Properties

Label 8007.2.a.e.1.20
Level 8007
Weight 2
Character 8007.1
Self dual Yes
Analytic conductor 63.936
Analytic rank 1
Dimension 46
CM No

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Newspace parameters

Level: \( N \) = \( 8007 = 3 \cdot 17 \cdot 157 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8007.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.9362168984\)
Analytic rank: \(1\)
Dimension: \(46\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.20
Character \(\chi\) = 8007.1

$q$-expansion

\(f(q)\) \(=\) \(q-0.576474 q^{2} +1.00000 q^{3} -1.66768 q^{4} +0.828352 q^{5} -0.576474 q^{6} -0.479856 q^{7} +2.11432 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-0.576474 q^{2} +1.00000 q^{3} -1.66768 q^{4} +0.828352 q^{5} -0.576474 q^{6} -0.479856 q^{7} +2.11432 q^{8} +1.00000 q^{9} -0.477524 q^{10} +5.91719 q^{11} -1.66768 q^{12} -2.47116 q^{13} +0.276625 q^{14} +0.828352 q^{15} +2.11650 q^{16} -1.00000 q^{17} -0.576474 q^{18} +2.75787 q^{19} -1.38142 q^{20} -0.479856 q^{21} -3.41111 q^{22} +4.50266 q^{23} +2.11432 q^{24} -4.31383 q^{25} +1.42456 q^{26} +1.00000 q^{27} +0.800245 q^{28} -6.59210 q^{29} -0.477524 q^{30} -2.35371 q^{31} -5.44875 q^{32} +5.91719 q^{33} +0.576474 q^{34} -0.397490 q^{35} -1.66768 q^{36} -9.35003 q^{37} -1.58984 q^{38} -2.47116 q^{39} +1.75140 q^{40} -7.84656 q^{41} +0.276625 q^{42} -10.6454 q^{43} -9.86797 q^{44} +0.828352 q^{45} -2.59567 q^{46} -10.0395 q^{47} +2.11650 q^{48} -6.76974 q^{49} +2.48681 q^{50} -1.00000 q^{51} +4.12110 q^{52} +10.7649 q^{53} -0.576474 q^{54} +4.90152 q^{55} -1.01457 q^{56} +2.75787 q^{57} +3.80018 q^{58} +0.266454 q^{59} -1.38142 q^{60} -7.69049 q^{61} +1.35685 q^{62} -0.479856 q^{63} -1.09194 q^{64} -2.04699 q^{65} -3.41111 q^{66} -12.4138 q^{67} +1.66768 q^{68} +4.50266 q^{69} +0.229143 q^{70} +7.86135 q^{71} +2.11432 q^{72} +2.29870 q^{73} +5.39005 q^{74} -4.31383 q^{75} -4.59924 q^{76} -2.83940 q^{77} +1.42456 q^{78} -6.28776 q^{79} +1.75321 q^{80} +1.00000 q^{81} +4.52334 q^{82} +11.7711 q^{83} +0.800245 q^{84} -0.828352 q^{85} +6.13679 q^{86} -6.59210 q^{87} +12.5108 q^{88} +10.1686 q^{89} -0.477524 q^{90} +1.18580 q^{91} -7.50899 q^{92} -2.35371 q^{93} +5.78749 q^{94} +2.28449 q^{95} -5.44875 q^{96} +0.346481 q^{97} +3.90258 q^{98} +5.91719 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 46q - 5q^{2} + 46q^{3} + 43q^{4} - 19q^{5} - 5q^{6} + q^{7} - 18q^{8} + 46q^{9} + O(q^{10}) \) \( 46q - 5q^{2} + 46q^{3} + 43q^{4} - 19q^{5} - 5q^{6} + q^{7} - 18q^{8} + 46q^{9} - 10q^{10} - 25q^{11} + 43q^{12} - 8q^{13} - 28q^{14} - 19q^{15} + 33q^{16} - 46q^{17} - 5q^{18} - 2q^{19} - 56q^{20} + q^{21} - 19q^{22} - 64q^{23} - 18q^{24} + 11q^{25} - 13q^{26} + 46q^{27} - 38q^{28} - 51q^{29} - 10q^{30} - 19q^{31} - 61q^{32} - 25q^{33} + 5q^{34} - 39q^{35} + 43q^{36} - 46q^{37} - 48q^{38} - 8q^{39} - 10q^{40} - 53q^{41} - 28q^{42} - 33q^{43} - 62q^{44} - 19q^{45} + 2q^{46} - 45q^{47} + 33q^{48} + 21q^{49} - 60q^{50} - 46q^{51} - 63q^{52} - 47q^{53} - 5q^{54} + 5q^{55} - 82q^{56} - 2q^{57} - 21q^{58} - 65q^{59} - 56q^{60} - 37q^{61} - 46q^{62} + q^{63} + 74q^{64} - 85q^{65} - 19q^{66} - 52q^{67} - 43q^{68} - 64q^{69} - 20q^{70} - 48q^{71} - 18q^{72} - 39q^{73} - 16q^{74} + 11q^{75} + 42q^{76} - 78q^{77} - 13q^{78} - 26q^{79} - 78q^{80} + 46q^{81} + 3q^{82} - 47q^{83} - 38q^{84} + 19q^{85} - 6q^{86} - 51q^{87} - 58q^{88} - 58q^{89} - 10q^{90} - 43q^{91} - 68q^{92} - 19q^{93} - 78q^{95} - 61q^{96} - 44q^{97} - 4q^{98} - 25q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.576474 −0.407629 −0.203814 0.979010i \(-0.565334\pi\)
−0.203814 + 0.979010i \(0.565334\pi\)
\(3\) 1.00000 0.577350
\(4\) −1.66768 −0.833839
\(5\) 0.828352 0.370450 0.185225 0.982696i \(-0.440699\pi\)
0.185225 + 0.982696i \(0.440699\pi\)
\(6\) −0.576474 −0.235345
\(7\) −0.479856 −0.181369 −0.0906843 0.995880i \(-0.528905\pi\)
−0.0906843 + 0.995880i \(0.528905\pi\)
\(8\) 2.11432 0.747525
\(9\) 1.00000 0.333333
\(10\) −0.477524 −0.151006
\(11\) 5.91719 1.78410 0.892050 0.451937i \(-0.149267\pi\)
0.892050 + 0.451937i \(0.149267\pi\)
\(12\) −1.66768 −0.481417
\(13\) −2.47116 −0.685377 −0.342688 0.939449i \(-0.611337\pi\)
−0.342688 + 0.939449i \(0.611337\pi\)
\(14\) 0.276625 0.0739310
\(15\) 0.828352 0.213880
\(16\) 2.11650 0.529126
\(17\) −1.00000 −0.242536
\(18\) −0.576474 −0.135876
\(19\) 2.75787 0.632699 0.316349 0.948643i \(-0.397543\pi\)
0.316349 + 0.948643i \(0.397543\pi\)
\(20\) −1.38142 −0.308896
\(21\) −0.479856 −0.104713
\(22\) −3.41111 −0.727250
\(23\) 4.50266 0.938870 0.469435 0.882967i \(-0.344458\pi\)
0.469435 + 0.882967i \(0.344458\pi\)
\(24\) 2.11432 0.431584
\(25\) −4.31383 −0.862767
\(26\) 1.42456 0.279379
\(27\) 1.00000 0.192450
\(28\) 0.800245 0.151232
\(29\) −6.59210 −1.22412 −0.612061 0.790810i \(-0.709659\pi\)
−0.612061 + 0.790810i \(0.709659\pi\)
\(30\) −0.477524 −0.0871835
\(31\) −2.35371 −0.422739 −0.211370 0.977406i \(-0.567792\pi\)
−0.211370 + 0.977406i \(0.567792\pi\)
\(32\) −5.44875 −0.963212
\(33\) 5.91719 1.03005
\(34\) 0.576474 0.0988645
\(35\) −0.397490 −0.0671880
\(36\) −1.66768 −0.277946
\(37\) −9.35003 −1.53713 −0.768567 0.639769i \(-0.779030\pi\)
−0.768567 + 0.639769i \(0.779030\pi\)
\(38\) −1.58984 −0.257906
\(39\) −2.47116 −0.395702
\(40\) 1.75140 0.276921
\(41\) −7.84656 −1.22543 −0.612713 0.790305i \(-0.709922\pi\)
−0.612713 + 0.790305i \(0.709922\pi\)
\(42\) 0.276625 0.0426841
\(43\) −10.6454 −1.62341 −0.811703 0.584071i \(-0.801459\pi\)
−0.811703 + 0.584071i \(0.801459\pi\)
\(44\) −9.86797 −1.48765
\(45\) 0.828352 0.123483
\(46\) −2.59567 −0.382711
\(47\) −10.0395 −1.46441 −0.732203 0.681087i \(-0.761508\pi\)
−0.732203 + 0.681087i \(0.761508\pi\)
\(48\) 2.11650 0.305491
\(49\) −6.76974 −0.967105
\(50\) 2.48681 0.351688
\(51\) −1.00000 −0.140028
\(52\) 4.12110 0.571494
\(53\) 10.7649 1.47867 0.739335 0.673338i \(-0.235140\pi\)
0.739335 + 0.673338i \(0.235140\pi\)
\(54\) −0.576474 −0.0784482
\(55\) 4.90152 0.660920
\(56\) −1.01457 −0.135578
\(57\) 2.75787 0.365289
\(58\) 3.80018 0.498988
\(59\) 0.266454 0.0346893 0.0173447 0.999850i \(-0.494479\pi\)
0.0173447 + 0.999850i \(0.494479\pi\)
\(60\) −1.38142 −0.178341
\(61\) −7.69049 −0.984666 −0.492333 0.870407i \(-0.663856\pi\)
−0.492333 + 0.870407i \(0.663856\pi\)
\(62\) 1.35685 0.172321
\(63\) −0.479856 −0.0604562
\(64\) −1.09194 −0.136493
\(65\) −2.04699 −0.253898
\(66\) −3.41111 −0.419878
\(67\) −12.4138 −1.51659 −0.758293 0.651914i \(-0.773966\pi\)
−0.758293 + 0.651914i \(0.773966\pi\)
\(68\) 1.66768 0.202236
\(69\) 4.50266 0.542057
\(70\) 0.229143 0.0273878
\(71\) 7.86135 0.932970 0.466485 0.884529i \(-0.345520\pi\)
0.466485 + 0.884529i \(0.345520\pi\)
\(72\) 2.11432 0.249175
\(73\) 2.29870 0.269043 0.134521 0.990911i \(-0.457050\pi\)
0.134521 + 0.990911i \(0.457050\pi\)
\(74\) 5.39005 0.626580
\(75\) −4.31383 −0.498118
\(76\) −4.59924 −0.527569
\(77\) −2.83940 −0.323580
\(78\) 1.42456 0.161300
\(79\) −6.28776 −0.707428 −0.353714 0.935354i \(-0.615081\pi\)
−0.353714 + 0.935354i \(0.615081\pi\)
\(80\) 1.75321 0.196015
\(81\) 1.00000 0.111111
\(82\) 4.52334 0.499519
\(83\) 11.7711 1.29204 0.646022 0.763319i \(-0.276432\pi\)
0.646022 + 0.763319i \(0.276432\pi\)
\(84\) 0.800245 0.0873139
\(85\) −0.828352 −0.0898474
\(86\) 6.13679 0.661747
\(87\) −6.59210 −0.706748
\(88\) 12.5108 1.33366
\(89\) 10.1686 1.07787 0.538934 0.842348i \(-0.318827\pi\)
0.538934 + 0.842348i \(0.318827\pi\)
\(90\) −0.477524 −0.0503354
\(91\) 1.18580 0.124306
\(92\) −7.50899 −0.782867
\(93\) −2.35371 −0.244069
\(94\) 5.78749 0.596934
\(95\) 2.28449 0.234384
\(96\) −5.44875 −0.556111
\(97\) 0.346481 0.0351798 0.0175899 0.999845i \(-0.494401\pi\)
0.0175899 + 0.999845i \(0.494401\pi\)
\(98\) 3.90258 0.394220
\(99\) 5.91719 0.594700
\(100\) 7.19408 0.719408
\(101\) 11.5452 1.14879 0.574397 0.818577i \(-0.305237\pi\)
0.574397 + 0.818577i \(0.305237\pi\)
\(102\) 0.576474 0.0570794
\(103\) 7.18519 0.707978 0.353989 0.935250i \(-0.384825\pi\)
0.353989 + 0.935250i \(0.384825\pi\)
\(104\) −5.22483 −0.512336
\(105\) −0.397490 −0.0387910
\(106\) −6.20568 −0.602749
\(107\) −2.35202 −0.227379 −0.113689 0.993516i \(-0.536267\pi\)
−0.113689 + 0.993516i \(0.536267\pi\)
\(108\) −1.66768 −0.160472
\(109\) 3.67918 0.352402 0.176201 0.984354i \(-0.443619\pi\)
0.176201 + 0.984354i \(0.443619\pi\)
\(110\) −2.82560 −0.269410
\(111\) −9.35003 −0.887465
\(112\) −1.01562 −0.0959668
\(113\) 10.6804 1.00473 0.502366 0.864655i \(-0.332463\pi\)
0.502366 + 0.864655i \(0.332463\pi\)
\(114\) −1.58984 −0.148902
\(115\) 3.72979 0.347805
\(116\) 10.9935 1.02072
\(117\) −2.47116 −0.228459
\(118\) −0.153604 −0.0141404
\(119\) 0.479856 0.0439883
\(120\) 1.75140 0.159880
\(121\) 24.0131 2.18301
\(122\) 4.43337 0.401378
\(123\) −7.84656 −0.707500
\(124\) 3.92523 0.352496
\(125\) −7.71513 −0.690063
\(126\) 0.276625 0.0246437
\(127\) −7.23512 −0.642013 −0.321007 0.947077i \(-0.604021\pi\)
−0.321007 + 0.947077i \(0.604021\pi\)
\(128\) 11.5270 1.01885
\(129\) −10.6454 −0.937274
\(130\) 1.18004 0.103496
\(131\) −16.6001 −1.45036 −0.725180 0.688560i \(-0.758243\pi\)
−0.725180 + 0.688560i \(0.758243\pi\)
\(132\) −9.86797 −0.858896
\(133\) −1.32338 −0.114752
\(134\) 7.15623 0.618204
\(135\) 0.828352 0.0712932
\(136\) −2.11432 −0.181302
\(137\) −8.81614 −0.753214 −0.376607 0.926373i \(-0.622909\pi\)
−0.376607 + 0.926373i \(0.622909\pi\)
\(138\) −2.59567 −0.220958
\(139\) −1.60980 −0.136542 −0.0682709 0.997667i \(-0.521748\pi\)
−0.0682709 + 0.997667i \(0.521748\pi\)
\(140\) 0.662885 0.0560240
\(141\) −10.0395 −0.845475
\(142\) −4.53186 −0.380306
\(143\) −14.6223 −1.22278
\(144\) 2.11650 0.176375
\(145\) −5.46058 −0.453477
\(146\) −1.32514 −0.109670
\(147\) −6.76974 −0.558359
\(148\) 15.5928 1.28172
\(149\) 1.20969 0.0991016 0.0495508 0.998772i \(-0.484221\pi\)
0.0495508 + 0.998772i \(0.484221\pi\)
\(150\) 2.48681 0.203047
\(151\) −19.6838 −1.60184 −0.800922 0.598769i \(-0.795657\pi\)
−0.800922 + 0.598769i \(0.795657\pi\)
\(152\) 5.83103 0.472959
\(153\) −1.00000 −0.0808452
\(154\) 1.63684 0.131900
\(155\) −1.94970 −0.156604
\(156\) 4.12110 0.329952
\(157\) 1.00000 0.0798087
\(158\) 3.62473 0.288368
\(159\) 10.7649 0.853711
\(160\) −4.51349 −0.356822
\(161\) −2.16063 −0.170282
\(162\) −0.576474 −0.0452921
\(163\) −13.6542 −1.06948 −0.534742 0.845016i \(-0.679591\pi\)
−0.534742 + 0.845016i \(0.679591\pi\)
\(164\) 13.0855 1.02181
\(165\) 4.90152 0.381583
\(166\) −6.78572 −0.526674
\(167\) 18.4779 1.42986 0.714930 0.699196i \(-0.246459\pi\)
0.714930 + 0.699196i \(0.246459\pi\)
\(168\) −1.01457 −0.0782758
\(169\) −6.89337 −0.530259
\(170\) 0.477524 0.0366244
\(171\) 2.75787 0.210900
\(172\) 17.7531 1.35366
\(173\) 12.7582 0.969989 0.484995 0.874517i \(-0.338822\pi\)
0.484995 + 0.874517i \(0.338822\pi\)
\(174\) 3.80018 0.288091
\(175\) 2.07002 0.156479
\(176\) 12.5238 0.944013
\(177\) 0.266454 0.0200279
\(178\) −5.86193 −0.439370
\(179\) 9.56385 0.714836 0.357418 0.933945i \(-0.383657\pi\)
0.357418 + 0.933945i \(0.383657\pi\)
\(180\) −1.38142 −0.102965
\(181\) −18.9044 −1.40516 −0.702578 0.711607i \(-0.747968\pi\)
−0.702578 + 0.711607i \(0.747968\pi\)
\(182\) −0.683584 −0.0506706
\(183\) −7.69049 −0.568497
\(184\) 9.52008 0.701830
\(185\) −7.74511 −0.569432
\(186\) 1.35685 0.0994894
\(187\) −5.91719 −0.432708
\(188\) 16.7426 1.22108
\(189\) −0.479856 −0.0349044
\(190\) −1.31695 −0.0955415
\(191\) −19.8281 −1.43471 −0.717355 0.696707i \(-0.754648\pi\)
−0.717355 + 0.696707i \(0.754648\pi\)
\(192\) −1.09194 −0.0788041
\(193\) −23.4458 −1.68766 −0.843831 0.536608i \(-0.819705\pi\)
−0.843831 + 0.536608i \(0.819705\pi\)
\(194\) −0.199737 −0.0143403
\(195\) −2.04699 −0.146588
\(196\) 11.2897 0.806410
\(197\) 9.98421 0.711346 0.355673 0.934611i \(-0.384252\pi\)
0.355673 + 0.934611i \(0.384252\pi\)
\(198\) −3.41111 −0.242417
\(199\) 4.12796 0.292623 0.146311 0.989239i \(-0.453260\pi\)
0.146311 + 0.989239i \(0.453260\pi\)
\(200\) −9.12083 −0.644940
\(201\) −12.4138 −0.875601
\(202\) −6.65553 −0.468282
\(203\) 3.16326 0.222017
\(204\) 1.66768 0.116761
\(205\) −6.49971 −0.453960
\(206\) −4.14208 −0.288592
\(207\) 4.50266 0.312957
\(208\) −5.23022 −0.362650
\(209\) 16.3188 1.12880
\(210\) 0.229143 0.0158123
\(211\) −8.50287 −0.585362 −0.292681 0.956210i \(-0.594547\pi\)
−0.292681 + 0.956210i \(0.594547\pi\)
\(212\) −17.9524 −1.23297
\(213\) 7.86135 0.538651
\(214\) 1.35588 0.0926861
\(215\) −8.81813 −0.601391
\(216\) 2.11432 0.143861
\(217\) 1.12944 0.0766716
\(218\) −2.12095 −0.143649
\(219\) 2.29870 0.155332
\(220\) −8.17415 −0.551101
\(221\) 2.47116 0.166228
\(222\) 5.39005 0.361756
\(223\) −15.1528 −1.01471 −0.507354 0.861738i \(-0.669376\pi\)
−0.507354 + 0.861738i \(0.669376\pi\)
\(224\) 2.61462 0.174696
\(225\) −4.31383 −0.287589
\(226\) −6.15700 −0.409557
\(227\) −22.2243 −1.47508 −0.737539 0.675305i \(-0.764012\pi\)
−0.737539 + 0.675305i \(0.764012\pi\)
\(228\) −4.59924 −0.304592
\(229\) 11.3305 0.748742 0.374371 0.927279i \(-0.377859\pi\)
0.374371 + 0.927279i \(0.377859\pi\)
\(230\) −2.15013 −0.141775
\(231\) −2.83940 −0.186819
\(232\) −13.9378 −0.915063
\(233\) 4.18406 0.274107 0.137053 0.990564i \(-0.456237\pi\)
0.137053 + 0.990564i \(0.456237\pi\)
\(234\) 1.42456 0.0931264
\(235\) −8.31621 −0.542490
\(236\) −0.444359 −0.0289253
\(237\) −6.28776 −0.408434
\(238\) −0.276625 −0.0179309
\(239\) 9.78127 0.632698 0.316349 0.948643i \(-0.397543\pi\)
0.316349 + 0.948643i \(0.397543\pi\)
\(240\) 1.75321 0.113169
\(241\) −21.7377 −1.40025 −0.700125 0.714020i \(-0.746873\pi\)
−0.700125 + 0.714020i \(0.746873\pi\)
\(242\) −13.8430 −0.889859
\(243\) 1.00000 0.0641500
\(244\) 12.8253 0.821053
\(245\) −5.60773 −0.358265
\(246\) 4.52334 0.288397
\(247\) −6.81514 −0.433637
\(248\) −4.97651 −0.316008
\(249\) 11.7711 0.745962
\(250\) 4.44758 0.281289
\(251\) −23.3319 −1.47270 −0.736349 0.676602i \(-0.763452\pi\)
−0.736349 + 0.676602i \(0.763452\pi\)
\(252\) 0.800245 0.0504107
\(253\) 26.6431 1.67504
\(254\) 4.17086 0.261703
\(255\) −0.828352 −0.0518734
\(256\) −4.46112 −0.278820
\(257\) 13.3221 0.831011 0.415505 0.909591i \(-0.363605\pi\)
0.415505 + 0.909591i \(0.363605\pi\)
\(258\) 6.13679 0.382060
\(259\) 4.48667 0.278788
\(260\) 3.41372 0.211710
\(261\) −6.59210 −0.408041
\(262\) 9.56954 0.591208
\(263\) −13.5052 −0.832765 −0.416382 0.909190i \(-0.636702\pi\)
−0.416382 + 0.909190i \(0.636702\pi\)
\(264\) 12.5108 0.769989
\(265\) 8.91711 0.547774
\(266\) 0.762895 0.0467761
\(267\) 10.1686 0.622308
\(268\) 20.7022 1.26459
\(269\) −11.2883 −0.688259 −0.344129 0.938922i \(-0.611826\pi\)
−0.344129 + 0.938922i \(0.611826\pi\)
\(270\) −0.477524 −0.0290612
\(271\) 8.30026 0.504205 0.252103 0.967701i \(-0.418878\pi\)
0.252103 + 0.967701i \(0.418878\pi\)
\(272\) −2.11650 −0.128332
\(273\) 1.18580 0.0717680
\(274\) 5.08228 0.307032
\(275\) −25.5258 −1.53926
\(276\) −7.50899 −0.451988
\(277\) 23.1419 1.39046 0.695232 0.718786i \(-0.255302\pi\)
0.695232 + 0.718786i \(0.255302\pi\)
\(278\) 0.928010 0.0556583
\(279\) −2.35371 −0.140913
\(280\) −0.840421 −0.0502248
\(281\) −10.0789 −0.601255 −0.300627 0.953742i \(-0.597196\pi\)
−0.300627 + 0.953742i \(0.597196\pi\)
\(282\) 5.78749 0.344640
\(283\) −13.2197 −0.785828 −0.392914 0.919575i \(-0.628533\pi\)
−0.392914 + 0.919575i \(0.628533\pi\)
\(284\) −13.1102 −0.777947
\(285\) 2.28449 0.135321
\(286\) 8.42939 0.498440
\(287\) 3.76522 0.222254
\(288\) −5.44875 −0.321071
\(289\) 1.00000 0.0588235
\(290\) 3.14788 0.184850
\(291\) 0.346481 0.0203111
\(292\) −3.83349 −0.224338
\(293\) 18.9435 1.10669 0.553346 0.832952i \(-0.313351\pi\)
0.553346 + 0.832952i \(0.313351\pi\)
\(294\) 3.90258 0.227603
\(295\) 0.220718 0.0128507
\(296\) −19.7690 −1.14905
\(297\) 5.91719 0.343350
\(298\) −0.697354 −0.0403966
\(299\) −11.1268 −0.643480
\(300\) 7.19408 0.415351
\(301\) 5.10825 0.294435
\(302\) 11.3472 0.652958
\(303\) 11.5452 0.663257
\(304\) 5.83704 0.334777
\(305\) −6.37043 −0.364770
\(306\) 0.576474 0.0329548
\(307\) 22.9698 1.31096 0.655479 0.755213i \(-0.272467\pi\)
0.655479 + 0.755213i \(0.272467\pi\)
\(308\) 4.73520 0.269813
\(309\) 7.18519 0.408751
\(310\) 1.12395 0.0638363
\(311\) 21.1653 1.20017 0.600086 0.799935i \(-0.295133\pi\)
0.600086 + 0.799935i \(0.295133\pi\)
\(312\) −5.22483 −0.295798
\(313\) 13.2039 0.746329 0.373164 0.927765i \(-0.378273\pi\)
0.373164 + 0.927765i \(0.378273\pi\)
\(314\) −0.576474 −0.0325323
\(315\) −0.397490 −0.0223960
\(316\) 10.4860 0.589881
\(317\) −10.0021 −0.561775 −0.280887 0.959741i \(-0.590629\pi\)
−0.280887 + 0.959741i \(0.590629\pi\)
\(318\) −6.20568 −0.347997
\(319\) −39.0067 −2.18396
\(320\) −0.904513 −0.0505638
\(321\) −2.35202 −0.131277
\(322\) 1.24555 0.0694117
\(323\) −2.75787 −0.153452
\(324\) −1.66768 −0.0926488
\(325\) 10.6602 0.591320
\(326\) 7.87132 0.435952
\(327\) 3.67918 0.203459
\(328\) −16.5901 −0.916037
\(329\) 4.81750 0.265597
\(330\) −2.82560 −0.155544
\(331\) 12.4144 0.682360 0.341180 0.939998i \(-0.389173\pi\)
0.341180 + 0.939998i \(0.389173\pi\)
\(332\) −19.6304 −1.07736
\(333\) −9.35003 −0.512378
\(334\) −10.6520 −0.582852
\(335\) −10.2830 −0.561820
\(336\) −1.01562 −0.0554065
\(337\) −5.55921 −0.302829 −0.151415 0.988470i \(-0.548383\pi\)
−0.151415 + 0.988470i \(0.548383\pi\)
\(338\) 3.97385 0.216149
\(339\) 10.6804 0.580082
\(340\) 1.38142 0.0749183
\(341\) −13.9274 −0.754209
\(342\) −1.58984 −0.0859688
\(343\) 6.60749 0.356771
\(344\) −22.5078 −1.21354
\(345\) 3.72979 0.200805
\(346\) −7.35478 −0.395396
\(347\) −12.7321 −0.683494 −0.341747 0.939792i \(-0.611019\pi\)
−0.341747 + 0.939792i \(0.611019\pi\)
\(348\) 10.9935 0.589313
\(349\) 19.5735 1.04775 0.523874 0.851796i \(-0.324486\pi\)
0.523874 + 0.851796i \(0.324486\pi\)
\(350\) −1.19331 −0.0637852
\(351\) −2.47116 −0.131901
\(352\) −32.2413 −1.71847
\(353\) −16.4742 −0.876834 −0.438417 0.898772i \(-0.644461\pi\)
−0.438417 + 0.898772i \(0.644461\pi\)
\(354\) −0.153604 −0.00816395
\(355\) 6.51197 0.345619
\(356\) −16.9579 −0.898769
\(357\) 0.479856 0.0253967
\(358\) −5.51331 −0.291388
\(359\) −10.4095 −0.549391 −0.274695 0.961531i \(-0.588577\pi\)
−0.274695 + 0.961531i \(0.588577\pi\)
\(360\) 1.75140 0.0923070
\(361\) −11.3941 −0.599692
\(362\) 10.8979 0.572782
\(363\) 24.0131 1.26036
\(364\) −1.97753 −0.103651
\(365\) 1.90413 0.0996669
\(366\) 4.43337 0.231736
\(367\) −22.6560 −1.18263 −0.591316 0.806440i \(-0.701391\pi\)
−0.591316 + 0.806440i \(0.701391\pi\)
\(368\) 9.52991 0.496781
\(369\) −7.84656 −0.408475
\(370\) 4.46486 0.232117
\(371\) −5.16559 −0.268184
\(372\) 3.92523 0.203514
\(373\) 23.1860 1.20052 0.600262 0.799803i \(-0.295063\pi\)
0.600262 + 0.799803i \(0.295063\pi\)
\(374\) 3.41111 0.176384
\(375\) −7.71513 −0.398408
\(376\) −21.2266 −1.09468
\(377\) 16.2901 0.838985
\(378\) 0.276625 0.0142280
\(379\) 18.9940 0.975654 0.487827 0.872940i \(-0.337790\pi\)
0.487827 + 0.872940i \(0.337790\pi\)
\(380\) −3.80979 −0.195438
\(381\) −7.23512 −0.370667
\(382\) 11.4304 0.584829
\(383\) 1.12690 0.0575818 0.0287909 0.999585i \(-0.490834\pi\)
0.0287909 + 0.999585i \(0.490834\pi\)
\(384\) 11.5270 0.588234
\(385\) −2.35202 −0.119870
\(386\) 13.5159 0.687940
\(387\) −10.6454 −0.541135
\(388\) −0.577818 −0.0293343
\(389\) −28.1550 −1.42751 −0.713757 0.700393i \(-0.753008\pi\)
−0.713757 + 0.700393i \(0.753008\pi\)
\(390\) 1.18004 0.0597535
\(391\) −4.50266 −0.227710
\(392\) −14.3134 −0.722936
\(393\) −16.6001 −0.837365
\(394\) −5.75564 −0.289965
\(395\) −5.20848 −0.262067
\(396\) −9.86797 −0.495884
\(397\) −28.7826 −1.44456 −0.722278 0.691603i \(-0.756905\pi\)
−0.722278 + 0.691603i \(0.756905\pi\)
\(398\) −2.37966 −0.119282
\(399\) −1.32338 −0.0662519
\(400\) −9.13024 −0.456512
\(401\) 19.0968 0.953649 0.476825 0.878998i \(-0.341788\pi\)
0.476825 + 0.878998i \(0.341788\pi\)
\(402\) 7.15623 0.356920
\(403\) 5.81640 0.289736
\(404\) −19.2537 −0.957909
\(405\) 0.828352 0.0411612
\(406\) −1.82354 −0.0905007
\(407\) −55.3259 −2.74240
\(408\) −2.11432 −0.104675
\(409\) 30.9140 1.52860 0.764300 0.644861i \(-0.223085\pi\)
0.764300 + 0.644861i \(0.223085\pi\)
\(410\) 3.74692 0.185047
\(411\) −8.81614 −0.434868
\(412\) −11.9826 −0.590339
\(413\) −0.127860 −0.00629156
\(414\) −2.59567 −0.127570
\(415\) 9.75060 0.478638
\(416\) 13.4647 0.660163
\(417\) −1.60980 −0.0788324
\(418\) −9.40739 −0.460131
\(419\) 14.4095 0.703952 0.351976 0.936009i \(-0.385510\pi\)
0.351976 + 0.936009i \(0.385510\pi\)
\(420\) 0.662885 0.0323455
\(421\) 6.23018 0.303640 0.151820 0.988408i \(-0.451487\pi\)
0.151820 + 0.988408i \(0.451487\pi\)
\(422\) 4.90168 0.238610
\(423\) −10.0395 −0.488135
\(424\) 22.7604 1.10534
\(425\) 4.31383 0.209252
\(426\) −4.53186 −0.219570
\(427\) 3.69033 0.178587
\(428\) 3.92242 0.189597
\(429\) −14.6223 −0.705973
\(430\) 5.08342 0.245144
\(431\) 8.93404 0.430337 0.215169 0.976577i \(-0.430970\pi\)
0.215169 + 0.976577i \(0.430970\pi\)
\(432\) 2.11650 0.101830
\(433\) −38.2328 −1.83735 −0.918677 0.395010i \(-0.870741\pi\)
−0.918677 + 0.395010i \(0.870741\pi\)
\(434\) −0.651095 −0.0312536
\(435\) −5.46058 −0.261815
\(436\) −6.13569 −0.293846
\(437\) 12.4178 0.594022
\(438\) −1.32514 −0.0633177
\(439\) −7.98160 −0.380941 −0.190471 0.981693i \(-0.561001\pi\)
−0.190471 + 0.981693i \(0.561001\pi\)
\(440\) 10.3634 0.494055
\(441\) −6.76974 −0.322368
\(442\) −1.42456 −0.0677594
\(443\) −6.80632 −0.323378 −0.161689 0.986842i \(-0.551694\pi\)
−0.161689 + 0.986842i \(0.551694\pi\)
\(444\) 15.5928 0.740003
\(445\) 8.42318 0.399297
\(446\) 8.73521 0.413624
\(447\) 1.20969 0.0572163
\(448\) 0.523975 0.0247555
\(449\) −2.60492 −0.122934 −0.0614669 0.998109i \(-0.519578\pi\)
−0.0614669 + 0.998109i \(0.519578\pi\)
\(450\) 2.48681 0.117229
\(451\) −46.4296 −2.18628
\(452\) −17.8115 −0.837784
\(453\) −19.6838 −0.924825
\(454\) 12.8117 0.601284
\(455\) 0.982261 0.0460491
\(456\) 5.83103 0.273063
\(457\) 36.9769 1.72971 0.864853 0.502026i \(-0.167412\pi\)
0.864853 + 0.502026i \(0.167412\pi\)
\(458\) −6.53176 −0.305209
\(459\) −1.00000 −0.0466760
\(460\) −6.22009 −0.290013
\(461\) −11.9000 −0.554239 −0.277119 0.960835i \(-0.589380\pi\)
−0.277119 + 0.960835i \(0.589380\pi\)
\(462\) 1.63684 0.0761527
\(463\) −18.0312 −0.837983 −0.418991 0.907990i \(-0.637616\pi\)
−0.418991 + 0.907990i \(0.637616\pi\)
\(464\) −13.9522 −0.647715
\(465\) −1.94970 −0.0904153
\(466\) −2.41200 −0.111734
\(467\) −36.7066 −1.69858 −0.849289 0.527929i \(-0.822969\pi\)
−0.849289 + 0.527929i \(0.822969\pi\)
\(468\) 4.12110 0.190498
\(469\) 5.95683 0.275061
\(470\) 4.79408 0.221134
\(471\) 1.00000 0.0460776
\(472\) 0.563369 0.0259312
\(473\) −62.9908 −2.89632
\(474\) 3.62473 0.166489
\(475\) −11.8970 −0.545872
\(476\) −0.800245 −0.0366792
\(477\) 10.7649 0.492890
\(478\) −5.63865 −0.257906
\(479\) −39.4505 −1.80254 −0.901269 0.433260i \(-0.857363\pi\)
−0.901269 + 0.433260i \(0.857363\pi\)
\(480\) −4.51349 −0.206011
\(481\) 23.1054 1.05352
\(482\) 12.5312 0.570782
\(483\) −2.16063 −0.0983121
\(484\) −40.0462 −1.82028
\(485\) 0.287008 0.0130324
\(486\) −0.576474 −0.0261494
\(487\) 37.0843 1.68045 0.840225 0.542239i \(-0.182423\pi\)
0.840225 + 0.542239i \(0.182423\pi\)
\(488\) −16.2602 −0.736063
\(489\) −13.6542 −0.617466
\(490\) 3.23271 0.146039
\(491\) 35.3651 1.59601 0.798003 0.602653i \(-0.205890\pi\)
0.798003 + 0.602653i \(0.205890\pi\)
\(492\) 13.0855 0.589941
\(493\) 6.59210 0.296893
\(494\) 3.92875 0.176763
\(495\) 4.90152 0.220307
\(496\) −4.98164 −0.223682
\(497\) −3.77232 −0.169211
\(498\) −6.78572 −0.304075
\(499\) −23.6503 −1.05873 −0.529366 0.848394i \(-0.677570\pi\)
−0.529366 + 0.848394i \(0.677570\pi\)
\(500\) 12.8664 0.575401
\(501\) 18.4779 0.825530
\(502\) 13.4503 0.600314
\(503\) 5.15704 0.229941 0.114971 0.993369i \(-0.463323\pi\)
0.114971 + 0.993369i \(0.463323\pi\)
\(504\) −1.01457 −0.0451925
\(505\) 9.56353 0.425571
\(506\) −15.3591 −0.682794
\(507\) −6.89337 −0.306145
\(508\) 12.0659 0.535336
\(509\) 14.8015 0.656066 0.328033 0.944666i \(-0.393614\pi\)
0.328033 + 0.944666i \(0.393614\pi\)
\(510\) 0.477524 0.0211451
\(511\) −1.10305 −0.0487959
\(512\) −20.4822 −0.905196
\(513\) 2.75787 0.121763
\(514\) −7.67986 −0.338744
\(515\) 5.95187 0.262271
\(516\) 17.7531 0.781535
\(517\) −59.4054 −2.61265
\(518\) −2.58645 −0.113642
\(519\) 12.7582 0.560024
\(520\) −4.32800 −0.189795
\(521\) −6.86900 −0.300936 −0.150468 0.988615i \(-0.548078\pi\)
−0.150468 + 0.988615i \(0.548078\pi\)
\(522\) 3.80018 0.166329
\(523\) −43.1892 −1.88853 −0.944267 0.329181i \(-0.893227\pi\)
−0.944267 + 0.329181i \(0.893227\pi\)
\(524\) 27.6837 1.20937
\(525\) 2.07002 0.0903430
\(526\) 7.78538 0.339459
\(527\) 2.35371 0.102529
\(528\) 12.5238 0.545026
\(529\) −2.72601 −0.118522
\(530\) −5.14049 −0.223288
\(531\) 0.266454 0.0115631
\(532\) 2.20697 0.0956844
\(533\) 19.3901 0.839878
\(534\) −5.86193 −0.253671
\(535\) −1.94830 −0.0842325
\(536\) −26.2467 −1.13369
\(537\) 9.56385 0.412711
\(538\) 6.50740 0.280554
\(539\) −40.0578 −1.72541
\(540\) −1.38142 −0.0594470
\(541\) 44.4463 1.91089 0.955447 0.295162i \(-0.0953737\pi\)
0.955447 + 0.295162i \(0.0953737\pi\)
\(542\) −4.78489 −0.205528
\(543\) −18.9044 −0.811267
\(544\) 5.44875 0.233613
\(545\) 3.04766 0.130547
\(546\) −0.683584 −0.0292547
\(547\) 12.2060 0.521890 0.260945 0.965354i \(-0.415966\pi\)
0.260945 + 0.965354i \(0.415966\pi\)
\(548\) 14.7025 0.628059
\(549\) −7.69049 −0.328222
\(550\) 14.7149 0.627447
\(551\) −18.1802 −0.774501
\(552\) 9.52008 0.405202
\(553\) 3.01722 0.128305
\(554\) −13.3407 −0.566793
\(555\) −7.74511 −0.328762
\(556\) 2.68463 0.113854
\(557\) 42.0547 1.78191 0.890956 0.454089i \(-0.150035\pi\)
0.890956 + 0.454089i \(0.150035\pi\)
\(558\) 1.35685 0.0574402
\(559\) 26.3064 1.11264
\(560\) −0.841289 −0.0355509
\(561\) −5.91719 −0.249824
\(562\) 5.81021 0.245089
\(563\) −9.38469 −0.395518 −0.197759 0.980251i \(-0.563366\pi\)
−0.197759 + 0.980251i \(0.563366\pi\)
\(564\) 16.7426 0.704990
\(565\) 8.84717 0.372203
\(566\) 7.62080 0.320326
\(567\) −0.479856 −0.0201521
\(568\) 16.6214 0.697419
\(569\) 26.4031 1.10688 0.553438 0.832890i \(-0.313316\pi\)
0.553438 + 0.832890i \(0.313316\pi\)
\(570\) −1.31695 −0.0551609
\(571\) 45.7159 1.91315 0.956575 0.291487i \(-0.0941500\pi\)
0.956575 + 0.291487i \(0.0941500\pi\)
\(572\) 24.3853 1.01960
\(573\) −19.8281 −0.828331
\(574\) −2.17055 −0.0905970
\(575\) −19.4237 −0.810026
\(576\) −1.09194 −0.0454976
\(577\) −39.1130 −1.62830 −0.814148 0.580658i \(-0.802795\pi\)
−0.814148 + 0.580658i \(0.802795\pi\)
\(578\) −0.576474 −0.0239782
\(579\) −23.4458 −0.974372
\(580\) 9.10649 0.378126
\(581\) −5.64842 −0.234336
\(582\) −0.199737 −0.00827937
\(583\) 63.6979 2.63810
\(584\) 4.86019 0.201116
\(585\) −2.04699 −0.0846327
\(586\) −10.9204 −0.451119
\(587\) −15.3040 −0.631662 −0.315831 0.948815i \(-0.602283\pi\)
−0.315831 + 0.948815i \(0.602283\pi\)
\(588\) 11.2897 0.465581
\(589\) −6.49124 −0.267467
\(590\) −0.127238 −0.00523831
\(591\) 9.98421 0.410696
\(592\) −19.7894 −0.813338
\(593\) 17.9368 0.736574 0.368287 0.929712i \(-0.379944\pi\)
0.368287 + 0.929712i \(0.379944\pi\)
\(594\) −3.41111 −0.139959
\(595\) 0.397490 0.0162955
\(596\) −2.01737 −0.0826347
\(597\) 4.12796 0.168946
\(598\) 6.41432 0.262301
\(599\) 34.6784 1.41692 0.708460 0.705751i \(-0.249390\pi\)
0.708460 + 0.705751i \(0.249390\pi\)
\(600\) −9.12083 −0.372356
\(601\) −8.64543 −0.352655 −0.176327 0.984332i \(-0.556422\pi\)
−0.176327 + 0.984332i \(0.556422\pi\)
\(602\) −2.94477 −0.120020
\(603\) −12.4138 −0.505529
\(604\) 32.8262 1.33568
\(605\) 19.8913 0.808698
\(606\) −6.65553 −0.270363
\(607\) 9.90149 0.401889 0.200945 0.979603i \(-0.435599\pi\)
0.200945 + 0.979603i \(0.435599\pi\)
\(608\) −15.0270 −0.609424
\(609\) 3.16326 0.128182
\(610\) 3.67239 0.148691
\(611\) 24.8091 1.00367
\(612\) 1.66768 0.0674119
\(613\) −24.5725 −0.992473 −0.496236 0.868188i \(-0.665285\pi\)
−0.496236 + 0.868188i \(0.665285\pi\)
\(614\) −13.2415 −0.534384
\(615\) −6.49971 −0.262094
\(616\) −6.00340 −0.241884
\(617\) −44.2221 −1.78031 −0.890157 0.455654i \(-0.849406\pi\)
−0.890157 + 0.455654i \(0.849406\pi\)
\(618\) −4.14208 −0.166619
\(619\) −0.932339 −0.0374739 −0.0187369 0.999824i \(-0.505965\pi\)
−0.0187369 + 0.999824i \(0.505965\pi\)
\(620\) 3.25148 0.130582
\(621\) 4.50266 0.180686
\(622\) −12.2012 −0.489225
\(623\) −4.87946 −0.195491
\(624\) −5.23022 −0.209376
\(625\) 15.1783 0.607133
\(626\) −7.61171 −0.304225
\(627\) 16.3188 0.651712
\(628\) −1.66768 −0.0665476
\(629\) 9.35003 0.372810
\(630\) 0.229143 0.00912926
\(631\) 41.6049 1.65627 0.828133 0.560532i \(-0.189403\pi\)
0.828133 + 0.560532i \(0.189403\pi\)
\(632\) −13.2943 −0.528821
\(633\) −8.50287 −0.337959
\(634\) 5.76596 0.228995
\(635\) −5.99323 −0.237834
\(636\) −17.9524 −0.711857
\(637\) 16.7291 0.662831
\(638\) 22.4864 0.890244
\(639\) 7.86135 0.310990
\(640\) 9.54840 0.377434
\(641\) 34.7701 1.37334 0.686669 0.726970i \(-0.259072\pi\)
0.686669 + 0.726970i \(0.259072\pi\)
\(642\) 1.35588 0.0535124
\(643\) −0.624812 −0.0246402 −0.0123201 0.999924i \(-0.503922\pi\)
−0.0123201 + 0.999924i \(0.503922\pi\)
\(644\) 3.60324 0.141987
\(645\) −8.81813 −0.347213
\(646\) 1.58984 0.0625515
\(647\) −13.1851 −0.518360 −0.259180 0.965829i \(-0.583452\pi\)
−0.259180 + 0.965829i \(0.583452\pi\)
\(648\) 2.11432 0.0830584
\(649\) 1.57666 0.0618893
\(650\) −6.14531 −0.241039
\(651\) 1.12944 0.0442664
\(652\) 22.7709 0.891777
\(653\) −12.6116 −0.493529 −0.246765 0.969075i \(-0.579367\pi\)
−0.246765 + 0.969075i \(0.579367\pi\)
\(654\) −2.12095 −0.0829358
\(655\) −13.7507 −0.537286
\(656\) −16.6073 −0.648405
\(657\) 2.29870 0.0896809
\(658\) −2.77716 −0.108265
\(659\) 29.2162 1.13810 0.569051 0.822302i \(-0.307311\pi\)
0.569051 + 0.822302i \(0.307311\pi\)
\(660\) −8.17415 −0.318178
\(661\) −18.3845 −0.715073 −0.357536 0.933899i \(-0.616383\pi\)
−0.357536 + 0.933899i \(0.616383\pi\)
\(662\) −7.15661 −0.278149
\(663\) 2.47116 0.0959719
\(664\) 24.8878 0.965835
\(665\) −1.09623 −0.0425098
\(666\) 5.39005 0.208860
\(667\) −29.6820 −1.14929
\(668\) −30.8151 −1.19227
\(669\) −15.1528 −0.585842
\(670\) 5.92788 0.229014
\(671\) −45.5061 −1.75674
\(672\) 2.61462 0.100861
\(673\) −21.1181 −0.814043 −0.407021 0.913419i \(-0.633433\pi\)
−0.407021 + 0.913419i \(0.633433\pi\)
\(674\) 3.20474 0.123442
\(675\) −4.31383 −0.166039
\(676\) 11.4959 0.442150
\(677\) 3.95528 0.152014 0.0760068 0.997107i \(-0.475783\pi\)
0.0760068 + 0.997107i \(0.475783\pi\)
\(678\) −6.15700 −0.236458
\(679\) −0.166261 −0.00638051
\(680\) −1.75140 −0.0671632
\(681\) −22.2243 −0.851636
\(682\) 8.02877 0.307437
\(683\) −10.9882 −0.420453 −0.210227 0.977653i \(-0.567420\pi\)
−0.210227 + 0.977653i \(0.567420\pi\)
\(684\) −4.59924 −0.175856
\(685\) −7.30287 −0.279028
\(686\) −3.80905 −0.145430
\(687\) 11.3305 0.432287
\(688\) −22.5310 −0.858986
\(689\) −26.6018 −1.01345
\(690\) −2.15013 −0.0818540
\(691\) 44.1142 1.67818 0.839092 0.543989i \(-0.183087\pi\)
0.839092 + 0.543989i \(0.183087\pi\)
\(692\) −21.2766 −0.808815
\(693\) −2.83940 −0.107860
\(694\) 7.33971 0.278612
\(695\) −1.33348 −0.0505819
\(696\) −13.9378 −0.528312
\(697\) 7.84656 0.297210
\(698\) −11.2836 −0.427092
\(699\) 4.18406 0.158256
\(700\) −3.45212 −0.130478
\(701\) −26.1733 −0.988553 −0.494277 0.869305i \(-0.664567\pi\)
−0.494277 + 0.869305i \(0.664567\pi\)
\(702\) 1.42456 0.0537666
\(703\) −25.7862 −0.972544
\(704\) −6.46123 −0.243517
\(705\) −8.31621 −0.313207
\(706\) 9.49696 0.357423
\(707\) −5.54005 −0.208355
\(708\) −0.444359 −0.0167000
\(709\) −1.69026 −0.0634792 −0.0317396 0.999496i \(-0.510105\pi\)
−0.0317396 + 0.999496i \(0.510105\pi\)
\(710\) −3.75398 −0.140884
\(711\) −6.28776 −0.235809
\(712\) 21.4997 0.805734
\(713\) −10.5980 −0.396897
\(714\) −0.276625 −0.0103524
\(715\) −12.1124 −0.452979
\(716\) −15.9494 −0.596058
\(717\) 9.78127 0.365288
\(718\) 6.00079 0.223948
\(719\) 3.93316 0.146682 0.0733411 0.997307i \(-0.476634\pi\)
0.0733411 + 0.997307i \(0.476634\pi\)
\(720\) 1.75321 0.0653383
\(721\) −3.44786 −0.128405
\(722\) 6.56843 0.244452
\(723\) −21.7377 −0.808435
\(724\) 31.5265 1.17167
\(725\) 28.4372 1.05613
\(726\) −13.8430 −0.513760
\(727\) −29.0999 −1.07926 −0.539628 0.841903i \(-0.681435\pi\)
−0.539628 + 0.841903i \(0.681435\pi\)
\(728\) 2.50716 0.0929217
\(729\) 1.00000 0.0370370
\(730\) −1.09768 −0.0406271
\(731\) 10.6454 0.393734
\(732\) 12.8253 0.474035
\(733\) −52.2535 −1.93003 −0.965013 0.262203i \(-0.915551\pi\)
−0.965013 + 0.262203i \(0.915551\pi\)
\(734\) 13.0606 0.482075
\(735\) −5.60773 −0.206844
\(736\) −24.5339 −0.904332
\(737\) −73.4548 −2.70574
\(738\) 4.52334 0.166506
\(739\) −4.32924 −0.159254 −0.0796268 0.996825i \(-0.525373\pi\)
−0.0796268 + 0.996825i \(0.525373\pi\)
\(740\) 12.9164 0.474815
\(741\) −6.81514 −0.250360
\(742\) 2.97783 0.109320
\(743\) 36.1019 1.32445 0.662226 0.749304i \(-0.269612\pi\)
0.662226 + 0.749304i \(0.269612\pi\)
\(744\) −4.97651 −0.182448
\(745\) 1.00205 0.0367122
\(746\) −13.3661 −0.489369
\(747\) 11.7711 0.430681
\(748\) 9.86797 0.360809
\(749\) 1.12863 0.0412394
\(750\) 4.44758 0.162402
\(751\) −2.95922 −0.107983 −0.0539917 0.998541i \(-0.517194\pi\)
−0.0539917 + 0.998541i \(0.517194\pi\)
\(752\) −21.2486 −0.774855
\(753\) −23.3319 −0.850263
\(754\) −9.39085 −0.341994
\(755\) −16.3051 −0.593404
\(756\) 0.800245 0.0291046
\(757\) 49.0765 1.78372 0.891859 0.452314i \(-0.149401\pi\)
0.891859 + 0.452314i \(0.149401\pi\)
\(758\) −10.9495 −0.397705
\(759\) 26.6431 0.967084
\(760\) 4.83014 0.175208
\(761\) 51.0121 1.84919 0.924593 0.380955i \(-0.124405\pi\)
0.924593 + 0.380955i \(0.124405\pi\)
\(762\) 4.17086 0.151094
\(763\) −1.76548 −0.0639146
\(764\) 33.0669 1.19632
\(765\) −0.828352 −0.0299491
\(766\) −0.649628 −0.0234720
\(767\) −0.658450 −0.0237753
\(768\) −4.46112 −0.160977
\(769\) −7.49780 −0.270378 −0.135189 0.990820i \(-0.543164\pi\)
−0.135189 + 0.990820i \(0.543164\pi\)
\(770\) 1.35588 0.0488625
\(771\) 13.3221 0.479784
\(772\) 39.1000 1.40724
\(773\) 53.9391 1.94005 0.970027 0.242996i \(-0.0781303\pi\)
0.970027 + 0.242996i \(0.0781303\pi\)
\(774\) 6.13679 0.220582
\(775\) 10.1535 0.364725
\(776\) 0.732572 0.0262978
\(777\) 4.48667 0.160958
\(778\) 16.2306 0.581896
\(779\) −21.6398 −0.775326
\(780\) 3.41372 0.122231
\(781\) 46.5171 1.66451
\(782\) 2.59567 0.0928210
\(783\) −6.59210 −0.235583
\(784\) −14.3282 −0.511721
\(785\) 0.828352 0.0295652
\(786\) 9.56954 0.341334
\(787\) 29.7518 1.06054 0.530268 0.847830i \(-0.322091\pi\)
0.530268 + 0.847830i \(0.322091\pi\)
\(788\) −16.6504 −0.593148
\(789\) −13.5052 −0.480797
\(790\) 3.00255 0.106826
\(791\) −5.12507 −0.182227
\(792\) 12.5108 0.444553
\(793\) 19.0044 0.674867
\(794\) 16.5924 0.588842
\(795\) 8.91711 0.316257
\(796\) −6.88410 −0.244000
\(797\) −41.0298 −1.45335 −0.726675 0.686981i \(-0.758936\pi\)
−0.726675 + 0.686981i \(0.758936\pi\)
\(798\) 0.762895 0.0270062
\(799\) 10.0395 0.355171
\(800\) 23.5050 0.831027
\(801\) 10.1686 0.359290
\(802\) −11.0088 −0.388735
\(803\) 13.6019 0.479999
\(804\) 20.7022 0.730110
\(805\) −1.78976 −0.0630809
\(806\) −3.35301 −0.118105
\(807\) −11.2883 −0.397366
\(808\) 24.4103 0.858753
\(809\) 14.8953 0.523692 0.261846 0.965110i \(-0.415669\pi\)
0.261846 + 0.965110i \(0.415669\pi\)
\(810\) −0.477524 −0.0167785
\(811\) −20.0677 −0.704673 −0.352336 0.935873i \(-0.614613\pi\)
−0.352336 + 0.935873i \(0.614613\pi\)
\(812\) −5.27530 −0.185127
\(813\) 8.30026 0.291103
\(814\) 31.8939 1.11788
\(815\) −11.3105 −0.396190
\(816\) −2.11650 −0.0740924
\(817\) −29.3586 −1.02713
\(818\) −17.8211 −0.623101
\(819\) 1.18580 0.0414352
\(820\) 10.8394 0.378529
\(821\) −37.3729 −1.30432 −0.652161 0.758080i \(-0.726137\pi\)
−0.652161 + 0.758080i \(0.726137\pi\)
\(822\) 5.08228 0.177265
\(823\) −25.4583 −0.887419 −0.443709 0.896171i \(-0.646338\pi\)
−0.443709 + 0.896171i \(0.646338\pi\)
\(824\) 15.1918 0.529231
\(825\) −25.5258 −0.888693
\(826\) 0.0737077 0.00256462
\(827\) −12.9303 −0.449631 −0.224815 0.974401i \(-0.572178\pi\)
−0.224815 + 0.974401i \(0.572178\pi\)
\(828\) −7.50899 −0.260956
\(829\) −14.7331 −0.511700 −0.255850 0.966716i \(-0.582355\pi\)
−0.255850 + 0.966716i \(0.582355\pi\)
\(830\) −5.62097 −0.195107
\(831\) 23.1419 0.802785
\(832\) 2.69836 0.0935490
\(833\) 6.76974 0.234558
\(834\) 0.928010 0.0321344
\(835\) 15.3062 0.529692
\(836\) −27.2146 −0.941236
\(837\) −2.35371 −0.0813562
\(838\) −8.30672 −0.286951
\(839\) 17.6593 0.609667 0.304834 0.952406i \(-0.401399\pi\)
0.304834 + 0.952406i \(0.401399\pi\)
\(840\) −0.840421 −0.0289973
\(841\) 14.4558 0.498476
\(842\) −3.59154 −0.123773
\(843\) −10.0789 −0.347135
\(844\) 14.1800 0.488097
\(845\) −5.71014 −0.196435
\(846\) 5.78749 0.198978
\(847\) −11.5228 −0.395930
\(848\) 22.7839 0.782403
\(849\) −13.2197 −0.453698
\(850\) −2.48681 −0.0852970
\(851\) −42.1000 −1.44317
\(852\) −13.1102 −0.449148
\(853\) −30.9734 −1.06051 −0.530255 0.847838i \(-0.677904\pi\)
−0.530255 + 0.847838i \(0.677904\pi\)
\(854\) −2.12738 −0.0727974
\(855\) 2.28449 0.0781279
\(856\) −4.97293 −0.169971
\(857\) −39.7544 −1.35799 −0.678993 0.734145i \(-0.737583\pi\)
−0.678993 + 0.734145i \(0.737583\pi\)
\(858\) 8.42939 0.287775
\(859\) 24.0479 0.820504 0.410252 0.911972i \(-0.365441\pi\)
0.410252 + 0.911972i \(0.365441\pi\)
\(860\) 14.7058 0.501463
\(861\) 3.76522 0.128318
\(862\) −5.15024 −0.175418
\(863\) 20.2167 0.688184 0.344092 0.938936i \(-0.388187\pi\)
0.344092 + 0.938936i \(0.388187\pi\)
\(864\) −5.44875 −0.185370
\(865\) 10.5683 0.359333
\(866\) 22.0402 0.748958
\(867\) 1.00000 0.0339618
\(868\) −1.88355 −0.0639318
\(869\) −37.2059 −1.26212
\(870\) 3.14788 0.106723
\(871\) 30.6765 1.03943
\(872\) 7.77897 0.263429
\(873\) 0.346481 0.0117266
\(874\) −7.15852 −0.242141
\(875\) 3.70215 0.125156
\(876\) −3.83349 −0.129522
\(877\) 20.0885 0.678341 0.339171 0.940725i \(-0.389854\pi\)
0.339171 + 0.940725i \(0.389854\pi\)
\(878\) 4.60119 0.155283
\(879\) 18.9435 0.638949
\(880\) 10.3741 0.349710
\(881\) −9.64903 −0.325084 −0.162542 0.986702i \(-0.551969\pi\)
−0.162542 + 0.986702i \(0.551969\pi\)
\(882\) 3.90258 0.131407
\(883\) −6.79260 −0.228589 −0.114295 0.993447i \(-0.536461\pi\)
−0.114295 + 0.993447i \(0.536461\pi\)
\(884\) −4.12110 −0.138608
\(885\) 0.220718 0.00741934
\(886\) 3.92367 0.131818
\(887\) 54.1860 1.81939 0.909693 0.415280i \(-0.136317\pi\)
0.909693 + 0.415280i \(0.136317\pi\)
\(888\) −19.7690 −0.663403
\(889\) 3.47182 0.116441
\(890\) −4.85574 −0.162765
\(891\) 5.91719 0.198233
\(892\) 25.2700 0.846103
\(893\) −27.6875 −0.926528
\(894\) −0.697354 −0.0233230
\(895\) 7.92224 0.264811
\(896\) −5.53129 −0.184787
\(897\) −11.1268 −0.371513
\(898\) 1.50167 0.0501114
\(899\) 15.5159 0.517485
\(900\) 7.19408 0.239803
\(901\) −10.7649 −0.358630
\(902\) 26.7654 0.891192
\(903\) 5.10825 0.169992
\(904\) 22.5819 0.751062
\(905\) −15.6595 −0.520540
\(906\) 11.3472 0.376985
\(907\) −20.9908 −0.696987 −0.348493 0.937311i \(-0.613307\pi\)
−0.348493 + 0.937311i \(0.613307\pi\)
\(908\) 37.0629 1.22998
\(909\) 11.5452 0.382931
\(910\) −0.566248 −0.0187709
\(911\) 33.3813 1.10597 0.552985 0.833191i \(-0.313489\pi\)
0.552985 + 0.833191i \(0.313489\pi\)
\(912\) 5.83704 0.193284
\(913\) 69.6517 2.30513
\(914\) −21.3162 −0.705078
\(915\) −6.37043 −0.210600
\(916\) −18.8957 −0.624330
\(917\) 7.96567 0.263050
\(918\) 0.576474 0.0190265
\(919\) 37.4810 1.23639 0.618193 0.786027i \(-0.287865\pi\)
0.618193 + 0.786027i \(0.287865\pi\)
\(920\) 7.88598 0.259993
\(921\) 22.9698 0.756882
\(922\) 6.86005 0.225924
\(923\) −19.4267 −0.639436
\(924\) 4.73520 0.155777
\(925\) 40.3344 1.32619
\(926\) 10.3945 0.341586
\(927\) 7.18519 0.235993
\(928\) 35.9187 1.17909
\(929\) 21.0780 0.691548 0.345774 0.938318i \(-0.387616\pi\)
0.345774 + 0.938318i \(0.387616\pi\)
\(930\) 1.12395 0.0368559
\(931\) −18.6701 −0.611887
\(932\) −6.97767 −0.228561
\(933\) 21.1653 0.692920
\(934\) 21.1604 0.692389
\(935\) −4.90152 −0.160297
\(936\) −5.22483 −0.170779
\(937\) −11.3980 −0.372356 −0.186178 0.982516i \(-0.559610\pi\)
−0.186178 + 0.982516i \(0.559610\pi\)
\(938\) −3.43396 −0.112123
\(939\) 13.2039 0.430893
\(940\) 13.8688 0.452349
\(941\) −12.5444 −0.408935 −0.204468 0.978873i \(-0.565546\pi\)
−0.204468 + 0.978873i \(0.565546\pi\)
\(942\) −0.576474 −0.0187825
\(943\) −35.3304 −1.15052
\(944\) 0.563951 0.0183550
\(945\) −0.397490 −0.0129303
\(946\) 36.3125 1.18062
\(947\) −0.0831248 −0.00270119 −0.00135060 0.999999i \(-0.500430\pi\)
−0.00135060 + 0.999999i \(0.500430\pi\)
\(948\) 10.4860 0.340568
\(949\) −5.68046 −0.184395
\(950\) 6.85831 0.222513
\(951\) −10.0021 −0.324341
\(952\) 1.01457 0.0328824
\(953\) −56.8291 −1.84088 −0.920438 0.390888i \(-0.872168\pi\)
−0.920438 + 0.390888i \(0.872168\pi\)
\(954\) −6.20568 −0.200916
\(955\) −16.4246 −0.531489
\(956\) −16.3120 −0.527568
\(957\) −39.0067 −1.26091
\(958\) 22.7422 0.734766
\(959\) 4.23048 0.136609
\(960\) −0.904513 −0.0291930
\(961\) −25.4600 −0.821291
\(962\) −13.3197 −0.429444
\(963\) −2.35202 −0.0757929
\(964\) 36.2515 1.16758
\(965\) −19.4213 −0.625195
\(966\) 1.24555 0.0400748
\(967\) −48.6775 −1.56536 −0.782682 0.622422i \(-0.786149\pi\)
−0.782682 + 0.622422i \(0.786149\pi\)
\(968\) 50.7715 1.63186
\(969\) −2.75787 −0.0885956
\(970\) −0.165453 −0.00531237
\(971\) −32.6531 −1.04789 −0.523943 0.851753i \(-0.675540\pi\)
−0.523943 + 0.851753i \(0.675540\pi\)
\(972\) −1.66768 −0.0534908
\(973\) 0.772474 0.0247644
\(974\) −21.3781 −0.684999
\(975\) 10.6602 0.341399
\(976\) −16.2769 −0.521012
\(977\) 1.95573 0.0625694 0.0312847 0.999511i \(-0.490040\pi\)
0.0312847 + 0.999511i \(0.490040\pi\)
\(978\) 7.87132 0.251697
\(979\) 60.1695 1.92303
\(980\) 9.35188 0.298735
\(981\) 3.67918 0.117467
\(982\) −20.3871 −0.650578
\(983\) −15.5246 −0.495157 −0.247578 0.968868i \(-0.579635\pi\)
−0.247578 + 0.968868i \(0.579635\pi\)
\(984\) −16.5901 −0.528874
\(985\) 8.27044 0.263518
\(986\) −3.80018 −0.121022
\(987\) 4.81750 0.153343
\(988\) 11.3655 0.361583
\(989\) −47.9326 −1.52417
\(990\) −2.82560 −0.0898034
\(991\) −27.8062 −0.883293 −0.441646 0.897189i \(-0.645605\pi\)
−0.441646 + 0.897189i \(0.645605\pi\)
\(992\) 12.8248 0.407188
\(993\) 12.4144 0.393961
\(994\) 2.17464 0.0689755
\(995\) 3.41940 0.108402
\(996\) −19.6304 −0.622012
\(997\) 58.8387 1.86344 0.931721 0.363175i \(-0.118307\pi\)
0.931721 + 0.363175i \(0.118307\pi\)
\(998\) 13.6338 0.431569
\(999\) −9.35003 −0.295822
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 \(a_p\))