Properties

Label 6047.2.a.a.1.20
Level 6047
Weight 2
Character 6047.1
Self dual Yes
Analytic conductor 48.286
Analytic rank 1
Dimension 217
CM No

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Newspace parameters

Level: \( N \) = \( 6047 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6047.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.2855381023\)
Analytic rank: \(1\)
Dimension: \(217\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.20
Character \(\chi\) = 6047.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.44753 q^{2} -2.68992 q^{3} +3.99041 q^{4} -1.41647 q^{5} +6.58366 q^{6} -0.890122 q^{7} -4.87158 q^{8} +4.23566 q^{9} +O(q^{10})\) \(q-2.44753 q^{2} -2.68992 q^{3} +3.99041 q^{4} -1.41647 q^{5} +6.58366 q^{6} -0.890122 q^{7} -4.87158 q^{8} +4.23566 q^{9} +3.46686 q^{10} +5.63194 q^{11} -10.7339 q^{12} +6.51825 q^{13} +2.17860 q^{14} +3.81019 q^{15} +3.94253 q^{16} +0.509200 q^{17} -10.3669 q^{18} +2.70183 q^{19} -5.65229 q^{20} +2.39435 q^{21} -13.7843 q^{22} +0.817422 q^{23} +13.1041 q^{24} -2.99361 q^{25} -15.9536 q^{26} -3.32382 q^{27} -3.55195 q^{28} +8.47541 q^{29} -9.32556 q^{30} +6.30475 q^{31} +0.0937034 q^{32} -15.1494 q^{33} -1.24628 q^{34} +1.26083 q^{35} +16.9020 q^{36} -9.26639 q^{37} -6.61280 q^{38} -17.5335 q^{39} +6.90045 q^{40} -0.0960551 q^{41} -5.86026 q^{42} -1.68517 q^{43} +22.4737 q^{44} -5.99969 q^{45} -2.00066 q^{46} -9.10936 q^{47} -10.6051 q^{48} -6.20768 q^{49} +7.32695 q^{50} -1.36971 q^{51} +26.0105 q^{52} -1.10602 q^{53} +8.13514 q^{54} -7.97748 q^{55} +4.33630 q^{56} -7.26769 q^{57} -20.7438 q^{58} -6.44584 q^{59} +15.2042 q^{60} -7.59288 q^{61} -15.4311 q^{62} -3.77025 q^{63} -8.11440 q^{64} -9.23291 q^{65} +37.0787 q^{66} -5.28086 q^{67} +2.03191 q^{68} -2.19880 q^{69} -3.08592 q^{70} +14.7116 q^{71} -20.6343 q^{72} +3.10261 q^{73} +22.6798 q^{74} +8.05256 q^{75} +10.7814 q^{76} -5.01311 q^{77} +42.9139 q^{78} -5.94542 q^{79} -5.58448 q^{80} -3.76618 q^{81} +0.235098 q^{82} -2.53055 q^{83} +9.55445 q^{84} -0.721267 q^{85} +4.12451 q^{86} -22.7982 q^{87} -27.4364 q^{88} +7.64966 q^{89} +14.6844 q^{90} -5.80203 q^{91} +3.26184 q^{92} -16.9592 q^{93} +22.2954 q^{94} -3.82706 q^{95} -0.252055 q^{96} +6.26189 q^{97} +15.1935 q^{98} +23.8550 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 217q - 20q^{2} - 27q^{3} + 184q^{4} - 19q^{5} - 17q^{6} - 48q^{7} - 57q^{8} + 152q^{9} + O(q^{10}) \) \( 217q - 20q^{2} - 27q^{3} + 184q^{4} - 19q^{5} - 17q^{6} - 48q^{7} - 57q^{8} + 152q^{9} - 46q^{10} - 32q^{11} - 72q^{12} - 80q^{13} - 22q^{14} - 43q^{15} + 122q^{16} - 61q^{17} - 88q^{18} - 43q^{19} - 41q^{20} - 61q^{21} - 93q^{22} - 60q^{23} - 41q^{24} + 26q^{25} - 9q^{26} - 93q^{27} - 126q^{28} - 47q^{29} - 36q^{30} - 100q^{31} - 114q^{32} - 133q^{33} - 75q^{34} - 37q^{35} + 75q^{36} - 264q^{37} - 35q^{38} - 47q^{39} - 118q^{40} - 72q^{41} - 64q^{42} - 107q^{43} - 59q^{44} - 69q^{45} - 111q^{46} - 54q^{47} - 135q^{48} + 33q^{49} - 42q^{50} - 26q^{51} - 173q^{52} - 103q^{53} - 28q^{54} - 78q^{55} - 44q^{56} - 205q^{57} - 189q^{58} - 38q^{59} - 105q^{60} - 108q^{61} - 14q^{62} - 116q^{63} + 39q^{64} - 146q^{65} + 5q^{66} - 206q^{67} - 62q^{68} - 55q^{69} - 125q^{70} - 78q^{71} - 225q^{72} - 326q^{73} + 3q^{74} - 95q^{75} - 84q^{76} - 79q^{77} - 86q^{78} - 117q^{79} - 39q^{80} + q^{81} - 96q^{82} - 23q^{83} - 57q^{84} - 224q^{85} - 7q^{86} - 45q^{87} - 250q^{88} - 104q^{89} - 36q^{90} - 96q^{91} - 137q^{92} - 155q^{93} - 48q^{94} - 38q^{95} - 33q^{96} - 447q^{97} - 46q^{98} - 94q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.44753 −1.73067 −0.865333 0.501198i \(-0.832893\pi\)
−0.865333 + 0.501198i \(0.832893\pi\)
\(3\) −2.68992 −1.55302 −0.776512 0.630102i \(-0.783013\pi\)
−0.776512 + 0.630102i \(0.783013\pi\)
\(4\) 3.99041 1.99520
\(5\) −1.41647 −0.633465 −0.316733 0.948515i \(-0.602586\pi\)
−0.316733 + 0.948515i \(0.602586\pi\)
\(6\) 6.58366 2.68777
\(7\) −0.890122 −0.336434 −0.168217 0.985750i \(-0.553801\pi\)
−0.168217 + 0.985750i \(0.553801\pi\)
\(8\) −4.87158 −1.72236
\(9\) 4.23566 1.41189
\(10\) 3.46686 1.09632
\(11\) 5.63194 1.69809 0.849046 0.528318i \(-0.177177\pi\)
0.849046 + 0.528318i \(0.177177\pi\)
\(12\) −10.7339 −3.09860
\(13\) 6.51825 1.80784 0.903918 0.427705i \(-0.140678\pi\)
0.903918 + 0.427705i \(0.140678\pi\)
\(14\) 2.17860 0.582256
\(15\) 3.81019 0.983787
\(16\) 3.94253 0.985632
\(17\) 0.509200 0.123499 0.0617495 0.998092i \(-0.480332\pi\)
0.0617495 + 0.998092i \(0.480332\pi\)
\(18\) −10.3669 −2.44350
\(19\) 2.70183 0.619842 0.309921 0.950762i \(-0.399697\pi\)
0.309921 + 0.950762i \(0.399697\pi\)
\(20\) −5.65229 −1.26389
\(21\) 2.39435 0.522491
\(22\) −13.7843 −2.93883
\(23\) 0.817422 0.170444 0.0852221 0.996362i \(-0.472840\pi\)
0.0852221 + 0.996362i \(0.472840\pi\)
\(24\) 13.1041 2.67487
\(25\) −2.99361 −0.598722
\(26\) −15.9536 −3.12876
\(27\) −3.32382 −0.639669
\(28\) −3.55195 −0.671255
\(29\) 8.47541 1.57384 0.786922 0.617052i \(-0.211673\pi\)
0.786922 + 0.617052i \(0.211673\pi\)
\(30\) −9.32556 −1.70261
\(31\) 6.30475 1.13237 0.566183 0.824280i \(-0.308420\pi\)
0.566183 + 0.824280i \(0.308420\pi\)
\(32\) 0.0937034 0.0165646
\(33\) −15.1494 −2.63718
\(34\) −1.24628 −0.213736
\(35\) 1.26083 0.213120
\(36\) 16.9020 2.81700
\(37\) −9.26639 −1.52339 −0.761693 0.647938i \(-0.775631\pi\)
−0.761693 + 0.647938i \(0.775631\pi\)
\(38\) −6.61280 −1.07274
\(39\) −17.5335 −2.80761
\(40\) 6.90045 1.09106
\(41\) −0.0960551 −0.0150013 −0.00750064 0.999972i \(-0.502388\pi\)
−0.00750064 + 0.999972i \(0.502388\pi\)
\(42\) −5.86026 −0.904257
\(43\) −1.68517 −0.256986 −0.128493 0.991710i \(-0.541014\pi\)
−0.128493 + 0.991710i \(0.541014\pi\)
\(44\) 22.4737 3.38804
\(45\) −5.99969 −0.894380
\(46\) −2.00066 −0.294982
\(47\) −9.10936 −1.32874 −0.664369 0.747405i \(-0.731300\pi\)
−0.664369 + 0.747405i \(0.731300\pi\)
\(48\) −10.6051 −1.53071
\(49\) −6.20768 −0.886812
\(50\) 7.32695 1.03619
\(51\) −1.36971 −0.191797
\(52\) 26.0105 3.60700
\(53\) −1.10602 −0.151923 −0.0759616 0.997111i \(-0.524203\pi\)
−0.0759616 + 0.997111i \(0.524203\pi\)
\(54\) 8.13514 1.10705
\(55\) −7.97748 −1.07568
\(56\) 4.33630 0.579462
\(57\) −7.26769 −0.962629
\(58\) −20.7438 −2.72380
\(59\) −6.44584 −0.839177 −0.419589 0.907714i \(-0.637826\pi\)
−0.419589 + 0.907714i \(0.637826\pi\)
\(60\) 15.2042 1.96285
\(61\) −7.59288 −0.972169 −0.486084 0.873912i \(-0.661575\pi\)
−0.486084 + 0.873912i \(0.661575\pi\)
\(62\) −15.4311 −1.95975
\(63\) −3.77025 −0.475007
\(64\) −8.11440 −1.01430
\(65\) −9.23291 −1.14520
\(66\) 37.0787 4.56408
\(67\) −5.28086 −0.645160 −0.322580 0.946542i \(-0.604550\pi\)
−0.322580 + 0.946542i \(0.604550\pi\)
\(68\) 2.03191 0.246406
\(69\) −2.19880 −0.264704
\(70\) −3.08592 −0.368839
\(71\) 14.7116 1.74595 0.872975 0.487766i \(-0.162188\pi\)
0.872975 + 0.487766i \(0.162188\pi\)
\(72\) −20.6343 −2.43178
\(73\) 3.10261 0.363133 0.181567 0.983379i \(-0.441883\pi\)
0.181567 + 0.983379i \(0.441883\pi\)
\(74\) 22.6798 2.63647
\(75\) 8.05256 0.929830
\(76\) 10.7814 1.23671
\(77\) −5.01311 −0.571297
\(78\) 42.9139 4.85904
\(79\) −5.94542 −0.668912 −0.334456 0.942411i \(-0.608553\pi\)
−0.334456 + 0.942411i \(0.608553\pi\)
\(80\) −5.58448 −0.624363
\(81\) −3.76618 −0.418464
\(82\) 0.235098 0.0259622
\(83\) −2.53055 −0.277763 −0.138882 0.990309i \(-0.544351\pi\)
−0.138882 + 0.990309i \(0.544351\pi\)
\(84\) 9.55445 1.04248
\(85\) −0.721267 −0.0782323
\(86\) 4.12451 0.444757
\(87\) −22.7982 −2.44422
\(88\) −27.4364 −2.92473
\(89\) 7.64966 0.810862 0.405431 0.914126i \(-0.367121\pi\)
0.405431 + 0.914126i \(0.367121\pi\)
\(90\) 14.6844 1.54787
\(91\) −5.80203 −0.608219
\(92\) 3.26184 0.340071
\(93\) −16.9592 −1.75859
\(94\) 22.2954 2.29960
\(95\) −3.82706 −0.392648
\(96\) −0.252055 −0.0257252
\(97\) 6.26189 0.635799 0.317899 0.948124i \(-0.397023\pi\)
0.317899 + 0.948124i \(0.397023\pi\)
\(98\) 15.1935 1.53477
\(99\) 23.8550 2.39751
\(100\) −11.9457 −1.19457
\(101\) −16.5310 −1.64489 −0.822446 0.568844i \(-0.807391\pi\)
−0.822446 + 0.568844i \(0.807391\pi\)
\(102\) 3.35240 0.331937
\(103\) −9.78801 −0.964441 −0.482221 0.876050i \(-0.660170\pi\)
−0.482221 + 0.876050i \(0.660170\pi\)
\(104\) −31.7542 −3.11375
\(105\) −3.39153 −0.330980
\(106\) 2.70701 0.262928
\(107\) −17.9574 −1.73601 −0.868006 0.496554i \(-0.834598\pi\)
−0.868006 + 0.496554i \(0.834598\pi\)
\(108\) −13.2634 −1.27627
\(109\) 4.19032 0.401359 0.200680 0.979657i \(-0.435685\pi\)
0.200680 + 0.979657i \(0.435685\pi\)
\(110\) 19.5251 1.86165
\(111\) 24.9258 2.36586
\(112\) −3.50933 −0.331600
\(113\) 2.11039 0.198529 0.0992645 0.995061i \(-0.468351\pi\)
0.0992645 + 0.995061i \(0.468351\pi\)
\(114\) 17.7879 1.66599
\(115\) −1.15785 −0.107970
\(116\) 33.8203 3.14014
\(117\) 27.6091 2.55246
\(118\) 15.7764 1.45234
\(119\) −0.453250 −0.0415493
\(120\) −18.5616 −1.69444
\(121\) 20.7187 1.88352
\(122\) 18.5838 1.68250
\(123\) 0.258380 0.0232974
\(124\) 25.1585 2.25930
\(125\) 11.3227 1.01273
\(126\) 9.22781 0.822078
\(127\) −10.3827 −0.921318 −0.460659 0.887577i \(-0.652387\pi\)
−0.460659 + 0.887577i \(0.652387\pi\)
\(128\) 19.6728 1.73885
\(129\) 4.53297 0.399106
\(130\) 22.5978 1.98196
\(131\) −8.52841 −0.745131 −0.372565 0.928006i \(-0.621522\pi\)
−0.372565 + 0.928006i \(0.621522\pi\)
\(132\) −60.4524 −5.26171
\(133\) −2.40496 −0.208536
\(134\) 12.9251 1.11656
\(135\) 4.70809 0.405208
\(136\) −2.48061 −0.212710
\(137\) −13.8047 −1.17941 −0.589707 0.807617i \(-0.700757\pi\)
−0.589707 + 0.807617i \(0.700757\pi\)
\(138\) 5.38162 0.458114
\(139\) −10.7081 −0.908253 −0.454126 0.890937i \(-0.650049\pi\)
−0.454126 + 0.890937i \(0.650049\pi\)
\(140\) 5.03123 0.425217
\(141\) 24.5034 2.06356
\(142\) −36.0072 −3.02165
\(143\) 36.7104 3.06987
\(144\) 16.6992 1.39160
\(145\) −12.0052 −0.996976
\(146\) −7.59374 −0.628462
\(147\) 16.6982 1.37724
\(148\) −36.9767 −3.03946
\(149\) −12.2400 −1.00274 −0.501372 0.865232i \(-0.667171\pi\)
−0.501372 + 0.865232i \(0.667171\pi\)
\(150\) −19.7089 −1.60922
\(151\) −12.3544 −1.00539 −0.502694 0.864464i \(-0.667658\pi\)
−0.502694 + 0.864464i \(0.667658\pi\)
\(152\) −13.1622 −1.06759
\(153\) 2.15680 0.174367
\(154\) 12.2697 0.988724
\(155\) −8.93049 −0.717314
\(156\) −69.9660 −5.60176
\(157\) −12.5772 −1.00377 −0.501885 0.864934i \(-0.667360\pi\)
−0.501885 + 0.864934i \(0.667360\pi\)
\(158\) 14.5516 1.15766
\(159\) 2.97510 0.235941
\(160\) −0.132728 −0.0104931
\(161\) −0.727605 −0.0573433
\(162\) 9.21784 0.724222
\(163\) −15.4289 −1.20848 −0.604241 0.796801i \(-0.706524\pi\)
−0.604241 + 0.796801i \(0.706524\pi\)
\(164\) −0.383299 −0.0299306
\(165\) 21.4588 1.67056
\(166\) 6.19359 0.480716
\(167\) 17.7040 1.36997 0.684987 0.728556i \(-0.259808\pi\)
0.684987 + 0.728556i \(0.259808\pi\)
\(168\) −11.6643 −0.899919
\(169\) 29.4875 2.26827
\(170\) 1.76532 0.135394
\(171\) 11.4440 0.875145
\(172\) −6.72451 −0.512739
\(173\) 6.90724 0.525148 0.262574 0.964912i \(-0.415429\pi\)
0.262574 + 0.964912i \(0.415429\pi\)
\(174\) 55.7992 4.23013
\(175\) 2.66468 0.201431
\(176\) 22.2041 1.67369
\(177\) 17.3388 1.30326
\(178\) −18.7228 −1.40333
\(179\) 6.94263 0.518916 0.259458 0.965754i \(-0.416456\pi\)
0.259458 + 0.965754i \(0.416456\pi\)
\(180\) −23.9412 −1.78447
\(181\) −15.5054 −1.15251 −0.576254 0.817271i \(-0.695486\pi\)
−0.576254 + 0.817271i \(0.695486\pi\)
\(182\) 14.2007 1.05262
\(183\) 20.4242 1.50980
\(184\) −3.98213 −0.293567
\(185\) 13.1256 0.965012
\(186\) 41.5083 3.04353
\(187\) 2.86778 0.209713
\(188\) −36.3501 −2.65110
\(189\) 2.95860 0.215207
\(190\) 9.36685 0.679542
\(191\) −7.70328 −0.557390 −0.278695 0.960380i \(-0.589902\pi\)
−0.278695 + 0.960380i \(0.589902\pi\)
\(192\) 21.8271 1.57523
\(193\) −17.1272 −1.23284 −0.616421 0.787417i \(-0.711418\pi\)
−0.616421 + 0.787417i \(0.711418\pi\)
\(194\) −15.3262 −1.10035
\(195\) 24.8358 1.77853
\(196\) −24.7712 −1.76937
\(197\) 18.1320 1.29185 0.645927 0.763399i \(-0.276471\pi\)
0.645927 + 0.763399i \(0.276471\pi\)
\(198\) −58.3857 −4.14929
\(199\) −23.2708 −1.64962 −0.824812 0.565407i \(-0.808719\pi\)
−0.824812 + 0.565407i \(0.808719\pi\)
\(200\) 14.5836 1.03122
\(201\) 14.2051 1.00195
\(202\) 40.4600 2.84676
\(203\) −7.54415 −0.529496
\(204\) −5.46568 −0.382674
\(205\) 0.136059 0.00950279
\(206\) 23.9565 1.66913
\(207\) 3.46232 0.240648
\(208\) 25.6984 1.78186
\(209\) 15.2165 1.05255
\(210\) 8.30088 0.572815
\(211\) 13.9098 0.957594 0.478797 0.877926i \(-0.341073\pi\)
0.478797 + 0.877926i \(0.341073\pi\)
\(212\) −4.41346 −0.303118
\(213\) −39.5731 −2.71150
\(214\) 43.9514 3.00445
\(215\) 2.38699 0.162792
\(216\) 16.1922 1.10174
\(217\) −5.61199 −0.380967
\(218\) −10.2559 −0.694619
\(219\) −8.34577 −0.563955
\(220\) −31.8334 −2.14621
\(221\) 3.31909 0.223266
\(222\) −61.0067 −4.09450
\(223\) 2.12520 0.142314 0.0711570 0.997465i \(-0.477331\pi\)
0.0711570 + 0.997465i \(0.477331\pi\)
\(224\) −0.0834075 −0.00557290
\(225\) −12.6799 −0.845327
\(226\) −5.16525 −0.343587
\(227\) 16.0941 1.06820 0.534102 0.845420i \(-0.320650\pi\)
0.534102 + 0.845420i \(0.320650\pi\)
\(228\) −29.0010 −1.92064
\(229\) 11.4833 0.758837 0.379418 0.925225i \(-0.376124\pi\)
0.379418 + 0.925225i \(0.376124\pi\)
\(230\) 2.83388 0.186861
\(231\) 13.4849 0.887238
\(232\) −41.2886 −2.71073
\(233\) 16.9021 1.10729 0.553645 0.832753i \(-0.313236\pi\)
0.553645 + 0.832753i \(0.313236\pi\)
\(234\) −67.5740 −4.41745
\(235\) 12.9032 0.841709
\(236\) −25.7215 −1.67433
\(237\) 15.9927 1.03884
\(238\) 1.10934 0.0719080
\(239\) −23.1196 −1.49548 −0.747740 0.663992i \(-0.768861\pi\)
−0.747740 + 0.663992i \(0.768861\pi\)
\(240\) 15.0218 0.969652
\(241\) −2.67252 −0.172152 −0.0860761 0.996289i \(-0.527433\pi\)
−0.0860761 + 0.996289i \(0.527433\pi\)
\(242\) −50.7097 −3.25974
\(243\) 20.1022 1.28955
\(244\) −30.2987 −1.93967
\(245\) 8.79300 0.561764
\(246\) −0.632393 −0.0403199
\(247\) 17.6112 1.12057
\(248\) −30.7141 −1.95035
\(249\) 6.80696 0.431373
\(250\) −27.7127 −1.75270
\(251\) 4.30218 0.271551 0.135776 0.990740i \(-0.456647\pi\)
0.135776 + 0.990740i \(0.456647\pi\)
\(252\) −15.0448 −0.947735
\(253\) 4.60367 0.289430
\(254\) 25.4120 1.59449
\(255\) 1.94015 0.121497
\(256\) −31.9210 −1.99507
\(257\) −22.4307 −1.39919 −0.699594 0.714541i \(-0.746636\pi\)
−0.699594 + 0.714541i \(0.746636\pi\)
\(258\) −11.0946 −0.690718
\(259\) 8.24822 0.512519
\(260\) −36.8431 −2.28491
\(261\) 35.8989 2.22209
\(262\) 20.8735 1.28957
\(263\) 19.7071 1.21519 0.607595 0.794247i \(-0.292134\pi\)
0.607595 + 0.794247i \(0.292134\pi\)
\(264\) 73.8017 4.54218
\(265\) 1.56664 0.0962381
\(266\) 5.88620 0.360906
\(267\) −20.5769 −1.25929
\(268\) −21.0728 −1.28723
\(269\) −32.2781 −1.96803 −0.984017 0.178076i \(-0.943013\pi\)
−0.984017 + 0.178076i \(0.943013\pi\)
\(270\) −11.5232 −0.701279
\(271\) 23.8537 1.44901 0.724503 0.689271i \(-0.242069\pi\)
0.724503 + 0.689271i \(0.242069\pi\)
\(272\) 2.00753 0.121725
\(273\) 15.6070 0.944578
\(274\) 33.7874 2.04117
\(275\) −16.8598 −1.01669
\(276\) −8.77409 −0.528138
\(277\) −27.4984 −1.65222 −0.826109 0.563511i \(-0.809450\pi\)
−0.826109 + 0.563511i \(0.809450\pi\)
\(278\) 26.2085 1.57188
\(279\) 26.7047 1.59877
\(280\) −6.14224 −0.367069
\(281\) 5.41702 0.323152 0.161576 0.986860i \(-0.448342\pi\)
0.161576 + 0.986860i \(0.448342\pi\)
\(282\) −59.9729 −3.57134
\(283\) −23.7937 −1.41439 −0.707195 0.707018i \(-0.750040\pi\)
−0.707195 + 0.707018i \(0.750040\pi\)
\(284\) 58.7054 3.48352
\(285\) 10.2945 0.609792
\(286\) −89.8497 −5.31292
\(287\) 0.0855007 0.00504695
\(288\) 0.396896 0.0233873
\(289\) −16.7407 −0.984748
\(290\) 29.3830 1.72543
\(291\) −16.8440 −0.987411
\(292\) 12.3807 0.724524
\(293\) 5.34461 0.312235 0.156118 0.987738i \(-0.450102\pi\)
0.156118 + 0.987738i \(0.450102\pi\)
\(294\) −40.8692 −2.38354
\(295\) 9.13035 0.531590
\(296\) 45.1420 2.62382
\(297\) −18.7195 −1.08622
\(298\) 29.9579 1.73541
\(299\) 5.32816 0.308135
\(300\) 32.1330 1.85520
\(301\) 1.50001 0.0864590
\(302\) 30.2378 1.73999
\(303\) 44.4669 2.55456
\(304\) 10.6520 0.610935
\(305\) 10.7551 0.615835
\(306\) −5.27882 −0.301770
\(307\) −31.8833 −1.81967 −0.909837 0.414965i \(-0.863794\pi\)
−0.909837 + 0.414965i \(0.863794\pi\)
\(308\) −20.0043 −1.13985
\(309\) 26.3289 1.49780
\(310\) 21.8576 1.24143
\(311\) 11.7871 0.668385 0.334193 0.942505i \(-0.391536\pi\)
0.334193 + 0.942505i \(0.391536\pi\)
\(312\) 85.4161 4.83573
\(313\) 17.5302 0.990867 0.495433 0.868646i \(-0.335009\pi\)
0.495433 + 0.868646i \(0.335009\pi\)
\(314\) 30.7831 1.73719
\(315\) 5.34045 0.300900
\(316\) −23.7247 −1.33462
\(317\) −12.3681 −0.694664 −0.347332 0.937742i \(-0.612912\pi\)
−0.347332 + 0.937742i \(0.612912\pi\)
\(318\) −7.28164 −0.408334
\(319\) 47.7330 2.67253
\(320\) 11.4938 0.642523
\(321\) 48.3040 2.69607
\(322\) 1.78084 0.0992421
\(323\) 1.37577 0.0765498
\(324\) −15.0286 −0.834921
\(325\) −19.5131 −1.08239
\(326\) 37.7626 2.09148
\(327\) −11.2716 −0.623321
\(328\) 0.467940 0.0258377
\(329\) 8.10845 0.447033
\(330\) −52.5210 −2.89118
\(331\) 15.9544 0.876931 0.438466 0.898748i \(-0.355522\pi\)
0.438466 + 0.898748i \(0.355522\pi\)
\(332\) −10.0979 −0.554194
\(333\) −39.2493 −2.15085
\(334\) −43.3310 −2.37097
\(335\) 7.48019 0.408686
\(336\) 9.43981 0.514984
\(337\) −21.1110 −1.14999 −0.574995 0.818157i \(-0.694996\pi\)
−0.574995 + 0.818157i \(0.694996\pi\)
\(338\) −72.1717 −3.92562
\(339\) −5.67678 −0.308321
\(340\) −2.87815 −0.156089
\(341\) 35.5079 1.92286
\(342\) −28.0096 −1.51458
\(343\) 11.7564 0.634789
\(344\) 8.20944 0.442623
\(345\) 3.11453 0.167681
\(346\) −16.9057 −0.908855
\(347\) 29.5371 1.58563 0.792817 0.609460i \(-0.208614\pi\)
0.792817 + 0.609460i \(0.208614\pi\)
\(348\) −90.9739 −4.87671
\(349\) 7.76249 0.415516 0.207758 0.978180i \(-0.433383\pi\)
0.207758 + 0.978180i \(0.433383\pi\)
\(350\) −6.52188 −0.348609
\(351\) −21.6655 −1.15642
\(352\) 0.527732 0.0281282
\(353\) −12.4518 −0.662745 −0.331372 0.943500i \(-0.607512\pi\)
−0.331372 + 0.943500i \(0.607512\pi\)
\(354\) −42.4372 −2.25551
\(355\) −20.8386 −1.10600
\(356\) 30.5252 1.61783
\(357\) 1.21920 0.0645272
\(358\) −16.9923 −0.898071
\(359\) 11.8809 0.627051 0.313525 0.949580i \(-0.398490\pi\)
0.313525 + 0.949580i \(0.398490\pi\)
\(360\) 29.2279 1.54045
\(361\) −11.7001 −0.615796
\(362\) 37.9500 1.99461
\(363\) −55.7316 −2.92515
\(364\) −23.1525 −1.21352
\(365\) −4.39476 −0.230032
\(366\) −49.9889 −2.61296
\(367\) 16.2758 0.849587 0.424794 0.905290i \(-0.360347\pi\)
0.424794 + 0.905290i \(0.360347\pi\)
\(368\) 3.22271 0.167995
\(369\) −0.406856 −0.0211801
\(370\) −32.1253 −1.67011
\(371\) 0.984491 0.0511122
\(372\) −67.6743 −3.50875
\(373\) −13.5560 −0.701906 −0.350953 0.936393i \(-0.614142\pi\)
−0.350953 + 0.936393i \(0.614142\pi\)
\(374\) −7.01898 −0.362943
\(375\) −30.4572 −1.57280
\(376\) 44.3770 2.28857
\(377\) 55.2448 2.84525
\(378\) −7.24127 −0.372451
\(379\) 34.0902 1.75110 0.875549 0.483130i \(-0.160500\pi\)
0.875549 + 0.483130i \(0.160500\pi\)
\(380\) −15.2715 −0.783412
\(381\) 27.9287 1.43083
\(382\) 18.8540 0.964656
\(383\) 3.42962 0.175245 0.0876226 0.996154i \(-0.472073\pi\)
0.0876226 + 0.996154i \(0.472073\pi\)
\(384\) −52.9183 −2.70047
\(385\) 7.10093 0.361897
\(386\) 41.9193 2.13364
\(387\) −7.13780 −0.362835
\(388\) 24.9875 1.26855
\(389\) −5.83791 −0.295994 −0.147997 0.988988i \(-0.547283\pi\)
−0.147997 + 0.988988i \(0.547283\pi\)
\(390\) −60.7863 −3.07803
\(391\) 0.416231 0.0210497
\(392\) 30.2412 1.52741
\(393\) 22.9407 1.15721
\(394\) −44.3787 −2.23577
\(395\) 8.42152 0.423733
\(396\) 95.1909 4.78353
\(397\) −23.9999 −1.20452 −0.602261 0.798299i \(-0.705733\pi\)
−0.602261 + 0.798299i \(0.705733\pi\)
\(398\) 56.9560 2.85495
\(399\) 6.46913 0.323862
\(400\) −11.8024 −0.590119
\(401\) −23.0233 −1.14973 −0.574865 0.818249i \(-0.694945\pi\)
−0.574865 + 0.818249i \(0.694945\pi\)
\(402\) −34.7674 −1.73404
\(403\) 41.0959 2.04713
\(404\) −65.9652 −3.28189
\(405\) 5.33468 0.265083
\(406\) 18.4645 0.916380
\(407\) −52.1877 −2.58685
\(408\) 6.67263 0.330344
\(409\) −34.0606 −1.68419 −0.842095 0.539329i \(-0.818678\pi\)
−0.842095 + 0.539329i \(0.818678\pi\)
\(410\) −0.333009 −0.0164461
\(411\) 37.1335 1.83166
\(412\) −39.0581 −1.92426
\(413\) 5.73759 0.282328
\(414\) −8.47413 −0.416481
\(415\) 3.58444 0.175953
\(416\) 0.610782 0.0299461
\(417\) 28.8040 1.41054
\(418\) −37.2429 −1.82161
\(419\) 14.9589 0.730790 0.365395 0.930853i \(-0.380934\pi\)
0.365395 + 0.930853i \(0.380934\pi\)
\(420\) −13.5336 −0.660372
\(421\) 5.09761 0.248442 0.124221 0.992255i \(-0.460357\pi\)
0.124221 + 0.992255i \(0.460357\pi\)
\(422\) −34.0448 −1.65727
\(423\) −38.5841 −1.87603
\(424\) 5.38805 0.261667
\(425\) −1.52434 −0.0739416
\(426\) 96.8563 4.69270
\(427\) 6.75859 0.327071
\(428\) −71.6575 −3.46369
\(429\) −98.7478 −4.76759
\(430\) −5.84224 −0.281738
\(431\) 4.41808 0.212811 0.106406 0.994323i \(-0.466066\pi\)
0.106406 + 0.994323i \(0.466066\pi\)
\(432\) −13.1042 −0.630478
\(433\) −18.6392 −0.895744 −0.447872 0.894098i \(-0.647818\pi\)
−0.447872 + 0.894098i \(0.647818\pi\)
\(434\) 13.7355 0.659326
\(435\) 32.2929 1.54833
\(436\) 16.7211 0.800793
\(437\) 2.20853 0.105648
\(438\) 20.4265 0.976017
\(439\) 18.9840 0.906058 0.453029 0.891496i \(-0.350343\pi\)
0.453029 + 0.891496i \(0.350343\pi\)
\(440\) 38.8629 1.85272
\(441\) −26.2936 −1.25208
\(442\) −8.12357 −0.386399
\(443\) 25.4883 1.21098 0.605492 0.795852i \(-0.292976\pi\)
0.605492 + 0.795852i \(0.292976\pi\)
\(444\) 99.4642 4.72036
\(445\) −10.8355 −0.513653
\(446\) −5.20149 −0.246298
\(447\) 32.9247 1.55729
\(448\) 7.22280 0.341245
\(449\) −31.4551 −1.48446 −0.742230 0.670145i \(-0.766232\pi\)
−0.742230 + 0.670145i \(0.766232\pi\)
\(450\) 31.0345 1.46298
\(451\) −0.540976 −0.0254736
\(452\) 8.42132 0.396106
\(453\) 33.2324 1.56139
\(454\) −39.3909 −1.84871
\(455\) 8.21841 0.385285
\(456\) 35.4051 1.65800
\(457\) −12.0040 −0.561526 −0.280763 0.959777i \(-0.590587\pi\)
−0.280763 + 0.959777i \(0.590587\pi\)
\(458\) −28.1057 −1.31329
\(459\) −1.69249 −0.0789985
\(460\) −4.62031 −0.215423
\(461\) −9.10238 −0.423940 −0.211970 0.977276i \(-0.567988\pi\)
−0.211970 + 0.977276i \(0.567988\pi\)
\(462\) −33.0046 −1.53551
\(463\) 27.2522 1.26652 0.633259 0.773940i \(-0.281717\pi\)
0.633259 + 0.773940i \(0.281717\pi\)
\(464\) 33.4145 1.55123
\(465\) 24.0223 1.11401
\(466\) −41.3683 −1.91635
\(467\) −3.39628 −0.157161 −0.0785805 0.996908i \(-0.525039\pi\)
−0.0785805 + 0.996908i \(0.525039\pi\)
\(468\) 110.171 5.09267
\(469\) 4.70061 0.217054
\(470\) −31.5809 −1.45672
\(471\) 33.8316 1.55888
\(472\) 31.4014 1.44537
\(473\) −9.49077 −0.436386
\(474\) −39.1426 −1.79788
\(475\) −8.08821 −0.371113
\(476\) −1.80865 −0.0828994
\(477\) −4.68471 −0.214498
\(478\) 56.5858 2.58817
\(479\) −23.7043 −1.08308 −0.541538 0.840676i \(-0.682158\pi\)
−0.541538 + 0.840676i \(0.682158\pi\)
\(480\) 0.357028 0.0162960
\(481\) −60.4006 −2.75403
\(482\) 6.54107 0.297938
\(483\) 1.95720 0.0890556
\(484\) 82.6761 3.75800
\(485\) −8.86979 −0.402756
\(486\) −49.2007 −2.23179
\(487\) −35.7815 −1.62141 −0.810706 0.585453i \(-0.800917\pi\)
−0.810706 + 0.585453i \(0.800917\pi\)
\(488\) 36.9893 1.67443
\(489\) 41.5024 1.87680
\(490\) −21.5211 −0.972226
\(491\) −31.7010 −1.43065 −0.715324 0.698793i \(-0.753721\pi\)
−0.715324 + 0.698793i \(0.753721\pi\)
\(492\) 1.03104 0.0464830
\(493\) 4.31568 0.194368
\(494\) −43.1039 −1.93934
\(495\) −33.7899 −1.51874
\(496\) 24.8566 1.11610
\(497\) −13.0951 −0.587398
\(498\) −16.6602 −0.746563
\(499\) −8.97807 −0.401914 −0.200957 0.979600i \(-0.564405\pi\)
−0.200957 + 0.979600i \(0.564405\pi\)
\(500\) 45.1822 2.02061
\(501\) −47.6222 −2.12760
\(502\) −10.5297 −0.469965
\(503\) −29.0742 −1.29635 −0.648177 0.761490i \(-0.724468\pi\)
−0.648177 + 0.761490i \(0.724468\pi\)
\(504\) 18.3671 0.818135
\(505\) 23.4156 1.04198
\(506\) −11.2676 −0.500907
\(507\) −79.3191 −3.52268
\(508\) −41.4313 −1.83822
\(509\) −18.2555 −0.809159 −0.404580 0.914503i \(-0.632582\pi\)
−0.404580 + 0.914503i \(0.632582\pi\)
\(510\) −4.74857 −0.210270
\(511\) −2.76170 −0.122171
\(512\) 38.7821 1.71394
\(513\) −8.98038 −0.396493
\(514\) 54.8998 2.42152
\(515\) 13.8644 0.610940
\(516\) 18.0884 0.796297
\(517\) −51.3034 −2.25632
\(518\) −20.1878 −0.887000
\(519\) −18.5799 −0.815568
\(520\) 44.9788 1.97245
\(521\) 9.18330 0.402328 0.201164 0.979558i \(-0.435528\pi\)
0.201164 + 0.979558i \(0.435528\pi\)
\(522\) −87.8638 −3.84569
\(523\) −13.6056 −0.594932 −0.297466 0.954732i \(-0.596141\pi\)
−0.297466 + 0.954732i \(0.596141\pi\)
\(524\) −34.0318 −1.48669
\(525\) −7.16776 −0.312827
\(526\) −48.2337 −2.10309
\(527\) 3.21037 0.139846
\(528\) −59.7271 −2.59929
\(529\) −22.3318 −0.970949
\(530\) −3.83441 −0.166556
\(531\) −27.3024 −1.18482
\(532\) −9.59675 −0.416072
\(533\) −0.626111 −0.0271199
\(534\) 50.3627 2.17941
\(535\) 25.4362 1.09970
\(536\) 25.7261 1.11120
\(537\) −18.6751 −0.805890
\(538\) 79.0018 3.40601
\(539\) −34.9613 −1.50589
\(540\) 18.7872 0.808472
\(541\) 15.2985 0.657734 0.328867 0.944376i \(-0.393333\pi\)
0.328867 + 0.944376i \(0.393333\pi\)
\(542\) −58.3826 −2.50775
\(543\) 41.7083 1.78987
\(544\) 0.0477138 0.00204571
\(545\) −5.93546 −0.254247
\(546\) −38.1986 −1.63475
\(547\) −11.1899 −0.478447 −0.239224 0.970965i \(-0.576893\pi\)
−0.239224 + 0.970965i \(0.576893\pi\)
\(548\) −55.0863 −2.35317
\(549\) −32.1608 −1.37259
\(550\) 41.2649 1.75954
\(551\) 22.8991 0.975534
\(552\) 10.7116 0.455917
\(553\) 5.29215 0.225045
\(554\) 67.3031 2.85944
\(555\) −35.3067 −1.49869
\(556\) −42.7298 −1.81215
\(557\) −31.1512 −1.31992 −0.659960 0.751301i \(-0.729427\pi\)
−0.659960 + 0.751301i \(0.729427\pi\)
\(558\) −65.3607 −2.76694
\(559\) −10.9844 −0.464589
\(560\) 4.97086 0.210057
\(561\) −7.71409 −0.325689
\(562\) −13.2583 −0.559268
\(563\) −27.2331 −1.14774 −0.573868 0.818948i \(-0.694558\pi\)
−0.573868 + 0.818948i \(0.694558\pi\)
\(564\) 97.7787 4.11722
\(565\) −2.98931 −0.125761
\(566\) 58.2359 2.44784
\(567\) 3.35236 0.140786
\(568\) −71.6689 −3.00716
\(569\) 21.4062 0.897393 0.448696 0.893684i \(-0.351888\pi\)
0.448696 + 0.893684i \(0.351888\pi\)
\(570\) −25.1960 −1.05535
\(571\) −4.12253 −0.172522 −0.0862612 0.996273i \(-0.527492\pi\)
−0.0862612 + 0.996273i \(0.527492\pi\)
\(572\) 146.489 6.12502
\(573\) 20.7212 0.865640
\(574\) −0.209266 −0.00873458
\(575\) −2.44704 −0.102049
\(576\) −34.3698 −1.43207
\(577\) 24.4685 1.01864 0.509319 0.860578i \(-0.329897\pi\)
0.509319 + 0.860578i \(0.329897\pi\)
\(578\) 40.9734 1.70427
\(579\) 46.0707 1.91463
\(580\) −47.9055 −1.98917
\(581\) 2.25249 0.0934492
\(582\) 41.2261 1.70888
\(583\) −6.22902 −0.257980
\(584\) −15.1146 −0.625447
\(585\) −39.1074 −1.61689
\(586\) −13.0811 −0.540375
\(587\) 33.1711 1.36912 0.684560 0.728957i \(-0.259994\pi\)
0.684560 + 0.728957i \(0.259994\pi\)
\(588\) 66.6324 2.74787
\(589\) 17.0343 0.701887
\(590\) −22.3468 −0.920004
\(591\) −48.7737 −2.00628
\(592\) −36.5330 −1.50150
\(593\) −30.1606 −1.23855 −0.619273 0.785175i \(-0.712573\pi\)
−0.619273 + 0.785175i \(0.712573\pi\)
\(594\) 45.8166 1.87988
\(595\) 0.642015 0.0263201
\(596\) −48.8427 −2.00068
\(597\) 62.5966 2.56191
\(598\) −13.0408 −0.533279
\(599\) −16.7701 −0.685208 −0.342604 0.939480i \(-0.611309\pi\)
−0.342604 + 0.939480i \(0.611309\pi\)
\(600\) −39.2287 −1.60150
\(601\) 32.8379 1.33949 0.669743 0.742593i \(-0.266404\pi\)
0.669743 + 0.742593i \(0.266404\pi\)
\(602\) −3.67131 −0.149632
\(603\) −22.3679 −0.910892
\(604\) −49.2992 −2.00595
\(605\) −29.3475 −1.19314
\(606\) −108.834 −4.42108
\(607\) 10.7068 0.434577 0.217289 0.976107i \(-0.430279\pi\)
0.217289 + 0.976107i \(0.430279\pi\)
\(608\) 0.253170 0.0102674
\(609\) 20.2931 0.822320
\(610\) −26.3234 −1.06580
\(611\) −59.3771 −2.40214
\(612\) 8.60649 0.347897
\(613\) −35.1182 −1.41841 −0.709206 0.705001i \(-0.750946\pi\)
−0.709206 + 0.705001i \(0.750946\pi\)
\(614\) 78.0353 3.14925
\(615\) −0.365988 −0.0147581
\(616\) 24.4218 0.983981
\(617\) −27.6583 −1.11348 −0.556740 0.830687i \(-0.687948\pi\)
−0.556740 + 0.830687i \(0.687948\pi\)
\(618\) −64.4409 −2.59219
\(619\) 46.1219 1.85380 0.926898 0.375313i \(-0.122465\pi\)
0.926898 + 0.375313i \(0.122465\pi\)
\(620\) −35.6363 −1.43119
\(621\) −2.71696 −0.109028
\(622\) −28.8493 −1.15675
\(623\) −6.80913 −0.272802
\(624\) −69.1265 −2.76727
\(625\) −1.07025 −0.0428102
\(626\) −42.9058 −1.71486
\(627\) −40.9312 −1.63463
\(628\) −50.1881 −2.00272
\(629\) −4.71844 −0.188137
\(630\) −13.0709 −0.520758
\(631\) −18.5482 −0.738392 −0.369196 0.929352i \(-0.620367\pi\)
−0.369196 + 0.929352i \(0.620367\pi\)
\(632\) 28.9636 1.15211
\(633\) −37.4164 −1.48717
\(634\) 30.2714 1.20223
\(635\) 14.7068 0.583623
\(636\) 11.8718 0.470749
\(637\) −40.4632 −1.60321
\(638\) −116.828 −4.62526
\(639\) 62.3134 2.46508
\(640\) −27.8660 −1.10150
\(641\) 16.4954 0.651528 0.325764 0.945451i \(-0.394379\pi\)
0.325764 + 0.945451i \(0.394379\pi\)
\(642\) −118.226 −4.66599
\(643\) 27.6160 1.08907 0.544535 0.838738i \(-0.316706\pi\)
0.544535 + 0.838738i \(0.316706\pi\)
\(644\) −2.90344 −0.114412
\(645\) −6.42082 −0.252820
\(646\) −3.36724 −0.132482
\(647\) −6.07994 −0.239027 −0.119514 0.992833i \(-0.538134\pi\)
−0.119514 + 0.992833i \(0.538134\pi\)
\(648\) 18.3472 0.720748
\(649\) −36.3026 −1.42500
\(650\) 47.7589 1.87326
\(651\) 15.0958 0.591651
\(652\) −61.5675 −2.41117
\(653\) 42.9964 1.68258 0.841289 0.540586i \(-0.181797\pi\)
0.841289 + 0.540586i \(0.181797\pi\)
\(654\) 27.5876 1.07876
\(655\) 12.0802 0.472014
\(656\) −0.378700 −0.0147857
\(657\) 13.1416 0.512703
\(658\) −19.8457 −0.773665
\(659\) −4.40998 −0.171788 −0.0858942 0.996304i \(-0.527375\pi\)
−0.0858942 + 0.996304i \(0.527375\pi\)
\(660\) 85.6291 3.33311
\(661\) −5.15605 −0.200547 −0.100274 0.994960i \(-0.531972\pi\)
−0.100274 + 0.994960i \(0.531972\pi\)
\(662\) −39.0488 −1.51767
\(663\) −8.92808 −0.346738
\(664\) 12.3277 0.478409
\(665\) 3.40655 0.132100
\(666\) 96.0638 3.72240
\(667\) 6.92799 0.268253
\(668\) 70.6460 2.73337
\(669\) −5.71662 −0.221017
\(670\) −18.3080 −0.707299
\(671\) −42.7626 −1.65083
\(672\) 0.224359 0.00865485
\(673\) −23.9965 −0.924997 −0.462499 0.886620i \(-0.653047\pi\)
−0.462499 + 0.886620i \(0.653047\pi\)
\(674\) 51.6699 1.99025
\(675\) 9.95021 0.382984
\(676\) 117.667 4.52566
\(677\) −45.6796 −1.75561 −0.877805 0.479019i \(-0.840993\pi\)
−0.877805 + 0.479019i \(0.840993\pi\)
\(678\) 13.8941 0.533600
\(679\) −5.57385 −0.213905
\(680\) 3.51371 0.134745
\(681\) −43.2919 −1.65895
\(682\) −86.9067 −3.32783
\(683\) 7.75642 0.296791 0.148396 0.988928i \(-0.452589\pi\)
0.148396 + 0.988928i \(0.452589\pi\)
\(684\) 45.6663 1.74609
\(685\) 19.5540 0.747118
\(686\) −28.7743 −1.09861
\(687\) −30.8891 −1.17849
\(688\) −6.64383 −0.253294
\(689\) −7.20930 −0.274652
\(690\) −7.62291 −0.290199
\(691\) −32.6197 −1.24091 −0.620456 0.784241i \(-0.713053\pi\)
−0.620456 + 0.784241i \(0.713053\pi\)
\(692\) 27.5627 1.04778
\(693\) −21.2338 −0.806606
\(694\) −72.2929 −2.74420
\(695\) 15.1678 0.575346
\(696\) 111.063 4.20983
\(697\) −0.0489112 −0.00185264
\(698\) −18.9989 −0.719120
\(699\) −45.4651 −1.71965
\(700\) 10.6331 0.401895
\(701\) 22.0897 0.834315 0.417157 0.908834i \(-0.363026\pi\)
0.417157 + 0.908834i \(0.363026\pi\)
\(702\) 53.0269 2.00137
\(703\) −25.0362 −0.944258
\(704\) −45.6998 −1.72237
\(705\) −34.7084 −1.30719
\(706\) 30.4763 1.14699
\(707\) 14.7146 0.553398
\(708\) 69.1888 2.60027
\(709\) 7.85616 0.295044 0.147522 0.989059i \(-0.452870\pi\)
0.147522 + 0.989059i \(0.452870\pi\)
\(710\) 51.0031 1.91411
\(711\) −25.1828 −0.944428
\(712\) −37.2659 −1.39660
\(713\) 5.15364 0.193005
\(714\) −2.98404 −0.111675
\(715\) −51.9992 −1.94466
\(716\) 27.7039 1.03534
\(717\) 62.1897 2.32252
\(718\) −29.0789 −1.08522
\(719\) 10.0478 0.374718 0.187359 0.982291i \(-0.440007\pi\)
0.187359 + 0.982291i \(0.440007\pi\)
\(720\) −23.6539 −0.881530
\(721\) 8.71252 0.324471
\(722\) 28.6364 1.06574
\(723\) 7.18886 0.267356
\(724\) −61.8729 −2.29949
\(725\) −25.3721 −0.942295
\(726\) 136.405 5.06246
\(727\) −5.68745 −0.210936 −0.105468 0.994423i \(-0.533634\pi\)
−0.105468 + 0.994423i \(0.533634\pi\)
\(728\) 28.2651 1.04757
\(729\) −42.7746 −1.58425
\(730\) 10.7563 0.398109
\(731\) −0.858088 −0.0317375
\(732\) 81.5009 3.01236
\(733\) 10.6157 0.392101 0.196050 0.980594i \(-0.437188\pi\)
0.196050 + 0.980594i \(0.437188\pi\)
\(734\) −39.8354 −1.47035
\(735\) −23.6525 −0.872434
\(736\) 0.0765952 0.00282334
\(737\) −29.7415 −1.09554
\(738\) 0.995793 0.0366557
\(739\) 35.3411 1.30004 0.650022 0.759916i \(-0.274760\pi\)
0.650022 + 0.759916i \(0.274760\pi\)
\(740\) 52.3764 1.92539
\(741\) −47.3726 −1.74028
\(742\) −2.40957 −0.0884582
\(743\) −49.6459 −1.82133 −0.910665 0.413146i \(-0.864430\pi\)
−0.910665 + 0.413146i \(0.864430\pi\)
\(744\) 82.6183 3.02893
\(745\) 17.3377 0.635203
\(746\) 33.1788 1.21476
\(747\) −10.7185 −0.392170
\(748\) 11.4436 0.418420
\(749\) 15.9843 0.584054
\(750\) 74.5449 2.72199
\(751\) −1.74195 −0.0635646 −0.0317823 0.999495i \(-0.510118\pi\)
−0.0317823 + 0.999495i \(0.510118\pi\)
\(752\) −35.9139 −1.30965
\(753\) −11.5725 −0.421726
\(754\) −135.213 −4.92418
\(755\) 17.4997 0.636879
\(756\) 11.8060 0.429381
\(757\) −21.0742 −0.765956 −0.382978 0.923757i \(-0.625102\pi\)
−0.382978 + 0.923757i \(0.625102\pi\)
\(758\) −83.4369 −3.03056
\(759\) −12.3835 −0.449492
\(760\) 18.6438 0.676283
\(761\) 17.9383 0.650263 0.325132 0.945669i \(-0.394591\pi\)
0.325132 + 0.945669i \(0.394591\pi\)
\(762\) −68.3563 −2.47629
\(763\) −3.72989 −0.135031
\(764\) −30.7392 −1.11211
\(765\) −3.05504 −0.110455
\(766\) −8.39409 −0.303291
\(767\) −42.0156 −1.51710
\(768\) 85.8650 3.09839
\(769\) −53.9528 −1.94559 −0.972794 0.231672i \(-0.925580\pi\)
−0.972794 + 0.231672i \(0.925580\pi\)
\(770\) −17.3797 −0.626322
\(771\) 60.3367 2.17297
\(772\) −68.3445 −2.45977
\(773\) 42.4103 1.52539 0.762697 0.646756i \(-0.223875\pi\)
0.762697 + 0.646756i \(0.223875\pi\)
\(774\) 17.4700 0.627946
\(775\) −18.8739 −0.677972
\(776\) −30.5053 −1.09508
\(777\) −22.1870 −0.795955
\(778\) 14.2885 0.512266
\(779\) −0.259524 −0.00929842
\(780\) 99.1048 3.54852
\(781\) 82.8550 2.96478
\(782\) −1.01874 −0.0364300
\(783\) −28.1707 −1.00674
\(784\) −24.4740 −0.874070
\(785\) 17.8152 0.635853
\(786\) −56.1481 −2.00274
\(787\) 5.50093 0.196087 0.0980434 0.995182i \(-0.468742\pi\)
0.0980434 + 0.995182i \(0.468742\pi\)
\(788\) 72.3542 2.57751
\(789\) −53.0104 −1.88722
\(790\) −20.6119 −0.733340
\(791\) −1.87851 −0.0667920
\(792\) −116.211 −4.12939
\(793\) −49.4923 −1.75752
\(794\) 58.7406 2.08463
\(795\) −4.21414 −0.149460
\(796\) −92.8600 −3.29134
\(797\) 13.7990 0.488787 0.244393 0.969676i \(-0.421411\pi\)
0.244393 + 0.969676i \(0.421411\pi\)
\(798\) −15.8334 −0.560496
\(799\) −4.63849 −0.164098
\(800\) −0.280512 −0.00991758
\(801\) 32.4013 1.14484
\(802\) 56.3502 1.98980
\(803\) 17.4737 0.616634
\(804\) 56.6841 1.99909
\(805\) 1.03063 0.0363250
\(806\) −100.583 −3.54290
\(807\) 86.8256 3.05640
\(808\) 80.5318 2.83310
\(809\) 8.46772 0.297709 0.148855 0.988859i \(-0.452441\pi\)
0.148855 + 0.988859i \(0.452441\pi\)
\(810\) −13.0568 −0.458769
\(811\) −2.76648 −0.0971444 −0.0485722 0.998820i \(-0.515467\pi\)
−0.0485722 + 0.998820i \(0.515467\pi\)
\(812\) −30.1042 −1.05645
\(813\) −64.1644 −2.25034
\(814\) 127.731 4.47697
\(815\) 21.8546 0.765532
\(816\) −5.40010 −0.189041
\(817\) −4.55304 −0.159291
\(818\) 83.3645 2.91477
\(819\) −24.5754 −0.858735
\(820\) 0.542932 0.0189600
\(821\) −40.3137 −1.40696 −0.703479 0.710716i \(-0.748371\pi\)
−0.703479 + 0.710716i \(0.748371\pi\)
\(822\) −90.8854 −3.16999
\(823\) −1.95277 −0.0680692 −0.0340346 0.999421i \(-0.510836\pi\)
−0.0340346 + 0.999421i \(0.510836\pi\)
\(824\) 47.6831 1.66112
\(825\) 45.3515 1.57894
\(826\) −14.0429 −0.488616
\(827\) −25.3430 −0.881262 −0.440631 0.897688i \(-0.645245\pi\)
−0.440631 + 0.897688i \(0.645245\pi\)
\(828\) 13.8161 0.480141
\(829\) −11.2952 −0.392298 −0.196149 0.980574i \(-0.562844\pi\)
−0.196149 + 0.980574i \(0.562844\pi\)
\(830\) −8.77304 −0.304517
\(831\) 73.9684 2.56593
\(832\) −52.8916 −1.83369
\(833\) −3.16095 −0.109520
\(834\) −70.4987 −2.44117
\(835\) −25.0771 −0.867830
\(836\) 60.7201 2.10005
\(837\) −20.9558 −0.724339
\(838\) −36.6123 −1.26475
\(839\) 50.8320 1.75492 0.877458 0.479654i \(-0.159238\pi\)
0.877458 + 0.479654i \(0.159238\pi\)
\(840\) 16.5221 0.570068
\(841\) 42.8326 1.47699
\(842\) −12.4765 −0.429970
\(843\) −14.5713 −0.501863
\(844\) 55.5059 1.91059
\(845\) −41.7683 −1.43687
\(846\) 94.4359 3.24677
\(847\) −18.4422 −0.633681
\(848\) −4.36051 −0.149740
\(849\) 64.0032 2.19658
\(850\) 3.73088 0.127968
\(851\) −7.57455 −0.259652
\(852\) −157.913 −5.41000
\(853\) −4.37117 −0.149666 −0.0748331 0.997196i \(-0.523842\pi\)
−0.0748331 + 0.997196i \(0.523842\pi\)
\(854\) −16.5419 −0.566051
\(855\) −16.2101 −0.554374
\(856\) 87.4811 2.99004
\(857\) −20.5532 −0.702083 −0.351041 0.936360i \(-0.614172\pi\)
−0.351041 + 0.936360i \(0.614172\pi\)
\(858\) 241.688 8.25110
\(859\) 29.4768 1.00573 0.502867 0.864364i \(-0.332278\pi\)
0.502867 + 0.864364i \(0.332278\pi\)
\(860\) 9.52508 0.324802
\(861\) −0.229990 −0.00783803
\(862\) −10.8134 −0.368305
\(863\) −9.45370 −0.321808 −0.160904 0.986970i \(-0.551441\pi\)
−0.160904 + 0.986970i \(0.551441\pi\)
\(864\) −0.311453 −0.0105958
\(865\) −9.78391 −0.332663
\(866\) 45.6201 1.55023
\(867\) 45.0311 1.52934
\(868\) −22.3941 −0.760106
\(869\) −33.4843 −1.13588
\(870\) −79.0380 −2.67964
\(871\) −34.4220 −1.16634
\(872\) −20.4135 −0.691287
\(873\) 26.5232 0.897675
\(874\) −5.40545 −0.182842
\(875\) −10.0786 −0.340719
\(876\) −33.3030 −1.12520
\(877\) −38.5399 −1.30140 −0.650700 0.759335i \(-0.725525\pi\)
−0.650700 + 0.759335i \(0.725525\pi\)
\(878\) −46.4640 −1.56808
\(879\) −14.3766 −0.484909
\(880\) −31.4514 −1.06023
\(881\) −16.0186 −0.539681 −0.269841 0.962905i \(-0.586971\pi\)
−0.269841 + 0.962905i \(0.586971\pi\)
\(882\) 64.3544 2.16693
\(883\) 4.96567 0.167108 0.0835540 0.996503i \(-0.473373\pi\)
0.0835540 + 0.996503i \(0.473373\pi\)
\(884\) 13.2445 0.445461
\(885\) −24.5599 −0.825572
\(886\) −62.3833 −2.09581
\(887\) 41.4801 1.39277 0.696383 0.717670i \(-0.254791\pi\)
0.696383 + 0.717670i \(0.254791\pi\)
\(888\) −121.428 −4.07486
\(889\) 9.24190 0.309963
\(890\) 26.5203 0.888961
\(891\) −21.2109 −0.710591
\(892\) 8.48041 0.283945
\(893\) −24.6119 −0.823607
\(894\) −80.5842 −2.69514
\(895\) −9.83403 −0.328715
\(896\) −17.5112 −0.585009
\(897\) −14.3323 −0.478542
\(898\) 76.9874 2.56910
\(899\) 53.4353 1.78217
\(900\) −50.5980 −1.68660
\(901\) −0.563184 −0.0187624
\(902\) 1.32406 0.0440862
\(903\) −4.03490 −0.134273
\(904\) −10.2809 −0.341939
\(905\) 21.9630 0.730074
\(906\) −81.3373 −2.70225
\(907\) 28.9150 0.960105 0.480053 0.877240i \(-0.340618\pi\)
0.480053 + 0.877240i \(0.340618\pi\)
\(908\) 64.2221 2.13129
\(909\) −70.0194 −2.32240
\(910\) −20.1148 −0.666800
\(911\) 6.43776 0.213293 0.106646 0.994297i \(-0.465989\pi\)
0.106646 + 0.994297i \(0.465989\pi\)
\(912\) −28.6531 −0.948798
\(913\) −14.2519 −0.471668
\(914\) 29.3803 0.971813
\(915\) −28.9303 −0.956407
\(916\) 45.8230 1.51403
\(917\) 7.59133 0.250688
\(918\) 4.14241 0.136720
\(919\) 44.3753 1.46381 0.731904 0.681408i \(-0.238632\pi\)
0.731904 + 0.681408i \(0.238632\pi\)
\(920\) 5.64058 0.185964
\(921\) 85.7634 2.82600
\(922\) 22.2783 0.733698
\(923\) 95.8940 3.15639
\(924\) 53.8100 1.77022
\(925\) 27.7400 0.912084
\(926\) −66.7007 −2.19192
\(927\) −41.4587 −1.36168
\(928\) 0.794175 0.0260701
\(929\) 51.0452 1.67474 0.837369 0.546638i \(-0.184093\pi\)
0.837369 + 0.546638i \(0.184093\pi\)
\(930\) −58.7953 −1.92797
\(931\) −16.7721 −0.549683
\(932\) 67.4461 2.20927
\(933\) −31.7063 −1.03802
\(934\) 8.31250 0.271993
\(935\) −4.06213 −0.132846
\(936\) −134.500 −4.39626
\(937\) 30.4957 0.996251 0.498125 0.867105i \(-0.334022\pi\)
0.498125 + 0.867105i \(0.334022\pi\)
\(938\) −11.5049 −0.375648
\(939\) −47.1549 −1.53884
\(940\) 51.4888 1.67938
\(941\) 1.47064 0.0479414 0.0239707 0.999713i \(-0.492369\pi\)
0.0239707 + 0.999713i \(0.492369\pi\)
\(942\) −82.8039 −2.69790
\(943\) −0.0785175 −0.00255688
\(944\) −25.4129 −0.827120
\(945\) −4.19077 −0.136326
\(946\) 23.2290 0.755238
\(947\) 34.8514 1.13252 0.566259 0.824228i \(-0.308390\pi\)
0.566259 + 0.824228i \(0.308390\pi\)
\(948\) 63.8174 2.07269
\(949\) 20.2236 0.656485
\(950\) 19.7962 0.642272
\(951\) 33.2693 1.07883
\(952\) 2.20804 0.0715631
\(953\) 12.2115 0.395570 0.197785 0.980245i \(-0.436625\pi\)
0.197785 + 0.980245i \(0.436625\pi\)
\(954\) 11.4660 0.371225
\(955\) 10.9115 0.353087
\(956\) −92.2564 −2.98379
\(957\) −128.398 −4.15051
\(958\) 58.0170 1.87444
\(959\) 12.2879 0.396796
\(960\) −30.9174 −0.997855
\(961\) 8.74981 0.282252
\(962\) 147.832 4.76631
\(963\) −76.0616 −2.45105
\(964\) −10.6644 −0.343478
\(965\) 24.2602 0.780963
\(966\) −4.79030 −0.154125
\(967\) −5.92843 −0.190645 −0.0953227 0.995446i \(-0.530388\pi\)
−0.0953227 + 0.995446i \(0.530388\pi\)
\(968\) −100.933 −3.24410
\(969\) −3.70071 −0.118884
\(970\) 21.7091 0.697036
\(971\) −23.5661 −0.756273 −0.378136 0.925750i \(-0.623435\pi\)
−0.378136 + 0.925750i \(0.623435\pi\)
\(972\) 80.2158 2.57292
\(973\) 9.53155 0.305568
\(974\) 87.5762 2.80612
\(975\) 52.4886 1.68098
\(976\) −29.9351 −0.958200
\(977\) 44.0856 1.41042 0.705211 0.708997i \(-0.250852\pi\)
0.705211 + 0.708997i \(0.250852\pi\)
\(978\) −101.578 −3.24812
\(979\) 43.0824 1.37692
\(980\) 35.0877 1.12083
\(981\) 17.7487 0.566674
\(982\) 77.5893 2.47597
\(983\) 2.18152 0.0695796 0.0347898 0.999395i \(-0.488924\pi\)
0.0347898 + 0.999395i \(0.488924\pi\)
\(984\) −1.25872 −0.0401265
\(985\) −25.6835 −0.818344
\(986\) −10.5628 −0.336387
\(987\) −21.8111 −0.694253
\(988\) 70.2757 2.23577
\(989\) −1.37749 −0.0438018
\(990\) 82.7017 2.62843
\(991\) −9.22446 −0.293025 −0.146512 0.989209i \(-0.546805\pi\)
−0.146512 + 0.989209i \(0.546805\pi\)
\(992\) 0.590776 0.0187572
\(993\) −42.9159 −1.36190
\(994\) 32.0508 1.01659
\(995\) 32.9624 1.04498
\(996\) 27.1625 0.860678
\(997\) −42.0745 −1.33251 −0.666257 0.745722i \(-0.732105\pi\)
−0.666257 + 0.745722i \(0.732105\pi\)
\(998\) 21.9741 0.695578
\(999\) 30.7998 0.974462
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 \(a_p\))