Properties

Label 6034.2.a.n.1.12
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 1.12
Character \(\chi\) = 6034.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} +0.430787 q^{3} +1.00000 q^{4} +1.34011 q^{5} -0.430787 q^{6} -1.00000 q^{7} -1.00000 q^{8} -2.81442 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +0.430787 q^{3} +1.00000 q^{4} +1.34011 q^{5} -0.430787 q^{6} -1.00000 q^{7} -1.00000 q^{8} -2.81442 q^{9} -1.34011 q^{10} +4.88156 q^{11} +0.430787 q^{12} +4.15645 q^{13} +1.00000 q^{14} +0.577304 q^{15} +1.00000 q^{16} +4.03673 q^{17} +2.81442 q^{18} -0.649997 q^{19} +1.34011 q^{20} -0.430787 q^{21} -4.88156 q^{22} -2.19781 q^{23} -0.430787 q^{24} -3.20409 q^{25} -4.15645 q^{26} -2.50478 q^{27} -1.00000 q^{28} -0.741706 q^{29} -0.577304 q^{30} -0.702478 q^{31} -1.00000 q^{32} +2.10291 q^{33} -4.03673 q^{34} -1.34011 q^{35} -2.81442 q^{36} +5.70012 q^{37} +0.649997 q^{38} +1.79054 q^{39} -1.34011 q^{40} +7.65210 q^{41} +0.430787 q^{42} +9.49126 q^{43} +4.88156 q^{44} -3.77165 q^{45} +2.19781 q^{46} +6.32719 q^{47} +0.430787 q^{48} +1.00000 q^{49} +3.20409 q^{50} +1.73897 q^{51} +4.15645 q^{52} -9.84296 q^{53} +2.50478 q^{54} +6.54185 q^{55} +1.00000 q^{56} -0.280010 q^{57} +0.741706 q^{58} -0.936742 q^{59} +0.577304 q^{60} -7.74852 q^{61} +0.702478 q^{62} +2.81442 q^{63} +1.00000 q^{64} +5.57012 q^{65} -2.10291 q^{66} -6.50275 q^{67} +4.03673 q^{68} -0.946788 q^{69} +1.34011 q^{70} -0.0975448 q^{71} +2.81442 q^{72} +11.8612 q^{73} -5.70012 q^{74} -1.38028 q^{75} -0.649997 q^{76} -4.88156 q^{77} -1.79054 q^{78} +15.4793 q^{79} +1.34011 q^{80} +7.36424 q^{81} -7.65210 q^{82} -15.5423 q^{83} -0.430787 q^{84} +5.40969 q^{85} -9.49126 q^{86} -0.319517 q^{87} -4.88156 q^{88} +15.5447 q^{89} +3.77165 q^{90} -4.15645 q^{91} -2.19781 q^{92} -0.302619 q^{93} -6.32719 q^{94} -0.871070 q^{95} -0.430787 q^{96} -17.7494 q^{97} -1.00000 q^{98} -13.7388 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q - 24q^{2} + 7q^{3} + 24q^{4} + 8q^{5} - 7q^{6} - 24q^{7} - 24q^{8} + 19q^{9} + O(q^{10}) \) \( 24q - 24q^{2} + 7q^{3} + 24q^{4} + 8q^{5} - 7q^{6} - 24q^{7} - 24q^{8} + 19q^{9} - 8q^{10} + 15q^{11} + 7q^{12} - 7q^{13} + 24q^{14} + 13q^{15} + 24q^{16} - 5q^{17} - 19q^{18} + 6q^{19} + 8q^{20} - 7q^{21} - 15q^{22} + 3q^{23} - 7q^{24} + 12q^{25} + 7q^{26} + 22q^{27} - 24q^{28} + 5q^{29} - 13q^{30} + 13q^{31} - 24q^{32} - 8q^{33} + 5q^{34} - 8q^{35} + 19q^{36} + 2q^{37} - 6q^{38} + 7q^{39} - 8q^{40} + 25q^{41} + 7q^{42} - 15q^{43} + 15q^{44} + 41q^{45} - 3q^{46} + 35q^{47} + 7q^{48} + 24q^{49} - 12q^{50} + 31q^{51} - 7q^{52} + 2q^{53} - 22q^{54} + 14q^{55} + 24q^{56} - 13q^{57} - 5q^{58} + 35q^{59} + 13q^{60} - 7q^{61} - 13q^{62} - 19q^{63} + 24q^{64} - 4q^{65} + 8q^{66} + 10q^{67} - 5q^{68} + 6q^{69} + 8q^{70} + 58q^{71} - 19q^{72} + 9q^{73} - 2q^{74} + 7q^{75} + 6q^{76} - 15q^{77} - 7q^{78} + 31q^{79} + 8q^{80} + 16q^{81} - 25q^{82} - q^{83} - 7q^{84} - 4q^{85} + 15q^{86} + 30q^{87} - 15q^{88} + 45q^{89} - 41q^{90} + 7q^{91} + 3q^{92} + 25q^{93} - 35q^{94} - 10q^{95} - 7q^{96} - 9q^{97} - 24q^{98} + 64q^{99} + O(q^{100}) \)

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
\(3\) 0.430787 0.248715 0.124358 0.992237i \(-0.460313\pi\)
0.124358 + 0.992237i \(0.460313\pi\)
\(4\) 1.00000 0.500000
\(5\) 1.34011 0.599317 0.299659 0.954046i \(-0.403127\pi\)
0.299659 + 0.954046i \(0.403127\pi\)
\(6\) −0.430787 −0.175868
\(7\) −1.00000 −0.377964
\(8\) −1.00000 −0.353553
\(9\) −2.81442 −0.938141
\(10\) −1.34011 −0.423781
\(11\) 4.88156 1.47185 0.735923 0.677065i \(-0.236749\pi\)
0.735923 + 0.677065i \(0.236749\pi\)
\(12\) 0.430787 0.124358
\(13\) 4.15645 1.15279 0.576396 0.817171i \(-0.304459\pi\)
0.576396 + 0.817171i \(0.304459\pi\)
\(14\) 1.00000 0.267261
\(15\) 0.577304 0.149059
\(16\) 1.00000 0.250000
\(17\) 4.03673 0.979052 0.489526 0.871989i \(-0.337170\pi\)
0.489526 + 0.871989i \(0.337170\pi\)
\(18\) 2.81442 0.663366
\(19\) −0.649997 −0.149120 −0.0745598 0.997217i \(-0.523755\pi\)
−0.0745598 + 0.997217i \(0.523755\pi\)
\(20\) 1.34011 0.299659
\(21\) −0.430787 −0.0940055
\(22\) −4.88156 −1.04075
\(23\) −2.19781 −0.458275 −0.229138 0.973394i \(-0.573591\pi\)
−0.229138 + 0.973394i \(0.573591\pi\)
\(24\) −0.430787 −0.0879340
\(25\) −3.20409 −0.640819
\(26\) −4.15645 −0.815147
\(27\) −2.50478 −0.482045
\(28\) −1.00000 −0.188982
\(29\) −0.741706 −0.137731 −0.0688657 0.997626i \(-0.521938\pi\)
−0.0688657 + 0.997626i \(0.521938\pi\)
\(30\) −0.577304 −0.105401
\(31\) −0.702478 −0.126169 −0.0630844 0.998008i \(-0.520094\pi\)
−0.0630844 + 0.998008i \(0.520094\pi\)
\(32\) −1.00000 −0.176777
\(33\) 2.10291 0.366070
\(34\) −4.03673 −0.692294
\(35\) −1.34011 −0.226521
\(36\) −2.81442 −0.469070
\(37\) 5.70012 0.937093 0.468547 0.883439i \(-0.344778\pi\)
0.468547 + 0.883439i \(0.344778\pi\)
\(38\) 0.649997 0.105443
\(39\) 1.79054 0.286717
\(40\) −1.34011 −0.211891
\(41\) 7.65210 1.19506 0.597528 0.801848i \(-0.296150\pi\)
0.597528 + 0.801848i \(0.296150\pi\)
\(42\) 0.430787 0.0664719
\(43\) 9.49126 1.44740 0.723702 0.690113i \(-0.242439\pi\)
0.723702 + 0.690113i \(0.242439\pi\)
\(44\) 4.88156 0.735923
\(45\) −3.77165 −0.562244
\(46\) 2.19781 0.324049
\(47\) 6.32719 0.922916 0.461458 0.887162i \(-0.347326\pi\)
0.461458 + 0.887162i \(0.347326\pi\)
\(48\) 0.430787 0.0621788
\(49\) 1.00000 0.142857
\(50\) 3.20409 0.453127
\(51\) 1.73897 0.243505
\(52\) 4.15645 0.576396
\(53\) −9.84296 −1.35204 −0.676018 0.736886i \(-0.736296\pi\)
−0.676018 + 0.736886i \(0.736296\pi\)
\(54\) 2.50478 0.340857
\(55\) 6.54185 0.882103
\(56\) 1.00000 0.133631
\(57\) −0.280010 −0.0370883
\(58\) 0.741706 0.0973908
\(59\) −0.936742 −0.121953 −0.0609767 0.998139i \(-0.519422\pi\)
−0.0609767 + 0.998139i \(0.519422\pi\)
\(60\) 0.577304 0.0745296
\(61\) −7.74852 −0.992096 −0.496048 0.868295i \(-0.665216\pi\)
−0.496048 + 0.868295i \(0.665216\pi\)
\(62\) 0.702478 0.0892148
\(63\) 2.81442 0.354584
\(64\) 1.00000 0.125000
\(65\) 5.57012 0.690888
\(66\) −2.10291 −0.258851
\(67\) −6.50275 −0.794438 −0.397219 0.917724i \(-0.630025\pi\)
−0.397219 + 0.917724i \(0.630025\pi\)
\(68\) 4.03673 0.489526
\(69\) −0.946788 −0.113980
\(70\) 1.34011 0.160174
\(71\) −0.0975448 −0.0115764 −0.00578822 0.999983i \(-0.501842\pi\)
−0.00578822 + 0.999983i \(0.501842\pi\)
\(72\) 2.81442 0.331683
\(73\) 11.8612 1.38825 0.694126 0.719854i \(-0.255791\pi\)
0.694126 + 0.719854i \(0.255791\pi\)
\(74\) −5.70012 −0.662625
\(75\) −1.38028 −0.159381
\(76\) −0.649997 −0.0745598
\(77\) −4.88156 −0.556306
\(78\) −1.79054 −0.202739
\(79\) 15.4793 1.74156 0.870780 0.491672i \(-0.163614\pi\)
0.870780 + 0.491672i \(0.163614\pi\)
\(80\) 1.34011 0.149829
\(81\) 7.36424 0.818249
\(82\) −7.65210 −0.845033
\(83\) −15.5423 −1.70599 −0.852996 0.521918i \(-0.825217\pi\)
−0.852996 + 0.521918i \(0.825217\pi\)
\(84\) −0.430787 −0.0470027
\(85\) 5.40969 0.586763
\(86\) −9.49126 −1.02347
\(87\) −0.319517 −0.0342559
\(88\) −4.88156 −0.520376
\(89\) 15.5447 1.64773 0.823867 0.566783i \(-0.191812\pi\)
0.823867 + 0.566783i \(0.191812\pi\)
\(90\) 3.77165 0.397567
\(91\) −4.15645 −0.435714
\(92\) −2.19781 −0.229138
\(93\) −0.302619 −0.0313801
\(94\) −6.32719 −0.652600
\(95\) −0.871070 −0.0893699
\(96\) −0.430787 −0.0439670
\(97\) −17.7494 −1.80218 −0.901088 0.433637i \(-0.857230\pi\)
−0.901088 + 0.433637i \(0.857230\pi\)
\(98\) −1.00000 −0.101015
\(99\) −13.7388 −1.38080
\(100\) −3.20409 −0.320409
\(101\) −10.4204 −1.03687 −0.518436 0.855117i \(-0.673485\pi\)
−0.518436 + 0.855117i \(0.673485\pi\)
\(102\) −1.73897 −0.172184
\(103\) −2.75557 −0.271514 −0.135757 0.990742i \(-0.543347\pi\)
−0.135757 + 0.990742i \(0.543347\pi\)
\(104\) −4.15645 −0.407573
\(105\) −0.577304 −0.0563391
\(106\) 9.84296 0.956033
\(107\) 12.7989 1.23732 0.618660 0.785659i \(-0.287676\pi\)
0.618660 + 0.785659i \(0.287676\pi\)
\(108\) −2.50478 −0.241022
\(109\) 11.2023 1.07298 0.536491 0.843906i \(-0.319750\pi\)
0.536491 + 0.843906i \(0.319750\pi\)
\(110\) −6.54185 −0.623741
\(111\) 2.45554 0.233069
\(112\) −1.00000 −0.0944911
\(113\) −19.6197 −1.84566 −0.922832 0.385203i \(-0.874132\pi\)
−0.922832 + 0.385203i \(0.874132\pi\)
\(114\) 0.280010 0.0262254
\(115\) −2.94532 −0.274652
\(116\) −0.741706 −0.0688657
\(117\) −11.6980 −1.08148
\(118\) 0.936742 0.0862341
\(119\) −4.03673 −0.370047
\(120\) −0.577304 −0.0527004
\(121\) 12.8296 1.16633
\(122\) 7.74852 0.701518
\(123\) 3.29642 0.297229
\(124\) −0.702478 −0.0630844
\(125\) −10.9944 −0.983371
\(126\) −2.81442 −0.250729
\(127\) 12.5057 1.10970 0.554850 0.831950i \(-0.312776\pi\)
0.554850 + 0.831950i \(0.312776\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 4.08871 0.359991
\(130\) −5.57012 −0.488532
\(131\) 0.741535 0.0647882 0.0323941 0.999475i \(-0.489687\pi\)
0.0323941 + 0.999475i \(0.489687\pi\)
\(132\) 2.10291 0.183035
\(133\) 0.649997 0.0563619
\(134\) 6.50275 0.561752
\(135\) −3.35669 −0.288898
\(136\) −4.03673 −0.346147
\(137\) 1.63537 0.139719 0.0698597 0.997557i \(-0.477745\pi\)
0.0698597 + 0.997557i \(0.477745\pi\)
\(138\) 0.946788 0.0805960
\(139\) 3.83022 0.324875 0.162438 0.986719i \(-0.448064\pi\)
0.162438 + 0.986719i \(0.448064\pi\)
\(140\) −1.34011 −0.113260
\(141\) 2.72567 0.229543
\(142\) 0.0975448 0.00818577
\(143\) 20.2900 1.69673
\(144\) −2.81442 −0.234535
\(145\) −0.993971 −0.0825448
\(146\) −11.8612 −0.981642
\(147\) 0.430787 0.0355307
\(148\) 5.70012 0.468547
\(149\) 2.41200 0.197599 0.0987994 0.995107i \(-0.468500\pi\)
0.0987994 + 0.995107i \(0.468500\pi\)
\(150\) 1.38028 0.112700
\(151\) −4.16767 −0.339160 −0.169580 0.985516i \(-0.554241\pi\)
−0.169580 + 0.985516i \(0.554241\pi\)
\(152\) 0.649997 0.0527217
\(153\) −11.3611 −0.918489
\(154\) 4.88156 0.393367
\(155\) −0.941401 −0.0756151
\(156\) 1.79054 0.143358
\(157\) 10.7568 0.858486 0.429243 0.903189i \(-0.358780\pi\)
0.429243 + 0.903189i \(0.358780\pi\)
\(158\) −15.4793 −1.23147
\(159\) −4.24022 −0.336271
\(160\) −1.34011 −0.105945
\(161\) 2.19781 0.173212
\(162\) −7.36424 −0.578589
\(163\) 9.37959 0.734666 0.367333 0.930089i \(-0.380271\pi\)
0.367333 + 0.930089i \(0.380271\pi\)
\(164\) 7.65210 0.597528
\(165\) 2.81814 0.219392
\(166\) 15.5423 1.20632
\(167\) 2.71386 0.210004 0.105002 0.994472i \(-0.466515\pi\)
0.105002 + 0.994472i \(0.466515\pi\)
\(168\) 0.430787 0.0332359
\(169\) 4.27608 0.328929
\(170\) −5.40969 −0.414904
\(171\) 1.82937 0.139895
\(172\) 9.49126 0.723702
\(173\) 13.1768 1.00181 0.500906 0.865502i \(-0.333000\pi\)
0.500906 + 0.865502i \(0.333000\pi\)
\(174\) 0.319517 0.0242225
\(175\) 3.20409 0.242207
\(176\) 4.88156 0.367962
\(177\) −0.403537 −0.0303317
\(178\) −15.5447 −1.16512
\(179\) −20.3611 −1.52186 −0.760931 0.648833i \(-0.775257\pi\)
−0.760931 + 0.648833i \(0.775257\pi\)
\(180\) −3.77165 −0.281122
\(181\) −8.58940 −0.638445 −0.319222 0.947680i \(-0.603422\pi\)
−0.319222 + 0.947680i \(0.603422\pi\)
\(182\) 4.15645 0.308097
\(183\) −3.33796 −0.246749
\(184\) 2.19781 0.162025
\(185\) 7.63881 0.561616
\(186\) 0.302619 0.0221891
\(187\) 19.7056 1.44101
\(188\) 6.32719 0.461458
\(189\) 2.50478 0.182196
\(190\) 0.871070 0.0631941
\(191\) 10.8353 0.784012 0.392006 0.919963i \(-0.371781\pi\)
0.392006 + 0.919963i \(0.371781\pi\)
\(192\) 0.430787 0.0310894
\(193\) 0.879349 0.0632970 0.0316485 0.999499i \(-0.489924\pi\)
0.0316485 + 0.999499i \(0.489924\pi\)
\(194\) 17.7494 1.27433
\(195\) 2.39953 0.171834
\(196\) 1.00000 0.0714286
\(197\) 9.38391 0.668576 0.334288 0.942471i \(-0.391504\pi\)
0.334288 + 0.942471i \(0.391504\pi\)
\(198\) 13.7388 0.976372
\(199\) 13.0525 0.925268 0.462634 0.886549i \(-0.346904\pi\)
0.462634 + 0.886549i \(0.346904\pi\)
\(200\) 3.20409 0.226564
\(201\) −2.80130 −0.197589
\(202\) 10.4204 0.733179
\(203\) 0.741706 0.0520576
\(204\) 1.73897 0.121752
\(205\) 10.2547 0.716218
\(206\) 2.75557 0.191990
\(207\) 6.18557 0.429927
\(208\) 4.15645 0.288198
\(209\) −3.17300 −0.219481
\(210\) 0.577304 0.0398378
\(211\) −18.5945 −1.28010 −0.640049 0.768334i \(-0.721086\pi\)
−0.640049 + 0.768334i \(0.721086\pi\)
\(212\) −9.84296 −0.676018
\(213\) −0.0420210 −0.00287923
\(214\) −12.7989 −0.874917
\(215\) 12.7194 0.867454
\(216\) 2.50478 0.170429
\(217\) 0.702478 0.0476873
\(218\) −11.2023 −0.758712
\(219\) 5.10966 0.345279
\(220\) 6.54185 0.441051
\(221\) 16.7785 1.12864
\(222\) −2.45554 −0.164805
\(223\) −10.4623 −0.700609 −0.350304 0.936636i \(-0.613922\pi\)
−0.350304 + 0.936636i \(0.613922\pi\)
\(224\) 1.00000 0.0668153
\(225\) 9.01767 0.601178
\(226\) 19.6197 1.30508
\(227\) 19.7535 1.31109 0.655544 0.755157i \(-0.272439\pi\)
0.655544 + 0.755157i \(0.272439\pi\)
\(228\) −0.280010 −0.0185441
\(229\) −3.62847 −0.239776 −0.119888 0.992787i \(-0.538254\pi\)
−0.119888 + 0.992787i \(0.538254\pi\)
\(230\) 2.94532 0.194208
\(231\) −2.10291 −0.138362
\(232\) 0.741706 0.0486954
\(233\) 27.7185 1.81590 0.907948 0.419083i \(-0.137648\pi\)
0.907948 + 0.419083i \(0.137648\pi\)
\(234\) 11.6980 0.764723
\(235\) 8.47916 0.553120
\(236\) −0.936742 −0.0609767
\(237\) 6.66830 0.433152
\(238\) 4.03673 0.261663
\(239\) 21.6785 1.40227 0.701134 0.713029i \(-0.252677\pi\)
0.701134 + 0.713029i \(0.252677\pi\)
\(240\) 0.577304 0.0372648
\(241\) −1.63500 −0.105319 −0.0526597 0.998613i \(-0.516770\pi\)
−0.0526597 + 0.998613i \(0.516770\pi\)
\(242\) −12.8296 −0.824720
\(243\) 10.6868 0.685556
\(244\) −7.74852 −0.496048
\(245\) 1.34011 0.0856168
\(246\) −3.29642 −0.210172
\(247\) −2.70168 −0.171904
\(248\) 0.702478 0.0446074
\(249\) −6.69543 −0.424306
\(250\) 10.9944 0.695348
\(251\) −2.99230 −0.188872 −0.0944362 0.995531i \(-0.530105\pi\)
−0.0944362 + 0.995531i \(0.530105\pi\)
\(252\) 2.81442 0.177292
\(253\) −10.7287 −0.674510
\(254\) −12.5057 −0.784677
\(255\) 2.33042 0.145937
\(256\) 1.00000 0.0625000
\(257\) 3.37565 0.210567 0.105283 0.994442i \(-0.466425\pi\)
0.105283 + 0.994442i \(0.466425\pi\)
\(258\) −4.08871 −0.254552
\(259\) −5.70012 −0.354188
\(260\) 5.57012 0.345444
\(261\) 2.08747 0.129211
\(262\) −0.741535 −0.0458122
\(263\) 17.1718 1.05886 0.529428 0.848355i \(-0.322406\pi\)
0.529428 + 0.848355i \(0.322406\pi\)
\(264\) −2.10291 −0.129425
\(265\) −13.1907 −0.810298
\(266\) −0.649997 −0.0398539
\(267\) 6.69645 0.409816
\(268\) −6.50275 −0.397219
\(269\) 16.9482 1.03335 0.516677 0.856181i \(-0.327169\pi\)
0.516677 + 0.856181i \(0.327169\pi\)
\(270\) 3.35669 0.204282
\(271\) −31.9627 −1.94160 −0.970798 0.239897i \(-0.922886\pi\)
−0.970798 + 0.239897i \(0.922886\pi\)
\(272\) 4.03673 0.244763
\(273\) −1.79054 −0.108369
\(274\) −1.63537 −0.0987966
\(275\) −15.6410 −0.943187
\(276\) −0.946788 −0.0569900
\(277\) 4.60896 0.276926 0.138463 0.990368i \(-0.455784\pi\)
0.138463 + 0.990368i \(0.455784\pi\)
\(278\) −3.83022 −0.229721
\(279\) 1.97707 0.118364
\(280\) 1.34011 0.0800871
\(281\) −9.61992 −0.573876 −0.286938 0.957949i \(-0.592637\pi\)
−0.286938 + 0.957949i \(0.592637\pi\)
\(282\) −2.72567 −0.162311
\(283\) 7.24549 0.430700 0.215350 0.976537i \(-0.430911\pi\)
0.215350 + 0.976537i \(0.430911\pi\)
\(284\) −0.0975448 −0.00578822
\(285\) −0.375246 −0.0222276
\(286\) −20.2900 −1.19977
\(287\) −7.65210 −0.451689
\(288\) 2.81442 0.165841
\(289\) −0.704773 −0.0414572
\(290\) 0.993971 0.0583680
\(291\) −7.64620 −0.448228
\(292\) 11.8612 0.694126
\(293\) −18.1385 −1.05966 −0.529830 0.848104i \(-0.677744\pi\)
−0.529830 + 0.848104i \(0.677744\pi\)
\(294\) −0.430787 −0.0251240
\(295\) −1.25534 −0.0730888
\(296\) −5.70012 −0.331312
\(297\) −12.2272 −0.709496
\(298\) −2.41200 −0.139723
\(299\) −9.13509 −0.528296
\(300\) −1.38028 −0.0796906
\(301\) −9.49126 −0.547067
\(302\) 4.16767 0.239823
\(303\) −4.48899 −0.257886
\(304\) −0.649997 −0.0372799
\(305\) −10.3839 −0.594581
\(306\) 11.3611 0.649470
\(307\) 11.1722 0.637633 0.318817 0.947816i \(-0.396715\pi\)
0.318817 + 0.947816i \(0.396715\pi\)
\(308\) −4.88156 −0.278153
\(309\) −1.18706 −0.0675297
\(310\) 0.941401 0.0534680
\(311\) −4.16414 −0.236127 −0.118063 0.993006i \(-0.537669\pi\)
−0.118063 + 0.993006i \(0.537669\pi\)
\(312\) −1.79054 −0.101370
\(313\) −29.5696 −1.67137 −0.835686 0.549207i \(-0.814930\pi\)
−0.835686 + 0.549207i \(0.814930\pi\)
\(314\) −10.7568 −0.607041
\(315\) 3.77165 0.212508
\(316\) 15.4793 0.870780
\(317\) −21.6998 −1.21878 −0.609391 0.792869i \(-0.708586\pi\)
−0.609391 + 0.792869i \(0.708586\pi\)
\(318\) 4.24022 0.237780
\(319\) −3.62068 −0.202719
\(320\) 1.34011 0.0749147
\(321\) 5.51362 0.307740
\(322\) −2.19781 −0.122479
\(323\) −2.62387 −0.145996
\(324\) 7.36424 0.409125
\(325\) −13.3177 −0.738731
\(326\) −9.37959 −0.519487
\(327\) 4.82579 0.266867
\(328\) −7.65210 −0.422516
\(329\) −6.32719 −0.348829
\(330\) −2.81814 −0.155134
\(331\) 11.5089 0.632588 0.316294 0.948661i \(-0.397561\pi\)
0.316294 + 0.948661i \(0.397561\pi\)
\(332\) −15.5423 −0.852996
\(333\) −16.0425 −0.879125
\(334\) −2.71386 −0.148496
\(335\) −8.71443 −0.476120
\(336\) −0.430787 −0.0235014
\(337\) 29.5972 1.61226 0.806131 0.591737i \(-0.201558\pi\)
0.806131 + 0.591737i \(0.201558\pi\)
\(338\) −4.27608 −0.232588
\(339\) −8.45190 −0.459044
\(340\) 5.40969 0.293381
\(341\) −3.42919 −0.185701
\(342\) −1.82937 −0.0989208
\(343\) −1.00000 −0.0539949
\(344\) −9.49126 −0.511734
\(345\) −1.26880 −0.0683101
\(346\) −13.1768 −0.708388
\(347\) 6.38658 0.342850 0.171425 0.985197i \(-0.445163\pi\)
0.171425 + 0.985197i \(0.445163\pi\)
\(348\) −0.319517 −0.0171279
\(349\) 27.9382 1.49550 0.747750 0.663981i \(-0.231134\pi\)
0.747750 + 0.663981i \(0.231134\pi\)
\(350\) −3.20409 −0.171266
\(351\) −10.4110 −0.555697
\(352\) −4.88156 −0.260188
\(353\) −13.6389 −0.725925 −0.362962 0.931804i \(-0.618235\pi\)
−0.362962 + 0.931804i \(0.618235\pi\)
\(354\) 0.403537 0.0214477
\(355\) −0.130721 −0.00693796
\(356\) 15.5447 0.823867
\(357\) −1.73897 −0.0920362
\(358\) 20.3611 1.07612
\(359\) −11.1803 −0.590072 −0.295036 0.955486i \(-0.595332\pi\)
−0.295036 + 0.955486i \(0.595332\pi\)
\(360\) 3.77165 0.198783
\(361\) −18.5775 −0.977763
\(362\) 8.58940 0.451449
\(363\) 5.52684 0.290084
\(364\) −4.15645 −0.217857
\(365\) 15.8954 0.832003
\(366\) 3.33796 0.174478
\(367\) 7.47025 0.389944 0.194972 0.980809i \(-0.437538\pi\)
0.194972 + 0.980809i \(0.437538\pi\)
\(368\) −2.19781 −0.114569
\(369\) −21.5362 −1.12113
\(370\) −7.63881 −0.397123
\(371\) 9.84296 0.511021
\(372\) −0.302619 −0.0156900
\(373\) −2.71431 −0.140541 −0.0702707 0.997528i \(-0.522386\pi\)
−0.0702707 + 0.997528i \(0.522386\pi\)
\(374\) −19.7056 −1.01895
\(375\) −4.73626 −0.244579
\(376\) −6.32719 −0.326300
\(377\) −3.08286 −0.158776
\(378\) −2.50478 −0.128832
\(379\) 21.9547 1.12774 0.563870 0.825864i \(-0.309312\pi\)
0.563870 + 0.825864i \(0.309312\pi\)
\(380\) −0.871070 −0.0446850
\(381\) 5.38729 0.275999
\(382\) −10.8353 −0.554380
\(383\) 26.7345 1.36607 0.683036 0.730385i \(-0.260659\pi\)
0.683036 + 0.730385i \(0.260659\pi\)
\(384\) −0.430787 −0.0219835
\(385\) −6.54185 −0.333404
\(386\) −0.879349 −0.0447577
\(387\) −26.7124 −1.35787
\(388\) −17.7494 −0.901088
\(389\) 20.1810 1.02322 0.511608 0.859219i \(-0.329050\pi\)
0.511608 + 0.859219i \(0.329050\pi\)
\(390\) −2.39953 −0.121505
\(391\) −8.87198 −0.448675
\(392\) −1.00000 −0.0505076
\(393\) 0.319444 0.0161138
\(394\) −9.38391 −0.472754
\(395\) 20.7441 1.04375
\(396\) −13.7388 −0.690399
\(397\) 28.5751 1.43414 0.717071 0.697000i \(-0.245482\pi\)
0.717071 + 0.697000i \(0.245482\pi\)
\(398\) −13.0525 −0.654263
\(399\) 0.280010 0.0140180
\(400\) −3.20409 −0.160205
\(401\) 33.5997 1.67789 0.838945 0.544216i \(-0.183173\pi\)
0.838945 + 0.544216i \(0.183173\pi\)
\(402\) 2.80130 0.139716
\(403\) −2.91981 −0.145446
\(404\) −10.4204 −0.518436
\(405\) 9.86892 0.490391
\(406\) −0.741706 −0.0368103
\(407\) 27.8255 1.37926
\(408\) −1.73897 −0.0860920
\(409\) −33.6397 −1.66338 −0.831688 0.555243i \(-0.812625\pi\)
−0.831688 + 0.555243i \(0.812625\pi\)
\(410\) −10.2547 −0.506443
\(411\) 0.704498 0.0347503
\(412\) −2.75557 −0.135757
\(413\) 0.936742 0.0460941
\(414\) −6.18557 −0.304004
\(415\) −20.8285 −1.02243
\(416\) −4.15645 −0.203787
\(417\) 1.65001 0.0808014
\(418\) 3.17300 0.155196
\(419\) −34.7028 −1.69534 −0.847672 0.530520i \(-0.821997\pi\)
−0.847672 + 0.530520i \(0.821997\pi\)
\(420\) −0.577304 −0.0281695
\(421\) 5.70276 0.277936 0.138968 0.990297i \(-0.455622\pi\)
0.138968 + 0.990297i \(0.455622\pi\)
\(422\) 18.5945 0.905165
\(423\) −17.8074 −0.865825
\(424\) 9.84296 0.478017
\(425\) −12.9341 −0.627395
\(426\) 0.0420210 0.00203593
\(427\) 7.74852 0.374977
\(428\) 12.7989 0.618660
\(429\) 8.74065 0.422003
\(430\) −12.7194 −0.613383
\(431\) 1.00000 0.0481683
\(432\) −2.50478 −0.120511
\(433\) 34.2697 1.64690 0.823449 0.567391i \(-0.192047\pi\)
0.823449 + 0.567391i \(0.192047\pi\)
\(434\) −0.702478 −0.0337200
\(435\) −0.428190 −0.0205301
\(436\) 11.2023 0.536491
\(437\) 1.42857 0.0683378
\(438\) −5.10966 −0.244149
\(439\) 34.0457 1.62491 0.812456 0.583022i \(-0.198130\pi\)
0.812456 + 0.583022i \(0.198130\pi\)
\(440\) −6.54185 −0.311870
\(441\) −2.81442 −0.134020
\(442\) −16.7785 −0.798071
\(443\) 7.48293 0.355525 0.177762 0.984073i \(-0.443114\pi\)
0.177762 + 0.984073i \(0.443114\pi\)
\(444\) 2.45554 0.116535
\(445\) 20.8317 0.987516
\(446\) 10.4623 0.495405
\(447\) 1.03906 0.0491458
\(448\) −1.00000 −0.0472456
\(449\) 12.2137 0.576401 0.288201 0.957570i \(-0.406943\pi\)
0.288201 + 0.957570i \(0.406943\pi\)
\(450\) −9.01767 −0.425097
\(451\) 37.3542 1.75894
\(452\) −19.6197 −0.922832
\(453\) −1.79538 −0.0843543
\(454\) −19.7535 −0.927080
\(455\) −5.57012 −0.261131
\(456\) 0.280010 0.0131127
\(457\) −15.9275 −0.745058 −0.372529 0.928021i \(-0.621509\pi\)
−0.372529 + 0.928021i \(0.621509\pi\)
\(458\) 3.62847 0.169547
\(459\) −10.1111 −0.471947
\(460\) −2.94532 −0.137326
\(461\) 2.32168 0.108131 0.0540657 0.998537i \(-0.482782\pi\)
0.0540657 + 0.998537i \(0.482782\pi\)
\(462\) 2.10291 0.0978364
\(463\) −41.1923 −1.91437 −0.957185 0.289478i \(-0.906518\pi\)
−0.957185 + 0.289478i \(0.906518\pi\)
\(464\) −0.741706 −0.0344328
\(465\) −0.405543 −0.0188066
\(466\) −27.7185 −1.28403
\(467\) 29.7574 1.37701 0.688505 0.725232i \(-0.258267\pi\)
0.688505 + 0.725232i \(0.258267\pi\)
\(468\) −11.6980 −0.540741
\(469\) 6.50275 0.300269
\(470\) −8.47916 −0.391115
\(471\) 4.63389 0.213518
\(472\) 0.936742 0.0431171
\(473\) 46.3322 2.13036
\(474\) −6.66830 −0.306285
\(475\) 2.08265 0.0955586
\(476\) −4.03673 −0.185023
\(477\) 27.7023 1.26840
\(478\) −21.6785 −0.991553
\(479\) 23.4244 1.07029 0.535143 0.844761i \(-0.320258\pi\)
0.535143 + 0.844761i \(0.320258\pi\)
\(480\) −0.577304 −0.0263502
\(481\) 23.6922 1.08027
\(482\) 1.63500 0.0744721
\(483\) 0.946788 0.0430804
\(484\) 12.8296 0.583165
\(485\) −23.7862 −1.08007
\(486\) −10.6868 −0.484761
\(487\) −29.0791 −1.31770 −0.658849 0.752275i \(-0.728956\pi\)
−0.658849 + 0.752275i \(0.728956\pi\)
\(488\) 7.74852 0.350759
\(489\) 4.04061 0.182723
\(490\) −1.34011 −0.0605402
\(491\) −2.65854 −0.119978 −0.0599892 0.998199i \(-0.519107\pi\)
−0.0599892 + 0.998199i \(0.519107\pi\)
\(492\) 3.29642 0.148614
\(493\) −2.99407 −0.134846
\(494\) 2.70168 0.121554
\(495\) −18.4115 −0.827537
\(496\) −0.702478 −0.0315422
\(497\) 0.0975448 0.00437548
\(498\) 6.69543 0.300029
\(499\) 3.77022 0.168778 0.0843891 0.996433i \(-0.473106\pi\)
0.0843891 + 0.996433i \(0.473106\pi\)
\(500\) −10.9944 −0.491686
\(501\) 1.16909 0.0522313
\(502\) 2.99230 0.133553
\(503\) −4.51264 −0.201209 −0.100604 0.994927i \(-0.532078\pi\)
−0.100604 + 0.994927i \(0.532078\pi\)
\(504\) −2.81442 −0.125364
\(505\) −13.9646 −0.621415
\(506\) 10.7287 0.476951
\(507\) 1.84208 0.0818096
\(508\) 12.5057 0.554850
\(509\) 28.8521 1.27885 0.639423 0.768855i \(-0.279173\pi\)
0.639423 + 0.768855i \(0.279173\pi\)
\(510\) −2.33042 −0.103193
\(511\) −11.8612 −0.524710
\(512\) −1.00000 −0.0441942
\(513\) 1.62810 0.0718823
\(514\) −3.37565 −0.148893
\(515\) −3.69278 −0.162723
\(516\) 4.08871 0.179996
\(517\) 30.8866 1.35839
\(518\) 5.70012 0.250449
\(519\) 5.67639 0.249166
\(520\) −5.57012 −0.244266
\(521\) −38.8458 −1.70186 −0.850932 0.525275i \(-0.823962\pi\)
−0.850932 + 0.525275i \(0.823962\pi\)
\(522\) −2.08747 −0.0913663
\(523\) −3.37912 −0.147759 −0.0738793 0.997267i \(-0.523538\pi\)
−0.0738793 + 0.997267i \(0.523538\pi\)
\(524\) 0.741535 0.0323941
\(525\) 1.38028 0.0602405
\(526\) −17.1718 −0.748725
\(527\) −2.83572 −0.123526
\(528\) 2.10291 0.0915176
\(529\) −18.1696 −0.789984
\(530\) 13.1907 0.572967
\(531\) 2.63639 0.114410
\(532\) 0.649997 0.0281809
\(533\) 31.8056 1.37765
\(534\) −6.69645 −0.289784
\(535\) 17.1520 0.741547
\(536\) 6.50275 0.280876
\(537\) −8.77131 −0.378510
\(538\) −16.9482 −0.730691
\(539\) 4.88156 0.210264
\(540\) −3.35669 −0.144449
\(541\) 3.53030 0.151779 0.0758897 0.997116i \(-0.475820\pi\)
0.0758897 + 0.997116i \(0.475820\pi\)
\(542\) 31.9627 1.37292
\(543\) −3.70020 −0.158791
\(544\) −4.03673 −0.173074
\(545\) 15.0123 0.643056
\(546\) 1.79054 0.0766283
\(547\) 7.76405 0.331967 0.165983 0.986129i \(-0.446920\pi\)
0.165983 + 0.986129i \(0.446920\pi\)
\(548\) 1.63537 0.0698597
\(549\) 21.8076 0.930726
\(550\) 15.6410 0.666934
\(551\) 0.482107 0.0205384
\(552\) 0.946788 0.0402980
\(553\) −15.4793 −0.658248
\(554\) −4.60896 −0.195816
\(555\) 3.29070 0.139682
\(556\) 3.83022 0.162438
\(557\) −10.6707 −0.452134 −0.226067 0.974112i \(-0.572587\pi\)
−0.226067 + 0.974112i \(0.572587\pi\)
\(558\) −1.97707 −0.0836961
\(559\) 39.4499 1.66855
\(560\) −1.34011 −0.0566302
\(561\) 8.48890 0.358402
\(562\) 9.61992 0.405792
\(563\) 2.69831 0.113720 0.0568601 0.998382i \(-0.481891\pi\)
0.0568601 + 0.998382i \(0.481891\pi\)
\(564\) 2.72567 0.114772
\(565\) −26.2926 −1.10614
\(566\) −7.24549 −0.304551
\(567\) −7.36424 −0.309269
\(568\) 0.0975448 0.00409289
\(569\) 42.2056 1.76935 0.884676 0.466207i \(-0.154380\pi\)
0.884676 + 0.466207i \(0.154380\pi\)
\(570\) 0.375246 0.0157173
\(571\) 20.1271 0.842295 0.421147 0.906992i \(-0.361628\pi\)
0.421147 + 0.906992i \(0.361628\pi\)
\(572\) 20.2900 0.848366
\(573\) 4.66769 0.194996
\(574\) 7.65210 0.319392
\(575\) 7.04199 0.293671
\(576\) −2.81442 −0.117268
\(577\) 3.40226 0.141638 0.0708189 0.997489i \(-0.477439\pi\)
0.0708189 + 0.997489i \(0.477439\pi\)
\(578\) 0.704773 0.0293147
\(579\) 0.378812 0.0157429
\(580\) −0.993971 −0.0412724
\(581\) 15.5423 0.644804
\(582\) 7.64620 0.316945
\(583\) −48.0490 −1.98999
\(584\) −11.8612 −0.490821
\(585\) −15.6767 −0.648150
\(586\) 18.1385 0.749293
\(587\) 30.0353 1.23969 0.619845 0.784724i \(-0.287195\pi\)
0.619845 + 0.784724i \(0.287195\pi\)
\(588\) 0.430787 0.0177654
\(589\) 0.456609 0.0188142
\(590\) 1.25534 0.0516816
\(591\) 4.04247 0.166285
\(592\) 5.70012 0.234273
\(593\) −20.9550 −0.860517 −0.430258 0.902706i \(-0.641578\pi\)
−0.430258 + 0.902706i \(0.641578\pi\)
\(594\) 12.2272 0.501689
\(595\) −5.40969 −0.221775
\(596\) 2.41200 0.0987994
\(597\) 5.62285 0.230128
\(598\) 9.13509 0.373562
\(599\) −40.6386 −1.66045 −0.830224 0.557429i \(-0.811788\pi\)
−0.830224 + 0.557429i \(0.811788\pi\)
\(600\) 1.38028 0.0563498
\(601\) −4.80383 −0.195952 −0.0979762 0.995189i \(-0.531237\pi\)
−0.0979762 + 0.995189i \(0.531237\pi\)
\(602\) 9.49126 0.386835
\(603\) 18.3015 0.745295
\(604\) −4.16767 −0.169580
\(605\) 17.1932 0.699002
\(606\) 4.48899 0.182353
\(607\) 2.03334 0.0825305 0.0412653 0.999148i \(-0.486861\pi\)
0.0412653 + 0.999148i \(0.486861\pi\)
\(608\) 0.649997 0.0263609
\(609\) 0.319517 0.0129475
\(610\) 10.3839 0.420432
\(611\) 26.2987 1.06393
\(612\) −11.3611 −0.459244
\(613\) −24.2911 −0.981107 −0.490554 0.871411i \(-0.663205\pi\)
−0.490554 + 0.871411i \(0.663205\pi\)
\(614\) −11.1722 −0.450875
\(615\) 4.41759 0.178134
\(616\) 4.88156 0.196684
\(617\) 2.09995 0.0845406 0.0422703 0.999106i \(-0.486541\pi\)
0.0422703 + 0.999106i \(0.486541\pi\)
\(618\) 1.18706 0.0477507
\(619\) 13.2849 0.533966 0.266983 0.963701i \(-0.413973\pi\)
0.266983 + 0.963701i \(0.413973\pi\)
\(620\) −0.941401 −0.0378076
\(621\) 5.50503 0.220909
\(622\) 4.16414 0.166967
\(623\) −15.5447 −0.622785
\(624\) 1.79054 0.0716792
\(625\) 1.28669 0.0514674
\(626\) 29.5696 1.18184
\(627\) −1.36689 −0.0545882
\(628\) 10.7568 0.429243
\(629\) 23.0099 0.917463
\(630\) −3.77165 −0.150266
\(631\) −21.8282 −0.868969 −0.434484 0.900679i \(-0.643069\pi\)
−0.434484 + 0.900679i \(0.643069\pi\)
\(632\) −15.4793 −0.615735
\(633\) −8.01026 −0.318379
\(634\) 21.6998 0.861810
\(635\) 16.7591 0.665063
\(636\) −4.24022 −0.168136
\(637\) 4.15645 0.164685
\(638\) 3.62068 0.143344
\(639\) 0.274532 0.0108603
\(640\) −1.34011 −0.0529727
\(641\) 34.0399 1.34449 0.672247 0.740327i \(-0.265329\pi\)
0.672247 + 0.740327i \(0.265329\pi\)
\(642\) −5.51362 −0.217605
\(643\) −47.9847 −1.89233 −0.946167 0.323680i \(-0.895080\pi\)
−0.946167 + 0.323680i \(0.895080\pi\)
\(644\) 2.19781 0.0866059
\(645\) 5.47934 0.215749
\(646\) 2.62387 0.103235
\(647\) 29.7922 1.17125 0.585627 0.810581i \(-0.300848\pi\)
0.585627 + 0.810581i \(0.300848\pi\)
\(648\) −7.36424 −0.289295
\(649\) −4.57277 −0.179497
\(650\) 13.3177 0.522361
\(651\) 0.302619 0.0118606
\(652\) 9.37959 0.367333
\(653\) −43.9740 −1.72084 −0.860418 0.509589i \(-0.829798\pi\)
−0.860418 + 0.509589i \(0.829798\pi\)
\(654\) −4.82579 −0.188703
\(655\) 0.993742 0.0388287
\(656\) 7.65210 0.298764
\(657\) −33.3825 −1.30238
\(658\) 6.32719 0.246660
\(659\) −3.83502 −0.149391 −0.0746956 0.997206i \(-0.523799\pi\)
−0.0746956 + 0.997206i \(0.523799\pi\)
\(660\) 2.81814 0.109696
\(661\) 30.1940 1.17441 0.587204 0.809439i \(-0.300228\pi\)
0.587204 + 0.809439i \(0.300228\pi\)
\(662\) −11.5089 −0.447307
\(663\) 7.22796 0.280711
\(664\) 15.5423 0.603159
\(665\) 0.871070 0.0337787
\(666\) 16.0425 0.621636
\(667\) 1.63013 0.0631188
\(668\) 2.71386 0.105002
\(669\) −4.50703 −0.174252
\(670\) 8.71443 0.336668
\(671\) −37.8249 −1.46021
\(672\) 0.430787 0.0166180
\(673\) 35.9020 1.38392 0.691960 0.721936i \(-0.256747\pi\)
0.691960 + 0.721936i \(0.256747\pi\)
\(674\) −29.5972 −1.14004
\(675\) 8.02554 0.308903
\(676\) 4.27608 0.164464
\(677\) 30.0257 1.15398 0.576990 0.816751i \(-0.304227\pi\)
0.576990 + 0.816751i \(0.304227\pi\)
\(678\) 8.45190 0.324593
\(679\) 17.7494 0.681158
\(680\) −5.40969 −0.207452
\(681\) 8.50957 0.326087
\(682\) 3.42919 0.131310
\(683\) 27.8495 1.06563 0.532815 0.846232i \(-0.321134\pi\)
0.532815 + 0.846232i \(0.321134\pi\)
\(684\) 1.82937 0.0699476
\(685\) 2.19159 0.0837363
\(686\) 1.00000 0.0381802
\(687\) −1.56310 −0.0596358
\(688\) 9.49126 0.361851
\(689\) −40.9118 −1.55861
\(690\) 1.26880 0.0483026
\(691\) −10.1730 −0.386998 −0.193499 0.981100i \(-0.561984\pi\)
−0.193499 + 0.981100i \(0.561984\pi\)
\(692\) 13.1768 0.500906
\(693\) 13.7388 0.521893
\(694\) −6.38658 −0.242431
\(695\) 5.13294 0.194703
\(696\) 0.319517 0.0121113
\(697\) 30.8895 1.17002
\(698\) −27.9382 −1.05748
\(699\) 11.9408 0.451641
\(700\) 3.20409 0.121103
\(701\) 8.82854 0.333449 0.166725 0.986003i \(-0.446681\pi\)
0.166725 + 0.986003i \(0.446681\pi\)
\(702\) 10.4110 0.392937
\(703\) −3.70506 −0.139739
\(704\) 4.88156 0.183981
\(705\) 3.65271 0.137569
\(706\) 13.6389 0.513306
\(707\) 10.4204 0.391901
\(708\) −0.403537 −0.0151658
\(709\) 19.6513 0.738021 0.369010 0.929425i \(-0.379697\pi\)
0.369010 + 0.929425i \(0.379697\pi\)
\(710\) 0.130721 0.00490588
\(711\) −43.5654 −1.63383
\(712\) −15.5447 −0.582562
\(713\) 1.54391 0.0578200
\(714\) 1.73897 0.0650794
\(715\) 27.1909 1.01688
\(716\) −20.3611 −0.760931
\(717\) 9.33883 0.348765
\(718\) 11.1803 0.417244
\(719\) 13.1445 0.490205 0.245103 0.969497i \(-0.421178\pi\)
0.245103 + 0.969497i \(0.421178\pi\)
\(720\) −3.77165 −0.140561
\(721\) 2.75557 0.102623
\(722\) 18.5775 0.691383
\(723\) −0.704336 −0.0261945
\(724\) −8.58940 −0.319222
\(725\) 2.37650 0.0882608
\(726\) −5.52684 −0.205120
\(727\) −48.0135 −1.78072 −0.890362 0.455254i \(-0.849549\pi\)
−0.890362 + 0.455254i \(0.849549\pi\)
\(728\) 4.15645 0.154048
\(729\) −17.4890 −0.647741
\(730\) −15.8954 −0.588315
\(731\) 38.3137 1.41708
\(732\) −3.33796 −0.123375
\(733\) −37.1431 −1.37191 −0.685956 0.727643i \(-0.740616\pi\)
−0.685956 + 0.727643i \(0.740616\pi\)
\(734\) −7.47025 −0.275732
\(735\) 0.577304 0.0212942
\(736\) 2.19781 0.0810124
\(737\) −31.7436 −1.16929
\(738\) 21.5362 0.792760
\(739\) 48.0802 1.76866 0.884329 0.466865i \(-0.154617\pi\)
0.884329 + 0.466865i \(0.154617\pi\)
\(740\) 7.63881 0.280808
\(741\) −1.16385 −0.0427550
\(742\) −9.84296 −0.361347
\(743\) 16.4613 0.603907 0.301953 0.953323i \(-0.402361\pi\)
0.301953 + 0.953323i \(0.402361\pi\)
\(744\) 0.302619 0.0110945
\(745\) 3.23236 0.118424
\(746\) 2.71431 0.0993778
\(747\) 43.7427 1.60046
\(748\) 19.7056 0.720507
\(749\) −12.7989 −0.467663
\(750\) 4.73626 0.172944
\(751\) 27.5165 1.00409 0.502046 0.864841i \(-0.332581\pi\)
0.502046 + 0.864841i \(0.332581\pi\)
\(752\) 6.32719 0.230729
\(753\) −1.28904 −0.0469754
\(754\) 3.08286 0.112271
\(755\) −5.58516 −0.203265
\(756\) 2.50478 0.0910979
\(757\) −47.5239 −1.72728 −0.863642 0.504105i \(-0.831822\pi\)
−0.863642 + 0.504105i \(0.831822\pi\)
\(758\) −21.9547 −0.797432
\(759\) −4.62181 −0.167761
\(760\) 0.871070 0.0315970
\(761\) 34.8551 1.26350 0.631748 0.775174i \(-0.282338\pi\)
0.631748 + 0.775174i \(0.282338\pi\)
\(762\) −5.38729 −0.195161
\(763\) −11.2023 −0.405549
\(764\) 10.8353 0.392006
\(765\) −15.2251 −0.550466
\(766\) −26.7345 −0.965958
\(767\) −3.89352 −0.140587
\(768\) 0.430787 0.0155447
\(769\) −50.4464 −1.81914 −0.909571 0.415548i \(-0.863590\pi\)
−0.909571 + 0.415548i \(0.863590\pi\)
\(770\) 6.54185 0.235752
\(771\) 1.45418 0.0523712
\(772\) 0.879349 0.0316485
\(773\) −38.0991 −1.37033 −0.685166 0.728387i \(-0.740270\pi\)
−0.685166 + 0.728387i \(0.740270\pi\)
\(774\) 26.7124 0.960158
\(775\) 2.25081 0.0808513
\(776\) 17.7494 0.637165
\(777\) −2.45554 −0.0880919
\(778\) −20.1810 −0.723523
\(779\) −4.97384 −0.178206
\(780\) 2.39953 0.0859171
\(781\) −0.476171 −0.0170387
\(782\) 8.87198 0.317261
\(783\) 1.85781 0.0663927
\(784\) 1.00000 0.0357143
\(785\) 14.4153 0.514505
\(786\) −0.319444 −0.0113942
\(787\) 0.613328 0.0218628 0.0109314 0.999940i \(-0.496520\pi\)
0.0109314 + 0.999940i \(0.496520\pi\)
\(788\) 9.38391 0.334288
\(789\) 7.39738 0.263354
\(790\) −20.7441 −0.738041
\(791\) 19.6197 0.697595
\(792\) 13.7388 0.488186
\(793\) −32.2063 −1.14368
\(794\) −28.5751 −1.01409
\(795\) −5.68238 −0.201533
\(796\) 13.0525 0.462634
\(797\) −23.3911 −0.828555 −0.414277 0.910151i \(-0.635966\pi\)
−0.414277 + 0.910151i \(0.635966\pi\)
\(798\) −0.280010 −0.00991226
\(799\) 25.5412 0.903583
\(800\) 3.20409 0.113282
\(801\) −43.7493 −1.54581
\(802\) −33.5997 −1.18645
\(803\) 57.9013 2.04329
\(804\) −2.80130 −0.0987943
\(805\) 2.94532 0.103809
\(806\) 2.91981 0.102846
\(807\) 7.30109 0.257010
\(808\) 10.4204 0.366589
\(809\) −0.394250 −0.0138611 −0.00693055 0.999976i \(-0.502206\pi\)
−0.00693055 + 0.999976i \(0.502206\pi\)
\(810\) −9.86892 −0.346759
\(811\) −17.7317 −0.622645 −0.311322 0.950304i \(-0.600772\pi\)
−0.311322 + 0.950304i \(0.600772\pi\)
\(812\) 0.741706 0.0260288
\(813\) −13.7691 −0.482904
\(814\) −27.8255 −0.975282
\(815\) 12.5697 0.440298
\(816\) 1.73897 0.0608762
\(817\) −6.16929 −0.215836
\(818\) 33.6397 1.17618
\(819\) 11.6980 0.408761
\(820\) 10.2547 0.358109
\(821\) 36.3206 1.26760 0.633798 0.773498i \(-0.281495\pi\)
0.633798 + 0.773498i \(0.281495\pi\)
\(822\) −0.704498 −0.0245722
\(823\) 37.3726 1.30273 0.651363 0.758766i \(-0.274198\pi\)
0.651363 + 0.758766i \(0.274198\pi\)
\(824\) 2.75557 0.0959948
\(825\) −6.73793 −0.234585
\(826\) −0.936742 −0.0325934
\(827\) −48.5754 −1.68913 −0.844566 0.535451i \(-0.820142\pi\)
−0.844566 + 0.535451i \(0.820142\pi\)
\(828\) 6.18557 0.214963
\(829\) 35.5307 1.23403 0.617016 0.786950i \(-0.288341\pi\)
0.617016 + 0.786950i \(0.288341\pi\)
\(830\) 20.8285 0.722967
\(831\) 1.98548 0.0688756
\(832\) 4.15645 0.144099
\(833\) 4.03673 0.139865
\(834\) −1.65001 −0.0571352
\(835\) 3.63688 0.125859
\(836\) −3.17300 −0.109740
\(837\) 1.75955 0.0608190
\(838\) 34.7028 1.19879
\(839\) 50.9183 1.75789 0.878947 0.476919i \(-0.158247\pi\)
0.878947 + 0.476919i \(0.158247\pi\)
\(840\) 0.577304 0.0199189
\(841\) −28.4499 −0.981030
\(842\) −5.70276 −0.196530
\(843\) −4.14414 −0.142732
\(844\) −18.5945 −0.640049
\(845\) 5.73043 0.197133
\(846\) 17.8074 0.612231
\(847\) −12.8296 −0.440832
\(848\) −9.84296 −0.338009
\(849\) 3.12126 0.107121
\(850\) 12.9341 0.443635
\(851\) −12.5278 −0.429447
\(852\) −0.0420210 −0.00143962
\(853\) −30.8860 −1.05752 −0.528758 0.848773i \(-0.677342\pi\)
−0.528758 + 0.848773i \(0.677342\pi\)
\(854\) −7.74852 −0.265149
\(855\) 2.45156 0.0838416
\(856\) −12.7989 −0.437459
\(857\) −30.4730 −1.04094 −0.520468 0.853881i \(-0.674243\pi\)
−0.520468 + 0.853881i \(0.674243\pi\)
\(858\) −8.74065 −0.298401
\(859\) 15.1849 0.518104 0.259052 0.965863i \(-0.416590\pi\)
0.259052 + 0.965863i \(0.416590\pi\)
\(860\) 12.7194 0.433727
\(861\) −3.29642 −0.112342
\(862\) −1.00000 −0.0340601
\(863\) −30.8906 −1.05153 −0.525764 0.850631i \(-0.676220\pi\)
−0.525764 + 0.850631i \(0.676220\pi\)
\(864\) 2.50478 0.0852143
\(865\) 17.6584 0.600403
\(866\) −34.2697 −1.16453
\(867\) −0.303607 −0.0103110
\(868\) 0.702478 0.0238437
\(869\) 75.5633 2.56331
\(870\) 0.428190 0.0145170
\(871\) −27.0284 −0.915822
\(872\) −11.2023 −0.379356
\(873\) 49.9542 1.69069
\(874\) −1.42857 −0.0483221
\(875\) 10.9944 0.371679
\(876\) 5.10966 0.172639
\(877\) −39.0901 −1.31998 −0.659990 0.751274i \(-0.729440\pi\)
−0.659990 + 0.751274i \(0.729440\pi\)
\(878\) −34.0457 −1.14899
\(879\) −7.81381 −0.263553
\(880\) 6.54185 0.220526
\(881\) −27.2364 −0.917618 −0.458809 0.888535i \(-0.651724\pi\)
−0.458809 + 0.888535i \(0.651724\pi\)
\(882\) 2.81442 0.0947665
\(883\) −42.8350 −1.44151 −0.720756 0.693189i \(-0.756205\pi\)
−0.720756 + 0.693189i \(0.756205\pi\)
\(884\) 16.7785 0.564322
\(885\) −0.540785 −0.0181783
\(886\) −7.48293 −0.251394
\(887\) 6.67724 0.224200 0.112100 0.993697i \(-0.464242\pi\)
0.112100 + 0.993697i \(0.464242\pi\)
\(888\) −2.45554 −0.0824024
\(889\) −12.5057 −0.419427
\(890\) −20.8317 −0.698279
\(891\) 35.9490 1.20434
\(892\) −10.4623 −0.350304
\(893\) −4.11266 −0.137625
\(894\) −1.03906 −0.0347513
\(895\) −27.2862 −0.912078
\(896\) 1.00000 0.0334077
\(897\) −3.93528 −0.131395
\(898\) −12.2137 −0.407577
\(899\) 0.521032 0.0173774
\(900\) 9.01767 0.300589
\(901\) −39.7334 −1.32371
\(902\) −37.3542 −1.24376
\(903\) −4.08871 −0.136064
\(904\) 19.6197 0.652541
\(905\) −11.5108 −0.382631
\(906\) 1.79538 0.0596475
\(907\) 22.1262 0.734689 0.367344 0.930085i \(-0.380267\pi\)
0.367344 + 0.930085i \(0.380267\pi\)
\(908\) 19.7535 0.655544
\(909\) 29.3275 0.972732
\(910\) 5.57012 0.184648
\(911\) −0.254712 −0.00843898 −0.00421949 0.999991i \(-0.501343\pi\)
−0.00421949 + 0.999991i \(0.501343\pi\)
\(912\) −0.280010 −0.00927207
\(913\) −75.8708 −2.51096
\(914\) 15.9275 0.526836
\(915\) −4.47325 −0.147881
\(916\) −3.62847 −0.119888
\(917\) −0.741535 −0.0244876
\(918\) 10.1111 0.333717
\(919\) 24.6580 0.813393 0.406697 0.913563i \(-0.366681\pi\)
0.406697 + 0.913563i \(0.366681\pi\)
\(920\) 2.94532 0.0971042
\(921\) 4.81286 0.158589
\(922\) −2.32168 −0.0764604
\(923\) −0.405440 −0.0133452
\(924\) −2.10291 −0.0691808
\(925\) −18.2637 −0.600507
\(926\) 41.1923 1.35366
\(927\) 7.75534 0.254719
\(928\) 0.741706 0.0243477
\(929\) −35.0089 −1.14860 −0.574302 0.818644i \(-0.694726\pi\)
−0.574302 + 0.818644i \(0.694726\pi\)
\(930\) 0.405543 0.0132983
\(931\) −0.649997 −0.0213028
\(932\) 27.7185 0.907948
\(933\) −1.79386 −0.0587283
\(934\) −29.7574 −0.973693
\(935\) 26.4077 0.863625
\(936\) 11.6980 0.382361
\(937\) 3.16836 0.103506 0.0517529 0.998660i \(-0.483519\pi\)
0.0517529 + 0.998660i \(0.483519\pi\)
\(938\) −6.50275 −0.212322
\(939\) −12.7382 −0.415696
\(940\) 8.47916 0.276560
\(941\) −50.2110 −1.63683 −0.818417 0.574625i \(-0.805148\pi\)
−0.818417 + 0.574625i \(0.805148\pi\)
\(942\) −4.63389 −0.150980
\(943\) −16.8179 −0.547665
\(944\) −0.936742 −0.0304884
\(945\) 3.35669 0.109193
\(946\) −46.3322 −1.50639
\(947\) 5.39318 0.175255 0.0876274 0.996153i \(-0.472072\pi\)
0.0876274 + 0.996153i \(0.472072\pi\)
\(948\) 6.66830 0.216576
\(949\) 49.3006 1.60036
\(950\) −2.08265 −0.0675701
\(951\) −9.34800 −0.303130
\(952\) 4.03673 0.130831
\(953\) −28.4611 −0.921945 −0.460972 0.887414i \(-0.652499\pi\)
−0.460972 + 0.887414i \(0.652499\pi\)
\(954\) −27.7023 −0.896894
\(955\) 14.5205 0.469872
\(956\) 21.6785 0.701134
\(957\) −1.55974 −0.0504194
\(958\) −23.4244 −0.756807
\(959\) −1.63537 −0.0528090
\(960\) 0.577304 0.0186324
\(961\) −30.5065 −0.984081
\(962\) −23.6922 −0.763869
\(963\) −36.0216 −1.16078
\(964\) −1.63500 −0.0526597
\(965\) 1.17843 0.0379350
\(966\) −0.946788 −0.0304624
\(967\) 21.9445 0.705686 0.352843 0.935682i \(-0.385215\pi\)
0.352843 + 0.935682i \(0.385215\pi\)
\(968\) −12.8296 −0.412360
\(969\) −1.13033 −0.0363113
\(970\) 23.7862 0.763728
\(971\) 54.2138 1.73980 0.869901 0.493226i \(-0.164182\pi\)
0.869901 + 0.493226i \(0.164182\pi\)
\(972\) 10.6868 0.342778
\(973\) −3.83022 −0.122791
\(974\) 29.0791 0.931753
\(975\) −5.73707 −0.183733
\(976\) −7.74852 −0.248024
\(977\) −28.2083 −0.902463 −0.451231 0.892407i \(-0.649015\pi\)
−0.451231 + 0.892407i \(0.649015\pi\)
\(978\) −4.04061 −0.129204
\(979\) 75.8824 2.42521
\(980\) 1.34011 0.0428084
\(981\) −31.5279 −1.00661
\(982\) 2.65854 0.0848376
\(983\) 7.99127 0.254882 0.127441 0.991846i \(-0.459324\pi\)
0.127441 + 0.991846i \(0.459324\pi\)
\(984\) −3.29642 −0.105086
\(985\) 12.5755 0.400689
\(986\) 2.99407 0.0953506
\(987\) −2.72567 −0.0867591
\(988\) −2.70168 −0.0859519
\(989\) −20.8600 −0.663309
\(990\) 18.4115 0.585157
\(991\) 19.3967 0.616156 0.308078 0.951361i \(-0.400314\pi\)
0.308078 + 0.951361i \(0.400314\pi\)
\(992\) 0.702478 0.0223037
\(993\) 4.95790 0.157334
\(994\) −0.0975448 −0.00309393
\(995\) 17.4919 0.554529
\(996\) −6.69543 −0.212153
\(997\) 33.4010 1.05782 0.528911 0.848677i \(-0.322601\pi\)
0.528911 + 0.848677i \(0.322601\pi\)
\(998\) −3.77022 −0.119344
\(999\) −14.2775 −0.451721
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 \(a_p\))