Properties

Label 8015.2.a.l.1.52
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 1.52
Character \(\chi\) = 8015.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.01854 q^{2} -0.120356 q^{3} +2.07451 q^{4} -1.00000 q^{5} -0.242944 q^{6} -1.00000 q^{7} +0.150396 q^{8} -2.98551 q^{9} +O(q^{10})\) \(q+2.01854 q^{2} -0.120356 q^{3} +2.07451 q^{4} -1.00000 q^{5} -0.242944 q^{6} -1.00000 q^{7} +0.150396 q^{8} -2.98551 q^{9} -2.01854 q^{10} +2.98599 q^{11} -0.249680 q^{12} -0.821835 q^{13} -2.01854 q^{14} +0.120356 q^{15} -3.84543 q^{16} -1.51410 q^{17} -6.02638 q^{18} -2.64727 q^{19} -2.07451 q^{20} +0.120356 q^{21} +6.02734 q^{22} -3.02307 q^{23} -0.0181011 q^{24} +1.00000 q^{25} -1.65891 q^{26} +0.720394 q^{27} -2.07451 q^{28} +0.285570 q^{29} +0.242944 q^{30} +10.8458 q^{31} -8.06296 q^{32} -0.359383 q^{33} -3.05627 q^{34} +1.00000 q^{35} -6.19347 q^{36} +8.77302 q^{37} -5.34363 q^{38} +0.0989130 q^{39} -0.150396 q^{40} +4.58429 q^{41} +0.242944 q^{42} +11.3637 q^{43} +6.19446 q^{44} +2.98551 q^{45} -6.10218 q^{46} -4.30252 q^{47} +0.462822 q^{48} +1.00000 q^{49} +2.01854 q^{50} +0.182231 q^{51} -1.70490 q^{52} -14.5128 q^{53} +1.45414 q^{54} -2.98599 q^{55} -0.150396 q^{56} +0.318616 q^{57} +0.576434 q^{58} +7.32785 q^{59} +0.249680 q^{60} -7.06064 q^{61} +21.8926 q^{62} +2.98551 q^{63} -8.58454 q^{64} +0.821835 q^{65} -0.725428 q^{66} +13.8295 q^{67} -3.14101 q^{68} +0.363845 q^{69} +2.01854 q^{70} +2.79792 q^{71} -0.449009 q^{72} +14.0562 q^{73} +17.7087 q^{74} -0.120356 q^{75} -5.49179 q^{76} -2.98599 q^{77} +0.199660 q^{78} -9.81451 q^{79} +3.84543 q^{80} +8.86984 q^{81} +9.25358 q^{82} +8.73512 q^{83} +0.249680 q^{84} +1.51410 q^{85} +22.9381 q^{86} -0.0343701 q^{87} +0.449080 q^{88} +5.44007 q^{89} +6.02638 q^{90} +0.821835 q^{91} -6.27137 q^{92} -1.30535 q^{93} -8.68482 q^{94} +2.64727 q^{95} +0.970427 q^{96} -0.253552 q^{97} +2.01854 q^{98} -8.91472 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 62q + 2q^{2} + 11q^{3} + 64q^{4} - 62q^{5} + 3q^{6} - 62q^{7} + 15q^{8} + 69q^{9} + O(q^{10}) \) \( 62q + 2q^{2} + 11q^{3} + 64q^{4} - 62q^{5} + 3q^{6} - 62q^{7} + 15q^{8} + 69q^{9} - 2q^{10} - 13q^{11} + 37q^{12} + 31q^{13} - 2q^{14} - 11q^{15} + 64q^{16} + 30q^{17} + 18q^{18} + 20q^{19} - 64q^{20} - 11q^{21} + 7q^{22} + 29q^{24} + 62q^{25} + 59q^{27} - 64q^{28} - 29q^{29} - 3q^{30} + 20q^{31} + 22q^{32} + 72q^{33} + 13q^{34} + 62q^{35} + 53q^{36} + 35q^{37} + 34q^{38} - 6q^{39} - 15q^{40} + 13q^{41} - 3q^{42} - 4q^{43} - 44q^{44} - 69q^{45} - 19q^{46} + 58q^{47} + 64q^{48} + 62q^{49} + 2q^{50} - 30q^{51} + 82q^{52} + 18q^{53} + 22q^{54} + 13q^{55} - 15q^{56} + 21q^{57} + 18q^{58} - 11q^{59} - 37q^{60} + 24q^{61} + 48q^{62} - 69q^{63} + 65q^{64} - 31q^{65} + 25q^{66} - 6q^{67} + 65q^{68} + 27q^{69} + 2q^{70} - 35q^{71} + 53q^{72} + 116q^{73} - 69q^{74} + 11q^{75} + 65q^{76} + 13q^{77} + 102q^{78} - 83q^{79} - 64q^{80} + 126q^{81} + 71q^{82} + 84q^{83} - 37q^{84} - 30q^{85} + 24q^{86} + 49q^{87} + 20q^{88} - 16q^{89} - 18q^{90} - 31q^{91} + 19q^{92} + 65q^{93} + 54q^{94} - 20q^{95} + 17q^{96} + 155q^{97} + 2q^{98} + 6q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.01854 1.42732 0.713662 0.700490i \(-0.247035\pi\)
0.713662 + 0.700490i \(0.247035\pi\)
\(3\) −0.120356 −0.0694877 −0.0347439 0.999396i \(-0.511062\pi\)
−0.0347439 + 0.999396i \(0.511062\pi\)
\(4\) 2.07451 1.03725
\(5\) −1.00000 −0.447214
\(6\) −0.242944 −0.0991815
\(7\) −1.00000 −0.377964
\(8\) 0.150396 0.0531729
\(9\) −2.98551 −0.995171
\(10\) −2.01854 −0.638319
\(11\) 2.98599 0.900310 0.450155 0.892950i \(-0.351369\pi\)
0.450155 + 0.892950i \(0.351369\pi\)
\(12\) −0.249680 −0.0720764
\(13\) −0.821835 −0.227936 −0.113968 0.993484i \(-0.536356\pi\)
−0.113968 + 0.993484i \(0.536356\pi\)
\(14\) −2.01854 −0.539478
\(15\) 0.120356 0.0310758
\(16\) −3.84543 −0.961359
\(17\) −1.51410 −0.367223 −0.183612 0.982999i \(-0.558779\pi\)
−0.183612 + 0.982999i \(0.558779\pi\)
\(18\) −6.02638 −1.42043
\(19\) −2.64727 −0.607326 −0.303663 0.952779i \(-0.598210\pi\)
−0.303663 + 0.952779i \(0.598210\pi\)
\(20\) −2.07451 −0.463874
\(21\) 0.120356 0.0262639
\(22\) 6.02734 1.28503
\(23\) −3.02307 −0.630353 −0.315176 0.949033i \(-0.602064\pi\)
−0.315176 + 0.949033i \(0.602064\pi\)
\(24\) −0.0181011 −0.00369486
\(25\) 1.00000 0.200000
\(26\) −1.65891 −0.325339
\(27\) 0.720394 0.138640
\(28\) −2.07451 −0.392045
\(29\) 0.285570 0.0530290 0.0265145 0.999648i \(-0.491559\pi\)
0.0265145 + 0.999648i \(0.491559\pi\)
\(30\) 0.242944 0.0443553
\(31\) 10.8458 1.94796 0.973978 0.226643i \(-0.0727750\pi\)
0.973978 + 0.226643i \(0.0727750\pi\)
\(32\) −8.06296 −1.42534
\(33\) −0.359383 −0.0625605
\(34\) −3.05627 −0.524147
\(35\) 1.00000 0.169031
\(36\) −6.19347 −1.03225
\(37\) 8.77302 1.44228 0.721138 0.692792i \(-0.243620\pi\)
0.721138 + 0.692792i \(0.243620\pi\)
\(38\) −5.34363 −0.866851
\(39\) 0.0989130 0.0158388
\(40\) −0.150396 −0.0237797
\(41\) 4.58429 0.715946 0.357973 0.933732i \(-0.383468\pi\)
0.357973 + 0.933732i \(0.383468\pi\)
\(42\) 0.242944 0.0374871
\(43\) 11.3637 1.73295 0.866476 0.499219i \(-0.166380\pi\)
0.866476 + 0.499219i \(0.166380\pi\)
\(44\) 6.19446 0.933850
\(45\) 2.98551 0.445054
\(46\) −6.10218 −0.899718
\(47\) −4.30252 −0.627587 −0.313794 0.949491i \(-0.601600\pi\)
−0.313794 + 0.949491i \(0.601600\pi\)
\(48\) 0.462822 0.0668026
\(49\) 1.00000 0.142857
\(50\) 2.01854 0.285465
\(51\) 0.182231 0.0255175
\(52\) −1.70490 −0.236427
\(53\) −14.5128 −1.99349 −0.996743 0.0806401i \(-0.974304\pi\)
−0.996743 + 0.0806401i \(0.974304\pi\)
\(54\) 1.45414 0.197884
\(55\) −2.98599 −0.402631
\(56\) −0.150396 −0.0200975
\(57\) 0.318616 0.0422017
\(58\) 0.576434 0.0756895
\(59\) 7.32785 0.954005 0.477002 0.878902i \(-0.341723\pi\)
0.477002 + 0.878902i \(0.341723\pi\)
\(60\) 0.249680 0.0322335
\(61\) −7.06064 −0.904022 −0.452011 0.892012i \(-0.649293\pi\)
−0.452011 + 0.892012i \(0.649293\pi\)
\(62\) 21.8926 2.78036
\(63\) 2.98551 0.376139
\(64\) −8.58454 −1.07307
\(65\) 0.821835 0.101936
\(66\) −0.725428 −0.0892941
\(67\) 13.8295 1.68954 0.844772 0.535127i \(-0.179736\pi\)
0.844772 + 0.535127i \(0.179736\pi\)
\(68\) −3.14101 −0.380904
\(69\) 0.363845 0.0438018
\(70\) 2.01854 0.241262
\(71\) 2.79792 0.332052 0.166026 0.986121i \(-0.446906\pi\)
0.166026 + 0.986121i \(0.446906\pi\)
\(72\) −0.449009 −0.0529162
\(73\) 14.0562 1.64515 0.822577 0.568654i \(-0.192536\pi\)
0.822577 + 0.568654i \(0.192536\pi\)
\(74\) 17.7087 2.05859
\(75\) −0.120356 −0.0138975
\(76\) −5.49179 −0.629951
\(77\) −2.98599 −0.340285
\(78\) 0.199660 0.0226070
\(79\) −9.81451 −1.10422 −0.552109 0.833772i \(-0.686177\pi\)
−0.552109 + 0.833772i \(0.686177\pi\)
\(80\) 3.84543 0.429933
\(81\) 8.86984 0.985538
\(82\) 9.25358 1.02189
\(83\) 8.73512 0.958804 0.479402 0.877596i \(-0.340854\pi\)
0.479402 + 0.877596i \(0.340854\pi\)
\(84\) 0.249680 0.0272423
\(85\) 1.51410 0.164227
\(86\) 22.9381 2.47348
\(87\) −0.0343701 −0.00368486
\(88\) 0.449080 0.0478721
\(89\) 5.44007 0.576646 0.288323 0.957533i \(-0.406902\pi\)
0.288323 + 0.957533i \(0.406902\pi\)
\(90\) 6.02638 0.635237
\(91\) 0.821835 0.0861517
\(92\) −6.27137 −0.653836
\(93\) −1.30535 −0.135359
\(94\) −8.68482 −0.895771
\(95\) 2.64727 0.271605
\(96\) 0.970427 0.0990438
\(97\) −0.253552 −0.0257443 −0.0128722 0.999917i \(-0.504097\pi\)
−0.0128722 + 0.999917i \(0.504097\pi\)
\(98\) 2.01854 0.203903
\(99\) −8.91472 −0.895963
\(100\) 2.07451 0.207451
\(101\) 11.9362 1.18769 0.593847 0.804578i \(-0.297608\pi\)
0.593847 + 0.804578i \(0.297608\pi\)
\(102\) 0.367842 0.0364217
\(103\) −10.7124 −1.05552 −0.527761 0.849393i \(-0.676969\pi\)
−0.527761 + 0.849393i \(0.676969\pi\)
\(104\) −0.123600 −0.0121200
\(105\) −0.120356 −0.0117456
\(106\) −29.2947 −2.84535
\(107\) 2.14088 0.206967 0.103484 0.994631i \(-0.467001\pi\)
0.103484 + 0.994631i \(0.467001\pi\)
\(108\) 1.49446 0.143805
\(109\) 3.50768 0.335975 0.167988 0.985789i \(-0.446273\pi\)
0.167988 + 0.985789i \(0.446273\pi\)
\(110\) −6.02734 −0.574685
\(111\) −1.05589 −0.100220
\(112\) 3.84543 0.363359
\(113\) −7.79191 −0.733001 −0.366501 0.930418i \(-0.619444\pi\)
−0.366501 + 0.930418i \(0.619444\pi\)
\(114\) 0.643139 0.0602355
\(115\) 3.02307 0.281902
\(116\) 0.592417 0.0550045
\(117\) 2.45360 0.226835
\(118\) 14.7916 1.36167
\(119\) 1.51410 0.138797
\(120\) 0.0181011 0.00165239
\(121\) −2.08386 −0.189442
\(122\) −14.2522 −1.29033
\(123\) −0.551748 −0.0497494
\(124\) 22.4996 2.02052
\(125\) −1.00000 −0.0894427
\(126\) 6.02638 0.536873
\(127\) 19.1524 1.69950 0.849749 0.527187i \(-0.176753\pi\)
0.849749 + 0.527187i \(0.176753\pi\)
\(128\) −1.20233 −0.106272
\(129\) −1.36769 −0.120419
\(130\) 1.65891 0.145496
\(131\) −4.72072 −0.412452 −0.206226 0.978504i \(-0.566118\pi\)
−0.206226 + 0.978504i \(0.566118\pi\)
\(132\) −0.745542 −0.0648911
\(133\) 2.64727 0.229548
\(134\) 27.9154 2.41153
\(135\) −0.720394 −0.0620016
\(136\) −0.227714 −0.0195263
\(137\) 4.06542 0.347332 0.173666 0.984805i \(-0.444439\pi\)
0.173666 + 0.984805i \(0.444439\pi\)
\(138\) 0.734436 0.0625193
\(139\) 11.0486 0.937129 0.468565 0.883429i \(-0.344771\pi\)
0.468565 + 0.883429i \(0.344771\pi\)
\(140\) 2.07451 0.175328
\(141\) 0.517835 0.0436096
\(142\) 5.64772 0.473946
\(143\) −2.45399 −0.205213
\(144\) 11.4806 0.956717
\(145\) −0.285570 −0.0237153
\(146\) 28.3730 2.34817
\(147\) −0.120356 −0.00992681
\(148\) 18.1997 1.49601
\(149\) −22.9093 −1.87680 −0.938402 0.345545i \(-0.887694\pi\)
−0.938402 + 0.345545i \(0.887694\pi\)
\(150\) −0.242944 −0.0198363
\(151\) −0.773441 −0.0629418 −0.0314709 0.999505i \(-0.510019\pi\)
−0.0314709 + 0.999505i \(0.510019\pi\)
\(152\) −0.398139 −0.0322933
\(153\) 4.52037 0.365450
\(154\) −6.02734 −0.485697
\(155\) −10.8458 −0.871152
\(156\) 0.205196 0.0164288
\(157\) 12.7942 1.02109 0.510546 0.859851i \(-0.329443\pi\)
0.510546 + 0.859851i \(0.329443\pi\)
\(158\) −19.8110 −1.57608
\(159\) 1.74671 0.138523
\(160\) 8.06296 0.637433
\(161\) 3.02307 0.238251
\(162\) 17.9041 1.40668
\(163\) 10.1285 0.793322 0.396661 0.917965i \(-0.370169\pi\)
0.396661 + 0.917965i \(0.370169\pi\)
\(164\) 9.51014 0.742617
\(165\) 0.359383 0.0279779
\(166\) 17.6322 1.36852
\(167\) 14.3083 1.10721 0.553604 0.832780i \(-0.313252\pi\)
0.553604 + 0.832780i \(0.313252\pi\)
\(168\) 0.0181011 0.00139653
\(169\) −12.3246 −0.948045
\(170\) 3.05627 0.234405
\(171\) 7.90347 0.604394
\(172\) 23.5741 1.79751
\(173\) −0.230042 −0.0174897 −0.00874487 0.999962i \(-0.502784\pi\)
−0.00874487 + 0.999962i \(0.502784\pi\)
\(174\) −0.0693775 −0.00525949
\(175\) −1.00000 −0.0755929
\(176\) −11.4824 −0.865521
\(177\) −0.881952 −0.0662916
\(178\) 10.9810 0.823061
\(179\) 2.12800 0.159054 0.0795270 0.996833i \(-0.474659\pi\)
0.0795270 + 0.996833i \(0.474659\pi\)
\(180\) 6.19347 0.461634
\(181\) −4.12887 −0.306897 −0.153448 0.988157i \(-0.549038\pi\)
−0.153448 + 0.988157i \(0.549038\pi\)
\(182\) 1.65891 0.122966
\(183\) 0.849792 0.0628184
\(184\) −0.454656 −0.0335177
\(185\) −8.77302 −0.645005
\(186\) −2.63491 −0.193201
\(187\) −4.52109 −0.330615
\(188\) −8.92561 −0.650967
\(189\) −0.720394 −0.0524009
\(190\) 5.34363 0.387668
\(191\) −17.8444 −1.29118 −0.645589 0.763685i \(-0.723388\pi\)
−0.645589 + 0.763685i \(0.723388\pi\)
\(192\) 1.03320 0.0745650
\(193\) 14.3542 1.03324 0.516620 0.856215i \(-0.327190\pi\)
0.516620 + 0.856215i \(0.327190\pi\)
\(194\) −0.511805 −0.0367455
\(195\) −0.0989130 −0.00708330
\(196\) 2.07451 0.148179
\(197\) −5.18092 −0.369125 −0.184563 0.982821i \(-0.559087\pi\)
−0.184563 + 0.982821i \(0.559087\pi\)
\(198\) −17.9947 −1.27883
\(199\) 13.9001 0.985349 0.492675 0.870214i \(-0.336019\pi\)
0.492675 + 0.870214i \(0.336019\pi\)
\(200\) 0.150396 0.0106346
\(201\) −1.66447 −0.117402
\(202\) 24.0937 1.69523
\(203\) −0.285570 −0.0200431
\(204\) 0.378040 0.0264681
\(205\) −4.58429 −0.320181
\(206\) −21.6234 −1.50657
\(207\) 9.02541 0.627309
\(208\) 3.16031 0.219128
\(209\) −7.90473 −0.546782
\(210\) −0.242944 −0.0167647
\(211\) 13.9829 0.962623 0.481311 0.876550i \(-0.340161\pi\)
0.481311 + 0.876550i \(0.340161\pi\)
\(212\) −30.1069 −2.06775
\(213\) −0.336747 −0.0230735
\(214\) 4.32146 0.295409
\(215\) −11.3637 −0.774999
\(216\) 0.108344 0.00737189
\(217\) −10.8458 −0.736258
\(218\) 7.08040 0.479545
\(219\) −1.69175 −0.114318
\(220\) −6.19446 −0.417630
\(221\) 1.24434 0.0837034
\(222\) −2.13135 −0.143047
\(223\) −1.92404 −0.128843 −0.0644217 0.997923i \(-0.520520\pi\)
−0.0644217 + 0.997923i \(0.520520\pi\)
\(224\) 8.06296 0.538729
\(225\) −2.98551 −0.199034
\(226\) −15.7283 −1.04623
\(227\) −25.9778 −1.72421 −0.862105 0.506730i \(-0.830854\pi\)
−0.862105 + 0.506730i \(0.830854\pi\)
\(228\) 0.660971 0.0437739
\(229\) 1.00000 0.0660819
\(230\) 6.10218 0.402366
\(231\) 0.359383 0.0236456
\(232\) 0.0429485 0.00281971
\(233\) 3.83628 0.251323 0.125662 0.992073i \(-0.459895\pi\)
0.125662 + 0.992073i \(0.459895\pi\)
\(234\) 4.95269 0.323768
\(235\) 4.30252 0.280666
\(236\) 15.2017 0.989545
\(237\) 1.18124 0.0767296
\(238\) 3.05627 0.198109
\(239\) 2.97210 0.192249 0.0961247 0.995369i \(-0.469355\pi\)
0.0961247 + 0.995369i \(0.469355\pi\)
\(240\) −0.462822 −0.0298750
\(241\) −8.38102 −0.539869 −0.269934 0.962879i \(-0.587002\pi\)
−0.269934 + 0.962879i \(0.587002\pi\)
\(242\) −4.20636 −0.270395
\(243\) −3.22872 −0.207123
\(244\) −14.6473 −0.937700
\(245\) −1.00000 −0.0638877
\(246\) −1.11373 −0.0710086
\(247\) 2.17562 0.138432
\(248\) 1.63116 0.103579
\(249\) −1.05133 −0.0666251
\(250\) −2.01854 −0.127664
\(251\) −10.8118 −0.682433 −0.341217 0.939985i \(-0.610839\pi\)
−0.341217 + 0.939985i \(0.610839\pi\)
\(252\) 6.19347 0.390152
\(253\) −9.02685 −0.567513
\(254\) 38.6599 2.42574
\(255\) −0.182231 −0.0114118
\(256\) 14.7421 0.921383
\(257\) −2.99285 −0.186689 −0.0933443 0.995634i \(-0.529756\pi\)
−0.0933443 + 0.995634i \(0.529756\pi\)
\(258\) −2.76075 −0.171877
\(259\) −8.77302 −0.545129
\(260\) 1.70490 0.105734
\(261\) −0.852573 −0.0527729
\(262\) −9.52898 −0.588702
\(263\) −9.74849 −0.601117 −0.300559 0.953763i \(-0.597173\pi\)
−0.300559 + 0.953763i \(0.597173\pi\)
\(264\) −0.0540496 −0.00332652
\(265\) 14.5128 0.891514
\(266\) 5.34363 0.327639
\(267\) −0.654746 −0.0400698
\(268\) 28.6894 1.75248
\(269\) 14.7391 0.898659 0.449330 0.893366i \(-0.351663\pi\)
0.449330 + 0.893366i \(0.351663\pi\)
\(270\) −1.45414 −0.0884964
\(271\) 28.1816 1.71191 0.855954 0.517052i \(-0.172971\pi\)
0.855954 + 0.517052i \(0.172971\pi\)
\(272\) 5.82237 0.353033
\(273\) −0.0989130 −0.00598649
\(274\) 8.20621 0.495755
\(275\) 2.98599 0.180062
\(276\) 0.754799 0.0454335
\(277\) −25.0942 −1.50776 −0.753882 0.657009i \(-0.771821\pi\)
−0.753882 + 0.657009i \(0.771821\pi\)
\(278\) 22.3020 1.33759
\(279\) −32.3802 −1.93855
\(280\) 0.150396 0.00898786
\(281\) 1.34593 0.0802917 0.0401458 0.999194i \(-0.487218\pi\)
0.0401458 + 0.999194i \(0.487218\pi\)
\(282\) 1.04527 0.0622450
\(283\) 4.90900 0.291809 0.145905 0.989299i \(-0.453391\pi\)
0.145905 + 0.989299i \(0.453391\pi\)
\(284\) 5.80430 0.344422
\(285\) −0.318616 −0.0188732
\(286\) −4.95348 −0.292906
\(287\) −4.58429 −0.270602
\(288\) 24.0721 1.41846
\(289\) −14.7075 −0.865147
\(290\) −0.576434 −0.0338494
\(291\) 0.0305166 0.00178891
\(292\) 29.1597 1.70644
\(293\) −4.75988 −0.278075 −0.139038 0.990287i \(-0.544401\pi\)
−0.139038 + 0.990287i \(0.544401\pi\)
\(294\) −0.242944 −0.0141688
\(295\) −7.32785 −0.426644
\(296\) 1.31942 0.0766900
\(297\) 2.15109 0.124819
\(298\) −46.2434 −2.67881
\(299\) 2.48446 0.143680
\(300\) −0.249680 −0.0144153
\(301\) −11.3637 −0.654994
\(302\) −1.56122 −0.0898383
\(303\) −1.43659 −0.0825302
\(304\) 10.1799 0.583858
\(305\) 7.06064 0.404291
\(306\) 9.12455 0.521616
\(307\) 6.36296 0.363153 0.181577 0.983377i \(-0.441880\pi\)
0.181577 + 0.983377i \(0.441880\pi\)
\(308\) −6.19446 −0.352962
\(309\) 1.28930 0.0733459
\(310\) −21.8926 −1.24342
\(311\) 7.14344 0.405067 0.202534 0.979275i \(-0.435082\pi\)
0.202534 + 0.979275i \(0.435082\pi\)
\(312\) 0.0148761 0.000842193 0
\(313\) 32.8188 1.85503 0.927515 0.373785i \(-0.121940\pi\)
0.927515 + 0.373785i \(0.121940\pi\)
\(314\) 25.8257 1.45743
\(315\) −2.98551 −0.168215
\(316\) −20.3603 −1.14535
\(317\) 20.8644 1.17186 0.585931 0.810361i \(-0.300729\pi\)
0.585931 + 0.810361i \(0.300729\pi\)
\(318\) 3.52580 0.197717
\(319\) 0.852709 0.0477425
\(320\) 8.58454 0.479890
\(321\) −0.257669 −0.0143817
\(322\) 6.10218 0.340061
\(323\) 4.00824 0.223024
\(324\) 18.4005 1.02225
\(325\) −0.821835 −0.0455872
\(326\) 20.4447 1.13233
\(327\) −0.422172 −0.0233461
\(328\) 0.689458 0.0380689
\(329\) 4.30252 0.237206
\(330\) 0.725428 0.0399335
\(331\) 22.7009 1.24775 0.623877 0.781523i \(-0.285557\pi\)
0.623877 + 0.781523i \(0.285557\pi\)
\(332\) 18.1211 0.994523
\(333\) −26.1920 −1.43531
\(334\) 28.8819 1.58034
\(335\) −13.8295 −0.755587
\(336\) −0.462822 −0.0252490
\(337\) 26.0804 1.42069 0.710346 0.703852i \(-0.248538\pi\)
0.710346 + 0.703852i \(0.248538\pi\)
\(338\) −24.8777 −1.35317
\(339\) 0.937805 0.0509346
\(340\) 3.14101 0.170345
\(341\) 32.3853 1.75376
\(342\) 15.9535 0.862666
\(343\) −1.00000 −0.0539949
\(344\) 1.70905 0.0921461
\(345\) −0.363845 −0.0195887
\(346\) −0.464348 −0.0249635
\(347\) 26.9574 1.44715 0.723574 0.690247i \(-0.242498\pi\)
0.723574 + 0.690247i \(0.242498\pi\)
\(348\) −0.0713010 −0.00382214
\(349\) −12.6296 −0.676049 −0.338024 0.941137i \(-0.609759\pi\)
−0.338024 + 0.941137i \(0.609759\pi\)
\(350\) −2.01854 −0.107896
\(351\) −0.592045 −0.0316010
\(352\) −24.0759 −1.28325
\(353\) −24.6136 −1.31005 −0.655025 0.755607i \(-0.727342\pi\)
−0.655025 + 0.755607i \(0.727342\pi\)
\(354\) −1.78026 −0.0946196
\(355\) −2.79792 −0.148498
\(356\) 11.2855 0.598128
\(357\) −0.182231 −0.00964471
\(358\) 4.29545 0.227022
\(359\) −27.3321 −1.44253 −0.721266 0.692658i \(-0.756439\pi\)
−0.721266 + 0.692658i \(0.756439\pi\)
\(360\) 0.449009 0.0236648
\(361\) −11.9919 −0.631155
\(362\) −8.33430 −0.438041
\(363\) 0.250806 0.0131639
\(364\) 1.70490 0.0893612
\(365\) −14.0562 −0.735735
\(366\) 1.71534 0.0896623
\(367\) 4.72242 0.246508 0.123254 0.992375i \(-0.460667\pi\)
0.123254 + 0.992375i \(0.460667\pi\)
\(368\) 11.6250 0.605995
\(369\) −13.6865 −0.712489
\(370\) −17.7087 −0.920631
\(371\) 14.5128 0.753467
\(372\) −2.70797 −0.140402
\(373\) −27.7541 −1.43705 −0.718526 0.695500i \(-0.755183\pi\)
−0.718526 + 0.695500i \(0.755183\pi\)
\(374\) −9.12600 −0.471894
\(375\) 0.120356 0.00621517
\(376\) −0.647081 −0.0333707
\(377\) −0.234691 −0.0120872
\(378\) −1.45414 −0.0747931
\(379\) −11.8613 −0.609273 −0.304636 0.952469i \(-0.598535\pi\)
−0.304636 + 0.952469i \(0.598535\pi\)
\(380\) 5.49179 0.281723
\(381\) −2.30511 −0.118094
\(382\) −36.0197 −1.84293
\(383\) −3.24910 −0.166021 −0.0830106 0.996549i \(-0.526454\pi\)
−0.0830106 + 0.996549i \(0.526454\pi\)
\(384\) 0.144708 0.00738460
\(385\) 2.98599 0.152180
\(386\) 28.9746 1.47477
\(387\) −33.9266 −1.72458
\(388\) −0.525996 −0.0267034
\(389\) −27.5946 −1.39910 −0.699550 0.714583i \(-0.746616\pi\)
−0.699550 + 0.714583i \(0.746616\pi\)
\(390\) −0.199660 −0.0101102
\(391\) 4.57723 0.231480
\(392\) 0.150396 0.00759613
\(393\) 0.568169 0.0286603
\(394\) −10.4579 −0.526861
\(395\) 9.81451 0.493821
\(396\) −18.4936 −0.929341
\(397\) 23.7727 1.19312 0.596559 0.802570i \(-0.296534\pi\)
0.596559 + 0.802570i \(0.296534\pi\)
\(398\) 28.0578 1.40641
\(399\) −0.318616 −0.0159507
\(400\) −3.84543 −0.192272
\(401\) −1.62548 −0.0811728 −0.0405864 0.999176i \(-0.512923\pi\)
−0.0405864 + 0.999176i \(0.512923\pi\)
\(402\) −3.35980 −0.167571
\(403\) −8.91343 −0.444009
\(404\) 24.7617 1.23194
\(405\) −8.86984 −0.440746
\(406\) −0.576434 −0.0286080
\(407\) 26.1961 1.29849
\(408\) 0.0274068 0.00135684
\(409\) −11.1149 −0.549596 −0.274798 0.961502i \(-0.588611\pi\)
−0.274798 + 0.961502i \(0.588611\pi\)
\(410\) −9.25358 −0.457002
\(411\) −0.489298 −0.0241353
\(412\) −22.2229 −1.09484
\(413\) −7.32785 −0.360580
\(414\) 18.2182 0.895373
\(415\) −8.73512 −0.428790
\(416\) 6.62642 0.324887
\(417\) −1.32977 −0.0651190
\(418\) −15.9560 −0.780435
\(419\) 36.4669 1.78152 0.890762 0.454470i \(-0.150171\pi\)
0.890762 + 0.454470i \(0.150171\pi\)
\(420\) −0.249680 −0.0121831
\(421\) −6.47846 −0.315741 −0.157870 0.987460i \(-0.550463\pi\)
−0.157870 + 0.987460i \(0.550463\pi\)
\(422\) 28.2251 1.37397
\(423\) 12.8452 0.624557
\(424\) −2.18266 −0.105999
\(425\) −1.51410 −0.0734447
\(426\) −0.679738 −0.0329334
\(427\) 7.06064 0.341688
\(428\) 4.44128 0.214677
\(429\) 0.295353 0.0142598
\(430\) −22.9381 −1.10618
\(431\) 0.605717 0.0291764 0.0145882 0.999894i \(-0.495356\pi\)
0.0145882 + 0.999894i \(0.495356\pi\)
\(432\) −2.77023 −0.133283
\(433\) 40.0413 1.92426 0.962132 0.272585i \(-0.0878786\pi\)
0.962132 + 0.272585i \(0.0878786\pi\)
\(434\) −21.8926 −1.05088
\(435\) 0.0343701 0.00164792
\(436\) 7.27672 0.348491
\(437\) 8.00288 0.382830
\(438\) −3.41487 −0.163169
\(439\) 14.0004 0.668201 0.334101 0.942537i \(-0.391567\pi\)
0.334101 + 0.942537i \(0.391567\pi\)
\(440\) −0.449080 −0.0214091
\(441\) −2.98551 −0.142167
\(442\) 2.51175 0.119472
\(443\) 30.6569 1.45655 0.728277 0.685283i \(-0.240321\pi\)
0.728277 + 0.685283i \(0.240321\pi\)
\(444\) −2.19045 −0.103954
\(445\) −5.44007 −0.257884
\(446\) −3.88376 −0.183901
\(447\) 2.75728 0.130415
\(448\) 8.58454 0.405581
\(449\) 20.4269 0.964006 0.482003 0.876170i \(-0.339909\pi\)
0.482003 + 0.876170i \(0.339909\pi\)
\(450\) −6.02638 −0.284086
\(451\) 13.6886 0.644573
\(452\) −16.1644 −0.760308
\(453\) 0.0930885 0.00437368
\(454\) −52.4373 −2.46101
\(455\) −0.821835 −0.0385282
\(456\) 0.0479185 0.00224399
\(457\) −26.9185 −1.25920 −0.629598 0.776921i \(-0.716780\pi\)
−0.629598 + 0.776921i \(0.716780\pi\)
\(458\) 2.01854 0.0943202
\(459\) −1.09075 −0.0509118
\(460\) 6.27137 0.292404
\(461\) 40.7205 1.89654 0.948271 0.317462i \(-0.102830\pi\)
0.948271 + 0.317462i \(0.102830\pi\)
\(462\) 0.725428 0.0337500
\(463\) −19.8876 −0.924256 −0.462128 0.886813i \(-0.652914\pi\)
−0.462128 + 0.886813i \(0.652914\pi\)
\(464\) −1.09814 −0.0509799
\(465\) 1.30535 0.0605344
\(466\) 7.74369 0.358720
\(467\) −19.1949 −0.888232 −0.444116 0.895969i \(-0.646482\pi\)
−0.444116 + 0.895969i \(0.646482\pi\)
\(468\) 5.09001 0.235286
\(469\) −13.8295 −0.638587
\(470\) 8.68482 0.400601
\(471\) −1.53987 −0.0709533
\(472\) 1.10208 0.0507272
\(473\) 33.9320 1.56019
\(474\) 2.38438 0.109518
\(475\) −2.64727 −0.121465
\(476\) 3.14101 0.143968
\(477\) 43.3282 1.98386
\(478\) 5.99931 0.274402
\(479\) −13.0349 −0.595579 −0.297789 0.954632i \(-0.596249\pi\)
−0.297789 + 0.954632i \(0.596249\pi\)
\(480\) −0.970427 −0.0442937
\(481\) −7.20997 −0.328747
\(482\) −16.9174 −0.770567
\(483\) −0.363845 −0.0165555
\(484\) −4.32299 −0.196499
\(485\) 0.253552 0.0115132
\(486\) −6.51731 −0.295631
\(487\) −1.39679 −0.0632944 −0.0316472 0.999499i \(-0.510075\pi\)
−0.0316472 + 0.999499i \(0.510075\pi\)
\(488\) −1.06189 −0.0480695
\(489\) −1.21902 −0.0551261
\(490\) −2.01854 −0.0911884
\(491\) 19.4386 0.877251 0.438625 0.898670i \(-0.355465\pi\)
0.438625 + 0.898670i \(0.355465\pi\)
\(492\) −1.14461 −0.0516028
\(493\) −0.432381 −0.0194735
\(494\) 4.39158 0.197587
\(495\) 8.91472 0.400687
\(496\) −41.7067 −1.87268
\(497\) −2.79792 −0.125504
\(498\) −2.12214 −0.0950956
\(499\) 16.8089 0.752470 0.376235 0.926524i \(-0.377219\pi\)
0.376235 + 0.926524i \(0.377219\pi\)
\(500\) −2.07451 −0.0927748
\(501\) −1.72209 −0.0769374
\(502\) −21.8240 −0.974054
\(503\) 40.5525 1.80815 0.904073 0.427378i \(-0.140562\pi\)
0.904073 + 0.427378i \(0.140562\pi\)
\(504\) 0.449009 0.0200004
\(505\) −11.9362 −0.531153
\(506\) −18.2211 −0.810025
\(507\) 1.48334 0.0658775
\(508\) 39.7317 1.76281
\(509\) −0.740309 −0.0328136 −0.0164068 0.999865i \(-0.505223\pi\)
−0.0164068 + 0.999865i \(0.505223\pi\)
\(510\) −0.367842 −0.0162883
\(511\) −14.0562 −0.621810
\(512\) 32.1622 1.42138
\(513\) −1.90708 −0.0841996
\(514\) −6.04118 −0.266465
\(515\) 10.7124 0.472044
\(516\) −2.83729 −0.124905
\(517\) −12.8473 −0.565023
\(518\) −17.7087 −0.778075
\(519\) 0.0276869 0.00121532
\(520\) 0.123600 0.00542024
\(521\) −35.4362 −1.55249 −0.776245 0.630432i \(-0.782878\pi\)
−0.776245 + 0.630432i \(0.782878\pi\)
\(522\) −1.72095 −0.0753241
\(523\) 11.4006 0.498513 0.249257 0.968437i \(-0.419814\pi\)
0.249257 + 0.968437i \(0.419814\pi\)
\(524\) −9.79318 −0.427817
\(525\) 0.120356 0.00525278
\(526\) −19.6777 −0.857989
\(527\) −16.4216 −0.715335
\(528\) 1.38198 0.0601430
\(529\) −13.8611 −0.602655
\(530\) 29.2947 1.27248
\(531\) −21.8774 −0.949398
\(532\) 5.49179 0.238099
\(533\) −3.76753 −0.163190
\(534\) −1.32163 −0.0571926
\(535\) −2.14088 −0.0925585
\(536\) 2.07990 0.0898380
\(537\) −0.256118 −0.0110523
\(538\) 29.7515 1.28268
\(539\) 2.98599 0.128616
\(540\) −1.49446 −0.0643114
\(541\) 23.4058 1.00629 0.503146 0.864201i \(-0.332176\pi\)
0.503146 + 0.864201i \(0.332176\pi\)
\(542\) 56.8856 2.44345
\(543\) 0.496935 0.0213255
\(544\) 12.2081 0.523419
\(545\) −3.50768 −0.150253
\(546\) −0.199660 −0.00854465
\(547\) −13.1125 −0.560649 −0.280325 0.959905i \(-0.590442\pi\)
−0.280325 + 0.959905i \(0.590442\pi\)
\(548\) 8.43374 0.360271
\(549\) 21.0796 0.899657
\(550\) 6.02734 0.257007
\(551\) −0.755981 −0.0322059
\(552\) 0.0547207 0.00232907
\(553\) 9.81451 0.417355
\(554\) −50.6537 −2.15207
\(555\) 1.05589 0.0448199
\(556\) 22.9204 0.972041
\(557\) 4.01859 0.170273 0.0851365 0.996369i \(-0.472867\pi\)
0.0851365 + 0.996369i \(0.472867\pi\)
\(558\) −65.3607 −2.76694
\(559\) −9.33910 −0.395002
\(560\) −3.84543 −0.162499
\(561\) 0.544141 0.0229737
\(562\) 2.71682 0.114602
\(563\) 23.6255 0.995695 0.497847 0.867265i \(-0.334124\pi\)
0.497847 + 0.867265i \(0.334124\pi\)
\(564\) 1.07425 0.0452342
\(565\) 7.79191 0.327808
\(566\) 9.90901 0.416507
\(567\) −8.86984 −0.372498
\(568\) 0.420795 0.0176562
\(569\) 0.466002 0.0195358 0.00976792 0.999952i \(-0.496891\pi\)
0.00976792 + 0.999952i \(0.496891\pi\)
\(570\) −0.643139 −0.0269381
\(571\) 9.13380 0.382238 0.191119 0.981567i \(-0.438788\pi\)
0.191119 + 0.981567i \(0.438788\pi\)
\(572\) −5.09082 −0.212858
\(573\) 2.14769 0.0897211
\(574\) −9.25358 −0.386237
\(575\) −3.02307 −0.126071
\(576\) 25.6293 1.06789
\(577\) 17.2137 0.716616 0.358308 0.933604i \(-0.383354\pi\)
0.358308 + 0.933604i \(0.383354\pi\)
\(578\) −29.6877 −1.23485
\(579\) −1.72762 −0.0717975
\(580\) −0.592417 −0.0245988
\(581\) −8.73512 −0.362394
\(582\) 0.0615990 0.00255336
\(583\) −43.3351 −1.79476
\(584\) 2.11399 0.0874776
\(585\) −2.45360 −0.101444
\(586\) −9.60801 −0.396903
\(587\) 13.5138 0.557775 0.278887 0.960324i \(-0.410034\pi\)
0.278887 + 0.960324i \(0.410034\pi\)
\(588\) −0.249680 −0.0102966
\(589\) −28.7117 −1.18304
\(590\) −14.7916 −0.608959
\(591\) 0.623556 0.0256497
\(592\) −33.7361 −1.38654
\(593\) −21.3194 −0.875484 −0.437742 0.899101i \(-0.644222\pi\)
−0.437742 + 0.899101i \(0.644222\pi\)
\(594\) 4.34206 0.178157
\(595\) −1.51410 −0.0620721
\(596\) −47.5255 −1.94672
\(597\) −1.67296 −0.0684696
\(598\) 5.01499 0.205078
\(599\) −23.9550 −0.978775 −0.489388 0.872066i \(-0.662780\pi\)
−0.489388 + 0.872066i \(0.662780\pi\)
\(600\) −0.0181011 −0.000738973 0
\(601\) 20.0702 0.818681 0.409340 0.912382i \(-0.365759\pi\)
0.409340 + 0.912382i \(0.365759\pi\)
\(602\) −22.9381 −0.934889
\(603\) −41.2882 −1.68139
\(604\) −1.60451 −0.0652866
\(605\) 2.08386 0.0847210
\(606\) −2.89982 −0.117797
\(607\) 5.41787 0.219905 0.109952 0.993937i \(-0.464930\pi\)
0.109952 + 0.993937i \(0.464930\pi\)
\(608\) 21.3449 0.865648
\(609\) 0.0343701 0.00139275
\(610\) 14.2522 0.577054
\(611\) 3.53596 0.143050
\(612\) 9.37754 0.379064
\(613\) −10.8001 −0.436213 −0.218106 0.975925i \(-0.569988\pi\)
−0.218106 + 0.975925i \(0.569988\pi\)
\(614\) 12.8439 0.518337
\(615\) 0.551748 0.0222486
\(616\) −0.449080 −0.0180940
\(617\) −6.15143 −0.247647 −0.123824 0.992304i \(-0.539516\pi\)
−0.123824 + 0.992304i \(0.539516\pi\)
\(618\) 2.60251 0.104688
\(619\) 11.3119 0.454665 0.227333 0.973817i \(-0.427000\pi\)
0.227333 + 0.973817i \(0.427000\pi\)
\(620\) −22.4996 −0.903606
\(621\) −2.17780 −0.0873920
\(622\) 14.4193 0.578162
\(623\) −5.44007 −0.217952
\(624\) −0.380363 −0.0152267
\(625\) 1.00000 0.0400000
\(626\) 66.2462 2.64773
\(627\) 0.951384 0.0379946
\(628\) 26.5417 1.05913
\(629\) −13.2832 −0.529637
\(630\) −6.02638 −0.240097
\(631\) −31.9598 −1.27230 −0.636150 0.771566i \(-0.719474\pi\)
−0.636150 + 0.771566i \(0.719474\pi\)
\(632\) −1.47606 −0.0587145
\(633\) −1.68293 −0.0668904
\(634\) 42.1157 1.67263
\(635\) −19.1524 −0.760039
\(636\) 3.62355 0.143683
\(637\) −0.821835 −0.0325623
\(638\) 1.72123 0.0681440
\(639\) −8.35323 −0.330449
\(640\) 1.20233 0.0475263
\(641\) −1.77275 −0.0700196 −0.0350098 0.999387i \(-0.511146\pi\)
−0.0350098 + 0.999387i \(0.511146\pi\)
\(642\) −0.520115 −0.0205273
\(643\) −8.92532 −0.351980 −0.175990 0.984392i \(-0.556313\pi\)
−0.175990 + 0.984392i \(0.556313\pi\)
\(644\) 6.27137 0.247127
\(645\) 1.36769 0.0538529
\(646\) 8.09079 0.318328
\(647\) −33.4910 −1.31667 −0.658334 0.752726i \(-0.728739\pi\)
−0.658334 + 0.752726i \(0.728739\pi\)
\(648\) 1.33399 0.0524039
\(649\) 21.8809 0.858900
\(650\) −1.65891 −0.0650677
\(651\) 1.30535 0.0511609
\(652\) 21.0115 0.822876
\(653\) 24.1848 0.946426 0.473213 0.880948i \(-0.343094\pi\)
0.473213 + 0.880948i \(0.343094\pi\)
\(654\) −0.852171 −0.0333225
\(655\) 4.72072 0.184454
\(656\) −17.6286 −0.688281
\(657\) −41.9650 −1.63721
\(658\) 8.68482 0.338569
\(659\) −24.4776 −0.953512 −0.476756 0.879036i \(-0.658187\pi\)
−0.476756 + 0.879036i \(0.658187\pi\)
\(660\) 0.745542 0.0290202
\(661\) 36.2043 1.40818 0.704091 0.710109i \(-0.251355\pi\)
0.704091 + 0.710109i \(0.251355\pi\)
\(662\) 45.8227 1.78095
\(663\) −0.149764 −0.00581636
\(664\) 1.31372 0.0509824
\(665\) −2.64727 −0.102657
\(666\) −52.8696 −2.04865
\(667\) −0.863296 −0.0334270
\(668\) 29.6826 1.14846
\(669\) 0.231571 0.00895303
\(670\) −27.9154 −1.07847
\(671\) −21.0830 −0.813900
\(672\) −0.970427 −0.0374350
\(673\) −10.8707 −0.419034 −0.209517 0.977805i \(-0.567189\pi\)
−0.209517 + 0.977805i \(0.567189\pi\)
\(674\) 52.6444 2.02779
\(675\) 0.720394 0.0277280
\(676\) −25.5674 −0.983363
\(677\) −13.4130 −0.515503 −0.257752 0.966211i \(-0.582982\pi\)
−0.257752 + 0.966211i \(0.582982\pi\)
\(678\) 1.89300 0.0727002
\(679\) 0.253552 0.00973044
\(680\) 0.227714 0.00873244
\(681\) 3.12659 0.119811
\(682\) 65.3711 2.50319
\(683\) 28.0061 1.07162 0.535811 0.844338i \(-0.320006\pi\)
0.535811 + 0.844338i \(0.320006\pi\)
\(684\) 16.3958 0.626910
\(685\) −4.06542 −0.155332
\(686\) −2.01854 −0.0770682
\(687\) −0.120356 −0.00459188
\(688\) −43.6984 −1.66599
\(689\) 11.9271 0.454387
\(690\) −0.734436 −0.0279595
\(691\) −41.6412 −1.58411 −0.792053 0.610452i \(-0.790988\pi\)
−0.792053 + 0.610452i \(0.790988\pi\)
\(692\) −0.477223 −0.0181413
\(693\) 8.91472 0.338642
\(694\) 54.4146 2.06555
\(695\) −11.0486 −0.419097
\(696\) −0.00516912 −0.000195935 0
\(697\) −6.94108 −0.262912
\(698\) −25.4934 −0.964941
\(699\) −0.461721 −0.0174639
\(700\) −2.07451 −0.0784090
\(701\) −13.0563 −0.493129 −0.246564 0.969126i \(-0.579302\pi\)
−0.246564 + 0.969126i \(0.579302\pi\)
\(702\) −1.19507 −0.0451049
\(703\) −23.2246 −0.875932
\(704\) −25.6334 −0.966093
\(705\) −0.517835 −0.0195028
\(706\) −49.6836 −1.86987
\(707\) −11.9362 −0.448906
\(708\) −1.82962 −0.0687612
\(709\) −35.4715 −1.33216 −0.666081 0.745879i \(-0.732030\pi\)
−0.666081 + 0.745879i \(0.732030\pi\)
\(710\) −5.64772 −0.211955
\(711\) 29.3014 1.09889
\(712\) 0.818163 0.0306620
\(713\) −32.7874 −1.22790
\(714\) −0.367842 −0.0137661
\(715\) 2.45399 0.0917741
\(716\) 4.41455 0.164979
\(717\) −0.357711 −0.0133590
\(718\) −55.1709 −2.05896
\(719\) 3.15811 0.117778 0.0588889 0.998265i \(-0.481244\pi\)
0.0588889 + 0.998265i \(0.481244\pi\)
\(720\) −11.4806 −0.427857
\(721\) 10.7124 0.398950
\(722\) −24.2062 −0.900862
\(723\) 1.00871 0.0375142
\(724\) −8.56537 −0.318330
\(725\) 0.285570 0.0106058
\(726\) 0.506262 0.0187891
\(727\) −2.07992 −0.0771401 −0.0385701 0.999256i \(-0.512280\pi\)
−0.0385701 + 0.999256i \(0.512280\pi\)
\(728\) 0.123600 0.00458094
\(729\) −26.2209 −0.971145
\(730\) −28.3730 −1.05013
\(731\) −17.2058 −0.636380
\(732\) 1.76290 0.0651586
\(733\) −16.5428 −0.611022 −0.305511 0.952189i \(-0.598827\pi\)
−0.305511 + 0.952189i \(0.598827\pi\)
\(734\) 9.53239 0.351847
\(735\) 0.120356 0.00443941
\(736\) 24.3749 0.898469
\(737\) 41.2948 1.52111
\(738\) −27.6267 −1.01695
\(739\) 17.3838 0.639472 0.319736 0.947507i \(-0.396406\pi\)
0.319736 + 0.947507i \(0.396406\pi\)
\(740\) −18.1997 −0.669034
\(741\) −0.261850 −0.00961929
\(742\) 29.2947 1.07544
\(743\) −7.12855 −0.261521 −0.130761 0.991414i \(-0.541742\pi\)
−0.130761 + 0.991414i \(0.541742\pi\)
\(744\) −0.196320 −0.00719743
\(745\) 22.9093 0.839332
\(746\) −56.0228 −2.05114
\(747\) −26.0788 −0.954174
\(748\) −9.37903 −0.342931
\(749\) −2.14088 −0.0782262
\(750\) 0.242944 0.00887106
\(751\) −45.6608 −1.66618 −0.833092 0.553134i \(-0.813432\pi\)
−0.833092 + 0.553134i \(0.813432\pi\)
\(752\) 16.5451 0.603337
\(753\) 1.30126 0.0474207
\(754\) −0.473734 −0.0172524
\(755\) 0.773441 0.0281484
\(756\) −1.49446 −0.0543531
\(757\) 23.3090 0.847180 0.423590 0.905854i \(-0.360770\pi\)
0.423590 + 0.905854i \(0.360770\pi\)
\(758\) −23.9425 −0.869630
\(759\) 1.08644 0.0394352
\(760\) 0.398139 0.0144420
\(761\) 36.5513 1.32498 0.662492 0.749069i \(-0.269499\pi\)
0.662492 + 0.749069i \(0.269499\pi\)
\(762\) −4.65296 −0.168559
\(763\) −3.50768 −0.126987
\(764\) −37.0184 −1.33928
\(765\) −4.52037 −0.163434
\(766\) −6.55844 −0.236966
\(767\) −6.02228 −0.217452
\(768\) −1.77431 −0.0640248
\(769\) 32.8931 1.18616 0.593078 0.805145i \(-0.297913\pi\)
0.593078 + 0.805145i \(0.297913\pi\)
\(770\) 6.02734 0.217210
\(771\) 0.360208 0.0129726
\(772\) 29.7780 1.07173
\(773\) −22.2418 −0.799981 −0.399991 0.916519i \(-0.630987\pi\)
−0.399991 + 0.916519i \(0.630987\pi\)
\(774\) −68.4821 −2.46154
\(775\) 10.8458 0.389591
\(776\) −0.0381332 −0.00136890
\(777\) 1.05589 0.0378798
\(778\) −55.7008 −1.99697
\(779\) −12.1359 −0.434813
\(780\) −0.205196 −0.00734718
\(781\) 8.35456 0.298950
\(782\) 9.23932 0.330397
\(783\) 0.205723 0.00735193
\(784\) −3.84543 −0.137337
\(785\) −12.7942 −0.456646
\(786\) 1.14687 0.0409076
\(787\) 1.42465 0.0507831 0.0253916 0.999678i \(-0.491917\pi\)
0.0253916 + 0.999678i \(0.491917\pi\)
\(788\) −10.7479 −0.382877
\(789\) 1.17329 0.0417703
\(790\) 19.8110 0.704843
\(791\) 7.79191 0.277049
\(792\) −1.34074 −0.0476410
\(793\) 5.80268 0.206059
\(794\) 47.9861 1.70296
\(795\) −1.74671 −0.0619493
\(796\) 28.8358 1.02206
\(797\) −37.2617 −1.31988 −0.659939 0.751319i \(-0.729418\pi\)
−0.659939 + 0.751319i \(0.729418\pi\)
\(798\) −0.643139 −0.0227669
\(799\) 6.51445 0.230465
\(800\) −8.06296 −0.285069
\(801\) −16.2414 −0.573862
\(802\) −3.28110 −0.115860
\(803\) 41.9717 1.48115
\(804\) −3.45295 −0.121776
\(805\) −3.02307 −0.106549
\(806\) −17.9921 −0.633745
\(807\) −1.77394 −0.0624458
\(808\) 1.79515 0.0631532
\(809\) −19.9105 −0.700016 −0.350008 0.936747i \(-0.613821\pi\)
−0.350008 + 0.936747i \(0.613821\pi\)
\(810\) −17.9041 −0.629087
\(811\) 17.9295 0.629589 0.314795 0.949160i \(-0.398064\pi\)
0.314795 + 0.949160i \(0.398064\pi\)
\(812\) −0.592417 −0.0207897
\(813\) −3.39183 −0.118957
\(814\) 52.8780 1.85337
\(815\) −10.1285 −0.354784
\(816\) −0.700759 −0.0245315
\(817\) −30.0829 −1.05247
\(818\) −22.4358 −0.784451
\(819\) −2.45360 −0.0857357
\(820\) −9.51014 −0.332109
\(821\) −5.29890 −0.184933 −0.0924664 0.995716i \(-0.529475\pi\)
−0.0924664 + 0.995716i \(0.529475\pi\)
\(822\) −0.987669 −0.0344489
\(823\) −12.2789 −0.428017 −0.214008 0.976832i \(-0.568652\pi\)
−0.214008 + 0.976832i \(0.568652\pi\)
\(824\) −1.61110 −0.0561252
\(825\) −0.359383 −0.0125121
\(826\) −14.7916 −0.514664
\(827\) 29.5684 1.02819 0.514097 0.857732i \(-0.328127\pi\)
0.514097 + 0.857732i \(0.328127\pi\)
\(828\) 18.7233 0.650679
\(829\) −31.3691 −1.08950 −0.544748 0.838600i \(-0.683375\pi\)
−0.544748 + 0.838600i \(0.683375\pi\)
\(830\) −17.6322 −0.612022
\(831\) 3.02024 0.104771
\(832\) 7.05508 0.244591
\(833\) −1.51410 −0.0524605
\(834\) −2.68419 −0.0929459
\(835\) −14.3083 −0.495159
\(836\) −16.3984 −0.567151
\(837\) 7.81322 0.270064
\(838\) 73.6099 2.54281
\(839\) 34.7611 1.20009 0.600044 0.799967i \(-0.295150\pi\)
0.600044 + 0.799967i \(0.295150\pi\)
\(840\) −0.0181011 −0.000624546 0
\(841\) −28.9184 −0.997188
\(842\) −13.0770 −0.450665
\(843\) −0.161992 −0.00557928
\(844\) 29.0076 0.998484
\(845\) 12.3246 0.423979
\(846\) 25.9286 0.891445
\(847\) 2.08386 0.0716023
\(848\) 55.8080 1.91646
\(849\) −0.590828 −0.0202772
\(850\) −3.05627 −0.104829
\(851\) −26.5214 −0.909142
\(852\) −0.698584 −0.0239331
\(853\) −32.0906 −1.09876 −0.549381 0.835572i \(-0.685137\pi\)
−0.549381 + 0.835572i \(0.685137\pi\)
\(854\) 14.2522 0.487700
\(855\) −7.90347 −0.270293
\(856\) 0.321980 0.0110050
\(857\) 37.3455 1.27570 0.637849 0.770161i \(-0.279824\pi\)
0.637849 + 0.770161i \(0.279824\pi\)
\(858\) 0.596182 0.0203533
\(859\) −48.6768 −1.66083 −0.830416 0.557144i \(-0.811897\pi\)
−0.830416 + 0.557144i \(0.811897\pi\)
\(860\) −23.5741 −0.803871
\(861\) 0.551748 0.0188035
\(862\) 1.22266 0.0416441
\(863\) 3.21053 0.109288 0.0546438 0.998506i \(-0.482598\pi\)
0.0546438 + 0.998506i \(0.482598\pi\)
\(864\) −5.80851 −0.197609
\(865\) 0.230042 0.00782165
\(866\) 80.8251 2.74655
\(867\) 1.77014 0.0601171
\(868\) −22.4996 −0.763686
\(869\) −29.3060 −0.994139
\(870\) 0.0693775 0.00235212
\(871\) −11.3656 −0.385108
\(872\) 0.527541 0.0178648
\(873\) 0.756984 0.0256200
\(874\) 16.1541 0.546422
\(875\) 1.00000 0.0338062
\(876\) −3.50955 −0.118577
\(877\) 18.4976 0.624621 0.312310 0.949980i \(-0.398897\pi\)
0.312310 + 0.949980i \(0.398897\pi\)
\(878\) 28.2603 0.953740
\(879\) 0.572881 0.0193228
\(880\) 11.4824 0.387073
\(881\) 18.7894 0.633032 0.316516 0.948587i \(-0.397487\pi\)
0.316516 + 0.948587i \(0.397487\pi\)
\(882\) −6.02638 −0.202919
\(883\) −10.1513 −0.341618 −0.170809 0.985304i \(-0.554638\pi\)
−0.170809 + 0.985304i \(0.554638\pi\)
\(884\) 2.58139 0.0868217
\(885\) 0.881952 0.0296465
\(886\) 61.8823 2.07897
\(887\) 15.7594 0.529149 0.264575 0.964365i \(-0.414768\pi\)
0.264575 + 0.964365i \(0.414768\pi\)
\(888\) −0.158801 −0.00532901
\(889\) −19.1524 −0.642350
\(890\) −10.9810 −0.368084
\(891\) 26.4853 0.887289
\(892\) −3.99144 −0.133643
\(893\) 11.3900 0.381150
\(894\) 5.56568 0.186144
\(895\) −2.12800 −0.0711311
\(896\) 1.20233 0.0401671
\(897\) −0.299020 −0.00998400
\(898\) 41.2326 1.37595
\(899\) 3.09722 0.103298
\(900\) −6.19347 −0.206449
\(901\) 21.9738 0.732055
\(902\) 27.6311 0.920015
\(903\) 1.36769 0.0455140
\(904\) −1.17187 −0.0389758
\(905\) 4.12887 0.137248
\(906\) 0.187903 0.00624266
\(907\) −45.6118 −1.51451 −0.757257 0.653117i \(-0.773461\pi\)
−0.757257 + 0.653117i \(0.773461\pi\)
\(908\) −53.8912 −1.78844
\(909\) −35.6356 −1.18196
\(910\) −1.65891 −0.0549923
\(911\) 13.9943 0.463651 0.231826 0.972757i \(-0.425530\pi\)
0.231826 + 0.972757i \(0.425530\pi\)
\(912\) −1.22522 −0.0405710
\(913\) 26.0830 0.863221
\(914\) −54.3362 −1.79728
\(915\) −0.849792 −0.0280933
\(916\) 2.07451 0.0685436
\(917\) 4.72072 0.155892
\(918\) −2.20172 −0.0726676
\(919\) 20.6800 0.682170 0.341085 0.940033i \(-0.389206\pi\)
0.341085 + 0.940033i \(0.389206\pi\)
\(920\) 0.454656 0.0149896
\(921\) −0.765821 −0.0252347
\(922\) 82.1960 2.70698
\(923\) −2.29943 −0.0756866
\(924\) 0.745542 0.0245265
\(925\) 8.77302 0.288455
\(926\) −40.1440 −1.31921
\(927\) 31.9820 1.05043
\(928\) −2.30254 −0.0755845
\(929\) −7.05111 −0.231339 −0.115670 0.993288i \(-0.536901\pi\)
−0.115670 + 0.993288i \(0.536901\pi\)
\(930\) 2.63491 0.0864022
\(931\) −2.64727 −0.0867609
\(932\) 7.95840 0.260686
\(933\) −0.859757 −0.0281472
\(934\) −38.7456 −1.26780
\(935\) 4.52109 0.147855
\(936\) 0.369011 0.0120615
\(937\) 18.9884 0.620325 0.310163 0.950684i \(-0.399617\pi\)
0.310163 + 0.950684i \(0.399617\pi\)
\(938\) −27.9154 −0.911471
\(939\) −3.94995 −0.128902
\(940\) 8.92561 0.291121
\(941\) 5.49813 0.179234 0.0896170 0.995976i \(-0.471436\pi\)
0.0896170 + 0.995976i \(0.471436\pi\)
\(942\) −3.10828 −0.101273
\(943\) −13.8586 −0.451299
\(944\) −28.1788 −0.917140
\(945\) 0.720394 0.0234344
\(946\) 68.4930 2.22690
\(947\) 60.6523 1.97093 0.985467 0.169868i \(-0.0543342\pi\)
0.985467 + 0.169868i \(0.0543342\pi\)
\(948\) 2.45048 0.0795881
\(949\) −11.5519 −0.374990
\(950\) −5.34363 −0.173370
\(951\) −2.51116 −0.0814300
\(952\) 0.227714 0.00738026
\(953\) −32.2600 −1.04500 −0.522502 0.852638i \(-0.675001\pi\)
−0.522502 + 0.852638i \(0.675001\pi\)
\(954\) 87.4597 2.83161
\(955\) 17.8444 0.577433
\(956\) 6.16565 0.199411
\(957\) −0.102629 −0.00331752
\(958\) −26.3114 −0.850084
\(959\) −4.06542 −0.131279
\(960\) −1.03320 −0.0333465
\(961\) 86.6305 2.79453
\(962\) −14.5536 −0.469228
\(963\) −6.39164 −0.205968
\(964\) −17.3865 −0.559981
\(965\) −14.3542 −0.462079
\(966\) −0.734436 −0.0236301
\(967\) 2.64984 0.0852132 0.0426066 0.999092i \(-0.486434\pi\)
0.0426066 + 0.999092i \(0.486434\pi\)
\(968\) −0.313404 −0.0100732
\(969\) −0.482416 −0.0154974
\(970\) 0.511805 0.0164331
\(971\) −10.1530 −0.325825 −0.162913 0.986640i \(-0.552089\pi\)
−0.162913 + 0.986640i \(0.552089\pi\)
\(972\) −6.69801 −0.214839
\(973\) −11.0486 −0.354202
\(974\) −2.81947 −0.0903416
\(975\) 0.0989130 0.00316775
\(976\) 27.1512 0.869090
\(977\) 44.2425 1.41544 0.707722 0.706491i \(-0.249723\pi\)
0.707722 + 0.706491i \(0.249723\pi\)
\(978\) −2.46065 −0.0786828
\(979\) 16.2440 0.519160
\(980\) −2.07451 −0.0662677
\(981\) −10.4722 −0.334353
\(982\) 39.2376 1.25212
\(983\) 32.2834 1.02968 0.514840 0.857286i \(-0.327851\pi\)
0.514840 + 0.857286i \(0.327851\pi\)
\(984\) −0.0829805 −0.00264532
\(985\) 5.18092 0.165078
\(986\) −0.872779 −0.0277950
\(987\) −0.517835 −0.0164829
\(988\) 4.51334 0.143589
\(989\) −34.3533 −1.09237
\(990\) 17.9947 0.571910
\(991\) −5.92942 −0.188354 −0.0941770 0.995555i \(-0.530022\pi\)
−0.0941770 + 0.995555i \(0.530022\pi\)
\(992\) −87.4489 −2.77651
\(993\) −2.73219 −0.0867035
\(994\) −5.64772 −0.179135
\(995\) −13.9001 −0.440662
\(996\) −2.18098 −0.0691071
\(997\) 11.2013 0.354748 0.177374 0.984143i \(-0.443240\pi\)
0.177374 + 0.984143i \(0.443240\pi\)
\(998\) 33.9295 1.07402
\(999\) 6.32003 0.199957
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 \(a_p\))