Properties

Label 8047.2.a.b.1.8
Level 8047
Weight 2
Character 8047.1
Self dual Yes
Analytic conductor 64.256
Analytic rank 1
Dimension 142
CM No

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Newspace parameters

Level: \( N \) = \( 8047 = 13 \cdot 619 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8047.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2556185065\)
Analytic rank: \(1\)
Dimension: \(142\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.8
Character \(\chi\) = 8047.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.56842 q^{2} +0.368799 q^{3} +4.59680 q^{4} -0.479572 q^{5} -0.947232 q^{6} +4.01594 q^{7} -6.66967 q^{8} -2.86399 q^{9} +O(q^{10})\) \(q-2.56842 q^{2} +0.368799 q^{3} +4.59680 q^{4} -0.479572 q^{5} -0.947232 q^{6} +4.01594 q^{7} -6.66967 q^{8} -2.86399 q^{9} +1.23174 q^{10} +2.41061 q^{11} +1.69529 q^{12} +1.00000 q^{13} -10.3146 q^{14} -0.176866 q^{15} +7.93693 q^{16} -0.131894 q^{17} +7.35593 q^{18} -3.90661 q^{19} -2.20449 q^{20} +1.48107 q^{21} -6.19146 q^{22} +6.17118 q^{23} -2.45977 q^{24} -4.77001 q^{25} -2.56842 q^{26} -2.16263 q^{27} +18.4604 q^{28} -1.74972 q^{29} +0.454266 q^{30} -5.54174 q^{31} -7.04607 q^{32} +0.889030 q^{33} +0.338759 q^{34} -1.92593 q^{35} -13.1652 q^{36} +5.17598 q^{37} +10.0338 q^{38} +0.368799 q^{39} +3.19858 q^{40} -8.47513 q^{41} -3.80402 q^{42} +6.79359 q^{43} +11.0811 q^{44} +1.37349 q^{45} -15.8502 q^{46} +1.05395 q^{47} +2.92713 q^{48} +9.12774 q^{49} +12.2514 q^{50} -0.0486423 q^{51} +4.59680 q^{52} -7.74698 q^{53} +5.55456 q^{54} -1.15606 q^{55} -26.7850 q^{56} -1.44075 q^{57} +4.49403 q^{58} -7.30694 q^{59} -0.813015 q^{60} +0.0733858 q^{61} +14.2335 q^{62} -11.5016 q^{63} +2.22341 q^{64} -0.479572 q^{65} -2.28340 q^{66} +10.6328 q^{67} -0.606288 q^{68} +2.27593 q^{69} +4.94660 q^{70} -6.14530 q^{71} +19.1018 q^{72} -3.87192 q^{73} -13.2941 q^{74} -1.75918 q^{75} -17.9579 q^{76} +9.68084 q^{77} -0.947232 q^{78} -3.76051 q^{79} -3.80633 q^{80} +7.79438 q^{81} +21.7677 q^{82} -6.77790 q^{83} +6.80819 q^{84} +0.0632525 q^{85} -17.4488 q^{86} -0.645296 q^{87} -16.0779 q^{88} -7.48139 q^{89} -3.52770 q^{90} +4.01594 q^{91} +28.3677 q^{92} -2.04379 q^{93} -2.70698 q^{94} +1.87350 q^{95} -2.59858 q^{96} -4.17090 q^{97} -23.4439 q^{98} -6.90395 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 142q - 13q^{2} - 26q^{3} + 129q^{4} - 37q^{5} - 15q^{6} - 14q^{7} - 39q^{8} + 98q^{9} + O(q^{10}) \) \( 142q - 13q^{2} - 26q^{3} + 129q^{4} - 37q^{5} - 15q^{6} - 14q^{7} - 39q^{8} + 98q^{9} - 25q^{10} - 25q^{11} - 62q^{12} + 142q^{13} - 57q^{14} - 14q^{15} + 111q^{16} - 141q^{17} - 29q^{18} - 3q^{19} - 87q^{20} - 19q^{21} - 24q^{22} - 69q^{23} - 40q^{24} + 87q^{25} - 13q^{26} - 95q^{27} - 34q^{28} - 147q^{29} - 2q^{30} - 21q^{31} - 66q^{32} - 62q^{33} - 6q^{34} - 59q^{35} + 74q^{36} - 37q^{37} - 76q^{38} - 26q^{39} - 61q^{40} - 97q^{41} - 29q^{42} - 33q^{43} - 57q^{44} - 86q^{45} - q^{46} - 102q^{47} - 141q^{48} + 70q^{49} - 28q^{50} - 13q^{51} + 129q^{52} - 137q^{53} - 29q^{54} - 24q^{55} - 130q^{56} - 65q^{57} - 15q^{58} - 56q^{59} + 11q^{60} - 77q^{61} - 150q^{62} - 32q^{63} + 73q^{64} - 37q^{65} - 32q^{66} - 9q^{67} - 226q^{68} - 113q^{69} + 6q^{70} - 18q^{71} - 82q^{72} - 117q^{73} - 70q^{74} - 83q^{75} + 40q^{76} - 214q^{77} - 15q^{78} - 52q^{79} - 161q^{80} - 10q^{81} - 36q^{82} - 74q^{83} + 53q^{84} + 2q^{85} + 17q^{86} - 49q^{87} - 29q^{88} - 171q^{89} - 57q^{90} - 14q^{91} - 187q^{92} - 39q^{93} + 13q^{94} - 150q^{95} - 47q^{96} - 126q^{97} - 85q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.56842 −1.81615 −0.908075 0.418809i \(-0.862448\pi\)
−0.908075 + 0.418809i \(0.862448\pi\)
\(3\) 0.368799 0.212926 0.106463 0.994317i \(-0.466047\pi\)
0.106463 + 0.994317i \(0.466047\pi\)
\(4\) 4.59680 2.29840
\(5\) −0.479572 −0.214471 −0.107235 0.994234i \(-0.534200\pi\)
−0.107235 + 0.994234i \(0.534200\pi\)
\(6\) −0.947232 −0.386706
\(7\) 4.01594 1.51788 0.758940 0.651160i \(-0.225717\pi\)
0.758940 + 0.651160i \(0.225717\pi\)
\(8\) −6.66967 −2.35808
\(9\) −2.86399 −0.954662
\(10\) 1.23174 0.389511
\(11\) 2.41061 0.726825 0.363413 0.931628i \(-0.381612\pi\)
0.363413 + 0.931628i \(0.381612\pi\)
\(12\) 1.69529 0.489389
\(13\) 1.00000 0.277350
\(14\) −10.3146 −2.75670
\(15\) −0.176866 −0.0456665
\(16\) 7.93693 1.98423
\(17\) −0.131894 −0.0319889 −0.0159945 0.999872i \(-0.505091\pi\)
−0.0159945 + 0.999872i \(0.505091\pi\)
\(18\) 7.35593 1.73381
\(19\) −3.90661 −0.896237 −0.448118 0.893974i \(-0.647906\pi\)
−0.448118 + 0.893974i \(0.647906\pi\)
\(20\) −2.20449 −0.492940
\(21\) 1.48107 0.323197
\(22\) −6.19146 −1.32002
\(23\) 6.17118 1.28678 0.643390 0.765538i \(-0.277527\pi\)
0.643390 + 0.765538i \(0.277527\pi\)
\(24\) −2.45977 −0.502098
\(25\) −4.77001 −0.954002
\(26\) −2.56842 −0.503709
\(27\) −2.16263 −0.416199
\(28\) 18.4604 3.48869
\(29\) −1.74972 −0.324915 −0.162458 0.986716i \(-0.551942\pi\)
−0.162458 + 0.986716i \(0.551942\pi\)
\(30\) 0.454266 0.0829372
\(31\) −5.54174 −0.995325 −0.497663 0.867371i \(-0.665808\pi\)
−0.497663 + 0.867371i \(0.665808\pi\)
\(32\) −7.04607 −1.24558
\(33\) 0.889030 0.154760
\(34\) 0.338759 0.0580966
\(35\) −1.92593 −0.325541
\(36\) −13.1652 −2.19419
\(37\) 5.17598 0.850926 0.425463 0.904976i \(-0.360111\pi\)
0.425463 + 0.904976i \(0.360111\pi\)
\(38\) 10.0338 1.62770
\(39\) 0.368799 0.0590551
\(40\) 3.19858 0.505740
\(41\) −8.47513 −1.32359 −0.661796 0.749684i \(-0.730206\pi\)
−0.661796 + 0.749684i \(0.730206\pi\)
\(42\) −3.80402 −0.586973
\(43\) 6.79359 1.03601 0.518006 0.855377i \(-0.326674\pi\)
0.518006 + 0.855377i \(0.326674\pi\)
\(44\) 11.0811 1.67053
\(45\) 1.37349 0.204747
\(46\) −15.8502 −2.33698
\(47\) 1.05395 0.153734 0.0768670 0.997041i \(-0.475508\pi\)
0.0768670 + 0.997041i \(0.475508\pi\)
\(48\) 2.92713 0.422495
\(49\) 9.12774 1.30396
\(50\) 12.2514 1.73261
\(51\) −0.0486423 −0.00681128
\(52\) 4.59680 0.637461
\(53\) −7.74698 −1.06413 −0.532065 0.846704i \(-0.678584\pi\)
−0.532065 + 0.846704i \(0.678584\pi\)
\(54\) 5.55456 0.755879
\(55\) −1.15606 −0.155883
\(56\) −26.7850 −3.57929
\(57\) −1.44075 −0.190832
\(58\) 4.49403 0.590095
\(59\) −7.30694 −0.951282 −0.475641 0.879639i \(-0.657784\pi\)
−0.475641 + 0.879639i \(0.657784\pi\)
\(60\) −0.813015 −0.104960
\(61\) 0.0733858 0.00939608 0.00469804 0.999989i \(-0.498505\pi\)
0.00469804 + 0.999989i \(0.498505\pi\)
\(62\) 14.2335 1.80766
\(63\) −11.5016 −1.44906
\(64\) 2.22341 0.277927
\(65\) −0.479572 −0.0594835
\(66\) −2.28340 −0.281068
\(67\) 10.6328 1.29901 0.649505 0.760358i \(-0.274976\pi\)
0.649505 + 0.760358i \(0.274976\pi\)
\(68\) −0.606288 −0.0735232
\(69\) 2.27593 0.273989
\(70\) 4.94660 0.591232
\(71\) −6.14530 −0.729313 −0.364657 0.931142i \(-0.618814\pi\)
−0.364657 + 0.931142i \(0.618814\pi\)
\(72\) 19.1018 2.25117
\(73\) −3.87192 −0.453174 −0.226587 0.973991i \(-0.572757\pi\)
−0.226587 + 0.973991i \(0.572757\pi\)
\(74\) −13.2941 −1.54541
\(75\) −1.75918 −0.203132
\(76\) −17.9579 −2.05991
\(77\) 9.68084 1.10323
\(78\) −0.947232 −0.107253
\(79\) −3.76051 −0.423090 −0.211545 0.977368i \(-0.567850\pi\)
−0.211545 + 0.977368i \(0.567850\pi\)
\(80\) −3.80633 −0.425560
\(81\) 7.79438 0.866043
\(82\) 21.7677 2.40384
\(83\) −6.77790 −0.743972 −0.371986 0.928238i \(-0.621323\pi\)
−0.371986 + 0.928238i \(0.621323\pi\)
\(84\) 6.80819 0.742834
\(85\) 0.0632525 0.00686069
\(86\) −17.4488 −1.88155
\(87\) −0.645296 −0.0691830
\(88\) −16.0779 −1.71391
\(89\) −7.48139 −0.793025 −0.396513 0.918029i \(-0.629780\pi\)
−0.396513 + 0.918029i \(0.629780\pi\)
\(90\) −3.52770 −0.371852
\(91\) 4.01594 0.420984
\(92\) 28.3677 2.95753
\(93\) −2.04379 −0.211931
\(94\) −2.70698 −0.279204
\(95\) 1.87350 0.192217
\(96\) −2.59858 −0.265217
\(97\) −4.17090 −0.423491 −0.211745 0.977325i \(-0.567915\pi\)
−0.211745 + 0.977325i \(0.567915\pi\)
\(98\) −23.4439 −2.36819
\(99\) −6.90395 −0.693873
\(100\) −21.9268 −2.19268
\(101\) −12.2721 −1.22112 −0.610561 0.791969i \(-0.709056\pi\)
−0.610561 + 0.791969i \(0.709056\pi\)
\(102\) 0.124934 0.0123703
\(103\) 5.15437 0.507876 0.253938 0.967221i \(-0.418274\pi\)
0.253938 + 0.967221i \(0.418274\pi\)
\(104\) −6.66967 −0.654015
\(105\) −0.710281 −0.0693163
\(106\) 19.8975 1.93262
\(107\) 4.40399 0.425749 0.212875 0.977080i \(-0.431717\pi\)
0.212875 + 0.977080i \(0.431717\pi\)
\(108\) −9.94118 −0.956591
\(109\) 17.6203 1.68772 0.843858 0.536566i \(-0.180279\pi\)
0.843858 + 0.536566i \(0.180279\pi\)
\(110\) 2.96925 0.283107
\(111\) 1.90890 0.181185
\(112\) 31.8742 3.01183
\(113\) 8.27697 0.778632 0.389316 0.921104i \(-0.372711\pi\)
0.389316 + 0.921104i \(0.372711\pi\)
\(114\) 3.70046 0.346580
\(115\) −2.95952 −0.275977
\(116\) −8.04312 −0.746785
\(117\) −2.86399 −0.264776
\(118\) 18.7673 1.72767
\(119\) −0.529677 −0.0485554
\(120\) 1.17963 0.107685
\(121\) −5.18898 −0.471725
\(122\) −0.188486 −0.0170647
\(123\) −3.12562 −0.281828
\(124\) −25.4742 −2.28765
\(125\) 4.68542 0.419077
\(126\) 29.5409 2.63172
\(127\) −3.99235 −0.354264 −0.177132 0.984187i \(-0.556682\pi\)
−0.177132 + 0.984187i \(0.556682\pi\)
\(128\) 8.38147 0.740825
\(129\) 2.50547 0.220594
\(130\) 1.23174 0.108031
\(131\) −13.3045 −1.16242 −0.581211 0.813753i \(-0.697421\pi\)
−0.581211 + 0.813753i \(0.697421\pi\)
\(132\) 4.08669 0.355700
\(133\) −15.6887 −1.36038
\(134\) −27.3096 −2.35919
\(135\) 1.03714 0.0892626
\(136\) 0.879687 0.0754325
\(137\) −14.6116 −1.24836 −0.624179 0.781282i \(-0.714566\pi\)
−0.624179 + 0.781282i \(0.714566\pi\)
\(138\) −5.84554 −0.497605
\(139\) −7.35278 −0.623654 −0.311827 0.950139i \(-0.600941\pi\)
−0.311827 + 0.950139i \(0.600941\pi\)
\(140\) −8.85310 −0.748223
\(141\) 0.388695 0.0327340
\(142\) 15.7837 1.32454
\(143\) 2.41061 0.201585
\(144\) −22.7313 −1.89427
\(145\) 0.839118 0.0696849
\(146\) 9.94473 0.823032
\(147\) 3.36630 0.277648
\(148\) 23.7929 1.95577
\(149\) −7.00050 −0.573503 −0.286751 0.958005i \(-0.592575\pi\)
−0.286751 + 0.958005i \(0.592575\pi\)
\(150\) 4.51831 0.368918
\(151\) 9.06306 0.737541 0.368771 0.929520i \(-0.379779\pi\)
0.368771 + 0.929520i \(0.379779\pi\)
\(152\) 26.0558 2.11340
\(153\) 0.377742 0.0305386
\(154\) −24.8645 −2.00364
\(155\) 2.65766 0.213468
\(156\) 1.69529 0.135732
\(157\) −10.6148 −0.847157 −0.423578 0.905859i \(-0.639226\pi\)
−0.423578 + 0.905859i \(0.639226\pi\)
\(158\) 9.65858 0.768395
\(159\) −2.85708 −0.226581
\(160\) 3.37909 0.267141
\(161\) 24.7831 1.95318
\(162\) −20.0193 −1.57286
\(163\) 5.56277 0.435710 0.217855 0.975981i \(-0.430094\pi\)
0.217855 + 0.975981i \(0.430094\pi\)
\(164\) −38.9584 −3.04214
\(165\) −0.426353 −0.0331916
\(166\) 17.4085 1.35116
\(167\) −2.96439 −0.229392 −0.114696 0.993401i \(-0.536589\pi\)
−0.114696 + 0.993401i \(0.536589\pi\)
\(168\) −9.87827 −0.762125
\(169\) 1.00000 0.0769231
\(170\) −0.162459 −0.0124600
\(171\) 11.1885 0.855604
\(172\) 31.2287 2.38117
\(173\) −10.0208 −0.761868 −0.380934 0.924602i \(-0.624397\pi\)
−0.380934 + 0.924602i \(0.624397\pi\)
\(174\) 1.65739 0.125647
\(175\) −19.1561 −1.44806
\(176\) 19.1328 1.44219
\(177\) −2.69479 −0.202553
\(178\) 19.2154 1.44025
\(179\) −12.1357 −0.907066 −0.453533 0.891239i \(-0.649837\pi\)
−0.453533 + 0.891239i \(0.649837\pi\)
\(180\) 6.31364 0.470591
\(181\) 2.15195 0.159953 0.0799767 0.996797i \(-0.474515\pi\)
0.0799767 + 0.996797i \(0.474515\pi\)
\(182\) −10.3146 −0.764570
\(183\) 0.0270646 0.00200067
\(184\) −41.1597 −3.03434
\(185\) −2.48225 −0.182499
\(186\) 5.24931 0.384898
\(187\) −0.317944 −0.0232504
\(188\) 4.84478 0.353342
\(189\) −8.68499 −0.631740
\(190\) −4.81193 −0.349094
\(191\) −18.0945 −1.30927 −0.654635 0.755945i \(-0.727178\pi\)
−0.654635 + 0.755945i \(0.727178\pi\)
\(192\) 0.819993 0.0591779
\(193\) −11.6503 −0.838607 −0.419304 0.907846i \(-0.637726\pi\)
−0.419304 + 0.907846i \(0.637726\pi\)
\(194\) 10.7126 0.769122
\(195\) −0.176866 −0.0126656
\(196\) 41.9583 2.99702
\(197\) −7.06627 −0.503451 −0.251725 0.967799i \(-0.580998\pi\)
−0.251725 + 0.967799i \(0.580998\pi\)
\(198\) 17.7323 1.26018
\(199\) −2.51466 −0.178259 −0.0891297 0.996020i \(-0.528409\pi\)
−0.0891297 + 0.996020i \(0.528409\pi\)
\(200\) 31.8144 2.24962
\(201\) 3.92138 0.276593
\(202\) 31.5200 2.21774
\(203\) −7.02678 −0.493183
\(204\) −0.223599 −0.0156550
\(205\) 4.06443 0.283872
\(206\) −13.2386 −0.922378
\(207\) −17.6742 −1.22844
\(208\) 7.93693 0.550327
\(209\) −9.41729 −0.651408
\(210\) 1.82430 0.125889
\(211\) 11.0007 0.757316 0.378658 0.925537i \(-0.376386\pi\)
0.378658 + 0.925537i \(0.376386\pi\)
\(212\) −35.6113 −2.44579
\(213\) −2.26638 −0.155290
\(214\) −11.3113 −0.773224
\(215\) −3.25801 −0.222195
\(216\) 14.4240 0.981432
\(217\) −22.2553 −1.51079
\(218\) −45.2563 −3.06514
\(219\) −1.42796 −0.0964927
\(220\) −5.31416 −0.358281
\(221\) −0.131894 −0.00887213
\(222\) −4.90286 −0.329058
\(223\) 21.8612 1.46393 0.731967 0.681340i \(-0.238603\pi\)
0.731967 + 0.681340i \(0.238603\pi\)
\(224\) −28.2966 −1.89064
\(225\) 13.6613 0.910750
\(226\) −21.2588 −1.41411
\(227\) −20.6778 −1.37243 −0.686217 0.727397i \(-0.740730\pi\)
−0.686217 + 0.727397i \(0.740730\pi\)
\(228\) −6.62284 −0.438609
\(229\) −11.1303 −0.735512 −0.367756 0.929922i \(-0.619874\pi\)
−0.367756 + 0.929922i \(0.619874\pi\)
\(230\) 7.60131 0.501215
\(231\) 3.57029 0.234908
\(232\) 11.6701 0.766178
\(233\) 9.68517 0.634497 0.317248 0.948342i \(-0.397241\pi\)
0.317248 + 0.948342i \(0.397241\pi\)
\(234\) 7.35593 0.480872
\(235\) −0.505443 −0.0329715
\(236\) −33.5885 −2.18642
\(237\) −1.38687 −0.0900871
\(238\) 1.36043 0.0881838
\(239\) −2.97535 −0.192460 −0.0962298 0.995359i \(-0.530678\pi\)
−0.0962298 + 0.995359i \(0.530678\pi\)
\(240\) −1.40377 −0.0906130
\(241\) 15.2082 0.979648 0.489824 0.871821i \(-0.337061\pi\)
0.489824 + 0.871821i \(0.337061\pi\)
\(242\) 13.3275 0.856723
\(243\) 9.36246 0.600602
\(244\) 0.337339 0.0215959
\(245\) −4.37740 −0.279662
\(246\) 8.02791 0.511841
\(247\) −3.90661 −0.248571
\(248\) 36.9615 2.34706
\(249\) −2.49968 −0.158411
\(250\) −12.0341 −0.761106
\(251\) −15.2988 −0.965649 −0.482825 0.875717i \(-0.660389\pi\)
−0.482825 + 0.875717i \(0.660389\pi\)
\(252\) −52.8704 −3.33052
\(253\) 14.8763 0.935264
\(254\) 10.2540 0.643396
\(255\) 0.0233275 0.00146082
\(256\) −25.9740 −1.62337
\(257\) −1.13315 −0.0706843 −0.0353421 0.999375i \(-0.511252\pi\)
−0.0353421 + 0.999375i \(0.511252\pi\)
\(258\) −6.43510 −0.400632
\(259\) 20.7864 1.29160
\(260\) −2.20449 −0.136717
\(261\) 5.01119 0.310185
\(262\) 34.1717 2.11113
\(263\) 18.6583 1.15052 0.575261 0.817970i \(-0.304901\pi\)
0.575261 + 0.817970i \(0.304901\pi\)
\(264\) −5.92953 −0.364937
\(265\) 3.71523 0.228225
\(266\) 40.2952 2.47065
\(267\) −2.75913 −0.168856
\(268\) 48.8770 2.98564
\(269\) −13.0785 −0.797408 −0.398704 0.917080i \(-0.630540\pi\)
−0.398704 + 0.917080i \(0.630540\pi\)
\(270\) −2.66381 −0.162114
\(271\) −4.51980 −0.274558 −0.137279 0.990532i \(-0.543836\pi\)
−0.137279 + 0.990532i \(0.543836\pi\)
\(272\) −1.04683 −0.0634735
\(273\) 1.48107 0.0896386
\(274\) 37.5289 2.26720
\(275\) −11.4986 −0.693393
\(276\) 10.4620 0.629736
\(277\) 16.8578 1.01289 0.506445 0.862272i \(-0.330959\pi\)
0.506445 + 0.862272i \(0.330959\pi\)
\(278\) 18.8850 1.13265
\(279\) 15.8715 0.950200
\(280\) 12.8453 0.767654
\(281\) 13.6399 0.813686 0.406843 0.913498i \(-0.366630\pi\)
0.406843 + 0.913498i \(0.366630\pi\)
\(282\) −0.998333 −0.0594498
\(283\) −11.0997 −0.659811 −0.329906 0.944014i \(-0.607017\pi\)
−0.329906 + 0.944014i \(0.607017\pi\)
\(284\) −28.2487 −1.67625
\(285\) 0.690944 0.0409280
\(286\) −6.19146 −0.366109
\(287\) −34.0356 −2.00906
\(288\) 20.1799 1.18911
\(289\) −16.9826 −0.998977
\(290\) −2.15521 −0.126558
\(291\) −1.53822 −0.0901723
\(292\) −17.7984 −1.04157
\(293\) −9.09262 −0.531197 −0.265598 0.964084i \(-0.585570\pi\)
−0.265598 + 0.964084i \(0.585570\pi\)
\(294\) −8.64608 −0.504250
\(295\) 3.50420 0.204022
\(296\) −34.5221 −2.00656
\(297\) −5.21326 −0.302504
\(298\) 17.9802 1.04157
\(299\) 6.17118 0.356889
\(300\) −8.08657 −0.466878
\(301\) 27.2826 1.57254
\(302\) −23.2778 −1.33948
\(303\) −4.52595 −0.260009
\(304\) −31.0065 −1.77834
\(305\) −0.0351937 −0.00201519
\(306\) −0.970201 −0.0554627
\(307\) −21.7706 −1.24251 −0.621257 0.783607i \(-0.713378\pi\)
−0.621257 + 0.783607i \(0.713378\pi\)
\(308\) 44.5008 2.53567
\(309\) 1.90093 0.108140
\(310\) −6.82599 −0.387690
\(311\) −16.9656 −0.962030 −0.481015 0.876712i \(-0.659732\pi\)
−0.481015 + 0.876712i \(0.659732\pi\)
\(312\) −2.45977 −0.139257
\(313\) −6.47578 −0.366033 −0.183016 0.983110i \(-0.558586\pi\)
−0.183016 + 0.983110i \(0.558586\pi\)
\(314\) 27.2634 1.53856
\(315\) 5.51584 0.310782
\(316\) −17.2863 −0.972430
\(317\) 1.61941 0.0909551 0.0454776 0.998965i \(-0.485519\pi\)
0.0454776 + 0.998965i \(0.485519\pi\)
\(318\) 7.33818 0.411505
\(319\) −4.21789 −0.236157
\(320\) −1.06629 −0.0596072
\(321\) 1.62419 0.0906532
\(322\) −63.6534 −3.54726
\(323\) 0.515257 0.0286696
\(324\) 35.8292 1.99051
\(325\) −4.77001 −0.264593
\(326\) −14.2876 −0.791315
\(327\) 6.49834 0.359359
\(328\) 56.5263 3.12114
\(329\) 4.23258 0.233350
\(330\) 1.09506 0.0602808
\(331\) −20.9317 −1.15051 −0.575254 0.817975i \(-0.695097\pi\)
−0.575254 + 0.817975i \(0.695097\pi\)
\(332\) −31.1566 −1.70994
\(333\) −14.8239 −0.812347
\(334\) 7.61382 0.416610
\(335\) −5.09921 −0.278600
\(336\) 11.7552 0.641298
\(337\) 19.9951 1.08920 0.544600 0.838696i \(-0.316681\pi\)
0.544600 + 0.838696i \(0.316681\pi\)
\(338\) −2.56842 −0.139704
\(339\) 3.05254 0.165791
\(340\) 0.290759 0.0157686
\(341\) −13.3589 −0.723428
\(342\) −28.7367 −1.55390
\(343\) 8.54485 0.461379
\(344\) −45.3110 −2.44300
\(345\) −1.09147 −0.0587627
\(346\) 25.7377 1.38367
\(347\) 1.66682 0.0894797 0.0447399 0.998999i \(-0.485754\pi\)
0.0447399 + 0.998999i \(0.485754\pi\)
\(348\) −2.96630 −0.159010
\(349\) 13.5560 0.725638 0.362819 0.931860i \(-0.381814\pi\)
0.362819 + 0.931860i \(0.381814\pi\)
\(350\) 49.2008 2.62990
\(351\) −2.16263 −0.115433
\(352\) −16.9853 −0.905319
\(353\) 24.5343 1.30583 0.652915 0.757431i \(-0.273546\pi\)
0.652915 + 0.757431i \(0.273546\pi\)
\(354\) 6.92137 0.367866
\(355\) 2.94711 0.156417
\(356\) −34.3904 −1.82269
\(357\) −0.195344 −0.0103387
\(358\) 31.1697 1.64737
\(359\) 11.8041 0.622994 0.311497 0.950247i \(-0.399170\pi\)
0.311497 + 0.950247i \(0.399170\pi\)
\(360\) −9.16070 −0.482811
\(361\) −3.73843 −0.196760
\(362\) −5.52713 −0.290499
\(363\) −1.91369 −0.100443
\(364\) 18.4604 0.967590
\(365\) 1.85686 0.0971927
\(366\) −0.0695133 −0.00363352
\(367\) −22.7889 −1.18957 −0.594786 0.803884i \(-0.702763\pi\)
−0.594786 + 0.803884i \(0.702763\pi\)
\(368\) 48.9803 2.55327
\(369\) 24.2727 1.26358
\(370\) 6.37548 0.331445
\(371\) −31.1114 −1.61522
\(372\) −9.39487 −0.487101
\(373\) 12.4489 0.644580 0.322290 0.946641i \(-0.395547\pi\)
0.322290 + 0.946641i \(0.395547\pi\)
\(374\) 0.816614 0.0422261
\(375\) 1.72798 0.0892324
\(376\) −7.02948 −0.362518
\(377\) −1.74972 −0.0901153
\(378\) 22.3067 1.14733
\(379\) 35.2004 1.80812 0.904062 0.427401i \(-0.140571\pi\)
0.904062 + 0.427401i \(0.140571\pi\)
\(380\) 8.61208 0.441791
\(381\) −1.47238 −0.0754321
\(382\) 46.4743 2.37783
\(383\) 25.5242 1.30423 0.652114 0.758121i \(-0.273882\pi\)
0.652114 + 0.758121i \(0.273882\pi\)
\(384\) 3.09108 0.157741
\(385\) −4.64266 −0.236612
\(386\) 29.9229 1.52304
\(387\) −19.4567 −0.989042
\(388\) −19.1728 −0.973350
\(389\) 15.6986 0.795952 0.397976 0.917396i \(-0.369713\pi\)
0.397976 + 0.917396i \(0.369713\pi\)
\(390\) 0.454266 0.0230026
\(391\) −0.813940 −0.0411627
\(392\) −60.8790 −3.07485
\(393\) −4.90670 −0.247510
\(394\) 18.1492 0.914341
\(395\) 1.80343 0.0907406
\(396\) −31.7360 −1.59480
\(397\) 18.1259 0.909714 0.454857 0.890565i \(-0.349690\pi\)
0.454857 + 0.890565i \(0.349690\pi\)
\(398\) 6.45871 0.323746
\(399\) −5.78597 −0.289661
\(400\) −37.8593 −1.89296
\(401\) 16.0335 0.800676 0.400338 0.916367i \(-0.368893\pi\)
0.400338 + 0.916367i \(0.368893\pi\)
\(402\) −10.0718 −0.502334
\(403\) −5.54174 −0.276054
\(404\) −56.4125 −2.80663
\(405\) −3.73797 −0.185741
\(406\) 18.0477 0.895694
\(407\) 12.4773 0.618475
\(408\) 0.324428 0.0160616
\(409\) 7.30829 0.361372 0.180686 0.983541i \(-0.442168\pi\)
0.180686 + 0.983541i \(0.442168\pi\)
\(410\) −10.4392 −0.515554
\(411\) −5.38876 −0.265808
\(412\) 23.6936 1.16730
\(413\) −29.3442 −1.44393
\(414\) 45.3948 2.23103
\(415\) 3.25049 0.159560
\(416\) −7.04607 −0.345462
\(417\) −2.71170 −0.132792
\(418\) 24.1876 1.18305
\(419\) 16.3226 0.797413 0.398707 0.917078i \(-0.369459\pi\)
0.398707 + 0.917078i \(0.369459\pi\)
\(420\) −3.26501 −0.159316
\(421\) 10.0501 0.489812 0.244906 0.969547i \(-0.421243\pi\)
0.244906 + 0.969547i \(0.421243\pi\)
\(422\) −28.2543 −1.37540
\(423\) −3.01849 −0.146764
\(424\) 51.6698 2.50931
\(425\) 0.629134 0.0305175
\(426\) 5.82103 0.282030
\(427\) 0.294712 0.0142621
\(428\) 20.2442 0.978541
\(429\) 0.889030 0.0429227
\(430\) 8.36795 0.403538
\(431\) 19.3204 0.930630 0.465315 0.885145i \(-0.345941\pi\)
0.465315 + 0.885145i \(0.345941\pi\)
\(432\) −17.1647 −0.825836
\(433\) −7.51856 −0.361319 −0.180660 0.983546i \(-0.557823\pi\)
−0.180660 + 0.983546i \(0.557823\pi\)
\(434\) 57.1609 2.74381
\(435\) 0.309466 0.0148378
\(436\) 80.9968 3.87904
\(437\) −24.1084 −1.15326
\(438\) 3.66761 0.175245
\(439\) −14.9288 −0.712511 −0.356256 0.934389i \(-0.615947\pi\)
−0.356256 + 0.934389i \(0.615947\pi\)
\(440\) 7.71053 0.367585
\(441\) −26.1417 −1.24484
\(442\) 0.338759 0.0161131
\(443\) −40.9005 −1.94324 −0.971621 0.236542i \(-0.923986\pi\)
−0.971621 + 0.236542i \(0.923986\pi\)
\(444\) 8.77481 0.416434
\(445\) 3.58786 0.170081
\(446\) −56.1488 −2.65872
\(447\) −2.58178 −0.122114
\(448\) 8.92908 0.421859
\(449\) 8.13521 0.383924 0.191962 0.981402i \(-0.438515\pi\)
0.191962 + 0.981402i \(0.438515\pi\)
\(450\) −35.0879 −1.65406
\(451\) −20.4302 −0.962021
\(452\) 38.0475 1.78961
\(453\) 3.34245 0.157042
\(454\) 53.1093 2.49254
\(455\) −1.92593 −0.0902889
\(456\) 9.60934 0.449999
\(457\) 8.32422 0.389391 0.194695 0.980864i \(-0.437628\pi\)
0.194695 + 0.980864i \(0.437628\pi\)
\(458\) 28.5874 1.33580
\(459\) 0.285238 0.0133138
\(460\) −13.6043 −0.634305
\(461\) −4.81487 −0.224251 −0.112125 0.993694i \(-0.535766\pi\)
−0.112125 + 0.993694i \(0.535766\pi\)
\(462\) −9.17000 −0.426627
\(463\) 9.14969 0.425222 0.212611 0.977137i \(-0.431803\pi\)
0.212611 + 0.977137i \(0.431803\pi\)
\(464\) −13.8874 −0.644708
\(465\) 0.980143 0.0454530
\(466\) −24.8756 −1.15234
\(467\) 7.61442 0.352353 0.176177 0.984359i \(-0.443627\pi\)
0.176177 + 0.984359i \(0.443627\pi\)
\(468\) −13.1652 −0.608560
\(469\) 42.7008 1.97174
\(470\) 1.29819 0.0598811
\(471\) −3.91475 −0.180382
\(472\) 48.7348 2.24320
\(473\) 16.3767 0.753000
\(474\) 3.56208 0.163612
\(475\) 18.6346 0.855012
\(476\) −2.43481 −0.111600
\(477\) 22.1872 1.01588
\(478\) 7.64196 0.349535
\(479\) −32.2113 −1.47177 −0.735886 0.677105i \(-0.763234\pi\)
−0.735886 + 0.677105i \(0.763234\pi\)
\(480\) 1.24621 0.0568813
\(481\) 5.17598 0.236004
\(482\) −39.0611 −1.77919
\(483\) 9.13997 0.415883
\(484\) −23.8527 −1.08421
\(485\) 2.00025 0.0908265
\(486\) −24.0468 −1.09078
\(487\) 24.9603 1.13106 0.565529 0.824728i \(-0.308672\pi\)
0.565529 + 0.824728i \(0.308672\pi\)
\(488\) −0.489459 −0.0221567
\(489\) 2.05155 0.0927741
\(490\) 11.2430 0.507908
\(491\) −14.0313 −0.633225 −0.316613 0.948555i \(-0.602546\pi\)
−0.316613 + 0.948555i \(0.602546\pi\)
\(492\) −14.3678 −0.647752
\(493\) 0.230777 0.0103937
\(494\) 10.0338 0.451443
\(495\) 3.31094 0.148816
\(496\) −43.9844 −1.97496
\(497\) −24.6791 −1.10701
\(498\) 6.42025 0.287698
\(499\) −26.5386 −1.18803 −0.594015 0.804454i \(-0.702458\pi\)
−0.594015 + 0.804454i \(0.702458\pi\)
\(500\) 21.5379 0.963205
\(501\) −1.09327 −0.0488435
\(502\) 39.2937 1.75376
\(503\) −38.4138 −1.71279 −0.856394 0.516323i \(-0.827300\pi\)
−0.856394 + 0.516323i \(0.827300\pi\)
\(504\) 76.7118 3.41701
\(505\) 5.88537 0.261895
\(506\) −38.2086 −1.69858
\(507\) 0.368799 0.0163789
\(508\) −18.3520 −0.814239
\(509\) 5.83637 0.258692 0.129346 0.991599i \(-0.458712\pi\)
0.129346 + 0.991599i \(0.458712\pi\)
\(510\) −0.0599148 −0.00265307
\(511\) −15.5494 −0.687865
\(512\) 49.9492 2.20747
\(513\) 8.44856 0.373013
\(514\) 2.91042 0.128373
\(515\) −2.47189 −0.108925
\(516\) 11.5171 0.507013
\(517\) 2.54065 0.111738
\(518\) −53.3883 −2.34575
\(519\) −3.69567 −0.162222
\(520\) 3.19858 0.140267
\(521\) 33.2484 1.45664 0.728320 0.685237i \(-0.240302\pi\)
0.728320 + 0.685237i \(0.240302\pi\)
\(522\) −12.8708 −0.563341
\(523\) −7.99914 −0.349778 −0.174889 0.984588i \(-0.555957\pi\)
−0.174889 + 0.984588i \(0.555957\pi\)
\(524\) −61.1582 −2.67171
\(525\) −7.06474 −0.308330
\(526\) −47.9225 −2.08952
\(527\) 0.730920 0.0318394
\(528\) 7.05617 0.307080
\(529\) 15.0835 0.655804
\(530\) −9.54228 −0.414490
\(531\) 20.9270 0.908153
\(532\) −72.1176 −3.12670
\(533\) −8.47513 −0.367099
\(534\) 7.08661 0.306667
\(535\) −2.11203 −0.0913109
\(536\) −70.9176 −3.06317
\(537\) −4.47564 −0.193138
\(538\) 33.5910 1.44821
\(539\) 22.0034 0.947753
\(540\) 4.76751 0.205161
\(541\) −33.3220 −1.43263 −0.716313 0.697779i \(-0.754172\pi\)
−0.716313 + 0.697779i \(0.754172\pi\)
\(542\) 11.6088 0.498639
\(543\) 0.793638 0.0340583
\(544\) 0.929332 0.0398448
\(545\) −8.45018 −0.361966
\(546\) −3.80402 −0.162797
\(547\) 2.05136 0.0877097 0.0438548 0.999038i \(-0.486036\pi\)
0.0438548 + 0.999038i \(0.486036\pi\)
\(548\) −67.1667 −2.86922
\(549\) −0.210176 −0.00897009
\(550\) 29.5333 1.25930
\(551\) 6.83548 0.291201
\(552\) −15.1797 −0.646090
\(553\) −15.1020 −0.642201
\(554\) −43.2981 −1.83956
\(555\) −0.915453 −0.0388588
\(556\) −33.7992 −1.43341
\(557\) −32.5707 −1.38007 −0.690033 0.723778i \(-0.742404\pi\)
−0.690033 + 0.723778i \(0.742404\pi\)
\(558\) −40.7646 −1.72570
\(559\) 6.79359 0.287338
\(560\) −15.2860 −0.645950
\(561\) −0.117257 −0.00495061
\(562\) −35.0329 −1.47778
\(563\) 5.63834 0.237628 0.118814 0.992917i \(-0.462091\pi\)
0.118814 + 0.992917i \(0.462091\pi\)
\(564\) 1.78675 0.0752358
\(565\) −3.96940 −0.166994
\(566\) 28.5088 1.19832
\(567\) 31.3017 1.31455
\(568\) 40.9871 1.71978
\(569\) 17.5228 0.734594 0.367297 0.930104i \(-0.380283\pi\)
0.367297 + 0.930104i \(0.380283\pi\)
\(570\) −1.77464 −0.0743313
\(571\) 19.0269 0.796253 0.398126 0.917331i \(-0.369661\pi\)
0.398126 + 0.917331i \(0.369661\pi\)
\(572\) 11.0811 0.463323
\(573\) −6.67323 −0.278778
\(574\) 87.4177 3.64875
\(575\) −29.4366 −1.22759
\(576\) −6.36783 −0.265326
\(577\) −0.0625611 −0.00260445 −0.00130223 0.999999i \(-0.500415\pi\)
−0.00130223 + 0.999999i \(0.500415\pi\)
\(578\) 43.6185 1.81429
\(579\) −4.29662 −0.178561
\(580\) 3.85725 0.160164
\(581\) −27.2196 −1.12926
\(582\) 3.95081 0.163766
\(583\) −18.6749 −0.773436
\(584\) 25.8244 1.06862
\(585\) 1.37349 0.0567867
\(586\) 23.3537 0.964733
\(587\) 20.4159 0.842652 0.421326 0.906909i \(-0.361565\pi\)
0.421326 + 0.906909i \(0.361565\pi\)
\(588\) 15.4742 0.638145
\(589\) 21.6494 0.892047
\(590\) −9.00027 −0.370535
\(591\) −2.60603 −0.107198
\(592\) 41.0814 1.68844
\(593\) −31.3283 −1.28650 −0.643250 0.765656i \(-0.722414\pi\)
−0.643250 + 0.765656i \(0.722414\pi\)
\(594\) 13.3898 0.549392
\(595\) 0.254018 0.0104137
\(596\) −32.1798 −1.31814
\(597\) −0.927404 −0.0379561
\(598\) −15.8502 −0.648163
\(599\) 6.56814 0.268367 0.134183 0.990957i \(-0.457159\pi\)
0.134183 + 0.990957i \(0.457159\pi\)
\(600\) 11.7331 0.479002
\(601\) 6.96170 0.283973 0.141987 0.989869i \(-0.454651\pi\)
0.141987 + 0.989869i \(0.454651\pi\)
\(602\) −70.0733 −2.85597
\(603\) −30.4523 −1.24012
\(604\) 41.6610 1.69516
\(605\) 2.48849 0.101171
\(606\) 11.6246 0.472215
\(607\) −22.9850 −0.932933 −0.466466 0.884539i \(-0.654473\pi\)
−0.466466 + 0.884539i \(0.654473\pi\)
\(608\) 27.5262 1.11634
\(609\) −2.59147 −0.105012
\(610\) 0.0903924 0.00365988
\(611\) 1.05395 0.0426381
\(612\) 1.73640 0.0701899
\(613\) −16.7191 −0.675278 −0.337639 0.941276i \(-0.609628\pi\)
−0.337639 + 0.941276i \(0.609628\pi\)
\(614\) 55.9161 2.25659
\(615\) 1.49896 0.0604438
\(616\) −64.5680 −2.60152
\(617\) 38.7760 1.56106 0.780532 0.625116i \(-0.214948\pi\)
0.780532 + 0.625116i \(0.214948\pi\)
\(618\) −4.88239 −0.196398
\(619\) 1.00000 0.0401934
\(620\) 12.2167 0.490635
\(621\) −13.3460 −0.535557
\(622\) 43.5748 1.74719
\(623\) −30.0448 −1.20372
\(624\) 2.92713 0.117179
\(625\) 21.6031 0.864122
\(626\) 16.6325 0.664770
\(627\) −3.47309 −0.138702
\(628\) −48.7943 −1.94710
\(629\) −0.682679 −0.0272202
\(630\) −14.1670 −0.564427
\(631\) 25.4322 1.01244 0.506221 0.862404i \(-0.331042\pi\)
0.506221 + 0.862404i \(0.331042\pi\)
\(632\) 25.0814 0.997683
\(633\) 4.05703 0.161253
\(634\) −4.15933 −0.165188
\(635\) 1.91462 0.0759793
\(636\) −13.1334 −0.520773
\(637\) 9.12774 0.361654
\(638\) 10.8333 0.428896
\(639\) 17.6001 0.696248
\(640\) −4.01952 −0.158885
\(641\) 35.6339 1.40745 0.703727 0.710471i \(-0.251518\pi\)
0.703727 + 0.710471i \(0.251518\pi\)
\(642\) −4.17160 −0.164640
\(643\) 41.3555 1.63090 0.815452 0.578825i \(-0.196489\pi\)
0.815452 + 0.578825i \(0.196489\pi\)
\(644\) 113.923 4.48918
\(645\) −1.20155 −0.0473111
\(646\) −1.32340 −0.0520684
\(647\) −14.6576 −0.576251 −0.288126 0.957593i \(-0.593032\pi\)
−0.288126 + 0.957593i \(0.593032\pi\)
\(648\) −51.9860 −2.04220
\(649\) −17.6142 −0.691416
\(650\) 12.2514 0.480540
\(651\) −8.20772 −0.321686
\(652\) 25.5709 1.00144
\(653\) 17.9419 0.702120 0.351060 0.936353i \(-0.385821\pi\)
0.351060 + 0.936353i \(0.385821\pi\)
\(654\) −16.6905 −0.652650
\(655\) 6.38047 0.249306
\(656\) −67.2665 −2.62632
\(657\) 11.0891 0.432628
\(658\) −10.8711 −0.423798
\(659\) −5.32562 −0.207457 −0.103728 0.994606i \(-0.533077\pi\)
−0.103728 + 0.994606i \(0.533077\pi\)
\(660\) −1.95986 −0.0762874
\(661\) −23.0577 −0.896839 −0.448420 0.893823i \(-0.648013\pi\)
−0.448420 + 0.893823i \(0.648013\pi\)
\(662\) 53.7613 2.08949
\(663\) −0.0486423 −0.00188911
\(664\) 45.2064 1.75435
\(665\) 7.52384 0.291762
\(666\) 38.0742 1.47534
\(667\) −10.7979 −0.418095
\(668\) −13.6267 −0.527233
\(669\) 8.06239 0.311710
\(670\) 13.0969 0.505979
\(671\) 0.176904 0.00682931
\(672\) −10.4357 −0.402568
\(673\) −9.88896 −0.381191 −0.190596 0.981669i \(-0.561042\pi\)
−0.190596 + 0.981669i \(0.561042\pi\)
\(674\) −51.3558 −1.97815
\(675\) 10.3158 0.397055
\(676\) 4.59680 0.176800
\(677\) −24.4486 −0.939637 −0.469818 0.882763i \(-0.655681\pi\)
−0.469818 + 0.882763i \(0.655681\pi\)
\(678\) −7.84021 −0.301101
\(679\) −16.7501 −0.642808
\(680\) −0.421873 −0.0161781
\(681\) −7.62595 −0.292227
\(682\) 34.3114 1.31385
\(683\) 6.00016 0.229590 0.114795 0.993389i \(-0.463379\pi\)
0.114795 + 0.993389i \(0.463379\pi\)
\(684\) 51.4311 1.96652
\(685\) 7.00733 0.267736
\(686\) −21.9468 −0.837932
\(687\) −4.10485 −0.156610
\(688\) 53.9203 2.05569
\(689\) −7.74698 −0.295136
\(690\) 2.80336 0.106722
\(691\) −40.0836 −1.52485 −0.762426 0.647076i \(-0.775992\pi\)
−0.762426 + 0.647076i \(0.775992\pi\)
\(692\) −46.0636 −1.75108
\(693\) −27.7258 −1.05322
\(694\) −4.28110 −0.162508
\(695\) 3.52618 0.133756
\(696\) 4.30391 0.163139
\(697\) 1.11782 0.0423403
\(698\) −34.8176 −1.31787
\(699\) 3.57188 0.135101
\(700\) −88.0565 −3.32822
\(701\) −15.1824 −0.573430 −0.286715 0.958016i \(-0.592563\pi\)
−0.286715 + 0.958016i \(0.592563\pi\)
\(702\) 5.55456 0.209643
\(703\) −20.2205 −0.762631
\(704\) 5.35977 0.202004
\(705\) −0.186407 −0.00702049
\(706\) −63.0145 −2.37158
\(707\) −49.2841 −1.85352
\(708\) −12.3874 −0.465547
\(709\) 47.3939 1.77992 0.889958 0.456043i \(-0.150734\pi\)
0.889958 + 0.456043i \(0.150734\pi\)
\(710\) −7.56943 −0.284076
\(711\) 10.7701 0.403909
\(712\) 49.8984 1.87002
\(713\) −34.1991 −1.28077
\(714\) 0.501727 0.0187766
\(715\) −1.15606 −0.0432341
\(716\) −55.7854 −2.08480
\(717\) −1.09731 −0.0409797
\(718\) −30.3178 −1.13145
\(719\) −38.0865 −1.42039 −0.710194 0.704006i \(-0.751393\pi\)
−0.710194 + 0.704006i \(0.751393\pi\)
\(720\) 10.9013 0.406267
\(721\) 20.6996 0.770895
\(722\) 9.60187 0.357345
\(723\) 5.60878 0.208593
\(724\) 9.89209 0.367637
\(725\) 8.34620 0.309970
\(726\) 4.91516 0.182419
\(727\) −50.4663 −1.87169 −0.935846 0.352409i \(-0.885362\pi\)
−0.935846 + 0.352409i \(0.885362\pi\)
\(728\) −26.7850 −0.992716
\(729\) −19.9303 −0.738159
\(730\) −4.76921 −0.176516
\(731\) −0.896031 −0.0331409
\(732\) 0.124410 0.00459834
\(733\) 0.741731 0.0273965 0.0136982 0.999906i \(-0.495640\pi\)
0.0136982 + 0.999906i \(0.495640\pi\)
\(734\) 58.5316 2.16044
\(735\) −1.61438 −0.0595474
\(736\) −43.4826 −1.60279
\(737\) 25.6316 0.944153
\(738\) −62.3424 −2.29486
\(739\) 5.69387 0.209452 0.104726 0.994501i \(-0.466603\pi\)
0.104726 + 0.994501i \(0.466603\pi\)
\(740\) −11.4104 −0.419455
\(741\) −1.44075 −0.0529274
\(742\) 79.9071 2.93348
\(743\) 31.9298 1.17139 0.585695 0.810532i \(-0.300822\pi\)
0.585695 + 0.810532i \(0.300822\pi\)
\(744\) 13.6314 0.499751
\(745\) 3.35724 0.123000
\(746\) −31.9741 −1.17065
\(747\) 19.4118 0.710242
\(748\) −1.46152 −0.0534386
\(749\) 17.6861 0.646237
\(750\) −4.43818 −0.162059
\(751\) −48.9484 −1.78615 −0.893076 0.449906i \(-0.851457\pi\)
−0.893076 + 0.449906i \(0.851457\pi\)
\(752\) 8.36511 0.305044
\(753\) −5.64217 −0.205612
\(754\) 4.49403 0.163663
\(755\) −4.34638 −0.158181
\(756\) −39.9231 −1.45199
\(757\) −27.6448 −1.00477 −0.502383 0.864645i \(-0.667543\pi\)
−0.502383 + 0.864645i \(0.667543\pi\)
\(758\) −90.4096 −3.28382
\(759\) 5.48636 0.199142
\(760\) −12.4956 −0.453263
\(761\) 0.685304 0.0248423 0.0124211 0.999923i \(-0.496046\pi\)
0.0124211 + 0.999923i \(0.496046\pi\)
\(762\) 3.78168 0.136996
\(763\) 70.7619 2.56175
\(764\) −83.1766 −3.00923
\(765\) −0.181154 −0.00654965
\(766\) −65.5570 −2.36867
\(767\) −7.30694 −0.263838
\(768\) −9.57918 −0.345659
\(769\) −11.5405 −0.416161 −0.208080 0.978112i \(-0.566722\pi\)
−0.208080 + 0.978112i \(0.566722\pi\)
\(770\) 11.9243 0.429722
\(771\) −0.417907 −0.0150505
\(772\) −53.5541 −1.92745
\(773\) 30.9551 1.11338 0.556689 0.830721i \(-0.312071\pi\)
0.556689 + 0.830721i \(0.312071\pi\)
\(774\) 49.9732 1.79625
\(775\) 26.4341 0.949543
\(776\) 27.8185 0.998626
\(777\) 7.66601 0.275017
\(778\) −40.3207 −1.44557
\(779\) 33.1090 1.18625
\(780\) −0.813015 −0.0291106
\(781\) −14.8139 −0.530083
\(782\) 2.09054 0.0747576
\(783\) 3.78401 0.135229
\(784\) 72.4462 2.58737
\(785\) 5.09058 0.181691
\(786\) 12.6025 0.449515
\(787\) −36.9734 −1.31796 −0.658979 0.752161i \(-0.729011\pi\)
−0.658979 + 0.752161i \(0.729011\pi\)
\(788\) −32.4822 −1.15713
\(789\) 6.88117 0.244976
\(790\) −4.63198 −0.164798
\(791\) 33.2398 1.18187
\(792\) 46.0470 1.63621
\(793\) 0.0733858 0.00260600
\(794\) −46.5550 −1.65218
\(795\) 1.37017 0.0485951
\(796\) −11.5594 −0.409711
\(797\) 1.25261 0.0443699 0.0221849 0.999754i \(-0.492938\pi\)
0.0221849 + 0.999754i \(0.492938\pi\)
\(798\) 14.8608 0.526067
\(799\) −0.139009 −0.00491779
\(800\) 33.6098 1.18829
\(801\) 21.4266 0.757071
\(802\) −41.1809 −1.45415
\(803\) −9.33368 −0.329378
\(804\) 18.0258 0.635721
\(805\) −11.8853 −0.418900
\(806\) 14.2335 0.501354
\(807\) −4.82332 −0.169789
\(808\) 81.8510 2.87951
\(809\) 35.3858 1.24410 0.622050 0.782978i \(-0.286300\pi\)
0.622050 + 0.782978i \(0.286300\pi\)
\(810\) 9.60068 0.337333
\(811\) 14.1638 0.497357 0.248678 0.968586i \(-0.420004\pi\)
0.248678 + 0.968586i \(0.420004\pi\)
\(812\) −32.3006 −1.13353
\(813\) −1.66690 −0.0584607
\(814\) −32.0469 −1.12324
\(815\) −2.66775 −0.0934472
\(816\) −0.386071 −0.0135152
\(817\) −26.5399 −0.928513
\(818\) −18.7708 −0.656305
\(819\) −11.5016 −0.401898
\(820\) 18.6834 0.652451
\(821\) −27.4236 −0.957090 −0.478545 0.878063i \(-0.658836\pi\)
−0.478545 + 0.878063i \(0.658836\pi\)
\(822\) 13.8406 0.482747
\(823\) 3.22768 0.112510 0.0562549 0.998416i \(-0.482084\pi\)
0.0562549 + 0.998416i \(0.482084\pi\)
\(824\) −34.3780 −1.19761
\(825\) −4.24068 −0.147642
\(826\) 75.3683 2.62240
\(827\) −48.2241 −1.67692 −0.838458 0.544967i \(-0.816542\pi\)
−0.838458 + 0.544967i \(0.816542\pi\)
\(828\) −81.2446 −2.82345
\(829\) −41.9537 −1.45711 −0.728557 0.684985i \(-0.759809\pi\)
−0.728557 + 0.684985i \(0.759809\pi\)
\(830\) −8.34863 −0.289785
\(831\) 6.21716 0.215671
\(832\) 2.22341 0.0770830
\(833\) −1.20389 −0.0417123
\(834\) 6.96478 0.241171
\(835\) 1.42164 0.0491979
\(836\) −43.2893 −1.49719
\(837\) 11.9847 0.414253
\(838\) −41.9235 −1.44822
\(839\) −4.87087 −0.168161 −0.0840805 0.996459i \(-0.526795\pi\)
−0.0840805 + 0.996459i \(0.526795\pi\)
\(840\) 4.73734 0.163454
\(841\) −25.9385 −0.894430
\(842\) −25.8129 −0.889571
\(843\) 5.03037 0.173255
\(844\) 50.5678 1.74061
\(845\) −0.479572 −0.0164978
\(846\) 7.75276 0.266545
\(847\) −20.8386 −0.716022
\(848\) −61.4873 −2.11148
\(849\) −4.09358 −0.140491
\(850\) −1.61588 −0.0554243
\(851\) 31.9419 1.09496
\(852\) −10.4181 −0.356918
\(853\) 43.2328 1.48026 0.740131 0.672462i \(-0.234763\pi\)
0.740131 + 0.672462i \(0.234763\pi\)
\(854\) −0.756946 −0.0259022
\(855\) −5.36567 −0.183502
\(856\) −29.3731 −1.00395
\(857\) −1.47221 −0.0502899 −0.0251449 0.999684i \(-0.508005\pi\)
−0.0251449 + 0.999684i \(0.508005\pi\)
\(858\) −2.28340 −0.0779541
\(859\) 0.204429 0.00697501 0.00348751 0.999994i \(-0.498890\pi\)
0.00348751 + 0.999994i \(0.498890\pi\)
\(860\) −14.9764 −0.510691
\(861\) −12.5523 −0.427781
\(862\) −49.6229 −1.69016
\(863\) −12.9219 −0.439866 −0.219933 0.975515i \(-0.570584\pi\)
−0.219933 + 0.975515i \(0.570584\pi\)
\(864\) 15.2381 0.518409
\(865\) 4.80570 0.163399
\(866\) 19.3109 0.656209
\(867\) −6.26317 −0.212708
\(868\) −102.303 −3.47239
\(869\) −9.06511 −0.307513
\(870\) −0.794839 −0.0269476
\(871\) 10.6328 0.360280
\(872\) −117.521 −3.97978
\(873\) 11.9454 0.404291
\(874\) 61.9205 2.09449
\(875\) 18.8163 0.636109
\(876\) −6.56405 −0.221779
\(877\) 15.6956 0.530004 0.265002 0.964248i \(-0.414627\pi\)
0.265002 + 0.964248i \(0.414627\pi\)
\(878\) 38.3434 1.29403
\(879\) −3.35335 −0.113106
\(880\) −9.17556 −0.309308
\(881\) −38.5668 −1.29935 −0.649675 0.760212i \(-0.725095\pi\)
−0.649675 + 0.760212i \(0.725095\pi\)
\(882\) 67.1430 2.26082
\(883\) −5.15729 −0.173557 −0.0867783 0.996228i \(-0.527657\pi\)
−0.0867783 + 0.996228i \(0.527657\pi\)
\(884\) −0.606288 −0.0203917
\(885\) 1.29235 0.0434417
\(886\) 105.050 3.52922
\(887\) 3.02348 0.101518 0.0507592 0.998711i \(-0.483836\pi\)
0.0507592 + 0.998711i \(0.483836\pi\)
\(888\) −12.7317 −0.427248
\(889\) −16.0330 −0.537730
\(890\) −9.21514 −0.308892
\(891\) 18.7892 0.629462
\(892\) 100.491 3.36470
\(893\) −4.11736 −0.137782
\(894\) 6.63109 0.221777
\(895\) 5.81995 0.194539
\(896\) 33.6595 1.12448
\(897\) 2.27593 0.0759910
\(898\) −20.8947 −0.697264
\(899\) 9.69651 0.323397
\(900\) 62.7980 2.09327
\(901\) 1.02178 0.0340403
\(902\) 52.4734 1.74717
\(903\) 10.0618 0.334836
\(904\) −55.2046 −1.83608
\(905\) −1.03202 −0.0343054
\(906\) −8.58482 −0.285211
\(907\) −35.6825 −1.18482 −0.592409 0.805637i \(-0.701823\pi\)
−0.592409 + 0.805637i \(0.701823\pi\)
\(908\) −95.0516 −3.15440
\(909\) 35.1472 1.16576
\(910\) 4.94660 0.163978
\(911\) −20.0467 −0.664178 −0.332089 0.943248i \(-0.607753\pi\)
−0.332089 + 0.943248i \(0.607753\pi\)
\(912\) −11.4352 −0.378656
\(913\) −16.3389 −0.540737
\(914\) −21.3801 −0.707192
\(915\) −0.0129794 −0.000429086 0
\(916\) −51.1638 −1.69050
\(917\) −53.4301 −1.76442
\(918\) −0.732611 −0.0241798
\(919\) −44.8216 −1.47853 −0.739264 0.673416i \(-0.764826\pi\)
−0.739264 + 0.673416i \(0.764826\pi\)
\(920\) 19.7390 0.650777
\(921\) −8.02898 −0.264564
\(922\) 12.3666 0.407273
\(923\) −6.14530 −0.202275
\(924\) 16.4119 0.539911
\(925\) −24.6895 −0.811786
\(926\) −23.5003 −0.772267
\(927\) −14.7621 −0.484850
\(928\) 12.3287 0.404708
\(929\) 31.8255 1.04416 0.522081 0.852896i \(-0.325156\pi\)
0.522081 + 0.852896i \(0.325156\pi\)
\(930\) −2.51742 −0.0825495
\(931\) −35.6585 −1.16866
\(932\) 44.5208 1.45833
\(933\) −6.25689 −0.204841
\(934\) −19.5570 −0.639926
\(935\) 0.152477 0.00498653
\(936\) 19.1018 0.624363
\(937\) −50.4418 −1.64786 −0.823930 0.566691i \(-0.808223\pi\)
−0.823930 + 0.566691i \(0.808223\pi\)
\(938\) −109.674 −3.58098
\(939\) −2.38826 −0.0779380
\(940\) −2.32342 −0.0757816
\(941\) −27.4312 −0.894232 −0.447116 0.894476i \(-0.647549\pi\)
−0.447116 + 0.894476i \(0.647549\pi\)
\(942\) 10.0547 0.327601
\(943\) −52.3016 −1.70317
\(944\) −57.9947 −1.88757
\(945\) 4.16508 0.135490
\(946\) −42.0622 −1.36756
\(947\) 7.05281 0.229186 0.114593 0.993413i \(-0.463444\pi\)
0.114593 + 0.993413i \(0.463444\pi\)
\(948\) −6.37517 −0.207056
\(949\) −3.87192 −0.125688
\(950\) −47.8614 −1.55283
\(951\) 0.597237 0.0193667
\(952\) 3.53277 0.114498
\(953\) 11.4772 0.371783 0.185892 0.982570i \(-0.440483\pi\)
0.185892 + 0.982570i \(0.440483\pi\)
\(954\) −56.9862 −1.84500
\(955\) 8.67760 0.280801
\(956\) −13.6771 −0.442349
\(957\) −1.55556 −0.0502840
\(958\) 82.7323 2.67296
\(959\) −58.6794 −1.89486
\(960\) −0.393245 −0.0126919
\(961\) −0.289150 −0.00932741
\(962\) −13.2941 −0.428619
\(963\) −12.6130 −0.406447
\(964\) 69.9091 2.25162
\(965\) 5.58715 0.179857
\(966\) −23.4753 −0.755306
\(967\) 7.94626 0.255534 0.127767 0.991804i \(-0.459219\pi\)
0.127767 + 0.991804i \(0.459219\pi\)
\(968\) 34.6087 1.11237
\(969\) 0.190026 0.00610452
\(970\) −5.13748 −0.164954
\(971\) 2.67528 0.0858538 0.0429269 0.999078i \(-0.486332\pi\)
0.0429269 + 0.999078i \(0.486332\pi\)
\(972\) 43.0373 1.38042
\(973\) −29.5283 −0.946633
\(974\) −64.1085 −2.05417
\(975\) −1.75918 −0.0563387
\(976\) 0.582458 0.0186440
\(977\) −39.8335 −1.27439 −0.637193 0.770704i \(-0.719905\pi\)
−0.637193 + 0.770704i \(0.719905\pi\)
\(978\) −5.26924 −0.168492
\(979\) −18.0347 −0.576391
\(980\) −20.1220 −0.642775
\(981\) −50.4642 −1.61120
\(982\) 36.0384 1.15003
\(983\) 59.7713 1.90641 0.953205 0.302326i \(-0.0977630\pi\)
0.953205 + 0.302326i \(0.0977630\pi\)
\(984\) 20.8468 0.664573
\(985\) 3.38878 0.107976
\(986\) −0.592734 −0.0188765
\(987\) 1.56097 0.0496863
\(988\) −17.9579 −0.571316
\(989\) 41.9245 1.33312
\(990\) −8.50389 −0.270271
\(991\) −60.1957 −1.91218 −0.956089 0.293076i \(-0.905321\pi\)
−0.956089 + 0.293076i \(0.905321\pi\)
\(992\) 39.0475 1.23976
\(993\) −7.71958 −0.244973
\(994\) 63.3865 2.01050
\(995\) 1.20596 0.0382315
\(996\) −11.4905 −0.364092
\(997\) −46.5265 −1.47351 −0.736755 0.676160i \(-0.763643\pi\)
−0.736755 + 0.676160i \(0.763643\pi\)
\(998\) 68.1623 2.15764
\(999\) −11.1938 −0.354155
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 \(a_p\))