Properties

Label 8046.2.a.h.1.5
Level 8046
Weight 2
Character 8046.1
Self dual Yes
Analytic conductor 64.248
Analytic rank 1
Dimension 9
CM No
Inner twists 1

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 8046 = 2 \cdot 3^{3} \cdot 149 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8046.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2476334663\)
Analytic rank: \(1\)
Dimension: \(9\)
Coefficient field: \(\mathbb{Q}[x]/(x^{9} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Root \(-0.584549\)
Character \(\chi\) = 8046.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} +1.00000 q^{4} -0.683695 q^{5} -0.639069 q^{7} +1.00000 q^{8} +O(q^{10})\) \(q+1.00000 q^{2} +1.00000 q^{4} -0.683695 q^{5} -0.639069 q^{7} +1.00000 q^{8} -0.683695 q^{10} -1.37847 q^{11} +1.22729 q^{13} -0.639069 q^{14} +1.00000 q^{16} -2.93824 q^{17} -1.25651 q^{19} -0.683695 q^{20} -1.37847 q^{22} +7.55461 q^{23} -4.53256 q^{25} +1.22729 q^{26} -0.639069 q^{28} -2.51033 q^{29} +5.78698 q^{31} +1.00000 q^{32} -2.93824 q^{34} +0.436928 q^{35} -2.36988 q^{37} -1.25651 q^{38} -0.683695 q^{40} -1.79132 q^{41} -10.0366 q^{43} -1.37847 q^{44} +7.55461 q^{46} -11.1030 q^{47} -6.59159 q^{49} -4.53256 q^{50} +1.22729 q^{52} +3.25589 q^{53} +0.942452 q^{55} -0.639069 q^{56} -2.51033 q^{58} +10.2114 q^{59} +1.02628 q^{61} +5.78698 q^{62} +1.00000 q^{64} -0.839089 q^{65} +8.00671 q^{67} -2.93824 q^{68} +0.436928 q^{70} +2.68750 q^{71} -15.4477 q^{73} -2.36988 q^{74} -1.25651 q^{76} +0.880936 q^{77} -7.08243 q^{79} -0.683695 q^{80} -1.79132 q^{82} +2.29043 q^{83} +2.00886 q^{85} -10.0366 q^{86} -1.37847 q^{88} -7.26133 q^{89} -0.784321 q^{91} +7.55461 q^{92} -11.1030 q^{94} +0.859067 q^{95} +0.495565 q^{97} -6.59159 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 9q + 9q^{2} + 9q^{4} - 4q^{5} - 4q^{7} + 9q^{8} + O(q^{10}) \) \( 9q + 9q^{2} + 9q^{4} - 4q^{5} - 4q^{7} + 9q^{8} - 4q^{10} - 4q^{11} - 8q^{13} - 4q^{14} + 9q^{16} - q^{17} - 10q^{19} - 4q^{20} - 4q^{22} - 8q^{23} - 3q^{25} - 8q^{26} - 4q^{28} - 4q^{29} - 17q^{31} + 9q^{32} - q^{34} - 10q^{35} - 11q^{37} - 10q^{38} - 4q^{40} - 16q^{43} - 4q^{44} - 8q^{46} - 7q^{47} - 5q^{49} - 3q^{50} - 8q^{52} - 12q^{53} - 23q^{55} - 4q^{56} - 4q^{58} - 6q^{59} - 13q^{61} - 17q^{62} + 9q^{64} + 24q^{65} - 14q^{67} - q^{68} - 10q^{70} - 30q^{71} - 12q^{73} - 11q^{74} - 10q^{76} - 12q^{77} - 35q^{79} - 4q^{80} - 5q^{83} - 27q^{85} - 16q^{86} - 4q^{88} - 23q^{89} - 28q^{91} - 8q^{92} - 7q^{94} - 32q^{95} - 21q^{97} - 5q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) 0 0
\(4\) 1.00000 0.500000
\(5\) −0.683695 −0.305758 −0.152879 0.988245i \(-0.548854\pi\)
−0.152879 + 0.988245i \(0.548854\pi\)
\(6\) 0 0
\(7\) −0.639069 −0.241545 −0.120773 0.992680i \(-0.538537\pi\)
−0.120773 + 0.992680i \(0.538537\pi\)
\(8\) 1.00000 0.353553
\(9\) 0 0
\(10\) −0.683695 −0.216203
\(11\) −1.37847 −0.415624 −0.207812 0.978169i \(-0.566634\pi\)
−0.207812 + 0.978169i \(0.566634\pi\)
\(12\) 0 0
\(13\) 1.22729 0.340388 0.170194 0.985411i \(-0.445561\pi\)
0.170194 + 0.985411i \(0.445561\pi\)
\(14\) −0.639069 −0.170798
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) −2.93824 −0.712627 −0.356313 0.934366i \(-0.615966\pi\)
−0.356313 + 0.934366i \(0.615966\pi\)
\(18\) 0 0
\(19\) −1.25651 −0.288262 −0.144131 0.989559i \(-0.546039\pi\)
−0.144131 + 0.989559i \(0.546039\pi\)
\(20\) −0.683695 −0.152879
\(21\) 0 0
\(22\) −1.37847 −0.293890
\(23\) 7.55461 1.57524 0.787622 0.616158i \(-0.211312\pi\)
0.787622 + 0.616158i \(0.211312\pi\)
\(24\) 0 0
\(25\) −4.53256 −0.906512
\(26\) 1.22729 0.240691
\(27\) 0 0
\(28\) −0.639069 −0.120773
\(29\) −2.51033 −0.466157 −0.233078 0.972458i \(-0.574880\pi\)
−0.233078 + 0.972458i \(0.574880\pi\)
\(30\) 0 0
\(31\) 5.78698 1.03937 0.519686 0.854357i \(-0.326049\pi\)
0.519686 + 0.854357i \(0.326049\pi\)
\(32\) 1.00000 0.176777
\(33\) 0 0
\(34\) −2.93824 −0.503903
\(35\) 0.436928 0.0738543
\(36\) 0 0
\(37\) −2.36988 −0.389606 −0.194803 0.980842i \(-0.562407\pi\)
−0.194803 + 0.980842i \(0.562407\pi\)
\(38\) −1.25651 −0.203832
\(39\) 0 0
\(40\) −0.683695 −0.108102
\(41\) −1.79132 −0.279758 −0.139879 0.990169i \(-0.544671\pi\)
−0.139879 + 0.990169i \(0.544671\pi\)
\(42\) 0 0
\(43\) −10.0366 −1.53056 −0.765282 0.643695i \(-0.777401\pi\)
−0.765282 + 0.643695i \(0.777401\pi\)
\(44\) −1.37847 −0.207812
\(45\) 0 0
\(46\) 7.55461 1.11387
\(47\) −11.1030 −1.61954 −0.809770 0.586748i \(-0.800408\pi\)
−0.809770 + 0.586748i \(0.800408\pi\)
\(48\) 0 0
\(49\) −6.59159 −0.941656
\(50\) −4.53256 −0.641001
\(51\) 0 0
\(52\) 1.22729 0.170194
\(53\) 3.25589 0.447231 0.223616 0.974677i \(-0.428214\pi\)
0.223616 + 0.974677i \(0.428214\pi\)
\(54\) 0 0
\(55\) 0.942452 0.127080
\(56\) −0.639069 −0.0853992
\(57\) 0 0
\(58\) −2.51033 −0.329623
\(59\) 10.2114 1.32941 0.664705 0.747106i \(-0.268557\pi\)
0.664705 + 0.747106i \(0.268557\pi\)
\(60\) 0 0
\(61\) 1.02628 0.131402 0.0657009 0.997839i \(-0.479072\pi\)
0.0657009 + 0.997839i \(0.479072\pi\)
\(62\) 5.78698 0.734947
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) −0.839089 −0.104076
\(66\) 0 0
\(67\) 8.00671 0.978175 0.489088 0.872235i \(-0.337330\pi\)
0.489088 + 0.872235i \(0.337330\pi\)
\(68\) −2.93824 −0.356313
\(69\) 0 0
\(70\) 0.436928 0.0522229
\(71\) 2.68750 0.318947 0.159474 0.987202i \(-0.449020\pi\)
0.159474 + 0.987202i \(0.449020\pi\)
\(72\) 0 0
\(73\) −15.4477 −1.80802 −0.904009 0.427513i \(-0.859390\pi\)
−0.904009 + 0.427513i \(0.859390\pi\)
\(74\) −2.36988 −0.275493
\(75\) 0 0
\(76\) −1.25651 −0.144131
\(77\) 0.880936 0.100392
\(78\) 0 0
\(79\) −7.08243 −0.796836 −0.398418 0.917204i \(-0.630441\pi\)
−0.398418 + 0.917204i \(0.630441\pi\)
\(80\) −0.683695 −0.0764394
\(81\) 0 0
\(82\) −1.79132 −0.197819
\(83\) 2.29043 0.251407 0.125703 0.992068i \(-0.459881\pi\)
0.125703 + 0.992068i \(0.459881\pi\)
\(84\) 0 0
\(85\) 2.00886 0.217891
\(86\) −10.0366 −1.08227
\(87\) 0 0
\(88\) −1.37847 −0.146945
\(89\) −7.26133 −0.769699 −0.384850 0.922979i \(-0.625747\pi\)
−0.384850 + 0.922979i \(0.625747\pi\)
\(90\) 0 0
\(91\) −0.784321 −0.0822191
\(92\) 7.55461 0.787622
\(93\) 0 0
\(94\) −11.1030 −1.14519
\(95\) 0.859067 0.0881384
\(96\) 0 0
\(97\) 0.495565 0.0503170 0.0251585 0.999683i \(-0.491991\pi\)
0.0251585 + 0.999683i \(0.491991\pi\)
\(98\) −6.59159 −0.665851
\(99\) 0 0
\(100\) −4.53256 −0.453256
\(101\) 18.5785 1.84863 0.924316 0.381628i \(-0.124637\pi\)
0.924316 + 0.381628i \(0.124637\pi\)
\(102\) 0 0
\(103\) 5.74954 0.566519 0.283260 0.959043i \(-0.408584\pi\)
0.283260 + 0.959043i \(0.408584\pi\)
\(104\) 1.22729 0.120345
\(105\) 0 0
\(106\) 3.25589 0.316240
\(107\) −5.00086 −0.483451 −0.241726 0.970345i \(-0.577713\pi\)
−0.241726 + 0.970345i \(0.577713\pi\)
\(108\) 0 0
\(109\) −7.81173 −0.748228 −0.374114 0.927383i \(-0.622053\pi\)
−0.374114 + 0.927383i \(0.622053\pi\)
\(110\) 0.942452 0.0898593
\(111\) 0 0
\(112\) −0.639069 −0.0603863
\(113\) −18.0793 −1.70076 −0.850379 0.526171i \(-0.823627\pi\)
−0.850379 + 0.526171i \(0.823627\pi\)
\(114\) 0 0
\(115\) −5.16505 −0.481643
\(116\) −2.51033 −0.233078
\(117\) 0 0
\(118\) 10.2114 0.940034
\(119\) 1.87774 0.172132
\(120\) 0 0
\(121\) −9.09982 −0.827257
\(122\) 1.02628 0.0929150
\(123\) 0 0
\(124\) 5.78698 0.519686
\(125\) 6.51736 0.582931
\(126\) 0 0
\(127\) 12.3765 1.09824 0.549120 0.835743i \(-0.314963\pi\)
0.549120 + 0.835743i \(0.314963\pi\)
\(128\) 1.00000 0.0883883
\(129\) 0 0
\(130\) −0.839089 −0.0735930
\(131\) −15.3165 −1.33821 −0.669104 0.743169i \(-0.733322\pi\)
−0.669104 + 0.743169i \(0.733322\pi\)
\(132\) 0 0
\(133\) 0.802994 0.0696284
\(134\) 8.00671 0.691674
\(135\) 0 0
\(136\) −2.93824 −0.251952
\(137\) 8.12377 0.694060 0.347030 0.937854i \(-0.387190\pi\)
0.347030 + 0.937854i \(0.387190\pi\)
\(138\) 0 0
\(139\) −15.8878 −1.34759 −0.673793 0.738920i \(-0.735336\pi\)
−0.673793 + 0.738920i \(0.735336\pi\)
\(140\) 0.436928 0.0369272
\(141\) 0 0
\(142\) 2.68750 0.225530
\(143\) −1.69178 −0.141473
\(144\) 0 0
\(145\) 1.71630 0.142531
\(146\) −15.4477 −1.27846
\(147\) 0 0
\(148\) −2.36988 −0.194803
\(149\) −1.00000 −0.0819232
\(150\) 0 0
\(151\) −4.92235 −0.400576 −0.200288 0.979737i \(-0.564188\pi\)
−0.200288 + 0.979737i \(0.564188\pi\)
\(152\) −1.25651 −0.101916
\(153\) 0 0
\(154\) 0.880936 0.0709879
\(155\) −3.95653 −0.317796
\(156\) 0 0
\(157\) −1.05732 −0.0843835 −0.0421918 0.999110i \(-0.513434\pi\)
−0.0421918 + 0.999110i \(0.513434\pi\)
\(158\) −7.08243 −0.563448
\(159\) 0 0
\(160\) −0.683695 −0.0540508
\(161\) −4.82791 −0.380493
\(162\) 0 0
\(163\) 5.30856 0.415798 0.207899 0.978150i \(-0.433337\pi\)
0.207899 + 0.978150i \(0.433337\pi\)
\(164\) −1.79132 −0.139879
\(165\) 0 0
\(166\) 2.29043 0.177771
\(167\) −7.75142 −0.599823 −0.299912 0.953967i \(-0.596957\pi\)
−0.299912 + 0.953967i \(0.596957\pi\)
\(168\) 0 0
\(169\) −11.4938 −0.884136
\(170\) 2.00886 0.154072
\(171\) 0 0
\(172\) −10.0366 −0.765282
\(173\) −1.91298 −0.145441 −0.0727206 0.997352i \(-0.523168\pi\)
−0.0727206 + 0.997352i \(0.523168\pi\)
\(174\) 0 0
\(175\) 2.89662 0.218964
\(176\) −1.37847 −0.103906
\(177\) 0 0
\(178\) −7.26133 −0.544260
\(179\) −23.0724 −1.72451 −0.862257 0.506470i \(-0.830950\pi\)
−0.862257 + 0.506470i \(0.830950\pi\)
\(180\) 0 0
\(181\) −0.420424 −0.0312499 −0.0156250 0.999878i \(-0.504974\pi\)
−0.0156250 + 0.999878i \(0.504974\pi\)
\(182\) −0.784321 −0.0581377
\(183\) 0 0
\(184\) 7.55461 0.556933
\(185\) 1.62027 0.119125
\(186\) 0 0
\(187\) 4.05027 0.296185
\(188\) −11.1030 −0.809770
\(189\) 0 0
\(190\) 0.859067 0.0623232
\(191\) 13.9592 1.01005 0.505026 0.863104i \(-0.331483\pi\)
0.505026 + 0.863104i \(0.331483\pi\)
\(192\) 0 0
\(193\) −26.1712 −1.88384 −0.941922 0.335831i \(-0.890983\pi\)
−0.941922 + 0.335831i \(0.890983\pi\)
\(194\) 0.495565 0.0355795
\(195\) 0 0
\(196\) −6.59159 −0.470828
\(197\) −13.2324 −0.942768 −0.471384 0.881928i \(-0.656245\pi\)
−0.471384 + 0.881928i \(0.656245\pi\)
\(198\) 0 0
\(199\) −22.0979 −1.56648 −0.783238 0.621722i \(-0.786433\pi\)
−0.783238 + 0.621722i \(0.786433\pi\)
\(200\) −4.53256 −0.320500
\(201\) 0 0
\(202\) 18.5785 1.30718
\(203\) 1.60428 0.112598
\(204\) 0 0
\(205\) 1.22472 0.0855380
\(206\) 5.74954 0.400589
\(207\) 0 0
\(208\) 1.22729 0.0850970
\(209\) 1.73205 0.119809
\(210\) 0 0
\(211\) 9.79151 0.674075 0.337038 0.941491i \(-0.390575\pi\)
0.337038 + 0.941491i \(0.390575\pi\)
\(212\) 3.25589 0.223616
\(213\) 0 0
\(214\) −5.00086 −0.341852
\(215\) 6.86196 0.467982
\(216\) 0 0
\(217\) −3.69828 −0.251055
\(218\) −7.81173 −0.529077
\(219\) 0 0
\(220\) 0.942452 0.0635401
\(221\) −3.60606 −0.242570
\(222\) 0 0
\(223\) −24.0602 −1.61119 −0.805597 0.592465i \(-0.798155\pi\)
−0.805597 + 0.592465i \(0.798155\pi\)
\(224\) −0.639069 −0.0426996
\(225\) 0 0
\(226\) −18.0793 −1.20262
\(227\) −14.1524 −0.939327 −0.469664 0.882845i \(-0.655625\pi\)
−0.469664 + 0.882845i \(0.655625\pi\)
\(228\) 0 0
\(229\) −7.88051 −0.520759 −0.260379 0.965506i \(-0.583848\pi\)
−0.260379 + 0.965506i \(0.583848\pi\)
\(230\) −5.16505 −0.340573
\(231\) 0 0
\(232\) −2.51033 −0.164811
\(233\) −4.07402 −0.266898 −0.133449 0.991056i \(-0.542605\pi\)
−0.133449 + 0.991056i \(0.542605\pi\)
\(234\) 0 0
\(235\) 7.59107 0.495187
\(236\) 10.2114 0.664705
\(237\) 0 0
\(238\) 1.87774 0.121715
\(239\) 13.7267 0.887909 0.443954 0.896049i \(-0.353575\pi\)
0.443954 + 0.896049i \(0.353575\pi\)
\(240\) 0 0
\(241\) 17.2144 1.10888 0.554439 0.832225i \(-0.312933\pi\)
0.554439 + 0.832225i \(0.312933\pi\)
\(242\) −9.09982 −0.584959
\(243\) 0 0
\(244\) 1.02628 0.0657009
\(245\) 4.50664 0.287918
\(246\) 0 0
\(247\) −1.54209 −0.0981210
\(248\) 5.78698 0.367473
\(249\) 0 0
\(250\) 6.51736 0.412194
\(251\) −11.7758 −0.743282 −0.371641 0.928377i \(-0.621205\pi\)
−0.371641 + 0.928377i \(0.621205\pi\)
\(252\) 0 0
\(253\) −10.4138 −0.654709
\(254\) 12.3765 0.776573
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) 21.0319 1.31193 0.655966 0.754791i \(-0.272262\pi\)
0.655966 + 0.754791i \(0.272262\pi\)
\(258\) 0 0
\(259\) 1.51452 0.0941074
\(260\) −0.839089 −0.0520381
\(261\) 0 0
\(262\) −15.3165 −0.946256
\(263\) 16.8639 1.03987 0.519936 0.854205i \(-0.325956\pi\)
0.519936 + 0.854205i \(0.325956\pi\)
\(264\) 0 0
\(265\) −2.22604 −0.136744
\(266\) 0.802994 0.0492347
\(267\) 0 0
\(268\) 8.00671 0.489088
\(269\) 22.4206 1.36701 0.683504 0.729947i \(-0.260455\pi\)
0.683504 + 0.729947i \(0.260455\pi\)
\(270\) 0 0
\(271\) −13.5262 −0.821661 −0.410830 0.911712i \(-0.634761\pi\)
−0.410830 + 0.911712i \(0.634761\pi\)
\(272\) −2.93824 −0.178157
\(273\) 0 0
\(274\) 8.12377 0.490775
\(275\) 6.24799 0.376768
\(276\) 0 0
\(277\) 11.6854 0.702109 0.351054 0.936355i \(-0.385823\pi\)
0.351054 + 0.936355i \(0.385823\pi\)
\(278\) −15.8878 −0.952887
\(279\) 0 0
\(280\) 0.436928 0.0261115
\(281\) −1.34141 −0.0800215 −0.0400108 0.999199i \(-0.512739\pi\)
−0.0400108 + 0.999199i \(0.512739\pi\)
\(282\) 0 0
\(283\) 24.3292 1.44622 0.723110 0.690732i \(-0.242712\pi\)
0.723110 + 0.690732i \(0.242712\pi\)
\(284\) 2.68750 0.159474
\(285\) 0 0
\(286\) −1.69178 −0.100037
\(287\) 1.14478 0.0675742
\(288\) 0 0
\(289\) −8.36677 −0.492163
\(290\) 1.71630 0.100785
\(291\) 0 0
\(292\) −15.4477 −0.904009
\(293\) 4.76293 0.278253 0.139127 0.990275i \(-0.455570\pi\)
0.139127 + 0.990275i \(0.455570\pi\)
\(294\) 0 0
\(295\) −6.98147 −0.406477
\(296\) −2.36988 −0.137746
\(297\) 0 0
\(298\) −1.00000 −0.0579284
\(299\) 9.27167 0.536194
\(300\) 0 0
\(301\) 6.41407 0.369701
\(302\) −4.92235 −0.283250
\(303\) 0 0
\(304\) −1.25651 −0.0720655
\(305\) −0.701663 −0.0401771
\(306\) 0 0
\(307\) −20.7130 −1.18215 −0.591077 0.806615i \(-0.701297\pi\)
−0.591077 + 0.806615i \(0.701297\pi\)
\(308\) 0.880936 0.0501960
\(309\) 0 0
\(310\) −3.95653 −0.224716
\(311\) −17.6892 −1.00306 −0.501532 0.865139i \(-0.667230\pi\)
−0.501532 + 0.865139i \(0.667230\pi\)
\(312\) 0 0
\(313\) 1.72775 0.0976583 0.0488291 0.998807i \(-0.484451\pi\)
0.0488291 + 0.998807i \(0.484451\pi\)
\(314\) −1.05732 −0.0596682
\(315\) 0 0
\(316\) −7.08243 −0.398418
\(317\) 27.4073 1.53935 0.769674 0.638437i \(-0.220419\pi\)
0.769674 + 0.638437i \(0.220419\pi\)
\(318\) 0 0
\(319\) 3.46041 0.193746
\(320\) −0.683695 −0.0382197
\(321\) 0 0
\(322\) −4.82791 −0.269049
\(323\) 3.69191 0.205423
\(324\) 0 0
\(325\) −5.56275 −0.308566
\(326\) 5.30856 0.294014
\(327\) 0 0
\(328\) −1.79132 −0.0989093
\(329\) 7.09558 0.391192
\(330\) 0 0
\(331\) −10.4910 −0.576636 −0.288318 0.957535i \(-0.593096\pi\)
−0.288318 + 0.957535i \(0.593096\pi\)
\(332\) 2.29043 0.125703
\(333\) 0 0
\(334\) −7.75142 −0.424139
\(335\) −5.47415 −0.299085
\(336\) 0 0
\(337\) 33.1109 1.80366 0.901832 0.432086i \(-0.142222\pi\)
0.901832 + 0.432086i \(0.142222\pi\)
\(338\) −11.4938 −0.625179
\(339\) 0 0
\(340\) 2.00886 0.108946
\(341\) −7.97717 −0.431988
\(342\) 0 0
\(343\) 8.68596 0.468998
\(344\) −10.0366 −0.541136
\(345\) 0 0
\(346\) −1.91298 −0.102843
\(347\) −24.7393 −1.32807 −0.664037 0.747700i \(-0.731158\pi\)
−0.664037 + 0.747700i \(0.731158\pi\)
\(348\) 0 0
\(349\) −27.8523 −1.49090 −0.745450 0.666561i \(-0.767765\pi\)
−0.745450 + 0.666561i \(0.767765\pi\)
\(350\) 2.89662 0.154831
\(351\) 0 0
\(352\) −1.37847 −0.0734726
\(353\) 18.3837 0.978466 0.489233 0.872153i \(-0.337277\pi\)
0.489233 + 0.872153i \(0.337277\pi\)
\(354\) 0 0
\(355\) −1.83743 −0.0975206
\(356\) −7.26133 −0.384850
\(357\) 0 0
\(358\) −23.0724 −1.21942
\(359\) 23.2473 1.22695 0.613473 0.789716i \(-0.289772\pi\)
0.613473 + 0.789716i \(0.289772\pi\)
\(360\) 0 0
\(361\) −17.4212 −0.916905
\(362\) −0.420424 −0.0220970
\(363\) 0 0
\(364\) −0.784321 −0.0411096
\(365\) 10.5615 0.552816
\(366\) 0 0
\(367\) −2.85101 −0.148821 −0.0744106 0.997228i \(-0.523708\pi\)
−0.0744106 + 0.997228i \(0.523708\pi\)
\(368\) 7.55461 0.393811
\(369\) 0 0
\(370\) 1.62027 0.0842340
\(371\) −2.08074 −0.108027
\(372\) 0 0
\(373\) −4.27241 −0.221217 −0.110608 0.993864i \(-0.535280\pi\)
−0.110608 + 0.993864i \(0.535280\pi\)
\(374\) 4.05027 0.209434
\(375\) 0 0
\(376\) −11.1030 −0.572594
\(377\) −3.08090 −0.158674
\(378\) 0 0
\(379\) 2.12935 0.109377 0.0546887 0.998503i \(-0.482583\pi\)
0.0546887 + 0.998503i \(0.482583\pi\)
\(380\) 0.859067 0.0440692
\(381\) 0 0
\(382\) 13.9592 0.714214
\(383\) −27.7927 −1.42014 −0.710071 0.704131i \(-0.751337\pi\)
−0.710071 + 0.704131i \(0.751337\pi\)
\(384\) 0 0
\(385\) −0.602292 −0.0306956
\(386\) −26.1712 −1.33208
\(387\) 0 0
\(388\) 0.495565 0.0251585
\(389\) 2.18146 0.110604 0.0553021 0.998470i \(-0.482388\pi\)
0.0553021 + 0.998470i \(0.482388\pi\)
\(390\) 0 0
\(391\) −22.1972 −1.12256
\(392\) −6.59159 −0.332926
\(393\) 0 0
\(394\) −13.2324 −0.666638
\(395\) 4.84222 0.243639
\(396\) 0 0
\(397\) 36.1692 1.81528 0.907640 0.419750i \(-0.137882\pi\)
0.907640 + 0.419750i \(0.137882\pi\)
\(398\) −22.0979 −1.10767
\(399\) 0 0
\(400\) −4.53256 −0.226628
\(401\) −38.0499 −1.90012 −0.950060 0.312068i \(-0.898978\pi\)
−0.950060 + 0.312068i \(0.898978\pi\)
\(402\) 0 0
\(403\) 7.10228 0.353790
\(404\) 18.5785 0.924316
\(405\) 0 0
\(406\) 1.60428 0.0796189
\(407\) 3.26680 0.161929
\(408\) 0 0
\(409\) −3.27404 −0.161891 −0.0809454 0.996719i \(-0.525794\pi\)
−0.0809454 + 0.996719i \(0.525794\pi\)
\(410\) 1.22472 0.0604845
\(411\) 0 0
\(412\) 5.74954 0.283260
\(413\) −6.52578 −0.321113
\(414\) 0 0
\(415\) −1.56595 −0.0768696
\(416\) 1.22729 0.0601727
\(417\) 0 0
\(418\) 1.73205 0.0847175
\(419\) −4.93454 −0.241068 −0.120534 0.992709i \(-0.538461\pi\)
−0.120534 + 0.992709i \(0.538461\pi\)
\(420\) 0 0
\(421\) −29.3725 −1.43153 −0.715764 0.698342i \(-0.753922\pi\)
−0.715764 + 0.698342i \(0.753922\pi\)
\(422\) 9.79151 0.476643
\(423\) 0 0
\(424\) 3.25589 0.158120
\(425\) 13.3177 0.646005
\(426\) 0 0
\(427\) −0.655864 −0.0317395
\(428\) −5.00086 −0.241726
\(429\) 0 0
\(430\) 6.86196 0.330913
\(431\) 2.39153 0.115196 0.0575981 0.998340i \(-0.481656\pi\)
0.0575981 + 0.998340i \(0.481656\pi\)
\(432\) 0 0
\(433\) −32.0988 −1.54257 −0.771285 0.636490i \(-0.780385\pi\)
−0.771285 + 0.636490i \(0.780385\pi\)
\(434\) −3.69828 −0.177523
\(435\) 0 0
\(436\) −7.81173 −0.374114
\(437\) −9.49241 −0.454083
\(438\) 0 0
\(439\) 13.9582 0.666188 0.333094 0.942894i \(-0.391907\pi\)
0.333094 + 0.942894i \(0.391907\pi\)
\(440\) 0.942452 0.0449296
\(441\) 0 0
\(442\) −3.60606 −0.171523
\(443\) −25.1491 −1.19487 −0.597436 0.801917i \(-0.703814\pi\)
−0.597436 + 0.801917i \(0.703814\pi\)
\(444\) 0 0
\(445\) 4.96453 0.235341
\(446\) −24.0602 −1.13929
\(447\) 0 0
\(448\) −0.639069 −0.0301932
\(449\) −11.0525 −0.521599 −0.260799 0.965393i \(-0.583986\pi\)
−0.260799 + 0.965393i \(0.583986\pi\)
\(450\) 0 0
\(451\) 2.46928 0.116274
\(452\) −18.0793 −0.850379
\(453\) 0 0
\(454\) −14.1524 −0.664205
\(455\) 0.536236 0.0251391
\(456\) 0 0
\(457\) −0.164071 −0.00767492 −0.00383746 0.999993i \(-0.501222\pi\)
−0.00383746 + 0.999993i \(0.501222\pi\)
\(458\) −7.88051 −0.368232
\(459\) 0 0
\(460\) −5.16505 −0.240822
\(461\) 9.62526 0.448293 0.224147 0.974555i \(-0.428041\pi\)
0.224147 + 0.974555i \(0.428041\pi\)
\(462\) 0 0
\(463\) 37.9510 1.76373 0.881866 0.471499i \(-0.156287\pi\)
0.881866 + 0.471499i \(0.156287\pi\)
\(464\) −2.51033 −0.116539
\(465\) 0 0
\(466\) −4.07402 −0.188725
\(467\) 27.8325 1.28793 0.643967 0.765054i \(-0.277288\pi\)
0.643967 + 0.765054i \(0.277288\pi\)
\(468\) 0 0
\(469\) −5.11684 −0.236274
\(470\) 7.59107 0.350150
\(471\) 0 0
\(472\) 10.2114 0.470017
\(473\) 13.8351 0.636139
\(474\) 0 0
\(475\) 5.69519 0.261313
\(476\) 1.87774 0.0860659
\(477\) 0 0
\(478\) 13.7267 0.627846
\(479\) 14.8934 0.680495 0.340248 0.940336i \(-0.389489\pi\)
0.340248 + 0.940336i \(0.389489\pi\)
\(480\) 0 0
\(481\) −2.90852 −0.132617
\(482\) 17.2144 0.784095
\(483\) 0 0
\(484\) −9.09982 −0.413628
\(485\) −0.338815 −0.0153848
\(486\) 0 0
\(487\) 18.5223 0.839326 0.419663 0.907680i \(-0.362148\pi\)
0.419663 + 0.907680i \(0.362148\pi\)
\(488\) 1.02628 0.0464575
\(489\) 0 0
\(490\) 4.50664 0.203589
\(491\) 33.3676 1.50586 0.752929 0.658102i \(-0.228641\pi\)
0.752929 + 0.658102i \(0.228641\pi\)
\(492\) 0 0
\(493\) 7.37595 0.332196
\(494\) −1.54209 −0.0693820
\(495\) 0 0
\(496\) 5.78698 0.259843
\(497\) −1.71750 −0.0770403
\(498\) 0 0
\(499\) −27.6463 −1.23762 −0.618808 0.785542i \(-0.712384\pi\)
−0.618808 + 0.785542i \(0.712384\pi\)
\(500\) 6.51736 0.291465
\(501\) 0 0
\(502\) −11.7758 −0.525580
\(503\) −20.7047 −0.923176 −0.461588 0.887094i \(-0.652720\pi\)
−0.461588 + 0.887094i \(0.652720\pi\)
\(504\) 0 0
\(505\) −12.7020 −0.565233
\(506\) −10.4138 −0.462949
\(507\) 0 0
\(508\) 12.3765 0.549120
\(509\) 17.9958 0.797648 0.398824 0.917028i \(-0.369418\pi\)
0.398824 + 0.917028i \(0.369418\pi\)
\(510\) 0 0
\(511\) 9.87216 0.436719
\(512\) 1.00000 0.0441942
\(513\) 0 0
\(514\) 21.0319 0.927675
\(515\) −3.93093 −0.173218
\(516\) 0 0
\(517\) 15.3051 0.673119
\(518\) 1.51452 0.0665440
\(519\) 0 0
\(520\) −0.839089 −0.0367965
\(521\) 26.7908 1.17373 0.586864 0.809686i \(-0.300363\pi\)
0.586864 + 0.809686i \(0.300363\pi\)
\(522\) 0 0
\(523\) −33.3656 −1.45897 −0.729487 0.683995i \(-0.760241\pi\)
−0.729487 + 0.683995i \(0.760241\pi\)
\(524\) −15.3165 −0.669104
\(525\) 0 0
\(526\) 16.8639 0.735300
\(527\) −17.0035 −0.740684
\(528\) 0 0
\(529\) 34.0721 1.48140
\(530\) −2.22604 −0.0966928
\(531\) 0 0
\(532\) 0.802994 0.0348142
\(533\) −2.19847 −0.0952261
\(534\) 0 0
\(535\) 3.41906 0.147819
\(536\) 8.00671 0.345837
\(537\) 0 0
\(538\) 22.4206 0.966621
\(539\) 9.08630 0.391375
\(540\) 0 0
\(541\) −14.4014 −0.619165 −0.309582 0.950873i \(-0.600189\pi\)
−0.309582 + 0.950873i \(0.600189\pi\)
\(542\) −13.5262 −0.581002
\(543\) 0 0
\(544\) −2.93824 −0.125976
\(545\) 5.34084 0.228776
\(546\) 0 0
\(547\) −24.5526 −1.04979 −0.524897 0.851166i \(-0.675896\pi\)
−0.524897 + 0.851166i \(0.675896\pi\)
\(548\) 8.12377 0.347030
\(549\) 0 0
\(550\) 6.24799 0.266415
\(551\) 3.15425 0.134375
\(552\) 0 0
\(553\) 4.52616 0.192472
\(554\) 11.6854 0.496466
\(555\) 0 0
\(556\) −15.8878 −0.673793
\(557\) −17.0938 −0.724290 −0.362145 0.932122i \(-0.617955\pi\)
−0.362145 + 0.932122i \(0.617955\pi\)
\(558\) 0 0
\(559\) −12.3178 −0.520986
\(560\) 0.436928 0.0184636
\(561\) 0 0
\(562\) −1.34141 −0.0565838
\(563\) −29.1527 −1.22864 −0.614321 0.789056i \(-0.710570\pi\)
−0.614321 + 0.789056i \(0.710570\pi\)
\(564\) 0 0
\(565\) 12.3607 0.520020
\(566\) 24.3292 1.02263
\(567\) 0 0
\(568\) 2.68750 0.112765
\(569\) 17.0923 0.716545 0.358273 0.933617i \(-0.383366\pi\)
0.358273 + 0.933617i \(0.383366\pi\)
\(570\) 0 0
\(571\) −6.80880 −0.284940 −0.142470 0.989799i \(-0.545504\pi\)
−0.142470 + 0.989799i \(0.545504\pi\)
\(572\) −1.69178 −0.0707367
\(573\) 0 0
\(574\) 1.14478 0.0477821
\(575\) −34.2417 −1.42798
\(576\) 0 0
\(577\) 42.9978 1.79002 0.895012 0.446043i \(-0.147167\pi\)
0.895012 + 0.446043i \(0.147167\pi\)
\(578\) −8.36677 −0.348012
\(579\) 0 0
\(580\) 1.71630 0.0712655
\(581\) −1.46374 −0.0607262
\(582\) 0 0
\(583\) −4.48814 −0.185880
\(584\) −15.4477 −0.639231
\(585\) 0 0
\(586\) 4.76293 0.196755
\(587\) 40.7800 1.68317 0.841585 0.540125i \(-0.181623\pi\)
0.841585 + 0.540125i \(0.181623\pi\)
\(588\) 0 0
\(589\) −7.27137 −0.299612
\(590\) −6.98147 −0.287423
\(591\) 0 0
\(592\) −2.36988 −0.0974014
\(593\) 13.2489 0.544066 0.272033 0.962288i \(-0.412304\pi\)
0.272033 + 0.962288i \(0.412304\pi\)
\(594\) 0 0
\(595\) −1.28380 −0.0526306
\(596\) −1.00000 −0.0409616
\(597\) 0 0
\(598\) 9.27167 0.379147
\(599\) −42.3211 −1.72919 −0.864597 0.502467i \(-0.832426\pi\)
−0.864597 + 0.502467i \(0.832426\pi\)
\(600\) 0 0
\(601\) 44.3599 1.80948 0.904739 0.425966i \(-0.140066\pi\)
0.904739 + 0.425966i \(0.140066\pi\)
\(602\) 6.41407 0.261418
\(603\) 0 0
\(604\) −4.92235 −0.200288
\(605\) 6.22150 0.252940
\(606\) 0 0
\(607\) −8.49059 −0.344622 −0.172311 0.985043i \(-0.555123\pi\)
−0.172311 + 0.985043i \(0.555123\pi\)
\(608\) −1.25651 −0.0509580
\(609\) 0 0
\(610\) −0.701663 −0.0284095
\(611\) −13.6266 −0.551272
\(612\) 0 0
\(613\) −40.3767 −1.63080 −0.815399 0.578899i \(-0.803482\pi\)
−0.815399 + 0.578899i \(0.803482\pi\)
\(614\) −20.7130 −0.835910
\(615\) 0 0
\(616\) 0.880936 0.0354939
\(617\) 41.2562 1.66091 0.830455 0.557085i \(-0.188080\pi\)
0.830455 + 0.557085i \(0.188080\pi\)
\(618\) 0 0
\(619\) 25.1365 1.01032 0.505160 0.863025i \(-0.331433\pi\)
0.505160 + 0.863025i \(0.331433\pi\)
\(620\) −3.95653 −0.158898
\(621\) 0 0
\(622\) −17.6892 −0.709274
\(623\) 4.64049 0.185917
\(624\) 0 0
\(625\) 18.2069 0.728277
\(626\) 1.72775 0.0690548
\(627\) 0 0
\(628\) −1.05732 −0.0421918
\(629\) 6.96326 0.277643
\(630\) 0 0
\(631\) −25.1878 −1.00271 −0.501355 0.865242i \(-0.667165\pi\)
−0.501355 + 0.865242i \(0.667165\pi\)
\(632\) −7.08243 −0.281724
\(633\) 0 0
\(634\) 27.4073 1.08848
\(635\) −8.46178 −0.335795
\(636\) 0 0
\(637\) −8.08977 −0.320528
\(638\) 3.46041 0.136999
\(639\) 0 0
\(640\) −0.683695 −0.0270254
\(641\) −22.2446 −0.878609 −0.439304 0.898338i \(-0.644775\pi\)
−0.439304 + 0.898338i \(0.644775\pi\)
\(642\) 0 0
\(643\) −35.5526 −1.40206 −0.701028 0.713133i \(-0.747275\pi\)
−0.701028 + 0.713133i \(0.747275\pi\)
\(644\) −4.82791 −0.190247
\(645\) 0 0
\(646\) 3.69191 0.145256
\(647\) 36.5412 1.43658 0.718291 0.695742i \(-0.244924\pi\)
0.718291 + 0.695742i \(0.244924\pi\)
\(648\) 0 0
\(649\) −14.0761 −0.552534
\(650\) −5.56275 −0.218189
\(651\) 0 0
\(652\) 5.30856 0.207899
\(653\) −19.4662 −0.761771 −0.380885 0.924622i \(-0.624381\pi\)
−0.380885 + 0.924622i \(0.624381\pi\)
\(654\) 0 0
\(655\) 10.4718 0.409167
\(656\) −1.79132 −0.0699394
\(657\) 0 0
\(658\) 7.09558 0.276615
\(659\) −1.02847 −0.0400637 −0.0200318 0.999799i \(-0.506377\pi\)
−0.0200318 + 0.999799i \(0.506377\pi\)
\(660\) 0 0
\(661\) −22.9972 −0.894488 −0.447244 0.894412i \(-0.647595\pi\)
−0.447244 + 0.894412i \(0.647595\pi\)
\(662\) −10.4910 −0.407743
\(663\) 0 0
\(664\) 2.29043 0.0888857
\(665\) −0.549003 −0.0212894
\(666\) 0 0
\(667\) −18.9646 −0.734311
\(668\) −7.75142 −0.299912
\(669\) 0 0
\(670\) −5.47415 −0.211485
\(671\) −1.41469 −0.0546137
\(672\) 0 0
\(673\) −13.8495 −0.533858 −0.266929 0.963716i \(-0.586009\pi\)
−0.266929 + 0.963716i \(0.586009\pi\)
\(674\) 33.1109 1.27538
\(675\) 0 0
\(676\) −11.4938 −0.442068
\(677\) −10.2057 −0.392235 −0.196118 0.980580i \(-0.562833\pi\)
−0.196118 + 0.980580i \(0.562833\pi\)
\(678\) 0 0
\(679\) −0.316700 −0.0121538
\(680\) 2.00886 0.0770361
\(681\) 0 0
\(682\) −7.97717 −0.305461
\(683\) 17.0019 0.650561 0.325280 0.945618i \(-0.394541\pi\)
0.325280 + 0.945618i \(0.394541\pi\)
\(684\) 0 0
\(685\) −5.55418 −0.212214
\(686\) 8.68596 0.331632
\(687\) 0 0
\(688\) −10.0366 −0.382641
\(689\) 3.99591 0.152232
\(690\) 0 0
\(691\) −15.9421 −0.606466 −0.303233 0.952916i \(-0.598066\pi\)
−0.303233 + 0.952916i \(0.598066\pi\)
\(692\) −1.91298 −0.0727206
\(693\) 0 0
\(694\) −24.7393 −0.939090
\(695\) 10.8624 0.412035
\(696\) 0 0
\(697\) 5.26333 0.199363
\(698\) −27.8523 −1.05423
\(699\) 0 0
\(700\) 2.89662 0.109482
\(701\) 29.6601 1.12024 0.560122 0.828410i \(-0.310754\pi\)
0.560122 + 0.828410i \(0.310754\pi\)
\(702\) 0 0
\(703\) 2.97777 0.112309
\(704\) −1.37847 −0.0519530
\(705\) 0 0
\(706\) 18.3837 0.691880
\(707\) −11.8730 −0.446528
\(708\) 0 0
\(709\) 28.9912 1.08879 0.544394 0.838829i \(-0.316760\pi\)
0.544394 + 0.838829i \(0.316760\pi\)
\(710\) −1.83743 −0.0689575
\(711\) 0 0
\(712\) −7.26133 −0.272130
\(713\) 43.7183 1.63726
\(714\) 0 0
\(715\) 1.15666 0.0432566
\(716\) −23.0724 −0.862257
\(717\) 0 0
\(718\) 23.2473 0.867582
\(719\) 28.5349 1.06417 0.532086 0.846690i \(-0.321408\pi\)
0.532086 + 0.846690i \(0.321408\pi\)
\(720\) 0 0
\(721\) −3.67435 −0.136840
\(722\) −17.4212 −0.648350
\(723\) 0 0
\(724\) −0.420424 −0.0156250
\(725\) 11.3782 0.422577
\(726\) 0 0
\(727\) −26.4341 −0.980388 −0.490194 0.871613i \(-0.663074\pi\)
−0.490194 + 0.871613i \(0.663074\pi\)
\(728\) −0.784321 −0.0290689
\(729\) 0 0
\(730\) 10.5615 0.390900
\(731\) 29.4898 1.09072
\(732\) 0 0
\(733\) −31.2748 −1.15516 −0.577581 0.816334i \(-0.696003\pi\)
−0.577581 + 0.816334i \(0.696003\pi\)
\(734\) −2.85101 −0.105233
\(735\) 0 0
\(736\) 7.55461 0.278467
\(737\) −11.0370 −0.406553
\(738\) 0 0
\(739\) −27.9612 −1.02857 −0.514284 0.857620i \(-0.671942\pi\)
−0.514284 + 0.857620i \(0.671942\pi\)
\(740\) 1.62027 0.0595625
\(741\) 0 0
\(742\) −2.08074 −0.0763863
\(743\) 20.2955 0.744570 0.372285 0.928118i \(-0.378574\pi\)
0.372285 + 0.928118i \(0.378574\pi\)
\(744\) 0 0
\(745\) 0.683695 0.0250486
\(746\) −4.27241 −0.156424
\(747\) 0 0
\(748\) 4.05027 0.148092
\(749\) 3.19589 0.116775
\(750\) 0 0
\(751\) 39.7018 1.44874 0.724369 0.689412i \(-0.242131\pi\)
0.724369 + 0.689412i \(0.242131\pi\)
\(752\) −11.1030 −0.404885
\(753\) 0 0
\(754\) −3.08090 −0.112200
\(755\) 3.36539 0.122479
\(756\) 0 0
\(757\) −1.35049 −0.0490843 −0.0245421 0.999699i \(-0.507813\pi\)
−0.0245421 + 0.999699i \(0.507813\pi\)
\(758\) 2.12935 0.0773416
\(759\) 0 0
\(760\) 0.859067 0.0311616
\(761\) 32.4735 1.17716 0.588582 0.808438i \(-0.299687\pi\)
0.588582 + 0.808438i \(0.299687\pi\)
\(762\) 0 0
\(763\) 4.99223 0.180731
\(764\) 13.9592 0.505026
\(765\) 0 0
\(766\) −27.7927 −1.00419
\(767\) 12.5323 0.452515
\(768\) 0 0
\(769\) 42.3996 1.52897 0.764485 0.644641i \(-0.222993\pi\)
0.764485 + 0.644641i \(0.222993\pi\)
\(770\) −0.602292 −0.0217051
\(771\) 0 0
\(772\) −26.1712 −0.941922
\(773\) 47.7751 1.71835 0.859175 0.511682i \(-0.170978\pi\)
0.859175 + 0.511682i \(0.170978\pi\)
\(774\) 0 0
\(775\) −26.2298 −0.942203
\(776\) 0.495565 0.0177897
\(777\) 0 0
\(778\) 2.18146 0.0782090
\(779\) 2.25081 0.0806435
\(780\) 0 0
\(781\) −3.70463 −0.132562
\(782\) −22.1972 −0.793771
\(783\) 0 0
\(784\) −6.59159 −0.235414
\(785\) 0.722886 0.0258009
\(786\) 0 0
\(787\) −9.34661 −0.333171 −0.166585 0.986027i \(-0.553274\pi\)
−0.166585 + 0.986027i \(0.553274\pi\)
\(788\) −13.2324 −0.471384
\(789\) 0 0
\(790\) 4.84222 0.172279
\(791\) 11.5539 0.410810
\(792\) 0 0
\(793\) 1.25954 0.0447276
\(794\) 36.1692 1.28360
\(795\) 0 0
\(796\) −22.0979 −0.783238
\(797\) 50.5937 1.79212 0.896061 0.443931i \(-0.146416\pi\)
0.896061 + 0.443931i \(0.146416\pi\)
\(798\) 0 0
\(799\) 32.6232 1.15413
\(800\) −4.53256 −0.160250
\(801\) 0 0
\(802\) −38.0499 −1.34359
\(803\) 21.2942 0.751456
\(804\) 0 0
\(805\) 3.30082 0.116339
\(806\) 7.10228 0.250167
\(807\) 0 0
\(808\) 18.5785 0.653590
\(809\) 3.65250 0.128415 0.0642075 0.997937i \(-0.479548\pi\)
0.0642075 + 0.997937i \(0.479548\pi\)
\(810\) 0 0
\(811\) −40.0359 −1.40585 −0.702925 0.711264i \(-0.748123\pi\)
−0.702925 + 0.711264i \(0.748123\pi\)
\(812\) 1.60428 0.0562990
\(813\) 0 0
\(814\) 3.26680 0.114501
\(815\) −3.62943 −0.127134
\(816\) 0 0
\(817\) 12.6110 0.441204
\(818\) −3.27404 −0.114474
\(819\) 0 0
\(820\) 1.22472 0.0427690
\(821\) 19.9066 0.694744 0.347372 0.937727i \(-0.387074\pi\)
0.347372 + 0.937727i \(0.387074\pi\)
\(822\) 0 0
\(823\) −2.99252 −0.104313 −0.0521564 0.998639i \(-0.516609\pi\)
−0.0521564 + 0.998639i \(0.516609\pi\)
\(824\) 5.74954 0.200295
\(825\) 0 0
\(826\) −6.52578 −0.227061
\(827\) −29.0535 −1.01029 −0.505145 0.863034i \(-0.668561\pi\)
−0.505145 + 0.863034i \(0.668561\pi\)
\(828\) 0 0
\(829\) 50.9263 1.76874 0.884371 0.466785i \(-0.154588\pi\)
0.884371 + 0.466785i \(0.154588\pi\)
\(830\) −1.56595 −0.0543550
\(831\) 0 0
\(832\) 1.22729 0.0425485
\(833\) 19.3676 0.671049
\(834\) 0 0
\(835\) 5.29961 0.183401
\(836\) 1.73205 0.0599043
\(837\) 0 0
\(838\) −4.93454 −0.170461
\(839\) 31.3519 1.08239 0.541194 0.840898i \(-0.317972\pi\)
0.541194 + 0.840898i \(0.317972\pi\)
\(840\) 0 0
\(841\) −22.6982 −0.782698
\(842\) −29.3725 −1.01224
\(843\) 0 0
\(844\) 9.79151 0.337038
\(845\) 7.85823 0.270331
\(846\) 0 0
\(847\) 5.81542 0.199820
\(848\) 3.25589 0.111808
\(849\) 0 0
\(850\) 13.3177 0.456794
\(851\) −17.9035 −0.613724
\(852\) 0 0
\(853\) −29.7165 −1.01747 −0.508736 0.860923i \(-0.669887\pi\)
−0.508736 + 0.860923i \(0.669887\pi\)
\(854\) −0.655864 −0.0224432
\(855\) 0 0
\(856\) −5.00086 −0.170926
\(857\) −54.8894 −1.87499 −0.937493 0.348005i \(-0.886859\pi\)
−0.937493 + 0.348005i \(0.886859\pi\)
\(858\) 0 0
\(859\) 21.5798 0.736295 0.368147 0.929767i \(-0.379992\pi\)
0.368147 + 0.929767i \(0.379992\pi\)
\(860\) 6.86196 0.233991
\(861\) 0 0
\(862\) 2.39153 0.0814560
\(863\) −20.8297 −0.709051 −0.354526 0.935046i \(-0.615358\pi\)
−0.354526 + 0.935046i \(0.615358\pi\)
\(864\) 0 0
\(865\) 1.30790 0.0444698
\(866\) −32.0988 −1.09076
\(867\) 0 0
\(868\) −3.69828 −0.125528
\(869\) 9.76291 0.331184
\(870\) 0 0
\(871\) 9.82652 0.332959
\(872\) −7.81173 −0.264538
\(873\) 0 0
\(874\) −9.49241 −0.321085
\(875\) −4.16504 −0.140804
\(876\) 0 0
\(877\) 19.7031 0.665328 0.332664 0.943045i \(-0.392053\pi\)
0.332664 + 0.943045i \(0.392053\pi\)
\(878\) 13.9582 0.471066
\(879\) 0 0
\(880\) 0.942452 0.0317700
\(881\) 30.5817 1.03032 0.515162 0.857093i \(-0.327732\pi\)
0.515162 + 0.857093i \(0.327732\pi\)
\(882\) 0 0
\(883\) −12.4083 −0.417573 −0.208786 0.977961i \(-0.566951\pi\)
−0.208786 + 0.977961i \(0.566951\pi\)
\(884\) −3.60606 −0.121285
\(885\) 0 0
\(886\) −25.1491 −0.844902
\(887\) 8.80165 0.295530 0.147765 0.989022i \(-0.452792\pi\)
0.147765 + 0.989022i \(0.452792\pi\)
\(888\) 0 0
\(889\) −7.90946 −0.265275
\(890\) 4.96453 0.166412
\(891\) 0 0
\(892\) −24.0602 −0.805597
\(893\) 13.9510 0.466852
\(894\) 0 0
\(895\) 15.7745 0.527284
\(896\) −0.639069 −0.0213498
\(897\) 0 0
\(898\) −11.0525 −0.368826
\(899\) −14.5272 −0.484510
\(900\) 0 0
\(901\) −9.56657 −0.318709
\(902\) 2.46928 0.0822181
\(903\) 0 0
\(904\) −18.0793 −0.601309
\(905\) 0.287442 0.00955490
\(906\) 0 0
\(907\) −40.8567 −1.35662 −0.678312 0.734774i \(-0.737288\pi\)
−0.678312 + 0.734774i \(0.737288\pi\)
\(908\) −14.1524 −0.469664
\(909\) 0 0
\(910\) 0.536236 0.0177760
\(911\) 50.3927 1.66958 0.834792 0.550566i \(-0.185588\pi\)
0.834792 + 0.550566i \(0.185588\pi\)
\(912\) 0 0
\(913\) −3.15728 −0.104491
\(914\) −0.164071 −0.00542699
\(915\) 0 0
\(916\) −7.88051 −0.260379
\(917\) 9.78829 0.323238
\(918\) 0 0
\(919\) 4.21729 0.139116 0.0695578 0.997578i \(-0.477841\pi\)
0.0695578 + 0.997578i \(0.477841\pi\)
\(920\) −5.16505 −0.170287
\(921\) 0 0
\(922\) 9.62526 0.316991
\(923\) 3.29833 0.108566
\(924\) 0 0
\(925\) 10.7416 0.353182
\(926\) 37.9510 1.24715
\(927\) 0 0
\(928\) −2.51033 −0.0824057
\(929\) 31.9962 1.04976 0.524881 0.851176i \(-0.324110\pi\)
0.524881 + 0.851176i \(0.324110\pi\)
\(930\) 0 0
\(931\) 8.28237 0.271444
\(932\) −4.07402 −0.133449
\(933\) 0 0
\(934\) 27.8325 0.910706
\(935\) −2.76915 −0.0905607
\(936\) 0 0
\(937\) −55.0823 −1.79946 −0.899730 0.436447i \(-0.856237\pi\)
−0.899730 + 0.436447i \(0.856237\pi\)
\(938\) −5.11684 −0.167071
\(939\) 0 0
\(940\) 7.59107 0.247593
\(941\) 3.82358 0.124645 0.0623225 0.998056i \(-0.480149\pi\)
0.0623225 + 0.998056i \(0.480149\pi\)
\(942\) 0 0
\(943\) −13.5327 −0.440687
\(944\) 10.2114 0.332352
\(945\) 0 0
\(946\) 13.8351 0.449818
\(947\) 20.1008 0.653188 0.326594 0.945165i \(-0.394099\pi\)
0.326594 + 0.945165i \(0.394099\pi\)
\(948\) 0 0
\(949\) −18.9588 −0.615428
\(950\) 5.69519 0.184776
\(951\) 0 0
\(952\) 1.87774 0.0608577
\(953\) 33.0458 1.07046 0.535229 0.844707i \(-0.320225\pi\)
0.535229 + 0.844707i \(0.320225\pi\)
\(954\) 0 0
\(955\) −9.54383 −0.308831
\(956\) 13.7267 0.443954
\(957\) 0 0
\(958\) 14.8934 0.481183
\(959\) −5.19165 −0.167647
\(960\) 0 0
\(961\) 2.48910 0.0802937
\(962\) −2.90852 −0.0937744
\(963\) 0 0
\(964\) 17.2144 0.554439
\(965\) 17.8931 0.576000
\(966\) 0 0
\(967\) 17.4137 0.559986 0.279993 0.960002i \(-0.409668\pi\)
0.279993 + 0.960002i \(0.409668\pi\)
\(968\) −9.09982 −0.292479
\(969\) 0 0
\(970\) −0.338815 −0.0108787
\(971\) −28.5581 −0.916474 −0.458237 0.888830i \(-0.651519\pi\)
−0.458237 + 0.888830i \(0.651519\pi\)
\(972\) 0 0
\(973\) 10.1534 0.325503
\(974\) 18.5223 0.593493
\(975\) 0 0
\(976\) 1.02628 0.0328504
\(977\) −33.7204 −1.07881 −0.539406 0.842046i \(-0.681351\pi\)
−0.539406 + 0.842046i \(0.681351\pi\)
\(978\) 0 0
\(979\) 10.0095 0.319905
\(980\) 4.50664 0.143959
\(981\) 0 0
\(982\) 33.3676 1.06480
\(983\) −26.3171 −0.839384 −0.419692 0.907667i \(-0.637862\pi\)
−0.419692 + 0.907667i \(0.637862\pi\)
\(984\) 0 0
\(985\) 9.04691 0.288258
\(986\) 7.37595 0.234898
\(987\) 0 0
\(988\) −1.54209 −0.0490605
\(989\) −75.8224 −2.41101
\(990\) 0 0
\(991\) 47.9413 1.52291 0.761453 0.648221i \(-0.224487\pi\)
0.761453 + 0.648221i \(0.224487\pi\)
\(992\) 5.78698 0.183737
\(993\) 0 0
\(994\) −1.71750 −0.0544757
\(995\) 15.1082 0.478962
\(996\) 0 0
\(997\) 40.7657 1.29106 0.645531 0.763734i \(-0.276636\pi\)
0.645531 + 0.763734i \(0.276636\pi\)
\(998\) −27.6463 −0.875127
\(999\) 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 \(a_p\))