Properties

Label 6003.2.a.t.1.17
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 1.17
Character \(\chi\) = 6003.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.16689 q^{2} -0.638362 q^{4} -1.66410 q^{5} -0.970636 q^{7} -3.07868 q^{8} +O(q^{10})\) \(q+1.16689 q^{2} -0.638362 q^{4} -1.66410 q^{5} -0.970636 q^{7} -3.07868 q^{8} -1.94183 q^{10} +3.13024 q^{11} +3.36483 q^{13} -1.13263 q^{14} -2.31577 q^{16} -3.46748 q^{17} +3.42577 q^{19} +1.06230 q^{20} +3.65265 q^{22} +1.00000 q^{23} -2.23076 q^{25} +3.92639 q^{26} +0.619617 q^{28} +1.00000 q^{29} -6.67837 q^{31} +3.45511 q^{32} -4.04618 q^{34} +1.61524 q^{35} -3.48322 q^{37} +3.99751 q^{38} +5.12325 q^{40} +7.11748 q^{41} +5.93664 q^{43} -1.99822 q^{44} +1.16689 q^{46} +6.42522 q^{47} -6.05787 q^{49} -2.60305 q^{50} -2.14798 q^{52} +8.21082 q^{53} -5.20904 q^{55} +2.98828 q^{56} +1.16689 q^{58} -13.8303 q^{59} -1.90373 q^{61} -7.79294 q^{62} +8.66329 q^{64} -5.59943 q^{65} -0.345727 q^{67} +2.21351 q^{68} +1.88481 q^{70} -9.30966 q^{71} +2.86037 q^{73} -4.06455 q^{74} -2.18688 q^{76} -3.03832 q^{77} +3.43789 q^{79} +3.85368 q^{80} +8.30533 q^{82} +1.04752 q^{83} +5.77025 q^{85} +6.92743 q^{86} -9.63701 q^{88} -9.73586 q^{89} -3.26602 q^{91} -0.638362 q^{92} +7.49754 q^{94} -5.70084 q^{95} -8.02056 q^{97} -7.06888 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 22q - 3q^{2} + 17q^{4} - 6q^{7} - 6q^{8} + O(q^{10}) \) \( 22q - 3q^{2} + 17q^{4} - 6q^{7} - 6q^{8} - 12q^{10} - 28q^{13} - q^{14} + 3q^{16} - 10q^{17} - 8q^{19} - 11q^{22} + 22q^{23} + 11q^{26} - 21q^{28} + 22q^{29} - 18q^{31} + 5q^{32} - 33q^{34} + 2q^{35} - 28q^{37} + 14q^{38} - 30q^{40} - 10q^{41} - 14q^{43} + 37q^{44} - 3q^{46} - 18q^{47} + 2q^{49} + 7q^{50} - 57q^{52} + 20q^{53} - 42q^{55} - 2q^{56} - 3q^{58} - 20q^{59} - 38q^{61} + 4q^{62} - 24q^{64} + 12q^{65} - 50q^{67} + 11q^{68} - 48q^{70} + 12q^{71} - 46q^{73} - 6q^{74} - 16q^{76} - 14q^{77} - 20q^{79} - 58q^{80} - 42q^{82} + 22q^{83} - 66q^{85} + 22q^{86} - 68q^{88} - 14q^{89} - 16q^{91} + 17q^{92} - 27q^{94} - 20q^{95} - 48q^{97} - 28q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.16689 0.825118 0.412559 0.910931i \(-0.364635\pi\)
0.412559 + 0.910931i \(0.364635\pi\)
\(3\) 0 0
\(4\) −0.638362 −0.319181
\(5\) −1.66410 −0.744210 −0.372105 0.928191i \(-0.621364\pi\)
−0.372105 + 0.928191i \(0.621364\pi\)
\(6\) 0 0
\(7\) −0.970636 −0.366866 −0.183433 0.983032i \(-0.558721\pi\)
−0.183433 + 0.983032i \(0.558721\pi\)
\(8\) −3.07868 −1.08848
\(9\) 0 0
\(10\) −1.94183 −0.614061
\(11\) 3.13024 0.943802 0.471901 0.881652i \(-0.343568\pi\)
0.471901 + 0.881652i \(0.343568\pi\)
\(12\) 0 0
\(13\) 3.36483 0.933236 0.466618 0.884459i \(-0.345472\pi\)
0.466618 + 0.884459i \(0.345472\pi\)
\(14\) −1.13263 −0.302707
\(15\) 0 0
\(16\) −2.31577 −0.578943
\(17\) −3.46748 −0.840988 −0.420494 0.907295i \(-0.638143\pi\)
−0.420494 + 0.907295i \(0.638143\pi\)
\(18\) 0 0
\(19\) 3.42577 0.785926 0.392963 0.919554i \(-0.371450\pi\)
0.392963 + 0.919554i \(0.371450\pi\)
\(20\) 1.06230 0.237538
\(21\) 0 0
\(22\) 3.65265 0.778748
\(23\) 1.00000 0.208514
\(24\) 0 0
\(25\) −2.23076 −0.446151
\(26\) 3.92639 0.770029
\(27\) 0 0
\(28\) 0.619617 0.117097
\(29\) 1.00000 0.185695
\(30\) 0 0
\(31\) −6.67837 −1.19947 −0.599735 0.800199i \(-0.704727\pi\)
−0.599735 + 0.800199i \(0.704727\pi\)
\(32\) 3.45511 0.610784
\(33\) 0 0
\(34\) −4.04618 −0.693914
\(35\) 1.61524 0.273025
\(36\) 0 0
\(37\) −3.48322 −0.572638 −0.286319 0.958134i \(-0.592432\pi\)
−0.286319 + 0.958134i \(0.592432\pi\)
\(38\) 3.99751 0.648481
\(39\) 0 0
\(40\) 5.12325 0.810058
\(41\) 7.11748 1.11156 0.555782 0.831328i \(-0.312419\pi\)
0.555782 + 0.831328i \(0.312419\pi\)
\(42\) 0 0
\(43\) 5.93664 0.905330 0.452665 0.891681i \(-0.350473\pi\)
0.452665 + 0.891681i \(0.350473\pi\)
\(44\) −1.99822 −0.301244
\(45\) 0 0
\(46\) 1.16689 0.172049
\(47\) 6.42522 0.937215 0.468607 0.883407i \(-0.344756\pi\)
0.468607 + 0.883407i \(0.344756\pi\)
\(48\) 0 0
\(49\) −6.05787 −0.865409
\(50\) −2.60305 −0.368127
\(51\) 0 0
\(52\) −2.14798 −0.297871
\(53\) 8.21082 1.12784 0.563921 0.825828i \(-0.309292\pi\)
0.563921 + 0.825828i \(0.309292\pi\)
\(54\) 0 0
\(55\) −5.20904 −0.702387
\(56\) 2.98828 0.399326
\(57\) 0 0
\(58\) 1.16689 0.153220
\(59\) −13.8303 −1.80056 −0.900278 0.435315i \(-0.856637\pi\)
−0.900278 + 0.435315i \(0.856637\pi\)
\(60\) 0 0
\(61\) −1.90373 −0.243748 −0.121874 0.992546i \(-0.538890\pi\)
−0.121874 + 0.992546i \(0.538890\pi\)
\(62\) −7.79294 −0.989704
\(63\) 0 0
\(64\) 8.66329 1.08291
\(65\) −5.59943 −0.694524
\(66\) 0 0
\(67\) −0.345727 −0.0422372 −0.0211186 0.999777i \(-0.506723\pi\)
−0.0211186 + 0.999777i \(0.506723\pi\)
\(68\) 2.21351 0.268427
\(69\) 0 0
\(70\) 1.88481 0.225278
\(71\) −9.30966 −1.10485 −0.552427 0.833561i \(-0.686298\pi\)
−0.552427 + 0.833561i \(0.686298\pi\)
\(72\) 0 0
\(73\) 2.86037 0.334781 0.167390 0.985891i \(-0.446466\pi\)
0.167390 + 0.985891i \(0.446466\pi\)
\(74\) −4.06455 −0.472494
\(75\) 0 0
\(76\) −2.18688 −0.250853
\(77\) −3.03832 −0.346249
\(78\) 0 0
\(79\) 3.43789 0.386793 0.193396 0.981121i \(-0.438050\pi\)
0.193396 + 0.981121i \(0.438050\pi\)
\(80\) 3.85368 0.430855
\(81\) 0 0
\(82\) 8.30533 0.917171
\(83\) 1.04752 0.114980 0.0574901 0.998346i \(-0.481690\pi\)
0.0574901 + 0.998346i \(0.481690\pi\)
\(84\) 0 0
\(85\) 5.77025 0.625872
\(86\) 6.92743 0.747004
\(87\) 0 0
\(88\) −9.63701 −1.02731
\(89\) −9.73586 −1.03200 −0.515999 0.856589i \(-0.672579\pi\)
−0.515999 + 0.856589i \(0.672579\pi\)
\(90\) 0 0
\(91\) −3.26602 −0.342372
\(92\) −0.638362 −0.0665538
\(93\) 0 0
\(94\) 7.49754 0.773312
\(95\) −5.70084 −0.584894
\(96\) 0 0
\(97\) −8.02056 −0.814364 −0.407182 0.913347i \(-0.633489\pi\)
−0.407182 + 0.913347i \(0.633489\pi\)
\(98\) −7.06888 −0.714065
\(99\) 0 0
\(100\) 1.42403 0.142403
\(101\) 14.3892 1.43178 0.715889 0.698215i \(-0.246022\pi\)
0.715889 + 0.698215i \(0.246022\pi\)
\(102\) 0 0
\(103\) −15.6662 −1.54364 −0.771818 0.635844i \(-0.780652\pi\)
−0.771818 + 0.635844i \(0.780652\pi\)
\(104\) −10.3592 −1.01581
\(105\) 0 0
\(106\) 9.58114 0.930603
\(107\) −6.90171 −0.667214 −0.333607 0.942712i \(-0.608266\pi\)
−0.333607 + 0.942712i \(0.608266\pi\)
\(108\) 0 0
\(109\) −11.1779 −1.07065 −0.535323 0.844647i \(-0.679810\pi\)
−0.535323 + 0.844647i \(0.679810\pi\)
\(110\) −6.07839 −0.579552
\(111\) 0 0
\(112\) 2.24777 0.212394
\(113\) −11.3063 −1.06360 −0.531802 0.846868i \(-0.678485\pi\)
−0.531802 + 0.846868i \(0.678485\pi\)
\(114\) 0 0
\(115\) −1.66410 −0.155179
\(116\) −0.638362 −0.0592704
\(117\) 0 0
\(118\) −16.1385 −1.48567
\(119\) 3.36566 0.308530
\(120\) 0 0
\(121\) −1.20161 −0.109238
\(122\) −2.22145 −0.201120
\(123\) 0 0
\(124\) 4.26322 0.382848
\(125\) 12.0327 1.07624
\(126\) 0 0
\(127\) 13.2943 1.17968 0.589840 0.807520i \(-0.299191\pi\)
0.589840 + 0.807520i \(0.299191\pi\)
\(128\) 3.19890 0.282745
\(129\) 0 0
\(130\) −6.53393 −0.573064
\(131\) 7.78581 0.680250 0.340125 0.940380i \(-0.389531\pi\)
0.340125 + 0.940380i \(0.389531\pi\)
\(132\) 0 0
\(133\) −3.32518 −0.288329
\(134\) −0.403426 −0.0348507
\(135\) 0 0
\(136\) 10.6753 0.915398
\(137\) −7.77414 −0.664189 −0.332095 0.943246i \(-0.607755\pi\)
−0.332095 + 0.943246i \(0.607755\pi\)
\(138\) 0 0
\(139\) −22.7573 −1.93025 −0.965123 0.261798i \(-0.915684\pi\)
−0.965123 + 0.261798i \(0.915684\pi\)
\(140\) −1.03111 −0.0871445
\(141\) 0 0
\(142\) −10.8634 −0.911634
\(143\) 10.5327 0.880790
\(144\) 0 0
\(145\) −1.66410 −0.138196
\(146\) 3.33774 0.276234
\(147\) 0 0
\(148\) 2.22356 0.182775
\(149\) −12.8192 −1.05019 −0.525093 0.851045i \(-0.675970\pi\)
−0.525093 + 0.851045i \(0.675970\pi\)
\(150\) 0 0
\(151\) −17.2566 −1.40432 −0.702159 0.712020i \(-0.747781\pi\)
−0.702159 + 0.712020i \(0.747781\pi\)
\(152\) −10.5469 −0.855464
\(153\) 0 0
\(154\) −3.54539 −0.285696
\(155\) 11.1135 0.892658
\(156\) 0 0
\(157\) −6.10782 −0.487457 −0.243728 0.969844i \(-0.578371\pi\)
−0.243728 + 0.969844i \(0.578371\pi\)
\(158\) 4.01165 0.319150
\(159\) 0 0
\(160\) −5.74967 −0.454551
\(161\) −0.970636 −0.0764968
\(162\) 0 0
\(163\) 19.4145 1.52066 0.760330 0.649537i \(-0.225037\pi\)
0.760330 + 0.649537i \(0.225037\pi\)
\(164\) −4.54353 −0.354790
\(165\) 0 0
\(166\) 1.22234 0.0948722
\(167\) 6.86540 0.531260 0.265630 0.964075i \(-0.414420\pi\)
0.265630 + 0.964075i \(0.414420\pi\)
\(168\) 0 0
\(169\) −1.67792 −0.129071
\(170\) 6.73327 0.516418
\(171\) 0 0
\(172\) −3.78973 −0.288964
\(173\) −5.77618 −0.439155 −0.219577 0.975595i \(-0.570468\pi\)
−0.219577 + 0.975595i \(0.570468\pi\)
\(174\) 0 0
\(175\) 2.16525 0.163678
\(176\) −7.24891 −0.546407
\(177\) 0 0
\(178\) −11.3607 −0.851520
\(179\) −19.9440 −1.49068 −0.745342 0.666682i \(-0.767714\pi\)
−0.745342 + 0.666682i \(0.767714\pi\)
\(180\) 0 0
\(181\) −7.56445 −0.562261 −0.281130 0.959670i \(-0.590709\pi\)
−0.281130 + 0.959670i \(0.590709\pi\)
\(182\) −3.81110 −0.282497
\(183\) 0 0
\(184\) −3.07868 −0.226964
\(185\) 5.79645 0.426163
\(186\) 0 0
\(187\) −10.8540 −0.793726
\(188\) −4.10162 −0.299141
\(189\) 0 0
\(190\) −6.65227 −0.482606
\(191\) −0.388024 −0.0280764 −0.0140382 0.999901i \(-0.504469\pi\)
−0.0140382 + 0.999901i \(0.504469\pi\)
\(192\) 0 0
\(193\) −6.75873 −0.486504 −0.243252 0.969963i \(-0.578214\pi\)
−0.243252 + 0.969963i \(0.578214\pi\)
\(194\) −9.35913 −0.671946
\(195\) 0 0
\(196\) 3.86711 0.276222
\(197\) 9.18467 0.654381 0.327190 0.944958i \(-0.393898\pi\)
0.327190 + 0.944958i \(0.393898\pi\)
\(198\) 0 0
\(199\) −3.41182 −0.241857 −0.120929 0.992661i \(-0.538587\pi\)
−0.120929 + 0.992661i \(0.538587\pi\)
\(200\) 6.86779 0.485626
\(201\) 0 0
\(202\) 16.7906 1.18138
\(203\) −0.970636 −0.0681253
\(204\) 0 0
\(205\) −11.8442 −0.827237
\(206\) −18.2808 −1.27368
\(207\) 0 0
\(208\) −7.79217 −0.540290
\(209\) 10.7235 0.741759
\(210\) 0 0
\(211\) −8.15205 −0.561210 −0.280605 0.959823i \(-0.590535\pi\)
−0.280605 + 0.959823i \(0.590535\pi\)
\(212\) −5.24147 −0.359986
\(213\) 0 0
\(214\) −8.05356 −0.550530
\(215\) −9.87920 −0.673756
\(216\) 0 0
\(217\) 6.48226 0.440045
\(218\) −13.0434 −0.883409
\(219\) 0 0
\(220\) 3.32525 0.224189
\(221\) −11.6675 −0.784840
\(222\) 0 0
\(223\) −18.2528 −1.22230 −0.611148 0.791516i \(-0.709292\pi\)
−0.611148 + 0.791516i \(0.709292\pi\)
\(224\) −3.35366 −0.224076
\(225\) 0 0
\(226\) −13.1932 −0.877599
\(227\) −21.0299 −1.39581 −0.697903 0.716193i \(-0.745883\pi\)
−0.697903 + 0.716193i \(0.745883\pi\)
\(228\) 0 0
\(229\) −2.19624 −0.145132 −0.0725659 0.997364i \(-0.523119\pi\)
−0.0725659 + 0.997364i \(0.523119\pi\)
\(230\) −1.94183 −0.128041
\(231\) 0 0
\(232\) −3.07868 −0.202126
\(233\) −17.1062 −1.12067 −0.560334 0.828267i \(-0.689327\pi\)
−0.560334 + 0.828267i \(0.689327\pi\)
\(234\) 0 0
\(235\) −10.6922 −0.697485
\(236\) 8.82876 0.574703
\(237\) 0 0
\(238\) 3.92737 0.254573
\(239\) 0.0237289 0.00153490 0.000767448 1.00000i \(-0.499756\pi\)
0.000767448 1.00000i \(0.499756\pi\)
\(240\) 0 0
\(241\) −18.0526 −1.16287 −0.581437 0.813592i \(-0.697509\pi\)
−0.581437 + 0.813592i \(0.697509\pi\)
\(242\) −1.40215 −0.0901338
\(243\) 0 0
\(244\) 1.21527 0.0777996
\(245\) 10.0809 0.644047
\(246\) 0 0
\(247\) 11.5271 0.733454
\(248\) 20.5606 1.30560
\(249\) 0 0
\(250\) 14.0409 0.888025
\(251\) −18.9850 −1.19833 −0.599163 0.800627i \(-0.704500\pi\)
−0.599163 + 0.800627i \(0.704500\pi\)
\(252\) 0 0
\(253\) 3.13024 0.196796
\(254\) 15.5130 0.973375
\(255\) 0 0
\(256\) −13.5938 −0.849613
\(257\) −7.95157 −0.496005 −0.248003 0.968759i \(-0.579774\pi\)
−0.248003 + 0.968759i \(0.579774\pi\)
\(258\) 0 0
\(259\) 3.38094 0.210082
\(260\) 3.57446 0.221679
\(261\) 0 0
\(262\) 9.08521 0.561286
\(263\) −6.77467 −0.417744 −0.208872 0.977943i \(-0.566979\pi\)
−0.208872 + 0.977943i \(0.566979\pi\)
\(264\) 0 0
\(265\) −13.6637 −0.839352
\(266\) −3.88012 −0.237906
\(267\) 0 0
\(268\) 0.220699 0.0134813
\(269\) 28.4683 1.73574 0.867872 0.496787i \(-0.165487\pi\)
0.867872 + 0.496787i \(0.165487\pi\)
\(270\) 0 0
\(271\) −21.1005 −1.28177 −0.640883 0.767639i \(-0.721432\pi\)
−0.640883 + 0.767639i \(0.721432\pi\)
\(272\) 8.02989 0.486884
\(273\) 0 0
\(274\) −9.07158 −0.548034
\(275\) −6.98280 −0.421078
\(276\) 0 0
\(277\) 22.0874 1.32710 0.663551 0.748131i \(-0.269049\pi\)
0.663551 + 0.748131i \(0.269049\pi\)
\(278\) −26.5553 −1.59268
\(279\) 0 0
\(280\) −4.97281 −0.297182
\(281\) 21.4004 1.27664 0.638320 0.769771i \(-0.279629\pi\)
0.638320 + 0.769771i \(0.279629\pi\)
\(282\) 0 0
\(283\) 14.7098 0.874406 0.437203 0.899363i \(-0.355969\pi\)
0.437203 + 0.899363i \(0.355969\pi\)
\(284\) 5.94293 0.352648
\(285\) 0 0
\(286\) 12.2905 0.726755
\(287\) −6.90848 −0.407795
\(288\) 0 0
\(289\) −4.97656 −0.292739
\(290\) −1.94183 −0.114028
\(291\) 0 0
\(292\) −1.82595 −0.106856
\(293\) 24.7990 1.44877 0.724387 0.689394i \(-0.242123\pi\)
0.724387 + 0.689394i \(0.242123\pi\)
\(294\) 0 0
\(295\) 23.0151 1.33999
\(296\) 10.7237 0.623305
\(297\) 0 0
\(298\) −14.9586 −0.866527
\(299\) 3.36483 0.194593
\(300\) 0 0
\(301\) −5.76232 −0.332135
\(302\) −20.1365 −1.15873
\(303\) 0 0
\(304\) −7.93330 −0.455006
\(305\) 3.16801 0.181400
\(306\) 0 0
\(307\) 32.1800 1.83661 0.918304 0.395877i \(-0.129559\pi\)
0.918304 + 0.395877i \(0.129559\pi\)
\(308\) 1.93955 0.110516
\(309\) 0 0
\(310\) 12.9683 0.736548
\(311\) −24.4553 −1.38673 −0.693366 0.720585i \(-0.743873\pi\)
−0.693366 + 0.720585i \(0.743873\pi\)
\(312\) 0 0
\(313\) 19.1018 1.07970 0.539848 0.841763i \(-0.318482\pi\)
0.539848 + 0.841763i \(0.318482\pi\)
\(314\) −7.12717 −0.402209
\(315\) 0 0
\(316\) −2.19462 −0.123457
\(317\) −0.189764 −0.0106582 −0.00532909 0.999986i \(-0.501696\pi\)
−0.00532909 + 0.999986i \(0.501696\pi\)
\(318\) 0 0
\(319\) 3.13024 0.175260
\(320\) −14.4166 −0.805913
\(321\) 0 0
\(322\) −1.13263 −0.0631189
\(323\) −11.8788 −0.660954
\(324\) 0 0
\(325\) −7.50611 −0.416364
\(326\) 22.6546 1.25472
\(327\) 0 0
\(328\) −21.9125 −1.20991
\(329\) −6.23655 −0.343832
\(330\) 0 0
\(331\) 1.51985 0.0835385 0.0417692 0.999127i \(-0.486701\pi\)
0.0417692 + 0.999127i \(0.486701\pi\)
\(332\) −0.668697 −0.0366995
\(333\) 0 0
\(334\) 8.01118 0.438352
\(335\) 0.575325 0.0314334
\(336\) 0 0
\(337\) −14.8217 −0.807389 −0.403694 0.914894i \(-0.632274\pi\)
−0.403694 + 0.914894i \(0.632274\pi\)
\(338\) −1.95796 −0.106499
\(339\) 0 0
\(340\) −3.68351 −0.199766
\(341\) −20.9049 −1.13206
\(342\) 0 0
\(343\) 12.6744 0.684355
\(344\) −18.2771 −0.985433
\(345\) 0 0
\(346\) −6.74018 −0.362355
\(347\) 0.764551 0.0410433 0.0205216 0.999789i \(-0.493467\pi\)
0.0205216 + 0.999789i \(0.493467\pi\)
\(348\) 0 0
\(349\) −18.8271 −1.00779 −0.503896 0.863764i \(-0.668101\pi\)
−0.503896 + 0.863764i \(0.668101\pi\)
\(350\) 2.52662 0.135053
\(351\) 0 0
\(352\) 10.8153 0.576459
\(353\) 19.6288 1.04473 0.522367 0.852721i \(-0.325049\pi\)
0.522367 + 0.852721i \(0.325049\pi\)
\(354\) 0 0
\(355\) 15.4922 0.822243
\(356\) 6.21500 0.329394
\(357\) 0 0
\(358\) −23.2725 −1.22999
\(359\) 8.40034 0.443353 0.221677 0.975120i \(-0.428847\pi\)
0.221677 + 0.975120i \(0.428847\pi\)
\(360\) 0 0
\(361\) −7.26409 −0.382321
\(362\) −8.82690 −0.463931
\(363\) 0 0
\(364\) 2.08491 0.109279
\(365\) −4.75995 −0.249147
\(366\) 0 0
\(367\) −30.7870 −1.60707 −0.803534 0.595260i \(-0.797049\pi\)
−0.803534 + 0.595260i \(0.797049\pi\)
\(368\) −2.31577 −0.120718
\(369\) 0 0
\(370\) 6.76383 0.351635
\(371\) −7.96972 −0.413767
\(372\) 0 0
\(373\) −3.79852 −0.196680 −0.0983399 0.995153i \(-0.531353\pi\)
−0.0983399 + 0.995153i \(0.531353\pi\)
\(374\) −12.6655 −0.654918
\(375\) 0 0
\(376\) −19.7812 −1.02014
\(377\) 3.36483 0.173298
\(378\) 0 0
\(379\) 10.4712 0.537867 0.268934 0.963159i \(-0.413329\pi\)
0.268934 + 0.963159i \(0.413329\pi\)
\(380\) 3.63920 0.186687
\(381\) 0 0
\(382\) −0.452783 −0.0231664
\(383\) −13.4398 −0.686740 −0.343370 0.939200i \(-0.611568\pi\)
−0.343370 + 0.939200i \(0.611568\pi\)
\(384\) 0 0
\(385\) 5.05608 0.257682
\(386\) −7.88671 −0.401423
\(387\) 0 0
\(388\) 5.12002 0.259930
\(389\) 29.5183 1.49664 0.748319 0.663339i \(-0.230861\pi\)
0.748319 + 0.663339i \(0.230861\pi\)
\(390\) 0 0
\(391\) −3.46748 −0.175358
\(392\) 18.6503 0.941980
\(393\) 0 0
\(394\) 10.7175 0.539941
\(395\) −5.72101 −0.287855
\(396\) 0 0
\(397\) −22.4511 −1.12679 −0.563394 0.826189i \(-0.690505\pi\)
−0.563394 + 0.826189i \(0.690505\pi\)
\(398\) −3.98123 −0.199561
\(399\) 0 0
\(400\) 5.16592 0.258296
\(401\) 31.5457 1.57532 0.787659 0.616111i \(-0.211293\pi\)
0.787659 + 0.616111i \(0.211293\pi\)
\(402\) 0 0
\(403\) −22.4716 −1.11939
\(404\) −9.18551 −0.456996
\(405\) 0 0
\(406\) −1.13263 −0.0562114
\(407\) −10.9033 −0.540457
\(408\) 0 0
\(409\) −36.5651 −1.80803 −0.904015 0.427501i \(-0.859394\pi\)
−0.904015 + 0.427501i \(0.859394\pi\)
\(410\) −13.8209 −0.682568
\(411\) 0 0
\(412\) 10.0007 0.492699
\(413\) 13.4242 0.660563
\(414\) 0 0
\(415\) −1.74318 −0.0855695
\(416\) 11.6259 0.570005
\(417\) 0 0
\(418\) 12.5131 0.612038
\(419\) 32.5009 1.58777 0.793887 0.608065i \(-0.208054\pi\)
0.793887 + 0.608065i \(0.208054\pi\)
\(420\) 0 0
\(421\) 22.1960 1.08177 0.540885 0.841097i \(-0.318090\pi\)
0.540885 + 0.841097i \(0.318090\pi\)
\(422\) −9.51256 −0.463064
\(423\) 0 0
\(424\) −25.2785 −1.22763
\(425\) 7.73511 0.375208
\(426\) 0 0
\(427\) 1.84783 0.0894227
\(428\) 4.40579 0.212962
\(429\) 0 0
\(430\) −11.5280 −0.555928
\(431\) −10.1047 −0.486726 −0.243363 0.969935i \(-0.578251\pi\)
−0.243363 + 0.969935i \(0.578251\pi\)
\(432\) 0 0
\(433\) 1.99683 0.0959617 0.0479808 0.998848i \(-0.484721\pi\)
0.0479808 + 0.998848i \(0.484721\pi\)
\(434\) 7.56410 0.363089
\(435\) 0 0
\(436\) 7.13553 0.341730
\(437\) 3.42577 0.163877
\(438\) 0 0
\(439\) −27.5731 −1.31599 −0.657997 0.753021i \(-0.728596\pi\)
−0.657997 + 0.753021i \(0.728596\pi\)
\(440\) 16.0370 0.764534
\(441\) 0 0
\(442\) −13.6147 −0.647585
\(443\) 11.2234 0.533240 0.266620 0.963802i \(-0.414093\pi\)
0.266620 + 0.963802i \(0.414093\pi\)
\(444\) 0 0
\(445\) 16.2015 0.768024
\(446\) −21.2990 −1.00854
\(447\) 0 0
\(448\) −8.40890 −0.397283
\(449\) 25.2119 1.18982 0.594911 0.803791i \(-0.297187\pi\)
0.594911 + 0.803791i \(0.297187\pi\)
\(450\) 0 0
\(451\) 22.2794 1.04910
\(452\) 7.21749 0.339482
\(453\) 0 0
\(454\) −24.5397 −1.15170
\(455\) 5.43501 0.254797
\(456\) 0 0
\(457\) 19.1195 0.894375 0.447187 0.894440i \(-0.352426\pi\)
0.447187 + 0.894440i \(0.352426\pi\)
\(458\) −2.56278 −0.119751
\(459\) 0 0
\(460\) 1.06230 0.0495300
\(461\) 28.0742 1.30754 0.653772 0.756692i \(-0.273186\pi\)
0.653772 + 0.756692i \(0.273186\pi\)
\(462\) 0 0
\(463\) −11.4780 −0.533430 −0.266715 0.963775i \(-0.585938\pi\)
−0.266715 + 0.963775i \(0.585938\pi\)
\(464\) −2.31577 −0.107507
\(465\) 0 0
\(466\) −19.9611 −0.924682
\(467\) 34.8739 1.61377 0.806886 0.590707i \(-0.201151\pi\)
0.806886 + 0.590707i \(0.201151\pi\)
\(468\) 0 0
\(469\) 0.335575 0.0154954
\(470\) −12.4767 −0.575507
\(471\) 0 0
\(472\) 42.5792 1.95987
\(473\) 18.5831 0.854452
\(474\) 0 0
\(475\) −7.64206 −0.350642
\(476\) −2.14851 −0.0984769
\(477\) 0 0
\(478\) 0.0276891 0.00126647
\(479\) 3.69004 0.168602 0.0843011 0.996440i \(-0.473134\pi\)
0.0843011 + 0.996440i \(0.473134\pi\)
\(480\) 0 0
\(481\) −11.7205 −0.534407
\(482\) −21.0655 −0.959507
\(483\) 0 0
\(484\) 0.767064 0.0348665
\(485\) 13.3470 0.606058
\(486\) 0 0
\(487\) −31.7082 −1.43684 −0.718418 0.695612i \(-0.755133\pi\)
−0.718418 + 0.695612i \(0.755133\pi\)
\(488\) 5.86098 0.265314
\(489\) 0 0
\(490\) 11.7634 0.531414
\(491\) 21.1652 0.955173 0.477587 0.878585i \(-0.341512\pi\)
0.477587 + 0.878585i \(0.341512\pi\)
\(492\) 0 0
\(493\) −3.46748 −0.156168
\(494\) 13.4509 0.605186
\(495\) 0 0
\(496\) 15.4656 0.694424
\(497\) 9.03629 0.405333
\(498\) 0 0
\(499\) 40.2349 1.80116 0.900582 0.434687i \(-0.143141\pi\)
0.900582 + 0.434687i \(0.143141\pi\)
\(500\) −7.68124 −0.343515
\(501\) 0 0
\(502\) −22.1535 −0.988759
\(503\) −5.43044 −0.242131 −0.121066 0.992644i \(-0.538631\pi\)
−0.121066 + 0.992644i \(0.538631\pi\)
\(504\) 0 0
\(505\) −23.9451 −1.06554
\(506\) 3.65265 0.162380
\(507\) 0 0
\(508\) −8.48659 −0.376531
\(509\) −0.165579 −0.00733915 −0.00366958 0.999993i \(-0.501168\pi\)
−0.00366958 + 0.999993i \(0.501168\pi\)
\(510\) 0 0
\(511\) −2.77638 −0.122820
\(512\) −22.2603 −0.983776
\(513\) 0 0
\(514\) −9.27862 −0.409263
\(515\) 26.0702 1.14879
\(516\) 0 0
\(517\) 20.1125 0.884545
\(518\) 3.94520 0.173342
\(519\) 0 0
\(520\) 17.2389 0.755975
\(521\) −2.11999 −0.0928786 −0.0464393 0.998921i \(-0.514787\pi\)
−0.0464393 + 0.998921i \(0.514787\pi\)
\(522\) 0 0
\(523\) −10.1662 −0.444538 −0.222269 0.974985i \(-0.571346\pi\)
−0.222269 + 0.974985i \(0.571346\pi\)
\(524\) −4.97017 −0.217123
\(525\) 0 0
\(526\) −7.90531 −0.344688
\(527\) 23.1571 1.00874
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) −15.9440 −0.692564
\(531\) 0 0
\(532\) 2.12267 0.0920293
\(533\) 23.9491 1.03735
\(534\) 0 0
\(535\) 11.4852 0.496547
\(536\) 1.06438 0.0459743
\(537\) 0 0
\(538\) 33.2195 1.43219
\(539\) −18.9626 −0.816775
\(540\) 0 0
\(541\) −17.0049 −0.731100 −0.365550 0.930792i \(-0.619119\pi\)
−0.365550 + 0.930792i \(0.619119\pi\)
\(542\) −24.6220 −1.05761
\(543\) 0 0
\(544\) −11.9806 −0.513662
\(545\) 18.6011 0.796786
\(546\) 0 0
\(547\) −5.79318 −0.247698 −0.123849 0.992301i \(-0.539524\pi\)
−0.123849 + 0.992301i \(0.539524\pi\)
\(548\) 4.96271 0.211997
\(549\) 0 0
\(550\) −8.14817 −0.347439
\(551\) 3.42577 0.145943
\(552\) 0 0
\(553\) −3.33694 −0.141901
\(554\) 25.7736 1.09502
\(555\) 0 0
\(556\) 14.5274 0.616097
\(557\) −11.4176 −0.483779 −0.241890 0.970304i \(-0.577767\pi\)
−0.241890 + 0.970304i \(0.577767\pi\)
\(558\) 0 0
\(559\) 19.9758 0.844886
\(560\) −3.74052 −0.158066
\(561\) 0 0
\(562\) 24.9720 1.05338
\(563\) 39.9407 1.68330 0.841650 0.540023i \(-0.181584\pi\)
0.841650 + 0.540023i \(0.181584\pi\)
\(564\) 0 0
\(565\) 18.8148 0.791546
\(566\) 17.1647 0.721488
\(567\) 0 0
\(568\) 28.6615 1.20261
\(569\) −9.79116 −0.410467 −0.205233 0.978713i \(-0.565795\pi\)
−0.205233 + 0.978713i \(0.565795\pi\)
\(570\) 0 0
\(571\) 29.3432 1.22798 0.613988 0.789315i \(-0.289564\pi\)
0.613988 + 0.789315i \(0.289564\pi\)
\(572\) −6.72368 −0.281131
\(573\) 0 0
\(574\) −8.06145 −0.336479
\(575\) −2.23076 −0.0930289
\(576\) 0 0
\(577\) −27.0324 −1.12537 −0.562687 0.826670i \(-0.690233\pi\)
−0.562687 + 0.826670i \(0.690233\pi\)
\(578\) −5.80711 −0.241544
\(579\) 0 0
\(580\) 1.06230 0.0441096
\(581\) −1.01676 −0.0421823
\(582\) 0 0
\(583\) 25.7018 1.06446
\(584\) −8.80618 −0.364402
\(585\) 0 0
\(586\) 28.9378 1.19541
\(587\) −4.30700 −0.177769 −0.0888845 0.996042i \(-0.528330\pi\)
−0.0888845 + 0.996042i \(0.528330\pi\)
\(588\) 0 0
\(589\) −22.8786 −0.942695
\(590\) 26.8562 1.10565
\(591\) 0 0
\(592\) 8.06635 0.331525
\(593\) −16.2048 −0.665453 −0.332727 0.943023i \(-0.607969\pi\)
−0.332727 + 0.943023i \(0.607969\pi\)
\(594\) 0 0
\(595\) −5.60082 −0.229611
\(596\) 8.18326 0.335200
\(597\) 0 0
\(598\) 3.92639 0.160562
\(599\) 14.9770 0.611945 0.305973 0.952040i \(-0.401018\pi\)
0.305973 + 0.952040i \(0.401018\pi\)
\(600\) 0 0
\(601\) 27.1354 1.10688 0.553438 0.832890i \(-0.313315\pi\)
0.553438 + 0.832890i \(0.313315\pi\)
\(602\) −6.72401 −0.274050
\(603\) 0 0
\(604\) 11.0159 0.448232
\(605\) 1.99961 0.0812957
\(606\) 0 0
\(607\) −4.67826 −0.189885 −0.0949423 0.995483i \(-0.530267\pi\)
−0.0949423 + 0.995483i \(0.530267\pi\)
\(608\) 11.8364 0.480031
\(609\) 0 0
\(610\) 3.69672 0.149676
\(611\) 21.6198 0.874642
\(612\) 0 0
\(613\) −39.1493 −1.58122 −0.790612 0.612317i \(-0.790238\pi\)
−0.790612 + 0.612317i \(0.790238\pi\)
\(614\) 37.5506 1.51542
\(615\) 0 0
\(616\) 9.35403 0.376885
\(617\) −5.78299 −0.232815 −0.116407 0.993202i \(-0.537138\pi\)
−0.116407 + 0.993202i \(0.537138\pi\)
\(618\) 0 0
\(619\) 49.3680 1.98427 0.992134 0.125181i \(-0.0399511\pi\)
0.992134 + 0.125181i \(0.0399511\pi\)
\(620\) −7.09444 −0.284919
\(621\) 0 0
\(622\) −28.5367 −1.14422
\(623\) 9.44997 0.378605
\(624\) 0 0
\(625\) −8.86995 −0.354798
\(626\) 22.2897 0.890876
\(627\) 0 0
\(628\) 3.89900 0.155587
\(629\) 12.0780 0.481582
\(630\) 0 0
\(631\) −16.3185 −0.649628 −0.324814 0.945778i \(-0.605302\pi\)
−0.324814 + 0.945778i \(0.605302\pi\)
\(632\) −10.5842 −0.421016
\(633\) 0 0
\(634\) −0.221434 −0.00879426
\(635\) −22.1231 −0.877930
\(636\) 0 0
\(637\) −20.3837 −0.807631
\(638\) 3.65265 0.144610
\(639\) 0 0
\(640\) −5.32330 −0.210422
\(641\) 11.2290 0.443521 0.221760 0.975101i \(-0.428820\pi\)
0.221760 + 0.975101i \(0.428820\pi\)
\(642\) 0 0
\(643\) 21.6694 0.854556 0.427278 0.904120i \(-0.359472\pi\)
0.427278 + 0.904120i \(0.359472\pi\)
\(644\) 0.619617 0.0244163
\(645\) 0 0
\(646\) −13.8613 −0.545365
\(647\) −6.83356 −0.268655 −0.134327 0.990937i \(-0.542887\pi\)
−0.134327 + 0.990937i \(0.542887\pi\)
\(648\) 0 0
\(649\) −43.2922 −1.69937
\(650\) −8.75883 −0.343549
\(651\) 0 0
\(652\) −12.3935 −0.485366
\(653\) −41.1434 −1.61006 −0.805032 0.593231i \(-0.797852\pi\)
−0.805032 + 0.593231i \(0.797852\pi\)
\(654\) 0 0
\(655\) −12.9564 −0.506249
\(656\) −16.4824 −0.643531
\(657\) 0 0
\(658\) −7.27738 −0.283702
\(659\) −37.5297 −1.46195 −0.730974 0.682405i \(-0.760934\pi\)
−0.730974 + 0.682405i \(0.760934\pi\)
\(660\) 0 0
\(661\) 13.9108 0.541068 0.270534 0.962710i \(-0.412800\pi\)
0.270534 + 0.962710i \(0.412800\pi\)
\(662\) 1.77350 0.0689291
\(663\) 0 0
\(664\) −3.22498 −0.125154
\(665\) 5.53344 0.214578
\(666\) 0 0
\(667\) 1.00000 0.0387202
\(668\) −4.38261 −0.169568
\(669\) 0 0
\(670\) 0.671343 0.0259362
\(671\) −5.95913 −0.230050
\(672\) 0 0
\(673\) −40.5659 −1.56370 −0.781850 0.623467i \(-0.785724\pi\)
−0.781850 + 0.623467i \(0.785724\pi\)
\(674\) −17.2953 −0.666191
\(675\) 0 0
\(676\) 1.07112 0.0411970
\(677\) −1.71291 −0.0658325 −0.0329163 0.999458i \(-0.510479\pi\)
−0.0329163 + 0.999458i \(0.510479\pi\)
\(678\) 0 0
\(679\) 7.78504 0.298762
\(680\) −17.7648 −0.681249
\(681\) 0 0
\(682\) −24.3937 −0.934085
\(683\) −8.39156 −0.321094 −0.160547 0.987028i \(-0.551326\pi\)
−0.160547 + 0.987028i \(0.551326\pi\)
\(684\) 0 0
\(685\) 12.9370 0.494296
\(686\) 14.7897 0.564673
\(687\) 0 0
\(688\) −13.7479 −0.524134
\(689\) 27.6280 1.05254
\(690\) 0 0
\(691\) 9.31311 0.354288 0.177144 0.984185i \(-0.443314\pi\)
0.177144 + 0.984185i \(0.443314\pi\)
\(692\) 3.68729 0.140170
\(693\) 0 0
\(694\) 0.892149 0.0338655
\(695\) 37.8705 1.43651
\(696\) 0 0
\(697\) −24.6797 −0.934812
\(698\) −21.9692 −0.831548
\(699\) 0 0
\(700\) −1.38221 −0.0522428
\(701\) 12.1056 0.457222 0.228611 0.973518i \(-0.426582\pi\)
0.228611 + 0.973518i \(0.426582\pi\)
\(702\) 0 0
\(703\) −11.9327 −0.450051
\(704\) 27.1181 1.02205
\(705\) 0 0
\(706\) 22.9046 0.862028
\(707\) −13.9667 −0.525270
\(708\) 0 0
\(709\) 33.0136 1.23985 0.619925 0.784661i \(-0.287163\pi\)
0.619925 + 0.784661i \(0.287163\pi\)
\(710\) 18.0778 0.678447
\(711\) 0 0
\(712\) 29.9736 1.12331
\(713\) −6.67837 −0.250107
\(714\) 0 0
\(715\) −17.5275 −0.655493
\(716\) 12.7315 0.475798
\(717\) 0 0
\(718\) 9.80230 0.365818
\(719\) 17.2610 0.643727 0.321864 0.946786i \(-0.395691\pi\)
0.321864 + 0.946786i \(0.395691\pi\)
\(720\) 0 0
\(721\) 15.2062 0.566307
\(722\) −8.47641 −0.315459
\(723\) 0 0
\(724\) 4.82885 0.179463
\(725\) −2.23076 −0.0828482
\(726\) 0 0
\(727\) −16.5001 −0.611955 −0.305977 0.952039i \(-0.598983\pi\)
−0.305977 + 0.952039i \(0.598983\pi\)
\(728\) 10.0551 0.372665
\(729\) 0 0
\(730\) −5.55435 −0.205576
\(731\) −20.5852 −0.761372
\(732\) 0 0
\(733\) −21.7144 −0.802039 −0.401020 0.916069i \(-0.631344\pi\)
−0.401020 + 0.916069i \(0.631344\pi\)
\(734\) −35.9251 −1.32602
\(735\) 0 0
\(736\) 3.45511 0.127357
\(737\) −1.08221 −0.0398636
\(738\) 0 0
\(739\) −15.4134 −0.566993 −0.283496 0.958973i \(-0.591494\pi\)
−0.283496 + 0.958973i \(0.591494\pi\)
\(740\) −3.70023 −0.136023
\(741\) 0 0
\(742\) −9.29980 −0.341406
\(743\) 47.2089 1.73193 0.865964 0.500106i \(-0.166706\pi\)
0.865964 + 0.500106i \(0.166706\pi\)
\(744\) 0 0
\(745\) 21.3324 0.781559
\(746\) −4.43246 −0.162284
\(747\) 0 0
\(748\) 6.92881 0.253342
\(749\) 6.69905 0.244778
\(750\) 0 0
\(751\) −1.92362 −0.0701939 −0.0350969 0.999384i \(-0.511174\pi\)
−0.0350969 + 0.999384i \(0.511174\pi\)
\(752\) −14.8793 −0.542594
\(753\) 0 0
\(754\) 3.92639 0.142991
\(755\) 28.7167 1.04511
\(756\) 0 0
\(757\) −33.3233 −1.21116 −0.605578 0.795786i \(-0.707058\pi\)
−0.605578 + 0.795786i \(0.707058\pi\)
\(758\) 12.2187 0.443804
\(759\) 0 0
\(760\) 17.5511 0.636645
\(761\) 12.2967 0.445754 0.222877 0.974847i \(-0.428455\pi\)
0.222877 + 0.974847i \(0.428455\pi\)
\(762\) 0 0
\(763\) 10.8496 0.392783
\(764\) 0.247700 0.00896147
\(765\) 0 0
\(766\) −15.6828 −0.566641
\(767\) −46.5367 −1.68034
\(768\) 0 0
\(769\) 21.7078 0.782803 0.391401 0.920220i \(-0.371990\pi\)
0.391401 + 0.920220i \(0.371990\pi\)
\(770\) 5.89991 0.212618
\(771\) 0 0
\(772\) 4.31452 0.155283
\(773\) −39.5976 −1.42423 −0.712114 0.702064i \(-0.752262\pi\)
−0.712114 + 0.702064i \(0.752262\pi\)
\(774\) 0 0
\(775\) 14.8978 0.535145
\(776\) 24.6928 0.886419
\(777\) 0 0
\(778\) 34.4447 1.23490
\(779\) 24.3829 0.873606
\(780\) 0 0
\(781\) −29.1414 −1.04276
\(782\) −4.04618 −0.144691
\(783\) 0 0
\(784\) 14.0286 0.501022
\(785\) 10.1640 0.362770
\(786\) 0 0
\(787\) −35.7413 −1.27404 −0.637020 0.770847i \(-0.719833\pi\)
−0.637020 + 0.770847i \(0.719833\pi\)
\(788\) −5.86314 −0.208866
\(789\) 0 0
\(790\) −6.67580 −0.237514
\(791\) 10.9743 0.390200
\(792\) 0 0
\(793\) −6.40573 −0.227474
\(794\) −26.1980 −0.929732
\(795\) 0 0
\(796\) 2.17798 0.0771963
\(797\) −42.4281 −1.50288 −0.751440 0.659801i \(-0.770640\pi\)
−0.751440 + 0.659801i \(0.770640\pi\)
\(798\) 0 0
\(799\) −22.2793 −0.788187
\(800\) −7.70752 −0.272502
\(801\) 0 0
\(802\) 36.8105 1.29982
\(803\) 8.95364 0.315967
\(804\) 0 0
\(805\) 1.61524 0.0569297
\(806\) −26.2219 −0.923627
\(807\) 0 0
\(808\) −44.2998 −1.55846
\(809\) −44.7480 −1.57325 −0.786627 0.617428i \(-0.788175\pi\)
−0.786627 + 0.617428i \(0.788175\pi\)
\(810\) 0 0
\(811\) −49.1461 −1.72575 −0.862877 0.505414i \(-0.831340\pi\)
−0.862877 + 0.505414i \(0.831340\pi\)
\(812\) 0.619617 0.0217443
\(813\) 0 0
\(814\) −12.7230 −0.445941
\(815\) −32.3078 −1.13169
\(816\) 0 0
\(817\) 20.3376 0.711522
\(818\) −42.6676 −1.49184
\(819\) 0 0
\(820\) 7.56090 0.264038
\(821\) −25.4417 −0.887921 −0.443960 0.896046i \(-0.646427\pi\)
−0.443960 + 0.896046i \(0.646427\pi\)
\(822\) 0 0
\(823\) −4.39388 −0.153161 −0.0765804 0.997063i \(-0.524400\pi\)
−0.0765804 + 0.997063i \(0.524400\pi\)
\(824\) 48.2313 1.68022
\(825\) 0 0
\(826\) 15.6646 0.545042
\(827\) −35.1132 −1.22101 −0.610503 0.792014i \(-0.709033\pi\)
−0.610503 + 0.792014i \(0.709033\pi\)
\(828\) 0 0
\(829\) 12.5291 0.435152 0.217576 0.976043i \(-0.430185\pi\)
0.217576 + 0.976043i \(0.430185\pi\)
\(830\) −2.03411 −0.0706049
\(831\) 0 0
\(832\) 29.1505 1.01061
\(833\) 21.0055 0.727799
\(834\) 0 0
\(835\) −11.4247 −0.395369
\(836\) −6.84546 −0.236755
\(837\) 0 0
\(838\) 37.9251 1.31010
\(839\) −1.22438 −0.0422703 −0.0211352 0.999777i \(-0.506728\pi\)
−0.0211352 + 0.999777i \(0.506728\pi\)
\(840\) 0 0
\(841\) 1.00000 0.0344828
\(842\) 25.9004 0.892587
\(843\) 0 0
\(844\) 5.20396 0.179128
\(845\) 2.79224 0.0960559
\(846\) 0 0
\(847\) 1.16633 0.0400755
\(848\) −19.0144 −0.652956
\(849\) 0 0
\(850\) 9.02604 0.309591
\(851\) −3.48322 −0.119403
\(852\) 0 0
\(853\) 32.0204 1.09636 0.548178 0.836361i \(-0.315322\pi\)
0.548178 + 0.836361i \(0.315322\pi\)
\(854\) 2.15622 0.0737842
\(855\) 0 0
\(856\) 21.2482 0.726248
\(857\) 31.7302 1.08388 0.541941 0.840416i \(-0.317690\pi\)
0.541941 + 0.840416i \(0.317690\pi\)
\(858\) 0 0
\(859\) 27.2799 0.930778 0.465389 0.885106i \(-0.345915\pi\)
0.465389 + 0.885106i \(0.345915\pi\)
\(860\) 6.30650 0.215050
\(861\) 0 0
\(862\) −11.7911 −0.401606
\(863\) −19.1687 −0.652512 −0.326256 0.945282i \(-0.605787\pi\)
−0.326256 + 0.945282i \(0.605787\pi\)
\(864\) 0 0
\(865\) 9.61217 0.326824
\(866\) 2.33009 0.0791797
\(867\) 0 0
\(868\) −4.13803 −0.140454
\(869\) 10.7614 0.365056
\(870\) 0 0
\(871\) −1.16331 −0.0394173
\(872\) 34.4131 1.16538
\(873\) 0 0
\(874\) 3.99751 0.135218
\(875\) −11.6794 −0.394836
\(876\) 0 0
\(877\) −18.5102 −0.625044 −0.312522 0.949911i \(-0.601174\pi\)
−0.312522 + 0.949911i \(0.601174\pi\)
\(878\) −32.1749 −1.08585
\(879\) 0 0
\(880\) 12.0629 0.406642
\(881\) 3.89803 0.131328 0.0656640 0.997842i \(-0.479083\pi\)
0.0656640 + 0.997842i \(0.479083\pi\)
\(882\) 0 0
\(883\) 21.4260 0.721043 0.360522 0.932751i \(-0.382599\pi\)
0.360522 + 0.932751i \(0.382599\pi\)
\(884\) 7.44808 0.250506
\(885\) 0 0
\(886\) 13.0965 0.439986
\(887\) −40.8605 −1.37196 −0.685981 0.727619i \(-0.740627\pi\)
−0.685981 + 0.727619i \(0.740627\pi\)
\(888\) 0 0
\(889\) −12.9039 −0.432784
\(890\) 18.9054 0.633710
\(891\) 0 0
\(892\) 11.6519 0.390133
\(893\) 22.0113 0.736581
\(894\) 0 0
\(895\) 33.1889 1.10938
\(896\) −3.10496 −0.103730
\(897\) 0 0
\(898\) 29.4196 0.981743
\(899\) −6.67837 −0.222736
\(900\) 0 0
\(901\) −28.4709 −0.948502
\(902\) 25.9977 0.865627
\(903\) 0 0
\(904\) 34.8085 1.15771
\(905\) 12.5880 0.418440
\(906\) 0 0
\(907\) 22.6638 0.752539 0.376269 0.926510i \(-0.377207\pi\)
0.376269 + 0.926510i \(0.377207\pi\)
\(908\) 13.4247 0.445515
\(909\) 0 0
\(910\) 6.34207 0.210238
\(911\) −25.2415 −0.836290 −0.418145 0.908380i \(-0.637320\pi\)
−0.418145 + 0.908380i \(0.637320\pi\)
\(912\) 0 0
\(913\) 3.27899 0.108519
\(914\) 22.3105 0.737964
\(915\) 0 0
\(916\) 1.40200 0.0463233
\(917\) −7.55719 −0.249560
\(918\) 0 0
\(919\) −16.3262 −0.538552 −0.269276 0.963063i \(-0.586784\pi\)
−0.269276 + 0.963063i \(0.586784\pi\)
\(920\) 5.12325 0.168909
\(921\) 0 0
\(922\) 32.7595 1.07888
\(923\) −31.3254 −1.03109
\(924\) 0 0
\(925\) 7.77022 0.255483
\(926\) −13.3936 −0.440142
\(927\) 0 0
\(928\) 3.45511 0.113420
\(929\) −17.1115 −0.561410 −0.280705 0.959794i \(-0.590568\pi\)
−0.280705 + 0.959794i \(0.590568\pi\)
\(930\) 0 0
\(931\) −20.7529 −0.680148
\(932\) 10.9200 0.357696
\(933\) 0 0
\(934\) 40.6941 1.33155
\(935\) 18.0623 0.590699
\(936\) 0 0
\(937\) −56.6451 −1.85051 −0.925257 0.379342i \(-0.876150\pi\)
−0.925257 + 0.379342i \(0.876150\pi\)
\(938\) 0.391579 0.0127855
\(939\) 0 0
\(940\) 6.82552 0.222624
\(941\) 17.5292 0.571435 0.285717 0.958314i \(-0.407768\pi\)
0.285717 + 0.958314i \(0.407768\pi\)
\(942\) 0 0
\(943\) 7.11748 0.231777
\(944\) 32.0279 1.04242
\(945\) 0 0
\(946\) 21.6845 0.705023
\(947\) 3.76309 0.122284 0.0611420 0.998129i \(-0.480526\pi\)
0.0611420 + 0.998129i \(0.480526\pi\)
\(948\) 0 0
\(949\) 9.62466 0.312430
\(950\) −8.91746 −0.289321
\(951\) 0 0
\(952\) −10.3618 −0.335828
\(953\) 49.0028 1.58736 0.793679 0.608337i \(-0.208163\pi\)
0.793679 + 0.608337i \(0.208163\pi\)
\(954\) 0 0
\(955\) 0.645713 0.0208948
\(956\) −0.0151476 −0.000489910 0
\(957\) 0 0
\(958\) 4.30588 0.139117
\(959\) 7.54585 0.243668
\(960\) 0 0
\(961\) 13.6006 0.438729
\(962\) −13.6765 −0.440948
\(963\) 0 0
\(964\) 11.5241 0.371167
\(965\) 11.2472 0.362061
\(966\) 0 0
\(967\) −7.49183 −0.240921 −0.120461 0.992718i \(-0.538437\pi\)
−0.120461 + 0.992718i \(0.538437\pi\)
\(968\) 3.69939 0.118903
\(969\) 0 0
\(970\) 15.5746 0.500069
\(971\) 27.8867 0.894926 0.447463 0.894303i \(-0.352328\pi\)
0.447463 + 0.894303i \(0.352328\pi\)
\(972\) 0 0
\(973\) 22.0890 0.708141
\(974\) −37.0001 −1.18556
\(975\) 0 0
\(976\) 4.40860 0.141116
\(977\) −50.8283 −1.62614 −0.813071 0.582165i \(-0.802206\pi\)
−0.813071 + 0.582165i \(0.802206\pi\)
\(978\) 0 0
\(979\) −30.4755 −0.974003
\(980\) −6.43528 −0.205567
\(981\) 0 0
\(982\) 24.6975 0.788130
\(983\) 41.3134 1.31769 0.658847 0.752277i \(-0.271044\pi\)
0.658847 + 0.752277i \(0.271044\pi\)
\(984\) 0 0
\(985\) −15.2843 −0.486997
\(986\) −4.04618 −0.128857
\(987\) 0 0
\(988\) −7.35849 −0.234105
\(989\) 5.93664 0.188774
\(990\) 0 0
\(991\) −37.8775 −1.20322 −0.601610 0.798790i \(-0.705474\pi\)
−0.601610 + 0.798790i \(0.705474\pi\)
\(992\) −23.0745 −0.732617
\(993\) 0 0
\(994\) 10.5444 0.334447
\(995\) 5.67762 0.179993
\(996\) 0 0
\(997\) −52.4367 −1.66069 −0.830344 0.557252i \(-0.811856\pi\)
−0.830344 + 0.557252i \(0.811856\pi\)
\(998\) 46.9498 1.48617
\(999\) 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 \(a_p\))