Properties

Label 6003.2.a.t.1.16
Level 6003
Weight 2
Character 6003.1
Self dual Yes
Analytic conductor 47.934
Analytic rank 1
Dimension 22
CM No

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Newspace parameters

Level: \( N \) = \( 6003 = 3^{2} \cdot 23 \cdot 29 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6003.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(47.9341963334\)
Analytic rank: \(1\)
Dimension: \(22\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.16
Character \(\chi\) = 6003.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.14621 q^{2} -0.686192 q^{4} +0.461250 q^{5} -3.03232 q^{7} -3.07895 q^{8} +O(q^{10})\) \(q+1.14621 q^{2} -0.686192 q^{4} +0.461250 q^{5} -3.03232 q^{7} -3.07895 q^{8} +0.528691 q^{10} +1.24022 q^{11} +3.02812 q^{13} -3.47569 q^{14} -2.15675 q^{16} +1.56446 q^{17} -0.758514 q^{19} -0.316506 q^{20} +1.42156 q^{22} +1.00000 q^{23} -4.78725 q^{25} +3.47087 q^{26} +2.08076 q^{28} +1.00000 q^{29} +5.58933 q^{31} +3.68580 q^{32} +1.79321 q^{34} -1.39866 q^{35} +11.3773 q^{37} -0.869420 q^{38} -1.42017 q^{40} +4.22535 q^{41} -3.44184 q^{43} -0.851030 q^{44} +1.14621 q^{46} -13.0870 q^{47} +2.19499 q^{49} -5.48721 q^{50} -2.07787 q^{52} -10.3082 q^{53} +0.572051 q^{55} +9.33638 q^{56} +1.14621 q^{58} +1.58780 q^{59} -11.2127 q^{61} +6.40657 q^{62} +8.53823 q^{64} +1.39672 q^{65} -4.97364 q^{67} -1.07352 q^{68} -1.60316 q^{70} +3.12927 q^{71} -13.6069 q^{73} +13.0408 q^{74} +0.520487 q^{76} -3.76075 q^{77} +5.95073 q^{79} -0.994802 q^{80} +4.84316 q^{82} +1.97198 q^{83} +0.721608 q^{85} -3.94508 q^{86} -3.81858 q^{88} -3.14877 q^{89} -9.18224 q^{91} -0.686192 q^{92} -15.0005 q^{94} -0.349864 q^{95} -14.1283 q^{97} +2.51593 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 22q - 3q^{2} + 17q^{4} - 6q^{7} - 6q^{8} + O(q^{10}) \) \( 22q - 3q^{2} + 17q^{4} - 6q^{7} - 6q^{8} - 12q^{10} - 28q^{13} - q^{14} + 3q^{16} - 10q^{17} - 8q^{19} - 11q^{22} + 22q^{23} + 11q^{26} - 21q^{28} + 22q^{29} - 18q^{31} + 5q^{32} - 33q^{34} + 2q^{35} - 28q^{37} + 14q^{38} - 30q^{40} - 10q^{41} - 14q^{43} + 37q^{44} - 3q^{46} - 18q^{47} + 2q^{49} + 7q^{50} - 57q^{52} + 20q^{53} - 42q^{55} - 2q^{56} - 3q^{58} - 20q^{59} - 38q^{61} + 4q^{62} - 24q^{64} + 12q^{65} - 50q^{67} + 11q^{68} - 48q^{70} + 12q^{71} - 46q^{73} - 6q^{74} - 16q^{76} - 14q^{77} - 20q^{79} - 58q^{80} - 42q^{82} + 22q^{83} - 66q^{85} + 22q^{86} - 68q^{88} - 14q^{89} - 16q^{91} + 17q^{92} - 27q^{94} - 20q^{95} - 48q^{97} - 28q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.14621 0.810496 0.405248 0.914207i \(-0.367185\pi\)
0.405248 + 0.914207i \(0.367185\pi\)
\(3\) 0 0
\(4\) −0.686192 −0.343096
\(5\) 0.461250 0.206277 0.103139 0.994667i \(-0.467112\pi\)
0.103139 + 0.994667i \(0.467112\pi\)
\(6\) 0 0
\(7\) −3.03232 −1.14611 −0.573056 0.819517i \(-0.694242\pi\)
−0.573056 + 0.819517i \(0.694242\pi\)
\(8\) −3.07895 −1.08857
\(9\) 0 0
\(10\) 0.528691 0.167187
\(11\) 1.24022 0.373941 0.186970 0.982366i \(-0.440133\pi\)
0.186970 + 0.982366i \(0.440133\pi\)
\(12\) 0 0
\(13\) 3.02812 0.839849 0.419924 0.907559i \(-0.362057\pi\)
0.419924 + 0.907559i \(0.362057\pi\)
\(14\) −3.47569 −0.928918
\(15\) 0 0
\(16\) −2.15675 −0.539189
\(17\) 1.56446 0.379438 0.189719 0.981838i \(-0.439242\pi\)
0.189719 + 0.981838i \(0.439242\pi\)
\(18\) 0 0
\(19\) −0.758514 −0.174015 −0.0870075 0.996208i \(-0.527730\pi\)
−0.0870075 + 0.996208i \(0.527730\pi\)
\(20\) −0.316506 −0.0707729
\(21\) 0 0
\(22\) 1.42156 0.303077
\(23\) 1.00000 0.208514
\(24\) 0 0
\(25\) −4.78725 −0.957450
\(26\) 3.47087 0.680694
\(27\) 0 0
\(28\) 2.08076 0.393226
\(29\) 1.00000 0.185695
\(30\) 0 0
\(31\) 5.58933 1.00387 0.501936 0.864905i \(-0.332621\pi\)
0.501936 + 0.864905i \(0.332621\pi\)
\(32\) 3.68580 0.651564
\(33\) 0 0
\(34\) 1.79321 0.307533
\(35\) −1.39866 −0.236416
\(36\) 0 0
\(37\) 11.3773 1.87042 0.935209 0.354097i \(-0.115212\pi\)
0.935209 + 0.354097i \(0.115212\pi\)
\(38\) −0.869420 −0.141038
\(39\) 0 0
\(40\) −1.42017 −0.224548
\(41\) 4.22535 0.659889 0.329944 0.944000i \(-0.392970\pi\)
0.329944 + 0.944000i \(0.392970\pi\)
\(42\) 0 0
\(43\) −3.44184 −0.524875 −0.262438 0.964949i \(-0.584526\pi\)
−0.262438 + 0.964949i \(0.584526\pi\)
\(44\) −0.851030 −0.128298
\(45\) 0 0
\(46\) 1.14621 0.169000
\(47\) −13.0870 −1.90894 −0.954468 0.298312i \(-0.903576\pi\)
−0.954468 + 0.298312i \(0.903576\pi\)
\(48\) 0 0
\(49\) 2.19499 0.313571
\(50\) −5.48721 −0.776009
\(51\) 0 0
\(52\) −2.07787 −0.288149
\(53\) −10.3082 −1.41594 −0.707970 0.706242i \(-0.750389\pi\)
−0.707970 + 0.706242i \(0.750389\pi\)
\(54\) 0 0
\(55\) 0.572051 0.0771354
\(56\) 9.33638 1.24763
\(57\) 0 0
\(58\) 1.14621 0.150505
\(59\) 1.58780 0.206714 0.103357 0.994644i \(-0.467042\pi\)
0.103357 + 0.994644i \(0.467042\pi\)
\(60\) 0 0
\(61\) −11.2127 −1.43564 −0.717819 0.696230i \(-0.754860\pi\)
−0.717819 + 0.696230i \(0.754860\pi\)
\(62\) 6.40657 0.813635
\(63\) 0 0
\(64\) 8.53823 1.06728
\(65\) 1.39672 0.173242
\(66\) 0 0
\(67\) −4.97364 −0.607627 −0.303813 0.952732i \(-0.598260\pi\)
−0.303813 + 0.952732i \(0.598260\pi\)
\(68\) −1.07352 −0.130184
\(69\) 0 0
\(70\) −1.60316 −0.191615
\(71\) 3.12927 0.371376 0.185688 0.982609i \(-0.440549\pi\)
0.185688 + 0.982609i \(0.440549\pi\)
\(72\) 0 0
\(73\) −13.6069 −1.59256 −0.796281 0.604927i \(-0.793202\pi\)
−0.796281 + 0.604927i \(0.793202\pi\)
\(74\) 13.0408 1.51597
\(75\) 0 0
\(76\) 0.520487 0.0597039
\(77\) −3.76075 −0.428578
\(78\) 0 0
\(79\) 5.95073 0.669509 0.334755 0.942305i \(-0.391347\pi\)
0.334755 + 0.942305i \(0.391347\pi\)
\(80\) −0.994802 −0.111222
\(81\) 0 0
\(82\) 4.84316 0.534837
\(83\) 1.97198 0.216453 0.108226 0.994126i \(-0.465483\pi\)
0.108226 + 0.994126i \(0.465483\pi\)
\(84\) 0 0
\(85\) 0.721608 0.0782694
\(86\) −3.94508 −0.425409
\(87\) 0 0
\(88\) −3.81858 −0.407062
\(89\) −3.14877 −0.333769 −0.166885 0.985976i \(-0.553371\pi\)
−0.166885 + 0.985976i \(0.553371\pi\)
\(90\) 0 0
\(91\) −9.18224 −0.962560
\(92\) −0.686192 −0.0715405
\(93\) 0 0
\(94\) −15.0005 −1.54719
\(95\) −0.349864 −0.0358953
\(96\) 0 0
\(97\) −14.1283 −1.43451 −0.717256 0.696809i \(-0.754602\pi\)
−0.717256 + 0.696809i \(0.754602\pi\)
\(98\) 2.51593 0.254148
\(99\) 0 0
\(100\) 3.28497 0.328497
\(101\) −14.3966 −1.43252 −0.716259 0.697835i \(-0.754147\pi\)
−0.716259 + 0.697835i \(0.754147\pi\)
\(102\) 0 0
\(103\) 10.1143 0.996595 0.498298 0.867006i \(-0.333959\pi\)
0.498298 + 0.867006i \(0.333959\pi\)
\(104\) −9.32343 −0.914238
\(105\) 0 0
\(106\) −11.8154 −1.14761
\(107\) −16.8285 −1.62687 −0.813435 0.581656i \(-0.802405\pi\)
−0.813435 + 0.581656i \(0.802405\pi\)
\(108\) 0 0
\(109\) 16.9409 1.62265 0.811323 0.584598i \(-0.198748\pi\)
0.811323 + 0.584598i \(0.198748\pi\)
\(110\) 0.655694 0.0625179
\(111\) 0 0
\(112\) 6.53998 0.617970
\(113\) −14.4070 −1.35530 −0.677651 0.735384i \(-0.737002\pi\)
−0.677651 + 0.735384i \(0.737002\pi\)
\(114\) 0 0
\(115\) 0.461250 0.0430117
\(116\) −0.686192 −0.0637114
\(117\) 0 0
\(118\) 1.81996 0.167541
\(119\) −4.74396 −0.434878
\(120\) 0 0
\(121\) −9.46185 −0.860168
\(122\) −12.8522 −1.16358
\(123\) 0 0
\(124\) −3.83535 −0.344425
\(125\) −4.51436 −0.403777
\(126\) 0 0
\(127\) 2.54119 0.225494 0.112747 0.993624i \(-0.464035\pi\)
0.112747 + 0.993624i \(0.464035\pi\)
\(128\) 2.41504 0.213461
\(129\) 0 0
\(130\) 1.60094 0.140412
\(131\) −3.71190 −0.324310 −0.162155 0.986765i \(-0.551844\pi\)
−0.162155 + 0.986765i \(0.551844\pi\)
\(132\) 0 0
\(133\) 2.30006 0.199441
\(134\) −5.70086 −0.492479
\(135\) 0 0
\(136\) −4.81691 −0.413047
\(137\) −8.98216 −0.767398 −0.383699 0.923458i \(-0.625350\pi\)
−0.383699 + 0.923458i \(0.625350\pi\)
\(138\) 0 0
\(139\) 2.13746 0.181297 0.0906487 0.995883i \(-0.471106\pi\)
0.0906487 + 0.995883i \(0.471106\pi\)
\(140\) 0.959749 0.0811136
\(141\) 0 0
\(142\) 3.58681 0.300999
\(143\) 3.75554 0.314054
\(144\) 0 0
\(145\) 0.461250 0.0383047
\(146\) −15.5964 −1.29076
\(147\) 0 0
\(148\) −7.80702 −0.641733
\(149\) 17.6412 1.44523 0.722614 0.691252i \(-0.242941\pi\)
0.722614 + 0.691252i \(0.242941\pi\)
\(150\) 0 0
\(151\) −5.41797 −0.440908 −0.220454 0.975397i \(-0.570754\pi\)
−0.220454 + 0.975397i \(0.570754\pi\)
\(152\) 2.33543 0.189428
\(153\) 0 0
\(154\) −4.31063 −0.347360
\(155\) 2.57807 0.207076
\(156\) 0 0
\(157\) −19.1808 −1.53080 −0.765399 0.643557i \(-0.777458\pi\)
−0.765399 + 0.643557i \(0.777458\pi\)
\(158\) 6.82081 0.542634
\(159\) 0 0
\(160\) 1.70007 0.134403
\(161\) −3.03232 −0.238981
\(162\) 0 0
\(163\) −15.2529 −1.19470 −0.597351 0.801980i \(-0.703780\pi\)
−0.597351 + 0.801980i \(0.703780\pi\)
\(164\) −2.89940 −0.226405
\(165\) 0 0
\(166\) 2.26031 0.175434
\(167\) 9.37038 0.725102 0.362551 0.931964i \(-0.381906\pi\)
0.362551 + 0.931964i \(0.381906\pi\)
\(168\) 0 0
\(169\) −3.83050 −0.294654
\(170\) 0.827118 0.0634370
\(171\) 0 0
\(172\) 2.36176 0.180083
\(173\) 5.08480 0.386591 0.193295 0.981141i \(-0.438082\pi\)
0.193295 + 0.981141i \(0.438082\pi\)
\(174\) 0 0
\(175\) 14.5165 1.09734
\(176\) −2.67485 −0.201625
\(177\) 0 0
\(178\) −3.60917 −0.270519
\(179\) 13.8992 1.03887 0.519437 0.854509i \(-0.326142\pi\)
0.519437 + 0.854509i \(0.326142\pi\)
\(180\) 0 0
\(181\) 14.4692 1.07549 0.537744 0.843108i \(-0.319277\pi\)
0.537744 + 0.843108i \(0.319277\pi\)
\(182\) −10.5248 −0.780151
\(183\) 0 0
\(184\) −3.07895 −0.226983
\(185\) 5.24778 0.385824
\(186\) 0 0
\(187\) 1.94028 0.141887
\(188\) 8.98021 0.654949
\(189\) 0 0
\(190\) −0.401019 −0.0290930
\(191\) 12.1024 0.875699 0.437849 0.899048i \(-0.355740\pi\)
0.437849 + 0.899048i \(0.355740\pi\)
\(192\) 0 0
\(193\) −4.52408 −0.325650 −0.162825 0.986655i \(-0.552061\pi\)
−0.162825 + 0.986655i \(0.552061\pi\)
\(194\) −16.1941 −1.16267
\(195\) 0 0
\(196\) −1.50619 −0.107585
\(197\) −26.4478 −1.88433 −0.942165 0.335149i \(-0.891213\pi\)
−0.942165 + 0.335149i \(0.891213\pi\)
\(198\) 0 0
\(199\) −2.65055 −0.187892 −0.0939462 0.995577i \(-0.529948\pi\)
−0.0939462 + 0.995577i \(0.529948\pi\)
\(200\) 14.7397 1.04226
\(201\) 0 0
\(202\) −16.5016 −1.16105
\(203\) −3.03232 −0.212827
\(204\) 0 0
\(205\) 1.94894 0.136120
\(206\) 11.5932 0.807737
\(207\) 0 0
\(208\) −6.53091 −0.452837
\(209\) −0.940725 −0.0650713
\(210\) 0 0
\(211\) 16.6333 1.14509 0.572543 0.819875i \(-0.305957\pi\)
0.572543 + 0.819875i \(0.305957\pi\)
\(212\) 7.07341 0.485804
\(213\) 0 0
\(214\) −19.2890 −1.31857
\(215\) −1.58755 −0.108270
\(216\) 0 0
\(217\) −16.9487 −1.15055
\(218\) 19.4179 1.31515
\(219\) 0 0
\(220\) −0.392537 −0.0264649
\(221\) 4.73738 0.318671
\(222\) 0 0
\(223\) 2.74786 0.184010 0.0920052 0.995759i \(-0.470672\pi\)
0.0920052 + 0.995759i \(0.470672\pi\)
\(224\) −11.1765 −0.746765
\(225\) 0 0
\(226\) −16.5136 −1.09847
\(227\) −14.8829 −0.987814 −0.493907 0.869515i \(-0.664432\pi\)
−0.493907 + 0.869515i \(0.664432\pi\)
\(228\) 0 0
\(229\) −18.8535 −1.24588 −0.622939 0.782271i \(-0.714061\pi\)
−0.622939 + 0.782271i \(0.714061\pi\)
\(230\) 0.528691 0.0348608
\(231\) 0 0
\(232\) −3.07895 −0.202143
\(233\) 0.877423 0.0574819 0.0287409 0.999587i \(-0.490850\pi\)
0.0287409 + 0.999587i \(0.490850\pi\)
\(234\) 0 0
\(235\) −6.03638 −0.393770
\(236\) −1.08954 −0.0709229
\(237\) 0 0
\(238\) −5.43760 −0.352467
\(239\) −16.3766 −1.05931 −0.529655 0.848213i \(-0.677679\pi\)
−0.529655 + 0.848213i \(0.677679\pi\)
\(240\) 0 0
\(241\) −22.2101 −1.43068 −0.715339 0.698778i \(-0.753727\pi\)
−0.715339 + 0.698778i \(0.753727\pi\)
\(242\) −10.8453 −0.697163
\(243\) 0 0
\(244\) 7.69407 0.492562
\(245\) 1.01244 0.0646824
\(246\) 0 0
\(247\) −2.29687 −0.146146
\(248\) −17.2093 −1.09279
\(249\) 0 0
\(250\) −5.17443 −0.327260
\(251\) 26.0956 1.64714 0.823571 0.567214i \(-0.191979\pi\)
0.823571 + 0.567214i \(0.191979\pi\)
\(252\) 0 0
\(253\) 1.24022 0.0779720
\(254\) 2.91275 0.182762
\(255\) 0 0
\(256\) −14.3083 −0.894269
\(257\) −10.7098 −0.668061 −0.334031 0.942562i \(-0.608409\pi\)
−0.334031 + 0.942562i \(0.608409\pi\)
\(258\) 0 0
\(259\) −34.4997 −2.14371
\(260\) −0.958417 −0.0594385
\(261\) 0 0
\(262\) −4.25463 −0.262852
\(263\) 7.99789 0.493171 0.246585 0.969121i \(-0.420691\pi\)
0.246585 + 0.969121i \(0.420691\pi\)
\(264\) 0 0
\(265\) −4.75465 −0.292076
\(266\) 2.63636 0.161646
\(267\) 0 0
\(268\) 3.41287 0.208474
\(269\) −7.58114 −0.462230 −0.231115 0.972926i \(-0.574237\pi\)
−0.231115 + 0.972926i \(0.574237\pi\)
\(270\) 0 0
\(271\) 2.48450 0.150923 0.0754613 0.997149i \(-0.475957\pi\)
0.0754613 + 0.997149i \(0.475957\pi\)
\(272\) −3.37417 −0.204589
\(273\) 0 0
\(274\) −10.2955 −0.621973
\(275\) −5.93725 −0.358029
\(276\) 0 0
\(277\) −1.86945 −0.112324 −0.0561621 0.998422i \(-0.517886\pi\)
−0.0561621 + 0.998422i \(0.517886\pi\)
\(278\) 2.44999 0.146941
\(279\) 0 0
\(280\) 4.30640 0.257357
\(281\) 19.7896 1.18055 0.590273 0.807204i \(-0.299020\pi\)
0.590273 + 0.807204i \(0.299020\pi\)
\(282\) 0 0
\(283\) 1.71272 0.101811 0.0509054 0.998703i \(-0.483789\pi\)
0.0509054 + 0.998703i \(0.483789\pi\)
\(284\) −2.14728 −0.127418
\(285\) 0 0
\(286\) 4.30465 0.254539
\(287\) −12.8126 −0.756306
\(288\) 0 0
\(289\) −14.5525 −0.856027
\(290\) 0.528691 0.0310458
\(291\) 0 0
\(292\) 9.33692 0.546402
\(293\) 10.0342 0.586202 0.293101 0.956081i \(-0.405313\pi\)
0.293101 + 0.956081i \(0.405313\pi\)
\(294\) 0 0
\(295\) 0.732373 0.0426404
\(296\) −35.0302 −2.03609
\(297\) 0 0
\(298\) 20.2207 1.17135
\(299\) 3.02812 0.175121
\(300\) 0 0
\(301\) 10.4368 0.601565
\(302\) −6.21015 −0.357354
\(303\) 0 0
\(304\) 1.63593 0.0938269
\(305\) −5.17185 −0.296139
\(306\) 0 0
\(307\) −9.23516 −0.527079 −0.263539 0.964649i \(-0.584890\pi\)
−0.263539 + 0.964649i \(0.584890\pi\)
\(308\) 2.58060 0.147043
\(309\) 0 0
\(310\) 2.95503 0.167834
\(311\) 26.4506 1.49988 0.749938 0.661509i \(-0.230083\pi\)
0.749938 + 0.661509i \(0.230083\pi\)
\(312\) 0 0
\(313\) −33.1867 −1.87582 −0.937912 0.346874i \(-0.887243\pi\)
−0.937912 + 0.346874i \(0.887243\pi\)
\(314\) −21.9853 −1.24070
\(315\) 0 0
\(316\) −4.08334 −0.229706
\(317\) 12.6620 0.711171 0.355586 0.934644i \(-0.384281\pi\)
0.355586 + 0.934644i \(0.384281\pi\)
\(318\) 0 0
\(319\) 1.24022 0.0694390
\(320\) 3.93825 0.220155
\(321\) 0 0
\(322\) −3.47569 −0.193693
\(323\) −1.18667 −0.0660279
\(324\) 0 0
\(325\) −14.4964 −0.804113
\(326\) −17.4831 −0.968301
\(327\) 0 0
\(328\) −13.0097 −0.718338
\(329\) 39.6841 2.18785
\(330\) 0 0
\(331\) 21.9555 1.20678 0.603391 0.797446i \(-0.293816\pi\)
0.603391 + 0.797446i \(0.293816\pi\)
\(332\) −1.35316 −0.0742641
\(333\) 0 0
\(334\) 10.7405 0.587692
\(335\) −2.29409 −0.125339
\(336\) 0 0
\(337\) 2.06225 0.112338 0.0561690 0.998421i \(-0.482111\pi\)
0.0561690 + 0.998421i \(0.482111\pi\)
\(338\) −4.39057 −0.238816
\(339\) 0 0
\(340\) −0.495162 −0.0268539
\(341\) 6.93200 0.375389
\(342\) 0 0
\(343\) 14.5703 0.786724
\(344\) 10.5973 0.571366
\(345\) 0 0
\(346\) 5.82828 0.313330
\(347\) −7.14692 −0.383667 −0.191833 0.981428i \(-0.561443\pi\)
−0.191833 + 0.981428i \(0.561443\pi\)
\(348\) 0 0
\(349\) −14.7917 −0.791783 −0.395892 0.918297i \(-0.629564\pi\)
−0.395892 + 0.918297i \(0.629564\pi\)
\(350\) 16.6390 0.889393
\(351\) 0 0
\(352\) 4.57121 0.243646
\(353\) 35.3093 1.87933 0.939663 0.342101i \(-0.111138\pi\)
0.939663 + 0.342101i \(0.111138\pi\)
\(354\) 0 0
\(355\) 1.44337 0.0766063
\(356\) 2.16066 0.114515
\(357\) 0 0
\(358\) 15.9315 0.842004
\(359\) −34.6918 −1.83097 −0.915483 0.402358i \(-0.868191\pi\)
−0.915483 + 0.402358i \(0.868191\pi\)
\(360\) 0 0
\(361\) −18.4247 −0.969719
\(362\) 16.5848 0.871679
\(363\) 0 0
\(364\) 6.30078 0.330251
\(365\) −6.27615 −0.328509
\(366\) 0 0
\(367\) −6.78620 −0.354237 −0.177118 0.984190i \(-0.556678\pi\)
−0.177118 + 0.984190i \(0.556678\pi\)
\(368\) −2.15675 −0.112429
\(369\) 0 0
\(370\) 6.01508 0.312709
\(371\) 31.2578 1.62282
\(372\) 0 0
\(373\) −31.1069 −1.61065 −0.805326 0.592832i \(-0.798010\pi\)
−0.805326 + 0.592832i \(0.798010\pi\)
\(374\) 2.22398 0.114999
\(375\) 0 0
\(376\) 40.2943 2.07802
\(377\) 3.02812 0.155956
\(378\) 0 0
\(379\) −37.0062 −1.90088 −0.950441 0.310904i \(-0.899368\pi\)
−0.950441 + 0.310904i \(0.899368\pi\)
\(380\) 0.240074 0.0123155
\(381\) 0 0
\(382\) 13.8719 0.709750
\(383\) −0.396982 −0.0202848 −0.0101424 0.999949i \(-0.503228\pi\)
−0.0101424 + 0.999949i \(0.503228\pi\)
\(384\) 0 0
\(385\) −1.73465 −0.0884057
\(386\) −5.18556 −0.263938
\(387\) 0 0
\(388\) 9.69474 0.492176
\(389\) −4.09069 −0.207406 −0.103703 0.994608i \(-0.533069\pi\)
−0.103703 + 0.994608i \(0.533069\pi\)
\(390\) 0 0
\(391\) 1.56446 0.0791183
\(392\) −6.75828 −0.341345
\(393\) 0 0
\(394\) −30.3149 −1.52724
\(395\) 2.74477 0.138104
\(396\) 0 0
\(397\) 3.63819 0.182596 0.0912978 0.995824i \(-0.470898\pi\)
0.0912978 + 0.995824i \(0.470898\pi\)
\(398\) −3.03810 −0.152286
\(399\) 0 0
\(400\) 10.3249 0.516246
\(401\) −17.3710 −0.867466 −0.433733 0.901042i \(-0.642804\pi\)
−0.433733 + 0.901042i \(0.642804\pi\)
\(402\) 0 0
\(403\) 16.9251 0.843101
\(404\) 9.87885 0.491491
\(405\) 0 0
\(406\) −3.47569 −0.172496
\(407\) 14.1104 0.699425
\(408\) 0 0
\(409\) 13.3595 0.660586 0.330293 0.943878i \(-0.392852\pi\)
0.330293 + 0.943878i \(0.392852\pi\)
\(410\) 2.23390 0.110325
\(411\) 0 0
\(412\) −6.94038 −0.341928
\(413\) −4.81473 −0.236917
\(414\) 0 0
\(415\) 0.909574 0.0446492
\(416\) 11.1610 0.547215
\(417\) 0 0
\(418\) −1.07827 −0.0527400
\(419\) 5.58865 0.273023 0.136512 0.990638i \(-0.456411\pi\)
0.136512 + 0.990638i \(0.456411\pi\)
\(420\) 0 0
\(421\) 19.4449 0.947687 0.473843 0.880609i \(-0.342866\pi\)
0.473843 + 0.880609i \(0.342866\pi\)
\(422\) 19.0654 0.928088
\(423\) 0 0
\(424\) 31.7385 1.54136
\(425\) −7.48948 −0.363293
\(426\) 0 0
\(427\) 34.0005 1.64540
\(428\) 11.5476 0.558173
\(429\) 0 0
\(430\) −1.81967 −0.0877522
\(431\) −2.38531 −0.114896 −0.0574481 0.998348i \(-0.518296\pi\)
−0.0574481 + 0.998348i \(0.518296\pi\)
\(432\) 0 0
\(433\) 5.06699 0.243504 0.121752 0.992561i \(-0.461149\pi\)
0.121752 + 0.992561i \(0.461149\pi\)
\(434\) −19.4268 −0.932516
\(435\) 0 0
\(436\) −11.6247 −0.556724
\(437\) −0.758514 −0.0362846
\(438\) 0 0
\(439\) −15.6379 −0.746354 −0.373177 0.927760i \(-0.621732\pi\)
−0.373177 + 0.927760i \(0.621732\pi\)
\(440\) −1.76132 −0.0839676
\(441\) 0 0
\(442\) 5.43005 0.258281
\(443\) 25.6358 1.21800 0.608998 0.793172i \(-0.291572\pi\)
0.608998 + 0.793172i \(0.291572\pi\)
\(444\) 0 0
\(445\) −1.45237 −0.0688490
\(446\) 3.14964 0.149140
\(447\) 0 0
\(448\) −25.8907 −1.22322
\(449\) 6.29801 0.297221 0.148611 0.988896i \(-0.452520\pi\)
0.148611 + 0.988896i \(0.452520\pi\)
\(450\) 0 0
\(451\) 5.24037 0.246759
\(452\) 9.88601 0.464999
\(453\) 0 0
\(454\) −17.0590 −0.800620
\(455\) −4.23530 −0.198554
\(456\) 0 0
\(457\) 4.88547 0.228533 0.114266 0.993450i \(-0.463548\pi\)
0.114266 + 0.993450i \(0.463548\pi\)
\(458\) −21.6102 −1.00978
\(459\) 0 0
\(460\) −0.316506 −0.0147572
\(461\) −9.79885 −0.456378 −0.228189 0.973617i \(-0.573280\pi\)
−0.228189 + 0.973617i \(0.573280\pi\)
\(462\) 0 0
\(463\) −6.06469 −0.281850 −0.140925 0.990020i \(-0.545008\pi\)
−0.140925 + 0.990020i \(0.545008\pi\)
\(464\) −2.15675 −0.100125
\(465\) 0 0
\(466\) 1.00571 0.0465888
\(467\) 25.8676 1.19701 0.598505 0.801119i \(-0.295762\pi\)
0.598505 + 0.801119i \(0.295762\pi\)
\(468\) 0 0
\(469\) 15.0817 0.696408
\(470\) −6.91898 −0.319149
\(471\) 0 0
\(472\) −4.88877 −0.225024
\(473\) −4.26864 −0.196272
\(474\) 0 0
\(475\) 3.63119 0.166611
\(476\) 3.25527 0.149205
\(477\) 0 0
\(478\) −18.7710 −0.858567
\(479\) −13.4965 −0.616673 −0.308336 0.951277i \(-0.599772\pi\)
−0.308336 + 0.951277i \(0.599772\pi\)
\(480\) 0 0
\(481\) 34.4518 1.57087
\(482\) −25.4575 −1.15956
\(483\) 0 0
\(484\) 6.49265 0.295121
\(485\) −6.51668 −0.295907
\(486\) 0 0
\(487\) −30.5042 −1.38228 −0.691139 0.722722i \(-0.742891\pi\)
−0.691139 + 0.722722i \(0.742891\pi\)
\(488\) 34.5234 1.56280
\(489\) 0 0
\(490\) 1.16047 0.0524249
\(491\) −35.2597 −1.59125 −0.795623 0.605792i \(-0.792856\pi\)
−0.795623 + 0.605792i \(0.792856\pi\)
\(492\) 0 0
\(493\) 1.56446 0.0704599
\(494\) −2.63271 −0.118451
\(495\) 0 0
\(496\) −12.0548 −0.541277
\(497\) −9.48896 −0.425638
\(498\) 0 0
\(499\) 18.0864 0.809658 0.404829 0.914392i \(-0.367331\pi\)
0.404829 + 0.914392i \(0.367331\pi\)
\(500\) 3.09772 0.138534
\(501\) 0 0
\(502\) 29.9112 1.33500
\(503\) 41.9591 1.87086 0.935432 0.353506i \(-0.115011\pi\)
0.935432 + 0.353506i \(0.115011\pi\)
\(504\) 0 0
\(505\) −6.64044 −0.295495
\(506\) 1.42156 0.0631960
\(507\) 0 0
\(508\) −1.74375 −0.0773663
\(509\) 0.134948 0.00598148 0.00299074 0.999996i \(-0.499048\pi\)
0.00299074 + 0.999996i \(0.499048\pi\)
\(510\) 0 0
\(511\) 41.2604 1.82525
\(512\) −21.2305 −0.938263
\(513\) 0 0
\(514\) −12.2758 −0.541461
\(515\) 4.66523 0.205575
\(516\) 0 0
\(517\) −16.2308 −0.713829
\(518\) −39.5440 −1.73747
\(519\) 0 0
\(520\) −4.30043 −0.188586
\(521\) 12.9612 0.567840 0.283920 0.958848i \(-0.408365\pi\)
0.283920 + 0.958848i \(0.408365\pi\)
\(522\) 0 0
\(523\) 23.8876 1.04453 0.522267 0.852782i \(-0.325087\pi\)
0.522267 + 0.852782i \(0.325087\pi\)
\(524\) 2.54708 0.111270
\(525\) 0 0
\(526\) 9.16729 0.399713
\(527\) 8.74430 0.380908
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) −5.44985 −0.236726
\(531\) 0 0
\(532\) −1.57828 −0.0684273
\(533\) 12.7949 0.554207
\(534\) 0 0
\(535\) −7.76212 −0.335586
\(536\) 15.3136 0.661447
\(537\) 0 0
\(538\) −8.68961 −0.374636
\(539\) 2.72228 0.117257
\(540\) 0 0
\(541\) −32.1719 −1.38318 −0.691588 0.722292i \(-0.743089\pi\)
−0.691588 + 0.722292i \(0.743089\pi\)
\(542\) 2.84777 0.122322
\(543\) 0 0
\(544\) 5.76630 0.247228
\(545\) 7.81399 0.334715
\(546\) 0 0
\(547\) −22.1022 −0.945022 −0.472511 0.881325i \(-0.656652\pi\)
−0.472511 + 0.881325i \(0.656652\pi\)
\(548\) 6.16349 0.263291
\(549\) 0 0
\(550\) −6.80536 −0.290181
\(551\) −0.758514 −0.0323138
\(552\) 0 0
\(553\) −18.0445 −0.767332
\(554\) −2.14279 −0.0910383
\(555\) 0 0
\(556\) −1.46671 −0.0622024
\(557\) 21.0377 0.891394 0.445697 0.895184i \(-0.352956\pi\)
0.445697 + 0.895184i \(0.352956\pi\)
\(558\) 0 0
\(559\) −10.4223 −0.440816
\(560\) 3.01656 0.127473
\(561\) 0 0
\(562\) 22.6831 0.956828
\(563\) 10.5927 0.446428 0.223214 0.974769i \(-0.428345\pi\)
0.223214 + 0.974769i \(0.428345\pi\)
\(564\) 0 0
\(565\) −6.64524 −0.279568
\(566\) 1.96315 0.0825172
\(567\) 0 0
\(568\) −9.63487 −0.404270
\(569\) 28.7234 1.20415 0.602074 0.798440i \(-0.294341\pi\)
0.602074 + 0.798440i \(0.294341\pi\)
\(570\) 0 0
\(571\) 3.70160 0.154907 0.0774535 0.996996i \(-0.475321\pi\)
0.0774535 + 0.996996i \(0.475321\pi\)
\(572\) −2.57702 −0.107751
\(573\) 0 0
\(574\) −14.6860 −0.612983
\(575\) −4.78725 −0.199642
\(576\) 0 0
\(577\) −31.7741 −1.32277 −0.661387 0.750045i \(-0.730032\pi\)
−0.661387 + 0.750045i \(0.730032\pi\)
\(578\) −16.6802 −0.693806
\(579\) 0 0
\(580\) −0.316506 −0.0131422
\(581\) −5.97968 −0.248079
\(582\) 0 0
\(583\) −12.7844 −0.529478
\(584\) 41.8949 1.73362
\(585\) 0 0
\(586\) 11.5013 0.475114
\(587\) 5.55049 0.229093 0.114547 0.993418i \(-0.463458\pi\)
0.114547 + 0.993418i \(0.463458\pi\)
\(588\) 0 0
\(589\) −4.23958 −0.174689
\(590\) 0.839456 0.0345599
\(591\) 0 0
\(592\) −24.5381 −1.00851
\(593\) 45.2481 1.85812 0.929058 0.369934i \(-0.120620\pi\)
0.929058 + 0.369934i \(0.120620\pi\)
\(594\) 0 0
\(595\) −2.18815 −0.0897054
\(596\) −12.1053 −0.495852
\(597\) 0 0
\(598\) 3.47087 0.141935
\(599\) −8.33358 −0.340501 −0.170251 0.985401i \(-0.554458\pi\)
−0.170251 + 0.985401i \(0.554458\pi\)
\(600\) 0 0
\(601\) −20.2780 −0.827158 −0.413579 0.910468i \(-0.635721\pi\)
−0.413579 + 0.910468i \(0.635721\pi\)
\(602\) 11.9628 0.487566
\(603\) 0 0
\(604\) 3.71777 0.151274
\(605\) −4.36427 −0.177433
\(606\) 0 0
\(607\) 46.1404 1.87278 0.936390 0.350962i \(-0.114145\pi\)
0.936390 + 0.350962i \(0.114145\pi\)
\(608\) −2.79573 −0.113382
\(609\) 0 0
\(610\) −5.92805 −0.240020
\(611\) −39.6290 −1.60322
\(612\) 0 0
\(613\) 39.2871 1.58679 0.793396 0.608706i \(-0.208311\pi\)
0.793396 + 0.608706i \(0.208311\pi\)
\(614\) −10.5855 −0.427195
\(615\) 0 0
\(616\) 11.5792 0.466538
\(617\) 38.1156 1.53448 0.767238 0.641362i \(-0.221630\pi\)
0.767238 + 0.641362i \(0.221630\pi\)
\(618\) 0 0
\(619\) −37.6762 −1.51433 −0.757167 0.653222i \(-0.773417\pi\)
−0.757167 + 0.653222i \(0.773417\pi\)
\(620\) −1.76906 −0.0710470
\(621\) 0 0
\(622\) 30.3180 1.21564
\(623\) 9.54811 0.382537
\(624\) 0 0
\(625\) 21.8540 0.874160
\(626\) −38.0391 −1.52035
\(627\) 0 0
\(628\) 13.1617 0.525211
\(629\) 17.7994 0.709708
\(630\) 0 0
\(631\) −24.2007 −0.963414 −0.481707 0.876332i \(-0.659983\pi\)
−0.481707 + 0.876332i \(0.659983\pi\)
\(632\) −18.3220 −0.728810
\(633\) 0 0
\(634\) 14.5134 0.576402
\(635\) 1.17212 0.0465143
\(636\) 0 0
\(637\) 6.64670 0.263352
\(638\) 1.42156 0.0562801
\(639\) 0 0
\(640\) 1.11394 0.0440322
\(641\) 34.1062 1.34711 0.673557 0.739135i \(-0.264766\pi\)
0.673557 + 0.739135i \(0.264766\pi\)
\(642\) 0 0
\(643\) −0.586521 −0.0231301 −0.0115651 0.999933i \(-0.503681\pi\)
−0.0115651 + 0.999933i \(0.503681\pi\)
\(644\) 2.08076 0.0819934
\(645\) 0 0
\(646\) −1.36018 −0.0535154
\(647\) −30.9753 −1.21776 −0.608882 0.793261i \(-0.708382\pi\)
−0.608882 + 0.793261i \(0.708382\pi\)
\(648\) 0 0
\(649\) 1.96922 0.0772988
\(650\) −16.6159 −0.651730
\(651\) 0 0
\(652\) 10.4664 0.409898
\(653\) 29.7907 1.16580 0.582900 0.812544i \(-0.301918\pi\)
0.582900 + 0.812544i \(0.301918\pi\)
\(654\) 0 0
\(655\) −1.71211 −0.0668977
\(656\) −9.11305 −0.355805
\(657\) 0 0
\(658\) 45.4865 1.77325
\(659\) 1.60411 0.0624871 0.0312436 0.999512i \(-0.490053\pi\)
0.0312436 + 0.999512i \(0.490053\pi\)
\(660\) 0 0
\(661\) −3.63035 −0.141204 −0.0706021 0.997505i \(-0.522492\pi\)
−0.0706021 + 0.997505i \(0.522492\pi\)
\(662\) 25.1657 0.978091
\(663\) 0 0
\(664\) −6.07163 −0.235625
\(665\) 1.06090 0.0411400
\(666\) 0 0
\(667\) 1.00000 0.0387202
\(668\) −6.42988 −0.248780
\(669\) 0 0
\(670\) −2.62952 −0.101587
\(671\) −13.9062 −0.536844
\(672\) 0 0
\(673\) −20.6602 −0.796390 −0.398195 0.917301i \(-0.630363\pi\)
−0.398195 + 0.917301i \(0.630363\pi\)
\(674\) 2.36378 0.0910495
\(675\) 0 0
\(676\) 2.62846 0.101095
\(677\) −19.9369 −0.766238 −0.383119 0.923699i \(-0.625150\pi\)
−0.383119 + 0.923699i \(0.625150\pi\)
\(678\) 0 0
\(679\) 42.8416 1.64411
\(680\) −2.22180 −0.0852020
\(681\) 0 0
\(682\) 7.94556 0.304251
\(683\) 32.8353 1.25641 0.628203 0.778049i \(-0.283791\pi\)
0.628203 + 0.778049i \(0.283791\pi\)
\(684\) 0 0
\(685\) −4.14302 −0.158297
\(686\) 16.7007 0.637637
\(687\) 0 0
\(688\) 7.42320 0.283007
\(689\) −31.2145 −1.18918
\(690\) 0 0
\(691\) 40.8340 1.55340 0.776699 0.629872i \(-0.216892\pi\)
0.776699 + 0.629872i \(0.216892\pi\)
\(692\) −3.48915 −0.132638
\(693\) 0 0
\(694\) −8.19190 −0.310960
\(695\) 0.985904 0.0373975
\(696\) 0 0
\(697\) 6.61041 0.250387
\(698\) −16.9545 −0.641737
\(699\) 0 0
\(700\) −9.96111 −0.376495
\(701\) −23.9089 −0.903028 −0.451514 0.892264i \(-0.649116\pi\)
−0.451514 + 0.892264i \(0.649116\pi\)
\(702\) 0 0
\(703\) −8.62984 −0.325481
\(704\) 10.5893 0.399099
\(705\) 0 0
\(706\) 40.4721 1.52319
\(707\) 43.6552 1.64182
\(708\) 0 0
\(709\) −7.52488 −0.282603 −0.141301 0.989967i \(-0.545129\pi\)
−0.141301 + 0.989967i \(0.545129\pi\)
\(710\) 1.65442 0.0620891
\(711\) 0 0
\(712\) 9.69493 0.363333
\(713\) 5.58933 0.209322
\(714\) 0 0
\(715\) 1.73224 0.0647821
\(716\) −9.53752 −0.356434
\(717\) 0 0
\(718\) −39.7643 −1.48399
\(719\) −42.2000 −1.57379 −0.786897 0.617084i \(-0.788314\pi\)
−0.786897 + 0.617084i \(0.788314\pi\)
\(720\) 0 0
\(721\) −30.6700 −1.14221
\(722\) −21.1186 −0.785953
\(723\) 0 0
\(724\) −9.92866 −0.368996
\(725\) −4.78725 −0.177794
\(726\) 0 0
\(727\) 26.6149 0.987093 0.493547 0.869719i \(-0.335700\pi\)
0.493547 + 0.869719i \(0.335700\pi\)
\(728\) 28.2717 1.04782
\(729\) 0 0
\(730\) −7.19382 −0.266255
\(731\) −5.38463 −0.199158
\(732\) 0 0
\(733\) −24.3128 −0.898015 −0.449007 0.893528i \(-0.648222\pi\)
−0.449007 + 0.893528i \(0.648222\pi\)
\(734\) −7.77844 −0.287107
\(735\) 0 0
\(736\) 3.68580 0.135860
\(737\) −6.16841 −0.227216
\(738\) 0 0
\(739\) −17.2467 −0.634429 −0.317214 0.948354i \(-0.602748\pi\)
−0.317214 + 0.948354i \(0.602748\pi\)
\(740\) −3.60098 −0.132375
\(741\) 0 0
\(742\) 35.8282 1.31529
\(743\) −27.2488 −0.999660 −0.499830 0.866124i \(-0.666604\pi\)
−0.499830 + 0.866124i \(0.666604\pi\)
\(744\) 0 0
\(745\) 8.13702 0.298117
\(746\) −35.6551 −1.30543
\(747\) 0 0
\(748\) −1.33141 −0.0486810
\(749\) 51.0294 1.86457
\(750\) 0 0
\(751\) −48.9353 −1.78567 −0.892836 0.450381i \(-0.851288\pi\)
−0.892836 + 0.450381i \(0.851288\pi\)
\(752\) 28.2255 1.02928
\(753\) 0 0
\(754\) 3.47087 0.126402
\(755\) −2.49903 −0.0909492
\(756\) 0 0
\(757\) −0.573928 −0.0208598 −0.0104299 0.999946i \(-0.503320\pi\)
−0.0104299 + 0.999946i \(0.503320\pi\)
\(758\) −42.4171 −1.54066
\(759\) 0 0
\(760\) 1.07722 0.0390747
\(761\) −47.1634 −1.70967 −0.854836 0.518898i \(-0.826342\pi\)
−0.854836 + 0.518898i \(0.826342\pi\)
\(762\) 0 0
\(763\) −51.3704 −1.85973
\(764\) −8.30457 −0.300449
\(765\) 0 0
\(766\) −0.455027 −0.0164408
\(767\) 4.80805 0.173609
\(768\) 0 0
\(769\) −40.2948 −1.45307 −0.726534 0.687130i \(-0.758870\pi\)
−0.726534 + 0.687130i \(0.758870\pi\)
\(770\) −1.98828 −0.0716525
\(771\) 0 0
\(772\) 3.10439 0.111729
\(773\) 2.89284 0.104048 0.0520241 0.998646i \(-0.483433\pi\)
0.0520241 + 0.998646i \(0.483433\pi\)
\(774\) 0 0
\(775\) −26.7575 −0.961158
\(776\) 43.5004 1.56157
\(777\) 0 0
\(778\) −4.68881 −0.168102
\(779\) −3.20499 −0.114831
\(780\) 0 0
\(781\) 3.88098 0.138872
\(782\) 1.79321 0.0641251
\(783\) 0 0
\(784\) −4.73407 −0.169074
\(785\) −8.84715 −0.315768
\(786\) 0 0
\(787\) 18.6559 0.665010 0.332505 0.943101i \(-0.392106\pi\)
0.332505 + 0.943101i \(0.392106\pi\)
\(788\) 18.1483 0.646507
\(789\) 0 0
\(790\) 3.14610 0.111933
\(791\) 43.6869 1.55333
\(792\) 0 0
\(793\) −33.9534 −1.20572
\(794\) 4.17015 0.147993
\(795\) 0 0
\(796\) 1.81879 0.0644652
\(797\) −21.1459 −0.749026 −0.374513 0.927222i \(-0.622190\pi\)
−0.374513 + 0.927222i \(0.622190\pi\)
\(798\) 0 0
\(799\) −20.4742 −0.724324
\(800\) −17.6448 −0.623840
\(801\) 0 0
\(802\) −19.9109 −0.703077
\(803\) −16.8755 −0.595524
\(804\) 0 0
\(805\) −1.39866 −0.0492962
\(806\) 19.3998 0.683330
\(807\) 0 0
\(808\) 44.3265 1.55940
\(809\) −3.28804 −0.115601 −0.0578007 0.998328i \(-0.518409\pi\)
−0.0578007 + 0.998328i \(0.518409\pi\)
\(810\) 0 0
\(811\) −2.39301 −0.0840299 −0.0420149 0.999117i \(-0.513378\pi\)
−0.0420149 + 0.999117i \(0.513378\pi\)
\(812\) 2.08076 0.0730203
\(813\) 0 0
\(814\) 16.1735 0.566881
\(815\) −7.03541 −0.246440
\(816\) 0 0
\(817\) 2.61068 0.0913362
\(818\) 15.3129 0.535403
\(819\) 0 0
\(820\) −1.33735 −0.0467022
\(821\) −33.4973 −1.16906 −0.584532 0.811370i \(-0.698722\pi\)
−0.584532 + 0.811370i \(0.698722\pi\)
\(822\) 0 0
\(823\) −45.2775 −1.57828 −0.789138 0.614216i \(-0.789472\pi\)
−0.789138 + 0.614216i \(0.789472\pi\)
\(824\) −31.1416 −1.08487
\(825\) 0 0
\(826\) −5.51871 −0.192021
\(827\) 32.4045 1.12682 0.563408 0.826179i \(-0.309490\pi\)
0.563408 + 0.826179i \(0.309490\pi\)
\(828\) 0 0
\(829\) 15.1470 0.526076 0.263038 0.964786i \(-0.415276\pi\)
0.263038 + 0.964786i \(0.415276\pi\)
\(830\) 1.04257 0.0361880
\(831\) 0 0
\(832\) 25.8548 0.896353
\(833\) 3.43399 0.118981
\(834\) 0 0
\(835\) 4.32208 0.149572
\(836\) 0.645518 0.0223257
\(837\) 0 0
\(838\) 6.40579 0.221284
\(839\) 41.2271 1.42332 0.711658 0.702526i \(-0.247944\pi\)
0.711658 + 0.702526i \(0.247944\pi\)
\(840\) 0 0
\(841\) 1.00000 0.0344828
\(842\) 22.2880 0.768096
\(843\) 0 0
\(844\) −11.4137 −0.392875
\(845\) −1.76682 −0.0607803
\(846\) 0 0
\(847\) 28.6914 0.985848
\(848\) 22.2323 0.763459
\(849\) 0 0
\(850\) −8.58455 −0.294448
\(851\) 11.3773 0.390009
\(852\) 0 0
\(853\) −13.5149 −0.462741 −0.231370 0.972866i \(-0.574321\pi\)
−0.231370 + 0.972866i \(0.574321\pi\)
\(854\) 38.9719 1.33359
\(855\) 0 0
\(856\) 51.8141 1.77097
\(857\) −44.7861 −1.52986 −0.764932 0.644111i \(-0.777227\pi\)
−0.764932 + 0.644111i \(0.777227\pi\)
\(858\) 0 0
\(859\) 41.0825 1.40172 0.700859 0.713300i \(-0.252800\pi\)
0.700859 + 0.713300i \(0.252800\pi\)
\(860\) 1.08936 0.0371469
\(861\) 0 0
\(862\) −2.73407 −0.0931229
\(863\) −35.5358 −1.20965 −0.604827 0.796357i \(-0.706758\pi\)
−0.604827 + 0.796357i \(0.706758\pi\)
\(864\) 0 0
\(865\) 2.34536 0.0797448
\(866\) 5.80786 0.197359
\(867\) 0 0
\(868\) 11.6300 0.394749
\(869\) 7.38022 0.250357
\(870\) 0 0
\(871\) −15.0608 −0.510315
\(872\) −52.1603 −1.76637
\(873\) 0 0
\(874\) −0.869420 −0.0294086
\(875\) 13.6890 0.462773
\(876\) 0 0
\(877\) 26.6815 0.900970 0.450485 0.892784i \(-0.351251\pi\)
0.450485 + 0.892784i \(0.351251\pi\)
\(878\) −17.9243 −0.604917
\(879\) 0 0
\(880\) −1.23377 −0.0415905
\(881\) 47.6041 1.60382 0.801911 0.597444i \(-0.203817\pi\)
0.801911 + 0.597444i \(0.203817\pi\)
\(882\) 0 0
\(883\) 9.91948 0.333817 0.166909 0.985972i \(-0.446622\pi\)
0.166909 + 0.985972i \(0.446622\pi\)
\(884\) −3.25076 −0.109335
\(885\) 0 0
\(886\) 29.3842 0.987180
\(887\) −50.8435 −1.70716 −0.853578 0.520965i \(-0.825572\pi\)
−0.853578 + 0.520965i \(0.825572\pi\)
\(888\) 0 0
\(889\) −7.70572 −0.258442
\(890\) −1.66473 −0.0558018
\(891\) 0 0
\(892\) −1.88556 −0.0631333
\(893\) 9.92668 0.332184
\(894\) 0 0
\(895\) 6.41100 0.214296
\(896\) −7.32318 −0.244650
\(897\) 0 0
\(898\) 7.21887 0.240897
\(899\) 5.58933 0.186414
\(900\) 0 0
\(901\) −16.1268 −0.537262
\(902\) 6.00659 0.199997
\(903\) 0 0
\(904\) 44.3586 1.47535
\(905\) 6.67392 0.221849
\(906\) 0 0
\(907\) −34.5190 −1.14618 −0.573092 0.819491i \(-0.694256\pi\)
−0.573092 + 0.819491i \(0.694256\pi\)
\(908\) 10.2126 0.338915
\(909\) 0 0
\(910\) −4.85457 −0.160927
\(911\) 41.7823 1.38431 0.692155 0.721749i \(-0.256661\pi\)
0.692155 + 0.721749i \(0.256661\pi\)
\(912\) 0 0
\(913\) 2.44569 0.0809405
\(914\) 5.59979 0.185225
\(915\) 0 0
\(916\) 12.9372 0.427456
\(917\) 11.2557 0.371695
\(918\) 0 0
\(919\) −1.38061 −0.0455422 −0.0227711 0.999741i \(-0.507249\pi\)
−0.0227711 + 0.999741i \(0.507249\pi\)
\(920\) −1.42017 −0.0468215
\(921\) 0 0
\(922\) −11.2316 −0.369892
\(923\) 9.47579 0.311899
\(924\) 0 0
\(925\) −54.4660 −1.79083
\(926\) −6.95144 −0.228439
\(927\) 0 0
\(928\) 3.68580 0.120992
\(929\) −35.2819 −1.15756 −0.578781 0.815483i \(-0.696471\pi\)
−0.578781 + 0.815483i \(0.696471\pi\)
\(930\) 0 0
\(931\) −1.66493 −0.0545660
\(932\) −0.602081 −0.0197218
\(933\) 0 0
\(934\) 29.6498 0.970171
\(935\) 0.894954 0.0292681
\(936\) 0 0
\(937\) −29.8035 −0.973638 −0.486819 0.873503i \(-0.661843\pi\)
−0.486819 + 0.873503i \(0.661843\pi\)
\(938\) 17.2869 0.564436
\(939\) 0 0
\(940\) 4.14212 0.135101
\(941\) −2.97294 −0.0969150 −0.0484575 0.998825i \(-0.515431\pi\)
−0.0484575 + 0.998825i \(0.515431\pi\)
\(942\) 0 0
\(943\) 4.22535 0.137596
\(944\) −3.42450 −0.111458
\(945\) 0 0
\(946\) −4.89278 −0.159078
\(947\) −53.9229 −1.75226 −0.876130 0.482075i \(-0.839883\pi\)
−0.876130 + 0.482075i \(0.839883\pi\)
\(948\) 0 0
\(949\) −41.2032 −1.33751
\(950\) 4.16213 0.135037
\(951\) 0 0
\(952\) 14.6064 0.473397
\(953\) 29.7467 0.963591 0.481796 0.876284i \(-0.339985\pi\)
0.481796 + 0.876284i \(0.339985\pi\)
\(954\) 0 0
\(955\) 5.58222 0.180637
\(956\) 11.2375 0.363446
\(957\) 0 0
\(958\) −15.4699 −0.499811
\(959\) 27.2368 0.879523
\(960\) 0 0
\(961\) 0.240574 0.00776044
\(962\) 39.4892 1.27318
\(963\) 0 0
\(964\) 15.2404 0.490860
\(965\) −2.08673 −0.0671742
\(966\) 0 0
\(967\) 36.8210 1.18408 0.592042 0.805907i \(-0.298322\pi\)
0.592042 + 0.805907i \(0.298322\pi\)
\(968\) 29.1326 0.936357
\(969\) 0 0
\(970\) −7.46951 −0.239832
\(971\) 4.91875 0.157850 0.0789251 0.996881i \(-0.474851\pi\)
0.0789251 + 0.996881i \(0.474851\pi\)
\(972\) 0 0
\(973\) −6.48149 −0.207787
\(974\) −34.9644 −1.12033
\(975\) 0 0
\(976\) 24.1830 0.774080
\(977\) −2.00780 −0.0642351 −0.0321175 0.999484i \(-0.510225\pi\)
−0.0321175 + 0.999484i \(0.510225\pi\)
\(978\) 0 0
\(979\) −3.90518 −0.124810
\(980\) −0.694729 −0.0221923
\(981\) 0 0
\(982\) −40.4151 −1.28970
\(983\) −17.0414 −0.543537 −0.271769 0.962363i \(-0.587609\pi\)
−0.271769 + 0.962363i \(0.587609\pi\)
\(984\) 0 0
\(985\) −12.1991 −0.388694
\(986\) 1.79321 0.0571075
\(987\) 0 0
\(988\) 1.57609 0.0501423
\(989\) −3.44184 −0.109444
\(990\) 0 0
\(991\) 26.4632 0.840630 0.420315 0.907378i \(-0.361920\pi\)
0.420315 + 0.907378i \(0.361920\pi\)
\(992\) 20.6011 0.654087
\(993\) 0 0
\(994\) −10.8764 −0.344978
\(995\) −1.22256 −0.0387579
\(996\) 0 0
\(997\) 34.2493 1.08469 0.542343 0.840157i \(-0.317537\pi\)
0.542343 + 0.840157i \(0.317537\pi\)
\(998\) 20.7309 0.656225
\(999\) 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 \(a_p\))