Properties

Label 4003.2.a.b.1.7
Level 4003
Weight 2
Character 4003.1
Self dual Yes
Analytic conductor 31.964
Analytic rank 1
Dimension 152
CM No

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Newspace parameters

Level: \( N \) = \( 4003 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4003.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(31.9641159291\)
Analytic rank: \(1\)
Dimension: \(152\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.7
Character \(\chi\) = 4003.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.68690 q^{2} +0.420690 q^{3} +5.21946 q^{4} -4.00007 q^{5} -1.13035 q^{6} -1.97783 q^{7} -8.65037 q^{8} -2.82302 q^{9} +O(q^{10})\) \(q-2.68690 q^{2} +0.420690 q^{3} +5.21946 q^{4} -4.00007 q^{5} -1.13035 q^{6} -1.97783 q^{7} -8.65037 q^{8} -2.82302 q^{9} +10.7478 q^{10} +3.47964 q^{11} +2.19577 q^{12} -2.54963 q^{13} +5.31424 q^{14} -1.68279 q^{15} +12.8038 q^{16} -4.33097 q^{17} +7.58519 q^{18} +4.38839 q^{19} -20.8782 q^{20} -0.832053 q^{21} -9.34945 q^{22} +4.51931 q^{23} -3.63912 q^{24} +11.0006 q^{25} +6.85061 q^{26} -2.44969 q^{27} -10.3232 q^{28} -4.29151 q^{29} +4.52149 q^{30} +0.697882 q^{31} -17.1019 q^{32} +1.46385 q^{33} +11.6369 q^{34} +7.91146 q^{35} -14.7346 q^{36} +0.561776 q^{37} -11.7912 q^{38} -1.07260 q^{39} +34.6021 q^{40} -9.09924 q^{41} +2.23565 q^{42} +3.56903 q^{43} +18.1618 q^{44} +11.2923 q^{45} -12.1430 q^{46} +1.73100 q^{47} +5.38643 q^{48} -3.08819 q^{49} -29.5575 q^{50} -1.82200 q^{51} -13.3077 q^{52} +3.98898 q^{53} +6.58207 q^{54} -13.9188 q^{55} +17.1090 q^{56} +1.84615 q^{57} +11.5309 q^{58} +13.7051 q^{59} -8.78325 q^{60} +7.04260 q^{61} -1.87514 q^{62} +5.58345 q^{63} +20.3435 q^{64} +10.1987 q^{65} -3.93322 q^{66} +10.0443 q^{67} -22.6053 q^{68} +1.90123 q^{69} -21.2573 q^{70} -14.2890 q^{71} +24.4202 q^{72} +13.0688 q^{73} -1.50944 q^{74} +4.62783 q^{75} +22.9050 q^{76} -6.88213 q^{77} +2.88198 q^{78} +3.64155 q^{79} -51.2161 q^{80} +7.43850 q^{81} +24.4488 q^{82} +1.94077 q^{83} -4.34286 q^{84} +17.3242 q^{85} -9.58964 q^{86} -1.80540 q^{87} -30.1001 q^{88} +12.2418 q^{89} -30.3413 q^{90} +5.04273 q^{91} +23.5883 q^{92} +0.293592 q^{93} -4.65104 q^{94} -17.5539 q^{95} -7.19458 q^{96} -5.49719 q^{97} +8.29768 q^{98} -9.82308 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 152q - 22q^{2} - 18q^{3} + 138q^{4} - 59q^{5} - 17q^{6} - 19q^{7} - 66q^{8} + 106q^{9} + O(q^{10}) \) \( 152q - 22q^{2} - 18q^{3} + 138q^{4} - 59q^{5} - 17q^{6} - 19q^{7} - 66q^{8} + 106q^{9} - 15q^{10} - 40q^{11} - 53q^{12} - 59q^{13} - 36q^{14} - 40q^{15} + 118q^{16} - 93q^{17} - 59q^{18} - 16q^{19} - 108q^{20} - 62q^{21} - 37q^{22} - 107q^{23} - 31q^{24} + 101q^{25} - 64q^{26} - 63q^{27} - 53q^{28} - 124q^{29} - 68q^{30} - 15q^{31} - 129q^{32} - 49q^{33} - 76q^{35} + 45q^{36} - 98q^{37} - 125q^{38} - 47q^{39} - 7q^{40} - 56q^{41} - 84q^{42} - 62q^{43} - 114q^{44} - 142q^{45} - 3q^{46} - 111q^{47} - 92q^{48} + 117q^{49} - 64q^{50} - 21q^{51} - 85q^{52} - 347q^{53} + 3q^{54} - 16q^{55} - 73q^{56} - 115q^{57} - 29q^{58} - 50q^{59} - 54q^{60} - 62q^{61} - 55q^{62} - 70q^{63} + 64q^{64} - 147q^{65} + 34q^{66} - 86q^{67} - 174q^{68} - 104q^{69} - 7q^{70} - 86q^{71} - 139q^{72} - 27q^{73} - 52q^{74} - 49q^{75} - 11q^{76} - 346q^{77} - 59q^{78} - 17q^{79} - 149q^{80} - 8q^{81} - 31q^{82} - 106q^{83} - 51q^{84} - 69q^{85} - 85q^{86} - 32q^{87} - 113q^{88} - 59q^{89} + 10q^{90} - 9q^{91} - 314q^{92} - 230q^{93} + 7q^{94} - 74q^{95} - 54q^{96} - 60q^{97} - 77q^{98} - 96q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.68690 −1.89993 −0.949964 0.312359i \(-0.898881\pi\)
−0.949964 + 0.312359i \(0.898881\pi\)
\(3\) 0.420690 0.242885 0.121443 0.992598i \(-0.461248\pi\)
0.121443 + 0.992598i \(0.461248\pi\)
\(4\) 5.21946 2.60973
\(5\) −4.00007 −1.78889 −0.894443 0.447182i \(-0.852428\pi\)
−0.894443 + 0.447182i \(0.852428\pi\)
\(6\) −1.13035 −0.461465
\(7\) −1.97783 −0.747549 −0.373775 0.927520i \(-0.621937\pi\)
−0.373775 + 0.927520i \(0.621937\pi\)
\(8\) −8.65037 −3.05837
\(9\) −2.82302 −0.941007
\(10\) 10.7478 3.39876
\(11\) 3.47964 1.04915 0.524575 0.851364i \(-0.324224\pi\)
0.524575 + 0.851364i \(0.324224\pi\)
\(12\) 2.19577 0.633865
\(13\) −2.54963 −0.707140 −0.353570 0.935408i \(-0.615032\pi\)
−0.353570 + 0.935408i \(0.615032\pi\)
\(14\) 5.31424 1.42029
\(15\) −1.68279 −0.434494
\(16\) 12.8038 3.20095
\(17\) −4.33097 −1.05041 −0.525207 0.850974i \(-0.676012\pi\)
−0.525207 + 0.850974i \(0.676012\pi\)
\(18\) 7.58519 1.78785
\(19\) 4.38839 1.00676 0.503382 0.864064i \(-0.332089\pi\)
0.503382 + 0.864064i \(0.332089\pi\)
\(20\) −20.8782 −4.66851
\(21\) −0.832053 −0.181569
\(22\) −9.34945 −1.99331
\(23\) 4.51931 0.942342 0.471171 0.882042i \(-0.343832\pi\)
0.471171 + 0.882042i \(0.343832\pi\)
\(24\) −3.63912 −0.742833
\(25\) 11.0006 2.20011
\(26\) 6.85061 1.34351
\(27\) −2.44969 −0.471442
\(28\) −10.3232 −1.95090
\(29\) −4.29151 −0.796914 −0.398457 0.917187i \(-0.630454\pi\)
−0.398457 + 0.917187i \(0.630454\pi\)
\(30\) 4.52149 0.825508
\(31\) 0.697882 0.125343 0.0626717 0.998034i \(-0.480038\pi\)
0.0626717 + 0.998034i \(0.480038\pi\)
\(32\) −17.1019 −3.02321
\(33\) 1.46385 0.254823
\(34\) 11.6369 1.99571
\(35\) 7.91146 1.33728
\(36\) −14.7346 −2.45577
\(37\) 0.561776 0.0923554 0.0461777 0.998933i \(-0.485296\pi\)
0.0461777 + 0.998933i \(0.485296\pi\)
\(38\) −11.7912 −1.91278
\(39\) −1.07260 −0.171754
\(40\) 34.6021 5.47107
\(41\) −9.09924 −1.42106 −0.710531 0.703666i \(-0.751545\pi\)
−0.710531 + 0.703666i \(0.751545\pi\)
\(42\) 2.23565 0.344968
\(43\) 3.56903 0.544272 0.272136 0.962259i \(-0.412270\pi\)
0.272136 + 0.962259i \(0.412270\pi\)
\(44\) 18.1618 2.73800
\(45\) 11.2923 1.68335
\(46\) −12.1430 −1.79038
\(47\) 1.73100 0.252493 0.126246 0.991999i \(-0.459707\pi\)
0.126246 + 0.991999i \(0.459707\pi\)
\(48\) 5.38643 0.777465
\(49\) −3.08819 −0.441170
\(50\) −29.5575 −4.18006
\(51\) −1.82200 −0.255130
\(52\) −13.3077 −1.84544
\(53\) 3.98898 0.547928 0.273964 0.961740i \(-0.411665\pi\)
0.273964 + 0.961740i \(0.411665\pi\)
\(54\) 6.58207 0.895707
\(55\) −13.9188 −1.87681
\(56\) 17.1090 2.28628
\(57\) 1.84615 0.244528
\(58\) 11.5309 1.51408
\(59\) 13.7051 1.78426 0.892129 0.451781i \(-0.149211\pi\)
0.892129 + 0.451781i \(0.149211\pi\)
\(60\) −8.78325 −1.13391
\(61\) 7.04260 0.901713 0.450856 0.892596i \(-0.351119\pi\)
0.450856 + 0.892596i \(0.351119\pi\)
\(62\) −1.87514 −0.238143
\(63\) 5.58345 0.703449
\(64\) 20.3435 2.54293
\(65\) 10.1987 1.26499
\(66\) −3.93322 −0.484146
\(67\) 10.0443 1.22711 0.613556 0.789651i \(-0.289738\pi\)
0.613556 + 0.789651i \(0.289738\pi\)
\(68\) −22.6053 −2.74130
\(69\) 1.90123 0.228881
\(70\) −21.2573 −2.54074
\(71\) −14.2890 −1.69579 −0.847894 0.530166i \(-0.822130\pi\)
−0.847894 + 0.530166i \(0.822130\pi\)
\(72\) 24.4202 2.87794
\(73\) 13.0688 1.52958 0.764792 0.644277i \(-0.222842\pi\)
0.764792 + 0.644277i \(0.222842\pi\)
\(74\) −1.50944 −0.175469
\(75\) 4.62783 0.534376
\(76\) 22.9050 2.62738
\(77\) −6.88213 −0.784291
\(78\) 2.88198 0.326320
\(79\) 3.64155 0.409706 0.204853 0.978793i \(-0.434328\pi\)
0.204853 + 0.978793i \(0.434328\pi\)
\(80\) −51.2161 −5.72614
\(81\) 7.43850 0.826500
\(82\) 24.4488 2.69992
\(83\) 1.94077 0.213027 0.106514 0.994311i \(-0.466031\pi\)
0.106514 + 0.994311i \(0.466031\pi\)
\(84\) −4.34286 −0.473845
\(85\) 17.3242 1.87907
\(86\) −9.58964 −1.03408
\(87\) −1.80540 −0.193559
\(88\) −30.1001 −3.20869
\(89\) 12.2418 1.29763 0.648813 0.760948i \(-0.275266\pi\)
0.648813 + 0.760948i \(0.275266\pi\)
\(90\) −30.3413 −3.19825
\(91\) 5.04273 0.528622
\(92\) 23.5883 2.45926
\(93\) 0.293592 0.0304441
\(94\) −4.65104 −0.479718
\(95\) −17.5539 −1.80099
\(96\) −7.19458 −0.734294
\(97\) −5.49719 −0.558155 −0.279078 0.960269i \(-0.590029\pi\)
−0.279078 + 0.960269i \(0.590029\pi\)
\(98\) 8.29768 0.838192
\(99\) −9.82308 −0.987257
\(100\) 57.4170 5.74170
\(101\) 14.3475 1.42763 0.713815 0.700334i \(-0.246966\pi\)
0.713815 + 0.700334i \(0.246966\pi\)
\(102\) 4.89553 0.484730
\(103\) −15.5032 −1.52757 −0.763787 0.645469i \(-0.776662\pi\)
−0.763787 + 0.645469i \(0.776662\pi\)
\(104\) 22.0552 2.16269
\(105\) 3.32827 0.324806
\(106\) −10.7180 −1.04102
\(107\) −10.5513 −1.02004 −0.510018 0.860164i \(-0.670361\pi\)
−0.510018 + 0.860164i \(0.670361\pi\)
\(108\) −12.7860 −1.23034
\(109\) 13.8055 1.32233 0.661164 0.750242i \(-0.270063\pi\)
0.661164 + 0.750242i \(0.270063\pi\)
\(110\) 37.3985 3.56580
\(111\) 0.236334 0.0224318
\(112\) −25.3237 −2.39287
\(113\) −16.9137 −1.59111 −0.795553 0.605884i \(-0.792819\pi\)
−0.795553 + 0.605884i \(0.792819\pi\)
\(114\) −4.96043 −0.464587
\(115\) −18.0776 −1.68574
\(116\) −22.3994 −2.07973
\(117\) 7.19765 0.665423
\(118\) −36.8244 −3.38996
\(119\) 8.56592 0.785237
\(120\) 14.5568 1.32884
\(121\) 1.10787 0.100715
\(122\) −18.9228 −1.71319
\(123\) −3.82796 −0.345155
\(124\) 3.64257 0.327112
\(125\) −24.0027 −2.14687
\(126\) −15.0022 −1.33650
\(127\) 11.7162 1.03965 0.519823 0.854274i \(-0.325998\pi\)
0.519823 + 0.854274i \(0.325998\pi\)
\(128\) −20.4572 −1.80818
\(129\) 1.50145 0.132196
\(130\) −27.4029 −2.40339
\(131\) 6.01570 0.525594 0.262797 0.964851i \(-0.415355\pi\)
0.262797 + 0.964851i \(0.415355\pi\)
\(132\) 7.64049 0.665019
\(133\) −8.67948 −0.752606
\(134\) −26.9882 −2.33143
\(135\) 9.79892 0.843357
\(136\) 37.4645 3.21255
\(137\) −17.6505 −1.50798 −0.753991 0.656884i \(-0.771874\pi\)
−0.753991 + 0.656884i \(0.771874\pi\)
\(138\) −5.10842 −0.434858
\(139\) 12.6521 1.07314 0.536570 0.843856i \(-0.319720\pi\)
0.536570 + 0.843856i \(0.319720\pi\)
\(140\) 41.2935 3.48994
\(141\) 0.728216 0.0613269
\(142\) 38.3931 3.22188
\(143\) −8.87178 −0.741895
\(144\) −36.1454 −3.01212
\(145\) 17.1664 1.42559
\(146\) −35.1145 −2.90610
\(147\) −1.29917 −0.107154
\(148\) 2.93217 0.241023
\(149\) 12.6293 1.03463 0.517317 0.855794i \(-0.326931\pi\)
0.517317 + 0.855794i \(0.326931\pi\)
\(150\) −12.4345 −1.01528
\(151\) −12.7417 −1.03691 −0.518453 0.855106i \(-0.673492\pi\)
−0.518453 + 0.855106i \(0.673492\pi\)
\(152\) −37.9612 −3.07906
\(153\) 12.2264 0.988447
\(154\) 18.4916 1.49010
\(155\) −2.79158 −0.224225
\(156\) −5.59840 −0.448231
\(157\) −15.4884 −1.23611 −0.618053 0.786136i \(-0.712078\pi\)
−0.618053 + 0.786136i \(0.712078\pi\)
\(158\) −9.78449 −0.778412
\(159\) 1.67812 0.133084
\(160\) 68.4087 5.40818
\(161\) −8.93843 −0.704447
\(162\) −19.9865 −1.57029
\(163\) −17.4478 −1.36662 −0.683310 0.730129i \(-0.739460\pi\)
−0.683310 + 0.730129i \(0.739460\pi\)
\(164\) −47.4931 −3.70859
\(165\) −5.85550 −0.455850
\(166\) −5.21467 −0.404737
\(167\) 4.31610 0.333990 0.166995 0.985958i \(-0.446594\pi\)
0.166995 + 0.985958i \(0.446594\pi\)
\(168\) 7.19757 0.555304
\(169\) −6.49939 −0.499953
\(170\) −46.5484 −3.57010
\(171\) −12.3885 −0.947372
\(172\) 18.6284 1.42040
\(173\) −24.6294 −1.87254 −0.936270 0.351282i \(-0.885746\pi\)
−0.936270 + 0.351282i \(0.885746\pi\)
\(174\) 4.85093 0.367748
\(175\) −21.7572 −1.64469
\(176\) 44.5526 3.35828
\(177\) 5.76562 0.433370
\(178\) −32.8925 −2.46540
\(179\) −2.56185 −0.191481 −0.0957407 0.995406i \(-0.530522\pi\)
−0.0957407 + 0.995406i \(0.530522\pi\)
\(180\) 58.9396 4.39309
\(181\) 17.8424 1.32621 0.663106 0.748525i \(-0.269238\pi\)
0.663106 + 0.748525i \(0.269238\pi\)
\(182\) −13.5493 −1.00434
\(183\) 2.96275 0.219013
\(184\) −39.0937 −2.88203
\(185\) −2.24714 −0.165213
\(186\) −0.788854 −0.0578416
\(187\) −15.0702 −1.10204
\(188\) 9.03490 0.658938
\(189\) 4.84506 0.352426
\(190\) 47.1655 3.42175
\(191\) 1.31894 0.0954349 0.0477174 0.998861i \(-0.484805\pi\)
0.0477174 + 0.998861i \(0.484805\pi\)
\(192\) 8.55829 0.617641
\(193\) 19.4965 1.40339 0.701694 0.712479i \(-0.252427\pi\)
0.701694 + 0.712479i \(0.252427\pi\)
\(194\) 14.7704 1.06045
\(195\) 4.29049 0.307248
\(196\) −16.1187 −1.15133
\(197\) −0.523930 −0.0373285 −0.0186642 0.999826i \(-0.505941\pi\)
−0.0186642 + 0.999826i \(0.505941\pi\)
\(198\) 26.3937 1.87572
\(199\) −10.3754 −0.735496 −0.367748 0.929926i \(-0.619871\pi\)
−0.367748 + 0.929926i \(0.619871\pi\)
\(200\) −95.1590 −6.72876
\(201\) 4.22556 0.298048
\(202\) −38.5504 −2.71240
\(203\) 8.48788 0.595732
\(204\) −9.50983 −0.665821
\(205\) 36.3976 2.54212
\(206\) 41.6555 2.90228
\(207\) −12.7581 −0.886750
\(208\) −32.6449 −2.26352
\(209\) 15.2700 1.05625
\(210\) −8.94274 −0.617108
\(211\) −14.6778 −1.01046 −0.505230 0.862985i \(-0.668592\pi\)
−0.505230 + 0.862985i \(0.668592\pi\)
\(212\) 20.8203 1.42994
\(213\) −6.01122 −0.411882
\(214\) 28.3504 1.93800
\(215\) −14.2764 −0.973640
\(216\) 21.1907 1.44184
\(217\) −1.38029 −0.0937003
\(218\) −37.0941 −2.51233
\(219\) 5.49790 0.371514
\(220\) −72.6485 −4.89796
\(221\) 11.0424 0.742790
\(222\) −0.635006 −0.0426188
\(223\) 8.12228 0.543908 0.271954 0.962310i \(-0.412330\pi\)
0.271954 + 0.962310i \(0.412330\pi\)
\(224\) 33.8246 2.26000
\(225\) −31.0548 −2.07032
\(226\) 45.4454 3.02299
\(227\) 21.9164 1.45464 0.727320 0.686298i \(-0.240766\pi\)
0.727320 + 0.686298i \(0.240766\pi\)
\(228\) 9.63590 0.638153
\(229\) 9.19255 0.607461 0.303730 0.952758i \(-0.401768\pi\)
0.303730 + 0.952758i \(0.401768\pi\)
\(230\) 48.5727 3.20279
\(231\) −2.89524 −0.190493
\(232\) 37.1232 2.43726
\(233\) −0.413316 −0.0270772 −0.0135386 0.999908i \(-0.504310\pi\)
−0.0135386 + 0.999908i \(0.504310\pi\)
\(234\) −19.3394 −1.26426
\(235\) −6.92414 −0.451681
\(236\) 71.5334 4.65643
\(237\) 1.53196 0.0995117
\(238\) −23.0158 −1.49189
\(239\) −17.5334 −1.13414 −0.567071 0.823669i \(-0.691924\pi\)
−0.567071 + 0.823669i \(0.691924\pi\)
\(240\) −21.5461 −1.39080
\(241\) 29.4233 1.89532 0.947662 0.319276i \(-0.103440\pi\)
0.947662 + 0.319276i \(0.103440\pi\)
\(242\) −2.97673 −0.191351
\(243\) 10.4784 0.672187
\(244\) 36.7586 2.35323
\(245\) 12.3530 0.789203
\(246\) 10.2854 0.655770
\(247\) −11.1888 −0.711923
\(248\) −6.03694 −0.383346
\(249\) 0.816463 0.0517412
\(250\) 64.4929 4.07889
\(251\) −10.6770 −0.673925 −0.336963 0.941518i \(-0.609400\pi\)
−0.336963 + 0.941518i \(0.609400\pi\)
\(252\) 29.1426 1.83581
\(253\) 15.7256 0.988657
\(254\) −31.4804 −1.97525
\(255\) 7.28811 0.456399
\(256\) 14.2797 0.892479
\(257\) −6.46137 −0.403049 −0.201524 0.979483i \(-0.564590\pi\)
−0.201524 + 0.979483i \(0.564590\pi\)
\(258\) −4.03426 −0.251162
\(259\) −1.11110 −0.0690402
\(260\) 53.2316 3.30129
\(261\) 12.1150 0.749901
\(262\) −16.1636 −0.998592
\(263\) −3.32295 −0.204902 −0.102451 0.994738i \(-0.532668\pi\)
−0.102451 + 0.994738i \(0.532668\pi\)
\(264\) −12.6628 −0.779343
\(265\) −15.9562 −0.980181
\(266\) 23.3209 1.42990
\(267\) 5.14999 0.315174
\(268\) 52.4260 3.20243
\(269\) 16.8635 1.02819 0.514094 0.857734i \(-0.328128\pi\)
0.514094 + 0.857734i \(0.328128\pi\)
\(270\) −26.3288 −1.60232
\(271\) −14.6528 −0.890096 −0.445048 0.895507i \(-0.646813\pi\)
−0.445048 + 0.895507i \(0.646813\pi\)
\(272\) −55.4529 −3.36233
\(273\) 2.12143 0.128395
\(274\) 47.4252 2.86506
\(275\) 38.2780 2.30825
\(276\) 9.92338 0.597317
\(277\) −26.2976 −1.58007 −0.790034 0.613062i \(-0.789937\pi\)
−0.790034 + 0.613062i \(0.789937\pi\)
\(278\) −33.9951 −2.03889
\(279\) −1.97014 −0.117949
\(280\) −68.4370 −4.08989
\(281\) 19.9818 1.19202 0.596009 0.802978i \(-0.296752\pi\)
0.596009 + 0.802978i \(0.296752\pi\)
\(282\) −1.95665 −0.116517
\(283\) −16.4821 −0.979762 −0.489881 0.871789i \(-0.662960\pi\)
−0.489881 + 0.871789i \(0.662960\pi\)
\(284\) −74.5806 −4.42555
\(285\) −7.38473 −0.437434
\(286\) 23.8376 1.40955
\(287\) 17.9967 1.06231
\(288\) 48.2789 2.84486
\(289\) 1.75731 0.103371
\(290\) −46.1243 −2.70851
\(291\) −2.31261 −0.135568
\(292\) 68.2119 3.99180
\(293\) −19.3464 −1.13023 −0.565113 0.825013i \(-0.691168\pi\)
−0.565113 + 0.825013i \(0.691168\pi\)
\(294\) 3.49075 0.203585
\(295\) −54.8216 −3.19183
\(296\) −4.85957 −0.282457
\(297\) −8.52402 −0.494614
\(298\) −33.9338 −1.96573
\(299\) −11.5226 −0.666367
\(300\) 24.1547 1.39457
\(301\) −7.05893 −0.406870
\(302\) 34.2357 1.97005
\(303\) 6.03585 0.346751
\(304\) 56.1880 3.22260
\(305\) −28.1709 −1.61306
\(306\) −32.8512 −1.87798
\(307\) −6.32371 −0.360913 −0.180457 0.983583i \(-0.557758\pi\)
−0.180457 + 0.983583i \(0.557758\pi\)
\(308\) −35.9209 −2.04679
\(309\) −6.52203 −0.371025
\(310\) 7.50071 0.426011
\(311\) 1.59636 0.0905212 0.0452606 0.998975i \(-0.485588\pi\)
0.0452606 + 0.998975i \(0.485588\pi\)
\(312\) 9.27841 0.525287
\(313\) −13.6077 −0.769154 −0.384577 0.923093i \(-0.625653\pi\)
−0.384577 + 0.923093i \(0.625653\pi\)
\(314\) 41.6158 2.34851
\(315\) −22.3342 −1.25839
\(316\) 19.0069 1.06922
\(317\) −21.6683 −1.21701 −0.608505 0.793550i \(-0.708231\pi\)
−0.608505 + 0.793550i \(0.708231\pi\)
\(318\) −4.50895 −0.252850
\(319\) −14.9329 −0.836082
\(320\) −81.3753 −4.54902
\(321\) −4.43884 −0.247752
\(322\) 24.0167 1.33840
\(323\) −19.0060 −1.05752
\(324\) 38.8249 2.15694
\(325\) −28.0474 −1.55579
\(326\) 46.8806 2.59648
\(327\) 5.80784 0.321174
\(328\) 78.7118 4.34613
\(329\) −3.42363 −0.188751
\(330\) 15.7332 0.866082
\(331\) 8.74663 0.480758 0.240379 0.970679i \(-0.422728\pi\)
0.240379 + 0.970679i \(0.422728\pi\)
\(332\) 10.1298 0.555943
\(333\) −1.58591 −0.0869071
\(334\) −11.5970 −0.634557
\(335\) −40.1781 −2.19516
\(336\) −10.6534 −0.581193
\(337\) 17.9330 0.976873 0.488437 0.872599i \(-0.337567\pi\)
0.488437 + 0.872599i \(0.337567\pi\)
\(338\) 17.4633 0.949876
\(339\) −7.11542 −0.386456
\(340\) 90.4228 4.90387
\(341\) 2.42838 0.131504
\(342\) 33.2867 1.79994
\(343\) 19.9527 1.07735
\(344\) −30.8734 −1.66458
\(345\) −7.60505 −0.409442
\(346\) 66.1769 3.55769
\(347\) 15.7807 0.847155 0.423577 0.905860i \(-0.360774\pi\)
0.423577 + 0.905860i \(0.360774\pi\)
\(348\) −9.42318 −0.505136
\(349\) 16.4879 0.882578 0.441289 0.897365i \(-0.354521\pi\)
0.441289 + 0.897365i \(0.354521\pi\)
\(350\) 58.4596 3.12480
\(351\) 6.24579 0.333376
\(352\) −59.5083 −3.17180
\(353\) 11.4594 0.609925 0.304962 0.952364i \(-0.401356\pi\)
0.304962 + 0.952364i \(0.401356\pi\)
\(354\) −15.4917 −0.823373
\(355\) 57.1569 3.03357
\(356\) 63.8954 3.38645
\(357\) 3.60360 0.190723
\(358\) 6.88344 0.363801
\(359\) −1.34046 −0.0707467 −0.0353733 0.999374i \(-0.511262\pi\)
−0.0353733 + 0.999374i \(0.511262\pi\)
\(360\) −97.6824 −5.14831
\(361\) 0.257925 0.0135750
\(362\) −47.9407 −2.51971
\(363\) 0.466068 0.0244622
\(364\) 26.3203 1.37956
\(365\) −52.2760 −2.73625
\(366\) −7.96063 −0.416109
\(367\) −35.7717 −1.86727 −0.933633 0.358230i \(-0.883380\pi\)
−0.933633 + 0.358230i \(0.883380\pi\)
\(368\) 57.8644 3.01639
\(369\) 25.6873 1.33723
\(370\) 6.03786 0.313894
\(371\) −7.88951 −0.409603
\(372\) 1.53239 0.0794508
\(373\) −14.5299 −0.752327 −0.376164 0.926553i \(-0.622757\pi\)
−0.376164 + 0.926553i \(0.622757\pi\)
\(374\) 40.4922 2.09380
\(375\) −10.0977 −0.521443
\(376\) −14.9738 −0.772216
\(377\) 10.9418 0.563529
\(378\) −13.0182 −0.669585
\(379\) 12.6017 0.647306 0.323653 0.946176i \(-0.395089\pi\)
0.323653 + 0.946176i \(0.395089\pi\)
\(380\) −91.6216 −4.70009
\(381\) 4.92890 0.252515
\(382\) −3.54386 −0.181319
\(383\) −16.7551 −0.856145 −0.428072 0.903744i \(-0.640807\pi\)
−0.428072 + 0.903744i \(0.640807\pi\)
\(384\) −8.60615 −0.439181
\(385\) 27.5290 1.40301
\(386\) −52.3852 −2.66634
\(387\) −10.0754 −0.512163
\(388\) −28.6923 −1.45663
\(389\) −29.5687 −1.49919 −0.749596 0.661896i \(-0.769752\pi\)
−0.749596 + 0.661896i \(0.769752\pi\)
\(390\) −11.5281 −0.583750
\(391\) −19.5730 −0.989849
\(392\) 26.7140 1.34926
\(393\) 2.53075 0.127659
\(394\) 1.40775 0.0709215
\(395\) −14.5665 −0.732918
\(396\) −51.2711 −2.57647
\(397\) −0.796357 −0.0399680 −0.0199840 0.999800i \(-0.506362\pi\)
−0.0199840 + 0.999800i \(0.506362\pi\)
\(398\) 27.8778 1.39739
\(399\) −3.65137 −0.182797
\(400\) 140.849 7.04246
\(401\) −10.5550 −0.527090 −0.263545 0.964647i \(-0.584892\pi\)
−0.263545 + 0.964647i \(0.584892\pi\)
\(402\) −11.3537 −0.566269
\(403\) −1.77934 −0.0886353
\(404\) 74.8862 3.72573
\(405\) −29.7545 −1.47851
\(406\) −22.8061 −1.13185
\(407\) 1.95478 0.0968947
\(408\) 15.7609 0.780283
\(409\) −13.9027 −0.687444 −0.343722 0.939071i \(-0.611688\pi\)
−0.343722 + 0.939071i \(0.611688\pi\)
\(410\) −97.7968 −4.82984
\(411\) −7.42538 −0.366267
\(412\) −80.9181 −3.98655
\(413\) −27.1064 −1.33382
\(414\) 34.2798 1.68476
\(415\) −7.76322 −0.381081
\(416\) 43.6034 2.13783
\(417\) 5.32262 0.260650
\(418\) −41.0290 −2.00679
\(419\) 17.8500 0.872031 0.436015 0.899939i \(-0.356389\pi\)
0.436015 + 0.899939i \(0.356389\pi\)
\(420\) 17.3718 0.847655
\(421\) −26.1225 −1.27313 −0.636566 0.771222i \(-0.719646\pi\)
−0.636566 + 0.771222i \(0.719646\pi\)
\(422\) 39.4378 1.91980
\(423\) −4.88666 −0.237598
\(424\) −34.5061 −1.67576
\(425\) −47.6431 −2.31103
\(426\) 16.1516 0.782547
\(427\) −13.9291 −0.674075
\(428\) −55.0722 −2.66202
\(429\) −3.73227 −0.180196
\(430\) 38.3592 1.84985
\(431\) −4.43438 −0.213597 −0.106798 0.994281i \(-0.534060\pi\)
−0.106798 + 0.994281i \(0.534060\pi\)
\(432\) −31.3653 −1.50906
\(433\) −31.1666 −1.49777 −0.748886 0.662699i \(-0.769411\pi\)
−0.748886 + 0.662699i \(0.769411\pi\)
\(434\) 3.70871 0.178024
\(435\) 7.22171 0.346255
\(436\) 72.0572 3.45091
\(437\) 19.8325 0.948716
\(438\) −14.7723 −0.705850
\(439\) −10.6341 −0.507536 −0.253768 0.967265i \(-0.581670\pi\)
−0.253768 + 0.967265i \(0.581670\pi\)
\(440\) 120.403 5.73997
\(441\) 8.71803 0.415144
\(442\) −29.6698 −1.41125
\(443\) 21.3500 1.01437 0.507185 0.861837i \(-0.330686\pi\)
0.507185 + 0.861837i \(0.330686\pi\)
\(444\) 1.23353 0.0585409
\(445\) −48.9680 −2.32130
\(446\) −21.8238 −1.03339
\(447\) 5.31302 0.251297
\(448\) −40.2359 −1.90097
\(449\) 16.6929 0.787787 0.393894 0.919156i \(-0.371128\pi\)
0.393894 + 0.919156i \(0.371128\pi\)
\(450\) 83.4413 3.93346
\(451\) −31.6620 −1.49091
\(452\) −88.2802 −4.15235
\(453\) −5.36031 −0.251849
\(454\) −58.8872 −2.76371
\(455\) −20.1713 −0.945644
\(456\) −15.9699 −0.747858
\(457\) −0.525670 −0.0245898 −0.0122949 0.999924i \(-0.503914\pi\)
−0.0122949 + 0.999924i \(0.503914\pi\)
\(458\) −24.6995 −1.15413
\(459\) 10.6095 0.495210
\(460\) −94.3551 −4.39933
\(461\) 6.21088 0.289270 0.144635 0.989485i \(-0.453799\pi\)
0.144635 + 0.989485i \(0.453799\pi\)
\(462\) 7.77924 0.361923
\(463\) 8.57996 0.398745 0.199372 0.979924i \(-0.436110\pi\)
0.199372 + 0.979924i \(0.436110\pi\)
\(464\) −54.9477 −2.55088
\(465\) −1.17439 −0.0544610
\(466\) 1.11054 0.0514448
\(467\) 25.3373 1.17247 0.586235 0.810141i \(-0.300610\pi\)
0.586235 + 0.810141i \(0.300610\pi\)
\(468\) 37.5678 1.73657
\(469\) −19.8660 −0.917327
\(470\) 18.6045 0.858162
\(471\) −6.51580 −0.300232
\(472\) −118.555 −5.45692
\(473\) 12.4189 0.571022
\(474\) −4.11624 −0.189065
\(475\) 48.2747 2.21500
\(476\) 44.7094 2.04925
\(477\) −11.2610 −0.515604
\(478\) 47.1106 2.15479
\(479\) −18.2777 −0.835130 −0.417565 0.908647i \(-0.637116\pi\)
−0.417565 + 0.908647i \(0.637116\pi\)
\(480\) 28.7788 1.31357
\(481\) −1.43232 −0.0653082
\(482\) −79.0577 −3.60098
\(483\) −3.76031 −0.171100
\(484\) 5.78246 0.262839
\(485\) 21.9892 0.998476
\(486\) −28.1544 −1.27711
\(487\) −12.6657 −0.573939 −0.286970 0.957940i \(-0.592648\pi\)
−0.286970 + 0.957940i \(0.592648\pi\)
\(488\) −60.9211 −2.75777
\(489\) −7.34012 −0.331932
\(490\) −33.1913 −1.49943
\(491\) −41.4093 −1.86878 −0.934389 0.356255i \(-0.884053\pi\)
−0.934389 + 0.356255i \(0.884053\pi\)
\(492\) −19.9799 −0.900761
\(493\) 18.5864 0.837090
\(494\) 30.0631 1.35260
\(495\) 39.2930 1.76609
\(496\) 8.93555 0.401218
\(497\) 28.2611 1.26769
\(498\) −2.19376 −0.0983046
\(499\) −18.7842 −0.840894 −0.420447 0.907317i \(-0.638127\pi\)
−0.420447 + 0.907317i \(0.638127\pi\)
\(500\) −125.281 −5.60274
\(501\) 1.81574 0.0811213
\(502\) 28.6880 1.28041
\(503\) −7.51792 −0.335207 −0.167604 0.985854i \(-0.553603\pi\)
−0.167604 + 0.985854i \(0.553603\pi\)
\(504\) −48.2989 −2.15140
\(505\) −57.3910 −2.55387
\(506\) −42.2531 −1.87838
\(507\) −2.73423 −0.121431
\(508\) 61.1523 2.71319
\(509\) −20.8304 −0.923292 −0.461646 0.887064i \(-0.652741\pi\)
−0.461646 + 0.887064i \(0.652741\pi\)
\(510\) −19.5825 −0.867126
\(511\) −25.8478 −1.14344
\(512\) 2.54635 0.112534
\(513\) −10.7502 −0.474631
\(514\) 17.3611 0.765764
\(515\) 62.0138 2.73265
\(516\) 7.83677 0.344995
\(517\) 6.02326 0.264903
\(518\) 2.98541 0.131172
\(519\) −10.3613 −0.454813
\(520\) −88.2225 −3.86881
\(521\) −1.95775 −0.0857706 −0.0428853 0.999080i \(-0.513655\pi\)
−0.0428853 + 0.999080i \(0.513655\pi\)
\(522\) −32.5519 −1.42476
\(523\) 2.70844 0.118432 0.0592159 0.998245i \(-0.481140\pi\)
0.0592159 + 0.998245i \(0.481140\pi\)
\(524\) 31.3987 1.37166
\(525\) −9.15305 −0.399472
\(526\) 8.92845 0.389299
\(527\) −3.02251 −0.131663
\(528\) 18.7428 0.815677
\(529\) −2.57582 −0.111992
\(530\) 42.8727 1.86227
\(531\) −38.6899 −1.67900
\(532\) −45.3021 −1.96410
\(533\) 23.1997 1.00489
\(534\) −13.8375 −0.598809
\(535\) 42.2061 1.82473
\(536\) −86.8873 −3.75296
\(537\) −1.07774 −0.0465081
\(538\) −45.3107 −1.95348
\(539\) −10.7458 −0.462854
\(540\) 51.1450 2.20093
\(541\) 12.4835 0.536706 0.268353 0.963321i \(-0.413521\pi\)
0.268353 + 0.963321i \(0.413521\pi\)
\(542\) 39.3707 1.69112
\(543\) 7.50610 0.322118
\(544\) 74.0677 3.17563
\(545\) −55.2230 −2.36549
\(546\) −5.70007 −0.243940
\(547\) 35.3280 1.51052 0.755259 0.655427i \(-0.227511\pi\)
0.755259 + 0.655427i \(0.227511\pi\)
\(548\) −92.1259 −3.93542
\(549\) −19.8814 −0.848518
\(550\) −102.849 −4.38551
\(551\) −18.8328 −0.802305
\(552\) −16.4463 −0.700002
\(553\) −7.20236 −0.306276
\(554\) 70.6591 3.00202
\(555\) −0.945351 −0.0401279
\(556\) 66.0372 2.80060
\(557\) 6.71952 0.284715 0.142358 0.989815i \(-0.454532\pi\)
0.142358 + 0.989815i \(0.454532\pi\)
\(558\) 5.29357 0.224095
\(559\) −9.09970 −0.384876
\(560\) 101.297 4.28057
\(561\) −6.33988 −0.267670
\(562\) −53.6893 −2.26475
\(563\) −2.26789 −0.0955800 −0.0477900 0.998857i \(-0.515218\pi\)
−0.0477900 + 0.998857i \(0.515218\pi\)
\(564\) 3.80089 0.160046
\(565\) 67.6559 2.84631
\(566\) 44.2859 1.86148
\(567\) −14.7121 −0.617850
\(568\) 123.605 5.18634
\(569\) 43.5035 1.82376 0.911880 0.410456i \(-0.134630\pi\)
0.911880 + 0.410456i \(0.134630\pi\)
\(570\) 19.8421 0.831092
\(571\) −43.3433 −1.81386 −0.906931 0.421279i \(-0.861581\pi\)
−0.906931 + 0.421279i \(0.861581\pi\)
\(572\) −46.3059 −1.93615
\(573\) 0.554863 0.0231797
\(574\) −48.3555 −2.01832
\(575\) 49.7150 2.07326
\(576\) −57.4300 −2.39292
\(577\) −3.99964 −0.166507 −0.0832536 0.996528i \(-0.526531\pi\)
−0.0832536 + 0.996528i \(0.526531\pi\)
\(578\) −4.72172 −0.196398
\(579\) 8.20198 0.340862
\(580\) 89.5990 3.72040
\(581\) −3.83851 −0.159248
\(582\) 6.21377 0.257569
\(583\) 13.8802 0.574858
\(584\) −113.050 −4.67803
\(585\) −28.7911 −1.19037
\(586\) 51.9818 2.14735
\(587\) −36.4316 −1.50369 −0.751846 0.659339i \(-0.770836\pi\)
−0.751846 + 0.659339i \(0.770836\pi\)
\(588\) −6.78097 −0.279642
\(589\) 3.06258 0.126191
\(590\) 147.300 6.06426
\(591\) −0.220412 −0.00906655
\(592\) 7.19287 0.295625
\(593\) −11.1919 −0.459594 −0.229797 0.973239i \(-0.573806\pi\)
−0.229797 + 0.973239i \(0.573806\pi\)
\(594\) 22.9032 0.939730
\(595\) −34.2643 −1.40470
\(596\) 65.9181 2.70011
\(597\) −4.36484 −0.178641
\(598\) 30.9600 1.26605
\(599\) 18.1366 0.741041 0.370521 0.928824i \(-0.379179\pi\)
0.370521 + 0.928824i \(0.379179\pi\)
\(600\) −40.0324 −1.63432
\(601\) 30.7298 1.25350 0.626748 0.779222i \(-0.284386\pi\)
0.626748 + 0.779222i \(0.284386\pi\)
\(602\) 18.9667 0.773024
\(603\) −28.3554 −1.15472
\(604\) −66.5048 −2.70604
\(605\) −4.43154 −0.180168
\(606\) −16.2178 −0.658801
\(607\) −39.8347 −1.61684 −0.808421 0.588605i \(-0.799677\pi\)
−0.808421 + 0.588605i \(0.799677\pi\)
\(608\) −75.0496 −3.04366
\(609\) 3.57076 0.144695
\(610\) 75.6926 3.06470
\(611\) −4.41342 −0.178548
\(612\) 63.8152 2.57958
\(613\) −4.08131 −0.164842 −0.0824212 0.996598i \(-0.526265\pi\)
−0.0824212 + 0.996598i \(0.526265\pi\)
\(614\) 16.9912 0.685710
\(615\) 15.3121 0.617443
\(616\) 59.5329 2.39865
\(617\) −25.1471 −1.01238 −0.506192 0.862421i \(-0.668947\pi\)
−0.506192 + 0.862421i \(0.668947\pi\)
\(618\) 17.5241 0.704922
\(619\) 40.9642 1.64649 0.823246 0.567685i \(-0.192161\pi\)
0.823246 + 0.567685i \(0.192161\pi\)
\(620\) −14.5705 −0.585166
\(621\) −11.0709 −0.444260
\(622\) −4.28926 −0.171984
\(623\) −24.2121 −0.970039
\(624\) −13.7334 −0.549776
\(625\) 41.0096 1.64039
\(626\) 36.5626 1.46134
\(627\) 6.42393 0.256547
\(628\) −80.8409 −3.22590
\(629\) −2.43304 −0.0970115
\(630\) 60.0099 2.39085
\(631\) −10.3066 −0.410299 −0.205149 0.978731i \(-0.565768\pi\)
−0.205149 + 0.978731i \(0.565768\pi\)
\(632\) −31.5007 −1.25303
\(633\) −6.17479 −0.245426
\(634\) 58.2206 2.31223
\(635\) −46.8657 −1.85981
\(636\) 8.75888 0.347312
\(637\) 7.87374 0.311969
\(638\) 40.1233 1.58850
\(639\) 40.3380 1.59575
\(640\) 81.8303 3.23463
\(641\) 21.1114 0.833851 0.416925 0.908941i \(-0.363108\pi\)
0.416925 + 0.908941i \(0.363108\pi\)
\(642\) 11.9267 0.470711
\(643\) 15.2860 0.602821 0.301410 0.953494i \(-0.402543\pi\)
0.301410 + 0.953494i \(0.402543\pi\)
\(644\) −46.6537 −1.83841
\(645\) −6.00592 −0.236483
\(646\) 51.0672 2.00921
\(647\) −7.47418 −0.293840 −0.146920 0.989148i \(-0.546936\pi\)
−0.146920 + 0.989148i \(0.546936\pi\)
\(648\) −64.3458 −2.52774
\(649\) 47.6889 1.87195
\(650\) 75.3606 2.95588
\(651\) −0.580675 −0.0227584
\(652\) −91.0682 −3.56650
\(653\) 13.0449 0.510486 0.255243 0.966877i \(-0.417844\pi\)
0.255243 + 0.966877i \(0.417844\pi\)
\(654\) −15.6051 −0.610208
\(655\) −24.0632 −0.940228
\(656\) −116.505 −4.54875
\(657\) −36.8934 −1.43935
\(658\) 9.19897 0.358613
\(659\) −31.6772 −1.23397 −0.616984 0.786975i \(-0.711646\pi\)
−0.616984 + 0.786975i \(0.711646\pi\)
\(660\) −30.5625 −1.18964
\(661\) −6.71929 −0.261350 −0.130675 0.991425i \(-0.541714\pi\)
−0.130675 + 0.991425i \(0.541714\pi\)
\(662\) −23.5013 −0.913406
\(663\) 4.64541 0.180413
\(664\) −16.7884 −0.651516
\(665\) 34.7185 1.34633
\(666\) 4.26118 0.165117
\(667\) −19.3947 −0.750965
\(668\) 22.5277 0.871623
\(669\) 3.41696 0.132107
\(670\) 107.955 4.17065
\(671\) 24.5057 0.946032
\(672\) 14.2297 0.548921
\(673\) −17.9538 −0.692069 −0.346034 0.938222i \(-0.612472\pi\)
−0.346034 + 0.938222i \(0.612472\pi\)
\(674\) −48.1843 −1.85599
\(675\) −26.9479 −1.03723
\(676\) −33.9233 −1.30474
\(677\) 36.6598 1.40895 0.704475 0.709729i \(-0.251183\pi\)
0.704475 + 0.709729i \(0.251183\pi\)
\(678\) 19.1184 0.734239
\(679\) 10.8725 0.417248
\(680\) −149.861 −5.74689
\(681\) 9.22000 0.353311
\(682\) −6.52482 −0.249848
\(683\) 32.0078 1.22474 0.612372 0.790570i \(-0.290216\pi\)
0.612372 + 0.790570i \(0.290216\pi\)
\(684\) −64.6612 −2.47238
\(685\) 70.6032 2.69761
\(686\) −53.6111 −2.04688
\(687\) 3.86721 0.147543
\(688\) 45.6971 1.74219
\(689\) −10.1704 −0.387462
\(690\) 20.4340 0.777911
\(691\) −14.5176 −0.552275 −0.276138 0.961118i \(-0.589055\pi\)
−0.276138 + 0.961118i \(0.589055\pi\)
\(692\) −128.552 −4.88682
\(693\) 19.4284 0.738023
\(694\) −42.4013 −1.60953
\(695\) −50.6094 −1.91972
\(696\) 15.6173 0.591974
\(697\) 39.4085 1.49270
\(698\) −44.3015 −1.67684
\(699\) −0.173878 −0.00657666
\(700\) −113.561 −4.29220
\(701\) 4.45492 0.168260 0.0841301 0.996455i \(-0.473189\pi\)
0.0841301 + 0.996455i \(0.473189\pi\)
\(702\) −16.7818 −0.633390
\(703\) 2.46529 0.0929802
\(704\) 70.7879 2.66792
\(705\) −2.91292 −0.109707
\(706\) −30.7904 −1.15881
\(707\) −28.3769 −1.06722
\(708\) 30.0934 1.13098
\(709\) −27.1358 −1.01911 −0.509554 0.860439i \(-0.670189\pi\)
−0.509554 + 0.860439i \(0.670189\pi\)
\(710\) −153.575 −5.76357
\(711\) −10.2802 −0.385536
\(712\) −105.896 −3.96862
\(713\) 3.15395 0.118116
\(714\) −9.68252 −0.362359
\(715\) 35.4877 1.32717
\(716\) −13.3714 −0.499714
\(717\) −7.37613 −0.275467
\(718\) 3.60168 0.134414
\(719\) −19.4840 −0.726632 −0.363316 0.931666i \(-0.618355\pi\)
−0.363316 + 0.931666i \(0.618355\pi\)
\(720\) 144.584 5.38833
\(721\) 30.6626 1.14194
\(722\) −0.693019 −0.0257915
\(723\) 12.3781 0.460347
\(724\) 93.1274 3.46105
\(725\) −47.2091 −1.75330
\(726\) −1.25228 −0.0464765
\(727\) 41.8194 1.55099 0.775497 0.631351i \(-0.217499\pi\)
0.775497 + 0.631351i \(0.217499\pi\)
\(728\) −43.6215 −1.61672
\(729\) −17.9074 −0.663236
\(730\) 140.461 5.19868
\(731\) −15.4574 −0.571711
\(732\) 15.4640 0.571564
\(733\) 11.8062 0.436072 0.218036 0.975941i \(-0.430035\pi\)
0.218036 + 0.975941i \(0.430035\pi\)
\(734\) 96.1151 3.54767
\(735\) 5.19678 0.191686
\(736\) −77.2887 −2.84890
\(737\) 34.9507 1.28742
\(738\) −69.0194 −2.54064
\(739\) 36.9572 1.35949 0.679746 0.733447i \(-0.262090\pi\)
0.679746 + 0.733447i \(0.262090\pi\)
\(740\) −11.7289 −0.431162
\(741\) −4.70700 −0.172916
\(742\) 21.1984 0.778216
\(743\) −1.71315 −0.0628495 −0.0314248 0.999506i \(-0.510004\pi\)
−0.0314248 + 0.999506i \(0.510004\pi\)
\(744\) −2.53968 −0.0931092
\(745\) −50.5181 −1.85084
\(746\) 39.0403 1.42937
\(747\) −5.47883 −0.200460
\(748\) −78.6582 −2.87603
\(749\) 20.8687 0.762527
\(750\) 27.1315 0.990703
\(751\) −13.0401 −0.475841 −0.237920 0.971285i \(-0.576466\pi\)
−0.237920 + 0.971285i \(0.576466\pi\)
\(752\) 22.1634 0.808218
\(753\) −4.49170 −0.163687
\(754\) −29.3995 −1.07067
\(755\) 50.9677 1.85491
\(756\) 25.2886 0.919737
\(757\) −9.32396 −0.338885 −0.169443 0.985540i \(-0.554197\pi\)
−0.169443 + 0.985540i \(0.554197\pi\)
\(758\) −33.8596 −1.22984
\(759\) 6.61558 0.240131
\(760\) 151.847 5.50808
\(761\) −34.5995 −1.25423 −0.627115 0.778927i \(-0.715764\pi\)
−0.627115 + 0.778927i \(0.715764\pi\)
\(762\) −13.2435 −0.479761
\(763\) −27.3049 −0.988505
\(764\) 6.88413 0.249059
\(765\) −48.9065 −1.76822
\(766\) 45.0193 1.62661
\(767\) −34.9430 −1.26172
\(768\) 6.00731 0.216770
\(769\) 42.3784 1.52820 0.764102 0.645096i \(-0.223183\pi\)
0.764102 + 0.645096i \(0.223183\pi\)
\(770\) −73.9678 −2.66561
\(771\) −2.71823 −0.0978947
\(772\) 101.761 3.66246
\(773\) 17.8026 0.640316 0.320158 0.947364i \(-0.396264\pi\)
0.320158 + 0.947364i \(0.396264\pi\)
\(774\) 27.0717 0.973074
\(775\) 7.67710 0.275770
\(776\) 47.5527 1.70704
\(777\) −0.467428 −0.0167689
\(778\) 79.4482 2.84836
\(779\) −39.9310 −1.43067
\(780\) 22.3940 0.801834
\(781\) −49.7204 −1.77914
\(782\) 52.5908 1.88064
\(783\) 10.5129 0.375699
\(784\) −39.5406 −1.41216
\(785\) 61.9546 2.21125
\(786\) −6.79987 −0.242543
\(787\) −7.07032 −0.252030 −0.126015 0.992028i \(-0.540219\pi\)
−0.126015 + 0.992028i \(0.540219\pi\)
\(788\) −2.73463 −0.0974172
\(789\) −1.39793 −0.0497677
\(790\) 39.1387 1.39249
\(791\) 33.4524 1.18943
\(792\) 84.9733 3.01939
\(793\) −17.9560 −0.637637
\(794\) 2.13974 0.0759364
\(795\) −6.71261 −0.238072
\(796\) −54.1542 −1.91944
\(797\) 31.6135 1.11981 0.559904 0.828558i \(-0.310838\pi\)
0.559904 + 0.828558i \(0.310838\pi\)
\(798\) 9.81088 0.347301
\(799\) −7.49693 −0.265222
\(800\) −188.130 −6.65141
\(801\) −34.5588 −1.22107
\(802\) 28.3602 1.00143
\(803\) 45.4746 1.60476
\(804\) 22.0551 0.777823
\(805\) 35.7543 1.26017
\(806\) 4.78092 0.168401
\(807\) 7.09432 0.249732
\(808\) −124.111 −4.36622
\(809\) −27.0891 −0.952403 −0.476201 0.879336i \(-0.657987\pi\)
−0.476201 + 0.879336i \(0.657987\pi\)
\(810\) 79.9476 2.80907
\(811\) 29.0111 1.01872 0.509359 0.860554i \(-0.329883\pi\)
0.509359 + 0.860554i \(0.329883\pi\)
\(812\) 44.3021 1.55470
\(813\) −6.16430 −0.216191
\(814\) −5.25230 −0.184093
\(815\) 69.7925 2.44473
\(816\) −23.3285 −0.816660
\(817\) 15.6623 0.547953
\(818\) 37.3552 1.30609
\(819\) −14.2357 −0.497437
\(820\) 189.976 6.63424
\(821\) −39.0357 −1.36236 −0.681178 0.732118i \(-0.738532\pi\)
−0.681178 + 0.732118i \(0.738532\pi\)
\(822\) 19.9513 0.695881
\(823\) 25.0475 0.873102 0.436551 0.899679i \(-0.356200\pi\)
0.436551 + 0.899679i \(0.356200\pi\)
\(824\) 134.108 4.67188
\(825\) 16.1032 0.560640
\(826\) 72.8324 2.53416
\(827\) −13.1012 −0.455573 −0.227787 0.973711i \(-0.573149\pi\)
−0.227787 + 0.973711i \(0.573149\pi\)
\(828\) −66.5904 −2.31418
\(829\) −38.1379 −1.32458 −0.662292 0.749246i \(-0.730416\pi\)
−0.662292 + 0.749246i \(0.730416\pi\)
\(830\) 20.8590 0.724028
\(831\) −11.0631 −0.383776
\(832\) −51.8683 −1.79821
\(833\) 13.3749 0.463412
\(834\) −14.3014 −0.495216
\(835\) −17.2647 −0.597470
\(836\) 79.7010 2.75652
\(837\) −1.70959 −0.0590922
\(838\) −47.9613 −1.65680
\(839\) −0.849033 −0.0293119 −0.0146559 0.999893i \(-0.504665\pi\)
−0.0146559 + 0.999893i \(0.504665\pi\)
\(840\) −28.7908 −0.993376
\(841\) −10.5829 −0.364929
\(842\) 70.1886 2.41886
\(843\) 8.40616 0.289524
\(844\) −76.6099 −2.63702
\(845\) 25.9980 0.894360
\(846\) 13.1300 0.451418
\(847\) −2.19117 −0.0752895
\(848\) 51.0741 1.75389
\(849\) −6.93387 −0.237970
\(850\) 128.013 4.39079
\(851\) 2.53884 0.0870304
\(852\) −31.3753 −1.07490
\(853\) 45.4746 1.55702 0.778510 0.627632i \(-0.215976\pi\)
0.778510 + 0.627632i \(0.215976\pi\)
\(854\) 37.4261 1.28069
\(855\) 49.5549 1.69474
\(856\) 91.2730 3.11965
\(857\) 45.9337 1.56907 0.784533 0.620087i \(-0.212903\pi\)
0.784533 + 0.620087i \(0.212903\pi\)
\(858\) 10.0282 0.342359
\(859\) −11.1390 −0.380058 −0.190029 0.981778i \(-0.560858\pi\)
−0.190029 + 0.981778i \(0.560858\pi\)
\(860\) −74.5149 −2.54094
\(861\) 7.57105 0.258021
\(862\) 11.9148 0.405818
\(863\) −26.3734 −0.897761 −0.448880 0.893592i \(-0.648177\pi\)
−0.448880 + 0.893592i \(0.648177\pi\)
\(864\) 41.8942 1.42527
\(865\) 98.5194 3.34976
\(866\) 83.7417 2.84566
\(867\) 0.739281 0.0251073
\(868\) −7.20437 −0.244532
\(869\) 12.6713 0.429843
\(870\) −19.4040 −0.657859
\(871\) −25.6093 −0.867740
\(872\) −119.423 −4.04416
\(873\) 15.5187 0.525228
\(874\) −53.2880 −1.80249
\(875\) 47.4732 1.60489
\(876\) 28.6961 0.969550
\(877\) −0.968243 −0.0326952 −0.0163476 0.999866i \(-0.505204\pi\)
−0.0163476 + 0.999866i \(0.505204\pi\)
\(878\) 28.5727 0.964283
\(879\) −8.13882 −0.274516
\(880\) −178.213 −6.00758
\(881\) −9.66838 −0.325736 −0.162868 0.986648i \(-0.552074\pi\)
−0.162868 + 0.986648i \(0.552074\pi\)
\(882\) −23.4245 −0.788744
\(883\) −18.6754 −0.628477 −0.314239 0.949344i \(-0.601749\pi\)
−0.314239 + 0.949344i \(0.601749\pi\)
\(884\) 57.6351 1.93848
\(885\) −23.0629 −0.775250
\(886\) −57.3655 −1.92723
\(887\) 1.42565 0.0478685 0.0239343 0.999714i \(-0.492381\pi\)
0.0239343 + 0.999714i \(0.492381\pi\)
\(888\) −2.04437 −0.0686047
\(889\) −23.1727 −0.777187
\(890\) 131.572 4.41031
\(891\) 25.8833 0.867122
\(892\) 42.3939 1.41945
\(893\) 7.59631 0.254201
\(894\) −14.2756 −0.477447
\(895\) 10.2476 0.342538
\(896\) 40.4609 1.35170
\(897\) −4.84743 −0.161851
\(898\) −44.8523 −1.49674
\(899\) −2.99497 −0.0998878
\(900\) −162.089 −5.40297
\(901\) −17.2761 −0.575552
\(902\) 85.0728 2.83262
\(903\) −2.96962 −0.0988228
\(904\) 146.310 4.86619
\(905\) −71.3707 −2.37244
\(906\) 14.4026 0.478495
\(907\) −19.2206 −0.638210 −0.319105 0.947719i \(-0.603382\pi\)
−0.319105 + 0.947719i \(0.603382\pi\)
\(908\) 114.392 3.79622
\(909\) −40.5033 −1.34341
\(910\) 54.1983 1.79666
\(911\) 16.6522 0.551711 0.275856 0.961199i \(-0.411039\pi\)
0.275856 + 0.961199i \(0.411039\pi\)
\(912\) 23.6377 0.782724
\(913\) 6.75318 0.223497
\(914\) 1.41242 0.0467188
\(915\) −11.8512 −0.391789
\(916\) 47.9801 1.58531
\(917\) −11.8980 −0.392908
\(918\) −28.5068 −0.940863
\(919\) −51.3896 −1.69519 −0.847593 0.530647i \(-0.821949\pi\)
−0.847593 + 0.530647i \(0.821949\pi\)
\(920\) 156.378 5.15562
\(921\) −2.66032 −0.0876606
\(922\) −16.6880 −0.549591
\(923\) 36.4316 1.19916
\(924\) −15.1116 −0.497135
\(925\) 6.17986 0.203192
\(926\) −23.0535 −0.757586
\(927\) 43.7658 1.43746
\(928\) 73.3929 2.40924
\(929\) 9.49538 0.311533 0.155767 0.987794i \(-0.450215\pi\)
0.155767 + 0.987794i \(0.450215\pi\)
\(930\) 3.15547 0.103472
\(931\) −13.5522 −0.444155
\(932\) −2.15728 −0.0706642
\(933\) 0.671572 0.0219863
\(934\) −68.0788 −2.22761
\(935\) 60.2819 1.97143
\(936\) −62.2624 −2.03511
\(937\) 29.4188 0.961071 0.480536 0.876975i \(-0.340442\pi\)
0.480536 + 0.876975i \(0.340442\pi\)
\(938\) 53.3780 1.74285
\(939\) −5.72463 −0.186816
\(940\) −36.1402 −1.17876
\(941\) −37.5242 −1.22325 −0.611626 0.791147i \(-0.709484\pi\)
−0.611626 + 0.791147i \(0.709484\pi\)
\(942\) 17.5073 0.570420
\(943\) −41.1223 −1.33913
\(944\) 175.478 5.71132
\(945\) −19.3806 −0.630450
\(946\) −33.3684 −1.08490
\(947\) 3.86902 0.125726 0.0628631 0.998022i \(-0.479977\pi\)
0.0628631 + 0.998022i \(0.479977\pi\)
\(948\) 7.99601 0.259698
\(949\) −33.3205 −1.08163
\(950\) −129.710 −4.20833
\(951\) −9.11562 −0.295594
\(952\) −74.0984 −2.40154
\(953\) 6.14411 0.199027 0.0995136 0.995036i \(-0.468271\pi\)
0.0995136 + 0.995036i \(0.468271\pi\)
\(954\) 30.2571 0.979610
\(955\) −5.27584 −0.170722
\(956\) −91.5149 −2.95980
\(957\) −6.28212 −0.203072
\(958\) 49.1105 1.58669
\(959\) 34.9096 1.12729
\(960\) −34.2338 −1.10489
\(961\) −30.5130 −0.984289
\(962\) 3.84851 0.124081
\(963\) 29.7866 0.959861
\(964\) 153.574 4.94628
\(965\) −77.9873 −2.51050
\(966\) 10.1036 0.325077
\(967\) −22.8244 −0.733983 −0.366992 0.930224i \(-0.619612\pi\)
−0.366992 + 0.930224i \(0.619612\pi\)
\(968\) −9.58345 −0.308024
\(969\) −7.99562 −0.256856
\(970\) −59.0828 −1.89703
\(971\) −29.1569 −0.935690 −0.467845 0.883811i \(-0.654969\pi\)
−0.467845 + 0.883811i \(0.654969\pi\)
\(972\) 54.6913 1.75423
\(973\) −25.0237 −0.802225
\(974\) 34.0316 1.09044
\(975\) −11.7992 −0.377878
\(976\) 90.1721 2.88634
\(977\) 50.9835 1.63111 0.815554 0.578681i \(-0.196433\pi\)
0.815554 + 0.578681i \(0.196433\pi\)
\(978\) 19.7222 0.630647
\(979\) 42.5969 1.36140
\(980\) 64.4759 2.05961
\(981\) −38.9732 −1.24432
\(982\) 111.263 3.55054
\(983\) 38.2064 1.21860 0.609298 0.792941i \(-0.291451\pi\)
0.609298 + 0.792941i \(0.291451\pi\)
\(984\) 33.1132 1.05561
\(985\) 2.09576 0.0667764
\(986\) −49.9399 −1.59041
\(987\) −1.44029 −0.0458448
\(988\) −58.3992 −1.85793
\(989\) 16.1296 0.512890
\(990\) −105.577 −3.35544
\(991\) 12.1005 0.384384 0.192192 0.981357i \(-0.438440\pi\)
0.192192 + 0.981357i \(0.438440\pi\)
\(992\) −11.9351 −0.378939
\(993\) 3.67962 0.116769
\(994\) −75.9350 −2.40851
\(995\) 41.5025 1.31572
\(996\) 4.26149 0.135031
\(997\) 7.02131 0.222367 0.111184 0.993800i \(-0.464536\pi\)
0.111184 + 0.993800i \(0.464536\pi\)
\(998\) 50.4712 1.59764
\(999\) −1.37618 −0.0435403
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 \(a_p\))