Properties

Label 6047.2.a.a.1.18
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 1.18
Character \(\chi\) = 6047.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.46358 q^{2} +2.70933 q^{3} +4.06925 q^{4} +0.207418 q^{5} -6.67465 q^{6} -2.27877 q^{7} -5.09776 q^{8} +4.34044 q^{9} +O(q^{10})\) \(q-2.46358 q^{2} +2.70933 q^{3} +4.06925 q^{4} +0.207418 q^{5} -6.67465 q^{6} -2.27877 q^{7} -5.09776 q^{8} +4.34044 q^{9} -0.510992 q^{10} +0.737352 q^{11} +11.0249 q^{12} -1.97568 q^{13} +5.61395 q^{14} +0.561963 q^{15} +4.42028 q^{16} -7.55846 q^{17} -10.6930 q^{18} +5.52880 q^{19} +0.844036 q^{20} -6.17394 q^{21} -1.81653 q^{22} +2.66109 q^{23} -13.8115 q^{24} -4.95698 q^{25} +4.86724 q^{26} +3.63170 q^{27} -9.27290 q^{28} +7.95097 q^{29} -1.38444 q^{30} -7.15763 q^{31} -0.694197 q^{32} +1.99773 q^{33} +18.6209 q^{34} -0.472659 q^{35} +17.6623 q^{36} +6.07020 q^{37} -13.6207 q^{38} -5.35275 q^{39} -1.05737 q^{40} -2.92883 q^{41} +15.2100 q^{42} +4.05631 q^{43} +3.00047 q^{44} +0.900287 q^{45} -6.55583 q^{46} -4.70183 q^{47} +11.9760 q^{48} -1.80719 q^{49} +12.2119 q^{50} -20.4783 q^{51} -8.03951 q^{52} -1.50496 q^{53} -8.94699 q^{54} +0.152940 q^{55} +11.6167 q^{56} +14.9793 q^{57} -19.5879 q^{58} +5.97409 q^{59} +2.28677 q^{60} +2.80794 q^{61} +17.6334 q^{62} -9.89089 q^{63} -7.13034 q^{64} -0.409791 q^{65} -4.92157 q^{66} +2.28444 q^{67} -30.7572 q^{68} +7.20977 q^{69} +1.16444 q^{70} -14.1479 q^{71} -22.1266 q^{72} +3.04156 q^{73} -14.9545 q^{74} -13.4301 q^{75} +22.4981 q^{76} -1.68026 q^{77} +13.1869 q^{78} -5.42532 q^{79} +0.916846 q^{80} -3.18188 q^{81} +7.21541 q^{82} +4.78846 q^{83} -25.1233 q^{84} -1.56776 q^{85} -9.99306 q^{86} +21.5418 q^{87} -3.75885 q^{88} -8.65761 q^{89} -2.21793 q^{90} +4.50212 q^{91} +10.8287 q^{92} -19.3923 q^{93} +11.5834 q^{94} +1.14677 q^{95} -1.88081 q^{96} -6.74444 q^{97} +4.45216 q^{98} +3.20043 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 217q - 20q^{2} - 27q^{3} + 184q^{4} - 19q^{5} - 17q^{6} - 48q^{7} - 57q^{8} + 152q^{9} + O(q^{10}) \) \( 217q - 20q^{2} - 27q^{3} + 184q^{4} - 19q^{5} - 17q^{6} - 48q^{7} - 57q^{8} + 152q^{9} - 46q^{10} - 32q^{11} - 72q^{12} - 80q^{13} - 22q^{14} - 43q^{15} + 122q^{16} - 61q^{17} - 88q^{18} - 43q^{19} - 41q^{20} - 61q^{21} - 93q^{22} - 60q^{23} - 41q^{24} + 26q^{25} - 9q^{26} - 93q^{27} - 126q^{28} - 47q^{29} - 36q^{30} - 100q^{31} - 114q^{32} - 133q^{33} - 75q^{34} - 37q^{35} + 75q^{36} - 264q^{37} - 35q^{38} - 47q^{39} - 118q^{40} - 72q^{41} - 64q^{42} - 107q^{43} - 59q^{44} - 69q^{45} - 111q^{46} - 54q^{47} - 135q^{48} + 33q^{49} - 42q^{50} - 26q^{51} - 173q^{52} - 103q^{53} - 28q^{54} - 78q^{55} - 44q^{56} - 205q^{57} - 189q^{58} - 38q^{59} - 105q^{60} - 108q^{61} - 14q^{62} - 116q^{63} + 39q^{64} - 146q^{65} + 5q^{66} - 206q^{67} - 62q^{68} - 55q^{69} - 125q^{70} - 78q^{71} - 225q^{72} - 326q^{73} + 3q^{74} - 95q^{75} - 84q^{76} - 79q^{77} - 86q^{78} - 117q^{79} - 39q^{80} + q^{81} - 96q^{82} - 23q^{83} - 57q^{84} - 224q^{85} - 7q^{86} - 45q^{87} - 250q^{88} - 104q^{89} - 36q^{90} - 96q^{91} - 137q^{92} - 155q^{93} - 48q^{94} - 38q^{95} - 33q^{96} - 447q^{97} - 46q^{98} - 94q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.46358 −1.74202 −0.871009 0.491268i \(-0.836534\pi\)
−0.871009 + 0.491268i \(0.836534\pi\)
\(3\) 2.70933 1.56423 0.782115 0.623134i \(-0.214141\pi\)
0.782115 + 0.623134i \(0.214141\pi\)
\(4\) 4.06925 2.03462
\(5\) 0.207418 0.0927602 0.0463801 0.998924i \(-0.485231\pi\)
0.0463801 + 0.998924i \(0.485231\pi\)
\(6\) −6.67465 −2.72491
\(7\) −2.27877 −0.861296 −0.430648 0.902520i \(-0.641715\pi\)
−0.430648 + 0.902520i \(0.641715\pi\)
\(8\) −5.09776 −1.80233
\(9\) 4.34044 1.44681
\(10\) −0.510992 −0.161590
\(11\) 0.737352 0.222320 0.111160 0.993803i \(-0.464543\pi\)
0.111160 + 0.993803i \(0.464543\pi\)
\(12\) 11.0249 3.18262
\(13\) −1.97568 −0.547954 −0.273977 0.961736i \(-0.588339\pi\)
−0.273977 + 0.961736i \(0.588339\pi\)
\(14\) 5.61395 1.50039
\(15\) 0.561963 0.145098
\(16\) 4.42028 1.10507
\(17\) −7.55846 −1.83319 −0.916597 0.399811i \(-0.869076\pi\)
−0.916597 + 0.399811i \(0.869076\pi\)
\(18\) −10.6930 −2.52038
\(19\) 5.52880 1.26839 0.634197 0.773171i \(-0.281331\pi\)
0.634197 + 0.773171i \(0.281331\pi\)
\(20\) 0.844036 0.188732
\(21\) −6.17394 −1.34726
\(22\) −1.81653 −0.387285
\(23\) 2.66109 0.554877 0.277438 0.960743i \(-0.410515\pi\)
0.277438 + 0.960743i \(0.410515\pi\)
\(24\) −13.8115 −2.81926
\(25\) −4.95698 −0.991396
\(26\) 4.86724 0.954545
\(27\) 3.63170 0.698920
\(28\) −9.27290 −1.75241
\(29\) 7.95097 1.47646 0.738229 0.674550i \(-0.235662\pi\)
0.738229 + 0.674550i \(0.235662\pi\)
\(30\) −1.38444 −0.252764
\(31\) −7.15763 −1.28555 −0.642774 0.766056i \(-0.722217\pi\)
−0.642774 + 0.766056i \(0.722217\pi\)
\(32\) −0.694197 −0.122718
\(33\) 1.99773 0.347759
\(34\) 18.6209 3.19346
\(35\) −0.472659 −0.0798940
\(36\) 17.6623 2.94372
\(37\) 6.07020 0.997935 0.498968 0.866621i \(-0.333713\pi\)
0.498968 + 0.866621i \(0.333713\pi\)
\(38\) −13.6207 −2.20957
\(39\) −5.35275 −0.857126
\(40\) −1.05737 −0.167185
\(41\) −2.92883 −0.457406 −0.228703 0.973496i \(-0.573448\pi\)
−0.228703 + 0.973496i \(0.573448\pi\)
\(42\) 15.2100 2.34696
\(43\) 4.05631 0.618581 0.309291 0.950968i \(-0.399908\pi\)
0.309291 + 0.950968i \(0.399908\pi\)
\(44\) 3.00047 0.452337
\(45\) 0.900287 0.134207
\(46\) −6.55583 −0.966605
\(47\) −4.70183 −0.685833 −0.342916 0.939366i \(-0.611415\pi\)
−0.342916 + 0.939366i \(0.611415\pi\)
\(48\) 11.9760 1.72858
\(49\) −1.80719 −0.258170
\(50\) 12.2119 1.72703
\(51\) −20.4783 −2.86754
\(52\) −8.03951 −1.11488
\(53\) −1.50496 −0.206722 −0.103361 0.994644i \(-0.532960\pi\)
−0.103361 + 0.994644i \(0.532960\pi\)
\(54\) −8.94699 −1.21753
\(55\) 0.152940 0.0206224
\(56\) 11.6167 1.55234
\(57\) 14.9793 1.98406
\(58\) −19.5879 −2.57202
\(59\) 5.97409 0.777760 0.388880 0.921288i \(-0.372862\pi\)
0.388880 + 0.921288i \(0.372862\pi\)
\(60\) 2.28677 0.295220
\(61\) 2.80794 0.359520 0.179760 0.983711i \(-0.442468\pi\)
0.179760 + 0.983711i \(0.442468\pi\)
\(62\) 17.6334 2.23945
\(63\) −9.89089 −1.24614
\(64\) −7.13034 −0.891293
\(65\) −0.409791 −0.0508283
\(66\) −4.92157 −0.605803
\(67\) 2.28444 0.279089 0.139545 0.990216i \(-0.455436\pi\)
0.139545 + 0.990216i \(0.455436\pi\)
\(68\) −30.7572 −3.72986
\(69\) 7.20977 0.867955
\(70\) 1.16444 0.139177
\(71\) −14.1479 −1.67904 −0.839522 0.543325i \(-0.817165\pi\)
−0.839522 + 0.543325i \(0.817165\pi\)
\(72\) −22.1266 −2.60764
\(73\) 3.04156 0.355987 0.177994 0.984032i \(-0.443039\pi\)
0.177994 + 0.984032i \(0.443039\pi\)
\(74\) −14.9545 −1.73842
\(75\) −13.4301 −1.55077
\(76\) 22.4981 2.58071
\(77\) −1.68026 −0.191483
\(78\) 13.1869 1.49313
\(79\) −5.42532 −0.610396 −0.305198 0.952289i \(-0.598723\pi\)
−0.305198 + 0.952289i \(0.598723\pi\)
\(80\) 0.916846 0.102506
\(81\) −3.18188 −0.353542
\(82\) 7.21541 0.796808
\(83\) 4.78846 0.525602 0.262801 0.964850i \(-0.415354\pi\)
0.262801 + 0.964850i \(0.415354\pi\)
\(84\) −25.1233 −2.74118
\(85\) −1.56776 −0.170048
\(86\) −9.99306 −1.07758
\(87\) 21.5418 2.30952
\(88\) −3.75885 −0.400694
\(89\) −8.65761 −0.917705 −0.458852 0.888512i \(-0.651739\pi\)
−0.458852 + 0.888512i \(0.651739\pi\)
\(90\) −2.21793 −0.233791
\(91\) 4.50212 0.471950
\(92\) 10.8287 1.12897
\(93\) −19.3923 −2.01089
\(94\) 11.5834 1.19473
\(95\) 1.14677 0.117657
\(96\) −1.88081 −0.191959
\(97\) −6.74444 −0.684794 −0.342397 0.939555i \(-0.611239\pi\)
−0.342397 + 0.939555i \(0.611239\pi\)
\(98\) 4.45216 0.449736
\(99\) 3.20043 0.321656
\(100\) −20.1712 −2.01712
\(101\) 18.0958 1.80060 0.900299 0.435272i \(-0.143348\pi\)
0.900299 + 0.435272i \(0.143348\pi\)
\(102\) 50.4501 4.99530
\(103\) −15.7262 −1.54955 −0.774773 0.632239i \(-0.782136\pi\)
−0.774773 + 0.632239i \(0.782136\pi\)
\(104\) 10.0715 0.987595
\(105\) −1.28059 −0.124973
\(106\) 3.70760 0.360114
\(107\) −4.98626 −0.482040 −0.241020 0.970520i \(-0.577482\pi\)
−0.241020 + 0.970520i \(0.577482\pi\)
\(108\) 14.7783 1.42204
\(109\) −11.2628 −1.07878 −0.539389 0.842057i \(-0.681345\pi\)
−0.539389 + 0.842057i \(0.681345\pi\)
\(110\) −0.376781 −0.0359247
\(111\) 16.4462 1.56100
\(112\) −10.0728 −0.951792
\(113\) −0.733892 −0.0690388 −0.0345194 0.999404i \(-0.510990\pi\)
−0.0345194 + 0.999404i \(0.510990\pi\)
\(114\) −36.9028 −3.45627
\(115\) 0.551959 0.0514705
\(116\) 32.3545 3.00404
\(117\) −8.57531 −0.792788
\(118\) −14.7177 −1.35487
\(119\) 17.2240 1.57892
\(120\) −2.86476 −0.261515
\(121\) −10.4563 −0.950574
\(122\) −6.91760 −0.626290
\(123\) −7.93514 −0.715487
\(124\) −29.1262 −2.61561
\(125\) −2.06526 −0.184722
\(126\) 24.3670 2.17079
\(127\) 14.4144 1.27907 0.639534 0.768763i \(-0.279127\pi\)
0.639534 + 0.768763i \(0.279127\pi\)
\(128\) 18.9546 1.67537
\(129\) 10.9899 0.967603
\(130\) 1.00955 0.0885438
\(131\) 15.4389 1.34890 0.674452 0.738319i \(-0.264380\pi\)
0.674452 + 0.738319i \(0.264380\pi\)
\(132\) 8.12924 0.707560
\(133\) −12.5989 −1.09246
\(134\) −5.62792 −0.486178
\(135\) 0.753280 0.0648320
\(136\) 38.5312 3.30403
\(137\) −12.3279 −1.05324 −0.526621 0.850100i \(-0.676541\pi\)
−0.526621 + 0.850100i \(0.676541\pi\)
\(138\) −17.7619 −1.51199
\(139\) 7.49102 0.635380 0.317690 0.948195i \(-0.397093\pi\)
0.317690 + 0.948195i \(0.397093\pi\)
\(140\) −1.92337 −0.162554
\(141\) −12.7388 −1.07280
\(142\) 34.8545 2.92492
\(143\) −1.45677 −0.121821
\(144\) 19.1860 1.59883
\(145\) 1.64918 0.136957
\(146\) −7.49313 −0.620136
\(147\) −4.89626 −0.403837
\(148\) 24.7012 2.03042
\(149\) 8.88590 0.727961 0.363981 0.931407i \(-0.381417\pi\)
0.363981 + 0.931407i \(0.381417\pi\)
\(150\) 33.0861 2.70147
\(151\) −5.98210 −0.486816 −0.243408 0.969924i \(-0.578265\pi\)
−0.243408 + 0.969924i \(0.578265\pi\)
\(152\) −28.1845 −2.28607
\(153\) −32.8071 −2.65229
\(154\) 4.13946 0.333567
\(155\) −1.48462 −0.119248
\(156\) −21.7817 −1.74393
\(157\) 15.4856 1.23588 0.617942 0.786224i \(-0.287967\pi\)
0.617942 + 0.786224i \(0.287967\pi\)
\(158\) 13.3657 1.06332
\(159\) −4.07743 −0.323361
\(160\) −0.143989 −0.0113833
\(161\) −6.06403 −0.477913
\(162\) 7.83883 0.615877
\(163\) −22.5815 −1.76872 −0.884358 0.466810i \(-0.845403\pi\)
−0.884358 + 0.466810i \(0.845403\pi\)
\(164\) −11.9181 −0.930648
\(165\) 0.414365 0.0322582
\(166\) −11.7968 −0.915608
\(167\) −6.24287 −0.483087 −0.241544 0.970390i \(-0.577654\pi\)
−0.241544 + 0.970390i \(0.577654\pi\)
\(168\) 31.4733 2.42822
\(169\) −9.09670 −0.699746
\(170\) 3.86231 0.296226
\(171\) 23.9975 1.83513
\(172\) 16.5061 1.25858
\(173\) −20.3542 −1.54750 −0.773749 0.633492i \(-0.781621\pi\)
−0.773749 + 0.633492i \(0.781621\pi\)
\(174\) −53.0700 −4.02322
\(175\) 11.2958 0.853885
\(176\) 3.25930 0.245679
\(177\) 16.1857 1.21660
\(178\) 21.3288 1.59866
\(179\) 4.81935 0.360215 0.180108 0.983647i \(-0.442355\pi\)
0.180108 + 0.983647i \(0.442355\pi\)
\(180\) 3.66349 0.273060
\(181\) −22.2852 −1.65645 −0.828225 0.560396i \(-0.810649\pi\)
−0.828225 + 0.560396i \(0.810649\pi\)
\(182\) −11.0914 −0.822146
\(183\) 7.60762 0.562372
\(184\) −13.5656 −1.00007
\(185\) 1.25907 0.0925687
\(186\) 47.7747 3.50301
\(187\) −5.57324 −0.407556
\(188\) −19.1329 −1.39541
\(189\) −8.27582 −0.601977
\(190\) −2.82518 −0.204960
\(191\) −17.4157 −1.26016 −0.630080 0.776531i \(-0.716978\pi\)
−0.630080 + 0.776531i \(0.716978\pi\)
\(192\) −19.3184 −1.39419
\(193\) −19.1191 −1.37622 −0.688111 0.725605i \(-0.741560\pi\)
−0.688111 + 0.725605i \(0.741560\pi\)
\(194\) 16.6155 1.19292
\(195\) −1.11026 −0.0795072
\(196\) −7.35390 −0.525278
\(197\) −22.1170 −1.57577 −0.787884 0.615824i \(-0.788823\pi\)
−0.787884 + 0.615824i \(0.788823\pi\)
\(198\) −7.88454 −0.560330
\(199\) −9.02073 −0.639463 −0.319731 0.947508i \(-0.603593\pi\)
−0.319731 + 0.947508i \(0.603593\pi\)
\(200\) 25.2695 1.78682
\(201\) 6.18930 0.436559
\(202\) −44.5805 −3.13667
\(203\) −18.1185 −1.27167
\(204\) −83.3313 −5.83436
\(205\) −0.607492 −0.0424290
\(206\) 38.7428 2.69934
\(207\) 11.5503 0.802804
\(208\) −8.73304 −0.605527
\(209\) 4.07667 0.281989
\(210\) 3.15483 0.217704
\(211\) −16.3882 −1.12821 −0.564104 0.825704i \(-0.690778\pi\)
−0.564104 + 0.825704i \(0.690778\pi\)
\(212\) −6.12405 −0.420602
\(213\) −38.3312 −2.62641
\(214\) 12.2841 0.839722
\(215\) 0.841352 0.0573797
\(216\) −18.5135 −1.25969
\(217\) 16.3106 1.10724
\(218\) 27.7468 1.87925
\(219\) 8.24056 0.556846
\(220\) 0.622351 0.0419589
\(221\) 14.9331 1.00451
\(222\) −40.5165 −2.71929
\(223\) −5.27404 −0.353176 −0.176588 0.984285i \(-0.556506\pi\)
−0.176588 + 0.984285i \(0.556506\pi\)
\(224\) 1.58192 0.105696
\(225\) −21.5155 −1.43437
\(226\) 1.80801 0.120267
\(227\) −8.42635 −0.559276 −0.279638 0.960105i \(-0.590215\pi\)
−0.279638 + 0.960105i \(0.590215\pi\)
\(228\) 60.9546 4.03682
\(229\) 13.8065 0.912359 0.456179 0.889888i \(-0.349218\pi\)
0.456179 + 0.889888i \(0.349218\pi\)
\(230\) −1.35980 −0.0896625
\(231\) −4.55237 −0.299524
\(232\) −40.5322 −2.66107
\(233\) 14.9144 0.977074 0.488537 0.872543i \(-0.337531\pi\)
0.488537 + 0.872543i \(0.337531\pi\)
\(234\) 21.1260 1.38105
\(235\) −0.975245 −0.0636180
\(236\) 24.3100 1.58245
\(237\) −14.6989 −0.954799
\(238\) −42.4328 −2.75051
\(239\) −8.71360 −0.563636 −0.281818 0.959468i \(-0.590937\pi\)
−0.281818 + 0.959468i \(0.590937\pi\)
\(240\) 2.48403 0.160344
\(241\) −4.26170 −0.274520 −0.137260 0.990535i \(-0.543830\pi\)
−0.137260 + 0.990535i \(0.543830\pi\)
\(242\) 25.7600 1.65592
\(243\) −19.5158 −1.25194
\(244\) 11.4262 0.731487
\(245\) −0.374844 −0.0239479
\(246\) 19.5489 1.24639
\(247\) −10.9231 −0.695022
\(248\) 36.4879 2.31698
\(249\) 12.9735 0.822162
\(250\) 5.08794 0.321789
\(251\) −11.3520 −0.716534 −0.358267 0.933619i \(-0.616632\pi\)
−0.358267 + 0.933619i \(0.616632\pi\)
\(252\) −40.2485 −2.53542
\(253\) 1.96216 0.123360
\(254\) −35.5110 −2.22816
\(255\) −4.24757 −0.265993
\(256\) −32.4355 −2.02722
\(257\) −3.48585 −0.217441 −0.108721 0.994072i \(-0.534675\pi\)
−0.108721 + 0.994072i \(0.534675\pi\)
\(258\) −27.0744 −1.68558
\(259\) −13.8326 −0.859517
\(260\) −1.66754 −0.103417
\(261\) 34.5107 2.13616
\(262\) −38.0350 −2.34981
\(263\) −3.02880 −0.186764 −0.0933819 0.995630i \(-0.529768\pi\)
−0.0933819 + 0.995630i \(0.529768\pi\)
\(264\) −10.1839 −0.626778
\(265\) −0.312156 −0.0191756
\(266\) 31.0384 1.90309
\(267\) −23.4563 −1.43550
\(268\) 9.29596 0.567841
\(269\) 11.3537 0.692249 0.346124 0.938189i \(-0.387498\pi\)
0.346124 + 0.938189i \(0.387498\pi\)
\(270\) −1.85577 −0.112938
\(271\) −12.1364 −0.737236 −0.368618 0.929581i \(-0.620169\pi\)
−0.368618 + 0.929581i \(0.620169\pi\)
\(272\) −33.4105 −2.02581
\(273\) 12.1977 0.738239
\(274\) 30.3707 1.83476
\(275\) −3.65504 −0.220407
\(276\) 29.3383 1.76596
\(277\) −8.60539 −0.517048 −0.258524 0.966005i \(-0.583236\pi\)
−0.258524 + 0.966005i \(0.583236\pi\)
\(278\) −18.4548 −1.10684
\(279\) −31.0673 −1.85995
\(280\) 2.40951 0.143995
\(281\) 9.45790 0.564211 0.282105 0.959383i \(-0.408967\pi\)
0.282105 + 0.959383i \(0.408967\pi\)
\(282\) 31.3831 1.86884
\(283\) −23.5494 −1.39987 −0.699934 0.714208i \(-0.746787\pi\)
−0.699934 + 0.714208i \(0.746787\pi\)
\(284\) −57.5712 −3.41622
\(285\) 3.10698 0.184042
\(286\) 3.58887 0.212214
\(287\) 6.67413 0.393961
\(288\) −3.01312 −0.177550
\(289\) 40.1303 2.36060
\(290\) −4.06288 −0.238581
\(291\) −18.2729 −1.07117
\(292\) 12.3768 0.724300
\(293\) 5.90558 0.345008 0.172504 0.985009i \(-0.444814\pi\)
0.172504 + 0.985009i \(0.444814\pi\)
\(294\) 12.0623 0.703491
\(295\) 1.23913 0.0721452
\(296\) −30.9445 −1.79861
\(297\) 2.67784 0.155384
\(298\) −21.8912 −1.26812
\(299\) −5.25746 −0.304047
\(300\) −54.6503 −3.15523
\(301\) −9.24341 −0.532781
\(302\) 14.7374 0.848042
\(303\) 49.0274 2.81655
\(304\) 24.4388 1.40166
\(305\) 0.582418 0.0333491
\(306\) 80.8229 4.62034
\(307\) −22.0290 −1.25726 −0.628632 0.777703i \(-0.716385\pi\)
−0.628632 + 0.777703i \(0.716385\pi\)
\(308\) −6.83739 −0.389596
\(309\) −42.6073 −2.42385
\(310\) 3.65749 0.207732
\(311\) 32.3394 1.83380 0.916899 0.399118i \(-0.130684\pi\)
0.916899 + 0.399118i \(0.130684\pi\)
\(312\) 27.2871 1.54483
\(313\) −19.4592 −1.09990 −0.549950 0.835197i \(-0.685353\pi\)
−0.549950 + 0.835197i \(0.685353\pi\)
\(314\) −38.1500 −2.15293
\(315\) −2.05155 −0.115592
\(316\) −22.0770 −1.24193
\(317\) 10.4087 0.584609 0.292305 0.956325i \(-0.405578\pi\)
0.292305 + 0.956325i \(0.405578\pi\)
\(318\) 10.0451 0.563300
\(319\) 5.86266 0.328246
\(320\) −1.47896 −0.0826765
\(321\) −13.5094 −0.754022
\(322\) 14.9393 0.832532
\(323\) −41.7892 −2.32521
\(324\) −12.9479 −0.719326
\(325\) 9.79338 0.543239
\(326\) 55.6313 3.08113
\(327\) −30.5145 −1.68746
\(328\) 14.9305 0.824397
\(329\) 10.7144 0.590705
\(330\) −1.02082 −0.0561944
\(331\) −20.2037 −1.11050 −0.555248 0.831685i \(-0.687377\pi\)
−0.555248 + 0.831685i \(0.687377\pi\)
\(332\) 19.4854 1.06940
\(333\) 26.3474 1.44383
\(334\) 15.3798 0.841547
\(335\) 0.473835 0.0258884
\(336\) −27.2905 −1.48882
\(337\) −0.0108319 −0.000590049 0 −0.000295025 1.00000i \(-0.500094\pi\)
−0.000295025 1.00000i \(0.500094\pi\)
\(338\) 22.4105 1.21897
\(339\) −1.98835 −0.107993
\(340\) −6.37961 −0.345983
\(341\) −5.27769 −0.285803
\(342\) −59.1198 −3.19683
\(343\) 20.0696 1.08366
\(344\) −20.6781 −1.11489
\(345\) 1.49544 0.0805117
\(346\) 50.1442 2.69577
\(347\) −15.7900 −0.847654 −0.423827 0.905743i \(-0.639314\pi\)
−0.423827 + 0.905743i \(0.639314\pi\)
\(348\) 87.6588 4.69900
\(349\) 29.9566 1.60354 0.801770 0.597632i \(-0.203892\pi\)
0.801770 + 0.597632i \(0.203892\pi\)
\(350\) −27.8282 −1.48748
\(351\) −7.17506 −0.382976
\(352\) −0.511868 −0.0272826
\(353\) 17.3623 0.924102 0.462051 0.886853i \(-0.347114\pi\)
0.462051 + 0.886853i \(0.347114\pi\)
\(354\) −39.8749 −2.11933
\(355\) −2.93453 −0.155749
\(356\) −35.2300 −1.86718
\(357\) 46.6655 2.46980
\(358\) −11.8729 −0.627501
\(359\) 20.2900 1.07086 0.535432 0.844578i \(-0.320149\pi\)
0.535432 + 0.844578i \(0.320149\pi\)
\(360\) −4.58945 −0.241885
\(361\) 11.5677 0.608825
\(362\) 54.9016 2.88556
\(363\) −28.3296 −1.48692
\(364\) 18.3202 0.960241
\(365\) 0.630874 0.0330215
\(366\) −18.7420 −0.979661
\(367\) 14.1454 0.738384 0.369192 0.929353i \(-0.379634\pi\)
0.369192 + 0.929353i \(0.379634\pi\)
\(368\) 11.7628 0.613177
\(369\) −12.7124 −0.661781
\(370\) −3.10183 −0.161256
\(371\) 3.42946 0.178049
\(372\) −78.9122 −4.09141
\(373\) 10.7290 0.555526 0.277763 0.960650i \(-0.410407\pi\)
0.277763 + 0.960650i \(0.410407\pi\)
\(374\) 13.7302 0.709969
\(375\) −5.59546 −0.288948
\(376\) 23.9688 1.23610
\(377\) −15.7085 −0.809031
\(378\) 20.3882 1.04865
\(379\) 16.1912 0.831684 0.415842 0.909437i \(-0.363487\pi\)
0.415842 + 0.909437i \(0.363487\pi\)
\(380\) 4.66651 0.239387
\(381\) 39.0532 2.00076
\(382\) 42.9052 2.19522
\(383\) −17.0072 −0.869026 −0.434513 0.900666i \(-0.643079\pi\)
−0.434513 + 0.900666i \(0.643079\pi\)
\(384\) 51.3542 2.62066
\(385\) −0.348516 −0.0177620
\(386\) 47.1015 2.39740
\(387\) 17.6062 0.894972
\(388\) −27.4448 −1.39330
\(389\) 36.8718 1.86947 0.934736 0.355343i \(-0.115636\pi\)
0.934736 + 0.355343i \(0.115636\pi\)
\(390\) 2.73521 0.138503
\(391\) −20.1138 −1.01720
\(392\) 9.21262 0.465308
\(393\) 41.8290 2.10999
\(394\) 54.4870 2.74501
\(395\) −1.12531 −0.0566205
\(396\) 13.0234 0.654448
\(397\) −24.4544 −1.22733 −0.613667 0.789565i \(-0.710306\pi\)
−0.613667 + 0.789565i \(0.710306\pi\)
\(398\) 22.2233 1.11395
\(399\) −34.1345 −1.70886
\(400\) −21.9112 −1.09556
\(401\) 1.24939 0.0623916 0.0311958 0.999513i \(-0.490068\pi\)
0.0311958 + 0.999513i \(0.490068\pi\)
\(402\) −15.2479 −0.760494
\(403\) 14.1412 0.704421
\(404\) 73.6362 3.66354
\(405\) −0.659980 −0.0327947
\(406\) 44.6364 2.21527
\(407\) 4.47588 0.221861
\(408\) 104.394 5.16825
\(409\) 1.09338 0.0540644 0.0270322 0.999635i \(-0.491394\pi\)
0.0270322 + 0.999635i \(0.491394\pi\)
\(410\) 1.49661 0.0739121
\(411\) −33.4002 −1.64751
\(412\) −63.9937 −3.15274
\(413\) −13.6136 −0.669881
\(414\) −28.4552 −1.39850
\(415\) 0.993214 0.0487550
\(416\) 1.37151 0.0672437
\(417\) 20.2956 0.993881
\(418\) −10.0432 −0.491230
\(419\) 33.8754 1.65492 0.827460 0.561525i \(-0.189785\pi\)
0.827460 + 0.561525i \(0.189785\pi\)
\(420\) −5.21103 −0.254272
\(421\) 36.1210 1.76043 0.880216 0.474574i \(-0.157398\pi\)
0.880216 + 0.474574i \(0.157398\pi\)
\(422\) 40.3736 1.96536
\(423\) −20.4080 −0.992273
\(424\) 7.67193 0.372582
\(425\) 37.4671 1.81742
\(426\) 94.4322 4.57525
\(427\) −6.39866 −0.309653
\(428\) −20.2903 −0.980770
\(429\) −3.94686 −0.190556
\(430\) −2.07274 −0.0999565
\(431\) 10.5344 0.507425 0.253712 0.967280i \(-0.418348\pi\)
0.253712 + 0.967280i \(0.418348\pi\)
\(432\) 16.0531 0.772356
\(433\) −32.7762 −1.57512 −0.787562 0.616235i \(-0.788657\pi\)
−0.787562 + 0.616235i \(0.788657\pi\)
\(434\) −40.1826 −1.92883
\(435\) 4.46815 0.214232
\(436\) −45.8310 −2.19491
\(437\) 14.7127 0.703803
\(438\) −20.3013 −0.970035
\(439\) −10.5311 −0.502623 −0.251312 0.967906i \(-0.580862\pi\)
−0.251312 + 0.967906i \(0.580862\pi\)
\(440\) −0.779653 −0.0371685
\(441\) −7.84400 −0.373524
\(442\) −36.7889 −1.74987
\(443\) 6.98371 0.331806 0.165903 0.986142i \(-0.446946\pi\)
0.165903 + 0.986142i \(0.446946\pi\)
\(444\) 66.9235 3.17605
\(445\) −1.79575 −0.0851265
\(446\) 12.9931 0.615239
\(447\) 24.0748 1.13870
\(448\) 16.2484 0.767667
\(449\) 1.16615 0.0550338 0.0275169 0.999621i \(-0.491240\pi\)
0.0275169 + 0.999621i \(0.491240\pi\)
\(450\) 53.0052 2.49869
\(451\) −2.15957 −0.101690
\(452\) −2.98639 −0.140468
\(453\) −16.2074 −0.761492
\(454\) 20.7590 0.974269
\(455\) 0.933821 0.0437782
\(456\) −76.3611 −3.57594
\(457\) −26.0996 −1.22089 −0.610444 0.792060i \(-0.709009\pi\)
−0.610444 + 0.792060i \(0.709009\pi\)
\(458\) −34.0135 −1.58934
\(459\) −27.4500 −1.28126
\(460\) 2.24606 0.104723
\(461\) 13.5240 0.629874 0.314937 0.949113i \(-0.398017\pi\)
0.314937 + 0.949113i \(0.398017\pi\)
\(462\) 11.2151 0.521775
\(463\) 24.6147 1.14394 0.571971 0.820274i \(-0.306179\pi\)
0.571971 + 0.820274i \(0.306179\pi\)
\(464\) 35.1455 1.63159
\(465\) −4.02232 −0.186531
\(466\) −36.7429 −1.70208
\(467\) −9.72964 −0.450234 −0.225117 0.974332i \(-0.572276\pi\)
−0.225117 + 0.974332i \(0.572276\pi\)
\(468\) −34.8951 −1.61302
\(469\) −5.20573 −0.240378
\(470\) 2.40260 0.110824
\(471\) 41.9554 1.93320
\(472\) −30.4545 −1.40178
\(473\) 2.99093 0.137523
\(474\) 36.2121 1.66328
\(475\) −27.4062 −1.25748
\(476\) 70.0888 3.21251
\(477\) −6.53219 −0.299089
\(478\) 21.4667 0.981864
\(479\) −21.6866 −0.990885 −0.495443 0.868641i \(-0.664994\pi\)
−0.495443 + 0.868641i \(0.664994\pi\)
\(480\) −0.390113 −0.0178062
\(481\) −11.9928 −0.546822
\(482\) 10.4991 0.478219
\(483\) −16.4294 −0.747566
\(484\) −42.5493 −1.93406
\(485\) −1.39892 −0.0635216
\(486\) 48.0789 2.18090
\(487\) −4.13786 −0.187504 −0.0937522 0.995596i \(-0.529886\pi\)
−0.0937522 + 0.995596i \(0.529886\pi\)
\(488\) −14.3142 −0.647974
\(489\) −61.1805 −2.76668
\(490\) 0.923459 0.0417176
\(491\) 35.8806 1.61927 0.809634 0.586935i \(-0.199666\pi\)
0.809634 + 0.586935i \(0.199666\pi\)
\(492\) −32.2900 −1.45575
\(493\) −60.0971 −2.70664
\(494\) 26.9100 1.21074
\(495\) 0.663828 0.0298369
\(496\) −31.6387 −1.42062
\(497\) 32.2398 1.44615
\(498\) −31.9613 −1.43222
\(499\) −4.99660 −0.223678 −0.111839 0.993726i \(-0.535674\pi\)
−0.111839 + 0.993726i \(0.535674\pi\)
\(500\) −8.40405 −0.375840
\(501\) −16.9140 −0.755660
\(502\) 27.9667 1.24821
\(503\) 21.6242 0.964176 0.482088 0.876123i \(-0.339879\pi\)
0.482088 + 0.876123i \(0.339879\pi\)
\(504\) 50.4214 2.24595
\(505\) 3.75340 0.167024
\(506\) −4.83395 −0.214896
\(507\) −24.6459 −1.09456
\(508\) 58.6556 2.60242
\(509\) −37.6768 −1.66999 −0.834997 0.550254i \(-0.814531\pi\)
−0.834997 + 0.550254i \(0.814531\pi\)
\(510\) 10.4643 0.463365
\(511\) −6.93102 −0.306610
\(512\) 41.9985 1.85609
\(513\) 20.0789 0.886507
\(514\) 8.58768 0.378786
\(515\) −3.26189 −0.143736
\(516\) 44.7205 1.96871
\(517\) −3.46691 −0.152474
\(518\) 34.0778 1.49729
\(519\) −55.1461 −2.42064
\(520\) 2.08902 0.0916095
\(521\) 29.5897 1.29635 0.648174 0.761492i \(-0.275533\pi\)
0.648174 + 0.761492i \(0.275533\pi\)
\(522\) −85.0201 −3.72123
\(523\) −14.3667 −0.628213 −0.314106 0.949388i \(-0.601705\pi\)
−0.314106 + 0.949388i \(0.601705\pi\)
\(524\) 62.8247 2.74451
\(525\) 30.6041 1.33567
\(526\) 7.46170 0.325346
\(527\) 54.1006 2.35666
\(528\) 8.83050 0.384298
\(529\) −15.9186 −0.692112
\(530\) 0.769023 0.0334042
\(531\) 25.9302 1.12527
\(532\) −51.2680 −2.22275
\(533\) 5.78641 0.250637
\(534\) 57.7865 2.50067
\(535\) −1.03424 −0.0447142
\(536\) −11.6456 −0.503011
\(537\) 13.0572 0.563459
\(538\) −27.9709 −1.20591
\(539\) −1.33253 −0.0573963
\(540\) 3.06528 0.131909
\(541\) −9.05680 −0.389382 −0.194691 0.980865i \(-0.562370\pi\)
−0.194691 + 0.980865i \(0.562370\pi\)
\(542\) 29.8991 1.28428
\(543\) −60.3780 −2.59107
\(544\) 5.24706 0.224966
\(545\) −2.33610 −0.100068
\(546\) −30.0501 −1.28602
\(547\) 19.3570 0.827644 0.413822 0.910358i \(-0.364194\pi\)
0.413822 + 0.910358i \(0.364194\pi\)
\(548\) −50.1651 −2.14295
\(549\) 12.1877 0.520158
\(550\) 9.00449 0.383953
\(551\) 43.9594 1.87273
\(552\) −36.7537 −1.56434
\(553\) 12.3631 0.525731
\(554\) 21.2001 0.900707
\(555\) 3.41123 0.144799
\(556\) 30.4828 1.29276
\(557\) −33.0231 −1.39923 −0.699616 0.714519i \(-0.746646\pi\)
−0.699616 + 0.714519i \(0.746646\pi\)
\(558\) 76.5369 3.24006
\(559\) −8.01395 −0.338954
\(560\) −2.08928 −0.0882884
\(561\) −15.0997 −0.637511
\(562\) −23.3003 −0.982865
\(563\) −30.5218 −1.28634 −0.643171 0.765723i \(-0.722381\pi\)
−0.643171 + 0.765723i \(0.722381\pi\)
\(564\) −51.8373 −2.18274
\(565\) −0.152223 −0.00640405
\(566\) 58.0160 2.43859
\(567\) 7.25079 0.304504
\(568\) 72.1226 3.02620
\(569\) 17.7482 0.744042 0.372021 0.928224i \(-0.378665\pi\)
0.372021 + 0.928224i \(0.378665\pi\)
\(570\) −7.65432 −0.320604
\(571\) 22.4174 0.938140 0.469070 0.883161i \(-0.344589\pi\)
0.469070 + 0.883161i \(0.344589\pi\)
\(572\) −5.92795 −0.247860
\(573\) −47.1849 −1.97118
\(574\) −16.4423 −0.686288
\(575\) −13.1910 −0.550102
\(576\) −30.9488 −1.28954
\(577\) 26.7970 1.11557 0.557787 0.829984i \(-0.311651\pi\)
0.557787 + 0.829984i \(0.311651\pi\)
\(578\) −98.8643 −4.11221
\(579\) −51.7998 −2.15273
\(580\) 6.71090 0.278655
\(581\) −10.9118 −0.452699
\(582\) 45.0168 1.86601
\(583\) −1.10969 −0.0459585
\(584\) −15.5051 −0.641607
\(585\) −1.77868 −0.0735392
\(586\) −14.5489 −0.601010
\(587\) −15.1774 −0.626437 −0.313218 0.949681i \(-0.601407\pi\)
−0.313218 + 0.949681i \(0.601407\pi\)
\(588\) −19.9241 −0.821656
\(589\) −39.5731 −1.63058
\(590\) −3.05271 −0.125678
\(591\) −59.9220 −2.46486
\(592\) 26.8320 1.10279
\(593\) 30.2545 1.24240 0.621202 0.783650i \(-0.286645\pi\)
0.621202 + 0.783650i \(0.286645\pi\)
\(594\) −6.59708 −0.270682
\(595\) 3.57257 0.146461
\(596\) 36.1589 1.48113
\(597\) −24.4401 −1.00027
\(598\) 12.9522 0.529655
\(599\) −46.9611 −1.91878 −0.959389 0.282088i \(-0.908973\pi\)
−0.959389 + 0.282088i \(0.908973\pi\)
\(600\) 68.4633 2.79500
\(601\) 39.2464 1.60089 0.800446 0.599405i \(-0.204596\pi\)
0.800446 + 0.599405i \(0.204596\pi\)
\(602\) 22.7719 0.928114
\(603\) 9.91549 0.403790
\(604\) −24.3426 −0.990487
\(605\) −2.16883 −0.0881754
\(606\) −120.783 −4.90648
\(607\) 4.12177 0.167297 0.0836487 0.996495i \(-0.473343\pi\)
0.0836487 + 0.996495i \(0.473343\pi\)
\(608\) −3.83808 −0.155655
\(609\) −49.0888 −1.98918
\(610\) −1.43483 −0.0580948
\(611\) 9.28930 0.375805
\(612\) −133.500 −5.39642
\(613\) −27.3466 −1.10452 −0.552260 0.833672i \(-0.686234\pi\)
−0.552260 + 0.833672i \(0.686234\pi\)
\(614\) 54.2704 2.19018
\(615\) −1.64589 −0.0663688
\(616\) 8.56556 0.345116
\(617\) −8.86438 −0.356867 −0.178433 0.983952i \(-0.557103\pi\)
−0.178433 + 0.983952i \(0.557103\pi\)
\(618\) 104.967 4.22238
\(619\) −28.6808 −1.15278 −0.576388 0.817176i \(-0.695538\pi\)
−0.576388 + 0.817176i \(0.695538\pi\)
\(620\) −6.04129 −0.242624
\(621\) 9.66429 0.387815
\(622\) −79.6708 −3.19451
\(623\) 19.7287 0.790415
\(624\) −23.6606 −0.947184
\(625\) 24.3565 0.974261
\(626\) 47.9395 1.91605
\(627\) 11.0450 0.441096
\(628\) 63.0146 2.51456
\(629\) −45.8814 −1.82941
\(630\) 5.05417 0.201363
\(631\) 32.0498 1.27588 0.637940 0.770086i \(-0.279787\pi\)
0.637940 + 0.770086i \(0.279787\pi\)
\(632\) 27.6570 1.10014
\(633\) −44.4009 −1.76478
\(634\) −25.6426 −1.01840
\(635\) 2.98980 0.118647
\(636\) −16.5921 −0.657918
\(637\) 3.57042 0.141465
\(638\) −14.4432 −0.571810
\(639\) −61.4081 −2.42927
\(640\) 3.93153 0.155407
\(641\) −34.9964 −1.38227 −0.691137 0.722724i \(-0.742890\pi\)
−0.691137 + 0.722724i \(0.742890\pi\)
\(642\) 33.2816 1.31352
\(643\) −21.8340 −0.861050 −0.430525 0.902579i \(-0.641672\pi\)
−0.430525 + 0.902579i \(0.641672\pi\)
\(644\) −24.6761 −0.972373
\(645\) 2.27950 0.0897551
\(646\) 102.951 4.05056
\(647\) −9.50571 −0.373708 −0.186854 0.982388i \(-0.559829\pi\)
−0.186854 + 0.982388i \(0.559829\pi\)
\(648\) 16.2205 0.637201
\(649\) 4.40500 0.172912
\(650\) −24.1268 −0.946332
\(651\) 44.1908 1.73197
\(652\) −91.8895 −3.59867
\(653\) −4.17745 −0.163476 −0.0817382 0.996654i \(-0.526047\pi\)
−0.0817382 + 0.996654i \(0.526047\pi\)
\(654\) 75.1751 2.93958
\(655\) 3.20231 0.125125
\(656\) −12.9462 −0.505465
\(657\) 13.2017 0.515047
\(658\) −26.3959 −1.02902
\(659\) 33.0039 1.28565 0.642825 0.766013i \(-0.277762\pi\)
0.642825 + 0.766013i \(0.277762\pi\)
\(660\) 1.68615 0.0656334
\(661\) 20.9557 0.815083 0.407541 0.913187i \(-0.366386\pi\)
0.407541 + 0.913187i \(0.366386\pi\)
\(662\) 49.7735 1.93450
\(663\) 40.4585 1.57128
\(664\) −24.4105 −0.947309
\(665\) −2.61324 −0.101337
\(666\) −64.9090 −2.51517
\(667\) 21.1583 0.819252
\(668\) −25.4038 −0.982901
\(669\) −14.2891 −0.552449
\(670\) −1.16733 −0.0450980
\(671\) 2.07044 0.0799284
\(672\) 4.28593 0.165333
\(673\) −7.61339 −0.293475 −0.146737 0.989175i \(-0.546877\pi\)
−0.146737 + 0.989175i \(0.546877\pi\)
\(674\) 0.0266852 0.00102788
\(675\) −18.0022 −0.692907
\(676\) −37.0167 −1.42372
\(677\) 30.0920 1.15653 0.578265 0.815849i \(-0.303730\pi\)
0.578265 + 0.815849i \(0.303730\pi\)
\(678\) 4.89848 0.188125
\(679\) 15.3691 0.589810
\(680\) 7.99208 0.306482
\(681\) −22.8297 −0.874837
\(682\) 13.0020 0.497874
\(683\) −10.3178 −0.394800 −0.197400 0.980323i \(-0.563250\pi\)
−0.197400 + 0.980323i \(0.563250\pi\)
\(684\) 97.6516 3.73380
\(685\) −2.55702 −0.0976989
\(686\) −49.4431 −1.88775
\(687\) 37.4063 1.42714
\(688\) 17.9300 0.683575
\(689\) 2.97331 0.113274
\(690\) −3.68414 −0.140253
\(691\) −37.2683 −1.41775 −0.708876 0.705333i \(-0.750797\pi\)
−0.708876 + 0.705333i \(0.750797\pi\)
\(692\) −82.8261 −3.14858
\(693\) −7.29307 −0.277041
\(694\) 38.9001 1.47663
\(695\) 1.55377 0.0589380
\(696\) −109.815 −4.16252
\(697\) 22.1374 0.838514
\(698\) −73.8006 −2.79340
\(699\) 40.4079 1.52837
\(700\) 45.9655 1.73733
\(701\) −17.9837 −0.679234 −0.339617 0.940564i \(-0.610297\pi\)
−0.339617 + 0.940564i \(0.610297\pi\)
\(702\) 17.6764 0.667151
\(703\) 33.5610 1.26578
\(704\) −5.25757 −0.198152
\(705\) −2.64226 −0.0995132
\(706\) −42.7735 −1.60980
\(707\) −41.2362 −1.55085
\(708\) 65.8638 2.47531
\(709\) −47.9511 −1.80084 −0.900420 0.435021i \(-0.856741\pi\)
−0.900420 + 0.435021i \(0.856741\pi\)
\(710\) 7.22946 0.271317
\(711\) −23.5483 −0.883130
\(712\) 44.1345 1.65401
\(713\) −19.0471 −0.713321
\(714\) −114.964 −4.30243
\(715\) −0.302160 −0.0113002
\(716\) 19.6111 0.732903
\(717\) −23.6080 −0.881656
\(718\) −49.9861 −1.86546
\(719\) 47.7537 1.78091 0.890456 0.455070i \(-0.150386\pi\)
0.890456 + 0.455070i \(0.150386\pi\)
\(720\) 3.97952 0.148308
\(721\) 35.8364 1.33462
\(722\) −28.4979 −1.06058
\(723\) −11.5463 −0.429413
\(724\) −90.6842 −3.37025
\(725\) −39.4128 −1.46375
\(726\) 69.7922 2.59023
\(727\) −10.5311 −0.390578 −0.195289 0.980746i \(-0.562565\pi\)
−0.195289 + 0.980746i \(0.562565\pi\)
\(728\) −22.9507 −0.850611
\(729\) −43.3291 −1.60478
\(730\) −1.55421 −0.0575239
\(731\) −30.6594 −1.13398
\(732\) 30.9573 1.14421
\(733\) 26.1614 0.966295 0.483147 0.875539i \(-0.339494\pi\)
0.483147 + 0.875539i \(0.339494\pi\)
\(734\) −34.8484 −1.28628
\(735\) −1.01557 −0.0374600
\(736\) −1.84732 −0.0680933
\(737\) 1.68444 0.0620471
\(738\) 31.3181 1.15283
\(739\) 23.6649 0.870526 0.435263 0.900303i \(-0.356655\pi\)
0.435263 + 0.900303i \(0.356655\pi\)
\(740\) 5.12347 0.188342
\(741\) −29.5943 −1.08717
\(742\) −8.44877 −0.310164
\(743\) −30.4320 −1.11644 −0.558220 0.829693i \(-0.688516\pi\)
−0.558220 + 0.829693i \(0.688516\pi\)
\(744\) 98.8576 3.62430
\(745\) 1.84310 0.0675259
\(746\) −26.4318 −0.967735
\(747\) 20.7841 0.760449
\(748\) −22.6789 −0.829223
\(749\) 11.3626 0.415179
\(750\) 13.7849 0.503353
\(751\) −22.0014 −0.802843 −0.401422 0.915893i \(-0.631484\pi\)
−0.401422 + 0.915893i \(0.631484\pi\)
\(752\) −20.7834 −0.757893
\(753\) −30.7563 −1.12082
\(754\) 38.6993 1.40935
\(755\) −1.24080 −0.0451572
\(756\) −33.6763 −1.22480
\(757\) 11.1472 0.405151 0.202576 0.979267i \(-0.435069\pi\)
0.202576 + 0.979267i \(0.435069\pi\)
\(758\) −39.8883 −1.44881
\(759\) 5.31614 0.192964
\(760\) −5.84599 −0.212056
\(761\) 14.2054 0.514945 0.257473 0.966286i \(-0.417110\pi\)
0.257473 + 0.966286i \(0.417110\pi\)
\(762\) −96.2109 −3.48535
\(763\) 25.6653 0.929147
\(764\) −70.8690 −2.56395
\(765\) −6.80478 −0.246027
\(766\) 41.8986 1.51386
\(767\) −11.8029 −0.426177
\(768\) −87.8785 −3.17104
\(769\) −26.2092 −0.945127 −0.472564 0.881297i \(-0.656671\pi\)
−0.472564 + 0.881297i \(0.656671\pi\)
\(770\) 0.858599 0.0309418
\(771\) −9.44429 −0.340128
\(772\) −77.8003 −2.80009
\(773\) 25.0060 0.899404 0.449702 0.893179i \(-0.351530\pi\)
0.449702 + 0.893179i \(0.351530\pi\)
\(774\) −43.3743 −1.55906
\(775\) 35.4802 1.27449
\(776\) 34.3816 1.23423
\(777\) −37.4771 −1.34448
\(778\) −90.8367 −3.25665
\(779\) −16.1929 −0.580171
\(780\) −4.51791 −0.161767
\(781\) −10.4320 −0.373285
\(782\) 49.5520 1.77197
\(783\) 28.8755 1.03193
\(784\) −7.98827 −0.285295
\(785\) 3.21199 0.114641
\(786\) −103.049 −3.67565
\(787\) −27.2848 −0.972600 −0.486300 0.873792i \(-0.661654\pi\)
−0.486300 + 0.873792i \(0.661654\pi\)
\(788\) −89.9994 −3.20609
\(789\) −8.20600 −0.292141
\(790\) 2.77229 0.0986338
\(791\) 1.67238 0.0594628
\(792\) −16.3151 −0.579730
\(793\) −5.54758 −0.197000
\(794\) 60.2456 2.13804
\(795\) −0.845732 −0.0299950
\(796\) −36.7076 −1.30107
\(797\) 29.0781 1.03000 0.514999 0.857191i \(-0.327792\pi\)
0.514999 + 0.857191i \(0.327792\pi\)
\(798\) 84.0932 2.97687
\(799\) 35.5386 1.25727
\(800\) 3.44112 0.121662
\(801\) −37.5779 −1.32775
\(802\) −3.07798 −0.108687
\(803\) 2.24270 0.0791431
\(804\) 25.1858 0.888234
\(805\) −1.25779 −0.0443313
\(806\) −34.8379 −1.22711
\(807\) 30.7609 1.08284
\(808\) −92.2481 −3.24528
\(809\) 9.73223 0.342167 0.171084 0.985257i \(-0.445273\pi\)
0.171084 + 0.985257i \(0.445273\pi\)
\(810\) 1.62592 0.0571289
\(811\) −18.4772 −0.648821 −0.324411 0.945916i \(-0.605166\pi\)
−0.324411 + 0.945916i \(0.605166\pi\)
\(812\) −73.7285 −2.58736
\(813\) −32.8816 −1.15321
\(814\) −11.0267 −0.386485
\(815\) −4.68380 −0.164066
\(816\) −90.5198 −3.16883
\(817\) 22.4265 0.784605
\(818\) −2.69365 −0.0941811
\(819\) 19.5412 0.682825
\(820\) −2.47203 −0.0863271
\(821\) −12.6750 −0.442360 −0.221180 0.975233i \(-0.570991\pi\)
−0.221180 + 0.975233i \(0.570991\pi\)
\(822\) 82.2842 2.86999
\(823\) 9.04786 0.315389 0.157694 0.987488i \(-0.449594\pi\)
0.157694 + 0.987488i \(0.449594\pi\)
\(824\) 80.1683 2.79280
\(825\) −9.90268 −0.344767
\(826\) 33.5382 1.16694
\(827\) −22.9582 −0.798335 −0.399167 0.916878i \(-0.630701\pi\)
−0.399167 + 0.916878i \(0.630701\pi\)
\(828\) 47.0012 1.63340
\(829\) 45.7039 1.58736 0.793681 0.608334i \(-0.208162\pi\)
0.793681 + 0.608334i \(0.208162\pi\)
\(830\) −2.44687 −0.0849320
\(831\) −23.3148 −0.808782
\(832\) 14.0872 0.488387
\(833\) 13.6596 0.473275
\(834\) −50.0000 −1.73136
\(835\) −1.29488 −0.0448113
\(836\) 16.5890 0.573742
\(837\) −25.9943 −0.898496
\(838\) −83.4548 −2.88290
\(839\) 0.284620 0.00982618 0.00491309 0.999988i \(-0.498436\pi\)
0.00491309 + 0.999988i \(0.498436\pi\)
\(840\) 6.52813 0.225242
\(841\) 34.2179 1.17993
\(842\) −88.9872 −3.06670
\(843\) 25.6245 0.882555
\(844\) −66.6875 −2.29548
\(845\) −1.88682 −0.0649086
\(846\) 50.2769 1.72856
\(847\) 23.8276 0.818725
\(848\) −6.65234 −0.228442
\(849\) −63.8030 −2.18971
\(850\) −92.3033 −3.16598
\(851\) 16.1534 0.553731
\(852\) −155.979 −5.34376
\(853\) 20.2275 0.692575 0.346288 0.938128i \(-0.387442\pi\)
0.346288 + 0.938128i \(0.387442\pi\)
\(854\) 15.7636 0.539421
\(855\) 4.97751 0.170227
\(856\) 25.4188 0.868796
\(857\) −8.92552 −0.304890 −0.152445 0.988312i \(-0.548715\pi\)
−0.152445 + 0.988312i \(0.548715\pi\)
\(858\) 9.72342 0.331952
\(859\) −19.6422 −0.670183 −0.335092 0.942186i \(-0.608767\pi\)
−0.335092 + 0.942186i \(0.608767\pi\)
\(860\) 3.42367 0.116746
\(861\) 18.0824 0.616246
\(862\) −25.9524 −0.883943
\(863\) 18.1000 0.616131 0.308066 0.951365i \(-0.400318\pi\)
0.308066 + 0.951365i \(0.400318\pi\)
\(864\) −2.52111 −0.0857700
\(865\) −4.22182 −0.143546
\(866\) 80.7469 2.74389
\(867\) 108.726 3.69253
\(868\) 66.3719 2.25281
\(869\) −4.00037 −0.135703
\(870\) −11.0077 −0.373195
\(871\) −4.51332 −0.152928
\(872\) 57.4150 1.94432
\(873\) −29.2739 −0.990770
\(874\) −36.2459 −1.22604
\(875\) 4.70626 0.159101
\(876\) 33.5329 1.13297
\(877\) 9.15545 0.309158 0.154579 0.987980i \(-0.450598\pi\)
0.154579 + 0.987980i \(0.450598\pi\)
\(878\) 25.9443 0.875578
\(879\) 16.0001 0.539672
\(880\) 0.676038 0.0227892
\(881\) −18.7061 −0.630224 −0.315112 0.949055i \(-0.602042\pi\)
−0.315112 + 0.949055i \(0.602042\pi\)
\(882\) 19.3243 0.650685
\(883\) 4.05251 0.136378 0.0681889 0.997672i \(-0.478278\pi\)
0.0681889 + 0.997672i \(0.478278\pi\)
\(884\) 60.7663 2.04379
\(885\) 3.35722 0.112852
\(886\) −17.2050 −0.578012
\(887\) 37.0743 1.24483 0.622417 0.782686i \(-0.286151\pi\)
0.622417 + 0.782686i \(0.286151\pi\)
\(888\) −83.8386 −2.81344
\(889\) −32.8471 −1.10166
\(890\) 4.42397 0.148292
\(891\) −2.34617 −0.0785995
\(892\) −21.4614 −0.718580
\(893\) −25.9955 −0.869907
\(894\) −59.3103 −1.98363
\(895\) 0.999621 0.0334137
\(896\) −43.1932 −1.44298
\(897\) −14.2442 −0.475599
\(898\) −2.87290 −0.0958699
\(899\) −56.9101 −1.89806
\(900\) −87.5518 −2.91839
\(901\) 11.3752 0.378962
\(902\) 5.32029 0.177146
\(903\) −25.0434 −0.833393
\(904\) 3.74121 0.124431
\(905\) −4.62236 −0.153653
\(906\) 39.9284 1.32653
\(907\) 36.4602 1.21064 0.605321 0.795981i \(-0.293045\pi\)
0.605321 + 0.795981i \(0.293045\pi\)
\(908\) −34.2889 −1.13792
\(909\) 78.5438 2.60513
\(910\) −2.30055 −0.0762624
\(911\) 44.5145 1.47483 0.737415 0.675440i \(-0.236046\pi\)
0.737415 + 0.675440i \(0.236046\pi\)
\(912\) 66.2128 2.19252
\(913\) 3.53078 0.116852
\(914\) 64.2985 2.12681
\(915\) 1.57796 0.0521657
\(916\) 56.1820 1.85631
\(917\) −35.1818 −1.16180
\(918\) 67.6254 2.23197
\(919\) −9.58116 −0.316053 −0.158027 0.987435i \(-0.550513\pi\)
−0.158027 + 0.987435i \(0.550513\pi\)
\(920\) −2.81376 −0.0927669
\(921\) −59.6839 −1.96665
\(922\) −33.3174 −1.09725
\(923\) 27.9516 0.920039
\(924\) −18.5247 −0.609418
\(925\) −30.0899 −0.989348
\(926\) −60.6404 −1.99277
\(927\) −68.2586 −2.24191
\(928\) −5.51954 −0.181188
\(929\) 42.3386 1.38908 0.694542 0.719452i \(-0.255607\pi\)
0.694542 + 0.719452i \(0.255607\pi\)
\(930\) 9.90933 0.324940
\(931\) −9.99159 −0.327461
\(932\) 60.6904 1.98798
\(933\) 87.6179 2.86848
\(934\) 23.9698 0.784315
\(935\) −1.15599 −0.0378050
\(936\) 43.7149 1.42887
\(937\) −22.3169 −0.729061 −0.364531 0.931191i \(-0.618771\pi\)
−0.364531 + 0.931191i \(0.618771\pi\)
\(938\) 12.8248 0.418743
\(939\) −52.7214 −1.72050
\(940\) −3.96851 −0.129439
\(941\) 24.0424 0.783761 0.391880 0.920016i \(-0.371825\pi\)
0.391880 + 0.920016i \(0.371825\pi\)
\(942\) −103.361 −3.36768
\(943\) −7.79388 −0.253804
\(944\) 26.4071 0.859479
\(945\) −1.71656 −0.0558395
\(946\) −7.36840 −0.239567
\(947\) −4.27489 −0.138915 −0.0694576 0.997585i \(-0.522127\pi\)
−0.0694576 + 0.997585i \(0.522127\pi\)
\(948\) −59.8137 −1.94266
\(949\) −6.00913 −0.195065
\(950\) 67.5174 2.19055
\(951\) 28.2005 0.914463
\(952\) −87.8040 −2.84574
\(953\) −39.3324 −1.27410 −0.637051 0.770822i \(-0.719846\pi\)
−0.637051 + 0.770822i \(0.719846\pi\)
\(954\) 16.0926 0.521018
\(955\) −3.61234 −0.116893
\(956\) −35.4578 −1.14679
\(957\) 15.8839 0.513452
\(958\) 53.4267 1.72614
\(959\) 28.0924 0.907152
\(960\) −4.00699 −0.129325
\(961\) 20.2316 0.652634
\(962\) 29.5452 0.952574
\(963\) −21.6426 −0.697423
\(964\) −17.3419 −0.558546
\(965\) −3.96565 −0.127659
\(966\) 40.4753 1.30227
\(967\) 42.9667 1.38172 0.690859 0.722990i \(-0.257233\pi\)
0.690859 + 0.722990i \(0.257233\pi\)
\(968\) 53.3038 1.71325
\(969\) −113.221 −3.63717
\(970\) 3.44635 0.110656
\(971\) 36.2576 1.16356 0.581780 0.813346i \(-0.302356\pi\)
0.581780 + 0.813346i \(0.302356\pi\)
\(972\) −79.4148 −2.54723
\(973\) −17.0704 −0.547250
\(974\) 10.1940 0.326636
\(975\) 26.5335 0.849751
\(976\) 12.4119 0.397294
\(977\) 5.49274 0.175728 0.0878641 0.996132i \(-0.471996\pi\)
0.0878641 + 0.996132i \(0.471996\pi\)
\(978\) 150.723 4.81960
\(979\) −6.38371 −0.204024
\(980\) −1.52533 −0.0487249
\(981\) −48.8854 −1.56079
\(982\) −88.3948 −2.82079
\(983\) −41.6338 −1.32791 −0.663956 0.747772i \(-0.731124\pi\)
−0.663956 + 0.747772i \(0.731124\pi\)
\(984\) 40.4515 1.28955
\(985\) −4.58746 −0.146169
\(986\) 148.054 4.71500
\(987\) 29.0288 0.923998
\(988\) −44.4489 −1.41411
\(989\) 10.7942 0.343236
\(990\) −1.63540 −0.0519763
\(991\) −39.7595 −1.26300 −0.631501 0.775375i \(-0.717561\pi\)
−0.631501 + 0.775375i \(0.717561\pi\)
\(992\) 4.96881 0.157760
\(993\) −54.7384 −1.73707
\(994\) −79.4255 −2.51923
\(995\) −1.87106 −0.0593167
\(996\) 52.7924 1.67279
\(997\) 6.99188 0.221435 0.110718 0.993852i \(-0.464685\pi\)
0.110718 + 0.993852i \(0.464685\pi\)
\(998\) 12.3095 0.389652
\(999\) 22.0451 0.697477
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 \(a_p\))