Properties

Label 6018.2.a.p.1.4
Level 6018
Weight 2
Character 6018.1
Self dual Yes
Analytic conductor 48.054
Analytic rank 0
Dimension 5
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 6018 = 2 \cdot 3 \cdot 17 \cdot 59 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6018.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.0539719364\)
Analytic rank: \(0\)
Dimension: \(5\)
Coefficient field: 5.5.1668357.1
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Root \(3.61712\)
Character \(\chi\) = 6018.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.96737 q^{5} -1.00000 q^{6} -3.61712 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.96737 q^{5} -1.00000 q^{6} -3.61712 q^{7} -1.00000 q^{8} +1.00000 q^{9} -1.96737 q^{10} +0.322205 q^{11} +1.00000 q^{12} +2.69718 q^{13} +3.61712 q^{14} +1.96737 q^{15} +1.00000 q^{16} -1.00000 q^{17} -1.00000 q^{18} -3.90670 q^{19} +1.96737 q^{20} -3.61712 q^{21} -0.322205 q^{22} -4.79401 q^{23} -1.00000 q^{24} -1.12946 q^{25} -2.69718 q^{26} +1.00000 q^{27} -3.61712 q^{28} -0.708609 q^{29} -1.96737 q^{30} +6.38640 q^{31} -1.00000 q^{32} +0.322205 q^{33} +1.00000 q^{34} -7.11622 q^{35} +1.00000 q^{36} -8.47640 q^{37} +3.90670 q^{38} +2.69718 q^{39} -1.96737 q^{40} +1.55976 q^{41} +3.61712 q^{42} +10.0935 q^{43} +0.322205 q^{44} +1.96737 q^{45} +4.79401 q^{46} +12.0456 q^{47} +1.00000 q^{48} +6.08358 q^{49} +1.12946 q^{50} -1.00000 q^{51} +2.69718 q^{52} -1.01479 q^{53} -1.00000 q^{54} +0.633897 q^{55} +3.61712 q^{56} -3.90670 q^{57} +0.708609 q^{58} -1.00000 q^{59} +1.96737 q^{60} +10.7660 q^{61} -6.38640 q^{62} -3.61712 q^{63} +1.00000 q^{64} +5.30635 q^{65} -0.322205 q^{66} +12.2702 q^{67} -1.00000 q^{68} -4.79401 q^{69} +7.11622 q^{70} +7.07215 q^{71} -1.00000 q^{72} +3.18832 q^{73} +8.47640 q^{74} -1.12946 q^{75} -3.90670 q^{76} -1.16546 q^{77} -2.69718 q^{78} -0.0479121 q^{79} +1.96737 q^{80} +1.00000 q^{81} -1.55976 q^{82} +0.102752 q^{83} -3.61712 q^{84} -1.96737 q^{85} -10.0935 q^{86} -0.708609 q^{87} -0.322205 q^{88} +3.15216 q^{89} -1.96737 q^{90} -9.75603 q^{91} -4.79401 q^{92} +6.38640 q^{93} -12.0456 q^{94} -7.68591 q^{95} -1.00000 q^{96} +2.11803 q^{97} -6.08358 q^{98} +0.322205 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 5q - 5q^{2} + 5q^{3} + 5q^{4} - q^{5} - 5q^{6} - q^{7} - 5q^{8} + 5q^{9} + O(q^{10}) \) \( 5q - 5q^{2} + 5q^{3} + 5q^{4} - q^{5} - 5q^{6} - q^{7} - 5q^{8} + 5q^{9} + q^{10} + 6q^{11} + 5q^{12} - 2q^{13} + q^{14} - q^{15} + 5q^{16} - 5q^{17} - 5q^{18} + 4q^{19} - q^{20} - q^{21} - 6q^{22} + 12q^{23} - 5q^{24} + 4q^{25} + 2q^{26} + 5q^{27} - q^{28} + 19q^{29} + q^{30} + 5q^{31} - 5q^{32} + 6q^{33} + 5q^{34} - 4q^{35} + 5q^{36} - 11q^{37} - 4q^{38} - 2q^{39} + q^{40} + 6q^{41} + q^{42} + 2q^{43} + 6q^{44} - q^{45} - 12q^{46} + 22q^{47} + 5q^{48} - 12q^{49} - 4q^{50} - 5q^{51} - 2q^{52} + 15q^{53} - 5q^{54} - 36q^{55} + q^{56} + 4q^{57} - 19q^{58} - 5q^{59} - q^{60} + 16q^{61} - 5q^{62} - q^{63} + 5q^{64} - 2q^{65} - 6q^{66} + 25q^{67} - 5q^{68} + 12q^{69} + 4q^{70} - 5q^{72} - 10q^{73} + 11q^{74} + 4q^{75} + 4q^{76} + 6q^{77} + 2q^{78} + 10q^{79} - q^{80} + 5q^{81} - 6q^{82} + 19q^{83} - q^{84} + q^{85} - 2q^{86} + 19q^{87} - 6q^{88} + 23q^{89} + q^{90} - 17q^{91} + 12q^{92} + 5q^{93} - 22q^{94} + q^{95} - 5q^{96} + 8q^{97} + 12q^{98} + 6q^{99} + O(q^{100}) \)

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
\(3\) 1.00000 0.577350
\(4\) 1.00000 0.500000
\(5\) 1.96737 0.879834 0.439917 0.898038i \(-0.355008\pi\)
0.439917 + 0.898038i \(0.355008\pi\)
\(6\) −1.00000 −0.408248
\(7\) −3.61712 −1.36714 −0.683572 0.729883i \(-0.739575\pi\)
−0.683572 + 0.729883i \(0.739575\pi\)
\(8\) −1.00000 −0.353553
\(9\) 1.00000 0.333333
\(10\) −1.96737 −0.622137
\(11\) 0.322205 0.0971486 0.0485743 0.998820i \(-0.484532\pi\)
0.0485743 + 0.998820i \(0.484532\pi\)
\(12\) 1.00000 0.288675
\(13\) 2.69718 0.748063 0.374032 0.927416i \(-0.377975\pi\)
0.374032 + 0.927416i \(0.377975\pi\)
\(14\) 3.61712 0.966717
\(15\) 1.96737 0.507972
\(16\) 1.00000 0.250000
\(17\) −1.00000 −0.242536
\(18\) −1.00000 −0.235702
\(19\) −3.90670 −0.896258 −0.448129 0.893969i \(-0.647909\pi\)
−0.448129 + 0.893969i \(0.647909\pi\)
\(20\) 1.96737 0.439917
\(21\) −3.61712 −0.789321
\(22\) −0.322205 −0.0686944
\(23\) −4.79401 −0.999620 −0.499810 0.866135i \(-0.666597\pi\)
−0.499810 + 0.866135i \(0.666597\pi\)
\(24\) −1.00000 −0.204124
\(25\) −1.12946 −0.225892
\(26\) −2.69718 −0.528961
\(27\) 1.00000 0.192450
\(28\) −3.61712 −0.683572
\(29\) −0.708609 −0.131585 −0.0657927 0.997833i \(-0.520958\pi\)
−0.0657927 + 0.997833i \(0.520958\pi\)
\(30\) −1.96737 −0.359191
\(31\) 6.38640 1.14703 0.573516 0.819194i \(-0.305579\pi\)
0.573516 + 0.819194i \(0.305579\pi\)
\(32\) −1.00000 −0.176777
\(33\) 0.322205 0.0560888
\(34\) 1.00000 0.171499
\(35\) −7.11622 −1.20286
\(36\) 1.00000 0.166667
\(37\) −8.47640 −1.39351 −0.696755 0.717309i \(-0.745374\pi\)
−0.696755 + 0.717309i \(0.745374\pi\)
\(38\) 3.90670 0.633750
\(39\) 2.69718 0.431894
\(40\) −1.96737 −0.311068
\(41\) 1.55976 0.243594 0.121797 0.992555i \(-0.461134\pi\)
0.121797 + 0.992555i \(0.461134\pi\)
\(42\) 3.61712 0.558134
\(43\) 10.0935 1.53925 0.769624 0.638498i \(-0.220444\pi\)
0.769624 + 0.638498i \(0.220444\pi\)
\(44\) 0.322205 0.0485743
\(45\) 1.96737 0.293278
\(46\) 4.79401 0.706838
\(47\) 12.0456 1.75703 0.878516 0.477712i \(-0.158534\pi\)
0.878516 + 0.477712i \(0.158534\pi\)
\(48\) 1.00000 0.144338
\(49\) 6.08358 0.869083
\(50\) 1.12946 0.159730
\(51\) −1.00000 −0.140028
\(52\) 2.69718 0.374032
\(53\) −1.01479 −0.139393 −0.0696963 0.997568i \(-0.522203\pi\)
−0.0696963 + 0.997568i \(0.522203\pi\)
\(54\) −1.00000 −0.136083
\(55\) 0.633897 0.0854746
\(56\) 3.61712 0.483358
\(57\) −3.90670 −0.517455
\(58\) 0.708609 0.0930449
\(59\) −1.00000 −0.130189
\(60\) 1.96737 0.253986
\(61\) 10.7660 1.37844 0.689221 0.724552i \(-0.257953\pi\)
0.689221 + 0.724552i \(0.257953\pi\)
\(62\) −6.38640 −0.811074
\(63\) −3.61712 −0.455715
\(64\) 1.00000 0.125000
\(65\) 5.30635 0.658171
\(66\) −0.322205 −0.0396608
\(67\) 12.2702 1.49905 0.749524 0.661977i \(-0.230282\pi\)
0.749524 + 0.661977i \(0.230282\pi\)
\(68\) −1.00000 −0.121268
\(69\) −4.79401 −0.577131
\(70\) 7.11622 0.850550
\(71\) 7.07215 0.839310 0.419655 0.907684i \(-0.362151\pi\)
0.419655 + 0.907684i \(0.362151\pi\)
\(72\) −1.00000 −0.117851
\(73\) 3.18832 0.373164 0.186582 0.982439i \(-0.440259\pi\)
0.186582 + 0.982439i \(0.440259\pi\)
\(74\) 8.47640 0.985361
\(75\) −1.12946 −0.130419
\(76\) −3.90670 −0.448129
\(77\) −1.16546 −0.132816
\(78\) −2.69718 −0.305396
\(79\) −0.0479121 −0.00539053 −0.00269526 0.999996i \(-0.500858\pi\)
−0.00269526 + 0.999996i \(0.500858\pi\)
\(80\) 1.96737 0.219958
\(81\) 1.00000 0.111111
\(82\) −1.55976 −0.172247
\(83\) 0.102752 0.0112784 0.00563922 0.999984i \(-0.498205\pi\)
0.00563922 + 0.999984i \(0.498205\pi\)
\(84\) −3.61712 −0.394661
\(85\) −1.96737 −0.213391
\(86\) −10.0935 −1.08841
\(87\) −0.708609 −0.0759709
\(88\) −0.322205 −0.0343472
\(89\) 3.15216 0.334128 0.167064 0.985946i \(-0.446571\pi\)
0.167064 + 0.985946i \(0.446571\pi\)
\(90\) −1.96737 −0.207379
\(91\) −9.75603 −1.02271
\(92\) −4.79401 −0.499810
\(93\) 6.38640 0.662239
\(94\) −12.0456 −1.24241
\(95\) −7.68591 −0.788558
\(96\) −1.00000 −0.102062
\(97\) 2.11803 0.215054 0.107527 0.994202i \(-0.465707\pi\)
0.107527 + 0.994202i \(0.465707\pi\)
\(98\) −6.08358 −0.614535
\(99\) 0.322205 0.0323829
\(100\) −1.12946 −0.112946
\(101\) −3.31580 −0.329934 −0.164967 0.986299i \(-0.552752\pi\)
−0.164967 + 0.986299i \(0.552752\pi\)
\(102\) 1.00000 0.0990148
\(103\) −5.84405 −0.575831 −0.287916 0.957656i \(-0.592962\pi\)
−0.287916 + 0.957656i \(0.592962\pi\)
\(104\) −2.69718 −0.264480
\(105\) −7.11622 −0.694471
\(106\) 1.01479 0.0985655
\(107\) 15.5098 1.49939 0.749694 0.661785i \(-0.230201\pi\)
0.749694 + 0.661785i \(0.230201\pi\)
\(108\) 1.00000 0.0962250
\(109\) 6.44376 0.617201 0.308600 0.951192i \(-0.400139\pi\)
0.308600 + 0.951192i \(0.400139\pi\)
\(110\) −0.633897 −0.0604397
\(111\) −8.47640 −0.804544
\(112\) −3.61712 −0.341786
\(113\) 15.0555 1.41631 0.708153 0.706059i \(-0.249529\pi\)
0.708153 + 0.706059i \(0.249529\pi\)
\(114\) 3.90670 0.365896
\(115\) −9.43158 −0.879500
\(116\) −0.708609 −0.0657927
\(117\) 2.69718 0.249354
\(118\) 1.00000 0.0920575
\(119\) 3.61712 0.331581
\(120\) −1.96737 −0.179595
\(121\) −10.8962 −0.990562
\(122\) −10.7660 −0.974705
\(123\) 1.55976 0.140639
\(124\) 6.38640 0.573516
\(125\) −12.0589 −1.07858
\(126\) 3.61712 0.322239
\(127\) 19.4634 1.72710 0.863549 0.504264i \(-0.168236\pi\)
0.863549 + 0.504264i \(0.168236\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 10.0935 0.888685
\(130\) −5.30635 −0.465397
\(131\) −6.93292 −0.605732 −0.302866 0.953033i \(-0.597943\pi\)
−0.302866 + 0.953033i \(0.597943\pi\)
\(132\) 0.322205 0.0280444
\(133\) 14.1310 1.22531
\(134\) −12.2702 −1.05999
\(135\) 1.96737 0.169324
\(136\) 1.00000 0.0857493
\(137\) −16.3204 −1.39435 −0.697175 0.716901i \(-0.745560\pi\)
−0.697175 + 0.716901i \(0.745560\pi\)
\(138\) 4.79401 0.408093
\(139\) 1.77264 0.150354 0.0751769 0.997170i \(-0.476048\pi\)
0.0751769 + 0.997170i \(0.476048\pi\)
\(140\) −7.11622 −0.601430
\(141\) 12.0456 1.01442
\(142\) −7.07215 −0.593482
\(143\) 0.869046 0.0726733
\(144\) 1.00000 0.0833333
\(145\) −1.39410 −0.115773
\(146\) −3.18832 −0.263867
\(147\) 6.08358 0.501766
\(148\) −8.47640 −0.696755
\(149\) −1.92331 −0.157564 −0.0787818 0.996892i \(-0.525103\pi\)
−0.0787818 + 0.996892i \(0.525103\pi\)
\(150\) 1.12946 0.0922201
\(151\) 19.1004 1.55437 0.777185 0.629273i \(-0.216647\pi\)
0.777185 + 0.629273i \(0.216647\pi\)
\(152\) 3.90670 0.316875
\(153\) −1.00000 −0.0808452
\(154\) 1.16546 0.0939152
\(155\) 12.5644 1.00920
\(156\) 2.69718 0.215947
\(157\) −3.76548 −0.300518 −0.150259 0.988647i \(-0.548011\pi\)
−0.150259 + 0.988647i \(0.548011\pi\)
\(158\) 0.0479121 0.00381168
\(159\) −1.01479 −0.0804784
\(160\) −1.96737 −0.155534
\(161\) 17.3405 1.36662
\(162\) −1.00000 −0.0785674
\(163\) −4.05277 −0.317437 −0.158719 0.987324i \(-0.550736\pi\)
−0.158719 + 0.987324i \(0.550736\pi\)
\(164\) 1.55976 0.121797
\(165\) 0.633897 0.0493488
\(166\) −0.102752 −0.00797507
\(167\) 8.12354 0.628618 0.314309 0.949321i \(-0.398227\pi\)
0.314309 + 0.949321i \(0.398227\pi\)
\(168\) 3.61712 0.279067
\(169\) −5.72522 −0.440401
\(170\) 1.96737 0.150890
\(171\) −3.90670 −0.298753
\(172\) 10.0935 0.769624
\(173\) 12.3655 0.940133 0.470067 0.882631i \(-0.344230\pi\)
0.470067 + 0.882631i \(0.344230\pi\)
\(174\) 0.708609 0.0537195
\(175\) 4.08540 0.308827
\(176\) 0.322205 0.0242872
\(177\) −1.00000 −0.0751646
\(178\) −3.15216 −0.236264
\(179\) 16.6961 1.24793 0.623963 0.781454i \(-0.285522\pi\)
0.623963 + 0.781454i \(0.285522\pi\)
\(180\) 1.96737 0.146639
\(181\) −26.2946 −1.95447 −0.977233 0.212169i \(-0.931947\pi\)
−0.977233 + 0.212169i \(0.931947\pi\)
\(182\) 9.75603 0.723165
\(183\) 10.7660 0.795843
\(184\) 4.79401 0.353419
\(185\) −16.6762 −1.22606
\(186\) −6.38640 −0.468274
\(187\) −0.322205 −0.0235620
\(188\) 12.0456 0.878516
\(189\) −3.61712 −0.263107
\(190\) 7.68591 0.557595
\(191\) 5.70129 0.412531 0.206265 0.978496i \(-0.433869\pi\)
0.206265 + 0.978496i \(0.433869\pi\)
\(192\) 1.00000 0.0721688
\(193\) 6.01143 0.432712 0.216356 0.976315i \(-0.430583\pi\)
0.216356 + 0.976315i \(0.430583\pi\)
\(194\) −2.11803 −0.152066
\(195\) 5.30635 0.379995
\(196\) 6.08358 0.434542
\(197\) 8.44024 0.601342 0.300671 0.953728i \(-0.402789\pi\)
0.300671 + 0.953728i \(0.402789\pi\)
\(198\) −0.322205 −0.0228981
\(199\) −10.3059 −0.730563 −0.365282 0.930897i \(-0.619027\pi\)
−0.365282 + 0.930897i \(0.619027\pi\)
\(200\) 1.12946 0.0798650
\(201\) 12.2702 0.865476
\(202\) 3.31580 0.233299
\(203\) 2.56313 0.179896
\(204\) −1.00000 −0.0700140
\(205\) 3.06863 0.214322
\(206\) 5.84405 0.407174
\(207\) −4.79401 −0.333207
\(208\) 2.69718 0.187016
\(209\) −1.25876 −0.0870702
\(210\) 7.11622 0.491066
\(211\) −8.45060 −0.581763 −0.290882 0.956759i \(-0.593949\pi\)
−0.290882 + 0.956759i \(0.593949\pi\)
\(212\) −1.01479 −0.0696963
\(213\) 7.07215 0.484576
\(214\) −15.5098 −1.06023
\(215\) 19.8577 1.35428
\(216\) −1.00000 −0.0680414
\(217\) −23.1004 −1.56816
\(218\) −6.44376 −0.436427
\(219\) 3.18832 0.215446
\(220\) 0.633897 0.0427373
\(221\) −2.69718 −0.181432
\(222\) 8.47640 0.568898
\(223\) 23.4257 1.56870 0.784349 0.620320i \(-0.212997\pi\)
0.784349 + 0.620320i \(0.212997\pi\)
\(224\) 3.61712 0.241679
\(225\) −1.12946 −0.0752974
\(226\) −15.0555 −1.00148
\(227\) 23.5348 1.56206 0.781030 0.624493i \(-0.214694\pi\)
0.781030 + 0.624493i \(0.214694\pi\)
\(228\) −3.90670 −0.258727
\(229\) −29.8732 −1.97408 −0.987039 0.160481i \(-0.948695\pi\)
−0.987039 + 0.160481i \(0.948695\pi\)
\(230\) 9.43158 0.621900
\(231\) −1.16546 −0.0766814
\(232\) 0.708609 0.0465225
\(233\) 13.5825 0.889820 0.444910 0.895575i \(-0.353236\pi\)
0.444910 + 0.895575i \(0.353236\pi\)
\(234\) −2.69718 −0.176320
\(235\) 23.6981 1.54590
\(236\) −1.00000 −0.0650945
\(237\) −0.0479121 −0.00311222
\(238\) −3.61712 −0.234463
\(239\) 5.64131 0.364906 0.182453 0.983215i \(-0.441596\pi\)
0.182453 + 0.983215i \(0.441596\pi\)
\(240\) 1.96737 0.126993
\(241\) 22.6870 1.46140 0.730698 0.682701i \(-0.239195\pi\)
0.730698 + 0.682701i \(0.239195\pi\)
\(242\) 10.8962 0.700433
\(243\) 1.00000 0.0641500
\(244\) 10.7660 0.689221
\(245\) 11.9687 0.764649
\(246\) −1.55976 −0.0994468
\(247\) −10.5371 −0.670458
\(248\) −6.38640 −0.405537
\(249\) 0.102752 0.00651162
\(250\) 12.0589 0.762672
\(251\) −6.93425 −0.437686 −0.218843 0.975760i \(-0.570228\pi\)
−0.218843 + 0.975760i \(0.570228\pi\)
\(252\) −3.61712 −0.227857
\(253\) −1.54466 −0.0971117
\(254\) −19.4634 −1.22124
\(255\) −1.96737 −0.123201
\(256\) 1.00000 0.0625000
\(257\) 9.25097 0.577059 0.288530 0.957471i \(-0.406834\pi\)
0.288530 + 0.957471i \(0.406834\pi\)
\(258\) −10.0935 −0.628395
\(259\) 30.6602 1.90513
\(260\) 5.30635 0.329086
\(261\) −0.708609 −0.0438618
\(262\) 6.93292 0.428317
\(263\) −1.77066 −0.109184 −0.0545919 0.998509i \(-0.517386\pi\)
−0.0545919 + 0.998509i \(0.517386\pi\)
\(264\) −0.322205 −0.0198304
\(265\) −1.99647 −0.122642
\(266\) −14.1310 −0.866428
\(267\) 3.15216 0.192909
\(268\) 12.2702 0.749524
\(269\) 1.30106 0.0793269 0.0396634 0.999213i \(-0.487371\pi\)
0.0396634 + 0.999213i \(0.487371\pi\)
\(270\) −1.96737 −0.119730
\(271\) 7.25086 0.440458 0.220229 0.975448i \(-0.429319\pi\)
0.220229 + 0.975448i \(0.429319\pi\)
\(272\) −1.00000 −0.0606339
\(273\) −9.75603 −0.590462
\(274\) 16.3204 0.985954
\(275\) −0.363919 −0.0219451
\(276\) −4.79401 −0.288565
\(277\) 12.3108 0.739683 0.369841 0.929095i \(-0.379412\pi\)
0.369841 + 0.929095i \(0.379412\pi\)
\(278\) −1.77264 −0.106316
\(279\) 6.38640 0.382344
\(280\) 7.11622 0.425275
\(281\) −22.8921 −1.36563 −0.682813 0.730593i \(-0.739244\pi\)
−0.682813 + 0.730593i \(0.739244\pi\)
\(282\) −12.0456 −0.717306
\(283\) 0.128131 0.00761662 0.00380831 0.999993i \(-0.498788\pi\)
0.00380831 + 0.999993i \(0.498788\pi\)
\(284\) 7.07215 0.419655
\(285\) −7.68591 −0.455274
\(286\) −0.869046 −0.0513878
\(287\) −5.64185 −0.333028
\(288\) −1.00000 −0.0589256
\(289\) 1.00000 0.0588235
\(290\) 1.39410 0.0818641
\(291\) 2.11803 0.124161
\(292\) 3.18832 0.186582
\(293\) −21.9385 −1.28166 −0.640830 0.767683i \(-0.721410\pi\)
−0.640830 + 0.767683i \(0.721410\pi\)
\(294\) −6.08358 −0.354802
\(295\) −1.96737 −0.114545
\(296\) 8.47640 0.492681
\(297\) 0.322205 0.0186963
\(298\) 1.92331 0.111414
\(299\) −12.9303 −0.747779
\(300\) −1.12946 −0.0652095
\(301\) −36.5095 −2.10437
\(302\) −19.1004 −1.09911
\(303\) −3.31580 −0.190488
\(304\) −3.90670 −0.224064
\(305\) 21.1806 1.21280
\(306\) 1.00000 0.0571662
\(307\) −12.9495 −0.739066 −0.369533 0.929218i \(-0.620482\pi\)
−0.369533 + 0.929218i \(0.620482\pi\)
\(308\) −1.16546 −0.0664081
\(309\) −5.84405 −0.332456
\(310\) −12.5644 −0.713611
\(311\) 26.8328 1.52155 0.760774 0.649017i \(-0.224820\pi\)
0.760774 + 0.649017i \(0.224820\pi\)
\(312\) −2.69718 −0.152698
\(313\) −16.8957 −0.955001 −0.477501 0.878631i \(-0.658457\pi\)
−0.477501 + 0.878631i \(0.658457\pi\)
\(314\) 3.76548 0.212499
\(315\) −7.11622 −0.400953
\(316\) −0.0479121 −0.00269526
\(317\) 21.1631 1.18864 0.594318 0.804230i \(-0.297422\pi\)
0.594318 + 0.804230i \(0.297422\pi\)
\(318\) 1.01479 0.0569068
\(319\) −0.228318 −0.0127833
\(320\) 1.96737 0.109979
\(321\) 15.5098 0.865672
\(322\) −17.3405 −0.966350
\(323\) 3.90670 0.217374
\(324\) 1.00000 0.0555556
\(325\) −3.04636 −0.168982
\(326\) 4.05277 0.224462
\(327\) 6.44376 0.356341
\(328\) −1.55976 −0.0861235
\(329\) −43.5705 −2.40212
\(330\) −0.633897 −0.0348949
\(331\) −27.4693 −1.50985 −0.754924 0.655812i \(-0.772326\pi\)
−0.754924 + 0.655812i \(0.772326\pi\)
\(332\) 0.102752 0.00563922
\(333\) −8.47640 −0.464504
\(334\) −8.12354 −0.444500
\(335\) 24.1401 1.31891
\(336\) −3.61712 −0.197330
\(337\) −12.5651 −0.684465 −0.342232 0.939615i \(-0.611183\pi\)
−0.342232 + 0.939615i \(0.611183\pi\)
\(338\) 5.72522 0.311411
\(339\) 15.0555 0.817705
\(340\) −1.96737 −0.106696
\(341\) 2.05773 0.111433
\(342\) 3.90670 0.211250
\(343\) 3.31479 0.178982
\(344\) −10.0935 −0.544206
\(345\) −9.43158 −0.507779
\(346\) −12.3655 −0.664775
\(347\) −7.80090 −0.418774 −0.209387 0.977833i \(-0.567147\pi\)
−0.209387 + 0.977833i \(0.567147\pi\)
\(348\) −0.708609 −0.0379854
\(349\) −25.2540 −1.35181 −0.675907 0.736987i \(-0.736248\pi\)
−0.675907 + 0.736987i \(0.736248\pi\)
\(350\) −4.08540 −0.218374
\(351\) 2.69718 0.143965
\(352\) −0.322205 −0.0171736
\(353\) 4.56034 0.242722 0.121361 0.992608i \(-0.461274\pi\)
0.121361 + 0.992608i \(0.461274\pi\)
\(354\) 1.00000 0.0531494
\(355\) 13.9135 0.738454
\(356\) 3.15216 0.167064
\(357\) 3.61712 0.191438
\(358\) −16.6961 −0.882417
\(359\) 14.4272 0.761436 0.380718 0.924691i \(-0.375677\pi\)
0.380718 + 0.924691i \(0.375677\pi\)
\(360\) −1.96737 −0.103689
\(361\) −3.73771 −0.196722
\(362\) 26.2946 1.38202
\(363\) −10.8962 −0.571901
\(364\) −9.75603 −0.511355
\(365\) 6.27259 0.328322
\(366\) −10.7660 −0.562746
\(367\) −24.9628 −1.30305 −0.651525 0.758628i \(-0.725870\pi\)
−0.651525 + 0.758628i \(0.725870\pi\)
\(368\) −4.79401 −0.249905
\(369\) 1.55976 0.0811980
\(370\) 16.6762 0.866954
\(371\) 3.67063 0.190570
\(372\) 6.38640 0.331120
\(373\) 4.05351 0.209883 0.104941 0.994478i \(-0.466535\pi\)
0.104941 + 0.994478i \(0.466535\pi\)
\(374\) 0.322205 0.0166608
\(375\) −12.0589 −0.622719
\(376\) −12.0456 −0.621205
\(377\) −1.91125 −0.0984342
\(378\) 3.61712 0.186045
\(379\) 2.67315 0.137310 0.0686552 0.997640i \(-0.478129\pi\)
0.0686552 + 0.997640i \(0.478129\pi\)
\(380\) −7.68591 −0.394279
\(381\) 19.4634 0.997141
\(382\) −5.70129 −0.291703
\(383\) 12.6525 0.646512 0.323256 0.946312i \(-0.395223\pi\)
0.323256 + 0.946312i \(0.395223\pi\)
\(384\) −1.00000 −0.0510310
\(385\) −2.29288 −0.116856
\(386\) −6.01143 −0.305974
\(387\) 10.0935 0.513082
\(388\) 2.11803 0.107527
\(389\) 19.4285 0.985066 0.492533 0.870294i \(-0.336071\pi\)
0.492533 + 0.870294i \(0.336071\pi\)
\(390\) −5.30635 −0.268697
\(391\) 4.79401 0.242443
\(392\) −6.08358 −0.307267
\(393\) −6.93292 −0.349720
\(394\) −8.44024 −0.425213
\(395\) −0.0942607 −0.00474277
\(396\) 0.322205 0.0161914
\(397\) −12.0808 −0.606318 −0.303159 0.952940i \(-0.598041\pi\)
−0.303159 + 0.952940i \(0.598041\pi\)
\(398\) 10.3059 0.516586
\(399\) 14.1310 0.707435
\(400\) −1.12946 −0.0564731
\(401\) −6.06618 −0.302930 −0.151465 0.988463i \(-0.548399\pi\)
−0.151465 + 0.988463i \(0.548399\pi\)
\(402\) −12.2702 −0.611984
\(403\) 17.2253 0.858052
\(404\) −3.31580 −0.164967
\(405\) 1.96737 0.0977593
\(406\) −2.56313 −0.127206
\(407\) −2.73114 −0.135378
\(408\) 1.00000 0.0495074
\(409\) 29.2302 1.44534 0.722670 0.691194i \(-0.242915\pi\)
0.722670 + 0.691194i \(0.242915\pi\)
\(410\) −3.06863 −0.151549
\(411\) −16.3204 −0.805028
\(412\) −5.84405 −0.287916
\(413\) 3.61712 0.177987
\(414\) 4.79401 0.235613
\(415\) 0.202150 0.00992316
\(416\) −2.69718 −0.132240
\(417\) 1.77264 0.0868068
\(418\) 1.25876 0.0615679
\(419\) 7.51927 0.367341 0.183670 0.982988i \(-0.441202\pi\)
0.183670 + 0.982988i \(0.441202\pi\)
\(420\) −7.11622 −0.347236
\(421\) −4.10410 −0.200022 −0.100011 0.994986i \(-0.531888\pi\)
−0.100011 + 0.994986i \(0.531888\pi\)
\(422\) 8.45060 0.411369
\(423\) 12.0456 0.585678
\(424\) 1.01479 0.0492827
\(425\) 1.12946 0.0547869
\(426\) −7.07215 −0.342647
\(427\) −38.9418 −1.88453
\(428\) 15.5098 0.749694
\(429\) 0.869046 0.0419579
\(430\) −19.8577 −0.957622
\(431\) −25.4463 −1.22571 −0.612853 0.790197i \(-0.709978\pi\)
−0.612853 + 0.790197i \(0.709978\pi\)
\(432\) 1.00000 0.0481125
\(433\) 26.8467 1.29017 0.645086 0.764110i \(-0.276822\pi\)
0.645086 + 0.764110i \(0.276822\pi\)
\(434\) 23.1004 1.10886
\(435\) −1.39410 −0.0668418
\(436\) 6.44376 0.308600
\(437\) 18.7287 0.895917
\(438\) −3.18832 −0.152344
\(439\) −2.80058 −0.133664 −0.0668322 0.997764i \(-0.521289\pi\)
−0.0668322 + 0.997764i \(0.521289\pi\)
\(440\) −0.633897 −0.0302198
\(441\) 6.08358 0.289694
\(442\) 2.69718 0.128292
\(443\) −11.2291 −0.533509 −0.266755 0.963765i \(-0.585951\pi\)
−0.266755 + 0.963765i \(0.585951\pi\)
\(444\) −8.47640 −0.402272
\(445\) 6.20145 0.293977
\(446\) −23.4257 −1.10924
\(447\) −1.92331 −0.0909693
\(448\) −3.61712 −0.170893
\(449\) −5.64645 −0.266472 −0.133236 0.991084i \(-0.542537\pi\)
−0.133236 + 0.991084i \(0.542537\pi\)
\(450\) 1.12946 0.0532433
\(451\) 0.502564 0.0236648
\(452\) 15.0555 0.708153
\(453\) 19.1004 0.897416
\(454\) −23.5348 −1.10454
\(455\) −19.1937 −0.899815
\(456\) 3.90670 0.182948
\(457\) −25.8898 −1.21108 −0.605538 0.795817i \(-0.707042\pi\)
−0.605538 + 0.795817i \(0.707042\pi\)
\(458\) 29.8732 1.39588
\(459\) −1.00000 −0.0466760
\(460\) −9.43158 −0.439750
\(461\) −12.3982 −0.577440 −0.288720 0.957414i \(-0.593230\pi\)
−0.288720 + 0.957414i \(0.593230\pi\)
\(462\) 1.16546 0.0542220
\(463\) −23.5345 −1.09374 −0.546871 0.837217i \(-0.684181\pi\)
−0.546871 + 0.837217i \(0.684181\pi\)
\(464\) −0.708609 −0.0328964
\(465\) 12.5644 0.582661
\(466\) −13.5825 −0.629198
\(467\) 13.3905 0.619637 0.309818 0.950796i \(-0.399732\pi\)
0.309818 + 0.950796i \(0.399732\pi\)
\(468\) 2.69718 0.124677
\(469\) −44.3830 −2.04942
\(470\) −23.6981 −1.09311
\(471\) −3.76548 −0.173504
\(472\) 1.00000 0.0460287
\(473\) 3.25219 0.149536
\(474\) 0.0479121 0.00220067
\(475\) 4.41246 0.202458
\(476\) 3.61712 0.165791
\(477\) −1.01479 −0.0464642
\(478\) −5.64131 −0.258028
\(479\) 26.8921 1.22873 0.614365 0.789022i \(-0.289412\pi\)
0.614365 + 0.789022i \(0.289412\pi\)
\(480\) −1.96737 −0.0897977
\(481\) −22.8624 −1.04243
\(482\) −22.6870 −1.03336
\(483\) 17.3405 0.789021
\(484\) −10.8962 −0.495281
\(485\) 4.16695 0.189211
\(486\) −1.00000 −0.0453609
\(487\) −16.0458 −0.727106 −0.363553 0.931574i \(-0.618436\pi\)
−0.363553 + 0.931574i \(0.618436\pi\)
\(488\) −10.7660 −0.487353
\(489\) −4.05277 −0.183273
\(490\) −11.9687 −0.540689
\(491\) 33.1658 1.49675 0.748377 0.663274i \(-0.230833\pi\)
0.748377 + 0.663274i \(0.230833\pi\)
\(492\) 1.55976 0.0703195
\(493\) 0.708609 0.0319141
\(494\) 10.5371 0.474085
\(495\) 0.633897 0.0284915
\(496\) 6.38640 0.286758
\(497\) −25.5809 −1.14746
\(498\) −0.102752 −0.00460441
\(499\) −19.1598 −0.857712 −0.428856 0.903373i \(-0.641083\pi\)
−0.428856 + 0.903373i \(0.641083\pi\)
\(500\) −12.0589 −0.539291
\(501\) 8.12354 0.362933
\(502\) 6.93425 0.309491
\(503\) 5.88667 0.262474 0.131237 0.991351i \(-0.458105\pi\)
0.131237 + 0.991351i \(0.458105\pi\)
\(504\) 3.61712 0.161119
\(505\) −6.52339 −0.290287
\(506\) 1.54466 0.0686683
\(507\) −5.72522 −0.254266
\(508\) 19.4634 0.863549
\(509\) −18.1966 −0.806550 −0.403275 0.915079i \(-0.632128\pi\)
−0.403275 + 0.915079i \(0.632128\pi\)
\(510\) 1.96737 0.0871165
\(511\) −11.5325 −0.510169
\(512\) −1.00000 −0.0441942
\(513\) −3.90670 −0.172485
\(514\) −9.25097 −0.408043
\(515\) −11.4974 −0.506636
\(516\) 10.0935 0.444342
\(517\) 3.88116 0.170693
\(518\) −30.6602 −1.34713
\(519\) 12.3655 0.542786
\(520\) −5.30635 −0.232699
\(521\) 35.2454 1.54413 0.772064 0.635545i \(-0.219225\pi\)
0.772064 + 0.635545i \(0.219225\pi\)
\(522\) 0.708609 0.0310150
\(523\) −13.7504 −0.601265 −0.300632 0.953740i \(-0.597198\pi\)
−0.300632 + 0.953740i \(0.597198\pi\)
\(524\) −6.93292 −0.302866
\(525\) 4.08540 0.178302
\(526\) 1.77066 0.0772046
\(527\) −6.38640 −0.278196
\(528\) 0.322205 0.0140222
\(529\) −0.0174704 −0.000759583 0
\(530\) 1.99647 0.0867212
\(531\) −1.00000 −0.0433963
\(532\) 14.1310 0.612657
\(533\) 4.20696 0.182224
\(534\) −3.15216 −0.136407
\(535\) 30.5135 1.31921
\(536\) −12.2702 −0.529994
\(537\) 16.6961 0.720491
\(538\) −1.30106 −0.0560926
\(539\) 1.96016 0.0844302
\(540\) 1.96737 0.0846621
\(541\) 23.7807 1.02241 0.511206 0.859459i \(-0.329199\pi\)
0.511206 + 0.859459i \(0.329199\pi\)
\(542\) −7.25086 −0.311451
\(543\) −26.2946 −1.12841
\(544\) 1.00000 0.0428746
\(545\) 12.6773 0.543034
\(546\) 9.75603 0.417520
\(547\) 20.1274 0.860584 0.430292 0.902690i \(-0.358411\pi\)
0.430292 + 0.902690i \(0.358411\pi\)
\(548\) −16.3204 −0.697175
\(549\) 10.7660 0.459480
\(550\) 0.363919 0.0155175
\(551\) 2.76832 0.117934
\(552\) 4.79401 0.204047
\(553\) 0.173304 0.00736963
\(554\) −12.3108 −0.523035
\(555\) −16.6762 −0.707865
\(556\) 1.77264 0.0751769
\(557\) −1.30667 −0.0553654 −0.0276827 0.999617i \(-0.508813\pi\)
−0.0276827 + 0.999617i \(0.508813\pi\)
\(558\) −6.38640 −0.270358
\(559\) 27.2240 1.15145
\(560\) −7.11622 −0.300715
\(561\) −0.322205 −0.0136035
\(562\) 22.8921 0.965643
\(563\) 32.0223 1.34958 0.674790 0.738010i \(-0.264234\pi\)
0.674790 + 0.738010i \(0.264234\pi\)
\(564\) 12.0456 0.507212
\(565\) 29.6198 1.24611
\(566\) −0.128131 −0.00538576
\(567\) −3.61712 −0.151905
\(568\) −7.07215 −0.296741
\(569\) −30.1329 −1.26324 −0.631619 0.775279i \(-0.717609\pi\)
−0.631619 + 0.775279i \(0.717609\pi\)
\(570\) 7.68591 0.321928
\(571\) −27.7915 −1.16304 −0.581519 0.813533i \(-0.697541\pi\)
−0.581519 + 0.813533i \(0.697541\pi\)
\(572\) 0.869046 0.0363366
\(573\) 5.70129 0.238175
\(574\) 5.64185 0.235486
\(575\) 5.41465 0.225806
\(576\) 1.00000 0.0416667
\(577\) −18.7594 −0.780964 −0.390482 0.920611i \(-0.627692\pi\)
−0.390482 + 0.920611i \(0.627692\pi\)
\(578\) −1.00000 −0.0415945
\(579\) 6.01143 0.249826
\(580\) −1.39410 −0.0578867
\(581\) −0.371665 −0.0154193
\(582\) −2.11803 −0.0877953
\(583\) −0.326972 −0.0135418
\(584\) −3.18832 −0.131933
\(585\) 5.30635 0.219390
\(586\) 21.9385 0.906270
\(587\) 22.0372 0.909572 0.454786 0.890601i \(-0.349716\pi\)
0.454786 + 0.890601i \(0.349716\pi\)
\(588\) 6.08358 0.250883
\(589\) −24.9497 −1.02804
\(590\) 1.96737 0.0809953
\(591\) 8.44024 0.347185
\(592\) −8.47640 −0.348378
\(593\) 31.9702 1.31286 0.656428 0.754388i \(-0.272066\pi\)
0.656428 + 0.754388i \(0.272066\pi\)
\(594\) −0.322205 −0.0132203
\(595\) 7.11622 0.291736
\(596\) −1.92331 −0.0787818
\(597\) −10.3059 −0.421791
\(598\) 12.9303 0.528760
\(599\) 36.8990 1.50765 0.753825 0.657075i \(-0.228206\pi\)
0.753825 + 0.657075i \(0.228206\pi\)
\(600\) 1.12946 0.0461101
\(601\) 29.8024 1.21567 0.607833 0.794065i \(-0.292039\pi\)
0.607833 + 0.794065i \(0.292039\pi\)
\(602\) 36.5095 1.48802
\(603\) 12.2702 0.499683
\(604\) 19.1004 0.777185
\(605\) −21.4368 −0.871530
\(606\) 3.31580 0.134695
\(607\) −5.56057 −0.225697 −0.112848 0.993612i \(-0.535997\pi\)
−0.112848 + 0.993612i \(0.535997\pi\)
\(608\) 3.90670 0.158438
\(609\) 2.56313 0.103863
\(610\) −21.1806 −0.857579
\(611\) 32.4892 1.31437
\(612\) −1.00000 −0.0404226
\(613\) 42.5174 1.71726 0.858630 0.512596i \(-0.171316\pi\)
0.858630 + 0.512596i \(0.171316\pi\)
\(614\) 12.9495 0.522599
\(615\) 3.06863 0.123739
\(616\) 1.16546 0.0469576
\(617\) −9.21261 −0.370886 −0.185443 0.982655i \(-0.559372\pi\)
−0.185443 + 0.982655i \(0.559372\pi\)
\(618\) 5.84405 0.235082
\(619\) 18.2750 0.734534 0.367267 0.930116i \(-0.380294\pi\)
0.367267 + 0.930116i \(0.380294\pi\)
\(620\) 12.5644 0.504599
\(621\) −4.79401 −0.192377
\(622\) −26.8328 −1.07590
\(623\) −11.4017 −0.456801
\(624\) 2.69718 0.107974
\(625\) −18.0770 −0.723080
\(626\) 16.8957 0.675288
\(627\) −1.25876 −0.0502700
\(628\) −3.76548 −0.150259
\(629\) 8.47640 0.337976
\(630\) 7.11622 0.283517
\(631\) 18.4487 0.734430 0.367215 0.930136i \(-0.380311\pi\)
0.367215 + 0.930136i \(0.380311\pi\)
\(632\) 0.0479121 0.00190584
\(633\) −8.45060 −0.335881
\(634\) −21.1631 −0.840493
\(635\) 38.2917 1.51956
\(636\) −1.01479 −0.0402392
\(637\) 16.4085 0.650129
\(638\) 0.228318 0.00903919
\(639\) 7.07215 0.279770
\(640\) −1.96737 −0.0777671
\(641\) −18.0312 −0.712189 −0.356094 0.934450i \(-0.615892\pi\)
−0.356094 + 0.934450i \(0.615892\pi\)
\(642\) −15.5098 −0.612122
\(643\) 17.6645 0.696620 0.348310 0.937379i \(-0.386756\pi\)
0.348310 + 0.937379i \(0.386756\pi\)
\(644\) 17.3405 0.683312
\(645\) 19.8577 0.781895
\(646\) −3.90670 −0.153707
\(647\) −17.2650 −0.678756 −0.339378 0.940650i \(-0.610217\pi\)
−0.339378 + 0.940650i \(0.610217\pi\)
\(648\) −1.00000 −0.0392837
\(649\) −0.322205 −0.0126477
\(650\) 3.04636 0.119488
\(651\) −23.1004 −0.905377
\(652\) −4.05277 −0.158719
\(653\) 33.7022 1.31887 0.659435 0.751762i \(-0.270796\pi\)
0.659435 + 0.751762i \(0.270796\pi\)
\(654\) −6.44376 −0.251971
\(655\) −13.6396 −0.532944
\(656\) 1.55976 0.0608985
\(657\) 3.18832 0.124388
\(658\) 43.5705 1.69855
\(659\) −8.24578 −0.321210 −0.160605 0.987019i \(-0.551345\pi\)
−0.160605 + 0.987019i \(0.551345\pi\)
\(660\) 0.633897 0.0246744
\(661\) 34.8127 1.35406 0.677029 0.735957i \(-0.263267\pi\)
0.677029 + 0.735957i \(0.263267\pi\)
\(662\) 27.4693 1.06762
\(663\) −2.69718 −0.104750
\(664\) −0.102752 −0.00398753
\(665\) 27.8009 1.07807
\(666\) 8.47640 0.328454
\(667\) 3.39708 0.131535
\(668\) 8.12354 0.314309
\(669\) 23.4257 0.905688
\(670\) −24.1401 −0.932613
\(671\) 3.46885 0.133914
\(672\) 3.61712 0.139534
\(673\) 41.1376 1.58574 0.792870 0.609391i \(-0.208586\pi\)
0.792870 + 0.609391i \(0.208586\pi\)
\(674\) 12.5651 0.483990
\(675\) −1.12946 −0.0434730
\(676\) −5.72522 −0.220201
\(677\) 6.78056 0.260598 0.130299 0.991475i \(-0.458406\pi\)
0.130299 + 0.991475i \(0.458406\pi\)
\(678\) −15.0555 −0.578205
\(679\) −7.66118 −0.294009
\(680\) 1.96737 0.0754451
\(681\) 23.5348 0.901856
\(682\) −2.05773 −0.0787947
\(683\) 25.8919 0.990726 0.495363 0.868686i \(-0.335035\pi\)
0.495363 + 0.868686i \(0.335035\pi\)
\(684\) −3.90670 −0.149376
\(685\) −32.1083 −1.22680
\(686\) −3.31479 −0.126559
\(687\) −29.8732 −1.13973
\(688\) 10.0935 0.384812
\(689\) −2.73708 −0.104274
\(690\) 9.43158 0.359054
\(691\) −34.2953 −1.30465 −0.652327 0.757937i \(-0.726207\pi\)
−0.652327 + 0.757937i \(0.726207\pi\)
\(692\) 12.3655 0.470067
\(693\) −1.16546 −0.0442721
\(694\) 7.80090 0.296118
\(695\) 3.48744 0.132286
\(696\) 0.708609 0.0268598
\(697\) −1.55976 −0.0590802
\(698\) 25.2540 0.955876
\(699\) 13.5825 0.513738
\(700\) 4.08540 0.154414
\(701\) −0.148640 −0.00561407 −0.00280704 0.999996i \(-0.500894\pi\)
−0.00280704 + 0.999996i \(0.500894\pi\)
\(702\) −2.69718 −0.101799
\(703\) 33.1147 1.24895
\(704\) 0.322205 0.0121436
\(705\) 23.6981 0.892524
\(706\) −4.56034 −0.171631
\(707\) 11.9936 0.451067
\(708\) −1.00000 −0.0375823
\(709\) −51.8127 −1.94587 −0.972933 0.231089i \(-0.925771\pi\)
−0.972933 + 0.231089i \(0.925771\pi\)
\(710\) −13.9135 −0.522166
\(711\) −0.0479121 −0.00179684
\(712\) −3.15216 −0.118132
\(713\) −30.6165 −1.14660
\(714\) −3.61712 −0.135367
\(715\) 1.70973 0.0639404
\(716\) 16.6961 0.623963
\(717\) 5.64131 0.210679
\(718\) −14.4272 −0.538417
\(719\) 40.7377 1.51926 0.759629 0.650356i \(-0.225380\pi\)
0.759629 + 0.650356i \(0.225380\pi\)
\(720\) 1.96737 0.0733195
\(721\) 21.1386 0.787244
\(722\) 3.73771 0.139103
\(723\) 22.6870 0.843738
\(724\) −26.2946 −0.977233
\(725\) 0.800346 0.0297241
\(726\) 10.8962 0.404395
\(727\) −36.1177 −1.33953 −0.669766 0.742572i \(-0.733606\pi\)
−0.669766 + 0.742572i \(0.733606\pi\)
\(728\) 9.75603 0.361583
\(729\) 1.00000 0.0370370
\(730\) −6.27259 −0.232159
\(731\) −10.0935 −0.373322
\(732\) 10.7660 0.397922
\(733\) 51.8615 1.91555 0.957774 0.287521i \(-0.0928312\pi\)
0.957774 + 0.287521i \(0.0928312\pi\)
\(734\) 24.9628 0.921395
\(735\) 11.9687 0.441470
\(736\) 4.79401 0.176710
\(737\) 3.95354 0.145631
\(738\) −1.55976 −0.0574156
\(739\) −16.1912 −0.595603 −0.297801 0.954628i \(-0.596253\pi\)
−0.297801 + 0.954628i \(0.596253\pi\)
\(740\) −16.6762 −0.613029
\(741\) −10.5371 −0.387089
\(742\) −3.67063 −0.134753
\(743\) 6.64667 0.243843 0.121921 0.992540i \(-0.461094\pi\)
0.121921 + 0.992540i \(0.461094\pi\)
\(744\) −6.38640 −0.234137
\(745\) −3.78386 −0.138630
\(746\) −4.05351 −0.148410
\(747\) 0.102752 0.00375948
\(748\) −0.322205 −0.0117810
\(749\) −56.1008 −2.04988
\(750\) 12.0589 0.440329
\(751\) −15.5930 −0.568995 −0.284498 0.958677i \(-0.591827\pi\)
−0.284498 + 0.958677i \(0.591827\pi\)
\(752\) 12.0456 0.439258
\(753\) −6.93425 −0.252698
\(754\) 1.91125 0.0696035
\(755\) 37.5775 1.36759
\(756\) −3.61712 −0.131554
\(757\) 13.4225 0.487849 0.243924 0.969794i \(-0.421565\pi\)
0.243924 + 0.969794i \(0.421565\pi\)
\(758\) −2.67315 −0.0970931
\(759\) −1.54466 −0.0560675
\(760\) 7.68591 0.278797
\(761\) −2.63485 −0.0955134 −0.0477567 0.998859i \(-0.515207\pi\)
−0.0477567 + 0.998859i \(0.515207\pi\)
\(762\) −19.4634 −0.705085
\(763\) −23.3079 −0.843802
\(764\) 5.70129 0.206265
\(765\) −1.96737 −0.0711304
\(766\) −12.6525 −0.457153
\(767\) −2.69718 −0.0973895
\(768\) 1.00000 0.0360844
\(769\) −47.1868 −1.70160 −0.850799 0.525491i \(-0.823882\pi\)
−0.850799 + 0.525491i \(0.823882\pi\)
\(770\) 2.29288 0.0826298
\(771\) 9.25097 0.333165
\(772\) 6.01143 0.216356
\(773\) −28.2857 −1.01737 −0.508683 0.860954i \(-0.669867\pi\)
−0.508683 + 0.860954i \(0.669867\pi\)
\(774\) −10.0935 −0.362804
\(775\) −7.21319 −0.259106
\(776\) −2.11803 −0.0760329
\(777\) 30.6602 1.09993
\(778\) −19.4285 −0.696547
\(779\) −6.09352 −0.218323
\(780\) 5.30635 0.189998
\(781\) 2.27869 0.0815378
\(782\) −4.79401 −0.171433
\(783\) −0.708609 −0.0253236
\(784\) 6.08358 0.217271
\(785\) −7.40809 −0.264406
\(786\) 6.93292 0.247289
\(787\) 17.4523 0.622108 0.311054 0.950392i \(-0.399318\pi\)
0.311054 + 0.950392i \(0.399318\pi\)
\(788\) 8.44024 0.300671
\(789\) −1.77066 −0.0630373
\(790\) 0.0942607 0.00335364
\(791\) −54.4578 −1.93630
\(792\) −0.322205 −0.0114491
\(793\) 29.0378 1.03116
\(794\) 12.0808 0.428732
\(795\) −1.99647 −0.0708076
\(796\) −10.3059 −0.365282
\(797\) −29.7203 −1.05275 −0.526373 0.850254i \(-0.676448\pi\)
−0.526373 + 0.850254i \(0.676448\pi\)
\(798\) −14.1310 −0.500232
\(799\) −12.0456 −0.426143
\(800\) 1.12946 0.0399325
\(801\) 3.15216 0.111376
\(802\) 6.06618 0.214204
\(803\) 1.02729 0.0362524
\(804\) 12.2702 0.432738
\(805\) 34.1152 1.20240
\(806\) −17.2253 −0.606735
\(807\) 1.30106 0.0457994
\(808\) 3.31580 0.116649
\(809\) −19.9190 −0.700314 −0.350157 0.936691i \(-0.613872\pi\)
−0.350157 + 0.936691i \(0.613872\pi\)
\(810\) −1.96737 −0.0691263
\(811\) 35.6195 1.25077 0.625385 0.780316i \(-0.284942\pi\)
0.625385 + 0.780316i \(0.284942\pi\)
\(812\) 2.56313 0.0899481
\(813\) 7.25086 0.254299
\(814\) 2.73114 0.0957265
\(815\) −7.97329 −0.279292
\(816\) −1.00000 −0.0350070
\(817\) −39.4323 −1.37956
\(818\) −29.2302 −1.02201
\(819\) −9.75603 −0.340903
\(820\) 3.06863 0.107161
\(821\) 35.0511 1.22329 0.611646 0.791131i \(-0.290508\pi\)
0.611646 + 0.791131i \(0.290508\pi\)
\(822\) 16.3204 0.569241
\(823\) 5.80101 0.202210 0.101105 0.994876i \(-0.467762\pi\)
0.101105 + 0.994876i \(0.467762\pi\)
\(824\) 5.84405 0.203587
\(825\) −0.363919 −0.0126700
\(826\) −3.61712 −0.125856
\(827\) −44.0917 −1.53322 −0.766608 0.642115i \(-0.778057\pi\)
−0.766608 + 0.642115i \(0.778057\pi\)
\(828\) −4.79401 −0.166603
\(829\) 7.17727 0.249277 0.124638 0.992202i \(-0.460223\pi\)
0.124638 + 0.992202i \(0.460223\pi\)
\(830\) −0.202150 −0.00701674
\(831\) 12.3108 0.427056
\(832\) 2.69718 0.0935079
\(833\) −6.08358 −0.210784
\(834\) −1.77264 −0.0613817
\(835\) 15.9820 0.553080
\(836\) −1.25876 −0.0435351
\(837\) 6.38640 0.220746
\(838\) −7.51927 −0.259749
\(839\) −7.56212 −0.261073 −0.130537 0.991443i \(-0.541670\pi\)
−0.130537 + 0.991443i \(0.541670\pi\)
\(840\) 7.11622 0.245533
\(841\) −28.4979 −0.982685
\(842\) 4.10410 0.141437
\(843\) −22.8921 −0.788445
\(844\) −8.45060 −0.290882
\(845\) −11.2636 −0.387480
\(846\) −12.0456 −0.414137
\(847\) 39.4128 1.35424
\(848\) −1.01479 −0.0348482
\(849\) 0.128131 0.00439746
\(850\) −1.12946 −0.0387402
\(851\) 40.6359 1.39298
\(852\) 7.07215 0.242288
\(853\) −4.18783 −0.143388 −0.0716942 0.997427i \(-0.522841\pi\)
−0.0716942 + 0.997427i \(0.522841\pi\)
\(854\) 38.9418 1.33256
\(855\) −7.68591 −0.262853
\(856\) −15.5098 −0.530113
\(857\) 26.8730 0.917965 0.458982 0.888445i \(-0.348214\pi\)
0.458982 + 0.888445i \(0.348214\pi\)
\(858\) −0.869046 −0.0296687
\(859\) 18.3419 0.625816 0.312908 0.949783i \(-0.398697\pi\)
0.312908 + 0.949783i \(0.398697\pi\)
\(860\) 19.8577 0.677141
\(861\) −5.64185 −0.192274
\(862\) 25.4463 0.866705
\(863\) −48.6135 −1.65482 −0.827411 0.561597i \(-0.810187\pi\)
−0.827411 + 0.561597i \(0.810187\pi\)
\(864\) −1.00000 −0.0340207
\(865\) 24.3275 0.827161
\(866\) −26.8467 −0.912289
\(867\) 1.00000 0.0339618
\(868\) −23.1004 −0.784079
\(869\) −0.0154375 −0.000523682 0
\(870\) 1.39410 0.0472643
\(871\) 33.0951 1.12138
\(872\) −6.44376 −0.218213
\(873\) 2.11803 0.0716845
\(874\) −18.7287 −0.633509
\(875\) 43.6186 1.47458
\(876\) 3.18832 0.107723
\(877\) −0.851478 −0.0287524 −0.0143762 0.999897i \(-0.504576\pi\)
−0.0143762 + 0.999897i \(0.504576\pi\)
\(878\) 2.80058 0.0945151
\(879\) −21.9385 −0.739967
\(880\) 0.633897 0.0213687
\(881\) 36.3285 1.22394 0.611969 0.790881i \(-0.290378\pi\)
0.611969 + 0.790881i \(0.290378\pi\)
\(882\) −6.08358 −0.204845
\(883\) −56.4060 −1.89821 −0.949107 0.314955i \(-0.898011\pi\)
−0.949107 + 0.314955i \(0.898011\pi\)
\(884\) −2.69718 −0.0907160
\(885\) −1.96737 −0.0661324
\(886\) 11.2291 0.377248
\(887\) 31.0751 1.04340 0.521701 0.853129i \(-0.325298\pi\)
0.521701 + 0.853129i \(0.325298\pi\)
\(888\) 8.47640 0.284449
\(889\) −70.4016 −2.36119
\(890\) −6.20145 −0.207873
\(891\) 0.322205 0.0107943
\(892\) 23.4257 0.784349
\(893\) −47.0585 −1.57475
\(894\) 1.92331 0.0643250
\(895\) 32.8474 1.09797
\(896\) 3.61712 0.120840
\(897\) −12.9303 −0.431730
\(898\) 5.64645 0.188424
\(899\) −4.52546 −0.150933
\(900\) −1.12946 −0.0376487
\(901\) 1.01479 0.0338077
\(902\) −0.502564 −0.0167336
\(903\) −36.5095 −1.21496
\(904\) −15.0555 −0.500740
\(905\) −51.7313 −1.71961
\(906\) −19.1004 −0.634569
\(907\) −55.9171 −1.85670 −0.928349 0.371711i \(-0.878771\pi\)
−0.928349 + 0.371711i \(0.878771\pi\)
\(908\) 23.5348 0.781030
\(909\) −3.31580 −0.109978
\(910\) 19.1937 0.636265
\(911\) −41.9901 −1.39119 −0.695597 0.718433i \(-0.744860\pi\)
−0.695597 + 0.718433i \(0.744860\pi\)
\(912\) −3.90670 −0.129364
\(913\) 0.0331071 0.00109569
\(914\) 25.8898 0.856359
\(915\) 21.1806 0.700210
\(916\) −29.8732 −0.987039
\(917\) 25.0772 0.828123
\(918\) 1.00000 0.0330049
\(919\) −38.2639 −1.26221 −0.631106 0.775697i \(-0.717399\pi\)
−0.631106 + 0.775697i \(0.717399\pi\)
\(920\) 9.43158 0.310950
\(921\) −12.9495 −0.426700
\(922\) 12.3982 0.408312
\(923\) 19.0749 0.627857
\(924\) −1.16546 −0.0383407
\(925\) 9.57376 0.314783
\(926\) 23.5345 0.773392
\(927\) −5.84405 −0.191944
\(928\) 0.708609 0.0232612
\(929\) 0.719669 0.0236116 0.0118058 0.999930i \(-0.496242\pi\)
0.0118058 + 0.999930i \(0.496242\pi\)
\(930\) −12.5644 −0.412003
\(931\) −23.7667 −0.778923
\(932\) 13.5825 0.444910
\(933\) 26.8328 0.878466
\(934\) −13.3905 −0.438149
\(935\) −0.633897 −0.0207306
\(936\) −2.69718 −0.0881601
\(937\) −52.1853 −1.70482 −0.852410 0.522874i \(-0.824860\pi\)
−0.852410 + 0.522874i \(0.824860\pi\)
\(938\) 44.3830 1.44916
\(939\) −16.8957 −0.551370
\(940\) 23.6981 0.772948
\(941\) 6.51151 0.212269 0.106135 0.994352i \(-0.466153\pi\)
0.106135 + 0.994352i \(0.466153\pi\)
\(942\) 3.76548 0.122686
\(943\) −7.47752 −0.243501
\(944\) −1.00000 −0.0325472
\(945\) −7.11622 −0.231490
\(946\) −3.25219 −0.105738
\(947\) 50.1578 1.62991 0.814955 0.579524i \(-0.196762\pi\)
0.814955 + 0.579524i \(0.196762\pi\)
\(948\) −0.0479121 −0.00155611
\(949\) 8.59946 0.279150
\(950\) −4.41246 −0.143159
\(951\) 21.1631 0.686259
\(952\) −3.61712 −0.117232
\(953\) 30.9124 1.00135 0.500676 0.865635i \(-0.333085\pi\)
0.500676 + 0.865635i \(0.333085\pi\)
\(954\) 1.01479 0.0328552
\(955\) 11.2165 0.362958
\(956\) 5.64131 0.182453
\(957\) −0.228318 −0.00738046
\(958\) −26.8921 −0.868843
\(959\) 59.0331 1.90628
\(960\) 1.96737 0.0634965
\(961\) 9.78615 0.315682
\(962\) 22.8624 0.737112
\(963\) 15.5098 0.499796
\(964\) 22.6870 0.730698
\(965\) 11.8267 0.380715
\(966\) −17.3405 −0.557922
\(967\) −41.9689 −1.34963 −0.674815 0.737987i \(-0.735776\pi\)
−0.674815 + 0.737987i \(0.735776\pi\)
\(968\) 10.8962 0.350217
\(969\) 3.90670 0.125501
\(970\) −4.16695 −0.133793
\(971\) −6.27634 −0.201417 −0.100709 0.994916i \(-0.532111\pi\)
−0.100709 + 0.994916i \(0.532111\pi\)
\(972\) 1.00000 0.0320750
\(973\) −6.41187 −0.205555
\(974\) 16.0458 0.514141
\(975\) −3.04636 −0.0975616
\(976\) 10.7660 0.344610
\(977\) −45.0880 −1.44249 −0.721247 0.692678i \(-0.756431\pi\)
−0.721247 + 0.692678i \(0.756431\pi\)
\(978\) 4.05277 0.129593
\(979\) 1.01564 0.0324601
\(980\) 11.9687 0.382325
\(981\) 6.44376 0.205734
\(982\) −33.1658 −1.05836
\(983\) 9.23375 0.294511 0.147255 0.989098i \(-0.452956\pi\)
0.147255 + 0.989098i \(0.452956\pi\)
\(984\) −1.55976 −0.0497234
\(985\) 16.6051 0.529081
\(986\) −0.708609 −0.0225667
\(987\) −43.5705 −1.38686
\(988\) −10.5371 −0.335229
\(989\) −48.3884 −1.53866
\(990\) −0.633897 −0.0201466
\(991\) 18.0309 0.572771 0.286386 0.958114i \(-0.407546\pi\)
0.286386 + 0.958114i \(0.407546\pi\)
\(992\) −6.38640 −0.202769
\(993\) −27.4693 −0.871712
\(994\) 25.5809 0.811376
\(995\) −20.2754 −0.642774
\(996\) 0.102752 0.00325581
\(997\) −31.7402 −1.00522 −0.502611 0.864513i \(-0.667627\pi\)
−0.502611 + 0.864513i \(0.667627\pi\)
\(998\) 19.1598 0.606494
\(999\) −8.47640 −0.268181
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 \(a_p\))