Properties

Label 8041.2.a.i.1.3
Level 8041
Weight 2
Character 8041.1
Self dual Yes
Analytic conductor 64.208
Analytic rank 0
Dimension 78
CM No

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Newspace parameters

Level: \( N \) = \( 8041 = 11 \cdot 17 \cdot 43 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8041.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2077082653\)
Analytic rank: \(0\)
Dimension: \(78\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Character \(\chi\) = 8041.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.66059 q^{2} -0.870455 q^{3} +5.07876 q^{4} -2.53728 q^{5} +2.31593 q^{6} +1.57807 q^{7} -8.19134 q^{8} -2.24231 q^{9} +O(q^{10})\) \(q-2.66059 q^{2} -0.870455 q^{3} +5.07876 q^{4} -2.53728 q^{5} +2.31593 q^{6} +1.57807 q^{7} -8.19134 q^{8} -2.24231 q^{9} +6.75067 q^{10} +1.00000 q^{11} -4.42083 q^{12} -5.54559 q^{13} -4.19860 q^{14} +2.20859 q^{15} +11.6363 q^{16} -1.00000 q^{17} +5.96587 q^{18} -7.29705 q^{19} -12.8862 q^{20} -1.37364 q^{21} -2.66059 q^{22} +7.87110 q^{23} +7.13019 q^{24} +1.43779 q^{25} +14.7546 q^{26} +4.56319 q^{27} +8.01463 q^{28} +1.60580 q^{29} -5.87616 q^{30} +5.64012 q^{31} -14.5768 q^{32} -0.870455 q^{33} +2.66059 q^{34} -4.00400 q^{35} -11.3881 q^{36} -2.01159 q^{37} +19.4145 q^{38} +4.82719 q^{39} +20.7837 q^{40} -8.14727 q^{41} +3.65469 q^{42} -1.00000 q^{43} +5.07876 q^{44} +5.68936 q^{45} -20.9418 q^{46} +3.48904 q^{47} -10.1289 q^{48} -4.50970 q^{49} -3.82537 q^{50} +0.870455 q^{51} -28.1647 q^{52} -4.47992 q^{53} -12.1408 q^{54} -2.53728 q^{55} -12.9265 q^{56} +6.35175 q^{57} -4.27238 q^{58} +4.63908 q^{59} +11.2169 q^{60} +1.59035 q^{61} -15.0061 q^{62} -3.53851 q^{63} +15.5103 q^{64} +14.0707 q^{65} +2.31593 q^{66} -14.5722 q^{67} -5.07876 q^{68} -6.85144 q^{69} +10.6530 q^{70} -2.40885 q^{71} +18.3675 q^{72} -12.2347 q^{73} +5.35202 q^{74} -1.25153 q^{75} -37.0600 q^{76} +1.57807 q^{77} -12.8432 q^{78} -12.1757 q^{79} -29.5245 q^{80} +2.75487 q^{81} +21.6766 q^{82} -4.85369 q^{83} -6.97637 q^{84} +2.53728 q^{85} +2.66059 q^{86} -1.39777 q^{87} -8.19134 q^{88} +18.3671 q^{89} -15.1371 q^{90} -8.75132 q^{91} +39.9754 q^{92} -4.90947 q^{93} -9.28292 q^{94} +18.5147 q^{95} +12.6884 q^{96} -2.70432 q^{97} +11.9985 q^{98} -2.24231 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 78q + 7q^{2} + 10q^{3} + 91q^{4} + 17q^{5} + 12q^{6} + 11q^{7} + 33q^{8} + 102q^{9} + O(q^{10}) \) \( 78q + 7q^{2} + 10q^{3} + 91q^{4} + 17q^{5} + 12q^{6} + 11q^{7} + 33q^{8} + 102q^{9} + 3q^{10} + 78q^{11} + 31q^{12} - 16q^{13} + 31q^{14} + 38q^{15} + 121q^{16} - 78q^{17} + 11q^{18} + 51q^{20} + 6q^{21} + 7q^{22} + 48q^{23} + 11q^{24} + 101q^{25} + 18q^{26} + 46q^{27} + 27q^{28} + 22q^{29} + 14q^{30} + 56q^{31} + 83q^{32} + 10q^{33} - 7q^{34} + 24q^{35} + 139q^{36} + 53q^{37} + 10q^{38} + 79q^{39} - q^{40} + 23q^{41} + 17q^{42} - 78q^{43} + 91q^{44} + 76q^{45} + 21q^{46} + 57q^{47} + 78q^{48} + 115q^{49} + 58q^{50} - 10q^{51} - 63q^{52} + 22q^{53} - 18q^{54} + 17q^{55} + 111q^{56} - 11q^{57} + 36q^{58} + 71q^{59} + 36q^{60} + 4q^{61} - 5q^{62} + 71q^{63} + 183q^{64} + 47q^{65} + 12q^{66} + 11q^{67} - 91q^{68} + 31q^{69} + 33q^{70} + 159q^{71} + 59q^{72} + 2q^{73} - 4q^{74} + 83q^{75} - 44q^{76} + 11q^{77} + 101q^{78} + 35q^{79} + 85q^{80} + 170q^{81} + 98q^{82} - 32q^{83} + 44q^{84} - 17q^{85} - 7q^{86} - 6q^{87} + 33q^{88} + 50q^{89} - 5q^{90} + 86q^{91} + 106q^{92} + 68q^{93} - q^{94} + 109q^{95} - 50q^{96} + 40q^{97} + 106q^{98} + 102q^{99} + O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.66059 −1.88132 −0.940662 0.339345i \(-0.889795\pi\)
−0.940662 + 0.339345i \(0.889795\pi\)
\(3\) −0.870455 −0.502557 −0.251279 0.967915i \(-0.580851\pi\)
−0.251279 + 0.967915i \(0.580851\pi\)
\(4\) 5.07876 2.53938
\(5\) −2.53728 −1.13471 −0.567353 0.823475i \(-0.692032\pi\)
−0.567353 + 0.823475i \(0.692032\pi\)
\(6\) 2.31593 0.945474
\(7\) 1.57807 0.596453 0.298227 0.954495i \(-0.403605\pi\)
0.298227 + 0.954495i \(0.403605\pi\)
\(8\) −8.19134 −2.89607
\(9\) −2.24231 −0.747436
\(10\) 6.75067 2.13475
\(11\) 1.00000 0.301511
\(12\) −4.42083 −1.27618
\(13\) −5.54559 −1.53807 −0.769035 0.639206i \(-0.779263\pi\)
−0.769035 + 0.639206i \(0.779263\pi\)
\(14\) −4.19860 −1.12212
\(15\) 2.20859 0.570255
\(16\) 11.6363 2.90907
\(17\) −1.00000 −0.242536
\(18\) 5.96587 1.40617
\(19\) −7.29705 −1.67406 −0.837029 0.547159i \(-0.815709\pi\)
−0.837029 + 0.547159i \(0.815709\pi\)
\(20\) −12.8862 −2.88145
\(21\) −1.37364 −0.299752
\(22\) −2.66059 −0.567241
\(23\) 7.87110 1.64124 0.820619 0.571476i \(-0.193629\pi\)
0.820619 + 0.571476i \(0.193629\pi\)
\(24\) 7.13019 1.45544
\(25\) 1.43779 0.287558
\(26\) 14.7546 2.89361
\(27\) 4.56319 0.878187
\(28\) 8.01463 1.51462
\(29\) 1.60580 0.298189 0.149095 0.988823i \(-0.452364\pi\)
0.149095 + 0.988823i \(0.452364\pi\)
\(30\) −5.87616 −1.07283
\(31\) 5.64012 1.01300 0.506498 0.862241i \(-0.330940\pi\)
0.506498 + 0.862241i \(0.330940\pi\)
\(32\) −14.5768 −2.57684
\(33\) −0.870455 −0.151527
\(34\) 2.66059 0.456288
\(35\) −4.00400 −0.676799
\(36\) −11.3881 −1.89802
\(37\) −2.01159 −0.330703 −0.165351 0.986235i \(-0.552876\pi\)
−0.165351 + 0.986235i \(0.552876\pi\)
\(38\) 19.4145 3.14945
\(39\) 4.82719 0.772969
\(40\) 20.7837 3.28619
\(41\) −8.14727 −1.27239 −0.636195 0.771528i \(-0.719493\pi\)
−0.636195 + 0.771528i \(0.719493\pi\)
\(42\) 3.65469 0.563931
\(43\) −1.00000 −0.152499
\(44\) 5.07876 0.765652
\(45\) 5.68936 0.848120
\(46\) −20.9418 −3.08770
\(47\) 3.48904 0.508929 0.254464 0.967082i \(-0.418101\pi\)
0.254464 + 0.967082i \(0.418101\pi\)
\(48\) −10.1289 −1.46198
\(49\) −4.50970 −0.644243
\(50\) −3.82537 −0.540989
\(51\) 0.870455 0.121888
\(52\) −28.1647 −3.90575
\(53\) −4.47992 −0.615364 −0.307682 0.951489i \(-0.599553\pi\)
−0.307682 + 0.951489i \(0.599553\pi\)
\(54\) −12.1408 −1.65215
\(55\) −2.53728 −0.342127
\(56\) −12.9265 −1.72737
\(57\) 6.35175 0.841310
\(58\) −4.27238 −0.560990
\(59\) 4.63908 0.603956 0.301978 0.953315i \(-0.402353\pi\)
0.301978 + 0.953315i \(0.402353\pi\)
\(60\) 11.2169 1.44809
\(61\) 1.59035 0.203624 0.101812 0.994804i \(-0.467536\pi\)
0.101812 + 0.994804i \(0.467536\pi\)
\(62\) −15.0061 −1.90577
\(63\) −3.53851 −0.445811
\(64\) 15.5103 1.93879
\(65\) 14.0707 1.74526
\(66\) 2.31593 0.285071
\(67\) −14.5722 −1.78028 −0.890139 0.455689i \(-0.849393\pi\)
−0.890139 + 0.455689i \(0.849393\pi\)
\(68\) −5.07876 −0.615890
\(69\) −6.85144 −0.824816
\(70\) 10.6530 1.27328
\(71\) −2.40885 −0.285877 −0.142939 0.989732i \(-0.545655\pi\)
−0.142939 + 0.989732i \(0.545655\pi\)
\(72\) 18.3675 2.16463
\(73\) −12.2347 −1.43196 −0.715980 0.698121i \(-0.754020\pi\)
−0.715980 + 0.698121i \(0.754020\pi\)
\(74\) 5.35202 0.622159
\(75\) −1.25153 −0.144514
\(76\) −37.0600 −4.25107
\(77\) 1.57807 0.179837
\(78\) −12.8432 −1.45420
\(79\) −12.1757 −1.36987 −0.684935 0.728604i \(-0.740169\pi\)
−0.684935 + 0.728604i \(0.740169\pi\)
\(80\) −29.5245 −3.30094
\(81\) 2.75487 0.306097
\(82\) 21.6766 2.39378
\(83\) −4.85369 −0.532762 −0.266381 0.963868i \(-0.585828\pi\)
−0.266381 + 0.963868i \(0.585828\pi\)
\(84\) −6.97637 −0.761185
\(85\) 2.53728 0.275207
\(86\) 2.66059 0.286899
\(87\) −1.39777 −0.149857
\(88\) −8.19134 −0.873199
\(89\) 18.3671 1.94690 0.973452 0.228891i \(-0.0735098\pi\)
0.973452 + 0.228891i \(0.0735098\pi\)
\(90\) −15.1371 −1.59559
\(91\) −8.75132 −0.917387
\(92\) 39.9754 4.16773
\(93\) −4.90947 −0.509089
\(94\) −9.28292 −0.957460
\(95\) 18.5147 1.89956
\(96\) 12.6884 1.29501
\(97\) −2.70432 −0.274582 −0.137291 0.990531i \(-0.543840\pi\)
−0.137291 + 0.990531i \(0.543840\pi\)
\(98\) 11.9985 1.21203
\(99\) −2.24231 −0.225360
\(100\) 7.30218 0.730218
\(101\) −15.5569 −1.54797 −0.773986 0.633202i \(-0.781740\pi\)
−0.773986 + 0.633202i \(0.781740\pi\)
\(102\) −2.31593 −0.229311
\(103\) −10.3576 −1.02056 −0.510282 0.860007i \(-0.670459\pi\)
−0.510282 + 0.860007i \(0.670459\pi\)
\(104\) 45.4258 4.45437
\(105\) 3.48530 0.340130
\(106\) 11.9193 1.15770
\(107\) −10.5750 −1.02232 −0.511161 0.859485i \(-0.670784\pi\)
−0.511161 + 0.859485i \(0.670784\pi\)
\(108\) 23.1754 2.23005
\(109\) −10.7814 −1.03267 −0.516333 0.856388i \(-0.672703\pi\)
−0.516333 + 0.856388i \(0.672703\pi\)
\(110\) 6.75067 0.643651
\(111\) 1.75100 0.166197
\(112\) 18.3629 1.73513
\(113\) 15.4711 1.45540 0.727701 0.685894i \(-0.240589\pi\)
0.727701 + 0.685894i \(0.240589\pi\)
\(114\) −16.8994 −1.58278
\(115\) −19.9712 −1.86232
\(116\) 8.15546 0.757216
\(117\) 12.4349 1.14961
\(118\) −12.3427 −1.13624
\(119\) −1.57807 −0.144661
\(120\) −18.0913 −1.65150
\(121\) 1.00000 0.0909091
\(122\) −4.23128 −0.383082
\(123\) 7.09184 0.639449
\(124\) 28.6448 2.57238
\(125\) 9.03833 0.808413
\(126\) 9.41455 0.838714
\(127\) 17.1175 1.51893 0.759467 0.650546i \(-0.225460\pi\)
0.759467 + 0.650546i \(0.225460\pi\)
\(128\) −12.1131 −1.07066
\(129\) 0.870455 0.0766393
\(130\) −37.4365 −3.28340
\(131\) −0.830164 −0.0725318 −0.0362659 0.999342i \(-0.511546\pi\)
−0.0362659 + 0.999342i \(0.511546\pi\)
\(132\) −4.42083 −0.384784
\(133\) −11.5152 −0.998497
\(134\) 38.7707 3.34928
\(135\) −11.5781 −0.996484
\(136\) 8.19134 0.702401
\(137\) −14.4097 −1.23110 −0.615550 0.788098i \(-0.711066\pi\)
−0.615550 + 0.788098i \(0.711066\pi\)
\(138\) 18.2289 1.55175
\(139\) −19.3602 −1.64211 −0.821053 0.570851i \(-0.806613\pi\)
−0.821053 + 0.570851i \(0.806613\pi\)
\(140\) −20.3354 −1.71865
\(141\) −3.03705 −0.255766
\(142\) 6.40896 0.537828
\(143\) −5.54559 −0.463746
\(144\) −26.0922 −2.17435
\(145\) −4.07436 −0.338357
\(146\) 32.5515 2.69398
\(147\) 3.92549 0.323769
\(148\) −10.2164 −0.839780
\(149\) 19.9891 1.63757 0.818786 0.574099i \(-0.194648\pi\)
0.818786 + 0.574099i \(0.194648\pi\)
\(150\) 3.32981 0.271878
\(151\) 16.8923 1.37468 0.687338 0.726337i \(-0.258779\pi\)
0.687338 + 0.726337i \(0.258779\pi\)
\(152\) 59.7726 4.84820
\(153\) 2.24231 0.181280
\(154\) −4.19860 −0.338333
\(155\) −14.3106 −1.14945
\(156\) 24.5161 1.96286
\(157\) −16.6329 −1.32745 −0.663726 0.747976i \(-0.731026\pi\)
−0.663726 + 0.747976i \(0.731026\pi\)
\(158\) 32.3945 2.57717
\(159\) 3.89957 0.309256
\(160\) 36.9854 2.92395
\(161\) 12.4211 0.978921
\(162\) −7.32959 −0.575867
\(163\) −13.0658 −1.02339 −0.511694 0.859168i \(-0.670982\pi\)
−0.511694 + 0.859168i \(0.670982\pi\)
\(164\) −41.3781 −3.23108
\(165\) 2.20859 0.171938
\(166\) 12.9137 1.00230
\(167\) −18.8842 −1.46131 −0.730653 0.682749i \(-0.760784\pi\)
−0.730653 + 0.682749i \(0.760784\pi\)
\(168\) 11.2519 0.868104
\(169\) 17.7536 1.36566
\(170\) −6.75067 −0.517753
\(171\) 16.3622 1.25125
\(172\) −5.07876 −0.387252
\(173\) −13.9903 −1.06366 −0.531832 0.846850i \(-0.678496\pi\)
−0.531832 + 0.846850i \(0.678496\pi\)
\(174\) 3.71891 0.281930
\(175\) 2.26893 0.171515
\(176\) 11.6363 0.877119
\(177\) −4.03811 −0.303523
\(178\) −48.8673 −3.66276
\(179\) 5.09962 0.381163 0.190582 0.981671i \(-0.438963\pi\)
0.190582 + 0.981671i \(0.438963\pi\)
\(180\) 28.8949 2.15370
\(181\) −15.7689 −1.17209 −0.586046 0.810277i \(-0.699316\pi\)
−0.586046 + 0.810277i \(0.699316\pi\)
\(182\) 23.2837 1.72590
\(183\) −1.38433 −0.102333
\(184\) −64.4748 −4.75315
\(185\) 5.10396 0.375250
\(186\) 13.0621 0.957761
\(187\) −1.00000 −0.0731272
\(188\) 17.7200 1.29236
\(189\) 7.20103 0.523798
\(190\) −49.2600 −3.57369
\(191\) −24.3575 −1.76245 −0.881223 0.472702i \(-0.843279\pi\)
−0.881223 + 0.472702i \(0.843279\pi\)
\(192\) −13.5011 −0.974355
\(193\) 6.37501 0.458883 0.229442 0.973322i \(-0.426310\pi\)
0.229442 + 0.973322i \(0.426310\pi\)
\(194\) 7.19510 0.516578
\(195\) −12.2479 −0.877092
\(196\) −22.9037 −1.63598
\(197\) 3.81198 0.271592 0.135796 0.990737i \(-0.456641\pi\)
0.135796 + 0.990737i \(0.456641\pi\)
\(198\) 5.96587 0.423976
\(199\) −17.0808 −1.21082 −0.605412 0.795913i \(-0.706991\pi\)
−0.605412 + 0.795913i \(0.706991\pi\)
\(200\) −11.7774 −0.832788
\(201\) 12.6844 0.894692
\(202\) 41.3907 2.91224
\(203\) 2.53406 0.177856
\(204\) 4.42083 0.309520
\(205\) 20.6719 1.44379
\(206\) 27.5574 1.92001
\(207\) −17.6494 −1.22672
\(208\) −64.5302 −4.47436
\(209\) −7.29705 −0.504747
\(210\) −9.27297 −0.639896
\(211\) 21.9914 1.51395 0.756977 0.653442i \(-0.226676\pi\)
0.756977 + 0.653442i \(0.226676\pi\)
\(212\) −22.7525 −1.56264
\(213\) 2.09679 0.143670
\(214\) 28.1357 1.92332
\(215\) 2.53728 0.173041
\(216\) −37.3787 −2.54330
\(217\) 8.90049 0.604205
\(218\) 28.6848 1.94278
\(219\) 10.6497 0.719642
\(220\) −12.8862 −0.868790
\(221\) 5.54559 0.373037
\(222\) −4.65869 −0.312671
\(223\) 13.4686 0.901926 0.450963 0.892543i \(-0.351081\pi\)
0.450963 + 0.892543i \(0.351081\pi\)
\(224\) −23.0032 −1.53696
\(225\) −3.22396 −0.214931
\(226\) −41.1624 −2.73808
\(227\) −7.93654 −0.526767 −0.263383 0.964691i \(-0.584838\pi\)
−0.263383 + 0.964691i \(0.584838\pi\)
\(228\) 32.2590 2.13641
\(229\) 4.11295 0.271792 0.135896 0.990723i \(-0.456609\pi\)
0.135896 + 0.990723i \(0.456609\pi\)
\(230\) 53.1352 3.50363
\(231\) −1.37364 −0.0903787
\(232\) −13.1536 −0.863578
\(233\) 11.7614 0.770517 0.385258 0.922809i \(-0.374112\pi\)
0.385258 + 0.922809i \(0.374112\pi\)
\(234\) −33.0843 −2.16279
\(235\) −8.85267 −0.577484
\(236\) 23.5608 1.53368
\(237\) 10.5984 0.688438
\(238\) 4.19860 0.272155
\(239\) 22.2846 1.44147 0.720737 0.693209i \(-0.243804\pi\)
0.720737 + 0.693209i \(0.243804\pi\)
\(240\) 25.6998 1.65891
\(241\) 20.2341 1.30339 0.651695 0.758481i \(-0.274058\pi\)
0.651695 + 0.758481i \(0.274058\pi\)
\(242\) −2.66059 −0.171029
\(243\) −16.0876 −1.03202
\(244\) 8.07702 0.517078
\(245\) 11.4424 0.731027
\(246\) −18.8685 −1.20301
\(247\) 40.4664 2.57482
\(248\) −46.2001 −2.93371
\(249\) 4.22492 0.267743
\(250\) −24.0473 −1.52089
\(251\) 9.69461 0.611918 0.305959 0.952045i \(-0.401023\pi\)
0.305959 + 0.952045i \(0.401023\pi\)
\(252\) −17.9713 −1.13208
\(253\) 7.87110 0.494852
\(254\) −45.5428 −2.85761
\(255\) −2.20859 −0.138307
\(256\) 1.20747 0.0754671
\(257\) −26.8705 −1.67613 −0.838067 0.545568i \(-0.816314\pi\)
−0.838067 + 0.545568i \(0.816314\pi\)
\(258\) −2.31593 −0.144183
\(259\) −3.17442 −0.197249
\(260\) 71.4618 4.43187
\(261\) −3.60069 −0.222877
\(262\) 2.20873 0.136456
\(263\) −30.2390 −1.86461 −0.932307 0.361668i \(-0.882207\pi\)
−0.932307 + 0.361668i \(0.882207\pi\)
\(264\) 7.13019 0.438833
\(265\) 11.3668 0.698258
\(266\) 30.6374 1.87850
\(267\) −15.9877 −0.978431
\(268\) −74.0088 −4.52080
\(269\) −15.5140 −0.945903 −0.472952 0.881088i \(-0.656811\pi\)
−0.472952 + 0.881088i \(0.656811\pi\)
\(270\) 30.8046 1.87471
\(271\) −14.6783 −0.891644 −0.445822 0.895122i \(-0.647088\pi\)
−0.445822 + 0.895122i \(0.647088\pi\)
\(272\) −11.6363 −0.705554
\(273\) 7.61763 0.461040
\(274\) 38.3383 2.31610
\(275\) 1.43779 0.0867019
\(276\) −34.7968 −2.09452
\(277\) −3.14366 −0.188884 −0.0944422 0.995530i \(-0.530107\pi\)
−0.0944422 + 0.995530i \(0.530107\pi\)
\(278\) 51.5095 3.08934
\(279\) −12.6469 −0.757150
\(280\) 32.7981 1.96006
\(281\) 1.01999 0.0608473 0.0304236 0.999537i \(-0.490314\pi\)
0.0304236 + 0.999537i \(0.490314\pi\)
\(282\) 8.08036 0.481178
\(283\) 3.69869 0.219865 0.109932 0.993939i \(-0.464937\pi\)
0.109932 + 0.993939i \(0.464937\pi\)
\(284\) −12.2340 −0.725952
\(285\) −16.1162 −0.954640
\(286\) 14.7546 0.872456
\(287\) −12.8569 −0.758921
\(288\) 32.6857 1.92602
\(289\) 1.00000 0.0588235
\(290\) 10.8402 0.636559
\(291\) 2.35399 0.137993
\(292\) −62.1370 −3.63629
\(293\) 1.45167 0.0848075 0.0424037 0.999101i \(-0.486498\pi\)
0.0424037 + 0.999101i \(0.486498\pi\)
\(294\) −10.4441 −0.609115
\(295\) −11.7706 −0.685313
\(296\) 16.4776 0.957740
\(297\) 4.56319 0.264783
\(298\) −53.1829 −3.08080
\(299\) −43.6499 −2.52434
\(300\) −6.35622 −0.366977
\(301\) −1.57807 −0.0909583
\(302\) −44.9436 −2.58621
\(303\) 13.5416 0.777945
\(304\) −84.9106 −4.86996
\(305\) −4.03517 −0.231053
\(306\) −5.96587 −0.341046
\(307\) 8.53719 0.487243 0.243622 0.969870i \(-0.421664\pi\)
0.243622 + 0.969870i \(0.421664\pi\)
\(308\) 8.01463 0.456676
\(309\) 9.01582 0.512892
\(310\) 38.0746 2.16249
\(311\) 10.0213 0.568258 0.284129 0.958786i \(-0.408296\pi\)
0.284129 + 0.958786i \(0.408296\pi\)
\(312\) −39.5411 −2.23858
\(313\) 14.2659 0.806359 0.403180 0.915121i \(-0.367905\pi\)
0.403180 + 0.915121i \(0.367905\pi\)
\(314\) 44.2535 2.49737
\(315\) 8.97820 0.505864
\(316\) −61.8373 −3.47862
\(317\) −23.8586 −1.34003 −0.670015 0.742347i \(-0.733713\pi\)
−0.670015 + 0.742347i \(0.733713\pi\)
\(318\) −10.3752 −0.581811
\(319\) 1.60580 0.0899074
\(320\) −39.3541 −2.19996
\(321\) 9.20504 0.513775
\(322\) −33.0476 −1.84167
\(323\) 7.29705 0.406019
\(324\) 13.9913 0.777296
\(325\) −7.97338 −0.442284
\(326\) 34.7627 1.92533
\(327\) 9.38469 0.518974
\(328\) 66.7371 3.68494
\(329\) 5.50594 0.303552
\(330\) −5.87616 −0.323472
\(331\) 23.6822 1.30169 0.650846 0.759210i \(-0.274414\pi\)
0.650846 + 0.759210i \(0.274414\pi\)
\(332\) −24.6507 −1.35288
\(333\) 4.51060 0.247179
\(334\) 50.2433 2.74919
\(335\) 36.9738 2.02009
\(336\) −15.9840 −0.872001
\(337\) −7.38517 −0.402296 −0.201148 0.979561i \(-0.564467\pi\)
−0.201148 + 0.979561i \(0.564467\pi\)
\(338\) −47.2351 −2.56925
\(339\) −13.4669 −0.731423
\(340\) 12.8862 0.698854
\(341\) 5.64012 0.305430
\(342\) −43.5333 −2.35401
\(343\) −18.1631 −0.980714
\(344\) 8.19134 0.441647
\(345\) 17.3840 0.935924
\(346\) 37.2225 2.00110
\(347\) −25.9513 −1.39314 −0.696570 0.717489i \(-0.745291\pi\)
−0.696570 + 0.717489i \(0.745291\pi\)
\(348\) −7.09896 −0.380544
\(349\) 3.22080 0.172405 0.0862027 0.996278i \(-0.472527\pi\)
0.0862027 + 0.996278i \(0.472527\pi\)
\(350\) −6.03669 −0.322675
\(351\) −25.3056 −1.35071
\(352\) −14.5768 −0.776946
\(353\) 17.6835 0.941198 0.470599 0.882347i \(-0.344038\pi\)
0.470599 + 0.882347i \(0.344038\pi\)
\(354\) 10.7438 0.571025
\(355\) 6.11192 0.324387
\(356\) 93.2819 4.94393
\(357\) 1.37364 0.0727006
\(358\) −13.5680 −0.717092
\(359\) 0.130807 0.00690375 0.00345187 0.999994i \(-0.498901\pi\)
0.00345187 + 0.999994i \(0.498901\pi\)
\(360\) −46.6035 −2.45622
\(361\) 34.2469 1.80247
\(362\) 41.9546 2.20509
\(363\) −0.870455 −0.0456870
\(364\) −44.4459 −2.32960
\(365\) 31.0428 1.62485
\(366\) 3.68314 0.192521
\(367\) −2.06773 −0.107935 −0.0539673 0.998543i \(-0.517187\pi\)
−0.0539673 + 0.998543i \(0.517187\pi\)
\(368\) 91.5904 4.77448
\(369\) 18.2687 0.951030
\(370\) −13.5796 −0.705968
\(371\) −7.06962 −0.367036
\(372\) −24.9340 −1.29277
\(373\) 3.04369 0.157596 0.0787982 0.996891i \(-0.474892\pi\)
0.0787982 + 0.996891i \(0.474892\pi\)
\(374\) 2.66059 0.137576
\(375\) −7.86746 −0.406274
\(376\) −28.5799 −1.47390
\(377\) −8.90510 −0.458636
\(378\) −19.1590 −0.985433
\(379\) −19.1476 −0.983545 −0.491772 0.870724i \(-0.663651\pi\)
−0.491772 + 0.870724i \(0.663651\pi\)
\(380\) 94.0315 4.82371
\(381\) −14.9000 −0.763352
\(382\) 64.8054 3.31573
\(383\) −27.1862 −1.38915 −0.694574 0.719421i \(-0.744407\pi\)
−0.694574 + 0.719421i \(0.744407\pi\)
\(384\) 10.5440 0.538069
\(385\) −4.00400 −0.204063
\(386\) −16.9613 −0.863308
\(387\) 2.24231 0.113983
\(388\) −13.7346 −0.697269
\(389\) −11.6206 −0.589190 −0.294595 0.955622i \(-0.595185\pi\)
−0.294595 + 0.955622i \(0.595185\pi\)
\(390\) 32.5868 1.65009
\(391\) −7.87110 −0.398058
\(392\) 36.9405 1.86578
\(393\) 0.722621 0.0364514
\(394\) −10.1421 −0.510953
\(395\) 30.8931 1.55440
\(396\) −11.3881 −0.572276
\(397\) −2.83727 −0.142398 −0.0711992 0.997462i \(-0.522683\pi\)
−0.0711992 + 0.997462i \(0.522683\pi\)
\(398\) 45.4450 2.27795
\(399\) 10.0235 0.501802
\(400\) 16.7305 0.836526
\(401\) 28.6063 1.42853 0.714265 0.699876i \(-0.246761\pi\)
0.714265 + 0.699876i \(0.246761\pi\)
\(402\) −33.7482 −1.68321
\(403\) −31.2778 −1.55806
\(404\) −79.0099 −3.93089
\(405\) −6.98987 −0.347330
\(406\) −6.74210 −0.334605
\(407\) −2.01159 −0.0997106
\(408\) −7.13019 −0.352997
\(409\) 7.05543 0.348868 0.174434 0.984669i \(-0.444190\pi\)
0.174434 + 0.984669i \(0.444190\pi\)
\(410\) −54.9996 −2.71624
\(411\) 12.5430 0.618699
\(412\) −52.6038 −2.59160
\(413\) 7.32077 0.360232
\(414\) 46.9580 2.30786
\(415\) 12.3152 0.604528
\(416\) 80.8370 3.96336
\(417\) 16.8521 0.825253
\(418\) 19.4145 0.949593
\(419\) 16.6105 0.811478 0.405739 0.913989i \(-0.367014\pi\)
0.405739 + 0.913989i \(0.367014\pi\)
\(420\) 17.7010 0.863721
\(421\) 34.4380 1.67840 0.839202 0.543819i \(-0.183022\pi\)
0.839202 + 0.543819i \(0.183022\pi\)
\(422\) −58.5103 −2.84824
\(423\) −7.82350 −0.380391
\(424\) 36.6965 1.78214
\(425\) −1.43779 −0.0697430
\(426\) −5.57871 −0.270290
\(427\) 2.50968 0.121452
\(428\) −53.7078 −2.59606
\(429\) 4.82719 0.233059
\(430\) −6.75067 −0.325546
\(431\) 12.9384 0.623220 0.311610 0.950210i \(-0.399132\pi\)
0.311610 + 0.950210i \(0.399132\pi\)
\(432\) 53.0987 2.55471
\(433\) 23.7005 1.13897 0.569486 0.822001i \(-0.307142\pi\)
0.569486 + 0.822001i \(0.307142\pi\)
\(434\) −23.6806 −1.13671
\(435\) 3.54654 0.170044
\(436\) −54.7560 −2.62233
\(437\) −57.4358 −2.74753
\(438\) −28.3346 −1.35388
\(439\) −12.5017 −0.596674 −0.298337 0.954461i \(-0.596432\pi\)
−0.298337 + 0.954461i \(0.596432\pi\)
\(440\) 20.7837 0.990825
\(441\) 10.1121 0.481531
\(442\) −14.7546 −0.701803
\(443\) 28.6698 1.36214 0.681072 0.732217i \(-0.261514\pi\)
0.681072 + 0.732217i \(0.261514\pi\)
\(444\) 8.89289 0.422038
\(445\) −46.6024 −2.20916
\(446\) −35.8345 −1.69682
\(447\) −17.3996 −0.822974
\(448\) 24.4764 1.15640
\(449\) −19.9595 −0.941945 −0.470972 0.882148i \(-0.656097\pi\)
−0.470972 + 0.882148i \(0.656097\pi\)
\(450\) 8.57766 0.404355
\(451\) −8.14727 −0.383640
\(452\) 78.5742 3.69582
\(453\) −14.7040 −0.690854
\(454\) 21.1159 0.991019
\(455\) 22.2045 1.04096
\(456\) −52.0293 −2.43650
\(457\) −26.9453 −1.26045 −0.630224 0.776414i \(-0.717037\pi\)
−0.630224 + 0.776414i \(0.717037\pi\)
\(458\) −10.9429 −0.511328
\(459\) −4.56319 −0.212992
\(460\) −101.429 −4.72914
\(461\) −26.1593 −1.21836 −0.609179 0.793033i \(-0.708501\pi\)
−0.609179 + 0.793033i \(0.708501\pi\)
\(462\) 3.65469 0.170032
\(463\) −30.0923 −1.39851 −0.699254 0.714873i \(-0.746484\pi\)
−0.699254 + 0.714873i \(0.746484\pi\)
\(464\) 18.6855 0.867454
\(465\) 12.4567 0.577666
\(466\) −31.2924 −1.44959
\(467\) −38.0326 −1.75994 −0.879969 0.475031i \(-0.842437\pi\)
−0.879969 + 0.475031i \(0.842437\pi\)
\(468\) 63.1540 2.91930
\(469\) −22.9959 −1.06185
\(470\) 23.5534 1.08644
\(471\) 14.4782 0.667121
\(472\) −38.0002 −1.74910
\(473\) −1.00000 −0.0459800
\(474\) −28.1980 −1.29518
\(475\) −10.4916 −0.481388
\(476\) −8.01463 −0.367350
\(477\) 10.0454 0.459946
\(478\) −59.2904 −2.71188
\(479\) −15.3441 −0.701090 −0.350545 0.936546i \(-0.614004\pi\)
−0.350545 + 0.936546i \(0.614004\pi\)
\(480\) −32.1941 −1.46945
\(481\) 11.1554 0.508644
\(482\) −53.8346 −2.45210
\(483\) −10.8120 −0.491964
\(484\) 5.07876 0.230853
\(485\) 6.86162 0.311570
\(486\) 42.8025 1.94156
\(487\) −4.98060 −0.225693 −0.112846 0.993612i \(-0.535997\pi\)
−0.112846 + 0.993612i \(0.535997\pi\)
\(488\) −13.0271 −0.589710
\(489\) 11.3731 0.514312
\(490\) −30.4435 −1.37530
\(491\) 24.3655 1.09960 0.549801 0.835296i \(-0.314704\pi\)
0.549801 + 0.835296i \(0.314704\pi\)
\(492\) 36.0177 1.62381
\(493\) −1.60580 −0.0723215
\(494\) −107.665 −4.84407
\(495\) 5.68936 0.255718
\(496\) 65.6302 2.94688
\(497\) −3.80132 −0.170513
\(498\) −11.2408 −0.503712
\(499\) −15.6279 −0.699599 −0.349800 0.936825i \(-0.613750\pi\)
−0.349800 + 0.936825i \(0.613750\pi\)
\(500\) 45.9035 2.05287
\(501\) 16.4379 0.734390
\(502\) −25.7934 −1.15122
\(503\) −4.60234 −0.205208 −0.102604 0.994722i \(-0.532717\pi\)
−0.102604 + 0.994722i \(0.532717\pi\)
\(504\) 28.9851 1.29110
\(505\) 39.4723 1.75649
\(506\) −20.9418 −0.930976
\(507\) −15.4537 −0.686323
\(508\) 86.9358 3.85715
\(509\) 18.2928 0.810816 0.405408 0.914136i \(-0.367130\pi\)
0.405408 + 0.914136i \(0.367130\pi\)
\(510\) 5.87616 0.260201
\(511\) −19.3071 −0.854097
\(512\) 21.0137 0.928683
\(513\) −33.2978 −1.47014
\(514\) 71.4914 3.15335
\(515\) 26.2801 1.15804
\(516\) 4.42083 0.194616
\(517\) 3.48904 0.153448
\(518\) 8.44584 0.371089
\(519\) 12.1779 0.534552
\(520\) −115.258 −5.05440
\(521\) −2.19257 −0.0960584 −0.0480292 0.998846i \(-0.515294\pi\)
−0.0480292 + 0.998846i \(0.515294\pi\)
\(522\) 9.57998 0.419304
\(523\) 13.2329 0.578636 0.289318 0.957233i \(-0.406571\pi\)
0.289318 + 0.957233i \(0.406571\pi\)
\(524\) −4.21621 −0.184186
\(525\) −1.97500 −0.0861960
\(526\) 80.4536 3.50794
\(527\) −5.64012 −0.245688
\(528\) −10.1289 −0.440803
\(529\) 38.9542 1.69366
\(530\) −30.2425 −1.31365
\(531\) −10.4022 −0.451419
\(532\) −58.4831 −2.53556
\(533\) 45.1815 1.95703
\(534\) 42.5368 1.84075
\(535\) 26.8317 1.16003
\(536\) 119.366 5.15582
\(537\) −4.43899 −0.191556
\(538\) 41.2764 1.77955
\(539\) −4.50970 −0.194247
\(540\) −58.8024 −2.53045
\(541\) −14.6820 −0.631228 −0.315614 0.948888i \(-0.602211\pi\)
−0.315614 + 0.948888i \(0.602211\pi\)
\(542\) 39.0530 1.67747
\(543\) 13.7261 0.589044
\(544\) 14.5768 0.624975
\(545\) 27.3553 1.17177
\(546\) −20.2674 −0.867365
\(547\) −0.0899527 −0.00384610 −0.00192305 0.999998i \(-0.500612\pi\)
−0.00192305 + 0.999998i \(0.500612\pi\)
\(548\) −73.1832 −3.12623
\(549\) −3.56606 −0.152196
\(550\) −3.82537 −0.163114
\(551\) −11.7176 −0.499186
\(552\) 56.1224 2.38873
\(553\) −19.2140 −0.817063
\(554\) 8.36401 0.355353
\(555\) −4.44277 −0.188585
\(556\) −98.3256 −4.16993
\(557\) 21.5747 0.914150 0.457075 0.889428i \(-0.348897\pi\)
0.457075 + 0.889428i \(0.348897\pi\)
\(558\) 33.6482 1.42444
\(559\) 5.54559 0.234554
\(560\) −46.5917 −1.96886
\(561\) 0.870455 0.0367506
\(562\) −2.71377 −0.114473
\(563\) 18.8013 0.792382 0.396191 0.918168i \(-0.370332\pi\)
0.396191 + 0.918168i \(0.370332\pi\)
\(564\) −15.4245 −0.649487
\(565\) −39.2546 −1.65145
\(566\) −9.84072 −0.413637
\(567\) 4.34737 0.182572
\(568\) 19.7317 0.827923
\(569\) −26.6804 −1.11850 −0.559251 0.828998i \(-0.688911\pi\)
−0.559251 + 0.828998i \(0.688911\pi\)
\(570\) 42.8786 1.79599
\(571\) −3.77200 −0.157853 −0.0789267 0.996880i \(-0.525149\pi\)
−0.0789267 + 0.996880i \(0.525149\pi\)
\(572\) −28.1647 −1.17763
\(573\) 21.2021 0.885730
\(574\) 34.2071 1.42778
\(575\) 11.3170 0.471950
\(576\) −34.7790 −1.44912
\(577\) −21.6186 −0.899994 −0.449997 0.893030i \(-0.648575\pi\)
−0.449997 + 0.893030i \(0.648575\pi\)
\(578\) −2.66059 −0.110666
\(579\) −5.54916 −0.230615
\(580\) −20.6927 −0.859217
\(581\) −7.65945 −0.317767
\(582\) −6.26301 −0.259610
\(583\) −4.47992 −0.185539
\(584\) 100.218 4.14706
\(585\) −31.5509 −1.30447
\(586\) −3.86231 −0.159550
\(587\) −24.0630 −0.993187 −0.496594 0.867983i \(-0.665416\pi\)
−0.496594 + 0.867983i \(0.665416\pi\)
\(588\) 19.9367 0.822174
\(589\) −41.1562 −1.69581
\(590\) 31.3169 1.28930
\(591\) −3.31816 −0.136491
\(592\) −23.4074 −0.962039
\(593\) 22.3368 0.917264 0.458632 0.888626i \(-0.348340\pi\)
0.458632 + 0.888626i \(0.348340\pi\)
\(594\) −12.1408 −0.498143
\(595\) 4.00400 0.164148
\(596\) 101.520 4.15842
\(597\) 14.8680 0.608508
\(598\) 116.135 4.74910
\(599\) 18.5635 0.758484 0.379242 0.925297i \(-0.376185\pi\)
0.379242 + 0.925297i \(0.376185\pi\)
\(600\) 10.2517 0.418524
\(601\) −2.90206 −0.118377 −0.0591887 0.998247i \(-0.518851\pi\)
−0.0591887 + 0.998247i \(0.518851\pi\)
\(602\) 4.19860 0.171122
\(603\) 32.6754 1.33064
\(604\) 85.7920 3.49083
\(605\) −2.53728 −0.103155
\(606\) −36.0287 −1.46357
\(607\) −34.9208 −1.41739 −0.708696 0.705514i \(-0.750716\pi\)
−0.708696 + 0.705514i \(0.750716\pi\)
\(608\) 106.368 4.31378
\(609\) −2.20578 −0.0893828
\(610\) 10.7359 0.434686
\(611\) −19.3488 −0.782768
\(612\) 11.3881 0.460339
\(613\) −32.4176 −1.30934 −0.654668 0.755917i \(-0.727191\pi\)
−0.654668 + 0.755917i \(0.727191\pi\)
\(614\) −22.7140 −0.916663
\(615\) −17.9940 −0.725587
\(616\) −12.9265 −0.520823
\(617\) 0.469553 0.0189035 0.00945174 0.999955i \(-0.496991\pi\)
0.00945174 + 0.999955i \(0.496991\pi\)
\(618\) −23.9874 −0.964916
\(619\) 33.4134 1.34300 0.671500 0.741005i \(-0.265650\pi\)
0.671500 + 0.741005i \(0.265650\pi\)
\(620\) −72.6800 −2.91890
\(621\) 35.9173 1.44131
\(622\) −26.6627 −1.06908
\(623\) 28.9845 1.16124
\(624\) 56.1706 2.24862
\(625\) −30.1217 −1.20487
\(626\) −37.9559 −1.51702
\(627\) 6.35175 0.253665
\(628\) −84.4747 −3.37091
\(629\) 2.01159 0.0802072
\(630\) −23.8873 −0.951694
\(631\) 33.8593 1.34792 0.673959 0.738769i \(-0.264592\pi\)
0.673959 + 0.738769i \(0.264592\pi\)
\(632\) 99.7350 3.96724
\(633\) −19.1426 −0.760849
\(634\) 63.4780 2.52103
\(635\) −43.4319 −1.72354
\(636\) 19.8050 0.785319
\(637\) 25.0090 0.990892
\(638\) −4.27238 −0.169145
\(639\) 5.40138 0.213675
\(640\) 30.7344 1.21489
\(641\) 6.38117 0.252041 0.126021 0.992028i \(-0.459779\pi\)
0.126021 + 0.992028i \(0.459779\pi\)
\(642\) −24.4909 −0.966578
\(643\) 17.3845 0.685577 0.342788 0.939413i \(-0.388629\pi\)
0.342788 + 0.939413i \(0.388629\pi\)
\(644\) 63.0839 2.48585
\(645\) −2.20859 −0.0869631
\(646\) −19.4145 −0.763853
\(647\) 18.5926 0.730949 0.365475 0.930821i \(-0.380907\pi\)
0.365475 + 0.930821i \(0.380907\pi\)
\(648\) −22.5661 −0.886478
\(649\) 4.63908 0.182100
\(650\) 21.2139 0.832079
\(651\) −7.74748 −0.303648
\(652\) −66.3578 −2.59877
\(653\) 40.0788 1.56840 0.784202 0.620505i \(-0.213073\pi\)
0.784202 + 0.620505i \(0.213073\pi\)
\(654\) −24.9688 −0.976359
\(655\) 2.10636 0.0823023
\(656\) −94.8041 −3.70148
\(657\) 27.4339 1.07030
\(658\) −14.6491 −0.571080
\(659\) −36.6028 −1.42584 −0.712921 0.701244i \(-0.752628\pi\)
−0.712921 + 0.701244i \(0.752628\pi\)
\(660\) 11.2169 0.436617
\(661\) −12.3226 −0.479293 −0.239646 0.970860i \(-0.577031\pi\)
−0.239646 + 0.970860i \(0.577031\pi\)
\(662\) −63.0087 −2.44890
\(663\) −4.82719 −0.187472
\(664\) 39.7582 1.54292
\(665\) 29.2174 1.13300
\(666\) −12.0009 −0.465024
\(667\) 12.6394 0.489399
\(668\) −95.9085 −3.71081
\(669\) −11.7238 −0.453270
\(670\) −98.3722 −3.80045
\(671\) 1.59035 0.0613949
\(672\) 20.0232 0.772413
\(673\) 47.4646 1.82962 0.914812 0.403880i \(-0.132339\pi\)
0.914812 + 0.403880i \(0.132339\pi\)
\(674\) 19.6489 0.756849
\(675\) 6.56090 0.252529
\(676\) 90.1662 3.46793
\(677\) 0.548743 0.0210899 0.0105449 0.999944i \(-0.496643\pi\)
0.0105449 + 0.999944i \(0.496643\pi\)
\(678\) 35.8300 1.37604
\(679\) −4.26760 −0.163776
\(680\) −20.7837 −0.797019
\(681\) 6.90840 0.264731
\(682\) −15.0061 −0.574612
\(683\) 14.6486 0.560512 0.280256 0.959925i \(-0.409581\pi\)
0.280256 + 0.959925i \(0.409581\pi\)
\(684\) 83.0999 3.17740
\(685\) 36.5613 1.39694
\(686\) 48.3246 1.84504
\(687\) −3.58014 −0.136591
\(688\) −11.6363 −0.443630
\(689\) 24.8438 0.946474
\(690\) −46.2518 −1.76078
\(691\) −30.2219 −1.14969 −0.574847 0.818261i \(-0.694939\pi\)
−0.574847 + 0.818261i \(0.694939\pi\)
\(692\) −71.0534 −2.70105
\(693\) −3.53851 −0.134417
\(694\) 69.0459 2.62095
\(695\) 49.1221 1.86331
\(696\) 11.4496 0.433998
\(697\) 8.14727 0.308600
\(698\) −8.56924 −0.324350
\(699\) −10.2378 −0.387229
\(700\) 11.5233 0.435541
\(701\) −46.9706 −1.77406 −0.887028 0.461716i \(-0.847234\pi\)
−0.887028 + 0.461716i \(0.847234\pi\)
\(702\) 67.3280 2.54113
\(703\) 14.6786 0.553616
\(704\) 15.5103 0.584568
\(705\) 7.70585 0.290219
\(706\) −47.0486 −1.77070
\(707\) −24.5499 −0.923293
\(708\) −20.5086 −0.770760
\(709\) 35.2164 1.32258 0.661290 0.750130i \(-0.270009\pi\)
0.661290 + 0.750130i \(0.270009\pi\)
\(710\) −16.2613 −0.610277
\(711\) 27.3016 1.02389
\(712\) −150.451 −5.63838
\(713\) 44.3940 1.66257
\(714\) −3.65469 −0.136773
\(715\) 14.0707 0.526215
\(716\) 25.8997 0.967919
\(717\) −19.3978 −0.724423
\(718\) −0.348025 −0.0129882
\(719\) 42.6654 1.59115 0.795576 0.605854i \(-0.207168\pi\)
0.795576 + 0.605854i \(0.207168\pi\)
\(720\) 66.2031 2.46724
\(721\) −16.3450 −0.608719
\(722\) −91.1171 −3.39103
\(723\) −17.6128 −0.655029
\(724\) −80.0865 −2.97639
\(725\) 2.30880 0.0857465
\(726\) 2.31593 0.0859521
\(727\) −41.1159 −1.52490 −0.762452 0.647045i \(-0.776005\pi\)
−0.762452 + 0.647045i \(0.776005\pi\)
\(728\) 71.6850 2.65682
\(729\) 5.73890 0.212552
\(730\) −82.5922 −3.05688
\(731\) 1.00000 0.0369863
\(732\) −7.03068 −0.259862
\(733\) 29.0554 1.07319 0.536593 0.843841i \(-0.319711\pi\)
0.536593 + 0.843841i \(0.319711\pi\)
\(734\) 5.50139 0.203060
\(735\) −9.96008 −0.367383
\(736\) −114.735 −4.22920
\(737\) −14.5722 −0.536774
\(738\) −48.6056 −1.78920
\(739\) 15.3390 0.564253 0.282127 0.959377i \(-0.408960\pi\)
0.282127 + 0.959377i \(0.408960\pi\)
\(740\) 25.9218 0.952904
\(741\) −35.2242 −1.29399
\(742\) 18.8094 0.690514
\(743\) −7.58541 −0.278282 −0.139141 0.990273i \(-0.544434\pi\)
−0.139141 + 0.990273i \(0.544434\pi\)
\(744\) 40.2151 1.47436
\(745\) −50.7179 −1.85816
\(746\) −8.09803 −0.296490
\(747\) 10.8835 0.398205
\(748\) −5.07876 −0.185698
\(749\) −16.6880 −0.609767
\(750\) 20.9321 0.764333
\(751\) 22.8706 0.834559 0.417279 0.908778i \(-0.362984\pi\)
0.417279 + 0.908778i \(0.362984\pi\)
\(752\) 40.5995 1.48051
\(753\) −8.43872 −0.307524
\(754\) 23.6928 0.862843
\(755\) −42.8605 −1.55985
\(756\) 36.5723 1.33012
\(757\) −32.4872 −1.18077 −0.590384 0.807123i \(-0.701024\pi\)
−0.590384 + 0.807123i \(0.701024\pi\)
\(758\) 50.9439 1.85037
\(759\) −6.85144 −0.248691
\(760\) −151.660 −5.50128
\(761\) 38.9926 1.41348 0.706740 0.707474i \(-0.250165\pi\)
0.706740 + 0.707474i \(0.250165\pi\)
\(762\) 39.6429 1.43611
\(763\) −17.0137 −0.615938
\(764\) −123.706 −4.47552
\(765\) −5.68936 −0.205699
\(766\) 72.3313 2.61344
\(767\) −25.7264 −0.928927
\(768\) −1.05105 −0.0379265
\(769\) −9.05845 −0.326656 −0.163328 0.986572i \(-0.552223\pi\)
−0.163328 + 0.986572i \(0.552223\pi\)
\(770\) 10.6530 0.383908
\(771\) 23.3895 0.842353
\(772\) 32.3771 1.16528
\(773\) −5.78595 −0.208106 −0.104053 0.994572i \(-0.533181\pi\)
−0.104053 + 0.994572i \(0.533181\pi\)
\(774\) −5.96587 −0.214439
\(775\) 8.10930 0.291295
\(776\) 22.1520 0.795211
\(777\) 2.76319 0.0991289
\(778\) 30.9178 1.10846
\(779\) 59.4510 2.13005
\(780\) −62.2043 −2.22727
\(781\) −2.40885 −0.0861953
\(782\) 20.9418 0.748877
\(783\) 7.32756 0.261866
\(784\) −52.4763 −1.87415
\(785\) 42.2024 1.50627
\(786\) −1.92260 −0.0685769
\(787\) −13.3593 −0.476207 −0.238104 0.971240i \(-0.576526\pi\)
−0.238104 + 0.971240i \(0.576526\pi\)
\(788\) 19.3601 0.689676
\(789\) 26.3217 0.937076
\(790\) −82.1939 −2.92433
\(791\) 24.4145 0.868079
\(792\) 18.3675 0.652661
\(793\) −8.81944 −0.313188
\(794\) 7.54882 0.267898
\(795\) −9.89430 −0.350915
\(796\) −86.7491 −3.07474
\(797\) 8.87297 0.314297 0.157148 0.987575i \(-0.449770\pi\)
0.157148 + 0.987575i \(0.449770\pi\)
\(798\) −26.6684 −0.944053
\(799\) −3.48904 −0.123433
\(800\) −20.9583 −0.740989
\(801\) −41.1846 −1.45519
\(802\) −76.1097 −2.68753
\(803\) −12.2347 −0.431752
\(804\) 64.4213 2.27196
\(805\) −31.5159 −1.11079
\(806\) 83.2176 2.93121
\(807\) 13.5042 0.475371
\(808\) 127.432 4.48304
\(809\) −12.3372 −0.433754 −0.216877 0.976199i \(-0.569587\pi\)
−0.216877 + 0.976199i \(0.569587\pi\)
\(810\) 18.5972 0.653440
\(811\) 31.3233 1.09991 0.549955 0.835194i \(-0.314645\pi\)
0.549955 + 0.835194i \(0.314645\pi\)
\(812\) 12.8699 0.451644
\(813\) 12.7768 0.448102
\(814\) 5.35202 0.187588
\(815\) 33.1515 1.16125
\(816\) 10.1289 0.354582
\(817\) 7.29705 0.255291
\(818\) −18.7716 −0.656335
\(819\) 19.6231 0.685688
\(820\) 104.988 3.66633
\(821\) 56.9650 1.98809 0.994047 0.108956i \(-0.0347507\pi\)
0.994047 + 0.108956i \(0.0347507\pi\)
\(822\) −33.3717 −1.16397
\(823\) −6.52318 −0.227384 −0.113692 0.993516i \(-0.536268\pi\)
−0.113692 + 0.993516i \(0.536268\pi\)
\(824\) 84.8425 2.95563
\(825\) −1.25153 −0.0435727
\(826\) −19.4776 −0.677713
\(827\) 34.5198 1.20037 0.600185 0.799861i \(-0.295093\pi\)
0.600185 + 0.799861i \(0.295093\pi\)
\(828\) −89.6372 −3.11511
\(829\) 13.1429 0.456473 0.228237 0.973606i \(-0.426704\pi\)
0.228237 + 0.973606i \(0.426704\pi\)
\(830\) −32.7657 −1.13731
\(831\) 2.73642 0.0949253
\(832\) −86.0141 −2.98200
\(833\) 4.50970 0.156252
\(834\) −44.8367 −1.55257
\(835\) 47.9146 1.65815
\(836\) −37.0600 −1.28175
\(837\) 25.7370 0.889600
\(838\) −44.1939 −1.52665
\(839\) 29.5728 1.02097 0.510483 0.859888i \(-0.329467\pi\)
0.510483 + 0.859888i \(0.329467\pi\)
\(840\) −28.5493 −0.985043
\(841\) −26.4214 −0.911083
\(842\) −91.6255 −3.15762
\(843\) −0.887852 −0.0305792
\(844\) 111.689 3.84450
\(845\) −45.0458 −1.54962
\(846\) 20.8152 0.715640
\(847\) 1.57807 0.0542230
\(848\) −52.1297 −1.79014
\(849\) −3.21955 −0.110495
\(850\) 3.82537 0.131209
\(851\) −15.8334 −0.542762
\(852\) 10.6491 0.364833
\(853\) 29.4565 1.00857 0.504285 0.863537i \(-0.331756\pi\)
0.504285 + 0.863537i \(0.331756\pi\)
\(854\) −6.67725 −0.228491
\(855\) −41.5155 −1.41980
\(856\) 86.6232 2.96072
\(857\) 15.0929 0.515564 0.257782 0.966203i \(-0.417008\pi\)
0.257782 + 0.966203i \(0.417008\pi\)
\(858\) −12.8432 −0.438459
\(859\) 8.36317 0.285348 0.142674 0.989770i \(-0.454430\pi\)
0.142674 + 0.989770i \(0.454430\pi\)
\(860\) 12.8862 0.439417
\(861\) 11.1914 0.381402
\(862\) −34.4238 −1.17248
\(863\) 3.72873 0.126927 0.0634637 0.997984i \(-0.479785\pi\)
0.0634637 + 0.997984i \(0.479785\pi\)
\(864\) −66.5168 −2.26295
\(865\) 35.4973 1.20694
\(866\) −63.0574 −2.14278
\(867\) −0.870455 −0.0295622
\(868\) 45.2035 1.53431
\(869\) −12.1757 −0.413031
\(870\) −9.43592 −0.319908
\(871\) 80.8115 2.73819
\(872\) 88.3137 2.99068
\(873\) 6.06392 0.205233
\(874\) 152.813 5.16899
\(875\) 14.2631 0.482180
\(876\) 54.0875 1.82745
\(877\) 42.0489 1.41989 0.709945 0.704257i \(-0.248720\pi\)
0.709945 + 0.704257i \(0.248720\pi\)
\(878\) 33.2620 1.12254
\(879\) −1.26361 −0.0426206
\(880\) −29.5245 −0.995272
\(881\) 3.70250 0.124740 0.0623702 0.998053i \(-0.480134\pi\)
0.0623702 + 0.998053i \(0.480134\pi\)
\(882\) −26.9043 −0.905915
\(883\) 5.52888 0.186062 0.0930309 0.995663i \(-0.470344\pi\)
0.0930309 + 0.995663i \(0.470344\pi\)
\(884\) 28.1647 0.947283
\(885\) 10.2458 0.344409
\(886\) −76.2787 −2.56263
\(887\) 38.8050 1.30294 0.651472 0.758673i \(-0.274152\pi\)
0.651472 + 0.758673i \(0.274152\pi\)
\(888\) −14.3430 −0.481319
\(889\) 27.0126 0.905973
\(890\) 123.990 4.15615
\(891\) 2.75487 0.0922916
\(892\) 68.4039 2.29033
\(893\) −25.4597 −0.851976
\(894\) 46.2933 1.54828
\(895\) −12.9392 −0.432508
\(896\) −19.1154 −0.638599
\(897\) 37.9953 1.26863
\(898\) 53.1040 1.77210
\(899\) 9.05689 0.302064
\(900\) −16.3737 −0.545791
\(901\) 4.47992 0.149248
\(902\) 21.6766 0.721751
\(903\) 1.37364 0.0457118
\(904\) −126.729 −4.21495
\(905\) 40.0101 1.32998
\(906\) 39.1214 1.29972
\(907\) 15.8936 0.527737 0.263869 0.964559i \(-0.415001\pi\)
0.263869 + 0.964559i \(0.415001\pi\)
\(908\) −40.3078 −1.33766
\(909\) 34.8834 1.15701
\(910\) −59.0773 −1.95839
\(911\) −17.9616 −0.595094 −0.297547 0.954707i \(-0.596169\pi\)
−0.297547 + 0.954707i \(0.596169\pi\)
\(912\) 73.9109 2.44743
\(913\) −4.85369 −0.160634
\(914\) 71.6905 2.37131
\(915\) 3.51243 0.116117
\(916\) 20.8887 0.690182
\(917\) −1.31006 −0.0432618
\(918\) 12.1408 0.400706
\(919\) −49.0097 −1.61668 −0.808340 0.588715i \(-0.799634\pi\)
−0.808340 + 0.588715i \(0.799634\pi\)
\(920\) 163.591 5.39342
\(921\) −7.43124 −0.244868
\(922\) 69.5992 2.29213
\(923\) 13.3585 0.439700
\(924\) −6.97637 −0.229506
\(925\) −2.89223 −0.0950961
\(926\) 80.0635 2.63105
\(927\) 23.2249 0.762806
\(928\) −23.4074 −0.768385
\(929\) −27.1642 −0.891228 −0.445614 0.895225i \(-0.647015\pi\)
−0.445614 + 0.895225i \(0.647015\pi\)
\(930\) −33.1422 −1.08678
\(931\) 32.9075 1.07850
\(932\) 59.7335 1.95664
\(933\) −8.72313 −0.285582
\(934\) 101.189 3.31101
\(935\) 2.53728 0.0829779
\(936\) −101.859 −3.32935
\(937\) 19.4721 0.636124 0.318062 0.948070i \(-0.396968\pi\)
0.318062 + 0.948070i \(0.396968\pi\)
\(938\) 61.1828 1.99769
\(939\) −12.4179 −0.405242
\(940\) −44.9606 −1.46645
\(941\) 31.3309 1.02136 0.510679 0.859772i \(-0.329394\pi\)
0.510679 + 0.859772i \(0.329394\pi\)
\(942\) −38.5206 −1.25507
\(943\) −64.1280 −2.08829
\(944\) 53.9817 1.75695
\(945\) −18.2710 −0.594356
\(946\) 2.66059 0.0865034
\(947\) 14.5406 0.472505 0.236253 0.971692i \(-0.424081\pi\)
0.236253 + 0.971692i \(0.424081\pi\)
\(948\) 53.8266 1.74821
\(949\) 67.8485 2.20246
\(950\) 27.9139 0.905647
\(951\) 20.7678 0.673443
\(952\) 12.9265 0.418950
\(953\) 30.6007 0.991254 0.495627 0.868535i \(-0.334938\pi\)
0.495627 + 0.868535i \(0.334938\pi\)
\(954\) −26.7266 −0.865307
\(955\) 61.8017 1.99986
\(956\) 113.178 3.66045
\(957\) −1.39777 −0.0451836
\(958\) 40.8244 1.31898
\(959\) −22.7394 −0.734294
\(960\) 34.2560 1.10561
\(961\) 0.810984 0.0261608
\(962\) −29.6801 −0.956925
\(963\) 23.7124 0.764120
\(964\) 102.764 3.30981
\(965\) −16.1752 −0.520697
\(966\) 28.7664 0.925544
\(967\) 23.5641 0.757770 0.378885 0.925444i \(-0.376308\pi\)
0.378885 + 0.925444i \(0.376308\pi\)
\(968\) −8.19134 −0.263280
\(969\) −6.35175 −0.204048
\(970\) −18.2560 −0.586165
\(971\) 25.4869 0.817913 0.408957 0.912554i \(-0.365893\pi\)
0.408957 + 0.912554i \(0.365893\pi\)
\(972\) −81.7049 −2.62069
\(973\) −30.5516 −0.979440
\(974\) 13.2514 0.424601
\(975\) 6.94047 0.222273
\(976\) 18.5058 0.592357
\(977\) 17.4287 0.557592 0.278796 0.960350i \(-0.410065\pi\)
0.278796 + 0.960350i \(0.410065\pi\)
\(978\) −30.2593 −0.967587
\(979\) 18.3671 0.587014
\(980\) 58.1131 1.85636
\(981\) 24.1751 0.771852
\(982\) −64.8268 −2.06871
\(983\) 24.3019 0.775110 0.387555 0.921847i \(-0.373320\pi\)
0.387555 + 0.921847i \(0.373320\pi\)
\(984\) −58.0916 −1.85189
\(985\) −9.67206 −0.308177
\(986\) 4.27238 0.136060
\(987\) −4.79267 −0.152552
\(988\) 205.519 6.53845
\(989\) −7.87110 −0.250286
\(990\) −15.1371 −0.481088
\(991\) 46.5378 1.47832 0.739161 0.673529i \(-0.235222\pi\)
0.739161 + 0.673529i \(0.235222\pi\)
\(992\) −82.2149 −2.61033
\(993\) −20.6143 −0.654175
\(994\) 10.1138 0.320789
\(995\) 43.3387 1.37393
\(996\) 21.4574 0.679902
\(997\) −52.3932 −1.65931 −0.829654 0.558278i \(-0.811462\pi\)
−0.829654 + 0.558278i \(0.811462\pi\)
\(998\) 41.5794 1.31617
\(999\) −9.17926 −0.290419
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 \(a_p\))