Properties

Label 6027.2.a.bk.1.4
Level 6027
Weight 2
Character 6027.1
Self dual Yes
Analytic conductor 48.126
Analytic rank 1
Dimension 14
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 6027 = 3 \cdot 7^{2} \cdot 41 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6027.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.1258372982\)
Analytic rank: \(1\)
Dimension: \(14\)
Coefficient field: \(\mathbb{Q}[x]/(x^{14} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Root \(1.64093\)
Character \(\chi\) = 6027.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.64093 q^{2} +1.00000 q^{3} +0.692668 q^{4} +0.0817657 q^{5} -1.64093 q^{6} +2.14525 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.64093 q^{2} +1.00000 q^{3} +0.692668 q^{4} +0.0817657 q^{5} -1.64093 q^{6} +2.14525 q^{8} +1.00000 q^{9} -0.134172 q^{10} -4.94328 q^{11} +0.692668 q^{12} +1.23171 q^{13} +0.0817657 q^{15} -4.90555 q^{16} -0.810235 q^{17} -1.64093 q^{18} +6.55953 q^{19} +0.0566365 q^{20} +8.11161 q^{22} -5.53945 q^{23} +2.14525 q^{24} -4.99331 q^{25} -2.02116 q^{26} +1.00000 q^{27} -0.0447280 q^{29} -0.134172 q^{30} +7.20734 q^{31} +3.75919 q^{32} -4.94328 q^{33} +1.32954 q^{34} +0.692668 q^{36} +5.22958 q^{37} -10.7638 q^{38} +1.23171 q^{39} +0.175408 q^{40} -1.00000 q^{41} -8.64881 q^{43} -3.42405 q^{44} +0.0817657 q^{45} +9.08988 q^{46} +10.9081 q^{47} -4.90555 q^{48} +8.19370 q^{50} -0.810235 q^{51} +0.853167 q^{52} -5.99240 q^{53} -1.64093 q^{54} -0.404191 q^{55} +6.55953 q^{57} +0.0733957 q^{58} -4.34053 q^{59} +0.0566365 q^{60} +1.13380 q^{61} -11.8268 q^{62} +3.64251 q^{64} +0.100712 q^{65} +8.11161 q^{66} -2.70626 q^{67} -0.561224 q^{68} -5.53945 q^{69} -5.56029 q^{71} +2.14525 q^{72} -14.5072 q^{73} -8.58140 q^{74} -4.99331 q^{75} +4.54357 q^{76} -2.02116 q^{78} +15.5574 q^{79} -0.401106 q^{80} +1.00000 q^{81} +1.64093 q^{82} +9.02538 q^{83} -0.0662495 q^{85} +14.1921 q^{86} -0.0447280 q^{87} -10.6046 q^{88} +7.38768 q^{89} -0.134172 q^{90} -3.83700 q^{92} +7.20734 q^{93} -17.8995 q^{94} +0.536345 q^{95} +3.75919 q^{96} +5.44556 q^{97} -4.94328 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 14q - 2q^{2} + 14q^{3} + 14q^{4} - 10q^{5} - 2q^{6} - 6q^{8} + 14q^{9} + O(q^{10}) \) \( 14q - 2q^{2} + 14q^{3} + 14q^{4} - 10q^{5} - 2q^{6} - 6q^{8} + 14q^{9} - 3q^{10} - 16q^{11} + 14q^{12} - 21q^{13} - 10q^{15} + 22q^{16} - 12q^{17} - 2q^{18} - 2q^{19} - 40q^{20} + q^{22} - 7q^{23} - 6q^{24} + 22q^{25} - 2q^{26} + 14q^{27} - 16q^{29} - 3q^{30} - 8q^{31} - 19q^{32} - 16q^{33} - 33q^{34} + 14q^{36} + q^{37} - 32q^{38} - 21q^{39} + 13q^{40} - 14q^{41} + 14q^{43} - 36q^{44} - 10q^{45} - 12q^{46} - 12q^{47} + 22q^{48} - q^{50} - 12q^{51} - 60q^{52} - 20q^{53} - 2q^{54} + 11q^{55} - 2q^{57} + 21q^{58} - 25q^{59} - 40q^{60} - 26q^{61} + 33q^{62} + 42q^{64} - 8q^{65} + q^{66} - 22q^{67} - 15q^{68} - 7q^{69} - 36q^{71} - 6q^{72} - 31q^{73} - 65q^{74} + 22q^{75} + 2q^{76} - 2q^{78} + 12q^{79} - 112q^{80} + 14q^{81} + 2q^{82} - 20q^{83} + 40q^{85} - 9q^{86} - 16q^{87} - 54q^{88} - 39q^{89} - 3q^{90} + 63q^{92} - 8q^{93} - 14q^{94} - 55q^{95} - 19q^{96} - 18q^{97} - 16q^{99} + O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.64093 −1.16032 −0.580158 0.814504i \(-0.697009\pi\)
−0.580158 + 0.814504i \(0.697009\pi\)
\(3\) 1.00000 0.577350
\(4\) 0.692668 0.346334
\(5\) 0.0817657 0.0365667 0.0182834 0.999833i \(-0.494180\pi\)
0.0182834 + 0.999833i \(0.494180\pi\)
\(6\) −1.64093 −0.669909
\(7\) 0 0
\(8\) 2.14525 0.758459
\(9\) 1.00000 0.333333
\(10\) −0.134172 −0.0424290
\(11\) −4.94328 −1.49046 −0.745228 0.666810i \(-0.767659\pi\)
−0.745228 + 0.666810i \(0.767659\pi\)
\(12\) 0.692668 0.199956
\(13\) 1.23171 0.341616 0.170808 0.985304i \(-0.445362\pi\)
0.170808 + 0.985304i \(0.445362\pi\)
\(14\) 0 0
\(15\) 0.0817657 0.0211118
\(16\) −4.90555 −1.22639
\(17\) −0.810235 −0.196511 −0.0982555 0.995161i \(-0.531326\pi\)
−0.0982555 + 0.995161i \(0.531326\pi\)
\(18\) −1.64093 −0.386772
\(19\) 6.55953 1.50486 0.752430 0.658673i \(-0.228882\pi\)
0.752430 + 0.658673i \(0.228882\pi\)
\(20\) 0.0566365 0.0126643
\(21\) 0 0
\(22\) 8.11161 1.72940
\(23\) −5.53945 −1.15506 −0.577528 0.816371i \(-0.695983\pi\)
−0.577528 + 0.816371i \(0.695983\pi\)
\(24\) 2.14525 0.437897
\(25\) −4.99331 −0.998663
\(26\) −2.02116 −0.396382
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) −0.0447280 −0.00830578 −0.00415289 0.999991i \(-0.501322\pi\)
−0.00415289 + 0.999991i \(0.501322\pi\)
\(30\) −0.134172 −0.0244964
\(31\) 7.20734 1.29448 0.647238 0.762288i \(-0.275924\pi\)
0.647238 + 0.762288i \(0.275924\pi\)
\(32\) 3.75919 0.664537
\(33\) −4.94328 −0.860515
\(34\) 1.32954 0.228015
\(35\) 0 0
\(36\) 0.692668 0.115445
\(37\) 5.22958 0.859737 0.429869 0.902891i \(-0.358560\pi\)
0.429869 + 0.902891i \(0.358560\pi\)
\(38\) −10.7638 −1.74611
\(39\) 1.23171 0.197232
\(40\) 0.175408 0.0277344
\(41\) −1.00000 −0.156174
\(42\) 0 0
\(43\) −8.64881 −1.31893 −0.659466 0.751735i \(-0.729217\pi\)
−0.659466 + 0.751735i \(0.729217\pi\)
\(44\) −3.42405 −0.516195
\(45\) 0.0817657 0.0121889
\(46\) 9.08988 1.34023
\(47\) 10.9081 1.59111 0.795556 0.605881i \(-0.207179\pi\)
0.795556 + 0.605881i \(0.207179\pi\)
\(48\) −4.90555 −0.708055
\(49\) 0 0
\(50\) 8.19370 1.15876
\(51\) −0.810235 −0.113456
\(52\) 0.853167 0.118313
\(53\) −5.99240 −0.823120 −0.411560 0.911383i \(-0.635016\pi\)
−0.411560 + 0.911383i \(0.635016\pi\)
\(54\) −1.64093 −0.223303
\(55\) −0.404191 −0.0545011
\(56\) 0 0
\(57\) 6.55953 0.868831
\(58\) 0.0733957 0.00963733
\(59\) −4.34053 −0.565089 −0.282544 0.959254i \(-0.591178\pi\)
−0.282544 + 0.959254i \(0.591178\pi\)
\(60\) 0.0566365 0.00731174
\(61\) 1.13380 0.145168 0.0725842 0.997362i \(-0.476875\pi\)
0.0725842 + 0.997362i \(0.476875\pi\)
\(62\) −11.8268 −1.50200
\(63\) 0 0
\(64\) 3.64251 0.455314
\(65\) 0.100712 0.0124918
\(66\) 8.11161 0.998470
\(67\) −2.70626 −0.330622 −0.165311 0.986241i \(-0.552863\pi\)
−0.165311 + 0.986241i \(0.552863\pi\)
\(68\) −0.561224 −0.0680584
\(69\) −5.53945 −0.666872
\(70\) 0 0
\(71\) −5.56029 −0.659885 −0.329943 0.944001i \(-0.607029\pi\)
−0.329943 + 0.944001i \(0.607029\pi\)
\(72\) 2.14525 0.252820
\(73\) −14.5072 −1.69794 −0.848972 0.528438i \(-0.822778\pi\)
−0.848972 + 0.528438i \(0.822778\pi\)
\(74\) −8.58140 −0.997567
\(75\) −4.99331 −0.576578
\(76\) 4.54357 0.521184
\(77\) 0 0
\(78\) −2.02116 −0.228851
\(79\) 15.5574 1.75034 0.875171 0.483813i \(-0.160749\pi\)
0.875171 + 0.483813i \(0.160749\pi\)
\(80\) −0.401106 −0.0448450
\(81\) 1.00000 0.111111
\(82\) 1.64093 0.181211
\(83\) 9.02538 0.990664 0.495332 0.868704i \(-0.335046\pi\)
0.495332 + 0.868704i \(0.335046\pi\)
\(84\) 0 0
\(85\) −0.0662495 −0.00718577
\(86\) 14.1921 1.53038
\(87\) −0.0447280 −0.00479534
\(88\) −10.6046 −1.13045
\(89\) 7.38768 0.783093 0.391546 0.920158i \(-0.371940\pi\)
0.391546 + 0.920158i \(0.371940\pi\)
\(90\) −0.134172 −0.0141430
\(91\) 0 0
\(92\) −3.83700 −0.400035
\(93\) 7.20734 0.747366
\(94\) −17.8995 −1.84619
\(95\) 0.536345 0.0550278
\(96\) 3.75919 0.383671
\(97\) 5.44556 0.552912 0.276456 0.961027i \(-0.410840\pi\)
0.276456 + 0.961027i \(0.410840\pi\)
\(98\) 0 0
\(99\) −4.94328 −0.496819
\(100\) −3.45871 −0.345871
\(101\) −3.78486 −0.376607 −0.188304 0.982111i \(-0.560299\pi\)
−0.188304 + 0.982111i \(0.560299\pi\)
\(102\) 1.32954 0.131644
\(103\) −19.1368 −1.88561 −0.942804 0.333349i \(-0.891821\pi\)
−0.942804 + 0.333349i \(0.891821\pi\)
\(104\) 2.64233 0.259102
\(105\) 0 0
\(106\) 9.83314 0.955079
\(107\) −13.5411 −1.30907 −0.654534 0.756032i \(-0.727135\pi\)
−0.654534 + 0.756032i \(0.727135\pi\)
\(108\) 0.692668 0.0666520
\(109\) 0.705015 0.0675282 0.0337641 0.999430i \(-0.489251\pi\)
0.0337641 + 0.999430i \(0.489251\pi\)
\(110\) 0.663251 0.0632385
\(111\) 5.22958 0.496370
\(112\) 0 0
\(113\) −11.6339 −1.09443 −0.547213 0.836993i \(-0.684311\pi\)
−0.547213 + 0.836993i \(0.684311\pi\)
\(114\) −10.7638 −1.00812
\(115\) −0.452937 −0.0422366
\(116\) −0.0309816 −0.00287657
\(117\) 1.23171 0.113872
\(118\) 7.12253 0.655682
\(119\) 0 0
\(120\) 0.175408 0.0160125
\(121\) 13.4360 1.22146
\(122\) −1.86049 −0.168441
\(123\) −1.00000 −0.0901670
\(124\) 4.99229 0.448321
\(125\) −0.817110 −0.0730846
\(126\) 0 0
\(127\) −2.52451 −0.224014 −0.112007 0.993707i \(-0.535728\pi\)
−0.112007 + 0.993707i \(0.535728\pi\)
\(128\) −13.4955 −1.19284
\(129\) −8.64881 −0.761485
\(130\) −0.165262 −0.0144944
\(131\) −10.8567 −0.948553 −0.474277 0.880376i \(-0.657290\pi\)
−0.474277 + 0.880376i \(0.657290\pi\)
\(132\) −3.42405 −0.298025
\(133\) 0 0
\(134\) 4.44080 0.383626
\(135\) 0.0817657 0.00703727
\(136\) −1.73816 −0.149046
\(137\) −10.3736 −0.886277 −0.443138 0.896453i \(-0.646135\pi\)
−0.443138 + 0.896453i \(0.646135\pi\)
\(138\) 9.08988 0.773782
\(139\) −3.46799 −0.294151 −0.147075 0.989125i \(-0.546986\pi\)
−0.147075 + 0.989125i \(0.546986\pi\)
\(140\) 0 0
\(141\) 10.9081 0.918628
\(142\) 9.12408 0.765676
\(143\) −6.08870 −0.509163
\(144\) −4.90555 −0.408796
\(145\) −0.00365722 −0.000303715 0
\(146\) 23.8054 1.97015
\(147\) 0 0
\(148\) 3.62236 0.297756
\(149\) 22.9065 1.87657 0.938287 0.345857i \(-0.112412\pi\)
0.938287 + 0.345857i \(0.112412\pi\)
\(150\) 8.19370 0.669013
\(151\) −22.3577 −1.81945 −0.909724 0.415214i \(-0.863707\pi\)
−0.909724 + 0.415214i \(0.863707\pi\)
\(152\) 14.0718 1.14137
\(153\) −0.810235 −0.0655037
\(154\) 0 0
\(155\) 0.589313 0.0473348
\(156\) 0.853167 0.0683081
\(157\) 12.9470 1.03328 0.516640 0.856203i \(-0.327182\pi\)
0.516640 + 0.856203i \(0.327182\pi\)
\(158\) −25.5287 −2.03095
\(159\) −5.99240 −0.475228
\(160\) 0.307373 0.0242999
\(161\) 0 0
\(162\) −1.64093 −0.128924
\(163\) 2.36528 0.185263 0.0926313 0.995700i \(-0.470472\pi\)
0.0926313 + 0.995700i \(0.470472\pi\)
\(164\) −0.692668 −0.0540883
\(165\) −0.404191 −0.0314662
\(166\) −14.8101 −1.14948
\(167\) 14.7792 1.14365 0.571824 0.820377i \(-0.306236\pi\)
0.571824 + 0.820377i \(0.306236\pi\)
\(168\) 0 0
\(169\) −11.4829 −0.883299
\(170\) 0.108711 0.00833776
\(171\) 6.55953 0.501620
\(172\) −5.99075 −0.456790
\(173\) −10.5024 −0.798479 −0.399239 0.916847i \(-0.630726\pi\)
−0.399239 + 0.916847i \(0.630726\pi\)
\(174\) 0.0733957 0.00556411
\(175\) 0 0
\(176\) 24.2495 1.82788
\(177\) −4.34053 −0.326254
\(178\) −12.1227 −0.908635
\(179\) −6.55231 −0.489743 −0.244871 0.969556i \(-0.578746\pi\)
−0.244871 + 0.969556i \(0.578746\pi\)
\(180\) 0.0566365 0.00422143
\(181\) −2.05872 −0.153023 −0.0765115 0.997069i \(-0.524378\pi\)
−0.0765115 + 0.997069i \(0.524378\pi\)
\(182\) 0 0
\(183\) 1.13380 0.0838130
\(184\) −11.8835 −0.876063
\(185\) 0.427600 0.0314378
\(186\) −11.8268 −0.867181
\(187\) 4.00522 0.292891
\(188\) 7.55569 0.551056
\(189\) 0 0
\(190\) −0.880107 −0.0638496
\(191\) −18.4559 −1.33542 −0.667712 0.744419i \(-0.732726\pi\)
−0.667712 + 0.744419i \(0.732726\pi\)
\(192\) 3.64251 0.262875
\(193\) 22.7365 1.63661 0.818304 0.574786i \(-0.194915\pi\)
0.818304 + 0.574786i \(0.194915\pi\)
\(194\) −8.93580 −0.641553
\(195\) 0.100712 0.00721213
\(196\) 0 0
\(197\) 1.89397 0.134940 0.0674698 0.997721i \(-0.478507\pi\)
0.0674698 + 0.997721i \(0.478507\pi\)
\(198\) 8.11161 0.576467
\(199\) 20.6802 1.46598 0.732989 0.680241i \(-0.238125\pi\)
0.732989 + 0.680241i \(0.238125\pi\)
\(200\) −10.7119 −0.757445
\(201\) −2.70626 −0.190885
\(202\) 6.21070 0.436984
\(203\) 0 0
\(204\) −0.561224 −0.0392935
\(205\) −0.0817657 −0.00571077
\(206\) 31.4023 2.18790
\(207\) −5.53945 −0.385019
\(208\) −6.04222 −0.418953
\(209\) −32.4256 −2.24293
\(210\) 0 0
\(211\) −8.73506 −0.601346 −0.300673 0.953727i \(-0.597211\pi\)
−0.300673 + 0.953727i \(0.597211\pi\)
\(212\) −4.15074 −0.285074
\(213\) −5.56029 −0.380985
\(214\) 22.2201 1.51893
\(215\) −0.707176 −0.0482290
\(216\) 2.14525 0.145966
\(217\) 0 0
\(218\) −1.15688 −0.0783541
\(219\) −14.5072 −0.980308
\(220\) −0.279970 −0.0188756
\(221\) −0.997977 −0.0671312
\(222\) −8.58140 −0.575946
\(223\) 12.8945 0.863483 0.431741 0.901997i \(-0.357899\pi\)
0.431741 + 0.901997i \(0.357899\pi\)
\(224\) 0 0
\(225\) −4.99331 −0.332888
\(226\) 19.0905 1.26988
\(227\) −18.9009 −1.25450 −0.627248 0.778820i \(-0.715819\pi\)
−0.627248 + 0.778820i \(0.715819\pi\)
\(228\) 4.54357 0.300905
\(229\) −1.43656 −0.0949305 −0.0474652 0.998873i \(-0.515114\pi\)
−0.0474652 + 0.998873i \(0.515114\pi\)
\(230\) 0.743241 0.0490078
\(231\) 0 0
\(232\) −0.0959526 −0.00629960
\(233\) −14.7809 −0.968331 −0.484166 0.874976i \(-0.660877\pi\)
−0.484166 + 0.874976i \(0.660877\pi\)
\(234\) −2.02116 −0.132127
\(235\) 0.891909 0.0581817
\(236\) −3.00655 −0.195709
\(237\) 15.5574 1.01056
\(238\) 0 0
\(239\) −1.03844 −0.0671712 −0.0335856 0.999436i \(-0.510693\pi\)
−0.0335856 + 0.999436i \(0.510693\pi\)
\(240\) −0.401106 −0.0258913
\(241\) −24.3864 −1.57087 −0.785433 0.618947i \(-0.787559\pi\)
−0.785433 + 0.618947i \(0.787559\pi\)
\(242\) −22.0477 −1.41728
\(243\) 1.00000 0.0641500
\(244\) 0.785347 0.0502767
\(245\) 0 0
\(246\) 1.64093 0.104622
\(247\) 8.07945 0.514083
\(248\) 15.4615 0.981808
\(249\) 9.02538 0.571960
\(250\) 1.34083 0.0848012
\(251\) −10.4072 −0.656898 −0.328449 0.944522i \(-0.606526\pi\)
−0.328449 + 0.944522i \(0.606526\pi\)
\(252\) 0 0
\(253\) 27.3831 1.72156
\(254\) 4.14255 0.259927
\(255\) −0.0662495 −0.00414870
\(256\) 14.8602 0.928764
\(257\) 18.1220 1.13042 0.565210 0.824947i \(-0.308795\pi\)
0.565210 + 0.824947i \(0.308795\pi\)
\(258\) 14.1921 0.883564
\(259\) 0 0
\(260\) 0.0697598 0.00432632
\(261\) −0.0447280 −0.00276859
\(262\) 17.8151 1.10062
\(263\) −2.84868 −0.175657 −0.0878284 0.996136i \(-0.527993\pi\)
−0.0878284 + 0.996136i \(0.527993\pi\)
\(264\) −10.6046 −0.652666
\(265\) −0.489973 −0.0300988
\(266\) 0 0
\(267\) 7.38768 0.452119
\(268\) −1.87454 −0.114506
\(269\) −7.26180 −0.442760 −0.221380 0.975188i \(-0.571056\pi\)
−0.221380 + 0.975188i \(0.571056\pi\)
\(270\) −0.134172 −0.00816546
\(271\) 4.19299 0.254706 0.127353 0.991857i \(-0.459352\pi\)
0.127353 + 0.991857i \(0.459352\pi\)
\(272\) 3.97465 0.240998
\(273\) 0 0
\(274\) 17.0224 1.02836
\(275\) 24.6834 1.48846
\(276\) −3.83700 −0.230960
\(277\) 8.00920 0.481226 0.240613 0.970621i \(-0.422652\pi\)
0.240613 + 0.970621i \(0.422652\pi\)
\(278\) 5.69074 0.341308
\(279\) 7.20734 0.431492
\(280\) 0 0
\(281\) −2.19975 −0.131226 −0.0656131 0.997845i \(-0.520900\pi\)
−0.0656131 + 0.997845i \(0.520900\pi\)
\(282\) −17.8995 −1.06590
\(283\) −3.83526 −0.227983 −0.113991 0.993482i \(-0.536364\pi\)
−0.113991 + 0.993482i \(0.536364\pi\)
\(284\) −3.85144 −0.228541
\(285\) 0.536345 0.0317703
\(286\) 9.99117 0.590790
\(287\) 0 0
\(288\) 3.75919 0.221512
\(289\) −16.3435 −0.961383
\(290\) 0.00600125 0.000352406 0
\(291\) 5.44556 0.319224
\(292\) −10.0487 −0.588055
\(293\) −7.82147 −0.456935 −0.228468 0.973552i \(-0.573371\pi\)
−0.228468 + 0.973552i \(0.573371\pi\)
\(294\) 0 0
\(295\) −0.354907 −0.0206635
\(296\) 11.2187 0.652076
\(297\) −4.94328 −0.286838
\(298\) −37.5881 −2.17742
\(299\) −6.82301 −0.394585
\(300\) −3.45871 −0.199689
\(301\) 0 0
\(302\) 36.6876 2.11113
\(303\) −3.78486 −0.217434
\(304\) −32.1781 −1.84554
\(305\) 0.0927060 0.00530833
\(306\) 1.32954 0.0760050
\(307\) 1.95055 0.111324 0.0556619 0.998450i \(-0.482273\pi\)
0.0556619 + 0.998450i \(0.482273\pi\)
\(308\) 0 0
\(309\) −19.1368 −1.08866
\(310\) −0.967025 −0.0549233
\(311\) 25.3798 1.43916 0.719578 0.694412i \(-0.244336\pi\)
0.719578 + 0.694412i \(0.244336\pi\)
\(312\) 2.64233 0.149592
\(313\) −16.7300 −0.945636 −0.472818 0.881160i \(-0.656763\pi\)
−0.472818 + 0.881160i \(0.656763\pi\)
\(314\) −21.2451 −1.19893
\(315\) 0 0
\(316\) 10.7761 0.606203
\(317\) −27.1439 −1.52455 −0.762277 0.647250i \(-0.775919\pi\)
−0.762277 + 0.647250i \(0.775919\pi\)
\(318\) 9.83314 0.551415
\(319\) 0.221103 0.0123794
\(320\) 0.297832 0.0166493
\(321\) −13.5411 −0.755791
\(322\) 0 0
\(323\) −5.31476 −0.295721
\(324\) 0.692668 0.0384815
\(325\) −6.15033 −0.341159
\(326\) −3.88126 −0.214963
\(327\) 0.705015 0.0389874
\(328\) −2.14525 −0.118451
\(329\) 0 0
\(330\) 0.663251 0.0365108
\(331\) −1.13038 −0.0621311 −0.0310656 0.999517i \(-0.509890\pi\)
−0.0310656 + 0.999517i \(0.509890\pi\)
\(332\) 6.25159 0.343101
\(333\) 5.22958 0.286579
\(334\) −24.2517 −1.32699
\(335\) −0.221279 −0.0120898
\(336\) 0 0
\(337\) 27.0417 1.47306 0.736529 0.676406i \(-0.236464\pi\)
0.736529 + 0.676406i \(0.236464\pi\)
\(338\) 18.8427 1.02491
\(339\) −11.6339 −0.631867
\(340\) −0.0458889 −0.00248867
\(341\) −35.6279 −1.92936
\(342\) −10.7638 −0.582037
\(343\) 0 0
\(344\) −18.5538 −1.00036
\(345\) −0.452937 −0.0243853
\(346\) 17.2337 0.926488
\(347\) −17.4737 −0.938039 −0.469020 0.883188i \(-0.655393\pi\)
−0.469020 + 0.883188i \(0.655393\pi\)
\(348\) −0.0309816 −0.00166079
\(349\) 22.4220 1.20022 0.600112 0.799916i \(-0.295123\pi\)
0.600112 + 0.799916i \(0.295123\pi\)
\(350\) 0 0
\(351\) 1.23171 0.0657439
\(352\) −18.5827 −0.990463
\(353\) −9.96215 −0.530232 −0.265116 0.964217i \(-0.585410\pi\)
−0.265116 + 0.964217i \(0.585410\pi\)
\(354\) 7.12253 0.378558
\(355\) −0.454641 −0.0241299
\(356\) 5.11721 0.271212
\(357\) 0 0
\(358\) 10.7519 0.568256
\(359\) −21.0085 −1.10879 −0.554394 0.832254i \(-0.687050\pi\)
−0.554394 + 0.832254i \(0.687050\pi\)
\(360\) 0.175408 0.00924480
\(361\) 24.0274 1.26460
\(362\) 3.37822 0.177555
\(363\) 13.4360 0.705209
\(364\) 0 0
\(365\) −1.18619 −0.0620882
\(366\) −1.86049 −0.0972496
\(367\) −31.8537 −1.66275 −0.831376 0.555711i \(-0.812446\pi\)
−0.831376 + 0.555711i \(0.812446\pi\)
\(368\) 27.1740 1.41655
\(369\) −1.00000 −0.0520579
\(370\) −0.701664 −0.0364778
\(371\) 0 0
\(372\) 4.99229 0.258838
\(373\) −22.2169 −1.15035 −0.575175 0.818031i \(-0.695066\pi\)
−0.575175 + 0.818031i \(0.695066\pi\)
\(374\) −6.57231 −0.339846
\(375\) −0.817110 −0.0421954
\(376\) 23.4006 1.20679
\(377\) −0.0550920 −0.00283738
\(378\) 0 0
\(379\) 28.0974 1.44327 0.721633 0.692276i \(-0.243392\pi\)
0.721633 + 0.692276i \(0.243392\pi\)
\(380\) 0.371509 0.0190580
\(381\) −2.52451 −0.129334
\(382\) 30.2850 1.54952
\(383\) 7.97911 0.407714 0.203857 0.979001i \(-0.434652\pi\)
0.203857 + 0.979001i \(0.434652\pi\)
\(384\) −13.4955 −0.688689
\(385\) 0 0
\(386\) −37.3091 −1.89898
\(387\) −8.64881 −0.439644
\(388\) 3.77196 0.191492
\(389\) −34.4544 −1.74691 −0.873453 0.486908i \(-0.838125\pi\)
−0.873453 + 0.486908i \(0.838125\pi\)
\(390\) −0.165262 −0.00836835
\(391\) 4.48826 0.226981
\(392\) 0 0
\(393\) −10.8567 −0.547647
\(394\) −3.10788 −0.156573
\(395\) 1.27206 0.0640043
\(396\) −3.42405 −0.172065
\(397\) −23.1863 −1.16369 −0.581843 0.813301i \(-0.697668\pi\)
−0.581843 + 0.813301i \(0.697668\pi\)
\(398\) −33.9348 −1.70100
\(399\) 0 0
\(400\) 24.4949 1.22475
\(401\) −10.7495 −0.536804 −0.268402 0.963307i \(-0.586496\pi\)
−0.268402 + 0.963307i \(0.586496\pi\)
\(402\) 4.44080 0.221487
\(403\) 8.87737 0.442213
\(404\) −2.62165 −0.130432
\(405\) 0.0817657 0.00406297
\(406\) 0 0
\(407\) −25.8513 −1.28140
\(408\) −1.73816 −0.0860515
\(409\) −15.6989 −0.776261 −0.388130 0.921604i \(-0.626879\pi\)
−0.388130 + 0.921604i \(0.626879\pi\)
\(410\) 0.134172 0.00662629
\(411\) −10.3736 −0.511692
\(412\) −13.2555 −0.653050
\(413\) 0 0
\(414\) 9.08988 0.446743
\(415\) 0.737967 0.0362254
\(416\) 4.63024 0.227016
\(417\) −3.46799 −0.169828
\(418\) 53.2083 2.60250
\(419\) −27.5809 −1.34741 −0.673707 0.738999i \(-0.735299\pi\)
−0.673707 + 0.738999i \(0.735299\pi\)
\(420\) 0 0
\(421\) 24.8712 1.21215 0.606075 0.795408i \(-0.292743\pi\)
0.606075 + 0.795408i \(0.292743\pi\)
\(422\) 14.3337 0.697752
\(423\) 10.9081 0.530370
\(424\) −12.8552 −0.624303
\(425\) 4.04576 0.196248
\(426\) 9.12408 0.442063
\(427\) 0 0
\(428\) −9.37949 −0.453375
\(429\) −6.08870 −0.293965
\(430\) 1.16043 0.0559609
\(431\) 38.0558 1.83308 0.916541 0.399942i \(-0.130970\pi\)
0.916541 + 0.399942i \(0.130970\pi\)
\(432\) −4.90555 −0.236018
\(433\) 21.6978 1.04273 0.521365 0.853334i \(-0.325423\pi\)
0.521365 + 0.853334i \(0.325423\pi\)
\(434\) 0 0
\(435\) −0.00365722 −0.000175350 0
\(436\) 0.488341 0.0233873
\(437\) −36.3362 −1.73820
\(438\) 23.8054 1.13747
\(439\) −36.9921 −1.76554 −0.882769 0.469807i \(-0.844323\pi\)
−0.882769 + 0.469807i \(0.844323\pi\)
\(440\) −0.867090 −0.0413369
\(441\) 0 0
\(442\) 1.63762 0.0778934
\(443\) 10.9047 0.518100 0.259050 0.965864i \(-0.416591\pi\)
0.259050 + 0.965864i \(0.416591\pi\)
\(444\) 3.62236 0.171910
\(445\) 0.604059 0.0286352
\(446\) −21.1591 −1.00191
\(447\) 22.9065 1.08344
\(448\) 0 0
\(449\) −28.3090 −1.33599 −0.667993 0.744168i \(-0.732846\pi\)
−0.667993 + 0.744168i \(0.732846\pi\)
\(450\) 8.19370 0.386255
\(451\) 4.94328 0.232770
\(452\) −8.05843 −0.379037
\(453\) −22.3577 −1.05046
\(454\) 31.0151 1.45561
\(455\) 0 0
\(456\) 14.0718 0.658973
\(457\) 0.0300373 0.00140509 0.000702543 1.00000i \(-0.499776\pi\)
0.000702543 1.00000i \(0.499776\pi\)
\(458\) 2.35730 0.110149
\(459\) −0.810235 −0.0378186
\(460\) −0.313735 −0.0146280
\(461\) −33.9313 −1.58034 −0.790169 0.612889i \(-0.790007\pi\)
−0.790169 + 0.612889i \(0.790007\pi\)
\(462\) 0 0
\(463\) 29.9962 1.39404 0.697020 0.717052i \(-0.254509\pi\)
0.697020 + 0.717052i \(0.254509\pi\)
\(464\) 0.219415 0.0101861
\(465\) 0.589313 0.0273288
\(466\) 24.2546 1.12357
\(467\) −16.3034 −0.754429 −0.377215 0.926126i \(-0.623118\pi\)
−0.377215 + 0.926126i \(0.623118\pi\)
\(468\) 0.853167 0.0394377
\(469\) 0 0
\(470\) −1.46356 −0.0675092
\(471\) 12.9470 0.596565
\(472\) −9.31151 −0.428597
\(473\) 42.7535 1.96581
\(474\) −25.5287 −1.17257
\(475\) −32.7538 −1.50285
\(476\) 0 0
\(477\) −5.99240 −0.274373
\(478\) 1.70401 0.0779398
\(479\) 1.76809 0.0807862 0.0403931 0.999184i \(-0.487139\pi\)
0.0403931 + 0.999184i \(0.487139\pi\)
\(480\) 0.307373 0.0140296
\(481\) 6.44134 0.293700
\(482\) 40.0165 1.82270
\(483\) 0 0
\(484\) 9.30671 0.423032
\(485\) 0.445260 0.0202182
\(486\) −1.64093 −0.0744343
\(487\) 12.5458 0.568503 0.284252 0.958750i \(-0.408255\pi\)
0.284252 + 0.958750i \(0.408255\pi\)
\(488\) 2.43228 0.110104
\(489\) 2.36528 0.106961
\(490\) 0 0
\(491\) −0.480203 −0.0216713 −0.0108356 0.999941i \(-0.503449\pi\)
−0.0108356 + 0.999941i \(0.503449\pi\)
\(492\) −0.692668 −0.0312279
\(493\) 0.0362402 0.00163218
\(494\) −13.2579 −0.596499
\(495\) −0.404191 −0.0181670
\(496\) −35.3559 −1.58753
\(497\) 0 0
\(498\) −14.8101 −0.663655
\(499\) 44.0725 1.97296 0.986479 0.163889i \(-0.0524038\pi\)
0.986479 + 0.163889i \(0.0524038\pi\)
\(500\) −0.565986 −0.0253117
\(501\) 14.7792 0.660285
\(502\) 17.0776 0.762209
\(503\) −28.8604 −1.28682 −0.643411 0.765521i \(-0.722481\pi\)
−0.643411 + 0.765521i \(0.722481\pi\)
\(504\) 0 0
\(505\) −0.309471 −0.0137713
\(506\) −44.9339 −1.99755
\(507\) −11.4829 −0.509973
\(508\) −1.74864 −0.0775836
\(509\) 29.3896 1.30267 0.651336 0.758789i \(-0.274209\pi\)
0.651336 + 0.758789i \(0.274209\pi\)
\(510\) 0.108711 0.00481381
\(511\) 0 0
\(512\) 2.60635 0.115185
\(513\) 6.55953 0.289610
\(514\) −29.7371 −1.31165
\(515\) −1.56474 −0.0689505
\(516\) −5.99075 −0.263728
\(517\) −53.9219 −2.37148
\(518\) 0 0
\(519\) −10.5024 −0.461002
\(520\) 0.216052 0.00947450
\(521\) −4.09206 −0.179277 −0.0896383 0.995974i \(-0.528571\pi\)
−0.0896383 + 0.995974i \(0.528571\pi\)
\(522\) 0.0733957 0.00321244
\(523\) −7.40617 −0.323849 −0.161925 0.986803i \(-0.551770\pi\)
−0.161925 + 0.986803i \(0.551770\pi\)
\(524\) −7.52008 −0.328516
\(525\) 0 0
\(526\) 4.67449 0.203818
\(527\) −5.83964 −0.254379
\(528\) 24.2495 1.05532
\(529\) 7.68555 0.334154
\(530\) 0.804014 0.0349241
\(531\) −4.34053 −0.188363
\(532\) 0 0
\(533\) −1.23171 −0.0533514
\(534\) −12.1227 −0.524601
\(535\) −1.10720 −0.0478684
\(536\) −5.80560 −0.250764
\(537\) −6.55231 −0.282753
\(538\) 11.9161 0.513742
\(539\) 0 0
\(540\) 0.0566365 0.00243725
\(541\) −31.6011 −1.35864 −0.679319 0.733843i \(-0.737725\pi\)
−0.679319 + 0.733843i \(0.737725\pi\)
\(542\) −6.88043 −0.295540
\(543\) −2.05872 −0.0883479
\(544\) −3.04583 −0.130589
\(545\) 0.0576461 0.00246929
\(546\) 0 0
\(547\) −13.6853 −0.585143 −0.292571 0.956244i \(-0.594511\pi\)
−0.292571 + 0.956244i \(0.594511\pi\)
\(548\) −7.18546 −0.306948
\(549\) 1.13380 0.0483894
\(550\) −40.5038 −1.72709
\(551\) −0.293394 −0.0124990
\(552\) −11.8835 −0.505795
\(553\) 0 0
\(554\) −13.1426 −0.558374
\(555\) 0.427600 0.0181506
\(556\) −2.40216 −0.101874
\(557\) 4.80505 0.203597 0.101798 0.994805i \(-0.467540\pi\)
0.101798 + 0.994805i \(0.467540\pi\)
\(558\) −11.8268 −0.500667
\(559\) −10.6528 −0.450567
\(560\) 0 0
\(561\) 4.00522 0.169101
\(562\) 3.60965 0.152264
\(563\) 8.15180 0.343558 0.171779 0.985136i \(-0.445049\pi\)
0.171779 + 0.985136i \(0.445049\pi\)
\(564\) 7.55569 0.318152
\(565\) −0.951255 −0.0400196
\(566\) 6.29341 0.264532
\(567\) 0 0
\(568\) −11.9282 −0.500496
\(569\) −34.3425 −1.43971 −0.719857 0.694122i \(-0.755793\pi\)
−0.719857 + 0.694122i \(0.755793\pi\)
\(570\) −0.880107 −0.0368636
\(571\) −8.17313 −0.342035 −0.171017 0.985268i \(-0.554705\pi\)
−0.171017 + 0.985268i \(0.554705\pi\)
\(572\) −4.21745 −0.176340
\(573\) −18.4559 −0.771008
\(574\) 0 0
\(575\) 27.6602 1.15351
\(576\) 3.64251 0.151771
\(577\) −1.24503 −0.0518312 −0.0259156 0.999664i \(-0.508250\pi\)
−0.0259156 + 0.999664i \(0.508250\pi\)
\(578\) 26.8187 1.11551
\(579\) 22.7365 0.944896
\(580\) −0.00253323 −0.000105187 0
\(581\) 0 0
\(582\) −8.93580 −0.370401
\(583\) 29.6221 1.22682
\(584\) −31.1216 −1.28782
\(585\) 0.100712 0.00416392
\(586\) 12.8345 0.530189
\(587\) 9.16561 0.378305 0.189153 0.981948i \(-0.439426\pi\)
0.189153 + 0.981948i \(0.439426\pi\)
\(588\) 0 0
\(589\) 47.2768 1.94800
\(590\) 0.582379 0.0239761
\(591\) 1.89397 0.0779074
\(592\) −25.6539 −1.05437
\(593\) 19.9726 0.820177 0.410089 0.912046i \(-0.365498\pi\)
0.410089 + 0.912046i \(0.365498\pi\)
\(594\) 8.11161 0.332823
\(595\) 0 0
\(596\) 15.8666 0.649921
\(597\) 20.6802 0.846382
\(598\) 11.1961 0.457844
\(599\) −9.37301 −0.382971 −0.191485 0.981495i \(-0.561330\pi\)
−0.191485 + 0.981495i \(0.561330\pi\)
\(600\) −10.7119 −0.437311
\(601\) 1.48167 0.0604388 0.0302194 0.999543i \(-0.490379\pi\)
0.0302194 + 0.999543i \(0.490379\pi\)
\(602\) 0 0
\(603\) −2.70626 −0.110207
\(604\) −15.4865 −0.630136
\(605\) 1.09861 0.0446647
\(606\) 6.21070 0.252293
\(607\) −23.5439 −0.955617 −0.477809 0.878464i \(-0.658569\pi\)
−0.477809 + 0.878464i \(0.658569\pi\)
\(608\) 24.6585 1.00003
\(609\) 0 0
\(610\) −0.152125 −0.00615934
\(611\) 13.4357 0.543548
\(612\) −0.561224 −0.0226861
\(613\) −23.4070 −0.945401 −0.472700 0.881223i \(-0.656721\pi\)
−0.472700 + 0.881223i \(0.656721\pi\)
\(614\) −3.20073 −0.129171
\(615\) −0.0817657 −0.00329711
\(616\) 0 0
\(617\) −32.4731 −1.30732 −0.653658 0.756790i \(-0.726767\pi\)
−0.653658 + 0.756790i \(0.726767\pi\)
\(618\) 31.4023 1.26318
\(619\) 9.07557 0.364778 0.182389 0.983226i \(-0.441617\pi\)
0.182389 + 0.983226i \(0.441617\pi\)
\(620\) 0.408198 0.0163936
\(621\) −5.53945 −0.222291
\(622\) −41.6466 −1.66987
\(623\) 0 0
\(624\) −6.04222 −0.241883
\(625\) 24.8998 0.995990
\(626\) 27.4528 1.09724
\(627\) −32.4256 −1.29495
\(628\) 8.96795 0.357860
\(629\) −4.23719 −0.168948
\(630\) 0 0
\(631\) −4.18697 −0.166681 −0.0833404 0.996521i \(-0.526559\pi\)
−0.0833404 + 0.996521i \(0.526559\pi\)
\(632\) 33.3744 1.32756
\(633\) −8.73506 −0.347187
\(634\) 44.5414 1.76897
\(635\) −0.206418 −0.00819145
\(636\) −4.15074 −0.164588
\(637\) 0 0
\(638\) −0.362816 −0.0143640
\(639\) −5.56029 −0.219962
\(640\) −1.10347 −0.0436184
\(641\) −28.6487 −1.13156 −0.565778 0.824558i \(-0.691424\pi\)
−0.565778 + 0.824558i \(0.691424\pi\)
\(642\) 22.2201 0.876957
\(643\) −26.3904 −1.04073 −0.520367 0.853943i \(-0.674205\pi\)
−0.520367 + 0.853943i \(0.674205\pi\)
\(644\) 0 0
\(645\) −0.707176 −0.0278450
\(646\) 8.72118 0.343130
\(647\) 16.5423 0.650344 0.325172 0.945655i \(-0.394578\pi\)
0.325172 + 0.945655i \(0.394578\pi\)
\(648\) 2.14525 0.0842733
\(649\) 21.4565 0.842240
\(650\) 10.0923 0.395852
\(651\) 0 0
\(652\) 1.63835 0.0641627
\(653\) 37.0887 1.45139 0.725697 0.688015i \(-0.241518\pi\)
0.725697 + 0.688015i \(0.241518\pi\)
\(654\) −1.15688 −0.0452377
\(655\) −0.887705 −0.0346855
\(656\) 4.90555 0.191529
\(657\) −14.5072 −0.565981
\(658\) 0 0
\(659\) −4.20478 −0.163795 −0.0818975 0.996641i \(-0.526098\pi\)
−0.0818975 + 0.996641i \(0.526098\pi\)
\(660\) −0.279970 −0.0108978
\(661\) 11.6207 0.451994 0.225997 0.974128i \(-0.427436\pi\)
0.225997 + 0.974128i \(0.427436\pi\)
\(662\) 1.85488 0.0720918
\(663\) −0.997977 −0.0387582
\(664\) 19.3617 0.751379
\(665\) 0 0
\(666\) −8.58140 −0.332522
\(667\) 0.247769 0.00959364
\(668\) 10.2371 0.396084
\(669\) 12.8945 0.498532
\(670\) 0.363105 0.0140280
\(671\) −5.60470 −0.216367
\(672\) 0 0
\(673\) −33.7947 −1.30269 −0.651346 0.758781i \(-0.725795\pi\)
−0.651346 + 0.758781i \(0.725795\pi\)
\(674\) −44.3737 −1.70921
\(675\) −4.99331 −0.192193
\(676\) −7.95382 −0.305916
\(677\) 22.3305 0.858229 0.429115 0.903250i \(-0.358826\pi\)
0.429115 + 0.903250i \(0.358826\pi\)
\(678\) 19.0905 0.733166
\(679\) 0 0
\(680\) −0.142122 −0.00545011
\(681\) −18.9009 −0.724283
\(682\) 58.4631 2.23867
\(683\) 1.70074 0.0650769 0.0325385 0.999470i \(-0.489641\pi\)
0.0325385 + 0.999470i \(0.489641\pi\)
\(684\) 4.54357 0.173728
\(685\) −0.848205 −0.0324082
\(686\) 0 0
\(687\) −1.43656 −0.0548081
\(688\) 42.4271 1.61752
\(689\) −7.38091 −0.281190
\(690\) 0.743241 0.0282947
\(691\) 18.1625 0.690934 0.345467 0.938431i \(-0.387721\pi\)
0.345467 + 0.938431i \(0.387721\pi\)
\(692\) −7.27464 −0.276540
\(693\) 0 0
\(694\) 28.6733 1.08842
\(695\) −0.283562 −0.0107561
\(696\) −0.0959526 −0.00363707
\(697\) 0.810235 0.0306899
\(698\) −36.7931 −1.39264
\(699\) −14.7809 −0.559066
\(700\) 0 0
\(701\) −16.2740 −0.614662 −0.307331 0.951603i \(-0.599436\pi\)
−0.307331 + 0.951603i \(0.599436\pi\)
\(702\) −2.02116 −0.0762838
\(703\) 34.3036 1.29378
\(704\) −18.0060 −0.678625
\(705\) 0.891909 0.0335912
\(706\) 16.3472 0.615236
\(707\) 0 0
\(708\) −3.00655 −0.112993
\(709\) −29.3971 −1.10403 −0.552016 0.833833i \(-0.686141\pi\)
−0.552016 + 0.833833i \(0.686141\pi\)
\(710\) 0.746037 0.0279983
\(711\) 15.5574 0.583447
\(712\) 15.8484 0.593944
\(713\) −39.9247 −1.49519
\(714\) 0 0
\(715\) −0.497847 −0.0186184
\(716\) −4.53857 −0.169614
\(717\) −1.03844 −0.0387813
\(718\) 34.4736 1.28655
\(719\) −21.6187 −0.806240 −0.403120 0.915147i \(-0.632074\pi\)
−0.403120 + 0.915147i \(0.632074\pi\)
\(720\) −0.401106 −0.0149483
\(721\) 0 0
\(722\) −39.4274 −1.46734
\(723\) −24.3864 −0.906939
\(724\) −1.42601 −0.0529971
\(725\) 0.223341 0.00829467
\(726\) −22.0477 −0.818266
\(727\) −30.5668 −1.13366 −0.566830 0.823834i \(-0.691831\pi\)
−0.566830 + 0.823834i \(0.691831\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 1.94647 0.0720420
\(731\) 7.00757 0.259184
\(732\) 0.785347 0.0290273
\(733\) −6.44019 −0.237874 −0.118937 0.992902i \(-0.537949\pi\)
−0.118937 + 0.992902i \(0.537949\pi\)
\(734\) 52.2699 1.92932
\(735\) 0 0
\(736\) −20.8239 −0.767577
\(737\) 13.3778 0.492778
\(738\) 1.64093 0.0604037
\(739\) −17.7546 −0.653114 −0.326557 0.945178i \(-0.605889\pi\)
−0.326557 + 0.945178i \(0.605889\pi\)
\(740\) 0.296185 0.0108880
\(741\) 8.07945 0.296806
\(742\) 0 0
\(743\) −13.7838 −0.505678 −0.252839 0.967508i \(-0.581364\pi\)
−0.252839 + 0.967508i \(0.581364\pi\)
\(744\) 15.4615 0.566847
\(745\) 1.87297 0.0686202
\(746\) 36.4565 1.33477
\(747\) 9.02538 0.330221
\(748\) 2.77429 0.101438
\(749\) 0 0
\(750\) 1.34083 0.0489600
\(751\) −31.6129 −1.15357 −0.576785 0.816896i \(-0.695693\pi\)
−0.576785 + 0.816896i \(0.695693\pi\)
\(752\) −53.5102 −1.95132
\(753\) −10.4072 −0.379260
\(754\) 0.0904024 0.00329226
\(755\) −1.82810 −0.0665313
\(756\) 0 0
\(757\) 25.1875 0.915454 0.457727 0.889093i \(-0.348664\pi\)
0.457727 + 0.889093i \(0.348664\pi\)
\(758\) −46.1060 −1.67464
\(759\) 27.3831 0.993943
\(760\) 1.15059 0.0417363
\(761\) −24.5389 −0.889534 −0.444767 0.895646i \(-0.646714\pi\)
−0.444767 + 0.895646i \(0.646714\pi\)
\(762\) 4.14255 0.150069
\(763\) 0 0
\(764\) −12.7838 −0.462503
\(765\) −0.0662495 −0.00239526
\(766\) −13.0932 −0.473077
\(767\) −5.34629 −0.193043
\(768\) 14.8602 0.536222
\(769\) 27.2252 0.981766 0.490883 0.871226i \(-0.336674\pi\)
0.490883 + 0.871226i \(0.336674\pi\)
\(770\) 0 0
\(771\) 18.1220 0.652649
\(772\) 15.7488 0.566813
\(773\) −39.2782 −1.41274 −0.706369 0.707844i \(-0.749668\pi\)
−0.706369 + 0.707844i \(0.749668\pi\)
\(774\) 14.1921 0.510126
\(775\) −35.9885 −1.29275
\(776\) 11.6821 0.419362
\(777\) 0 0
\(778\) 56.5374 2.02696
\(779\) −6.55953 −0.235019
\(780\) 0.0697598 0.00249780
\(781\) 27.4861 0.983530
\(782\) −7.36495 −0.263370
\(783\) −0.0447280 −0.00159845
\(784\) 0 0
\(785\) 1.05862 0.0377837
\(786\) 17.8151 0.635444
\(787\) −54.3409 −1.93704 −0.968522 0.248927i \(-0.919922\pi\)
−0.968522 + 0.248927i \(0.919922\pi\)
\(788\) 1.31189 0.0467341
\(789\) −2.84868 −0.101416
\(790\) −2.08737 −0.0742652
\(791\) 0 0
\(792\) −10.6046 −0.376817
\(793\) 1.39652 0.0495918
\(794\) 38.0472 1.35024
\(795\) −0.489973 −0.0173775
\(796\) 14.3245 0.507718
\(797\) −45.0852 −1.59700 −0.798500 0.601995i \(-0.794373\pi\)
−0.798500 + 0.601995i \(0.794373\pi\)
\(798\) 0 0
\(799\) −8.83814 −0.312671
\(800\) −18.7708 −0.663648
\(801\) 7.38768 0.261031
\(802\) 17.6392 0.622862
\(803\) 71.7134 2.53071
\(804\) −1.87454 −0.0661099
\(805\) 0 0
\(806\) −14.5672 −0.513107
\(807\) −7.26180 −0.255628
\(808\) −8.11945 −0.285641
\(809\) 44.8906 1.57827 0.789135 0.614220i \(-0.210529\pi\)
0.789135 + 0.614220i \(0.210529\pi\)
\(810\) −0.134172 −0.00471433
\(811\) 43.9625 1.54373 0.771865 0.635786i \(-0.219324\pi\)
0.771865 + 0.635786i \(0.219324\pi\)
\(812\) 0 0
\(813\) 4.19299 0.147055
\(814\) 42.4203 1.48683
\(815\) 0.193398 0.00677445
\(816\) 3.97465 0.139141
\(817\) −56.7321 −1.98481
\(818\) 25.7609 0.900708
\(819\) 0 0
\(820\) −0.0566365 −0.00197783
\(821\) −9.16765 −0.319953 −0.159977 0.987121i \(-0.551142\pi\)
−0.159977 + 0.987121i \(0.551142\pi\)
\(822\) 17.0224 0.593725
\(823\) −8.42471 −0.293667 −0.146834 0.989161i \(-0.546908\pi\)
−0.146834 + 0.989161i \(0.546908\pi\)
\(824\) −41.0532 −1.43016
\(825\) 24.6834 0.859364
\(826\) 0 0
\(827\) 48.2599 1.67816 0.839080 0.544008i \(-0.183094\pi\)
0.839080 + 0.544008i \(0.183094\pi\)
\(828\) −3.83700 −0.133345
\(829\) 0.597727 0.0207599 0.0103800 0.999946i \(-0.496696\pi\)
0.0103800 + 0.999946i \(0.496696\pi\)
\(830\) −1.21096 −0.0420329
\(831\) 8.00920 0.277836
\(832\) 4.48652 0.155542
\(833\) 0 0
\(834\) 5.69074 0.197054
\(835\) 1.20843 0.0418195
\(836\) −22.4602 −0.776801
\(837\) 7.20734 0.249122
\(838\) 45.2584 1.56343
\(839\) 12.7920 0.441630 0.220815 0.975316i \(-0.429128\pi\)
0.220815 + 0.975316i \(0.429128\pi\)
\(840\) 0 0
\(841\) −28.9980 −0.999931
\(842\) −40.8121 −1.40648
\(843\) −2.19975 −0.0757635
\(844\) −6.05049 −0.208267
\(845\) −0.938906 −0.0322994
\(846\) −17.8995 −0.615397
\(847\) 0 0
\(848\) 29.3960 1.00946
\(849\) −3.83526 −0.131626
\(850\) −6.63883 −0.227710
\(851\) −28.9690 −0.993045
\(852\) −3.85144 −0.131948
\(853\) −14.5985 −0.499841 −0.249921 0.968266i \(-0.580405\pi\)
−0.249921 + 0.968266i \(0.580405\pi\)
\(854\) 0 0
\(855\) 0.536345 0.0183426
\(856\) −29.0490 −0.992875
\(857\) −7.40299 −0.252881 −0.126441 0.991974i \(-0.540355\pi\)
−0.126441 + 0.991974i \(0.540355\pi\)
\(858\) 9.99117 0.341093
\(859\) −43.1440 −1.47206 −0.736028 0.676951i \(-0.763301\pi\)
−0.736028 + 0.676951i \(0.763301\pi\)
\(860\) −0.489838 −0.0167033
\(861\) 0 0
\(862\) −62.4470 −2.12695
\(863\) 27.0789 0.921776 0.460888 0.887458i \(-0.347531\pi\)
0.460888 + 0.887458i \(0.347531\pi\)
\(864\) 3.75919 0.127890
\(865\) −0.858732 −0.0291978
\(866\) −35.6047 −1.20990
\(867\) −16.3435 −0.555055
\(868\) 0 0
\(869\) −76.9045 −2.60881
\(870\) 0.00600125 0.000203462 0
\(871\) −3.33333 −0.112946
\(872\) 1.51243 0.0512174
\(873\) 5.44556 0.184304
\(874\) 59.6253 2.01686
\(875\) 0 0
\(876\) −10.0487 −0.339514
\(877\) 33.0013 1.11438 0.557188 0.830387i \(-0.311880\pi\)
0.557188 + 0.830387i \(0.311880\pi\)
\(878\) 60.7017 2.04858
\(879\) −7.82147 −0.263812
\(880\) 1.98278 0.0668394
\(881\) −22.3933 −0.754451 −0.377225 0.926122i \(-0.623122\pi\)
−0.377225 + 0.926122i \(0.623122\pi\)
\(882\) 0 0
\(883\) 12.8447 0.432257 0.216129 0.976365i \(-0.430657\pi\)
0.216129 + 0.976365i \(0.430657\pi\)
\(884\) −0.691266 −0.0232498
\(885\) −0.354907 −0.0119301
\(886\) −17.8940 −0.601160
\(887\) −26.8473 −0.901445 −0.450722 0.892664i \(-0.648834\pi\)
−0.450722 + 0.892664i \(0.648834\pi\)
\(888\) 11.2187 0.376476
\(889\) 0 0
\(890\) −0.991222 −0.0332258
\(891\) −4.94328 −0.165606
\(892\) 8.93164 0.299053
\(893\) 71.5520 2.39440
\(894\) −37.5881 −1.25713
\(895\) −0.535754 −0.0179083
\(896\) 0 0
\(897\) −6.82301 −0.227814
\(898\) 46.4533 1.55017
\(899\) −0.322370 −0.0107516
\(900\) −3.45871 −0.115290
\(901\) 4.85526 0.161752
\(902\) −8.11161 −0.270087
\(903\) 0 0
\(904\) −24.9576 −0.830078
\(905\) −0.168332 −0.00559556
\(906\) 36.6876 1.21886
\(907\) −32.9319 −1.09349 −0.546743 0.837300i \(-0.684133\pi\)
−0.546743 + 0.837300i \(0.684133\pi\)
\(908\) −13.0920 −0.434474
\(909\) −3.78486 −0.125536
\(910\) 0 0
\(911\) −1.75669 −0.0582018 −0.0291009 0.999576i \(-0.509264\pi\)
−0.0291009 + 0.999576i \(0.509264\pi\)
\(912\) −32.1781 −1.06552
\(913\) −44.6150 −1.47654
\(914\) −0.0492893 −0.00163034
\(915\) 0.0927060 0.00306477
\(916\) −0.995058 −0.0328776
\(917\) 0 0
\(918\) 1.32954 0.0438815
\(919\) −31.1103 −1.02623 −0.513117 0.858319i \(-0.671509\pi\)
−0.513117 + 0.858319i \(0.671509\pi\)
\(920\) −0.971663 −0.0320348
\(921\) 1.95055 0.0642728
\(922\) 55.6790 1.83369
\(923\) −6.84868 −0.225427
\(924\) 0 0
\(925\) −26.1129 −0.858588
\(926\) −49.2217 −1.61753
\(927\) −19.1368 −0.628536
\(928\) −0.168141 −0.00551950
\(929\) −14.9878 −0.491734 −0.245867 0.969304i \(-0.579073\pi\)
−0.245867 + 0.969304i \(0.579073\pi\)
\(930\) −0.967025 −0.0317100
\(931\) 0 0
\(932\) −10.2383 −0.335366
\(933\) 25.3798 0.830897
\(934\) 26.7527 0.875376
\(935\) 0.327490 0.0107101
\(936\) 2.64233 0.0863672
\(937\) −46.7766 −1.52812 −0.764062 0.645143i \(-0.776798\pi\)
−0.764062 + 0.645143i \(0.776798\pi\)
\(938\) 0 0
\(939\) −16.7300 −0.545963
\(940\) 0.617797 0.0201503
\(941\) −1.19448 −0.0389391 −0.0194695 0.999810i \(-0.506198\pi\)
−0.0194695 + 0.999810i \(0.506198\pi\)
\(942\) −21.2451 −0.692204
\(943\) 5.53945 0.180389
\(944\) 21.2927 0.693018
\(945\) 0 0
\(946\) −70.1557 −2.28096
\(947\) 0.760030 0.0246977 0.0123488 0.999924i \(-0.496069\pi\)
0.0123488 + 0.999924i \(0.496069\pi\)
\(948\) 10.7761 0.349991
\(949\) −17.8687 −0.580044
\(950\) 53.7468 1.74378
\(951\) −27.1439 −0.880202
\(952\) 0 0
\(953\) −45.9749 −1.48927 −0.744637 0.667470i \(-0.767377\pi\)
−0.744637 + 0.667470i \(0.767377\pi\)
\(954\) 9.83314 0.318360
\(955\) −1.50906 −0.0488321
\(956\) −0.719295 −0.0232636
\(957\) 0.221103 0.00714725
\(958\) −2.90132 −0.0937376
\(959\) 0 0
\(960\) 0.297832 0.00961250
\(961\) 20.9458 0.675670
\(962\) −10.5698 −0.340784
\(963\) −13.5411 −0.436356
\(964\) −16.8917 −0.544044
\(965\) 1.85906 0.0598454
\(966\) 0 0
\(967\) 20.1637 0.648421 0.324211 0.945985i \(-0.394901\pi\)
0.324211 + 0.945985i \(0.394901\pi\)
\(968\) 28.8236 0.926427
\(969\) −5.31476 −0.170735
\(970\) −0.730642 −0.0234595
\(971\) −35.0294 −1.12415 −0.562074 0.827087i \(-0.689996\pi\)
−0.562074 + 0.827087i \(0.689996\pi\)
\(972\) 0.692668 0.0222173
\(973\) 0 0
\(974\) −20.5868 −0.659644
\(975\) −6.15033 −0.196968
\(976\) −5.56191 −0.178033
\(977\) −58.3885 −1.86801 −0.934006 0.357257i \(-0.883712\pi\)
−0.934006 + 0.357257i \(0.883712\pi\)
\(978\) −3.88126 −0.124109
\(979\) −36.5194 −1.16717
\(980\) 0 0
\(981\) 0.705015 0.0225094
\(982\) 0.787983 0.0251455
\(983\) 36.7120 1.17093 0.585465 0.810698i \(-0.300912\pi\)
0.585465 + 0.810698i \(0.300912\pi\)
\(984\) −2.14525 −0.0683880
\(985\) 0.154862 0.00493430
\(986\) −0.0594678 −0.00189384
\(987\) 0 0
\(988\) 5.59638 0.178044
\(989\) 47.9097 1.52344
\(990\) 0.663251 0.0210795
\(991\) 25.4394 0.808108 0.404054 0.914735i \(-0.367601\pi\)
0.404054 + 0.914735i \(0.367601\pi\)
\(992\) 27.0938 0.860228
\(993\) −1.13038 −0.0358714
\(994\) 0 0
\(995\) 1.69093 0.0536060
\(996\) 6.25159 0.198089
\(997\) −23.9681 −0.759076 −0.379538 0.925176i \(-0.623917\pi\)
−0.379538 + 0.925176i \(0.623917\pi\)
\(998\) −72.3202 −2.28925
\(999\) 5.22958 0.165457
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 \(a_p\))