Properties

Label 8027.2.a.f.1.7
Level 8027
Weight 2
Character 8027.1
Self dual Yes
Analytic conductor 64.096
Analytic rank 0
Dimension 176
CM No

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Newspace parameters

Level: \( N \) = \( 8027 = 23 \cdot 349 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8027.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0959177025\)
Analytic rank: \(0\)
Dimension: \(176\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.7
Character \(\chi\) = 8027.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.63657 q^{2} +1.64340 q^{3} +4.95152 q^{4} -0.607936 q^{5} -4.33295 q^{6} -1.90677 q^{7} -7.78191 q^{8} -0.299236 q^{9} +O(q^{10})\) \(q-2.63657 q^{2} +1.64340 q^{3} +4.95152 q^{4} -0.607936 q^{5} -4.33295 q^{6} -1.90677 q^{7} -7.78191 q^{8} -0.299236 q^{9} +1.60287 q^{10} -1.70915 q^{11} +8.13733 q^{12} +5.00785 q^{13} +5.02735 q^{14} -0.999082 q^{15} +10.6145 q^{16} +4.32864 q^{17} +0.788958 q^{18} +2.36317 q^{19} -3.01021 q^{20} -3.13359 q^{21} +4.50630 q^{22} +1.00000 q^{23} -12.7888 q^{24} -4.63041 q^{25} -13.2036 q^{26} -5.42196 q^{27} -9.44144 q^{28} +9.97868 q^{29} +2.63415 q^{30} +2.03651 q^{31} -12.4222 q^{32} -2.80882 q^{33} -11.4128 q^{34} +1.15920 q^{35} -1.48167 q^{36} +6.33509 q^{37} -6.23068 q^{38} +8.22991 q^{39} +4.73090 q^{40} -2.18062 q^{41} +8.26195 q^{42} +4.94696 q^{43} -8.46290 q^{44} +0.181916 q^{45} -2.63657 q^{46} -10.8495 q^{47} +17.4439 q^{48} -3.36421 q^{49} +12.2084 q^{50} +7.11369 q^{51} +24.7965 q^{52} -10.8360 q^{53} +14.2954 q^{54} +1.03905 q^{55} +14.8384 q^{56} +3.88364 q^{57} -26.3095 q^{58} -3.53380 q^{59} -4.94698 q^{60} +5.69234 q^{61} -5.36940 q^{62} +0.570576 q^{63} +11.5230 q^{64} -3.04445 q^{65} +7.40566 q^{66} +10.5950 q^{67} +21.4334 q^{68} +1.64340 q^{69} -3.05631 q^{70} +9.59204 q^{71} +2.32863 q^{72} +14.6035 q^{73} -16.7029 q^{74} -7.60962 q^{75} +11.7013 q^{76} +3.25896 q^{77} -21.6988 q^{78} -13.0776 q^{79} -6.45296 q^{80} -8.01275 q^{81} +5.74937 q^{82} +10.5285 q^{83} -15.5161 q^{84} -2.63154 q^{85} -13.0430 q^{86} +16.3990 q^{87} +13.3005 q^{88} +11.2687 q^{89} -0.479636 q^{90} -9.54885 q^{91} +4.95152 q^{92} +3.34680 q^{93} +28.6055 q^{94} -1.43666 q^{95} -20.4146 q^{96} -9.14110 q^{97} +8.86999 q^{98} +0.511439 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 176q + 19q^{2} + 22q^{3} + 203q^{4} + 28q^{5} + 9q^{6} + 30q^{7} + 51q^{8} + 204q^{9} + O(q^{10}) \) \( 176q + 19q^{2} + 22q^{3} + 203q^{4} + 28q^{5} + 9q^{6} + 30q^{7} + 51q^{8} + 204q^{9} + 18q^{10} + 11q^{11} + 46q^{12} + 87q^{13} - 6q^{14} + 29q^{15} + 257q^{16} + 14q^{17} + 72q^{18} + 34q^{19} + 45q^{20} + 23q^{21} + 62q^{22} + 176q^{23} + 33q^{24} + 272q^{25} + 31q^{26} + 82q^{27} + 80q^{28} + 75q^{29} - 30q^{30} + 73q^{31} + 71q^{32} + 30q^{33} + 23q^{34} + 44q^{35} + 264q^{36} + 236q^{37} - 21q^{38} + 17q^{39} + 43q^{40} + 51q^{41} + 38q^{42} + 51q^{43} + 12q^{44} + 127q^{45} + 19q^{46} + 45q^{47} + 61q^{48} + 268q^{49} + 55q^{50} - 3q^{51} + 166q^{52} + 63q^{53} - 32q^{54} + 11q^{55} - 9q^{56} + 72q^{57} + 98q^{58} + 95q^{59} - 7q^{60} + 73q^{61} + 12q^{62} + 19q^{63} + 365q^{64} + 19q^{65} - 28q^{66} + 138q^{67} + 16q^{68} + 22q^{69} + 100q^{70} + 85q^{71} + 129q^{72} + 118q^{73} - 21q^{74} - 12q^{75} + 52q^{76} + 75q^{77} + 97q^{78} + 74q^{79} + 8q^{80} + 280q^{81} + 67q^{82} + 10q^{83} - 51q^{84} + 169q^{85} - 39q^{86} - 6q^{87} + 159q^{88} + 38q^{89} + 22q^{90} + 90q^{91} + 203q^{92} + 230q^{93} + 63q^{94} + 30q^{95} + 107q^{96} + 161q^{97} + 58q^{98} + 7q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.63657 −1.86434 −0.932170 0.362021i \(-0.882087\pi\)
−0.932170 + 0.362021i \(0.882087\pi\)
\(3\) 1.64340 0.948818 0.474409 0.880305i \(-0.342662\pi\)
0.474409 + 0.880305i \(0.342662\pi\)
\(4\) 4.95152 2.47576
\(5\) −0.607936 −0.271877 −0.135939 0.990717i \(-0.543405\pi\)
−0.135939 + 0.990717i \(0.543405\pi\)
\(6\) −4.33295 −1.76892
\(7\) −1.90677 −0.720693 −0.360347 0.932819i \(-0.617342\pi\)
−0.360347 + 0.932819i \(0.617342\pi\)
\(8\) −7.78191 −2.75132
\(9\) −0.299236 −0.0997453
\(10\) 1.60287 0.506871
\(11\) −1.70915 −0.515328 −0.257664 0.966235i \(-0.582953\pi\)
−0.257664 + 0.966235i \(0.582953\pi\)
\(12\) 8.13733 2.34905
\(13\) 5.00785 1.38893 0.694464 0.719527i \(-0.255641\pi\)
0.694464 + 0.719527i \(0.255641\pi\)
\(14\) 5.02735 1.34362
\(15\) −0.999082 −0.257962
\(16\) 10.6145 2.65363
\(17\) 4.32864 1.04985 0.524925 0.851149i \(-0.324093\pi\)
0.524925 + 0.851149i \(0.324093\pi\)
\(18\) 0.788958 0.185959
\(19\) 2.36317 0.542149 0.271075 0.962558i \(-0.412621\pi\)
0.271075 + 0.962558i \(0.412621\pi\)
\(20\) −3.01021 −0.673103
\(21\) −3.13359 −0.683806
\(22\) 4.50630 0.960747
\(23\) 1.00000 0.208514
\(24\) −12.7888 −2.61050
\(25\) −4.63041 −0.926083
\(26\) −13.2036 −2.58943
\(27\) −5.42196 −1.04346
\(28\) −9.44144 −1.78426
\(29\) 9.97868 1.85300 0.926498 0.376301i \(-0.122804\pi\)
0.926498 + 0.376301i \(0.122804\pi\)
\(30\) 2.63415 0.480928
\(31\) 2.03651 0.365768 0.182884 0.983135i \(-0.441457\pi\)
0.182884 + 0.983135i \(0.441457\pi\)
\(32\) −12.4222 −2.19595
\(33\) −2.80882 −0.488952
\(34\) −11.4128 −1.95728
\(35\) 1.15920 0.195940
\(36\) −1.48167 −0.246946
\(37\) 6.33509 1.04148 0.520741 0.853715i \(-0.325656\pi\)
0.520741 + 0.853715i \(0.325656\pi\)
\(38\) −6.23068 −1.01075
\(39\) 8.22991 1.31784
\(40\) 4.73090 0.748021
\(41\) −2.18062 −0.340556 −0.170278 0.985396i \(-0.554467\pi\)
−0.170278 + 0.985396i \(0.554467\pi\)
\(42\) 8.26195 1.27485
\(43\) 4.94696 0.754404 0.377202 0.926131i \(-0.376886\pi\)
0.377202 + 0.926131i \(0.376886\pi\)
\(44\) −8.46290 −1.27583
\(45\) 0.181916 0.0271185
\(46\) −2.63657 −0.388742
\(47\) −10.8495 −1.58256 −0.791282 0.611452i \(-0.790586\pi\)
−0.791282 + 0.611452i \(0.790586\pi\)
\(48\) 17.4439 2.51781
\(49\) −3.36421 −0.480601
\(50\) 12.2084 1.72653
\(51\) 7.11369 0.996116
\(52\) 24.7965 3.43866
\(53\) −10.8360 −1.48844 −0.744218 0.667937i \(-0.767178\pi\)
−0.744218 + 0.667937i \(0.767178\pi\)
\(54\) 14.2954 1.94536
\(55\) 1.03905 0.140106
\(56\) 14.8384 1.98286
\(57\) 3.88364 0.514401
\(58\) −26.3095 −3.45461
\(59\) −3.53380 −0.460061 −0.230031 0.973183i \(-0.573883\pi\)
−0.230031 + 0.973183i \(0.573883\pi\)
\(60\) −4.94698 −0.638652
\(61\) 5.69234 0.728830 0.364415 0.931237i \(-0.381269\pi\)
0.364415 + 0.931237i \(0.381269\pi\)
\(62\) −5.36940 −0.681915
\(63\) 0.570576 0.0718858
\(64\) 11.5230 1.44037
\(65\) −3.04445 −0.377618
\(66\) 7.40566 0.911573
\(67\) 10.5950 1.29439 0.647194 0.762325i \(-0.275942\pi\)
0.647194 + 0.762325i \(0.275942\pi\)
\(68\) 21.4334 2.59918
\(69\) 1.64340 0.197842
\(70\) −3.05631 −0.365299
\(71\) 9.59204 1.13837 0.569183 0.822211i \(-0.307260\pi\)
0.569183 + 0.822211i \(0.307260\pi\)
\(72\) 2.32863 0.274431
\(73\) 14.6035 1.70921 0.854606 0.519277i \(-0.173799\pi\)
0.854606 + 0.519277i \(0.173799\pi\)
\(74\) −16.7029 −1.94168
\(75\) −7.60962 −0.878684
\(76\) 11.7013 1.34223
\(77\) 3.25896 0.371394
\(78\) −21.6988 −2.45690
\(79\) −13.0776 −1.47135 −0.735675 0.677335i \(-0.763135\pi\)
−0.735675 + 0.677335i \(0.763135\pi\)
\(80\) −6.45296 −0.721462
\(81\) −8.01275 −0.890306
\(82\) 5.74937 0.634911
\(83\) 10.5285 1.15565 0.577825 0.816161i \(-0.303902\pi\)
0.577825 + 0.816161i \(0.303902\pi\)
\(84\) −15.5161 −1.69294
\(85\) −2.63154 −0.285430
\(86\) −13.0430 −1.40646
\(87\) 16.3990 1.75815
\(88\) 13.3005 1.41783
\(89\) 11.2687 1.19449 0.597243 0.802061i \(-0.296263\pi\)
0.597243 + 0.802061i \(0.296263\pi\)
\(90\) −0.479636 −0.0505580
\(91\) −9.54885 −1.00099
\(92\) 4.95152 0.516232
\(93\) 3.34680 0.347047
\(94\) 28.6055 2.95044
\(95\) −1.43666 −0.147398
\(96\) −20.4146 −2.08356
\(97\) −9.14110 −0.928138 −0.464069 0.885799i \(-0.653611\pi\)
−0.464069 + 0.885799i \(0.653611\pi\)
\(98\) 8.86999 0.896004
\(99\) 0.511439 0.0514016
\(100\) −22.9276 −2.29276
\(101\) −8.84196 −0.879808 −0.439904 0.898045i \(-0.644988\pi\)
−0.439904 + 0.898045i \(0.644988\pi\)
\(102\) −18.7558 −1.85710
\(103\) −1.70094 −0.167599 −0.0837993 0.996483i \(-0.526705\pi\)
−0.0837993 + 0.996483i \(0.526705\pi\)
\(104\) −38.9707 −3.82139
\(105\) 1.90502 0.185911
\(106\) 28.5699 2.77495
\(107\) −11.4304 −1.10502 −0.552508 0.833508i \(-0.686329\pi\)
−0.552508 + 0.833508i \(0.686329\pi\)
\(108\) −26.8470 −2.58335
\(109\) 9.49004 0.908981 0.454490 0.890752i \(-0.349821\pi\)
0.454490 + 0.890752i \(0.349821\pi\)
\(110\) −2.73954 −0.261205
\(111\) 10.4111 0.988177
\(112\) −20.2395 −1.91246
\(113\) −11.3169 −1.06461 −0.532304 0.846553i \(-0.678674\pi\)
−0.532304 + 0.846553i \(0.678674\pi\)
\(114\) −10.2395 −0.959017
\(115\) −0.607936 −0.0566903
\(116\) 49.4097 4.58757
\(117\) −1.49853 −0.138539
\(118\) 9.31711 0.857710
\(119\) −8.25374 −0.756619
\(120\) 7.77476 0.709736
\(121\) −8.07880 −0.734437
\(122\) −15.0083 −1.35879
\(123\) −3.58363 −0.323125
\(124\) 10.0838 0.905553
\(125\) 5.85467 0.523658
\(126\) −1.50436 −0.134019
\(127\) −10.8972 −0.966968 −0.483484 0.875353i \(-0.660629\pi\)
−0.483484 + 0.875353i \(0.660629\pi\)
\(128\) −5.53676 −0.489385
\(129\) 8.12983 0.715791
\(130\) 8.02692 0.704008
\(131\) −2.15149 −0.187977 −0.0939885 0.995573i \(-0.529962\pi\)
−0.0939885 + 0.995573i \(0.529962\pi\)
\(132\) −13.9079 −1.21053
\(133\) −4.50604 −0.390723
\(134\) −27.9346 −2.41318
\(135\) 3.29621 0.283692
\(136\) −33.6851 −2.88847
\(137\) 0.344286 0.0294144 0.0147072 0.999892i \(-0.495318\pi\)
0.0147072 + 0.999892i \(0.495318\pi\)
\(138\) −4.33295 −0.368845
\(139\) 20.2372 1.71650 0.858250 0.513232i \(-0.171552\pi\)
0.858250 + 0.513232i \(0.171552\pi\)
\(140\) 5.73979 0.485101
\(141\) −17.8301 −1.50156
\(142\) −25.2901 −2.12230
\(143\) −8.55917 −0.715754
\(144\) −3.17625 −0.264688
\(145\) −6.06640 −0.503787
\(146\) −38.5032 −3.18655
\(147\) −5.52874 −0.456003
\(148\) 31.3683 2.57846
\(149\) −18.0257 −1.47672 −0.738361 0.674405i \(-0.764400\pi\)
−0.738361 + 0.674405i \(0.764400\pi\)
\(150\) 20.0633 1.63816
\(151\) −13.5923 −1.10613 −0.553064 0.833138i \(-0.686542\pi\)
−0.553064 + 0.833138i \(0.686542\pi\)
\(152\) −18.3900 −1.49163
\(153\) −1.29528 −0.104718
\(154\) −8.59250 −0.692404
\(155\) −1.23807 −0.0994438
\(156\) 40.7506 3.26266
\(157\) −14.7510 −1.17726 −0.588628 0.808404i \(-0.700332\pi\)
−0.588628 + 0.808404i \(0.700332\pi\)
\(158\) 34.4802 2.74310
\(159\) −17.8078 −1.41225
\(160\) 7.55190 0.597030
\(161\) −1.90677 −0.150275
\(162\) 21.1262 1.65983
\(163\) 2.47996 0.194246 0.0971228 0.995272i \(-0.469036\pi\)
0.0971228 + 0.995272i \(0.469036\pi\)
\(164\) −10.7974 −0.843135
\(165\) 1.70758 0.132935
\(166\) −27.7591 −2.15452
\(167\) −9.48227 −0.733760 −0.366880 0.930268i \(-0.619574\pi\)
−0.366880 + 0.930268i \(0.619574\pi\)
\(168\) 24.3853 1.88137
\(169\) 12.0786 0.929122
\(170\) 6.93824 0.532139
\(171\) −0.707146 −0.0540768
\(172\) 24.4950 1.86772
\(173\) 19.6984 1.49764 0.748820 0.662774i \(-0.230621\pi\)
0.748820 + 0.662774i \(0.230621\pi\)
\(174\) −43.2371 −3.27780
\(175\) 8.82916 0.667421
\(176\) −18.1418 −1.36749
\(177\) −5.80744 −0.436514
\(178\) −29.7109 −2.22693
\(179\) −8.03467 −0.600540 −0.300270 0.953854i \(-0.597077\pi\)
−0.300270 + 0.953854i \(0.597077\pi\)
\(180\) 0.900762 0.0671389
\(181\) 12.8014 0.951524 0.475762 0.879574i \(-0.342172\pi\)
0.475762 + 0.879574i \(0.342172\pi\)
\(182\) 25.1762 1.86619
\(183\) 9.35479 0.691526
\(184\) −7.78191 −0.573690
\(185\) −3.85133 −0.283155
\(186\) −8.82408 −0.647013
\(187\) −7.39830 −0.541017
\(188\) −53.7216 −3.91805
\(189\) 10.3385 0.752013
\(190\) 3.78785 0.274800
\(191\) 9.57623 0.692911 0.346456 0.938066i \(-0.387385\pi\)
0.346456 + 0.938066i \(0.387385\pi\)
\(192\) 18.9368 1.36665
\(193\) 20.3494 1.46478 0.732392 0.680884i \(-0.238404\pi\)
0.732392 + 0.680884i \(0.238404\pi\)
\(194\) 24.1012 1.73037
\(195\) −5.00325 −0.358290
\(196\) −16.6580 −1.18985
\(197\) −7.49801 −0.534211 −0.267106 0.963667i \(-0.586067\pi\)
−0.267106 + 0.963667i \(0.586067\pi\)
\(198\) −1.34845 −0.0958300
\(199\) 7.63098 0.540946 0.270473 0.962728i \(-0.412820\pi\)
0.270473 + 0.962728i \(0.412820\pi\)
\(200\) 36.0335 2.54795
\(201\) 17.4119 1.22814
\(202\) 23.3125 1.64026
\(203\) −19.0271 −1.33544
\(204\) 35.2236 2.46614
\(205\) 1.32568 0.0925893
\(206\) 4.48465 0.312461
\(207\) −0.299236 −0.0207983
\(208\) 53.1560 3.68571
\(209\) −4.03902 −0.279385
\(210\) −5.02274 −0.346602
\(211\) 24.7488 1.70378 0.851890 0.523721i \(-0.175457\pi\)
0.851890 + 0.523721i \(0.175457\pi\)
\(212\) −53.6546 −3.68501
\(213\) 15.7636 1.08010
\(214\) 30.1370 2.06012
\(215\) −3.00743 −0.205105
\(216\) 42.1932 2.87089
\(217\) −3.88316 −0.263606
\(218\) −25.0212 −1.69465
\(219\) 23.9994 1.62173
\(220\) 5.14490 0.346869
\(221\) 21.6772 1.45817
\(222\) −27.4496 −1.84230
\(223\) 29.5235 1.97704 0.988519 0.151100i \(-0.0482815\pi\)
0.988519 + 0.151100i \(0.0482815\pi\)
\(224\) 23.6863 1.58261
\(225\) 1.38559 0.0923724
\(226\) 29.8379 1.98479
\(227\) −18.0587 −1.19860 −0.599298 0.800526i \(-0.704554\pi\)
−0.599298 + 0.800526i \(0.704554\pi\)
\(228\) 19.2299 1.27353
\(229\) 22.8986 1.51318 0.756590 0.653889i \(-0.226864\pi\)
0.756590 + 0.653889i \(0.226864\pi\)
\(230\) 1.60287 0.105690
\(231\) 5.35578 0.352385
\(232\) −77.6532 −5.09818
\(233\) 12.1725 0.797447 0.398724 0.917071i \(-0.369453\pi\)
0.398724 + 0.917071i \(0.369453\pi\)
\(234\) 3.95098 0.258284
\(235\) 6.59580 0.430263
\(236\) −17.4977 −1.13900
\(237\) −21.4918 −1.39604
\(238\) 21.7616 1.41060
\(239\) −0.105377 −0.00681629 −0.00340814 0.999994i \(-0.501085\pi\)
−0.00340814 + 0.999994i \(0.501085\pi\)
\(240\) −10.6048 −0.684536
\(241\) −1.70718 −0.109969 −0.0549845 0.998487i \(-0.517511\pi\)
−0.0549845 + 0.998487i \(0.517511\pi\)
\(242\) 21.3004 1.36924
\(243\) 3.09774 0.198720
\(244\) 28.1858 1.80441
\(245\) 2.04522 0.130665
\(246\) 9.44851 0.602415
\(247\) 11.8344 0.753006
\(248\) −15.8479 −1.00634
\(249\) 17.3025 1.09650
\(250\) −15.4363 −0.976276
\(251\) −0.779810 −0.0492211 −0.0246106 0.999697i \(-0.507835\pi\)
−0.0246106 + 0.999697i \(0.507835\pi\)
\(252\) 2.82522 0.177972
\(253\) −1.70915 −0.107453
\(254\) 28.7312 1.80276
\(255\) −4.32467 −0.270821
\(256\) −8.44785 −0.527991
\(257\) 9.04524 0.564227 0.282113 0.959381i \(-0.408965\pi\)
0.282113 + 0.959381i \(0.408965\pi\)
\(258\) −21.4349 −1.33448
\(259\) −12.0796 −0.750589
\(260\) −15.0747 −0.934892
\(261\) −2.98598 −0.184828
\(262\) 5.67258 0.350453
\(263\) 16.7032 1.02996 0.514981 0.857202i \(-0.327799\pi\)
0.514981 + 0.857202i \(0.327799\pi\)
\(264\) 21.8580 1.34527
\(265\) 6.58758 0.404672
\(266\) 11.8805 0.728440
\(267\) 18.5191 1.13335
\(268\) 52.4615 3.20460
\(269\) −15.9918 −0.975038 −0.487519 0.873112i \(-0.662098\pi\)
−0.487519 + 0.873112i \(0.662098\pi\)
\(270\) −8.69069 −0.528899
\(271\) 11.5420 0.701129 0.350565 0.936539i \(-0.385990\pi\)
0.350565 + 0.936539i \(0.385990\pi\)
\(272\) 45.9465 2.78592
\(273\) −15.6926 −0.949758
\(274\) −0.907736 −0.0548384
\(275\) 7.91407 0.477237
\(276\) 8.13733 0.489810
\(277\) 14.0530 0.844363 0.422181 0.906511i \(-0.361265\pi\)
0.422181 + 0.906511i \(0.361265\pi\)
\(278\) −53.3570 −3.20014
\(279\) −0.609396 −0.0364836
\(280\) −9.02076 −0.539094
\(281\) 7.90708 0.471697 0.235848 0.971790i \(-0.424213\pi\)
0.235848 + 0.971790i \(0.424213\pi\)
\(282\) 47.0103 2.79942
\(283\) −15.5998 −0.927314 −0.463657 0.886015i \(-0.653463\pi\)
−0.463657 + 0.886015i \(0.653463\pi\)
\(284\) 47.4952 2.81832
\(285\) −2.36100 −0.139854
\(286\) 22.5669 1.33441
\(287\) 4.15795 0.245436
\(288\) 3.71717 0.219036
\(289\) 1.73713 0.102184
\(290\) 15.9945 0.939230
\(291\) −15.0225 −0.880634
\(292\) 72.3096 4.23160
\(293\) 5.63033 0.328927 0.164464 0.986383i \(-0.447411\pi\)
0.164464 + 0.986383i \(0.447411\pi\)
\(294\) 14.5769 0.850145
\(295\) 2.14832 0.125080
\(296\) −49.2991 −2.86545
\(297\) 9.26695 0.537723
\(298\) 47.5261 2.75311
\(299\) 5.00785 0.289612
\(300\) −37.6792 −2.17541
\(301\) −9.43273 −0.543693
\(302\) 35.8372 2.06220
\(303\) −14.5309 −0.834777
\(304\) 25.0840 1.43867
\(305\) −3.46058 −0.198152
\(306\) 3.41511 0.195229
\(307\) 11.9256 0.680627 0.340314 0.940312i \(-0.389467\pi\)
0.340314 + 0.940312i \(0.389467\pi\)
\(308\) 16.1368 0.919482
\(309\) −2.79532 −0.159020
\(310\) 3.26425 0.185397
\(311\) −1.29915 −0.0736682 −0.0368341 0.999321i \(-0.511727\pi\)
−0.0368341 + 0.999321i \(0.511727\pi\)
\(312\) −64.0444 −3.62580
\(313\) 18.0288 1.01905 0.509525 0.860456i \(-0.329821\pi\)
0.509525 + 0.860456i \(0.329821\pi\)
\(314\) 38.8921 2.19481
\(315\) −0.346873 −0.0195441
\(316\) −64.7543 −3.64271
\(317\) 13.5054 0.758537 0.379268 0.925287i \(-0.376176\pi\)
0.379268 + 0.925287i \(0.376176\pi\)
\(318\) 46.9517 2.63292
\(319\) −17.0551 −0.954901
\(320\) −7.00522 −0.391604
\(321\) −18.7847 −1.04846
\(322\) 5.02735 0.280163
\(323\) 10.2293 0.569175
\(324\) −39.6753 −2.20418
\(325\) −23.1884 −1.28626
\(326\) −6.53861 −0.362140
\(327\) 15.5959 0.862457
\(328\) 16.9694 0.936978
\(329\) 20.6876 1.14054
\(330\) −4.50216 −0.247836
\(331\) −3.16347 −0.173880 −0.0869401 0.996214i \(-0.527709\pi\)
−0.0869401 + 0.996214i \(0.527709\pi\)
\(332\) 52.1320 2.86111
\(333\) −1.89569 −0.103883
\(334\) 25.0007 1.36798
\(335\) −6.44109 −0.351914
\(336\) −33.2616 −1.81457
\(337\) −4.88725 −0.266226 −0.133113 0.991101i \(-0.542497\pi\)
−0.133113 + 0.991101i \(0.542497\pi\)
\(338\) −31.8461 −1.73220
\(339\) −18.5982 −1.01012
\(340\) −13.0301 −0.706657
\(341\) −3.48070 −0.188490
\(342\) 1.86444 0.100818
\(343\) 19.7622 1.06706
\(344\) −38.4968 −2.07561
\(345\) −0.999082 −0.0537887
\(346\) −51.9362 −2.79211
\(347\) −13.6511 −0.732829 −0.366414 0.930452i \(-0.619415\pi\)
−0.366414 + 0.930452i \(0.619415\pi\)
\(348\) 81.1999 4.35277
\(349\) −1.00000 −0.0535288
\(350\) −23.2787 −1.24430
\(351\) −27.1524 −1.44929
\(352\) 21.2314 1.13164
\(353\) 8.13096 0.432768 0.216384 0.976308i \(-0.430574\pi\)
0.216384 + 0.976308i \(0.430574\pi\)
\(354\) 15.3117 0.813810
\(355\) −5.83134 −0.309496
\(356\) 55.7975 2.95726
\(357\) −13.5642 −0.717894
\(358\) 21.1840 1.11961
\(359\) −7.63110 −0.402754 −0.201377 0.979514i \(-0.564542\pi\)
−0.201377 + 0.979514i \(0.564542\pi\)
\(360\) −1.41566 −0.0746116
\(361\) −13.4154 −0.706074
\(362\) −33.7519 −1.77396
\(363\) −13.2767 −0.696846
\(364\) −47.2813 −2.47822
\(365\) −8.87800 −0.464696
\(366\) −24.6646 −1.28924
\(367\) −24.4133 −1.27436 −0.637182 0.770713i \(-0.719900\pi\)
−0.637182 + 0.770713i \(0.719900\pi\)
\(368\) 10.6145 0.553321
\(369\) 0.652520 0.0339688
\(370\) 10.1543 0.527897
\(371\) 20.6618 1.07271
\(372\) 16.5717 0.859205
\(373\) 9.23433 0.478136 0.239068 0.971003i \(-0.423158\pi\)
0.239068 + 0.971003i \(0.423158\pi\)
\(374\) 19.5062 1.00864
\(375\) 9.62157 0.496856
\(376\) 84.4299 4.35414
\(377\) 49.9718 2.57368
\(378\) −27.2581 −1.40201
\(379\) 17.6248 0.905324 0.452662 0.891682i \(-0.350474\pi\)
0.452662 + 0.891682i \(0.350474\pi\)
\(380\) −7.11364 −0.364922
\(381\) −17.9084 −0.917476
\(382\) −25.2484 −1.29182
\(383\) 23.6066 1.20624 0.603121 0.797650i \(-0.293924\pi\)
0.603121 + 0.797650i \(0.293924\pi\)
\(384\) −9.09911 −0.464337
\(385\) −1.98124 −0.100973
\(386\) −53.6527 −2.73085
\(387\) −1.48031 −0.0752482
\(388\) −45.2624 −2.29785
\(389\) 0.662173 0.0335735 0.0167867 0.999859i \(-0.494656\pi\)
0.0167867 + 0.999859i \(0.494656\pi\)
\(390\) 13.1914 0.667975
\(391\) 4.32864 0.218909
\(392\) 26.1800 1.32229
\(393\) −3.53577 −0.178356
\(394\) 19.7691 0.995951
\(395\) 7.95037 0.400026
\(396\) 2.53240 0.127258
\(397\) −5.83901 −0.293051 −0.146526 0.989207i \(-0.546809\pi\)
−0.146526 + 0.989207i \(0.546809\pi\)
\(398\) −20.1197 −1.00851
\(399\) −7.40522 −0.370725
\(400\) −49.1497 −2.45749
\(401\) 20.8106 1.03923 0.519615 0.854401i \(-0.326075\pi\)
0.519615 + 0.854401i \(0.326075\pi\)
\(402\) −45.9077 −2.28967
\(403\) 10.1985 0.508025
\(404\) −43.7812 −2.17819
\(405\) 4.87124 0.242054
\(406\) 50.1664 2.48971
\(407\) −10.8276 −0.536705
\(408\) −55.3581 −2.74063
\(409\) 19.9880 0.988341 0.494171 0.869365i \(-0.335472\pi\)
0.494171 + 0.869365i \(0.335472\pi\)
\(410\) −3.49525 −0.172618
\(411\) 0.565800 0.0279089
\(412\) −8.42224 −0.414934
\(413\) 6.73815 0.331563
\(414\) 0.788958 0.0387752
\(415\) −6.40063 −0.314195
\(416\) −62.2085 −3.05002
\(417\) 33.2579 1.62864
\(418\) 10.6492 0.520868
\(419\) −35.6823 −1.74319 −0.871597 0.490223i \(-0.836915\pi\)
−0.871597 + 0.490223i \(0.836915\pi\)
\(420\) 9.43277 0.460272
\(421\) 16.5533 0.806760 0.403380 0.915033i \(-0.367835\pi\)
0.403380 + 0.915033i \(0.367835\pi\)
\(422\) −65.2521 −3.17642
\(423\) 3.24656 0.157853
\(424\) 84.3246 4.09516
\(425\) −20.0434 −0.972248
\(426\) −41.5618 −2.01368
\(427\) −10.8540 −0.525262
\(428\) −56.5978 −2.73576
\(429\) −14.0661 −0.679120
\(430\) 7.92931 0.382385
\(431\) 1.66686 0.0802899 0.0401450 0.999194i \(-0.487218\pi\)
0.0401450 + 0.999194i \(0.487218\pi\)
\(432\) −57.5517 −2.76896
\(433\) 30.4107 1.46144 0.730722 0.682675i \(-0.239184\pi\)
0.730722 + 0.682675i \(0.239184\pi\)
\(434\) 10.2382 0.491451
\(435\) −9.96952 −0.478002
\(436\) 46.9902 2.25042
\(437\) 2.36317 0.113046
\(438\) −63.2762 −3.02346
\(439\) −22.1759 −1.05840 −0.529198 0.848498i \(-0.677507\pi\)
−0.529198 + 0.848498i \(0.677507\pi\)
\(440\) −8.08582 −0.385476
\(441\) 1.00669 0.0479377
\(442\) −57.1535 −2.71852
\(443\) 18.7735 0.891956 0.445978 0.895044i \(-0.352856\pi\)
0.445978 + 0.895044i \(0.352856\pi\)
\(444\) 51.5507 2.44649
\(445\) −6.85068 −0.324753
\(446\) −77.8408 −3.68587
\(447\) −29.6234 −1.40114
\(448\) −21.9717 −1.03807
\(449\) 26.8482 1.26704 0.633522 0.773725i \(-0.281609\pi\)
0.633522 + 0.773725i \(0.281609\pi\)
\(450\) −3.65320 −0.172214
\(451\) 3.72701 0.175498
\(452\) −56.0361 −2.63571
\(453\) −22.3377 −1.04951
\(454\) 47.6130 2.23459
\(455\) 5.80508 0.272147
\(456\) −30.2221 −1.41528
\(457\) −15.3981 −0.720291 −0.360146 0.932896i \(-0.617273\pi\)
−0.360146 + 0.932896i \(0.617273\pi\)
\(458\) −60.3738 −2.82108
\(459\) −23.4697 −1.09547
\(460\) −3.01021 −0.140352
\(461\) −4.94351 −0.230242 −0.115121 0.993351i \(-0.536726\pi\)
−0.115121 + 0.993351i \(0.536726\pi\)
\(462\) −14.1209 −0.656965
\(463\) 20.7293 0.963374 0.481687 0.876343i \(-0.340024\pi\)
0.481687 + 0.876343i \(0.340024\pi\)
\(464\) 105.919 4.91717
\(465\) −2.03464 −0.0943540
\(466\) −32.0937 −1.48671
\(467\) 19.9019 0.920952 0.460476 0.887672i \(-0.347679\pi\)
0.460476 + 0.887672i \(0.347679\pi\)
\(468\) −7.42000 −0.342990
\(469\) −20.2023 −0.932857
\(470\) −17.3903 −0.802156
\(471\) −24.2418 −1.11700
\(472\) 27.4997 1.26578
\(473\) −8.45509 −0.388765
\(474\) 56.6647 2.60270
\(475\) −10.9425 −0.502075
\(476\) −40.8686 −1.87321
\(477\) 3.24251 0.148465
\(478\) 0.277835 0.0127079
\(479\) −28.2127 −1.28907 −0.644536 0.764574i \(-0.722949\pi\)
−0.644536 + 0.764574i \(0.722949\pi\)
\(480\) 12.4108 0.566472
\(481\) 31.7252 1.44654
\(482\) 4.50110 0.205020
\(483\) −3.13359 −0.142583
\(484\) −40.0024 −1.81829
\(485\) 5.55720 0.252340
\(486\) −8.16742 −0.370482
\(487\) 14.3970 0.652389 0.326195 0.945303i \(-0.394234\pi\)
0.326195 + 0.945303i \(0.394234\pi\)
\(488\) −44.2973 −2.00524
\(489\) 4.07557 0.184304
\(490\) −5.39238 −0.243603
\(491\) 8.47476 0.382461 0.191230 0.981545i \(-0.438752\pi\)
0.191230 + 0.981545i \(0.438752\pi\)
\(492\) −17.7444 −0.799981
\(493\) 43.1941 1.94537
\(494\) −31.2023 −1.40386
\(495\) −0.310922 −0.0139749
\(496\) 21.6166 0.970613
\(497\) −18.2899 −0.820412
\(498\) −45.6193 −2.04425
\(499\) −23.9521 −1.07224 −0.536122 0.844141i \(-0.680111\pi\)
−0.536122 + 0.844141i \(0.680111\pi\)
\(500\) 28.9895 1.29645
\(501\) −15.5832 −0.696205
\(502\) 2.05603 0.0917649
\(503\) 17.4413 0.777670 0.388835 0.921307i \(-0.372878\pi\)
0.388835 + 0.921307i \(0.372878\pi\)
\(504\) −4.44017 −0.197781
\(505\) 5.37534 0.239200
\(506\) 4.50630 0.200330
\(507\) 19.8500 0.881567
\(508\) −53.9576 −2.39398
\(509\) 19.9721 0.885250 0.442625 0.896707i \(-0.354047\pi\)
0.442625 + 0.896707i \(0.354047\pi\)
\(510\) 11.4023 0.504902
\(511\) −27.8456 −1.23182
\(512\) 33.3469 1.47374
\(513\) −12.8130 −0.565710
\(514\) −23.8484 −1.05191
\(515\) 1.03406 0.0455662
\(516\) 40.2550 1.77213
\(517\) 18.5434 0.815540
\(518\) 31.8487 1.39935
\(519\) 32.3723 1.42099
\(520\) 23.6917 1.03895
\(521\) 23.4574 1.02769 0.513844 0.857884i \(-0.328221\pi\)
0.513844 + 0.857884i \(0.328221\pi\)
\(522\) 7.87276 0.344581
\(523\) −23.1124 −1.01063 −0.505317 0.862934i \(-0.668625\pi\)
−0.505317 + 0.862934i \(0.668625\pi\)
\(524\) −10.6532 −0.465386
\(525\) 14.5098 0.633261
\(526\) −44.0392 −1.92020
\(527\) 8.81531 0.384001
\(528\) −29.8143 −1.29750
\(529\) 1.00000 0.0434783
\(530\) −17.3686 −0.754445
\(531\) 1.05744 0.0458889
\(532\) −22.3118 −0.967337
\(533\) −10.9202 −0.473008
\(534\) −48.8269 −2.11295
\(535\) 6.94893 0.300429
\(536\) −82.4495 −3.56128
\(537\) −13.2042 −0.569803
\(538\) 42.1636 1.81780
\(539\) 5.74994 0.247668
\(540\) 16.3212 0.702354
\(541\) 12.6756 0.544965 0.272483 0.962161i \(-0.412155\pi\)
0.272483 + 0.962161i \(0.412155\pi\)
\(542\) −30.4315 −1.30714
\(543\) 21.0379 0.902822
\(544\) −53.7712 −2.30542
\(545\) −5.76933 −0.247131
\(546\) 41.3746 1.77067
\(547\) −17.1411 −0.732902 −0.366451 0.930437i \(-0.619427\pi\)
−0.366451 + 0.930437i \(0.619427\pi\)
\(548\) 1.70474 0.0728230
\(549\) −1.70335 −0.0726973
\(550\) −20.8660 −0.889731
\(551\) 23.5814 1.00460
\(552\) −12.7888 −0.544327
\(553\) 24.9361 1.06039
\(554\) −37.0518 −1.57418
\(555\) −6.32927 −0.268663
\(556\) 100.205 4.24964
\(557\) −32.7913 −1.38941 −0.694705 0.719294i \(-0.744465\pi\)
−0.694705 + 0.719294i \(0.744465\pi\)
\(558\) 1.60672 0.0680178
\(559\) 24.7736 1.04781
\(560\) 12.3043 0.519953
\(561\) −12.1584 −0.513327
\(562\) −20.8476 −0.879403
\(563\) −10.3633 −0.436760 −0.218380 0.975864i \(-0.570077\pi\)
−0.218380 + 0.975864i \(0.570077\pi\)
\(564\) −88.2861 −3.71751
\(565\) 6.87997 0.289442
\(566\) 41.1301 1.72883
\(567\) 15.2785 0.641637
\(568\) −74.6444 −3.13201
\(569\) −38.1386 −1.59885 −0.799426 0.600765i \(-0.794863\pi\)
−0.799426 + 0.600765i \(0.794863\pi\)
\(570\) 6.22496 0.260735
\(571\) 10.5721 0.442428 0.221214 0.975225i \(-0.428998\pi\)
0.221214 + 0.975225i \(0.428998\pi\)
\(572\) −42.3809 −1.77204
\(573\) 15.7376 0.657447
\(574\) −10.9627 −0.457576
\(575\) −4.63041 −0.193102
\(576\) −3.44809 −0.143670
\(577\) 21.8011 0.907592 0.453796 0.891106i \(-0.350070\pi\)
0.453796 + 0.891106i \(0.350070\pi\)
\(578\) −4.58007 −0.190506
\(579\) 33.4422 1.38981
\(580\) −30.0379 −1.24726
\(581\) −20.0754 −0.832869
\(582\) 39.6079 1.64180
\(583\) 18.5203 0.767033
\(584\) −113.643 −4.70259
\(585\) 0.911010 0.0376656
\(586\) −14.8448 −0.613232
\(587\) −16.4416 −0.678617 −0.339309 0.940675i \(-0.610193\pi\)
−0.339309 + 0.940675i \(0.610193\pi\)
\(588\) −27.3757 −1.12896
\(589\) 4.81262 0.198301
\(590\) −5.66421 −0.233192
\(591\) −12.3222 −0.506869
\(592\) 67.2440 2.76371
\(593\) 18.7070 0.768203 0.384101 0.923291i \(-0.374511\pi\)
0.384101 + 0.923291i \(0.374511\pi\)
\(594\) −24.4330 −1.00250
\(595\) 5.01774 0.205707
\(596\) −89.2547 −3.65601
\(597\) 12.5408 0.513259
\(598\) −13.2036 −0.539934
\(599\) −10.8483 −0.443248 −0.221624 0.975132i \(-0.571136\pi\)
−0.221624 + 0.975132i \(0.571136\pi\)
\(600\) 59.2174 2.41754
\(601\) 2.36883 0.0966267 0.0483134 0.998832i \(-0.484615\pi\)
0.0483134 + 0.998832i \(0.484615\pi\)
\(602\) 24.8701 1.01363
\(603\) −3.17041 −0.129109
\(604\) −67.3028 −2.73851
\(605\) 4.91139 0.199677
\(606\) 38.3117 1.55631
\(607\) 20.9624 0.850838 0.425419 0.904996i \(-0.360127\pi\)
0.425419 + 0.904996i \(0.360127\pi\)
\(608\) −29.3558 −1.19053
\(609\) −31.2691 −1.26709
\(610\) 9.12407 0.369423
\(611\) −54.3327 −2.19807
\(612\) −6.41363 −0.259256
\(613\) −23.1952 −0.936843 −0.468422 0.883505i \(-0.655177\pi\)
−0.468422 + 0.883505i \(0.655177\pi\)
\(614\) −31.4426 −1.26892
\(615\) 2.17862 0.0878504
\(616\) −25.3610 −1.02182
\(617\) 30.6906 1.23556 0.617779 0.786352i \(-0.288033\pi\)
0.617779 + 0.786352i \(0.288033\pi\)
\(618\) 7.37008 0.296468
\(619\) 19.9187 0.800601 0.400301 0.916384i \(-0.368906\pi\)
0.400301 + 0.916384i \(0.368906\pi\)
\(620\) −6.13031 −0.246199
\(621\) −5.42196 −0.217576
\(622\) 3.42531 0.137342
\(623\) −21.4870 −0.860857
\(624\) 87.3566 3.49706
\(625\) 19.5928 0.783712
\(626\) −47.5344 −1.89985
\(627\) −6.63772 −0.265085
\(628\) −73.0398 −2.91461
\(629\) 27.4223 1.09340
\(630\) 0.914557 0.0364368
\(631\) 16.9341 0.674134 0.337067 0.941481i \(-0.390565\pi\)
0.337067 + 0.941481i \(0.390565\pi\)
\(632\) 101.769 4.04816
\(633\) 40.6722 1.61658
\(634\) −35.6079 −1.41417
\(635\) 6.62478 0.262896
\(636\) −88.1760 −3.49640
\(637\) −16.8475 −0.667521
\(638\) 44.9670 1.78026
\(639\) −2.87028 −0.113547
\(640\) 3.36599 0.133053
\(641\) −42.3221 −1.67162 −0.835811 0.549017i \(-0.815002\pi\)
−0.835811 + 0.549017i \(0.815002\pi\)
\(642\) 49.5272 1.95468
\(643\) 47.3934 1.86901 0.934507 0.355945i \(-0.115841\pi\)
0.934507 + 0.355945i \(0.115841\pi\)
\(644\) −9.44144 −0.372045
\(645\) −4.94241 −0.194607
\(646\) −26.9704 −1.06114
\(647\) −22.9751 −0.903245 −0.451623 0.892209i \(-0.649155\pi\)
−0.451623 + 0.892209i \(0.649155\pi\)
\(648\) 62.3545 2.44952
\(649\) 6.03979 0.237082
\(650\) 61.1380 2.39803
\(651\) −6.38159 −0.250114
\(652\) 12.2796 0.480906
\(653\) 30.0338 1.17531 0.587657 0.809110i \(-0.300051\pi\)
0.587657 + 0.809110i \(0.300051\pi\)
\(654\) −41.1198 −1.60791
\(655\) 1.30797 0.0511066
\(656\) −23.1463 −0.903710
\(657\) −4.36990 −0.170486
\(658\) −54.5443 −2.12636
\(659\) 31.2967 1.21914 0.609572 0.792730i \(-0.291341\pi\)
0.609572 + 0.792730i \(0.291341\pi\)
\(660\) 8.45513 0.329115
\(661\) 22.4784 0.874307 0.437154 0.899387i \(-0.355987\pi\)
0.437154 + 0.899387i \(0.355987\pi\)
\(662\) 8.34073 0.324172
\(663\) 35.6243 1.38353
\(664\) −81.9316 −3.17956
\(665\) 2.73938 0.106229
\(666\) 4.99812 0.193673
\(667\) 9.97868 0.386376
\(668\) −46.9517 −1.81662
\(669\) 48.5189 1.87585
\(670\) 16.9824 0.656088
\(671\) −9.72907 −0.375586
\(672\) 38.9261 1.50161
\(673\) 0.599637 0.0231143 0.0115572 0.999933i \(-0.496321\pi\)
0.0115572 + 0.999933i \(0.496321\pi\)
\(674\) 12.8856 0.496335
\(675\) 25.1059 0.966328
\(676\) 59.8074 2.30028
\(677\) 45.6605 1.75487 0.877437 0.479691i \(-0.159251\pi\)
0.877437 + 0.479691i \(0.159251\pi\)
\(678\) 49.0357 1.88320
\(679\) 17.4300 0.668903
\(680\) 20.4784 0.785310
\(681\) −29.6776 −1.13725
\(682\) 9.17712 0.351410
\(683\) 7.89455 0.302077 0.151038 0.988528i \(-0.451738\pi\)
0.151038 + 0.988528i \(0.451738\pi\)
\(684\) −3.50145 −0.133881
\(685\) −0.209304 −0.00799709
\(686\) −52.1045 −1.98936
\(687\) 37.6315 1.43573
\(688\) 52.5096 2.00191
\(689\) −54.2650 −2.06733
\(690\) 2.63415 0.100280
\(691\) 11.2730 0.428847 0.214423 0.976741i \(-0.431213\pi\)
0.214423 + 0.976741i \(0.431213\pi\)
\(692\) 97.5370 3.70780
\(693\) −0.975200 −0.0370448
\(694\) 35.9921 1.36624
\(695\) −12.3029 −0.466677
\(696\) −127.615 −4.83725
\(697\) −9.43912 −0.357532
\(698\) 2.63657 0.0997958
\(699\) 20.0043 0.756632
\(700\) 43.7178 1.65238
\(701\) 17.1738 0.648645 0.324322 0.945947i \(-0.394864\pi\)
0.324322 + 0.945947i \(0.394864\pi\)
\(702\) 71.5893 2.70196
\(703\) 14.9709 0.564639
\(704\) −19.6945 −0.742264
\(705\) 10.8395 0.408241
\(706\) −21.4379 −0.806826
\(707\) 16.8596 0.634071
\(708\) −28.7557 −1.08070
\(709\) 3.12657 0.117421 0.0587104 0.998275i \(-0.481301\pi\)
0.0587104 + 0.998275i \(0.481301\pi\)
\(710\) 15.3748 0.577005
\(711\) 3.91330 0.146760
\(712\) −87.6924 −3.28641
\(713\) 2.03651 0.0762678
\(714\) 35.7630 1.33840
\(715\) 5.20343 0.194597
\(716\) −39.7839 −1.48679
\(717\) −0.173177 −0.00646741
\(718\) 20.1200 0.750870
\(719\) 0.247381 0.00922577 0.00461288 0.999989i \(-0.498532\pi\)
0.00461288 + 0.999989i \(0.498532\pi\)
\(720\) 1.93096 0.0719625
\(721\) 3.24331 0.120787
\(722\) 35.3707 1.31636
\(723\) −2.80558 −0.104341
\(724\) 63.3866 2.35575
\(725\) −46.2054 −1.71603
\(726\) 35.0050 1.29916
\(727\) −1.34779 −0.0499869 −0.0249934 0.999688i \(-0.507956\pi\)
−0.0249934 + 0.999688i \(0.507956\pi\)
\(728\) 74.3083 2.75405
\(729\) 29.1291 1.07885
\(730\) 23.4075 0.866350
\(731\) 21.4136 0.792010
\(732\) 46.3205 1.71205
\(733\) −33.5556 −1.23940 −0.619702 0.784837i \(-0.712747\pi\)
−0.619702 + 0.784837i \(0.712747\pi\)
\(734\) 64.3675 2.37585
\(735\) 3.36112 0.123977
\(736\) −12.4222 −0.457888
\(737\) −18.1085 −0.667035
\(738\) −1.72042 −0.0633295
\(739\) −24.4577 −0.899690 −0.449845 0.893107i \(-0.648521\pi\)
−0.449845 + 0.893107i \(0.648521\pi\)
\(740\) −19.0699 −0.701025
\(741\) 19.4487 0.714465
\(742\) −54.4763 −1.99989
\(743\) −5.00269 −0.183531 −0.0917655 0.995781i \(-0.529251\pi\)
−0.0917655 + 0.995781i \(0.529251\pi\)
\(744\) −26.0445 −0.954837
\(745\) 10.9585 0.401487
\(746\) −24.3470 −0.891407
\(747\) −3.15050 −0.115271
\(748\) −36.6328 −1.33943
\(749\) 21.7951 0.796377
\(750\) −25.3680 −0.926308
\(751\) 37.8714 1.38195 0.690974 0.722880i \(-0.257182\pi\)
0.690974 + 0.722880i \(0.257182\pi\)
\(752\) −115.163 −4.19954
\(753\) −1.28154 −0.0467019
\(754\) −131.754 −4.79821
\(755\) 8.26327 0.300731
\(756\) 51.1912 1.86180
\(757\) 34.6620 1.25981 0.629907 0.776671i \(-0.283093\pi\)
0.629907 + 0.776671i \(0.283093\pi\)
\(758\) −46.4691 −1.68783
\(759\) −2.80882 −0.101954
\(760\) 11.1799 0.405539
\(761\) 47.1092 1.70771 0.853854 0.520513i \(-0.174259\pi\)
0.853854 + 0.520513i \(0.174259\pi\)
\(762\) 47.2169 1.71049
\(763\) −18.0954 −0.655096
\(764\) 47.4169 1.71548
\(765\) 0.787450 0.0284703
\(766\) −62.2406 −2.24884
\(767\) −17.6967 −0.638992
\(768\) −13.8832 −0.500967
\(769\) −22.3289 −0.805201 −0.402601 0.915376i \(-0.631894\pi\)
−0.402601 + 0.915376i \(0.631894\pi\)
\(770\) 5.22369 0.188249
\(771\) 14.8649 0.535348
\(772\) 100.761 3.62645
\(773\) 30.2420 1.08773 0.543865 0.839173i \(-0.316961\pi\)
0.543865 + 0.839173i \(0.316961\pi\)
\(774\) 3.90294 0.140288
\(775\) −9.42987 −0.338731
\(776\) 71.1352 2.55361
\(777\) −19.8516 −0.712172
\(778\) −1.74587 −0.0625924
\(779\) −5.15318 −0.184632
\(780\) −24.7737 −0.887042
\(781\) −16.3942 −0.586632
\(782\) −11.4128 −0.408120
\(783\) −54.1041 −1.93352
\(784\) −35.7095 −1.27534
\(785\) 8.96765 0.320069
\(786\) 9.32231 0.332516
\(787\) −10.2073 −0.363852 −0.181926 0.983312i \(-0.558233\pi\)
−0.181926 + 0.983312i \(0.558233\pi\)
\(788\) −37.1266 −1.32258
\(789\) 27.4500 0.977246
\(790\) −20.9617 −0.745785
\(791\) 21.5788 0.767255
\(792\) −3.97997 −0.141422
\(793\) 28.5064 1.01229
\(794\) 15.3950 0.546347
\(795\) 10.8260 0.383960
\(796\) 37.7850 1.33925
\(797\) −9.11218 −0.322770 −0.161385 0.986892i \(-0.551596\pi\)
−0.161385 + 0.986892i \(0.551596\pi\)
\(798\) 19.5244 0.691157
\(799\) −46.9636 −1.66145
\(800\) 57.5199 2.03364
\(801\) −3.37202 −0.119144
\(802\) −54.8686 −1.93748
\(803\) −24.9596 −0.880805
\(804\) 86.2152 3.04058
\(805\) 1.15920 0.0408563
\(806\) −26.8892 −0.947131
\(807\) −26.2810 −0.925133
\(808\) 68.8073 2.42063
\(809\) −21.6998 −0.762923 −0.381462 0.924385i \(-0.624579\pi\)
−0.381462 + 0.924385i \(0.624579\pi\)
\(810\) −12.8434 −0.451270
\(811\) −34.7346 −1.21970 −0.609848 0.792518i \(-0.708770\pi\)
−0.609848 + 0.792518i \(0.708770\pi\)
\(812\) −94.2131 −3.30623
\(813\) 18.9682 0.665244
\(814\) 28.5478 1.00060
\(815\) −1.50766 −0.0528110
\(816\) 75.5085 2.64333
\(817\) 11.6905 0.408999
\(818\) −52.6998 −1.84260
\(819\) 2.85736 0.0998442
\(820\) 6.56412 0.229229
\(821\) 26.5019 0.924924 0.462462 0.886639i \(-0.346966\pi\)
0.462462 + 0.886639i \(0.346966\pi\)
\(822\) −1.49177 −0.0520316
\(823\) −32.7115 −1.14025 −0.570125 0.821558i \(-0.693105\pi\)
−0.570125 + 0.821558i \(0.693105\pi\)
\(824\) 13.2366 0.461117
\(825\) 13.0060 0.452810
\(826\) −17.7656 −0.618146
\(827\) −22.8742 −0.795414 −0.397707 0.917512i \(-0.630194\pi\)
−0.397707 + 0.917512i \(0.630194\pi\)
\(828\) −1.48167 −0.0514917
\(829\) 15.6517 0.543607 0.271804 0.962353i \(-0.412380\pi\)
0.271804 + 0.962353i \(0.412380\pi\)
\(830\) 16.8757 0.585765
\(831\) 23.0947 0.801146
\(832\) 57.7053 2.00057
\(833\) −14.5625 −0.504559
\(834\) −87.6868 −3.03635
\(835\) 5.76461 0.199493
\(836\) −19.9993 −0.691690
\(837\) −11.0419 −0.381663
\(838\) 94.0790 3.24991
\(839\) −1.39286 −0.0480867 −0.0240434 0.999711i \(-0.507654\pi\)
−0.0240434 + 0.999711i \(0.507654\pi\)
\(840\) −14.8247 −0.511502
\(841\) 70.5741 2.43359
\(842\) −43.6441 −1.50407
\(843\) 12.9945 0.447554
\(844\) 122.544 4.21815
\(845\) −7.34300 −0.252607
\(846\) −8.55980 −0.294292
\(847\) 15.4045 0.529304
\(848\) −115.019 −3.94976
\(849\) −25.6368 −0.879852
\(850\) 52.8459 1.81260
\(851\) 6.33509 0.217164
\(852\) 78.0537 2.67407
\(853\) −12.5718 −0.430450 −0.215225 0.976565i \(-0.569048\pi\)
−0.215225 + 0.976565i \(0.569048\pi\)
\(854\) 28.6174 0.979268
\(855\) 0.429900 0.0147023
\(856\) 88.9502 3.04025
\(857\) −5.87878 −0.200815 −0.100408 0.994946i \(-0.532015\pi\)
−0.100408 + 0.994946i \(0.532015\pi\)
\(858\) 37.0864 1.26611
\(859\) 48.9229 1.66923 0.834613 0.550837i \(-0.185691\pi\)
0.834613 + 0.550837i \(0.185691\pi\)
\(860\) −14.8914 −0.507791
\(861\) 6.83318 0.232874
\(862\) −4.39481 −0.149688
\(863\) 32.8555 1.11841 0.559207 0.829028i \(-0.311106\pi\)
0.559207 + 0.829028i \(0.311106\pi\)
\(864\) 67.3527 2.29139
\(865\) −11.9753 −0.407174
\(866\) −80.1800 −2.72463
\(867\) 2.85480 0.0969539
\(868\) −19.2276 −0.652626
\(869\) 22.3517 0.758228
\(870\) 26.2854 0.891158
\(871\) 53.0583 1.79781
\(872\) −73.8506 −2.50090
\(873\) 2.73535 0.0925775
\(874\) −6.23068 −0.210756
\(875\) −11.1635 −0.377397
\(876\) 118.834 4.01502
\(877\) 8.68321 0.293211 0.146606 0.989195i \(-0.453165\pi\)
0.146606 + 0.989195i \(0.453165\pi\)
\(878\) 58.4683 1.97321
\(879\) 9.25288 0.312092
\(880\) 11.0291 0.371790
\(881\) −15.9274 −0.536607 −0.268304 0.963334i \(-0.586463\pi\)
−0.268304 + 0.963334i \(0.586463\pi\)
\(882\) −2.65422 −0.0893722
\(883\) −19.6399 −0.660935 −0.330467 0.943817i \(-0.607206\pi\)
−0.330467 + 0.943817i \(0.607206\pi\)
\(884\) 107.335 3.61007
\(885\) 3.53055 0.118678
\(886\) −49.4977 −1.66291
\(887\) −5.25326 −0.176387 −0.0881935 0.996103i \(-0.528109\pi\)
−0.0881935 + 0.996103i \(0.528109\pi\)
\(888\) −81.0181 −2.71879
\(889\) 20.7784 0.696887
\(890\) 18.0623 0.605450
\(891\) 13.6950 0.458800
\(892\) 146.186 4.89467
\(893\) −25.6393 −0.857985
\(894\) 78.1044 2.61220
\(895\) 4.88457 0.163273
\(896\) 10.5574 0.352696
\(897\) 8.22991 0.274789
\(898\) −70.7872 −2.36220
\(899\) 20.3217 0.677766
\(900\) 6.86076 0.228692
\(901\) −46.9050 −1.56263
\(902\) −9.82653 −0.327188
\(903\) −15.5017 −0.515866
\(904\) 88.0674 2.92908
\(905\) −7.78245 −0.258697
\(906\) 58.8949 1.95665
\(907\) −25.8865 −0.859547 −0.429774 0.902937i \(-0.641407\pi\)
−0.429774 + 0.902937i \(0.641407\pi\)
\(908\) −89.4180 −2.96744
\(909\) 2.64583 0.0877567
\(910\) −15.3055 −0.507374
\(911\) −4.88285 −0.161776 −0.0808880 0.996723i \(-0.525776\pi\)
−0.0808880 + 0.996723i \(0.525776\pi\)
\(912\) 41.2230 1.36503
\(913\) −17.9947 −0.595539
\(914\) 40.5982 1.34287
\(915\) −5.68711 −0.188010
\(916\) 113.383 3.74627
\(917\) 4.10242 0.135474
\(918\) 61.8797 2.04233
\(919\) 2.16483 0.0714111 0.0357056 0.999362i \(-0.488632\pi\)
0.0357056 + 0.999362i \(0.488632\pi\)
\(920\) 4.73090 0.155973
\(921\) 19.5985 0.645791
\(922\) 13.0339 0.429250
\(923\) 48.0355 1.58111
\(924\) 26.5193 0.872420
\(925\) −29.3341 −0.964499
\(926\) −54.6544 −1.79606
\(927\) 0.508982 0.0167172
\(928\) −123.957 −4.06909
\(929\) 33.1333 1.08707 0.543534 0.839387i \(-0.317086\pi\)
0.543534 + 0.839387i \(0.317086\pi\)
\(930\) 5.36447 0.175908
\(931\) −7.95021 −0.260558
\(932\) 60.2724 1.97429
\(933\) −2.13503 −0.0698977
\(934\) −52.4729 −1.71697
\(935\) 4.49769 0.147090
\(936\) 11.6614 0.381166
\(937\) 20.5124 0.670109 0.335055 0.942199i \(-0.391245\pi\)
0.335055 + 0.942199i \(0.391245\pi\)
\(938\) 53.2649 1.73916
\(939\) 29.6286 0.966892
\(940\) 32.6593 1.06523
\(941\) −38.6191 −1.25895 −0.629473 0.777022i \(-0.716729\pi\)
−0.629473 + 0.777022i \(0.716729\pi\)
\(942\) 63.9152 2.08247
\(943\) −2.18062 −0.0710108
\(944\) −37.5096 −1.22083
\(945\) −6.28512 −0.204455
\(946\) 22.2925 0.724791
\(947\) −42.5206 −1.38174 −0.690868 0.722981i \(-0.742771\pi\)
−0.690868 + 0.722981i \(0.742771\pi\)
\(948\) −106.417 −3.45627
\(949\) 73.1322 2.37397
\(950\) 28.8506 0.936038
\(951\) 22.1947 0.719713
\(952\) 64.2299 2.08170
\(953\) 39.8417 1.29060 0.645299 0.763930i \(-0.276733\pi\)
0.645299 + 0.763930i \(0.276733\pi\)
\(954\) −8.54913 −0.276788
\(955\) −5.82173 −0.188387
\(956\) −0.521778 −0.0168755
\(957\) −28.0283 −0.906027
\(958\) 74.3849 2.40327
\(959\) −0.656476 −0.0211987
\(960\) −11.5124 −0.371561
\(961\) −26.8526 −0.866214
\(962\) −83.6458 −2.69685
\(963\) 3.42038 0.110220
\(964\) −8.45313 −0.272257
\(965\) −12.3711 −0.398241
\(966\) 8.26195 0.265824
\(967\) 44.1313 1.41917 0.709584 0.704621i \(-0.248883\pi\)
0.709584 + 0.704621i \(0.248883\pi\)
\(968\) 62.8685 2.02067
\(969\) 16.8109 0.540043
\(970\) −14.6520 −0.470447
\(971\) −33.5441 −1.07648 −0.538240 0.842791i \(-0.680911\pi\)
−0.538240 + 0.842791i \(0.680911\pi\)
\(972\) 15.3385 0.491984
\(973\) −38.5878 −1.23707
\(974\) −37.9587 −1.21628
\(975\) −38.1079 −1.22043
\(976\) 60.4216 1.93405
\(977\) 15.5289 0.496815 0.248408 0.968656i \(-0.420093\pi\)
0.248408 + 0.968656i \(0.420093\pi\)
\(978\) −10.7455 −0.343605
\(979\) −19.2600 −0.615552
\(980\) 10.1270 0.323494
\(981\) −2.83976 −0.0906666
\(982\) −22.3443 −0.713037
\(983\) −32.0934 −1.02362 −0.511811 0.859098i \(-0.671025\pi\)
−0.511811 + 0.859098i \(0.671025\pi\)
\(984\) 27.8875 0.889021
\(985\) 4.55831 0.145240
\(986\) −113.885 −3.62682
\(987\) 33.9980 1.08217
\(988\) 58.5984 1.86426
\(989\) 4.94696 0.157304
\(990\) 0.819769 0.0260540
\(991\) −0.298428 −0.00947987 −0.00473994 0.999989i \(-0.501509\pi\)
−0.00473994 + 0.999989i \(0.501509\pi\)
\(992\) −25.2979 −0.803209
\(993\) −5.19885 −0.164980
\(994\) 48.2226 1.52953
\(995\) −4.63915 −0.147071
\(996\) 85.6737 2.71467
\(997\) −54.0188 −1.71079 −0.855396 0.517975i \(-0.826686\pi\)
−0.855396 + 0.517975i \(0.826686\pi\)
\(998\) 63.1515 1.99903
\(999\) −34.3486 −1.08674
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 \(a_p\))