Properties

Label 8001.2.a.v.1.5
Level 8001
Weight 2
Character 8001.1
Self dual Yes
Analytic conductor 63.888
Analytic rank 0
Dimension 19
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8001 = 3^{2} \cdot 7 \cdot 127 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8001.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.8883066572\)
Analytic rank: \(0\)
Dimension: \(19\)
Coefficient field: \(\mathbb{Q}[x]/(x^{19} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{2} \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Root \(1.88777\)
Character \(\chi\) = 8001.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.88777 q^{2} +1.56369 q^{4} +3.95777 q^{5} +1.00000 q^{7} +0.823654 q^{8} +O(q^{10})\) \(q-1.88777 q^{2} +1.56369 q^{4} +3.95777 q^{5} +1.00000 q^{7} +0.823654 q^{8} -7.47138 q^{10} -2.14742 q^{11} +4.63999 q^{13} -1.88777 q^{14} -4.68225 q^{16} +2.02948 q^{17} +5.69266 q^{19} +6.18873 q^{20} +4.05384 q^{22} +1.45406 q^{23} +10.6640 q^{25} -8.75925 q^{26} +1.56369 q^{28} +7.67597 q^{29} +9.00443 q^{31} +7.19173 q^{32} -3.83120 q^{34} +3.95777 q^{35} +7.50700 q^{37} -10.7465 q^{38} +3.25984 q^{40} -1.70524 q^{41} +11.2877 q^{43} -3.35790 q^{44} -2.74493 q^{46} -10.1989 q^{47} +1.00000 q^{49} -20.1312 q^{50} +7.25551 q^{52} -7.66310 q^{53} -8.49900 q^{55} +0.823654 q^{56} -14.4905 q^{58} +3.85596 q^{59} -7.14847 q^{61} -16.9983 q^{62} -4.21185 q^{64} +18.3640 q^{65} -5.67445 q^{67} +3.17348 q^{68} -7.47138 q^{70} +6.26208 q^{71} -9.32720 q^{73} -14.1715 q^{74} +8.90157 q^{76} -2.14742 q^{77} +8.47237 q^{79} -18.5313 q^{80} +3.21911 q^{82} -6.28388 q^{83} +8.03222 q^{85} -21.3087 q^{86} -1.76873 q^{88} -10.4894 q^{89} +4.63999 q^{91} +2.27370 q^{92} +19.2533 q^{94} +22.5303 q^{95} -1.36340 q^{97} -1.88777 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 19q - 4q^{2} + 22q^{4} - 5q^{5} + 19q^{7} - 9q^{8} + O(q^{10}) \) \( 19q - 4q^{2} + 22q^{4} - 5q^{5} + 19q^{7} - 9q^{8} + 9q^{11} + 24q^{13} - 4q^{14} + 20q^{16} - 17q^{17} + 23q^{19} - 5q^{20} - 3q^{22} + 17q^{23} + 38q^{25} - 28q^{26} + 22q^{28} - 2q^{29} + 16q^{31} - 17q^{32} + 29q^{34} - 5q^{35} + 56q^{37} - 2q^{38} - 13q^{40} + 7q^{41} + 19q^{43} + 29q^{44} + 10q^{46} - 25q^{47} + 19q^{49} + 9q^{50} + 16q^{52} - 18q^{53} + 10q^{55} - 9q^{56} + 31q^{58} - 11q^{59} + 26q^{61} - 26q^{62} + 45q^{64} - 27q^{65} + 24q^{67} - 14q^{68} + 32q^{71} + 51q^{73} + 12q^{76} + 9q^{77} + 30q^{79} + 30q^{80} - 52q^{82} - q^{83} + 44q^{85} + 24q^{86} - 30q^{88} - 5q^{89} + 24q^{91} + 88q^{92} + 7q^{94} + 24q^{95} + 5q^{97} - 4q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.88777 −1.33486 −0.667429 0.744674i \(-0.732605\pi\)
−0.667429 + 0.744674i \(0.732605\pi\)
\(3\) 0 0
\(4\) 1.56369 0.781845
\(5\) 3.95777 1.76997 0.884985 0.465619i \(-0.154168\pi\)
0.884985 + 0.465619i \(0.154168\pi\)
\(6\) 0 0
\(7\) 1.00000 0.377964
\(8\) 0.823654 0.291206
\(9\) 0 0
\(10\) −7.47138 −2.36266
\(11\) −2.14742 −0.647471 −0.323736 0.946148i \(-0.604939\pi\)
−0.323736 + 0.946148i \(0.604939\pi\)
\(12\) 0 0
\(13\) 4.63999 1.28690 0.643451 0.765488i \(-0.277502\pi\)
0.643451 + 0.765488i \(0.277502\pi\)
\(14\) −1.88777 −0.504529
\(15\) 0 0
\(16\) −4.68225 −1.17056
\(17\) 2.02948 0.492221 0.246111 0.969242i \(-0.420847\pi\)
0.246111 + 0.969242i \(0.420847\pi\)
\(18\) 0 0
\(19\) 5.69266 1.30599 0.652993 0.757364i \(-0.273513\pi\)
0.652993 + 0.757364i \(0.273513\pi\)
\(20\) 6.18873 1.38384
\(21\) 0 0
\(22\) 4.05384 0.864282
\(23\) 1.45406 0.303192 0.151596 0.988443i \(-0.451559\pi\)
0.151596 + 0.988443i \(0.451559\pi\)
\(24\) 0 0
\(25\) 10.6640 2.13280
\(26\) −8.75925 −1.71783
\(27\) 0 0
\(28\) 1.56369 0.295510
\(29\) 7.67597 1.42539 0.712696 0.701473i \(-0.247474\pi\)
0.712696 + 0.701473i \(0.247474\pi\)
\(30\) 0 0
\(31\) 9.00443 1.61724 0.808622 0.588329i \(-0.200214\pi\)
0.808622 + 0.588329i \(0.200214\pi\)
\(32\) 7.19173 1.27133
\(33\) 0 0
\(34\) −3.83120 −0.657045
\(35\) 3.95777 0.668986
\(36\) 0 0
\(37\) 7.50700 1.23414 0.617071 0.786907i \(-0.288319\pi\)
0.617071 + 0.786907i \(0.288319\pi\)
\(38\) −10.7465 −1.74331
\(39\) 0 0
\(40\) 3.25984 0.515425
\(41\) −1.70524 −0.266314 −0.133157 0.991095i \(-0.542511\pi\)
−0.133157 + 0.991095i \(0.542511\pi\)
\(42\) 0 0
\(43\) 11.2877 1.72136 0.860681 0.509144i \(-0.170038\pi\)
0.860681 + 0.509144i \(0.170038\pi\)
\(44\) −3.35790 −0.506222
\(45\) 0 0
\(46\) −2.74493 −0.404719
\(47\) −10.1989 −1.48767 −0.743835 0.668363i \(-0.766995\pi\)
−0.743835 + 0.668363i \(0.766995\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) −20.1312 −2.84698
\(51\) 0 0
\(52\) 7.25551 1.00616
\(53\) −7.66310 −1.05261 −0.526304 0.850297i \(-0.676423\pi\)
−0.526304 + 0.850297i \(0.676423\pi\)
\(54\) 0 0
\(55\) −8.49900 −1.14601
\(56\) 0.823654 0.110065
\(57\) 0 0
\(58\) −14.4905 −1.90270
\(59\) 3.85596 0.502004 0.251002 0.967987i \(-0.419240\pi\)
0.251002 + 0.967987i \(0.419240\pi\)
\(60\) 0 0
\(61\) −7.14847 −0.915268 −0.457634 0.889141i \(-0.651303\pi\)
−0.457634 + 0.889141i \(0.651303\pi\)
\(62\) −16.9983 −2.15879
\(63\) 0 0
\(64\) −4.21185 −0.526481
\(65\) 18.3640 2.27778
\(66\) 0 0
\(67\) −5.67445 −0.693245 −0.346622 0.938005i \(-0.612671\pi\)
−0.346622 + 0.938005i \(0.612671\pi\)
\(68\) 3.17348 0.384841
\(69\) 0 0
\(70\) −7.47138 −0.893001
\(71\) 6.26208 0.743172 0.371586 0.928398i \(-0.378814\pi\)
0.371586 + 0.928398i \(0.378814\pi\)
\(72\) 0 0
\(73\) −9.32720 −1.09167 −0.545833 0.837894i \(-0.683787\pi\)
−0.545833 + 0.837894i \(0.683787\pi\)
\(74\) −14.1715 −1.64741
\(75\) 0 0
\(76\) 8.90157 1.02108
\(77\) −2.14742 −0.244721
\(78\) 0 0
\(79\) 8.47237 0.953216 0.476608 0.879116i \(-0.341866\pi\)
0.476608 + 0.879116i \(0.341866\pi\)
\(80\) −18.5313 −2.07186
\(81\) 0 0
\(82\) 3.21911 0.355491
\(83\) −6.28388 −0.689746 −0.344873 0.938649i \(-0.612078\pi\)
−0.344873 + 0.938649i \(0.612078\pi\)
\(84\) 0 0
\(85\) 8.03222 0.871217
\(86\) −21.3087 −2.29777
\(87\) 0 0
\(88\) −1.76873 −0.188547
\(89\) −10.4894 −1.11187 −0.555935 0.831226i \(-0.687640\pi\)
−0.555935 + 0.831226i \(0.687640\pi\)
\(90\) 0 0
\(91\) 4.63999 0.486403
\(92\) 2.27370 0.237049
\(93\) 0 0
\(94\) 19.2533 1.98583
\(95\) 22.5303 2.31156
\(96\) 0 0
\(97\) −1.36340 −0.138432 −0.0692159 0.997602i \(-0.522050\pi\)
−0.0692159 + 0.997602i \(0.522050\pi\)
\(98\) −1.88777 −0.190694
\(99\) 0 0
\(100\) 16.6752 1.66752
\(101\) −11.4803 −1.14233 −0.571165 0.820835i \(-0.693508\pi\)
−0.571165 + 0.820835i \(0.693508\pi\)
\(102\) 0 0
\(103\) 8.90018 0.876961 0.438480 0.898741i \(-0.355517\pi\)
0.438480 + 0.898741i \(0.355517\pi\)
\(104\) 3.82174 0.374753
\(105\) 0 0
\(106\) 14.4662 1.40508
\(107\) 19.2178 1.85786 0.928929 0.370258i \(-0.120731\pi\)
0.928929 + 0.370258i \(0.120731\pi\)
\(108\) 0 0
\(109\) −16.3725 −1.56820 −0.784101 0.620633i \(-0.786876\pi\)
−0.784101 + 0.620633i \(0.786876\pi\)
\(110\) 16.0442 1.52975
\(111\) 0 0
\(112\) −4.68225 −0.442431
\(113\) 11.4751 1.07948 0.539742 0.841830i \(-0.318522\pi\)
0.539742 + 0.841830i \(0.318522\pi\)
\(114\) 0 0
\(115\) 5.75484 0.536641
\(116\) 12.0028 1.11444
\(117\) 0 0
\(118\) −7.27919 −0.670104
\(119\) 2.02948 0.186042
\(120\) 0 0
\(121\) −6.38859 −0.580781
\(122\) 13.4947 1.22175
\(123\) 0 0
\(124\) 14.0801 1.26443
\(125\) 22.4168 2.00502
\(126\) 0 0
\(127\) 1.00000 0.0887357
\(128\) −6.43243 −0.568552
\(129\) 0 0
\(130\) −34.6671 −3.04051
\(131\) −16.8610 −1.47315 −0.736577 0.676354i \(-0.763559\pi\)
−0.736577 + 0.676354i \(0.763559\pi\)
\(132\) 0 0
\(133\) 5.69266 0.493617
\(134\) 10.7121 0.925383
\(135\) 0 0
\(136\) 1.67159 0.143338
\(137\) 19.1796 1.63862 0.819311 0.573350i \(-0.194356\pi\)
0.819311 + 0.573350i \(0.194356\pi\)
\(138\) 0 0
\(139\) −8.01183 −0.679554 −0.339777 0.940506i \(-0.610352\pi\)
−0.339777 + 0.940506i \(0.610352\pi\)
\(140\) 6.18873 0.523044
\(141\) 0 0
\(142\) −11.8214 −0.992029
\(143\) −9.96400 −0.833232
\(144\) 0 0
\(145\) 30.3798 2.52290
\(146\) 17.6076 1.45722
\(147\) 0 0
\(148\) 11.7386 0.964909
\(149\) −13.1891 −1.08049 −0.540246 0.841507i \(-0.681669\pi\)
−0.540246 + 0.841507i \(0.681669\pi\)
\(150\) 0 0
\(151\) 13.0804 1.06447 0.532233 0.846598i \(-0.321353\pi\)
0.532233 + 0.846598i \(0.321353\pi\)
\(152\) 4.68878 0.380311
\(153\) 0 0
\(154\) 4.05384 0.326668
\(155\) 35.6375 2.86247
\(156\) 0 0
\(157\) −4.19203 −0.334560 −0.167280 0.985909i \(-0.553498\pi\)
−0.167280 + 0.985909i \(0.553498\pi\)
\(158\) −15.9939 −1.27241
\(159\) 0 0
\(160\) 28.4632 2.25022
\(161\) 1.45406 0.114596
\(162\) 0 0
\(163\) −15.0370 −1.17779 −0.588895 0.808210i \(-0.700437\pi\)
−0.588895 + 0.808210i \(0.700437\pi\)
\(164\) −2.66647 −0.208216
\(165\) 0 0
\(166\) 11.8625 0.920712
\(167\) −9.25065 −0.715837 −0.357919 0.933753i \(-0.616513\pi\)
−0.357919 + 0.933753i \(0.616513\pi\)
\(168\) 0 0
\(169\) 8.52949 0.656115
\(170\) −15.1630 −1.16295
\(171\) 0 0
\(172\) 17.6505 1.34584
\(173\) −7.57346 −0.575800 −0.287900 0.957661i \(-0.592957\pi\)
−0.287900 + 0.957661i \(0.592957\pi\)
\(174\) 0 0
\(175\) 10.6640 0.806121
\(176\) 10.0548 0.757906
\(177\) 0 0
\(178\) 19.8015 1.48419
\(179\) −7.28211 −0.544290 −0.272145 0.962256i \(-0.587733\pi\)
−0.272145 + 0.962256i \(0.587733\pi\)
\(180\) 0 0
\(181\) −23.4346 −1.74188 −0.870941 0.491388i \(-0.836490\pi\)
−0.870941 + 0.491388i \(0.836490\pi\)
\(182\) −8.75925 −0.649279
\(183\) 0 0
\(184\) 1.19764 0.0882913
\(185\) 29.7110 2.18440
\(186\) 0 0
\(187\) −4.35814 −0.318699
\(188\) −15.9480 −1.16313
\(189\) 0 0
\(190\) −42.5321 −3.08560
\(191\) −15.0684 −1.09031 −0.545157 0.838334i \(-0.683530\pi\)
−0.545157 + 0.838334i \(0.683530\pi\)
\(192\) 0 0
\(193\) −22.0680 −1.58849 −0.794243 0.607600i \(-0.792133\pi\)
−0.794243 + 0.607600i \(0.792133\pi\)
\(194\) 2.57378 0.184787
\(195\) 0 0
\(196\) 1.56369 0.111692
\(197\) −5.41669 −0.385923 −0.192962 0.981206i \(-0.561809\pi\)
−0.192962 + 0.981206i \(0.561809\pi\)
\(198\) 0 0
\(199\) 11.5150 0.816279 0.408140 0.912919i \(-0.366178\pi\)
0.408140 + 0.912919i \(0.366178\pi\)
\(200\) 8.78343 0.621082
\(201\) 0 0
\(202\) 21.6722 1.52485
\(203\) 7.67597 0.538748
\(204\) 0 0
\(205\) −6.74897 −0.471368
\(206\) −16.8015 −1.17062
\(207\) 0 0
\(208\) −21.7256 −1.50640
\(209\) −12.2245 −0.845589
\(210\) 0 0
\(211\) 5.20139 0.358079 0.179039 0.983842i \(-0.442701\pi\)
0.179039 + 0.983842i \(0.442701\pi\)
\(212\) −11.9827 −0.822976
\(213\) 0 0
\(214\) −36.2789 −2.47998
\(215\) 44.6743 3.04676
\(216\) 0 0
\(217\) 9.00443 0.611261
\(218\) 30.9076 2.09333
\(219\) 0 0
\(220\) −13.2898 −0.895999
\(221\) 9.41676 0.633440
\(222\) 0 0
\(223\) 21.3493 1.42965 0.714827 0.699301i \(-0.246505\pi\)
0.714827 + 0.699301i \(0.246505\pi\)
\(224\) 7.19173 0.480518
\(225\) 0 0
\(226\) −21.6623 −1.44096
\(227\) 6.08058 0.403582 0.201791 0.979429i \(-0.435324\pi\)
0.201791 + 0.979429i \(0.435324\pi\)
\(228\) 0 0
\(229\) 21.0455 1.39073 0.695364 0.718658i \(-0.255243\pi\)
0.695364 + 0.718658i \(0.255243\pi\)
\(230\) −10.8638 −0.716340
\(231\) 0 0
\(232\) 6.32234 0.415082
\(233\) −22.1764 −1.45282 −0.726411 0.687260i \(-0.758813\pi\)
−0.726411 + 0.687260i \(0.758813\pi\)
\(234\) 0 0
\(235\) −40.3651 −2.63313
\(236\) 6.02953 0.392489
\(237\) 0 0
\(238\) −3.83120 −0.248340
\(239\) 25.5967 1.65572 0.827858 0.560938i \(-0.189559\pi\)
0.827858 + 0.560938i \(0.189559\pi\)
\(240\) 0 0
\(241\) −19.9316 −1.28391 −0.641954 0.766743i \(-0.721876\pi\)
−0.641954 + 0.766743i \(0.721876\pi\)
\(242\) 12.0602 0.775260
\(243\) 0 0
\(244\) −11.1780 −0.715598
\(245\) 3.95777 0.252853
\(246\) 0 0
\(247\) 26.4139 1.68068
\(248\) 7.41653 0.470950
\(249\) 0 0
\(250\) −42.3178 −2.67641
\(251\) −10.1150 −0.638453 −0.319226 0.947679i \(-0.603423\pi\)
−0.319226 + 0.947679i \(0.603423\pi\)
\(252\) 0 0
\(253\) −3.12248 −0.196308
\(254\) −1.88777 −0.118449
\(255\) 0 0
\(256\) 20.5667 1.28542
\(257\) −11.7107 −0.730492 −0.365246 0.930911i \(-0.619015\pi\)
−0.365246 + 0.930911i \(0.619015\pi\)
\(258\) 0 0
\(259\) 7.50700 0.466462
\(260\) 28.7157 1.78087
\(261\) 0 0
\(262\) 31.8298 1.96645
\(263\) 11.8920 0.733292 0.366646 0.930360i \(-0.380506\pi\)
0.366646 + 0.930360i \(0.380506\pi\)
\(264\) 0 0
\(265\) −30.3288 −1.86308
\(266\) −10.7465 −0.658908
\(267\) 0 0
\(268\) −8.87309 −0.542010
\(269\) 3.47050 0.211600 0.105800 0.994387i \(-0.466260\pi\)
0.105800 + 0.994387i \(0.466260\pi\)
\(270\) 0 0
\(271\) −30.0603 −1.82603 −0.913015 0.407926i \(-0.866252\pi\)
−0.913015 + 0.407926i \(0.866252\pi\)
\(272\) −9.50254 −0.576176
\(273\) 0 0
\(274\) −36.2067 −2.18733
\(275\) −22.9000 −1.38092
\(276\) 0 0
\(277\) −27.2744 −1.63876 −0.819380 0.573251i \(-0.805682\pi\)
−0.819380 + 0.573251i \(0.805682\pi\)
\(278\) 15.1245 0.907108
\(279\) 0 0
\(280\) 3.25984 0.194812
\(281\) 17.7977 1.06172 0.530862 0.847459i \(-0.321868\pi\)
0.530862 + 0.847459i \(0.321868\pi\)
\(282\) 0 0
\(283\) 4.85009 0.288308 0.144154 0.989555i \(-0.453954\pi\)
0.144154 + 0.989555i \(0.453954\pi\)
\(284\) 9.79196 0.581046
\(285\) 0 0
\(286\) 18.8098 1.11225
\(287\) −1.70524 −0.100657
\(288\) 0 0
\(289\) −12.8812 −0.757718
\(290\) −57.3501 −3.36772
\(291\) 0 0
\(292\) −14.5849 −0.853514
\(293\) 14.8955 0.870207 0.435103 0.900381i \(-0.356712\pi\)
0.435103 + 0.900381i \(0.356712\pi\)
\(294\) 0 0
\(295\) 15.2610 0.888532
\(296\) 6.18317 0.359389
\(297\) 0 0
\(298\) 24.8980 1.44230
\(299\) 6.74682 0.390179
\(300\) 0 0
\(301\) 11.2877 0.650614
\(302\) −24.6928 −1.42091
\(303\) 0 0
\(304\) −26.6545 −1.52874
\(305\) −28.2920 −1.62000
\(306\) 0 0
\(307\) −1.06872 −0.0609948 −0.0304974 0.999535i \(-0.509709\pi\)
−0.0304974 + 0.999535i \(0.509709\pi\)
\(308\) −3.35790 −0.191334
\(309\) 0 0
\(310\) −67.2756 −3.82100
\(311\) 0.583290 0.0330754 0.0165377 0.999863i \(-0.494736\pi\)
0.0165377 + 0.999863i \(0.494736\pi\)
\(312\) 0 0
\(313\) −26.9052 −1.52077 −0.760385 0.649472i \(-0.774990\pi\)
−0.760385 + 0.649472i \(0.774990\pi\)
\(314\) 7.91360 0.446590
\(315\) 0 0
\(316\) 13.2482 0.745267
\(317\) −9.34430 −0.524828 −0.262414 0.964955i \(-0.584519\pi\)
−0.262414 + 0.964955i \(0.584519\pi\)
\(318\) 0 0
\(319\) −16.4835 −0.922901
\(320\) −16.6696 −0.931856
\(321\) 0 0
\(322\) −2.74493 −0.152969
\(323\) 11.5531 0.642834
\(324\) 0 0
\(325\) 49.4807 2.74470
\(326\) 28.3865 1.57218
\(327\) 0 0
\(328\) −1.40453 −0.0775522
\(329\) −10.1989 −0.562286
\(330\) 0 0
\(331\) −1.03557 −0.0569200 −0.0284600 0.999595i \(-0.509060\pi\)
−0.0284600 + 0.999595i \(0.509060\pi\)
\(332\) −9.82605 −0.539274
\(333\) 0 0
\(334\) 17.4631 0.955541
\(335\) −22.4582 −1.22702
\(336\) 0 0
\(337\) −14.1889 −0.772918 −0.386459 0.922307i \(-0.626302\pi\)
−0.386459 + 0.922307i \(0.626302\pi\)
\(338\) −16.1018 −0.875820
\(339\) 0 0
\(340\) 12.5599 0.681157
\(341\) −19.3363 −1.04712
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) 9.29718 0.501270
\(345\) 0 0
\(346\) 14.2970 0.768611
\(347\) −17.6484 −0.947416 −0.473708 0.880682i \(-0.657085\pi\)
−0.473708 + 0.880682i \(0.657085\pi\)
\(348\) 0 0
\(349\) 11.4412 0.612435 0.306218 0.951962i \(-0.400936\pi\)
0.306218 + 0.951962i \(0.400936\pi\)
\(350\) −20.1312 −1.07606
\(351\) 0 0
\(352\) −15.4437 −0.823150
\(353\) 20.3642 1.08388 0.541939 0.840418i \(-0.317691\pi\)
0.541939 + 0.840418i \(0.317691\pi\)
\(354\) 0 0
\(355\) 24.7839 1.31539
\(356\) −16.4021 −0.869310
\(357\) 0 0
\(358\) 13.7470 0.726550
\(359\) −3.45273 −0.182228 −0.0911140 0.995840i \(-0.529043\pi\)
−0.0911140 + 0.995840i \(0.529043\pi\)
\(360\) 0 0
\(361\) 13.4064 0.705602
\(362\) 44.2393 2.32516
\(363\) 0 0
\(364\) 7.25551 0.380292
\(365\) −36.9150 −1.93222
\(366\) 0 0
\(367\) 34.3928 1.79529 0.897645 0.440718i \(-0.145276\pi\)
0.897645 + 0.440718i \(0.145276\pi\)
\(368\) −6.80827 −0.354906
\(369\) 0 0
\(370\) −56.0877 −2.91586
\(371\) −7.66310 −0.397848
\(372\) 0 0
\(373\) −1.96560 −0.101775 −0.0508874 0.998704i \(-0.516205\pi\)
−0.0508874 + 0.998704i \(0.516205\pi\)
\(374\) 8.22719 0.425418
\(375\) 0 0
\(376\) −8.40040 −0.433218
\(377\) 35.6164 1.83434
\(378\) 0 0
\(379\) −8.58920 −0.441197 −0.220599 0.975365i \(-0.570801\pi\)
−0.220599 + 0.975365i \(0.570801\pi\)
\(380\) 35.2304 1.80728
\(381\) 0 0
\(382\) 28.4458 1.45541
\(383\) −10.3226 −0.527460 −0.263730 0.964597i \(-0.584953\pi\)
−0.263730 + 0.964597i \(0.584953\pi\)
\(384\) 0 0
\(385\) −8.49900 −0.433149
\(386\) 41.6593 2.12040
\(387\) 0 0
\(388\) −2.13193 −0.108232
\(389\) −19.6783 −0.997730 −0.498865 0.866680i \(-0.666250\pi\)
−0.498865 + 0.866680i \(0.666250\pi\)
\(390\) 0 0
\(391\) 2.95098 0.149238
\(392\) 0.823654 0.0416008
\(393\) 0 0
\(394\) 10.2255 0.515153
\(395\) 33.5317 1.68716
\(396\) 0 0
\(397\) −16.9533 −0.850863 −0.425432 0.904991i \(-0.639878\pi\)
−0.425432 + 0.904991i \(0.639878\pi\)
\(398\) −21.7378 −1.08962
\(399\) 0 0
\(400\) −49.9314 −2.49657
\(401\) 14.7737 0.737762 0.368881 0.929477i \(-0.379741\pi\)
0.368881 + 0.929477i \(0.379741\pi\)
\(402\) 0 0
\(403\) 41.7805 2.08123
\(404\) −17.9516 −0.893126
\(405\) 0 0
\(406\) −14.4905 −0.719152
\(407\) −16.1207 −0.799072
\(408\) 0 0
\(409\) −22.3107 −1.10319 −0.551596 0.834111i \(-0.685981\pi\)
−0.551596 + 0.834111i \(0.685981\pi\)
\(410\) 12.7405 0.629209
\(411\) 0 0
\(412\) 13.9171 0.685647
\(413\) 3.85596 0.189740
\(414\) 0 0
\(415\) −24.8702 −1.22083
\(416\) 33.3695 1.63608
\(417\) 0 0
\(418\) 23.0772 1.12874
\(419\) −3.91746 −0.191380 −0.0956901 0.995411i \(-0.530506\pi\)
−0.0956901 + 0.995411i \(0.530506\pi\)
\(420\) 0 0
\(421\) −9.93242 −0.484076 −0.242038 0.970267i \(-0.577816\pi\)
−0.242038 + 0.970267i \(0.577816\pi\)
\(422\) −9.81906 −0.477984
\(423\) 0 0
\(424\) −6.31174 −0.306525
\(425\) 21.6423 1.04981
\(426\) 0 0
\(427\) −7.14847 −0.345939
\(428\) 30.0507 1.45256
\(429\) 0 0
\(430\) −84.3349 −4.06699
\(431\) −4.01227 −0.193264 −0.0966320 0.995320i \(-0.530807\pi\)
−0.0966320 + 0.995320i \(0.530807\pi\)
\(432\) 0 0
\(433\) −16.6134 −0.798388 −0.399194 0.916867i \(-0.630710\pi\)
−0.399194 + 0.916867i \(0.630710\pi\)
\(434\) −16.9983 −0.815946
\(435\) 0 0
\(436\) −25.6015 −1.22609
\(437\) 8.27747 0.395965
\(438\) 0 0
\(439\) −1.61324 −0.0769956 −0.0384978 0.999259i \(-0.512257\pi\)
−0.0384978 + 0.999259i \(0.512257\pi\)
\(440\) −7.00024 −0.333723
\(441\) 0 0
\(442\) −17.7767 −0.845552
\(443\) −15.3314 −0.728416 −0.364208 0.931318i \(-0.618660\pi\)
−0.364208 + 0.931318i \(0.618660\pi\)
\(444\) 0 0
\(445\) −41.5145 −1.96798
\(446\) −40.3026 −1.90838
\(447\) 0 0
\(448\) −4.21185 −0.198991
\(449\) −25.6227 −1.20921 −0.604604 0.796526i \(-0.706669\pi\)
−0.604604 + 0.796526i \(0.706669\pi\)
\(450\) 0 0
\(451\) 3.66187 0.172431
\(452\) 17.9435 0.843989
\(453\) 0 0
\(454\) −11.4788 −0.538725
\(455\) 18.3640 0.860919
\(456\) 0 0
\(457\) 10.3360 0.483496 0.241748 0.970339i \(-0.422279\pi\)
0.241748 + 0.970339i \(0.422279\pi\)
\(458\) −39.7292 −1.85642
\(459\) 0 0
\(460\) 8.99879 0.419571
\(461\) 17.7774 0.827976 0.413988 0.910282i \(-0.364135\pi\)
0.413988 + 0.910282i \(0.364135\pi\)
\(462\) 0 0
\(463\) −17.3660 −0.807065 −0.403532 0.914965i \(-0.632218\pi\)
−0.403532 + 0.914965i \(0.632218\pi\)
\(464\) −35.9408 −1.66851
\(465\) 0 0
\(466\) 41.8640 1.93931
\(467\) 26.1427 1.20974 0.604869 0.796325i \(-0.293226\pi\)
0.604869 + 0.796325i \(0.293226\pi\)
\(468\) 0 0
\(469\) −5.67445 −0.262022
\(470\) 76.2003 3.51486
\(471\) 0 0
\(472\) 3.17598 0.146186
\(473\) −24.2395 −1.11453
\(474\) 0 0
\(475\) 60.7065 2.78540
\(476\) 3.17348 0.145456
\(477\) 0 0
\(478\) −48.3209 −2.21014
\(479\) −24.4009 −1.11490 −0.557452 0.830209i \(-0.688221\pi\)
−0.557452 + 0.830209i \(0.688221\pi\)
\(480\) 0 0
\(481\) 34.8324 1.58822
\(482\) 37.6264 1.71384
\(483\) 0 0
\(484\) −9.98977 −0.454081
\(485\) −5.39601 −0.245020
\(486\) 0 0
\(487\) 4.27526 0.193731 0.0968653 0.995298i \(-0.469118\pi\)
0.0968653 + 0.995298i \(0.469118\pi\)
\(488\) −5.88786 −0.266531
\(489\) 0 0
\(490\) −7.47138 −0.337523
\(491\) −19.5487 −0.882220 −0.441110 0.897453i \(-0.645415\pi\)
−0.441110 + 0.897453i \(0.645415\pi\)
\(492\) 0 0
\(493\) 15.5782 0.701608
\(494\) −49.8635 −2.24346
\(495\) 0 0
\(496\) −42.1610 −1.89309
\(497\) 6.26208 0.280893
\(498\) 0 0
\(499\) 15.2354 0.682029 0.341015 0.940058i \(-0.389229\pi\)
0.341015 + 0.940058i \(0.389229\pi\)
\(500\) 35.0529 1.56761
\(501\) 0 0
\(502\) 19.0948 0.852243
\(503\) −34.0607 −1.51869 −0.759346 0.650687i \(-0.774481\pi\)
−0.759346 + 0.650687i \(0.774481\pi\)
\(504\) 0 0
\(505\) −45.4364 −2.02189
\(506\) 5.89453 0.262044
\(507\) 0 0
\(508\) 1.56369 0.0693775
\(509\) −9.48321 −0.420336 −0.210168 0.977665i \(-0.567401\pi\)
−0.210168 + 0.977665i \(0.567401\pi\)
\(510\) 0 0
\(511\) −9.32720 −0.412611
\(512\) −25.9604 −1.14730
\(513\) 0 0
\(514\) 22.1071 0.975103
\(515\) 35.2249 1.55219
\(516\) 0 0
\(517\) 21.9014 0.963224
\(518\) −14.1715 −0.622661
\(519\) 0 0
\(520\) 15.1256 0.663301
\(521\) −14.5732 −0.638464 −0.319232 0.947677i \(-0.603425\pi\)
−0.319232 + 0.947677i \(0.603425\pi\)
\(522\) 0 0
\(523\) 12.4195 0.543068 0.271534 0.962429i \(-0.412469\pi\)
0.271534 + 0.962429i \(0.412469\pi\)
\(524\) −26.3654 −1.15178
\(525\) 0 0
\(526\) −22.4494 −0.978841
\(527\) 18.2743 0.796041
\(528\) 0 0
\(529\) −20.8857 −0.908074
\(530\) 57.2540 2.48695
\(531\) 0 0
\(532\) 8.90157 0.385932
\(533\) −7.91231 −0.342720
\(534\) 0 0
\(535\) 76.0598 3.28835
\(536\) −4.67379 −0.201877
\(537\) 0 0
\(538\) −6.55152 −0.282456
\(539\) −2.14742 −0.0924959
\(540\) 0 0
\(541\) −0.384270 −0.0165211 −0.00826053 0.999966i \(-0.502629\pi\)
−0.00826053 + 0.999966i \(0.502629\pi\)
\(542\) 56.7470 2.43749
\(543\) 0 0
\(544\) 14.5955 0.625775
\(545\) −64.7987 −2.77567
\(546\) 0 0
\(547\) 21.1127 0.902715 0.451358 0.892343i \(-0.350940\pi\)
0.451358 + 0.892343i \(0.350940\pi\)
\(548\) 29.9909 1.28115
\(549\) 0 0
\(550\) 43.2301 1.84334
\(551\) 43.6967 1.86154
\(552\) 0 0
\(553\) 8.47237 0.360282
\(554\) 51.4879 2.18751
\(555\) 0 0
\(556\) −12.5280 −0.531306
\(557\) 7.73413 0.327706 0.163853 0.986485i \(-0.447608\pi\)
0.163853 + 0.986485i \(0.447608\pi\)
\(558\) 0 0
\(559\) 52.3749 2.21522
\(560\) −18.5313 −0.783090
\(561\) 0 0
\(562\) −33.5981 −1.41725
\(563\) −36.6656 −1.54527 −0.772636 0.634849i \(-0.781062\pi\)
−0.772636 + 0.634849i \(0.781062\pi\)
\(564\) 0 0
\(565\) 45.4158 1.91066
\(566\) −9.15588 −0.384850
\(567\) 0 0
\(568\) 5.15779 0.216416
\(569\) 18.2910 0.766798 0.383399 0.923583i \(-0.374753\pi\)
0.383399 + 0.923583i \(0.374753\pi\)
\(570\) 0 0
\(571\) 19.4223 0.812800 0.406400 0.913695i \(-0.366784\pi\)
0.406400 + 0.913695i \(0.366784\pi\)
\(572\) −15.5806 −0.651458
\(573\) 0 0
\(574\) 3.21911 0.134363
\(575\) 15.5061 0.646647
\(576\) 0 0
\(577\) −39.4979 −1.64432 −0.822160 0.569257i \(-0.807231\pi\)
−0.822160 + 0.569257i \(0.807231\pi\)
\(578\) 24.3168 1.01145
\(579\) 0 0
\(580\) 47.5046 1.97252
\(581\) −6.28388 −0.260699
\(582\) 0 0
\(583\) 16.4559 0.681533
\(584\) −7.68239 −0.317899
\(585\) 0 0
\(586\) −28.1194 −1.16160
\(587\) 6.56836 0.271105 0.135553 0.990770i \(-0.456719\pi\)
0.135553 + 0.990770i \(0.456719\pi\)
\(588\) 0 0
\(589\) 51.2592 2.11210
\(590\) −28.8094 −1.18606
\(591\) 0 0
\(592\) −35.1497 −1.44464
\(593\) −36.5594 −1.50131 −0.750657 0.660693i \(-0.770263\pi\)
−0.750657 + 0.660693i \(0.770263\pi\)
\(594\) 0 0
\(595\) 8.03222 0.329289
\(596\) −20.6236 −0.844778
\(597\) 0 0
\(598\) −12.7365 −0.520833
\(599\) −10.1789 −0.415897 −0.207948 0.978140i \(-0.566679\pi\)
−0.207948 + 0.978140i \(0.566679\pi\)
\(600\) 0 0
\(601\) 20.3312 0.829328 0.414664 0.909975i \(-0.363899\pi\)
0.414664 + 0.909975i \(0.363899\pi\)
\(602\) −21.3087 −0.868477
\(603\) 0 0
\(604\) 20.4537 0.832247
\(605\) −25.2846 −1.02796
\(606\) 0 0
\(607\) 27.5219 1.11708 0.558540 0.829478i \(-0.311362\pi\)
0.558540 + 0.829478i \(0.311362\pi\)
\(608\) 40.9401 1.66034
\(609\) 0 0
\(610\) 53.4089 2.16246
\(611\) −47.3230 −1.91448
\(612\) 0 0
\(613\) 0.970338 0.0391916 0.0195958 0.999808i \(-0.493762\pi\)
0.0195958 + 0.999808i \(0.493762\pi\)
\(614\) 2.01749 0.0814194
\(615\) 0 0
\(616\) −1.76873 −0.0712642
\(617\) 6.80882 0.274113 0.137056 0.990563i \(-0.456236\pi\)
0.137056 + 0.990563i \(0.456236\pi\)
\(618\) 0 0
\(619\) −24.7537 −0.994936 −0.497468 0.867482i \(-0.665737\pi\)
−0.497468 + 0.867482i \(0.665737\pi\)
\(620\) 55.7260 2.23801
\(621\) 0 0
\(622\) −1.10112 −0.0441509
\(623\) −10.4894 −0.420247
\(624\) 0 0
\(625\) 35.4006 1.41602
\(626\) 50.7909 2.03001
\(627\) 0 0
\(628\) −6.55503 −0.261574
\(629\) 15.2353 0.607471
\(630\) 0 0
\(631\) −4.67050 −0.185930 −0.0929648 0.995669i \(-0.529634\pi\)
−0.0929648 + 0.995669i \(0.529634\pi\)
\(632\) 6.97830 0.277582
\(633\) 0 0
\(634\) 17.6399 0.700571
\(635\) 3.95777 0.157059
\(636\) 0 0
\(637\) 4.63999 0.183843
\(638\) 31.1172 1.23194
\(639\) 0 0
\(640\) −25.4581 −1.00632
\(641\) 25.9544 1.02514 0.512569 0.858646i \(-0.328694\pi\)
0.512569 + 0.858646i \(0.328694\pi\)
\(642\) 0 0
\(643\) 26.4794 1.04425 0.522123 0.852870i \(-0.325140\pi\)
0.522123 + 0.852870i \(0.325140\pi\)
\(644\) 2.27370 0.0895963
\(645\) 0 0
\(646\) −21.8097 −0.858092
\(647\) 30.6460 1.20482 0.602409 0.798187i \(-0.294208\pi\)
0.602409 + 0.798187i \(0.294208\pi\)
\(648\) 0 0
\(649\) −8.28037 −0.325033
\(650\) −93.4085 −3.66378
\(651\) 0 0
\(652\) −23.5132 −0.920849
\(653\) 46.1775 1.80706 0.903532 0.428521i \(-0.140965\pi\)
0.903532 + 0.428521i \(0.140965\pi\)
\(654\) 0 0
\(655\) −66.7321 −2.60744
\(656\) 7.98438 0.311738
\(657\) 0 0
\(658\) 19.2533 0.750572
\(659\) 33.6935 1.31251 0.656255 0.754539i \(-0.272139\pi\)
0.656255 + 0.754539i \(0.272139\pi\)
\(660\) 0 0
\(661\) −5.86710 −0.228204 −0.114102 0.993469i \(-0.536399\pi\)
−0.114102 + 0.993469i \(0.536399\pi\)
\(662\) 1.95492 0.0759801
\(663\) 0 0
\(664\) −5.17574 −0.200858
\(665\) 22.5303 0.873687
\(666\) 0 0
\(667\) 11.1613 0.432168
\(668\) −14.4652 −0.559674
\(669\) 0 0
\(670\) 42.3960 1.63790
\(671\) 15.3508 0.592610
\(672\) 0 0
\(673\) 42.5282 1.63934 0.819672 0.572833i \(-0.194156\pi\)
0.819672 + 0.572833i \(0.194156\pi\)
\(674\) 26.7854 1.03174
\(675\) 0 0
\(676\) 13.3375 0.512980
\(677\) 31.9041 1.22618 0.613088 0.790015i \(-0.289927\pi\)
0.613088 + 0.790015i \(0.289927\pi\)
\(678\) 0 0
\(679\) −1.36340 −0.0523223
\(680\) 6.61577 0.253703
\(681\) 0 0
\(682\) 36.5026 1.39776
\(683\) 20.7623 0.794445 0.397223 0.917722i \(-0.369974\pi\)
0.397223 + 0.917722i \(0.369974\pi\)
\(684\) 0 0
\(685\) 75.9084 2.90031
\(686\) −1.88777 −0.0720755
\(687\) 0 0
\(688\) −52.8520 −2.01496
\(689\) −35.5567 −1.35460
\(690\) 0 0
\(691\) 4.89130 0.186074 0.0930370 0.995663i \(-0.470343\pi\)
0.0930370 + 0.995663i \(0.470343\pi\)
\(692\) −11.8426 −0.450186
\(693\) 0 0
\(694\) 33.3162 1.26467
\(695\) −31.7090 −1.20279
\(696\) 0 0
\(697\) −3.46075 −0.131085
\(698\) −21.5985 −0.817514
\(699\) 0 0
\(700\) 16.6752 0.630262
\(701\) −46.2580 −1.74714 −0.873570 0.486699i \(-0.838201\pi\)
−0.873570 + 0.486699i \(0.838201\pi\)
\(702\) 0 0
\(703\) 42.7348 1.61177
\(704\) 9.04461 0.340882
\(705\) 0 0
\(706\) −38.4430 −1.44682
\(707\) −11.4803 −0.431760
\(708\) 0 0
\(709\) 6.50323 0.244234 0.122117 0.992516i \(-0.461032\pi\)
0.122117 + 0.992516i \(0.461032\pi\)
\(710\) −46.7864 −1.75586
\(711\) 0 0
\(712\) −8.63960 −0.323783
\(713\) 13.0930 0.490336
\(714\) 0 0
\(715\) −39.4353 −1.47480
\(716\) −11.3870 −0.425551
\(717\) 0 0
\(718\) 6.51797 0.243248
\(719\) −24.1984 −0.902449 −0.451224 0.892411i \(-0.649013\pi\)
−0.451224 + 0.892411i \(0.649013\pi\)
\(720\) 0 0
\(721\) 8.90018 0.331460
\(722\) −25.3083 −0.941878
\(723\) 0 0
\(724\) −36.6445 −1.36188
\(725\) 81.8564 3.04007
\(726\) 0 0
\(727\) −38.4129 −1.42466 −0.712328 0.701846i \(-0.752359\pi\)
−0.712328 + 0.701846i \(0.752359\pi\)
\(728\) 3.82174 0.141643
\(729\) 0 0
\(730\) 69.6871 2.57924
\(731\) 22.9082 0.847291
\(732\) 0 0
\(733\) 1.75404 0.0647869 0.0323934 0.999475i \(-0.489687\pi\)
0.0323934 + 0.999475i \(0.489687\pi\)
\(734\) −64.9259 −2.39646
\(735\) 0 0
\(736\) 10.4572 0.385457
\(737\) 12.1854 0.448856
\(738\) 0 0
\(739\) 51.1599 1.88195 0.940973 0.338480i \(-0.109913\pi\)
0.940973 + 0.338480i \(0.109913\pi\)
\(740\) 46.4588 1.70786
\(741\) 0 0
\(742\) 14.4662 0.531071
\(743\) −40.5974 −1.48937 −0.744686 0.667415i \(-0.767401\pi\)
−0.744686 + 0.667415i \(0.767401\pi\)
\(744\) 0 0
\(745\) −52.1994 −1.91244
\(746\) 3.71060 0.135855
\(747\) 0 0
\(748\) −6.81479 −0.249173
\(749\) 19.2178 0.702204
\(750\) 0 0
\(751\) 29.4652 1.07520 0.537601 0.843199i \(-0.319331\pi\)
0.537601 + 0.843199i \(0.319331\pi\)
\(752\) 47.7541 1.74141
\(753\) 0 0
\(754\) −67.2358 −2.44858
\(755\) 51.7692 1.88407
\(756\) 0 0
\(757\) 24.4676 0.889290 0.444645 0.895707i \(-0.353330\pi\)
0.444645 + 0.895707i \(0.353330\pi\)
\(758\) 16.2145 0.588936
\(759\) 0 0
\(760\) 18.5572 0.673139
\(761\) 9.90305 0.358985 0.179493 0.983759i \(-0.442554\pi\)
0.179493 + 0.983759i \(0.442554\pi\)
\(762\) 0 0
\(763\) −16.3725 −0.592725
\(764\) −23.5624 −0.852457
\(765\) 0 0
\(766\) 19.4867 0.704084
\(767\) 17.8916 0.646029
\(768\) 0 0
\(769\) 24.5030 0.883599 0.441800 0.897114i \(-0.354340\pi\)
0.441800 + 0.897114i \(0.354340\pi\)
\(770\) 16.0442 0.578193
\(771\) 0 0
\(772\) −34.5075 −1.24195
\(773\) 5.48889 0.197422 0.0987109 0.995116i \(-0.468528\pi\)
0.0987109 + 0.995116i \(0.468528\pi\)
\(774\) 0 0
\(775\) 96.0231 3.44925
\(776\) −1.12297 −0.0403121
\(777\) 0 0
\(778\) 37.1482 1.33183
\(779\) −9.70737 −0.347803
\(780\) 0 0
\(781\) −13.4473 −0.481183
\(782\) −5.57079 −0.199211
\(783\) 0 0
\(784\) −4.68225 −0.167223
\(785\) −16.5911 −0.592161
\(786\) 0 0
\(787\) 20.1270 0.717448 0.358724 0.933444i \(-0.383212\pi\)
0.358724 + 0.933444i \(0.383212\pi\)
\(788\) −8.47003 −0.301732
\(789\) 0 0
\(790\) −63.3003 −2.25212
\(791\) 11.4751 0.408007
\(792\) 0 0
\(793\) −33.1688 −1.17786
\(794\) 32.0041 1.13578
\(795\) 0 0
\(796\) 18.0060 0.638204
\(797\) 37.5515 1.33014 0.665071 0.746781i \(-0.268401\pi\)
0.665071 + 0.746781i \(0.268401\pi\)
\(798\) 0 0
\(799\) −20.6986 −0.732262
\(800\) 76.6924 2.71149
\(801\) 0 0
\(802\) −27.8894 −0.984808
\(803\) 20.0294 0.706823
\(804\) 0 0
\(805\) 5.75484 0.202831
\(806\) −78.8721 −2.77815
\(807\) 0 0
\(808\) −9.45577 −0.332653
\(809\) 15.5218 0.545719 0.272859 0.962054i \(-0.412031\pi\)
0.272859 + 0.962054i \(0.412031\pi\)
\(810\) 0 0
\(811\) −36.0347 −1.26535 −0.632675 0.774417i \(-0.718043\pi\)
−0.632675 + 0.774417i \(0.718043\pi\)
\(812\) 12.0028 0.421217
\(813\) 0 0
\(814\) 30.4322 1.06665
\(815\) −59.5131 −2.08465
\(816\) 0 0
\(817\) 64.2572 2.24808
\(818\) 42.1175 1.47261
\(819\) 0 0
\(820\) −10.5533 −0.368537
\(821\) 36.1102 1.26025 0.630127 0.776492i \(-0.283003\pi\)
0.630127 + 0.776492i \(0.283003\pi\)
\(822\) 0 0
\(823\) −40.1465 −1.39942 −0.699709 0.714428i \(-0.746687\pi\)
−0.699709 + 0.714428i \(0.746687\pi\)
\(824\) 7.33066 0.255376
\(825\) 0 0
\(826\) −7.27919 −0.253275
\(827\) 17.4221 0.605827 0.302914 0.953018i \(-0.402041\pi\)
0.302914 + 0.953018i \(0.402041\pi\)
\(828\) 0 0
\(829\) −52.1085 −1.80980 −0.904902 0.425620i \(-0.860056\pi\)
−0.904902 + 0.425620i \(0.860056\pi\)
\(830\) 46.9493 1.62963
\(831\) 0 0
\(832\) −19.5429 −0.677529
\(833\) 2.02948 0.0703173
\(834\) 0 0
\(835\) −36.6120 −1.26701
\(836\) −19.1154 −0.661120
\(837\) 0 0
\(838\) 7.39527 0.255465
\(839\) −11.3620 −0.392260 −0.196130 0.980578i \(-0.562837\pi\)
−0.196130 + 0.980578i \(0.562837\pi\)
\(840\) 0 0
\(841\) 29.9206 1.03174
\(842\) 18.7502 0.646173
\(843\) 0 0
\(844\) 8.13337 0.279962
\(845\) 33.7578 1.16130
\(846\) 0 0
\(847\) −6.38859 −0.219514
\(848\) 35.8806 1.23214
\(849\) 0 0
\(850\) −40.8558 −1.40134
\(851\) 10.9156 0.374183
\(852\) 0 0
\(853\) −11.4023 −0.390406 −0.195203 0.980763i \(-0.562537\pi\)
−0.195203 + 0.980763i \(0.562537\pi\)
\(854\) 13.4947 0.461779
\(855\) 0 0
\(856\) 15.8288 0.541019
\(857\) 0.950674 0.0324744 0.0162372 0.999868i \(-0.494831\pi\)
0.0162372 + 0.999868i \(0.494831\pi\)
\(858\) 0 0
\(859\) 0.210633 0.00718671 0.00359336 0.999994i \(-0.498856\pi\)
0.00359336 + 0.999994i \(0.498856\pi\)
\(860\) 69.8567 2.38210
\(861\) 0 0
\(862\) 7.57425 0.257980
\(863\) −10.9776 −0.373681 −0.186841 0.982390i \(-0.559825\pi\)
−0.186841 + 0.982390i \(0.559825\pi\)
\(864\) 0 0
\(865\) −29.9741 −1.01915
\(866\) 31.3623 1.06573
\(867\) 0 0
\(868\) 14.0801 0.477911
\(869\) −18.1937 −0.617180
\(870\) 0 0
\(871\) −26.3294 −0.892138
\(872\) −13.4853 −0.456669
\(873\) 0 0
\(874\) −15.6260 −0.528557
\(875\) 22.4168 0.757825
\(876\) 0 0
\(877\) 0.159264 0.00537796 0.00268898 0.999996i \(-0.499144\pi\)
0.00268898 + 0.999996i \(0.499144\pi\)
\(878\) 3.04542 0.102778
\(879\) 0 0
\(880\) 39.7945 1.34147
\(881\) 23.8224 0.802598 0.401299 0.915947i \(-0.368559\pi\)
0.401299 + 0.915947i \(0.368559\pi\)
\(882\) 0 0
\(883\) −13.0665 −0.439722 −0.219861 0.975531i \(-0.570560\pi\)
−0.219861 + 0.975531i \(0.570560\pi\)
\(884\) 14.7249 0.495252
\(885\) 0 0
\(886\) 28.9422 0.972332
\(887\) −30.3390 −1.01868 −0.509341 0.860565i \(-0.670111\pi\)
−0.509341 + 0.860565i \(0.670111\pi\)
\(888\) 0 0
\(889\) 1.00000 0.0335389
\(890\) 78.3700 2.62697
\(891\) 0 0
\(892\) 33.3837 1.11777
\(893\) −58.0592 −1.94288
\(894\) 0 0
\(895\) −28.8209 −0.963378
\(896\) −6.43243 −0.214893
\(897\) 0 0
\(898\) 48.3698 1.61412
\(899\) 69.1178 2.30521
\(900\) 0 0
\(901\) −15.5521 −0.518116
\(902\) −6.91279 −0.230171
\(903\) 0 0
\(904\) 9.45149 0.314352
\(905\) −92.7490 −3.08308
\(906\) 0 0
\(907\) −29.7564 −0.988044 −0.494022 0.869449i \(-0.664474\pi\)
−0.494022 + 0.869449i \(0.664474\pi\)
\(908\) 9.50814 0.315539
\(909\) 0 0
\(910\) −34.6671 −1.14920
\(911\) 60.0700 1.99021 0.995103 0.0988416i \(-0.0315137\pi\)
0.995103 + 0.0988416i \(0.0315137\pi\)
\(912\) 0 0
\(913\) 13.4941 0.446591
\(914\) −19.5119 −0.645398
\(915\) 0 0
\(916\) 32.9087 1.08733
\(917\) −16.8610 −0.556800
\(918\) 0 0
\(919\) 25.7936 0.850852 0.425426 0.904993i \(-0.360124\pi\)
0.425426 + 0.904993i \(0.360124\pi\)
\(920\) 4.73999 0.156273
\(921\) 0 0
\(922\) −33.5597 −1.10523
\(923\) 29.0560 0.956389
\(924\) 0 0
\(925\) 80.0545 2.63217
\(926\) 32.7830 1.07732
\(927\) 0 0
\(928\) 55.2035 1.81214
\(929\) 46.1737 1.51491 0.757455 0.652887i \(-0.226442\pi\)
0.757455 + 0.652887i \(0.226442\pi\)
\(930\) 0 0
\(931\) 5.69266 0.186570
\(932\) −34.6770 −1.13588
\(933\) 0 0
\(934\) −49.3514 −1.61483
\(935\) −17.2486 −0.564088
\(936\) 0 0
\(937\) −54.6743 −1.78613 −0.893066 0.449926i \(-0.851450\pi\)
−0.893066 + 0.449926i \(0.851450\pi\)
\(938\) 10.7121 0.349762
\(939\) 0 0
\(940\) −63.1186 −2.05870
\(941\) −16.7357 −0.545569 −0.272785 0.962075i \(-0.587945\pi\)
−0.272785 + 0.962075i \(0.587945\pi\)
\(942\) 0 0
\(943\) −2.47952 −0.0807444
\(944\) −18.0546 −0.587627
\(945\) 0 0
\(946\) 45.7587 1.48774
\(947\) −60.2549 −1.95802 −0.979011 0.203808i \(-0.934668\pi\)
−0.979011 + 0.203808i \(0.934668\pi\)
\(948\) 0 0
\(949\) −43.2781 −1.40487
\(950\) −114.600 −3.71812
\(951\) 0 0
\(952\) 1.67159 0.0541765
\(953\) −8.73051 −0.282809 −0.141405 0.989952i \(-0.545162\pi\)
−0.141405 + 0.989952i \(0.545162\pi\)
\(954\) 0 0
\(955\) −59.6375 −1.92982
\(956\) 40.0254 1.29451
\(957\) 0 0
\(958\) 46.0634 1.48824
\(959\) 19.1796 0.619341
\(960\) 0 0
\(961\) 50.0798 1.61548
\(962\) −65.7557 −2.12005
\(963\) 0 0
\(964\) −31.1669 −1.00382
\(965\) −87.3400 −2.81157
\(966\) 0 0
\(967\) 59.2643 1.90581 0.952905 0.303268i \(-0.0980777\pi\)
0.952905 + 0.303268i \(0.0980777\pi\)
\(968\) −5.26198 −0.169127
\(969\) 0 0
\(970\) 10.1865 0.327067
\(971\) 15.3180 0.491577 0.245789 0.969323i \(-0.420953\pi\)
0.245789 + 0.969323i \(0.420953\pi\)
\(972\) 0 0
\(973\) −8.01183 −0.256847
\(974\) −8.07073 −0.258603
\(975\) 0 0
\(976\) 33.4709 1.07138
\(977\) 55.5903 1.77849 0.889245 0.457431i \(-0.151230\pi\)
0.889245 + 0.457431i \(0.151230\pi\)
\(978\) 0 0
\(979\) 22.5251 0.719904
\(980\) 6.18873 0.197692
\(981\) 0 0
\(982\) 36.9035 1.17764
\(983\) −2.43713 −0.0777323 −0.0388662 0.999244i \(-0.512375\pi\)
−0.0388662 + 0.999244i \(0.512375\pi\)
\(984\) 0 0
\(985\) −21.4380 −0.683073
\(986\) −29.4082 −0.936547
\(987\) 0 0
\(988\) 41.3032 1.31403
\(989\) 16.4130 0.521904
\(990\) 0 0
\(991\) −8.15365 −0.259009 −0.129505 0.991579i \(-0.541339\pi\)
−0.129505 + 0.991579i \(0.541339\pi\)
\(992\) 64.7574 2.05605
\(993\) 0 0
\(994\) −11.8214 −0.374952
\(995\) 45.5739 1.44479
\(996\) 0 0
\(997\) −33.5398 −1.06222 −0.531109 0.847304i \(-0.678224\pi\)
−0.531109 + 0.847304i \(0.678224\pi\)
\(998\) −28.7609 −0.910412
\(999\) 0 0
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 \(a_p\))