Properties

Label 8027.2.a.f.1.14
Level 8027
Weight 2
Character 8027.1
Self dual Yes
Analytic conductor 64.096
Analytic rank 0
Dimension 176
CM No

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Newspace parameters

Level: \( N \) = \( 8027 = 23 \cdot 349 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8027.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0959177025\)
Analytic rank: \(0\)
Dimension: \(176\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.14
Character \(\chi\) = 8027.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.45769 q^{2} +0.342548 q^{3} +4.04026 q^{4} -0.529727 q^{5} -0.841878 q^{6} -2.69173 q^{7} -5.01433 q^{8} -2.88266 q^{9} +O(q^{10})\) \(q-2.45769 q^{2} +0.342548 q^{3} +4.04026 q^{4} -0.529727 q^{5} -0.841878 q^{6} -2.69173 q^{7} -5.01433 q^{8} -2.88266 q^{9} +1.30191 q^{10} +3.44506 q^{11} +1.38398 q^{12} -3.97647 q^{13} +6.61545 q^{14} -0.181457 q^{15} +4.24317 q^{16} +4.73579 q^{17} +7.08470 q^{18} +0.229013 q^{19} -2.14024 q^{20} -0.922047 q^{21} -8.46689 q^{22} +1.00000 q^{23} -1.71765 q^{24} -4.71939 q^{25} +9.77295 q^{26} -2.01509 q^{27} -10.8753 q^{28} +1.12006 q^{29} +0.445966 q^{30} -2.98049 q^{31} -0.399747 q^{32} +1.18010 q^{33} -11.6391 q^{34} +1.42588 q^{35} -11.6467 q^{36} +1.41985 q^{37} -0.562845 q^{38} -1.36213 q^{39} +2.65623 q^{40} +4.11935 q^{41} +2.26611 q^{42} -8.35321 q^{43} +13.9189 q^{44} +1.52702 q^{45} -2.45769 q^{46} +4.03088 q^{47} +1.45349 q^{48} +0.245415 q^{49} +11.5988 q^{50} +1.62223 q^{51} -16.0660 q^{52} -2.06114 q^{53} +4.95248 q^{54} -1.82494 q^{55} +13.4972 q^{56} +0.0784480 q^{57} -2.75276 q^{58} -4.70019 q^{59} -0.733133 q^{60} +5.09790 q^{61} +7.32514 q^{62} +7.75935 q^{63} -7.50388 q^{64} +2.10645 q^{65} -2.90032 q^{66} +11.6013 q^{67} +19.1338 q^{68} +0.342548 q^{69} -3.50439 q^{70} -9.99153 q^{71} +14.4546 q^{72} +4.39154 q^{73} -3.48956 q^{74} -1.61662 q^{75} +0.925273 q^{76} -9.27316 q^{77} +3.34770 q^{78} +6.05625 q^{79} -2.24772 q^{80} +7.95772 q^{81} -10.1241 q^{82} -4.61756 q^{83} -3.72531 q^{84} -2.50868 q^{85} +20.5296 q^{86} +0.383673 q^{87} -17.2746 q^{88} -16.5032 q^{89} -3.75296 q^{90} +10.7036 q^{91} +4.04026 q^{92} -1.02096 q^{93} -9.90666 q^{94} -0.121315 q^{95} -0.136932 q^{96} -18.0047 q^{97} -0.603154 q^{98} -9.93093 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 176q + 19q^{2} + 22q^{3} + 203q^{4} + 28q^{5} + 9q^{6} + 30q^{7} + 51q^{8} + 204q^{9} + O(q^{10}) \) \( 176q + 19q^{2} + 22q^{3} + 203q^{4} + 28q^{5} + 9q^{6} + 30q^{7} + 51q^{8} + 204q^{9} + 18q^{10} + 11q^{11} + 46q^{12} + 87q^{13} - 6q^{14} + 29q^{15} + 257q^{16} + 14q^{17} + 72q^{18} + 34q^{19} + 45q^{20} + 23q^{21} + 62q^{22} + 176q^{23} + 33q^{24} + 272q^{25} + 31q^{26} + 82q^{27} + 80q^{28} + 75q^{29} - 30q^{30} + 73q^{31} + 71q^{32} + 30q^{33} + 23q^{34} + 44q^{35} + 264q^{36} + 236q^{37} - 21q^{38} + 17q^{39} + 43q^{40} + 51q^{41} + 38q^{42} + 51q^{43} + 12q^{44} + 127q^{45} + 19q^{46} + 45q^{47} + 61q^{48} + 268q^{49} + 55q^{50} - 3q^{51} + 166q^{52} + 63q^{53} - 32q^{54} + 11q^{55} - 9q^{56} + 72q^{57} + 98q^{58} + 95q^{59} - 7q^{60} + 73q^{61} + 12q^{62} + 19q^{63} + 365q^{64} + 19q^{65} - 28q^{66} + 138q^{67} + 16q^{68} + 22q^{69} + 100q^{70} + 85q^{71} + 129q^{72} + 118q^{73} - 21q^{74} - 12q^{75} + 52q^{76} + 75q^{77} + 97q^{78} + 74q^{79} + 8q^{80} + 280q^{81} + 67q^{82} + 10q^{83} - 51q^{84} + 169q^{85} - 39q^{86} - 6q^{87} + 159q^{88} + 38q^{89} + 22q^{90} + 90q^{91} + 203q^{92} + 230q^{93} + 63q^{94} + 30q^{95} + 107q^{96} + 161q^{97} + 58q^{98} + 7q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.45769 −1.73785 −0.868926 0.494942i \(-0.835189\pi\)
−0.868926 + 0.494942i \(0.835189\pi\)
\(3\) 0.342548 0.197770 0.0988851 0.995099i \(-0.468472\pi\)
0.0988851 + 0.995099i \(0.468472\pi\)
\(4\) 4.04026 2.02013
\(5\) −0.529727 −0.236901 −0.118451 0.992960i \(-0.537793\pi\)
−0.118451 + 0.992960i \(0.537793\pi\)
\(6\) −0.841878 −0.343695
\(7\) −2.69173 −1.01738 −0.508689 0.860950i \(-0.669870\pi\)
−0.508689 + 0.860950i \(0.669870\pi\)
\(8\) −5.01433 −1.77283
\(9\) −2.88266 −0.960887
\(10\) 1.30191 0.411699
\(11\) 3.44506 1.03872 0.519362 0.854555i \(-0.326170\pi\)
0.519362 + 0.854555i \(0.326170\pi\)
\(12\) 1.38398 0.399521
\(13\) −3.97647 −1.10287 −0.551437 0.834216i \(-0.685920\pi\)
−0.551437 + 0.834216i \(0.685920\pi\)
\(14\) 6.61545 1.76805
\(15\) −0.181457 −0.0468520
\(16\) 4.24317 1.06079
\(17\) 4.73579 1.14860 0.574299 0.818646i \(-0.305275\pi\)
0.574299 + 0.818646i \(0.305275\pi\)
\(18\) 7.08470 1.66988
\(19\) 0.229013 0.0525393 0.0262696 0.999655i \(-0.491637\pi\)
0.0262696 + 0.999655i \(0.491637\pi\)
\(20\) −2.14024 −0.478571
\(21\) −0.922047 −0.201207
\(22\) −8.46689 −1.80515
\(23\) 1.00000 0.208514
\(24\) −1.71765 −0.350613
\(25\) −4.71939 −0.943878
\(26\) 9.77295 1.91663
\(27\) −2.01509 −0.387805
\(28\) −10.8753 −2.05524
\(29\) 1.12006 0.207989 0.103995 0.994578i \(-0.466838\pi\)
0.103995 + 0.994578i \(0.466838\pi\)
\(30\) 0.445966 0.0814218
\(31\) −2.98049 −0.535313 −0.267656 0.963514i \(-0.586249\pi\)
−0.267656 + 0.963514i \(0.586249\pi\)
\(32\) −0.399747 −0.0706660
\(33\) 1.18010 0.205428
\(34\) −11.6391 −1.99609
\(35\) 1.42588 0.241018
\(36\) −11.6467 −1.94112
\(37\) 1.41985 0.233422 0.116711 0.993166i \(-0.462765\pi\)
0.116711 + 0.993166i \(0.462765\pi\)
\(38\) −0.562845 −0.0913055
\(39\) −1.36213 −0.218116
\(40\) 2.65623 0.419986
\(41\) 4.11935 0.643334 0.321667 0.946853i \(-0.395757\pi\)
0.321667 + 0.946853i \(0.395757\pi\)
\(42\) 2.26611 0.349668
\(43\) −8.35321 −1.27385 −0.636926 0.770925i \(-0.719794\pi\)
−0.636926 + 0.770925i \(0.719794\pi\)
\(44\) 13.9189 2.09836
\(45\) 1.52702 0.227635
\(46\) −2.45769 −0.362367
\(47\) 4.03088 0.587964 0.293982 0.955811i \(-0.405019\pi\)
0.293982 + 0.955811i \(0.405019\pi\)
\(48\) 1.45349 0.209793
\(49\) 0.245415 0.0350593
\(50\) 11.5988 1.64032
\(51\) 1.62223 0.227158
\(52\) −16.0660 −2.22795
\(53\) −2.06114 −0.283119 −0.141559 0.989930i \(-0.545212\pi\)
−0.141559 + 0.989930i \(0.545212\pi\)
\(54\) 4.95248 0.673947
\(55\) −1.82494 −0.246075
\(56\) 13.4972 1.80364
\(57\) 0.0784480 0.0103907
\(58\) −2.75276 −0.361455
\(59\) −4.70019 −0.611913 −0.305956 0.952046i \(-0.598976\pi\)
−0.305956 + 0.952046i \(0.598976\pi\)
\(60\) −0.733133 −0.0946471
\(61\) 5.09790 0.652720 0.326360 0.945246i \(-0.394178\pi\)
0.326360 + 0.945246i \(0.394178\pi\)
\(62\) 7.32514 0.930294
\(63\) 7.75935 0.977586
\(64\) −7.50388 −0.937985
\(65\) 2.10645 0.261272
\(66\) −2.90032 −0.357004
\(67\) 11.6013 1.41732 0.708660 0.705550i \(-0.249300\pi\)
0.708660 + 0.705550i \(0.249300\pi\)
\(68\) 19.1338 2.32031
\(69\) 0.342548 0.0412379
\(70\) −3.50439 −0.418854
\(71\) −9.99153 −1.18578 −0.592888 0.805285i \(-0.702012\pi\)
−0.592888 + 0.805285i \(0.702012\pi\)
\(72\) 14.4546 1.70349
\(73\) 4.39154 0.513991 0.256996 0.966413i \(-0.417267\pi\)
0.256996 + 0.966413i \(0.417267\pi\)
\(74\) −3.48956 −0.405653
\(75\) −1.61662 −0.186671
\(76\) 0.925273 0.106136
\(77\) −9.27316 −1.05677
\(78\) 3.34770 0.379053
\(79\) 6.05625 0.681382 0.340691 0.940175i \(-0.389339\pi\)
0.340691 + 0.940175i \(0.389339\pi\)
\(80\) −2.24772 −0.251303
\(81\) 7.95772 0.884191
\(82\) −10.1241 −1.11802
\(83\) −4.61756 −0.506843 −0.253422 0.967356i \(-0.581556\pi\)
−0.253422 + 0.967356i \(0.581556\pi\)
\(84\) −3.72531 −0.406464
\(85\) −2.50868 −0.272104
\(86\) 20.5296 2.21377
\(87\) 0.383673 0.0411341
\(88\) −17.2746 −1.84148
\(89\) −16.5032 −1.74933 −0.874666 0.484725i \(-0.838920\pi\)
−0.874666 + 0.484725i \(0.838920\pi\)
\(90\) −3.75296 −0.395597
\(91\) 10.7036 1.12204
\(92\) 4.04026 0.421226
\(93\) −1.02096 −0.105869
\(94\) −9.90666 −1.02179
\(95\) −0.121315 −0.0124466
\(96\) −0.136932 −0.0139756
\(97\) −18.0047 −1.82810 −0.914049 0.405603i \(-0.867062\pi\)
−0.914049 + 0.405603i \(0.867062\pi\)
\(98\) −0.603154 −0.0609278
\(99\) −9.93093 −0.998096
\(100\) −19.0675 −1.90675
\(101\) −12.7298 −1.26667 −0.633334 0.773879i \(-0.718314\pi\)
−0.633334 + 0.773879i \(0.718314\pi\)
\(102\) −3.98696 −0.394767
\(103\) −7.48581 −0.737599 −0.368800 0.929509i \(-0.620231\pi\)
−0.368800 + 0.929509i \(0.620231\pi\)
\(104\) 19.9393 1.95521
\(105\) 0.488433 0.0476662
\(106\) 5.06564 0.492019
\(107\) 11.1675 1.07960 0.539799 0.841794i \(-0.318500\pi\)
0.539799 + 0.841794i \(0.318500\pi\)
\(108\) −8.14150 −0.783416
\(109\) −15.8363 −1.51685 −0.758423 0.651762i \(-0.774030\pi\)
−0.758423 + 0.651762i \(0.774030\pi\)
\(110\) 4.48514 0.427642
\(111\) 0.486368 0.0461640
\(112\) −11.4215 −1.07923
\(113\) 13.8554 1.30341 0.651705 0.758473i \(-0.274054\pi\)
0.651705 + 0.758473i \(0.274054\pi\)
\(114\) −0.192801 −0.0180575
\(115\) −0.529727 −0.0493973
\(116\) 4.52532 0.420165
\(117\) 11.4628 1.05974
\(118\) 11.5516 1.06341
\(119\) −12.7475 −1.16856
\(120\) 0.909885 0.0830608
\(121\) 0.868409 0.0789463
\(122\) −12.5291 −1.13433
\(123\) 1.41107 0.127232
\(124\) −12.0420 −1.08140
\(125\) 5.14863 0.460507
\(126\) −19.0701 −1.69890
\(127\) 20.8679 1.85173 0.925865 0.377855i \(-0.123338\pi\)
0.925865 + 0.377855i \(0.123338\pi\)
\(128\) 19.2417 1.70074
\(129\) −2.86137 −0.251930
\(130\) −5.17700 −0.454053
\(131\) −6.97451 −0.609366 −0.304683 0.952454i \(-0.598550\pi\)
−0.304683 + 0.952454i \(0.598550\pi\)
\(132\) 4.76789 0.414992
\(133\) −0.616442 −0.0534523
\(134\) −28.5123 −2.46309
\(135\) 1.06745 0.0918715
\(136\) −23.7468 −2.03627
\(137\) −12.2238 −1.04435 −0.522175 0.852838i \(-0.674879\pi\)
−0.522175 + 0.852838i \(0.674879\pi\)
\(138\) −0.841878 −0.0716654
\(139\) 3.15644 0.267726 0.133863 0.991000i \(-0.457262\pi\)
0.133863 + 0.991000i \(0.457262\pi\)
\(140\) 5.76094 0.486888
\(141\) 1.38077 0.116282
\(142\) 24.5561 2.06070
\(143\) −13.6992 −1.14558
\(144\) −12.2316 −1.01930
\(145\) −0.593325 −0.0492729
\(146\) −10.7931 −0.893240
\(147\) 0.0840663 0.00693367
\(148\) 5.73657 0.471543
\(149\) −1.72361 −0.141204 −0.0706020 0.997505i \(-0.522492\pi\)
−0.0706020 + 0.997505i \(0.522492\pi\)
\(150\) 3.97315 0.324406
\(151\) −9.43083 −0.767470 −0.383735 0.923443i \(-0.625362\pi\)
−0.383735 + 0.923443i \(0.625362\pi\)
\(152\) −1.14835 −0.0931433
\(153\) −13.6517 −1.10367
\(154\) 22.7906 1.83652
\(155\) 1.57885 0.126816
\(156\) −5.50336 −0.440622
\(157\) 7.00554 0.559103 0.279552 0.960131i \(-0.409814\pi\)
0.279552 + 0.960131i \(0.409814\pi\)
\(158\) −14.8844 −1.18414
\(159\) −0.706038 −0.0559924
\(160\) 0.211757 0.0167409
\(161\) −2.69173 −0.212138
\(162\) −19.5576 −1.53659
\(163\) −9.05829 −0.709500 −0.354750 0.934961i \(-0.615434\pi\)
−0.354750 + 0.934961i \(0.615434\pi\)
\(164\) 16.6432 1.29962
\(165\) −0.625130 −0.0486663
\(166\) 11.3486 0.880819
\(167\) 4.62025 0.357525 0.178763 0.983892i \(-0.442791\pi\)
0.178763 + 0.983892i \(0.442791\pi\)
\(168\) 4.62344 0.356707
\(169\) 2.81232 0.216332
\(170\) 6.16556 0.472877
\(171\) −0.660168 −0.0504843
\(172\) −33.7491 −2.57335
\(173\) −11.0639 −0.841174 −0.420587 0.907252i \(-0.638176\pi\)
−0.420587 + 0.907252i \(0.638176\pi\)
\(174\) −0.942951 −0.0714849
\(175\) 12.7033 0.960281
\(176\) 14.6179 1.10187
\(177\) −1.61004 −0.121018
\(178\) 40.5597 3.04008
\(179\) −21.3674 −1.59707 −0.798537 0.601945i \(-0.794392\pi\)
−0.798537 + 0.601945i \(0.794392\pi\)
\(180\) 6.16957 0.459853
\(181\) 21.5933 1.60502 0.802510 0.596639i \(-0.203497\pi\)
0.802510 + 0.596639i \(0.203497\pi\)
\(182\) −26.3061 −1.94994
\(183\) 1.74628 0.129088
\(184\) −5.01433 −0.369661
\(185\) −0.752135 −0.0552981
\(186\) 2.50921 0.183984
\(187\) 16.3151 1.19308
\(188\) 16.2858 1.18776
\(189\) 5.42409 0.394544
\(190\) 0.298154 0.0216304
\(191\) 3.09135 0.223683 0.111841 0.993726i \(-0.464325\pi\)
0.111841 + 0.993726i \(0.464325\pi\)
\(192\) −2.57044 −0.185505
\(193\) 9.88437 0.711492 0.355746 0.934583i \(-0.384227\pi\)
0.355746 + 0.934583i \(0.384227\pi\)
\(194\) 44.2500 3.17696
\(195\) 0.721559 0.0516719
\(196\) 0.991539 0.0708242
\(197\) 11.9903 0.854271 0.427135 0.904188i \(-0.359523\pi\)
0.427135 + 0.904188i \(0.359523\pi\)
\(198\) 24.4072 1.73454
\(199\) −7.49757 −0.531488 −0.265744 0.964044i \(-0.585618\pi\)
−0.265744 + 0.964044i \(0.585618\pi\)
\(200\) 23.6646 1.67334
\(201\) 3.97399 0.280304
\(202\) 31.2861 2.20128
\(203\) −3.01489 −0.211604
\(204\) 6.55425 0.458889
\(205\) −2.18213 −0.152407
\(206\) 18.3978 1.28184
\(207\) −2.88266 −0.200359
\(208\) −16.8728 −1.16992
\(209\) 0.788964 0.0545738
\(210\) −1.20042 −0.0828368
\(211\) −22.4754 −1.54727 −0.773634 0.633633i \(-0.781563\pi\)
−0.773634 + 0.633633i \(0.781563\pi\)
\(212\) −8.32752 −0.571936
\(213\) −3.42258 −0.234511
\(214\) −27.4462 −1.87618
\(215\) 4.42493 0.301777
\(216\) 10.1043 0.687513
\(217\) 8.02269 0.544615
\(218\) 38.9209 2.63605
\(219\) 1.50431 0.101652
\(220\) −7.37323 −0.497103
\(221\) −18.8317 −1.26676
\(222\) −1.19534 −0.0802261
\(223\) 24.4105 1.63465 0.817325 0.576176i \(-0.195456\pi\)
0.817325 + 0.576176i \(0.195456\pi\)
\(224\) 1.07601 0.0718940
\(225\) 13.6044 0.906960
\(226\) −34.0524 −2.26513
\(227\) 25.1855 1.67162 0.835810 0.549019i \(-0.184999\pi\)
0.835810 + 0.549019i \(0.184999\pi\)
\(228\) 0.316950 0.0209905
\(229\) 27.0410 1.78692 0.893458 0.449146i \(-0.148272\pi\)
0.893458 + 0.449146i \(0.148272\pi\)
\(230\) 1.30191 0.0858453
\(231\) −3.17650 −0.208999
\(232\) −5.61633 −0.368730
\(233\) −3.00162 −0.196643 −0.0983213 0.995155i \(-0.531347\pi\)
−0.0983213 + 0.995155i \(0.531347\pi\)
\(234\) −28.1721 −1.84167
\(235\) −2.13527 −0.139289
\(236\) −18.9900 −1.23614
\(237\) 2.07456 0.134757
\(238\) 31.3294 2.03078
\(239\) 24.4826 1.58364 0.791822 0.610751i \(-0.209132\pi\)
0.791822 + 0.610751i \(0.209132\pi\)
\(240\) −0.769952 −0.0497002
\(241\) 3.93065 0.253196 0.126598 0.991954i \(-0.459594\pi\)
0.126598 + 0.991954i \(0.459594\pi\)
\(242\) −2.13428 −0.137197
\(243\) 8.77118 0.562671
\(244\) 20.5968 1.31858
\(245\) −0.130003 −0.00830558
\(246\) −3.46799 −0.221111
\(247\) −0.910665 −0.0579442
\(248\) 14.9452 0.949020
\(249\) −1.58174 −0.100238
\(250\) −12.6537 −0.800293
\(251\) 8.37786 0.528806 0.264403 0.964412i \(-0.414825\pi\)
0.264403 + 0.964412i \(0.414825\pi\)
\(252\) 31.3498 1.97485
\(253\) 3.44506 0.216589
\(254\) −51.2870 −3.21803
\(255\) −0.859342 −0.0538141
\(256\) −32.2825 −2.01766
\(257\) −1.23759 −0.0771989 −0.0385995 0.999255i \(-0.512290\pi\)
−0.0385995 + 0.999255i \(0.512290\pi\)
\(258\) 7.03238 0.437817
\(259\) −3.82186 −0.237479
\(260\) 8.51058 0.527804
\(261\) −3.22874 −0.199854
\(262\) 17.1412 1.05899
\(263\) −18.4230 −1.13601 −0.568005 0.823025i \(-0.692284\pi\)
−0.568005 + 0.823025i \(0.692284\pi\)
\(264\) −5.91739 −0.364190
\(265\) 1.09184 0.0670712
\(266\) 1.51503 0.0928922
\(267\) −5.65313 −0.345966
\(268\) 46.8721 2.86317
\(269\) −10.0610 −0.613428 −0.306714 0.951802i \(-0.599230\pi\)
−0.306714 + 0.951802i \(0.599230\pi\)
\(270\) −2.62347 −0.159659
\(271\) −26.6162 −1.61682 −0.808410 0.588620i \(-0.799672\pi\)
−0.808410 + 0.588620i \(0.799672\pi\)
\(272\) 20.0947 1.21842
\(273\) 3.66649 0.221906
\(274\) 30.0424 1.81493
\(275\) −16.2586 −0.980428
\(276\) 1.38398 0.0833059
\(277\) 2.68365 0.161245 0.0806223 0.996745i \(-0.474309\pi\)
0.0806223 + 0.996745i \(0.474309\pi\)
\(278\) −7.75756 −0.465268
\(279\) 8.59175 0.514375
\(280\) −7.14985 −0.427285
\(281\) 11.6101 0.692598 0.346299 0.938124i \(-0.387438\pi\)
0.346299 + 0.938124i \(0.387438\pi\)
\(282\) −3.39350 −0.202080
\(283\) 20.7572 1.23389 0.616945 0.787006i \(-0.288370\pi\)
0.616945 + 0.787006i \(0.288370\pi\)
\(284\) −40.3684 −2.39542
\(285\) −0.0415561 −0.00246157
\(286\) 33.6683 1.99085
\(287\) −11.0882 −0.654515
\(288\) 1.15234 0.0679020
\(289\) 5.42769 0.319276
\(290\) 1.45821 0.0856291
\(291\) −6.16747 −0.361543
\(292\) 17.7430 1.03833
\(293\) 3.31042 0.193397 0.0966985 0.995314i \(-0.469172\pi\)
0.0966985 + 0.995314i \(0.469172\pi\)
\(294\) −0.206609 −0.0120497
\(295\) 2.48982 0.144963
\(296\) −7.11961 −0.413819
\(297\) −6.94211 −0.402822
\(298\) 4.23612 0.245392
\(299\) −3.97647 −0.229965
\(300\) −6.53155 −0.377099
\(301\) 22.4846 1.29599
\(302\) 23.1781 1.33375
\(303\) −4.36058 −0.250509
\(304\) 0.971742 0.0557332
\(305\) −2.70050 −0.154630
\(306\) 33.5516 1.91802
\(307\) −32.2315 −1.83955 −0.919774 0.392448i \(-0.871628\pi\)
−0.919774 + 0.392448i \(0.871628\pi\)
\(308\) −37.4660 −2.13482
\(309\) −2.56425 −0.145875
\(310\) −3.88033 −0.220388
\(311\) 5.42662 0.307715 0.153858 0.988093i \(-0.450830\pi\)
0.153858 + 0.988093i \(0.450830\pi\)
\(312\) 6.83018 0.386683
\(313\) 21.1179 1.19365 0.596826 0.802371i \(-0.296428\pi\)
0.596826 + 0.802371i \(0.296428\pi\)
\(314\) −17.2175 −0.971638
\(315\) −4.11034 −0.231591
\(316\) 24.4688 1.37648
\(317\) 10.1993 0.572852 0.286426 0.958102i \(-0.407533\pi\)
0.286426 + 0.958102i \(0.407533\pi\)
\(318\) 1.73522 0.0973066
\(319\) 3.85866 0.216043
\(320\) 3.97501 0.222210
\(321\) 3.82539 0.213512
\(322\) 6.61545 0.368665
\(323\) 1.08456 0.0603465
\(324\) 32.1512 1.78618
\(325\) 18.7665 1.04098
\(326\) 22.2625 1.23301
\(327\) −5.42471 −0.299987
\(328\) −20.6558 −1.14052
\(329\) −10.8500 −0.598182
\(330\) 1.53638 0.0845748
\(331\) 21.6720 1.19120 0.595601 0.803281i \(-0.296914\pi\)
0.595601 + 0.803281i \(0.296914\pi\)
\(332\) −18.6561 −1.02389
\(333\) −4.09295 −0.224293
\(334\) −11.3552 −0.621326
\(335\) −6.14551 −0.335765
\(336\) −3.91240 −0.213439
\(337\) 36.2570 1.97505 0.987523 0.157472i \(-0.0503344\pi\)
0.987523 + 0.157472i \(0.0503344\pi\)
\(338\) −6.91182 −0.375953
\(339\) 4.74615 0.257775
\(340\) −10.1357 −0.549686
\(341\) −10.2680 −0.556042
\(342\) 1.62249 0.0877342
\(343\) 18.1815 0.981710
\(344\) 41.8857 2.25833
\(345\) −0.181457 −0.00976932
\(346\) 27.1917 1.46184
\(347\) −21.0934 −1.13235 −0.566175 0.824285i \(-0.691578\pi\)
−0.566175 + 0.824285i \(0.691578\pi\)
\(348\) 1.55014 0.0830961
\(349\) −1.00000 −0.0535288
\(350\) −31.2209 −1.66883
\(351\) 8.01296 0.427700
\(352\) −1.37715 −0.0734024
\(353\) −13.0137 −0.692650 −0.346325 0.938115i \(-0.612571\pi\)
−0.346325 + 0.938115i \(0.612571\pi\)
\(354\) 3.95699 0.210311
\(355\) 5.29279 0.280912
\(356\) −66.6771 −3.53388
\(357\) −4.36662 −0.231106
\(358\) 52.5145 2.77548
\(359\) 20.0172 1.05647 0.528234 0.849099i \(-0.322855\pi\)
0.528234 + 0.849099i \(0.322855\pi\)
\(360\) −7.65700 −0.403559
\(361\) −18.9476 −0.997240
\(362\) −53.0698 −2.78929
\(363\) 0.297472 0.0156132
\(364\) 43.2453 2.26667
\(365\) −2.32632 −0.121765
\(366\) −4.29181 −0.224337
\(367\) 10.2313 0.534067 0.267034 0.963687i \(-0.413957\pi\)
0.267034 + 0.963687i \(0.413957\pi\)
\(368\) 4.24317 0.221190
\(369\) −11.8747 −0.618172
\(370\) 1.84852 0.0960998
\(371\) 5.54802 0.288039
\(372\) −4.12495 −0.213869
\(373\) −24.1064 −1.24818 −0.624090 0.781352i \(-0.714530\pi\)
−0.624090 + 0.781352i \(0.714530\pi\)
\(374\) −40.0974 −2.07339
\(375\) 1.76365 0.0910746
\(376\) −20.2121 −1.04236
\(377\) −4.45387 −0.229386
\(378\) −13.3307 −0.685660
\(379\) 25.5176 1.31075 0.655376 0.755303i \(-0.272510\pi\)
0.655376 + 0.755303i \(0.272510\pi\)
\(380\) −0.490142 −0.0251438
\(381\) 7.14827 0.366217
\(382\) −7.59760 −0.388727
\(383\) −11.2623 −0.575478 −0.287739 0.957709i \(-0.592904\pi\)
−0.287739 + 0.957709i \(0.592904\pi\)
\(384\) 6.59121 0.336356
\(385\) 4.91225 0.250351
\(386\) −24.2927 −1.23647
\(387\) 24.0795 1.22403
\(388\) −72.7436 −3.69300
\(389\) 31.5865 1.60150 0.800751 0.598998i \(-0.204434\pi\)
0.800751 + 0.598998i \(0.204434\pi\)
\(390\) −1.77337 −0.0897981
\(391\) 4.73579 0.239499
\(392\) −1.23059 −0.0621542
\(393\) −2.38910 −0.120514
\(394\) −29.4684 −1.48460
\(395\) −3.20816 −0.161420
\(396\) −40.1235 −2.01628
\(397\) 17.2659 0.866549 0.433274 0.901262i \(-0.357358\pi\)
0.433274 + 0.901262i \(0.357358\pi\)
\(398\) 18.4267 0.923648
\(399\) −0.211161 −0.0105713
\(400\) −20.0252 −1.00126
\(401\) −9.22126 −0.460488 −0.230244 0.973133i \(-0.573952\pi\)
−0.230244 + 0.973133i \(0.573952\pi\)
\(402\) −9.76685 −0.487126
\(403\) 11.8518 0.590383
\(404\) −51.4319 −2.55883
\(405\) −4.21542 −0.209466
\(406\) 7.40968 0.367736
\(407\) 4.89147 0.242461
\(408\) −8.13442 −0.402714
\(409\) −33.5080 −1.65686 −0.828432 0.560090i \(-0.810766\pi\)
−0.828432 + 0.560090i \(0.810766\pi\)
\(410\) 5.36301 0.264860
\(411\) −4.18724 −0.206541
\(412\) −30.2446 −1.49005
\(413\) 12.6517 0.622547
\(414\) 7.08470 0.348194
\(415\) 2.44605 0.120072
\(416\) 1.58958 0.0779357
\(417\) 1.08123 0.0529482
\(418\) −1.93903 −0.0948411
\(419\) −23.7481 −1.16017 −0.580086 0.814555i \(-0.696981\pi\)
−0.580086 + 0.814555i \(0.696981\pi\)
\(420\) 1.97340 0.0962919
\(421\) 7.08343 0.345225 0.172613 0.984990i \(-0.444779\pi\)
0.172613 + 0.984990i \(0.444779\pi\)
\(422\) 55.2376 2.68892
\(423\) −11.6196 −0.564967
\(424\) 10.3352 0.501922
\(425\) −22.3500 −1.08414
\(426\) 8.41165 0.407546
\(427\) −13.7222 −0.664063
\(428\) 45.1194 2.18093
\(429\) −4.69262 −0.226562
\(430\) −10.8751 −0.524444
\(431\) 28.5327 1.37437 0.687187 0.726481i \(-0.258845\pi\)
0.687187 + 0.726481i \(0.258845\pi\)
\(432\) −8.55038 −0.411380
\(433\) −3.77190 −0.181266 −0.0906330 0.995884i \(-0.528889\pi\)
−0.0906330 + 0.995884i \(0.528889\pi\)
\(434\) −19.7173 −0.946461
\(435\) −0.203242 −0.00974471
\(436\) −63.9829 −3.06423
\(437\) 0.229013 0.0109552
\(438\) −3.69714 −0.176656
\(439\) 2.63964 0.125983 0.0629916 0.998014i \(-0.479936\pi\)
0.0629916 + 0.998014i \(0.479936\pi\)
\(440\) 9.15085 0.436250
\(441\) −0.707448 −0.0336880
\(442\) 46.2826 2.20144
\(443\) 5.94252 0.282338 0.141169 0.989986i \(-0.454914\pi\)
0.141169 + 0.989986i \(0.454914\pi\)
\(444\) 1.96505 0.0932572
\(445\) 8.74218 0.414419
\(446\) −59.9936 −2.84078
\(447\) −0.590420 −0.0279259
\(448\) 20.1984 0.954286
\(449\) −13.8175 −0.652090 −0.326045 0.945354i \(-0.605716\pi\)
−0.326045 + 0.945354i \(0.605716\pi\)
\(450\) −33.4354 −1.57616
\(451\) 14.1914 0.668246
\(452\) 55.9795 2.63306
\(453\) −3.23051 −0.151783
\(454\) −61.8982 −2.90503
\(455\) −5.66998 −0.265813
\(456\) −0.393364 −0.0184210
\(457\) 23.9348 1.11962 0.559810 0.828621i \(-0.310874\pi\)
0.559810 + 0.828621i \(0.310874\pi\)
\(458\) −66.4584 −3.10540
\(459\) −9.54306 −0.445432
\(460\) −2.14024 −0.0997890
\(461\) −13.6400 −0.635279 −0.317640 0.948211i \(-0.602890\pi\)
−0.317640 + 0.948211i \(0.602890\pi\)
\(462\) 7.80687 0.363208
\(463\) −8.63044 −0.401091 −0.200545 0.979684i \(-0.564271\pi\)
−0.200545 + 0.979684i \(0.564271\pi\)
\(464\) 4.75259 0.220633
\(465\) 0.540832 0.0250805
\(466\) 7.37706 0.341736
\(467\) 1.62345 0.0751242 0.0375621 0.999294i \(-0.488041\pi\)
0.0375621 + 0.999294i \(0.488041\pi\)
\(468\) 46.3127 2.14081
\(469\) −31.2275 −1.44195
\(470\) 5.24783 0.242064
\(471\) 2.39973 0.110574
\(472\) 23.5683 1.08482
\(473\) −28.7773 −1.32318
\(474\) −5.09863 −0.234188
\(475\) −1.08080 −0.0495906
\(476\) −51.5031 −2.36064
\(477\) 5.94156 0.272045
\(478\) −60.1706 −2.75214
\(479\) −2.92359 −0.133582 −0.0667911 0.997767i \(-0.521276\pi\)
−0.0667911 + 0.997767i \(0.521276\pi\)
\(480\) 0.0725369 0.00331084
\(481\) −5.64600 −0.257436
\(482\) −9.66034 −0.440017
\(483\) −0.922047 −0.0419546
\(484\) 3.50860 0.159482
\(485\) 9.53758 0.433079
\(486\) −21.5569 −0.977839
\(487\) −6.32402 −0.286569 −0.143284 0.989682i \(-0.545766\pi\)
−0.143284 + 0.989682i \(0.545766\pi\)
\(488\) −25.5626 −1.15716
\(489\) −3.10290 −0.140318
\(490\) 0.319507 0.0144339
\(491\) 3.48555 0.157301 0.0786504 0.996902i \(-0.474939\pi\)
0.0786504 + 0.996902i \(0.474939\pi\)
\(492\) 5.70110 0.257026
\(493\) 5.30435 0.238896
\(494\) 2.23814 0.100698
\(495\) 5.26068 0.236450
\(496\) −12.6467 −0.567855
\(497\) 26.8945 1.20638
\(498\) 3.88742 0.174200
\(499\) 24.7377 1.10741 0.553706 0.832712i \(-0.313213\pi\)
0.553706 + 0.832712i \(0.313213\pi\)
\(500\) 20.8018 0.930284
\(501\) 1.58266 0.0707079
\(502\) −20.5902 −0.918987
\(503\) −6.94866 −0.309825 −0.154913 0.987928i \(-0.549510\pi\)
−0.154913 + 0.987928i \(0.549510\pi\)
\(504\) −38.9079 −1.73310
\(505\) 6.74335 0.300075
\(506\) −8.46689 −0.376399
\(507\) 0.963354 0.0427841
\(508\) 84.3118 3.74073
\(509\) 28.6540 1.27007 0.635033 0.772485i \(-0.280987\pi\)
0.635033 + 0.772485i \(0.280987\pi\)
\(510\) 2.11200 0.0935209
\(511\) −11.8208 −0.522924
\(512\) 40.8571 1.80564
\(513\) −0.461483 −0.0203750
\(514\) 3.04162 0.134160
\(515\) 3.96544 0.174738
\(516\) −11.5607 −0.508931
\(517\) 13.8866 0.610732
\(518\) 9.39297 0.412703
\(519\) −3.78992 −0.166359
\(520\) −10.5624 −0.463192
\(521\) −6.04848 −0.264989 −0.132494 0.991184i \(-0.542299\pi\)
−0.132494 + 0.991184i \(0.542299\pi\)
\(522\) 7.93526 0.347317
\(523\) −39.7852 −1.73968 −0.869842 0.493331i \(-0.835779\pi\)
−0.869842 + 0.493331i \(0.835779\pi\)
\(524\) −28.1788 −1.23100
\(525\) 4.35150 0.189915
\(526\) 45.2780 1.97422
\(527\) −14.1150 −0.614859
\(528\) 5.00735 0.217917
\(529\) 1.00000 0.0434783
\(530\) −2.68341 −0.116560
\(531\) 13.5491 0.587979
\(532\) −2.49059 −0.107981
\(533\) −16.3805 −0.709517
\(534\) 13.8937 0.601237
\(535\) −5.91571 −0.255758
\(536\) −58.1725 −2.51267
\(537\) −7.31936 −0.315854
\(538\) 24.7268 1.06605
\(539\) 0.845468 0.0364169
\(540\) 4.31277 0.185592
\(541\) −37.5995 −1.61653 −0.808265 0.588819i \(-0.799593\pi\)
−0.808265 + 0.588819i \(0.799593\pi\)
\(542\) 65.4145 2.80979
\(543\) 7.39675 0.317425
\(544\) −1.89312 −0.0811667
\(545\) 8.38895 0.359343
\(546\) −9.01111 −0.385640
\(547\) 15.1906 0.649503 0.324751 0.945799i \(-0.394719\pi\)
0.324751 + 0.945799i \(0.394719\pi\)
\(548\) −49.3873 −2.10972
\(549\) −14.6955 −0.627190
\(550\) 39.9586 1.70384
\(551\) 0.256508 0.0109276
\(552\) −1.71765 −0.0731079
\(553\) −16.3018 −0.693223
\(554\) −6.59558 −0.280219
\(555\) −0.257642 −0.0109363
\(556\) 12.7528 0.540841
\(557\) −37.4321 −1.58605 −0.793024 0.609191i \(-0.791494\pi\)
−0.793024 + 0.609191i \(0.791494\pi\)
\(558\) −21.1159 −0.893907
\(559\) 33.2163 1.40490
\(560\) 6.05026 0.255670
\(561\) 5.58869 0.235955
\(562\) −28.5340 −1.20363
\(563\) 15.3323 0.646180 0.323090 0.946368i \(-0.395278\pi\)
0.323090 + 0.946368i \(0.395278\pi\)
\(564\) 5.57866 0.234904
\(565\) −7.33960 −0.308779
\(566\) −51.0149 −2.14432
\(567\) −21.4200 −0.899557
\(568\) 50.1008 2.10218
\(569\) 15.8440 0.664214 0.332107 0.943242i \(-0.392240\pi\)
0.332107 + 0.943242i \(0.392240\pi\)
\(570\) 0.102132 0.00427784
\(571\) 25.1086 1.05076 0.525380 0.850867i \(-0.323923\pi\)
0.525380 + 0.850867i \(0.323923\pi\)
\(572\) −55.3481 −2.31422
\(573\) 1.05894 0.0442377
\(574\) 27.2514 1.13745
\(575\) −4.71939 −0.196812
\(576\) 21.6311 0.901297
\(577\) 12.1029 0.503849 0.251925 0.967747i \(-0.418936\pi\)
0.251925 + 0.967747i \(0.418936\pi\)
\(578\) −13.3396 −0.554855
\(579\) 3.38587 0.140712
\(580\) −2.39718 −0.0995377
\(581\) 12.4292 0.515652
\(582\) 15.1577 0.628309
\(583\) −7.10073 −0.294082
\(584\) −22.0206 −0.911220
\(585\) −6.07217 −0.251053
\(586\) −8.13601 −0.336095
\(587\) 39.2732 1.62098 0.810490 0.585753i \(-0.199201\pi\)
0.810490 + 0.585753i \(0.199201\pi\)
\(588\) 0.339650 0.0140069
\(589\) −0.682573 −0.0281249
\(590\) −6.11922 −0.251924
\(591\) 4.10724 0.168949
\(592\) 6.02467 0.247613
\(593\) 13.0513 0.535953 0.267976 0.963425i \(-0.413645\pi\)
0.267976 + 0.963425i \(0.413645\pi\)
\(594\) 17.0616 0.700045
\(595\) 6.75268 0.276833
\(596\) −6.96384 −0.285250
\(597\) −2.56828 −0.105113
\(598\) 9.77295 0.399646
\(599\) 36.4842 1.49070 0.745352 0.666671i \(-0.232282\pi\)
0.745352 + 0.666671i \(0.232282\pi\)
\(600\) 8.10625 0.330936
\(601\) −4.04469 −0.164986 −0.0824932 0.996592i \(-0.526288\pi\)
−0.0824932 + 0.996592i \(0.526288\pi\)
\(602\) −55.2602 −2.25224
\(603\) −33.4425 −1.36188
\(604\) −38.1030 −1.55039
\(605\) −0.460020 −0.0187025
\(606\) 10.7170 0.435347
\(607\) 21.2322 0.861789 0.430895 0.902402i \(-0.358198\pi\)
0.430895 + 0.902402i \(0.358198\pi\)
\(608\) −0.0915474 −0.00371274
\(609\) −1.03274 −0.0418489
\(610\) 6.63700 0.268724
\(611\) −16.0287 −0.648450
\(612\) −55.1563 −2.22956
\(613\) −13.7027 −0.553447 −0.276723 0.960950i \(-0.589249\pi\)
−0.276723 + 0.960950i \(0.589249\pi\)
\(614\) 79.2151 3.19686
\(615\) −0.747485 −0.0301415
\(616\) 46.4987 1.87349
\(617\) −3.77209 −0.151859 −0.0759293 0.997113i \(-0.524192\pi\)
−0.0759293 + 0.997113i \(0.524192\pi\)
\(618\) 6.30214 0.253509
\(619\) −46.0495 −1.85089 −0.925443 0.378887i \(-0.876307\pi\)
−0.925443 + 0.378887i \(0.876307\pi\)
\(620\) 6.37896 0.256185
\(621\) −2.01509 −0.0808629
\(622\) −13.3370 −0.534763
\(623\) 44.4221 1.77973
\(624\) −5.77975 −0.231375
\(625\) 20.8696 0.834783
\(626\) −51.9012 −2.07439
\(627\) 0.270258 0.0107931
\(628\) 28.3042 1.12946
\(629\) 6.72412 0.268108
\(630\) 10.1020 0.402471
\(631\) 44.3267 1.76462 0.882308 0.470672i \(-0.155988\pi\)
0.882308 + 0.470672i \(0.155988\pi\)
\(632\) −30.3680 −1.20798
\(633\) −7.69889 −0.306003
\(634\) −25.0669 −0.995532
\(635\) −11.0543 −0.438677
\(636\) −2.85257 −0.113112
\(637\) −0.975885 −0.0386660
\(638\) −9.48340 −0.375451
\(639\) 28.8022 1.13940
\(640\) −10.1929 −0.402909
\(641\) −10.3322 −0.408098 −0.204049 0.978961i \(-0.565410\pi\)
−0.204049 + 0.978961i \(0.565410\pi\)
\(642\) −9.40163 −0.371053
\(643\) 36.5123 1.43991 0.719953 0.694023i \(-0.244163\pi\)
0.719953 + 0.694023i \(0.244163\pi\)
\(644\) −10.8753 −0.428546
\(645\) 1.51575 0.0596825
\(646\) −2.66551 −0.104873
\(647\) −28.2373 −1.11012 −0.555062 0.831809i \(-0.687306\pi\)
−0.555062 + 0.831809i \(0.687306\pi\)
\(648\) −39.9026 −1.56752
\(649\) −16.1924 −0.635608
\(650\) −46.1223 −1.80907
\(651\) 2.74815 0.107709
\(652\) −36.5978 −1.43328
\(653\) 29.1424 1.14043 0.570215 0.821496i \(-0.306860\pi\)
0.570215 + 0.821496i \(0.306860\pi\)
\(654\) 13.3323 0.521333
\(655\) 3.69459 0.144359
\(656\) 17.4791 0.682444
\(657\) −12.6593 −0.493887
\(658\) 26.6661 1.03955
\(659\) −25.8166 −1.00567 −0.502836 0.864382i \(-0.667710\pi\)
−0.502836 + 0.864382i \(0.667710\pi\)
\(660\) −2.52568 −0.0983121
\(661\) 9.69006 0.376900 0.188450 0.982083i \(-0.439654\pi\)
0.188450 + 0.982083i \(0.439654\pi\)
\(662\) −53.2632 −2.07013
\(663\) −6.45077 −0.250527
\(664\) 23.1540 0.898549
\(665\) 0.326546 0.0126629
\(666\) 10.0592 0.389787
\(667\) 1.12006 0.0433688
\(668\) 18.6670 0.722248
\(669\) 8.36178 0.323285
\(670\) 15.1038 0.583510
\(671\) 17.5626 0.677995
\(672\) 0.368585 0.0142185
\(673\) −21.8461 −0.842107 −0.421053 0.907036i \(-0.638340\pi\)
−0.421053 + 0.907036i \(0.638340\pi\)
\(674\) −89.1087 −3.43234
\(675\) 9.51001 0.366040
\(676\) 11.3625 0.437019
\(677\) −11.7608 −0.452003 −0.226002 0.974127i \(-0.572565\pi\)
−0.226002 + 0.974127i \(0.572565\pi\)
\(678\) −11.6646 −0.447976
\(679\) 48.4638 1.85987
\(680\) 12.5793 0.482395
\(681\) 8.62724 0.330596
\(682\) 25.2355 0.966318
\(683\) −6.44571 −0.246638 −0.123319 0.992367i \(-0.539354\pi\)
−0.123319 + 0.992367i \(0.539354\pi\)
\(684\) −2.66725 −0.101985
\(685\) 6.47528 0.247408
\(686\) −44.6846 −1.70607
\(687\) 9.26282 0.353399
\(688\) −35.4441 −1.35129
\(689\) 8.19605 0.312245
\(690\) 0.445966 0.0169776
\(691\) −10.2801 −0.391075 −0.195538 0.980696i \(-0.562645\pi\)
−0.195538 + 0.980696i \(0.562645\pi\)
\(692\) −44.7011 −1.69928
\(693\) 26.7314 1.01544
\(694\) 51.8410 1.96786
\(695\) −1.67205 −0.0634246
\(696\) −1.92386 −0.0729238
\(697\) 19.5084 0.738932
\(698\) 2.45769 0.0930251
\(699\) −1.02820 −0.0388900
\(700\) 51.3247 1.93989
\(701\) 43.4816 1.64228 0.821138 0.570729i \(-0.193339\pi\)
0.821138 + 0.570729i \(0.193339\pi\)
\(702\) −19.6934 −0.743279
\(703\) 0.325165 0.0122638
\(704\) −25.8513 −0.974307
\(705\) −0.731431 −0.0275473
\(706\) 31.9837 1.20372
\(707\) 34.2653 1.28868
\(708\) −6.50498 −0.244472
\(709\) 39.0848 1.46786 0.733930 0.679225i \(-0.237684\pi\)
0.733930 + 0.679225i \(0.237684\pi\)
\(710\) −13.0081 −0.488183
\(711\) −17.4581 −0.654731
\(712\) 82.7523 3.10127
\(713\) −2.98049 −0.111620
\(714\) 10.7318 0.401628
\(715\) 7.25682 0.271390
\(716\) −86.3298 −3.22630
\(717\) 8.38645 0.313198
\(718\) −49.1961 −1.83598
\(719\) 9.07212 0.338333 0.169166 0.985588i \(-0.445892\pi\)
0.169166 + 0.985588i \(0.445892\pi\)
\(720\) 6.47942 0.241474
\(721\) 20.1498 0.750418
\(722\) 46.5673 1.73305
\(723\) 1.34644 0.0500745
\(724\) 87.2426 3.24235
\(725\) −5.28598 −0.196316
\(726\) −0.731095 −0.0271335
\(727\) 30.1795 1.11930 0.559649 0.828730i \(-0.310936\pi\)
0.559649 + 0.828730i \(0.310936\pi\)
\(728\) −53.6713 −1.98919
\(729\) −20.8686 −0.772911
\(730\) 5.71738 0.211610
\(731\) −39.5590 −1.46314
\(732\) 7.05541 0.260775
\(733\) 7.85867 0.290267 0.145133 0.989412i \(-0.453639\pi\)
0.145133 + 0.989412i \(0.453639\pi\)
\(734\) −25.1453 −0.928129
\(735\) −0.0445322 −0.00164260
\(736\) −0.399747 −0.0147349
\(737\) 39.9670 1.47220
\(738\) 29.1843 1.07429
\(739\) 24.0500 0.884694 0.442347 0.896844i \(-0.354146\pi\)
0.442347 + 0.896844i \(0.354146\pi\)
\(740\) −3.03882 −0.111709
\(741\) −0.311946 −0.0114596
\(742\) −13.6353 −0.500569
\(743\) 6.46266 0.237092 0.118546 0.992949i \(-0.462177\pi\)
0.118546 + 0.992949i \(0.462177\pi\)
\(744\) 5.11944 0.187688
\(745\) 0.913046 0.0334514
\(746\) 59.2460 2.16915
\(747\) 13.3109 0.487019
\(748\) 65.9170 2.41017
\(749\) −30.0598 −1.09836
\(750\) −4.33451 −0.158274
\(751\) 22.5664 0.823458 0.411729 0.911306i \(-0.364925\pi\)
0.411729 + 0.911306i \(0.364925\pi\)
\(752\) 17.1037 0.623707
\(753\) 2.86982 0.104582
\(754\) 10.9463 0.398639
\(755\) 4.99577 0.181815
\(756\) 21.9147 0.797030
\(757\) −43.7231 −1.58914 −0.794572 0.607171i \(-0.792304\pi\)
−0.794572 + 0.607171i \(0.792304\pi\)
\(758\) −62.7145 −2.27789
\(759\) 1.18010 0.0428348
\(760\) 0.608311 0.0220658
\(761\) −32.3972 −1.17440 −0.587199 0.809443i \(-0.699769\pi\)
−0.587199 + 0.809443i \(0.699769\pi\)
\(762\) −17.5682 −0.636431
\(763\) 42.6272 1.54321
\(764\) 12.4899 0.451868
\(765\) 7.23167 0.261461
\(766\) 27.6794 1.00010
\(767\) 18.6902 0.674863
\(768\) −11.0583 −0.399032
\(769\) 25.2783 0.911560 0.455780 0.890092i \(-0.349360\pi\)
0.455780 + 0.890092i \(0.349360\pi\)
\(770\) −12.0728 −0.435074
\(771\) −0.423935 −0.0152676
\(772\) 39.9354 1.43731
\(773\) 45.2638 1.62803 0.814013 0.580846i \(-0.197278\pi\)
0.814013 + 0.580846i \(0.197278\pi\)
\(774\) −59.1800 −2.12718
\(775\) 14.0661 0.505270
\(776\) 90.2814 3.24091
\(777\) −1.30917 −0.0469662
\(778\) −77.6301 −2.78317
\(779\) 0.943386 0.0338003
\(780\) 2.91528 0.104384
\(781\) −34.4214 −1.23169
\(782\) −11.6391 −0.416214
\(783\) −2.25702 −0.0806592
\(784\) 1.04134 0.0371906
\(785\) −3.71103 −0.132452
\(786\) 5.87168 0.209436
\(787\) −17.0656 −0.608321 −0.304161 0.952621i \(-0.598376\pi\)
−0.304161 + 0.952621i \(0.598376\pi\)
\(788\) 48.4437 1.72574
\(789\) −6.31075 −0.224669
\(790\) 7.88469 0.280525
\(791\) −37.2951 −1.32606
\(792\) 49.7969 1.76946
\(793\) −20.2717 −0.719868
\(794\) −42.4342 −1.50593
\(795\) 0.374008 0.0132647
\(796\) −30.2921 −1.07367
\(797\) 26.8771 0.952037 0.476019 0.879435i \(-0.342079\pi\)
0.476019 + 0.879435i \(0.342079\pi\)
\(798\) 0.518969 0.0183713
\(799\) 19.0894 0.675333
\(800\) 1.88656 0.0667000
\(801\) 47.5731 1.68091
\(802\) 22.6630 0.800260
\(803\) 15.1291 0.533895
\(804\) 16.0559 0.566249
\(805\) 1.42588 0.0502558
\(806\) −29.1282 −1.02600
\(807\) −3.44637 −0.121318
\(808\) 63.8316 2.24559
\(809\) 44.2709 1.55648 0.778241 0.627966i \(-0.216112\pi\)
0.778241 + 0.627966i \(0.216112\pi\)
\(810\) 10.3602 0.364021
\(811\) −35.7084 −1.25389 −0.626947 0.779062i \(-0.715696\pi\)
−0.626947 + 0.779062i \(0.715696\pi\)
\(812\) −12.1809 −0.427467
\(813\) −9.11733 −0.319759
\(814\) −12.0217 −0.421362
\(815\) 4.79842 0.168081
\(816\) 6.88341 0.240968
\(817\) −1.91300 −0.0669273
\(818\) 82.3523 2.87938
\(819\) −30.8548 −1.07815
\(820\) −8.81638 −0.307881
\(821\) −52.9856 −1.84921 −0.924605 0.380928i \(-0.875605\pi\)
−0.924605 + 0.380928i \(0.875605\pi\)
\(822\) 10.2909 0.358938
\(823\) −25.6366 −0.893634 −0.446817 0.894625i \(-0.647443\pi\)
−0.446817 + 0.894625i \(0.647443\pi\)
\(824\) 37.5363 1.30764
\(825\) −5.56933 −0.193899
\(826\) −31.0939 −1.08189
\(827\) 47.9151 1.66617 0.833085 0.553144i \(-0.186572\pi\)
0.833085 + 0.553144i \(0.186572\pi\)
\(828\) −11.6467 −0.404751
\(829\) 7.03956 0.244494 0.122247 0.992500i \(-0.460990\pi\)
0.122247 + 0.992500i \(0.460990\pi\)
\(830\) −6.01164 −0.208667
\(831\) 0.919277 0.0318894
\(832\) 29.8389 1.03448
\(833\) 1.16223 0.0402690
\(834\) −2.65734 −0.0920161
\(835\) −2.44747 −0.0846983
\(836\) 3.18762 0.110246
\(837\) 6.00597 0.207597
\(838\) 58.3656 2.01621
\(839\) −5.24467 −0.181066 −0.0905330 0.995893i \(-0.528857\pi\)
−0.0905330 + 0.995893i \(0.528857\pi\)
\(840\) −2.44917 −0.0845042
\(841\) −27.7455 −0.956740
\(842\) −17.4089 −0.599950
\(843\) 3.97700 0.136975
\(844\) −90.8063 −3.12568
\(845\) −1.48976 −0.0512494
\(846\) 28.5575 0.981828
\(847\) −2.33752 −0.0803183
\(848\) −8.74574 −0.300330
\(849\) 7.11035 0.244026
\(850\) 54.9295 1.88407
\(851\) 1.41985 0.0486719
\(852\) −13.8281 −0.473743
\(853\) 35.6976 1.22226 0.611131 0.791530i \(-0.290715\pi\)
0.611131 + 0.791530i \(0.290715\pi\)
\(854\) 33.7249 1.15404
\(855\) 0.349709 0.0119598
\(856\) −55.9973 −1.91395
\(857\) −10.3044 −0.351993 −0.175997 0.984391i \(-0.556315\pi\)
−0.175997 + 0.984391i \(0.556315\pi\)
\(858\) 11.5330 0.393731
\(859\) 45.9304 1.56712 0.783562 0.621313i \(-0.213401\pi\)
0.783562 + 0.621313i \(0.213401\pi\)
\(860\) 17.8778 0.609629
\(861\) −3.79823 −0.129443
\(862\) −70.1247 −2.38846
\(863\) −8.63962 −0.294096 −0.147048 0.989129i \(-0.546977\pi\)
−0.147048 + 0.989129i \(0.546977\pi\)
\(864\) 0.805527 0.0274046
\(865\) 5.86086 0.199275
\(866\) 9.27018 0.315014
\(867\) 1.85925 0.0631433
\(868\) 32.4137 1.10019
\(869\) 20.8641 0.707767
\(870\) 0.499507 0.0169349
\(871\) −46.1321 −1.56313
\(872\) 79.4086 2.68912
\(873\) 51.9014 1.75660
\(874\) −0.562845 −0.0190385
\(875\) −13.8587 −0.468510
\(876\) 6.07781 0.205350
\(877\) 35.0843 1.18471 0.592356 0.805677i \(-0.298198\pi\)
0.592356 + 0.805677i \(0.298198\pi\)
\(878\) −6.48743 −0.218940
\(879\) 1.13398 0.0382481
\(880\) −7.74353 −0.261034
\(881\) 9.11522 0.307099 0.153550 0.988141i \(-0.450929\pi\)
0.153550 + 0.988141i \(0.450929\pi\)
\(882\) 1.73869 0.0585447
\(883\) 49.5173 1.66639 0.833196 0.552978i \(-0.186509\pi\)
0.833196 + 0.552978i \(0.186509\pi\)
\(884\) −76.0850 −2.55902
\(885\) 0.852883 0.0286693
\(886\) −14.6049 −0.490661
\(887\) 41.0102 1.37699 0.688493 0.725243i \(-0.258273\pi\)
0.688493 + 0.725243i \(0.258273\pi\)
\(888\) −2.43881 −0.0818410
\(889\) −56.1709 −1.88391
\(890\) −21.4856 −0.720199
\(891\) 27.4148 0.918430
\(892\) 98.6249 3.30220
\(893\) 0.923124 0.0308912
\(894\) 1.45107 0.0485311
\(895\) 11.3189 0.378349
\(896\) −51.7935 −1.73030
\(897\) −1.36213 −0.0454803
\(898\) 33.9593 1.13324
\(899\) −3.33832 −0.111339
\(900\) 54.9653 1.83218
\(901\) −9.76111 −0.325190
\(902\) −34.8781 −1.16131
\(903\) 7.70205 0.256308
\(904\) −69.4757 −2.31073
\(905\) −11.4386 −0.380231
\(906\) 7.93961 0.263776
\(907\) 7.35913 0.244356 0.122178 0.992508i \(-0.461012\pi\)
0.122178 + 0.992508i \(0.461012\pi\)
\(908\) 101.756 3.37689
\(909\) 36.6958 1.21712
\(910\) 13.9351 0.461944
\(911\) −18.4435 −0.611059 −0.305530 0.952183i \(-0.598833\pi\)
−0.305530 + 0.952183i \(0.598833\pi\)
\(912\) 0.332868 0.0110224
\(913\) −15.9078 −0.526470
\(914\) −58.8243 −1.94573
\(915\) −0.925050 −0.0305812
\(916\) 109.252 3.60980
\(917\) 18.7735 0.619955
\(918\) 23.4539 0.774094
\(919\) 34.4076 1.13500 0.567501 0.823373i \(-0.307910\pi\)
0.567501 + 0.823373i \(0.307910\pi\)
\(920\) 2.65623 0.0875732
\(921\) −11.0408 −0.363808
\(922\) 33.5230 1.10402
\(923\) 39.7310 1.30776
\(924\) −12.8339 −0.422204
\(925\) −6.70084 −0.220322
\(926\) 21.2110 0.697036
\(927\) 21.5791 0.708749
\(928\) −0.447739 −0.0146978
\(929\) 32.6774 1.07211 0.536056 0.844183i \(-0.319914\pi\)
0.536056 + 0.844183i \(0.319914\pi\)
\(930\) −1.32920 −0.0435861
\(931\) 0.0562033 0.00184199
\(932\) −12.1273 −0.397243
\(933\) 1.85888 0.0608569
\(934\) −3.98994 −0.130555
\(935\) −8.64253 −0.282641
\(936\) −57.4783 −1.87874
\(937\) −21.0126 −0.686452 −0.343226 0.939253i \(-0.611520\pi\)
−0.343226 + 0.939253i \(0.611520\pi\)
\(938\) 76.7476 2.50590
\(939\) 7.23388 0.236069
\(940\) −8.62702 −0.281382
\(941\) 3.79551 0.123730 0.0618650 0.998085i \(-0.480295\pi\)
0.0618650 + 0.998085i \(0.480295\pi\)
\(942\) −5.89781 −0.192161
\(943\) 4.11935 0.134144
\(944\) −19.9437 −0.649112
\(945\) −2.87329 −0.0934681
\(946\) 70.7257 2.29949
\(947\) 2.07168 0.0673206 0.0336603 0.999433i \(-0.489284\pi\)
0.0336603 + 0.999433i \(0.489284\pi\)
\(948\) 8.38175 0.272226
\(949\) −17.4628 −0.566868
\(950\) 2.65628 0.0861812
\(951\) 3.49376 0.113293
\(952\) 63.9200 2.07166
\(953\) 11.3256 0.366872 0.183436 0.983032i \(-0.441278\pi\)
0.183436 + 0.983032i \(0.441278\pi\)
\(954\) −14.6025 −0.472774
\(955\) −1.63757 −0.0529907
\(956\) 98.9158 3.19917
\(957\) 1.32177 0.0427269
\(958\) 7.18529 0.232146
\(959\) 32.9032 1.06250
\(960\) 1.36163 0.0439465
\(961\) −22.1167 −0.713441
\(962\) 13.8761 0.447385
\(963\) −32.1920 −1.03737
\(964\) 15.8809 0.511488
\(965\) −5.23602 −0.168553
\(966\) 2.26611 0.0729108
\(967\) 24.7639 0.796352 0.398176 0.917309i \(-0.369643\pi\)
0.398176 + 0.917309i \(0.369643\pi\)
\(968\) −4.35449 −0.139959
\(969\) 0.371513 0.0119347
\(970\) −23.4404 −0.752627
\(971\) 51.9814 1.66816 0.834082 0.551641i \(-0.185998\pi\)
0.834082 + 0.551641i \(0.185998\pi\)
\(972\) 35.4378 1.13667
\(973\) −8.49629 −0.272379
\(974\) 15.5425 0.498014
\(975\) 6.42843 0.205874
\(976\) 21.6313 0.692400
\(977\) 20.0648 0.641930 0.320965 0.947091i \(-0.395993\pi\)
0.320965 + 0.947091i \(0.395993\pi\)
\(978\) 7.62597 0.243852
\(979\) −56.8543 −1.81707
\(980\) −0.525245 −0.0167783
\(981\) 45.6508 1.45752
\(982\) −8.56642 −0.273365
\(983\) 54.2228 1.72944 0.864720 0.502255i \(-0.167496\pi\)
0.864720 + 0.502255i \(0.167496\pi\)
\(984\) −7.07559 −0.225562
\(985\) −6.35157 −0.202378
\(986\) −13.0365 −0.415166
\(987\) −3.71666 −0.118302
\(988\) −3.67932 −0.117055
\(989\) −8.35321 −0.265617
\(990\) −12.9292 −0.410915
\(991\) −20.6690 −0.656572 −0.328286 0.944578i \(-0.606471\pi\)
−0.328286 + 0.944578i \(0.606471\pi\)
\(992\) 1.19144 0.0378284
\(993\) 7.42370 0.235584
\(994\) −66.0985 −2.09652
\(995\) 3.97167 0.125910
\(996\) −6.39062 −0.202495
\(997\) −20.0372 −0.634585 −0.317293 0.948328i \(-0.602774\pi\)
−0.317293 + 0.948328i \(0.602774\pi\)
\(998\) −60.7978 −1.92452
\(999\) −2.86114 −0.0905223
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 \(a_p\))