Properties

Label 6027.2.a.bn.1.1
Level 6027
Weight 2
Character 6027.1
Self dual Yes
Analytic conductor 48.126
Analytic rank 0
Dimension 24
CM No

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Newspace parameters

Level: \( N \) = \( 6027 = 3 \cdot 7^{2} \cdot 41 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6027.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.1258372982\)
Analytic rank: \(0\)
Dimension: \(24\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) = 6027.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.69245 q^{2} -1.00000 q^{3} +5.24930 q^{4} -3.40876 q^{5} +2.69245 q^{6} -8.74860 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-2.69245 q^{2} -1.00000 q^{3} +5.24930 q^{4} -3.40876 q^{5} +2.69245 q^{6} -8.74860 q^{8} +1.00000 q^{9} +9.17792 q^{10} +2.47740 q^{11} -5.24930 q^{12} +2.61944 q^{13} +3.40876 q^{15} +13.0566 q^{16} +5.06684 q^{17} -2.69245 q^{18} +2.94589 q^{19} -17.8936 q^{20} -6.67027 q^{22} +2.48116 q^{23} +8.74860 q^{24} +6.61964 q^{25} -7.05272 q^{26} -1.00000 q^{27} +0.267181 q^{29} -9.17792 q^{30} +6.04056 q^{31} -17.6570 q^{32} -2.47740 q^{33} -13.6422 q^{34} +5.24930 q^{36} +9.78122 q^{37} -7.93167 q^{38} -2.61944 q^{39} +29.8219 q^{40} +1.00000 q^{41} +7.25634 q^{43} +13.0046 q^{44} -3.40876 q^{45} -6.68041 q^{46} +8.30624 q^{47} -13.0566 q^{48} -17.8231 q^{50} -5.06684 q^{51} +13.7502 q^{52} +10.8096 q^{53} +2.69245 q^{54} -8.44485 q^{55} -2.94589 q^{57} -0.719372 q^{58} +2.98222 q^{59} +17.8936 q^{60} +7.07265 q^{61} -16.2639 q^{62} +21.4276 q^{64} -8.92904 q^{65} +6.67027 q^{66} +14.1114 q^{67} +26.5974 q^{68} -2.48116 q^{69} +8.21376 q^{71} -8.74860 q^{72} +6.66722 q^{73} -26.3355 q^{74} -6.61964 q^{75} +15.4639 q^{76} +7.05272 q^{78} -10.7721 q^{79} -44.5067 q^{80} +1.00000 q^{81} -2.69245 q^{82} -14.0497 q^{83} -17.2716 q^{85} -19.5374 q^{86} -0.267181 q^{87} -21.6737 q^{88} -15.6068 q^{89} +9.17792 q^{90} +13.0244 q^{92} -6.04056 q^{93} -22.3642 q^{94} -10.0418 q^{95} +17.6570 q^{96} +7.72850 q^{97} +2.47740 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q + 8q^{2} - 24q^{3} + 32q^{4} - 4q^{5} - 8q^{6} + 24q^{8} + 24q^{9} + O(q^{10}) \) \( 24q + 8q^{2} - 24q^{3} + 32q^{4} - 4q^{5} - 8q^{6} + 24q^{8} + 24q^{9} + 4q^{10} + 12q^{11} - 32q^{12} + 4q^{15} + 44q^{16} - 8q^{17} + 8q^{18} + 4q^{19} - 28q^{20} + 16q^{22} + 20q^{23} - 24q^{24} + 48q^{25} - 32q^{26} - 24q^{27} + 24q^{29} - 4q^{30} + 4q^{31} + 36q^{32} - 12q^{33} - 16q^{34} + 32q^{36} + 64q^{37} - 20q^{38} + 48q^{40} + 24q^{41} + 20q^{43} + 48q^{44} - 4q^{45} + 28q^{46} - 32q^{47} - 44q^{48} - 20q^{50} + 8q^{51} + 76q^{53} - 8q^{54} + 24q^{55} - 4q^{57} + 28q^{58} - 28q^{59} + 28q^{60} + 28q^{61} + 4q^{62} + 48q^{64} + 28q^{65} - 16q^{66} + 44q^{67} + 32q^{68} - 20q^{69} + 20q^{71} + 24q^{72} + 16q^{73} + 44q^{74} - 48q^{75} + 16q^{76} + 32q^{78} + 4q^{79} - 44q^{80} + 24q^{81} + 8q^{82} - 8q^{83} + 28q^{85} + 56q^{86} - 24q^{87} + 60q^{88} - 60q^{89} + 4q^{90} + 60q^{92} - 4q^{93} - 24q^{94} + 28q^{95} - 36q^{96} + 48q^{97} + 12q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.69245 −1.90385 −0.951926 0.306328i \(-0.900899\pi\)
−0.951926 + 0.306328i \(0.900899\pi\)
\(3\) −1.00000 −0.577350
\(4\) 5.24930 2.62465
\(5\) −3.40876 −1.52444 −0.762222 0.647316i \(-0.775891\pi\)
−0.762222 + 0.647316i \(0.775891\pi\)
\(6\) 2.69245 1.09919
\(7\) 0 0
\(8\) −8.74860 −3.09310
\(9\) 1.00000 0.333333
\(10\) 9.17792 2.90231
\(11\) 2.47740 0.746963 0.373482 0.927638i \(-0.378164\pi\)
0.373482 + 0.927638i \(0.378164\pi\)
\(12\) −5.24930 −1.51534
\(13\) 2.61944 0.726502 0.363251 0.931691i \(-0.381667\pi\)
0.363251 + 0.931691i \(0.381667\pi\)
\(14\) 0 0
\(15\) 3.40876 0.880138
\(16\) 13.0566 3.26414
\(17\) 5.06684 1.22889 0.614445 0.788960i \(-0.289380\pi\)
0.614445 + 0.788960i \(0.289380\pi\)
\(18\) −2.69245 −0.634617
\(19\) 2.94589 0.675833 0.337917 0.941176i \(-0.390278\pi\)
0.337917 + 0.941176i \(0.390278\pi\)
\(20\) −17.8936 −4.00113
\(21\) 0 0
\(22\) −6.67027 −1.42211
\(23\) 2.48116 0.517358 0.258679 0.965963i \(-0.416713\pi\)
0.258679 + 0.965963i \(0.416713\pi\)
\(24\) 8.74860 1.78580
\(25\) 6.61964 1.32393
\(26\) −7.05272 −1.38315
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) 0.267181 0.0496142 0.0248071 0.999692i \(-0.492103\pi\)
0.0248071 + 0.999692i \(0.492103\pi\)
\(30\) −9.17792 −1.67565
\(31\) 6.04056 1.08492 0.542459 0.840083i \(-0.317494\pi\)
0.542459 + 0.840083i \(0.317494\pi\)
\(32\) −17.6570 −3.12135
\(33\) −2.47740 −0.431259
\(34\) −13.6422 −2.33962
\(35\) 0 0
\(36\) 5.24930 0.874884
\(37\) 9.78122 1.60802 0.804012 0.594614i \(-0.202695\pi\)
0.804012 + 0.594614i \(0.202695\pi\)
\(38\) −7.93167 −1.28669
\(39\) −2.61944 −0.419446
\(40\) 29.8219 4.71525
\(41\) 1.00000 0.156174
\(42\) 0 0
\(43\) 7.25634 1.10658 0.553291 0.832988i \(-0.313372\pi\)
0.553291 + 0.832988i \(0.313372\pi\)
\(44\) 13.0046 1.96052
\(45\) −3.40876 −0.508148
\(46\) −6.68041 −0.984973
\(47\) 8.30624 1.21159 0.605795 0.795621i \(-0.292855\pi\)
0.605795 + 0.795621i \(0.292855\pi\)
\(48\) −13.0566 −1.88455
\(49\) 0 0
\(50\) −17.8231 −2.52056
\(51\) −5.06684 −0.709500
\(52\) 13.7502 1.90682
\(53\) 10.8096 1.48481 0.742406 0.669951i \(-0.233685\pi\)
0.742406 + 0.669951i \(0.233685\pi\)
\(54\) 2.69245 0.366396
\(55\) −8.44485 −1.13870
\(56\) 0 0
\(57\) −2.94589 −0.390192
\(58\) −0.719372 −0.0944581
\(59\) 2.98222 0.388252 0.194126 0.980977i \(-0.437813\pi\)
0.194126 + 0.980977i \(0.437813\pi\)
\(60\) 17.8936 2.31005
\(61\) 7.07265 0.905560 0.452780 0.891622i \(-0.350432\pi\)
0.452780 + 0.891622i \(0.350432\pi\)
\(62\) −16.2639 −2.06552
\(63\) 0 0
\(64\) 21.4276 2.67845
\(65\) −8.92904 −1.10751
\(66\) 6.67027 0.821054
\(67\) 14.1114 1.72398 0.861989 0.506927i \(-0.169219\pi\)
0.861989 + 0.506927i \(0.169219\pi\)
\(68\) 26.5974 3.22541
\(69\) −2.48116 −0.298697
\(70\) 0 0
\(71\) 8.21376 0.974794 0.487397 0.873181i \(-0.337946\pi\)
0.487397 + 0.873181i \(0.337946\pi\)
\(72\) −8.74860 −1.03103
\(73\) 6.66722 0.780339 0.390169 0.920743i \(-0.372416\pi\)
0.390169 + 0.920743i \(0.372416\pi\)
\(74\) −26.3355 −3.06144
\(75\) −6.61964 −0.764370
\(76\) 15.4639 1.77383
\(77\) 0 0
\(78\) 7.05272 0.798564
\(79\) −10.7721 −1.21196 −0.605979 0.795481i \(-0.707218\pi\)
−0.605979 + 0.795481i \(0.707218\pi\)
\(80\) −44.5067 −4.97600
\(81\) 1.00000 0.111111
\(82\) −2.69245 −0.297332
\(83\) −14.0497 −1.54215 −0.771077 0.636743i \(-0.780281\pi\)
−0.771077 + 0.636743i \(0.780281\pi\)
\(84\) 0 0
\(85\) −17.2716 −1.87337
\(86\) −19.5374 −2.10677
\(87\) −0.267181 −0.0286448
\(88\) −21.6737 −2.31043
\(89\) −15.6068 −1.65432 −0.827161 0.561966i \(-0.810045\pi\)
−0.827161 + 0.561966i \(0.810045\pi\)
\(90\) 9.17792 0.967438
\(91\) 0 0
\(92\) 13.0244 1.35788
\(93\) −6.04056 −0.626377
\(94\) −22.3642 −2.30669
\(95\) −10.0418 −1.03027
\(96\) 17.6570 1.80211
\(97\) 7.72850 0.784710 0.392355 0.919814i \(-0.371660\pi\)
0.392355 + 0.919814i \(0.371660\pi\)
\(98\) 0 0
\(99\) 2.47740 0.248988
\(100\) 34.7485 3.47485
\(101\) −9.67726 −0.962923 −0.481462 0.876467i \(-0.659894\pi\)
−0.481462 + 0.876467i \(0.659894\pi\)
\(102\) 13.6422 1.35078
\(103\) 4.45587 0.439050 0.219525 0.975607i \(-0.429549\pi\)
0.219525 + 0.975607i \(0.429549\pi\)
\(104\) −22.9164 −2.24714
\(105\) 0 0
\(106\) −29.1043 −2.82686
\(107\) 10.3878 1.00423 0.502115 0.864801i \(-0.332555\pi\)
0.502115 + 0.864801i \(0.332555\pi\)
\(108\) −5.24930 −0.505114
\(109\) −7.88580 −0.755322 −0.377661 0.925944i \(-0.623272\pi\)
−0.377661 + 0.925944i \(0.623272\pi\)
\(110\) 22.7373 2.16792
\(111\) −9.78122 −0.928393
\(112\) 0 0
\(113\) 18.9778 1.78528 0.892641 0.450768i \(-0.148850\pi\)
0.892641 + 0.450768i \(0.148850\pi\)
\(114\) 7.93167 0.742869
\(115\) −8.45768 −0.788683
\(116\) 1.40251 0.130220
\(117\) 2.61944 0.242167
\(118\) −8.02950 −0.739175
\(119\) 0 0
\(120\) −29.8219 −2.72235
\(121\) −4.86251 −0.442046
\(122\) −19.0428 −1.72405
\(123\) −1.00000 −0.0901670
\(124\) 31.7087 2.84753
\(125\) −5.52095 −0.493809
\(126\) 0 0
\(127\) 13.4451 1.19306 0.596529 0.802592i \(-0.296546\pi\)
0.596529 + 0.802592i \(0.296546\pi\)
\(128\) −22.3787 −1.97801
\(129\) −7.25634 −0.638885
\(130\) 24.0410 2.10854
\(131\) −1.31500 −0.114892 −0.0574460 0.998349i \(-0.518296\pi\)
−0.0574460 + 0.998349i \(0.518296\pi\)
\(132\) −13.0046 −1.13191
\(133\) 0 0
\(134\) −37.9942 −3.28220
\(135\) 3.40876 0.293379
\(136\) −44.3278 −3.80107
\(137\) 14.4957 1.23845 0.619224 0.785214i \(-0.287447\pi\)
0.619224 + 0.785214i \(0.287447\pi\)
\(138\) 6.68041 0.568674
\(139\) −3.68532 −0.312585 −0.156292 0.987711i \(-0.549954\pi\)
−0.156292 + 0.987711i \(0.549954\pi\)
\(140\) 0 0
\(141\) −8.30624 −0.699512
\(142\) −22.1152 −1.85586
\(143\) 6.48939 0.542670
\(144\) 13.0566 1.08805
\(145\) −0.910755 −0.0756341
\(146\) −17.9512 −1.48565
\(147\) 0 0
\(148\) 51.3446 4.22050
\(149\) 15.8559 1.29897 0.649485 0.760375i \(-0.274985\pi\)
0.649485 + 0.760375i \(0.274985\pi\)
\(150\) 17.8231 1.45525
\(151\) 11.0469 0.898987 0.449493 0.893284i \(-0.351605\pi\)
0.449493 + 0.893284i \(0.351605\pi\)
\(152\) −25.7724 −2.09042
\(153\) 5.06684 0.409630
\(154\) 0 0
\(155\) −20.5908 −1.65389
\(156\) −13.7502 −1.10090
\(157\) −8.18928 −0.653576 −0.326788 0.945098i \(-0.605966\pi\)
−0.326788 + 0.945098i \(0.605966\pi\)
\(158\) 29.0034 2.30739
\(159\) −10.8096 −0.857256
\(160\) 60.1885 4.75832
\(161\) 0 0
\(162\) −2.69245 −0.211539
\(163\) −0.540625 −0.0423450 −0.0211725 0.999776i \(-0.506740\pi\)
−0.0211725 + 0.999776i \(0.506740\pi\)
\(164\) 5.24930 0.409902
\(165\) 8.44485 0.657430
\(166\) 37.8281 2.93603
\(167\) −22.1797 −1.71631 −0.858157 0.513388i \(-0.828390\pi\)
−0.858157 + 0.513388i \(0.828390\pi\)
\(168\) 0 0
\(169\) −6.13853 −0.472194
\(170\) 46.5031 3.56662
\(171\) 2.94589 0.225278
\(172\) 38.0908 2.90439
\(173\) −18.9158 −1.43814 −0.719070 0.694937i \(-0.755432\pi\)
−0.719070 + 0.694937i \(0.755432\pi\)
\(174\) 0.719372 0.0545354
\(175\) 0 0
\(176\) 32.3463 2.43820
\(177\) −2.98222 −0.224158
\(178\) 42.0207 3.14958
\(179\) −4.70118 −0.351383 −0.175691 0.984445i \(-0.556216\pi\)
−0.175691 + 0.984445i \(0.556216\pi\)
\(180\) −17.8936 −1.33371
\(181\) −20.8428 −1.54923 −0.774616 0.632432i \(-0.782057\pi\)
−0.774616 + 0.632432i \(0.782057\pi\)
\(182\) 0 0
\(183\) −7.07265 −0.522825
\(184\) −21.7067 −1.60024
\(185\) −33.3418 −2.45134
\(186\) 16.2639 1.19253
\(187\) 12.5526 0.917935
\(188\) 43.6020 3.18000
\(189\) 0 0
\(190\) 27.0371 1.96148
\(191\) 2.02143 0.146266 0.0731329 0.997322i \(-0.476700\pi\)
0.0731329 + 0.997322i \(0.476700\pi\)
\(192\) −21.4276 −1.54640
\(193\) 0.759337 0.0546583 0.0273291 0.999626i \(-0.491300\pi\)
0.0273291 + 0.999626i \(0.491300\pi\)
\(194\) −20.8086 −1.49397
\(195\) 8.92904 0.639422
\(196\) 0 0
\(197\) 17.2289 1.22751 0.613755 0.789496i \(-0.289658\pi\)
0.613755 + 0.789496i \(0.289658\pi\)
\(198\) −6.67027 −0.474036
\(199\) −20.8621 −1.47887 −0.739436 0.673227i \(-0.764908\pi\)
−0.739436 + 0.673227i \(0.764908\pi\)
\(200\) −57.9125 −4.09503
\(201\) −14.1114 −0.995339
\(202\) 26.0556 1.83326
\(203\) 0 0
\(204\) −26.5974 −1.86219
\(205\) −3.40876 −0.238078
\(206\) −11.9972 −0.835887
\(207\) 2.48116 0.172453
\(208\) 34.2009 2.37141
\(209\) 7.29813 0.504822
\(210\) 0 0
\(211\) −12.7824 −0.879978 −0.439989 0.898003i \(-0.645018\pi\)
−0.439989 + 0.898003i \(0.645018\pi\)
\(212\) 56.7428 3.89711
\(213\) −8.21376 −0.562798
\(214\) −27.9688 −1.91190
\(215\) −24.7351 −1.68692
\(216\) 8.74860 0.595267
\(217\) 0 0
\(218\) 21.2321 1.43802
\(219\) −6.66722 −0.450529
\(220\) −44.3296 −2.98870
\(221\) 13.2723 0.892791
\(222\) 26.3355 1.76752
\(223\) −7.42145 −0.496977 −0.248489 0.968635i \(-0.579934\pi\)
−0.248489 + 0.968635i \(0.579934\pi\)
\(224\) 0 0
\(225\) 6.61964 0.441309
\(226\) −51.0969 −3.39891
\(227\) −12.4666 −0.827437 −0.413718 0.910405i \(-0.635770\pi\)
−0.413718 + 0.910405i \(0.635770\pi\)
\(228\) −15.4639 −1.02412
\(229\) 14.2997 0.944948 0.472474 0.881345i \(-0.343361\pi\)
0.472474 + 0.881345i \(0.343361\pi\)
\(230\) 22.7719 1.50154
\(231\) 0 0
\(232\) −2.33746 −0.153462
\(233\) −23.7816 −1.55798 −0.778991 0.627035i \(-0.784268\pi\)
−0.778991 + 0.627035i \(0.784268\pi\)
\(234\) −7.05272 −0.461051
\(235\) −28.3140 −1.84700
\(236\) 15.6546 1.01903
\(237\) 10.7721 0.699724
\(238\) 0 0
\(239\) 10.0560 0.650472 0.325236 0.945633i \(-0.394556\pi\)
0.325236 + 0.945633i \(0.394556\pi\)
\(240\) 44.5067 2.87290
\(241\) 9.20788 0.593132 0.296566 0.955012i \(-0.404159\pi\)
0.296566 + 0.955012i \(0.404159\pi\)
\(242\) 13.0921 0.841591
\(243\) −1.00000 −0.0641500
\(244\) 37.1265 2.37678
\(245\) 0 0
\(246\) 2.69245 0.171665
\(247\) 7.71658 0.490994
\(248\) −52.8464 −3.35575
\(249\) 14.0497 0.890362
\(250\) 14.8649 0.940138
\(251\) 25.0778 1.58290 0.791450 0.611234i \(-0.209327\pi\)
0.791450 + 0.611234i \(0.209327\pi\)
\(252\) 0 0
\(253\) 6.14682 0.386447
\(254\) −36.2002 −2.27140
\(255\) 17.2716 1.08159
\(256\) 17.3983 1.08740
\(257\) −22.7564 −1.41950 −0.709752 0.704452i \(-0.751193\pi\)
−0.709752 + 0.704452i \(0.751193\pi\)
\(258\) 19.5374 1.21634
\(259\) 0 0
\(260\) −46.8713 −2.90683
\(261\) 0.267181 0.0165381
\(262\) 3.54057 0.218737
\(263\) −5.98638 −0.369136 −0.184568 0.982820i \(-0.559089\pi\)
−0.184568 + 0.982820i \(0.559089\pi\)
\(264\) 21.6737 1.33393
\(265\) −36.8473 −2.26351
\(266\) 0 0
\(267\) 15.6068 0.955123
\(268\) 74.0749 4.52484
\(269\) 31.2140 1.90315 0.951575 0.307418i \(-0.0994649\pi\)
0.951575 + 0.307418i \(0.0994649\pi\)
\(270\) −9.17792 −0.558551
\(271\) 6.47522 0.393342 0.196671 0.980470i \(-0.436987\pi\)
0.196671 + 0.980470i \(0.436987\pi\)
\(272\) 66.1556 4.01127
\(273\) 0 0
\(274\) −39.0289 −2.35782
\(275\) 16.3995 0.988925
\(276\) −13.0244 −0.783975
\(277\) 20.3614 1.22340 0.611699 0.791091i \(-0.290486\pi\)
0.611699 + 0.791091i \(0.290486\pi\)
\(278\) 9.92255 0.595115
\(279\) 6.04056 0.361639
\(280\) 0 0
\(281\) 18.5325 1.10556 0.552778 0.833328i \(-0.313568\pi\)
0.552778 + 0.833328i \(0.313568\pi\)
\(282\) 22.3642 1.33177
\(283\) 5.17781 0.307789 0.153894 0.988087i \(-0.450818\pi\)
0.153894 + 0.988087i \(0.450818\pi\)
\(284\) 43.1165 2.55849
\(285\) 10.0418 0.594826
\(286\) −17.4724 −1.03316
\(287\) 0 0
\(288\) −17.6570 −1.04045
\(289\) 8.67290 0.510171
\(290\) 2.45216 0.143996
\(291\) −7.72850 −0.453053
\(292\) 34.9982 2.04812
\(293\) 5.72975 0.334735 0.167368 0.985895i \(-0.446473\pi\)
0.167368 + 0.985895i \(0.446473\pi\)
\(294\) 0 0
\(295\) −10.1657 −0.591869
\(296\) −85.5720 −4.97377
\(297\) −2.47740 −0.143753
\(298\) −42.6914 −2.47305
\(299\) 6.49926 0.375862
\(300\) −34.7485 −2.00620
\(301\) 0 0
\(302\) −29.7434 −1.71154
\(303\) 9.67726 0.555944
\(304\) 38.4632 2.20602
\(305\) −24.1089 −1.38047
\(306\) −13.6422 −0.779875
\(307\) −1.87189 −0.106835 −0.0534173 0.998572i \(-0.517011\pi\)
−0.0534173 + 0.998572i \(0.517011\pi\)
\(308\) 0 0
\(309\) −4.45587 −0.253486
\(310\) 55.4398 3.14877
\(311\) 14.0836 0.798608 0.399304 0.916819i \(-0.369252\pi\)
0.399304 + 0.916819i \(0.369252\pi\)
\(312\) 22.9164 1.29739
\(313\) −26.4775 −1.49659 −0.748297 0.663363i \(-0.769128\pi\)
−0.748297 + 0.663363i \(0.769128\pi\)
\(314\) 22.0493 1.24431
\(315\) 0 0
\(316\) −56.5461 −3.18097
\(317\) −2.22286 −0.124848 −0.0624242 0.998050i \(-0.519883\pi\)
−0.0624242 + 0.998050i \(0.519883\pi\)
\(318\) 29.1043 1.63209
\(319\) 0.661913 0.0370600
\(320\) −73.0414 −4.08314
\(321\) −10.3878 −0.579792
\(322\) 0 0
\(323\) 14.9264 0.830525
\(324\) 5.24930 0.291628
\(325\) 17.3397 0.961836
\(326\) 1.45561 0.0806187
\(327\) 7.88580 0.436086
\(328\) −8.74860 −0.483060
\(329\) 0 0
\(330\) −22.7373 −1.25165
\(331\) −18.1534 −0.997800 −0.498900 0.866660i \(-0.666262\pi\)
−0.498900 + 0.866660i \(0.666262\pi\)
\(332\) −73.7510 −4.04761
\(333\) 9.78122 0.536008
\(334\) 59.7177 3.26761
\(335\) −48.1023 −2.62811
\(336\) 0 0
\(337\) −7.69887 −0.419384 −0.209692 0.977767i \(-0.567246\pi\)
−0.209692 + 0.977767i \(0.567246\pi\)
\(338\) 16.5277 0.898988
\(339\) −18.9778 −1.03073
\(340\) −90.6641 −4.91695
\(341\) 14.9649 0.810393
\(342\) −7.93167 −0.428895
\(343\) 0 0
\(344\) −63.4828 −3.42276
\(345\) 8.45768 0.455346
\(346\) 50.9299 2.73801
\(347\) −28.2126 −1.51453 −0.757266 0.653107i \(-0.773465\pi\)
−0.757266 + 0.653107i \(0.773465\pi\)
\(348\) −1.40251 −0.0751826
\(349\) −24.3427 −1.30303 −0.651517 0.758634i \(-0.725867\pi\)
−0.651517 + 0.758634i \(0.725867\pi\)
\(350\) 0 0
\(351\) −2.61944 −0.139815
\(352\) −43.7435 −2.33153
\(353\) 34.9906 1.86236 0.931180 0.364559i \(-0.118780\pi\)
0.931180 + 0.364559i \(0.118780\pi\)
\(354\) 8.02950 0.426763
\(355\) −27.9987 −1.48602
\(356\) −81.9250 −4.34202
\(357\) 0 0
\(358\) 12.6577 0.668980
\(359\) −34.5993 −1.82608 −0.913039 0.407871i \(-0.866271\pi\)
−0.913039 + 0.407871i \(0.866271\pi\)
\(360\) 29.8219 1.57175
\(361\) −10.3217 −0.543250
\(362\) 56.1182 2.94951
\(363\) 4.86251 0.255216
\(364\) 0 0
\(365\) −22.7269 −1.18958
\(366\) 19.0428 0.995381
\(367\) 23.3100 1.21677 0.608387 0.793640i \(-0.291817\pi\)
0.608387 + 0.793640i \(0.291817\pi\)
\(368\) 32.3955 1.68873
\(369\) 1.00000 0.0520579
\(370\) 89.7713 4.66699
\(371\) 0 0
\(372\) −31.7087 −1.64402
\(373\) −19.5468 −1.01209 −0.506047 0.862506i \(-0.668894\pi\)
−0.506047 + 0.862506i \(0.668894\pi\)
\(374\) −33.7972 −1.74761
\(375\) 5.52095 0.285101
\(376\) −72.6679 −3.74756
\(377\) 0.699865 0.0360449
\(378\) 0 0
\(379\) 3.74324 0.192277 0.0961386 0.995368i \(-0.469351\pi\)
0.0961386 + 0.995368i \(0.469351\pi\)
\(380\) −52.7126 −2.70410
\(381\) −13.4451 −0.688812
\(382\) −5.44262 −0.278468
\(383\) 4.35761 0.222664 0.111332 0.993783i \(-0.464488\pi\)
0.111332 + 0.993783i \(0.464488\pi\)
\(384\) 22.3787 1.14201
\(385\) 0 0
\(386\) −2.04448 −0.104061
\(387\) 7.25634 0.368861
\(388\) 40.5692 2.05959
\(389\) −28.6074 −1.45045 −0.725226 0.688511i \(-0.758265\pi\)
−0.725226 + 0.688511i \(0.758265\pi\)
\(390\) −24.0410 −1.21736
\(391\) 12.5717 0.635776
\(392\) 0 0
\(393\) 1.31500 0.0663329
\(394\) −46.3881 −2.33700
\(395\) 36.7195 1.84756
\(396\) 13.0046 0.653506
\(397\) 11.4747 0.575898 0.287949 0.957646i \(-0.407027\pi\)
0.287949 + 0.957646i \(0.407027\pi\)
\(398\) 56.1701 2.81555
\(399\) 0 0
\(400\) 86.4298 4.32149
\(401\) −16.8298 −0.840442 −0.420221 0.907422i \(-0.638047\pi\)
−0.420221 + 0.907422i \(0.638047\pi\)
\(402\) 37.9942 1.89498
\(403\) 15.8229 0.788195
\(404\) −50.7989 −2.52734
\(405\) −3.40876 −0.169383
\(406\) 0 0
\(407\) 24.2320 1.20113
\(408\) 44.3278 2.19455
\(409\) −33.7391 −1.66829 −0.834144 0.551546i \(-0.814038\pi\)
−0.834144 + 0.551546i \(0.814038\pi\)
\(410\) 9.17792 0.453265
\(411\) −14.4957 −0.715019
\(412\) 23.3902 1.15235
\(413\) 0 0
\(414\) −6.68041 −0.328324
\(415\) 47.8920 2.35092
\(416\) −46.2516 −2.26767
\(417\) 3.68532 0.180471
\(418\) −19.6499 −0.961107
\(419\) −13.3241 −0.650923 −0.325461 0.945555i \(-0.605520\pi\)
−0.325461 + 0.945555i \(0.605520\pi\)
\(420\) 0 0
\(421\) −25.0597 −1.22134 −0.610668 0.791887i \(-0.709099\pi\)
−0.610668 + 0.791887i \(0.709099\pi\)
\(422\) 34.4161 1.67535
\(423\) 8.30624 0.403863
\(424\) −94.5687 −4.59266
\(425\) 33.5407 1.62696
\(426\) 22.1152 1.07148
\(427\) 0 0
\(428\) 54.5289 2.63575
\(429\) −6.48939 −0.313311
\(430\) 66.5982 3.21165
\(431\) 6.65870 0.320738 0.160369 0.987057i \(-0.448732\pi\)
0.160369 + 0.987057i \(0.448732\pi\)
\(432\) −13.0566 −0.628185
\(433\) −30.8114 −1.48070 −0.740352 0.672220i \(-0.765341\pi\)
−0.740352 + 0.672220i \(0.765341\pi\)
\(434\) 0 0
\(435\) 0.910755 0.0436674
\(436\) −41.3949 −1.98246
\(437\) 7.30923 0.349648
\(438\) 17.9512 0.857740
\(439\) 9.81611 0.468497 0.234249 0.972177i \(-0.424737\pi\)
0.234249 + 0.972177i \(0.424737\pi\)
\(440\) 73.8805 3.52212
\(441\) 0 0
\(442\) −35.7350 −1.69974
\(443\) −21.1360 −1.00420 −0.502101 0.864809i \(-0.667439\pi\)
−0.502101 + 0.864809i \(0.667439\pi\)
\(444\) −51.3446 −2.43671
\(445\) 53.1999 2.52192
\(446\) 19.9819 0.946171
\(447\) −15.8559 −0.749960
\(448\) 0 0
\(449\) 29.6148 1.39761 0.698805 0.715312i \(-0.253715\pi\)
0.698805 + 0.715312i \(0.253715\pi\)
\(450\) −17.8231 −0.840187
\(451\) 2.47740 0.116656
\(452\) 99.6203 4.68574
\(453\) −11.0469 −0.519030
\(454\) 33.5657 1.57532
\(455\) 0 0
\(456\) 25.7724 1.20690
\(457\) −8.41928 −0.393837 −0.196919 0.980420i \(-0.563094\pi\)
−0.196919 + 0.980420i \(0.563094\pi\)
\(458\) −38.5012 −1.79904
\(459\) −5.06684 −0.236500
\(460\) −44.3969 −2.07002
\(461\) 16.5792 0.772171 0.386086 0.922463i \(-0.373827\pi\)
0.386086 + 0.922463i \(0.373827\pi\)
\(462\) 0 0
\(463\) 7.25788 0.337302 0.168651 0.985676i \(-0.446059\pi\)
0.168651 + 0.985676i \(0.446059\pi\)
\(464\) 3.48847 0.161948
\(465\) 20.5908 0.954876
\(466\) 64.0307 2.96617
\(467\) 33.5488 1.55245 0.776226 0.630454i \(-0.217131\pi\)
0.776226 + 0.630454i \(0.217131\pi\)
\(468\) 13.7502 0.635605
\(469\) 0 0
\(470\) 76.2340 3.51641
\(471\) 8.18928 0.377342
\(472\) −26.0903 −1.20090
\(473\) 17.9768 0.826576
\(474\) −29.0034 −1.33217
\(475\) 19.5007 0.894754
\(476\) 0 0
\(477\) 10.8096 0.494937
\(478\) −27.0754 −1.23840
\(479\) −18.5081 −0.845656 −0.422828 0.906210i \(-0.638963\pi\)
−0.422828 + 0.906210i \(0.638963\pi\)
\(480\) −60.1885 −2.74722
\(481\) 25.6213 1.16823
\(482\) −24.7918 −1.12923
\(483\) 0 0
\(484\) −25.5248 −1.16022
\(485\) −26.3446 −1.19625
\(486\) 2.69245 0.122132
\(487\) −43.5938 −1.97542 −0.987711 0.156290i \(-0.950046\pi\)
−0.987711 + 0.156290i \(0.950046\pi\)
\(488\) −61.8757 −2.80098
\(489\) 0.540625 0.0244479
\(490\) 0 0
\(491\) 33.8439 1.52735 0.763676 0.645599i \(-0.223392\pi\)
0.763676 + 0.645599i \(0.223392\pi\)
\(492\) −5.24930 −0.236657
\(493\) 1.35376 0.0609704
\(494\) −20.7765 −0.934781
\(495\) −8.44485 −0.379568
\(496\) 78.8691 3.54133
\(497\) 0 0
\(498\) −37.8281 −1.69512
\(499\) 35.4016 1.58479 0.792396 0.610008i \(-0.208834\pi\)
0.792396 + 0.610008i \(0.208834\pi\)
\(500\) −28.9811 −1.29608
\(501\) 22.1797 0.990914
\(502\) −67.5209 −3.01361
\(503\) −35.0856 −1.56439 −0.782195 0.623033i \(-0.785900\pi\)
−0.782195 + 0.623033i \(0.785900\pi\)
\(504\) 0 0
\(505\) 32.9874 1.46792
\(506\) −16.5500 −0.735738
\(507\) 6.13853 0.272622
\(508\) 70.5773 3.13136
\(509\) 24.7682 1.09783 0.548917 0.835877i \(-0.315040\pi\)
0.548917 + 0.835877i \(0.315040\pi\)
\(510\) −46.5031 −2.05919
\(511\) 0 0
\(512\) −2.08691 −0.0922294
\(513\) −2.94589 −0.130064
\(514\) 61.2705 2.70253
\(515\) −15.1890 −0.669307
\(516\) −38.0908 −1.67685
\(517\) 20.5778 0.905013
\(518\) 0 0
\(519\) 18.9158 0.830311
\(520\) 78.1166 3.42564
\(521\) 20.6917 0.906520 0.453260 0.891378i \(-0.350261\pi\)
0.453260 + 0.891378i \(0.350261\pi\)
\(522\) −0.719372 −0.0314860
\(523\) −3.14418 −0.137485 −0.0687426 0.997634i \(-0.521899\pi\)
−0.0687426 + 0.997634i \(0.521899\pi\)
\(524\) −6.90283 −0.301551
\(525\) 0 0
\(526\) 16.1180 0.702780
\(527\) 30.6066 1.33324
\(528\) −32.3463 −1.40769
\(529\) −16.8438 −0.732341
\(530\) 99.2096 4.30939
\(531\) 2.98222 0.129417
\(532\) 0 0
\(533\) 2.61944 0.113461
\(534\) −42.0207 −1.81841
\(535\) −35.4096 −1.53089
\(536\) −123.455 −5.33243
\(537\) 4.70118 0.202871
\(538\) −84.0421 −3.62331
\(539\) 0 0
\(540\) 17.8936 0.770018
\(541\) −1.25034 −0.0537565 −0.0268782 0.999639i \(-0.508557\pi\)
−0.0268782 + 0.999639i \(0.508557\pi\)
\(542\) −17.4342 −0.748864
\(543\) 20.8428 0.894449
\(544\) −89.4654 −3.83580
\(545\) 26.8808 1.15145
\(546\) 0 0
\(547\) −27.9208 −1.19381 −0.596903 0.802313i \(-0.703602\pi\)
−0.596903 + 0.802313i \(0.703602\pi\)
\(548\) 76.0922 3.25050
\(549\) 7.07265 0.301853
\(550\) −44.1548 −1.88277
\(551\) 0.787085 0.0335309
\(552\) 21.7067 0.923898
\(553\) 0 0
\(554\) −54.8221 −2.32917
\(555\) 33.3418 1.41528
\(556\) −19.3454 −0.820426
\(557\) −3.83843 −0.162639 −0.0813197 0.996688i \(-0.525913\pi\)
−0.0813197 + 0.996688i \(0.525913\pi\)
\(558\) −16.2639 −0.688507
\(559\) 19.0076 0.803935
\(560\) 0 0
\(561\) −12.5526 −0.529970
\(562\) −49.8979 −2.10482
\(563\) 19.5595 0.824335 0.412167 0.911108i \(-0.364772\pi\)
0.412167 + 0.911108i \(0.364772\pi\)
\(564\) −43.6020 −1.83597
\(565\) −64.6908 −2.72156
\(566\) −13.9410 −0.585984
\(567\) 0 0
\(568\) −71.8589 −3.01513
\(569\) −4.77753 −0.200284 −0.100142 0.994973i \(-0.531930\pi\)
−0.100142 + 0.994973i \(0.531930\pi\)
\(570\) −27.0371 −1.13246
\(571\) 16.0786 0.672870 0.336435 0.941707i \(-0.390779\pi\)
0.336435 + 0.941707i \(0.390779\pi\)
\(572\) 34.0648 1.42432
\(573\) −2.02143 −0.0844466
\(574\) 0 0
\(575\) 16.4244 0.684944
\(576\) 21.4276 0.892815
\(577\) −2.45923 −0.102379 −0.0511896 0.998689i \(-0.516301\pi\)
−0.0511896 + 0.998689i \(0.516301\pi\)
\(578\) −23.3514 −0.971289
\(579\) −0.759337 −0.0315570
\(580\) −4.78083 −0.198513
\(581\) 0 0
\(582\) 20.8086 0.862545
\(583\) 26.7796 1.10910
\(584\) −58.3288 −2.41366
\(585\) −8.92904 −0.369171
\(586\) −15.4271 −0.637286
\(587\) 16.0272 0.661512 0.330756 0.943716i \(-0.392696\pi\)
0.330756 + 0.943716i \(0.392696\pi\)
\(588\) 0 0
\(589\) 17.7948 0.733223
\(590\) 27.3706 1.12683
\(591\) −17.2289 −0.708704
\(592\) 127.709 5.24882
\(593\) −15.5184 −0.637266 −0.318633 0.947878i \(-0.603224\pi\)
−0.318633 + 0.947878i \(0.603224\pi\)
\(594\) 6.67027 0.273685
\(595\) 0 0
\(596\) 83.2327 3.40934
\(597\) 20.8621 0.853827
\(598\) −17.4989 −0.715585
\(599\) 21.8286 0.891892 0.445946 0.895060i \(-0.352867\pi\)
0.445946 + 0.895060i \(0.352867\pi\)
\(600\) 57.9125 2.36427
\(601\) −2.88582 −0.117715 −0.0588575 0.998266i \(-0.518746\pi\)
−0.0588575 + 0.998266i \(0.518746\pi\)
\(602\) 0 0
\(603\) 14.1114 0.574659
\(604\) 57.9887 2.35953
\(605\) 16.5751 0.673874
\(606\) −26.0556 −1.05844
\(607\) 6.38555 0.259182 0.129591 0.991568i \(-0.458634\pi\)
0.129591 + 0.991568i \(0.458634\pi\)
\(608\) −52.0156 −2.10951
\(609\) 0 0
\(610\) 64.9122 2.62822
\(611\) 21.7577 0.880223
\(612\) 26.5974 1.07514
\(613\) 17.3087 0.699092 0.349546 0.936919i \(-0.386336\pi\)
0.349546 + 0.936919i \(0.386336\pi\)
\(614\) 5.03998 0.203397
\(615\) 3.40876 0.137454
\(616\) 0 0
\(617\) 2.81470 0.113316 0.0566579 0.998394i \(-0.481956\pi\)
0.0566579 + 0.998394i \(0.481956\pi\)
\(618\) 11.9972 0.482599
\(619\) 28.7390 1.15512 0.577559 0.816349i \(-0.304005\pi\)
0.577559 + 0.816349i \(0.304005\pi\)
\(620\) −108.087 −4.34090
\(621\) −2.48116 −0.0995656
\(622\) −37.9194 −1.52043
\(623\) 0 0
\(624\) −34.2009 −1.36913
\(625\) −14.2786 −0.571144
\(626\) 71.2893 2.84929
\(627\) −7.29813 −0.291459
\(628\) −42.9880 −1.71541
\(629\) 49.5599 1.97608
\(630\) 0 0
\(631\) 0.108140 0.00430497 0.00215249 0.999998i \(-0.499315\pi\)
0.00215249 + 0.999998i \(0.499315\pi\)
\(632\) 94.2409 3.74870
\(633\) 12.7824 0.508056
\(634\) 5.98496 0.237693
\(635\) −45.8310 −1.81875
\(636\) −56.7428 −2.25000
\(637\) 0 0
\(638\) −1.78217 −0.0705567
\(639\) 8.21376 0.324931
\(640\) 76.2834 3.01537
\(641\) 14.5924 0.576366 0.288183 0.957575i \(-0.406949\pi\)
0.288183 + 0.957575i \(0.406949\pi\)
\(642\) 27.9688 1.10384
\(643\) 19.0479 0.751178 0.375589 0.926786i \(-0.377440\pi\)
0.375589 + 0.926786i \(0.377440\pi\)
\(644\) 0 0
\(645\) 24.7351 0.973945
\(646\) −40.1885 −1.58120
\(647\) 2.49785 0.0982008 0.0491004 0.998794i \(-0.484365\pi\)
0.0491004 + 0.998794i \(0.484365\pi\)
\(648\) −8.74860 −0.343677
\(649\) 7.38815 0.290010
\(650\) −46.6865 −1.83119
\(651\) 0 0
\(652\) −2.83791 −0.111141
\(653\) 7.16644 0.280444 0.140222 0.990120i \(-0.455218\pi\)
0.140222 + 0.990120i \(0.455218\pi\)
\(654\) −21.2321 −0.830242
\(655\) 4.48251 0.175146
\(656\) 13.0566 0.509774
\(657\) 6.66722 0.260113
\(658\) 0 0
\(659\) 24.4135 0.951016 0.475508 0.879712i \(-0.342264\pi\)
0.475508 + 0.879712i \(0.342264\pi\)
\(660\) 44.3296 1.72553
\(661\) 22.6127 0.879530 0.439765 0.898113i \(-0.355062\pi\)
0.439765 + 0.898113i \(0.355062\pi\)
\(662\) 48.8771 1.89966
\(663\) −13.2723 −0.515453
\(664\) 122.915 4.77003
\(665\) 0 0
\(666\) −26.3355 −1.02048
\(667\) 0.662919 0.0256683
\(668\) −116.428 −4.50473
\(669\) 7.42145 0.286930
\(670\) 129.513 5.00353
\(671\) 17.5217 0.676419
\(672\) 0 0
\(673\) 11.8973 0.458607 0.229303 0.973355i \(-0.426355\pi\)
0.229303 + 0.973355i \(0.426355\pi\)
\(674\) 20.7288 0.798445
\(675\) −6.61964 −0.254790
\(676\) −32.2230 −1.23935
\(677\) 4.70172 0.180702 0.0903509 0.995910i \(-0.471201\pi\)
0.0903509 + 0.995910i \(0.471201\pi\)
\(678\) 51.0969 1.96236
\(679\) 0 0
\(680\) 151.103 5.79452
\(681\) 12.4666 0.477721
\(682\) −40.2922 −1.54287
\(683\) −16.7037 −0.639149 −0.319575 0.947561i \(-0.603540\pi\)
−0.319575 + 0.947561i \(0.603540\pi\)
\(684\) 15.4639 0.591276
\(685\) −49.4122 −1.88794
\(686\) 0 0
\(687\) −14.2997 −0.545566
\(688\) 94.7430 3.61204
\(689\) 28.3151 1.07872
\(690\) −22.7719 −0.866912
\(691\) 1.53565 0.0584187 0.0292093 0.999573i \(-0.490701\pi\)
0.0292093 + 0.999573i \(0.490701\pi\)
\(692\) −99.2947 −3.77462
\(693\) 0 0
\(694\) 75.9611 2.88344
\(695\) 12.5624 0.476518
\(696\) 2.33746 0.0886011
\(697\) 5.06684 0.191920
\(698\) 65.5415 2.48078
\(699\) 23.7816 0.899501
\(700\) 0 0
\(701\) −18.6576 −0.704687 −0.352343 0.935871i \(-0.614615\pi\)
−0.352343 + 0.935871i \(0.614615\pi\)
\(702\) 7.05272 0.266188
\(703\) 28.8144 1.08676
\(704\) 53.0846 2.00070
\(705\) 28.3140 1.06637
\(706\) −94.2105 −3.54566
\(707\) 0 0
\(708\) −15.6546 −0.588336
\(709\) 17.4961 0.657079 0.328540 0.944490i \(-0.393444\pi\)
0.328540 + 0.944490i \(0.393444\pi\)
\(710\) 75.3853 2.82916
\(711\) −10.7721 −0.403986
\(712\) 136.538 5.11697
\(713\) 14.9876 0.561291
\(714\) 0 0
\(715\) −22.1208 −0.827270
\(716\) −24.6779 −0.922257
\(717\) −10.0560 −0.375550
\(718\) 93.1569 3.47658
\(719\) −10.4177 −0.388513 −0.194257 0.980951i \(-0.562229\pi\)
−0.194257 + 0.980951i \(0.562229\pi\)
\(720\) −44.5067 −1.65867
\(721\) 0 0
\(722\) 27.7908 1.03427
\(723\) −9.20788 −0.342445
\(724\) −109.410 −4.06619
\(725\) 1.76864 0.0656856
\(726\) −13.0921 −0.485893
\(727\) −13.3290 −0.494346 −0.247173 0.968971i \(-0.579502\pi\)
−0.247173 + 0.968971i \(0.579502\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 61.1912 2.26479
\(731\) 36.7668 1.35987
\(732\) −37.1265 −1.37223
\(733\) −10.0515 −0.371262 −0.185631 0.982620i \(-0.559433\pi\)
−0.185631 + 0.982620i \(0.559433\pi\)
\(734\) −62.7612 −2.31656
\(735\) 0 0
\(736\) −43.8099 −1.61486
\(737\) 34.9595 1.28775
\(738\) −2.69245 −0.0991106
\(739\) 22.6282 0.832392 0.416196 0.909275i \(-0.363363\pi\)
0.416196 + 0.909275i \(0.363363\pi\)
\(740\) −175.021 −6.43391
\(741\) −7.71658 −0.283476
\(742\) 0 0
\(743\) 45.5658 1.67165 0.835823 0.548999i \(-0.184991\pi\)
0.835823 + 0.548999i \(0.184991\pi\)
\(744\) 52.8464 1.93744
\(745\) −54.0491 −1.98021
\(746\) 52.6288 1.92688
\(747\) −14.0497 −0.514051
\(748\) 65.8923 2.40926
\(749\) 0 0
\(750\) −14.8649 −0.542789
\(751\) −24.9793 −0.911507 −0.455753 0.890106i \(-0.650630\pi\)
−0.455753 + 0.890106i \(0.650630\pi\)
\(752\) 108.451 3.95480
\(753\) −25.0778 −0.913888
\(754\) −1.88435 −0.0686241
\(755\) −37.6563 −1.37045
\(756\) 0 0
\(757\) −25.3070 −0.919799 −0.459899 0.887971i \(-0.652115\pi\)
−0.459899 + 0.887971i \(0.652115\pi\)
\(758\) −10.0785 −0.366067
\(759\) −6.14682 −0.223115
\(760\) 87.8518 3.18672
\(761\) 23.9832 0.869391 0.434695 0.900578i \(-0.356856\pi\)
0.434695 + 0.900578i \(0.356856\pi\)
\(762\) 36.2002 1.31140
\(763\) 0 0
\(764\) 10.6111 0.383897
\(765\) −17.2716 −0.624458
\(766\) −11.7327 −0.423919
\(767\) 7.81176 0.282066
\(768\) −17.3983 −0.627809
\(769\) 9.22042 0.332497 0.166248 0.986084i \(-0.446835\pi\)
0.166248 + 0.986084i \(0.446835\pi\)
\(770\) 0 0
\(771\) 22.7564 0.819551
\(772\) 3.98599 0.143459
\(773\) −12.9567 −0.466020 −0.233010 0.972474i \(-0.574858\pi\)
−0.233010 + 0.972474i \(0.574858\pi\)
\(774\) −19.5374 −0.702256
\(775\) 39.9863 1.43635
\(776\) −67.6135 −2.42718
\(777\) 0 0
\(778\) 77.0240 2.76144
\(779\) 2.94589 0.105547
\(780\) 46.8713 1.67826
\(781\) 20.3487 0.728135
\(782\) −33.8486 −1.21042
\(783\) −0.267181 −0.00954826
\(784\) 0 0
\(785\) 27.9153 0.996339
\(786\) −3.54057 −0.126288
\(787\) 21.9896 0.783845 0.391923 0.919998i \(-0.371810\pi\)
0.391923 + 0.919998i \(0.371810\pi\)
\(788\) 90.4399 3.22179
\(789\) 5.98638 0.213121
\(790\) −98.8656 −3.51748
\(791\) 0 0
\(792\) −21.6737 −0.770143
\(793\) 18.5264 0.657891
\(794\) −30.8950 −1.09642
\(795\) 36.8473 1.30684
\(796\) −109.511 −3.88152
\(797\) −54.7322 −1.93871 −0.969356 0.245658i \(-0.920996\pi\)
−0.969356 + 0.245658i \(0.920996\pi\)
\(798\) 0 0
\(799\) 42.0864 1.48891
\(800\) −116.883 −4.13244
\(801\) −15.6068 −0.551440
\(802\) 45.3136 1.60008
\(803\) 16.5173 0.582884
\(804\) −74.0749 −2.61242
\(805\) 0 0
\(806\) −42.6024 −1.50061
\(807\) −31.2140 −1.09878
\(808\) 84.6624 2.97841
\(809\) 43.6588 1.53496 0.767482 0.641071i \(-0.221510\pi\)
0.767482 + 0.641071i \(0.221510\pi\)
\(810\) 9.17792 0.322479
\(811\) 1.40296 0.0492645 0.0246322 0.999697i \(-0.492159\pi\)
0.0246322 + 0.999697i \(0.492159\pi\)
\(812\) 0 0
\(813\) −6.47522 −0.227096
\(814\) −65.2434 −2.28678
\(815\) 1.84286 0.0645526
\(816\) −66.1556 −2.31591
\(817\) 21.3764 0.747865
\(818\) 90.8408 3.17617
\(819\) 0 0
\(820\) −17.8936 −0.624872
\(821\) −31.7107 −1.10671 −0.553355 0.832946i \(-0.686653\pi\)
−0.553355 + 0.832946i \(0.686653\pi\)
\(822\) 39.0289 1.36129
\(823\) −31.6705 −1.10396 −0.551981 0.833856i \(-0.686128\pi\)
−0.551981 + 0.833856i \(0.686128\pi\)
\(824\) −38.9826 −1.35802
\(825\) −16.3995 −0.570956
\(826\) 0 0
\(827\) −11.7291 −0.407861 −0.203931 0.978985i \(-0.565372\pi\)
−0.203931 + 0.978985i \(0.565372\pi\)
\(828\) 13.0244 0.452628
\(829\) 37.7160 1.30993 0.654965 0.755659i \(-0.272683\pi\)
0.654965 + 0.755659i \(0.272683\pi\)
\(830\) −128.947 −4.47581
\(831\) −20.3614 −0.706329
\(832\) 56.1283 1.94590
\(833\) 0 0
\(834\) −9.92255 −0.343590
\(835\) 75.6051 2.61642
\(836\) 38.3101 1.32498
\(837\) −6.04056 −0.208792
\(838\) 35.8744 1.23926
\(839\) 26.0811 0.900420 0.450210 0.892923i \(-0.351349\pi\)
0.450210 + 0.892923i \(0.351349\pi\)
\(840\) 0 0
\(841\) −28.9286 −0.997538
\(842\) 67.4721 2.32524
\(843\) −18.5325 −0.638293
\(844\) −67.0988 −2.30964
\(845\) 20.9248 0.719833
\(846\) −22.3642 −0.768896
\(847\) 0 0
\(848\) 141.136 4.84664
\(849\) −5.17781 −0.177702
\(850\) −90.3066 −3.09749
\(851\) 24.2688 0.831924
\(852\) −43.1165 −1.47715
\(853\) 48.0414 1.64491 0.822453 0.568833i \(-0.192605\pi\)
0.822453 + 0.568833i \(0.192605\pi\)
\(854\) 0 0
\(855\) −10.0418 −0.343423
\(856\) −90.8790 −3.10618
\(857\) 41.5181 1.41823 0.709116 0.705092i \(-0.249094\pi\)
0.709116 + 0.705092i \(0.249094\pi\)
\(858\) 17.4724 0.596498
\(859\) −47.5478 −1.62231 −0.811156 0.584830i \(-0.801161\pi\)
−0.811156 + 0.584830i \(0.801161\pi\)
\(860\) −129.842 −4.42758
\(861\) 0 0
\(862\) −17.9282 −0.610638
\(863\) 3.80787 0.129621 0.0648107 0.997898i \(-0.479356\pi\)
0.0648107 + 0.997898i \(0.479356\pi\)
\(864\) 17.6570 0.600704
\(865\) 64.4794 2.19236
\(866\) 82.9584 2.81904
\(867\) −8.67290 −0.294547
\(868\) 0 0
\(869\) −26.6868 −0.905288
\(870\) −2.45216 −0.0831362
\(871\) 36.9639 1.25247
\(872\) 68.9897 2.33628
\(873\) 7.72850 0.261570
\(874\) −19.6797 −0.665677
\(875\) 0 0
\(876\) −34.9982 −1.18248
\(877\) −46.2498 −1.56175 −0.780873 0.624690i \(-0.785226\pi\)
−0.780873 + 0.624690i \(0.785226\pi\)
\(878\) −26.4294 −0.891949
\(879\) −5.72975 −0.193260
\(880\) −110.261 −3.71689
\(881\) 8.19976 0.276257 0.138128 0.990414i \(-0.455891\pi\)
0.138128 + 0.990414i \(0.455891\pi\)
\(882\) 0 0
\(883\) −37.2720 −1.25430 −0.627151 0.778898i \(-0.715779\pi\)
−0.627151 + 0.778898i \(0.715779\pi\)
\(884\) 69.6703 2.34327
\(885\) 10.1657 0.341716
\(886\) 56.9077 1.91185
\(887\) 24.8683 0.834996 0.417498 0.908678i \(-0.362907\pi\)
0.417498 + 0.908678i \(0.362907\pi\)
\(888\) 85.5720 2.87161
\(889\) 0 0
\(890\) −143.238 −4.80136
\(891\) 2.47740 0.0829959
\(892\) −38.9574 −1.30439
\(893\) 24.4693 0.818832
\(894\) 42.6914 1.42781
\(895\) 16.0252 0.535663
\(896\) 0 0
\(897\) −6.49926 −0.217004
\(898\) −79.7366 −2.66084
\(899\) 1.61392 0.0538273
\(900\) 34.7485 1.15828
\(901\) 54.7705 1.82467
\(902\) −6.67027 −0.222096
\(903\) 0 0
\(904\) −166.029 −5.52205
\(905\) 71.0480 2.36172
\(906\) 29.7434 0.988157
\(907\) −10.1610 −0.337389 −0.168694 0.985668i \(-0.553955\pi\)
−0.168694 + 0.985668i \(0.553955\pi\)
\(908\) −65.4409 −2.17173
\(909\) −9.67726 −0.320974
\(910\) 0 0
\(911\) −16.7737 −0.555738 −0.277869 0.960619i \(-0.589628\pi\)
−0.277869 + 0.960619i \(0.589628\pi\)
\(912\) −38.4632 −1.27364
\(913\) −34.8066 −1.15193
\(914\) 22.6685 0.749808
\(915\) 24.1089 0.797017
\(916\) 75.0632 2.48016
\(917\) 0 0
\(918\) 13.6422 0.450261
\(919\) 2.31695 0.0764290 0.0382145 0.999270i \(-0.487833\pi\)
0.0382145 + 0.999270i \(0.487833\pi\)
\(920\) 73.9928 2.43947
\(921\) 1.87189 0.0616810
\(922\) −44.6388 −1.47010
\(923\) 21.5155 0.708190
\(924\) 0 0
\(925\) 64.7481 2.12891
\(926\) −19.5415 −0.642173
\(927\) 4.45587 0.146350
\(928\) −4.71762 −0.154863
\(929\) −48.6233 −1.59528 −0.797640 0.603134i \(-0.793918\pi\)
−0.797640 + 0.603134i \(0.793918\pi\)
\(930\) −55.4398 −1.81794
\(931\) 0 0
\(932\) −124.837 −4.08916
\(933\) −14.0836 −0.461077
\(934\) −90.3285 −2.95564
\(935\) −42.7887 −1.39934
\(936\) −22.9164 −0.749047
\(937\) −9.53054 −0.311349 −0.155675 0.987808i \(-0.549755\pi\)
−0.155675 + 0.987808i \(0.549755\pi\)
\(938\) 0 0
\(939\) 26.4775 0.864059
\(940\) −148.629 −4.84773
\(941\) −47.8808 −1.56087 −0.780434 0.625238i \(-0.785002\pi\)
−0.780434 + 0.625238i \(0.785002\pi\)
\(942\) −22.0493 −0.718403
\(943\) 2.48116 0.0807977
\(944\) 38.9376 1.26731
\(945\) 0 0
\(946\) −48.4018 −1.57368
\(947\) −40.4665 −1.31498 −0.657492 0.753461i \(-0.728383\pi\)
−0.657492 + 0.753461i \(0.728383\pi\)
\(948\) 56.5461 1.83653
\(949\) 17.4644 0.566918
\(950\) −52.5047 −1.70348
\(951\) 2.22286 0.0720813
\(952\) 0 0
\(953\) −39.0547 −1.26511 −0.632554 0.774517i \(-0.717993\pi\)
−0.632554 + 0.774517i \(0.717993\pi\)
\(954\) −29.1043 −0.942287
\(955\) −6.89058 −0.222974
\(956\) 52.7872 1.70726
\(957\) −0.661913 −0.0213966
\(958\) 49.8321 1.61000
\(959\) 0 0
\(960\) 73.0414 2.35740
\(961\) 5.48840 0.177045
\(962\) −68.9843 −2.22414
\(963\) 10.3878 0.334743
\(964\) 48.3350 1.55676
\(965\) −2.58840 −0.0833234
\(966\) 0 0
\(967\) −18.3993 −0.591681 −0.295840 0.955237i \(-0.595600\pi\)
−0.295840 + 0.955237i \(0.595600\pi\)
\(968\) 42.5401 1.36729
\(969\) −14.9264 −0.479504
\(970\) 70.9316 2.27748
\(971\) −31.1119 −0.998429 −0.499215 0.866478i \(-0.666378\pi\)
−0.499215 + 0.866478i \(0.666378\pi\)
\(972\) −5.24930 −0.168371
\(973\) 0 0
\(974\) 117.374 3.76091
\(975\) −17.3397 −0.555316
\(976\) 92.3445 2.95588
\(977\) −13.4478 −0.430232 −0.215116 0.976588i \(-0.569013\pi\)
−0.215116 + 0.976588i \(0.569013\pi\)
\(978\) −1.45561 −0.0465452
\(979\) −38.6643 −1.23572
\(980\) 0 0
\(981\) −7.88580 −0.251774
\(982\) −91.1230 −2.90785
\(983\) 23.3009 0.743184 0.371592 0.928396i \(-0.378812\pi\)
0.371592 + 0.928396i \(0.378812\pi\)
\(984\) 8.74860 0.278895
\(985\) −58.7293 −1.87127
\(986\) −3.64494 −0.116079
\(987\) 0 0
\(988\) 40.5067 1.28869
\(989\) 18.0042 0.572499
\(990\) 22.7373 0.722640
\(991\) 23.4475 0.744835 0.372417 0.928065i \(-0.378529\pi\)
0.372417 + 0.928065i \(0.378529\pi\)
\(992\) −106.658 −3.38641
\(993\) 18.1534 0.576080
\(994\) 0 0
\(995\) 71.1137 2.25446
\(996\) 73.7510 2.33689
\(997\) −0.865413 −0.0274079 −0.0137039 0.999906i \(-0.504362\pi\)
−0.0137039 + 0.999906i \(0.504362\pi\)
\(998\) −95.3170 −3.01721
\(999\) −9.78122 −0.309464
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 \(a_p\))