Properties

Label 8002.2.a.e.1.14
Level 8002
Weight 2
Character 8002.1
Self dual Yes
Analytic conductor 63.896
Analytic rank 0
Dimension 77
CM No

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Newspace parameters

Level: \( N \) = \( 8002 = 2 \cdot 4001 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8002.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.8962916974\)
Analytic rank: \(0\)
Dimension: \(77\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.14
Character \(\chi\) = 8002.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} -2.17233 q^{3} +1.00000 q^{4} -1.31184 q^{5} +2.17233 q^{6} -2.50290 q^{7} -1.00000 q^{8} +1.71901 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -2.17233 q^{3} +1.00000 q^{4} -1.31184 q^{5} +2.17233 q^{6} -2.50290 q^{7} -1.00000 q^{8} +1.71901 q^{9} +1.31184 q^{10} -0.100565 q^{11} -2.17233 q^{12} +2.06885 q^{13} +2.50290 q^{14} +2.84976 q^{15} +1.00000 q^{16} -2.01258 q^{17} -1.71901 q^{18} +4.95546 q^{19} -1.31184 q^{20} +5.43713 q^{21} +0.100565 q^{22} +5.18712 q^{23} +2.17233 q^{24} -3.27907 q^{25} -2.06885 q^{26} +2.78273 q^{27} -2.50290 q^{28} +9.97044 q^{29} -2.84976 q^{30} -7.91975 q^{31} -1.00000 q^{32} +0.218460 q^{33} +2.01258 q^{34} +3.28342 q^{35} +1.71901 q^{36} +3.73621 q^{37} -4.95546 q^{38} -4.49422 q^{39} +1.31184 q^{40} +3.49399 q^{41} -5.43713 q^{42} +7.18482 q^{43} -0.100565 q^{44} -2.25507 q^{45} -5.18712 q^{46} -6.40829 q^{47} -2.17233 q^{48} -0.735476 q^{49} +3.27907 q^{50} +4.37198 q^{51} +2.06885 q^{52} -2.04402 q^{53} -2.78273 q^{54} +0.131926 q^{55} +2.50290 q^{56} -10.7649 q^{57} -9.97044 q^{58} -0.710808 q^{59} +2.84976 q^{60} -0.711142 q^{61} +7.91975 q^{62} -4.30252 q^{63} +1.00000 q^{64} -2.71401 q^{65} -0.218460 q^{66} +2.07100 q^{67} -2.01258 q^{68} -11.2681 q^{69} -3.28342 q^{70} -12.5268 q^{71} -1.71901 q^{72} -4.08400 q^{73} -3.73621 q^{74} +7.12321 q^{75} +4.95546 q^{76} +0.251705 q^{77} +4.49422 q^{78} +2.72361 q^{79} -1.31184 q^{80} -11.2020 q^{81} -3.49399 q^{82} +7.12661 q^{83} +5.43713 q^{84} +2.64019 q^{85} -7.18482 q^{86} -21.6591 q^{87} +0.100565 q^{88} -9.67029 q^{89} +2.25507 q^{90} -5.17813 q^{91} +5.18712 q^{92} +17.2043 q^{93} +6.40829 q^{94} -6.50079 q^{95} +2.17233 q^{96} +13.5076 q^{97} +0.735476 q^{98} -0.172872 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 77q - 77q^{2} + 10q^{3} + 77q^{4} + 18q^{5} - 10q^{6} + 21q^{7} - 77q^{8} + 71q^{9} + O(q^{10}) \) \( 77q - 77q^{2} + 10q^{3} + 77q^{4} + 18q^{5} - 10q^{6} + 21q^{7} - 77q^{8} + 71q^{9} - 18q^{10} + 30q^{11} + 10q^{12} - 2q^{13} - 21q^{14} + 21q^{15} + 77q^{16} + 60q^{17} - 71q^{18} - 3q^{19} + 18q^{20} + 10q^{21} - 30q^{22} + 53q^{23} - 10q^{24} + 59q^{25} + 2q^{26} + 43q^{27} + 21q^{28} + 30q^{29} - 21q^{30} + 22q^{31} - 77q^{32} + 31q^{33} - 60q^{34} + 41q^{35} + 71q^{36} - 3q^{37} + 3q^{38} + 44q^{39} - 18q^{40} + 48q^{41} - 10q^{42} + 21q^{43} + 30q^{44} + 33q^{45} - 53q^{46} + 107q^{47} + 10q^{48} + 24q^{49} - 59q^{50} + 18q^{51} - 2q^{52} + 42q^{53} - 43q^{54} + 49q^{55} - 21q^{56} + 32q^{57} - 30q^{58} + 42q^{59} + 21q^{60} - 31q^{61} - 22q^{62} + 109q^{63} + 77q^{64} + 39q^{65} - 31q^{66} - q^{67} + 60q^{68} - 33q^{69} - 41q^{70} + 58q^{71} - 71q^{72} + 35q^{73} + 3q^{74} + 34q^{75} - 3q^{76} + 86q^{77} - 44q^{78} + 25q^{79} + 18q^{80} + 53q^{81} - 48q^{82} + 107q^{83} + 10q^{84} + 21q^{85} - 21q^{86} + 100q^{87} - 30q^{88} + 34q^{89} - 33q^{90} - 51q^{91} + 53q^{92} + 48q^{93} - 107q^{94} + 118q^{95} - 10q^{96} - 13q^{97} - 24q^{98} + 63q^{99} + O(q^{100}) \)

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
\(3\) −2.17233 −1.25419 −0.627097 0.778941i \(-0.715757\pi\)
−0.627097 + 0.778941i \(0.715757\pi\)
\(4\) 1.00000 0.500000
\(5\) −1.31184 −0.586674 −0.293337 0.956009i \(-0.594766\pi\)
−0.293337 + 0.956009i \(0.594766\pi\)
\(6\) 2.17233 0.886849
\(7\) −2.50290 −0.946008 −0.473004 0.881060i \(-0.656830\pi\)
−0.473004 + 0.881060i \(0.656830\pi\)
\(8\) −1.00000 −0.353553
\(9\) 1.71901 0.573003
\(10\) 1.31184 0.414841
\(11\) −0.100565 −0.0303215 −0.0151608 0.999885i \(-0.504826\pi\)
−0.0151608 + 0.999885i \(0.504826\pi\)
\(12\) −2.17233 −0.627097
\(13\) 2.06885 0.573796 0.286898 0.957961i \(-0.407376\pi\)
0.286898 + 0.957961i \(0.407376\pi\)
\(14\) 2.50290 0.668929
\(15\) 2.84976 0.735804
\(16\) 1.00000 0.250000
\(17\) −2.01258 −0.488122 −0.244061 0.969760i \(-0.578480\pi\)
−0.244061 + 0.969760i \(0.578480\pi\)
\(18\) −1.71901 −0.405175
\(19\) 4.95546 1.13686 0.568430 0.822731i \(-0.307551\pi\)
0.568430 + 0.822731i \(0.307551\pi\)
\(20\) −1.31184 −0.293337
\(21\) 5.43713 1.18648
\(22\) 0.100565 0.0214405
\(23\) 5.18712 1.08159 0.540795 0.841155i \(-0.318124\pi\)
0.540795 + 0.841155i \(0.318124\pi\)
\(24\) 2.17233 0.443425
\(25\) −3.27907 −0.655813
\(26\) −2.06885 −0.405735
\(27\) 2.78273 0.535537
\(28\) −2.50290 −0.473004
\(29\) 9.97044 1.85146 0.925732 0.378180i \(-0.123450\pi\)
0.925732 + 0.378180i \(0.123450\pi\)
\(30\) −2.84976 −0.520292
\(31\) −7.91975 −1.42243 −0.711215 0.702975i \(-0.751855\pi\)
−0.711215 + 0.702975i \(0.751855\pi\)
\(32\) −1.00000 −0.176777
\(33\) 0.218460 0.0380291
\(34\) 2.01258 0.345155
\(35\) 3.28342 0.554999
\(36\) 1.71901 0.286502
\(37\) 3.73621 0.614229 0.307114 0.951673i \(-0.400637\pi\)
0.307114 + 0.951673i \(0.400637\pi\)
\(38\) −4.95546 −0.803882
\(39\) −4.49422 −0.719652
\(40\) 1.31184 0.207421
\(41\) 3.49399 0.545670 0.272835 0.962061i \(-0.412039\pi\)
0.272835 + 0.962061i \(0.412039\pi\)
\(42\) −5.43713 −0.838967
\(43\) 7.18482 1.09568 0.547838 0.836585i \(-0.315451\pi\)
0.547838 + 0.836585i \(0.315451\pi\)
\(44\) −0.100565 −0.0151608
\(45\) −2.25507 −0.336166
\(46\) −5.18712 −0.764799
\(47\) −6.40829 −0.934745 −0.467372 0.884061i \(-0.654799\pi\)
−0.467372 + 0.884061i \(0.654799\pi\)
\(48\) −2.17233 −0.313549
\(49\) −0.735476 −0.105068
\(50\) 3.27907 0.463730
\(51\) 4.37198 0.612200
\(52\) 2.06885 0.286898
\(53\) −2.04402 −0.280768 −0.140384 0.990097i \(-0.544834\pi\)
−0.140384 + 0.990097i \(0.544834\pi\)
\(54\) −2.78273 −0.378682
\(55\) 0.131926 0.0177889
\(56\) 2.50290 0.334465
\(57\) −10.7649 −1.42584
\(58\) −9.97044 −1.30918
\(59\) −0.710808 −0.0925394 −0.0462697 0.998929i \(-0.514733\pi\)
−0.0462697 + 0.998929i \(0.514733\pi\)
\(60\) 2.84976 0.367902
\(61\) −0.711142 −0.0910524 −0.0455262 0.998963i \(-0.514496\pi\)
−0.0455262 + 0.998963i \(0.514496\pi\)
\(62\) 7.91975 1.00581
\(63\) −4.30252 −0.542066
\(64\) 1.00000 0.125000
\(65\) −2.71401 −0.336631
\(66\) −0.218460 −0.0268906
\(67\) 2.07100 0.253013 0.126507 0.991966i \(-0.459623\pi\)
0.126507 + 0.991966i \(0.459623\pi\)
\(68\) −2.01258 −0.244061
\(69\) −11.2681 −1.35652
\(70\) −3.28342 −0.392444
\(71\) −12.5268 −1.48666 −0.743331 0.668924i \(-0.766755\pi\)
−0.743331 + 0.668924i \(0.766755\pi\)
\(72\) −1.71901 −0.202587
\(73\) −4.08400 −0.477997 −0.238998 0.971020i \(-0.576819\pi\)
−0.238998 + 0.971020i \(0.576819\pi\)
\(74\) −3.73621 −0.434325
\(75\) 7.12321 0.822517
\(76\) 4.95546 0.568430
\(77\) 0.251705 0.0286844
\(78\) 4.49422 0.508871
\(79\) 2.72361 0.306430 0.153215 0.988193i \(-0.451037\pi\)
0.153215 + 0.988193i \(0.451037\pi\)
\(80\) −1.31184 −0.146669
\(81\) −11.2020 −1.24467
\(82\) −3.49399 −0.385847
\(83\) 7.12661 0.782247 0.391124 0.920338i \(-0.372087\pi\)
0.391124 + 0.920338i \(0.372087\pi\)
\(84\) 5.43713 0.593239
\(85\) 2.64019 0.286369
\(86\) −7.18482 −0.774759
\(87\) −21.6591 −2.32210
\(88\) 0.100565 0.0107203
\(89\) −9.67029 −1.02505 −0.512524 0.858673i \(-0.671290\pi\)
−0.512524 + 0.858673i \(0.671290\pi\)
\(90\) 2.25507 0.237706
\(91\) −5.17813 −0.542816
\(92\) 5.18712 0.540795
\(93\) 17.2043 1.78400
\(94\) 6.40829 0.660964
\(95\) −6.50079 −0.666967
\(96\) 2.17233 0.221712
\(97\) 13.5076 1.37149 0.685746 0.727841i \(-0.259476\pi\)
0.685746 + 0.727841i \(0.259476\pi\)
\(98\) 0.735476 0.0742943
\(99\) −0.172872 −0.0173743
\(100\) −3.27907 −0.327907
\(101\) −8.75991 −0.871644 −0.435822 0.900033i \(-0.643542\pi\)
−0.435822 + 0.900033i \(0.643542\pi\)
\(102\) −4.37198 −0.432891
\(103\) 10.1373 0.998862 0.499431 0.866354i \(-0.333542\pi\)
0.499431 + 0.866354i \(0.333542\pi\)
\(104\) −2.06885 −0.202868
\(105\) −7.13266 −0.696077
\(106\) 2.04402 0.198533
\(107\) 9.92879 0.959853 0.479926 0.877309i \(-0.340663\pi\)
0.479926 + 0.877309i \(0.340663\pi\)
\(108\) 2.78273 0.267768
\(109\) −16.1257 −1.54456 −0.772279 0.635284i \(-0.780883\pi\)
−0.772279 + 0.635284i \(0.780883\pi\)
\(110\) −0.131926 −0.0125786
\(111\) −8.11627 −0.770362
\(112\) −2.50290 −0.236502
\(113\) −11.7020 −1.10083 −0.550416 0.834891i \(-0.685531\pi\)
−0.550416 + 0.834891i \(0.685531\pi\)
\(114\) 10.7649 1.00822
\(115\) −6.80469 −0.634541
\(116\) 9.97044 0.925732
\(117\) 3.55638 0.328787
\(118\) 0.710808 0.0654352
\(119\) 5.03729 0.461768
\(120\) −2.84976 −0.260146
\(121\) −10.9899 −0.999081
\(122\) 0.711142 0.0643838
\(123\) −7.59010 −0.684376
\(124\) −7.91975 −0.711215
\(125\) 10.8608 0.971423
\(126\) 4.30252 0.383299
\(127\) −4.84397 −0.429833 −0.214917 0.976632i \(-0.568948\pi\)
−0.214917 + 0.976632i \(0.568948\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −15.6078 −1.37419
\(130\) 2.71401 0.238034
\(131\) 5.91413 0.516720 0.258360 0.966049i \(-0.416818\pi\)
0.258360 + 0.966049i \(0.416818\pi\)
\(132\) 0.218460 0.0190145
\(133\) −12.4030 −1.07548
\(134\) −2.07100 −0.178908
\(135\) −3.65051 −0.314186
\(136\) 2.01258 0.172577
\(137\) 13.2312 1.13041 0.565207 0.824949i \(-0.308796\pi\)
0.565207 + 0.824949i \(0.308796\pi\)
\(138\) 11.2681 0.959207
\(139\) −5.31410 −0.450736 −0.225368 0.974274i \(-0.572358\pi\)
−0.225368 + 0.974274i \(0.572358\pi\)
\(140\) 3.28342 0.277499
\(141\) 13.9209 1.17235
\(142\) 12.5268 1.05123
\(143\) −0.208054 −0.0173984
\(144\) 1.71901 0.143251
\(145\) −13.0797 −1.08621
\(146\) 4.08400 0.337995
\(147\) 1.59770 0.131776
\(148\) 3.73621 0.307114
\(149\) −4.04539 −0.331411 −0.165706 0.986175i \(-0.552990\pi\)
−0.165706 + 0.986175i \(0.552990\pi\)
\(150\) −7.12321 −0.581607
\(151\) 3.91908 0.318931 0.159465 0.987204i \(-0.449023\pi\)
0.159465 + 0.987204i \(0.449023\pi\)
\(152\) −4.95546 −0.401941
\(153\) −3.45964 −0.279696
\(154\) −0.251705 −0.0202829
\(155\) 10.3895 0.834503
\(156\) −4.49422 −0.359826
\(157\) 1.29450 0.103312 0.0516560 0.998665i \(-0.483550\pi\)
0.0516560 + 0.998665i \(0.483550\pi\)
\(158\) −2.72361 −0.216679
\(159\) 4.44028 0.352137
\(160\) 1.31184 0.103710
\(161\) −12.9829 −1.02319
\(162\) 11.2020 0.880115
\(163\) −5.00829 −0.392280 −0.196140 0.980576i \(-0.562841\pi\)
−0.196140 + 0.980576i \(0.562841\pi\)
\(164\) 3.49399 0.272835
\(165\) −0.286586 −0.0223107
\(166\) −7.12661 −0.553132
\(167\) 14.5968 1.12953 0.564765 0.825252i \(-0.308967\pi\)
0.564765 + 0.825252i \(0.308967\pi\)
\(168\) −5.43713 −0.419483
\(169\) −8.71986 −0.670758
\(170\) −2.64019 −0.202493
\(171\) 8.51849 0.651425
\(172\) 7.18482 0.547838
\(173\) −18.7254 −1.42367 −0.711833 0.702348i \(-0.752135\pi\)
−0.711833 + 0.702348i \(0.752135\pi\)
\(174\) 21.6591 1.64197
\(175\) 8.20718 0.620405
\(176\) −0.100565 −0.00758038
\(177\) 1.54411 0.116062
\(178\) 9.67029 0.724819
\(179\) 16.4101 1.22655 0.613276 0.789869i \(-0.289851\pi\)
0.613276 + 0.789869i \(0.289851\pi\)
\(180\) −2.25507 −0.168083
\(181\) 16.1897 1.20337 0.601686 0.798732i \(-0.294496\pi\)
0.601686 + 0.798732i \(0.294496\pi\)
\(182\) 5.17813 0.383829
\(183\) 1.54483 0.114197
\(184\) −5.18712 −0.382400
\(185\) −4.90132 −0.360352
\(186\) −17.2043 −1.26148
\(187\) 0.202395 0.0148006
\(188\) −6.40829 −0.467372
\(189\) −6.96491 −0.506622
\(190\) 6.50079 0.471617
\(191\) −24.9052 −1.80208 −0.901039 0.433738i \(-0.857194\pi\)
−0.901039 + 0.433738i \(0.857194\pi\)
\(192\) −2.17233 −0.156774
\(193\) −16.9546 −1.22042 −0.610208 0.792241i \(-0.708914\pi\)
−0.610208 + 0.792241i \(0.708914\pi\)
\(194\) −13.5076 −0.969791
\(195\) 5.89572 0.422201
\(196\) −0.735476 −0.0525340
\(197\) 19.7851 1.40963 0.704815 0.709391i \(-0.251030\pi\)
0.704815 + 0.709391i \(0.251030\pi\)
\(198\) 0.172872 0.0122855
\(199\) −10.1142 −0.716979 −0.358490 0.933534i \(-0.616708\pi\)
−0.358490 + 0.933534i \(0.616708\pi\)
\(200\) 3.27907 0.231865
\(201\) −4.49890 −0.317328
\(202\) 8.75991 0.616345
\(203\) −24.9550 −1.75150
\(204\) 4.37198 0.306100
\(205\) −4.58357 −0.320131
\(206\) −10.1373 −0.706302
\(207\) 8.91671 0.619754
\(208\) 2.06885 0.143449
\(209\) −0.498346 −0.0344713
\(210\) 7.13266 0.492200
\(211\) −25.2032 −1.73506 −0.867532 0.497382i \(-0.834295\pi\)
−0.867532 + 0.497382i \(0.834295\pi\)
\(212\) −2.04402 −0.140384
\(213\) 27.2124 1.86456
\(214\) −9.92879 −0.678718
\(215\) −9.42537 −0.642805
\(216\) −2.78273 −0.189341
\(217\) 19.8224 1.34563
\(218\) 16.1257 1.09217
\(219\) 8.87180 0.599501
\(220\) 0.131926 0.00889443
\(221\) −4.16373 −0.280083
\(222\) 8.11627 0.544728
\(223\) 14.7802 0.989757 0.494879 0.868962i \(-0.335213\pi\)
0.494879 + 0.868962i \(0.335213\pi\)
\(224\) 2.50290 0.167232
\(225\) −5.63675 −0.375783
\(226\) 11.7020 0.778405
\(227\) −10.1598 −0.674330 −0.337165 0.941446i \(-0.609468\pi\)
−0.337165 + 0.941446i \(0.609468\pi\)
\(228\) −10.7649 −0.712922
\(229\) 19.5203 1.28994 0.644970 0.764208i \(-0.276870\pi\)
0.644970 + 0.764208i \(0.276870\pi\)
\(230\) 6.80469 0.448688
\(231\) −0.546785 −0.0359758
\(232\) −9.97044 −0.654592
\(233\) −9.34433 −0.612168 −0.306084 0.952005i \(-0.599019\pi\)
−0.306084 + 0.952005i \(0.599019\pi\)
\(234\) −3.55638 −0.232488
\(235\) 8.40667 0.548391
\(236\) −0.710808 −0.0462697
\(237\) −5.91658 −0.384323
\(238\) −5.03729 −0.326519
\(239\) 20.5513 1.32935 0.664676 0.747132i \(-0.268570\pi\)
0.664676 + 0.747132i \(0.268570\pi\)
\(240\) 2.84976 0.183951
\(241\) 6.41466 0.413204 0.206602 0.978425i \(-0.433759\pi\)
0.206602 + 0.978425i \(0.433759\pi\)
\(242\) 10.9899 0.706457
\(243\) 15.9863 1.02552
\(244\) −0.711142 −0.0455262
\(245\) 0.964830 0.0616407
\(246\) 7.59010 0.483927
\(247\) 10.2521 0.652326
\(248\) 7.91975 0.502905
\(249\) −15.4813 −0.981090
\(250\) −10.8608 −0.686900
\(251\) 10.7601 0.679170 0.339585 0.940575i \(-0.389713\pi\)
0.339585 + 0.940575i \(0.389713\pi\)
\(252\) −4.30252 −0.271033
\(253\) −0.521643 −0.0327954
\(254\) 4.84397 0.303938
\(255\) −5.73536 −0.359162
\(256\) 1.00000 0.0625000
\(257\) 1.29400 0.0807178 0.0403589 0.999185i \(-0.487150\pi\)
0.0403589 + 0.999185i \(0.487150\pi\)
\(258\) 15.6078 0.971699
\(259\) −9.35137 −0.581066
\(260\) −2.71401 −0.168316
\(261\) 17.1393 1.06090
\(262\) −5.91413 −0.365376
\(263\) −7.04882 −0.434649 −0.217324 0.976099i \(-0.569733\pi\)
−0.217324 + 0.976099i \(0.569733\pi\)
\(264\) −0.218460 −0.0134453
\(265\) 2.68143 0.164719
\(266\) 12.4030 0.760479
\(267\) 21.0070 1.28561
\(268\) 2.07100 0.126507
\(269\) 26.9814 1.64509 0.822543 0.568702i \(-0.192554\pi\)
0.822543 + 0.568702i \(0.192554\pi\)
\(270\) 3.65051 0.222163
\(271\) −1.38607 −0.0841978 −0.0420989 0.999113i \(-0.513404\pi\)
−0.0420989 + 0.999113i \(0.513404\pi\)
\(272\) −2.01258 −0.122031
\(273\) 11.2486 0.680797
\(274\) −13.2312 −0.799324
\(275\) 0.329759 0.0198852
\(276\) −11.2681 −0.678262
\(277\) −11.3658 −0.682905 −0.341453 0.939899i \(-0.610919\pi\)
−0.341453 + 0.939899i \(0.610919\pi\)
\(278\) 5.31410 0.318719
\(279\) −13.6141 −0.815057
\(280\) −3.28342 −0.196222
\(281\) 9.12180 0.544161 0.272080 0.962275i \(-0.412288\pi\)
0.272080 + 0.962275i \(0.412288\pi\)
\(282\) −13.9209 −0.828978
\(283\) 1.86684 0.110972 0.0554860 0.998459i \(-0.482329\pi\)
0.0554860 + 0.998459i \(0.482329\pi\)
\(284\) −12.5268 −0.743331
\(285\) 14.1219 0.836506
\(286\) 0.208054 0.0123025
\(287\) −8.74513 −0.516208
\(288\) −1.71901 −0.101294
\(289\) −12.9495 −0.761737
\(290\) 13.0797 0.768064
\(291\) −29.3430 −1.72012
\(292\) −4.08400 −0.238998
\(293\) 5.28826 0.308943 0.154472 0.987997i \(-0.450632\pi\)
0.154472 + 0.987997i \(0.450632\pi\)
\(294\) −1.59770 −0.0931795
\(295\) 0.932469 0.0542905
\(296\) −3.73621 −0.217163
\(297\) −0.279845 −0.0162383
\(298\) 4.04539 0.234343
\(299\) 10.7314 0.620612
\(300\) 7.12321 0.411259
\(301\) −17.9829 −1.03652
\(302\) −3.91908 −0.225518
\(303\) 19.0294 1.09321
\(304\) 4.95546 0.284215
\(305\) 0.932907 0.0534181
\(306\) 3.45964 0.197775
\(307\) 27.5283 1.57113 0.785563 0.618782i \(-0.212373\pi\)
0.785563 + 0.618782i \(0.212373\pi\)
\(308\) 0.251705 0.0143422
\(309\) −22.0216 −1.25277
\(310\) −10.3895 −0.590083
\(311\) 3.05641 0.173313 0.0866566 0.996238i \(-0.472382\pi\)
0.0866566 + 0.996238i \(0.472382\pi\)
\(312\) 4.49422 0.254435
\(313\) −21.5109 −1.21587 −0.607933 0.793988i \(-0.708001\pi\)
−0.607933 + 0.793988i \(0.708001\pi\)
\(314\) −1.29450 −0.0730526
\(315\) 5.64423 0.318016
\(316\) 2.72361 0.153215
\(317\) −5.45734 −0.306515 −0.153257 0.988186i \(-0.548976\pi\)
−0.153257 + 0.988186i \(0.548976\pi\)
\(318\) −4.44028 −0.248999
\(319\) −1.00268 −0.0561392
\(320\) −1.31184 −0.0733343
\(321\) −21.5686 −1.20384
\(322\) 12.9829 0.723506
\(323\) −9.97326 −0.554927
\(324\) −11.2020 −0.622335
\(325\) −6.78390 −0.376303
\(326\) 5.00829 0.277384
\(327\) 35.0302 1.93718
\(328\) −3.49399 −0.192923
\(329\) 16.0393 0.884276
\(330\) 0.286586 0.0157760
\(331\) −10.4352 −0.573569 −0.286785 0.957995i \(-0.592586\pi\)
−0.286785 + 0.957995i \(0.592586\pi\)
\(332\) 7.12661 0.391124
\(333\) 6.42258 0.351955
\(334\) −14.5968 −0.798699
\(335\) −2.71683 −0.148437
\(336\) 5.43713 0.296620
\(337\) 28.2649 1.53969 0.769844 0.638233i \(-0.220334\pi\)
0.769844 + 0.638233i \(0.220334\pi\)
\(338\) 8.71986 0.474298
\(339\) 25.4206 1.38066
\(340\) 2.64019 0.143184
\(341\) 0.796450 0.0431302
\(342\) −8.51849 −0.460627
\(343\) 19.3611 1.04540
\(344\) −7.18482 −0.387380
\(345\) 14.7820 0.795837
\(346\) 18.7254 1.00668
\(347\) 4.29931 0.230799 0.115400 0.993319i \(-0.463185\pi\)
0.115400 + 0.993319i \(0.463185\pi\)
\(348\) −21.6591 −1.16105
\(349\) −15.7538 −0.843283 −0.421642 0.906763i \(-0.638546\pi\)
−0.421642 + 0.906763i \(0.638546\pi\)
\(350\) −8.20718 −0.438692
\(351\) 5.75706 0.307289
\(352\) 0.100565 0.00536014
\(353\) −32.0369 −1.70515 −0.852577 0.522602i \(-0.824961\pi\)
−0.852577 + 0.522602i \(0.824961\pi\)
\(354\) −1.54411 −0.0820685
\(355\) 16.4333 0.872187
\(356\) −9.67029 −0.512524
\(357\) −10.9426 −0.579146
\(358\) −16.4101 −0.867303
\(359\) −25.5931 −1.35075 −0.675377 0.737472i \(-0.736019\pi\)
−0.675377 + 0.737472i \(0.736019\pi\)
\(360\) 2.25507 0.118853
\(361\) 5.55659 0.292452
\(362\) −16.1897 −0.850913
\(363\) 23.8736 1.25304
\(364\) −5.17813 −0.271408
\(365\) 5.35758 0.280428
\(366\) −1.54483 −0.0807497
\(367\) −26.2220 −1.36878 −0.684390 0.729116i \(-0.739931\pi\)
−0.684390 + 0.729116i \(0.739931\pi\)
\(368\) 5.18712 0.270397
\(369\) 6.00621 0.312671
\(370\) 4.90132 0.254808
\(371\) 5.11598 0.265609
\(372\) 17.2043 0.892002
\(373\) 36.7040 1.90046 0.950231 0.311546i \(-0.100847\pi\)
0.950231 + 0.311546i \(0.100847\pi\)
\(374\) −0.202395 −0.0104656
\(375\) −23.5933 −1.21835
\(376\) 6.40829 0.330482
\(377\) 20.6274 1.06236
\(378\) 6.96491 0.358236
\(379\) −29.0002 −1.48964 −0.744821 0.667265i \(-0.767465\pi\)
−0.744821 + 0.667265i \(0.767465\pi\)
\(380\) −6.50079 −0.333484
\(381\) 10.5227 0.539094
\(382\) 24.9052 1.27426
\(383\) 25.2690 1.29118 0.645592 0.763683i \(-0.276611\pi\)
0.645592 + 0.763683i \(0.276611\pi\)
\(384\) 2.17233 0.110856
\(385\) −0.330197 −0.0168284
\(386\) 16.9546 0.862964
\(387\) 12.3508 0.627826
\(388\) 13.5076 0.685746
\(389\) −6.33010 −0.320949 −0.160474 0.987040i \(-0.551302\pi\)
−0.160474 + 0.987040i \(0.551302\pi\)
\(390\) −5.89572 −0.298541
\(391\) −10.4395 −0.527948
\(392\) 0.735476 0.0371471
\(393\) −12.8474 −0.648067
\(394\) −19.7851 −0.996759
\(395\) −3.57296 −0.179775
\(396\) −0.172872 −0.00868716
\(397\) −13.9127 −0.698256 −0.349128 0.937075i \(-0.613522\pi\)
−0.349128 + 0.937075i \(0.613522\pi\)
\(398\) 10.1142 0.506981
\(399\) 26.9435 1.34886
\(400\) −3.27907 −0.163953
\(401\) −32.7694 −1.63642 −0.818212 0.574916i \(-0.805035\pi\)
−0.818212 + 0.574916i \(0.805035\pi\)
\(402\) 4.49890 0.224385
\(403\) −16.3848 −0.816184
\(404\) −8.75991 −0.435822
\(405\) 14.6953 0.730216
\(406\) 24.9550 1.23850
\(407\) −0.375732 −0.0186243
\(408\) −4.37198 −0.216445
\(409\) −30.9075 −1.52828 −0.764138 0.645053i \(-0.776835\pi\)
−0.764138 + 0.645053i \(0.776835\pi\)
\(410\) 4.58357 0.226367
\(411\) −28.7424 −1.41776
\(412\) 10.1373 0.499431
\(413\) 1.77908 0.0875430
\(414\) −8.91671 −0.438232
\(415\) −9.34900 −0.458924
\(416\) −2.06885 −0.101434
\(417\) 11.5440 0.565311
\(418\) 0.498346 0.0243749
\(419\) 34.5512 1.68794 0.843968 0.536394i \(-0.180214\pi\)
0.843968 + 0.536394i \(0.180214\pi\)
\(420\) −7.13266 −0.348038
\(421\) 10.0270 0.488687 0.244344 0.969689i \(-0.421428\pi\)
0.244344 + 0.969689i \(0.421428\pi\)
\(422\) 25.2032 1.22687
\(423\) −11.0159 −0.535612
\(424\) 2.04402 0.0992663
\(425\) 6.59938 0.320117
\(426\) −27.2124 −1.31845
\(427\) 1.77992 0.0861363
\(428\) 9.92879 0.479926
\(429\) 0.451962 0.0218209
\(430\) 9.42537 0.454532
\(431\) 12.7690 0.615062 0.307531 0.951538i \(-0.400497\pi\)
0.307531 + 0.951538i \(0.400497\pi\)
\(432\) 2.78273 0.133884
\(433\) 7.62871 0.366612 0.183306 0.983056i \(-0.441320\pi\)
0.183306 + 0.983056i \(0.441320\pi\)
\(434\) −19.8224 −0.951504
\(435\) 28.4133 1.36231
\(436\) −16.1257 −0.772279
\(437\) 25.7046 1.22962
\(438\) −8.87180 −0.423911
\(439\) −0.892723 −0.0426073 −0.0213037 0.999773i \(-0.506782\pi\)
−0.0213037 + 0.999773i \(0.506782\pi\)
\(440\) −0.131926 −0.00628931
\(441\) −1.26429 −0.0602043
\(442\) 4.16373 0.198048
\(443\) 25.6792 1.22005 0.610027 0.792380i \(-0.291158\pi\)
0.610027 + 0.792380i \(0.291158\pi\)
\(444\) −8.11627 −0.385181
\(445\) 12.6859 0.601370
\(446\) −14.7802 −0.699864
\(447\) 8.78791 0.415654
\(448\) −2.50290 −0.118251
\(449\) 26.4059 1.24617 0.623087 0.782153i \(-0.285878\pi\)
0.623087 + 0.782153i \(0.285878\pi\)
\(450\) 5.63675 0.265719
\(451\) −0.351374 −0.0165455
\(452\) −11.7020 −0.550416
\(453\) −8.51354 −0.400001
\(454\) 10.1598 0.476823
\(455\) 6.79290 0.318456
\(456\) 10.7649 0.504112
\(457\) −16.0306 −0.749880 −0.374940 0.927049i \(-0.622337\pi\)
−0.374940 + 0.927049i \(0.622337\pi\)
\(458\) −19.5203 −0.912126
\(459\) −5.60047 −0.261407
\(460\) −6.80469 −0.317270
\(461\) 19.3403 0.900767 0.450383 0.892835i \(-0.351287\pi\)
0.450383 + 0.892835i \(0.351287\pi\)
\(462\) 0.546785 0.0254387
\(463\) 2.26727 0.105369 0.0526844 0.998611i \(-0.483222\pi\)
0.0526844 + 0.998611i \(0.483222\pi\)
\(464\) 9.97044 0.462866
\(465\) −22.5694 −1.04663
\(466\) 9.34433 0.432868
\(467\) 24.3815 1.12824 0.564121 0.825692i \(-0.309215\pi\)
0.564121 + 0.825692i \(0.309215\pi\)
\(468\) 3.55638 0.164394
\(469\) −5.18352 −0.239353
\(470\) −8.40667 −0.387771
\(471\) −2.81207 −0.129573
\(472\) 0.710808 0.0327176
\(473\) −0.722542 −0.0332225
\(474\) 5.91658 0.271758
\(475\) −16.2493 −0.745568
\(476\) 5.03729 0.230884
\(477\) −3.51369 −0.160881
\(478\) −20.5513 −0.939994
\(479\) 23.3231 1.06566 0.532831 0.846222i \(-0.321128\pi\)
0.532831 + 0.846222i \(0.321128\pi\)
\(480\) −2.84976 −0.130073
\(481\) 7.72966 0.352442
\(482\) −6.41466 −0.292180
\(483\) 28.2030 1.28328
\(484\) −10.9899 −0.499540
\(485\) −17.7199 −0.804619
\(486\) −15.9863 −0.725153
\(487\) 11.4534 0.519005 0.259503 0.965742i \(-0.416441\pi\)
0.259503 + 0.965742i \(0.416441\pi\)
\(488\) 0.711142 0.0321919
\(489\) 10.8797 0.491995
\(490\) −0.964830 −0.0435866
\(491\) −18.5596 −0.837581 −0.418790 0.908083i \(-0.637546\pi\)
−0.418790 + 0.908083i \(0.637546\pi\)
\(492\) −7.59010 −0.342188
\(493\) −20.0663 −0.903741
\(494\) −10.2521 −0.461264
\(495\) 0.226782 0.0101931
\(496\) −7.91975 −0.355607
\(497\) 31.3535 1.40640
\(498\) 15.4813 0.693735
\(499\) 14.5750 0.652464 0.326232 0.945290i \(-0.394221\pi\)
0.326232 + 0.945290i \(0.394221\pi\)
\(500\) 10.8608 0.485712
\(501\) −31.7089 −1.41665
\(502\) −10.7601 −0.480246
\(503\) 35.3826 1.57763 0.788816 0.614629i \(-0.210694\pi\)
0.788816 + 0.614629i \(0.210694\pi\)
\(504\) 4.30252 0.191649
\(505\) 11.4916 0.511371
\(506\) 0.521643 0.0231899
\(507\) 18.9424 0.841261
\(508\) −4.84397 −0.214917
\(509\) 18.7107 0.829337 0.414669 0.909972i \(-0.363897\pi\)
0.414669 + 0.909972i \(0.363897\pi\)
\(510\) 5.73536 0.253966
\(511\) 10.2219 0.452189
\(512\) −1.00000 −0.0441942
\(513\) 13.7897 0.608831
\(514\) −1.29400 −0.0570761
\(515\) −13.2986 −0.586007
\(516\) −15.6078 −0.687095
\(517\) 0.644450 0.0283429
\(518\) 9.35137 0.410875
\(519\) 40.6777 1.78555
\(520\) 2.71401 0.119017
\(521\) −1.20896 −0.0529655 −0.0264827 0.999649i \(-0.508431\pi\)
−0.0264827 + 0.999649i \(0.508431\pi\)
\(522\) −17.1393 −0.750166
\(523\) 13.4025 0.586052 0.293026 0.956104i \(-0.405338\pi\)
0.293026 + 0.956104i \(0.405338\pi\)
\(524\) 5.91413 0.258360
\(525\) −17.8287 −0.778108
\(526\) 7.04882 0.307343
\(527\) 15.9391 0.694319
\(528\) 0.218460 0.00950726
\(529\) 3.90621 0.169835
\(530\) −2.68143 −0.116474
\(531\) −1.22189 −0.0530254
\(532\) −12.4030 −0.537740
\(533\) 7.22855 0.313103
\(534\) −21.0070 −0.909064
\(535\) −13.0250 −0.563121
\(536\) −2.07100 −0.0894538
\(537\) −35.6482 −1.53833
\(538\) −26.9814 −1.16325
\(539\) 0.0739632 0.00318582
\(540\) −3.65051 −0.157093
\(541\) −41.9329 −1.80284 −0.901418 0.432950i \(-0.857472\pi\)
−0.901418 + 0.432950i \(0.857472\pi\)
\(542\) 1.38607 0.0595369
\(543\) −35.1694 −1.50926
\(544\) 2.01258 0.0862886
\(545\) 21.1543 0.906153
\(546\) −11.2486 −0.481396
\(547\) −31.9661 −1.36677 −0.683385 0.730058i \(-0.739493\pi\)
−0.683385 + 0.730058i \(0.739493\pi\)
\(548\) 13.2312 0.565207
\(549\) −1.22246 −0.0521733
\(550\) −0.329759 −0.0140610
\(551\) 49.4081 2.10486
\(552\) 11.2681 0.479603
\(553\) −6.81694 −0.289886
\(554\) 11.3658 0.482887
\(555\) 10.6473 0.451952
\(556\) −5.31410 −0.225368
\(557\) 43.1997 1.83043 0.915215 0.402967i \(-0.132021\pi\)
0.915215 + 0.402967i \(0.132021\pi\)
\(558\) 13.6141 0.576332
\(559\) 14.8643 0.628694
\(560\) 3.28342 0.138750
\(561\) −0.439669 −0.0185628
\(562\) −9.12180 −0.384780
\(563\) −13.9123 −0.586332 −0.293166 0.956062i \(-0.594709\pi\)
−0.293166 + 0.956062i \(0.594709\pi\)
\(564\) 13.9209 0.586176
\(565\) 15.3512 0.645830
\(566\) −1.86684 −0.0784690
\(567\) 28.0376 1.17747
\(568\) 12.5268 0.525614
\(569\) −11.1738 −0.468430 −0.234215 0.972185i \(-0.575252\pi\)
−0.234215 + 0.972185i \(0.575252\pi\)
\(570\) −14.1219 −0.591499
\(571\) −14.9473 −0.625523 −0.312762 0.949832i \(-0.601254\pi\)
−0.312762 + 0.949832i \(0.601254\pi\)
\(572\) −0.208054 −0.00869918
\(573\) 54.1023 2.26016
\(574\) 8.74513 0.365015
\(575\) −17.0089 −0.709320
\(576\) 1.71901 0.0716254
\(577\) 27.2187 1.13313 0.566566 0.824017i \(-0.308272\pi\)
0.566566 + 0.824017i \(0.308272\pi\)
\(578\) 12.9495 0.538629
\(579\) 36.8309 1.53064
\(580\) −13.0797 −0.543103
\(581\) −17.8372 −0.740012
\(582\) 29.3430 1.21631
\(583\) 0.205557 0.00851330
\(584\) 4.08400 0.168997
\(585\) −4.66541 −0.192891
\(586\) −5.28826 −0.218456
\(587\) −10.4117 −0.429737 −0.214869 0.976643i \(-0.568932\pi\)
−0.214869 + 0.976643i \(0.568932\pi\)
\(588\) 1.59770 0.0658878
\(589\) −39.2460 −1.61710
\(590\) −0.932469 −0.0383892
\(591\) −42.9797 −1.76795
\(592\) 3.73621 0.153557
\(593\) −30.0513 −1.23406 −0.617030 0.786940i \(-0.711664\pi\)
−0.617030 + 0.786940i \(0.711664\pi\)
\(594\) 0.279845 0.0114822
\(595\) −6.60814 −0.270907
\(596\) −4.04539 −0.165706
\(597\) 21.9714 0.899231
\(598\) −10.7314 −0.438839
\(599\) 12.5523 0.512873 0.256436 0.966561i \(-0.417452\pi\)
0.256436 + 0.966561i \(0.417452\pi\)
\(600\) −7.12321 −0.290804
\(601\) −31.2086 −1.27303 −0.636513 0.771266i \(-0.719624\pi\)
−0.636513 + 0.771266i \(0.719624\pi\)
\(602\) 17.9829 0.732929
\(603\) 3.56008 0.144978
\(604\) 3.91908 0.159465
\(605\) 14.4170 0.586135
\(606\) −19.0294 −0.773017
\(607\) −24.8789 −1.00980 −0.504901 0.863177i \(-0.668471\pi\)
−0.504901 + 0.863177i \(0.668471\pi\)
\(608\) −4.95546 −0.200970
\(609\) 54.2106 2.19672
\(610\) −0.932907 −0.0377723
\(611\) −13.2578 −0.536353
\(612\) −3.45964 −0.139848
\(613\) 30.6685 1.23869 0.619345 0.785119i \(-0.287398\pi\)
0.619345 + 0.785119i \(0.287398\pi\)
\(614\) −27.5283 −1.11095
\(615\) 9.95703 0.401506
\(616\) −0.251705 −0.0101415
\(617\) 30.5353 1.22930 0.614651 0.788799i \(-0.289297\pi\)
0.614651 + 0.788799i \(0.289297\pi\)
\(618\) 22.0216 0.885840
\(619\) 44.7812 1.79991 0.899954 0.435986i \(-0.143600\pi\)
0.899954 + 0.435986i \(0.143600\pi\)
\(620\) 10.3895 0.417252
\(621\) 14.4344 0.579231
\(622\) −3.05641 −0.122551
\(623\) 24.2038 0.969705
\(624\) −4.49422 −0.179913
\(625\) 2.14760 0.0859039
\(626\) 21.5109 0.859747
\(627\) 1.08257 0.0432337
\(628\) 1.29450 0.0516560
\(629\) −7.51941 −0.299819
\(630\) −5.64423 −0.224871
\(631\) −30.4326 −1.21150 −0.605752 0.795653i \(-0.707128\pi\)
−0.605752 + 0.795653i \(0.707128\pi\)
\(632\) −2.72361 −0.108340
\(633\) 54.7497 2.17611
\(634\) 5.45734 0.216739
\(635\) 6.35454 0.252172
\(636\) 4.44028 0.176069
\(637\) −1.52159 −0.0602876
\(638\) 1.00268 0.0396964
\(639\) −21.5338 −0.851862
\(640\) 1.31184 0.0518552
\(641\) 33.3018 1.31534 0.657671 0.753306i \(-0.271542\pi\)
0.657671 + 0.753306i \(0.271542\pi\)
\(642\) 21.5686 0.851245
\(643\) −27.4330 −1.08185 −0.540926 0.841070i \(-0.681926\pi\)
−0.540926 + 0.841070i \(0.681926\pi\)
\(644\) −12.9829 −0.511596
\(645\) 20.4750 0.806202
\(646\) 9.97326 0.392393
\(647\) −26.7203 −1.05048 −0.525242 0.850953i \(-0.676025\pi\)
−0.525242 + 0.850953i \(0.676025\pi\)
\(648\) 11.2020 0.440057
\(649\) 0.0714825 0.00280593
\(650\) 6.78390 0.266086
\(651\) −43.0607 −1.68768
\(652\) −5.00829 −0.196140
\(653\) 17.2176 0.673776 0.336888 0.941545i \(-0.390626\pi\)
0.336888 + 0.941545i \(0.390626\pi\)
\(654\) −35.0302 −1.36979
\(655\) −7.75841 −0.303146
\(656\) 3.49399 0.136418
\(657\) −7.02044 −0.273894
\(658\) −16.0393 −0.625278
\(659\) 7.61250 0.296541 0.148270 0.988947i \(-0.452629\pi\)
0.148270 + 0.988947i \(0.452629\pi\)
\(660\) −0.286586 −0.0111553
\(661\) 12.9707 0.504502 0.252251 0.967662i \(-0.418829\pi\)
0.252251 + 0.967662i \(0.418829\pi\)
\(662\) 10.4352 0.405575
\(663\) 9.04498 0.351278
\(664\) −7.12661 −0.276566
\(665\) 16.2708 0.630956
\(666\) −6.42258 −0.248870
\(667\) 51.7179 2.00252
\(668\) 14.5968 0.564765
\(669\) −32.1075 −1.24135
\(670\) 2.71683 0.104960
\(671\) 0.0715160 0.00276084
\(672\) −5.43713 −0.209742
\(673\) 39.5644 1.52509 0.762547 0.646932i \(-0.223948\pi\)
0.762547 + 0.646932i \(0.223948\pi\)
\(674\) −28.2649 −1.08872
\(675\) −9.12476 −0.351212
\(676\) −8.71986 −0.335379
\(677\) 16.6832 0.641188 0.320594 0.947217i \(-0.396117\pi\)
0.320594 + 0.947217i \(0.396117\pi\)
\(678\) −25.4206 −0.976272
\(679\) −33.8083 −1.29744
\(680\) −2.64019 −0.101247
\(681\) 22.0704 0.845741
\(682\) −0.796450 −0.0304977
\(683\) 47.6884 1.82475 0.912373 0.409360i \(-0.134248\pi\)
0.912373 + 0.409360i \(0.134248\pi\)
\(684\) 8.51849 0.325712
\(685\) −17.3572 −0.663185
\(686\) −19.3611 −0.739212
\(687\) −42.4046 −1.61784
\(688\) 7.18482 0.273919
\(689\) −4.22877 −0.161103
\(690\) −14.7820 −0.562742
\(691\) 47.1497 1.79366 0.896829 0.442377i \(-0.145865\pi\)
0.896829 + 0.442377i \(0.145865\pi\)
\(692\) −18.7254 −0.711833
\(693\) 0.432683 0.0164363
\(694\) −4.29931 −0.163200
\(695\) 6.97127 0.264435
\(696\) 21.6591 0.820985
\(697\) −7.03194 −0.266354
\(698\) 15.7538 0.596291
\(699\) 20.2990 0.767777
\(700\) 8.20718 0.310202
\(701\) 18.2319 0.688610 0.344305 0.938858i \(-0.388115\pi\)
0.344305 + 0.938858i \(0.388115\pi\)
\(702\) −5.75706 −0.217286
\(703\) 18.5146 0.698292
\(704\) −0.100565 −0.00379019
\(705\) −18.2621 −0.687789
\(706\) 32.0369 1.20573
\(707\) 21.9252 0.824582
\(708\) 1.54411 0.0580312
\(709\) −30.6601 −1.15146 −0.575731 0.817639i \(-0.695283\pi\)
−0.575731 + 0.817639i \(0.695283\pi\)
\(710\) −16.4333 −0.616729
\(711\) 4.68192 0.175586
\(712\) 9.67029 0.362410
\(713\) −41.0807 −1.53848
\(714\) 10.9426 0.409518
\(715\) 0.272935 0.0102072
\(716\) 16.4101 0.613276
\(717\) −44.6441 −1.66727
\(718\) 25.5931 0.955128
\(719\) −6.05972 −0.225989 −0.112995 0.993596i \(-0.536044\pi\)
−0.112995 + 0.993596i \(0.536044\pi\)
\(720\) −2.25507 −0.0840416
\(721\) −25.3728 −0.944932
\(722\) −5.55659 −0.206795
\(723\) −13.9347 −0.518239
\(724\) 16.1897 0.601686
\(725\) −32.6937 −1.21421
\(726\) −23.8736 −0.886034
\(727\) 52.9498 1.96380 0.981901 0.189397i \(-0.0606534\pi\)
0.981901 + 0.189397i \(0.0606534\pi\)
\(728\) 5.17813 0.191914
\(729\) −1.12140 −0.0415332
\(730\) −5.35758 −0.198293
\(731\) −14.4600 −0.534823
\(732\) 1.54483 0.0570987
\(733\) −42.0710 −1.55393 −0.776965 0.629544i \(-0.783242\pi\)
−0.776965 + 0.629544i \(0.783242\pi\)
\(734\) 26.2220 0.967873
\(735\) −2.09593 −0.0773094
\(736\) −5.18712 −0.191200
\(737\) −0.208271 −0.00767175
\(738\) −6.00621 −0.221092
\(739\) 11.0290 0.405707 0.202853 0.979209i \(-0.434979\pi\)
0.202853 + 0.979209i \(0.434979\pi\)
\(740\) −4.90132 −0.180176
\(741\) −22.2709 −0.818144
\(742\) −5.11598 −0.187814
\(743\) 14.0240 0.514489 0.257244 0.966346i \(-0.417185\pi\)
0.257244 + 0.966346i \(0.417185\pi\)
\(744\) −17.2043 −0.630740
\(745\) 5.30692 0.194430
\(746\) −36.7040 −1.34383
\(747\) 12.2507 0.448230
\(748\) 0.202395 0.00740030
\(749\) −24.8508 −0.908029
\(750\) 23.5933 0.861506
\(751\) 34.0777 1.24351 0.621757 0.783210i \(-0.286419\pi\)
0.621757 + 0.783210i \(0.286419\pi\)
\(752\) −6.40829 −0.233686
\(753\) −23.3744 −0.851811
\(754\) −20.6274 −0.751204
\(755\) −5.14123 −0.187108
\(756\) −6.96491 −0.253311
\(757\) −23.6972 −0.861290 −0.430645 0.902521i \(-0.641714\pi\)
−0.430645 + 0.902521i \(0.641714\pi\)
\(758\) 29.0002 1.05334
\(759\) 1.13318 0.0411318
\(760\) 6.50079 0.235808
\(761\) 4.04853 0.146759 0.0733795 0.997304i \(-0.476622\pi\)
0.0733795 + 0.997304i \(0.476622\pi\)
\(762\) −10.5227 −0.381197
\(763\) 40.3610 1.46116
\(764\) −24.9052 −0.901039
\(765\) 4.53851 0.164090
\(766\) −25.2690 −0.913005
\(767\) −1.47056 −0.0530987
\(768\) −2.17233 −0.0783871
\(769\) 40.7296 1.46875 0.734374 0.678745i \(-0.237476\pi\)
0.734374 + 0.678745i \(0.237476\pi\)
\(770\) 0.330197 0.0118995
\(771\) −2.81100 −0.101236
\(772\) −16.9546 −0.610208
\(773\) −21.4110 −0.770100 −0.385050 0.922896i \(-0.625816\pi\)
−0.385050 + 0.922896i \(0.625816\pi\)
\(774\) −12.3508 −0.443940
\(775\) 25.9694 0.932848
\(776\) −13.5076 −0.484895
\(777\) 20.3142 0.728769
\(778\) 6.33010 0.226945
\(779\) 17.3143 0.620351
\(780\) 5.89572 0.211101
\(781\) 1.25976 0.0450778
\(782\) 10.4395 0.373315
\(783\) 27.7451 0.991527
\(784\) −0.735476 −0.0262670
\(785\) −1.69818 −0.0606105
\(786\) 12.8474 0.458253
\(787\) 25.0065 0.891385 0.445693 0.895186i \(-0.352957\pi\)
0.445693 + 0.895186i \(0.352957\pi\)
\(788\) 19.7851 0.704815
\(789\) 15.3123 0.545134
\(790\) 3.57296 0.127120
\(791\) 29.2890 1.04140
\(792\) 0.172872 0.00614275
\(793\) −1.47125 −0.0522455
\(794\) 13.9127 0.493742
\(795\) −5.82495 −0.206590
\(796\) −10.1142 −0.358490
\(797\) −34.9899 −1.23940 −0.619702 0.784837i \(-0.712747\pi\)
−0.619702 + 0.784837i \(0.712747\pi\)
\(798\) −26.9435 −0.953788
\(799\) 12.8972 0.456270
\(800\) 3.27907 0.115932
\(801\) −16.6233 −0.587356
\(802\) 32.7694 1.15713
\(803\) 0.410708 0.0144936
\(804\) −4.49890 −0.158664
\(805\) 17.0315 0.600281
\(806\) 16.3848 0.577130
\(807\) −58.6125 −2.06326
\(808\) 8.75991 0.308173
\(809\) −29.7270 −1.04515 −0.522573 0.852595i \(-0.675028\pi\)
−0.522573 + 0.852595i \(0.675028\pi\)
\(810\) −14.6953 −0.516341
\(811\) 21.0565 0.739395 0.369697 0.929152i \(-0.379461\pi\)
0.369697 + 0.929152i \(0.379461\pi\)
\(812\) −24.9550 −0.875751
\(813\) 3.01100 0.105600
\(814\) 0.375732 0.0131694
\(815\) 6.57010 0.230140
\(816\) 4.37198 0.153050
\(817\) 35.6041 1.24563
\(818\) 30.9075 1.08065
\(819\) −8.90126 −0.311035
\(820\) −4.58357 −0.160065
\(821\) 14.8753 0.519153 0.259577 0.965723i \(-0.416417\pi\)
0.259577 + 0.965723i \(0.416417\pi\)
\(822\) 28.7424 1.00251
\(823\) 37.0263 1.29066 0.645328 0.763906i \(-0.276721\pi\)
0.645328 + 0.763906i \(0.276721\pi\)
\(824\) −10.1373 −0.353151
\(825\) −0.716346 −0.0249400
\(826\) −1.77908 −0.0619023
\(827\) 34.3635 1.19493 0.597467 0.801893i \(-0.296174\pi\)
0.597467 + 0.801893i \(0.296174\pi\)
\(828\) 8.91671 0.309877
\(829\) −15.8069 −0.548996 −0.274498 0.961588i \(-0.588512\pi\)
−0.274498 + 0.961588i \(0.588512\pi\)
\(830\) 9.34900 0.324509
\(831\) 24.6903 0.856496
\(832\) 2.06885 0.0717245
\(833\) 1.48020 0.0512860
\(834\) −11.5440 −0.399735
\(835\) −19.1487 −0.662667
\(836\) −0.498346 −0.0172357
\(837\) −22.0385 −0.761763
\(838\) −34.5512 −1.19355
\(839\) 37.3168 1.28832 0.644159 0.764891i \(-0.277207\pi\)
0.644159 + 0.764891i \(0.277207\pi\)
\(840\) 7.13266 0.246100
\(841\) 70.4097 2.42792
\(842\) −10.0270 −0.345554
\(843\) −19.8155 −0.682483
\(844\) −25.2032 −0.867532
\(845\) 11.4391 0.393517
\(846\) 11.0159 0.378735
\(847\) 27.5066 0.945139
\(848\) −2.04402 −0.0701919
\(849\) −4.05538 −0.139180
\(850\) −6.59938 −0.226357
\(851\) 19.3802 0.664343
\(852\) 27.2124 0.932282
\(853\) −39.4222 −1.34979 −0.674895 0.737914i \(-0.735811\pi\)
−0.674895 + 0.737914i \(0.735811\pi\)
\(854\) −1.77992 −0.0609076
\(855\) −11.1749 −0.382174
\(856\) −9.92879 −0.339359
\(857\) −46.8985 −1.60202 −0.801012 0.598648i \(-0.795705\pi\)
−0.801012 + 0.598648i \(0.795705\pi\)
\(858\) −0.451962 −0.0154297
\(859\) 21.0160 0.717055 0.358528 0.933519i \(-0.383279\pi\)
0.358528 + 0.933519i \(0.383279\pi\)
\(860\) −9.42537 −0.321402
\(861\) 18.9973 0.647426
\(862\) −12.7690 −0.434914
\(863\) 1.99957 0.0680661 0.0340331 0.999421i \(-0.489165\pi\)
0.0340331 + 0.999421i \(0.489165\pi\)
\(864\) −2.78273 −0.0946704
\(865\) 24.5648 0.835229
\(866\) −7.62871 −0.259234
\(867\) 28.1306 0.955366
\(868\) 19.8224 0.672815
\(869\) −0.273900 −0.00929143
\(870\) −28.4133 −0.963302
\(871\) 4.28460 0.145178
\(872\) 16.1257 0.546084
\(873\) 23.2197 0.785869
\(874\) −25.7046 −0.869470
\(875\) −27.1836 −0.918975
\(876\) 8.87180 0.299750
\(877\) −29.4135 −0.993224 −0.496612 0.867973i \(-0.665423\pi\)
−0.496612 + 0.867973i \(0.665423\pi\)
\(878\) 0.892723 0.0301279
\(879\) −11.4878 −0.387475
\(880\) 0.131926 0.00444721
\(881\) 6.76250 0.227834 0.113917 0.993490i \(-0.463660\pi\)
0.113917 + 0.993490i \(0.463660\pi\)
\(882\) 1.26429 0.0425709
\(883\) −14.9701 −0.503782 −0.251891 0.967756i \(-0.581053\pi\)
−0.251891 + 0.967756i \(0.581053\pi\)
\(884\) −4.16373 −0.140041
\(885\) −2.02563 −0.0680908
\(886\) −25.6792 −0.862709
\(887\) −26.0458 −0.874534 −0.437267 0.899332i \(-0.644053\pi\)
−0.437267 + 0.899332i \(0.644053\pi\)
\(888\) 8.11627 0.272364
\(889\) 12.1240 0.406626
\(890\) −12.6859 −0.425233
\(891\) 1.12653 0.0377403
\(892\) 14.7802 0.494879
\(893\) −31.7560 −1.06267
\(894\) −8.78791 −0.293912
\(895\) −21.5275 −0.719587
\(896\) 2.50290 0.0836161
\(897\) −23.3121 −0.778368
\(898\) −26.4059 −0.881177
\(899\) −78.9634 −2.63358
\(900\) −5.63675 −0.187892
\(901\) 4.11375 0.137049
\(902\) 0.351374 0.0116995
\(903\) 39.0648 1.29999
\(904\) 11.7020 0.389203
\(905\) −21.2384 −0.705988
\(906\) 8.51354 0.282843
\(907\) 38.2589 1.27036 0.635182 0.772362i \(-0.280925\pi\)
0.635182 + 0.772362i \(0.280925\pi\)
\(908\) −10.1598 −0.337165
\(909\) −15.0584 −0.499455
\(910\) −6.79290 −0.225183
\(911\) 17.7130 0.586859 0.293430 0.955981i \(-0.405203\pi\)
0.293430 + 0.955981i \(0.405203\pi\)
\(912\) −10.7649 −0.356461
\(913\) −0.716688 −0.0237189
\(914\) 16.0306 0.530245
\(915\) −2.02658 −0.0669967
\(916\) 19.5203 0.644970
\(917\) −14.8025 −0.488821
\(918\) 5.60047 0.184843
\(919\) −58.4634 −1.92853 −0.964264 0.264942i \(-0.914647\pi\)
−0.964264 + 0.264942i \(0.914647\pi\)
\(920\) 6.80469 0.224344
\(921\) −59.8006 −1.97050
\(922\) −19.3403 −0.636938
\(923\) −25.9162 −0.853041
\(924\) −0.546785 −0.0179879
\(925\) −12.2513 −0.402819
\(926\) −2.26727 −0.0745070
\(927\) 17.4262 0.572351
\(928\) −9.97044 −0.327296
\(929\) 47.1093 1.54561 0.772803 0.634646i \(-0.218854\pi\)
0.772803 + 0.634646i \(0.218854\pi\)
\(930\) 22.5694 0.740078
\(931\) −3.64462 −0.119448
\(932\) −9.34433 −0.306084
\(933\) −6.63953 −0.217368
\(934\) −24.3815 −0.797788
\(935\) −0.265511 −0.00868313
\(936\) −3.55638 −0.116244
\(937\) 16.6377 0.543530 0.271765 0.962364i \(-0.412393\pi\)
0.271765 + 0.962364i \(0.412393\pi\)
\(938\) 5.18352 0.169248
\(939\) 46.7287 1.52493
\(940\) 8.40667 0.274195
\(941\) 46.3653 1.51146 0.755732 0.654881i \(-0.227281\pi\)
0.755732 + 0.654881i \(0.227281\pi\)
\(942\) 2.81207 0.0916222
\(943\) 18.1238 0.590191
\(944\) −0.710808 −0.0231348
\(945\) 9.13687 0.297222
\(946\) 0.722542 0.0234919
\(947\) 49.7566 1.61687 0.808436 0.588585i \(-0.200315\pi\)
0.808436 + 0.588585i \(0.200315\pi\)
\(948\) −5.91658 −0.192162
\(949\) −8.44920 −0.274273
\(950\) 16.2493 0.527196
\(951\) 11.8551 0.384429
\(952\) −5.03729 −0.163260
\(953\) −53.0218 −1.71754 −0.858772 0.512358i \(-0.828772\pi\)
−0.858772 + 0.512358i \(0.828772\pi\)
\(954\) 3.51369 0.113760
\(955\) 32.6718 1.05723
\(956\) 20.5513 0.664676
\(957\) 2.17815 0.0704094
\(958\) −23.3231 −0.753536
\(959\) −33.1163 −1.06938
\(960\) 2.84976 0.0919755
\(961\) 31.7225 1.02331
\(962\) −7.72966 −0.249214
\(963\) 17.0677 0.549999
\(964\) 6.41466 0.206602
\(965\) 22.2417 0.715987
\(966\) −28.2030 −0.907418
\(967\) −31.5421 −1.01433 −0.507163 0.861850i \(-0.669306\pi\)
−0.507163 + 0.861850i \(0.669306\pi\)
\(968\) 10.9899 0.353228
\(969\) 21.6652 0.695986
\(970\) 17.7199 0.568951
\(971\) 35.8122 1.14927 0.574634 0.818410i \(-0.305144\pi\)
0.574634 + 0.818410i \(0.305144\pi\)
\(972\) 15.9863 0.512761
\(973\) 13.3007 0.426400
\(974\) −11.4534 −0.366992
\(975\) 14.7369 0.471957
\(976\) −0.711142 −0.0227631
\(977\) −0.0185896 −0.000594735 0 −0.000297368 1.00000i \(-0.500095\pi\)
−0.000297368 1.00000i \(0.500095\pi\)
\(978\) −10.8797 −0.347893
\(979\) 0.972493 0.0310810
\(980\) 0.964830 0.0308203
\(981\) −27.7202 −0.885037
\(982\) 18.5596 0.592259
\(983\) 11.2924 0.360172 0.180086 0.983651i \(-0.442362\pi\)
0.180086 + 0.983651i \(0.442362\pi\)
\(984\) 7.59010 0.241964
\(985\) −25.9550 −0.826994
\(986\) 20.0663 0.639041
\(987\) −34.8427 −1.10905
\(988\) 10.2521 0.326163
\(989\) 37.2685 1.18507
\(990\) −0.226782 −0.00720759
\(991\) 20.6817 0.656974 0.328487 0.944508i \(-0.393461\pi\)
0.328487 + 0.944508i \(0.393461\pi\)
\(992\) 7.91975 0.251452
\(993\) 22.6686 0.719367
\(994\) −31.3535 −0.994472
\(995\) 13.2683 0.420633
\(996\) −15.4813 −0.490545
\(997\) 28.7917 0.911842 0.455921 0.890020i \(-0.349310\pi\)
0.455921 + 0.890020i \(0.349310\pi\)
\(998\) −14.5750 −0.461362
\(999\) 10.3969 0.328942
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 \(a_p\))