Properties

Label 8047.2.a.b.1.15
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 1.15
Character \(\chi\) = 8047.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.43267 q^{2} -0.839960 q^{3} +3.91786 q^{4} -3.64522 q^{5} +2.04334 q^{6} -2.93716 q^{7} -4.66552 q^{8} -2.29447 q^{9} +O(q^{10})\) \(q-2.43267 q^{2} -0.839960 q^{3} +3.91786 q^{4} -3.64522 q^{5} +2.04334 q^{6} -2.93716 q^{7} -4.66552 q^{8} -2.29447 q^{9} +8.86761 q^{10} -1.95237 q^{11} -3.29085 q^{12} +1.00000 q^{13} +7.14513 q^{14} +3.06184 q^{15} +3.51393 q^{16} -6.09230 q^{17} +5.58167 q^{18} +6.19342 q^{19} -14.2815 q^{20} +2.46710 q^{21} +4.74947 q^{22} -5.35888 q^{23} +3.91885 q^{24} +8.28765 q^{25} -2.43267 q^{26} +4.44714 q^{27} -11.5074 q^{28} -3.08816 q^{29} -7.44844 q^{30} -2.60935 q^{31} +0.782822 q^{32} +1.63992 q^{33} +14.8205 q^{34} +10.7066 q^{35} -8.98941 q^{36} +0.220676 q^{37} -15.0665 q^{38} -0.839960 q^{39} +17.0069 q^{40} -9.64711 q^{41} -6.00162 q^{42} -11.3459 q^{43} -7.64914 q^{44} +8.36384 q^{45} +13.0364 q^{46} -0.488560 q^{47} -2.95156 q^{48} +1.62691 q^{49} -20.1611 q^{50} +5.11729 q^{51} +3.91786 q^{52} -2.57418 q^{53} -10.8184 q^{54} +7.11684 q^{55} +13.7034 q^{56} -5.20223 q^{57} +7.51246 q^{58} +0.288421 q^{59} +11.9959 q^{60} +11.8875 q^{61} +6.34767 q^{62} +6.73922 q^{63} -8.93221 q^{64} -3.64522 q^{65} -3.98937 q^{66} -4.74662 q^{67} -23.8688 q^{68} +4.50124 q^{69} -26.0456 q^{70} +4.41906 q^{71} +10.7049 q^{72} -10.0232 q^{73} -0.536831 q^{74} -6.96129 q^{75} +24.2650 q^{76} +5.73444 q^{77} +2.04334 q^{78} +4.45139 q^{79} -12.8091 q^{80} +3.14798 q^{81} +23.4682 q^{82} +7.46556 q^{83} +9.66575 q^{84} +22.2078 q^{85} +27.6008 q^{86} +2.59393 q^{87} +9.10885 q^{88} +7.26752 q^{89} -20.3464 q^{90} -2.93716 q^{91} -20.9954 q^{92} +2.19175 q^{93} +1.18850 q^{94} -22.5764 q^{95} -0.657539 q^{96} +12.9408 q^{97} -3.95773 q^{98} +4.47966 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 142q - 13q^{2} - 26q^{3} + 129q^{4} - 37q^{5} - 15q^{6} - 14q^{7} - 39q^{8} + 98q^{9} + O(q^{10}) \) \( 142q - 13q^{2} - 26q^{3} + 129q^{4} - 37q^{5} - 15q^{6} - 14q^{7} - 39q^{8} + 98q^{9} - 25q^{10} - 25q^{11} - 62q^{12} + 142q^{13} - 57q^{14} - 14q^{15} + 111q^{16} - 141q^{17} - 29q^{18} - 3q^{19} - 87q^{20} - 19q^{21} - 24q^{22} - 69q^{23} - 40q^{24} + 87q^{25} - 13q^{26} - 95q^{27} - 34q^{28} - 147q^{29} - 2q^{30} - 21q^{31} - 66q^{32} - 62q^{33} - 6q^{34} - 59q^{35} + 74q^{36} - 37q^{37} - 76q^{38} - 26q^{39} - 61q^{40} - 97q^{41} - 29q^{42} - 33q^{43} - 57q^{44} - 86q^{45} - q^{46} - 102q^{47} - 141q^{48} + 70q^{49} - 28q^{50} - 13q^{51} + 129q^{52} - 137q^{53} - 29q^{54} - 24q^{55} - 130q^{56} - 65q^{57} - 15q^{58} - 56q^{59} + 11q^{60} - 77q^{61} - 150q^{62} - 32q^{63} + 73q^{64} - 37q^{65} - 32q^{66} - 9q^{67} - 226q^{68} - 113q^{69} + 6q^{70} - 18q^{71} - 82q^{72} - 117q^{73} - 70q^{74} - 83q^{75} + 40q^{76} - 214q^{77} - 15q^{78} - 52q^{79} - 161q^{80} - 10q^{81} - 36q^{82} - 74q^{83} + 53q^{84} + 2q^{85} + 17q^{86} - 49q^{87} - 29q^{88} - 171q^{89} - 57q^{90} - 14q^{91} - 187q^{92} - 39q^{93} + 13q^{94} - 150q^{95} - 47q^{96} - 126q^{97} - 85q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.43267 −1.72015 −0.860077 0.510164i \(-0.829585\pi\)
−0.860077 + 0.510164i \(0.829585\pi\)
\(3\) −0.839960 −0.484951 −0.242476 0.970158i \(-0.577959\pi\)
−0.242476 + 0.970158i \(0.577959\pi\)
\(4\) 3.91786 1.95893
\(5\) −3.64522 −1.63019 −0.815097 0.579325i \(-0.803316\pi\)
−0.815097 + 0.579325i \(0.803316\pi\)
\(6\) 2.04334 0.834191
\(7\) −2.93716 −1.11014 −0.555071 0.831803i \(-0.687309\pi\)
−0.555071 + 0.831803i \(0.687309\pi\)
\(8\) −4.66552 −1.64951
\(9\) −2.29447 −0.764822
\(10\) 8.86761 2.80418
\(11\) −1.95237 −0.588663 −0.294331 0.955703i \(-0.595097\pi\)
−0.294331 + 0.955703i \(0.595097\pi\)
\(12\) −3.29085 −0.949986
\(13\) 1.00000 0.277350
\(14\) 7.14513 1.90962
\(15\) 3.06184 0.790564
\(16\) 3.51393 0.878483
\(17\) −6.09230 −1.47760 −0.738800 0.673925i \(-0.764607\pi\)
−0.738800 + 0.673925i \(0.764607\pi\)
\(18\) 5.58167 1.31561
\(19\) 6.19342 1.42087 0.710434 0.703763i \(-0.248498\pi\)
0.710434 + 0.703763i \(0.248498\pi\)
\(20\) −14.2815 −3.19344
\(21\) 2.46710 0.538365
\(22\) 4.74947 1.01259
\(23\) −5.35888 −1.11740 −0.558702 0.829369i \(-0.688700\pi\)
−0.558702 + 0.829369i \(0.688700\pi\)
\(24\) 3.91885 0.799933
\(25\) 8.28765 1.65753
\(26\) −2.43267 −0.477085
\(27\) 4.44714 0.855853
\(28\) −11.5074 −2.17469
\(29\) −3.08816 −0.573456 −0.286728 0.958012i \(-0.592568\pi\)
−0.286728 + 0.958012i \(0.592568\pi\)
\(30\) −7.44844 −1.35989
\(31\) −2.60935 −0.468652 −0.234326 0.972158i \(-0.575288\pi\)
−0.234326 + 0.972158i \(0.575288\pi\)
\(32\) 0.782822 0.138385
\(33\) 1.63992 0.285473
\(34\) 14.8205 2.54170
\(35\) 10.7066 1.80975
\(36\) −8.98941 −1.49824
\(37\) 0.220676 0.0362789 0.0181395 0.999835i \(-0.494226\pi\)
0.0181395 + 0.999835i \(0.494226\pi\)
\(38\) −15.0665 −2.44411
\(39\) −0.839960 −0.134501
\(40\) 17.0069 2.68902
\(41\) −9.64711 −1.50663 −0.753313 0.657663i \(-0.771545\pi\)
−0.753313 + 0.657663i \(0.771545\pi\)
\(42\) −6.00162 −0.926071
\(43\) −11.3459 −1.73023 −0.865117 0.501570i \(-0.832756\pi\)
−0.865117 + 0.501570i \(0.832756\pi\)
\(44\) −7.64914 −1.15315
\(45\) 8.36384 1.24681
\(46\) 13.0364 1.92211
\(47\) −0.488560 −0.0712638 −0.0356319 0.999365i \(-0.511344\pi\)
−0.0356319 + 0.999365i \(0.511344\pi\)
\(48\) −2.95156 −0.426022
\(49\) 1.62691 0.232416
\(50\) −20.1611 −2.85121
\(51\) 5.11729 0.716564
\(52\) 3.91786 0.543310
\(53\) −2.57418 −0.353591 −0.176795 0.984248i \(-0.556573\pi\)
−0.176795 + 0.984248i \(0.556573\pi\)
\(54\) −10.8184 −1.47220
\(55\) 7.11684 0.959634
\(56\) 13.7034 1.83119
\(57\) −5.20223 −0.689052
\(58\) 7.51246 0.986434
\(59\) 0.288421 0.0375493 0.0187746 0.999824i \(-0.494023\pi\)
0.0187746 + 0.999824i \(0.494023\pi\)
\(60\) 11.9959 1.54866
\(61\) 11.8875 1.52204 0.761021 0.648728i \(-0.224699\pi\)
0.761021 + 0.648728i \(0.224699\pi\)
\(62\) 6.34767 0.806154
\(63\) 6.73922 0.849062
\(64\) −8.93221 −1.11653
\(65\) −3.64522 −0.452134
\(66\) −3.98937 −0.491057
\(67\) −4.74662 −0.579892 −0.289946 0.957043i \(-0.593637\pi\)
−0.289946 + 0.957043i \(0.593637\pi\)
\(68\) −23.8688 −2.89452
\(69\) 4.50124 0.541886
\(70\) −26.0456 −3.11304
\(71\) 4.41906 0.524446 0.262223 0.965007i \(-0.415544\pi\)
0.262223 + 0.965007i \(0.415544\pi\)
\(72\) 10.7049 1.26158
\(73\) −10.0232 −1.17313 −0.586564 0.809903i \(-0.699520\pi\)
−0.586564 + 0.809903i \(0.699520\pi\)
\(74\) −0.536831 −0.0624053
\(75\) −6.96129 −0.803821
\(76\) 24.2650 2.78339
\(77\) 5.73444 0.653500
\(78\) 2.04334 0.231363
\(79\) 4.45139 0.500821 0.250410 0.968140i \(-0.419434\pi\)
0.250410 + 0.968140i \(0.419434\pi\)
\(80\) −12.8091 −1.43210
\(81\) 3.14798 0.349776
\(82\) 23.4682 2.59163
\(83\) 7.46556 0.819452 0.409726 0.912209i \(-0.365624\pi\)
0.409726 + 0.912209i \(0.365624\pi\)
\(84\) 9.66575 1.05462
\(85\) 22.2078 2.40877
\(86\) 27.6008 2.97627
\(87\) 2.59393 0.278098
\(88\) 9.10885 0.971006
\(89\) 7.26752 0.770356 0.385178 0.922842i \(-0.374140\pi\)
0.385178 + 0.922842i \(0.374140\pi\)
\(90\) −20.3464 −2.14470
\(91\) −2.93716 −0.307898
\(92\) −20.9954 −2.18892
\(93\) 2.19175 0.227273
\(94\) 1.18850 0.122585
\(95\) −22.5764 −2.31629
\(96\) −0.657539 −0.0671098
\(97\) 12.9408 1.31393 0.656967 0.753919i \(-0.271839\pi\)
0.656967 + 0.753919i \(0.271839\pi\)
\(98\) −3.95773 −0.399791
\(99\) 4.47966 0.450223
\(100\) 32.4699 3.24699
\(101\) −9.44266 −0.939580 −0.469790 0.882778i \(-0.655670\pi\)
−0.469790 + 0.882778i \(0.655670\pi\)
\(102\) −12.4487 −1.23260
\(103\) 5.51149 0.543063 0.271532 0.962429i \(-0.412470\pi\)
0.271532 + 0.962429i \(0.412470\pi\)
\(104\) −4.66552 −0.457492
\(105\) −8.99312 −0.877639
\(106\) 6.26212 0.608230
\(107\) −13.8940 −1.34318 −0.671591 0.740922i \(-0.734389\pi\)
−0.671591 + 0.740922i \(0.734389\pi\)
\(108\) 17.4233 1.67656
\(109\) 10.8139 1.03578 0.517892 0.855446i \(-0.326717\pi\)
0.517892 + 0.855446i \(0.326717\pi\)
\(110\) −17.3129 −1.65072
\(111\) −0.185359 −0.0175935
\(112\) −10.3210 −0.975241
\(113\) 9.00074 0.846719 0.423359 0.905962i \(-0.360851\pi\)
0.423359 + 0.905962i \(0.360851\pi\)
\(114\) 12.6553 1.18528
\(115\) 19.5343 1.82158
\(116\) −12.0990 −1.12336
\(117\) −2.29447 −0.212124
\(118\) −0.701633 −0.0645905
\(119\) 17.8941 1.64035
\(120\) −14.2851 −1.30404
\(121\) −7.18824 −0.653476
\(122\) −28.9184 −2.61815
\(123\) 8.10319 0.730640
\(124\) −10.2231 −0.918058
\(125\) −11.9842 −1.07190
\(126\) −16.3943 −1.46052
\(127\) −0.678367 −0.0601954 −0.0300977 0.999547i \(-0.509582\pi\)
−0.0300977 + 0.999547i \(0.509582\pi\)
\(128\) 20.1634 1.78221
\(129\) 9.53011 0.839079
\(130\) 8.86761 0.777741
\(131\) 11.6202 1.01526 0.507629 0.861576i \(-0.330522\pi\)
0.507629 + 0.861576i \(0.330522\pi\)
\(132\) 6.42497 0.559222
\(133\) −18.1911 −1.57737
\(134\) 11.5469 0.997504
\(135\) −16.2108 −1.39521
\(136\) 28.4238 2.43732
\(137\) 12.8243 1.09566 0.547828 0.836591i \(-0.315455\pi\)
0.547828 + 0.836591i \(0.315455\pi\)
\(138\) −10.9500 −0.932128
\(139\) 3.89399 0.330284 0.165142 0.986270i \(-0.447192\pi\)
0.165142 + 0.986270i \(0.447192\pi\)
\(140\) 41.9470 3.54517
\(141\) 0.410371 0.0345595
\(142\) −10.7501 −0.902128
\(143\) −1.95237 −0.163266
\(144\) −8.06260 −0.671884
\(145\) 11.2570 0.934845
\(146\) 24.3831 2.01796
\(147\) −1.36654 −0.112710
\(148\) 0.864578 0.0710679
\(149\) 9.41585 0.771376 0.385688 0.922629i \(-0.373964\pi\)
0.385688 + 0.922629i \(0.373964\pi\)
\(150\) 16.9345 1.38270
\(151\) 22.2475 1.81048 0.905238 0.424906i \(-0.139693\pi\)
0.905238 + 0.424906i \(0.139693\pi\)
\(152\) −28.8956 −2.34374
\(153\) 13.9786 1.13010
\(154\) −13.9500 −1.12412
\(155\) 9.51165 0.763994
\(156\) −3.29085 −0.263479
\(157\) 7.35290 0.586826 0.293413 0.955986i \(-0.405209\pi\)
0.293413 + 0.955986i \(0.405209\pi\)
\(158\) −10.8287 −0.861489
\(159\) 2.16221 0.171474
\(160\) −2.85356 −0.225594
\(161\) 15.7399 1.24048
\(162\) −7.65799 −0.601668
\(163\) −14.3471 −1.12375 −0.561877 0.827221i \(-0.689921\pi\)
−0.561877 + 0.827221i \(0.689921\pi\)
\(164\) −37.7961 −2.95138
\(165\) −5.97786 −0.465376
\(166\) −18.1612 −1.40958
\(167\) 23.6284 1.82842 0.914210 0.405242i \(-0.132813\pi\)
0.914210 + 0.405242i \(0.132813\pi\)
\(168\) −11.5103 −0.888039
\(169\) 1.00000 0.0769231
\(170\) −54.0241 −4.14346
\(171\) −14.2106 −1.08671
\(172\) −44.4517 −3.38941
\(173\) −10.0254 −0.762219 −0.381109 0.924530i \(-0.624458\pi\)
−0.381109 + 0.924530i \(0.624458\pi\)
\(174\) −6.31016 −0.478372
\(175\) −24.3422 −1.84009
\(176\) −6.86051 −0.517131
\(177\) −0.242262 −0.0182096
\(178\) −17.6795 −1.32513
\(179\) 19.1672 1.43262 0.716310 0.697782i \(-0.245830\pi\)
0.716310 + 0.697782i \(0.245830\pi\)
\(180\) 32.7684 2.44241
\(181\) 4.06058 0.301820 0.150910 0.988547i \(-0.451780\pi\)
0.150910 + 0.988547i \(0.451780\pi\)
\(182\) 7.14513 0.529632
\(183\) −9.98504 −0.738116
\(184\) 25.0020 1.84317
\(185\) −0.804413 −0.0591416
\(186\) −5.33179 −0.390946
\(187\) 11.8944 0.869808
\(188\) −1.91411 −0.139601
\(189\) −13.0620 −0.950118
\(190\) 54.9209 3.98438
\(191\) −14.5472 −1.05260 −0.526300 0.850299i \(-0.676421\pi\)
−0.526300 + 0.850299i \(0.676421\pi\)
\(192\) 7.50270 0.541461
\(193\) 15.2869 1.10038 0.550189 0.835040i \(-0.314556\pi\)
0.550189 + 0.835040i \(0.314556\pi\)
\(194\) −31.4805 −2.26017
\(195\) 3.06184 0.219263
\(196\) 6.37402 0.455287
\(197\) −2.35092 −0.167496 −0.0837482 0.996487i \(-0.526689\pi\)
−0.0837482 + 0.996487i \(0.526689\pi\)
\(198\) −10.8975 −0.774452
\(199\) −4.48196 −0.317718 −0.158859 0.987301i \(-0.550782\pi\)
−0.158859 + 0.987301i \(0.550782\pi\)
\(200\) −38.6662 −2.73411
\(201\) 3.98697 0.281219
\(202\) 22.9708 1.61622
\(203\) 9.07041 0.636618
\(204\) 20.0488 1.40370
\(205\) 35.1659 2.45609
\(206\) −13.4076 −0.934153
\(207\) 12.2958 0.854615
\(208\) 3.51393 0.243647
\(209\) −12.0919 −0.836413
\(210\) 21.8773 1.50967
\(211\) 0.549258 0.0378125 0.0189062 0.999821i \(-0.493982\pi\)
0.0189062 + 0.999821i \(0.493982\pi\)
\(212\) −10.0853 −0.692660
\(213\) −3.71183 −0.254331
\(214\) 33.7994 2.31048
\(215\) 41.3584 2.82062
\(216\) −20.7482 −1.41174
\(217\) 7.66407 0.520271
\(218\) −26.3066 −1.78171
\(219\) 8.41910 0.568910
\(220\) 27.8828 1.87986
\(221\) −6.09230 −0.409812
\(222\) 0.450917 0.0302635
\(223\) 0.0405410 0.00271482 0.00135741 0.999999i \(-0.499568\pi\)
0.00135741 + 0.999999i \(0.499568\pi\)
\(224\) −2.29927 −0.153627
\(225\) −19.0157 −1.26772
\(226\) −21.8958 −1.45649
\(227\) −4.64935 −0.308588 −0.154294 0.988025i \(-0.549310\pi\)
−0.154294 + 0.988025i \(0.549310\pi\)
\(228\) −20.3816 −1.34981
\(229\) −18.9317 −1.25104 −0.625520 0.780209i \(-0.715113\pi\)
−0.625520 + 0.780209i \(0.715113\pi\)
\(230\) −47.5204 −3.13341
\(231\) −4.81670 −0.316915
\(232\) 14.4079 0.945923
\(233\) 16.0613 1.05221 0.526104 0.850420i \(-0.323652\pi\)
0.526104 + 0.850420i \(0.323652\pi\)
\(234\) 5.58167 0.364885
\(235\) 1.78091 0.116174
\(236\) 1.13000 0.0735565
\(237\) −3.73899 −0.242874
\(238\) −43.5303 −2.82165
\(239\) −21.3159 −1.37881 −0.689405 0.724376i \(-0.742128\pi\)
−0.689405 + 0.724376i \(0.742128\pi\)
\(240\) 10.7591 0.694497
\(241\) 20.4739 1.31884 0.659419 0.751776i \(-0.270803\pi\)
0.659419 + 0.751776i \(0.270803\pi\)
\(242\) 17.4866 1.12408
\(243\) −15.9856 −1.02548
\(244\) 46.5737 2.98158
\(245\) −5.93045 −0.378883
\(246\) −19.7123 −1.25681
\(247\) 6.19342 0.394078
\(248\) 12.1740 0.773047
\(249\) −6.27077 −0.397394
\(250\) 29.1536 1.84383
\(251\) −9.23733 −0.583055 −0.291527 0.956562i \(-0.594163\pi\)
−0.291527 + 0.956562i \(0.594163\pi\)
\(252\) 26.4033 1.66325
\(253\) 10.4625 0.657774
\(254\) 1.65024 0.103545
\(255\) −18.6537 −1.16814
\(256\) −31.1865 −1.94916
\(257\) −6.66713 −0.415884 −0.207942 0.978141i \(-0.566677\pi\)
−0.207942 + 0.978141i \(0.566677\pi\)
\(258\) −23.1836 −1.44335
\(259\) −0.648161 −0.0402747
\(260\) −14.2815 −0.885700
\(261\) 7.08567 0.438592
\(262\) −28.2680 −1.74640
\(263\) 0.311831 0.0192283 0.00961417 0.999954i \(-0.496940\pi\)
0.00961417 + 0.999954i \(0.496940\pi\)
\(264\) −7.65107 −0.470891
\(265\) 9.38345 0.576421
\(266\) 44.2528 2.71331
\(267\) −6.10443 −0.373585
\(268\) −18.5966 −1.13597
\(269\) 8.93944 0.545047 0.272524 0.962149i \(-0.412142\pi\)
0.272524 + 0.962149i \(0.412142\pi\)
\(270\) 39.4355 2.39997
\(271\) 1.73849 0.105606 0.0528029 0.998605i \(-0.483184\pi\)
0.0528029 + 0.998605i \(0.483184\pi\)
\(272\) −21.4079 −1.29805
\(273\) 2.46710 0.149316
\(274\) −31.1973 −1.88470
\(275\) −16.1806 −0.975726
\(276\) 17.6353 1.06152
\(277\) −17.5446 −1.05415 −0.527077 0.849818i \(-0.676712\pi\)
−0.527077 + 0.849818i \(0.676712\pi\)
\(278\) −9.47277 −0.568139
\(279\) 5.98706 0.358436
\(280\) −49.9519 −2.98520
\(281\) 14.6425 0.873496 0.436748 0.899584i \(-0.356130\pi\)
0.436748 + 0.899584i \(0.356130\pi\)
\(282\) −0.998295 −0.0594476
\(283\) −19.9903 −1.18830 −0.594150 0.804355i \(-0.702511\pi\)
−0.594150 + 0.804355i \(0.702511\pi\)
\(284\) 17.3133 1.02735
\(285\) 18.9633 1.12329
\(286\) 4.74947 0.280842
\(287\) 28.3351 1.67257
\(288\) −1.79616 −0.105840
\(289\) 20.1161 1.18330
\(290\) −27.3846 −1.60808
\(291\) −10.8697 −0.637194
\(292\) −39.2696 −2.29808
\(293\) −30.9640 −1.80894 −0.904469 0.426540i \(-0.859732\pi\)
−0.904469 + 0.426540i \(0.859732\pi\)
\(294\) 3.32434 0.193879
\(295\) −1.05136 −0.0612125
\(296\) −1.02957 −0.0598425
\(297\) −8.68248 −0.503809
\(298\) −22.9056 −1.32689
\(299\) −5.35888 −0.309912
\(300\) −27.2734 −1.57463
\(301\) 33.3247 1.92081
\(302\) −54.1207 −3.11430
\(303\) 7.93146 0.455650
\(304\) 21.7633 1.24821
\(305\) −43.3327 −2.48122
\(306\) −34.0052 −1.94395
\(307\) 21.9702 1.25390 0.626952 0.779058i \(-0.284302\pi\)
0.626952 + 0.779058i \(0.284302\pi\)
\(308\) 22.4667 1.28016
\(309\) −4.62943 −0.263359
\(310\) −23.1387 −1.31419
\(311\) 5.77549 0.327498 0.163749 0.986502i \(-0.447641\pi\)
0.163749 + 0.986502i \(0.447641\pi\)
\(312\) 3.91885 0.221861
\(313\) −21.5018 −1.21535 −0.607675 0.794185i \(-0.707898\pi\)
−0.607675 + 0.794185i \(0.707898\pi\)
\(314\) −17.8872 −1.00943
\(315\) −24.5659 −1.38413
\(316\) 17.4399 0.981074
\(317\) −22.8103 −1.28116 −0.640578 0.767893i \(-0.721305\pi\)
−0.640578 + 0.767893i \(0.721305\pi\)
\(318\) −5.25993 −0.294962
\(319\) 6.02924 0.337573
\(320\) 32.5599 1.82015
\(321\) 11.6704 0.651378
\(322\) −38.2899 −2.13381
\(323\) −37.7322 −2.09947
\(324\) 12.3334 0.685187
\(325\) 8.28765 0.459716
\(326\) 34.9018 1.93303
\(327\) −9.08324 −0.502304
\(328\) 45.0088 2.48520
\(329\) 1.43498 0.0791130
\(330\) 14.5421 0.800518
\(331\) −20.9138 −1.14952 −0.574762 0.818320i \(-0.694906\pi\)
−0.574762 + 0.818320i \(0.694906\pi\)
\(332\) 29.2491 1.60525
\(333\) −0.506334 −0.0277469
\(334\) −57.4800 −3.14516
\(335\) 17.3025 0.945336
\(336\) 8.66922 0.472944
\(337\) −3.13546 −0.170799 −0.0853996 0.996347i \(-0.527217\pi\)
−0.0853996 + 0.996347i \(0.527217\pi\)
\(338\) −2.43267 −0.132320
\(339\) −7.56026 −0.410617
\(340\) 87.0071 4.71862
\(341\) 5.09442 0.275878
\(342\) 34.5697 1.86931
\(343\) 15.7816 0.852128
\(344\) 52.9346 2.85404
\(345\) −16.4080 −0.883379
\(346\) 24.3885 1.31113
\(347\) 28.6562 1.53835 0.769173 0.639041i \(-0.220668\pi\)
0.769173 + 0.639041i \(0.220668\pi\)
\(348\) 10.1627 0.544776
\(349\) −16.8790 −0.903514 −0.451757 0.892141i \(-0.649203\pi\)
−0.451757 + 0.892141i \(0.649203\pi\)
\(350\) 59.2163 3.16525
\(351\) 4.44714 0.237371
\(352\) −1.52836 −0.0814619
\(353\) 28.1451 1.49801 0.749006 0.662563i \(-0.230531\pi\)
0.749006 + 0.662563i \(0.230531\pi\)
\(354\) 0.589344 0.0313233
\(355\) −16.1085 −0.854948
\(356\) 28.4732 1.50907
\(357\) −15.0303 −0.795487
\(358\) −46.6273 −2.46433
\(359\) −18.7833 −0.991344 −0.495672 0.868510i \(-0.665078\pi\)
−0.495672 + 0.868510i \(0.665078\pi\)
\(360\) −39.0217 −2.05662
\(361\) 19.3585 1.01887
\(362\) −9.87803 −0.519178
\(363\) 6.03783 0.316904
\(364\) −11.5074 −0.603151
\(365\) 36.5368 1.91243
\(366\) 24.2903 1.26967
\(367\) −9.81686 −0.512436 −0.256218 0.966619i \(-0.582476\pi\)
−0.256218 + 0.966619i \(0.582476\pi\)
\(368\) −18.8307 −0.981620
\(369\) 22.1350 1.15230
\(370\) 1.95687 0.101733
\(371\) 7.56077 0.392536
\(372\) 8.58696 0.445213
\(373\) 17.6484 0.913799 0.456899 0.889518i \(-0.348960\pi\)
0.456899 + 0.889518i \(0.348960\pi\)
\(374\) −28.9352 −1.49620
\(375\) 10.0663 0.519819
\(376\) 2.27939 0.117550
\(377\) −3.08816 −0.159048
\(378\) 31.7754 1.63435
\(379\) −15.6693 −0.804879 −0.402439 0.915447i \(-0.631838\pi\)
−0.402439 + 0.915447i \(0.631838\pi\)
\(380\) −88.4513 −4.53746
\(381\) 0.569802 0.0291918
\(382\) 35.3885 1.81064
\(383\) 0.0432659 0.00221078 0.00110539 0.999999i \(-0.499648\pi\)
0.00110539 + 0.999999i \(0.499648\pi\)
\(384\) −16.9365 −0.864286
\(385\) −20.9033 −1.06533
\(386\) −37.1880 −1.89282
\(387\) 26.0328 1.32332
\(388\) 50.7001 2.57391
\(389\) 39.1737 1.98619 0.993094 0.117325i \(-0.0374318\pi\)
0.993094 + 0.117325i \(0.0374318\pi\)
\(390\) −7.44844 −0.377166
\(391\) 32.6479 1.65107
\(392\) −7.59039 −0.383373
\(393\) −9.76047 −0.492351
\(394\) 5.71901 0.288120
\(395\) −16.2263 −0.816434
\(396\) 17.5507 0.881956
\(397\) −25.7581 −1.29276 −0.646381 0.763015i \(-0.723718\pi\)
−0.646381 + 0.763015i \(0.723718\pi\)
\(398\) 10.9031 0.546524
\(399\) 15.2798 0.764946
\(400\) 29.1222 1.45611
\(401\) 2.56358 0.128019 0.0640095 0.997949i \(-0.479611\pi\)
0.0640095 + 0.997949i \(0.479611\pi\)
\(402\) −9.69897 −0.483741
\(403\) −2.60935 −0.129981
\(404\) −36.9951 −1.84057
\(405\) −11.4751 −0.570202
\(406\) −22.0653 −1.09508
\(407\) −0.430842 −0.0213560
\(408\) −23.8748 −1.18198
\(409\) 26.2935 1.30013 0.650066 0.759878i \(-0.274741\pi\)
0.650066 + 0.759878i \(0.274741\pi\)
\(410\) −85.5468 −4.22486
\(411\) −10.7719 −0.531340
\(412\) 21.5933 1.06382
\(413\) −0.847140 −0.0416850
\(414\) −29.9115 −1.47007
\(415\) −27.2136 −1.33586
\(416\) 0.782822 0.0383810
\(417\) −3.27079 −0.160171
\(418\) 29.4155 1.43876
\(419\) 12.1058 0.591406 0.295703 0.955280i \(-0.404446\pi\)
0.295703 + 0.955280i \(0.404446\pi\)
\(420\) −35.2338 −1.71923
\(421\) 14.5550 0.709366 0.354683 0.934987i \(-0.384589\pi\)
0.354683 + 0.934987i \(0.384589\pi\)
\(422\) −1.33616 −0.0650433
\(423\) 1.12098 0.0545041
\(424\) 12.0099 0.583252
\(425\) −50.4908 −2.44916
\(426\) 9.02965 0.437488
\(427\) −34.9156 −1.68968
\(428\) −54.4347 −2.63120
\(429\) 1.63992 0.0791759
\(430\) −100.611 −4.85190
\(431\) 20.9584 1.00953 0.504764 0.863257i \(-0.331579\pi\)
0.504764 + 0.863257i \(0.331579\pi\)
\(432\) 15.6270 0.751852
\(433\) 4.52672 0.217540 0.108770 0.994067i \(-0.465309\pi\)
0.108770 + 0.994067i \(0.465309\pi\)
\(434\) −18.6441 −0.894946
\(435\) −9.45545 −0.453354
\(436\) 42.3674 2.02903
\(437\) −33.1898 −1.58768
\(438\) −20.4809 −0.978613
\(439\) −36.8148 −1.75707 −0.878537 0.477675i \(-0.841480\pi\)
−0.878537 + 0.477675i \(0.841480\pi\)
\(440\) −33.2038 −1.58293
\(441\) −3.73289 −0.177757
\(442\) 14.8205 0.704941
\(443\) −28.7694 −1.36688 −0.683438 0.730008i \(-0.739516\pi\)
−0.683438 + 0.730008i \(0.739516\pi\)
\(444\) −0.726211 −0.0344645
\(445\) −26.4917 −1.25583
\(446\) −0.0986226 −0.00466992
\(447\) −7.90893 −0.374080
\(448\) 26.2353 1.23950
\(449\) 2.50012 0.117988 0.0589940 0.998258i \(-0.481211\pi\)
0.0589940 + 0.998258i \(0.481211\pi\)
\(450\) 46.2589 2.18067
\(451\) 18.8348 0.886894
\(452\) 35.2637 1.65866
\(453\) −18.6870 −0.877992
\(454\) 11.3103 0.530819
\(455\) 10.7066 0.501933
\(456\) 24.2711 1.13660
\(457\) 35.5183 1.66148 0.830739 0.556663i \(-0.187918\pi\)
0.830739 + 0.556663i \(0.187918\pi\)
\(458\) 46.0544 2.15198
\(459\) −27.0933 −1.26461
\(460\) 76.5328 3.56836
\(461\) 21.5051 1.00159 0.500795 0.865566i \(-0.333041\pi\)
0.500795 + 0.865566i \(0.333041\pi\)
\(462\) 11.7174 0.545143
\(463\) −31.1781 −1.44897 −0.724485 0.689290i \(-0.757923\pi\)
−0.724485 + 0.689290i \(0.757923\pi\)
\(464\) −10.8516 −0.503772
\(465\) −7.98940 −0.370500
\(466\) −39.0717 −1.80996
\(467\) 13.4678 0.623215 0.311608 0.950211i \(-0.399133\pi\)
0.311608 + 0.950211i \(0.399133\pi\)
\(468\) −8.98941 −0.415536
\(469\) 13.9416 0.643763
\(470\) −4.33236 −0.199837
\(471\) −6.17615 −0.284582
\(472\) −1.34564 −0.0619379
\(473\) 22.1515 1.01852
\(474\) 9.09572 0.417780
\(475\) 51.3289 2.35513
\(476\) 70.1065 3.21333
\(477\) 5.90637 0.270434
\(478\) 51.8544 2.37177
\(479\) 3.89369 0.177907 0.0889536 0.996036i \(-0.471648\pi\)
0.0889536 + 0.996036i \(0.471648\pi\)
\(480\) 2.39688 0.109402
\(481\) 0.220676 0.0100620
\(482\) −49.8061 −2.26860
\(483\) −13.2209 −0.601571
\(484\) −28.1625 −1.28012
\(485\) −47.1719 −2.14197
\(486\) 38.8876 1.76398
\(487\) 36.8745 1.67094 0.835472 0.549534i \(-0.185195\pi\)
0.835472 + 0.549534i \(0.185195\pi\)
\(488\) −55.4615 −2.51063
\(489\) 12.0510 0.544966
\(490\) 14.4268 0.651737
\(491\) −18.3643 −0.828769 −0.414384 0.910102i \(-0.636003\pi\)
−0.414384 + 0.910102i \(0.636003\pi\)
\(492\) 31.7472 1.43127
\(493\) 18.8140 0.847339
\(494\) −15.0665 −0.677875
\(495\) −16.3294 −0.733950
\(496\) −9.16907 −0.411703
\(497\) −12.9795 −0.582210
\(498\) 15.2547 0.683579
\(499\) −9.08841 −0.406853 −0.203427 0.979090i \(-0.565208\pi\)
−0.203427 + 0.979090i \(0.565208\pi\)
\(500\) −46.9525 −2.09978
\(501\) −19.8469 −0.886694
\(502\) 22.4713 1.00294
\(503\) −1.07688 −0.0480157 −0.0240078 0.999712i \(-0.507643\pi\)
−0.0240078 + 0.999712i \(0.507643\pi\)
\(504\) −31.4420 −1.40054
\(505\) 34.4206 1.53170
\(506\) −25.4519 −1.13147
\(507\) −0.839960 −0.0373039
\(508\) −2.65775 −0.117919
\(509\) 40.4809 1.79429 0.897143 0.441740i \(-0.145639\pi\)
0.897143 + 0.441740i \(0.145639\pi\)
\(510\) 45.3781 2.00938
\(511\) 29.4398 1.30234
\(512\) 35.5395 1.57064
\(513\) 27.5430 1.21605
\(514\) 16.2189 0.715385
\(515\) −20.0906 −0.885298
\(516\) 37.3377 1.64370
\(517\) 0.953852 0.0419504
\(518\) 1.57676 0.0692788
\(519\) 8.42096 0.369639
\(520\) 17.0069 0.745801
\(521\) −7.01078 −0.307148 −0.153574 0.988137i \(-0.549078\pi\)
−0.153574 + 0.988137i \(0.549078\pi\)
\(522\) −17.2371 −0.754447
\(523\) 29.3279 1.28242 0.641210 0.767365i \(-0.278433\pi\)
0.641210 + 0.767365i \(0.278433\pi\)
\(524\) 45.5262 1.98882
\(525\) 20.4464 0.892356
\(526\) −0.758582 −0.0330757
\(527\) 15.8969 0.692480
\(528\) 5.76256 0.250783
\(529\) 5.71759 0.248591
\(530\) −22.8268 −0.991533
\(531\) −0.661773 −0.0287185
\(532\) −71.2702 −3.08995
\(533\) −9.64711 −0.417863
\(534\) 14.8500 0.642624
\(535\) 50.6467 2.18965
\(536\) 22.1455 0.956539
\(537\) −16.0996 −0.694751
\(538\) −21.7467 −0.937566
\(539\) −3.17634 −0.136815
\(540\) −63.5118 −2.73311
\(541\) 33.6492 1.44669 0.723346 0.690485i \(-0.242603\pi\)
0.723346 + 0.690485i \(0.242603\pi\)
\(542\) −4.22917 −0.181658
\(543\) −3.41072 −0.146368
\(544\) −4.76918 −0.204477
\(545\) −39.4191 −1.68853
\(546\) −6.00162 −0.256846
\(547\) −23.9739 −1.02505 −0.512525 0.858672i \(-0.671290\pi\)
−0.512525 + 0.858672i \(0.671290\pi\)
\(548\) 50.2440 2.14632
\(549\) −27.2755 −1.16409
\(550\) 39.3620 1.67840
\(551\) −19.1263 −0.814806
\(552\) −21.0007 −0.893848
\(553\) −13.0745 −0.555982
\(554\) 42.6802 1.81331
\(555\) 0.675675 0.0286808
\(556\) 15.2561 0.647003
\(557\) −12.7715 −0.541145 −0.270572 0.962700i \(-0.587213\pi\)
−0.270572 + 0.962700i \(0.587213\pi\)
\(558\) −14.5645 −0.616565
\(559\) −11.3459 −0.479881
\(560\) 37.6223 1.58983
\(561\) −9.99086 −0.421814
\(562\) −35.6202 −1.50255
\(563\) 23.8832 1.00656 0.503278 0.864125i \(-0.332127\pi\)
0.503278 + 0.864125i \(0.332127\pi\)
\(564\) 1.60778 0.0676996
\(565\) −32.8097 −1.38031
\(566\) 48.6297 2.04406
\(567\) −9.24612 −0.388301
\(568\) −20.6172 −0.865080
\(569\) −30.4046 −1.27463 −0.637314 0.770605i \(-0.719954\pi\)
−0.637314 + 0.770605i \(0.719954\pi\)
\(570\) −46.1313 −1.93223
\(571\) 12.0930 0.506075 0.253037 0.967457i \(-0.418570\pi\)
0.253037 + 0.967457i \(0.418570\pi\)
\(572\) −7.64914 −0.319826
\(573\) 12.2191 0.510460
\(574\) −68.9298 −2.87708
\(575\) −44.4125 −1.85213
\(576\) 20.4947 0.853944
\(577\) 33.6188 1.39957 0.699785 0.714354i \(-0.253279\pi\)
0.699785 + 0.714354i \(0.253279\pi\)
\(578\) −48.9358 −2.03546
\(579\) −12.8404 −0.533630
\(580\) 44.1035 1.83130
\(581\) −21.9275 −0.909708
\(582\) 26.4424 1.09607
\(583\) 5.02576 0.208146
\(584\) 46.7635 1.93509
\(585\) 8.36384 0.345802
\(586\) 75.3251 3.11165
\(587\) −0.476412 −0.0196636 −0.00983181 0.999952i \(-0.503130\pi\)
−0.00983181 + 0.999952i \(0.503130\pi\)
\(588\) −5.35392 −0.220792
\(589\) −16.1608 −0.665893
\(590\) 2.55761 0.105295
\(591\) 1.97468 0.0812275
\(592\) 0.775441 0.0318704
\(593\) 10.3245 0.423978 0.211989 0.977272i \(-0.432006\pi\)
0.211989 + 0.977272i \(0.432006\pi\)
\(594\) 21.1216 0.866629
\(595\) −65.2278 −2.67408
\(596\) 36.8900 1.51107
\(597\) 3.76467 0.154078
\(598\) 13.0364 0.533097
\(599\) 21.0777 0.861212 0.430606 0.902540i \(-0.358300\pi\)
0.430606 + 0.902540i \(0.358300\pi\)
\(600\) 32.4781 1.32591
\(601\) −14.2327 −0.580564 −0.290282 0.956941i \(-0.593749\pi\)
−0.290282 + 0.956941i \(0.593749\pi\)
\(602\) −81.0680 −3.30408
\(603\) 10.8910 0.443514
\(604\) 87.1627 3.54660
\(605\) 26.2027 1.06529
\(606\) −19.2946 −0.783789
\(607\) −33.3191 −1.35238 −0.676190 0.736727i \(-0.736370\pi\)
−0.676190 + 0.736727i \(0.736370\pi\)
\(608\) 4.84835 0.196626
\(609\) −7.61878 −0.308729
\(610\) 105.414 4.26808
\(611\) −0.488560 −0.0197650
\(612\) 54.7662 2.21379
\(613\) −47.3358 −1.91187 −0.955937 0.293570i \(-0.905156\pi\)
−0.955937 + 0.293570i \(0.905156\pi\)
\(614\) −53.4461 −2.15691
\(615\) −29.5379 −1.19108
\(616\) −26.7541 −1.07796
\(617\) −0.451673 −0.0181837 −0.00909184 0.999959i \(-0.502894\pi\)
−0.00909184 + 0.999959i \(0.502894\pi\)
\(618\) 11.2619 0.453019
\(619\) 1.00000 0.0401934
\(620\) 37.2653 1.49661
\(621\) −23.8317 −0.956333
\(622\) −14.0498 −0.563348
\(623\) −21.3459 −0.855205
\(624\) −2.95156 −0.118157
\(625\) 2.24688 0.0898750
\(626\) 52.3066 2.09059
\(627\) 10.1567 0.405619
\(628\) 28.8077 1.14955
\(629\) −1.34442 −0.0536057
\(630\) 59.7608 2.38093
\(631\) 16.4564 0.655118 0.327559 0.944831i \(-0.393774\pi\)
0.327559 + 0.944831i \(0.393774\pi\)
\(632\) −20.7681 −0.826110
\(633\) −0.461355 −0.0183372
\(634\) 55.4899 2.20379
\(635\) 2.47280 0.0981301
\(636\) 8.47123 0.335906
\(637\) 1.62691 0.0644605
\(638\) −14.6671 −0.580677
\(639\) −10.1394 −0.401108
\(640\) −73.5002 −2.90535
\(641\) −40.9811 −1.61866 −0.809328 0.587358i \(-0.800168\pi\)
−0.809328 + 0.587358i \(0.800168\pi\)
\(642\) −28.3902 −1.12047
\(643\) 35.0821 1.38350 0.691752 0.722135i \(-0.256839\pi\)
0.691752 + 0.722135i \(0.256839\pi\)
\(644\) 61.6667 2.43001
\(645\) −34.7394 −1.36786
\(646\) 91.7898 3.61142
\(647\) −9.70406 −0.381506 −0.190753 0.981638i \(-0.561093\pi\)
−0.190753 + 0.981638i \(0.561093\pi\)
\(648\) −14.6870 −0.576959
\(649\) −0.563106 −0.0221039
\(650\) −20.1611 −0.790783
\(651\) −6.43751 −0.252306
\(652\) −56.2102 −2.20136
\(653\) −28.0300 −1.09690 −0.548450 0.836184i \(-0.684782\pi\)
−0.548450 + 0.836184i \(0.684782\pi\)
\(654\) 22.0965 0.864041
\(655\) −42.3581 −1.65507
\(656\) −33.8993 −1.32355
\(657\) 22.9979 0.897235
\(658\) −3.49082 −0.136087
\(659\) −4.00968 −0.156195 −0.0780975 0.996946i \(-0.524885\pi\)
−0.0780975 + 0.996946i \(0.524885\pi\)
\(660\) −23.4204 −0.911640
\(661\) −15.9496 −0.620367 −0.310183 0.950677i \(-0.600390\pi\)
−0.310183 + 0.950677i \(0.600390\pi\)
\(662\) 50.8762 1.97736
\(663\) 5.11729 0.198739
\(664\) −34.8307 −1.35170
\(665\) 66.3105 2.57141
\(666\) 1.23174 0.0477290
\(667\) 16.5491 0.640782
\(668\) 92.5728 3.58175
\(669\) −0.0340528 −0.00131656
\(670\) −42.0912 −1.62612
\(671\) −23.2089 −0.895969
\(672\) 1.93130 0.0745014
\(673\) 8.33607 0.321332 0.160666 0.987009i \(-0.448636\pi\)
0.160666 + 0.987009i \(0.448636\pi\)
\(674\) 7.62752 0.293801
\(675\) 36.8563 1.41860
\(676\) 3.91786 0.150687
\(677\) −40.8130 −1.56857 −0.784286 0.620399i \(-0.786971\pi\)
−0.784286 + 0.620399i \(0.786971\pi\)
\(678\) 18.3916 0.706325
\(679\) −38.0091 −1.45865
\(680\) −103.611 −3.97330
\(681\) 3.90526 0.149650
\(682\) −12.3930 −0.474553
\(683\) 35.1141 1.34361 0.671803 0.740730i \(-0.265520\pi\)
0.671803 + 0.740730i \(0.265520\pi\)
\(684\) −55.6752 −2.12880
\(685\) −46.7476 −1.78613
\(686\) −38.3914 −1.46579
\(687\) 15.9018 0.606693
\(688\) −39.8688 −1.51998
\(689\) −2.57418 −0.0980684
\(690\) 39.9153 1.51955
\(691\) 3.16458 0.120386 0.0601932 0.998187i \(-0.480828\pi\)
0.0601932 + 0.998187i \(0.480828\pi\)
\(692\) −39.2783 −1.49314
\(693\) −13.1575 −0.499811
\(694\) −69.7110 −2.64619
\(695\) −14.1944 −0.538426
\(696\) −12.1020 −0.458726
\(697\) 58.7731 2.22619
\(698\) 41.0610 1.55418
\(699\) −13.4908 −0.510269
\(700\) −95.3693 −3.60462
\(701\) −17.4612 −0.659500 −0.329750 0.944068i \(-0.606965\pi\)
−0.329750 + 0.944068i \(0.606965\pi\)
\(702\) −10.8184 −0.408315
\(703\) 1.36674 0.0515476
\(704\) 17.4390 0.657258
\(705\) −1.49589 −0.0563386
\(706\) −68.4676 −2.57681
\(707\) 27.7346 1.04307
\(708\) −0.949151 −0.0356713
\(709\) −29.7660 −1.11789 −0.558943 0.829206i \(-0.688793\pi\)
−0.558943 + 0.829206i \(0.688793\pi\)
\(710\) 39.1865 1.47064
\(711\) −10.2136 −0.383039
\(712\) −33.9068 −1.27071
\(713\) 13.9832 0.523674
\(714\) 36.5637 1.36836
\(715\) 7.11684 0.266155
\(716\) 75.0943 2.80641
\(717\) 17.9045 0.668656
\(718\) 45.6934 1.70526
\(719\) 40.4446 1.50833 0.754164 0.656686i \(-0.228042\pi\)
0.754164 + 0.656686i \(0.228042\pi\)
\(720\) 29.3900 1.09530
\(721\) −16.1881 −0.602878
\(722\) −47.0928 −1.75261
\(723\) −17.1972 −0.639572
\(724\) 15.9088 0.591246
\(725\) −25.5936 −0.950521
\(726\) −14.6880 −0.545124
\(727\) −47.9207 −1.77728 −0.888641 0.458603i \(-0.848350\pi\)
−0.888641 + 0.458603i \(0.848350\pi\)
\(728\) 13.7034 0.507881
\(729\) 3.98332 0.147531
\(730\) −88.8820 −3.28967
\(731\) 69.1227 2.55659
\(732\) −39.1201 −1.44592
\(733\) 0.795034 0.0293652 0.0146826 0.999892i \(-0.495326\pi\)
0.0146826 + 0.999892i \(0.495326\pi\)
\(734\) 23.8811 0.881469
\(735\) 4.98134 0.183740
\(736\) −4.19505 −0.154631
\(737\) 9.26718 0.341361
\(738\) −53.8470 −1.98214
\(739\) −33.3608 −1.22720 −0.613599 0.789618i \(-0.710279\pi\)
−0.613599 + 0.789618i \(0.710279\pi\)
\(740\) −3.15158 −0.115854
\(741\) −5.20223 −0.191109
\(742\) −18.3928 −0.675222
\(743\) −5.17500 −0.189852 −0.0949262 0.995484i \(-0.530262\pi\)
−0.0949262 + 0.995484i \(0.530262\pi\)
\(744\) −10.2256 −0.374890
\(745\) −34.3229 −1.25749
\(746\) −42.9326 −1.57188
\(747\) −17.1295 −0.626735
\(748\) 46.6008 1.70389
\(749\) 40.8089 1.49112
\(750\) −24.4878 −0.894170
\(751\) −34.1669 −1.24677 −0.623383 0.781916i \(-0.714242\pi\)
−0.623383 + 0.781916i \(0.714242\pi\)
\(752\) −1.71677 −0.0626041
\(753\) 7.75899 0.282753
\(754\) 7.51246 0.273587
\(755\) −81.0971 −2.95142
\(756\) −51.1750 −1.86122
\(757\) 33.8610 1.23070 0.615350 0.788254i \(-0.289015\pi\)
0.615350 + 0.788254i \(0.289015\pi\)
\(758\) 38.1182 1.38452
\(759\) −8.78811 −0.318988
\(760\) 105.331 3.82075
\(761\) 14.4804 0.524914 0.262457 0.964944i \(-0.415467\pi\)
0.262457 + 0.964944i \(0.415467\pi\)
\(762\) −1.38614 −0.0502144
\(763\) −31.7622 −1.14987
\(764\) −56.9941 −2.06197
\(765\) −50.9550 −1.84228
\(766\) −0.105251 −0.00380289
\(767\) 0.288421 0.0104143
\(768\) 26.1954 0.945246
\(769\) −34.3195 −1.23759 −0.618797 0.785551i \(-0.712380\pi\)
−0.618797 + 0.785551i \(0.712380\pi\)
\(770\) 50.8507 1.83253
\(771\) 5.60012 0.201683
\(772\) 59.8922 2.15557
\(773\) 6.88095 0.247490 0.123745 0.992314i \(-0.460509\pi\)
0.123745 + 0.992314i \(0.460509\pi\)
\(774\) −63.3291 −2.27632
\(775\) −21.6253 −0.776805
\(776\) −60.3754 −2.16735
\(777\) 0.544429 0.0195313
\(778\) −95.2966 −3.41655
\(779\) −59.7486 −2.14072
\(780\) 11.9959 0.429521
\(781\) −8.62766 −0.308722
\(782\) −79.4214 −2.84010
\(783\) −13.7335 −0.490794
\(784\) 5.71686 0.204173
\(785\) −26.8030 −0.956639
\(786\) 23.7440 0.846919
\(787\) −17.4441 −0.621814 −0.310907 0.950440i \(-0.600633\pi\)
−0.310907 + 0.950440i \(0.600633\pi\)
\(788\) −9.21060 −0.328114
\(789\) −0.261926 −0.00932481
\(790\) 39.4732 1.40439
\(791\) −26.4366 −0.939978
\(792\) −20.9000 −0.742647
\(793\) 11.8875 0.422138
\(794\) 62.6609 2.22375
\(795\) −7.88173 −0.279536
\(796\) −17.5597 −0.622388
\(797\) −36.1084 −1.27903 −0.639513 0.768780i \(-0.720864\pi\)
−0.639513 + 0.768780i \(0.720864\pi\)
\(798\) −37.1706 −1.31583
\(799\) 2.97645 0.105299
\(800\) 6.48775 0.229377
\(801\) −16.6751 −0.589185
\(802\) −6.23633 −0.220212
\(803\) 19.5691 0.690577
\(804\) 15.6204 0.550890
\(805\) −57.3754 −2.02222
\(806\) 6.34767 0.223587
\(807\) −7.50877 −0.264321
\(808\) 44.0550 1.54985
\(809\) 45.2575 1.59117 0.795585 0.605842i \(-0.207164\pi\)
0.795585 + 0.605842i \(0.207164\pi\)
\(810\) 27.9151 0.980835
\(811\) 50.4390 1.77115 0.885576 0.464494i \(-0.153764\pi\)
0.885576 + 0.464494i \(0.153764\pi\)
\(812\) 35.5366 1.24709
\(813\) −1.46026 −0.0512137
\(814\) 1.04809 0.0367357
\(815\) 52.2985 1.83194
\(816\) 17.9818 0.629489
\(817\) −70.2700 −2.45844
\(818\) −63.9634 −2.23643
\(819\) 6.73922 0.235487
\(820\) 137.775 4.81131
\(821\) −19.5226 −0.681343 −0.340671 0.940182i \(-0.610654\pi\)
−0.340671 + 0.940182i \(0.610654\pi\)
\(822\) 26.2045 0.913987
\(823\) 46.8485 1.63304 0.816518 0.577321i \(-0.195902\pi\)
0.816518 + 0.577321i \(0.195902\pi\)
\(824\) −25.7140 −0.895790
\(825\) 13.5910 0.473180
\(826\) 2.06081 0.0717047
\(827\) −52.0032 −1.80833 −0.904164 0.427185i \(-0.859505\pi\)
−0.904164 + 0.427185i \(0.859505\pi\)
\(828\) 48.1732 1.67413
\(829\) 41.9539 1.45712 0.728560 0.684982i \(-0.240190\pi\)
0.728560 + 0.684982i \(0.240190\pi\)
\(830\) 66.2017 2.29789
\(831\) 14.7368 0.511213
\(832\) −8.93221 −0.309669
\(833\) −9.91162 −0.343417
\(834\) 7.95674 0.275520
\(835\) −86.1307 −2.98068
\(836\) −47.3743 −1.63848
\(837\) −11.6041 −0.401097
\(838\) −29.4493 −1.01731
\(839\) 43.9044 1.51575 0.757875 0.652400i \(-0.226238\pi\)
0.757875 + 0.652400i \(0.226238\pi\)
\(840\) 41.9576 1.44768
\(841\) −19.4633 −0.671148
\(842\) −35.4074 −1.22022
\(843\) −12.2991 −0.423603
\(844\) 2.15192 0.0740721
\(845\) −3.64522 −0.125399
\(846\) −2.72698 −0.0937556
\(847\) 21.1130 0.725451
\(848\) −9.04549 −0.310623
\(849\) 16.7910 0.576267
\(850\) 122.827 4.21294
\(851\) −1.18258 −0.0405382
\(852\) −14.5425 −0.498217
\(853\) 2.05638 0.0704091 0.0352046 0.999380i \(-0.488792\pi\)
0.0352046 + 0.999380i \(0.488792\pi\)
\(854\) 84.9379 2.90652
\(855\) 51.8008 1.77155
\(856\) 64.8227 2.21559
\(857\) −40.5263 −1.38435 −0.692176 0.721729i \(-0.743348\pi\)
−0.692176 + 0.721729i \(0.743348\pi\)
\(858\) −3.98937 −0.136195
\(859\) 43.4286 1.48177 0.740883 0.671635i \(-0.234408\pi\)
0.740883 + 0.671635i \(0.234408\pi\)
\(860\) 162.036 5.52540
\(861\) −23.8004 −0.811114
\(862\) −50.9847 −1.73654
\(863\) −45.4429 −1.54690 −0.773448 0.633860i \(-0.781469\pi\)
−0.773448 + 0.633860i \(0.781469\pi\)
\(864\) 3.48132 0.118437
\(865\) 36.5449 1.24256
\(866\) −11.0120 −0.374203
\(867\) −16.8967 −0.573843
\(868\) 30.0268 1.01918
\(869\) −8.69078 −0.294815
\(870\) 23.0019 0.779839
\(871\) −4.74662 −0.160833
\(872\) −50.4525 −1.70854
\(873\) −29.6921 −1.00493
\(874\) 80.7397 2.73106
\(875\) 35.1995 1.18996
\(876\) 32.9849 1.11446
\(877\) −48.2621 −1.62970 −0.814848 0.579675i \(-0.803180\pi\)
−0.814848 + 0.579675i \(0.803180\pi\)
\(878\) 89.5581 3.02244
\(879\) 26.0085 0.877246
\(880\) 25.0081 0.843023
\(881\) −32.7464 −1.10326 −0.551628 0.834090i \(-0.685993\pi\)
−0.551628 + 0.834090i \(0.685993\pi\)
\(882\) 9.08088 0.305769
\(883\) −1.19651 −0.0402658 −0.0201329 0.999797i \(-0.506409\pi\)
−0.0201329 + 0.999797i \(0.506409\pi\)
\(884\) −23.8688 −0.802795
\(885\) 0.883100 0.0296851
\(886\) 69.9864 2.35124
\(887\) −25.5300 −0.857214 −0.428607 0.903491i \(-0.640995\pi\)
−0.428607 + 0.903491i \(0.640995\pi\)
\(888\) 0.864797 0.0290207
\(889\) 1.99247 0.0668254
\(890\) 64.4456 2.16022
\(891\) −6.14604 −0.205900
\(892\) 0.158834 0.00531816
\(893\) −3.02586 −0.101257
\(894\) 19.2398 0.643475
\(895\) −69.8685 −2.33545
\(896\) −59.2233 −1.97851
\(897\) 4.50124 0.150292
\(898\) −6.08196 −0.202958
\(899\) 8.05807 0.268752
\(900\) −74.5011 −2.48337
\(901\) 15.6827 0.522465
\(902\) −45.8187 −1.52560
\(903\) −27.9915 −0.931497
\(904\) −41.9932 −1.39667
\(905\) −14.8017 −0.492025
\(906\) 45.4592 1.51028
\(907\) −7.60563 −0.252541 −0.126270 0.991996i \(-0.540301\pi\)
−0.126270 + 0.991996i \(0.540301\pi\)
\(908\) −18.2155 −0.604503
\(909\) 21.6659 0.718612
\(910\) −26.0456 −0.863403
\(911\) 39.0561 1.29399 0.646993 0.762496i \(-0.276026\pi\)
0.646993 + 0.762496i \(0.276026\pi\)
\(912\) −18.2803 −0.605321
\(913\) −14.5756 −0.482381
\(914\) −86.4042 −2.85800
\(915\) 36.3977 1.20327
\(916\) −74.1717 −2.45070
\(917\) −34.1303 −1.12708
\(918\) 65.9090 2.17532
\(919\) −15.9975 −0.527710 −0.263855 0.964562i \(-0.584994\pi\)
−0.263855 + 0.964562i \(0.584994\pi\)
\(920\) −91.1378 −3.00472
\(921\) −18.4541 −0.608082
\(922\) −52.3146 −1.72289
\(923\) 4.41906 0.145455
\(924\) −18.8712 −0.620816
\(925\) 1.82888 0.0601334
\(926\) 75.8460 2.49245
\(927\) −12.6459 −0.415347
\(928\) −2.41748 −0.0793575
\(929\) 36.3506 1.19263 0.596313 0.802752i \(-0.296632\pi\)
0.596313 + 0.802752i \(0.296632\pi\)
\(930\) 19.4355 0.637317
\(931\) 10.0761 0.330232
\(932\) 62.9258 2.06120
\(933\) −4.85118 −0.158821
\(934\) −32.7626 −1.07203
\(935\) −43.3579 −1.41796
\(936\) 10.7049 0.349900
\(937\) −43.0018 −1.40481 −0.702404 0.711779i \(-0.747890\pi\)
−0.702404 + 0.711779i \(0.747890\pi\)
\(938\) −33.9152 −1.10737
\(939\) 18.0606 0.589386
\(940\) 6.97736 0.227577
\(941\) −7.30276 −0.238063 −0.119032 0.992890i \(-0.537979\pi\)
−0.119032 + 0.992890i \(0.537979\pi\)
\(942\) 15.0245 0.489525
\(943\) 51.6977 1.68351
\(944\) 1.01349 0.0329864
\(945\) 47.6138 1.54888
\(946\) −53.8871 −1.75202
\(947\) −52.9038 −1.71914 −0.859571 0.511016i \(-0.829269\pi\)
−0.859571 + 0.511016i \(0.829269\pi\)
\(948\) −14.6489 −0.475773
\(949\) −10.0232 −0.325367
\(950\) −124.866 −4.05119
\(951\) 19.1598 0.621298
\(952\) −83.4852 −2.70577
\(953\) −7.50053 −0.242966 −0.121483 0.992594i \(-0.538765\pi\)
−0.121483 + 0.992594i \(0.538765\pi\)
\(954\) −14.3682 −0.465188
\(955\) 53.0279 1.71594
\(956\) −83.5128 −2.70100
\(957\) −5.06432 −0.163706
\(958\) −9.47204 −0.306028
\(959\) −37.6671 −1.21633
\(960\) −27.3490 −0.882686
\(961\) −24.1913 −0.780365
\(962\) −0.536831 −0.0173081
\(963\) 31.8793 1.02730
\(964\) 80.2138 2.58351
\(965\) −55.7243 −1.79383
\(966\) 32.1620 1.03479
\(967\) −13.8994 −0.446973 −0.223487 0.974707i \(-0.571744\pi\)
−0.223487 + 0.974707i \(0.571744\pi\)
\(968\) 33.5369 1.07792
\(969\) 31.6935 1.01814
\(970\) 114.754 3.68451
\(971\) 15.3058 0.491187 0.245593 0.969373i \(-0.421017\pi\)
0.245593 + 0.969373i \(0.421017\pi\)
\(972\) −62.6294 −2.00884
\(973\) −11.4373 −0.366662
\(974\) −89.7033 −2.87428
\(975\) −6.96129 −0.222940
\(976\) 41.7720 1.33709
\(977\) −7.75540 −0.248117 −0.124059 0.992275i \(-0.539591\pi\)
−0.124059 + 0.992275i \(0.539591\pi\)
\(978\) −29.3161 −0.937426
\(979\) −14.1889 −0.453480
\(980\) −23.2347 −0.742205
\(981\) −24.8121 −0.792190
\(982\) 44.6742 1.42561
\(983\) −13.0950 −0.417666 −0.208833 0.977951i \(-0.566966\pi\)
−0.208833 + 0.977951i \(0.566966\pi\)
\(984\) −37.8056 −1.20520
\(985\) 8.56964 0.273051
\(986\) −45.7681 −1.45755
\(987\) −1.20533 −0.0383659
\(988\) 24.2650 0.771972
\(989\) 60.8013 1.93337
\(990\) 39.7239 1.26251
\(991\) −29.3422 −0.932087 −0.466043 0.884762i \(-0.654321\pi\)
−0.466043 + 0.884762i \(0.654321\pi\)
\(992\) −2.04265 −0.0648543
\(993\) 17.5667 0.557463
\(994\) 31.5748 1.00149
\(995\) 16.3378 0.517942
\(996\) −24.5680 −0.778468
\(997\) 35.6671 1.12959 0.564794 0.825232i \(-0.308956\pi\)
0.564794 + 0.825232i \(0.308956\pi\)
\(998\) 22.1091 0.699850
\(999\) 0.981377 0.0310494
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 \(a_p\))