Properties

Label 6027.2.a.s.1.1
Level 6027
Weight 2
Character 6027.1
Self dual Yes
Analytic conductor 48.126
Analytic rank 1
Dimension 3
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 6027 = 3 \cdot 7^{2} \cdot 41 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6027.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.1258372982\)
Analytic rank: \(1\)
Dimension: \(3\)
Coefficient field: 3.3.316.1
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-1.81361\)
Character \(\chi\) = 6027.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.81361 q^{2} +1.00000 q^{3} +1.28917 q^{4} +1.10278 q^{5} -1.81361 q^{6} +1.28917 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.81361 q^{2} +1.00000 q^{3} +1.28917 q^{4} +1.10278 q^{5} -1.81361 q^{6} +1.28917 q^{8} +1.00000 q^{9} -2.00000 q^{10} +0.813607 q^{11} +1.28917 q^{12} -5.10278 q^{13} +1.10278 q^{15} -4.91638 q^{16} -3.39194 q^{17} -1.81361 q^{18} -3.10278 q^{19} +1.42166 q^{20} -1.47556 q^{22} -0.897225 q^{23} +1.28917 q^{24} -3.78389 q^{25} +9.25443 q^{26} +1.00000 q^{27} +4.44082 q^{29} -2.00000 q^{30} +8.96526 q^{31} +6.33804 q^{32} +0.813607 q^{33} +6.15165 q^{34} +1.28917 q^{36} +2.08362 q^{37} +5.62721 q^{38} -5.10278 q^{39} +1.42166 q^{40} -1.00000 q^{41} +9.07306 q^{43} +1.04888 q^{44} +1.10278 q^{45} +1.62721 q^{46} +0.235269 q^{47} -4.91638 q^{48} +6.86248 q^{50} -3.39194 q^{51} -6.57834 q^{52} +13.8328 q^{53} -1.81361 q^{54} +0.897225 q^{55} -3.10278 q^{57} -8.05390 q^{58} -1.04888 q^{59} +1.42166 q^{60} -1.91638 q^{61} -16.2594 q^{62} -1.66196 q^{64} -5.62721 q^{65} -1.47556 q^{66} -10.0383 q^{67} -4.37279 q^{68} -0.897225 q^{69} -12.8136 q^{71} +1.28917 q^{72} -4.75971 q^{73} -3.77886 q^{74} -3.78389 q^{75} -4.00000 q^{76} +9.25443 q^{78} -15.8328 q^{79} -5.42166 q^{80} +1.00000 q^{81} +1.81361 q^{82} +7.68111 q^{83} -3.74055 q^{85} -16.4550 q^{86} +4.44082 q^{87} +1.04888 q^{88} -13.2544 q^{89} -2.00000 q^{90} -1.15667 q^{92} +8.96526 q^{93} -0.426686 q^{94} -3.42166 q^{95} +6.33804 q^{96} -2.72999 q^{97} +0.813607 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3q + q^{2} + 3q^{3} + 3q^{4} - 4q^{5} + q^{6} + 3q^{8} + 3q^{9} + O(q^{10}) \) \( 3q + q^{2} + 3q^{3} + 3q^{4} - 4q^{5} + q^{6} + 3q^{8} + 3q^{9} - 6q^{10} - 4q^{11} + 3q^{12} - 8q^{13} - 4q^{15} - q^{16} - 2q^{17} + q^{18} - 2q^{19} + 6q^{20} - 10q^{22} - 10q^{23} + 3q^{24} + 5q^{25} + 2q^{26} + 3q^{27} - 6q^{29} - 6q^{30} + 2q^{31} + 7q^{32} - 4q^{33} + 3q^{36} + 20q^{37} + 4q^{38} - 8q^{39} + 6q^{40} - 3q^{41} + 10q^{43} - 8q^{44} - 4q^{45} - 8q^{46} - 4q^{47} - q^{48} + 3q^{50} - 2q^{51} - 18q^{52} + 14q^{53} + q^{54} + 10q^{55} - 2q^{57} - 28q^{58} + 8q^{59} + 6q^{60} + 8q^{61} - 38q^{62} - 17q^{64} - 4q^{65} - 10q^{66} + 12q^{67} - 26q^{68} - 10q^{69} - 32q^{71} + 3q^{72} - 4q^{73} + 20q^{74} + 5q^{75} - 12q^{76} + 2q^{78} - 20q^{79} - 18q^{80} + 3q^{81} - q^{82} + 14q^{83} - 22q^{85} + 6q^{86} - 6q^{87} - 8q^{88} - 14q^{89} - 6q^{90} + 2q^{93} - 18q^{94} - 12q^{95} + 7q^{96} + 12q^{97} - 4q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.81361 −1.28241 −0.641207 0.767368i \(-0.721566\pi\)
−0.641207 + 0.767368i \(0.721566\pi\)
\(3\) 1.00000 0.577350
\(4\) 1.28917 0.644584
\(5\) 1.10278 0.493176 0.246588 0.969120i \(-0.420691\pi\)
0.246588 + 0.969120i \(0.420691\pi\)
\(6\) −1.81361 −0.740402
\(7\) 0 0
\(8\) 1.28917 0.455790
\(9\) 1.00000 0.333333
\(10\) −2.00000 −0.632456
\(11\) 0.813607 0.245312 0.122656 0.992449i \(-0.460859\pi\)
0.122656 + 0.992449i \(0.460859\pi\)
\(12\) 1.28917 0.372151
\(13\) −5.10278 −1.41526 −0.707628 0.706586i \(-0.750235\pi\)
−0.707628 + 0.706586i \(0.750235\pi\)
\(14\) 0 0
\(15\) 1.10278 0.284735
\(16\) −4.91638 −1.22910
\(17\) −3.39194 −0.822667 −0.411334 0.911485i \(-0.634937\pi\)
−0.411334 + 0.911485i \(0.634937\pi\)
\(18\) −1.81361 −0.427471
\(19\) −3.10278 −0.711825 −0.355913 0.934519i \(-0.615830\pi\)
−0.355913 + 0.934519i \(0.615830\pi\)
\(20\) 1.42166 0.317893
\(21\) 0 0
\(22\) −1.47556 −0.314591
\(23\) −0.897225 −0.187084 −0.0935422 0.995615i \(-0.529819\pi\)
−0.0935422 + 0.995615i \(0.529819\pi\)
\(24\) 1.28917 0.263150
\(25\) −3.78389 −0.756777
\(26\) 9.25443 1.81494
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) 4.44082 0.824639 0.412320 0.911039i \(-0.364719\pi\)
0.412320 + 0.911039i \(0.364719\pi\)
\(30\) −2.00000 −0.365148
\(31\) 8.96526 1.61021 0.805104 0.593134i \(-0.202110\pi\)
0.805104 + 0.593134i \(0.202110\pi\)
\(32\) 6.33804 1.12042
\(33\) 0.813607 0.141631
\(34\) 6.15165 1.05500
\(35\) 0 0
\(36\) 1.28917 0.214861
\(37\) 2.08362 0.342545 0.171272 0.985224i \(-0.445212\pi\)
0.171272 + 0.985224i \(0.445212\pi\)
\(38\) 5.62721 0.912854
\(39\) −5.10278 −0.817098
\(40\) 1.42166 0.224785
\(41\) −1.00000 −0.156174
\(42\) 0 0
\(43\) 9.07306 1.38363 0.691814 0.722076i \(-0.256812\pi\)
0.691814 + 0.722076i \(0.256812\pi\)
\(44\) 1.04888 0.158124
\(45\) 1.10278 0.164392
\(46\) 1.62721 0.239919
\(47\) 0.235269 0.0343176 0.0171588 0.999853i \(-0.494538\pi\)
0.0171588 + 0.999853i \(0.494538\pi\)
\(48\) −4.91638 −0.709619
\(49\) 0 0
\(50\) 6.86248 0.970502
\(51\) −3.39194 −0.474967
\(52\) −6.57834 −0.912251
\(53\) 13.8328 1.90008 0.950038 0.312134i \(-0.101044\pi\)
0.950038 + 0.312134i \(0.101044\pi\)
\(54\) −1.81361 −0.246801
\(55\) 0.897225 0.120982
\(56\) 0 0
\(57\) −3.10278 −0.410973
\(58\) −8.05390 −1.05753
\(59\) −1.04888 −0.136552 −0.0682760 0.997666i \(-0.521750\pi\)
−0.0682760 + 0.997666i \(0.521750\pi\)
\(60\) 1.42166 0.183536
\(61\) −1.91638 −0.245368 −0.122684 0.992446i \(-0.539150\pi\)
−0.122684 + 0.992446i \(0.539150\pi\)
\(62\) −16.2594 −2.06495
\(63\) 0 0
\(64\) −1.66196 −0.207744
\(65\) −5.62721 −0.697970
\(66\) −1.47556 −0.181629
\(67\) −10.0383 −1.22638 −0.613188 0.789937i \(-0.710113\pi\)
−0.613188 + 0.789937i \(0.710113\pi\)
\(68\) −4.37279 −0.530278
\(69\) −0.897225 −0.108013
\(70\) 0 0
\(71\) −12.8136 −1.52070 −0.760348 0.649516i \(-0.774971\pi\)
−0.760348 + 0.649516i \(0.774971\pi\)
\(72\) 1.28917 0.151930
\(73\) −4.75971 −0.557082 −0.278541 0.960424i \(-0.589851\pi\)
−0.278541 + 0.960424i \(0.589851\pi\)
\(74\) −3.77886 −0.439284
\(75\) −3.78389 −0.436926
\(76\) −4.00000 −0.458831
\(77\) 0 0
\(78\) 9.25443 1.04786
\(79\) −15.8328 −1.78133 −0.890663 0.454665i \(-0.849759\pi\)
−0.890663 + 0.454665i \(0.849759\pi\)
\(80\) −5.42166 −0.606160
\(81\) 1.00000 0.111111
\(82\) 1.81361 0.200279
\(83\) 7.68111 0.843112 0.421556 0.906802i \(-0.361484\pi\)
0.421556 + 0.906802i \(0.361484\pi\)
\(84\) 0 0
\(85\) −3.74055 −0.405720
\(86\) −16.4550 −1.77438
\(87\) 4.44082 0.476106
\(88\) 1.04888 0.111811
\(89\) −13.2544 −1.40497 −0.702483 0.711700i \(-0.747925\pi\)
−0.702483 + 0.711700i \(0.747925\pi\)
\(90\) −2.00000 −0.210819
\(91\) 0 0
\(92\) −1.15667 −0.120592
\(93\) 8.96526 0.929654
\(94\) −0.426686 −0.0440093
\(95\) −3.42166 −0.351055
\(96\) 6.33804 0.646874
\(97\) −2.72999 −0.277188 −0.138594 0.990349i \(-0.544258\pi\)
−0.138594 + 0.990349i \(0.544258\pi\)
\(98\) 0 0
\(99\) 0.813607 0.0817705
\(100\) −4.87807 −0.487807
\(101\) 11.8625 1.18036 0.590181 0.807271i \(-0.299057\pi\)
0.590181 + 0.807271i \(0.299057\pi\)
\(102\) 6.15165 0.609104
\(103\) 0.494719 0.0487461 0.0243730 0.999703i \(-0.492241\pi\)
0.0243730 + 0.999703i \(0.492241\pi\)
\(104\) −6.57834 −0.645059
\(105\) 0 0
\(106\) −25.0872 −2.43668
\(107\) −15.0872 −1.45853 −0.729267 0.684229i \(-0.760139\pi\)
−0.729267 + 0.684229i \(0.760139\pi\)
\(108\) 1.28917 0.124050
\(109\) 5.10278 0.488757 0.244379 0.969680i \(-0.421416\pi\)
0.244379 + 0.969680i \(0.421416\pi\)
\(110\) −1.62721 −0.155149
\(111\) 2.08362 0.197768
\(112\) 0 0
\(113\) −17.5139 −1.64757 −0.823783 0.566905i \(-0.808141\pi\)
−0.823783 + 0.566905i \(0.808141\pi\)
\(114\) 5.62721 0.527037
\(115\) −0.989437 −0.0922655
\(116\) 5.72496 0.531550
\(117\) −5.10278 −0.471752
\(118\) 1.90225 0.175116
\(119\) 0 0
\(120\) 1.42166 0.129779
\(121\) −10.3380 −0.939822
\(122\) 3.47556 0.314663
\(123\) −1.00000 −0.0901670
\(124\) 11.5577 1.03791
\(125\) −9.68665 −0.866400
\(126\) 0 0
\(127\) 12.8816 1.14306 0.571530 0.820581i \(-0.306350\pi\)
0.571530 + 0.820581i \(0.306350\pi\)
\(128\) −9.66196 −0.854004
\(129\) 9.07306 0.798838
\(130\) 10.2056 0.895086
\(131\) 6.35720 0.555431 0.277716 0.960663i \(-0.410423\pi\)
0.277716 + 0.960663i \(0.410423\pi\)
\(132\) 1.04888 0.0912929
\(133\) 0 0
\(134\) 18.2056 1.57272
\(135\) 1.10278 0.0949118
\(136\) −4.37279 −0.374963
\(137\) −17.4897 −1.49425 −0.747123 0.664686i \(-0.768565\pi\)
−0.747123 + 0.664686i \(0.768565\pi\)
\(138\) 1.62721 0.138518
\(139\) −15.7250 −1.33377 −0.666887 0.745159i \(-0.732374\pi\)
−0.666887 + 0.745159i \(0.732374\pi\)
\(140\) 0 0
\(141\) 0.235269 0.0198133
\(142\) 23.2388 1.95016
\(143\) −4.15165 −0.347178
\(144\) −4.91638 −0.409698
\(145\) 4.89722 0.406692
\(146\) 8.63224 0.714409
\(147\) 0 0
\(148\) 2.68614 0.220799
\(149\) 11.5678 0.947669 0.473835 0.880614i \(-0.342869\pi\)
0.473835 + 0.880614i \(0.342869\pi\)
\(150\) 6.86248 0.560319
\(151\) 19.2544 1.56690 0.783451 0.621453i \(-0.213457\pi\)
0.783451 + 0.621453i \(0.213457\pi\)
\(152\) −4.00000 −0.324443
\(153\) −3.39194 −0.274222
\(154\) 0 0
\(155\) 9.88666 0.794116
\(156\) −6.57834 −0.526688
\(157\) 20.9200 1.66959 0.834797 0.550558i \(-0.185585\pi\)
0.834797 + 0.550558i \(0.185585\pi\)
\(158\) 28.7144 2.28440
\(159\) 13.8328 1.09701
\(160\) 6.98944 0.552564
\(161\) 0 0
\(162\) −1.81361 −0.142490
\(163\) −12.7980 −1.00242 −0.501209 0.865326i \(-0.667111\pi\)
−0.501209 + 0.865326i \(0.667111\pi\)
\(164\) −1.28917 −0.100667
\(165\) 0.897225 0.0698489
\(166\) −13.9305 −1.08122
\(167\) −9.62721 −0.744976 −0.372488 0.928037i \(-0.621495\pi\)
−0.372488 + 0.928037i \(0.621495\pi\)
\(168\) 0 0
\(169\) 13.0383 1.00295
\(170\) 6.78389 0.520300
\(171\) −3.10278 −0.237275
\(172\) 11.6967 0.891865
\(173\) −11.9461 −0.908245 −0.454123 0.890939i \(-0.650047\pi\)
−0.454123 + 0.890939i \(0.650047\pi\)
\(174\) −8.05390 −0.610565
\(175\) 0 0
\(176\) −4.00000 −0.301511
\(177\) −1.04888 −0.0788383
\(178\) 24.0383 1.80175
\(179\) −2.13752 −0.159766 −0.0798828 0.996804i \(-0.525455\pi\)
−0.0798828 + 0.996804i \(0.525455\pi\)
\(180\) 1.42166 0.105964
\(181\) 1.83276 0.136228 0.0681141 0.997678i \(-0.478302\pi\)
0.0681141 + 0.997678i \(0.478302\pi\)
\(182\) 0 0
\(183\) −1.91638 −0.141663
\(184\) −1.15667 −0.0852712
\(185\) 2.29776 0.168935
\(186\) −16.2594 −1.19220
\(187\) −2.75971 −0.201810
\(188\) 0.303302 0.0221206
\(189\) 0 0
\(190\) 6.20555 0.450198
\(191\) −18.6167 −1.34705 −0.673527 0.739163i \(-0.735221\pi\)
−0.673527 + 0.739163i \(0.735221\pi\)
\(192\) −1.66196 −0.119941
\(193\) 15.6116 1.12375 0.561875 0.827222i \(-0.310080\pi\)
0.561875 + 0.827222i \(0.310080\pi\)
\(194\) 4.95112 0.355470
\(195\) −5.62721 −0.402973
\(196\) 0 0
\(197\) −5.21057 −0.371238 −0.185619 0.982622i \(-0.559429\pi\)
−0.185619 + 0.982622i \(0.559429\pi\)
\(198\) −1.47556 −0.104864
\(199\) −2.05390 −0.145597 −0.0727985 0.997347i \(-0.523193\pi\)
−0.0727985 + 0.997347i \(0.523193\pi\)
\(200\) −4.87807 −0.344932
\(201\) −10.0383 −0.708048
\(202\) −21.5139 −1.51371
\(203\) 0 0
\(204\) −4.37279 −0.306156
\(205\) −1.10278 −0.0770212
\(206\) −0.897225 −0.0625126
\(207\) −0.897225 −0.0623614
\(208\) 25.0872 1.73948
\(209\) −2.52444 −0.174619
\(210\) 0 0
\(211\) −9.04888 −0.622950 −0.311475 0.950254i \(-0.600823\pi\)
−0.311475 + 0.950254i \(0.600823\pi\)
\(212\) 17.8328 1.22476
\(213\) −12.8136 −0.877974
\(214\) 27.3622 1.87044
\(215\) 10.0055 0.682372
\(216\) 1.28917 0.0877168
\(217\) 0 0
\(218\) −9.25443 −0.626789
\(219\) −4.75971 −0.321631
\(220\) 1.15667 0.0779830
\(221\) 17.3083 1.16428
\(222\) −3.77886 −0.253621
\(223\) −24.8222 −1.66222 −0.831109 0.556110i \(-0.812293\pi\)
−0.831109 + 0.556110i \(0.812293\pi\)
\(224\) 0 0
\(225\) −3.78389 −0.252259
\(226\) 31.7633 2.11286
\(227\) −16.6464 −1.10486 −0.552429 0.833560i \(-0.686299\pi\)
−0.552429 + 0.833560i \(0.686299\pi\)
\(228\) −4.00000 −0.264906
\(229\) 15.7789 1.04270 0.521348 0.853344i \(-0.325429\pi\)
0.521348 + 0.853344i \(0.325429\pi\)
\(230\) 1.79445 0.118323
\(231\) 0 0
\(232\) 5.72496 0.375862
\(233\) −24.9200 −1.63256 −0.816280 0.577656i \(-0.803967\pi\)
−0.816280 + 0.577656i \(0.803967\pi\)
\(234\) 9.25443 0.604981
\(235\) 0.259449 0.0169246
\(236\) −1.35218 −0.0880193
\(237\) −15.8328 −1.02845
\(238\) 0 0
\(239\) −2.95112 −0.190892 −0.0954462 0.995435i \(-0.530428\pi\)
−0.0954462 + 0.995435i \(0.530428\pi\)
\(240\) −5.42166 −0.349967
\(241\) 16.5925 1.06881 0.534407 0.845227i \(-0.320535\pi\)
0.534407 + 0.845227i \(0.320535\pi\)
\(242\) 18.7491 1.20524
\(243\) 1.00000 0.0641500
\(244\) −2.47054 −0.158160
\(245\) 0 0
\(246\) 1.81361 0.115631
\(247\) 15.8328 1.00741
\(248\) 11.5577 0.733916
\(249\) 7.68111 0.486771
\(250\) 17.5678 1.11108
\(251\) 20.1361 1.27098 0.635489 0.772110i \(-0.280799\pi\)
0.635489 + 0.772110i \(0.280799\pi\)
\(252\) 0 0
\(253\) −0.729988 −0.0458940
\(254\) −23.3622 −1.46588
\(255\) −3.74055 −0.234242
\(256\) 20.8469 1.30293
\(257\) −25.9008 −1.61565 −0.807824 0.589424i \(-0.799355\pi\)
−0.807824 + 0.589424i \(0.799355\pi\)
\(258\) −16.4550 −1.02444
\(259\) 0 0
\(260\) −7.25443 −0.449900
\(261\) 4.44082 0.274880
\(262\) −11.5295 −0.712292
\(263\) −22.4408 −1.38376 −0.691880 0.722012i \(-0.743217\pi\)
−0.691880 + 0.722012i \(0.743217\pi\)
\(264\) 1.04888 0.0645538
\(265\) 15.2544 0.937072
\(266\) 0 0
\(267\) −13.2544 −0.811158
\(268\) −12.9411 −0.790502
\(269\) −7.62721 −0.465039 −0.232520 0.972592i \(-0.574697\pi\)
−0.232520 + 0.972592i \(0.574697\pi\)
\(270\) −2.00000 −0.121716
\(271\) −19.9164 −1.20983 −0.604917 0.796289i \(-0.706794\pi\)
−0.604917 + 0.796289i \(0.706794\pi\)
\(272\) 16.6761 1.01114
\(273\) 0 0
\(274\) 31.7194 1.91624
\(275\) −3.07860 −0.185646
\(276\) −1.15667 −0.0696236
\(277\) −17.6413 −1.05997 −0.529983 0.848008i \(-0.677802\pi\)
−0.529983 + 0.848008i \(0.677802\pi\)
\(278\) 28.5189 1.71045
\(279\) 8.96526 0.536736
\(280\) 0 0
\(281\) −0.0297193 −0.00177291 −0.000886453 1.00000i \(-0.500282\pi\)
−0.000886453 1.00000i \(0.500282\pi\)
\(282\) −0.426686 −0.0254088
\(283\) 10.1814 0.605220 0.302610 0.953115i \(-0.402142\pi\)
0.302610 + 0.953115i \(0.402142\pi\)
\(284\) −16.5189 −0.980216
\(285\) −3.42166 −0.202682
\(286\) 7.52946 0.445226
\(287\) 0 0
\(288\) 6.33804 0.373473
\(289\) −5.49472 −0.323219
\(290\) −8.88164 −0.521548
\(291\) −2.72999 −0.160035
\(292\) −6.13607 −0.359086
\(293\) −3.14808 −0.183913 −0.0919564 0.995763i \(-0.529312\pi\)
−0.0919564 + 0.995763i \(0.529312\pi\)
\(294\) 0 0
\(295\) −1.15667 −0.0673442
\(296\) 2.68614 0.156128
\(297\) 0.813607 0.0472102
\(298\) −20.9794 −1.21530
\(299\) 4.57834 0.264772
\(300\) −4.87807 −0.281635
\(301\) 0 0
\(302\) −34.9200 −2.00942
\(303\) 11.8625 0.681482
\(304\) 15.2544 0.874901
\(305\) −2.11334 −0.121009
\(306\) 6.15165 0.351666
\(307\) 12.7980 0.730422 0.365211 0.930925i \(-0.380997\pi\)
0.365211 + 0.930925i \(0.380997\pi\)
\(308\) 0 0
\(309\) 0.494719 0.0281436
\(310\) −17.9305 −1.01838
\(311\) −26.6167 −1.50929 −0.754646 0.656132i \(-0.772191\pi\)
−0.754646 + 0.656132i \(0.772191\pi\)
\(312\) −6.57834 −0.372425
\(313\) 3.00502 0.169854 0.0849270 0.996387i \(-0.472934\pi\)
0.0849270 + 0.996387i \(0.472934\pi\)
\(314\) −37.9406 −2.14111
\(315\) 0 0
\(316\) −20.4111 −1.14821
\(317\) −4.33302 −0.243367 −0.121683 0.992569i \(-0.538829\pi\)
−0.121683 + 0.992569i \(0.538829\pi\)
\(318\) −25.0872 −1.40682
\(319\) 3.61308 0.202294
\(320\) −1.83276 −0.102455
\(321\) −15.0872 −0.842085
\(322\) 0 0
\(323\) 10.5244 0.585595
\(324\) 1.28917 0.0716205
\(325\) 19.3083 1.07103
\(326\) 23.2106 1.28551
\(327\) 5.10278 0.282184
\(328\) −1.28917 −0.0711824
\(329\) 0 0
\(330\) −1.62721 −0.0895751
\(331\) 5.53500 0.304231 0.152116 0.988363i \(-0.451391\pi\)
0.152116 + 0.988363i \(0.451391\pi\)
\(332\) 9.90225 0.543456
\(333\) 2.08362 0.114182
\(334\) 17.4600 0.955367
\(335\) −11.0700 −0.604819
\(336\) 0 0
\(337\) −3.71083 −0.202142 −0.101071 0.994879i \(-0.532227\pi\)
−0.101071 + 0.994879i \(0.532227\pi\)
\(338\) −23.6464 −1.28619
\(339\) −17.5139 −0.951223
\(340\) −4.82220 −0.261521
\(341\) 7.29419 0.395003
\(342\) 5.62721 0.304285
\(343\) 0 0
\(344\) 11.6967 0.630644
\(345\) −0.989437 −0.0532695
\(346\) 21.6655 1.16475
\(347\) 3.07860 0.165268 0.0826338 0.996580i \(-0.473667\pi\)
0.0826338 + 0.996580i \(0.473667\pi\)
\(348\) 5.72496 0.306890
\(349\) −14.7980 −0.792120 −0.396060 0.918225i \(-0.629623\pi\)
−0.396060 + 0.918225i \(0.629623\pi\)
\(350\) 0 0
\(351\) −5.10278 −0.272366
\(352\) 5.15667 0.274852
\(353\) −26.8222 −1.42760 −0.713801 0.700349i \(-0.753028\pi\)
−0.713801 + 0.700349i \(0.753028\pi\)
\(354\) 1.90225 0.101103
\(355\) −14.1305 −0.749970
\(356\) −17.0872 −0.905619
\(357\) 0 0
\(358\) 3.87662 0.204886
\(359\) 2.35720 0.124408 0.0622042 0.998063i \(-0.480187\pi\)
0.0622042 + 0.998063i \(0.480187\pi\)
\(360\) 1.42166 0.0749282
\(361\) −9.37279 −0.493305
\(362\) −3.32391 −0.174701
\(363\) −10.3380 −0.542607
\(364\) 0 0
\(365\) −5.24889 −0.274739
\(366\) 3.47556 0.181671
\(367\) −23.1708 −1.20951 −0.604753 0.796413i \(-0.706728\pi\)
−0.604753 + 0.796413i \(0.706728\pi\)
\(368\) 4.41110 0.229944
\(369\) −1.00000 −0.0520579
\(370\) −4.16724 −0.216644
\(371\) 0 0
\(372\) 11.5577 0.599240
\(373\) 35.2091 1.82306 0.911530 0.411235i \(-0.134902\pi\)
0.911530 + 0.411235i \(0.134902\pi\)
\(374\) 5.00502 0.258804
\(375\) −9.68665 −0.500217
\(376\) 0.303302 0.0156416
\(377\) −22.6605 −1.16708
\(378\) 0 0
\(379\) −26.0383 −1.33750 −0.668749 0.743488i \(-0.733170\pi\)
−0.668749 + 0.743488i \(0.733170\pi\)
\(380\) −4.41110 −0.226285
\(381\) 12.8816 0.659946
\(382\) 33.7633 1.72748
\(383\) −15.3819 −0.785978 −0.392989 0.919543i \(-0.628559\pi\)
−0.392989 + 0.919543i \(0.628559\pi\)
\(384\) −9.66196 −0.493060
\(385\) 0 0
\(386\) −28.3133 −1.44111
\(387\) 9.07306 0.461209
\(388\) −3.51941 −0.178671
\(389\) 4.46500 0.226384 0.113192 0.993573i \(-0.463892\pi\)
0.113192 + 0.993573i \(0.463892\pi\)
\(390\) 10.2056 0.516778
\(391\) 3.04334 0.153908
\(392\) 0 0
\(393\) 6.35720 0.320678
\(394\) 9.44993 0.476081
\(395\) −17.4600 −0.878507
\(396\) 1.04888 0.0527080
\(397\) 10.5628 0.530129 0.265065 0.964231i \(-0.414607\pi\)
0.265065 + 0.964231i \(0.414607\pi\)
\(398\) 3.72496 0.186716
\(399\) 0 0
\(400\) 18.6030 0.930152
\(401\) 13.0872 0.653543 0.326772 0.945103i \(-0.394039\pi\)
0.326772 + 0.945103i \(0.394039\pi\)
\(402\) 18.2056 0.908010
\(403\) −45.7477 −2.27885
\(404\) 15.2927 0.760842
\(405\) 1.10278 0.0547973
\(406\) 0 0
\(407\) 1.69525 0.0840302
\(408\) −4.37279 −0.216485
\(409\) 18.5542 0.917444 0.458722 0.888580i \(-0.348307\pi\)
0.458722 + 0.888580i \(0.348307\pi\)
\(410\) 2.00000 0.0987730
\(411\) −17.4897 −0.862703
\(412\) 0.637776 0.0314210
\(413\) 0 0
\(414\) 1.62721 0.0799732
\(415\) 8.47054 0.415802
\(416\) −32.3416 −1.58568
\(417\) −15.7250 −0.770055
\(418\) 4.57834 0.223934
\(419\) 25.6116 1.25121 0.625605 0.780140i \(-0.284852\pi\)
0.625605 + 0.780140i \(0.284852\pi\)
\(420\) 0 0
\(421\) −8.67609 −0.422847 −0.211423 0.977395i \(-0.567810\pi\)
−0.211423 + 0.977395i \(0.567810\pi\)
\(422\) 16.4111 0.798880
\(423\) 0.235269 0.0114392
\(424\) 17.8328 0.866036
\(425\) 12.8347 0.622576
\(426\) 23.2388 1.12593
\(427\) 0 0
\(428\) −19.4499 −0.940148
\(429\) −4.15165 −0.200444
\(430\) −18.1461 −0.875083
\(431\) 7.10278 0.342129 0.171064 0.985260i \(-0.445279\pi\)
0.171064 + 0.985260i \(0.445279\pi\)
\(432\) −4.91638 −0.236540
\(433\) 11.0247 0.529813 0.264907 0.964274i \(-0.414659\pi\)
0.264907 + 0.964274i \(0.414659\pi\)
\(434\) 0 0
\(435\) 4.89722 0.234804
\(436\) 6.57834 0.315045
\(437\) 2.78389 0.133171
\(438\) 8.63224 0.412464
\(439\) 1.32391 0.0631868 0.0315934 0.999501i \(-0.489942\pi\)
0.0315934 + 0.999501i \(0.489942\pi\)
\(440\) 1.15667 0.0551423
\(441\) 0 0
\(442\) −31.3905 −1.49309
\(443\) 15.5889 0.740651 0.370325 0.928902i \(-0.379246\pi\)
0.370325 + 0.928902i \(0.379246\pi\)
\(444\) 2.68614 0.127478
\(445\) −14.6167 −0.692896
\(446\) 45.0177 2.13165
\(447\) 11.5678 0.547137
\(448\) 0 0
\(449\) −32.7839 −1.54717 −0.773584 0.633694i \(-0.781538\pi\)
−0.773584 + 0.633694i \(0.781538\pi\)
\(450\) 6.86248 0.323501
\(451\) −0.813607 −0.0383112
\(452\) −22.5783 −1.06200
\(453\) 19.2544 0.904652
\(454\) 30.1900 1.41689
\(455\) 0 0
\(456\) −4.00000 −0.187317
\(457\) −14.1672 −0.662715 −0.331358 0.943505i \(-0.607507\pi\)
−0.331358 + 0.943505i \(0.607507\pi\)
\(458\) −28.6167 −1.33717
\(459\) −3.39194 −0.158322
\(460\) −1.27555 −0.0594729
\(461\) 30.0766 1.40081 0.700404 0.713747i \(-0.253003\pi\)
0.700404 + 0.713747i \(0.253003\pi\)
\(462\) 0 0
\(463\) −23.8766 −1.10964 −0.554820 0.831970i \(-0.687213\pi\)
−0.554820 + 0.831970i \(0.687213\pi\)
\(464\) −21.8328 −1.01356
\(465\) 9.88666 0.458483
\(466\) 45.1950 2.09362
\(467\) 9.73501 0.450483 0.225241 0.974303i \(-0.427683\pi\)
0.225241 + 0.974303i \(0.427683\pi\)
\(468\) −6.57834 −0.304084
\(469\) 0 0
\(470\) −0.470539 −0.0217043
\(471\) 20.9200 0.963941
\(472\) −1.35218 −0.0622390
\(473\) 7.38190 0.339420
\(474\) 28.7144 1.31890
\(475\) 11.7406 0.538693
\(476\) 0 0
\(477\) 13.8328 0.633359
\(478\) 5.35218 0.244803
\(479\) 1.17635 0.0537487 0.0268743 0.999639i \(-0.491445\pi\)
0.0268743 + 0.999639i \(0.491445\pi\)
\(480\) 6.98944 0.319023
\(481\) −10.6322 −0.484788
\(482\) −30.0922 −1.37066
\(483\) 0 0
\(484\) −13.3275 −0.605795
\(485\) −3.01056 −0.136703
\(486\) −1.81361 −0.0822669
\(487\) 20.6025 0.933589 0.466795 0.884366i \(-0.345409\pi\)
0.466795 + 0.884366i \(0.345409\pi\)
\(488\) −2.47054 −0.111836
\(489\) −12.7980 −0.578746
\(490\) 0 0
\(491\) 14.1900 0.640384 0.320192 0.947353i \(-0.396253\pi\)
0.320192 + 0.947353i \(0.396253\pi\)
\(492\) −1.28917 −0.0581202
\(493\) −15.0630 −0.678404
\(494\) −28.7144 −1.29192
\(495\) 0.897225 0.0403273
\(496\) −44.0766 −1.97910
\(497\) 0 0
\(498\) −13.9305 −0.624241
\(499\) −21.4600 −0.960680 −0.480340 0.877082i \(-0.659487\pi\)
−0.480340 + 0.877082i \(0.659487\pi\)
\(500\) −12.4877 −0.558468
\(501\) −9.62721 −0.430112
\(502\) −36.5189 −1.62992
\(503\) 15.5491 0.693302 0.346651 0.937994i \(-0.387319\pi\)
0.346651 + 0.937994i \(0.387319\pi\)
\(504\) 0 0
\(505\) 13.0816 0.582126
\(506\) 1.32391 0.0588550
\(507\) 13.0383 0.579052
\(508\) 16.6066 0.736799
\(509\) −22.7542 −1.00856 −0.504280 0.863540i \(-0.668242\pi\)
−0.504280 + 0.863540i \(0.668242\pi\)
\(510\) 6.78389 0.300396
\(511\) 0 0
\(512\) −18.4842 −0.816892
\(513\) −3.10278 −0.136991
\(514\) 46.9739 2.07193
\(515\) 0.545563 0.0240404
\(516\) 11.6967 0.514918
\(517\) 0.191417 0.00841850
\(518\) 0 0
\(519\) −11.9461 −0.524376
\(520\) −7.25443 −0.318128
\(521\) 38.7230 1.69649 0.848243 0.529608i \(-0.177661\pi\)
0.848243 + 0.529608i \(0.177661\pi\)
\(522\) −8.05390 −0.352510
\(523\) −6.56829 −0.287211 −0.143606 0.989635i \(-0.545870\pi\)
−0.143606 + 0.989635i \(0.545870\pi\)
\(524\) 8.19550 0.358022
\(525\) 0 0
\(526\) 40.6988 1.77455
\(527\) −30.4096 −1.32467
\(528\) −4.00000 −0.174078
\(529\) −22.1950 −0.964999
\(530\) −27.6655 −1.20171
\(531\) −1.04888 −0.0455173
\(532\) 0 0
\(533\) 5.10278 0.221026
\(534\) 24.0383 1.04024
\(535\) −16.6378 −0.719314
\(536\) −12.9411 −0.558969
\(537\) −2.13752 −0.0922407
\(538\) 13.8328 0.596373
\(539\) 0 0
\(540\) 1.42166 0.0611786
\(541\) 42.0766 1.80902 0.904508 0.426457i \(-0.140239\pi\)
0.904508 + 0.426457i \(0.140239\pi\)
\(542\) 36.1205 1.55151
\(543\) 1.83276 0.0786514
\(544\) −21.4983 −0.921732
\(545\) 5.62721 0.241043
\(546\) 0 0
\(547\) 19.9688 0.853805 0.426903 0.904298i \(-0.359605\pi\)
0.426903 + 0.904298i \(0.359605\pi\)
\(548\) −22.5472 −0.963167
\(549\) −1.91638 −0.0817892
\(550\) 5.58336 0.238075
\(551\) −13.7789 −0.586999
\(552\) −1.15667 −0.0492313
\(553\) 0 0
\(554\) 31.9945 1.35931
\(555\) 2.29776 0.0975346
\(556\) −20.2721 −0.859730
\(557\) 13.5491 0.574095 0.287048 0.957916i \(-0.407326\pi\)
0.287048 + 0.957916i \(0.407326\pi\)
\(558\) −16.2594 −0.688317
\(559\) −46.2978 −1.95819
\(560\) 0 0
\(561\) −2.75971 −0.116515
\(562\) 0.0538991 0.00227360
\(563\) −9.75468 −0.411111 −0.205555 0.978645i \(-0.565900\pi\)
−0.205555 + 0.978645i \(0.565900\pi\)
\(564\) 0.303302 0.0127713
\(565\) −19.3139 −0.812540
\(566\) −18.4650 −0.776142
\(567\) 0 0
\(568\) −16.5189 −0.693118
\(569\) −21.4544 −0.899417 −0.449708 0.893175i \(-0.648472\pi\)
−0.449708 + 0.893175i \(0.648472\pi\)
\(570\) 6.20555 0.259922
\(571\) 20.9411 0.876357 0.438178 0.898888i \(-0.355624\pi\)
0.438178 + 0.898888i \(0.355624\pi\)
\(572\) −5.35218 −0.223786
\(573\) −18.6167 −0.777722
\(574\) 0 0
\(575\) 3.39500 0.141581
\(576\) −1.66196 −0.0692481
\(577\) −18.4705 −0.768939 −0.384469 0.923138i \(-0.625616\pi\)
−0.384469 + 0.923138i \(0.625616\pi\)
\(578\) 9.96526 0.414500
\(579\) 15.6116 0.648797
\(580\) 6.31335 0.262148
\(581\) 0 0
\(582\) 4.95112 0.205231
\(583\) 11.2544 0.466111
\(584\) −6.13607 −0.253912
\(585\) −5.62721 −0.232657
\(586\) 5.70938 0.235852
\(587\) 0.127471 0.00526130 0.00263065 0.999997i \(-0.499163\pi\)
0.00263065 + 0.999997i \(0.499163\pi\)
\(588\) 0 0
\(589\) −27.8172 −1.14619
\(590\) 2.09775 0.0863631
\(591\) −5.21057 −0.214334
\(592\) −10.2439 −0.421020
\(593\) 27.2841 1.12043 0.560213 0.828349i \(-0.310719\pi\)
0.560213 + 0.828349i \(0.310719\pi\)
\(594\) −1.47556 −0.0605430
\(595\) 0 0
\(596\) 14.9128 0.610853
\(597\) −2.05390 −0.0840605
\(598\) −8.30330 −0.339547
\(599\) −42.3260 −1.72939 −0.864697 0.502293i \(-0.832490\pi\)
−0.864697 + 0.502293i \(0.832490\pi\)
\(600\) −4.87807 −0.199146
\(601\) 15.6756 0.639420 0.319710 0.947515i \(-0.396415\pi\)
0.319710 + 0.947515i \(0.396415\pi\)
\(602\) 0 0
\(603\) −10.0383 −0.408792
\(604\) 24.8222 1.01000
\(605\) −11.4005 −0.463498
\(606\) −21.5139 −0.873941
\(607\) 1.93051 0.0783572 0.0391786 0.999232i \(-0.487526\pi\)
0.0391786 + 0.999232i \(0.487526\pi\)
\(608\) −19.6655 −0.797542
\(609\) 0 0
\(610\) 3.83276 0.155184
\(611\) −1.20053 −0.0485681
\(612\) −4.37279 −0.176759
\(613\) −0.372787 −0.0150567 −0.00752836 0.999972i \(-0.502396\pi\)
−0.00752836 + 0.999972i \(0.502396\pi\)
\(614\) −23.2106 −0.936703
\(615\) −1.10278 −0.0444682
\(616\) 0 0
\(617\) 31.3083 1.26043 0.630213 0.776422i \(-0.282968\pi\)
0.630213 + 0.776422i \(0.282968\pi\)
\(618\) −0.897225 −0.0360917
\(619\) −34.3658 −1.38128 −0.690639 0.723200i \(-0.742671\pi\)
−0.690639 + 0.723200i \(0.742671\pi\)
\(620\) 12.7456 0.511875
\(621\) −0.897225 −0.0360044
\(622\) 48.2721 1.93554
\(623\) 0 0
\(624\) 25.0872 1.00429
\(625\) 8.23724 0.329490
\(626\) −5.44993 −0.217823
\(627\) −2.52444 −0.100816
\(628\) 26.9693 1.07619
\(629\) −7.06752 −0.281800
\(630\) 0 0
\(631\) 7.33804 0.292123 0.146061 0.989276i \(-0.453340\pi\)
0.146061 + 0.989276i \(0.453340\pi\)
\(632\) −20.4111 −0.811910
\(633\) −9.04888 −0.359661
\(634\) 7.85840 0.312097
\(635\) 14.2056 0.563730
\(636\) 17.8328 0.707115
\(637\) 0 0
\(638\) −6.55270 −0.259424
\(639\) −12.8136 −0.506898
\(640\) −10.6550 −0.421174
\(641\) −31.5764 −1.24719 −0.623596 0.781747i \(-0.714329\pi\)
−0.623596 + 0.781747i \(0.714329\pi\)
\(642\) 27.3622 1.07990
\(643\) 4.51890 0.178208 0.0891040 0.996022i \(-0.471600\pi\)
0.0891040 + 0.996022i \(0.471600\pi\)
\(644\) 0 0
\(645\) 10.0055 0.393968
\(646\) −19.0872 −0.750975
\(647\) 20.6705 0.812643 0.406322 0.913730i \(-0.366811\pi\)
0.406322 + 0.913730i \(0.366811\pi\)
\(648\) 1.28917 0.0506433
\(649\) −0.853372 −0.0334978
\(650\) −35.0177 −1.37351
\(651\) 0 0
\(652\) −16.4988 −0.646143
\(653\) 0.381381 0.0149246 0.00746229 0.999972i \(-0.497625\pi\)
0.00746229 + 0.999972i \(0.497625\pi\)
\(654\) −9.25443 −0.361877
\(655\) 7.01056 0.273925
\(656\) 4.91638 0.191952
\(657\) −4.75971 −0.185694
\(658\) 0 0
\(659\) 13.4600 0.524326 0.262163 0.965024i \(-0.415564\pi\)
0.262163 + 0.965024i \(0.415564\pi\)
\(660\) 1.15667 0.0450235
\(661\) −30.7738 −1.19696 −0.598482 0.801136i \(-0.704229\pi\)
−0.598482 + 0.801136i \(0.704229\pi\)
\(662\) −10.0383 −0.390150
\(663\) 17.3083 0.672200
\(664\) 9.90225 0.384282
\(665\) 0 0
\(666\) −3.77886 −0.146428
\(667\) −3.98441 −0.154277
\(668\) −12.4111 −0.480200
\(669\) −24.8222 −0.959682
\(670\) 20.0766 0.775628
\(671\) −1.55918 −0.0601915
\(672\) 0 0
\(673\) 1.48110 0.0570923 0.0285461 0.999592i \(-0.490912\pi\)
0.0285461 + 0.999592i \(0.490912\pi\)
\(674\) 6.72999 0.259229
\(675\) −3.78389 −0.145642
\(676\) 16.8086 0.646484
\(677\) −45.3749 −1.74390 −0.871950 0.489596i \(-0.837144\pi\)
−0.871950 + 0.489596i \(0.837144\pi\)
\(678\) 31.7633 1.21986
\(679\) 0 0
\(680\) −4.82220 −0.184923
\(681\) −16.6464 −0.637890
\(682\) −13.2288 −0.506557
\(683\) −0.0594386 −0.00227436 −0.00113718 0.999999i \(-0.500362\pi\)
−0.00113718 + 0.999999i \(0.500362\pi\)
\(684\) −4.00000 −0.152944
\(685\) −19.2872 −0.736926
\(686\) 0 0
\(687\) 15.7789 0.602001
\(688\) −44.6066 −1.70061
\(689\) −70.5855 −2.68909
\(690\) 1.79445 0.0683135
\(691\) 18.9355 0.720342 0.360171 0.932886i \(-0.382718\pi\)
0.360171 + 0.932886i \(0.382718\pi\)
\(692\) −15.4005 −0.585441
\(693\) 0 0
\(694\) −5.58336 −0.211941
\(695\) −17.3411 −0.657785
\(696\) 5.72496 0.217004
\(697\) 3.39194 0.128479
\(698\) 26.8378 1.01583
\(699\) −24.9200 −0.942559
\(700\) 0 0
\(701\) −0.540024 −0.0203964 −0.0101982 0.999948i \(-0.503246\pi\)
−0.0101982 + 0.999948i \(0.503246\pi\)
\(702\) 9.25443 0.349286
\(703\) −6.46500 −0.243832
\(704\) −1.35218 −0.0509621
\(705\) 0.259449 0.00977142
\(706\) 48.6449 1.83078
\(707\) 0 0
\(708\) −1.35218 −0.0508180
\(709\) 28.0867 1.05482 0.527409 0.849612i \(-0.323164\pi\)
0.527409 + 0.849612i \(0.323164\pi\)
\(710\) 25.6272 0.961772
\(711\) −15.8328 −0.593775
\(712\) −17.0872 −0.640369
\(713\) −8.04385 −0.301245
\(714\) 0 0
\(715\) −4.57834 −0.171220
\(716\) −2.75562 −0.102982
\(717\) −2.95112 −0.110212
\(718\) −4.27504 −0.159543
\(719\) −9.86248 −0.367809 −0.183904 0.982944i \(-0.558874\pi\)
−0.183904 + 0.982944i \(0.558874\pi\)
\(720\) −5.42166 −0.202053
\(721\) 0 0
\(722\) 16.9985 0.632620
\(723\) 16.5925 0.617081
\(724\) 2.36274 0.0878106
\(725\) −16.8036 −0.624069
\(726\) 18.7491 0.695846
\(727\) 30.4650 1.12988 0.564942 0.825131i \(-0.308898\pi\)
0.564942 + 0.825131i \(0.308898\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 9.51941 0.352329
\(731\) −30.7753 −1.13827
\(732\) −2.47054 −0.0913137
\(733\) −27.5436 −1.01735 −0.508673 0.860960i \(-0.669864\pi\)
−0.508673 + 0.860960i \(0.669864\pi\)
\(734\) 42.0227 1.55109
\(735\) 0 0
\(736\) −5.68665 −0.209613
\(737\) −8.16724 −0.300844
\(738\) 1.81361 0.0667598
\(739\) 13.1013 0.481940 0.240970 0.970533i \(-0.422534\pi\)
0.240970 + 0.970533i \(0.422534\pi\)
\(740\) 2.96220 0.108893
\(741\) 15.8328 0.581631
\(742\) 0 0
\(743\) 34.7527 1.27495 0.637477 0.770470i \(-0.279978\pi\)
0.637477 + 0.770470i \(0.279978\pi\)
\(744\) 11.5577 0.423727
\(745\) 12.7567 0.467368
\(746\) −63.8555 −2.33792
\(747\) 7.68111 0.281037
\(748\) −3.55773 −0.130083
\(749\) 0 0
\(750\) 17.5678 0.641484
\(751\) 32.7738 1.19593 0.597967 0.801521i \(-0.295975\pi\)
0.597967 + 0.801521i \(0.295975\pi\)
\(752\) −1.15667 −0.0421796
\(753\) 20.1361 0.733799
\(754\) 41.0972 1.49667
\(755\) 21.2333 0.772759
\(756\) 0 0
\(757\) −32.2978 −1.17388 −0.586941 0.809630i \(-0.699668\pi\)
−0.586941 + 0.809630i \(0.699668\pi\)
\(758\) 47.2233 1.71523
\(759\) −0.729988 −0.0264969
\(760\) −4.41110 −0.160007
\(761\) −44.4494 −1.61129 −0.805645 0.592399i \(-0.798181\pi\)
−0.805645 + 0.592399i \(0.798181\pi\)
\(762\) −23.3622 −0.846324
\(763\) 0 0
\(764\) −24.0000 −0.868290
\(765\) −3.74055 −0.135240
\(766\) 27.8967 1.00795
\(767\) 5.35218 0.193256
\(768\) 20.8469 0.752248
\(769\) 19.7108 0.710791 0.355395 0.934716i \(-0.384346\pi\)
0.355395 + 0.934716i \(0.384346\pi\)
\(770\) 0 0
\(771\) −25.9008 −0.932794
\(772\) 20.1260 0.724351
\(773\) −43.2530 −1.55570 −0.777851 0.628449i \(-0.783690\pi\)
−0.777851 + 0.628449i \(0.783690\pi\)
\(774\) −16.4550 −0.591461
\(775\) −33.9235 −1.21857
\(776\) −3.51941 −0.126340
\(777\) 0 0
\(778\) −8.09775 −0.290318
\(779\) 3.10278 0.111168
\(780\) −7.25443 −0.259750
\(781\) −10.4252 −0.373044
\(782\) −5.51941 −0.197374
\(783\) 4.44082 0.158702
\(784\) 0 0
\(785\) 23.0700 0.823404
\(786\) −11.5295 −0.411242
\(787\) 21.4358 0.764104 0.382052 0.924141i \(-0.375218\pi\)
0.382052 + 0.924141i \(0.375218\pi\)
\(788\) −6.71731 −0.239294
\(789\) −22.4408 −0.798914
\(790\) 31.6655 1.12661
\(791\) 0 0
\(792\) 1.04888 0.0372702
\(793\) 9.77886 0.347258
\(794\) −19.1567 −0.679845
\(795\) 15.2544 0.541019
\(796\) −2.64782 −0.0938496
\(797\) 4.40105 0.155893 0.0779467 0.996958i \(-0.475164\pi\)
0.0779467 + 0.996958i \(0.475164\pi\)
\(798\) 0 0
\(799\) −0.798021 −0.0282319
\(800\) −23.9824 −0.847907
\(801\) −13.2544 −0.468322
\(802\) −23.7350 −0.838112
\(803\) −3.87253 −0.136659
\(804\) −12.9411 −0.456397
\(805\) 0 0
\(806\) 82.9683 2.92243
\(807\) −7.62721 −0.268491
\(808\) 15.2927 0.537997
\(809\) −26.3799 −0.927469 −0.463734 0.885974i \(-0.653491\pi\)
−0.463734 + 0.885974i \(0.653491\pi\)
\(810\) −2.00000 −0.0702728
\(811\) −4.96526 −0.174354 −0.0871769 0.996193i \(-0.527785\pi\)
−0.0871769 + 0.996193i \(0.527785\pi\)
\(812\) 0 0
\(813\) −19.9164 −0.698498
\(814\) −3.07451 −0.107761
\(815\) −14.1133 −0.494369
\(816\) 16.6761 0.583780
\(817\) −28.1517 −0.984902
\(818\) −33.6499 −1.17654
\(819\) 0 0
\(820\) −1.42166 −0.0496466
\(821\) −15.7789 −0.550686 −0.275343 0.961346i \(-0.588791\pi\)
−0.275343 + 0.961346i \(0.588791\pi\)
\(822\) 31.7194 1.10634
\(823\) −8.35166 −0.291121 −0.145560 0.989349i \(-0.546498\pi\)
−0.145560 + 0.989349i \(0.546498\pi\)
\(824\) 0.637776 0.0222180
\(825\) −3.07860 −0.107183
\(826\) 0 0
\(827\) −18.3925 −0.639568 −0.319784 0.947490i \(-0.603610\pi\)
−0.319784 + 0.947490i \(0.603610\pi\)
\(828\) −1.15667 −0.0401972
\(829\) 29.4147 1.02161 0.510807 0.859695i \(-0.329347\pi\)
0.510807 + 0.859695i \(0.329347\pi\)
\(830\) −15.3622 −0.533231
\(831\) −17.6413 −0.611972
\(832\) 8.48059 0.294011
\(833\) 0 0
\(834\) 28.5189 0.987529
\(835\) −10.6167 −0.367404
\(836\) −3.25443 −0.112557
\(837\) 8.96526 0.309885
\(838\) −46.4494 −1.60457
\(839\) 33.4600 1.15517 0.577583 0.816332i \(-0.303996\pi\)
0.577583 + 0.816332i \(0.303996\pi\)
\(840\) 0 0
\(841\) −9.27912 −0.319970
\(842\) 15.7350 0.542264
\(843\) −0.0297193 −0.00102359
\(844\) −11.6655 −0.401544
\(845\) 14.3783 0.494629
\(846\) −0.426686 −0.0146698
\(847\) 0 0
\(848\) −68.0071 −2.33537
\(849\) 10.1814 0.349424
\(850\) −23.2772 −0.798400
\(851\) −1.86947 −0.0640848
\(852\) −16.5189 −0.565928
\(853\) −40.4494 −1.38496 −0.692481 0.721436i \(-0.743482\pi\)
−0.692481 + 0.721436i \(0.743482\pi\)
\(854\) 0 0
\(855\) −3.42166 −0.117018
\(856\) −19.4499 −0.664785
\(857\) −12.4494 −0.425264 −0.212632 0.977132i \(-0.568204\pi\)
−0.212632 + 0.977132i \(0.568204\pi\)
\(858\) 7.52946 0.257052
\(859\) 21.6514 0.738736 0.369368 0.929283i \(-0.379574\pi\)
0.369368 + 0.929283i \(0.379574\pi\)
\(860\) 12.8988 0.439846
\(861\) 0 0
\(862\) −12.8816 −0.438750
\(863\) 19.3778 0.659628 0.329814 0.944046i \(-0.393014\pi\)
0.329814 + 0.944046i \(0.393014\pi\)
\(864\) 6.33804 0.215625
\(865\) −13.1739 −0.447925
\(866\) −19.9945 −0.679439
\(867\) −5.49472 −0.186610
\(868\) 0 0
\(869\) −12.8816 −0.436980
\(870\) −8.88164 −0.301116
\(871\) 51.2233 1.73563
\(872\) 6.57834 0.222771
\(873\) −2.72999 −0.0923961
\(874\) −5.04888 −0.170781
\(875\) 0 0
\(876\) −6.13607 −0.207318
\(877\) −3.08413 −0.104144 −0.0520719 0.998643i \(-0.516583\pi\)
−0.0520719 + 0.998643i \(0.516583\pi\)
\(878\) −2.40105 −0.0810316
\(879\) −3.14808 −0.106182
\(880\) −4.41110 −0.148698
\(881\) 34.5783 1.16497 0.582487 0.812840i \(-0.302080\pi\)
0.582487 + 0.812840i \(0.302080\pi\)
\(882\) 0 0
\(883\) −9.64280 −0.324506 −0.162253 0.986749i \(-0.551876\pi\)
−0.162253 + 0.986749i \(0.551876\pi\)
\(884\) 22.3133 0.750479
\(885\) −1.15667 −0.0388812
\(886\) −28.2721 −0.949821
\(887\) −32.2041 −1.08131 −0.540654 0.841245i \(-0.681823\pi\)
−0.540654 + 0.841245i \(0.681823\pi\)
\(888\) 2.68614 0.0901408
\(889\) 0 0
\(890\) 26.5089 0.888579
\(891\) 0.813607 0.0272568
\(892\) −32.0000 −1.07144
\(893\) −0.729988 −0.0244281
\(894\) −20.9794 −0.701656
\(895\) −2.35720 −0.0787925
\(896\) 0 0
\(897\) 4.57834 0.152866
\(898\) 59.4571 1.98411
\(899\) 39.8131 1.32784
\(900\) −4.87807 −0.162602
\(901\) −46.9200 −1.56313
\(902\) 1.47556 0.0491308
\(903\) 0 0
\(904\) −22.5783 −0.750944
\(905\) 2.02113 0.0671845
\(906\) −34.9200 −1.16014
\(907\) −17.8227 −0.591794 −0.295897 0.955220i \(-0.595618\pi\)
−0.295897 + 0.955220i \(0.595618\pi\)
\(908\) −21.4600 −0.712174
\(909\) 11.8625 0.393454
\(910\) 0 0
\(911\) −20.7894 −0.688784 −0.344392 0.938826i \(-0.611915\pi\)
−0.344392 + 0.938826i \(0.611915\pi\)
\(912\) 15.2544 0.505125
\(913\) 6.24940 0.206825
\(914\) 25.6938 0.849875
\(915\) −2.11334 −0.0698648
\(916\) 20.3416 0.672106
\(917\) 0 0
\(918\) 6.15165 0.203035
\(919\) 33.8555 1.11679 0.558395 0.829575i \(-0.311417\pi\)
0.558395 + 0.829575i \(0.311417\pi\)
\(920\) −1.27555 −0.0420537
\(921\) 12.7980 0.421709
\(922\) −54.5472 −1.79642
\(923\) 65.3850 2.15217
\(924\) 0 0
\(925\) −7.88418 −0.259230
\(926\) 43.3028 1.42302
\(927\) 0.494719 0.0162487
\(928\) 28.1461 0.923941
\(929\) 4.10635 0.134725 0.0673624 0.997729i \(-0.478542\pi\)
0.0673624 + 0.997729i \(0.478542\pi\)
\(930\) −17.9305 −0.587965
\(931\) 0 0
\(932\) −32.1260 −1.05232
\(933\) −26.6167 −0.871390
\(934\) −17.6555 −0.577705
\(935\) −3.04334 −0.0995277
\(936\) −6.57834 −0.215020
\(937\) −13.3028 −0.434583 −0.217292 0.976107i \(-0.569722\pi\)
−0.217292 + 0.976107i \(0.569722\pi\)
\(938\) 0 0
\(939\) 3.00502 0.0980652
\(940\) 0.334474 0.0109093
\(941\) 11.7633 0.383472 0.191736 0.981447i \(-0.438588\pi\)
0.191736 + 0.981447i \(0.438588\pi\)
\(942\) −37.9406 −1.23617
\(943\) 0.897225 0.0292177
\(944\) 5.15667 0.167835
\(945\) 0 0
\(946\) −13.3879 −0.435277
\(947\) 1.40054 0.0455114 0.0227557 0.999741i \(-0.492756\pi\)
0.0227557 + 0.999741i \(0.492756\pi\)
\(948\) −20.4111 −0.662922
\(949\) 24.2877 0.788413
\(950\) −21.2927 −0.690828
\(951\) −4.33302 −0.140508
\(952\) 0 0
\(953\) 33.7577 1.09352 0.546760 0.837289i \(-0.315861\pi\)
0.546760 + 0.837289i \(0.315861\pi\)
\(954\) −25.0872 −0.812228
\(955\) −20.5300 −0.664334
\(956\) −3.80450 −0.123046
\(957\) 3.61308 0.116794
\(958\) −2.13343 −0.0689280
\(959\) 0 0
\(960\) −1.83276 −0.0591522
\(961\) 49.3758 1.59277
\(962\) 19.2827 0.621699
\(963\) −15.0872 −0.486178
\(964\) 21.3905 0.688941
\(965\) 17.2161 0.554206
\(966\) 0 0
\(967\) −10.4806 −0.337033 −0.168516 0.985699i \(-0.553898\pi\)
−0.168516 + 0.985699i \(0.553898\pi\)
\(968\) −13.3275 −0.428361
\(969\) 10.5244 0.338094
\(970\) 5.45998 0.175309
\(971\) −57.6358 −1.84962 −0.924811 0.380428i \(-0.875777\pi\)
−0.924811 + 0.380428i \(0.875777\pi\)
\(972\) 1.28917 0.0413501
\(973\) 0 0
\(974\) −37.3649 −1.19725
\(975\) 19.3083 0.618361
\(976\) 9.42166 0.301580
\(977\) 41.9008 1.34053 0.670263 0.742124i \(-0.266181\pi\)
0.670263 + 0.742124i \(0.266181\pi\)
\(978\) 23.2106 0.742192
\(979\) −10.7839 −0.344655
\(980\) 0 0
\(981\) 5.10278 0.162919
\(982\) −25.7350 −0.821237
\(983\) 18.4056 0.587046 0.293523 0.955952i \(-0.405172\pi\)
0.293523 + 0.955952i \(0.405172\pi\)
\(984\) −1.28917 −0.0410972
\(985\) −5.74609 −0.183086
\(986\) 27.3184 0.869994
\(987\) 0 0
\(988\) 20.4111 0.649364
\(989\) −8.14057 −0.258855
\(990\) −1.62721 −0.0517162
\(991\) 26.0666 0.828032 0.414016 0.910270i \(-0.364126\pi\)
0.414016 + 0.910270i \(0.364126\pi\)
\(992\) 56.8222 1.80411
\(993\) 5.53500 0.175648
\(994\) 0 0
\(995\) −2.26499 −0.0718050
\(996\) 9.90225 0.313765
\(997\) 29.8483 0.945307 0.472653 0.881248i \(-0.343296\pi\)
0.472653 + 0.881248i \(0.343296\pi\)
\(998\) 38.9200 1.23199
\(999\) 2.08362 0.0659228
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 \(a_p\))