Properties

Label 8015.2.a.l.1.33
Level 8015
Weight 2
Character 8015.1
Self dual Yes
Analytic conductor 64.000
Analytic rank 0
Dimension 62
CM No

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Newspace parameters

Level: \( N \) = \( 8015 = 5 \cdot 7 \cdot 229 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8015.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0000972201\)
Analytic rank: \(0\)
Dimension: \(62\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.33
Character \(\chi\) = 8015.1

$q$-expansion

\(f(q)\) \(=\) \(q+0.177306 q^{2} -1.77336 q^{3} -1.96856 q^{4} -1.00000 q^{5} -0.314428 q^{6} -1.00000 q^{7} -0.703651 q^{8} +0.144804 q^{9} +O(q^{10})\) \(q+0.177306 q^{2} -1.77336 q^{3} -1.96856 q^{4} -1.00000 q^{5} -0.314428 q^{6} -1.00000 q^{7} -0.703651 q^{8} +0.144804 q^{9} -0.177306 q^{10} -0.639776 q^{11} +3.49097 q^{12} -2.64003 q^{13} -0.177306 q^{14} +1.77336 q^{15} +3.81236 q^{16} +6.32556 q^{17} +0.0256746 q^{18} -6.95789 q^{19} +1.96856 q^{20} +1.77336 q^{21} -0.113436 q^{22} -3.01957 q^{23} +1.24783 q^{24} +1.00000 q^{25} -0.468094 q^{26} +5.06329 q^{27} +1.96856 q^{28} -1.66003 q^{29} +0.314428 q^{30} -5.14184 q^{31} +2.08326 q^{32} +1.13455 q^{33} +1.12156 q^{34} +1.00000 q^{35} -0.285055 q^{36} -0.896079 q^{37} -1.23368 q^{38} +4.68172 q^{39} +0.703651 q^{40} +1.25216 q^{41} +0.314428 q^{42} -9.47924 q^{43} +1.25944 q^{44} -0.144804 q^{45} -0.535389 q^{46} -7.01227 q^{47} -6.76069 q^{48} +1.00000 q^{49} +0.177306 q^{50} -11.2175 q^{51} +5.19706 q^{52} -9.00910 q^{53} +0.897753 q^{54} +0.639776 q^{55} +0.703651 q^{56} +12.3388 q^{57} -0.294334 q^{58} -10.4486 q^{59} -3.49097 q^{60} -4.57798 q^{61} -0.911681 q^{62} -0.144804 q^{63} -7.25535 q^{64} +2.64003 q^{65} +0.201163 q^{66} -5.16197 q^{67} -12.4523 q^{68} +5.35479 q^{69} +0.177306 q^{70} +9.51234 q^{71} -0.101891 q^{72} +5.65625 q^{73} -0.158880 q^{74} -1.77336 q^{75} +13.6971 q^{76} +0.639776 q^{77} +0.830098 q^{78} +1.21962 q^{79} -3.81236 q^{80} -9.41344 q^{81} +0.222015 q^{82} -17.2730 q^{83} -3.49097 q^{84} -6.32556 q^{85} -1.68073 q^{86} +2.94383 q^{87} +0.450179 q^{88} +7.76378 q^{89} -0.0256746 q^{90} +2.64003 q^{91} +5.94422 q^{92} +9.11834 q^{93} -1.24332 q^{94} +6.95789 q^{95} -3.69437 q^{96} -18.6292 q^{97} +0.177306 q^{98} -0.0926419 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 62q + 2q^{2} + 11q^{3} + 64q^{4} - 62q^{5} + 3q^{6} - 62q^{7} + 15q^{8} + 69q^{9} + O(q^{10}) \) \( 62q + 2q^{2} + 11q^{3} + 64q^{4} - 62q^{5} + 3q^{6} - 62q^{7} + 15q^{8} + 69q^{9} - 2q^{10} - 13q^{11} + 37q^{12} + 31q^{13} - 2q^{14} - 11q^{15} + 64q^{16} + 30q^{17} + 18q^{18} + 20q^{19} - 64q^{20} - 11q^{21} + 7q^{22} + 29q^{24} + 62q^{25} + 59q^{27} - 64q^{28} - 29q^{29} - 3q^{30} + 20q^{31} + 22q^{32} + 72q^{33} + 13q^{34} + 62q^{35} + 53q^{36} + 35q^{37} + 34q^{38} - 6q^{39} - 15q^{40} + 13q^{41} - 3q^{42} - 4q^{43} - 44q^{44} - 69q^{45} - 19q^{46} + 58q^{47} + 64q^{48} + 62q^{49} + 2q^{50} - 30q^{51} + 82q^{52} + 18q^{53} + 22q^{54} + 13q^{55} - 15q^{56} + 21q^{57} + 18q^{58} - 11q^{59} - 37q^{60} + 24q^{61} + 48q^{62} - 69q^{63} + 65q^{64} - 31q^{65} + 25q^{66} - 6q^{67} + 65q^{68} + 27q^{69} + 2q^{70} - 35q^{71} + 53q^{72} + 116q^{73} - 69q^{74} + 11q^{75} + 65q^{76} + 13q^{77} + 102q^{78} - 83q^{79} - 64q^{80} + 126q^{81} + 71q^{82} + 84q^{83} - 37q^{84} - 30q^{85} + 24q^{86} + 49q^{87} + 20q^{88} - 16q^{89} - 18q^{90} - 31q^{91} + 19q^{92} + 65q^{93} + 54q^{94} - 20q^{95} + 17q^{96} + 155q^{97} + 2q^{98} + 6q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.177306 0.125375 0.0626873 0.998033i \(-0.480033\pi\)
0.0626873 + 0.998033i \(0.480033\pi\)
\(3\) −1.77336 −1.02385 −0.511925 0.859030i \(-0.671067\pi\)
−0.511925 + 0.859030i \(0.671067\pi\)
\(4\) −1.96856 −0.984281
\(5\) −1.00000 −0.447214
\(6\) −0.314428 −0.128365
\(7\) −1.00000 −0.377964
\(8\) −0.703651 −0.248778
\(9\) 0.144804 0.0482679
\(10\) −0.177306 −0.0560692
\(11\) −0.639776 −0.192900 −0.0964499 0.995338i \(-0.530749\pi\)
−0.0964499 + 0.995338i \(0.530749\pi\)
\(12\) 3.49097 1.00776
\(13\) −2.64003 −0.732212 −0.366106 0.930573i \(-0.619309\pi\)
−0.366106 + 0.930573i \(0.619309\pi\)
\(14\) −0.177306 −0.0473871
\(15\) 1.77336 0.457879
\(16\) 3.81236 0.953091
\(17\) 6.32556 1.53417 0.767087 0.641543i \(-0.221705\pi\)
0.767087 + 0.641543i \(0.221705\pi\)
\(18\) 0.0256746 0.00605156
\(19\) −6.95789 −1.59625 −0.798125 0.602492i \(-0.794175\pi\)
−0.798125 + 0.602492i \(0.794175\pi\)
\(20\) 1.96856 0.440184
\(21\) 1.77336 0.386979
\(22\) −0.113436 −0.0241847
\(23\) −3.01957 −0.629624 −0.314812 0.949154i \(-0.601942\pi\)
−0.314812 + 0.949154i \(0.601942\pi\)
\(24\) 1.24783 0.254712
\(25\) 1.00000 0.200000
\(26\) −0.468094 −0.0918007
\(27\) 5.06329 0.974430
\(28\) 1.96856 0.372023
\(29\) −1.66003 −0.308260 −0.154130 0.988051i \(-0.549257\pi\)
−0.154130 + 0.988051i \(0.549257\pi\)
\(30\) 0.314428 0.0574064
\(31\) −5.14184 −0.923502 −0.461751 0.887010i \(-0.652779\pi\)
−0.461751 + 0.887010i \(0.652779\pi\)
\(32\) 2.08326 0.368272
\(33\) 1.13455 0.197500
\(34\) 1.12156 0.192346
\(35\) 1.00000 0.169031
\(36\) −0.285055 −0.0475092
\(37\) −0.896079 −0.147314 −0.0736572 0.997284i \(-0.523467\pi\)
−0.0736572 + 0.997284i \(0.523467\pi\)
\(38\) −1.23368 −0.200129
\(39\) 4.68172 0.749675
\(40\) 0.703651 0.111257
\(41\) 1.25216 0.195554 0.0977770 0.995208i \(-0.468827\pi\)
0.0977770 + 0.995208i \(0.468827\pi\)
\(42\) 0.314428 0.0485173
\(43\) −9.47924 −1.44557 −0.722785 0.691073i \(-0.757138\pi\)
−0.722785 + 0.691073i \(0.757138\pi\)
\(44\) 1.25944 0.189868
\(45\) −0.144804 −0.0215861
\(46\) −0.535389 −0.0789388
\(47\) −7.01227 −1.02284 −0.511422 0.859330i \(-0.670881\pi\)
−0.511422 + 0.859330i \(0.670881\pi\)
\(48\) −6.76069 −0.975822
\(49\) 1.00000 0.142857
\(50\) 0.177306 0.0250749
\(51\) −11.2175 −1.57076
\(52\) 5.19706 0.720703
\(53\) −9.00910 −1.23749 −0.618747 0.785590i \(-0.712360\pi\)
−0.618747 + 0.785590i \(0.712360\pi\)
\(54\) 0.897753 0.122169
\(55\) 0.639776 0.0862674
\(56\) 0.703651 0.0940294
\(57\) 12.3388 1.63432
\(58\) −0.294334 −0.0386480
\(59\) −10.4486 −1.36029 −0.680144 0.733079i \(-0.738083\pi\)
−0.680144 + 0.733079i \(0.738083\pi\)
\(60\) −3.49097 −0.450682
\(61\) −4.57798 −0.586150 −0.293075 0.956090i \(-0.594679\pi\)
−0.293075 + 0.956090i \(0.594679\pi\)
\(62\) −0.911681 −0.115784
\(63\) −0.144804 −0.0182435
\(64\) −7.25535 −0.906919
\(65\) 2.64003 0.327455
\(66\) 0.201163 0.0247615
\(67\) −5.16197 −0.630635 −0.315317 0.948986i \(-0.602111\pi\)
−0.315317 + 0.948986i \(0.602111\pi\)
\(68\) −12.4523 −1.51006
\(69\) 5.35479 0.644641
\(70\) 0.177306 0.0211922
\(71\) 9.51234 1.12891 0.564454 0.825465i \(-0.309087\pi\)
0.564454 + 0.825465i \(0.309087\pi\)
\(72\) −0.101891 −0.0120080
\(73\) 5.65625 0.662015 0.331007 0.943628i \(-0.392612\pi\)
0.331007 + 0.943628i \(0.392612\pi\)
\(74\) −0.158880 −0.0184695
\(75\) −1.77336 −0.204770
\(76\) 13.6971 1.57116
\(77\) 0.639776 0.0729093
\(78\) 0.830098 0.0939901
\(79\) 1.21962 0.137218 0.0686091 0.997644i \(-0.478144\pi\)
0.0686091 + 0.997644i \(0.478144\pi\)
\(80\) −3.81236 −0.426235
\(81\) −9.41344 −1.04594
\(82\) 0.222015 0.0245175
\(83\) −17.2730 −1.89595 −0.947977 0.318339i \(-0.896875\pi\)
−0.947977 + 0.318339i \(0.896875\pi\)
\(84\) −3.49097 −0.380896
\(85\) −6.32556 −0.686104
\(86\) −1.68073 −0.181238
\(87\) 2.94383 0.315612
\(88\) 0.450179 0.0479893
\(89\) 7.76378 0.822959 0.411480 0.911419i \(-0.365012\pi\)
0.411480 + 0.911419i \(0.365012\pi\)
\(90\) −0.0256746 −0.00270634
\(91\) 2.64003 0.276750
\(92\) 5.94422 0.619727
\(93\) 9.11834 0.945527
\(94\) −1.24332 −0.128239
\(95\) 6.95789 0.713865
\(96\) −3.69437 −0.377055
\(97\) −18.6292 −1.89151 −0.945753 0.324885i \(-0.894674\pi\)
−0.945753 + 0.324885i \(0.894674\pi\)
\(98\) 0.177306 0.0179106
\(99\) −0.0926419 −0.00931086
\(100\) −1.96856 −0.196856
\(101\) 9.10274 0.905756 0.452878 0.891572i \(-0.350397\pi\)
0.452878 + 0.891572i \(0.350397\pi\)
\(102\) −1.98893 −0.196934
\(103\) −13.0303 −1.28391 −0.641957 0.766741i \(-0.721877\pi\)
−0.641957 + 0.766741i \(0.721877\pi\)
\(104\) 1.85766 0.182158
\(105\) −1.77336 −0.173062
\(106\) −1.59737 −0.155150
\(107\) −7.46844 −0.722001 −0.361001 0.932566i \(-0.617565\pi\)
−0.361001 + 0.932566i \(0.617565\pi\)
\(108\) −9.96740 −0.959114
\(109\) −20.0020 −1.91585 −0.957923 0.287025i \(-0.907334\pi\)
−0.957923 + 0.287025i \(0.907334\pi\)
\(110\) 0.113436 0.0108157
\(111\) 1.58907 0.150828
\(112\) −3.81236 −0.360234
\(113\) −13.3848 −1.25914 −0.629570 0.776944i \(-0.716769\pi\)
−0.629570 + 0.776944i \(0.716769\pi\)
\(114\) 2.18776 0.204902
\(115\) 3.01957 0.281577
\(116\) 3.26788 0.303415
\(117\) −0.382286 −0.0353423
\(118\) −1.85260 −0.170545
\(119\) −6.32556 −0.579863
\(120\) −1.24783 −0.113910
\(121\) −10.5907 −0.962790
\(122\) −0.811704 −0.0734882
\(123\) −2.22052 −0.200218
\(124\) 10.1220 0.908986
\(125\) −1.00000 −0.0894427
\(126\) −0.0256746 −0.00228728
\(127\) −9.93366 −0.881469 −0.440735 0.897637i \(-0.645282\pi\)
−0.440735 + 0.897637i \(0.645282\pi\)
\(128\) −5.45294 −0.481976
\(129\) 16.8101 1.48005
\(130\) 0.468094 0.0410545
\(131\) 5.00799 0.437551 0.218775 0.975775i \(-0.429794\pi\)
0.218775 + 0.975775i \(0.429794\pi\)
\(132\) −2.23344 −0.194396
\(133\) 6.95789 0.603326
\(134\) −0.915250 −0.0790655
\(135\) −5.06329 −0.435779
\(136\) −4.45099 −0.381669
\(137\) 22.7945 1.94746 0.973731 0.227701i \(-0.0731209\pi\)
0.973731 + 0.227701i \(0.0731209\pi\)
\(138\) 0.949438 0.0808215
\(139\) 21.9719 1.86363 0.931815 0.362935i \(-0.118225\pi\)
0.931815 + 0.362935i \(0.118225\pi\)
\(140\) −1.96856 −0.166374
\(141\) 12.4353 1.04724
\(142\) 1.68660 0.141536
\(143\) 1.68903 0.141244
\(144\) 0.552044 0.0460037
\(145\) 1.66003 0.137858
\(146\) 1.00289 0.0829997
\(147\) −1.77336 −0.146264
\(148\) 1.76399 0.144999
\(149\) 6.86559 0.562451 0.281226 0.959642i \(-0.409259\pi\)
0.281226 + 0.959642i \(0.409259\pi\)
\(150\) −0.314428 −0.0256729
\(151\) −1.72727 −0.140564 −0.0702818 0.997527i \(-0.522390\pi\)
−0.0702818 + 0.997527i \(0.522390\pi\)
\(152\) 4.89593 0.397112
\(153\) 0.915965 0.0740514
\(154\) 0.113436 0.00914096
\(155\) 5.14184 0.413003
\(156\) −9.21626 −0.737891
\(157\) 7.85732 0.627082 0.313541 0.949575i \(-0.398485\pi\)
0.313541 + 0.949575i \(0.398485\pi\)
\(158\) 0.216247 0.0172037
\(159\) 15.9764 1.26701
\(160\) −2.08326 −0.164696
\(161\) 3.01957 0.237976
\(162\) −1.66906 −0.131134
\(163\) 10.9697 0.859212 0.429606 0.903016i \(-0.358652\pi\)
0.429606 + 0.903016i \(0.358652\pi\)
\(164\) −2.46495 −0.192480
\(165\) −1.13455 −0.0883248
\(166\) −3.06261 −0.237704
\(167\) −0.101144 −0.00782677 −0.00391339 0.999992i \(-0.501246\pi\)
−0.00391339 + 0.999992i \(0.501246\pi\)
\(168\) −1.24783 −0.0962719
\(169\) −6.03025 −0.463865
\(170\) −1.12156 −0.0860199
\(171\) −1.00753 −0.0770476
\(172\) 18.6605 1.42285
\(173\) −2.37379 −0.180476 −0.0902379 0.995920i \(-0.528763\pi\)
−0.0902379 + 0.995920i \(0.528763\pi\)
\(174\) 0.521960 0.0395697
\(175\) −1.00000 −0.0755929
\(176\) −2.43906 −0.183851
\(177\) 18.5291 1.39273
\(178\) 1.37657 0.103178
\(179\) −16.7854 −1.25460 −0.627298 0.778779i \(-0.715839\pi\)
−0.627298 + 0.778779i \(0.715839\pi\)
\(180\) 0.285055 0.0212467
\(181\) −14.2181 −1.05682 −0.528410 0.848989i \(-0.677212\pi\)
−0.528410 + 0.848989i \(0.677212\pi\)
\(182\) 0.468094 0.0346974
\(183\) 8.11840 0.600129
\(184\) 2.12473 0.156637
\(185\) 0.896079 0.0658810
\(186\) 1.61674 0.118545
\(187\) −4.04694 −0.295942
\(188\) 13.8041 1.00677
\(189\) −5.06329 −0.368300
\(190\) 1.23368 0.0895005
\(191\) −9.13370 −0.660892 −0.330446 0.943825i \(-0.607199\pi\)
−0.330446 + 0.943825i \(0.607199\pi\)
\(192\) 12.8663 0.928549
\(193\) 22.3999 1.61238 0.806189 0.591658i \(-0.201526\pi\)
0.806189 + 0.591658i \(0.201526\pi\)
\(194\) −3.30307 −0.237147
\(195\) −4.68172 −0.335265
\(196\) −1.96856 −0.140612
\(197\) −10.5228 −0.749718 −0.374859 0.927082i \(-0.622309\pi\)
−0.374859 + 0.927082i \(0.622309\pi\)
\(198\) −0.0164260 −0.00116734
\(199\) −22.9550 −1.62724 −0.813619 0.581399i \(-0.802506\pi\)
−0.813619 + 0.581399i \(0.802506\pi\)
\(200\) −0.703651 −0.0497557
\(201\) 9.15403 0.645675
\(202\) 1.61397 0.113559
\(203\) 1.66003 0.116511
\(204\) 22.0823 1.54607
\(205\) −1.25216 −0.0874544
\(206\) −2.31035 −0.160970
\(207\) −0.437245 −0.0303906
\(208\) −10.0647 −0.697865
\(209\) 4.45149 0.307916
\(210\) −0.314428 −0.0216976
\(211\) −21.4441 −1.47627 −0.738136 0.674651i \(-0.764294\pi\)
−0.738136 + 0.674651i \(0.764294\pi\)
\(212\) 17.7350 1.21804
\(213\) −16.8688 −1.15583
\(214\) −1.32420 −0.0905206
\(215\) 9.47924 0.646479
\(216\) −3.56279 −0.242417
\(217\) 5.14184 0.349051
\(218\) −3.54648 −0.240198
\(219\) −10.0306 −0.677803
\(220\) −1.25944 −0.0849114
\(221\) −16.6997 −1.12334
\(222\) 0.281752 0.0189100
\(223\) −11.6626 −0.780986 −0.390493 0.920606i \(-0.627695\pi\)
−0.390493 + 0.920606i \(0.627695\pi\)
\(224\) −2.08326 −0.139194
\(225\) 0.144804 0.00965358
\(226\) −2.37322 −0.157864
\(227\) 3.51032 0.232988 0.116494 0.993191i \(-0.462834\pi\)
0.116494 + 0.993191i \(0.462834\pi\)
\(228\) −24.2898 −1.60863
\(229\) 1.00000 0.0660819
\(230\) 0.535389 0.0353025
\(231\) −1.13455 −0.0746481
\(232\) 1.16808 0.0766884
\(233\) 14.0683 0.921643 0.460821 0.887493i \(-0.347555\pi\)
0.460821 + 0.887493i \(0.347555\pi\)
\(234\) −0.0677817 −0.00443103
\(235\) 7.01227 0.457430
\(236\) 20.5687 1.33891
\(237\) −2.16283 −0.140491
\(238\) −1.12156 −0.0727001
\(239\) 6.38400 0.412947 0.206473 0.978452i \(-0.433801\pi\)
0.206473 + 0.978452i \(0.433801\pi\)
\(240\) 6.76069 0.436401
\(241\) 1.06088 0.0683375 0.0341687 0.999416i \(-0.489122\pi\)
0.0341687 + 0.999416i \(0.489122\pi\)
\(242\) −1.87780 −0.120709
\(243\) 1.50355 0.0964528
\(244\) 9.01203 0.576936
\(245\) −1.00000 −0.0638877
\(246\) −0.393713 −0.0251022
\(247\) 18.3690 1.16879
\(248\) 3.61806 0.229747
\(249\) 30.6312 1.94117
\(250\) −0.177306 −0.0112138
\(251\) −26.1553 −1.65091 −0.825455 0.564468i \(-0.809081\pi\)
−0.825455 + 0.564468i \(0.809081\pi\)
\(252\) 0.285055 0.0179568
\(253\) 1.93185 0.121454
\(254\) −1.76130 −0.110514
\(255\) 11.2175 0.702467
\(256\) 13.5439 0.846491
\(257\) −1.74763 −0.109014 −0.0545071 0.998513i \(-0.517359\pi\)
−0.0545071 + 0.998513i \(0.517359\pi\)
\(258\) 2.98054 0.185560
\(259\) 0.896079 0.0556796
\(260\) −5.19706 −0.322308
\(261\) −0.240379 −0.0148791
\(262\) 0.887949 0.0548577
\(263\) 9.21353 0.568131 0.284065 0.958805i \(-0.408317\pi\)
0.284065 + 0.958805i \(0.408317\pi\)
\(264\) −0.798330 −0.0491338
\(265\) 9.00910 0.553424
\(266\) 1.23368 0.0756417
\(267\) −13.7680 −0.842586
\(268\) 10.1617 0.620722
\(269\) 18.3383 1.11811 0.559054 0.829131i \(-0.311164\pi\)
0.559054 + 0.829131i \(0.311164\pi\)
\(270\) −0.897753 −0.0546355
\(271\) −22.9608 −1.39477 −0.697386 0.716696i \(-0.745654\pi\)
−0.697386 + 0.716696i \(0.745654\pi\)
\(272\) 24.1153 1.46221
\(273\) −4.68172 −0.283351
\(274\) 4.04160 0.244162
\(275\) −0.639776 −0.0385800
\(276\) −10.5412 −0.634508
\(277\) −10.7662 −0.646877 −0.323439 0.946249i \(-0.604839\pi\)
−0.323439 + 0.946249i \(0.604839\pi\)
\(278\) 3.89575 0.233652
\(279\) −0.744558 −0.0445755
\(280\) −0.703651 −0.0420512
\(281\) 18.7391 1.11788 0.558940 0.829208i \(-0.311208\pi\)
0.558940 + 0.829208i \(0.311208\pi\)
\(282\) 2.20485 0.131297
\(283\) 24.7051 1.46857 0.734283 0.678843i \(-0.237519\pi\)
0.734283 + 0.678843i \(0.237519\pi\)
\(284\) −18.7256 −1.11116
\(285\) −12.3388 −0.730890
\(286\) 0.299475 0.0177083
\(287\) −1.25216 −0.0739124
\(288\) 0.301663 0.0177757
\(289\) 23.0128 1.35369
\(290\) 0.294334 0.0172839
\(291\) 33.0362 1.93662
\(292\) −11.1347 −0.651609
\(293\) 33.2001 1.93957 0.969784 0.243966i \(-0.0784484\pi\)
0.969784 + 0.243966i \(0.0784484\pi\)
\(294\) −0.314428 −0.0183378
\(295\) 10.4486 0.608339
\(296\) 0.630527 0.0366486
\(297\) −3.23937 −0.187967
\(298\) 1.21731 0.0705171
\(299\) 7.97176 0.461019
\(300\) 3.49097 0.201551
\(301\) 9.47924 0.546374
\(302\) −0.306257 −0.0176231
\(303\) −16.1424 −0.927358
\(304\) −26.5260 −1.52137
\(305\) 4.57798 0.262134
\(306\) 0.162406 0.00928415
\(307\) 24.7066 1.41008 0.705039 0.709169i \(-0.250930\pi\)
0.705039 + 0.709169i \(0.250930\pi\)
\(308\) −1.25944 −0.0717632
\(309\) 23.1074 1.31453
\(310\) 0.911681 0.0517800
\(311\) 18.8964 1.07152 0.535759 0.844371i \(-0.320026\pi\)
0.535759 + 0.844371i \(0.320026\pi\)
\(312\) −3.29430 −0.186503
\(313\) −24.5126 −1.38554 −0.692768 0.721160i \(-0.743609\pi\)
−0.692768 + 0.721160i \(0.743609\pi\)
\(314\) 1.39315 0.0786201
\(315\) 0.144804 0.00815876
\(316\) −2.40090 −0.135061
\(317\) 7.11436 0.399582 0.199791 0.979839i \(-0.435974\pi\)
0.199791 + 0.979839i \(0.435974\pi\)
\(318\) 2.83271 0.158851
\(319\) 1.06205 0.0594633
\(320\) 7.25535 0.405586
\(321\) 13.2442 0.739221
\(322\) 0.535389 0.0298361
\(323\) −44.0126 −2.44893
\(324\) 18.5310 1.02950
\(325\) −2.64003 −0.146442
\(326\) 1.94499 0.107723
\(327\) 35.4708 1.96154
\(328\) −0.881081 −0.0486496
\(329\) 7.01227 0.386599
\(330\) −0.201163 −0.0110737
\(331\) −26.6025 −1.46221 −0.731103 0.682267i \(-0.760994\pi\)
−0.731103 + 0.682267i \(0.760994\pi\)
\(332\) 34.0029 1.86615
\(333\) −0.129756 −0.00711056
\(334\) −0.0179335 −0.000981277 0
\(335\) 5.16197 0.282029
\(336\) 6.76069 0.368826
\(337\) −20.5741 −1.12074 −0.560371 0.828242i \(-0.689342\pi\)
−0.560371 + 0.828242i \(0.689342\pi\)
\(338\) −1.06920 −0.0581569
\(339\) 23.7361 1.28917
\(340\) 12.4523 0.675319
\(341\) 3.28963 0.178143
\(342\) −0.178641 −0.00965981
\(343\) −1.00000 −0.0539949
\(344\) 6.67008 0.359627
\(345\) −5.35479 −0.288292
\(346\) −0.420888 −0.0226271
\(347\) 19.1273 1.02681 0.513404 0.858147i \(-0.328384\pi\)
0.513404 + 0.858147i \(0.328384\pi\)
\(348\) −5.79512 −0.310651
\(349\) −22.1849 −1.18753 −0.593765 0.804638i \(-0.702359\pi\)
−0.593765 + 0.804638i \(0.702359\pi\)
\(350\) −0.177306 −0.00947742
\(351\) −13.3672 −0.713490
\(352\) −1.33282 −0.0710395
\(353\) 2.55318 0.135892 0.0679462 0.997689i \(-0.478355\pi\)
0.0679462 + 0.997689i \(0.478355\pi\)
\(354\) 3.28532 0.174613
\(355\) −9.51234 −0.504863
\(356\) −15.2835 −0.810023
\(357\) 11.2175 0.593693
\(358\) −2.97615 −0.157294
\(359\) 14.3040 0.754938 0.377469 0.926022i \(-0.376794\pi\)
0.377469 + 0.926022i \(0.376794\pi\)
\(360\) 0.101891 0.00537014
\(361\) 29.4123 1.54802
\(362\) −2.52095 −0.132498
\(363\) 18.7811 0.985752
\(364\) −5.19706 −0.272400
\(365\) −5.65625 −0.296062
\(366\) 1.43944 0.0752409
\(367\) 3.02815 0.158068 0.0790341 0.996872i \(-0.474816\pi\)
0.0790341 + 0.996872i \(0.474816\pi\)
\(368\) −11.5117 −0.600089
\(369\) 0.181317 0.00943898
\(370\) 0.158880 0.00825980
\(371\) 9.00910 0.467729
\(372\) −17.9500 −0.930665
\(373\) −20.0667 −1.03901 −0.519507 0.854466i \(-0.673884\pi\)
−0.519507 + 0.854466i \(0.673884\pi\)
\(374\) −0.717549 −0.0371036
\(375\) 1.77336 0.0915759
\(376\) 4.93419 0.254461
\(377\) 4.38253 0.225712
\(378\) −0.897753 −0.0461754
\(379\) −31.0196 −1.59337 −0.796686 0.604394i \(-0.793415\pi\)
−0.796686 + 0.604394i \(0.793415\pi\)
\(380\) −13.6971 −0.702644
\(381\) 17.6159 0.902492
\(382\) −1.61946 −0.0828590
\(383\) 28.4889 1.45572 0.727858 0.685728i \(-0.240516\pi\)
0.727858 + 0.685728i \(0.240516\pi\)
\(384\) 9.67002 0.493471
\(385\) −0.639776 −0.0326060
\(386\) 3.97164 0.202151
\(387\) −1.37263 −0.0697746
\(388\) 36.6727 1.86177
\(389\) −13.7177 −0.695517 −0.347759 0.937584i \(-0.613057\pi\)
−0.347759 + 0.937584i \(0.613057\pi\)
\(390\) −0.830098 −0.0420337
\(391\) −19.1005 −0.965954
\(392\) −0.703651 −0.0355398
\(393\) −8.88097 −0.447986
\(394\) −1.86576 −0.0939955
\(395\) −1.21962 −0.0613659
\(396\) 0.182371 0.00916451
\(397\) 14.8305 0.744323 0.372161 0.928168i \(-0.378617\pi\)
0.372161 + 0.928168i \(0.378617\pi\)
\(398\) −4.07007 −0.204014
\(399\) −12.3388 −0.617715
\(400\) 3.81236 0.190618
\(401\) 34.4861 1.72216 0.861078 0.508473i \(-0.169790\pi\)
0.861078 + 0.508473i \(0.169790\pi\)
\(402\) 1.62307 0.0809512
\(403\) 13.5746 0.676200
\(404\) −17.9193 −0.891519
\(405\) 9.41344 0.467758
\(406\) 0.294334 0.0146076
\(407\) 0.573290 0.0284169
\(408\) 7.89321 0.390772
\(409\) 17.7653 0.878438 0.439219 0.898380i \(-0.355255\pi\)
0.439219 + 0.898380i \(0.355255\pi\)
\(410\) −0.222015 −0.0109645
\(411\) −40.4228 −1.99391
\(412\) 25.6509 1.26373
\(413\) 10.4486 0.514140
\(414\) −0.0775263 −0.00381021
\(415\) 17.2730 0.847896
\(416\) −5.49986 −0.269653
\(417\) −38.9640 −1.90808
\(418\) 0.789278 0.0386049
\(419\) −14.0985 −0.688758 −0.344379 0.938831i \(-0.611910\pi\)
−0.344379 + 0.938831i \(0.611910\pi\)
\(420\) 3.49097 0.170342
\(421\) 2.43136 0.118497 0.0592485 0.998243i \(-0.481130\pi\)
0.0592485 + 0.998243i \(0.481130\pi\)
\(422\) −3.80217 −0.185087
\(423\) −1.01540 −0.0493705
\(424\) 6.33926 0.307862
\(425\) 6.32556 0.306835
\(426\) −2.99095 −0.144912
\(427\) 4.57798 0.221544
\(428\) 14.7021 0.710652
\(429\) −2.99525 −0.144612
\(430\) 1.68073 0.0810520
\(431\) 11.5551 0.556592 0.278296 0.960495i \(-0.410230\pi\)
0.278296 + 0.960495i \(0.410230\pi\)
\(432\) 19.3031 0.928721
\(433\) 35.1114 1.68735 0.843673 0.536858i \(-0.180389\pi\)
0.843673 + 0.536858i \(0.180389\pi\)
\(434\) 0.911681 0.0437621
\(435\) −2.94383 −0.141146
\(436\) 39.3752 1.88573
\(437\) 21.0099 1.00504
\(438\) −1.77848 −0.0849793
\(439\) 8.10691 0.386922 0.193461 0.981108i \(-0.438029\pi\)
0.193461 + 0.981108i \(0.438029\pi\)
\(440\) −0.450179 −0.0214615
\(441\) 0.144804 0.00689541
\(442\) −2.96096 −0.140838
\(443\) 13.4712 0.640035 0.320018 0.947412i \(-0.396311\pi\)
0.320018 + 0.947412i \(0.396311\pi\)
\(444\) −3.12818 −0.148457
\(445\) −7.76378 −0.368038
\(446\) −2.06785 −0.0979157
\(447\) −12.1752 −0.575866
\(448\) 7.25535 0.342783
\(449\) −35.2371 −1.66294 −0.831470 0.555570i \(-0.812500\pi\)
−0.831470 + 0.555570i \(0.812500\pi\)
\(450\) 0.0256746 0.00121031
\(451\) −0.801100 −0.0377223
\(452\) 26.3489 1.23935
\(453\) 3.06308 0.143916
\(454\) 0.622402 0.0292108
\(455\) −2.64003 −0.123766
\(456\) −8.68225 −0.406583
\(457\) −24.5476 −1.14829 −0.574145 0.818754i \(-0.694665\pi\)
−0.574145 + 0.818754i \(0.694665\pi\)
\(458\) 0.177306 0.00828498
\(459\) 32.0282 1.49495
\(460\) −5.94422 −0.277151
\(461\) 6.05338 0.281934 0.140967 0.990014i \(-0.454979\pi\)
0.140967 + 0.990014i \(0.454979\pi\)
\(462\) −0.201163 −0.00935897
\(463\) −4.03738 −0.187633 −0.0938166 0.995590i \(-0.529907\pi\)
−0.0938166 + 0.995590i \(0.529907\pi\)
\(464\) −6.32864 −0.293800
\(465\) −9.11834 −0.422853
\(466\) 2.49439 0.115551
\(467\) −21.9718 −1.01673 −0.508366 0.861141i \(-0.669750\pi\)
−0.508366 + 0.861141i \(0.669750\pi\)
\(468\) 0.752553 0.0347868
\(469\) 5.16197 0.238358
\(470\) 1.24332 0.0573500
\(471\) −13.9338 −0.642038
\(472\) 7.35215 0.338410
\(473\) 6.06459 0.278850
\(474\) −0.383483 −0.0176140
\(475\) −6.95789 −0.319250
\(476\) 12.4523 0.570749
\(477\) −1.30455 −0.0597313
\(478\) 1.13192 0.0517730
\(479\) −6.64512 −0.303623 −0.151812 0.988409i \(-0.548511\pi\)
−0.151812 + 0.988409i \(0.548511\pi\)
\(480\) 3.69437 0.168624
\(481\) 2.36567 0.107865
\(482\) 0.188101 0.00856778
\(483\) −5.35479 −0.243651
\(484\) 20.8484 0.947656
\(485\) 18.6292 0.845908
\(486\) 0.266589 0.0120927
\(487\) 12.7097 0.575933 0.287967 0.957640i \(-0.407021\pi\)
0.287967 + 0.957640i \(0.407021\pi\)
\(488\) 3.22130 0.145821
\(489\) −19.4532 −0.879704
\(490\) −0.177306 −0.00800988
\(491\) −27.5861 −1.24494 −0.622472 0.782642i \(-0.713872\pi\)
−0.622472 + 0.782642i \(0.713872\pi\)
\(492\) 4.37124 0.197071
\(493\) −10.5006 −0.472925
\(494\) 3.25695 0.146537
\(495\) 0.0926419 0.00416394
\(496\) −19.6026 −0.880181
\(497\) −9.51234 −0.426687
\(498\) 5.43110 0.243373
\(499\) −37.3390 −1.67152 −0.835761 0.549094i \(-0.814973\pi\)
−0.835761 + 0.549094i \(0.814973\pi\)
\(500\) 1.96856 0.0880368
\(501\) 0.179365 0.00801344
\(502\) −4.63750 −0.206982
\(503\) 24.5926 1.09653 0.548264 0.836305i \(-0.315289\pi\)
0.548264 + 0.836305i \(0.315289\pi\)
\(504\) 0.101891 0.00453860
\(505\) −9.10274 −0.405067
\(506\) 0.342529 0.0152273
\(507\) 10.6938 0.474928
\(508\) 19.5550 0.867614
\(509\) −17.4789 −0.774737 −0.387369 0.921925i \(-0.626616\pi\)
−0.387369 + 0.921925i \(0.626616\pi\)
\(510\) 1.98893 0.0880714
\(511\) −5.65625 −0.250218
\(512\) 13.3073 0.588105
\(513\) −35.2298 −1.55544
\(514\) −0.309866 −0.0136676
\(515\) 13.0303 0.574183
\(516\) −33.0917 −1.45678
\(517\) 4.48628 0.197306
\(518\) 0.158880 0.00698081
\(519\) 4.20958 0.184780
\(520\) −1.85766 −0.0814637
\(521\) −1.48819 −0.0651990 −0.0325995 0.999468i \(-0.510379\pi\)
−0.0325995 + 0.999468i \(0.510379\pi\)
\(522\) −0.0426207 −0.00186546
\(523\) 2.09180 0.0914679 0.0457339 0.998954i \(-0.485437\pi\)
0.0457339 + 0.998954i \(0.485437\pi\)
\(524\) −9.85855 −0.430673
\(525\) 1.77336 0.0773958
\(526\) 1.63362 0.0712291
\(527\) −32.5251 −1.41681
\(528\) 4.32533 0.188236
\(529\) −13.8822 −0.603573
\(530\) 1.59737 0.0693853
\(531\) −1.51299 −0.0656582
\(532\) −13.6971 −0.593842
\(533\) −3.30573 −0.143187
\(534\) −2.44115 −0.105639
\(535\) 7.46844 0.322889
\(536\) 3.63223 0.156888
\(537\) 29.7665 1.28452
\(538\) 3.25150 0.140182
\(539\) −0.639776 −0.0275571
\(540\) 9.96740 0.428929
\(541\) −14.6748 −0.630920 −0.315460 0.948939i \(-0.602159\pi\)
−0.315460 + 0.948939i \(0.602159\pi\)
\(542\) −4.07110 −0.174869
\(543\) 25.2137 1.08202
\(544\) 13.1778 0.564993
\(545\) 20.0020 0.856792
\(546\) −0.830098 −0.0355249
\(547\) 39.9747 1.70920 0.854598 0.519290i \(-0.173804\pi\)
0.854598 + 0.519290i \(0.173804\pi\)
\(548\) −44.8723 −1.91685
\(549\) −0.662908 −0.0282922
\(550\) −0.113436 −0.00483694
\(551\) 11.5503 0.492060
\(552\) −3.76790 −0.160373
\(553\) −1.21962 −0.0518636
\(554\) −1.90891 −0.0811019
\(555\) −1.58907 −0.0674523
\(556\) −43.2530 −1.83434
\(557\) −25.7840 −1.09250 −0.546251 0.837621i \(-0.683946\pi\)
−0.546251 + 0.837621i \(0.683946\pi\)
\(558\) −0.132015 −0.00558863
\(559\) 25.0255 1.05846
\(560\) 3.81236 0.161102
\(561\) 7.17669 0.303000
\(562\) 3.32256 0.140154
\(563\) 15.4832 0.652537 0.326269 0.945277i \(-0.394209\pi\)
0.326269 + 0.945277i \(0.394209\pi\)
\(564\) −24.4796 −1.03078
\(565\) 13.3848 0.563104
\(566\) 4.38037 0.184121
\(567\) 9.41344 0.395327
\(568\) −6.69337 −0.280848
\(569\) −26.5208 −1.11181 −0.555906 0.831245i \(-0.687628\pi\)
−0.555906 + 0.831245i \(0.687628\pi\)
\(570\) −2.18776 −0.0916350
\(571\) 27.6779 1.15828 0.579142 0.815227i \(-0.303388\pi\)
0.579142 + 0.815227i \(0.303388\pi\)
\(572\) −3.32496 −0.139023
\(573\) 16.1973 0.676654
\(574\) −0.222015 −0.00926674
\(575\) −3.01957 −0.125925
\(576\) −1.05060 −0.0437751
\(577\) 19.0810 0.794352 0.397176 0.917743i \(-0.369990\pi\)
0.397176 + 0.917743i \(0.369990\pi\)
\(578\) 4.08031 0.169718
\(579\) −39.7230 −1.65083
\(580\) −3.26788 −0.135691
\(581\) 17.2730 0.716603
\(582\) 5.85753 0.242803
\(583\) 5.76381 0.238712
\(584\) −3.98003 −0.164695
\(585\) 0.382286 0.0158056
\(586\) 5.88658 0.243172
\(587\) −34.9330 −1.44184 −0.720920 0.693018i \(-0.756281\pi\)
−0.720920 + 0.693018i \(0.756281\pi\)
\(588\) 3.49097 0.143965
\(589\) 35.7764 1.47414
\(590\) 1.85260 0.0762702
\(591\) 18.6607 0.767599
\(592\) −3.41618 −0.140404
\(593\) −3.83915 −0.157655 −0.0788275 0.996888i \(-0.525118\pi\)
−0.0788275 + 0.996888i \(0.525118\pi\)
\(594\) −0.574361 −0.0235663
\(595\) 6.32556 0.259323
\(596\) −13.5153 −0.553610
\(597\) 40.7075 1.66605
\(598\) 1.41344 0.0578000
\(599\) 40.6855 1.66237 0.831183 0.555999i \(-0.187664\pi\)
0.831183 + 0.555999i \(0.187664\pi\)
\(600\) 1.24783 0.0509423
\(601\) 22.7544 0.928170 0.464085 0.885791i \(-0.346383\pi\)
0.464085 + 0.885791i \(0.346383\pi\)
\(602\) 1.68073 0.0685014
\(603\) −0.747472 −0.0304394
\(604\) 3.40025 0.138354
\(605\) 10.5907 0.430573
\(606\) −2.86215 −0.116267
\(607\) 23.9724 0.973010 0.486505 0.873678i \(-0.338272\pi\)
0.486505 + 0.873678i \(0.338272\pi\)
\(608\) −14.4951 −0.587854
\(609\) −2.94383 −0.119290
\(610\) 0.811704 0.0328649
\(611\) 18.5126 0.748939
\(612\) −1.80313 −0.0728874
\(613\) 3.34662 0.135169 0.0675845 0.997714i \(-0.478471\pi\)
0.0675845 + 0.997714i \(0.478471\pi\)
\(614\) 4.38063 0.176788
\(615\) 2.22052 0.0895401
\(616\) −0.450179 −0.0181382
\(617\) −10.9995 −0.442822 −0.221411 0.975181i \(-0.571066\pi\)
−0.221411 + 0.975181i \(0.571066\pi\)
\(618\) 4.09709 0.164809
\(619\) 16.3619 0.657640 0.328820 0.944393i \(-0.393349\pi\)
0.328820 + 0.944393i \(0.393349\pi\)
\(620\) −10.1220 −0.406511
\(621\) −15.2890 −0.613525
\(622\) 3.35046 0.134341
\(623\) −7.76378 −0.311049
\(624\) 17.8484 0.714508
\(625\) 1.00000 0.0400000
\(626\) −4.34625 −0.173711
\(627\) −7.89410 −0.315260
\(628\) −15.4676 −0.617225
\(629\) −5.66820 −0.226006
\(630\) 0.0256746 0.00102290
\(631\) 36.1886 1.44065 0.720323 0.693639i \(-0.243994\pi\)
0.720323 + 0.693639i \(0.243994\pi\)
\(632\) −0.858189 −0.0341369
\(633\) 38.0281 1.51148
\(634\) 1.26142 0.0500974
\(635\) 9.93366 0.394205
\(636\) −31.4505 −1.24709
\(637\) −2.64003 −0.104602
\(638\) 0.188308 0.00745518
\(639\) 1.37742 0.0544900
\(640\) 5.45294 0.215546
\(641\) −25.6413 −1.01277 −0.506385 0.862308i \(-0.669018\pi\)
−0.506385 + 0.862308i \(0.669018\pi\)
\(642\) 2.34829 0.0926794
\(643\) 0.144796 0.00571018 0.00285509 0.999996i \(-0.499091\pi\)
0.00285509 + 0.999996i \(0.499091\pi\)
\(644\) −5.94422 −0.234235
\(645\) −16.8101 −0.661897
\(646\) −7.80371 −0.307033
\(647\) −14.2312 −0.559486 −0.279743 0.960075i \(-0.590249\pi\)
−0.279743 + 0.960075i \(0.590249\pi\)
\(648\) 6.62378 0.260207
\(649\) 6.68474 0.262399
\(650\) −0.468094 −0.0183601
\(651\) −9.11834 −0.357376
\(652\) −21.5945 −0.845706
\(653\) −5.41349 −0.211846 −0.105923 0.994374i \(-0.533780\pi\)
−0.105923 + 0.994374i \(0.533780\pi\)
\(654\) 6.28919 0.245927
\(655\) −5.00799 −0.195679
\(656\) 4.77367 0.186381
\(657\) 0.819046 0.0319540
\(658\) 1.24332 0.0484696
\(659\) −32.2234 −1.25524 −0.627622 0.778518i \(-0.715972\pi\)
−0.627622 + 0.778518i \(0.715972\pi\)
\(660\) 2.23344 0.0869365
\(661\) −29.6861 −1.15466 −0.577328 0.816513i \(-0.695904\pi\)
−0.577328 + 0.816513i \(0.695904\pi\)
\(662\) −4.71679 −0.183323
\(663\) 29.6145 1.15013
\(664\) 12.1541 0.471672
\(665\) −6.95789 −0.269816
\(666\) −0.0230065 −0.000891483 0
\(667\) 5.01259 0.194088
\(668\) 0.199109 0.00770374
\(669\) 20.6820 0.799612
\(670\) 0.915250 0.0353592
\(671\) 2.92888 0.113068
\(672\) 3.69437 0.142513
\(673\) −11.2206 −0.432523 −0.216262 0.976335i \(-0.569386\pi\)
−0.216262 + 0.976335i \(0.569386\pi\)
\(674\) −3.64792 −0.140513
\(675\) 5.06329 0.194886
\(676\) 11.8709 0.456574
\(677\) 31.2202 1.19989 0.599944 0.800042i \(-0.295189\pi\)
0.599944 + 0.800042i \(0.295189\pi\)
\(678\) 4.20856 0.161629
\(679\) 18.6292 0.714922
\(680\) 4.45099 0.170688
\(681\) −6.22506 −0.238545
\(682\) 0.583272 0.0223346
\(683\) 35.5516 1.36034 0.680172 0.733053i \(-0.261905\pi\)
0.680172 + 0.733053i \(0.261905\pi\)
\(684\) 1.98338 0.0758365
\(685\) −22.7945 −0.870932
\(686\) −0.177306 −0.00676959
\(687\) −1.77336 −0.0676579
\(688\) −36.1383 −1.37776
\(689\) 23.7843 0.906109
\(690\) −0.949438 −0.0361445
\(691\) −21.0442 −0.800560 −0.400280 0.916393i \(-0.631087\pi\)
−0.400280 + 0.916393i \(0.631087\pi\)
\(692\) 4.67295 0.177639
\(693\) 0.0926419 0.00351918
\(694\) 3.39139 0.128735
\(695\) −21.9719 −0.833440
\(696\) −2.07143 −0.0785174
\(697\) 7.92059 0.300014
\(698\) −3.93352 −0.148886
\(699\) −24.9481 −0.943624
\(700\) 1.96856 0.0744047
\(701\) −22.3782 −0.845212 −0.422606 0.906313i \(-0.638885\pi\)
−0.422606 + 0.906313i \(0.638885\pi\)
\(702\) −2.37009 −0.0894534
\(703\) 6.23482 0.235151
\(704\) 4.64180 0.174944
\(705\) −12.4353 −0.468339
\(706\) 0.452696 0.0170374
\(707\) −9.10274 −0.342344
\(708\) −36.4756 −1.37084
\(709\) 45.5067 1.70904 0.854520 0.519419i \(-0.173851\pi\)
0.854520 + 0.519419i \(0.173851\pi\)
\(710\) −1.68660 −0.0632969
\(711\) 0.176606 0.00662324
\(712\) −5.46299 −0.204734
\(713\) 15.5262 0.581460
\(714\) 1.98893 0.0744340
\(715\) −1.68903 −0.0631660
\(716\) 33.0430 1.23488
\(717\) −11.3211 −0.422795
\(718\) 2.53620 0.0946500
\(719\) 18.7149 0.697950 0.348975 0.937132i \(-0.386530\pi\)
0.348975 + 0.937132i \(0.386530\pi\)
\(720\) −0.552044 −0.0205735
\(721\) 13.0303 0.485274
\(722\) 5.21499 0.194082
\(723\) −1.88133 −0.0699673
\(724\) 27.9891 1.04021
\(725\) −1.66003 −0.0616520
\(726\) 3.33001 0.123588
\(727\) −20.3001 −0.752888 −0.376444 0.926439i \(-0.622853\pi\)
−0.376444 + 0.926439i \(0.622853\pi\)
\(728\) −1.85766 −0.0688494
\(729\) 25.5740 0.947185
\(730\) −1.00289 −0.0371186
\(731\) −59.9615 −2.21776
\(732\) −15.9816 −0.590696
\(733\) −5.90820 −0.218224 −0.109112 0.994029i \(-0.534801\pi\)
−0.109112 + 0.994029i \(0.534801\pi\)
\(734\) 0.536911 0.0198177
\(735\) 1.77336 0.0654113
\(736\) −6.29055 −0.231873
\(737\) 3.30250 0.121649
\(738\) 0.0321486 0.00118341
\(739\) 25.3524 0.932604 0.466302 0.884625i \(-0.345586\pi\)
0.466302 + 0.884625i \(0.345586\pi\)
\(740\) −1.76399 −0.0648455
\(741\) −32.5749 −1.19667
\(742\) 1.59737 0.0586413
\(743\) 41.4168 1.51943 0.759717 0.650253i \(-0.225337\pi\)
0.759717 + 0.650253i \(0.225337\pi\)
\(744\) −6.41613 −0.235227
\(745\) −6.86559 −0.251536
\(746\) −3.55795 −0.130266
\(747\) −2.50119 −0.0915137
\(748\) 7.96666 0.291290
\(749\) 7.46844 0.272891
\(750\) 0.314428 0.0114813
\(751\) 11.5455 0.421300 0.210650 0.977562i \(-0.432442\pi\)
0.210650 + 0.977562i \(0.432442\pi\)
\(752\) −26.7333 −0.974863
\(753\) 46.3828 1.69028
\(754\) 0.777050 0.0282985
\(755\) 1.72727 0.0628620
\(756\) 9.96740 0.362511
\(757\) −14.3446 −0.521363 −0.260681 0.965425i \(-0.583947\pi\)
−0.260681 + 0.965425i \(0.583947\pi\)
\(758\) −5.49998 −0.199768
\(759\) −3.42587 −0.124351
\(760\) −4.89593 −0.177594
\(761\) 3.31937 0.120327 0.0601635 0.998189i \(-0.480838\pi\)
0.0601635 + 0.998189i \(0.480838\pi\)
\(762\) 3.12342 0.113149
\(763\) 20.0020 0.724122
\(764\) 17.9803 0.650503
\(765\) −0.915965 −0.0331168
\(766\) 5.05127 0.182510
\(767\) 27.5845 0.996019
\(768\) −24.0181 −0.866680
\(769\) −3.61887 −0.130500 −0.0652499 0.997869i \(-0.520784\pi\)
−0.0652499 + 0.997869i \(0.520784\pi\)
\(770\) −0.113436 −0.00408796
\(771\) 3.09918 0.111614
\(772\) −44.0956 −1.58703
\(773\) −43.6956 −1.57162 −0.785810 0.618468i \(-0.787754\pi\)
−0.785810 + 0.618468i \(0.787754\pi\)
\(774\) −0.243376 −0.00874796
\(775\) −5.14184 −0.184700
\(776\) 13.1084 0.470566
\(777\) −1.58907 −0.0570076
\(778\) −2.43224 −0.0872001
\(779\) −8.71237 −0.312153
\(780\) 9.21626 0.329995
\(781\) −6.08577 −0.217766
\(782\) −3.38664 −0.121106
\(783\) −8.40522 −0.300378
\(784\) 3.81236 0.136156
\(785\) −7.85732 −0.280440
\(786\) −1.57465 −0.0561660
\(787\) 22.2010 0.791379 0.395689 0.918384i \(-0.370506\pi\)
0.395689 + 0.918384i \(0.370506\pi\)
\(788\) 20.7148 0.737933
\(789\) −16.3389 −0.581680
\(790\) −0.216247 −0.00769372
\(791\) 13.3848 0.475910
\(792\) 0.0651876 0.00231634
\(793\) 12.0860 0.429186
\(794\) 2.62955 0.0933191
\(795\) −15.9764 −0.566623
\(796\) 45.1884 1.60166
\(797\) 0.552766 0.0195800 0.00978999 0.999952i \(-0.496884\pi\)
0.00978999 + 0.999952i \(0.496884\pi\)
\(798\) −2.18776 −0.0774457
\(799\) −44.3565 −1.56922
\(800\) 2.08326 0.0736543
\(801\) 1.12422 0.0397225
\(802\) 6.11461 0.215914
\(803\) −3.61874 −0.127702
\(804\) −18.0203 −0.635526
\(805\) −3.01957 −0.106426
\(806\) 2.40686 0.0847782
\(807\) −32.5205 −1.14477
\(808\) −6.40515 −0.225332
\(809\) −23.4047 −0.822866 −0.411433 0.911440i \(-0.634972\pi\)
−0.411433 + 0.911440i \(0.634972\pi\)
\(810\) 1.66906 0.0586449
\(811\) 30.7889 1.08115 0.540573 0.841297i \(-0.318207\pi\)
0.540573 + 0.841297i \(0.318207\pi\)
\(812\) −3.26788 −0.114680
\(813\) 40.7178 1.42804
\(814\) 0.101648 0.00356276
\(815\) −10.9697 −0.384251
\(816\) −42.7652 −1.49708
\(817\) 65.9556 2.30749
\(818\) 3.14990 0.110134
\(819\) 0.382286 0.0133581
\(820\) 2.46495 0.0860797
\(821\) −53.9264 −1.88204 −0.941022 0.338344i \(-0.890133\pi\)
−0.941022 + 0.338344i \(0.890133\pi\)
\(822\) −7.16721 −0.249985
\(823\) −20.4217 −0.711856 −0.355928 0.934513i \(-0.615835\pi\)
−0.355928 + 0.934513i \(0.615835\pi\)
\(824\) 9.16878 0.319410
\(825\) 1.13455 0.0395001
\(826\) 1.85260 0.0644601
\(827\) 32.6957 1.13694 0.568470 0.822704i \(-0.307535\pi\)
0.568470 + 0.822704i \(0.307535\pi\)
\(828\) 0.860744 0.0299129
\(829\) 37.3968 1.29884 0.649422 0.760428i \(-0.275011\pi\)
0.649422 + 0.760428i \(0.275011\pi\)
\(830\) 3.06261 0.106305
\(831\) 19.0923 0.662305
\(832\) 19.1543 0.664057
\(833\) 6.32556 0.219168
\(834\) −6.90857 −0.239224
\(835\) 0.101144 0.00350024
\(836\) −8.76305 −0.303076
\(837\) −26.0346 −0.899889
\(838\) −2.49976 −0.0863527
\(839\) −17.2708 −0.596254 −0.298127 0.954526i \(-0.596362\pi\)
−0.298127 + 0.954526i \(0.596362\pi\)
\(840\) 1.24783 0.0430541
\(841\) −26.2443 −0.904976
\(842\) 0.431095 0.0148565
\(843\) −33.2311 −1.14454
\(844\) 42.2141 1.45307
\(845\) 6.03025 0.207447
\(846\) −0.180037 −0.00618981
\(847\) 10.5907 0.363900
\(848\) −34.3459 −1.17944
\(849\) −43.8110 −1.50359
\(850\) 1.12156 0.0384693
\(851\) 2.70578 0.0927528
\(852\) 33.2073 1.13766
\(853\) −26.6556 −0.912672 −0.456336 0.889808i \(-0.650838\pi\)
−0.456336 + 0.889808i \(0.650838\pi\)
\(854\) 0.811704 0.0277759
\(855\) 1.00753 0.0344568
\(856\) 5.25518 0.179618
\(857\) 44.4595 1.51871 0.759354 0.650678i \(-0.225515\pi\)
0.759354 + 0.650678i \(0.225515\pi\)
\(858\) −0.531077 −0.0181307
\(859\) 14.5481 0.496375 0.248187 0.968712i \(-0.420165\pi\)
0.248187 + 0.968712i \(0.420165\pi\)
\(860\) −18.6605 −0.636317
\(861\) 2.22052 0.0756752
\(862\) 2.04880 0.0697824
\(863\) −32.4779 −1.10556 −0.552780 0.833327i \(-0.686433\pi\)
−0.552780 + 0.833327i \(0.686433\pi\)
\(864\) 10.5481 0.358855
\(865\) 2.37379 0.0807112
\(866\) 6.22547 0.211550
\(867\) −40.8099 −1.38598
\(868\) −10.1220 −0.343564
\(869\) −0.780286 −0.0264694
\(870\) −0.521960 −0.0176961
\(871\) 13.6277 0.461759
\(872\) 14.0744 0.476621
\(873\) −2.69757 −0.0912990
\(874\) 3.72518 0.126006
\(875\) 1.00000 0.0338062
\(876\) 19.7458 0.667149
\(877\) 29.5104 0.996495 0.498247 0.867035i \(-0.333977\pi\)
0.498247 + 0.867035i \(0.333977\pi\)
\(878\) 1.43741 0.0485101
\(879\) −58.8756 −1.98583
\(880\) 2.43906 0.0822207
\(881\) 28.8388 0.971605 0.485802 0.874069i \(-0.338527\pi\)
0.485802 + 0.874069i \(0.338527\pi\)
\(882\) 0.0256746 0.000864509 0
\(883\) −6.08332 −0.204720 −0.102360 0.994747i \(-0.532639\pi\)
−0.102360 + 0.994747i \(0.532639\pi\)
\(884\) 32.8743 1.10568
\(885\) −18.5291 −0.622848
\(886\) 2.38853 0.0802441
\(887\) 4.67202 0.156871 0.0784355 0.996919i \(-0.475008\pi\)
0.0784355 + 0.996919i \(0.475008\pi\)
\(888\) −1.11815 −0.0375227
\(889\) 9.93366 0.333164
\(890\) −1.37657 −0.0461426
\(891\) 6.02250 0.201761
\(892\) 22.9586 0.768709
\(893\) 48.7906 1.63272
\(894\) −2.15873 −0.0721989
\(895\) 16.7854 0.561073
\(896\) 5.45294 0.182170
\(897\) −14.1368 −0.472014
\(898\) −6.24775 −0.208490
\(899\) 8.53562 0.284679
\(900\) −0.285055 −0.00950184
\(901\) −56.9876 −1.89853
\(902\) −0.142040 −0.00472942
\(903\) −16.8101 −0.559405
\(904\) 9.41826 0.313247
\(905\) 14.2181 0.472624
\(906\) 0.543103 0.0180434
\(907\) 37.0421 1.22996 0.614981 0.788542i \(-0.289164\pi\)
0.614981 + 0.788542i \(0.289164\pi\)
\(908\) −6.91028 −0.229326
\(909\) 1.31811 0.0437189
\(910\) −0.468094 −0.0155172
\(911\) 3.87020 0.128226 0.0641128 0.997943i \(-0.479578\pi\)
0.0641128 + 0.997943i \(0.479578\pi\)
\(912\) 47.0402 1.55766
\(913\) 11.0508 0.365729
\(914\) −4.35245 −0.143966
\(915\) −8.11840 −0.268386
\(916\) −1.96856 −0.0650431
\(917\) −5.00799 −0.165379
\(918\) 5.67879 0.187428
\(919\) −42.9788 −1.41774 −0.708870 0.705339i \(-0.750795\pi\)
−0.708870 + 0.705339i \(0.750795\pi\)
\(920\) −2.12473 −0.0700501
\(921\) −43.8136 −1.44371
\(922\) 1.07330 0.0353473
\(923\) −25.1129 −0.826600
\(924\) 2.23344 0.0734747
\(925\) −0.896079 −0.0294629
\(926\) −0.715854 −0.0235244
\(927\) −1.88683 −0.0619718
\(928\) −3.45827 −0.113523
\(929\) −17.7526 −0.582445 −0.291222 0.956655i \(-0.594062\pi\)
−0.291222 + 0.956655i \(0.594062\pi\)
\(930\) −1.61674 −0.0530149
\(931\) −6.95789 −0.228036
\(932\) −27.6943 −0.907156
\(933\) −33.5101 −1.09707
\(934\) −3.89573 −0.127472
\(935\) 4.04694 0.132349
\(936\) 0.268996 0.00879240
\(937\) 45.9827 1.50219 0.751094 0.660195i \(-0.229526\pi\)
0.751094 + 0.660195i \(0.229526\pi\)
\(938\) 0.915250 0.0298840
\(939\) 43.4697 1.41858
\(940\) −13.8041 −0.450240
\(941\) 18.7917 0.612591 0.306295 0.951937i \(-0.400910\pi\)
0.306295 + 0.951937i \(0.400910\pi\)
\(942\) −2.47056 −0.0804952
\(943\) −3.78098 −0.123126
\(944\) −39.8337 −1.29648
\(945\) 5.06329 0.164709
\(946\) 1.07529 0.0349607
\(947\) −21.7088 −0.705440 −0.352720 0.935729i \(-0.614743\pi\)
−0.352720 + 0.935729i \(0.614743\pi\)
\(948\) 4.25767 0.138283
\(949\) −14.9327 −0.484735
\(950\) −1.23368 −0.0400258
\(951\) −12.6163 −0.409112
\(952\) 4.45099 0.144257
\(953\) 14.7668 0.478344 0.239172 0.970977i \(-0.423124\pi\)
0.239172 + 0.970977i \(0.423124\pi\)
\(954\) −0.231305 −0.00748878
\(955\) 9.13370 0.295560
\(956\) −12.5673 −0.406456
\(957\) −1.88339 −0.0608815
\(958\) −1.17822 −0.0380666
\(959\) −22.7945 −0.736071
\(960\) −12.8663 −0.415260
\(961\) −4.56145 −0.147144
\(962\) 0.419449 0.0135236
\(963\) −1.08146 −0.0348495
\(964\) −2.08841 −0.0672633
\(965\) −22.3999 −0.721077
\(966\) −0.949438 −0.0305477
\(967\) −47.7645 −1.53600 −0.768001 0.640449i \(-0.778748\pi\)
−0.768001 + 0.640449i \(0.778748\pi\)
\(968\) 7.45215 0.239521
\(969\) 78.0502 2.50733
\(970\) 3.30307 0.106055
\(971\) −44.0116 −1.41240 −0.706199 0.708013i \(-0.749592\pi\)
−0.706199 + 0.708013i \(0.749592\pi\)
\(972\) −2.95983 −0.0949366
\(973\) −21.9719 −0.704386
\(974\) 2.25352 0.0722074
\(975\) 4.68172 0.149935
\(976\) −17.4529 −0.558654
\(977\) −3.25938 −0.104277 −0.0521384 0.998640i \(-0.516604\pi\)
−0.0521384 + 0.998640i \(0.516604\pi\)
\(978\) −3.44917 −0.110292
\(979\) −4.96708 −0.158749
\(980\) 1.96856 0.0628834
\(981\) −2.89637 −0.0924738
\(982\) −4.89119 −0.156084
\(983\) −52.0093 −1.65884 −0.829419 0.558627i \(-0.811328\pi\)
−0.829419 + 0.558627i \(0.811328\pi\)
\(984\) 1.56247 0.0498098
\(985\) 10.5228 0.335284
\(986\) −1.86183 −0.0592927
\(987\) −12.4353 −0.395819
\(988\) −36.1606 −1.15042
\(989\) 28.6233 0.910166
\(990\) 0.0164260 0.000522053 0
\(991\) −59.0845 −1.87688 −0.938440 0.345441i \(-0.887729\pi\)
−0.938440 + 0.345441i \(0.887729\pi\)
\(992\) −10.7118 −0.340100
\(993\) 47.1758 1.49708
\(994\) −1.68660 −0.0534957
\(995\) 22.9550 0.727723
\(996\) −60.2994 −1.91066
\(997\) 18.9426 0.599918 0.299959 0.953952i \(-0.403027\pi\)
0.299959 + 0.953952i \(0.403027\pi\)
\(998\) −6.62044 −0.209566
\(999\) −4.53711 −0.143548
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 \(a_p\))