Properties

Label 4005.2.a.p.1.6
Level 4005
Weight 2
Character 4005.1
Self dual Yes
Analytic conductor 31.980
Analytic rank 1
Dimension 8
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4005 = 3^{2} \cdot 5 \cdot 89 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4005.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(31.9800860095\)
Analytic rank: \(1\)
Dimension: \(8\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.6
Root \(-1.11667\)
Character \(\chi\) = 4005.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.11667 q^{2} -0.753041 q^{4} +1.00000 q^{5} -1.16728 q^{7} -3.07425 q^{8} +O(q^{10})\) \(q+1.11667 q^{2} -0.753041 q^{4} +1.00000 q^{5} -1.16728 q^{7} -3.07425 q^{8} +1.11667 q^{10} +2.19092 q^{11} +1.10132 q^{13} -1.30347 q^{14} -1.92685 q^{16} -7.78009 q^{17} +4.75115 q^{19} -0.753041 q^{20} +2.44654 q^{22} -2.26860 q^{23} +1.00000 q^{25} +1.22981 q^{26} +0.879008 q^{28} +6.01934 q^{29} -1.58614 q^{31} +3.99684 q^{32} -8.68782 q^{34} -1.16728 q^{35} -7.29224 q^{37} +5.30548 q^{38} -3.07425 q^{40} +2.30872 q^{41} -2.34975 q^{43} -1.64985 q^{44} -2.53328 q^{46} +0.949255 q^{47} -5.63746 q^{49} +1.11667 q^{50} -0.829338 q^{52} -8.03974 q^{53} +2.19092 q^{55} +3.58850 q^{56} +6.72163 q^{58} -3.82542 q^{59} -5.72557 q^{61} -1.77120 q^{62} +8.31685 q^{64} +1.10132 q^{65} -15.8843 q^{67} +5.85873 q^{68} -1.30347 q^{70} -2.59018 q^{71} -12.1497 q^{73} -8.14305 q^{74} -3.57781 q^{76} -2.55741 q^{77} +10.7999 q^{79} -1.92685 q^{80} +2.57809 q^{82} -3.60391 q^{83} -7.78009 q^{85} -2.62390 q^{86} -6.73543 q^{88} -1.00000 q^{89} -1.28554 q^{91} +1.70835 q^{92} +1.06001 q^{94} +4.75115 q^{95} -3.17508 q^{97} -6.29520 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - q^{2} + 7q^{4} + 8q^{5} - 6q^{7} - 3q^{8} + O(q^{10}) \) \( 8q - q^{2} + 7q^{4} + 8q^{5} - 6q^{7} - 3q^{8} - q^{10} - 14q^{11} - 7q^{13} - 15q^{14} + 9q^{16} - 17q^{17} + 17q^{19} + 7q^{20} + 2q^{22} + q^{23} + 8q^{25} - 3q^{26} - 29q^{28} - 10q^{29} + q^{31} - 2q^{32} - 16q^{34} - 6q^{35} - 11q^{37} + 30q^{38} - 3q^{40} - 15q^{41} - 5q^{43} - 7q^{44} - 12q^{46} - 12q^{47} + 4q^{49} - q^{50} - 14q^{52} + q^{53} - 14q^{55} - 3q^{56} - 37q^{58} - 26q^{59} + 13q^{61} - 22q^{62} - 15q^{64} - 7q^{65} - 25q^{67} - 23q^{68} - 15q^{70} - 28q^{71} - 17q^{73} + 5q^{74} + 8q^{76} - 7q^{79} + 9q^{80} + 5q^{82} - 44q^{83} - 17q^{85} + 13q^{86} - 66q^{88} - 8q^{89} + 27q^{91} - 15q^{92} - 27q^{94} + 17q^{95} + q^{97} + 34q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.11667 0.789607 0.394804 0.918766i \(-0.370813\pi\)
0.394804 + 0.918766i \(0.370813\pi\)
\(3\) 0 0
\(4\) −0.753041 −0.376520
\(5\) 1.00000 0.447214
\(6\) 0 0
\(7\) −1.16728 −0.441190 −0.220595 0.975366i \(-0.570800\pi\)
−0.220595 + 0.975366i \(0.570800\pi\)
\(8\) −3.07425 −1.08691
\(9\) 0 0
\(10\) 1.11667 0.353123
\(11\) 2.19092 0.660587 0.330294 0.943878i \(-0.392852\pi\)
0.330294 + 0.943878i \(0.392852\pi\)
\(12\) 0 0
\(13\) 1.10132 0.305451 0.152725 0.988269i \(-0.451195\pi\)
0.152725 + 0.988269i \(0.451195\pi\)
\(14\) −1.30347 −0.348366
\(15\) 0 0
\(16\) −1.92685 −0.481712
\(17\) −7.78009 −1.88695 −0.943475 0.331445i \(-0.892464\pi\)
−0.943475 + 0.331445i \(0.892464\pi\)
\(18\) 0 0
\(19\) 4.75115 1.08999 0.544994 0.838440i \(-0.316532\pi\)
0.544994 + 0.838440i \(0.316532\pi\)
\(20\) −0.753041 −0.168385
\(21\) 0 0
\(22\) 2.44654 0.521605
\(23\) −2.26860 −0.473035 −0.236517 0.971627i \(-0.576006\pi\)
−0.236517 + 0.971627i \(0.576006\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 1.22981 0.241186
\(27\) 0 0
\(28\) 0.879008 0.166117
\(29\) 6.01934 1.11776 0.558882 0.829248i \(-0.311231\pi\)
0.558882 + 0.829248i \(0.311231\pi\)
\(30\) 0 0
\(31\) −1.58614 −0.284879 −0.142440 0.989804i \(-0.545495\pi\)
−0.142440 + 0.989804i \(0.545495\pi\)
\(32\) 3.99684 0.706547
\(33\) 0 0
\(34\) −8.68782 −1.48995
\(35\) −1.16728 −0.197306
\(36\) 0 0
\(37\) −7.29224 −1.19884 −0.599418 0.800436i \(-0.704601\pi\)
−0.599418 + 0.800436i \(0.704601\pi\)
\(38\) 5.30548 0.860663
\(39\) 0 0
\(40\) −3.07425 −0.486081
\(41\) 2.30872 0.360562 0.180281 0.983615i \(-0.442299\pi\)
0.180281 + 0.983615i \(0.442299\pi\)
\(42\) 0 0
\(43\) −2.34975 −0.358333 −0.179167 0.983819i \(-0.557340\pi\)
−0.179167 + 0.983819i \(0.557340\pi\)
\(44\) −1.64985 −0.248725
\(45\) 0 0
\(46\) −2.53328 −0.373512
\(47\) 0.949255 0.138463 0.0692315 0.997601i \(-0.477945\pi\)
0.0692315 + 0.997601i \(0.477945\pi\)
\(48\) 0 0
\(49\) −5.63746 −0.805352
\(50\) 1.11667 0.157921
\(51\) 0 0
\(52\) −0.829338 −0.115008
\(53\) −8.03974 −1.10434 −0.552171 0.833731i \(-0.686201\pi\)
−0.552171 + 0.833731i \(0.686201\pi\)
\(54\) 0 0
\(55\) 2.19092 0.295424
\(56\) 3.58850 0.479534
\(57\) 0 0
\(58\) 6.72163 0.882594
\(59\) −3.82542 −0.498027 −0.249013 0.968500i \(-0.580106\pi\)
−0.249013 + 0.968500i \(0.580106\pi\)
\(60\) 0 0
\(61\) −5.72557 −0.733084 −0.366542 0.930402i \(-0.619458\pi\)
−0.366542 + 0.930402i \(0.619458\pi\)
\(62\) −1.77120 −0.224943
\(63\) 0 0
\(64\) 8.31685 1.03961
\(65\) 1.10132 0.136602
\(66\) 0 0
\(67\) −15.8843 −1.94057 −0.970285 0.241964i \(-0.922208\pi\)
−0.970285 + 0.241964i \(0.922208\pi\)
\(68\) 5.85873 0.710475
\(69\) 0 0
\(70\) −1.30347 −0.155794
\(71\) −2.59018 −0.307398 −0.153699 0.988118i \(-0.549119\pi\)
−0.153699 + 0.988118i \(0.549119\pi\)
\(72\) 0 0
\(73\) −12.1497 −1.42202 −0.711010 0.703182i \(-0.751762\pi\)
−0.711010 + 0.703182i \(0.751762\pi\)
\(74\) −8.14305 −0.946610
\(75\) 0 0
\(76\) −3.57781 −0.410403
\(77\) −2.55741 −0.291444
\(78\) 0 0
\(79\) 10.7999 1.21509 0.607544 0.794286i \(-0.292155\pi\)
0.607544 + 0.794286i \(0.292155\pi\)
\(80\) −1.92685 −0.215428
\(81\) 0 0
\(82\) 2.57809 0.284702
\(83\) −3.60391 −0.395581 −0.197790 0.980244i \(-0.563376\pi\)
−0.197790 + 0.980244i \(0.563376\pi\)
\(84\) 0 0
\(85\) −7.78009 −0.843869
\(86\) −2.62390 −0.282942
\(87\) 0 0
\(88\) −6.73543 −0.717999
\(89\) −1.00000 −0.106000
\(90\) 0 0
\(91\) −1.28554 −0.134762
\(92\) 1.70835 0.178107
\(93\) 0 0
\(94\) 1.06001 0.109331
\(95\) 4.75115 0.487458
\(96\) 0 0
\(97\) −3.17508 −0.322381 −0.161190 0.986923i \(-0.551533\pi\)
−0.161190 + 0.986923i \(0.551533\pi\)
\(98\) −6.29520 −0.635912
\(99\) 0 0
\(100\) −0.753041 −0.0753041
\(101\) 6.07838 0.604821 0.302411 0.953178i \(-0.402209\pi\)
0.302411 + 0.953178i \(0.402209\pi\)
\(102\) 0 0
\(103\) −15.4733 −1.52463 −0.762315 0.647206i \(-0.775937\pi\)
−0.762315 + 0.647206i \(0.775937\pi\)
\(104\) −3.38572 −0.331998
\(105\) 0 0
\(106\) −8.97776 −0.871997
\(107\) −3.75432 −0.362944 −0.181472 0.983396i \(-0.558086\pi\)
−0.181472 + 0.983396i \(0.558086\pi\)
\(108\) 0 0
\(109\) 14.3378 1.37331 0.686654 0.726984i \(-0.259079\pi\)
0.686654 + 0.726984i \(0.259079\pi\)
\(110\) 2.44654 0.233269
\(111\) 0 0
\(112\) 2.24917 0.212526
\(113\) 0.592705 0.0557570 0.0278785 0.999611i \(-0.491125\pi\)
0.0278785 + 0.999611i \(0.491125\pi\)
\(114\) 0 0
\(115\) −2.26860 −0.211548
\(116\) −4.53281 −0.420861
\(117\) 0 0
\(118\) −4.27174 −0.393246
\(119\) 9.08153 0.832502
\(120\) 0 0
\(121\) −6.19987 −0.563624
\(122\) −6.39359 −0.578848
\(123\) 0 0
\(124\) 1.19443 0.107263
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) −17.3069 −1.53574 −0.767869 0.640606i \(-0.778683\pi\)
−0.767869 + 0.640606i \(0.778683\pi\)
\(128\) 1.29354 0.114334
\(129\) 0 0
\(130\) 1.22981 0.107862
\(131\) −6.52966 −0.570499 −0.285250 0.958453i \(-0.592076\pi\)
−0.285250 + 0.958453i \(0.592076\pi\)
\(132\) 0 0
\(133\) −5.54591 −0.480891
\(134\) −17.7375 −1.53229
\(135\) 0 0
\(136\) 23.9179 2.05094
\(137\) 15.0929 1.28947 0.644737 0.764405i \(-0.276967\pi\)
0.644737 + 0.764405i \(0.276967\pi\)
\(138\) 0 0
\(139\) 11.1708 0.947492 0.473746 0.880662i \(-0.342901\pi\)
0.473746 + 0.880662i \(0.342901\pi\)
\(140\) 0.879008 0.0742897
\(141\) 0 0
\(142\) −2.89238 −0.242723
\(143\) 2.41290 0.201777
\(144\) 0 0
\(145\) 6.01934 0.499879
\(146\) −13.5673 −1.12284
\(147\) 0 0
\(148\) 5.49135 0.451387
\(149\) −7.56657 −0.619877 −0.309939 0.950757i \(-0.600309\pi\)
−0.309939 + 0.950757i \(0.600309\pi\)
\(150\) 0 0
\(151\) −4.28422 −0.348645 −0.174322 0.984689i \(-0.555773\pi\)
−0.174322 + 0.984689i \(0.555773\pi\)
\(152\) −14.6062 −1.18472
\(153\) 0 0
\(154\) −2.85579 −0.230126
\(155\) −1.58614 −0.127402
\(156\) 0 0
\(157\) −5.39518 −0.430582 −0.215291 0.976550i \(-0.569070\pi\)
−0.215291 + 0.976550i \(0.569070\pi\)
\(158\) 12.0600 0.959442
\(159\) 0 0
\(160\) 3.99684 0.315978
\(161\) 2.64808 0.208698
\(162\) 0 0
\(163\) 15.7496 1.23360 0.616801 0.787119i \(-0.288428\pi\)
0.616801 + 0.787119i \(0.288428\pi\)
\(164\) −1.73856 −0.135759
\(165\) 0 0
\(166\) −4.02439 −0.312353
\(167\) 18.1941 1.40790 0.703951 0.710248i \(-0.251417\pi\)
0.703951 + 0.710248i \(0.251417\pi\)
\(168\) 0 0
\(169\) −11.7871 −0.906700
\(170\) −8.68782 −0.666325
\(171\) 0 0
\(172\) 1.76946 0.134920
\(173\) −4.39190 −0.333910 −0.166955 0.985964i \(-0.553394\pi\)
−0.166955 + 0.985964i \(0.553394\pi\)
\(174\) 0 0
\(175\) −1.16728 −0.0882379
\(176\) −4.22157 −0.318213
\(177\) 0 0
\(178\) −1.11667 −0.0836982
\(179\) 22.7104 1.69745 0.848726 0.528833i \(-0.177370\pi\)
0.848726 + 0.528833i \(0.177370\pi\)
\(180\) 0 0
\(181\) −17.2204 −1.27999 −0.639993 0.768381i \(-0.721063\pi\)
−0.639993 + 0.768381i \(0.721063\pi\)
\(182\) −1.43553 −0.106409
\(183\) 0 0
\(184\) 6.97422 0.514147
\(185\) −7.29224 −0.536136
\(186\) 0 0
\(187\) −17.0456 −1.24649
\(188\) −0.714828 −0.0521342
\(189\) 0 0
\(190\) 5.30548 0.384900
\(191\) −20.5891 −1.48977 −0.744887 0.667190i \(-0.767497\pi\)
−0.744887 + 0.667190i \(0.767497\pi\)
\(192\) 0 0
\(193\) −9.48692 −0.682884 −0.341442 0.939903i \(-0.610915\pi\)
−0.341442 + 0.939903i \(0.610915\pi\)
\(194\) −3.54553 −0.254554
\(195\) 0 0
\(196\) 4.24524 0.303231
\(197\) −25.9622 −1.84973 −0.924865 0.380297i \(-0.875822\pi\)
−0.924865 + 0.380297i \(0.875822\pi\)
\(198\) 0 0
\(199\) −16.4243 −1.16429 −0.582143 0.813087i \(-0.697786\pi\)
−0.582143 + 0.813087i \(0.697786\pi\)
\(200\) −3.07425 −0.217382
\(201\) 0 0
\(202\) 6.78756 0.477571
\(203\) −7.02624 −0.493145
\(204\) 0 0
\(205\) 2.30872 0.161248
\(206\) −17.2786 −1.20386
\(207\) 0 0
\(208\) −2.12207 −0.147139
\(209\) 10.4094 0.720032
\(210\) 0 0
\(211\) 9.30596 0.640649 0.320324 0.947308i \(-0.396208\pi\)
0.320324 + 0.947308i \(0.396208\pi\)
\(212\) 6.05425 0.415808
\(213\) 0 0
\(214\) −4.19235 −0.286583
\(215\) −2.34975 −0.160251
\(216\) 0 0
\(217\) 1.85147 0.125686
\(218\) 16.0106 1.08437
\(219\) 0 0
\(220\) −1.64985 −0.111233
\(221\) −8.56835 −0.576370
\(222\) 0 0
\(223\) 5.64930 0.378305 0.189152 0.981948i \(-0.439426\pi\)
0.189152 + 0.981948i \(0.439426\pi\)
\(224\) −4.66542 −0.311721
\(225\) 0 0
\(226\) 0.661858 0.0440261
\(227\) −2.69793 −0.179068 −0.0895341 0.995984i \(-0.528538\pi\)
−0.0895341 + 0.995984i \(0.528538\pi\)
\(228\) 0 0
\(229\) 6.50881 0.430115 0.215057 0.976601i \(-0.431006\pi\)
0.215057 + 0.976601i \(0.431006\pi\)
\(230\) −2.53328 −0.167040
\(231\) 0 0
\(232\) −18.5049 −1.21491
\(233\) 16.6350 1.08980 0.544899 0.838502i \(-0.316568\pi\)
0.544899 + 0.838502i \(0.316568\pi\)
\(234\) 0 0
\(235\) 0.949255 0.0619225
\(236\) 2.88070 0.187517
\(237\) 0 0
\(238\) 10.1411 0.657350
\(239\) −21.1293 −1.36674 −0.683370 0.730072i \(-0.739486\pi\)
−0.683370 + 0.730072i \(0.739486\pi\)
\(240\) 0 0
\(241\) −5.60825 −0.361259 −0.180629 0.983551i \(-0.557813\pi\)
−0.180629 + 0.983551i \(0.557813\pi\)
\(242\) −6.92323 −0.445042
\(243\) 0 0
\(244\) 4.31159 0.276021
\(245\) −5.63746 −0.360164
\(246\) 0 0
\(247\) 5.23253 0.332938
\(248\) 4.87619 0.309638
\(249\) 0 0
\(250\) 1.11667 0.0706246
\(251\) −15.2914 −0.965187 −0.482593 0.875845i \(-0.660305\pi\)
−0.482593 + 0.875845i \(0.660305\pi\)
\(252\) 0 0
\(253\) −4.97031 −0.312481
\(254\) −19.3262 −1.21263
\(255\) 0 0
\(256\) −15.1892 −0.949328
\(257\) −3.40793 −0.212581 −0.106290 0.994335i \(-0.533897\pi\)
−0.106290 + 0.994335i \(0.533897\pi\)
\(258\) 0 0
\(259\) 8.51207 0.528914
\(260\) −0.829338 −0.0514333
\(261\) 0 0
\(262\) −7.29150 −0.450470
\(263\) −7.66796 −0.472827 −0.236413 0.971653i \(-0.575972\pi\)
−0.236413 + 0.971653i \(0.575972\pi\)
\(264\) 0 0
\(265\) −8.03974 −0.493877
\(266\) −6.19297 −0.379715
\(267\) 0 0
\(268\) 11.9615 0.730664
\(269\) 21.3290 1.30045 0.650227 0.759740i \(-0.274674\pi\)
0.650227 + 0.759740i \(0.274674\pi\)
\(270\) 0 0
\(271\) 2.10429 0.127827 0.0639134 0.997955i \(-0.479642\pi\)
0.0639134 + 0.997955i \(0.479642\pi\)
\(272\) 14.9910 0.908966
\(273\) 0 0
\(274\) 16.8538 1.01818
\(275\) 2.19092 0.132117
\(276\) 0 0
\(277\) 11.9745 0.719477 0.359738 0.933053i \(-0.382866\pi\)
0.359738 + 0.933053i \(0.382866\pi\)
\(278\) 12.4741 0.748147
\(279\) 0 0
\(280\) 3.58850 0.214454
\(281\) −17.4431 −1.04057 −0.520283 0.853994i \(-0.674174\pi\)
−0.520283 + 0.853994i \(0.674174\pi\)
\(282\) 0 0
\(283\) 22.5162 1.33845 0.669225 0.743060i \(-0.266626\pi\)
0.669225 + 0.743060i \(0.266626\pi\)
\(284\) 1.95051 0.115741
\(285\) 0 0
\(286\) 2.69442 0.159324
\(287\) −2.69492 −0.159076
\(288\) 0 0
\(289\) 43.5298 2.56058
\(290\) 6.72163 0.394708
\(291\) 0 0
\(292\) 9.14925 0.535420
\(293\) −10.1887 −0.595229 −0.297615 0.954686i \(-0.596191\pi\)
−0.297615 + 0.954686i \(0.596191\pi\)
\(294\) 0 0
\(295\) −3.82542 −0.222724
\(296\) 22.4181 1.30303
\(297\) 0 0
\(298\) −8.44938 −0.489460
\(299\) −2.49845 −0.144489
\(300\) 0 0
\(301\) 2.74281 0.158093
\(302\) −4.78407 −0.275292
\(303\) 0 0
\(304\) −9.15474 −0.525060
\(305\) −5.72557 −0.327845
\(306\) 0 0
\(307\) −10.2100 −0.582715 −0.291358 0.956614i \(-0.594107\pi\)
−0.291358 + 0.956614i \(0.594107\pi\)
\(308\) 1.92584 0.109735
\(309\) 0 0
\(310\) −1.77120 −0.100597
\(311\) −13.3442 −0.756678 −0.378339 0.925667i \(-0.623505\pi\)
−0.378339 + 0.925667i \(0.623505\pi\)
\(312\) 0 0
\(313\) −13.7779 −0.778772 −0.389386 0.921075i \(-0.627313\pi\)
−0.389386 + 0.921075i \(0.627313\pi\)
\(314\) −6.02465 −0.339991
\(315\) 0 0
\(316\) −8.13279 −0.457505
\(317\) 32.6813 1.83557 0.917784 0.397081i \(-0.129977\pi\)
0.917784 + 0.397081i \(0.129977\pi\)
\(318\) 0 0
\(319\) 13.1879 0.738380
\(320\) 8.31685 0.464926
\(321\) 0 0
\(322\) 2.95704 0.164790
\(323\) −36.9644 −2.05675
\(324\) 0 0
\(325\) 1.10132 0.0610901
\(326\) 17.5871 0.974061
\(327\) 0 0
\(328\) −7.09759 −0.391899
\(329\) −1.10804 −0.0610884
\(330\) 0 0
\(331\) −17.1541 −0.942873 −0.471437 0.881900i \(-0.656264\pi\)
−0.471437 + 0.881900i \(0.656264\pi\)
\(332\) 2.71389 0.148944
\(333\) 0 0
\(334\) 20.3169 1.11169
\(335\) −15.8843 −0.867849
\(336\) 0 0
\(337\) 14.8907 0.811149 0.405575 0.914062i \(-0.367071\pi\)
0.405575 + 0.914062i \(0.367071\pi\)
\(338\) −13.1623 −0.715937
\(339\) 0 0
\(340\) 5.85873 0.317734
\(341\) −3.47511 −0.188188
\(342\) 0 0
\(343\) 14.7514 0.796502
\(344\) 7.22370 0.389476
\(345\) 0 0
\(346\) −4.90432 −0.263658
\(347\) 24.1687 1.29745 0.648723 0.761024i \(-0.275303\pi\)
0.648723 + 0.761024i \(0.275303\pi\)
\(348\) 0 0
\(349\) 33.4055 1.78816 0.894078 0.447910i \(-0.147832\pi\)
0.894078 + 0.447910i \(0.147832\pi\)
\(350\) −1.30347 −0.0696733
\(351\) 0 0
\(352\) 8.75675 0.466736
\(353\) 24.5144 1.30477 0.652384 0.757889i \(-0.273769\pi\)
0.652384 + 0.757889i \(0.273769\pi\)
\(354\) 0 0
\(355\) −2.59018 −0.137472
\(356\) 0.753041 0.0399111
\(357\) 0 0
\(358\) 25.3601 1.34032
\(359\) −11.5135 −0.607657 −0.303829 0.952727i \(-0.598265\pi\)
−0.303829 + 0.952727i \(0.598265\pi\)
\(360\) 0 0
\(361\) 3.57341 0.188074
\(362\) −19.2296 −1.01069
\(363\) 0 0
\(364\) 0.968067 0.0507405
\(365\) −12.1497 −0.635947
\(366\) 0 0
\(367\) −1.52333 −0.0795173 −0.0397587 0.999209i \(-0.512659\pi\)
−0.0397587 + 0.999209i \(0.512659\pi\)
\(368\) 4.37124 0.227867
\(369\) 0 0
\(370\) −8.14305 −0.423337
\(371\) 9.38461 0.487225
\(372\) 0 0
\(373\) 29.7945 1.54270 0.771351 0.636410i \(-0.219581\pi\)
0.771351 + 0.636410i \(0.219581\pi\)
\(374\) −19.0343 −0.984241
\(375\) 0 0
\(376\) −2.91824 −0.150497
\(377\) 6.62921 0.341421
\(378\) 0 0
\(379\) 19.5814 1.00583 0.502914 0.864337i \(-0.332261\pi\)
0.502914 + 0.864337i \(0.332261\pi\)
\(380\) −3.57781 −0.183538
\(381\) 0 0
\(382\) −22.9913 −1.17634
\(383\) 15.6845 0.801440 0.400720 0.916201i \(-0.368760\pi\)
0.400720 + 0.916201i \(0.368760\pi\)
\(384\) 0 0
\(385\) −2.55741 −0.130338
\(386\) −10.5938 −0.539210
\(387\) 0 0
\(388\) 2.39097 0.121383
\(389\) −14.7385 −0.747273 −0.373636 0.927575i \(-0.621889\pi\)
−0.373636 + 0.927575i \(0.621889\pi\)
\(390\) 0 0
\(391\) 17.6499 0.892593
\(392\) 17.3310 0.875345
\(393\) 0 0
\(394\) −28.9913 −1.46056
\(395\) 10.7999 0.543404
\(396\) 0 0
\(397\) 7.30391 0.366573 0.183286 0.983060i \(-0.441326\pi\)
0.183286 + 0.983060i \(0.441326\pi\)
\(398\) −18.3405 −0.919328
\(399\) 0 0
\(400\) −1.92685 −0.0963424
\(401\) 7.65061 0.382053 0.191027 0.981585i \(-0.438818\pi\)
0.191027 + 0.981585i \(0.438818\pi\)
\(402\) 0 0
\(403\) −1.74684 −0.0870165
\(404\) −4.57727 −0.227728
\(405\) 0 0
\(406\) −7.84601 −0.389391
\(407\) −15.9767 −0.791936
\(408\) 0 0
\(409\) −23.1681 −1.14559 −0.572793 0.819700i \(-0.694140\pi\)
−0.572793 + 0.819700i \(0.694140\pi\)
\(410\) 2.57809 0.127323
\(411\) 0 0
\(412\) 11.6520 0.574055
\(413\) 4.46532 0.219724
\(414\) 0 0
\(415\) −3.60391 −0.176909
\(416\) 4.40179 0.215815
\(417\) 0 0
\(418\) 11.6239 0.568543
\(419\) 23.7901 1.16222 0.581112 0.813824i \(-0.302618\pi\)
0.581112 + 0.813824i \(0.302618\pi\)
\(420\) 0 0
\(421\) 10.2706 0.500560 0.250280 0.968174i \(-0.419477\pi\)
0.250280 + 0.968174i \(0.419477\pi\)
\(422\) 10.3917 0.505861
\(423\) 0 0
\(424\) 24.7161 1.20032
\(425\) −7.78009 −0.377390
\(426\) 0 0
\(427\) 6.68333 0.323429
\(428\) 2.82716 0.136656
\(429\) 0 0
\(430\) −2.62390 −0.126536
\(431\) −2.47844 −0.119382 −0.0596911 0.998217i \(-0.519012\pi\)
−0.0596911 + 0.998217i \(0.519012\pi\)
\(432\) 0 0
\(433\) −13.9612 −0.670931 −0.335465 0.942053i \(-0.608894\pi\)
−0.335465 + 0.942053i \(0.608894\pi\)
\(434\) 2.06748 0.0992423
\(435\) 0 0
\(436\) −10.7969 −0.517079
\(437\) −10.7784 −0.515603
\(438\) 0 0
\(439\) −3.44298 −0.164324 −0.0821622 0.996619i \(-0.526183\pi\)
−0.0821622 + 0.996619i \(0.526183\pi\)
\(440\) −6.73543 −0.321099
\(441\) 0 0
\(442\) −9.56805 −0.455106
\(443\) 16.7717 0.796847 0.398424 0.917201i \(-0.369557\pi\)
0.398424 + 0.917201i \(0.369557\pi\)
\(444\) 0 0
\(445\) −1.00000 −0.0474045
\(446\) 6.30842 0.298712
\(447\) 0 0
\(448\) −9.70808 −0.458664
\(449\) −7.85536 −0.370717 −0.185359 0.982671i \(-0.559345\pi\)
−0.185359 + 0.982671i \(0.559345\pi\)
\(450\) 0 0
\(451\) 5.05823 0.238183
\(452\) −0.446331 −0.0209936
\(453\) 0 0
\(454\) −3.01271 −0.141394
\(455\) −1.28554 −0.0602672
\(456\) 0 0
\(457\) −14.7105 −0.688129 −0.344064 0.938946i \(-0.611804\pi\)
−0.344064 + 0.938946i \(0.611804\pi\)
\(458\) 7.26822 0.339622
\(459\) 0 0
\(460\) 1.70835 0.0796520
\(461\) 9.79268 0.456090 0.228045 0.973651i \(-0.426767\pi\)
0.228045 + 0.973651i \(0.426767\pi\)
\(462\) 0 0
\(463\) −12.8936 −0.599216 −0.299608 0.954062i \(-0.596856\pi\)
−0.299608 + 0.954062i \(0.596856\pi\)
\(464\) −11.5983 −0.538440
\(465\) 0 0
\(466\) 18.5759 0.860513
\(467\) 2.35654 0.109048 0.0545239 0.998512i \(-0.482636\pi\)
0.0545239 + 0.998512i \(0.482636\pi\)
\(468\) 0 0
\(469\) 18.5413 0.856159
\(470\) 1.06001 0.0488945
\(471\) 0 0
\(472\) 11.7603 0.541311
\(473\) −5.14811 −0.236710
\(474\) 0 0
\(475\) 4.75115 0.217998
\(476\) −6.83876 −0.313454
\(477\) 0 0
\(478\) −23.5945 −1.07919
\(479\) −10.5084 −0.480142 −0.240071 0.970755i \(-0.577171\pi\)
−0.240071 + 0.970755i \(0.577171\pi\)
\(480\) 0 0
\(481\) −8.03107 −0.366185
\(482\) −6.26258 −0.285253
\(483\) 0 0
\(484\) 4.66875 0.212216
\(485\) −3.17508 −0.144173
\(486\) 0 0
\(487\) −22.3713 −1.01374 −0.506870 0.862023i \(-0.669198\pi\)
−0.506870 + 0.862023i \(0.669198\pi\)
\(488\) 17.6018 0.796796
\(489\) 0 0
\(490\) −6.29520 −0.284388
\(491\) −9.72458 −0.438864 −0.219432 0.975628i \(-0.570420\pi\)
−0.219432 + 0.975628i \(0.570420\pi\)
\(492\) 0 0
\(493\) −46.8310 −2.10916
\(494\) 5.84302 0.262890
\(495\) 0 0
\(496\) 3.05625 0.137230
\(497\) 3.02346 0.135621
\(498\) 0 0
\(499\) 21.5022 0.962570 0.481285 0.876564i \(-0.340170\pi\)
0.481285 + 0.876564i \(0.340170\pi\)
\(500\) −0.753041 −0.0336770
\(501\) 0 0
\(502\) −17.0755 −0.762118
\(503\) −31.3622 −1.39837 −0.699186 0.714940i \(-0.746454\pi\)
−0.699186 + 0.714940i \(0.746454\pi\)
\(504\) 0 0
\(505\) 6.07838 0.270484
\(506\) −5.55022 −0.246737
\(507\) 0 0
\(508\) 13.0328 0.578237
\(509\) 18.7676 0.831859 0.415929 0.909397i \(-0.363456\pi\)
0.415929 + 0.909397i \(0.363456\pi\)
\(510\) 0 0
\(511\) 14.1821 0.627380
\(512\) −19.5485 −0.863930
\(513\) 0 0
\(514\) −3.80554 −0.167855
\(515\) −15.4733 −0.681836
\(516\) 0 0
\(517\) 2.07974 0.0914669
\(518\) 9.50520 0.417634
\(519\) 0 0
\(520\) −3.38572 −0.148474
\(521\) −21.5513 −0.944180 −0.472090 0.881550i \(-0.656500\pi\)
−0.472090 + 0.881550i \(0.656500\pi\)
\(522\) 0 0
\(523\) −8.72082 −0.381335 −0.190667 0.981655i \(-0.561065\pi\)
−0.190667 + 0.981655i \(0.561065\pi\)
\(524\) 4.91710 0.214805
\(525\) 0 0
\(526\) −8.56260 −0.373347
\(527\) 12.3403 0.537552
\(528\) 0 0
\(529\) −17.8535 −0.776238
\(530\) −8.97776 −0.389969
\(531\) 0 0
\(532\) 4.17630 0.181065
\(533\) 2.54264 0.110134
\(534\) 0 0
\(535\) −3.75432 −0.162313
\(536\) 48.8321 2.10923
\(537\) 0 0
\(538\) 23.8176 1.02685
\(539\) −12.3512 −0.532005
\(540\) 0 0
\(541\) −35.1880 −1.51285 −0.756424 0.654081i \(-0.773055\pi\)
−0.756424 + 0.654081i \(0.773055\pi\)
\(542\) 2.34981 0.100933
\(543\) 0 0
\(544\) −31.0957 −1.33322
\(545\) 14.3378 0.614162
\(546\) 0 0
\(547\) 21.7368 0.929399 0.464700 0.885468i \(-0.346162\pi\)
0.464700 + 0.885468i \(0.346162\pi\)
\(548\) −11.3656 −0.485513
\(549\) 0 0
\(550\) 2.44654 0.104321
\(551\) 28.5988 1.21835
\(552\) 0 0
\(553\) −12.6065 −0.536084
\(554\) 13.3716 0.568104
\(555\) 0 0
\(556\) −8.41204 −0.356750
\(557\) 35.5213 1.50509 0.752544 0.658542i \(-0.228827\pi\)
0.752544 + 0.658542i \(0.228827\pi\)
\(558\) 0 0
\(559\) −2.58782 −0.109453
\(560\) 2.24917 0.0950446
\(561\) 0 0
\(562\) −19.4782 −0.821639
\(563\) −24.4265 −1.02946 −0.514728 0.857353i \(-0.672107\pi\)
−0.514728 + 0.857353i \(0.672107\pi\)
\(564\) 0 0
\(565\) 0.592705 0.0249353
\(566\) 25.1432 1.05685
\(567\) 0 0
\(568\) 7.96285 0.334114
\(569\) 4.52474 0.189687 0.0948435 0.995492i \(-0.469765\pi\)
0.0948435 + 0.995492i \(0.469765\pi\)
\(570\) 0 0
\(571\) 20.6420 0.863842 0.431921 0.901911i \(-0.357836\pi\)
0.431921 + 0.901911i \(0.357836\pi\)
\(572\) −1.81701 −0.0759731
\(573\) 0 0
\(574\) −3.00935 −0.125608
\(575\) −2.26860 −0.0946070
\(576\) 0 0
\(577\) 29.9774 1.24798 0.623989 0.781433i \(-0.285511\pi\)
0.623989 + 0.781433i \(0.285511\pi\)
\(578\) 48.6086 2.02185
\(579\) 0 0
\(580\) −4.53281 −0.188215
\(581\) 4.20676 0.174526
\(582\) 0 0
\(583\) −17.6144 −0.729515
\(584\) 37.3513 1.54561
\(585\) 0 0
\(586\) −11.3774 −0.469997
\(587\) −33.2868 −1.37389 −0.686947 0.726708i \(-0.741050\pi\)
−0.686947 + 0.726708i \(0.741050\pi\)
\(588\) 0 0
\(589\) −7.53599 −0.310515
\(590\) −4.27174 −0.175865
\(591\) 0 0
\(592\) 14.0510 0.577494
\(593\) 29.9369 1.22936 0.614681 0.788776i \(-0.289285\pi\)
0.614681 + 0.788776i \(0.289285\pi\)
\(594\) 0 0
\(595\) 9.08153 0.372306
\(596\) 5.69793 0.233396
\(597\) 0 0
\(598\) −2.78995 −0.114089
\(599\) 8.69422 0.355236 0.177618 0.984099i \(-0.443161\pi\)
0.177618 + 0.984099i \(0.443161\pi\)
\(600\) 0 0
\(601\) −3.33351 −0.135977 −0.0679884 0.997686i \(-0.521658\pi\)
−0.0679884 + 0.997686i \(0.521658\pi\)
\(602\) 3.06282 0.124831
\(603\) 0 0
\(604\) 3.22619 0.131272
\(605\) −6.19987 −0.252060
\(606\) 0 0
\(607\) 19.4556 0.789679 0.394839 0.918750i \(-0.370800\pi\)
0.394839 + 0.918750i \(0.370800\pi\)
\(608\) 18.9896 0.770128
\(609\) 0 0
\(610\) −6.39359 −0.258869
\(611\) 1.04543 0.0422936
\(612\) 0 0
\(613\) −7.99162 −0.322778 −0.161389 0.986891i \(-0.551597\pi\)
−0.161389 + 0.986891i \(0.551597\pi\)
\(614\) −11.4012 −0.460116
\(615\) 0 0
\(616\) 7.86212 0.316774
\(617\) −16.9756 −0.683414 −0.341707 0.939807i \(-0.611005\pi\)
−0.341707 + 0.939807i \(0.611005\pi\)
\(618\) 0 0
\(619\) −30.8826 −1.24128 −0.620638 0.784097i \(-0.713126\pi\)
−0.620638 + 0.784097i \(0.713126\pi\)
\(620\) 1.19443 0.0479694
\(621\) 0 0
\(622\) −14.9011 −0.597478
\(623\) 1.16728 0.0467660
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) −15.3854 −0.614924
\(627\) 0 0
\(628\) 4.06279 0.162123
\(629\) 56.7343 2.26214
\(630\) 0 0
\(631\) 21.6472 0.861763 0.430881 0.902409i \(-0.358203\pi\)
0.430881 + 0.902409i \(0.358203\pi\)
\(632\) −33.2017 −1.32069
\(633\) 0 0
\(634\) 36.4944 1.44938
\(635\) −17.3069 −0.686803
\(636\) 0 0
\(637\) −6.20864 −0.245995
\(638\) 14.7266 0.583030
\(639\) 0 0
\(640\) 1.29354 0.0511316
\(641\) −39.4212 −1.55704 −0.778522 0.627617i \(-0.784030\pi\)
−0.778522 + 0.627617i \(0.784030\pi\)
\(642\) 0 0
\(643\) 42.5193 1.67680 0.838398 0.545058i \(-0.183492\pi\)
0.838398 + 0.545058i \(0.183492\pi\)
\(644\) −1.99411 −0.0785791
\(645\) 0 0
\(646\) −41.2771 −1.62403
\(647\) 27.5508 1.08313 0.541566 0.840658i \(-0.317831\pi\)
0.541566 + 0.840658i \(0.317831\pi\)
\(648\) 0 0
\(649\) −8.38118 −0.328990
\(650\) 1.22981 0.0482372
\(651\) 0 0
\(652\) −11.8601 −0.464476
\(653\) 7.69506 0.301131 0.150566 0.988600i \(-0.451891\pi\)
0.150566 + 0.988600i \(0.451891\pi\)
\(654\) 0 0
\(655\) −6.52966 −0.255135
\(656\) −4.44856 −0.173687
\(657\) 0 0
\(658\) −1.23732 −0.0482359
\(659\) −23.7448 −0.924965 −0.462482 0.886628i \(-0.653041\pi\)
−0.462482 + 0.886628i \(0.653041\pi\)
\(660\) 0 0
\(661\) −13.5532 −0.527159 −0.263580 0.964638i \(-0.584903\pi\)
−0.263580 + 0.964638i \(0.584903\pi\)
\(662\) −19.1555 −0.744499
\(663\) 0 0
\(664\) 11.0793 0.429961
\(665\) −5.54591 −0.215061
\(666\) 0 0
\(667\) −13.6554 −0.528741
\(668\) −13.7009 −0.530104
\(669\) 0 0
\(670\) −17.7375 −0.685260
\(671\) −12.5443 −0.484266
\(672\) 0 0
\(673\) 34.2943 1.32195 0.660973 0.750409i \(-0.270144\pi\)
0.660973 + 0.750409i \(0.270144\pi\)
\(674\) 16.6281 0.640489
\(675\) 0 0
\(676\) 8.87617 0.341391
\(677\) 43.3280 1.66523 0.832616 0.553851i \(-0.186842\pi\)
0.832616 + 0.553851i \(0.186842\pi\)
\(678\) 0 0
\(679\) 3.70620 0.142231
\(680\) 23.9179 0.917210
\(681\) 0 0
\(682\) −3.88056 −0.148594
\(683\) 11.4828 0.439378 0.219689 0.975570i \(-0.429496\pi\)
0.219689 + 0.975570i \(0.429496\pi\)
\(684\) 0 0
\(685\) 15.0929 0.576670
\(686\) 16.4725 0.628924
\(687\) 0 0
\(688\) 4.52760 0.172613
\(689\) −8.85431 −0.337322
\(690\) 0 0
\(691\) −6.59111 −0.250738 −0.125369 0.992110i \(-0.540011\pi\)
−0.125369 + 0.992110i \(0.540011\pi\)
\(692\) 3.30728 0.125724
\(693\) 0 0
\(694\) 26.9886 1.02447
\(695\) 11.1708 0.423731
\(696\) 0 0
\(697\) −17.9621 −0.680362
\(698\) 37.3031 1.41194
\(699\) 0 0
\(700\) 0.879008 0.0332234
\(701\) 25.5796 0.966126 0.483063 0.875586i \(-0.339524\pi\)
0.483063 + 0.875586i \(0.339524\pi\)
\(702\) 0 0
\(703\) −34.6465 −1.30672
\(704\) 18.2216 0.686751
\(705\) 0 0
\(706\) 27.3745 1.03025
\(707\) −7.09516 −0.266841
\(708\) 0 0
\(709\) 33.3520 1.25256 0.626280 0.779598i \(-0.284577\pi\)
0.626280 + 0.779598i \(0.284577\pi\)
\(710\) −2.89238 −0.108549
\(711\) 0 0
\(712\) 3.07425 0.115212
\(713\) 3.59831 0.134758
\(714\) 0 0
\(715\) 2.41290 0.0902373
\(716\) −17.1018 −0.639126
\(717\) 0 0
\(718\) −12.8568 −0.479811
\(719\) −35.2920 −1.31617 −0.658084 0.752944i \(-0.728633\pi\)
−0.658084 + 0.752944i \(0.728633\pi\)
\(720\) 0 0
\(721\) 18.0617 0.672651
\(722\) 3.99033 0.148505
\(723\) 0 0
\(724\) 12.9677 0.481941
\(725\) 6.01934 0.223553
\(726\) 0 0
\(727\) −28.5760 −1.05982 −0.529912 0.848053i \(-0.677775\pi\)
−0.529912 + 0.848053i \(0.677775\pi\)
\(728\) 3.95208 0.146474
\(729\) 0 0
\(730\) −13.5673 −0.502148
\(731\) 18.2812 0.676156
\(732\) 0 0
\(733\) 40.9855 1.51384 0.756918 0.653510i \(-0.226704\pi\)
0.756918 + 0.653510i \(0.226704\pi\)
\(734\) −1.70106 −0.0627874
\(735\) 0 0
\(736\) −9.06720 −0.334222
\(737\) −34.8011 −1.28192
\(738\) 0 0
\(739\) −12.0594 −0.443613 −0.221807 0.975091i \(-0.571195\pi\)
−0.221807 + 0.975091i \(0.571195\pi\)
\(740\) 5.49135 0.201866
\(741\) 0 0
\(742\) 10.4795 0.384716
\(743\) 33.2440 1.21961 0.609803 0.792553i \(-0.291249\pi\)
0.609803 + 0.792553i \(0.291249\pi\)
\(744\) 0 0
\(745\) −7.56657 −0.277218
\(746\) 33.2707 1.21813
\(747\) 0 0
\(748\) 12.8360 0.469331
\(749\) 4.38234 0.160127
\(750\) 0 0
\(751\) 17.5671 0.641033 0.320516 0.947243i \(-0.396144\pi\)
0.320516 + 0.947243i \(0.396144\pi\)
\(752\) −1.82907 −0.0666993
\(753\) 0 0
\(754\) 7.40266 0.269589
\(755\) −4.28422 −0.155919
\(756\) 0 0
\(757\) 8.12514 0.295313 0.147657 0.989039i \(-0.452827\pi\)
0.147657 + 0.989039i \(0.452827\pi\)
\(758\) 21.8660 0.794208
\(759\) 0 0
\(760\) −14.6062 −0.529823
\(761\) 1.67104 0.0605750 0.0302875 0.999541i \(-0.490358\pi\)
0.0302875 + 0.999541i \(0.490358\pi\)
\(762\) 0 0
\(763\) −16.7362 −0.605890
\(764\) 15.5044 0.560931
\(765\) 0 0
\(766\) 17.5144 0.632823
\(767\) −4.21300 −0.152123
\(768\) 0 0
\(769\) −16.2382 −0.585563 −0.292782 0.956179i \(-0.594581\pi\)
−0.292782 + 0.956179i \(0.594581\pi\)
\(770\) −2.85579 −0.102916
\(771\) 0 0
\(772\) 7.14404 0.257120
\(773\) 20.2377 0.727898 0.363949 0.931419i \(-0.381428\pi\)
0.363949 + 0.931419i \(0.381428\pi\)
\(774\) 0 0
\(775\) −1.58614 −0.0569758
\(776\) 9.76099 0.350399
\(777\) 0 0
\(778\) −16.4581 −0.590052
\(779\) 10.9691 0.393008
\(780\) 0 0
\(781\) −5.67487 −0.203063
\(782\) 19.7092 0.704798
\(783\) 0 0
\(784\) 10.8625 0.387948
\(785\) −5.39518 −0.192562
\(786\) 0 0
\(787\) −19.8995 −0.709340 −0.354670 0.934991i \(-0.615407\pi\)
−0.354670 + 0.934991i \(0.615407\pi\)
\(788\) 19.5506 0.696461
\(789\) 0 0
\(790\) 12.0600 0.429076
\(791\) −0.691851 −0.0245994
\(792\) 0 0
\(793\) −6.30567 −0.223921
\(794\) 8.15609 0.289449
\(795\) 0 0
\(796\) 12.3681 0.438377
\(797\) 45.1119 1.59795 0.798973 0.601366i \(-0.205377\pi\)
0.798973 + 0.601366i \(0.205377\pi\)
\(798\) 0 0
\(799\) −7.38529 −0.261273
\(800\) 3.99684 0.141309
\(801\) 0 0
\(802\) 8.54324 0.301672
\(803\) −26.6191 −0.939368
\(804\) 0 0
\(805\) 2.64808 0.0933326
\(806\) −1.95065 −0.0687089
\(807\) 0 0
\(808\) −18.6864 −0.657387
\(809\) 10.7813 0.379049 0.189525 0.981876i \(-0.439305\pi\)
0.189525 + 0.981876i \(0.439305\pi\)
\(810\) 0 0
\(811\) 10.2037 0.358301 0.179150 0.983822i \(-0.442665\pi\)
0.179150 + 0.983822i \(0.442665\pi\)
\(812\) 5.29105 0.185679
\(813\) 0 0
\(814\) −17.8408 −0.625319
\(815\) 15.7496 0.551683
\(816\) 0 0
\(817\) −11.1640 −0.390579
\(818\) −25.8711 −0.904564
\(819\) 0 0
\(820\) −1.73856 −0.0607133
\(821\) 17.4466 0.608891 0.304445 0.952530i \(-0.401529\pi\)
0.304445 + 0.952530i \(0.401529\pi\)
\(822\) 0 0
\(823\) 1.89092 0.0659133 0.0329566 0.999457i \(-0.489508\pi\)
0.0329566 + 0.999457i \(0.489508\pi\)
\(824\) 47.5688 1.65714
\(825\) 0 0
\(826\) 4.98631 0.173496
\(827\) 10.1852 0.354173 0.177086 0.984195i \(-0.443333\pi\)
0.177086 + 0.984195i \(0.443333\pi\)
\(828\) 0 0
\(829\) −4.41864 −0.153466 −0.0767328 0.997052i \(-0.524449\pi\)
−0.0767328 + 0.997052i \(0.524449\pi\)
\(830\) −4.02439 −0.139689
\(831\) 0 0
\(832\) 9.15950 0.317549
\(833\) 43.8600 1.51966
\(834\) 0 0
\(835\) 18.1941 0.629633
\(836\) −7.83869 −0.271107
\(837\) 0 0
\(838\) 26.5658 0.917700
\(839\) −10.8397 −0.374227 −0.187113 0.982338i \(-0.559913\pi\)
−0.187113 + 0.982338i \(0.559913\pi\)
\(840\) 0 0
\(841\) 7.23243 0.249394
\(842\) 11.4689 0.395246
\(843\) 0 0
\(844\) −7.00777 −0.241217
\(845\) −11.7871 −0.405489
\(846\) 0 0
\(847\) 7.23697 0.248665
\(848\) 15.4913 0.531975
\(849\) 0 0
\(850\) −8.68782 −0.297990
\(851\) 16.5431 0.567092
\(852\) 0 0
\(853\) 38.3227 1.31214 0.656072 0.754698i \(-0.272217\pi\)
0.656072 + 0.754698i \(0.272217\pi\)
\(854\) 7.46309 0.255382
\(855\) 0 0
\(856\) 11.5417 0.394488
\(857\) 10.9435 0.373822 0.186911 0.982377i \(-0.440152\pi\)
0.186911 + 0.982377i \(0.440152\pi\)
\(858\) 0 0
\(859\) −11.3613 −0.387643 −0.193821 0.981037i \(-0.562088\pi\)
−0.193821 + 0.981037i \(0.562088\pi\)
\(860\) 1.76946 0.0603379
\(861\) 0 0
\(862\) −2.76761 −0.0942651
\(863\) −33.9378 −1.15526 −0.577628 0.816300i \(-0.696022\pi\)
−0.577628 + 0.816300i \(0.696022\pi\)
\(864\) 0 0
\(865\) −4.39190 −0.149329
\(866\) −15.5901 −0.529772
\(867\) 0 0
\(868\) −1.39423 −0.0473232
\(869\) 23.6618 0.802672
\(870\) 0 0
\(871\) −17.4936 −0.592748
\(872\) −44.0778 −1.49266
\(873\) 0 0
\(874\) −12.0360 −0.407123
\(875\) −1.16728 −0.0394612
\(876\) 0 0
\(877\) 30.3020 1.02322 0.511612 0.859216i \(-0.329048\pi\)
0.511612 + 0.859216i \(0.329048\pi\)
\(878\) −3.84468 −0.129752
\(879\) 0 0
\(880\) −4.22157 −0.142309
\(881\) 0.576968 0.0194385 0.00971927 0.999953i \(-0.496906\pi\)
0.00971927 + 0.999953i \(0.496906\pi\)
\(882\) 0 0
\(883\) 24.3155 0.818282 0.409141 0.912471i \(-0.365828\pi\)
0.409141 + 0.912471i \(0.365828\pi\)
\(884\) 6.45232 0.217015
\(885\) 0 0
\(886\) 18.7285 0.629196
\(887\) −36.5382 −1.22683 −0.613416 0.789760i \(-0.710205\pi\)
−0.613416 + 0.789760i \(0.710205\pi\)
\(888\) 0 0
\(889\) 20.2020 0.677552
\(890\) −1.11667 −0.0374310
\(891\) 0 0
\(892\) −4.25415 −0.142440
\(893\) 4.51005 0.150923
\(894\) 0 0
\(895\) 22.7104 0.759124
\(896\) −1.50992 −0.0504428
\(897\) 0 0
\(898\) −8.77187 −0.292721
\(899\) −9.54751 −0.318427
\(900\) 0 0
\(901\) 62.5499 2.08384
\(902\) 5.64839 0.188071
\(903\) 0 0
\(904\) −1.82212 −0.0606029
\(905\) −17.2204 −0.572427
\(906\) 0 0
\(907\) −34.4021 −1.14230 −0.571152 0.820845i \(-0.693503\pi\)
−0.571152 + 0.820845i \(0.693503\pi\)
\(908\) 2.03165 0.0674228
\(909\) 0 0
\(910\) −1.43553 −0.0475874
\(911\) −31.0883 −1.03000 −0.515001 0.857189i \(-0.672209\pi\)
−0.515001 + 0.857189i \(0.672209\pi\)
\(912\) 0 0
\(913\) −7.89588 −0.261315
\(914\) −16.4268 −0.543351
\(915\) 0 0
\(916\) −4.90140 −0.161947
\(917\) 7.62193 0.251698
\(918\) 0 0
\(919\) −12.3439 −0.407188 −0.203594 0.979055i \(-0.565262\pi\)
−0.203594 + 0.979055i \(0.565262\pi\)
\(920\) 6.97422 0.229933
\(921\) 0 0
\(922\) 10.9352 0.360132
\(923\) −2.85261 −0.0938948
\(924\) 0 0
\(925\) −7.29224 −0.239767
\(926\) −14.3979 −0.473145
\(927\) 0 0
\(928\) 24.0583 0.789752
\(929\) 5.59982 0.183724 0.0918621 0.995772i \(-0.470718\pi\)
0.0918621 + 0.995772i \(0.470718\pi\)
\(930\) 0 0
\(931\) −26.7844 −0.877824
\(932\) −12.5269 −0.410331
\(933\) 0 0
\(934\) 2.63149 0.0861050
\(935\) −17.0456 −0.557449
\(936\) 0 0
\(937\) −18.6418 −0.609002 −0.304501 0.952512i \(-0.598490\pi\)
−0.304501 + 0.952512i \(0.598490\pi\)
\(938\) 20.7046 0.676030
\(939\) 0 0
\(940\) −0.714828 −0.0233151
\(941\) −2.41923 −0.0788647 −0.0394324 0.999222i \(-0.512555\pi\)
−0.0394324 + 0.999222i \(0.512555\pi\)
\(942\) 0 0
\(943\) −5.23756 −0.170558
\(944\) 7.37099 0.239905
\(945\) 0 0
\(946\) −5.74876 −0.186908
\(947\) −42.9867 −1.39688 −0.698440 0.715669i \(-0.746122\pi\)
−0.698440 + 0.715669i \(0.746122\pi\)
\(948\) 0 0
\(949\) −13.3807 −0.434357
\(950\) 5.30548 0.172133
\(951\) 0 0
\(952\) −27.9189 −0.904856
\(953\) −1.84709 −0.0598332 −0.0299166 0.999552i \(-0.509524\pi\)
−0.0299166 + 0.999552i \(0.509524\pi\)
\(954\) 0 0
\(955\) −20.5891 −0.666247
\(956\) 15.9112 0.514606
\(957\) 0 0
\(958\) −11.7345 −0.379124
\(959\) −17.6176 −0.568902
\(960\) 0 0
\(961\) −28.4842 −0.918844
\(962\) −8.96808 −0.289143
\(963\) 0 0
\(964\) 4.22324 0.136021
\(965\) −9.48692 −0.305395
\(966\) 0 0
\(967\) −3.91413 −0.125870 −0.0629350 0.998018i \(-0.520046\pi\)
−0.0629350 + 0.998018i \(0.520046\pi\)
\(968\) 19.0599 0.612609
\(969\) 0 0
\(970\) −3.54553 −0.113840
\(971\) −0.764398 −0.0245307 −0.0122653 0.999925i \(-0.503904\pi\)
−0.0122653 + 0.999925i \(0.503904\pi\)
\(972\) 0 0
\(973\) −13.0394 −0.418024
\(974\) −24.9814 −0.800456
\(975\) 0 0
\(976\) 11.0323 0.353135
\(977\) −23.1991 −0.742204 −0.371102 0.928592i \(-0.621020\pi\)
−0.371102 + 0.928592i \(0.621020\pi\)
\(978\) 0 0
\(979\) −2.19092 −0.0700221
\(980\) 4.24524 0.135609
\(981\) 0 0
\(982\) −10.8592 −0.346530
\(983\) −58.1928 −1.85606 −0.928031 0.372503i \(-0.878500\pi\)
−0.928031 + 0.372503i \(0.878500\pi\)
\(984\) 0 0
\(985\) −25.9622 −0.827224
\(986\) −52.2949 −1.66541
\(987\) 0 0
\(988\) −3.94031 −0.125358
\(989\) 5.33063 0.169504
\(990\) 0 0
\(991\) −29.7580 −0.945295 −0.472648 0.881252i \(-0.656702\pi\)
−0.472648 + 0.881252i \(0.656702\pi\)
\(992\) −6.33954 −0.201281
\(993\) 0 0
\(994\) 3.37621 0.107087
\(995\) −16.4243 −0.520684
\(996\) 0 0
\(997\) 30.6497 0.970687 0.485343 0.874324i \(-0.338695\pi\)
0.485343 + 0.874324i \(0.338695\pi\)
\(998\) 24.0109 0.760053
\(999\) 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 \(a_p\))