Properties

Label 6034.2.a.n.1.6
Level 6034
Weight 2
Character 6034.1
Self dual Yes
Analytic conductor 48.182
Analytic rank 0
Dimension 24
CM No

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Newspace parameters

Level: \( N \) = \( 6034 = 2 \cdot 7 \cdot 431 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6034.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.1817325796\)
Analytic rank: \(0\)
Dimension: \(24\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.6
Character \(\chi\) = 6034.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} -1.69422 q^{3} +1.00000 q^{4} +3.76480 q^{5} +1.69422 q^{6} -1.00000 q^{7} -1.00000 q^{8} -0.129635 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -1.69422 q^{3} +1.00000 q^{4} +3.76480 q^{5} +1.69422 q^{6} -1.00000 q^{7} -1.00000 q^{8} -0.129635 q^{9} -3.76480 q^{10} +5.13106 q^{11} -1.69422 q^{12} +2.53139 q^{13} +1.00000 q^{14} -6.37839 q^{15} +1.00000 q^{16} +1.63388 q^{17} +0.129635 q^{18} +2.24224 q^{19} +3.76480 q^{20} +1.69422 q^{21} -5.13106 q^{22} +4.75107 q^{23} +1.69422 q^{24} +9.17374 q^{25} -2.53139 q^{26} +5.30227 q^{27} -1.00000 q^{28} +3.82147 q^{29} +6.37839 q^{30} +7.14240 q^{31} -1.00000 q^{32} -8.69311 q^{33} -1.63388 q^{34} -3.76480 q^{35} -0.129635 q^{36} +2.28449 q^{37} -2.24224 q^{38} -4.28873 q^{39} -3.76480 q^{40} -6.10878 q^{41} -1.69422 q^{42} -7.09119 q^{43} +5.13106 q^{44} -0.488049 q^{45} -4.75107 q^{46} +1.29990 q^{47} -1.69422 q^{48} +1.00000 q^{49} -9.17374 q^{50} -2.76814 q^{51} +2.53139 q^{52} +1.88649 q^{53} -5.30227 q^{54} +19.3174 q^{55} +1.00000 q^{56} -3.79883 q^{57} -3.82147 q^{58} +7.44350 q^{59} -6.37839 q^{60} -0.00800210 q^{61} -7.14240 q^{62} +0.129635 q^{63} +1.00000 q^{64} +9.53020 q^{65} +8.69311 q^{66} +0.701020 q^{67} +1.63388 q^{68} -8.04934 q^{69} +3.76480 q^{70} -3.28126 q^{71} +0.129635 q^{72} -2.75032 q^{73} -2.28449 q^{74} -15.5423 q^{75} +2.24224 q^{76} -5.13106 q^{77} +4.28873 q^{78} +3.70673 q^{79} +3.76480 q^{80} -8.59429 q^{81} +6.10878 q^{82} +7.74981 q^{83} +1.69422 q^{84} +6.15123 q^{85} +7.09119 q^{86} -6.47438 q^{87} -5.13106 q^{88} -8.90310 q^{89} +0.488049 q^{90} -2.53139 q^{91} +4.75107 q^{92} -12.1008 q^{93} -1.29990 q^{94} +8.44158 q^{95} +1.69422 q^{96} -8.92397 q^{97} -1.00000 q^{98} -0.665163 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q - 24q^{2} + 7q^{3} + 24q^{4} + 8q^{5} - 7q^{6} - 24q^{7} - 24q^{8} + 19q^{9} + O(q^{10}) \) \( 24q - 24q^{2} + 7q^{3} + 24q^{4} + 8q^{5} - 7q^{6} - 24q^{7} - 24q^{8} + 19q^{9} - 8q^{10} + 15q^{11} + 7q^{12} - 7q^{13} + 24q^{14} + 13q^{15} + 24q^{16} - 5q^{17} - 19q^{18} + 6q^{19} + 8q^{20} - 7q^{21} - 15q^{22} + 3q^{23} - 7q^{24} + 12q^{25} + 7q^{26} + 22q^{27} - 24q^{28} + 5q^{29} - 13q^{30} + 13q^{31} - 24q^{32} - 8q^{33} + 5q^{34} - 8q^{35} + 19q^{36} + 2q^{37} - 6q^{38} + 7q^{39} - 8q^{40} + 25q^{41} + 7q^{42} - 15q^{43} + 15q^{44} + 41q^{45} - 3q^{46} + 35q^{47} + 7q^{48} + 24q^{49} - 12q^{50} + 31q^{51} - 7q^{52} + 2q^{53} - 22q^{54} + 14q^{55} + 24q^{56} - 13q^{57} - 5q^{58} + 35q^{59} + 13q^{60} - 7q^{61} - 13q^{62} - 19q^{63} + 24q^{64} - 4q^{65} + 8q^{66} + 10q^{67} - 5q^{68} + 6q^{69} + 8q^{70} + 58q^{71} - 19q^{72} + 9q^{73} - 2q^{74} + 7q^{75} + 6q^{76} - 15q^{77} - 7q^{78} + 31q^{79} + 8q^{80} + 16q^{81} - 25q^{82} - q^{83} - 7q^{84} - 4q^{85} + 15q^{86} + 30q^{87} - 15q^{88} + 45q^{89} - 41q^{90} + 7q^{91} + 3q^{92} + 25q^{93} - 35q^{94} - 10q^{95} - 7q^{96} - 9q^{97} - 24q^{98} + 64q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) −1.69422 −0.978156 −0.489078 0.872240i \(-0.662667\pi\)
−0.489078 + 0.872240i \(0.662667\pi\)
\(4\) 1.00000 0.500000
\(5\) 3.76480 1.68367 0.841836 0.539734i \(-0.181475\pi\)
0.841836 + 0.539734i \(0.181475\pi\)
\(6\) 1.69422 0.691660
\(7\) −1.00000 −0.377964
\(8\) −1.00000 −0.353553
\(9\) −0.129635 −0.0432115
\(10\) −3.76480 −1.19054
\(11\) 5.13106 1.54707 0.773536 0.633753i \(-0.218486\pi\)
0.773536 + 0.633753i \(0.218486\pi\)
\(12\) −1.69422 −0.489078
\(13\) 2.53139 0.702082 0.351041 0.936360i \(-0.385828\pi\)
0.351041 + 0.936360i \(0.385828\pi\)
\(14\) 1.00000 0.267261
\(15\) −6.37839 −1.64689
\(16\) 1.00000 0.250000
\(17\) 1.63388 0.396273 0.198137 0.980174i \(-0.436511\pi\)
0.198137 + 0.980174i \(0.436511\pi\)
\(18\) 0.129635 0.0305552
\(19\) 2.24224 0.514404 0.257202 0.966358i \(-0.417199\pi\)
0.257202 + 0.966358i \(0.417199\pi\)
\(20\) 3.76480 0.841836
\(21\) 1.69422 0.369708
\(22\) −5.13106 −1.09394
\(23\) 4.75107 0.990668 0.495334 0.868703i \(-0.335046\pi\)
0.495334 + 0.868703i \(0.335046\pi\)
\(24\) 1.69422 0.345830
\(25\) 9.17374 1.83475
\(26\) −2.53139 −0.496447
\(27\) 5.30227 1.02042
\(28\) −1.00000 −0.188982
\(29\) 3.82147 0.709628 0.354814 0.934937i \(-0.384544\pi\)
0.354814 + 0.934937i \(0.384544\pi\)
\(30\) 6.37839 1.16453
\(31\) 7.14240 1.28281 0.641406 0.767202i \(-0.278351\pi\)
0.641406 + 0.767202i \(0.278351\pi\)
\(32\) −1.00000 −0.176777
\(33\) −8.69311 −1.51328
\(34\) −1.63388 −0.280208
\(35\) −3.76480 −0.636368
\(36\) −0.129635 −0.0216058
\(37\) 2.28449 0.375568 0.187784 0.982210i \(-0.439870\pi\)
0.187784 + 0.982210i \(0.439870\pi\)
\(38\) −2.24224 −0.363739
\(39\) −4.28873 −0.686746
\(40\) −3.76480 −0.595268
\(41\) −6.10878 −0.954031 −0.477015 0.878895i \(-0.658281\pi\)
−0.477015 + 0.878895i \(0.658281\pi\)
\(42\) −1.69422 −0.261423
\(43\) −7.09119 −1.08140 −0.540698 0.841217i \(-0.681840\pi\)
−0.540698 + 0.841217i \(0.681840\pi\)
\(44\) 5.13106 0.773536
\(45\) −0.488049 −0.0727540
\(46\) −4.75107 −0.700508
\(47\) 1.29990 0.189610 0.0948048 0.995496i \(-0.469777\pi\)
0.0948048 + 0.995496i \(0.469777\pi\)
\(48\) −1.69422 −0.244539
\(49\) 1.00000 0.142857
\(50\) −9.17374 −1.29736
\(51\) −2.76814 −0.387617
\(52\) 2.53139 0.351041
\(53\) 1.88649 0.259129 0.129564 0.991571i \(-0.458642\pi\)
0.129564 + 0.991571i \(0.458642\pi\)
\(54\) −5.30227 −0.721548
\(55\) 19.3174 2.60476
\(56\) 1.00000 0.133631
\(57\) −3.79883 −0.503167
\(58\) −3.82147 −0.501783
\(59\) 7.44350 0.969061 0.484530 0.874774i \(-0.338991\pi\)
0.484530 + 0.874774i \(0.338991\pi\)
\(60\) −6.37839 −0.823446
\(61\) −0.00800210 −0.00102456 −0.000512282 1.00000i \(-0.500163\pi\)
−0.000512282 1.00000i \(0.500163\pi\)
\(62\) −7.14240 −0.907085
\(63\) 0.129635 0.0163324
\(64\) 1.00000 0.125000
\(65\) 9.53020 1.18208
\(66\) 8.69311 1.07005
\(67\) 0.701020 0.0856432 0.0428216 0.999083i \(-0.486365\pi\)
0.0428216 + 0.999083i \(0.486365\pi\)
\(68\) 1.63388 0.198137
\(69\) −8.04934 −0.969027
\(70\) 3.76480 0.449980
\(71\) −3.28126 −0.389414 −0.194707 0.980861i \(-0.562376\pi\)
−0.194707 + 0.980861i \(0.562376\pi\)
\(72\) 0.129635 0.0152776
\(73\) −2.75032 −0.321900 −0.160950 0.986963i \(-0.551456\pi\)
−0.160950 + 0.986963i \(0.551456\pi\)
\(74\) −2.28449 −0.265567
\(75\) −15.5423 −1.79467
\(76\) 2.24224 0.257202
\(77\) −5.13106 −0.584738
\(78\) 4.28873 0.485603
\(79\) 3.70673 0.417040 0.208520 0.978018i \(-0.433135\pi\)
0.208520 + 0.978018i \(0.433135\pi\)
\(80\) 3.76480 0.420918
\(81\) −8.59429 −0.954921
\(82\) 6.10878 0.674601
\(83\) 7.74981 0.850653 0.425326 0.905040i \(-0.360159\pi\)
0.425326 + 0.905040i \(0.360159\pi\)
\(84\) 1.69422 0.184854
\(85\) 6.15123 0.667194
\(86\) 7.09119 0.764663
\(87\) −6.47438 −0.694127
\(88\) −5.13106 −0.546972
\(89\) −8.90310 −0.943727 −0.471864 0.881672i \(-0.656419\pi\)
−0.471864 + 0.881672i \(0.656419\pi\)
\(90\) 0.488049 0.0514449
\(91\) −2.53139 −0.265362
\(92\) 4.75107 0.495334
\(93\) −12.1008 −1.25479
\(94\) −1.29990 −0.134074
\(95\) 8.44158 0.866088
\(96\) 1.69422 0.172915
\(97\) −8.92397 −0.906092 −0.453046 0.891487i \(-0.649663\pi\)
−0.453046 + 0.891487i \(0.649663\pi\)
\(98\) −1.00000 −0.101015
\(99\) −0.665163 −0.0668514
\(100\) 9.17374 0.917374
\(101\) −10.5709 −1.05185 −0.525924 0.850532i \(-0.676280\pi\)
−0.525924 + 0.850532i \(0.676280\pi\)
\(102\) 2.76814 0.274087
\(103\) 0.247124 0.0243498 0.0121749 0.999926i \(-0.496125\pi\)
0.0121749 + 0.999926i \(0.496125\pi\)
\(104\) −2.53139 −0.248224
\(105\) 6.37839 0.622467
\(106\) −1.88649 −0.183232
\(107\) 4.44791 0.429996 0.214998 0.976614i \(-0.431026\pi\)
0.214998 + 0.976614i \(0.431026\pi\)
\(108\) 5.30227 0.510212
\(109\) 4.93957 0.473125 0.236563 0.971616i \(-0.423979\pi\)
0.236563 + 0.971616i \(0.423979\pi\)
\(110\) −19.3174 −1.84184
\(111\) −3.87042 −0.367364
\(112\) −1.00000 −0.0944911
\(113\) 3.76323 0.354015 0.177008 0.984209i \(-0.443358\pi\)
0.177008 + 0.984209i \(0.443358\pi\)
\(114\) 3.79883 0.355793
\(115\) 17.8869 1.66796
\(116\) 3.82147 0.354814
\(117\) −0.328156 −0.0303381
\(118\) −7.44350 −0.685229
\(119\) −1.63388 −0.149777
\(120\) 6.37839 0.582264
\(121\) 15.3277 1.39343
\(122\) 0.00800210 0.000724476 0
\(123\) 10.3496 0.933190
\(124\) 7.14240 0.641406
\(125\) 15.7133 1.40544
\(126\) −0.129635 −0.0115488
\(127\) −2.90453 −0.257735 −0.128868 0.991662i \(-0.541134\pi\)
−0.128868 + 0.991662i \(0.541134\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 12.0140 1.05777
\(130\) −9.53020 −0.835854
\(131\) −7.95468 −0.695003 −0.347502 0.937679i \(-0.612970\pi\)
−0.347502 + 0.937679i \(0.612970\pi\)
\(132\) −8.69311 −0.756638
\(133\) −2.24224 −0.194427
\(134\) −0.701020 −0.0605589
\(135\) 19.9620 1.71806
\(136\) −1.63388 −0.140104
\(137\) −0.336958 −0.0287883 −0.0143941 0.999896i \(-0.504582\pi\)
−0.0143941 + 0.999896i \(0.504582\pi\)
\(138\) 8.04934 0.685206
\(139\) 13.2883 1.12709 0.563547 0.826084i \(-0.309436\pi\)
0.563547 + 0.826084i \(0.309436\pi\)
\(140\) −3.76480 −0.318184
\(141\) −2.20231 −0.185468
\(142\) 3.28126 0.275358
\(143\) 12.9887 1.08617
\(144\) −0.129635 −0.0108029
\(145\) 14.3871 1.19478
\(146\) 2.75032 0.227618
\(147\) −1.69422 −0.139737
\(148\) 2.28449 0.187784
\(149\) −2.03542 −0.166748 −0.0833742 0.996518i \(-0.526570\pi\)
−0.0833742 + 0.996518i \(0.526570\pi\)
\(150\) 15.5423 1.26902
\(151\) 1.78140 0.144968 0.0724842 0.997370i \(-0.476907\pi\)
0.0724842 + 0.997370i \(0.476907\pi\)
\(152\) −2.24224 −0.181869
\(153\) −0.211807 −0.0171236
\(154\) 5.13106 0.413472
\(155\) 26.8897 2.15983
\(156\) −4.28873 −0.343373
\(157\) 4.79958 0.383049 0.191524 0.981488i \(-0.438657\pi\)
0.191524 + 0.981488i \(0.438657\pi\)
\(158\) −3.70673 −0.294892
\(159\) −3.19612 −0.253468
\(160\) −3.76480 −0.297634
\(161\) −4.75107 −0.374437
\(162\) 8.59429 0.675231
\(163\) 2.74208 0.214776 0.107388 0.994217i \(-0.465751\pi\)
0.107388 + 0.994217i \(0.465751\pi\)
\(164\) −6.10878 −0.477015
\(165\) −32.7279 −2.54786
\(166\) −7.74981 −0.601502
\(167\) −17.5930 −1.36139 −0.680693 0.732569i \(-0.738321\pi\)
−0.680693 + 0.732569i \(0.738321\pi\)
\(168\) −1.69422 −0.130712
\(169\) −6.59204 −0.507080
\(170\) −6.15123 −0.471778
\(171\) −0.290672 −0.0222282
\(172\) −7.09119 −0.540698
\(173\) −14.4727 −1.10034 −0.550168 0.835054i \(-0.685436\pi\)
−0.550168 + 0.835054i \(0.685436\pi\)
\(174\) 6.47438 0.490822
\(175\) −9.17374 −0.693470
\(176\) 5.13106 0.386768
\(177\) −12.6109 −0.947892
\(178\) 8.90310 0.667316
\(179\) −16.2018 −1.21098 −0.605491 0.795852i \(-0.707023\pi\)
−0.605491 + 0.795852i \(0.707023\pi\)
\(180\) −0.488049 −0.0363770
\(181\) 3.75290 0.278951 0.139475 0.990226i \(-0.455458\pi\)
0.139475 + 0.990226i \(0.455458\pi\)
\(182\) 2.53139 0.187639
\(183\) 0.0135573 0.00100218
\(184\) −4.75107 −0.350254
\(185\) 8.60066 0.632333
\(186\) 12.1008 0.887270
\(187\) 8.38352 0.613063
\(188\) 1.29990 0.0948048
\(189\) −5.30227 −0.385684
\(190\) −8.44158 −0.612416
\(191\) 15.4237 1.11602 0.558010 0.829834i \(-0.311565\pi\)
0.558010 + 0.829834i \(0.311565\pi\)
\(192\) −1.69422 −0.122269
\(193\) −24.4004 −1.75638 −0.878191 0.478310i \(-0.841250\pi\)
−0.878191 + 0.478310i \(0.841250\pi\)
\(194\) 8.92397 0.640704
\(195\) −16.1462 −1.15625
\(196\) 1.00000 0.0714286
\(197\) −14.1409 −1.00750 −0.503750 0.863849i \(-0.668047\pi\)
−0.503750 + 0.863849i \(0.668047\pi\)
\(198\) 0.665163 0.0472710
\(199\) 5.58283 0.395756 0.197878 0.980227i \(-0.436595\pi\)
0.197878 + 0.980227i \(0.436595\pi\)
\(200\) −9.17374 −0.648682
\(201\) −1.18768 −0.0837724
\(202\) 10.5709 0.743768
\(203\) −3.82147 −0.268214
\(204\) −2.76814 −0.193809
\(205\) −22.9983 −1.60627
\(206\) −0.247124 −0.0172179
\(207\) −0.615904 −0.0428083
\(208\) 2.53139 0.175521
\(209\) 11.5050 0.795820
\(210\) −6.37839 −0.440151
\(211\) 19.1382 1.31753 0.658765 0.752349i \(-0.271079\pi\)
0.658765 + 0.752349i \(0.271079\pi\)
\(212\) 1.88649 0.129564
\(213\) 5.55917 0.380908
\(214\) −4.44791 −0.304053
\(215\) −26.6969 −1.82072
\(216\) −5.30227 −0.360774
\(217\) −7.14240 −0.484857
\(218\) −4.93957 −0.334550
\(219\) 4.65963 0.314868
\(220\) 19.3174 1.30238
\(221\) 4.13599 0.278217
\(222\) 3.87042 0.259766
\(223\) −8.10489 −0.542744 −0.271372 0.962475i \(-0.587477\pi\)
−0.271372 + 0.962475i \(0.587477\pi\)
\(224\) 1.00000 0.0668153
\(225\) −1.18923 −0.0792823
\(226\) −3.76323 −0.250327
\(227\) −11.5098 −0.763934 −0.381967 0.924176i \(-0.624753\pi\)
−0.381967 + 0.924176i \(0.624753\pi\)
\(228\) −3.79883 −0.251584
\(229\) −7.41334 −0.489887 −0.244944 0.969537i \(-0.578769\pi\)
−0.244944 + 0.969537i \(0.578769\pi\)
\(230\) −17.8869 −1.17942
\(231\) 8.69311 0.571965
\(232\) −3.82147 −0.250891
\(233\) −26.0542 −1.70687 −0.853433 0.521202i \(-0.825484\pi\)
−0.853433 + 0.521202i \(0.825484\pi\)
\(234\) 0.328156 0.0214523
\(235\) 4.89386 0.319240
\(236\) 7.44350 0.484530
\(237\) −6.28000 −0.407930
\(238\) 1.63388 0.105909
\(239\) −4.13675 −0.267584 −0.133792 0.991009i \(-0.542715\pi\)
−0.133792 + 0.991009i \(0.542715\pi\)
\(240\) −6.37839 −0.411723
\(241\) 14.4204 0.928897 0.464448 0.885600i \(-0.346253\pi\)
0.464448 + 0.885600i \(0.346253\pi\)
\(242\) −15.3277 −0.985304
\(243\) −1.34625 −0.0863617
\(244\) −0.00800210 −0.000512282 0
\(245\) 3.76480 0.240524
\(246\) −10.3496 −0.659865
\(247\) 5.67598 0.361154
\(248\) −7.14240 −0.453543
\(249\) −13.1299 −0.832071
\(250\) −15.7133 −0.993798
\(251\) 13.2145 0.834091 0.417046 0.908886i \(-0.363066\pi\)
0.417046 + 0.908886i \(0.363066\pi\)
\(252\) 0.129635 0.00816622
\(253\) 24.3780 1.53263
\(254\) 2.90453 0.182246
\(255\) −10.4215 −0.652620
\(256\) 1.00000 0.0625000
\(257\) 3.32744 0.207560 0.103780 0.994600i \(-0.466906\pi\)
0.103780 + 0.994600i \(0.466906\pi\)
\(258\) −12.0140 −0.747959
\(259\) −2.28449 −0.141951
\(260\) 9.53020 0.591038
\(261\) −0.495394 −0.0306641
\(262\) 7.95468 0.491442
\(263\) −22.8100 −1.40653 −0.703264 0.710929i \(-0.748275\pi\)
−0.703264 + 0.710929i \(0.748275\pi\)
\(264\) 8.69311 0.535024
\(265\) 7.10225 0.436288
\(266\) 2.24224 0.137480
\(267\) 15.0838 0.923112
\(268\) 0.701020 0.0428216
\(269\) −2.36176 −0.143999 −0.0719995 0.997405i \(-0.522938\pi\)
−0.0719995 + 0.997405i \(0.522938\pi\)
\(270\) −19.9620 −1.21485
\(271\) −6.66509 −0.404875 −0.202438 0.979295i \(-0.564886\pi\)
−0.202438 + 0.979295i \(0.564886\pi\)
\(272\) 1.63388 0.0990684
\(273\) 4.28873 0.259566
\(274\) 0.336958 0.0203564
\(275\) 47.0710 2.83849
\(276\) −8.04934 −0.484514
\(277\) −25.7492 −1.54712 −0.773560 0.633723i \(-0.781526\pi\)
−0.773560 + 0.633723i \(0.781526\pi\)
\(278\) −13.2883 −0.796976
\(279\) −0.925902 −0.0554323
\(280\) 3.76480 0.224990
\(281\) 7.24230 0.432040 0.216020 0.976389i \(-0.430692\pi\)
0.216020 + 0.976389i \(0.430692\pi\)
\(282\) 2.20231 0.131146
\(283\) −5.52079 −0.328177 −0.164089 0.986446i \(-0.552468\pi\)
−0.164089 + 0.986446i \(0.552468\pi\)
\(284\) −3.28126 −0.194707
\(285\) −14.3019 −0.847169
\(286\) −12.9887 −0.768039
\(287\) 6.10878 0.360590
\(288\) 0.129635 0.00763879
\(289\) −14.3304 −0.842967
\(290\) −14.3871 −0.844838
\(291\) 15.1191 0.886299
\(292\) −2.75032 −0.160950
\(293\) 4.12082 0.240741 0.120370 0.992729i \(-0.461592\pi\)
0.120370 + 0.992729i \(0.461592\pi\)
\(294\) 1.69422 0.0988086
\(295\) 28.0233 1.63158
\(296\) −2.28449 −0.132783
\(297\) 27.2063 1.57867
\(298\) 2.03542 0.117909
\(299\) 12.0268 0.695530
\(300\) −15.5423 −0.897335
\(301\) 7.09119 0.408729
\(302\) −1.78140 −0.102508
\(303\) 17.9094 1.02887
\(304\) 2.24224 0.128601
\(305\) −0.0301263 −0.00172503
\(306\) 0.211807 0.0121082
\(307\) 15.1726 0.865944 0.432972 0.901407i \(-0.357465\pi\)
0.432972 + 0.901407i \(0.357465\pi\)
\(308\) −5.13106 −0.292369
\(309\) −0.418681 −0.0238179
\(310\) −26.8897 −1.52723
\(311\) −4.58694 −0.260101 −0.130051 0.991507i \(-0.541514\pi\)
−0.130051 + 0.991507i \(0.541514\pi\)
\(312\) 4.28873 0.242801
\(313\) −0.591030 −0.0334070 −0.0167035 0.999860i \(-0.505317\pi\)
−0.0167035 + 0.999860i \(0.505317\pi\)
\(314\) −4.79958 −0.270856
\(315\) 0.488049 0.0274984
\(316\) 3.70673 0.208520
\(317\) 18.1207 1.01776 0.508881 0.860837i \(-0.330059\pi\)
0.508881 + 0.860837i \(0.330059\pi\)
\(318\) 3.19612 0.179229
\(319\) 19.6082 1.09785
\(320\) 3.76480 0.210459
\(321\) −7.53572 −0.420603
\(322\) 4.75107 0.264767
\(323\) 3.66354 0.203845
\(324\) −8.59429 −0.477461
\(325\) 23.2224 1.28814
\(326\) −2.74208 −0.151870
\(327\) −8.36870 −0.462790
\(328\) 6.10878 0.337301
\(329\) −1.29990 −0.0716657
\(330\) 32.7279 1.80161
\(331\) 24.2633 1.33363 0.666816 0.745223i \(-0.267657\pi\)
0.666816 + 0.745223i \(0.267657\pi\)
\(332\) 7.74981 0.425326
\(333\) −0.296149 −0.0162289
\(334\) 17.5930 0.962645
\(335\) 2.63920 0.144195
\(336\) 1.69422 0.0924270
\(337\) 20.5308 1.11839 0.559193 0.829038i \(-0.311111\pi\)
0.559193 + 0.829038i \(0.311111\pi\)
\(338\) 6.59204 0.358560
\(339\) −6.37573 −0.346282
\(340\) 6.15123 0.333597
\(341\) 36.6480 1.98460
\(342\) 0.290672 0.0157177
\(343\) −1.00000 −0.0539949
\(344\) 7.09119 0.382331
\(345\) −30.3042 −1.63152
\(346\) 14.4727 0.778055
\(347\) 0.619877 0.0332767 0.0166384 0.999862i \(-0.494704\pi\)
0.0166384 + 0.999862i \(0.494704\pi\)
\(348\) −6.47438 −0.347063
\(349\) 0.293252 0.0156974 0.00784871 0.999969i \(-0.497502\pi\)
0.00784871 + 0.999969i \(0.497502\pi\)
\(350\) 9.17374 0.490357
\(351\) 13.4221 0.716421
\(352\) −5.13106 −0.273486
\(353\) −30.7987 −1.63925 −0.819625 0.572900i \(-0.805818\pi\)
−0.819625 + 0.572900i \(0.805818\pi\)
\(354\) 12.6109 0.670261
\(355\) −12.3533 −0.655646
\(356\) −8.90310 −0.471864
\(357\) 2.76814 0.146505
\(358\) 16.2018 0.856294
\(359\) −13.9496 −0.736231 −0.368116 0.929780i \(-0.619997\pi\)
−0.368116 + 0.929780i \(0.619997\pi\)
\(360\) 0.488049 0.0257224
\(361\) −13.9724 −0.735388
\(362\) −3.75290 −0.197248
\(363\) −25.9685 −1.36299
\(364\) −2.53139 −0.132681
\(365\) −10.3544 −0.541974
\(366\) −0.0135573 −0.000708650 0
\(367\) −18.7430 −0.978376 −0.489188 0.872178i \(-0.662707\pi\)
−0.489188 + 0.872178i \(0.662707\pi\)
\(368\) 4.75107 0.247667
\(369\) 0.791909 0.0412251
\(370\) −8.60066 −0.447127
\(371\) −1.88649 −0.0979416
\(372\) −12.1008 −0.627395
\(373\) 0.233693 0.0121002 0.00605009 0.999982i \(-0.498074\pi\)
0.00605009 + 0.999982i \(0.498074\pi\)
\(374\) −8.38352 −0.433501
\(375\) −26.6217 −1.37474
\(376\) −1.29990 −0.0670372
\(377\) 9.67364 0.498218
\(378\) 5.30227 0.272720
\(379\) 22.0112 1.13064 0.565319 0.824873i \(-0.308753\pi\)
0.565319 + 0.824873i \(0.308753\pi\)
\(380\) 8.44158 0.433044
\(381\) 4.92090 0.252105
\(382\) −15.4237 −0.789145
\(383\) 6.39092 0.326561 0.163280 0.986580i \(-0.447792\pi\)
0.163280 + 0.986580i \(0.447792\pi\)
\(384\) 1.69422 0.0864576
\(385\) −19.3174 −0.984507
\(386\) 24.4004 1.24195
\(387\) 0.919264 0.0467288
\(388\) −8.92397 −0.453046
\(389\) 26.6128 1.34932 0.674662 0.738127i \(-0.264289\pi\)
0.674662 + 0.738127i \(0.264289\pi\)
\(390\) 16.1462 0.817595
\(391\) 7.76267 0.392575
\(392\) −1.00000 −0.0505076
\(393\) 13.4769 0.679821
\(394\) 14.1409 0.712411
\(395\) 13.9551 0.702158
\(396\) −0.665163 −0.0334257
\(397\) −6.68899 −0.335711 −0.167856 0.985812i \(-0.553684\pi\)
−0.167856 + 0.985812i \(0.553684\pi\)
\(398\) −5.58283 −0.279842
\(399\) 3.79883 0.190179
\(400\) 9.17374 0.458687
\(401\) −8.28110 −0.413538 −0.206769 0.978390i \(-0.566295\pi\)
−0.206769 + 0.978390i \(0.566295\pi\)
\(402\) 1.18768 0.0592360
\(403\) 18.0802 0.900640
\(404\) −10.5709 −0.525924
\(405\) −32.3558 −1.60777
\(406\) 3.82147 0.189656
\(407\) 11.7218 0.581031
\(408\) 2.76814 0.137043
\(409\) 3.04974 0.150800 0.0753999 0.997153i \(-0.475977\pi\)
0.0753999 + 0.997153i \(0.475977\pi\)
\(410\) 22.9983 1.13581
\(411\) 0.570880 0.0281594
\(412\) 0.247124 0.0121749
\(413\) −7.44350 −0.366271
\(414\) 0.615904 0.0302700
\(415\) 29.1765 1.43222
\(416\) −2.53139 −0.124112
\(417\) −22.5132 −1.10247
\(418\) −11.5050 −0.562730
\(419\) 33.0604 1.61511 0.807554 0.589794i \(-0.200791\pi\)
0.807554 + 0.589794i \(0.200791\pi\)
\(420\) 6.37839 0.311233
\(421\) 26.2130 1.27754 0.638771 0.769397i \(-0.279443\pi\)
0.638771 + 0.769397i \(0.279443\pi\)
\(422\) −19.1382 −0.931635
\(423\) −0.168512 −0.00819333
\(424\) −1.88649 −0.0916159
\(425\) 14.9888 0.727062
\(426\) −5.55917 −0.269342
\(427\) 0.00800210 0.000387249 0
\(428\) 4.44791 0.214998
\(429\) −22.0057 −1.06245
\(430\) 26.6969 1.28744
\(431\) 1.00000 0.0481683
\(432\) 5.30227 0.255106
\(433\) 15.9959 0.768713 0.384356 0.923185i \(-0.374423\pi\)
0.384356 + 0.923185i \(0.374423\pi\)
\(434\) 7.14240 0.342846
\(435\) −24.3748 −1.16868
\(436\) 4.93957 0.236563
\(437\) 10.6530 0.509604
\(438\) −4.65963 −0.222646
\(439\) −31.2755 −1.49270 −0.746350 0.665554i \(-0.768195\pi\)
−0.746350 + 0.665554i \(0.768195\pi\)
\(440\) −19.3174 −0.920922
\(441\) −0.129635 −0.00617308
\(442\) −4.13599 −0.196729
\(443\) −26.1389 −1.24190 −0.620949 0.783851i \(-0.713253\pi\)
−0.620949 + 0.783851i \(0.713253\pi\)
\(444\) −3.87042 −0.183682
\(445\) −33.5184 −1.58893
\(446\) 8.10489 0.383778
\(447\) 3.44845 0.163106
\(448\) −1.00000 −0.0472456
\(449\) 14.1690 0.668678 0.334339 0.942453i \(-0.391487\pi\)
0.334339 + 0.942453i \(0.391487\pi\)
\(450\) 1.18923 0.0560611
\(451\) −31.3445 −1.47595
\(452\) 3.76323 0.177008
\(453\) −3.01808 −0.141802
\(454\) 11.5098 0.540183
\(455\) −9.53020 −0.446783
\(456\) 3.79883 0.177897
\(457\) 14.2280 0.665557 0.332779 0.943005i \(-0.392014\pi\)
0.332779 + 0.943005i \(0.392014\pi\)
\(458\) 7.41334 0.346402
\(459\) 8.66327 0.404367
\(460\) 17.8869 0.833979
\(461\) 19.6352 0.914504 0.457252 0.889337i \(-0.348834\pi\)
0.457252 + 0.889337i \(0.348834\pi\)
\(462\) −8.69311 −0.404440
\(463\) −12.0254 −0.558867 −0.279433 0.960165i \(-0.590147\pi\)
−0.279433 + 0.960165i \(0.590147\pi\)
\(464\) 3.82147 0.177407
\(465\) −45.5570 −2.11265
\(466\) 26.0542 1.20694
\(467\) −2.49381 −0.115400 −0.0576998 0.998334i \(-0.518377\pi\)
−0.0576998 + 0.998334i \(0.518377\pi\)
\(468\) −0.328156 −0.0151690
\(469\) −0.701020 −0.0323701
\(470\) −4.89386 −0.225737
\(471\) −8.13153 −0.374681
\(472\) −7.44350 −0.342615
\(473\) −36.3853 −1.67300
\(474\) 6.28000 0.288450
\(475\) 20.5697 0.943803
\(476\) −1.63388 −0.0748886
\(477\) −0.244554 −0.0111974
\(478\) 4.13675 0.189210
\(479\) 23.9177 1.09283 0.546415 0.837515i \(-0.315992\pi\)
0.546415 + 0.837515i \(0.315992\pi\)
\(480\) 6.37839 0.291132
\(481\) 5.78295 0.263680
\(482\) −14.4204 −0.656829
\(483\) 8.04934 0.366258
\(484\) 15.3277 0.696715
\(485\) −33.5970 −1.52556
\(486\) 1.34625 0.0610669
\(487\) 13.4212 0.608171 0.304085 0.952645i \(-0.401649\pi\)
0.304085 + 0.952645i \(0.401649\pi\)
\(488\) 0.00800210 0.000362238 0
\(489\) −4.64567 −0.210084
\(490\) −3.76480 −0.170076
\(491\) −12.6746 −0.571995 −0.285998 0.958230i \(-0.592325\pi\)
−0.285998 + 0.958230i \(0.592325\pi\)
\(492\) 10.3496 0.466595
\(493\) 6.24381 0.281207
\(494\) −5.67598 −0.255375
\(495\) −2.50421 −0.112556
\(496\) 7.14240 0.320703
\(497\) 3.28126 0.147185
\(498\) 13.1299 0.588363
\(499\) 30.7009 1.37436 0.687181 0.726486i \(-0.258848\pi\)
0.687181 + 0.726486i \(0.258848\pi\)
\(500\) 15.7133 0.702721
\(501\) 29.8063 1.33165
\(502\) −13.2145 −0.589792
\(503\) −5.63591 −0.251293 −0.125646 0.992075i \(-0.540100\pi\)
−0.125646 + 0.992075i \(0.540100\pi\)
\(504\) −0.129635 −0.00577439
\(505\) −39.7975 −1.77096
\(506\) −24.3780 −1.08374
\(507\) 11.1683 0.496003
\(508\) −2.90453 −0.128868
\(509\) 40.0652 1.77586 0.887930 0.459979i \(-0.152143\pi\)
0.887930 + 0.459979i \(0.152143\pi\)
\(510\) 10.4215 0.461472
\(511\) 2.75032 0.121667
\(512\) −1.00000 −0.0441942
\(513\) 11.8890 0.524910
\(514\) −3.32744 −0.146767
\(515\) 0.930373 0.0409971
\(516\) 12.0140 0.528887
\(517\) 6.66985 0.293340
\(518\) 2.28449 0.100375
\(519\) 24.5198 1.07630
\(520\) −9.53020 −0.417927
\(521\) −12.7582 −0.558947 −0.279474 0.960153i \(-0.590160\pi\)
−0.279474 + 0.960153i \(0.590160\pi\)
\(522\) 0.495394 0.0216828
\(523\) −22.1792 −0.969829 −0.484915 0.874561i \(-0.661149\pi\)
−0.484915 + 0.874561i \(0.661149\pi\)
\(524\) −7.95468 −0.347502
\(525\) 15.5423 0.678321
\(526\) 22.8100 0.994565
\(527\) 11.6698 0.508344
\(528\) −8.69311 −0.378319
\(529\) −0.427289 −0.0185778
\(530\) −7.10225 −0.308502
\(531\) −0.964935 −0.0418746
\(532\) −2.24224 −0.0972133
\(533\) −15.4637 −0.669808
\(534\) −15.0838 −0.652739
\(535\) 16.7455 0.723972
\(536\) −0.701020 −0.0302794
\(537\) 27.4494 1.18453
\(538\) 2.36176 0.101823
\(539\) 5.13106 0.221010
\(540\) 19.9620 0.859029
\(541\) −6.75570 −0.290450 −0.145225 0.989399i \(-0.546391\pi\)
−0.145225 + 0.989399i \(0.546391\pi\)
\(542\) 6.66509 0.286290
\(543\) −6.35821 −0.272857
\(544\) −1.63388 −0.0700519
\(545\) 18.5965 0.796587
\(546\) −4.28873 −0.183541
\(547\) 20.5399 0.878221 0.439110 0.898433i \(-0.355294\pi\)
0.439110 + 0.898433i \(0.355294\pi\)
\(548\) −0.336958 −0.0143941
\(549\) 0.00103735 4.42730e−5 0
\(550\) −47.0710 −2.00711
\(551\) 8.56863 0.365036
\(552\) 8.04934 0.342603
\(553\) −3.70673 −0.157626
\(554\) 25.7492 1.09398
\(555\) −14.5714 −0.618520
\(556\) 13.2883 0.563547
\(557\) 30.3295 1.28510 0.642550 0.766244i \(-0.277876\pi\)
0.642550 + 0.766244i \(0.277876\pi\)
\(558\) 0.925902 0.0391966
\(559\) −17.9506 −0.759230
\(560\) −3.76480 −0.159092
\(561\) −14.2035 −0.599671
\(562\) −7.24230 −0.305498
\(563\) 34.3651 1.44831 0.724157 0.689635i \(-0.242229\pi\)
0.724157 + 0.689635i \(0.242229\pi\)
\(564\) −2.20231 −0.0927339
\(565\) 14.1678 0.596045
\(566\) 5.52079 0.232056
\(567\) 8.59429 0.360926
\(568\) 3.28126 0.137679
\(569\) 37.0801 1.55448 0.777240 0.629204i \(-0.216619\pi\)
0.777240 + 0.629204i \(0.216619\pi\)
\(570\) 14.3019 0.599039
\(571\) 4.16167 0.174161 0.0870803 0.996201i \(-0.472246\pi\)
0.0870803 + 0.996201i \(0.472246\pi\)
\(572\) 12.9887 0.543086
\(573\) −26.1311 −1.09164
\(574\) −6.10878 −0.254975
\(575\) 43.5851 1.81763
\(576\) −0.129635 −0.00540144
\(577\) 2.02887 0.0844628 0.0422314 0.999108i \(-0.486553\pi\)
0.0422314 + 0.999108i \(0.486553\pi\)
\(578\) 14.3304 0.596068
\(579\) 41.3396 1.71801
\(580\) 14.3871 0.597390
\(581\) −7.74981 −0.321516
\(582\) −15.1191 −0.626708
\(583\) 9.67967 0.400891
\(584\) 2.75032 0.113809
\(585\) −1.23544 −0.0510793
\(586\) −4.12082 −0.170229
\(587\) 6.09047 0.251380 0.125690 0.992070i \(-0.459885\pi\)
0.125690 + 0.992070i \(0.459885\pi\)
\(588\) −1.69422 −0.0698683
\(589\) 16.0149 0.659884
\(590\) −28.0233 −1.15370
\(591\) 23.9578 0.985492
\(592\) 2.28449 0.0938920
\(593\) −6.16953 −0.253352 −0.126676 0.991944i \(-0.540431\pi\)
−0.126676 + 0.991944i \(0.540431\pi\)
\(594\) −27.2063 −1.11629
\(595\) −6.15123 −0.252176
\(596\) −2.03542 −0.0833742
\(597\) −9.45852 −0.387111
\(598\) −12.0268 −0.491814
\(599\) 11.2936 0.461444 0.230722 0.973020i \(-0.425891\pi\)
0.230722 + 0.973020i \(0.425891\pi\)
\(600\) 15.5423 0.634512
\(601\) −18.5052 −0.754844 −0.377422 0.926041i \(-0.623189\pi\)
−0.377422 + 0.926041i \(0.623189\pi\)
\(602\) −7.09119 −0.289015
\(603\) −0.0908764 −0.00370077
\(604\) 1.78140 0.0724842
\(605\) 57.7059 2.34608
\(606\) −17.9094 −0.727521
\(607\) 32.3535 1.31319 0.656593 0.754245i \(-0.271997\pi\)
0.656593 + 0.754245i \(0.271997\pi\)
\(608\) −2.24224 −0.0909347
\(609\) 6.47438 0.262355
\(610\) 0.0301263 0.00121978
\(611\) 3.29056 0.133122
\(612\) −0.211807 −0.00856179
\(613\) −33.5095 −1.35344 −0.676718 0.736243i \(-0.736598\pi\)
−0.676718 + 0.736243i \(0.736598\pi\)
\(614\) −15.1726 −0.612315
\(615\) 38.9641 1.57119
\(616\) 5.13106 0.206736
\(617\) −41.2052 −1.65886 −0.829429 0.558612i \(-0.811334\pi\)
−0.829429 + 0.558612i \(0.811334\pi\)
\(618\) 0.418681 0.0168418
\(619\) −20.2632 −0.814448 −0.407224 0.913328i \(-0.633503\pi\)
−0.407224 + 0.913328i \(0.633503\pi\)
\(620\) 26.8897 1.07992
\(621\) 25.1915 1.01090
\(622\) 4.58694 0.183919
\(623\) 8.90310 0.356695
\(624\) −4.28873 −0.171686
\(625\) 13.2888 0.531554
\(626\) 0.591030 0.0236223
\(627\) −19.4920 −0.778436
\(628\) 4.79958 0.191524
\(629\) 3.73258 0.148828
\(630\) −0.488049 −0.0194443
\(631\) −22.9496 −0.913610 −0.456805 0.889567i \(-0.651006\pi\)
−0.456805 + 0.889567i \(0.651006\pi\)
\(632\) −3.70673 −0.147446
\(633\) −32.4243 −1.28875
\(634\) −18.1207 −0.719666
\(635\) −10.9350 −0.433941
\(636\) −3.19612 −0.126734
\(637\) 2.53139 0.100297
\(638\) −19.6082 −0.776294
\(639\) 0.425365 0.0168272
\(640\) −3.76480 −0.148817
\(641\) −24.5916 −0.971310 −0.485655 0.874151i \(-0.661419\pi\)
−0.485655 + 0.874151i \(0.661419\pi\)
\(642\) 7.53572 0.297411
\(643\) 34.8580 1.37467 0.687333 0.726342i \(-0.258781\pi\)
0.687333 + 0.726342i \(0.258781\pi\)
\(644\) −4.75107 −0.187219
\(645\) 45.2304 1.78094
\(646\) −3.66354 −0.144140
\(647\) 16.9996 0.668322 0.334161 0.942516i \(-0.391547\pi\)
0.334161 + 0.942516i \(0.391547\pi\)
\(648\) 8.59429 0.337616
\(649\) 38.1930 1.49921
\(650\) −23.2224 −0.910856
\(651\) 12.1008 0.474266
\(652\) 2.74208 0.107388
\(653\) 20.4074 0.798602 0.399301 0.916820i \(-0.369253\pi\)
0.399301 + 0.916820i \(0.369253\pi\)
\(654\) 8.36870 0.327242
\(655\) −29.9478 −1.17016
\(656\) −6.10878 −0.238508
\(657\) 0.356536 0.0139098
\(658\) 1.29990 0.0506753
\(659\) 32.3364 1.25965 0.629824 0.776738i \(-0.283127\pi\)
0.629824 + 0.776738i \(0.283127\pi\)
\(660\) −32.7279 −1.27393
\(661\) −33.5586 −1.30528 −0.652639 0.757669i \(-0.726338\pi\)
−0.652639 + 0.757669i \(0.726338\pi\)
\(662\) −24.2633 −0.943020
\(663\) −7.00725 −0.272139
\(664\) −7.74981 −0.300751
\(665\) −8.44158 −0.327350
\(666\) 0.296149 0.0114755
\(667\) 18.1561 0.703006
\(668\) −17.5930 −0.680693
\(669\) 13.7314 0.530888
\(670\) −2.63920 −0.101961
\(671\) −0.0410592 −0.00158507
\(672\) −1.69422 −0.0653558
\(673\) 18.8291 0.725810 0.362905 0.931826i \(-0.381785\pi\)
0.362905 + 0.931826i \(0.381785\pi\)
\(674\) −20.5308 −0.790818
\(675\) 48.6417 1.87222
\(676\) −6.59204 −0.253540
\(677\) 23.0258 0.884954 0.442477 0.896780i \(-0.354100\pi\)
0.442477 + 0.896780i \(0.354100\pi\)
\(678\) 6.37573 0.244858
\(679\) 8.92397 0.342471
\(680\) −6.15123 −0.235889
\(681\) 19.5001 0.747247
\(682\) −36.6480 −1.40333
\(683\) 18.5392 0.709381 0.354690 0.934984i \(-0.384586\pi\)
0.354690 + 0.934984i \(0.384586\pi\)
\(684\) −0.290672 −0.0111141
\(685\) −1.26858 −0.0484700
\(686\) 1.00000 0.0381802
\(687\) 12.5598 0.479186
\(688\) −7.09119 −0.270349
\(689\) 4.77544 0.181930
\(690\) 30.3042 1.15366
\(691\) 1.70733 0.0649497 0.0324749 0.999473i \(-0.489661\pi\)
0.0324749 + 0.999473i \(0.489661\pi\)
\(692\) −14.4727 −0.550168
\(693\) 0.665163 0.0252674
\(694\) −0.619877 −0.0235302
\(695\) 50.0277 1.89766
\(696\) 6.47438 0.245411
\(697\) −9.98099 −0.378057
\(698\) −0.293252 −0.0110997
\(699\) 44.1414 1.66958
\(700\) −9.17374 −0.346735
\(701\) −8.58039 −0.324077 −0.162039 0.986784i \(-0.551807\pi\)
−0.162039 + 0.986784i \(0.551807\pi\)
\(702\) −13.4221 −0.506586
\(703\) 5.12237 0.193194
\(704\) 5.13106 0.193384
\(705\) −8.29126 −0.312267
\(706\) 30.7987 1.15912
\(707\) 10.5709 0.397561
\(708\) −12.6109 −0.473946
\(709\) −40.6934 −1.52827 −0.764136 0.645055i \(-0.776834\pi\)
−0.764136 + 0.645055i \(0.776834\pi\)
\(710\) 12.3533 0.463611
\(711\) −0.480521 −0.0180209
\(712\) 8.90310 0.333658
\(713\) 33.9341 1.27084
\(714\) −2.76814 −0.103595
\(715\) 48.9000 1.82876
\(716\) −16.2018 −0.605491
\(717\) 7.00854 0.261739
\(718\) 13.9496 0.520594
\(719\) 1.09263 0.0407482 0.0203741 0.999792i \(-0.493514\pi\)
0.0203741 + 0.999792i \(0.493514\pi\)
\(720\) −0.488049 −0.0181885
\(721\) −0.247124 −0.00920338
\(722\) 13.9724 0.519998
\(723\) −24.4312 −0.908605
\(724\) 3.75290 0.139475
\(725\) 35.0571 1.30199
\(726\) 25.9685 0.963781
\(727\) −1.68744 −0.0625837 −0.0312918 0.999510i \(-0.509962\pi\)
−0.0312918 + 0.999510i \(0.509962\pi\)
\(728\) 2.53139 0.0938197
\(729\) 28.0637 1.03940
\(730\) 10.3544 0.383234
\(731\) −11.5861 −0.428529
\(732\) 0.0135573 0.000501092 0
\(733\) 7.42652 0.274305 0.137152 0.990550i \(-0.456205\pi\)
0.137152 + 0.990550i \(0.456205\pi\)
\(734\) 18.7430 0.691817
\(735\) −6.37839 −0.235270
\(736\) −4.75107 −0.175127
\(737\) 3.59697 0.132496
\(738\) −0.791909 −0.0291506
\(739\) −32.7878 −1.20612 −0.603060 0.797696i \(-0.706052\pi\)
−0.603060 + 0.797696i \(0.706052\pi\)
\(740\) 8.60066 0.316166
\(741\) −9.61634 −0.353265
\(742\) 1.88649 0.0692551
\(743\) −21.9863 −0.806599 −0.403299 0.915068i \(-0.632137\pi\)
−0.403299 + 0.915068i \(0.632137\pi\)
\(744\) 12.1008 0.443635
\(745\) −7.66297 −0.280750
\(746\) −0.233693 −0.00855613
\(747\) −1.00464 −0.0367580
\(748\) 8.38352 0.306532
\(749\) −4.44791 −0.162523
\(750\) 26.6217 0.972089
\(751\) −20.6369 −0.753051 −0.376525 0.926406i \(-0.622881\pi\)
−0.376525 + 0.926406i \(0.622881\pi\)
\(752\) 1.29990 0.0474024
\(753\) −22.3882 −0.815871
\(754\) −9.67364 −0.352293
\(755\) 6.70663 0.244079
\(756\) −5.30227 −0.192842
\(757\) 23.4349 0.851756 0.425878 0.904781i \(-0.359965\pi\)
0.425878 + 0.904781i \(0.359965\pi\)
\(758\) −22.0112 −0.799481
\(759\) −41.3016 −1.49915
\(760\) −8.44158 −0.306208
\(761\) 32.1036 1.16375 0.581876 0.813277i \(-0.302319\pi\)
0.581876 + 0.813277i \(0.302319\pi\)
\(762\) −4.92090 −0.178265
\(763\) −4.93957 −0.178824
\(764\) 15.4237 0.558010
\(765\) −0.797412 −0.0288305
\(766\) −6.39092 −0.230913
\(767\) 18.8424 0.680361
\(768\) −1.69422 −0.0611347
\(769\) −28.6301 −1.03243 −0.516214 0.856459i \(-0.672659\pi\)
−0.516214 + 0.856459i \(0.672659\pi\)
\(770\) 19.3174 0.696151
\(771\) −5.63740 −0.203026
\(772\) −24.4004 −0.878191
\(773\) −12.4854 −0.449070 −0.224535 0.974466i \(-0.572086\pi\)
−0.224535 + 0.974466i \(0.572086\pi\)
\(774\) −0.919264 −0.0330423
\(775\) 65.5225 2.35364
\(776\) 8.92397 0.320352
\(777\) 3.87042 0.138851
\(778\) −26.6128 −0.954116
\(779\) −13.6973 −0.490757
\(780\) −16.1462 −0.578127
\(781\) −16.8363 −0.602452
\(782\) −7.76267 −0.277593
\(783\) 20.2625 0.724121
\(784\) 1.00000 0.0357143
\(785\) 18.0695 0.644928
\(786\) −13.4769 −0.480706
\(787\) −34.2854 −1.22214 −0.611071 0.791576i \(-0.709261\pi\)
−0.611071 + 0.791576i \(0.709261\pi\)
\(788\) −14.1409 −0.503750
\(789\) 38.6451 1.37580
\(790\) −13.9551 −0.496501
\(791\) −3.76323 −0.133805
\(792\) 0.665163 0.0236355
\(793\) −0.0202565 −0.000719328 0
\(794\) 6.68899 0.237384
\(795\) −12.0327 −0.426758
\(796\) 5.58283 0.197878
\(797\) 24.7988 0.878419 0.439209 0.898385i \(-0.355259\pi\)
0.439209 + 0.898385i \(0.355259\pi\)
\(798\) −3.79883 −0.134477
\(799\) 2.12387 0.0751373
\(800\) −9.17374 −0.324341
\(801\) 1.15415 0.0407799
\(802\) 8.28110 0.292416
\(803\) −14.1120 −0.498003
\(804\) −1.18768 −0.0418862
\(805\) −17.8869 −0.630429
\(806\) −18.0802 −0.636849
\(807\) 4.00133 0.140853
\(808\) 10.5709 0.371884
\(809\) −29.1838 −1.02605 −0.513024 0.858374i \(-0.671475\pi\)
−0.513024 + 0.858374i \(0.671475\pi\)
\(810\) 32.3558 1.13687
\(811\) 36.1041 1.26778 0.633892 0.773421i \(-0.281456\pi\)
0.633892 + 0.773421i \(0.281456\pi\)
\(812\) −3.82147 −0.134107
\(813\) 11.2921 0.396031
\(814\) −11.7218 −0.410851
\(815\) 10.3234 0.361612
\(816\) −2.76814 −0.0969043
\(817\) −15.9001 −0.556275
\(818\) −3.04974 −0.106632
\(819\) 0.328156 0.0114667
\(820\) −22.9983 −0.803137
\(821\) 39.8232 1.38984 0.694920 0.719087i \(-0.255440\pi\)
0.694920 + 0.719087i \(0.255440\pi\)
\(822\) −0.570880 −0.0199117
\(823\) −17.9944 −0.627244 −0.313622 0.949548i \(-0.601542\pi\)
−0.313622 + 0.949548i \(0.601542\pi\)
\(824\) −0.247124 −0.00860897
\(825\) −79.7484 −2.77648
\(826\) 7.44350 0.258992
\(827\) −12.4662 −0.433493 −0.216747 0.976228i \(-0.569545\pi\)
−0.216747 + 0.976228i \(0.569545\pi\)
\(828\) −0.615904 −0.0214041
\(829\) −48.1453 −1.67215 −0.836077 0.548612i \(-0.815157\pi\)
−0.836077 + 0.548612i \(0.815157\pi\)
\(830\) −29.1765 −1.01273
\(831\) 43.6247 1.51332
\(832\) 2.53139 0.0877603
\(833\) 1.63388 0.0566105
\(834\) 22.5132 0.779567
\(835\) −66.2341 −2.29213
\(836\) 11.5050 0.397910
\(837\) 37.8709 1.30901
\(838\) −33.0604 −1.14205
\(839\) −18.6641 −0.644358 −0.322179 0.946679i \(-0.604415\pi\)
−0.322179 + 0.946679i \(0.604415\pi\)
\(840\) −6.37839 −0.220075
\(841\) −14.3964 −0.496428
\(842\) −26.2130 −0.903358
\(843\) −12.2700 −0.422602
\(844\) 19.1382 0.658765
\(845\) −24.8177 −0.853756
\(846\) 0.168512 0.00579356
\(847\) −15.3277 −0.526667
\(848\) 1.88649 0.0647822
\(849\) 9.35341 0.321008
\(850\) −14.9888 −0.514111
\(851\) 10.8538 0.372063
\(852\) 5.55917 0.190454
\(853\) 34.9018 1.19502 0.597508 0.801863i \(-0.296158\pi\)
0.597508 + 0.801863i \(0.296158\pi\)
\(854\) −0.00800210 −0.000273826 0
\(855\) −1.09432 −0.0374250
\(856\) −4.44791 −0.152027
\(857\) −35.3858 −1.20876 −0.604378 0.796697i \(-0.706578\pi\)
−0.604378 + 0.796697i \(0.706578\pi\)
\(858\) 22.0057 0.751262
\(859\) −16.8970 −0.576518 −0.288259 0.957552i \(-0.593076\pi\)
−0.288259 + 0.957552i \(0.593076\pi\)
\(860\) −26.6969 −0.910358
\(861\) −10.3496 −0.352713
\(862\) −1.00000 −0.0340601
\(863\) −13.6174 −0.463543 −0.231772 0.972770i \(-0.574452\pi\)
−0.231772 + 0.972770i \(0.574452\pi\)
\(864\) −5.30227 −0.180387
\(865\) −54.4867 −1.85260
\(866\) −15.9959 −0.543562
\(867\) 24.2789 0.824553
\(868\) −7.14240 −0.242429
\(869\) 19.0194 0.645190
\(870\) 24.3748 0.826383
\(871\) 1.77456 0.0601286
\(872\) −4.93957 −0.167275
\(873\) 1.15686 0.0391536
\(874\) −10.6530 −0.360344
\(875\) −15.7133 −0.531207
\(876\) 4.65963 0.157434
\(877\) 55.3170 1.86792 0.933961 0.357376i \(-0.116328\pi\)
0.933961 + 0.357376i \(0.116328\pi\)
\(878\) 31.2755 1.05550
\(879\) −6.98156 −0.235482
\(880\) 19.3174 0.651190
\(881\) 37.1653 1.25213 0.626066 0.779770i \(-0.284664\pi\)
0.626066 + 0.779770i \(0.284664\pi\)
\(882\) 0.129635 0.00436503
\(883\) 20.0043 0.673199 0.336599 0.941648i \(-0.390723\pi\)
0.336599 + 0.941648i \(0.390723\pi\)
\(884\) 4.13599 0.139108
\(885\) −47.4775 −1.59594
\(886\) 26.1389 0.878155
\(887\) 35.2378 1.18317 0.591585 0.806242i \(-0.298502\pi\)
0.591585 + 0.806242i \(0.298502\pi\)
\(888\) 3.87042 0.129883
\(889\) 2.90453 0.0974148
\(890\) 33.5184 1.12354
\(891\) −44.0978 −1.47733
\(892\) −8.10489 −0.271372
\(893\) 2.91468 0.0975360
\(894\) −3.44845 −0.115333
\(895\) −60.9967 −2.03890
\(896\) 1.00000 0.0334077
\(897\) −20.3761 −0.680337
\(898\) −14.1690 −0.472827
\(899\) 27.2944 0.910320
\(900\) −1.18923 −0.0396412
\(901\) 3.08229 0.102686
\(902\) 31.3445 1.04366
\(903\) −12.0140 −0.399801
\(904\) −3.76323 −0.125163
\(905\) 14.1289 0.469661
\(906\) 3.01808 0.100269
\(907\) −16.3214 −0.541943 −0.270972 0.962587i \(-0.587345\pi\)
−0.270972 + 0.962587i \(0.587345\pi\)
\(908\) −11.5098 −0.381967
\(909\) 1.37036 0.0454519
\(910\) 9.53020 0.315923
\(911\) −12.9312 −0.428430 −0.214215 0.976787i \(-0.568719\pi\)
−0.214215 + 0.976787i \(0.568719\pi\)
\(912\) −3.79883 −0.125792
\(913\) 39.7647 1.31602
\(914\) −14.2280 −0.470620
\(915\) 0.0510405 0.00168735
\(916\) −7.41334 −0.244944
\(917\) 7.95468 0.262687
\(918\) −8.66327 −0.285930
\(919\) 4.11729 0.135817 0.0679085 0.997692i \(-0.478367\pi\)
0.0679085 + 0.997692i \(0.478367\pi\)
\(920\) −17.8869 −0.589712
\(921\) −25.7056 −0.847028
\(922\) −19.6352 −0.646652
\(923\) −8.30617 −0.273401
\(924\) 8.69311 0.285982
\(925\) 20.9573 0.689073
\(926\) 12.0254 0.395179
\(927\) −0.0320358 −0.00105219
\(928\) −3.82147 −0.125446
\(929\) 21.3527 0.700559 0.350280 0.936645i \(-0.386087\pi\)
0.350280 + 0.936645i \(0.386087\pi\)
\(930\) 45.5570 1.49387
\(931\) 2.24224 0.0734863
\(932\) −26.0542 −0.853433
\(933\) 7.77126 0.254420
\(934\) 2.49381 0.0815998
\(935\) 31.5623 1.03220
\(936\) 0.328156 0.0107261
\(937\) −19.5021 −0.637104 −0.318552 0.947905i \(-0.603197\pi\)
−0.318552 + 0.947905i \(0.603197\pi\)
\(938\) 0.701020 0.0228891
\(939\) 1.00133 0.0326772
\(940\) 4.89386 0.159620
\(941\) −5.14134 −0.167603 −0.0838014 0.996482i \(-0.526706\pi\)
−0.0838014 + 0.996482i \(0.526706\pi\)
\(942\) 8.13153 0.264940
\(943\) −29.0233 −0.945127
\(944\) 7.44350 0.242265
\(945\) −19.9620 −0.649365
\(946\) 36.3853 1.18299
\(947\) 57.8513 1.87991 0.939957 0.341293i \(-0.110865\pi\)
0.939957 + 0.341293i \(0.110865\pi\)
\(948\) −6.28000 −0.203965
\(949\) −6.96214 −0.226000
\(950\) −20.5697 −0.667369
\(951\) −30.7004 −0.995529
\(952\) 1.63388 0.0529543
\(953\) −43.7561 −1.41740 −0.708700 0.705510i \(-0.750718\pi\)
−0.708700 + 0.705510i \(0.750718\pi\)
\(954\) 0.244554 0.00791773
\(955\) 58.0672 1.87901
\(956\) −4.13675 −0.133792
\(957\) −33.2204 −1.07386
\(958\) −23.9177 −0.772747
\(959\) 0.336958 0.0108809
\(960\) −6.37839 −0.205862
\(961\) 20.0138 0.645607
\(962\) −5.78295 −0.186450
\(963\) −0.576604 −0.0185808
\(964\) 14.4204 0.464448
\(965\) −91.8628 −2.95717
\(966\) −8.04934 −0.258983
\(967\) −33.2809 −1.07024 −0.535121 0.844775i \(-0.679734\pi\)
−0.535121 + 0.844775i \(0.679734\pi\)
\(968\) −15.3277 −0.492652
\(969\) −6.20682 −0.199392
\(970\) 33.5970 1.07873
\(971\) 3.31961 0.106531 0.0532657 0.998580i \(-0.483037\pi\)
0.0532657 + 0.998580i \(0.483037\pi\)
\(972\) −1.34625 −0.0431808
\(973\) −13.2883 −0.426002
\(974\) −13.4212 −0.430042
\(975\) −39.3437 −1.26001
\(976\) −0.00800210 −0.000256141 0
\(977\) 4.02190 0.128672 0.0643360 0.997928i \(-0.479507\pi\)
0.0643360 + 0.997928i \(0.479507\pi\)
\(978\) 4.64567 0.148552
\(979\) −45.6823 −1.46001
\(980\) 3.76480 0.120262
\(981\) −0.640339 −0.0204445
\(982\) 12.6746 0.404462
\(983\) −23.2274 −0.740838 −0.370419 0.928865i \(-0.620786\pi\)
−0.370419 + 0.928865i \(0.620786\pi\)
\(984\) −10.3496 −0.329933
\(985\) −53.2379 −1.69630
\(986\) −6.24381 −0.198843
\(987\) 2.20231 0.0701002
\(988\) 5.67598 0.180577
\(989\) −33.6908 −1.07130
\(990\) 2.50421 0.0795889
\(991\) 39.7385 1.26234 0.631168 0.775646i \(-0.282576\pi\)
0.631168 + 0.775646i \(0.282576\pi\)
\(992\) −7.14240 −0.226771
\(993\) −41.1072 −1.30450
\(994\) −3.28126 −0.104075
\(995\) 21.0183 0.666324
\(996\) −13.1299 −0.416035
\(997\) −4.20588 −0.133202 −0.0666009 0.997780i \(-0.521215\pi\)
−0.0666009 + 0.997780i \(0.521215\pi\)
\(998\) −30.7009 −0.971821
\(999\) 12.1130 0.383238
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 \(a_p\))