Properties

Label 8041.2.a.i.1.20
Level 8041
Weight 2
Character 8041.1
Self dual Yes
Analytic conductor 64.208
Analytic rank 0
Dimension 78
CM No

Related objects

Downloads

Learn more about

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 1.20
Character \(\chi\) = 8041.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.52440 q^{2} -2.61179 q^{3} +0.323806 q^{4} +2.08851 q^{5} +3.98143 q^{6} +2.52784 q^{7} +2.55520 q^{8} +3.82147 q^{9} +O(q^{10})\) \(q-1.52440 q^{2} -2.61179 q^{3} +0.323806 q^{4} +2.08851 q^{5} +3.98143 q^{6} +2.52784 q^{7} +2.55520 q^{8} +3.82147 q^{9} -3.18374 q^{10} +1.00000 q^{11} -0.845713 q^{12} +4.21148 q^{13} -3.85345 q^{14} -5.45477 q^{15} -4.54276 q^{16} -1.00000 q^{17} -5.82546 q^{18} +4.62200 q^{19} +0.676273 q^{20} -6.60220 q^{21} -1.52440 q^{22} -2.56492 q^{23} -6.67365 q^{24} -0.638107 q^{25} -6.42000 q^{26} -2.14551 q^{27} +0.818528 q^{28} -4.16417 q^{29} +8.31527 q^{30} -10.2776 q^{31} +1.81461 q^{32} -2.61179 q^{33} +1.52440 q^{34} +5.27943 q^{35} +1.23741 q^{36} +3.37372 q^{37} -7.04579 q^{38} -10.9995 q^{39} +5.33656 q^{40} -2.06542 q^{41} +10.0644 q^{42} -1.00000 q^{43} +0.323806 q^{44} +7.98119 q^{45} +3.90998 q^{46} +8.00918 q^{47} +11.8648 q^{48} -0.610027 q^{49} +0.972733 q^{50} +2.61179 q^{51} +1.36370 q^{52} +11.1669 q^{53} +3.27062 q^{54} +2.08851 q^{55} +6.45913 q^{56} -12.0717 q^{57} +6.34788 q^{58} -10.6860 q^{59} -1.76628 q^{60} +0.218045 q^{61} +15.6673 q^{62} +9.66006 q^{63} +6.31933 q^{64} +8.79574 q^{65} +3.98143 q^{66} +11.1241 q^{67} -0.323806 q^{68} +6.69905 q^{69} -8.04798 q^{70} +0.842522 q^{71} +9.76461 q^{72} -7.25499 q^{73} -5.14291 q^{74} +1.66660 q^{75} +1.49663 q^{76} +2.52784 q^{77} +16.7677 q^{78} +16.3831 q^{79} -9.48762 q^{80} -5.86078 q^{81} +3.14854 q^{82} +2.32483 q^{83} -2.13783 q^{84} -2.08851 q^{85} +1.52440 q^{86} +10.8760 q^{87} +2.55520 q^{88} -3.90945 q^{89} -12.1666 q^{90} +10.6460 q^{91} -0.830536 q^{92} +26.8431 q^{93} -12.2092 q^{94} +9.65311 q^{95} -4.73938 q^{96} -9.93107 q^{97} +0.929927 q^{98} +3.82147 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 78q + 7q^{2} + 10q^{3} + 91q^{4} + 17q^{5} + 12q^{6} + 11q^{7} + 33q^{8} + 102q^{9} + O(q^{10}) \) \( 78q + 7q^{2} + 10q^{3} + 91q^{4} + 17q^{5} + 12q^{6} + 11q^{7} + 33q^{8} + 102q^{9} + 3q^{10} + 78q^{11} + 31q^{12} - 16q^{13} + 31q^{14} + 38q^{15} + 121q^{16} - 78q^{17} + 11q^{18} + 51q^{20} + 6q^{21} + 7q^{22} + 48q^{23} + 11q^{24} + 101q^{25} + 18q^{26} + 46q^{27} + 27q^{28} + 22q^{29} + 14q^{30} + 56q^{31} + 83q^{32} + 10q^{33} - 7q^{34} + 24q^{35} + 139q^{36} + 53q^{37} + 10q^{38} + 79q^{39} - q^{40} + 23q^{41} + 17q^{42} - 78q^{43} + 91q^{44} + 76q^{45} + 21q^{46} + 57q^{47} + 78q^{48} + 115q^{49} + 58q^{50} - 10q^{51} - 63q^{52} + 22q^{53} - 18q^{54} + 17q^{55} + 111q^{56} - 11q^{57} + 36q^{58} + 71q^{59} + 36q^{60} + 4q^{61} - 5q^{62} + 71q^{63} + 183q^{64} + 47q^{65} + 12q^{66} + 11q^{67} - 91q^{68} + 31q^{69} + 33q^{70} + 159q^{71} + 59q^{72} + 2q^{73} - 4q^{74} + 83q^{75} - 44q^{76} + 11q^{77} + 101q^{78} + 35q^{79} + 85q^{80} + 170q^{81} + 98q^{82} - 32q^{83} + 44q^{84} - 17q^{85} - 7q^{86} - 6q^{87} + 33q^{88} + 50q^{89} - 5q^{90} + 86q^{91} + 106q^{92} + 68q^{93} - q^{94} + 109q^{95} - 50q^{96} + 40q^{97} + 106q^{98} + 102q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.52440 −1.07792 −0.538958 0.842333i \(-0.681182\pi\)
−0.538958 + 0.842333i \(0.681182\pi\)
\(3\) −2.61179 −1.50792 −0.753960 0.656920i \(-0.771859\pi\)
−0.753960 + 0.656920i \(0.771859\pi\)
\(4\) 0.323806 0.161903
\(5\) 2.08851 0.934012 0.467006 0.884254i \(-0.345333\pi\)
0.467006 + 0.884254i \(0.345333\pi\)
\(6\) 3.98143 1.62541
\(7\) 2.52784 0.955434 0.477717 0.878514i \(-0.341465\pi\)
0.477717 + 0.878514i \(0.341465\pi\)
\(8\) 2.55520 0.903398
\(9\) 3.82147 1.27382
\(10\) −3.18374 −1.00679
\(11\) 1.00000 0.301511
\(12\) −0.845713 −0.244136
\(13\) 4.21148 1.16806 0.584028 0.811734i \(-0.301476\pi\)
0.584028 + 0.811734i \(0.301476\pi\)
\(14\) −3.85345 −1.02988
\(15\) −5.45477 −1.40842
\(16\) −4.54276 −1.13569
\(17\) −1.00000 −0.242536
\(18\) −5.82546 −1.37307
\(19\) 4.62200 1.06036 0.530180 0.847885i \(-0.322124\pi\)
0.530180 + 0.847885i \(0.322124\pi\)
\(20\) 0.676273 0.151219
\(21\) −6.60220 −1.44072
\(22\) −1.52440 −0.325004
\(23\) −2.56492 −0.534823 −0.267412 0.963582i \(-0.586168\pi\)
−0.267412 + 0.963582i \(0.586168\pi\)
\(24\) −6.67365 −1.36225
\(25\) −0.638107 −0.127621
\(26\) −6.42000 −1.25907
\(27\) −2.14551 −0.412903
\(28\) 0.818528 0.154687
\(29\) −4.16417 −0.773267 −0.386634 0.922233i \(-0.626362\pi\)
−0.386634 + 0.922233i \(0.626362\pi\)
\(30\) 8.31527 1.51815
\(31\) −10.2776 −1.84592 −0.922960 0.384896i \(-0.874237\pi\)
−0.922960 + 0.384896i \(0.874237\pi\)
\(32\) 1.81461 0.320780
\(33\) −2.61179 −0.454655
\(34\) 1.52440 0.261433
\(35\) 5.27943 0.892387
\(36\) 1.23741 0.206235
\(37\) 3.37372 0.554636 0.277318 0.960778i \(-0.410554\pi\)
0.277318 + 0.960778i \(0.410554\pi\)
\(38\) −7.04579 −1.14298
\(39\) −10.9995 −1.76133
\(40\) 5.33656 0.843785
\(41\) −2.06542 −0.322565 −0.161282 0.986908i \(-0.551563\pi\)
−0.161282 + 0.986908i \(0.551563\pi\)
\(42\) 10.0644 1.55297
\(43\) −1.00000 −0.152499
\(44\) 0.323806 0.0488155
\(45\) 7.98119 1.18977
\(46\) 3.90998 0.576494
\(47\) 8.00918 1.16826 0.584130 0.811660i \(-0.301436\pi\)
0.584130 + 0.811660i \(0.301436\pi\)
\(48\) 11.8648 1.71253
\(49\) −0.610027 −0.0871467
\(50\) 0.972733 0.137565
\(51\) 2.61179 0.365724
\(52\) 1.36370 0.189111
\(53\) 11.1669 1.53389 0.766946 0.641712i \(-0.221776\pi\)
0.766946 + 0.641712i \(0.221776\pi\)
\(54\) 3.27062 0.445075
\(55\) 2.08851 0.281615
\(56\) 6.45913 0.863137
\(57\) −12.0717 −1.59894
\(58\) 6.34788 0.833517
\(59\) −10.6860 −1.39120 −0.695602 0.718428i \(-0.744862\pi\)
−0.695602 + 0.718428i \(0.744862\pi\)
\(60\) −1.76628 −0.228026
\(61\) 0.218045 0.0279178 0.0139589 0.999903i \(-0.495557\pi\)
0.0139589 + 0.999903i \(0.495557\pi\)
\(62\) 15.6673 1.98975
\(63\) 9.66006 1.21705
\(64\) 6.31933 0.789916
\(65\) 8.79574 1.09098
\(66\) 3.98143 0.490080
\(67\) 11.1241 1.35903 0.679515 0.733661i \(-0.262190\pi\)
0.679515 + 0.733661i \(0.262190\pi\)
\(68\) −0.323806 −0.0392672
\(69\) 6.69905 0.806471
\(70\) −8.04798 −0.961918
\(71\) 0.842522 0.0999889 0.0499945 0.998749i \(-0.484080\pi\)
0.0499945 + 0.998749i \(0.484080\pi\)
\(72\) 9.76461 1.15077
\(73\) −7.25499 −0.849133 −0.424566 0.905397i \(-0.639573\pi\)
−0.424566 + 0.905397i \(0.639573\pi\)
\(74\) −5.14291 −0.597851
\(75\) 1.66660 0.192443
\(76\) 1.49663 0.171675
\(77\) 2.52784 0.288074
\(78\) 16.7677 1.89857
\(79\) 16.3831 1.84324 0.921621 0.388090i \(-0.126865\pi\)
0.921621 + 0.388090i \(0.126865\pi\)
\(80\) −9.48762 −1.06075
\(81\) −5.86078 −0.651198
\(82\) 3.14854 0.347698
\(83\) 2.32483 0.255183 0.127591 0.991827i \(-0.459275\pi\)
0.127591 + 0.991827i \(0.459275\pi\)
\(84\) −2.13783 −0.233256
\(85\) −2.08851 −0.226531
\(86\) 1.52440 0.164381
\(87\) 10.8760 1.16602
\(88\) 2.55520 0.272385
\(89\) −3.90945 −0.414401 −0.207200 0.978299i \(-0.566435\pi\)
−0.207200 + 0.978299i \(0.566435\pi\)
\(90\) −12.1666 −1.28247
\(91\) 10.6460 1.11600
\(92\) −0.830536 −0.0865894
\(93\) 26.8431 2.78350
\(94\) −12.2092 −1.25929
\(95\) 9.65311 0.990388
\(96\) −4.73938 −0.483711
\(97\) −9.93107 −1.00835 −0.504174 0.863602i \(-0.668203\pi\)
−0.504174 + 0.863602i \(0.668203\pi\)
\(98\) 0.929927 0.0939368
\(99\) 3.82147 0.384072
\(100\) −0.206623 −0.0206623
\(101\) 12.4528 1.23910 0.619551 0.784956i \(-0.287315\pi\)
0.619551 + 0.784956i \(0.287315\pi\)
\(102\) −3.98143 −0.394220
\(103\) −9.36852 −0.923108 −0.461554 0.887112i \(-0.652708\pi\)
−0.461554 + 0.887112i \(0.652708\pi\)
\(104\) 10.7612 1.05522
\(105\) −13.7888 −1.34565
\(106\) −17.0229 −1.65341
\(107\) 15.5898 1.50712 0.753561 0.657378i \(-0.228334\pi\)
0.753561 + 0.657378i \(0.228334\pi\)
\(108\) −0.694728 −0.0668502
\(109\) −11.4522 −1.09692 −0.548462 0.836175i \(-0.684787\pi\)
−0.548462 + 0.836175i \(0.684787\pi\)
\(110\) −3.18374 −0.303558
\(111\) −8.81147 −0.836347
\(112\) −11.4834 −1.08508
\(113\) 10.5061 0.988329 0.494164 0.869368i \(-0.335474\pi\)
0.494164 + 0.869368i \(0.335474\pi\)
\(114\) 18.4022 1.72352
\(115\) −5.35688 −0.499531
\(116\) −1.34838 −0.125194
\(117\) 16.0941 1.48790
\(118\) 16.2898 1.49960
\(119\) −2.52784 −0.231727
\(120\) −13.9380 −1.27236
\(121\) 1.00000 0.0909091
\(122\) −0.332388 −0.0300930
\(123\) 5.39446 0.486402
\(124\) −3.32796 −0.298860
\(125\) −11.7753 −1.05321
\(126\) −14.7258 −1.31188
\(127\) 0.0683139 0.00606188 0.00303094 0.999995i \(-0.499035\pi\)
0.00303094 + 0.999995i \(0.499035\pi\)
\(128\) −13.2624 −1.17224
\(129\) 2.61179 0.229956
\(130\) −13.4083 −1.17598
\(131\) 8.40815 0.734624 0.367312 0.930098i \(-0.380278\pi\)
0.367312 + 0.930098i \(0.380278\pi\)
\(132\) −0.845713 −0.0736099
\(133\) 11.6837 1.01310
\(134\) −16.9577 −1.46492
\(135\) −4.48093 −0.385657
\(136\) −2.55520 −0.219106
\(137\) −4.79750 −0.409878 −0.204939 0.978775i \(-0.565700\pi\)
−0.204939 + 0.978775i \(0.565700\pi\)
\(138\) −10.2121 −0.869308
\(139\) 20.4479 1.73437 0.867184 0.497988i \(-0.165928\pi\)
0.867184 + 0.497988i \(0.165928\pi\)
\(140\) 1.70951 0.144480
\(141\) −20.9183 −1.76164
\(142\) −1.28434 −0.107780
\(143\) 4.21148 0.352182
\(144\) −17.3600 −1.44667
\(145\) −8.69693 −0.722241
\(146\) 11.0595 0.915294
\(147\) 1.59326 0.131410
\(148\) 1.09243 0.0897972
\(149\) 13.8181 1.13202 0.566011 0.824398i \(-0.308486\pi\)
0.566011 + 0.824398i \(0.308486\pi\)
\(150\) −2.54058 −0.207437
\(151\) −9.14676 −0.744353 −0.372176 0.928162i \(-0.621388\pi\)
−0.372176 + 0.928162i \(0.621388\pi\)
\(152\) 11.8101 0.957927
\(153\) −3.82147 −0.308947
\(154\) −3.85345 −0.310520
\(155\) −21.4650 −1.72411
\(156\) −3.56171 −0.285165
\(157\) −6.75842 −0.539381 −0.269690 0.962947i \(-0.586921\pi\)
−0.269690 + 0.962947i \(0.586921\pi\)
\(158\) −24.9745 −1.98686
\(159\) −29.1656 −2.31299
\(160\) 3.78983 0.299613
\(161\) −6.48371 −0.510988
\(162\) 8.93419 0.701936
\(163\) 18.9536 1.48456 0.742281 0.670089i \(-0.233744\pi\)
0.742281 + 0.670089i \(0.233744\pi\)
\(164\) −0.668795 −0.0522241
\(165\) −5.45477 −0.424653
\(166\) −3.54397 −0.275066
\(167\) −4.16622 −0.322392 −0.161196 0.986922i \(-0.551535\pi\)
−0.161196 + 0.986922i \(0.551535\pi\)
\(168\) −16.8699 −1.30154
\(169\) 4.73659 0.364353
\(170\) 3.18374 0.244182
\(171\) 17.6628 1.35071
\(172\) −0.323806 −0.0246899
\(173\) 17.2976 1.31511 0.657554 0.753407i \(-0.271591\pi\)
0.657554 + 0.753407i \(0.271591\pi\)
\(174\) −16.5793 −1.25688
\(175\) −1.61303 −0.121934
\(176\) −4.54276 −0.342423
\(177\) 27.9097 2.09782
\(178\) 5.95957 0.446689
\(179\) −22.6720 −1.69458 −0.847292 0.531127i \(-0.821769\pi\)
−0.847292 + 0.531127i \(0.821769\pi\)
\(180\) 2.58435 0.192626
\(181\) 19.5544 1.45347 0.726733 0.686920i \(-0.241038\pi\)
0.726733 + 0.686920i \(0.241038\pi\)
\(182\) −16.2287 −1.20295
\(183\) −0.569488 −0.0420978
\(184\) −6.55388 −0.483158
\(185\) 7.04607 0.518037
\(186\) −40.9197 −3.00038
\(187\) −1.00000 −0.0731272
\(188\) 2.59342 0.189144
\(189\) −5.42350 −0.394502
\(190\) −14.7152 −1.06756
\(191\) 10.5745 0.765145 0.382573 0.923925i \(-0.375038\pi\)
0.382573 + 0.923925i \(0.375038\pi\)
\(192\) −16.5048 −1.19113
\(193\) −14.9762 −1.07801 −0.539006 0.842302i \(-0.681200\pi\)
−0.539006 + 0.842302i \(0.681200\pi\)
\(194\) 15.1390 1.08691
\(195\) −22.9727 −1.64511
\(196\) −0.197530 −0.0141093
\(197\) 15.0577 1.07282 0.536408 0.843959i \(-0.319781\pi\)
0.536408 + 0.843959i \(0.319781\pi\)
\(198\) −5.82546 −0.413997
\(199\) −11.2627 −0.798390 −0.399195 0.916866i \(-0.630710\pi\)
−0.399195 + 0.916866i \(0.630710\pi\)
\(200\) −1.63049 −0.115293
\(201\) −29.0540 −2.04931
\(202\) −18.9831 −1.33565
\(203\) −10.5264 −0.738805
\(204\) 0.845713 0.0592118
\(205\) −4.31366 −0.301279
\(206\) 14.2814 0.995033
\(207\) −9.80177 −0.681270
\(208\) −19.1318 −1.32655
\(209\) 4.62200 0.319710
\(210\) 21.0197 1.45049
\(211\) 25.5415 1.75835 0.879174 0.476501i \(-0.158095\pi\)
0.879174 + 0.476501i \(0.158095\pi\)
\(212\) 3.61590 0.248341
\(213\) −2.20049 −0.150775
\(214\) −23.7651 −1.62455
\(215\) −2.08851 −0.142436
\(216\) −5.48220 −0.373016
\(217\) −25.9802 −1.76365
\(218\) 17.4578 1.18239
\(219\) 18.9485 1.28042
\(220\) 0.676273 0.0455943
\(221\) −4.21148 −0.283295
\(222\) 13.4322 0.901512
\(223\) −7.14062 −0.478171 −0.239085 0.970999i \(-0.576848\pi\)
−0.239085 + 0.970999i \(0.576848\pi\)
\(224\) 4.58704 0.306484
\(225\) −2.43851 −0.162567
\(226\) −16.0155 −1.06534
\(227\) 19.8202 1.31551 0.657755 0.753232i \(-0.271506\pi\)
0.657755 + 0.753232i \(0.271506\pi\)
\(228\) −3.90889 −0.258872
\(229\) −11.5225 −0.761430 −0.380715 0.924692i \(-0.624322\pi\)
−0.380715 + 0.924692i \(0.624322\pi\)
\(230\) 8.16604 0.538453
\(231\) −6.60220 −0.434393
\(232\) −10.6403 −0.698568
\(233\) −0.684884 −0.0448683 −0.0224341 0.999748i \(-0.507142\pi\)
−0.0224341 + 0.999748i \(0.507142\pi\)
\(234\) −24.5338 −1.60383
\(235\) 16.7273 1.09117
\(236\) −3.46020 −0.225240
\(237\) −42.7893 −2.77946
\(238\) 3.85345 0.249782
\(239\) 15.6962 1.01530 0.507650 0.861563i \(-0.330514\pi\)
0.507650 + 0.861563i \(0.330514\pi\)
\(240\) 24.7797 1.59952
\(241\) 22.3618 1.44045 0.720226 0.693740i \(-0.244038\pi\)
0.720226 + 0.693740i \(0.244038\pi\)
\(242\) −1.52440 −0.0979924
\(243\) 21.7437 1.39486
\(244\) 0.0706041 0.00451997
\(245\) −1.27405 −0.0813961
\(246\) −8.22333 −0.524300
\(247\) 19.4655 1.23856
\(248\) −26.2614 −1.66760
\(249\) −6.07197 −0.384795
\(250\) 17.9503 1.13527
\(251\) −25.1249 −1.58587 −0.792936 0.609305i \(-0.791449\pi\)
−0.792936 + 0.609305i \(0.791449\pi\)
\(252\) 3.12798 0.197044
\(253\) −2.56492 −0.161255
\(254\) −0.104138 −0.00653420
\(255\) 5.45477 0.341591
\(256\) 7.57862 0.473664
\(257\) −16.0150 −0.998988 −0.499494 0.866317i \(-0.666481\pi\)
−0.499494 + 0.866317i \(0.666481\pi\)
\(258\) −3.98143 −0.247873
\(259\) 8.52823 0.529918
\(260\) 2.84811 0.176632
\(261\) −15.9133 −0.985005
\(262\) −12.8174 −0.791862
\(263\) −20.7177 −1.27751 −0.638754 0.769411i \(-0.720550\pi\)
−0.638754 + 0.769411i \(0.720550\pi\)
\(264\) −6.67365 −0.410735
\(265\) 23.3222 1.43267
\(266\) −17.8106 −1.09204
\(267\) 10.2107 0.624883
\(268\) 3.60206 0.220031
\(269\) 18.5811 1.13291 0.566455 0.824092i \(-0.308314\pi\)
0.566455 + 0.824092i \(0.308314\pi\)
\(270\) 6.83074 0.415706
\(271\) 15.8732 0.964227 0.482114 0.876109i \(-0.339869\pi\)
0.482114 + 0.876109i \(0.339869\pi\)
\(272\) 4.54276 0.275445
\(273\) −27.8050 −1.68284
\(274\) 7.31333 0.441814
\(275\) −0.638107 −0.0384793
\(276\) 2.16919 0.130570
\(277\) −9.94758 −0.597692 −0.298846 0.954301i \(-0.596602\pi\)
−0.298846 + 0.954301i \(0.596602\pi\)
\(278\) −31.1708 −1.86950
\(279\) −39.2757 −2.35138
\(280\) 13.4900 0.806181
\(281\) −9.31187 −0.555500 −0.277750 0.960653i \(-0.589589\pi\)
−0.277750 + 0.960653i \(0.589589\pi\)
\(282\) 31.8880 1.89890
\(283\) −1.88517 −0.112062 −0.0560310 0.998429i \(-0.517845\pi\)
−0.0560310 + 0.998429i \(0.517845\pi\)
\(284\) 0.272813 0.0161885
\(285\) −25.2119 −1.49343
\(286\) −6.42000 −0.379622
\(287\) −5.22106 −0.308189
\(288\) 6.93447 0.408617
\(289\) 1.00000 0.0588235
\(290\) 13.2576 0.778515
\(291\) 25.9379 1.52051
\(292\) −2.34921 −0.137477
\(293\) 29.5867 1.72847 0.864237 0.503085i \(-0.167802\pi\)
0.864237 + 0.503085i \(0.167802\pi\)
\(294\) −2.42878 −0.141649
\(295\) −22.3179 −1.29940
\(296\) 8.62052 0.501058
\(297\) −2.14551 −0.124495
\(298\) −21.0643 −1.22022
\(299\) −10.8021 −0.624703
\(300\) 0.539656 0.0311570
\(301\) −2.52784 −0.145702
\(302\) 13.9434 0.802350
\(303\) −32.5242 −1.86847
\(304\) −20.9966 −1.20424
\(305\) 0.455390 0.0260755
\(306\) 5.82546 0.333019
\(307\) 12.4896 0.712818 0.356409 0.934330i \(-0.384001\pi\)
0.356409 + 0.934330i \(0.384001\pi\)
\(308\) 0.818528 0.0466400
\(309\) 24.4687 1.39197
\(310\) 32.7213 1.85845
\(311\) −32.9977 −1.87113 −0.935564 0.353156i \(-0.885109\pi\)
−0.935564 + 0.353156i \(0.885109\pi\)
\(312\) −28.1060 −1.59119
\(313\) −17.5560 −0.992326 −0.496163 0.868229i \(-0.665258\pi\)
−0.496163 + 0.868229i \(0.665258\pi\)
\(314\) 10.3026 0.581407
\(315\) 20.1752 1.13674
\(316\) 5.30494 0.298426
\(317\) −25.5227 −1.43350 −0.716748 0.697332i \(-0.754370\pi\)
−0.716748 + 0.697332i \(0.754370\pi\)
\(318\) 44.4602 2.49320
\(319\) −4.16417 −0.233149
\(320\) 13.1980 0.737791
\(321\) −40.7173 −2.27262
\(322\) 9.88379 0.550802
\(323\) −4.62200 −0.257175
\(324\) −1.89775 −0.105431
\(325\) −2.68738 −0.149069
\(326\) −28.8930 −1.60023
\(327\) 29.9109 1.65407
\(328\) −5.27756 −0.291404
\(329\) 20.2459 1.11619
\(330\) 8.31527 0.457741
\(331\) −1.23874 −0.0680873 −0.0340437 0.999420i \(-0.510839\pi\)
−0.0340437 + 0.999420i \(0.510839\pi\)
\(332\) 0.752792 0.0413148
\(333\) 12.8926 0.706509
\(334\) 6.35100 0.347511
\(335\) 23.2329 1.26935
\(336\) 29.9922 1.63621
\(337\) 19.7330 1.07492 0.537462 0.843288i \(-0.319383\pi\)
0.537462 + 0.843288i \(0.319383\pi\)
\(338\) −7.22047 −0.392742
\(339\) −27.4397 −1.49032
\(340\) −0.676273 −0.0366760
\(341\) −10.2776 −0.556566
\(342\) −26.9253 −1.45595
\(343\) −19.2369 −1.03870
\(344\) −2.55520 −0.137767
\(345\) 13.9911 0.753253
\(346\) −26.3684 −1.41758
\(347\) 24.9505 1.33941 0.669707 0.742625i \(-0.266420\pi\)
0.669707 + 0.742625i \(0.266420\pi\)
\(348\) 3.52169 0.188783
\(349\) 5.02067 0.268750 0.134375 0.990931i \(-0.457097\pi\)
0.134375 + 0.990931i \(0.457097\pi\)
\(350\) 2.45891 0.131434
\(351\) −9.03578 −0.482294
\(352\) 1.81461 0.0967189
\(353\) −2.23938 −0.119190 −0.0595950 0.998223i \(-0.518981\pi\)
−0.0595950 + 0.998223i \(0.518981\pi\)
\(354\) −42.5457 −2.26128
\(355\) 1.75962 0.0933909
\(356\) −1.26590 −0.0670926
\(357\) 6.60220 0.349425
\(358\) 34.5613 1.82662
\(359\) 25.6692 1.35477 0.677383 0.735630i \(-0.263114\pi\)
0.677383 + 0.735630i \(0.263114\pi\)
\(360\) 20.3935 1.07483
\(361\) 2.36288 0.124362
\(362\) −29.8088 −1.56671
\(363\) −2.61179 −0.137084
\(364\) 3.44722 0.180683
\(365\) −15.1522 −0.793100
\(366\) 0.868130 0.0453779
\(367\) 8.89968 0.464560 0.232280 0.972649i \(-0.425381\pi\)
0.232280 + 0.972649i \(0.425381\pi\)
\(368\) 11.6518 0.607394
\(369\) −7.89295 −0.410890
\(370\) −10.7410 −0.558400
\(371\) 28.2281 1.46553
\(372\) 8.69194 0.450656
\(373\) −31.5846 −1.63539 −0.817695 0.575652i \(-0.804748\pi\)
−0.817695 + 0.575652i \(0.804748\pi\)
\(374\) 1.52440 0.0788250
\(375\) 30.7546 1.58816
\(376\) 20.4650 1.05540
\(377\) −17.5373 −0.903219
\(378\) 8.26761 0.425240
\(379\) 27.3785 1.40634 0.703168 0.711023i \(-0.251768\pi\)
0.703168 + 0.711023i \(0.251768\pi\)
\(380\) 3.12573 0.160347
\(381\) −0.178422 −0.00914083
\(382\) −16.1198 −0.824762
\(383\) −31.1780 −1.59312 −0.796561 0.604558i \(-0.793350\pi\)
−0.796561 + 0.604558i \(0.793350\pi\)
\(384\) 34.6387 1.76765
\(385\) 5.27943 0.269065
\(386\) 22.8298 1.16201
\(387\) −3.82147 −0.194256
\(388\) −3.21573 −0.163254
\(389\) 6.43830 0.326435 0.163217 0.986590i \(-0.447813\pi\)
0.163217 + 0.986590i \(0.447813\pi\)
\(390\) 35.0196 1.77329
\(391\) 2.56492 0.129714
\(392\) −1.55874 −0.0787282
\(393\) −21.9604 −1.10775
\(394\) −22.9540 −1.15641
\(395\) 34.2163 1.72161
\(396\) 1.23741 0.0621823
\(397\) −27.9240 −1.40147 −0.700733 0.713424i \(-0.747143\pi\)
−0.700733 + 0.713424i \(0.747143\pi\)
\(398\) 17.1689 0.860598
\(399\) −30.5154 −1.52768
\(400\) 2.89877 0.144938
\(401\) −14.1222 −0.705230 −0.352615 0.935769i \(-0.614707\pi\)
−0.352615 + 0.935769i \(0.614707\pi\)
\(402\) 44.2900 2.20898
\(403\) −43.2841 −2.15614
\(404\) 4.03229 0.200614
\(405\) −12.2403 −0.608227
\(406\) 16.0464 0.796370
\(407\) 3.37372 0.167229
\(408\) 6.67365 0.330395
\(409\) −1.78582 −0.0883030 −0.0441515 0.999025i \(-0.514058\pi\)
−0.0441515 + 0.999025i \(0.514058\pi\)
\(410\) 6.57576 0.324754
\(411\) 12.5301 0.618064
\(412\) −3.03358 −0.149454
\(413\) −27.0126 −1.32920
\(414\) 14.9419 0.734352
\(415\) 4.85543 0.238344
\(416\) 7.64219 0.374689
\(417\) −53.4057 −2.61529
\(418\) −7.04579 −0.344621
\(419\) −8.42087 −0.411386 −0.205693 0.978617i \(-0.565945\pi\)
−0.205693 + 0.978617i \(0.565945\pi\)
\(420\) −4.46488 −0.217864
\(421\) −29.8918 −1.45684 −0.728418 0.685133i \(-0.759744\pi\)
−0.728418 + 0.685133i \(0.759744\pi\)
\(422\) −38.9355 −1.89535
\(423\) 30.6069 1.48816
\(424\) 28.5336 1.38572
\(425\) 0.638107 0.0309527
\(426\) 3.35444 0.162523
\(427\) 0.551182 0.0266736
\(428\) 5.04806 0.244007
\(429\) −10.9995 −0.531062
\(430\) 3.18374 0.153534
\(431\) 24.5729 1.18363 0.591817 0.806072i \(-0.298411\pi\)
0.591817 + 0.806072i \(0.298411\pi\)
\(432\) 9.74654 0.468930
\(433\) 15.2346 0.732129 0.366064 0.930590i \(-0.380705\pi\)
0.366064 + 0.930590i \(0.380705\pi\)
\(434\) 39.6044 1.90107
\(435\) 22.7146 1.08908
\(436\) −3.70829 −0.177595
\(437\) −11.8551 −0.567105
\(438\) −28.8852 −1.38019
\(439\) 7.51213 0.358534 0.179267 0.983800i \(-0.442627\pi\)
0.179267 + 0.983800i \(0.442627\pi\)
\(440\) 5.33656 0.254411
\(441\) −2.33120 −0.111009
\(442\) 6.42000 0.305368
\(443\) −0.549215 −0.0260940 −0.0130470 0.999915i \(-0.504153\pi\)
−0.0130470 + 0.999915i \(0.504153\pi\)
\(444\) −2.85320 −0.135407
\(445\) −8.16494 −0.387055
\(446\) 10.8852 0.515428
\(447\) −36.0900 −1.70700
\(448\) 15.9743 0.754712
\(449\) 27.9509 1.31909 0.659543 0.751667i \(-0.270750\pi\)
0.659543 + 0.751667i \(0.270750\pi\)
\(450\) 3.71727 0.175234
\(451\) −2.06542 −0.0972569
\(452\) 3.40193 0.160013
\(453\) 23.8895 1.12242
\(454\) −30.2139 −1.41801
\(455\) 22.2342 1.04236
\(456\) −30.8456 −1.44448
\(457\) 17.8452 0.834764 0.417382 0.908731i \(-0.362948\pi\)
0.417382 + 0.908731i \(0.362948\pi\)
\(458\) 17.5650 0.820757
\(459\) 2.14551 0.100144
\(460\) −1.73459 −0.0808755
\(461\) −24.2712 −1.13042 −0.565211 0.824947i \(-0.691205\pi\)
−0.565211 + 0.824947i \(0.691205\pi\)
\(462\) 10.0644 0.468239
\(463\) 42.1441 1.95860 0.979301 0.202410i \(-0.0648774\pi\)
0.979301 + 0.202410i \(0.0648774\pi\)
\(464\) 18.9168 0.878192
\(465\) 56.0622 2.59982
\(466\) 1.04404 0.0483642
\(467\) 16.7816 0.776560 0.388280 0.921541i \(-0.373069\pi\)
0.388280 + 0.921541i \(0.373069\pi\)
\(468\) 5.21134 0.240894
\(469\) 28.1201 1.29846
\(470\) −25.4992 −1.17619
\(471\) 17.6516 0.813343
\(472\) −27.3049 −1.25681
\(473\) −1.00000 −0.0459800
\(474\) 65.2281 2.99603
\(475\) −2.94933 −0.135325
\(476\) −0.818528 −0.0375172
\(477\) 42.6740 1.95391
\(478\) −23.9273 −1.09441
\(479\) 24.7169 1.12934 0.564672 0.825315i \(-0.309003\pi\)
0.564672 + 0.825315i \(0.309003\pi\)
\(480\) −9.89827 −0.451792
\(481\) 14.2084 0.647846
\(482\) −34.0884 −1.55269
\(483\) 16.9341 0.770529
\(484\) 0.323806 0.0147184
\(485\) −20.7412 −0.941808
\(486\) −33.1461 −1.50354
\(487\) 19.1843 0.869323 0.434661 0.900594i \(-0.356868\pi\)
0.434661 + 0.900594i \(0.356868\pi\)
\(488\) 0.557147 0.0252209
\(489\) −49.5030 −2.23860
\(490\) 1.94217 0.0877381
\(491\) −17.2250 −0.777354 −0.388677 0.921374i \(-0.627068\pi\)
−0.388677 + 0.921374i \(0.627068\pi\)
\(492\) 1.74676 0.0787498
\(493\) 4.16417 0.187545
\(494\) −29.6732 −1.33506
\(495\) 7.98119 0.358728
\(496\) 46.6889 2.09639
\(497\) 2.12976 0.0955328
\(498\) 9.25613 0.414777
\(499\) 28.1566 1.26046 0.630230 0.776408i \(-0.282960\pi\)
0.630230 + 0.776408i \(0.282960\pi\)
\(500\) −3.81290 −0.170518
\(501\) 10.8813 0.486141
\(502\) 38.3005 1.70944
\(503\) 33.4928 1.49337 0.746684 0.665179i \(-0.231645\pi\)
0.746684 + 0.665179i \(0.231645\pi\)
\(504\) 24.6834 1.09948
\(505\) 26.0079 1.15734
\(506\) 3.90998 0.173820
\(507\) −12.3710 −0.549415
\(508\) 0.0221204 0.000981435 0
\(509\) 38.2477 1.69530 0.847650 0.530556i \(-0.178017\pi\)
0.847650 + 0.530556i \(0.178017\pi\)
\(510\) −8.31527 −0.368206
\(511\) −18.3395 −0.811290
\(512\) 14.9720 0.661674
\(513\) −9.91654 −0.437826
\(514\) 24.4133 1.07683
\(515\) −19.5663 −0.862194
\(516\) 0.845713 0.0372305
\(517\) 8.00918 0.352244
\(518\) −13.0005 −0.571207
\(519\) −45.1776 −1.98308
\(520\) 22.4749 0.985587
\(521\) 5.61957 0.246198 0.123099 0.992394i \(-0.460717\pi\)
0.123099 + 0.992394i \(0.460717\pi\)
\(522\) 24.2582 1.06175
\(523\) 29.0896 1.27200 0.635999 0.771690i \(-0.280588\pi\)
0.635999 + 0.771690i \(0.280588\pi\)
\(524\) 2.72261 0.118938
\(525\) 4.21291 0.183866
\(526\) 31.5821 1.37705
\(527\) 10.2776 0.447701
\(528\) 11.8648 0.516347
\(529\) −16.4212 −0.713964
\(530\) −35.5525 −1.54430
\(531\) −40.8364 −1.77215
\(532\) 3.78324 0.164024
\(533\) −8.69849 −0.376773
\(534\) −15.5652 −0.673571
\(535\) 32.5595 1.40767
\(536\) 28.4244 1.22775
\(537\) 59.2146 2.55530
\(538\) −28.3251 −1.22118
\(539\) −0.610027 −0.0262757
\(540\) −1.45095 −0.0624389
\(541\) −21.2457 −0.913423 −0.456711 0.889615i \(-0.650973\pi\)
−0.456711 + 0.889615i \(0.650973\pi\)
\(542\) −24.1971 −1.03936
\(543\) −51.0720 −2.19171
\(544\) −1.81461 −0.0778006
\(545\) −23.9181 −1.02454
\(546\) 42.3861 1.81396
\(547\) −41.3094 −1.76626 −0.883131 0.469127i \(-0.844569\pi\)
−0.883131 + 0.469127i \(0.844569\pi\)
\(548\) −1.55346 −0.0663604
\(549\) 0.833252 0.0355623
\(550\) 0.972733 0.0414775
\(551\) −19.2468 −0.819941
\(552\) 17.1174 0.728564
\(553\) 41.4138 1.76110
\(554\) 15.1641 0.644262
\(555\) −18.4029 −0.781158
\(556\) 6.62114 0.280799
\(557\) 31.1040 1.31792 0.658959 0.752179i \(-0.270997\pi\)
0.658959 + 0.752179i \(0.270997\pi\)
\(558\) 59.8720 2.53458
\(559\) −4.21148 −0.178127
\(560\) −23.9832 −1.01347
\(561\) 2.61179 0.110270
\(562\) 14.1951 0.598782
\(563\) −10.0863 −0.425088 −0.212544 0.977152i \(-0.568175\pi\)
−0.212544 + 0.977152i \(0.568175\pi\)
\(564\) −6.77348 −0.285215
\(565\) 21.9421 0.923111
\(566\) 2.87377 0.120793
\(567\) −14.8151 −0.622176
\(568\) 2.15281 0.0903298
\(569\) 34.2226 1.43468 0.717342 0.696721i \(-0.245359\pi\)
0.717342 + 0.696721i \(0.245359\pi\)
\(570\) 38.4332 1.60979
\(571\) 20.3009 0.849566 0.424783 0.905295i \(-0.360350\pi\)
0.424783 + 0.905295i \(0.360350\pi\)
\(572\) 1.36370 0.0570192
\(573\) −27.6185 −1.15378
\(574\) 7.95899 0.332202
\(575\) 1.63670 0.0682549
\(576\) 24.1491 1.00621
\(577\) 37.3636 1.55547 0.777734 0.628594i \(-0.216369\pi\)
0.777734 + 0.628594i \(0.216369\pi\)
\(578\) −1.52440 −0.0634068
\(579\) 39.1148 1.62556
\(580\) −2.81611 −0.116933
\(581\) 5.87679 0.243810
\(582\) −39.5398 −1.63898
\(583\) 11.1669 0.462486
\(584\) −18.5379 −0.767105
\(585\) 33.6127 1.38971
\(586\) −45.1021 −1.86315
\(587\) −7.72624 −0.318896 −0.159448 0.987206i \(-0.550971\pi\)
−0.159448 + 0.987206i \(0.550971\pi\)
\(588\) 0.515908 0.0212757
\(589\) −47.5033 −1.95734
\(590\) 34.0215 1.40064
\(591\) −39.3276 −1.61772
\(592\) −15.3260 −0.629895
\(593\) −17.6991 −0.726817 −0.363408 0.931630i \(-0.618387\pi\)
−0.363408 + 0.931630i \(0.618387\pi\)
\(594\) 3.27062 0.134195
\(595\) −5.27943 −0.216436
\(596\) 4.47437 0.183278
\(597\) 29.4158 1.20391
\(598\) 16.4668 0.673377
\(599\) 35.4275 1.44753 0.723763 0.690048i \(-0.242411\pi\)
0.723763 + 0.690048i \(0.242411\pi\)
\(600\) 4.25850 0.173853
\(601\) −44.0727 −1.79776 −0.898881 0.438192i \(-0.855619\pi\)
−0.898881 + 0.438192i \(0.855619\pi\)
\(602\) 3.85345 0.157055
\(603\) 42.5106 1.73116
\(604\) −2.96177 −0.120513
\(605\) 2.08851 0.0849102
\(606\) 49.5800 2.01405
\(607\) −19.2005 −0.779326 −0.389663 0.920958i \(-0.627408\pi\)
−0.389663 + 0.920958i \(0.627408\pi\)
\(608\) 8.38711 0.340142
\(609\) 27.4927 1.11406
\(610\) −0.694198 −0.0281073
\(611\) 33.7305 1.36459
\(612\) −1.23741 −0.0500195
\(613\) −26.8182 −1.08318 −0.541588 0.840644i \(-0.682177\pi\)
−0.541588 + 0.840644i \(0.682177\pi\)
\(614\) −19.0392 −0.768358
\(615\) 11.2664 0.454305
\(616\) 6.45913 0.260246
\(617\) −28.6889 −1.15497 −0.577487 0.816400i \(-0.695966\pi\)
−0.577487 + 0.816400i \(0.695966\pi\)
\(618\) −37.3001 −1.50043
\(619\) −2.58005 −0.103701 −0.0518505 0.998655i \(-0.516512\pi\)
−0.0518505 + 0.998655i \(0.516512\pi\)
\(620\) −6.95049 −0.279138
\(621\) 5.50306 0.220830
\(622\) 50.3018 2.01692
\(623\) −9.88246 −0.395932
\(624\) 49.9682 2.00033
\(625\) −21.4023 −0.856091
\(626\) 26.7625 1.06964
\(627\) −12.0717 −0.482098
\(628\) −2.18841 −0.0873272
\(629\) −3.37372 −0.134519
\(630\) −30.7551 −1.22531
\(631\) 40.8951 1.62801 0.814004 0.580860i \(-0.197284\pi\)
0.814004 + 0.580860i \(0.197284\pi\)
\(632\) 41.8620 1.66518
\(633\) −66.7091 −2.65145
\(634\) 38.9068 1.54519
\(635\) 0.142675 0.00566187
\(636\) −9.44400 −0.374479
\(637\) −2.56912 −0.101792
\(638\) 6.34788 0.251315
\(639\) 3.21967 0.127368
\(640\) −27.6988 −1.09489
\(641\) 24.5958 0.971476 0.485738 0.874104i \(-0.338551\pi\)
0.485738 + 0.874104i \(0.338551\pi\)
\(642\) 62.0696 2.44969
\(643\) 21.7586 0.858074 0.429037 0.903287i \(-0.358853\pi\)
0.429037 + 0.903287i \(0.358853\pi\)
\(644\) −2.09946 −0.0827304
\(645\) 5.45477 0.214781
\(646\) 7.04579 0.277213
\(647\) −20.5541 −0.808067 −0.404033 0.914744i \(-0.632392\pi\)
−0.404033 + 0.914744i \(0.632392\pi\)
\(648\) −14.9754 −0.588291
\(649\) −10.6860 −0.419464
\(650\) 4.09665 0.160684
\(651\) 67.8550 2.65945
\(652\) 6.13729 0.240355
\(653\) 29.8061 1.16640 0.583201 0.812328i \(-0.301800\pi\)
0.583201 + 0.812328i \(0.301800\pi\)
\(654\) −45.5962 −1.78295
\(655\) 17.5605 0.686147
\(656\) 9.38272 0.366334
\(657\) −27.7247 −1.08164
\(658\) −30.8630 −1.20316
\(659\) −11.6129 −0.452376 −0.226188 0.974084i \(-0.572626\pi\)
−0.226188 + 0.974084i \(0.572626\pi\)
\(660\) −1.76628 −0.0687525
\(661\) 1.60659 0.0624890 0.0312445 0.999512i \(-0.490053\pi\)
0.0312445 + 0.999512i \(0.490053\pi\)
\(662\) 1.88834 0.0733924
\(663\) 10.9995 0.427186
\(664\) 5.94039 0.230532
\(665\) 24.4015 0.946250
\(666\) −19.6535 −0.761557
\(667\) 10.6808 0.413561
\(668\) −1.34904 −0.0521961
\(669\) 18.6498 0.721044
\(670\) −35.4164 −1.36825
\(671\) 0.218045 0.00841753
\(672\) −11.9804 −0.462154
\(673\) 33.1063 1.27615 0.638076 0.769973i \(-0.279730\pi\)
0.638076 + 0.769973i \(0.279730\pi\)
\(674\) −30.0810 −1.15868
\(675\) 1.36906 0.0526953
\(676\) 1.53373 0.0589898
\(677\) 9.97795 0.383484 0.191742 0.981445i \(-0.438586\pi\)
0.191742 + 0.981445i \(0.438586\pi\)
\(678\) 41.8292 1.60644
\(679\) −25.1041 −0.963409
\(680\) −5.33656 −0.204648
\(681\) −51.7662 −1.98368
\(682\) 15.6673 0.599931
\(683\) 9.95038 0.380741 0.190370 0.981712i \(-0.439031\pi\)
0.190370 + 0.981712i \(0.439031\pi\)
\(684\) 5.71932 0.218684
\(685\) −10.0197 −0.382831
\(686\) 29.3248 1.11963
\(687\) 30.0945 1.14818
\(688\) 4.54276 0.173191
\(689\) 47.0292 1.79167
\(690\) −21.3280 −0.811944
\(691\) −16.8218 −0.639930 −0.319965 0.947429i \(-0.603671\pi\)
−0.319965 + 0.947429i \(0.603671\pi\)
\(692\) 5.60104 0.212920
\(693\) 9.66006 0.366955
\(694\) −38.0347 −1.44378
\(695\) 42.7057 1.61992
\(696\) 27.7902 1.05339
\(697\) 2.06542 0.0782334
\(698\) −7.65353 −0.289690
\(699\) 1.78878 0.0676578
\(700\) −0.522309 −0.0197414
\(701\) 28.4495 1.07452 0.537261 0.843416i \(-0.319459\pi\)
0.537261 + 0.843416i \(0.319459\pi\)
\(702\) 13.7742 0.519872
\(703\) 15.5933 0.588114
\(704\) 6.31933 0.238169
\(705\) −43.6883 −1.64540
\(706\) 3.41371 0.128477
\(707\) 31.4787 1.18388
\(708\) 9.03732 0.339643
\(709\) 2.01680 0.0757427 0.0378713 0.999283i \(-0.487942\pi\)
0.0378713 + 0.999283i \(0.487942\pi\)
\(710\) −2.68237 −0.100668
\(711\) 62.6075 2.34797
\(712\) −9.98941 −0.374369
\(713\) 26.3614 0.987241
\(714\) −10.0644 −0.376651
\(715\) 8.79574 0.328942
\(716\) −7.34132 −0.274358
\(717\) −40.9951 −1.53099
\(718\) −39.1302 −1.46032
\(719\) −2.61111 −0.0973778 −0.0486889 0.998814i \(-0.515504\pi\)
−0.0486889 + 0.998814i \(0.515504\pi\)
\(720\) −36.2567 −1.35121
\(721\) −23.6821 −0.881968
\(722\) −3.60198 −0.134052
\(723\) −58.4045 −2.17209
\(724\) 6.33182 0.235320
\(725\) 2.65719 0.0986854
\(726\) 3.98143 0.147765
\(727\) 13.6988 0.508060 0.254030 0.967196i \(-0.418244\pi\)
0.254030 + 0.967196i \(0.418244\pi\)
\(728\) 27.2025 1.00819
\(729\) −39.2077 −1.45214
\(730\) 23.0980 0.854895
\(731\) 1.00000 0.0369863
\(732\) −0.184403 −0.00681575
\(733\) −13.8959 −0.513256 −0.256628 0.966510i \(-0.582612\pi\)
−0.256628 + 0.966510i \(0.582612\pi\)
\(734\) −13.5667 −0.500756
\(735\) 3.32756 0.122739
\(736\) −4.65433 −0.171561
\(737\) 11.1241 0.409763
\(738\) 12.0320 0.442905
\(739\) −47.0982 −1.73254 −0.866268 0.499579i \(-0.833488\pi\)
−0.866268 + 0.499579i \(0.833488\pi\)
\(740\) 2.28155 0.0838716
\(741\) −50.8398 −1.86765
\(742\) −43.0311 −1.57972
\(743\) 12.2955 0.451078 0.225539 0.974234i \(-0.427586\pi\)
0.225539 + 0.974234i \(0.427586\pi\)
\(744\) 68.5894 2.51461
\(745\) 28.8593 1.05732
\(746\) 48.1477 1.76281
\(747\) 8.88426 0.325058
\(748\) −0.323806 −0.0118395
\(749\) 39.4085 1.43996
\(750\) −46.8824 −1.71190
\(751\) 19.0387 0.694731 0.347366 0.937730i \(-0.387076\pi\)
0.347366 + 0.937730i \(0.387076\pi\)
\(752\) −36.3838 −1.32678
\(753\) 65.6212 2.39137
\(754\) 26.7340 0.973594
\(755\) −19.1031 −0.695234
\(756\) −1.75616 −0.0638709
\(757\) −9.39774 −0.341567 −0.170783 0.985309i \(-0.554630\pi\)
−0.170783 + 0.985309i \(0.554630\pi\)
\(758\) −41.7358 −1.51591
\(759\) 6.69905 0.243160
\(760\) 24.6656 0.894715
\(761\) 0.287453 0.0104202 0.00521009 0.999986i \(-0.498342\pi\)
0.00521009 + 0.999986i \(0.498342\pi\)
\(762\) 0.271987 0.00985305
\(763\) −28.9494 −1.04804
\(764\) 3.42409 0.123879
\(765\) −7.98119 −0.288561
\(766\) 47.5279 1.71725
\(767\) −45.0041 −1.62500
\(768\) −19.7938 −0.714247
\(769\) −26.6207 −0.959966 −0.479983 0.877278i \(-0.659357\pi\)
−0.479983 + 0.877278i \(0.659357\pi\)
\(770\) −8.04798 −0.290029
\(771\) 41.8279 1.50639
\(772\) −4.84939 −0.174533
\(773\) 35.4018 1.27331 0.636656 0.771148i \(-0.280317\pi\)
0.636656 + 0.771148i \(0.280317\pi\)
\(774\) 5.82546 0.209392
\(775\) 6.55824 0.235579
\(776\) −25.3758 −0.910939
\(777\) −22.2740 −0.799074
\(778\) −9.81456 −0.351869
\(779\) −9.54638 −0.342035
\(780\) −7.43868 −0.266347
\(781\) 0.842522 0.0301478
\(782\) −3.90998 −0.139820
\(783\) 8.93427 0.319285
\(784\) 2.77121 0.0989716
\(785\) −14.1151 −0.503788
\(786\) 33.4764 1.19407
\(787\) 12.0085 0.428056 0.214028 0.976827i \(-0.431342\pi\)
0.214028 + 0.976827i \(0.431342\pi\)
\(788\) 4.87576 0.173692
\(789\) 54.1103 1.92638
\(790\) −52.1595 −1.85575
\(791\) 26.5577 0.944283
\(792\) 9.76461 0.346970
\(793\) 0.918292 0.0326095
\(794\) 42.5674 1.51066
\(795\) −60.9129 −2.16036
\(796\) −3.64692 −0.129262
\(797\) 4.59288 0.162688 0.0813440 0.996686i \(-0.474079\pi\)
0.0813440 + 0.996686i \(0.474079\pi\)
\(798\) 46.5177 1.64671
\(799\) −8.00918 −0.283345
\(800\) −1.15791 −0.0409384
\(801\) −14.9398 −0.527873
\(802\) 21.5279 0.760178
\(803\) −7.25499 −0.256023
\(804\) −9.40784 −0.331789
\(805\) −13.5413 −0.477269
\(806\) 65.9825 2.32413
\(807\) −48.5301 −1.70834
\(808\) 31.8194 1.11940
\(809\) 23.3934 0.822469 0.411234 0.911530i \(-0.365098\pi\)
0.411234 + 0.911530i \(0.365098\pi\)
\(810\) 18.6592 0.655617
\(811\) 24.9092 0.874679 0.437339 0.899297i \(-0.355921\pi\)
0.437339 + 0.899297i \(0.355921\pi\)
\(812\) −3.40849 −0.119615
\(813\) −41.4575 −1.45398
\(814\) −5.14291 −0.180259
\(815\) 39.5849 1.38660
\(816\) −11.8648 −0.415350
\(817\) −4.62200 −0.161703
\(818\) 2.72231 0.0951832
\(819\) 40.6832 1.42159
\(820\) −1.39679 −0.0487780
\(821\) 13.0771 0.456394 0.228197 0.973615i \(-0.426717\pi\)
0.228197 + 0.973615i \(0.426717\pi\)
\(822\) −19.1009 −0.666221
\(823\) −21.5599 −0.751532 −0.375766 0.926715i \(-0.622620\pi\)
−0.375766 + 0.926715i \(0.622620\pi\)
\(824\) −23.9384 −0.833934
\(825\) 1.66660 0.0580237
\(826\) 41.1781 1.43277
\(827\) −19.1172 −0.664771 −0.332385 0.943144i \(-0.607853\pi\)
−0.332385 + 0.943144i \(0.607853\pi\)
\(828\) −3.17387 −0.110300
\(829\) −47.1892 −1.63895 −0.819474 0.573117i \(-0.805734\pi\)
−0.819474 + 0.573117i \(0.805734\pi\)
\(830\) −7.40164 −0.256915
\(831\) 25.9810 0.901272
\(832\) 26.6137 0.922666
\(833\) 0.610027 0.0211362
\(834\) 81.4118 2.81906
\(835\) −8.70121 −0.301118
\(836\) 1.49663 0.0517620
\(837\) 22.0508 0.762187
\(838\) 12.8368 0.443440
\(839\) 8.34400 0.288067 0.144033 0.989573i \(-0.453993\pi\)
0.144033 + 0.989573i \(0.453993\pi\)
\(840\) −35.2331 −1.21566
\(841\) −11.6597 −0.402058
\(842\) 45.5671 1.57035
\(843\) 24.3207 0.837649
\(844\) 8.27047 0.284681
\(845\) 9.89244 0.340310
\(846\) −46.6572 −1.60411
\(847\) 2.52784 0.0868576
\(848\) −50.7286 −1.74203
\(849\) 4.92369 0.168980
\(850\) −0.972733 −0.0333645
\(851\) −8.65333 −0.296632
\(852\) −0.712532 −0.0244109
\(853\) 7.22404 0.247346 0.123673 0.992323i \(-0.460533\pi\)
0.123673 + 0.992323i \(0.460533\pi\)
\(854\) −0.840224 −0.0287519
\(855\) 36.8891 1.26158
\(856\) 39.8350 1.36153
\(857\) 21.1422 0.722203 0.361101 0.932527i \(-0.382401\pi\)
0.361101 + 0.932527i \(0.382401\pi\)
\(858\) 16.7677 0.572440
\(859\) −8.67517 −0.295993 −0.147997 0.988988i \(-0.547282\pi\)
−0.147997 + 0.988988i \(0.547282\pi\)
\(860\) −0.676273 −0.0230607
\(861\) 13.6363 0.464725
\(862\) −37.4590 −1.27586
\(863\) −52.2063 −1.77712 −0.888561 0.458758i \(-0.848294\pi\)
−0.888561 + 0.458758i \(0.848294\pi\)
\(864\) −3.89326 −0.132451
\(865\) 36.1262 1.22833
\(866\) −23.2237 −0.789173
\(867\) −2.61179 −0.0887012
\(868\) −8.41255 −0.285540
\(869\) 16.3831 0.555759
\(870\) −34.6262 −1.17394
\(871\) 46.8492 1.58742
\(872\) −29.2627 −0.990960
\(873\) −37.9513 −1.28446
\(874\) 18.0719 0.611291
\(875\) −29.7660 −1.00627
\(876\) 6.13564 0.207304
\(877\) −22.6792 −0.765824 −0.382912 0.923785i \(-0.625079\pi\)
−0.382912 + 0.923785i \(0.625079\pi\)
\(878\) −11.4515 −0.386470
\(879\) −77.2744 −2.60640
\(880\) −9.48762 −0.319828
\(881\) −6.28693 −0.211812 −0.105906 0.994376i \(-0.533774\pi\)
−0.105906 + 0.994376i \(0.533774\pi\)
\(882\) 3.55369 0.119659
\(883\) 6.94902 0.233853 0.116927 0.993141i \(-0.462696\pi\)
0.116927 + 0.993141i \(0.462696\pi\)
\(884\) −1.36370 −0.0458662
\(885\) 58.2899 1.95939
\(886\) 0.837224 0.0281271
\(887\) −23.3869 −0.785254 −0.392627 0.919698i \(-0.628434\pi\)
−0.392627 + 0.919698i \(0.628434\pi\)
\(888\) −22.5150 −0.755555
\(889\) 0.172687 0.00579172
\(890\) 12.4467 0.417213
\(891\) −5.86078 −0.196343
\(892\) −2.31217 −0.0774172
\(893\) 37.0184 1.23878
\(894\) 55.0157 1.84000
\(895\) −47.3508 −1.58276
\(896\) −33.5253 −1.12000
\(897\) 28.2129 0.942002
\(898\) −42.6085 −1.42186
\(899\) 42.7979 1.42739
\(900\) −0.789602 −0.0263201
\(901\) −11.1669 −0.372023
\(902\) 3.14854 0.104835
\(903\) 6.60220 0.219707
\(904\) 26.8451 0.892855
\(905\) 40.8396 1.35755
\(906\) −36.4172 −1.20988
\(907\) −2.47907 −0.0823163 −0.0411581 0.999153i \(-0.513105\pi\)
−0.0411581 + 0.999153i \(0.513105\pi\)
\(908\) 6.41788 0.212985
\(909\) 47.5881 1.57840
\(910\) −33.8939 −1.12357
\(911\) −51.1495 −1.69466 −0.847329 0.531068i \(-0.821791\pi\)
−0.847329 + 0.531068i \(0.821791\pi\)
\(912\) 54.8389 1.81590
\(913\) 2.32483 0.0769405
\(914\) −27.2033 −0.899805
\(915\) −1.18938 −0.0393198
\(916\) −3.73106 −0.123278
\(917\) 21.2545 0.701884
\(918\) −3.27062 −0.107947
\(919\) −14.0328 −0.462898 −0.231449 0.972847i \(-0.574347\pi\)
−0.231449 + 0.972847i \(0.574347\pi\)
\(920\) −13.6879 −0.451276
\(921\) −32.6202 −1.07487
\(922\) 36.9991 1.21850
\(923\) 3.54827 0.116793
\(924\) −2.13783 −0.0703294
\(925\) −2.15280 −0.0707835
\(926\) −64.2446 −2.11121
\(927\) −35.8015 −1.17588
\(928\) −7.55633 −0.248049
\(929\) −1.54785 −0.0507833 −0.0253916 0.999678i \(-0.508083\pi\)
−0.0253916 + 0.999678i \(0.508083\pi\)
\(930\) −85.4614 −2.80239
\(931\) −2.81954 −0.0924068
\(932\) −0.221769 −0.00726430
\(933\) 86.1833 2.82151
\(934\) −25.5819 −0.837067
\(935\) −2.08851 −0.0683017
\(936\) 41.1235 1.34416
\(937\) 47.6356 1.55619 0.778094 0.628147i \(-0.216187\pi\)
0.778094 + 0.628147i \(0.216187\pi\)
\(938\) −42.8663 −1.39963
\(939\) 45.8528 1.49635
\(940\) 5.41639 0.176663
\(941\) −2.10861 −0.0687386 −0.0343693 0.999409i \(-0.510942\pi\)
−0.0343693 + 0.999409i \(0.510942\pi\)
\(942\) −26.9082 −0.876715
\(943\) 5.29765 0.172515
\(944\) 48.5441 1.57998
\(945\) −11.3271 −0.368469
\(946\) 1.52440 0.0495626
\(947\) −22.8912 −0.743865 −0.371932 0.928260i \(-0.621305\pi\)
−0.371932 + 0.928260i \(0.621305\pi\)
\(948\) −13.8554 −0.450003
\(949\) −30.5543 −0.991834
\(950\) 4.49597 0.145869
\(951\) 66.6600 2.16160
\(952\) −6.45913 −0.209342
\(953\) −11.5615 −0.374513 −0.187257 0.982311i \(-0.559960\pi\)
−0.187257 + 0.982311i \(0.559960\pi\)
\(954\) −65.0523 −2.10615
\(955\) 22.0850 0.714655
\(956\) 5.08250 0.164380
\(957\) 10.8760 0.351570
\(958\) −37.6785 −1.21734
\(959\) −12.1273 −0.391611
\(960\) −34.4705 −1.11253
\(961\) 74.6300 2.40742
\(962\) −21.6593 −0.698323
\(963\) 59.5759 1.91981
\(964\) 7.24088 0.233213
\(965\) −31.2781 −1.00688
\(966\) −25.8144 −0.830566
\(967\) −9.38119 −0.301679 −0.150839 0.988558i \(-0.548198\pi\)
−0.150839 + 0.988558i \(0.548198\pi\)
\(968\) 2.55520 0.0821271
\(969\) 12.0717 0.387799
\(970\) 31.6179 1.01519
\(971\) −3.31428 −0.106360 −0.0531801 0.998585i \(-0.516936\pi\)
−0.0531801 + 0.998585i \(0.516936\pi\)
\(972\) 7.04072 0.225831
\(973\) 51.6890 1.65707
\(974\) −29.2446 −0.937057
\(975\) 7.01888 0.224784
\(976\) −0.990526 −0.0317060
\(977\) −16.5523 −0.529553 −0.264777 0.964310i \(-0.585298\pi\)
−0.264777 + 0.964310i \(0.585298\pi\)
\(978\) 75.4625 2.41302
\(979\) −3.90945 −0.124946
\(980\) −0.412544 −0.0131782
\(981\) −43.7643 −1.39729
\(982\) 26.2579 0.837922
\(983\) 8.68985 0.277163 0.138582 0.990351i \(-0.455746\pi\)
0.138582 + 0.990351i \(0.455746\pi\)
\(984\) 13.7839 0.439415
\(985\) 31.4482 1.00202
\(986\) −6.34788 −0.202158
\(987\) −52.8782 −1.68313
\(988\) 6.30303 0.200526
\(989\) 2.56492 0.0815598
\(990\) −12.1666 −0.386679
\(991\) 42.9911 1.36566 0.682828 0.730579i \(-0.260750\pi\)
0.682828 + 0.730579i \(0.260750\pi\)
\(992\) −18.6499 −0.592135
\(993\) 3.23534 0.102670
\(994\) −3.24661 −0.102976
\(995\) −23.5223 −0.745706
\(996\) −1.96614 −0.0622994
\(997\) 30.8130 0.975857 0.487928 0.872884i \(-0.337753\pi\)
0.487928 + 0.872884i \(0.337753\pi\)
\(998\) −42.9219 −1.35867
\(999\) −7.23835 −0.229011
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 \(a_p\))