Properties

Label 8047.2.a.b.1.2
Level 8047
Weight 2
Character 8047.1
Self dual Yes
Analytic conductor 64.256
Analytic rank 1
Dimension 142
CM No

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Newspace parameters

Level: \( N \) = \( 8047 = 13 \cdot 619 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8047.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2556185065\)
Analytic rank: \(1\)
Dimension: \(142\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Character \(\chi\) = 8047.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.78511 q^{2} -1.73890 q^{3} +5.75683 q^{4} -2.18885 q^{5} +4.84303 q^{6} +2.36535 q^{7} -10.4632 q^{8} +0.0237834 q^{9} +O(q^{10})\) \(q-2.78511 q^{2} -1.73890 q^{3} +5.75683 q^{4} -2.18885 q^{5} +4.84303 q^{6} +2.36535 q^{7} -10.4632 q^{8} +0.0237834 q^{9} +6.09618 q^{10} -0.884308 q^{11} -10.0106 q^{12} +1.00000 q^{13} -6.58775 q^{14} +3.80620 q^{15} +17.6275 q^{16} +2.18187 q^{17} -0.0662393 q^{18} +5.05652 q^{19} -12.6008 q^{20} -4.11311 q^{21} +2.46290 q^{22} -2.02538 q^{23} +18.1945 q^{24} -0.208939 q^{25} -2.78511 q^{26} +5.17535 q^{27} +13.6169 q^{28} +2.80291 q^{29} -10.6007 q^{30} -0.680434 q^{31} -28.1680 q^{32} +1.53773 q^{33} -6.07675 q^{34} -5.17739 q^{35} +0.136917 q^{36} -7.27254 q^{37} -14.0830 q^{38} -1.73890 q^{39} +22.9023 q^{40} +6.76115 q^{41} +11.4555 q^{42} -6.39506 q^{43} -5.09082 q^{44} -0.0520583 q^{45} +5.64092 q^{46} +1.37604 q^{47} -30.6524 q^{48} -1.40513 q^{49} +0.581917 q^{50} -3.79406 q^{51} +5.75683 q^{52} -9.65347 q^{53} -14.4139 q^{54} +1.93562 q^{55} -24.7491 q^{56} -8.79280 q^{57} -7.80640 q^{58} -2.37713 q^{59} +21.9116 q^{60} +2.69248 q^{61} +1.89508 q^{62} +0.0562560 q^{63} +43.1961 q^{64} -2.18885 q^{65} -4.28274 q^{66} +15.6747 q^{67} +12.5607 q^{68} +3.52195 q^{69} +14.4196 q^{70} -11.3057 q^{71} -0.248850 q^{72} +7.49476 q^{73} +20.2548 q^{74} +0.363324 q^{75} +29.1096 q^{76} -2.09170 q^{77} +4.84303 q^{78} +2.06278 q^{79} -38.5839 q^{80} -9.07078 q^{81} -18.8305 q^{82} -7.30157 q^{83} -23.6785 q^{84} -4.77579 q^{85} +17.8109 q^{86} -4.87398 q^{87} +9.25269 q^{88} +5.77496 q^{89} +0.144988 q^{90} +2.36535 q^{91} -11.6598 q^{92} +1.18321 q^{93} -3.83242 q^{94} -11.0680 q^{95} +48.9815 q^{96} -1.09513 q^{97} +3.91344 q^{98} -0.0210318 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 142q - 13q^{2} - 26q^{3} + 129q^{4} - 37q^{5} - 15q^{6} - 14q^{7} - 39q^{8} + 98q^{9} + O(q^{10}) \) \( 142q - 13q^{2} - 26q^{3} + 129q^{4} - 37q^{5} - 15q^{6} - 14q^{7} - 39q^{8} + 98q^{9} - 25q^{10} - 25q^{11} - 62q^{12} + 142q^{13} - 57q^{14} - 14q^{15} + 111q^{16} - 141q^{17} - 29q^{18} - 3q^{19} - 87q^{20} - 19q^{21} - 24q^{22} - 69q^{23} - 40q^{24} + 87q^{25} - 13q^{26} - 95q^{27} - 34q^{28} - 147q^{29} - 2q^{30} - 21q^{31} - 66q^{32} - 62q^{33} - 6q^{34} - 59q^{35} + 74q^{36} - 37q^{37} - 76q^{38} - 26q^{39} - 61q^{40} - 97q^{41} - 29q^{42} - 33q^{43} - 57q^{44} - 86q^{45} - q^{46} - 102q^{47} - 141q^{48} + 70q^{49} - 28q^{50} - 13q^{51} + 129q^{52} - 137q^{53} - 29q^{54} - 24q^{55} - 130q^{56} - 65q^{57} - 15q^{58} - 56q^{59} + 11q^{60} - 77q^{61} - 150q^{62} - 32q^{63} + 73q^{64} - 37q^{65} - 32q^{66} - 9q^{67} - 226q^{68} - 113q^{69} + 6q^{70} - 18q^{71} - 82q^{72} - 117q^{73} - 70q^{74} - 83q^{75} + 40q^{76} - 214q^{77} - 15q^{78} - 52q^{79} - 161q^{80} - 10q^{81} - 36q^{82} - 74q^{83} + 53q^{84} + 2q^{85} + 17q^{86} - 49q^{87} - 29q^{88} - 171q^{89} - 57q^{90} - 14q^{91} - 187q^{92} - 39q^{93} + 13q^{94} - 150q^{95} - 47q^{96} - 126q^{97} - 85q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.78511 −1.96937 −0.984685 0.174344i \(-0.944219\pi\)
−0.984685 + 0.174344i \(0.944219\pi\)
\(3\) −1.73890 −1.00396 −0.501978 0.864880i \(-0.667394\pi\)
−0.501978 + 0.864880i \(0.667394\pi\)
\(4\) 5.75683 2.87842
\(5\) −2.18885 −0.978883 −0.489442 0.872036i \(-0.662799\pi\)
−0.489442 + 0.872036i \(0.662799\pi\)
\(6\) 4.84303 1.97716
\(7\) 2.36535 0.894017 0.447009 0.894530i \(-0.352489\pi\)
0.447009 + 0.894530i \(0.352489\pi\)
\(8\) −10.4632 −3.69930
\(9\) 0.0237834 0.00792780
\(10\) 6.09618 1.92778
\(11\) −0.884308 −0.266629 −0.133315 0.991074i \(-0.542562\pi\)
−0.133315 + 0.991074i \(0.542562\pi\)
\(12\) −10.0106 −2.88980
\(13\) 1.00000 0.277350
\(14\) −6.58775 −1.76065
\(15\) 3.80620 0.982756
\(16\) 17.6275 4.40687
\(17\) 2.18187 0.529182 0.264591 0.964361i \(-0.414763\pi\)
0.264591 + 0.964361i \(0.414763\pi\)
\(18\) −0.0662393 −0.0156128
\(19\) 5.05652 1.16005 0.580023 0.814600i \(-0.303044\pi\)
0.580023 + 0.814600i \(0.303044\pi\)
\(20\) −12.6008 −2.81763
\(21\) −4.11311 −0.897554
\(22\) 2.46290 0.525091
\(23\) −2.02538 −0.422322 −0.211161 0.977451i \(-0.567724\pi\)
−0.211161 + 0.977451i \(0.567724\pi\)
\(24\) 18.1945 3.71393
\(25\) −0.208939 −0.0417877
\(26\) −2.78511 −0.546205
\(27\) 5.17535 0.995997
\(28\) 13.6169 2.57335
\(29\) 2.80291 0.520487 0.260243 0.965543i \(-0.416197\pi\)
0.260243 + 0.965543i \(0.416197\pi\)
\(30\) −10.6007 −1.93541
\(31\) −0.680434 −0.122210 −0.0611048 0.998131i \(-0.519462\pi\)
−0.0611048 + 0.998131i \(0.519462\pi\)
\(32\) −28.1680 −4.97945
\(33\) 1.53773 0.267684
\(34\) −6.07675 −1.04215
\(35\) −5.17739 −0.875139
\(36\) 0.136917 0.0228195
\(37\) −7.27254 −1.19560 −0.597799 0.801646i \(-0.703958\pi\)
−0.597799 + 0.801646i \(0.703958\pi\)
\(38\) −14.0830 −2.28456
\(39\) −1.73890 −0.278447
\(40\) 22.9023 3.62118
\(41\) 6.76115 1.05591 0.527957 0.849271i \(-0.322958\pi\)
0.527957 + 0.849271i \(0.322958\pi\)
\(42\) 11.4555 1.76762
\(43\) −6.39506 −0.975237 −0.487619 0.873057i \(-0.662134\pi\)
−0.487619 + 0.873057i \(0.662134\pi\)
\(44\) −5.09082 −0.767469
\(45\) −0.0520583 −0.00776039
\(46\) 5.64092 0.831708
\(47\) 1.37604 0.200716 0.100358 0.994951i \(-0.468001\pi\)
0.100358 + 0.994951i \(0.468001\pi\)
\(48\) −30.6524 −4.42430
\(49\) −1.40513 −0.200733
\(50\) 0.581917 0.0822954
\(51\) −3.79406 −0.531275
\(52\) 5.75683 0.798329
\(53\) −9.65347 −1.32601 −0.663003 0.748617i \(-0.730718\pi\)
−0.663003 + 0.748617i \(0.730718\pi\)
\(54\) −14.4139 −1.96149
\(55\) 1.93562 0.260999
\(56\) −24.7491 −3.30724
\(57\) −8.79280 −1.16464
\(58\) −7.80640 −1.02503
\(59\) −2.37713 −0.309476 −0.154738 0.987956i \(-0.549453\pi\)
−0.154738 + 0.987956i \(0.549453\pi\)
\(60\) 21.9116 2.82878
\(61\) 2.69248 0.344737 0.172368 0.985033i \(-0.444858\pi\)
0.172368 + 0.985033i \(0.444858\pi\)
\(62\) 1.89508 0.240676
\(63\) 0.0562560 0.00708759
\(64\) 43.1961 5.39951
\(65\) −2.18885 −0.271493
\(66\) −4.28274 −0.527168
\(67\) 15.6747 1.91497 0.957486 0.288478i \(-0.0931494\pi\)
0.957486 + 0.288478i \(0.0931494\pi\)
\(68\) 12.5607 1.52321
\(69\) 3.52195 0.423993
\(70\) 14.4196 1.72347
\(71\) −11.3057 −1.34174 −0.670868 0.741577i \(-0.734078\pi\)
−0.670868 + 0.741577i \(0.734078\pi\)
\(72\) −0.248850 −0.0293273
\(73\) 7.49476 0.877195 0.438598 0.898684i \(-0.355475\pi\)
0.438598 + 0.898684i \(0.355475\pi\)
\(74\) 20.2548 2.35458
\(75\) 0.363324 0.0419530
\(76\) 29.1096 3.33910
\(77\) −2.09170 −0.238371
\(78\) 4.84303 0.548366
\(79\) 2.06278 0.232080 0.116040 0.993245i \(-0.462980\pi\)
0.116040 + 0.993245i \(0.462980\pi\)
\(80\) −38.5839 −4.31381
\(81\) −9.07078 −1.00786
\(82\) −18.8305 −2.07949
\(83\) −7.30157 −0.801452 −0.400726 0.916198i \(-0.631242\pi\)
−0.400726 + 0.916198i \(0.631242\pi\)
\(84\) −23.6785 −2.58353
\(85\) −4.77579 −0.518007
\(86\) 17.8109 1.92060
\(87\) −4.87398 −0.522546
\(88\) 9.25269 0.986340
\(89\) 5.77496 0.612144 0.306072 0.952008i \(-0.400985\pi\)
0.306072 + 0.952008i \(0.400985\pi\)
\(90\) 0.144988 0.0152831
\(91\) 2.36535 0.247956
\(92\) −11.6598 −1.21562
\(93\) 1.18321 0.122693
\(94\) −3.83242 −0.395284
\(95\) −11.0680 −1.13555
\(96\) 48.9815 4.99915
\(97\) −1.09513 −0.111194 −0.0555969 0.998453i \(-0.517706\pi\)
−0.0555969 + 0.998453i \(0.517706\pi\)
\(98\) 3.91344 0.395317
\(99\) −0.0210318 −0.00211378
\(100\) −1.20282 −0.120282
\(101\) −3.54503 −0.352743 −0.176372 0.984324i \(-0.556436\pi\)
−0.176372 + 0.984324i \(0.556436\pi\)
\(102\) 10.5669 1.04628
\(103\) −8.55320 −0.842772 −0.421386 0.906881i \(-0.638456\pi\)
−0.421386 + 0.906881i \(0.638456\pi\)
\(104\) −10.4632 −1.02600
\(105\) 9.00298 0.878601
\(106\) 26.8860 2.61140
\(107\) 2.04408 0.197609 0.0988043 0.995107i \(-0.468498\pi\)
0.0988043 + 0.995107i \(0.468498\pi\)
\(108\) 29.7936 2.86689
\(109\) 2.71863 0.260398 0.130199 0.991488i \(-0.458438\pi\)
0.130199 + 0.991488i \(0.458438\pi\)
\(110\) −5.39091 −0.514003
\(111\) 12.6462 1.20033
\(112\) 41.6951 3.93981
\(113\) −0.565582 −0.0532055 −0.0266027 0.999646i \(-0.508469\pi\)
−0.0266027 + 0.999646i \(0.508469\pi\)
\(114\) 24.4889 2.29360
\(115\) 4.43326 0.413404
\(116\) 16.1359 1.49818
\(117\) 0.0237834 0.00219877
\(118\) 6.62056 0.609472
\(119\) 5.16089 0.473098
\(120\) −39.8250 −3.63550
\(121\) −10.2180 −0.928909
\(122\) −7.49885 −0.678914
\(123\) −11.7570 −1.06009
\(124\) −3.91715 −0.351770
\(125\) 11.4016 1.01979
\(126\) −0.156679 −0.0139581
\(127\) −2.01559 −0.178854 −0.0894272 0.995993i \(-0.528504\pi\)
−0.0894272 + 0.995993i \(0.528504\pi\)
\(128\) −63.9698 −5.65418
\(129\) 11.1204 0.979095
\(130\) 6.09618 0.534671
\(131\) 4.55412 0.397896 0.198948 0.980010i \(-0.436248\pi\)
0.198948 + 0.980010i \(0.436248\pi\)
\(132\) 8.85243 0.770505
\(133\) 11.9604 1.03710
\(134\) −43.6558 −3.77129
\(135\) −11.3281 −0.974965
\(136\) −22.8293 −1.95760
\(137\) 1.77598 0.151732 0.0758661 0.997118i \(-0.475828\pi\)
0.0758661 + 0.997118i \(0.475828\pi\)
\(138\) −9.80901 −0.834998
\(139\) −9.18282 −0.778876 −0.389438 0.921053i \(-0.627331\pi\)
−0.389438 + 0.921053i \(0.627331\pi\)
\(140\) −29.8054 −2.51901
\(141\) −2.39280 −0.201510
\(142\) 31.4875 2.64237
\(143\) −0.884308 −0.0739496
\(144\) 0.419241 0.0349367
\(145\) −6.13514 −0.509496
\(146\) −20.8737 −1.72752
\(147\) 2.44339 0.201527
\(148\) −41.8668 −3.44143
\(149\) 6.15017 0.503842 0.251921 0.967748i \(-0.418938\pi\)
0.251921 + 0.967748i \(0.418938\pi\)
\(150\) −1.01190 −0.0826210
\(151\) 0.941732 0.0766370 0.0383185 0.999266i \(-0.487800\pi\)
0.0383185 + 0.999266i \(0.487800\pi\)
\(152\) −52.9074 −4.29135
\(153\) 0.0518923 0.00419524
\(154\) 5.82560 0.469441
\(155\) 1.48937 0.119629
\(156\) −10.0106 −0.801487
\(157\) −0.495225 −0.0395232 −0.0197616 0.999805i \(-0.506291\pi\)
−0.0197616 + 0.999805i \(0.506291\pi\)
\(158\) −5.74505 −0.457052
\(159\) 16.7864 1.33125
\(160\) 61.6556 4.87430
\(161\) −4.79074 −0.377563
\(162\) 25.2631 1.98486
\(163\) −5.32403 −0.417010 −0.208505 0.978021i \(-0.566860\pi\)
−0.208505 + 0.978021i \(0.566860\pi\)
\(164\) 38.9228 3.03936
\(165\) −3.36585 −0.262031
\(166\) 20.3357 1.57835
\(167\) −9.14210 −0.707437 −0.353718 0.935352i \(-0.615083\pi\)
−0.353718 + 0.935352i \(0.615083\pi\)
\(168\) 43.0363 3.32032
\(169\) 1.00000 0.0769231
\(170\) 13.3011 1.02015
\(171\) 0.120261 0.00919661
\(172\) −36.8153 −2.80714
\(173\) −14.4980 −1.10226 −0.551132 0.834418i \(-0.685804\pi\)
−0.551132 + 0.834418i \(0.685804\pi\)
\(174\) 13.5746 1.02909
\(175\) −0.494212 −0.0373589
\(176\) −15.5881 −1.17500
\(177\) 4.13359 0.310700
\(178\) −16.0839 −1.20554
\(179\) 3.15629 0.235912 0.117956 0.993019i \(-0.462366\pi\)
0.117956 + 0.993019i \(0.462366\pi\)
\(180\) −0.299691 −0.0223376
\(181\) 14.3284 1.06502 0.532511 0.846423i \(-0.321249\pi\)
0.532511 + 0.846423i \(0.321249\pi\)
\(182\) −6.58775 −0.488317
\(183\) −4.68196 −0.346101
\(184\) 21.1920 1.56229
\(185\) 15.9185 1.17035
\(186\) −3.29537 −0.241628
\(187\) −1.92945 −0.141095
\(188\) 7.92163 0.577744
\(189\) 12.2415 0.890439
\(190\) 30.8255 2.23632
\(191\) −7.03178 −0.508802 −0.254401 0.967099i \(-0.581878\pi\)
−0.254401 + 0.967099i \(0.581878\pi\)
\(192\) −75.1138 −5.42087
\(193\) −17.5125 −1.26058 −0.630289 0.776360i \(-0.717064\pi\)
−0.630289 + 0.776360i \(0.717064\pi\)
\(194\) 3.05006 0.218982
\(195\) 3.80620 0.272567
\(196\) −8.08910 −0.577793
\(197\) 9.54771 0.680246 0.340123 0.940381i \(-0.389531\pi\)
0.340123 + 0.940381i \(0.389531\pi\)
\(198\) 0.0585760 0.00416281
\(199\) 12.7444 0.903423 0.451712 0.892164i \(-0.350814\pi\)
0.451712 + 0.892164i \(0.350814\pi\)
\(200\) 2.18616 0.154585
\(201\) −27.2568 −1.92255
\(202\) 9.87328 0.694682
\(203\) 6.62985 0.465324
\(204\) −21.8418 −1.52923
\(205\) −14.7991 −1.03362
\(206\) 23.8216 1.65973
\(207\) −0.0481705 −0.00334808
\(208\) 17.6275 1.22224
\(209\) −4.47153 −0.309302
\(210\) −25.0743 −1.73029
\(211\) −11.7716 −0.810389 −0.405195 0.914230i \(-0.632796\pi\)
−0.405195 + 0.914230i \(0.632796\pi\)
\(212\) −55.5734 −3.81680
\(213\) 19.6595 1.34704
\(214\) −5.69298 −0.389164
\(215\) 13.9978 0.954643
\(216\) −54.1507 −3.68449
\(217\) −1.60946 −0.109257
\(218\) −7.57169 −0.512820
\(219\) −13.0327 −0.880665
\(220\) 11.1430 0.751263
\(221\) 2.18187 0.146769
\(222\) −35.2212 −2.36389
\(223\) 2.34501 0.157034 0.0785169 0.996913i \(-0.474982\pi\)
0.0785169 + 0.996913i \(0.474982\pi\)
\(224\) −66.6272 −4.45171
\(225\) −0.00496927 −0.000331284 0
\(226\) 1.57521 0.104781
\(227\) 2.13254 0.141542 0.0707709 0.997493i \(-0.477454\pi\)
0.0707709 + 0.997493i \(0.477454\pi\)
\(228\) −50.6187 −3.35231
\(229\) 0.0358487 0.00236895 0.00118447 0.999999i \(-0.499623\pi\)
0.00118447 + 0.999999i \(0.499623\pi\)
\(230\) −12.3471 −0.814145
\(231\) 3.63726 0.239314
\(232\) −29.3274 −1.92544
\(233\) −8.03189 −0.526186 −0.263093 0.964770i \(-0.584743\pi\)
−0.263093 + 0.964770i \(0.584743\pi\)
\(234\) −0.0662393 −0.00433020
\(235\) −3.01194 −0.196477
\(236\) −13.6847 −0.890800
\(237\) −3.58697 −0.232998
\(238\) −14.3736 −0.931704
\(239\) 9.64443 0.623847 0.311923 0.950107i \(-0.399027\pi\)
0.311923 + 0.950107i \(0.399027\pi\)
\(240\) 67.0936 4.33087
\(241\) 27.7024 1.78447 0.892235 0.451572i \(-0.149136\pi\)
0.892235 + 0.451572i \(0.149136\pi\)
\(242\) 28.4582 1.82937
\(243\) 0.247158 0.0158552
\(244\) 15.5002 0.992296
\(245\) 3.07562 0.196494
\(246\) 32.7445 2.08771
\(247\) 5.05652 0.321739
\(248\) 7.11951 0.452089
\(249\) 12.6967 0.804622
\(250\) −31.7546 −2.00834
\(251\) 2.69835 0.170318 0.0851590 0.996367i \(-0.472860\pi\)
0.0851590 + 0.996367i \(0.472860\pi\)
\(252\) 0.323856 0.0204010
\(253\) 1.79106 0.112603
\(254\) 5.61363 0.352231
\(255\) 8.30463 0.520056
\(256\) 91.7707 5.73567
\(257\) 22.7630 1.41992 0.709958 0.704244i \(-0.248714\pi\)
0.709958 + 0.704244i \(0.248714\pi\)
\(258\) −30.9715 −1.92820
\(259\) −17.2021 −1.06889
\(260\) −12.6008 −0.781471
\(261\) 0.0666626 0.00412631
\(262\) −12.6837 −0.783603
\(263\) −23.4915 −1.44855 −0.724275 0.689511i \(-0.757825\pi\)
−0.724275 + 0.689511i \(0.757825\pi\)
\(264\) −16.0895 −0.990242
\(265\) 21.1300 1.29801
\(266\) −33.3111 −2.04244
\(267\) −10.0421 −0.614566
\(268\) 90.2368 5.51209
\(269\) 3.10455 0.189287 0.0946437 0.995511i \(-0.469829\pi\)
0.0946437 + 0.995511i \(0.469829\pi\)
\(270\) 31.5499 1.92007
\(271\) 8.07182 0.490328 0.245164 0.969482i \(-0.421158\pi\)
0.245164 + 0.969482i \(0.421158\pi\)
\(272\) 38.4609 2.33203
\(273\) −4.11311 −0.248937
\(274\) −4.94630 −0.298817
\(275\) 0.184766 0.0111418
\(276\) 20.2753 1.22043
\(277\) −7.11393 −0.427435 −0.213717 0.976896i \(-0.568557\pi\)
−0.213717 + 0.976896i \(0.568557\pi\)
\(278\) 25.5751 1.53390
\(279\) −0.0161830 −0.000968853 0
\(280\) 54.1720 3.23740
\(281\) 3.10347 0.185137 0.0925687 0.995706i \(-0.470492\pi\)
0.0925687 + 0.995706i \(0.470492\pi\)
\(282\) 6.66420 0.396848
\(283\) 2.59717 0.154386 0.0771929 0.997016i \(-0.475404\pi\)
0.0771929 + 0.997016i \(0.475404\pi\)
\(284\) −65.0848 −3.86207
\(285\) 19.2461 1.14004
\(286\) 2.46290 0.145634
\(287\) 15.9925 0.944006
\(288\) −0.669931 −0.0394761
\(289\) −12.2394 −0.719967
\(290\) 17.0870 1.00339
\(291\) 1.90433 0.111634
\(292\) 43.1461 2.52493
\(293\) 24.8172 1.44983 0.724917 0.688836i \(-0.241878\pi\)
0.724917 + 0.688836i \(0.241878\pi\)
\(294\) −6.80510 −0.396881
\(295\) 5.20318 0.302941
\(296\) 76.0940 4.42287
\(297\) −4.57661 −0.265562
\(298\) −17.1289 −0.992251
\(299\) −2.02538 −0.117131
\(300\) 2.09159 0.120758
\(301\) −15.1265 −0.871879
\(302\) −2.62283 −0.150927
\(303\) 6.16446 0.354139
\(304\) 89.1337 5.11217
\(305\) −5.89344 −0.337457
\(306\) −0.144526 −0.00826199
\(307\) 18.2343 1.04069 0.520344 0.853957i \(-0.325804\pi\)
0.520344 + 0.853957i \(0.325804\pi\)
\(308\) −12.0415 −0.686131
\(309\) 14.8732 0.846106
\(310\) −4.14805 −0.235594
\(311\) 11.6548 0.660885 0.330442 0.943826i \(-0.392802\pi\)
0.330442 + 0.943826i \(0.392802\pi\)
\(312\) 18.1945 1.03006
\(313\) 20.4370 1.15517 0.577583 0.816332i \(-0.303996\pi\)
0.577583 + 0.816332i \(0.303996\pi\)
\(314\) 1.37926 0.0778359
\(315\) −0.123136 −0.00693792
\(316\) 11.8751 0.668024
\(317\) −15.7017 −0.881893 −0.440946 0.897533i \(-0.645357\pi\)
−0.440946 + 0.897533i \(0.645357\pi\)
\(318\) −46.7521 −2.62173
\(319\) −2.47863 −0.138777
\(320\) −94.5497 −5.28549
\(321\) −3.55446 −0.198390
\(322\) 13.3427 0.743561
\(323\) 11.0327 0.613875
\(324\) −52.2190 −2.90106
\(325\) −0.208939 −0.0115898
\(326\) 14.8280 0.821247
\(327\) −4.72744 −0.261428
\(328\) −70.7432 −3.90614
\(329\) 3.25481 0.179444
\(330\) 9.37426 0.516036
\(331\) 6.21351 0.341525 0.170763 0.985312i \(-0.445377\pi\)
0.170763 + 0.985312i \(0.445377\pi\)
\(332\) −42.0339 −2.30691
\(333\) −0.172966 −0.00947846
\(334\) 25.4617 1.39320
\(335\) −34.3096 −1.87453
\(336\) −72.5037 −3.95540
\(337\) −7.97675 −0.434521 −0.217261 0.976114i \(-0.569712\pi\)
−0.217261 + 0.976114i \(0.569712\pi\)
\(338\) −2.78511 −0.151490
\(339\) 0.983492 0.0534159
\(340\) −27.4934 −1.49104
\(341\) 0.601714 0.0325846
\(342\) −0.334941 −0.0181115
\(343\) −19.8811 −1.07348
\(344\) 66.9127 3.60769
\(345\) −7.70901 −0.415039
\(346\) 40.3786 2.17077
\(347\) −14.6340 −0.785594 −0.392797 0.919625i \(-0.628492\pi\)
−0.392797 + 0.919625i \(0.628492\pi\)
\(348\) −28.0587 −1.50410
\(349\) 27.2934 1.46098 0.730491 0.682923i \(-0.239291\pi\)
0.730491 + 0.682923i \(0.239291\pi\)
\(350\) 1.37644 0.0735736
\(351\) 5.17535 0.276240
\(352\) 24.9092 1.32767
\(353\) −14.5383 −0.773797 −0.386899 0.922122i \(-0.626454\pi\)
−0.386899 + 0.922122i \(0.626454\pi\)
\(354\) −11.5125 −0.611883
\(355\) 24.7464 1.31340
\(356\) 33.2455 1.76201
\(357\) −8.97428 −0.474969
\(358\) −8.79061 −0.464598
\(359\) −26.0971 −1.37735 −0.688676 0.725070i \(-0.741808\pi\)
−0.688676 + 0.725070i \(0.741808\pi\)
\(360\) 0.544695 0.0287080
\(361\) 6.56844 0.345707
\(362\) −39.9061 −2.09742
\(363\) 17.7681 0.932584
\(364\) 13.6169 0.713720
\(365\) −16.4049 −0.858671
\(366\) 13.0398 0.681600
\(367\) 18.3993 0.960438 0.480219 0.877149i \(-0.340557\pi\)
0.480219 + 0.877149i \(0.340557\pi\)
\(368\) −35.7024 −1.86112
\(369\) 0.160803 0.00837107
\(370\) −44.3348 −2.30485
\(371\) −22.8338 −1.18547
\(372\) 6.81154 0.353162
\(373\) −11.8325 −0.612664 −0.306332 0.951925i \(-0.599102\pi\)
−0.306332 + 0.951925i \(0.599102\pi\)
\(374\) 5.37372 0.277869
\(375\) −19.8262 −1.02382
\(376\) −14.3978 −0.742508
\(377\) 2.80291 0.144357
\(378\) −34.0939 −1.75360
\(379\) 29.2141 1.50063 0.750315 0.661081i \(-0.229902\pi\)
0.750315 + 0.661081i \(0.229902\pi\)
\(380\) −63.7165 −3.26859
\(381\) 3.50491 0.179562
\(382\) 19.5843 1.00202
\(383\) 7.93469 0.405444 0.202722 0.979236i \(-0.435021\pi\)
0.202722 + 0.979236i \(0.435021\pi\)
\(384\) 111.237 5.67655
\(385\) 4.57841 0.233337
\(386\) 48.7743 2.48254
\(387\) −0.152096 −0.00773148
\(388\) −6.30449 −0.320062
\(389\) 27.9382 1.41652 0.708260 0.705951i \(-0.249480\pi\)
0.708260 + 0.705951i \(0.249480\pi\)
\(390\) −10.6007 −0.536786
\(391\) −4.41913 −0.223485
\(392\) 14.7021 0.742571
\(393\) −7.91918 −0.399470
\(394\) −26.5914 −1.33966
\(395\) −4.51510 −0.227180
\(396\) −0.121077 −0.00608434
\(397\) 3.21804 0.161509 0.0807544 0.996734i \(-0.474267\pi\)
0.0807544 + 0.996734i \(0.474267\pi\)
\(398\) −35.4944 −1.77917
\(399\) −20.7980 −1.04120
\(400\) −3.68306 −0.184153
\(401\) −32.3688 −1.61642 −0.808211 0.588893i \(-0.799564\pi\)
−0.808211 + 0.588893i \(0.799564\pi\)
\(402\) 75.9132 3.78621
\(403\) −0.680434 −0.0338948
\(404\) −20.4081 −1.01534
\(405\) 19.8546 0.986582
\(406\) −18.4649 −0.916396
\(407\) 6.43117 0.318781
\(408\) 39.6980 1.96534
\(409\) −23.3367 −1.15393 −0.576963 0.816770i \(-0.695762\pi\)
−0.576963 + 0.816770i \(0.695762\pi\)
\(410\) 41.2172 2.03557
\(411\) −3.08826 −0.152333
\(412\) −49.2394 −2.42585
\(413\) −5.62273 −0.276677
\(414\) 0.134160 0.00659361
\(415\) 15.9820 0.784527
\(416\) −28.1680 −1.38105
\(417\) 15.9680 0.781958
\(418\) 12.4537 0.609130
\(419\) 2.18340 0.106666 0.0533330 0.998577i \(-0.483016\pi\)
0.0533330 + 0.998577i \(0.483016\pi\)
\(420\) 51.8286 2.52898
\(421\) 32.2238 1.57049 0.785246 0.619183i \(-0.212536\pi\)
0.785246 + 0.619183i \(0.212536\pi\)
\(422\) 32.7851 1.59596
\(423\) 0.0327269 0.00159123
\(424\) 101.006 4.90529
\(425\) −0.455877 −0.0221133
\(426\) −54.7537 −2.65283
\(427\) 6.36865 0.308201
\(428\) 11.7674 0.568800
\(429\) 1.53773 0.0742421
\(430\) −38.9855 −1.88005
\(431\) −0.310143 −0.0149391 −0.00746953 0.999972i \(-0.502378\pi\)
−0.00746953 + 0.999972i \(0.502378\pi\)
\(432\) 91.2283 4.38922
\(433\) −17.2598 −0.829453 −0.414726 0.909946i \(-0.636123\pi\)
−0.414726 + 0.909946i \(0.636123\pi\)
\(434\) 4.48253 0.215168
\(435\) 10.6684 0.511511
\(436\) 15.6507 0.749534
\(437\) −10.2414 −0.489913
\(438\) 36.2974 1.73436
\(439\) 23.0890 1.10198 0.550989 0.834512i \(-0.314250\pi\)
0.550989 + 0.834512i \(0.314250\pi\)
\(440\) −20.2527 −0.965511
\(441\) −0.0334188 −0.00159137
\(442\) −6.07675 −0.289042
\(443\) 27.9719 1.32898 0.664492 0.747296i \(-0.268648\pi\)
0.664492 + 0.747296i \(0.268648\pi\)
\(444\) 72.8023 3.45505
\(445\) −12.6405 −0.599218
\(446\) −6.53112 −0.309257
\(447\) −10.6946 −0.505835
\(448\) 102.174 4.82726
\(449\) 1.94412 0.0917487 0.0458743 0.998947i \(-0.485393\pi\)
0.0458743 + 0.998947i \(0.485393\pi\)
\(450\) 0.0138399 0.000652421 0
\(451\) −5.97894 −0.281537
\(452\) −3.25596 −0.153147
\(453\) −1.63758 −0.0769402
\(454\) −5.93936 −0.278748
\(455\) −5.17739 −0.242720
\(456\) 92.0008 4.30833
\(457\) −5.89984 −0.275983 −0.137991 0.990433i \(-0.544065\pi\)
−0.137991 + 0.990433i \(0.544065\pi\)
\(458\) −0.0998426 −0.00466534
\(459\) 11.2920 0.527063
\(460\) 25.5215 1.18995
\(461\) 23.9756 1.11665 0.558327 0.829621i \(-0.311444\pi\)
0.558327 + 0.829621i \(0.311444\pi\)
\(462\) −10.1302 −0.471298
\(463\) 20.4156 0.948792 0.474396 0.880312i \(-0.342667\pi\)
0.474396 + 0.880312i \(0.342667\pi\)
\(464\) 49.4081 2.29372
\(465\) −2.58987 −0.120102
\(466\) 22.3697 1.03626
\(467\) 12.2422 0.566503 0.283251 0.959046i \(-0.408587\pi\)
0.283251 + 0.959046i \(0.408587\pi\)
\(468\) 0.136917 0.00632899
\(469\) 37.0762 1.71202
\(470\) 8.38859 0.386937
\(471\) 0.861148 0.0396796
\(472\) 24.8723 1.14484
\(473\) 5.65520 0.260027
\(474\) 9.99009 0.458860
\(475\) −1.05650 −0.0484757
\(476\) 29.7104 1.36177
\(477\) −0.229592 −0.0105123
\(478\) −26.8608 −1.22858
\(479\) 13.2697 0.606307 0.303153 0.952942i \(-0.401961\pi\)
0.303153 + 0.952942i \(0.401961\pi\)
\(480\) −107.213 −4.89358
\(481\) −7.27254 −0.331599
\(482\) −77.1543 −3.51428
\(483\) 8.33063 0.379057
\(484\) −58.8233 −2.67379
\(485\) 2.39708 0.108846
\(486\) −0.688363 −0.0312248
\(487\) −24.5619 −1.11300 −0.556502 0.830846i \(-0.687857\pi\)
−0.556502 + 0.830846i \(0.687857\pi\)
\(488\) −28.1719 −1.27528
\(489\) 9.25797 0.418660
\(490\) −8.56593 −0.386969
\(491\) −38.0697 −1.71806 −0.859030 0.511925i \(-0.828932\pi\)
−0.859030 + 0.511925i \(0.828932\pi\)
\(492\) −67.6830 −3.05138
\(493\) 6.11559 0.275432
\(494\) −14.0830 −0.633623
\(495\) 0.0460355 0.00206914
\(496\) −11.9943 −0.538561
\(497\) −26.7418 −1.19953
\(498\) −35.3618 −1.58460
\(499\) −27.6586 −1.23817 −0.619085 0.785324i \(-0.712497\pi\)
−0.619085 + 0.785324i \(0.712497\pi\)
\(500\) 65.6370 2.93538
\(501\) 15.8972 0.710235
\(502\) −7.51519 −0.335419
\(503\) −1.53629 −0.0685000 −0.0342500 0.999413i \(-0.510904\pi\)
−0.0342500 + 0.999413i \(0.510904\pi\)
\(504\) −0.588617 −0.0262191
\(505\) 7.75953 0.345294
\(506\) −4.98831 −0.221757
\(507\) −1.73890 −0.0772274
\(508\) −11.6034 −0.514818
\(509\) 32.1253 1.42393 0.711965 0.702215i \(-0.247805\pi\)
0.711965 + 0.702215i \(0.247805\pi\)
\(510\) −23.1293 −1.02418
\(511\) 17.7277 0.784228
\(512\) −127.652 −5.64146
\(513\) 26.1693 1.15540
\(514\) −63.3974 −2.79634
\(515\) 18.7217 0.824976
\(516\) 64.0182 2.81824
\(517\) −1.21684 −0.0535167
\(518\) 47.9097 2.10503
\(519\) 25.2107 1.10663
\(520\) 22.9023 1.00433
\(521\) 31.9753 1.40086 0.700431 0.713720i \(-0.252991\pi\)
0.700431 + 0.713720i \(0.252991\pi\)
\(522\) −0.185663 −0.00812624
\(523\) −7.59470 −0.332093 −0.166046 0.986118i \(-0.553100\pi\)
−0.166046 + 0.986118i \(0.553100\pi\)
\(524\) 26.2173 1.14531
\(525\) 0.859387 0.0375067
\(526\) 65.4265 2.85273
\(527\) −1.48462 −0.0646711
\(528\) 27.1062 1.17965
\(529\) −18.8978 −0.821644
\(530\) −58.8493 −2.55625
\(531\) −0.0565362 −0.00245346
\(532\) 68.8542 2.98521
\(533\) 6.76115 0.292858
\(534\) 27.9683 1.21031
\(535\) −4.47418 −0.193436
\(536\) −164.008 −7.08405
\(537\) −5.48848 −0.236845
\(538\) −8.64650 −0.372777
\(539\) 1.24257 0.0535212
\(540\) −65.2138 −2.80635
\(541\) −7.28592 −0.313246 −0.156623 0.987658i \(-0.550061\pi\)
−0.156623 + 0.987658i \(0.550061\pi\)
\(542\) −22.4809 −0.965638
\(543\) −24.9157 −1.06923
\(544\) −61.4590 −2.63503
\(545\) −5.95068 −0.254899
\(546\) 11.4555 0.490248
\(547\) −18.9473 −0.810128 −0.405064 0.914288i \(-0.632751\pi\)
−0.405064 + 0.914288i \(0.632751\pi\)
\(548\) 10.2240 0.436749
\(549\) 0.0640363 0.00273300
\(550\) −0.514594 −0.0219424
\(551\) 14.1730 0.603789
\(552\) −36.8508 −1.56847
\(553\) 4.87918 0.207484
\(554\) 19.8131 0.841777
\(555\) −27.6807 −1.17498
\(556\) −52.8639 −2.24193
\(557\) −12.2696 −0.519880 −0.259940 0.965625i \(-0.583703\pi\)
−0.259940 + 0.965625i \(0.583703\pi\)
\(558\) 0.0450715 0.00190803
\(559\) −6.39506 −0.270482
\(560\) −91.2642 −3.85662
\(561\) 3.35512 0.141653
\(562\) −8.64350 −0.364604
\(563\) −33.5383 −1.41347 −0.706736 0.707477i \(-0.749833\pi\)
−0.706736 + 0.707477i \(0.749833\pi\)
\(564\) −13.7749 −0.580030
\(565\) 1.23797 0.0520819
\(566\) −7.23340 −0.304043
\(567\) −21.4556 −0.901049
\(568\) 118.293 4.96348
\(569\) −12.1506 −0.509379 −0.254689 0.967023i \(-0.581973\pi\)
−0.254689 + 0.967023i \(0.581973\pi\)
\(570\) −53.6026 −2.24516
\(571\) −10.4274 −0.436372 −0.218186 0.975907i \(-0.570014\pi\)
−0.218186 + 0.975907i \(0.570014\pi\)
\(572\) −5.09082 −0.212858
\(573\) 12.2276 0.510815
\(574\) −44.5408 −1.85910
\(575\) 0.423181 0.0176479
\(576\) 1.02735 0.0428062
\(577\) −44.1920 −1.83974 −0.919868 0.392228i \(-0.871705\pi\)
−0.919868 + 0.392228i \(0.871705\pi\)
\(578\) 34.0882 1.41788
\(579\) 30.4526 1.26557
\(580\) −35.3190 −1.46654
\(581\) −17.2708 −0.716512
\(582\) −5.30376 −0.219848
\(583\) 8.53664 0.353552
\(584\) −78.4191 −3.24500
\(585\) −0.0520583 −0.00215234
\(586\) −69.1185 −2.85526
\(587\) −2.12312 −0.0876306 −0.0438153 0.999040i \(-0.513951\pi\)
−0.0438153 + 0.999040i \(0.513951\pi\)
\(588\) 14.0662 0.580079
\(589\) −3.44063 −0.141769
\(590\) −14.4914 −0.596602
\(591\) −16.6025 −0.682937
\(592\) −128.196 −5.26884
\(593\) 20.2349 0.830947 0.415474 0.909605i \(-0.363616\pi\)
0.415474 + 0.909605i \(0.363616\pi\)
\(594\) 12.7463 0.522989
\(595\) −11.2964 −0.463107
\(596\) 35.4055 1.45027
\(597\) −22.1612 −0.906997
\(598\) 5.64092 0.230674
\(599\) 42.2252 1.72528 0.862638 0.505821i \(-0.168810\pi\)
0.862638 + 0.505821i \(0.168810\pi\)
\(600\) −3.80153 −0.155197
\(601\) −30.8846 −1.25981 −0.629905 0.776672i \(-0.716906\pi\)
−0.629905 + 0.776672i \(0.716906\pi\)
\(602\) 42.1291 1.71705
\(603\) 0.372798 0.0151815
\(604\) 5.42139 0.220593
\(605\) 22.3657 0.909293
\(606\) −17.1687 −0.697430
\(607\) −5.26851 −0.213842 −0.106921 0.994268i \(-0.534099\pi\)
−0.106921 + 0.994268i \(0.534099\pi\)
\(608\) −142.432 −5.77639
\(609\) −11.5287 −0.467165
\(610\) 16.4139 0.664578
\(611\) 1.37604 0.0556686
\(612\) 0.298735 0.0120757
\(613\) 7.23983 0.292414 0.146207 0.989254i \(-0.453293\pi\)
0.146207 + 0.989254i \(0.453293\pi\)
\(614\) −50.7845 −2.04950
\(615\) 25.7343 1.03771
\(616\) 21.8858 0.881805
\(617\) 42.6756 1.71805 0.859027 0.511930i \(-0.171069\pi\)
0.859027 + 0.511930i \(0.171069\pi\)
\(618\) −41.4235 −1.66630
\(619\) 1.00000 0.0401934
\(620\) 8.57404 0.344342
\(621\) −10.4821 −0.420631
\(622\) −32.4600 −1.30153
\(623\) 13.6598 0.547268
\(624\) −30.6524 −1.22708
\(625\) −23.9117 −0.956466
\(626\) −56.9192 −2.27495
\(627\) 7.77555 0.310526
\(628\) −2.85093 −0.113764
\(629\) −15.8678 −0.632689
\(630\) 0.342947 0.0136633
\(631\) −15.1629 −0.603624 −0.301812 0.953367i \(-0.597591\pi\)
−0.301812 + 0.953367i \(0.597591\pi\)
\(632\) −21.5832 −0.858534
\(633\) 20.4696 0.813595
\(634\) 43.7308 1.73677
\(635\) 4.41182 0.175078
\(636\) 96.6368 3.83190
\(637\) −1.40513 −0.0556733
\(638\) 6.90327 0.273303
\(639\) −0.268887 −0.0106370
\(640\) 140.020 5.53479
\(641\) −1.88878 −0.0746022 −0.0373011 0.999304i \(-0.511876\pi\)
−0.0373011 + 0.999304i \(0.511876\pi\)
\(642\) 9.89955 0.390704
\(643\) −8.39620 −0.331114 −0.165557 0.986200i \(-0.552942\pi\)
−0.165557 + 0.986200i \(0.552942\pi\)
\(644\) −27.5795 −1.08678
\(645\) −24.3409 −0.958420
\(646\) −30.7272 −1.20895
\(647\) 12.9301 0.508335 0.254168 0.967160i \(-0.418198\pi\)
0.254168 + 0.967160i \(0.418198\pi\)
\(648\) 94.9093 3.72839
\(649\) 2.10211 0.0825152
\(650\) 0.581917 0.0228246
\(651\) 2.79870 0.109690
\(652\) −30.6495 −1.20033
\(653\) −12.9091 −0.505173 −0.252586 0.967574i \(-0.581281\pi\)
−0.252586 + 0.967574i \(0.581281\pi\)
\(654\) 13.1664 0.514848
\(655\) −9.96829 −0.389493
\(656\) 119.182 4.65327
\(657\) 0.178251 0.00695422
\(658\) −9.06500 −0.353391
\(659\) −3.49538 −0.136161 −0.0680804 0.997680i \(-0.521687\pi\)
−0.0680804 + 0.997680i \(0.521687\pi\)
\(660\) −19.3766 −0.754235
\(661\) 3.42826 0.133344 0.0666719 0.997775i \(-0.478762\pi\)
0.0666719 + 0.997775i \(0.478762\pi\)
\(662\) −17.3053 −0.672589
\(663\) −3.79406 −0.147349
\(664\) 76.3977 2.96481
\(665\) −26.1796 −1.01520
\(666\) 0.481728 0.0186666
\(667\) −5.67697 −0.219813
\(668\) −52.6295 −2.03630
\(669\) −4.07775 −0.157655
\(670\) 95.5560 3.69165
\(671\) −2.38098 −0.0919169
\(672\) 115.858 4.46933
\(673\) −33.7053 −1.29925 −0.649623 0.760257i \(-0.725073\pi\)
−0.649623 + 0.760257i \(0.725073\pi\)
\(674\) 22.2161 0.855733
\(675\) −1.08133 −0.0416204
\(676\) 5.75683 0.221417
\(677\) −33.5818 −1.29065 −0.645327 0.763907i \(-0.723279\pi\)
−0.645327 + 0.763907i \(0.723279\pi\)
\(678\) −2.73913 −0.105196
\(679\) −2.59037 −0.0994091
\(680\) 49.9700 1.91626
\(681\) −3.70829 −0.142102
\(682\) −1.67584 −0.0641712
\(683\) 8.32347 0.318489 0.159244 0.987239i \(-0.449094\pi\)
0.159244 + 0.987239i \(0.449094\pi\)
\(684\) 0.692324 0.0264717
\(685\) −3.88735 −0.148528
\(686\) 55.3709 2.11407
\(687\) −0.0623374 −0.00237832
\(688\) −112.729 −4.29774
\(689\) −9.65347 −0.367768
\(690\) 21.4704 0.817366
\(691\) −44.9027 −1.70818 −0.854090 0.520126i \(-0.825885\pi\)
−0.854090 + 0.520126i \(0.825885\pi\)
\(692\) −83.4627 −3.17278
\(693\) −0.0497476 −0.00188976
\(694\) 40.7573 1.54712
\(695\) 20.0998 0.762429
\(696\) 50.9974 1.93305
\(697\) 14.7520 0.558770
\(698\) −76.0150 −2.87721
\(699\) 13.9667 0.528268
\(700\) −2.84510 −0.107535
\(701\) 15.1048 0.570501 0.285251 0.958453i \(-0.407923\pi\)
0.285251 + 0.958453i \(0.407923\pi\)
\(702\) −14.4139 −0.544018
\(703\) −36.7738 −1.38695
\(704\) −38.1987 −1.43967
\(705\) 5.23747 0.197255
\(706\) 40.4908 1.52389
\(707\) −8.38522 −0.315359
\(708\) 23.7964 0.894324
\(709\) −40.0732 −1.50498 −0.752490 0.658603i \(-0.771148\pi\)
−0.752490 + 0.658603i \(0.771148\pi\)
\(710\) −68.9214 −2.58657
\(711\) 0.0490598 0.00183989
\(712\) −60.4245 −2.26450
\(713\) 1.37814 0.0516118
\(714\) 24.9943 0.935390
\(715\) 1.93562 0.0723880
\(716\) 18.1702 0.679053
\(717\) −16.7707 −0.626315
\(718\) 72.6832 2.71251
\(719\) −24.3610 −0.908513 −0.454257 0.890871i \(-0.650095\pi\)
−0.454257 + 0.890871i \(0.650095\pi\)
\(720\) −0.917655 −0.0341990
\(721\) −20.2313 −0.753453
\(722\) −18.2938 −0.680825
\(723\) −48.1718 −1.79153
\(724\) 82.4862 3.06557
\(725\) −0.585635 −0.0217500
\(726\) −49.4861 −1.83660
\(727\) 33.7910 1.25324 0.626619 0.779326i \(-0.284438\pi\)
0.626619 + 0.779326i \(0.284438\pi\)
\(728\) −24.7491 −0.917262
\(729\) 26.7826 0.991947
\(730\) 45.6894 1.69104
\(731\) −13.9532 −0.516078
\(732\) −26.9533 −0.996222
\(733\) −36.5543 −1.35016 −0.675082 0.737742i \(-0.735892\pi\)
−0.675082 + 0.737742i \(0.735892\pi\)
\(734\) −51.2442 −1.89146
\(735\) −5.34820 −0.197271
\(736\) 57.0511 2.10293
\(737\) −13.8613 −0.510587
\(738\) −0.447854 −0.0164857
\(739\) 43.9210 1.61566 0.807831 0.589414i \(-0.200641\pi\)
0.807831 + 0.589414i \(0.200641\pi\)
\(740\) 91.6401 3.36876
\(741\) −8.79280 −0.323012
\(742\) 63.5947 2.33463
\(743\) −22.6540 −0.831096 −0.415548 0.909571i \(-0.636410\pi\)
−0.415548 + 0.909571i \(0.636410\pi\)
\(744\) −12.3801 −0.453878
\(745\) −13.4618 −0.493202
\(746\) 32.9548 1.20656
\(747\) −0.173656 −0.00635374
\(748\) −11.1075 −0.406131
\(749\) 4.83496 0.176666
\(750\) 55.2183 2.01629
\(751\) 17.3085 0.631595 0.315798 0.948827i \(-0.397728\pi\)
0.315798 + 0.948827i \(0.397728\pi\)
\(752\) 24.2561 0.884528
\(753\) −4.69216 −0.170992
\(754\) −7.80640 −0.284292
\(755\) −2.06131 −0.0750187
\(756\) 70.4723 2.56305
\(757\) −13.5801 −0.493579 −0.246789 0.969069i \(-0.579376\pi\)
−0.246789 + 0.969069i \(0.579376\pi\)
\(758\) −81.3645 −2.95529
\(759\) −3.11449 −0.113049
\(760\) 115.806 4.20074
\(761\) 6.09679 0.221008 0.110504 0.993876i \(-0.464753\pi\)
0.110504 + 0.993876i \(0.464753\pi\)
\(762\) −9.76156 −0.353624
\(763\) 6.43051 0.232800
\(764\) −40.4808 −1.46454
\(765\) −0.113584 −0.00410665
\(766\) −22.0990 −0.798468
\(767\) −2.37713 −0.0858331
\(768\) −159.580 −5.75836
\(769\) −4.15339 −0.149775 −0.0748875 0.997192i \(-0.523860\pi\)
−0.0748875 + 0.997192i \(0.523860\pi\)
\(770\) −12.7514 −0.459527
\(771\) −39.5826 −1.42553
\(772\) −100.817 −3.62847
\(773\) −7.02831 −0.252791 −0.126395 0.991980i \(-0.540341\pi\)
−0.126395 + 0.991980i \(0.540341\pi\)
\(774\) 0.423604 0.0152261
\(775\) 0.142169 0.00510686
\(776\) 11.4586 0.411339
\(777\) 29.9128 1.07311
\(778\) −77.8108 −2.78965
\(779\) 34.1879 1.22491
\(780\) 21.9116 0.784562
\(781\) 9.99769 0.357746
\(782\) 12.3078 0.440124
\(783\) 14.5060 0.518403
\(784\) −24.7689 −0.884603
\(785\) 1.08397 0.0386886
\(786\) 22.0558 0.786703
\(787\) 53.5470 1.90874 0.954372 0.298619i \(-0.0965260\pi\)
0.954372 + 0.298619i \(0.0965260\pi\)
\(788\) 54.9646 1.95803
\(789\) 40.8495 1.45428
\(790\) 12.5751 0.447400
\(791\) −1.33780 −0.0475666
\(792\) 0.220060 0.00781950
\(793\) 2.69248 0.0956128
\(794\) −8.96259 −0.318070
\(795\) −36.7430 −1.30314
\(796\) 73.3671 2.60043
\(797\) −36.0855 −1.27821 −0.639107 0.769117i \(-0.720696\pi\)
−0.639107 + 0.769117i \(0.720696\pi\)
\(798\) 57.9248 2.05052
\(799\) 3.00234 0.106215
\(800\) 5.88539 0.208080
\(801\) 0.137348 0.00485296
\(802\) 90.1507 3.18333
\(803\) −6.62768 −0.233886
\(804\) −156.913 −5.53390
\(805\) 10.4862 0.369590
\(806\) 1.89508 0.0667515
\(807\) −5.39850 −0.190036
\(808\) 37.0923 1.30490
\(809\) 53.6120 1.88490 0.942448 0.334353i \(-0.108518\pi\)
0.942448 + 0.334353i \(0.108518\pi\)
\(810\) −55.2972 −1.94294
\(811\) −24.6502 −0.865584 −0.432792 0.901494i \(-0.642472\pi\)
−0.432792 + 0.901494i \(0.642472\pi\)
\(812\) 38.1669 1.33940
\(813\) −14.0361 −0.492268
\(814\) −17.9115 −0.627798
\(815\) 11.6535 0.408204
\(816\) −66.8797 −2.34126
\(817\) −32.3368 −1.13132
\(818\) 64.9953 2.27251
\(819\) 0.0562560 0.00196574
\(820\) −85.1962 −2.97518
\(821\) 37.2377 1.29960 0.649802 0.760103i \(-0.274852\pi\)
0.649802 + 0.760103i \(0.274852\pi\)
\(822\) 8.60114 0.299999
\(823\) −29.0038 −1.01101 −0.505505 0.862824i \(-0.668694\pi\)
−0.505505 + 0.862824i \(0.668694\pi\)
\(824\) 89.4938 3.11766
\(825\) −0.321290 −0.0111859
\(826\) 15.6599 0.544879
\(827\) −11.2891 −0.392562 −0.196281 0.980548i \(-0.562886\pi\)
−0.196281 + 0.980548i \(0.562886\pi\)
\(828\) −0.277310 −0.00963717
\(829\) 0.418251 0.0145265 0.00726323 0.999974i \(-0.497688\pi\)
0.00726323 + 0.999974i \(0.497688\pi\)
\(830\) −44.5117 −1.54502
\(831\) 12.3704 0.429126
\(832\) 43.1961 1.49756
\(833\) −3.06581 −0.106224
\(834\) −44.4727 −1.53996
\(835\) 20.0107 0.692498
\(836\) −25.7418 −0.890300
\(837\) −3.52149 −0.121720
\(838\) −6.08101 −0.210065
\(839\) −33.8156 −1.16744 −0.583721 0.811954i \(-0.698404\pi\)
−0.583721 + 0.811954i \(0.698404\pi\)
\(840\) −94.1999 −3.25020
\(841\) −21.1437 −0.729093
\(842\) −89.7468 −3.09288
\(843\) −5.39663 −0.185870
\(844\) −67.7670 −2.33264
\(845\) −2.18885 −0.0752987
\(846\) −0.0911479 −0.00313373
\(847\) −24.1691 −0.830461
\(848\) −170.166 −5.84353
\(849\) −4.51623 −0.154997
\(850\) 1.26967 0.0435492
\(851\) 14.7297 0.504927
\(852\) 113.176 3.87735
\(853\) −46.2914 −1.58499 −0.792494 0.609879i \(-0.791218\pi\)
−0.792494 + 0.609879i \(0.791218\pi\)
\(854\) −17.7374 −0.606961
\(855\) −0.263234 −0.00900241
\(856\) −21.3876 −0.731013
\(857\) −4.42340 −0.151100 −0.0755502 0.997142i \(-0.524071\pi\)
−0.0755502 + 0.997142i \(0.524071\pi\)
\(858\) −4.28274 −0.146210
\(859\) −28.9606 −0.988122 −0.494061 0.869427i \(-0.664488\pi\)
−0.494061 + 0.869427i \(0.664488\pi\)
\(860\) 80.5831 2.74786
\(861\) −27.8094 −0.947740
\(862\) 0.863782 0.0294205
\(863\) −29.5161 −1.00474 −0.502370 0.864653i \(-0.667539\pi\)
−0.502370 + 0.864653i \(0.667539\pi\)
\(864\) −145.779 −4.95952
\(865\) 31.7340 1.07899
\(866\) 48.0704 1.63350
\(867\) 21.2832 0.722815
\(868\) −9.26541 −0.314489
\(869\) −1.82413 −0.0618793
\(870\) −29.7127 −1.00736
\(871\) 15.6747 0.531118
\(872\) −28.4456 −0.963289
\(873\) −0.0260459 −0.000881521 0
\(874\) 28.5234 0.964819
\(875\) 26.9687 0.911709
\(876\) −75.0268 −2.53492
\(877\) 7.27417 0.245631 0.122816 0.992430i \(-0.460808\pi\)
0.122816 + 0.992430i \(0.460808\pi\)
\(878\) −64.3054 −2.17020
\(879\) −43.1547 −1.45557
\(880\) 34.1200 1.15019
\(881\) −23.5894 −0.794745 −0.397373 0.917657i \(-0.630078\pi\)
−0.397373 + 0.917657i \(0.630078\pi\)
\(882\) 0.0930749 0.00313400
\(883\) −45.3766 −1.52704 −0.763522 0.645781i \(-0.776532\pi\)
−0.763522 + 0.645781i \(0.776532\pi\)
\(884\) 12.5607 0.422461
\(885\) −9.04782 −0.304139
\(886\) −77.9047 −2.61726
\(887\) 37.9773 1.27515 0.637576 0.770387i \(-0.279937\pi\)
0.637576 + 0.770387i \(0.279937\pi\)
\(888\) −132.320 −4.44037
\(889\) −4.76756 −0.159899
\(890\) 35.2052 1.18008
\(891\) 8.02137 0.268726
\(892\) 13.4999 0.452008
\(893\) 6.95797 0.232840
\(894\) 29.7855 0.996176
\(895\) −6.90864 −0.230930
\(896\) −151.311 −5.05494
\(897\) 3.52195 0.117594
\(898\) −5.41459 −0.180687
\(899\) −1.90719 −0.0636085
\(900\) −0.0286072 −0.000953575 0
\(901\) −21.0626 −0.701698
\(902\) 16.6520 0.554451
\(903\) 26.3036 0.875328
\(904\) 5.91779 0.196823
\(905\) −31.3627 −1.04253
\(906\) 4.56084 0.151524
\(907\) 11.8516 0.393526 0.196763 0.980451i \(-0.436957\pi\)
0.196763 + 0.980451i \(0.436957\pi\)
\(908\) 12.2767 0.407416
\(909\) −0.0843127 −0.00279648
\(910\) 14.4196 0.478005
\(911\) −47.7316 −1.58142 −0.790710 0.612191i \(-0.790288\pi\)
−0.790710 + 0.612191i \(0.790288\pi\)
\(912\) −154.995 −5.13239
\(913\) 6.45684 0.213690
\(914\) 16.4317 0.543512
\(915\) 10.2481 0.338792
\(916\) 0.206375 0.00681882
\(917\) 10.7721 0.355726
\(918\) −31.4493 −1.03798
\(919\) −8.60726 −0.283927 −0.141964 0.989872i \(-0.545342\pi\)
−0.141964 + 0.989872i \(0.545342\pi\)
\(920\) −46.3861 −1.52930
\(921\) −31.7077 −1.04480
\(922\) −66.7745 −2.19910
\(923\) −11.3057 −0.372130
\(924\) 20.9391 0.688845
\(925\) 1.51951 0.0499613
\(926\) −56.8596 −1.86852
\(927\) −0.203424 −0.00668133
\(928\) −78.9524 −2.59174
\(929\) −1.03512 −0.0339613 −0.0169806 0.999856i \(-0.505405\pi\)
−0.0169806 + 0.999856i \(0.505405\pi\)
\(930\) 7.21306 0.236526
\(931\) −7.10508 −0.232859
\(932\) −46.2382 −1.51458
\(933\) −20.2666 −0.663499
\(934\) −34.0959 −1.11565
\(935\) 4.22327 0.138116
\(936\) −0.248850 −0.00813392
\(937\) −23.6121 −0.771373 −0.385686 0.922630i \(-0.626035\pi\)
−0.385686 + 0.922630i \(0.626035\pi\)
\(938\) −103.261 −3.37160
\(939\) −35.5379 −1.15974
\(940\) −17.3392 −0.565544
\(941\) 45.5882 1.48613 0.743066 0.669218i \(-0.233371\pi\)
0.743066 + 0.669218i \(0.233371\pi\)
\(942\) −2.39839 −0.0781438
\(943\) −13.6939 −0.445936
\(944\) −41.9027 −1.36382
\(945\) −26.7948 −0.871635
\(946\) −15.7504 −0.512088
\(947\) −41.0253 −1.33314 −0.666571 0.745442i \(-0.732239\pi\)
−0.666571 + 0.745442i \(0.732239\pi\)
\(948\) −20.6496 −0.670667
\(949\) 7.49476 0.243290
\(950\) 2.94248 0.0954665
\(951\) 27.3036 0.885381
\(952\) −53.9993 −1.75013
\(953\) −10.9272 −0.353967 −0.176983 0.984214i \(-0.556634\pi\)
−0.176983 + 0.984214i \(0.556634\pi\)
\(954\) 0.639439 0.0207026
\(955\) 15.3915 0.498058
\(956\) 55.5214 1.79569
\(957\) 4.31011 0.139326
\(958\) −36.9575 −1.19404
\(959\) 4.20081 0.135651
\(960\) 164.413 5.30640
\(961\) −30.5370 −0.985065
\(962\) 20.2548 0.653042
\(963\) 0.0486151 0.00156660
\(964\) 159.478 5.13645
\(965\) 38.3323 1.23396
\(966\) −23.2017 −0.746503
\(967\) 22.8433 0.734589 0.367295 0.930105i \(-0.380284\pi\)
0.367295 + 0.930105i \(0.380284\pi\)
\(968\) 106.913 3.43631
\(969\) −19.1848 −0.616304
\(970\) −6.67612 −0.214357
\(971\) −15.7174 −0.504394 −0.252197 0.967676i \(-0.581153\pi\)
−0.252197 + 0.967676i \(0.581153\pi\)
\(972\) 1.42285 0.0456379
\(973\) −21.7206 −0.696329
\(974\) 68.4075 2.19192
\(975\) 0.363324 0.0116357
\(976\) 47.4616 1.51921
\(977\) 42.5260 1.36053 0.680264 0.732968i \(-0.261865\pi\)
0.680264 + 0.732968i \(0.261865\pi\)
\(978\) −25.7844 −0.824496
\(979\) −5.10684 −0.163215
\(980\) 17.7058 0.565592
\(981\) 0.0646583 0.00206438
\(982\) 106.028 3.38349
\(983\) −46.3584 −1.47860 −0.739302 0.673374i \(-0.764844\pi\)
−0.739302 + 0.673374i \(0.764844\pi\)
\(984\) 123.016 3.92159
\(985\) −20.8985 −0.665882
\(986\) −17.0326 −0.542428
\(987\) −5.65980 −0.180153
\(988\) 29.1096 0.926099
\(989\) 12.9525 0.411864
\(990\) −0.128214 −0.00407491
\(991\) 4.06632 0.129171 0.0645855 0.997912i \(-0.479427\pi\)
0.0645855 + 0.997912i \(0.479427\pi\)
\(992\) 19.1665 0.608536
\(993\) −10.8047 −0.342876
\(994\) 74.4789 2.36233
\(995\) −27.8955 −0.884346
\(996\) 73.0929 2.31604
\(997\) −12.0591 −0.381917 −0.190958 0.981598i \(-0.561160\pi\)
−0.190958 + 0.981598i \(0.561160\pi\)
\(998\) 77.0323 2.43842
\(999\) −37.6380 −1.19081
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 \(a_p\))