Properties

Label 8008.2.a.k.1.1
Level 8008
Weight 2
Character 8008.1
Self dual Yes
Analytic conductor 63.944
Analytic rank 0
Dimension 6
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8008 = 2^{3} \cdot 7 \cdot 11 \cdot 13 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8008.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.9442019386\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: 6.6.244558277.1
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{2} \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(2.98317\)
Character \(\chi\) = 8008.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.98317 q^{3} +3.19751 q^{5} +1.00000 q^{7} +5.89931 q^{9} +O(q^{10})\) \(q-2.98317 q^{3} +3.19751 q^{5} +1.00000 q^{7} +5.89931 q^{9} -1.00000 q^{11} -1.00000 q^{13} -9.53872 q^{15} +1.18708 q^{17} +0.300378 q^{19} -2.98317 q^{21} -7.32438 q^{23} +5.22407 q^{25} -8.64913 q^{27} +3.24089 q^{29} -6.56527 q^{31} +2.98317 q^{33} +3.19751 q^{35} -4.73878 q^{37} +2.98317 q^{39} -4.72545 q^{41} +8.34121 q^{43} +18.8631 q^{45} -3.02365 q^{47} +1.00000 q^{49} -3.54127 q^{51} +9.50471 q^{53} -3.19751 q^{55} -0.896080 q^{57} +12.9166 q^{59} -1.00349 q^{61} +5.89931 q^{63} -3.19751 q^{65} -7.44408 q^{67} +21.8499 q^{69} -3.06703 q^{71} +10.3083 q^{73} -15.5843 q^{75} -1.00000 q^{77} +5.83010 q^{79} +8.10392 q^{81} +9.23729 q^{83} +3.79571 q^{85} -9.66814 q^{87} -1.07999 q^{89} -1.00000 q^{91} +19.5853 q^{93} +0.960462 q^{95} +12.0606 q^{97} -5.89931 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q - q^{3} + q^{5} + 6q^{7} + 9q^{9} + O(q^{10}) \) \( 6q - q^{3} + q^{5} + 6q^{7} + 9q^{9} - 6q^{11} - 6q^{13} - q^{15} + 2q^{19} - q^{21} + 11q^{23} + 9q^{25} - q^{27} + 14q^{29} + 21q^{31} + q^{33} + q^{35} - 5q^{37} + q^{39} + 12q^{43} + 2q^{45} + 2q^{47} + 6q^{49} - 16q^{51} + 2q^{53} - q^{55} - 12q^{57} + 3q^{59} - 18q^{61} + 9q^{63} - q^{65} - 25q^{67} + 29q^{69} - 11q^{71} + 14q^{73} - 42q^{75} - 6q^{77} + 24q^{79} + 42q^{81} + 24q^{83} - 46q^{85} - 16q^{87} + 55q^{89} - 6q^{91} + 41q^{93} - 30q^{95} + 37q^{97} - 9q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −2.98317 −1.72233 −0.861167 0.508322i \(-0.830266\pi\)
−0.861167 + 0.508322i \(0.830266\pi\)
\(4\) 0 0
\(5\) 3.19751 1.42997 0.714985 0.699140i \(-0.246434\pi\)
0.714985 + 0.699140i \(0.246434\pi\)
\(6\) 0 0
\(7\) 1.00000 0.377964
\(8\) 0 0
\(9\) 5.89931 1.96644
\(10\) 0 0
\(11\) −1.00000 −0.301511
\(12\) 0 0
\(13\) −1.00000 −0.277350
\(14\) 0 0
\(15\) −9.53872 −2.46289
\(16\) 0 0
\(17\) 1.18708 0.287910 0.143955 0.989584i \(-0.454018\pi\)
0.143955 + 0.989584i \(0.454018\pi\)
\(18\) 0 0
\(19\) 0.300378 0.0689115 0.0344557 0.999406i \(-0.489030\pi\)
0.0344557 + 0.999406i \(0.489030\pi\)
\(20\) 0 0
\(21\) −2.98317 −0.650981
\(22\) 0 0
\(23\) −7.32438 −1.52724 −0.763619 0.645667i \(-0.776579\pi\)
−0.763619 + 0.645667i \(0.776579\pi\)
\(24\) 0 0
\(25\) 5.22407 1.04481
\(26\) 0 0
\(27\) −8.64913 −1.66453
\(28\) 0 0
\(29\) 3.24089 0.601819 0.300909 0.953653i \(-0.402710\pi\)
0.300909 + 0.953653i \(0.402710\pi\)
\(30\) 0 0
\(31\) −6.56527 −1.17916 −0.589579 0.807711i \(-0.700706\pi\)
−0.589579 + 0.807711i \(0.700706\pi\)
\(32\) 0 0
\(33\) 2.98317 0.519303
\(34\) 0 0
\(35\) 3.19751 0.540478
\(36\) 0 0
\(37\) −4.73878 −0.779051 −0.389525 0.921016i \(-0.627361\pi\)
−0.389525 + 0.921016i \(0.627361\pi\)
\(38\) 0 0
\(39\) 2.98317 0.477690
\(40\) 0 0
\(41\) −4.72545 −0.737991 −0.368995 0.929431i \(-0.620298\pi\)
−0.368995 + 0.929431i \(0.620298\pi\)
\(42\) 0 0
\(43\) 8.34121 1.27202 0.636011 0.771680i \(-0.280583\pi\)
0.636011 + 0.771680i \(0.280583\pi\)
\(44\) 0 0
\(45\) 18.8631 2.81194
\(46\) 0 0
\(47\) −3.02365 −0.441044 −0.220522 0.975382i \(-0.570776\pi\)
−0.220522 + 0.975382i \(0.570776\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) −3.54127 −0.495877
\(52\) 0 0
\(53\) 9.50471 1.30557 0.652786 0.757542i \(-0.273600\pi\)
0.652786 + 0.757542i \(0.273600\pi\)
\(54\) 0 0
\(55\) −3.19751 −0.431152
\(56\) 0 0
\(57\) −0.896080 −0.118689
\(58\) 0 0
\(59\) 12.9166 1.68159 0.840796 0.541352i \(-0.182087\pi\)
0.840796 + 0.541352i \(0.182087\pi\)
\(60\) 0 0
\(61\) −1.00349 −0.128484 −0.0642422 0.997934i \(-0.520463\pi\)
−0.0642422 + 0.997934i \(0.520463\pi\)
\(62\) 0 0
\(63\) 5.89931 0.743243
\(64\) 0 0
\(65\) −3.19751 −0.396602
\(66\) 0 0
\(67\) −7.44408 −0.909439 −0.454719 0.890635i \(-0.650260\pi\)
−0.454719 + 0.890635i \(0.650260\pi\)
\(68\) 0 0
\(69\) 21.8499 2.63042
\(70\) 0 0
\(71\) −3.06703 −0.363990 −0.181995 0.983299i \(-0.558255\pi\)
−0.181995 + 0.983299i \(0.558255\pi\)
\(72\) 0 0
\(73\) 10.3083 1.20649 0.603246 0.797555i \(-0.293874\pi\)
0.603246 + 0.797555i \(0.293874\pi\)
\(74\) 0 0
\(75\) −15.5843 −1.79952
\(76\) 0 0
\(77\) −1.00000 −0.113961
\(78\) 0 0
\(79\) 5.83010 0.655937 0.327969 0.944689i \(-0.393636\pi\)
0.327969 + 0.944689i \(0.393636\pi\)
\(80\) 0 0
\(81\) 8.10392 0.900436
\(82\) 0 0
\(83\) 9.23729 1.01392 0.506962 0.861968i \(-0.330768\pi\)
0.506962 + 0.861968i \(0.330768\pi\)
\(84\) 0 0
\(85\) 3.79571 0.411703
\(86\) 0 0
\(87\) −9.66814 −1.03653
\(88\) 0 0
\(89\) −1.07999 −0.114479 −0.0572393 0.998360i \(-0.518230\pi\)
−0.0572393 + 0.998360i \(0.518230\pi\)
\(90\) 0 0
\(91\) −1.00000 −0.104828
\(92\) 0 0
\(93\) 19.5853 2.03090
\(94\) 0 0
\(95\) 0.960462 0.0985413
\(96\) 0 0
\(97\) 12.0606 1.22457 0.612286 0.790637i \(-0.290250\pi\)
0.612286 + 0.790637i \(0.290250\pi\)
\(98\) 0 0
\(99\) −5.89931 −0.592903
\(100\) 0 0
\(101\) 4.75550 0.473190 0.236595 0.971608i \(-0.423969\pi\)
0.236595 + 0.971608i \(0.423969\pi\)
\(102\) 0 0
\(103\) 8.00000 0.788263 0.394132 0.919054i \(-0.371045\pi\)
0.394132 + 0.919054i \(0.371045\pi\)
\(104\) 0 0
\(105\) −9.53872 −0.930883
\(106\) 0 0
\(107\) −12.7893 −1.23639 −0.618196 0.786024i \(-0.712136\pi\)
−0.618196 + 0.786024i \(0.712136\pi\)
\(108\) 0 0
\(109\) −2.45873 −0.235503 −0.117752 0.993043i \(-0.537569\pi\)
−0.117752 + 0.993043i \(0.537569\pi\)
\(110\) 0 0
\(111\) 14.1366 1.34179
\(112\) 0 0
\(113\) 10.4915 0.986956 0.493478 0.869758i \(-0.335725\pi\)
0.493478 + 0.869758i \(0.335725\pi\)
\(114\) 0 0
\(115\) −23.4198 −2.18390
\(116\) 0 0
\(117\) −5.89931 −0.545391
\(118\) 0 0
\(119\) 1.18708 0.108820
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) 0 0
\(123\) 14.0968 1.27107
\(124\) 0 0
\(125\) 0.716451 0.0640813
\(126\) 0 0
\(127\) 20.1578 1.78872 0.894358 0.447352i \(-0.147633\pi\)
0.894358 + 0.447352i \(0.147633\pi\)
\(128\) 0 0
\(129\) −24.8832 −2.19085
\(130\) 0 0
\(131\) −0.644494 −0.0563097 −0.0281549 0.999604i \(-0.508963\pi\)
−0.0281549 + 0.999604i \(0.508963\pi\)
\(132\) 0 0
\(133\) 0.300378 0.0260461
\(134\) 0 0
\(135\) −27.6557 −2.38022
\(136\) 0 0
\(137\) −0.565273 −0.0482945 −0.0241473 0.999708i \(-0.507687\pi\)
−0.0241473 + 0.999708i \(0.507687\pi\)
\(138\) 0 0
\(139\) −10.3614 −0.878839 −0.439420 0.898282i \(-0.644816\pi\)
−0.439420 + 0.898282i \(0.644816\pi\)
\(140\) 0 0
\(141\) 9.02006 0.759626
\(142\) 0 0
\(143\) 1.00000 0.0836242
\(144\) 0 0
\(145\) 10.3628 0.860583
\(146\) 0 0
\(147\) −2.98317 −0.246048
\(148\) 0 0
\(149\) −5.47396 −0.448444 −0.224222 0.974538i \(-0.571984\pi\)
−0.224222 + 0.974538i \(0.571984\pi\)
\(150\) 0 0
\(151\) 19.8029 1.61154 0.805769 0.592230i \(-0.201752\pi\)
0.805769 + 0.592230i \(0.201752\pi\)
\(152\) 0 0
\(153\) 7.00297 0.566157
\(154\) 0 0
\(155\) −20.9925 −1.68616
\(156\) 0 0
\(157\) 9.83045 0.784555 0.392278 0.919847i \(-0.371687\pi\)
0.392278 + 0.919847i \(0.371687\pi\)
\(158\) 0 0
\(159\) −28.3542 −2.24863
\(160\) 0 0
\(161\) −7.32438 −0.577242
\(162\) 0 0
\(163\) −5.58857 −0.437730 −0.218865 0.975755i \(-0.570236\pi\)
−0.218865 + 0.975755i \(0.570236\pi\)
\(164\) 0 0
\(165\) 9.53872 0.742588
\(166\) 0 0
\(167\) 6.73196 0.520935 0.260467 0.965483i \(-0.416123\pi\)
0.260467 + 0.965483i \(0.416123\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) 1.77202 0.135510
\(172\) 0 0
\(173\) 10.2331 0.778005 0.389003 0.921237i \(-0.372820\pi\)
0.389003 + 0.921237i \(0.372820\pi\)
\(174\) 0 0
\(175\) 5.22407 0.394902
\(176\) 0 0
\(177\) −38.5323 −2.89626
\(178\) 0 0
\(179\) −4.01191 −0.299864 −0.149932 0.988696i \(-0.547905\pi\)
−0.149932 + 0.988696i \(0.547905\pi\)
\(180\) 0 0
\(181\) −16.5881 −1.23299 −0.616493 0.787360i \(-0.711447\pi\)
−0.616493 + 0.787360i \(0.711447\pi\)
\(182\) 0 0
\(183\) 2.99360 0.221293
\(184\) 0 0
\(185\) −15.1523 −1.11402
\(186\) 0 0
\(187\) −1.18708 −0.0868081
\(188\) 0 0
\(189\) −8.64913 −0.629132
\(190\) 0 0
\(191\) 0.00182569 0.000132103 0 6.60513e−5 1.00000i \(-0.499979\pi\)
6.60513e−5 1.00000i \(0.499979\pi\)
\(192\) 0 0
\(193\) −9.55423 −0.687728 −0.343864 0.939019i \(-0.611736\pi\)
−0.343864 + 0.939019i \(0.611736\pi\)
\(194\) 0 0
\(195\) 9.53872 0.683082
\(196\) 0 0
\(197\) 0.975622 0.0695102 0.0347551 0.999396i \(-0.488935\pi\)
0.0347551 + 0.999396i \(0.488935\pi\)
\(198\) 0 0
\(199\) −3.43165 −0.243263 −0.121632 0.992575i \(-0.538813\pi\)
−0.121632 + 0.992575i \(0.538813\pi\)
\(200\) 0 0
\(201\) 22.2070 1.56636
\(202\) 0 0
\(203\) 3.24089 0.227466
\(204\) 0 0
\(205\) −15.1097 −1.05530
\(206\) 0 0
\(207\) −43.2088 −3.00322
\(208\) 0 0
\(209\) −0.300378 −0.0207776
\(210\) 0 0
\(211\) −0.582064 −0.0400709 −0.0200355 0.999799i \(-0.506378\pi\)
−0.0200355 + 0.999799i \(0.506378\pi\)
\(212\) 0 0
\(213\) 9.14948 0.626912
\(214\) 0 0
\(215\) 26.6711 1.81895
\(216\) 0 0
\(217\) −6.56527 −0.445680
\(218\) 0 0
\(219\) −30.7514 −2.07798
\(220\) 0 0
\(221\) −1.18708 −0.0798519
\(222\) 0 0
\(223\) 13.2528 0.887471 0.443735 0.896158i \(-0.353653\pi\)
0.443735 + 0.896158i \(0.353653\pi\)
\(224\) 0 0
\(225\) 30.8184 2.05456
\(226\) 0 0
\(227\) −16.5019 −1.09527 −0.547635 0.836717i \(-0.684472\pi\)
−0.547635 + 0.836717i \(0.684472\pi\)
\(228\) 0 0
\(229\) −29.6994 −1.96259 −0.981296 0.192507i \(-0.938338\pi\)
−0.981296 + 0.192507i \(0.938338\pi\)
\(230\) 0 0
\(231\) 2.98317 0.196278
\(232\) 0 0
\(233\) 7.50544 0.491697 0.245849 0.969308i \(-0.420933\pi\)
0.245849 + 0.969308i \(0.420933\pi\)
\(234\) 0 0
\(235\) −9.66814 −0.630680
\(236\) 0 0
\(237\) −17.3922 −1.12974
\(238\) 0 0
\(239\) 23.2680 1.50508 0.752541 0.658545i \(-0.228828\pi\)
0.752541 + 0.658545i \(0.228828\pi\)
\(240\) 0 0
\(241\) 9.98221 0.643010 0.321505 0.946908i \(-0.395811\pi\)
0.321505 + 0.946908i \(0.395811\pi\)
\(242\) 0 0
\(243\) 1.77202 0.113675
\(244\) 0 0
\(245\) 3.19751 0.204281
\(246\) 0 0
\(247\) −0.300378 −0.0191126
\(248\) 0 0
\(249\) −27.5564 −1.74632
\(250\) 0 0
\(251\) 15.8463 1.00021 0.500104 0.865966i \(-0.333295\pi\)
0.500104 + 0.865966i \(0.333295\pi\)
\(252\) 0 0
\(253\) 7.32438 0.460480
\(254\) 0 0
\(255\) −11.3233 −0.709090
\(256\) 0 0
\(257\) 19.9706 1.24573 0.622866 0.782328i \(-0.285968\pi\)
0.622866 + 0.782328i \(0.285968\pi\)
\(258\) 0 0
\(259\) −4.73878 −0.294454
\(260\) 0 0
\(261\) 19.1190 1.18344
\(262\) 0 0
\(263\) −19.5614 −1.20621 −0.603104 0.797663i \(-0.706070\pi\)
−0.603104 + 0.797663i \(0.706070\pi\)
\(264\) 0 0
\(265\) 30.3914 1.86693
\(266\) 0 0
\(267\) 3.22179 0.197171
\(268\) 0 0
\(269\) −9.07317 −0.553201 −0.276600 0.960985i \(-0.589208\pi\)
−0.276600 + 0.960985i \(0.589208\pi\)
\(270\) 0 0
\(271\) 17.0135 1.03350 0.516750 0.856137i \(-0.327142\pi\)
0.516750 + 0.856137i \(0.327142\pi\)
\(272\) 0 0
\(273\) 2.98317 0.180550
\(274\) 0 0
\(275\) −5.22407 −0.315023
\(276\) 0 0
\(277\) 3.99063 0.239773 0.119887 0.992788i \(-0.461747\pi\)
0.119887 + 0.992788i \(0.461747\pi\)
\(278\) 0 0
\(279\) −38.7306 −2.31874
\(280\) 0 0
\(281\) 26.3835 1.57391 0.786954 0.617011i \(-0.211657\pi\)
0.786954 + 0.617011i \(0.211657\pi\)
\(282\) 0 0
\(283\) −16.2739 −0.967384 −0.483692 0.875238i \(-0.660704\pi\)
−0.483692 + 0.875238i \(0.660704\pi\)
\(284\) 0 0
\(285\) −2.86522 −0.169721
\(286\) 0 0
\(287\) −4.72545 −0.278934
\(288\) 0 0
\(289\) −15.5908 −0.917108
\(290\) 0 0
\(291\) −35.9789 −2.10912
\(292\) 0 0
\(293\) 2.47530 0.144608 0.0723042 0.997383i \(-0.476965\pi\)
0.0723042 + 0.997383i \(0.476965\pi\)
\(294\) 0 0
\(295\) 41.3008 2.40463
\(296\) 0 0
\(297\) 8.64913 0.501874
\(298\) 0 0
\(299\) 7.32438 0.423580
\(300\) 0 0
\(301\) 8.34121 0.480779
\(302\) 0 0
\(303\) −14.1865 −0.814991
\(304\) 0 0
\(305\) −3.20868 −0.183729
\(306\) 0 0
\(307\) 7.12911 0.406880 0.203440 0.979087i \(-0.434788\pi\)
0.203440 + 0.979087i \(0.434788\pi\)
\(308\) 0 0
\(309\) −23.8654 −1.35765
\(310\) 0 0
\(311\) 10.8766 0.616755 0.308378 0.951264i \(-0.400214\pi\)
0.308378 + 0.951264i \(0.400214\pi\)
\(312\) 0 0
\(313\) −29.9258 −1.69151 −0.845754 0.533573i \(-0.820849\pi\)
−0.845754 + 0.533573i \(0.820849\pi\)
\(314\) 0 0
\(315\) 18.8631 1.06282
\(316\) 0 0
\(317\) 22.0112 1.23627 0.618136 0.786072i \(-0.287888\pi\)
0.618136 + 0.786072i \(0.287888\pi\)
\(318\) 0 0
\(319\) −3.24089 −0.181455
\(320\) 0 0
\(321\) 38.1528 2.12948
\(322\) 0 0
\(323\) 0.356574 0.0198403
\(324\) 0 0
\(325\) −5.22407 −0.289779
\(326\) 0 0
\(327\) 7.33480 0.405616
\(328\) 0 0
\(329\) −3.02365 −0.166699
\(330\) 0 0
\(331\) −29.1417 −1.60177 −0.800886 0.598817i \(-0.795637\pi\)
−0.800886 + 0.598817i \(0.795637\pi\)
\(332\) 0 0
\(333\) −27.9555 −1.53195
\(334\) 0 0
\(335\) −23.8025 −1.30047
\(336\) 0 0
\(337\) 15.3750 0.837527 0.418764 0.908095i \(-0.362464\pi\)
0.418764 + 0.908095i \(0.362464\pi\)
\(338\) 0 0
\(339\) −31.2979 −1.69987
\(340\) 0 0
\(341\) 6.56527 0.355529
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) 0 0
\(345\) 69.8652 3.76141
\(346\) 0 0
\(347\) −22.5334 −1.20966 −0.604828 0.796356i \(-0.706758\pi\)
−0.604828 + 0.796356i \(0.706758\pi\)
\(348\) 0 0
\(349\) 21.4403 1.14767 0.573835 0.818971i \(-0.305455\pi\)
0.573835 + 0.818971i \(0.305455\pi\)
\(350\) 0 0
\(351\) 8.64913 0.461657
\(352\) 0 0
\(353\) 33.1167 1.76262 0.881312 0.472536i \(-0.156661\pi\)
0.881312 + 0.472536i \(0.156661\pi\)
\(354\) 0 0
\(355\) −9.80687 −0.520494
\(356\) 0 0
\(357\) −3.54127 −0.187424
\(358\) 0 0
\(359\) −23.0681 −1.21749 −0.608743 0.793368i \(-0.708326\pi\)
−0.608743 + 0.793368i \(0.708326\pi\)
\(360\) 0 0
\(361\) −18.9098 −0.995251
\(362\) 0 0
\(363\) −2.98317 −0.156576
\(364\) 0 0
\(365\) 32.9608 1.72525
\(366\) 0 0
\(367\) 19.6427 1.02534 0.512671 0.858585i \(-0.328656\pi\)
0.512671 + 0.858585i \(0.328656\pi\)
\(368\) 0 0
\(369\) −27.8769 −1.45121
\(370\) 0 0
\(371\) 9.50471 0.493460
\(372\) 0 0
\(373\) 16.9691 0.878629 0.439314 0.898333i \(-0.355221\pi\)
0.439314 + 0.898333i \(0.355221\pi\)
\(374\) 0 0
\(375\) −2.13730 −0.110369
\(376\) 0 0
\(377\) −3.24089 −0.166915
\(378\) 0 0
\(379\) 2.34873 0.120646 0.0603230 0.998179i \(-0.480787\pi\)
0.0603230 + 0.998179i \(0.480787\pi\)
\(380\) 0 0
\(381\) −60.1342 −3.08077
\(382\) 0 0
\(383\) 28.8964 1.47654 0.738268 0.674508i \(-0.235644\pi\)
0.738268 + 0.674508i \(0.235644\pi\)
\(384\) 0 0
\(385\) −3.19751 −0.162960
\(386\) 0 0
\(387\) 49.2074 2.50135
\(388\) 0 0
\(389\) −17.3481 −0.879584 −0.439792 0.898100i \(-0.644948\pi\)
−0.439792 + 0.898100i \(0.644948\pi\)
\(390\) 0 0
\(391\) −8.69465 −0.439707
\(392\) 0 0
\(393\) 1.92264 0.0969841
\(394\) 0 0
\(395\) 18.6418 0.937970
\(396\) 0 0
\(397\) −9.97353 −0.500557 −0.250279 0.968174i \(-0.580522\pi\)
−0.250279 + 0.968174i \(0.580522\pi\)
\(398\) 0 0
\(399\) −0.896080 −0.0448601
\(400\) 0 0
\(401\) −30.2847 −1.51234 −0.756172 0.654373i \(-0.772933\pi\)
−0.756172 + 0.654373i \(0.772933\pi\)
\(402\) 0 0
\(403\) 6.56527 0.327040
\(404\) 0 0
\(405\) 25.9124 1.28760
\(406\) 0 0
\(407\) 4.73878 0.234893
\(408\) 0 0
\(409\) 11.9397 0.590379 0.295189 0.955439i \(-0.404617\pi\)
0.295189 + 0.955439i \(0.404617\pi\)
\(410\) 0 0
\(411\) 1.68631 0.0831793
\(412\) 0 0
\(413\) 12.9166 0.635582
\(414\) 0 0
\(415\) 29.5363 1.44988
\(416\) 0 0
\(417\) 30.9097 1.51365
\(418\) 0 0
\(419\) 2.53557 0.123871 0.0619353 0.998080i \(-0.480273\pi\)
0.0619353 + 0.998080i \(0.480273\pi\)
\(420\) 0 0
\(421\) 24.0444 1.17185 0.585926 0.810364i \(-0.300731\pi\)
0.585926 + 0.810364i \(0.300731\pi\)
\(422\) 0 0
\(423\) −17.8374 −0.867286
\(424\) 0 0
\(425\) 6.20140 0.300812
\(426\) 0 0
\(427\) −1.00349 −0.0485625
\(428\) 0 0
\(429\) −2.98317 −0.144029
\(430\) 0 0
\(431\) 13.8931 0.669205 0.334602 0.942359i \(-0.391398\pi\)
0.334602 + 0.942359i \(0.391398\pi\)
\(432\) 0 0
\(433\) 4.65198 0.223560 0.111780 0.993733i \(-0.464345\pi\)
0.111780 + 0.993733i \(0.464345\pi\)
\(434\) 0 0
\(435\) −30.9140 −1.48221
\(436\) 0 0
\(437\) −2.20008 −0.105244
\(438\) 0 0
\(439\) 39.3177 1.87653 0.938266 0.345916i \(-0.112432\pi\)
0.938266 + 0.345916i \(0.112432\pi\)
\(440\) 0 0
\(441\) 5.89931 0.280919
\(442\) 0 0
\(443\) 12.7875 0.607553 0.303776 0.952743i \(-0.401752\pi\)
0.303776 + 0.952743i \(0.401752\pi\)
\(444\) 0 0
\(445\) −3.45328 −0.163701
\(446\) 0 0
\(447\) 16.3297 0.772371
\(448\) 0 0
\(449\) 22.1827 1.04687 0.523433 0.852067i \(-0.324651\pi\)
0.523433 + 0.852067i \(0.324651\pi\)
\(450\) 0 0
\(451\) 4.72545 0.222513
\(452\) 0 0
\(453\) −59.0755 −2.77561
\(454\) 0 0
\(455\) −3.19751 −0.149902
\(456\) 0 0
\(457\) 2.48514 0.116250 0.0581250 0.998309i \(-0.481488\pi\)
0.0581250 + 0.998309i \(0.481488\pi\)
\(458\) 0 0
\(459\) −10.2672 −0.479234
\(460\) 0 0
\(461\) −23.0253 −1.07239 −0.536197 0.844093i \(-0.680140\pi\)
−0.536197 + 0.844093i \(0.680140\pi\)
\(462\) 0 0
\(463\) 20.0068 0.929796 0.464898 0.885364i \(-0.346091\pi\)
0.464898 + 0.885364i \(0.346091\pi\)
\(464\) 0 0
\(465\) 62.6243 2.90413
\(466\) 0 0
\(467\) −4.94951 −0.229036 −0.114518 0.993421i \(-0.536532\pi\)
−0.114518 + 0.993421i \(0.536532\pi\)
\(468\) 0 0
\(469\) −7.44408 −0.343736
\(470\) 0 0
\(471\) −29.3259 −1.35127
\(472\) 0 0
\(473\) −8.34121 −0.383529
\(474\) 0 0
\(475\) 1.56920 0.0719996
\(476\) 0 0
\(477\) 56.0712 2.56732
\(478\) 0 0
\(479\) 13.9476 0.637281 0.318640 0.947876i \(-0.396774\pi\)
0.318640 + 0.947876i \(0.396774\pi\)
\(480\) 0 0
\(481\) 4.73878 0.216070
\(482\) 0 0
\(483\) 21.8499 0.994204
\(484\) 0 0
\(485\) 38.5640 1.75110
\(486\) 0 0
\(487\) 15.5788 0.705945 0.352972 0.935634i \(-0.385171\pi\)
0.352972 + 0.935634i \(0.385171\pi\)
\(488\) 0 0
\(489\) 16.6717 0.753918
\(490\) 0 0
\(491\) −38.7362 −1.74814 −0.874069 0.485801i \(-0.838528\pi\)
−0.874069 + 0.485801i \(0.838528\pi\)
\(492\) 0 0
\(493\) 3.84721 0.173270
\(494\) 0 0
\(495\) −18.8631 −0.847833
\(496\) 0 0
\(497\) −3.06703 −0.137575
\(498\) 0 0
\(499\) 30.4777 1.36437 0.682184 0.731181i \(-0.261031\pi\)
0.682184 + 0.731181i \(0.261031\pi\)
\(500\) 0 0
\(501\) −20.0826 −0.897224
\(502\) 0 0
\(503\) −21.5999 −0.963091 −0.481545 0.876421i \(-0.659924\pi\)
−0.481545 + 0.876421i \(0.659924\pi\)
\(504\) 0 0
\(505\) 15.2058 0.676647
\(506\) 0 0
\(507\) −2.98317 −0.132487
\(508\) 0 0
\(509\) 37.8929 1.67957 0.839787 0.542916i \(-0.182680\pi\)
0.839787 + 0.542916i \(0.182680\pi\)
\(510\) 0 0
\(511\) 10.3083 0.456011
\(512\) 0 0
\(513\) −2.59801 −0.114705
\(514\) 0 0
\(515\) 25.5801 1.12719
\(516\) 0 0
\(517\) 3.02365 0.132980
\(518\) 0 0
\(519\) −30.5270 −1.33999
\(520\) 0 0
\(521\) 10.7631 0.471540 0.235770 0.971809i \(-0.424239\pi\)
0.235770 + 0.971809i \(0.424239\pi\)
\(522\) 0 0
\(523\) 13.5112 0.590804 0.295402 0.955373i \(-0.404546\pi\)
0.295402 + 0.955373i \(0.404546\pi\)
\(524\) 0 0
\(525\) −15.5843 −0.680154
\(526\) 0 0
\(527\) −7.79353 −0.339491
\(528\) 0 0
\(529\) 30.6465 1.33246
\(530\) 0 0
\(531\) 76.1987 3.30674
\(532\) 0 0
\(533\) 4.72545 0.204682
\(534\) 0 0
\(535\) −40.8940 −1.76800
\(536\) 0 0
\(537\) 11.9682 0.516466
\(538\) 0 0
\(539\) −1.00000 −0.0430730
\(540\) 0 0
\(541\) −29.7148 −1.27754 −0.638770 0.769397i \(-0.720557\pi\)
−0.638770 + 0.769397i \(0.720557\pi\)
\(542\) 0 0
\(543\) 49.4852 2.12361
\(544\) 0 0
\(545\) −7.86180 −0.336763
\(546\) 0 0
\(547\) 12.1263 0.518484 0.259242 0.965812i \(-0.416527\pi\)
0.259242 + 0.965812i \(0.416527\pi\)
\(548\) 0 0
\(549\) −5.91993 −0.252656
\(550\) 0 0
\(551\) 0.973494 0.0414722
\(552\) 0 0
\(553\) 5.83010 0.247921
\(554\) 0 0
\(555\) 45.2019 1.91871
\(556\) 0 0
\(557\) 29.9648 1.26965 0.634825 0.772656i \(-0.281072\pi\)
0.634825 + 0.772656i \(0.281072\pi\)
\(558\) 0 0
\(559\) −8.34121 −0.352795
\(560\) 0 0
\(561\) 3.54127 0.149513
\(562\) 0 0
\(563\) 25.9907 1.09538 0.547689 0.836682i \(-0.315508\pi\)
0.547689 + 0.836682i \(0.315508\pi\)
\(564\) 0 0
\(565\) 33.5466 1.41132
\(566\) 0 0
\(567\) 8.10392 0.340333
\(568\) 0 0
\(569\) −1.30119 −0.0545487 −0.0272743 0.999628i \(-0.508683\pi\)
−0.0272743 + 0.999628i \(0.508683\pi\)
\(570\) 0 0
\(571\) −2.13173 −0.0892101 −0.0446051 0.999005i \(-0.514203\pi\)
−0.0446051 + 0.999005i \(0.514203\pi\)
\(572\) 0 0
\(573\) −0.00544636 −0.000227525 0
\(574\) 0 0
\(575\) −38.2630 −1.59568
\(576\) 0 0
\(577\) 21.9561 0.914044 0.457022 0.889455i \(-0.348916\pi\)
0.457022 + 0.889455i \(0.348916\pi\)
\(578\) 0 0
\(579\) 28.5019 1.18450
\(580\) 0 0
\(581\) 9.23729 0.383227
\(582\) 0 0
\(583\) −9.50471 −0.393645
\(584\) 0 0
\(585\) −18.8631 −0.779893
\(586\) 0 0
\(587\) 16.8990 0.697496 0.348748 0.937217i \(-0.386607\pi\)
0.348748 + 0.937217i \(0.386607\pi\)
\(588\) 0 0
\(589\) −1.97207 −0.0812575
\(590\) 0 0
\(591\) −2.91045 −0.119720
\(592\) 0 0
\(593\) −20.8869 −0.857720 −0.428860 0.903371i \(-0.641085\pi\)
−0.428860 + 0.903371i \(0.641085\pi\)
\(594\) 0 0
\(595\) 3.79571 0.155609
\(596\) 0 0
\(597\) 10.2372 0.418980
\(598\) 0 0
\(599\) −28.9823 −1.18418 −0.592092 0.805870i \(-0.701698\pi\)
−0.592092 + 0.805870i \(0.701698\pi\)
\(600\) 0 0
\(601\) 9.34759 0.381296 0.190648 0.981658i \(-0.438941\pi\)
0.190648 + 0.981658i \(0.438941\pi\)
\(602\) 0 0
\(603\) −43.9149 −1.78835
\(604\) 0 0
\(605\) 3.19751 0.129997
\(606\) 0 0
\(607\) 32.7917 1.33097 0.665487 0.746409i \(-0.268224\pi\)
0.665487 + 0.746409i \(0.268224\pi\)
\(608\) 0 0
\(609\) −9.66814 −0.391773
\(610\) 0 0
\(611\) 3.02365 0.122324
\(612\) 0 0
\(613\) 23.1572 0.935311 0.467656 0.883911i \(-0.345099\pi\)
0.467656 + 0.883911i \(0.345099\pi\)
\(614\) 0 0
\(615\) 45.0747 1.81759
\(616\) 0 0
\(617\) −29.3083 −1.17991 −0.589954 0.807437i \(-0.700854\pi\)
−0.589954 + 0.807437i \(0.700854\pi\)
\(618\) 0 0
\(619\) −12.9366 −0.519966 −0.259983 0.965613i \(-0.583717\pi\)
−0.259983 + 0.965613i \(0.583717\pi\)
\(620\) 0 0
\(621\) 63.3495 2.54213
\(622\) 0 0
\(623\) −1.07999 −0.0432689
\(624\) 0 0
\(625\) −23.8295 −0.953179
\(626\) 0 0
\(627\) 0.896080 0.0357860
\(628\) 0 0
\(629\) −5.62533 −0.224297
\(630\) 0 0
\(631\) 11.6680 0.464495 0.232247 0.972657i \(-0.425392\pi\)
0.232247 + 0.972657i \(0.425392\pi\)
\(632\) 0 0
\(633\) 1.73640 0.0690155
\(634\) 0 0
\(635\) 64.4548 2.55781
\(636\) 0 0
\(637\) −1.00000 −0.0396214
\(638\) 0 0
\(639\) −18.0934 −0.715763
\(640\) 0 0
\(641\) 30.1282 1.18999 0.594995 0.803729i \(-0.297154\pi\)
0.594995 + 0.803729i \(0.297154\pi\)
\(642\) 0 0
\(643\) 30.2577 1.19325 0.596623 0.802522i \(-0.296509\pi\)
0.596623 + 0.802522i \(0.296509\pi\)
\(644\) 0 0
\(645\) −79.5644 −3.13285
\(646\) 0 0
\(647\) −25.7746 −1.01331 −0.506653 0.862150i \(-0.669117\pi\)
−0.506653 + 0.862150i \(0.669117\pi\)
\(648\) 0 0
\(649\) −12.9166 −0.507019
\(650\) 0 0
\(651\) 19.5853 0.767610
\(652\) 0 0
\(653\) 36.4729 1.42730 0.713648 0.700504i \(-0.247042\pi\)
0.713648 + 0.700504i \(0.247042\pi\)
\(654\) 0 0
\(655\) −2.06078 −0.0805212
\(656\) 0 0
\(657\) 60.8117 2.37249
\(658\) 0 0
\(659\) 19.9993 0.779062 0.389531 0.921013i \(-0.372637\pi\)
0.389531 + 0.921013i \(0.372637\pi\)
\(660\) 0 0
\(661\) −24.5502 −0.954891 −0.477445 0.878661i \(-0.658437\pi\)
−0.477445 + 0.878661i \(0.658437\pi\)
\(662\) 0 0
\(663\) 3.54127 0.137532
\(664\) 0 0
\(665\) 0.960462 0.0372451
\(666\) 0 0
\(667\) −23.7375 −0.919121
\(668\) 0 0
\(669\) −39.5353 −1.52852
\(670\) 0 0
\(671\) 1.00349 0.0387395
\(672\) 0 0
\(673\) 14.9857 0.577655 0.288828 0.957381i \(-0.406735\pi\)
0.288828 + 0.957381i \(0.406735\pi\)
\(674\) 0 0
\(675\) −45.1836 −1.73912
\(676\) 0 0
\(677\) −42.5415 −1.63500 −0.817501 0.575928i \(-0.804641\pi\)
−0.817501 + 0.575928i \(0.804641\pi\)
\(678\) 0 0
\(679\) 12.0606 0.462844
\(680\) 0 0
\(681\) 49.2280 1.88642
\(682\) 0 0
\(683\) −16.6831 −0.638362 −0.319181 0.947694i \(-0.603408\pi\)
−0.319181 + 0.947694i \(0.603408\pi\)
\(684\) 0 0
\(685\) −1.80746 −0.0690597
\(686\) 0 0
\(687\) 88.5984 3.38024
\(688\) 0 0
\(689\) −9.50471 −0.362100
\(690\) 0 0
\(691\) 46.8600 1.78264 0.891319 0.453377i \(-0.149781\pi\)
0.891319 + 0.453377i \(0.149781\pi\)
\(692\) 0 0
\(693\) −5.89931 −0.224096
\(694\) 0 0
\(695\) −33.1305 −1.25671
\(696\) 0 0
\(697\) −5.60950 −0.212475
\(698\) 0 0
\(699\) −22.3900 −0.846868
\(700\) 0 0
\(701\) −14.8465 −0.560746 −0.280373 0.959891i \(-0.590458\pi\)
−0.280373 + 0.959891i \(0.590458\pi\)
\(702\) 0 0
\(703\) −1.42343 −0.0536856
\(704\) 0 0
\(705\) 28.8417 1.08624
\(706\) 0 0
\(707\) 4.75550 0.178849
\(708\) 0 0
\(709\) −36.2226 −1.36037 −0.680184 0.733042i \(-0.738100\pi\)
−0.680184 + 0.733042i \(0.738100\pi\)
\(710\) 0 0
\(711\) 34.3936 1.28986
\(712\) 0 0
\(713\) 48.0865 1.80086
\(714\) 0 0
\(715\) 3.19751 0.119580
\(716\) 0 0
\(717\) −69.4125 −2.59226
\(718\) 0 0
\(719\) 10.0712 0.375592 0.187796 0.982208i \(-0.439866\pi\)
0.187796 + 0.982208i \(0.439866\pi\)
\(720\) 0 0
\(721\) 8.00000 0.297936
\(722\) 0 0
\(723\) −29.7786 −1.10748
\(724\) 0 0
\(725\) 16.9306 0.628788
\(726\) 0 0
\(727\) 19.2979 0.715719 0.357859 0.933775i \(-0.383507\pi\)
0.357859 + 0.933775i \(0.383507\pi\)
\(728\) 0 0
\(729\) −29.5980 −1.09622
\(730\) 0 0
\(731\) 9.90171 0.366228
\(732\) 0 0
\(733\) 8.72910 0.322417 0.161208 0.986920i \(-0.448461\pi\)
0.161208 + 0.986920i \(0.448461\pi\)
\(734\) 0 0
\(735\) −9.53872 −0.351841
\(736\) 0 0
\(737\) 7.44408 0.274206
\(738\) 0 0
\(739\) 20.3871 0.749951 0.374975 0.927035i \(-0.377651\pi\)
0.374975 + 0.927035i \(0.377651\pi\)
\(740\) 0 0
\(741\) 0.896080 0.0329183
\(742\) 0 0
\(743\) −40.1070 −1.47138 −0.735692 0.677316i \(-0.763143\pi\)
−0.735692 + 0.677316i \(0.763143\pi\)
\(744\) 0 0
\(745\) −17.5030 −0.641261
\(746\) 0 0
\(747\) 54.4936 1.99382
\(748\) 0 0
\(749\) −12.7893 −0.467312
\(750\) 0 0
\(751\) −47.4794 −1.73255 −0.866273 0.499570i \(-0.833491\pi\)
−0.866273 + 0.499570i \(0.833491\pi\)
\(752\) 0 0
\(753\) −47.2721 −1.72269
\(754\) 0 0
\(755\) 63.3200 2.30445
\(756\) 0 0
\(757\) 32.6137 1.18536 0.592682 0.805437i \(-0.298069\pi\)
0.592682 + 0.805437i \(0.298069\pi\)
\(758\) 0 0
\(759\) −21.8499 −0.793100
\(760\) 0 0
\(761\) 23.8173 0.863376 0.431688 0.902023i \(-0.357918\pi\)
0.431688 + 0.902023i \(0.357918\pi\)
\(762\) 0 0
\(763\) −2.45873 −0.0890119
\(764\) 0 0
\(765\) 22.3921 0.809587
\(766\) 0 0
\(767\) −12.9166 −0.466390
\(768\) 0 0
\(769\) 7.65466 0.276034 0.138017 0.990430i \(-0.455927\pi\)
0.138017 + 0.990430i \(0.455927\pi\)
\(770\) 0 0
\(771\) −59.5757 −2.14557
\(772\) 0 0
\(773\) −28.4596 −1.02362 −0.511811 0.859098i \(-0.671025\pi\)
−0.511811 + 0.859098i \(0.671025\pi\)
\(774\) 0 0
\(775\) −34.2974 −1.23200
\(776\) 0 0
\(777\) 14.1366 0.507148
\(778\) 0 0
\(779\) −1.41942 −0.0508561
\(780\) 0 0
\(781\) 3.06703 0.109747
\(782\) 0 0
\(783\) −28.0309 −1.00174
\(784\) 0 0
\(785\) 31.4330 1.12189
\(786\) 0 0
\(787\) −10.3402 −0.368588 −0.184294 0.982871i \(-0.559000\pi\)
−0.184294 + 0.982871i \(0.559000\pi\)
\(788\) 0 0
\(789\) 58.3550 2.07749
\(790\) 0 0
\(791\) 10.4915 0.373034
\(792\) 0 0
\(793\) 1.00349 0.0356351
\(794\) 0 0
\(795\) −90.6627 −3.21547
\(796\) 0 0
\(797\) 19.9378 0.706235 0.353117 0.935579i \(-0.385122\pi\)
0.353117 + 0.935579i \(0.385122\pi\)
\(798\) 0 0
\(799\) −3.58932 −0.126981
\(800\) 0 0
\(801\) −6.37119 −0.225115
\(802\) 0 0
\(803\) −10.3083 −0.363771
\(804\) 0 0
\(805\) −23.4198 −0.825438
\(806\) 0 0
\(807\) 27.0668 0.952797
\(808\) 0 0
\(809\) −28.6798 −1.00833 −0.504164 0.863608i \(-0.668199\pi\)
−0.504164 + 0.863608i \(0.668199\pi\)
\(810\) 0 0
\(811\) −25.1778 −0.884113 −0.442057 0.896987i \(-0.645751\pi\)
−0.442057 + 0.896987i \(0.645751\pi\)
\(812\) 0 0
\(813\) −50.7543 −1.78003
\(814\) 0 0
\(815\) −17.8695 −0.625941
\(816\) 0 0
\(817\) 2.50552 0.0876570
\(818\) 0 0
\(819\) −5.89931 −0.206139
\(820\) 0 0
\(821\) −22.9218 −0.799977 −0.399988 0.916520i \(-0.630986\pi\)
−0.399988 + 0.916520i \(0.630986\pi\)
\(822\) 0 0
\(823\) −25.4907 −0.888549 −0.444275 0.895891i \(-0.646539\pi\)
−0.444275 + 0.895891i \(0.646539\pi\)
\(824\) 0 0
\(825\) 15.5843 0.542575
\(826\) 0 0
\(827\) −5.50179 −0.191316 −0.0956579 0.995414i \(-0.530495\pi\)
−0.0956579 + 0.995414i \(0.530495\pi\)
\(828\) 0 0
\(829\) 40.0228 1.39005 0.695025 0.718986i \(-0.255393\pi\)
0.695025 + 0.718986i \(0.255393\pi\)
\(830\) 0 0
\(831\) −11.9047 −0.412970
\(832\) 0 0
\(833\) 1.18708 0.0411300
\(834\) 0 0
\(835\) 21.5255 0.744921
\(836\) 0 0
\(837\) 56.7839 1.96274
\(838\) 0 0
\(839\) 16.9393 0.584811 0.292406 0.956294i \(-0.405544\pi\)
0.292406 + 0.956294i \(0.405544\pi\)
\(840\) 0 0
\(841\) −18.4966 −0.637814
\(842\) 0 0
\(843\) −78.7065 −2.71080
\(844\) 0 0
\(845\) 3.19751 0.109998
\(846\) 0 0
\(847\) 1.00000 0.0343604
\(848\) 0 0
\(849\) 48.5479 1.66616
\(850\) 0 0
\(851\) 34.7086 1.18980
\(852\) 0 0
\(853\) −12.8030 −0.438366 −0.219183 0.975684i \(-0.570339\pi\)
−0.219183 + 0.975684i \(0.570339\pi\)
\(854\) 0 0
\(855\) 5.66606 0.193775
\(856\) 0 0
\(857\) 17.9534 0.613276 0.306638 0.951826i \(-0.400796\pi\)
0.306638 + 0.951826i \(0.400796\pi\)
\(858\) 0 0
\(859\) 36.9107 1.25938 0.629689 0.776848i \(-0.283182\pi\)
0.629689 + 0.776848i \(0.283182\pi\)
\(860\) 0 0
\(861\) 14.0968 0.480418
\(862\) 0 0
\(863\) −14.9728 −0.509680 −0.254840 0.966983i \(-0.582023\pi\)
−0.254840 + 0.966983i \(0.582023\pi\)
\(864\) 0 0
\(865\) 32.7203 1.11252
\(866\) 0 0
\(867\) 46.5101 1.57957
\(868\) 0 0
\(869\) −5.83010 −0.197773
\(870\) 0 0
\(871\) 7.44408 0.252233
\(872\) 0 0
\(873\) 71.1494 2.40804
\(874\) 0 0
\(875\) 0.716451 0.0242205
\(876\) 0 0
\(877\) −33.7707 −1.14036 −0.570178 0.821521i \(-0.693126\pi\)
−0.570178 + 0.821521i \(0.693126\pi\)
\(878\) 0 0
\(879\) −7.38424 −0.249064
\(880\) 0 0
\(881\) 16.9144 0.569860 0.284930 0.958548i \(-0.408030\pi\)
0.284930 + 0.958548i \(0.408030\pi\)
\(882\) 0 0
\(883\) 10.4990 0.353319 0.176660 0.984272i \(-0.443471\pi\)
0.176660 + 0.984272i \(0.443471\pi\)
\(884\) 0 0
\(885\) −123.207 −4.14157
\(886\) 0 0
\(887\) 4.11464 0.138156 0.0690781 0.997611i \(-0.477994\pi\)
0.0690781 + 0.997611i \(0.477994\pi\)
\(888\) 0 0
\(889\) 20.1578 0.676071
\(890\) 0 0
\(891\) −8.10392 −0.271492
\(892\) 0 0
\(893\) −0.908238 −0.0303930
\(894\) 0 0
\(895\) −12.8281 −0.428796
\(896\) 0 0
\(897\) −21.8499 −0.729546
\(898\) 0 0
\(899\) −21.2774 −0.709640
\(900\) 0 0
\(901\) 11.2829 0.375887
\(902\) 0 0
\(903\) −24.8832 −0.828063
\(904\) 0 0
\(905\) −53.0407 −1.76313
\(906\) 0 0
\(907\) 1.26804 0.0421047 0.0210523 0.999778i \(-0.493298\pi\)
0.0210523 + 0.999778i \(0.493298\pi\)
\(908\) 0 0
\(909\) 28.0542 0.930498
\(910\) 0 0
\(911\) 28.5742 0.946705 0.473353 0.880873i \(-0.343044\pi\)
0.473353 + 0.880873i \(0.343044\pi\)
\(912\) 0 0
\(913\) −9.23729 −0.305710
\(914\) 0 0
\(915\) 9.57205 0.316442
\(916\) 0 0
\(917\) −0.644494 −0.0212831
\(918\) 0 0
\(919\) 37.5286 1.23795 0.618977 0.785409i \(-0.287547\pi\)
0.618977 + 0.785409i \(0.287547\pi\)
\(920\) 0 0
\(921\) −21.2674 −0.700783
\(922\) 0 0
\(923\) 3.06703 0.100953
\(924\) 0 0
\(925\) −24.7557 −0.813963
\(926\) 0 0
\(927\) 47.1945 1.55007
\(928\) 0 0
\(929\) −14.9227 −0.489599 −0.244800 0.969574i \(-0.578722\pi\)
−0.244800 + 0.969574i \(0.578722\pi\)
\(930\) 0 0
\(931\) 0.300378 0.00984450
\(932\) 0 0
\(933\) −32.4468 −1.06226
\(934\) 0 0
\(935\) −3.79571 −0.124133
\(936\) 0 0
\(937\) −37.7125 −1.23201 −0.616007 0.787740i \(-0.711251\pi\)
−0.616007 + 0.787740i \(0.711251\pi\)
\(938\) 0 0
\(939\) 89.2739 2.91334
\(940\) 0 0
\(941\) 10.8319 0.353110 0.176555 0.984291i \(-0.443505\pi\)
0.176555 + 0.984291i \(0.443505\pi\)
\(942\) 0 0
\(943\) 34.6110 1.12709
\(944\) 0 0
\(945\) −27.6557 −0.899640
\(946\) 0 0
\(947\) −28.0606 −0.911848 −0.455924 0.890019i \(-0.650691\pi\)
−0.455924 + 0.890019i \(0.650691\pi\)
\(948\) 0 0
\(949\) −10.3083 −0.334621
\(950\) 0 0
\(951\) −65.6631 −2.12927
\(952\) 0 0
\(953\) −41.9586 −1.35917 −0.679586 0.733596i \(-0.737840\pi\)
−0.679586 + 0.733596i \(0.737840\pi\)
\(954\) 0 0
\(955\) 0.00583767 0.000188903 0
\(956\) 0 0
\(957\) 9.66814 0.312527
\(958\) 0 0
\(959\) −0.565273 −0.0182536
\(960\) 0 0
\(961\) 12.1028 0.390413
\(962\) 0 0
\(963\) −75.4483 −2.43129
\(964\) 0 0
\(965\) −30.5497 −0.983431
\(966\) 0 0
\(967\) 15.9842 0.514018 0.257009 0.966409i \(-0.417263\pi\)
0.257009 + 0.966409i \(0.417263\pi\)
\(968\) 0 0
\(969\) −1.06372 −0.0341717
\(970\) 0 0
\(971\) −37.9393 −1.21753 −0.608765 0.793351i \(-0.708335\pi\)
−0.608765 + 0.793351i \(0.708335\pi\)
\(972\) 0 0
\(973\) −10.3614 −0.332170
\(974\) 0 0
\(975\) 15.5843 0.499096
\(976\) 0 0
\(977\) 26.8666 0.859537 0.429769 0.902939i \(-0.358595\pi\)
0.429769 + 0.902939i \(0.358595\pi\)
\(978\) 0 0
\(979\) 1.07999 0.0345166
\(980\) 0 0
\(981\) −14.5048 −0.463102
\(982\) 0 0
\(983\) 42.1880 1.34559 0.672794 0.739830i \(-0.265094\pi\)
0.672794 + 0.739830i \(0.265094\pi\)
\(984\) 0 0
\(985\) 3.11956 0.0993975
\(986\) 0 0
\(987\) 9.02006 0.287112
\(988\) 0 0
\(989\) −61.0942 −1.94268
\(990\) 0 0
\(991\) 0.198655 0.00631048 0.00315524 0.999995i \(-0.498996\pi\)
0.00315524 + 0.999995i \(0.498996\pi\)
\(992\) 0 0
\(993\) 86.9346 2.75879
\(994\) 0 0
\(995\) −10.9727 −0.347859
\(996\) 0 0
\(997\) 58.2283 1.84411 0.922055 0.387060i \(-0.126509\pi\)
0.922055 + 0.387060i \(0.126509\pi\)
\(998\) 0 0
\(999\) 40.9864 1.29675
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 \(a_p\))