Properties

Label 4003.2.a.b.1.5
Level 4003
Weight 2
Character 4003.1
Self dual Yes
Analytic conductor 31.964
Analytic rank 1
Dimension 152
CM No

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Newspace parameters

Level: \( N \) = \( 4003 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4003.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(31.9641159291\)
Analytic rank: \(1\)
Dimension: \(152\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Character \(\chi\) = 4003.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.71344 q^{2} -2.64650 q^{3} +5.36273 q^{4} -1.98460 q^{5} +7.18110 q^{6} -4.86510 q^{7} -9.12456 q^{8} +4.00395 q^{9} +O(q^{10})\) \(q-2.71344 q^{2} -2.64650 q^{3} +5.36273 q^{4} -1.98460 q^{5} +7.18110 q^{6} -4.86510 q^{7} -9.12456 q^{8} +4.00395 q^{9} +5.38509 q^{10} +4.74904 q^{11} -14.1925 q^{12} -0.0343281 q^{13} +13.2011 q^{14} +5.25224 q^{15} +14.0334 q^{16} +3.60088 q^{17} -10.8645 q^{18} -3.71179 q^{19} -10.6429 q^{20} +12.8755 q^{21} -12.8862 q^{22} -5.09332 q^{23} +24.1481 q^{24} -1.06136 q^{25} +0.0931470 q^{26} -2.65695 q^{27} -26.0902 q^{28} -10.4557 q^{29} -14.2516 q^{30} -3.93498 q^{31} -19.8297 q^{32} -12.5683 q^{33} -9.77077 q^{34} +9.65528 q^{35} +21.4721 q^{36} +0.369241 q^{37} +10.0717 q^{38} +0.0908491 q^{39} +18.1086 q^{40} +2.32546 q^{41} -34.9367 q^{42} +7.81321 q^{43} +25.4678 q^{44} -7.94624 q^{45} +13.8204 q^{46} -3.83967 q^{47} -37.1394 q^{48} +16.6692 q^{49} +2.87993 q^{50} -9.52973 q^{51} -0.184092 q^{52} -12.6157 q^{53} +7.20945 q^{54} -9.42495 q^{55} +44.3919 q^{56} +9.82324 q^{57} +28.3709 q^{58} -1.72956 q^{59} +28.1664 q^{60} +2.62444 q^{61} +10.6773 q^{62} -19.4796 q^{63} +25.7398 q^{64} +0.0681275 q^{65} +34.1033 q^{66} +9.42755 q^{67} +19.3106 q^{68} +13.4794 q^{69} -26.1990 q^{70} +14.5835 q^{71} -36.5343 q^{72} -9.64534 q^{73} -1.00191 q^{74} +2.80888 q^{75} -19.9053 q^{76} -23.1045 q^{77} -0.246513 q^{78} +3.62057 q^{79} -27.8508 q^{80} -4.98024 q^{81} -6.31000 q^{82} +11.9062 q^{83} +69.0477 q^{84} -7.14632 q^{85} -21.2006 q^{86} +27.6710 q^{87} -43.3329 q^{88} +3.03326 q^{89} +21.5616 q^{90} +0.167009 q^{91} -27.3141 q^{92} +10.4139 q^{93} +10.4187 q^{94} +7.36642 q^{95} +52.4793 q^{96} +18.1865 q^{97} -45.2307 q^{98} +19.0149 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 152q - 22q^{2} - 18q^{3} + 138q^{4} - 59q^{5} - 17q^{6} - 19q^{7} - 66q^{8} + 106q^{9} + O(q^{10}) \) \( 152q - 22q^{2} - 18q^{3} + 138q^{4} - 59q^{5} - 17q^{6} - 19q^{7} - 66q^{8} + 106q^{9} - 15q^{10} - 40q^{11} - 53q^{12} - 59q^{13} - 36q^{14} - 40q^{15} + 118q^{16} - 93q^{17} - 59q^{18} - 16q^{19} - 108q^{20} - 62q^{21} - 37q^{22} - 107q^{23} - 31q^{24} + 101q^{25} - 64q^{26} - 63q^{27} - 53q^{28} - 124q^{29} - 68q^{30} - 15q^{31} - 129q^{32} - 49q^{33} - 76q^{35} + 45q^{36} - 98q^{37} - 125q^{38} - 47q^{39} - 7q^{40} - 56q^{41} - 84q^{42} - 62q^{43} - 114q^{44} - 142q^{45} - 3q^{46} - 111q^{47} - 92q^{48} + 117q^{49} - 64q^{50} - 21q^{51} - 85q^{52} - 347q^{53} + 3q^{54} - 16q^{55} - 73q^{56} - 115q^{57} - 29q^{58} - 50q^{59} - 54q^{60} - 62q^{61} - 55q^{62} - 70q^{63} + 64q^{64} - 147q^{65} + 34q^{66} - 86q^{67} - 174q^{68} - 104q^{69} - 7q^{70} - 86q^{71} - 139q^{72} - 27q^{73} - 52q^{74} - 49q^{75} - 11q^{76} - 346q^{77} - 59q^{78} - 17q^{79} - 149q^{80} - 8q^{81} - 31q^{82} - 106q^{83} - 51q^{84} - 69q^{85} - 85q^{86} - 32q^{87} - 113q^{88} - 59q^{89} + 10q^{90} - 9q^{91} - 314q^{92} - 230q^{93} + 7q^{94} - 74q^{95} - 54q^{96} - 60q^{97} - 77q^{98} - 96q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.71344 −1.91869 −0.959344 0.282238i \(-0.908923\pi\)
−0.959344 + 0.282238i \(0.908923\pi\)
\(3\) −2.64650 −1.52796 −0.763978 0.645242i \(-0.776756\pi\)
−0.763978 + 0.645242i \(0.776756\pi\)
\(4\) 5.36273 2.68137
\(5\) −1.98460 −0.887541 −0.443770 0.896141i \(-0.646359\pi\)
−0.443770 + 0.896141i \(0.646359\pi\)
\(6\) 7.18110 2.93167
\(7\) −4.86510 −1.83883 −0.919417 0.393284i \(-0.871339\pi\)
−0.919417 + 0.393284i \(0.871339\pi\)
\(8\) −9.12456 −3.22602
\(9\) 4.00395 1.33465
\(10\) 5.38509 1.70291
\(11\) 4.74904 1.43189 0.715944 0.698157i \(-0.245996\pi\)
0.715944 + 0.698157i \(0.245996\pi\)
\(12\) −14.1925 −4.09701
\(13\) −0.0343281 −0.00952089 −0.00476044 0.999989i \(-0.501515\pi\)
−0.00476044 + 0.999989i \(0.501515\pi\)
\(14\) 13.2011 3.52815
\(15\) 5.25224 1.35612
\(16\) 14.0334 3.50836
\(17\) 3.60088 0.873343 0.436671 0.899621i \(-0.356157\pi\)
0.436671 + 0.899621i \(0.356157\pi\)
\(18\) −10.8645 −2.56078
\(19\) −3.71179 −0.851543 −0.425771 0.904831i \(-0.639997\pi\)
−0.425771 + 0.904831i \(0.639997\pi\)
\(20\) −10.6429 −2.37982
\(21\) 12.8755 2.80966
\(22\) −12.8862 −2.74735
\(23\) −5.09332 −1.06203 −0.531015 0.847362i \(-0.678189\pi\)
−0.531015 + 0.847362i \(0.678189\pi\)
\(24\) 24.1481 4.92921
\(25\) −1.06136 −0.212272
\(26\) 0.0931470 0.0182676
\(27\) −2.65695 −0.511329
\(28\) −26.0902 −4.93059
\(29\) −10.4557 −1.94158 −0.970789 0.239937i \(-0.922873\pi\)
−0.970789 + 0.239937i \(0.922873\pi\)
\(30\) −14.2516 −2.60198
\(31\) −3.93498 −0.706744 −0.353372 0.935483i \(-0.614965\pi\)
−0.353372 + 0.935483i \(0.614965\pi\)
\(32\) −19.8297 −3.50543
\(33\) −12.5683 −2.18786
\(34\) −9.77077 −1.67567
\(35\) 9.65528 1.63204
\(36\) 21.4721 3.57868
\(37\) 0.369241 0.0607029 0.0303514 0.999539i \(-0.490337\pi\)
0.0303514 + 0.999539i \(0.490337\pi\)
\(38\) 10.0717 1.63385
\(39\) 0.0908491 0.0145475
\(40\) 18.1086 2.86322
\(41\) 2.32546 0.363176 0.181588 0.983375i \(-0.441876\pi\)
0.181588 + 0.983375i \(0.441876\pi\)
\(42\) −34.9367 −5.39086
\(43\) 7.81321 1.19150 0.595751 0.803169i \(-0.296854\pi\)
0.595751 + 0.803169i \(0.296854\pi\)
\(44\) 25.4678 3.83942
\(45\) −7.94624 −1.18456
\(46\) 13.8204 2.03770
\(47\) −3.83967 −0.560073 −0.280037 0.959989i \(-0.590347\pi\)
−0.280037 + 0.959989i \(0.590347\pi\)
\(48\) −37.1394 −5.36062
\(49\) 16.6692 2.38131
\(50\) 2.87993 0.407283
\(51\) −9.52973 −1.33443
\(52\) −0.184092 −0.0255290
\(53\) −12.6157 −1.73290 −0.866452 0.499261i \(-0.833605\pi\)
−0.866452 + 0.499261i \(0.833605\pi\)
\(54\) 7.20945 0.981082
\(55\) −9.42495 −1.27086
\(56\) 44.3919 5.93211
\(57\) 9.82324 1.30112
\(58\) 28.3709 3.72528
\(59\) −1.72956 −0.225170 −0.112585 0.993642i \(-0.535913\pi\)
−0.112585 + 0.993642i \(0.535913\pi\)
\(60\) 28.1664 3.63626
\(61\) 2.62444 0.336025 0.168013 0.985785i \(-0.446265\pi\)
0.168013 + 0.985785i \(0.446265\pi\)
\(62\) 10.6773 1.35602
\(63\) −19.4796 −2.45420
\(64\) 25.7398 3.21747
\(65\) 0.0681275 0.00845018
\(66\) 34.1033 4.19783
\(67\) 9.42755 1.15176 0.575879 0.817535i \(-0.304660\pi\)
0.575879 + 0.817535i \(0.304660\pi\)
\(68\) 19.3106 2.34175
\(69\) 13.4794 1.62274
\(70\) −26.1990 −3.13138
\(71\) 14.5835 1.73075 0.865374 0.501127i \(-0.167081\pi\)
0.865374 + 0.501127i \(0.167081\pi\)
\(72\) −36.5343 −4.30560
\(73\) −9.64534 −1.12890 −0.564451 0.825467i \(-0.690912\pi\)
−0.564451 + 0.825467i \(0.690912\pi\)
\(74\) −1.00191 −0.116470
\(75\) 2.80888 0.324342
\(76\) −19.9053 −2.28330
\(77\) −23.1045 −2.63301
\(78\) −0.246513 −0.0279121
\(79\) 3.62057 0.407346 0.203673 0.979039i \(-0.434712\pi\)
0.203673 + 0.979039i \(0.434712\pi\)
\(80\) −27.8508 −3.11381
\(81\) −4.98024 −0.553360
\(82\) −6.31000 −0.696822
\(83\) 11.9062 1.30688 0.653439 0.756979i \(-0.273326\pi\)
0.653439 + 0.756979i \(0.273326\pi\)
\(84\) 69.0477 7.53372
\(85\) −7.14632 −0.775127
\(86\) −21.2006 −2.28612
\(87\) 27.6710 2.96664
\(88\) −43.3329 −4.61930
\(89\) 3.03326 0.321525 0.160763 0.986993i \(-0.448605\pi\)
0.160763 + 0.986993i \(0.448605\pi\)
\(90\) 21.5616 2.27279
\(91\) 0.167009 0.0175073
\(92\) −27.3141 −2.84769
\(93\) 10.4139 1.07987
\(94\) 10.4187 1.07461
\(95\) 7.36642 0.755779
\(96\) 52.4793 5.35614
\(97\) 18.1865 1.84656 0.923280 0.384127i \(-0.125498\pi\)
0.923280 + 0.384127i \(0.125498\pi\)
\(98\) −45.2307 −4.56899
\(99\) 19.0149 1.91107
\(100\) −5.69178 −0.569178
\(101\) −15.8696 −1.57909 −0.789543 0.613696i \(-0.789682\pi\)
−0.789543 + 0.613696i \(0.789682\pi\)
\(102\) 25.8583 2.56035
\(103\) 8.79965 0.867055 0.433528 0.901140i \(-0.357269\pi\)
0.433528 + 0.901140i \(0.357269\pi\)
\(104\) 0.313228 0.0307146
\(105\) −25.5527 −2.49369
\(106\) 34.2320 3.32490
\(107\) −15.5394 −1.50225 −0.751127 0.660157i \(-0.770490\pi\)
−0.751127 + 0.660157i \(0.770490\pi\)
\(108\) −14.2485 −1.37106
\(109\) 8.64675 0.828209 0.414104 0.910229i \(-0.364095\pi\)
0.414104 + 0.910229i \(0.364095\pi\)
\(110\) 25.5740 2.43838
\(111\) −0.977196 −0.0927513
\(112\) −68.2740 −6.45129
\(113\) −6.44293 −0.606100 −0.303050 0.952975i \(-0.598005\pi\)
−0.303050 + 0.952975i \(0.598005\pi\)
\(114\) −26.6547 −2.49644
\(115\) 10.1082 0.942595
\(116\) −56.0712 −5.20608
\(117\) −0.137448 −0.0127070
\(118\) 4.69306 0.432031
\(119\) −17.5186 −1.60593
\(120\) −47.9244 −4.37488
\(121\) 11.5534 1.05031
\(122\) −7.12125 −0.644727
\(123\) −6.15433 −0.554918
\(124\) −21.1023 −1.89504
\(125\) 12.0294 1.07594
\(126\) 52.8566 4.70884
\(127\) 20.1579 1.78873 0.894363 0.447343i \(-0.147630\pi\)
0.894363 + 0.447343i \(0.147630\pi\)
\(128\) −30.1837 −2.66789
\(129\) −20.6776 −1.82056
\(130\) −0.184860 −0.0162133
\(131\) 14.5061 1.26741 0.633704 0.773576i \(-0.281534\pi\)
0.633704 + 0.773576i \(0.281534\pi\)
\(132\) −67.4005 −5.86646
\(133\) 18.0582 1.56585
\(134\) −25.5810 −2.20987
\(135\) 5.27298 0.453826
\(136\) −32.8565 −2.81742
\(137\) −10.7896 −0.921814 −0.460907 0.887448i \(-0.652476\pi\)
−0.460907 + 0.887448i \(0.652476\pi\)
\(138\) −36.5756 −3.11352
\(139\) 4.76264 0.403962 0.201981 0.979389i \(-0.435262\pi\)
0.201981 + 0.979389i \(0.435262\pi\)
\(140\) 51.7787 4.37610
\(141\) 10.1617 0.855767
\(142\) −39.5715 −3.32077
\(143\) −0.163025 −0.0136329
\(144\) 56.1891 4.68243
\(145\) 20.7504 1.72323
\(146\) 26.1720 2.16601
\(147\) −44.1149 −3.63854
\(148\) 1.98014 0.162767
\(149\) −18.5520 −1.51984 −0.759921 0.650015i \(-0.774762\pi\)
−0.759921 + 0.650015i \(0.774762\pi\)
\(150\) −7.62171 −0.622310
\(151\) 14.6621 1.19319 0.596594 0.802543i \(-0.296520\pi\)
0.596594 + 0.802543i \(0.296520\pi\)
\(152\) 33.8684 2.74709
\(153\) 14.4178 1.16561
\(154\) 62.6927 5.05192
\(155\) 7.80938 0.627264
\(156\) 0.487199 0.0390072
\(157\) 0.170936 0.0136422 0.00682109 0.999977i \(-0.497829\pi\)
0.00682109 + 0.999977i \(0.497829\pi\)
\(158\) −9.82418 −0.781569
\(159\) 33.3875 2.64780
\(160\) 39.3541 3.11121
\(161\) 24.7795 1.95290
\(162\) 13.5136 1.06173
\(163\) 2.94393 0.230587 0.115293 0.993331i \(-0.463219\pi\)
0.115293 + 0.993331i \(0.463219\pi\)
\(164\) 12.4708 0.973809
\(165\) 24.9431 1.94182
\(166\) −32.3068 −2.50749
\(167\) 16.9104 1.30856 0.654282 0.756251i \(-0.272971\pi\)
0.654282 + 0.756251i \(0.272971\pi\)
\(168\) −117.483 −9.06401
\(169\) −12.9988 −0.999909
\(170\) 19.3911 1.48723
\(171\) −14.8618 −1.13651
\(172\) 41.9001 3.19486
\(173\) 19.4805 1.48108 0.740538 0.672015i \(-0.234571\pi\)
0.740538 + 0.672015i \(0.234571\pi\)
\(174\) −75.0835 −5.69207
\(175\) 5.16361 0.390332
\(176\) 66.6453 5.02358
\(177\) 4.57729 0.344050
\(178\) −8.23056 −0.616907
\(179\) −5.95394 −0.445019 −0.222509 0.974931i \(-0.571425\pi\)
−0.222509 + 0.974931i \(0.571425\pi\)
\(180\) −42.6136 −3.17623
\(181\) 4.71521 0.350479 0.175239 0.984526i \(-0.443930\pi\)
0.175239 + 0.984526i \(0.443930\pi\)
\(182\) −0.453169 −0.0335911
\(183\) −6.94557 −0.513432
\(184\) 46.4743 3.42613
\(185\) −0.732797 −0.0538763
\(186\) −28.2575 −2.07194
\(187\) 17.1007 1.25053
\(188\) −20.5911 −1.50176
\(189\) 12.9263 0.940250
\(190\) −19.9883 −1.45010
\(191\) −2.28622 −0.165425 −0.0827124 0.996573i \(-0.526358\pi\)
−0.0827124 + 0.996573i \(0.526358\pi\)
\(192\) −68.1202 −4.91615
\(193\) −2.13543 −0.153712 −0.0768559 0.997042i \(-0.524488\pi\)
−0.0768559 + 0.997042i \(0.524488\pi\)
\(194\) −49.3479 −3.54297
\(195\) −0.180299 −0.0129115
\(196\) 89.3923 6.38516
\(197\) 3.40347 0.242487 0.121244 0.992623i \(-0.461312\pi\)
0.121244 + 0.992623i \(0.461312\pi\)
\(198\) −51.5957 −3.66675
\(199\) −17.1412 −1.21510 −0.607552 0.794280i \(-0.707849\pi\)
−0.607552 + 0.794280i \(0.707849\pi\)
\(200\) 9.68442 0.684792
\(201\) −24.9500 −1.75984
\(202\) 43.0612 3.02977
\(203\) 50.8681 3.57024
\(204\) −51.1054 −3.57809
\(205\) −4.61512 −0.322334
\(206\) −23.8773 −1.66361
\(207\) −20.3934 −1.41744
\(208\) −0.481740 −0.0334027
\(209\) −17.6274 −1.21931
\(210\) 69.3355 4.78461
\(211\) 28.0241 1.92926 0.964630 0.263609i \(-0.0849130\pi\)
0.964630 + 0.263609i \(0.0849130\pi\)
\(212\) −67.6548 −4.64655
\(213\) −38.5953 −2.64451
\(214\) 42.1653 2.88236
\(215\) −15.5061 −1.05751
\(216\) 24.2435 1.64956
\(217\) 19.1441 1.29959
\(218\) −23.4624 −1.58907
\(219\) 25.5264 1.72491
\(220\) −50.5435 −3.40764
\(221\) −0.123611 −0.00831500
\(222\) 2.65156 0.177961
\(223\) −17.2363 −1.15423 −0.577114 0.816663i \(-0.695821\pi\)
−0.577114 + 0.816663i \(0.695821\pi\)
\(224\) 96.4734 6.44590
\(225\) −4.24962 −0.283308
\(226\) 17.4825 1.16292
\(227\) 2.96262 0.196636 0.0983180 0.995155i \(-0.468654\pi\)
0.0983180 + 0.995155i \(0.468654\pi\)
\(228\) 52.6794 3.48878
\(229\) 7.21530 0.476801 0.238400 0.971167i \(-0.423377\pi\)
0.238400 + 0.971167i \(0.423377\pi\)
\(230\) −27.4280 −1.80855
\(231\) 61.1461 4.02312
\(232\) 95.4038 6.26356
\(233\) 11.0720 0.725353 0.362676 0.931915i \(-0.381863\pi\)
0.362676 + 0.931915i \(0.381863\pi\)
\(234\) 0.372956 0.0243809
\(235\) 7.62021 0.497088
\(236\) −9.27519 −0.603764
\(237\) −9.58182 −0.622406
\(238\) 47.5357 3.08128
\(239\) 9.33487 0.603823 0.301911 0.953336i \(-0.402375\pi\)
0.301911 + 0.953336i \(0.402375\pi\)
\(240\) 73.7070 4.75777
\(241\) −11.4957 −0.740506 −0.370253 0.928931i \(-0.620729\pi\)
−0.370253 + 0.928931i \(0.620729\pi\)
\(242\) −31.3493 −2.01521
\(243\) 21.1510 1.35684
\(244\) 14.0742 0.901006
\(245\) −33.0817 −2.11351
\(246\) 16.6994 1.06471
\(247\) 0.127418 0.00810744
\(248\) 35.9050 2.27997
\(249\) −31.5098 −1.99685
\(250\) −32.6409 −2.06439
\(251\) 5.70283 0.359959 0.179980 0.983670i \(-0.442397\pi\)
0.179980 + 0.983670i \(0.442397\pi\)
\(252\) −104.464 −6.58060
\(253\) −24.1884 −1.52071
\(254\) −54.6972 −3.43201
\(255\) 18.9127 1.18436
\(256\) 30.4222 1.90138
\(257\) 0.891949 0.0556383 0.0278191 0.999613i \(-0.491144\pi\)
0.0278191 + 0.999613i \(0.491144\pi\)
\(258\) 56.1074 3.49310
\(259\) −1.79639 −0.111623
\(260\) 0.365350 0.0226580
\(261\) −41.8641 −2.59132
\(262\) −39.3615 −2.43176
\(263\) −15.0509 −0.928079 −0.464039 0.885815i \(-0.653600\pi\)
−0.464039 + 0.885815i \(0.653600\pi\)
\(264\) 114.680 7.05809
\(265\) 25.0372 1.53802
\(266\) −48.9998 −3.00437
\(267\) −8.02752 −0.491276
\(268\) 50.5574 3.08829
\(269\) 0.133043 0.00811179 0.00405589 0.999992i \(-0.498709\pi\)
0.00405589 + 0.999992i \(0.498709\pi\)
\(270\) −14.3079 −0.870750
\(271\) 10.9188 0.663268 0.331634 0.943408i \(-0.392400\pi\)
0.331634 + 0.943408i \(0.392400\pi\)
\(272\) 50.5328 3.06400
\(273\) −0.441990 −0.0267504
\(274\) 29.2768 1.76867
\(275\) −5.04043 −0.303949
\(276\) 72.2867 4.35115
\(277\) 12.6256 0.758597 0.379298 0.925274i \(-0.376165\pi\)
0.379298 + 0.925274i \(0.376165\pi\)
\(278\) −12.9231 −0.775078
\(279\) −15.7555 −0.943256
\(280\) −88.1001 −5.26499
\(281\) 11.5896 0.691376 0.345688 0.938349i \(-0.387646\pi\)
0.345688 + 0.938349i \(0.387646\pi\)
\(282\) −27.5730 −1.64195
\(283\) −25.5451 −1.51850 −0.759250 0.650799i \(-0.774434\pi\)
−0.759250 + 0.650799i \(0.774434\pi\)
\(284\) 78.2076 4.64077
\(285\) −19.4952 −1.15480
\(286\) 0.442358 0.0261572
\(287\) −11.3136 −0.667821
\(288\) −79.3971 −4.67852
\(289\) −4.03364 −0.237273
\(290\) −56.3049 −3.30634
\(291\) −48.1306 −2.82146
\(292\) −51.7254 −3.02700
\(293\) −1.72183 −0.100590 −0.0502952 0.998734i \(-0.516016\pi\)
−0.0502952 + 0.998734i \(0.516016\pi\)
\(294\) 119.703 6.98122
\(295\) 3.43250 0.199848
\(296\) −3.36916 −0.195829
\(297\) −12.6179 −0.732167
\(298\) 50.3398 2.91610
\(299\) 0.174844 0.0101115
\(300\) 15.0633 0.869678
\(301\) −38.0120 −2.19098
\(302\) −39.7848 −2.28936
\(303\) 41.9989 2.41277
\(304\) −52.0891 −2.98752
\(305\) −5.20847 −0.298236
\(306\) −39.1216 −2.23644
\(307\) −14.9800 −0.854954 −0.427477 0.904026i \(-0.640597\pi\)
−0.427477 + 0.904026i \(0.640597\pi\)
\(308\) −123.903 −7.06005
\(309\) −23.2883 −1.32482
\(310\) −21.1902 −1.20352
\(311\) −30.3754 −1.72243 −0.861216 0.508240i \(-0.830296\pi\)
−0.861216 + 0.508240i \(0.830296\pi\)
\(312\) −0.828958 −0.0469305
\(313\) 8.96448 0.506702 0.253351 0.967374i \(-0.418467\pi\)
0.253351 + 0.967374i \(0.418467\pi\)
\(314\) −0.463824 −0.0261751
\(315\) 38.6592 2.17820
\(316\) 19.4161 1.09224
\(317\) −10.8579 −0.609842 −0.304921 0.952378i \(-0.598630\pi\)
−0.304921 + 0.952378i \(0.598630\pi\)
\(318\) −90.5948 −5.08030
\(319\) −49.6546 −2.78012
\(320\) −51.0831 −2.85563
\(321\) 41.1251 2.29538
\(322\) −67.2375 −3.74700
\(323\) −13.3657 −0.743689
\(324\) −26.7077 −1.48376
\(325\) 0.0364343 0.00202101
\(326\) −7.98817 −0.442424
\(327\) −22.8836 −1.26547
\(328\) −21.2188 −1.17161
\(329\) 18.6804 1.02988
\(330\) −67.6815 −3.72574
\(331\) 27.7984 1.52794 0.763969 0.645253i \(-0.223248\pi\)
0.763969 + 0.645253i \(0.223248\pi\)
\(332\) 63.8499 3.50422
\(333\) 1.47842 0.0810171
\(334\) −45.8852 −2.51073
\(335\) −18.7099 −1.02223
\(336\) 180.687 9.85728
\(337\) 5.20485 0.283526 0.141763 0.989901i \(-0.454723\pi\)
0.141763 + 0.989901i \(0.454723\pi\)
\(338\) 35.2715 1.91851
\(339\) 17.0512 0.926094
\(340\) −38.3238 −2.07840
\(341\) −18.6874 −1.01198
\(342\) 40.3266 2.18061
\(343\) −47.0415 −2.54000
\(344\) −71.2921 −3.84381
\(345\) −26.7513 −1.44024
\(346\) −52.8591 −2.84172
\(347\) 19.0644 1.02343 0.511714 0.859156i \(-0.329011\pi\)
0.511714 + 0.859156i \(0.329011\pi\)
\(348\) 148.392 7.95466
\(349\) 25.9284 1.38791 0.693957 0.720016i \(-0.255866\pi\)
0.693957 + 0.720016i \(0.255866\pi\)
\(350\) −14.0111 −0.748926
\(351\) 0.0912078 0.00486831
\(352\) −94.1720 −5.01939
\(353\) −12.0698 −0.642409 −0.321205 0.947010i \(-0.604088\pi\)
−0.321205 + 0.947010i \(0.604088\pi\)
\(354\) −12.4202 −0.660125
\(355\) −28.9425 −1.53611
\(356\) 16.2666 0.862127
\(357\) 46.3631 2.45379
\(358\) 16.1556 0.853852
\(359\) −21.2454 −1.12129 −0.560644 0.828057i \(-0.689446\pi\)
−0.560644 + 0.828057i \(0.689446\pi\)
\(360\) 72.5059 3.82140
\(361\) −5.22262 −0.274875
\(362\) −12.7944 −0.672460
\(363\) −30.5760 −1.60482
\(364\) 0.895626 0.0469436
\(365\) 19.1422 1.00195
\(366\) 18.8464 0.985115
\(367\) −8.83887 −0.461385 −0.230693 0.973027i \(-0.574099\pi\)
−0.230693 + 0.973027i \(0.574099\pi\)
\(368\) −71.4767 −3.72598
\(369\) 9.31104 0.484713
\(370\) 1.98840 0.103372
\(371\) 61.3767 3.18652
\(372\) 55.8471 2.89554
\(373\) −8.19249 −0.424191 −0.212096 0.977249i \(-0.568029\pi\)
−0.212096 + 0.977249i \(0.568029\pi\)
\(374\) −46.4017 −2.39938
\(375\) −31.8357 −1.64399
\(376\) 35.0353 1.80681
\(377\) 0.358924 0.0184855
\(378\) −35.0747 −1.80405
\(379\) −1.08109 −0.0555316 −0.0277658 0.999614i \(-0.508839\pi\)
−0.0277658 + 0.999614i \(0.508839\pi\)
\(380\) 39.5041 2.02652
\(381\) −53.3479 −2.73309
\(382\) 6.20350 0.317399
\(383\) 33.7632 1.72522 0.862611 0.505868i \(-0.168828\pi\)
0.862611 + 0.505868i \(0.168828\pi\)
\(384\) 79.8812 4.07642
\(385\) 45.8533 2.33690
\(386\) 5.79436 0.294925
\(387\) 31.2837 1.59024
\(388\) 97.5294 4.95131
\(389\) 12.9279 0.655469 0.327734 0.944770i \(-0.393715\pi\)
0.327734 + 0.944770i \(0.393715\pi\)
\(390\) 0.489230 0.0247731
\(391\) −18.3404 −0.927516
\(392\) −152.099 −7.68215
\(393\) −38.3905 −1.93654
\(394\) −9.23509 −0.465257
\(395\) −7.18538 −0.361536
\(396\) 101.972 5.12428
\(397\) 29.3298 1.47202 0.736010 0.676970i \(-0.236707\pi\)
0.736010 + 0.676970i \(0.236707\pi\)
\(398\) 46.5114 2.33141
\(399\) −47.7910 −2.39254
\(400\) −14.8945 −0.744725
\(401\) −16.6130 −0.829613 −0.414806 0.909910i \(-0.636151\pi\)
−0.414806 + 0.909910i \(0.636151\pi\)
\(402\) 67.7001 3.37658
\(403\) 0.135080 0.00672883
\(404\) −85.1045 −4.23411
\(405\) 9.88380 0.491130
\(406\) −138.027 −6.85017
\(407\) 1.75354 0.0869198
\(408\) 86.9546 4.30489
\(409\) −5.85432 −0.289477 −0.144739 0.989470i \(-0.546234\pi\)
−0.144739 + 0.989470i \(0.546234\pi\)
\(410\) 12.5228 0.618458
\(411\) 28.5545 1.40849
\(412\) 47.1902 2.32489
\(413\) 8.41450 0.414051
\(414\) 55.3361 2.71962
\(415\) −23.6291 −1.15991
\(416\) 0.680715 0.0333748
\(417\) −12.6043 −0.617236
\(418\) 47.8309 2.33949
\(419\) 11.1072 0.542620 0.271310 0.962492i \(-0.412543\pi\)
0.271310 + 0.962492i \(0.412543\pi\)
\(420\) −137.032 −6.68648
\(421\) 0.733952 0.0357706 0.0178853 0.999840i \(-0.494307\pi\)
0.0178853 + 0.999840i \(0.494307\pi\)
\(422\) −76.0416 −3.70165
\(423\) −15.3738 −0.747501
\(424\) 115.113 5.59038
\(425\) −3.82182 −0.185386
\(426\) 104.726 5.07398
\(427\) −12.7682 −0.617894
\(428\) −83.3339 −4.02809
\(429\) 0.431446 0.0208304
\(430\) 42.0748 2.02903
\(431\) 22.0473 1.06198 0.530990 0.847378i \(-0.321820\pi\)
0.530990 + 0.847378i \(0.321820\pi\)
\(432\) −37.2861 −1.79393
\(433\) 17.6984 0.850532 0.425266 0.905068i \(-0.360180\pi\)
0.425266 + 0.905068i \(0.360180\pi\)
\(434\) −51.9462 −2.49350
\(435\) −54.9159 −2.63302
\(436\) 46.3702 2.22073
\(437\) 18.9053 0.904364
\(438\) −69.2642 −3.30957
\(439\) 19.2876 0.920547 0.460274 0.887777i \(-0.347751\pi\)
0.460274 + 0.887777i \(0.347751\pi\)
\(440\) 85.9985 4.09982
\(441\) 66.7425 3.17821
\(442\) 0.335411 0.0159539
\(443\) −21.0561 −1.00041 −0.500203 0.865908i \(-0.666741\pi\)
−0.500203 + 0.865908i \(0.666741\pi\)
\(444\) −5.24044 −0.248700
\(445\) −6.01982 −0.285367
\(446\) 46.7696 2.21461
\(447\) 49.0979 2.32225
\(448\) −125.226 −5.91639
\(449\) −5.91283 −0.279044 −0.139522 0.990219i \(-0.544557\pi\)
−0.139522 + 0.990219i \(0.544557\pi\)
\(450\) 11.5311 0.543580
\(451\) 11.0437 0.520028
\(452\) −34.5517 −1.62518
\(453\) −38.8033 −1.82314
\(454\) −8.03888 −0.377283
\(455\) −0.331447 −0.0155385
\(456\) −89.6327 −4.19744
\(457\) −6.28400 −0.293953 −0.146977 0.989140i \(-0.546954\pi\)
−0.146977 + 0.989140i \(0.546954\pi\)
\(458\) −19.5783 −0.914832
\(459\) −9.56735 −0.446566
\(460\) 54.2076 2.52744
\(461\) −15.2872 −0.711998 −0.355999 0.934486i \(-0.615859\pi\)
−0.355999 + 0.934486i \(0.615859\pi\)
\(462\) −165.916 −7.71911
\(463\) −10.1649 −0.472401 −0.236200 0.971704i \(-0.575902\pi\)
−0.236200 + 0.971704i \(0.575902\pi\)
\(464\) −146.730 −6.81175
\(465\) −20.6675 −0.958432
\(466\) −30.0432 −1.39173
\(467\) 10.3905 0.480817 0.240409 0.970672i \(-0.422719\pi\)
0.240409 + 0.970672i \(0.422719\pi\)
\(468\) −0.737095 −0.0340722
\(469\) −45.8659 −2.11789
\(470\) −20.6769 −0.953756
\(471\) −0.452382 −0.0208447
\(472\) 15.7815 0.726403
\(473\) 37.1052 1.70610
\(474\) 25.9997 1.19420
\(475\) 3.93954 0.180758
\(476\) −93.9478 −4.30609
\(477\) −50.5127 −2.31282
\(478\) −25.3296 −1.15855
\(479\) −37.0241 −1.69168 −0.845838 0.533440i \(-0.820899\pi\)
−0.845838 + 0.533440i \(0.820899\pi\)
\(480\) −104.150 −4.75379
\(481\) −0.0126753 −0.000577945 0
\(482\) 31.1930 1.42080
\(483\) −65.5788 −2.98394
\(484\) 61.9576 2.81626
\(485\) −36.0930 −1.63890
\(486\) −57.3920 −2.60335
\(487\) −30.3561 −1.37557 −0.687784 0.725915i \(-0.741416\pi\)
−0.687784 + 0.725915i \(0.741416\pi\)
\(488\) −23.9469 −1.08402
\(489\) −7.79111 −0.352326
\(490\) 89.7650 4.05517
\(491\) −38.3828 −1.73219 −0.866096 0.499878i \(-0.833378\pi\)
−0.866096 + 0.499878i \(0.833378\pi\)
\(492\) −33.0040 −1.48794
\(493\) −37.6498 −1.69566
\(494\) −0.345742 −0.0155557
\(495\) −37.7370 −1.69615
\(496\) −55.2213 −2.47951
\(497\) −70.9503 −3.18256
\(498\) 85.4998 3.83134
\(499\) 16.5331 0.740122 0.370061 0.929007i \(-0.379337\pi\)
0.370061 + 0.929007i \(0.379337\pi\)
\(500\) 64.5103 2.88499
\(501\) −44.7533 −1.99943
\(502\) −15.4743 −0.690650
\(503\) 6.51841 0.290642 0.145321 0.989385i \(-0.453579\pi\)
0.145321 + 0.989385i \(0.453579\pi\)
\(504\) 177.743 7.91729
\(505\) 31.4948 1.40150
\(506\) 65.6336 2.91777
\(507\) 34.4013 1.52782
\(508\) 108.101 4.79623
\(509\) 1.01563 0.0450172 0.0225086 0.999747i \(-0.492835\pi\)
0.0225086 + 0.999747i \(0.492835\pi\)
\(510\) −51.3184 −2.27242
\(511\) 46.9255 2.07586
\(512\) −22.1811 −0.980274
\(513\) 9.86202 0.435419
\(514\) −2.42025 −0.106752
\(515\) −17.4638 −0.769547
\(516\) −110.889 −4.88160
\(517\) −18.2347 −0.801962
\(518\) 4.87440 0.214169
\(519\) −51.5551 −2.26302
\(520\) −0.621633 −0.0272604
\(521\) 2.06206 0.0903407 0.0451704 0.998979i \(-0.485617\pi\)
0.0451704 + 0.998979i \(0.485617\pi\)
\(522\) 113.596 4.97195
\(523\) −31.9386 −1.39658 −0.698288 0.715817i \(-0.746055\pi\)
−0.698288 + 0.715817i \(0.746055\pi\)
\(524\) 77.7925 3.39838
\(525\) −13.6655 −0.596410
\(526\) 40.8397 1.78069
\(527\) −14.1694 −0.617230
\(528\) −176.377 −7.67581
\(529\) 2.94188 0.127908
\(530\) −67.9368 −2.95099
\(531\) −6.92509 −0.300523
\(532\) 96.8414 4.19861
\(533\) −0.0798286 −0.00345776
\(534\) 21.7822 0.942606
\(535\) 30.8396 1.33331
\(536\) −86.0222 −3.71559
\(537\) 15.7571 0.679969
\(538\) −0.361004 −0.0155640
\(539\) 79.1625 3.40977
\(540\) 28.2776 1.21687
\(541\) −44.0977 −1.89591 −0.947953 0.318410i \(-0.896851\pi\)
−0.947953 + 0.318410i \(0.896851\pi\)
\(542\) −29.6274 −1.27261
\(543\) −12.4788 −0.535516
\(544\) −71.4044 −3.06144
\(545\) −17.1604 −0.735069
\(546\) 1.19931 0.0513258
\(547\) 19.6921 0.841975 0.420987 0.907067i \(-0.361684\pi\)
0.420987 + 0.907067i \(0.361684\pi\)
\(548\) −57.8615 −2.47172
\(549\) 10.5081 0.448476
\(550\) 13.6769 0.583184
\(551\) 38.8094 1.65334
\(552\) −122.994 −5.23497
\(553\) −17.6144 −0.749041
\(554\) −34.2587 −1.45551
\(555\) 1.93934 0.0823206
\(556\) 25.5408 1.08317
\(557\) −22.7118 −0.962331 −0.481166 0.876630i \(-0.659786\pi\)
−0.481166 + 0.876630i \(0.659786\pi\)
\(558\) 42.7515 1.80981
\(559\) −0.268212 −0.0113442
\(560\) 135.497 5.72578
\(561\) −45.2570 −1.91075
\(562\) −31.4476 −1.32654
\(563\) 12.9127 0.544206 0.272103 0.962268i \(-0.412281\pi\)
0.272103 + 0.962268i \(0.412281\pi\)
\(564\) 54.4943 2.29462
\(565\) 12.7867 0.537939
\(566\) 69.3151 2.91353
\(567\) 24.2294 1.01754
\(568\) −133.068 −5.58342
\(569\) −10.2081 −0.427945 −0.213973 0.976840i \(-0.568640\pi\)
−0.213973 + 0.976840i \(0.568640\pi\)
\(570\) 52.8990 2.21570
\(571\) −22.7597 −0.952462 −0.476231 0.879320i \(-0.657997\pi\)
−0.476231 + 0.879320i \(0.657997\pi\)
\(572\) −0.874261 −0.0365547
\(573\) 6.05046 0.252762
\(574\) 30.6987 1.28134
\(575\) 5.40583 0.225439
\(576\) 103.061 4.29419
\(577\) 3.75852 0.156469 0.0782347 0.996935i \(-0.475072\pi\)
0.0782347 + 0.996935i \(0.475072\pi\)
\(578\) 10.9450 0.455253
\(579\) 5.65142 0.234865
\(580\) 111.279 4.62061
\(581\) −57.9250 −2.40313
\(582\) 130.599 5.41351
\(583\) −59.9126 −2.48133
\(584\) 88.0095 3.64186
\(585\) 0.272779 0.0112780
\(586\) 4.67207 0.193002
\(587\) −5.02212 −0.207285 −0.103642 0.994615i \(-0.533050\pi\)
−0.103642 + 0.994615i \(0.533050\pi\)
\(588\) −236.576 −9.75625
\(589\) 14.6058 0.601823
\(590\) −9.31386 −0.383445
\(591\) −9.00727 −0.370510
\(592\) 5.18172 0.212968
\(593\) 6.96580 0.286051 0.143026 0.989719i \(-0.454317\pi\)
0.143026 + 0.989719i \(0.454317\pi\)
\(594\) 34.2380 1.40480
\(595\) 34.7675 1.42533
\(596\) −99.4896 −4.07525
\(597\) 45.3640 1.85663
\(598\) −0.474427 −0.0194008
\(599\) 27.3644 1.11808 0.559040 0.829141i \(-0.311170\pi\)
0.559040 + 0.829141i \(0.311170\pi\)
\(600\) −25.6298 −1.04633
\(601\) −4.02471 −0.164171 −0.0820857 0.996625i \(-0.526158\pi\)
−0.0820857 + 0.996625i \(0.526158\pi\)
\(602\) 103.143 4.20380
\(603\) 37.7474 1.53719
\(604\) 78.6291 3.19937
\(605\) −22.9288 −0.932189
\(606\) −113.961 −4.62936
\(607\) 36.7703 1.49246 0.746230 0.665688i \(-0.231862\pi\)
0.746230 + 0.665688i \(0.231862\pi\)
\(608\) 73.6037 2.98502
\(609\) −134.622 −5.45517
\(610\) 14.1328 0.572222
\(611\) 0.131808 0.00533239
\(612\) 77.3185 3.12542
\(613\) −6.94466 −0.280492 −0.140246 0.990117i \(-0.544789\pi\)
−0.140246 + 0.990117i \(0.544789\pi\)
\(614\) 40.6473 1.64039
\(615\) 12.2139 0.492512
\(616\) 210.819 8.49413
\(617\) −1.46402 −0.0589392 −0.0294696 0.999566i \(-0.509382\pi\)
−0.0294696 + 0.999566i \(0.509382\pi\)
\(618\) 63.1912 2.54192
\(619\) 13.4341 0.539961 0.269980 0.962866i \(-0.412983\pi\)
0.269980 + 0.962866i \(0.412983\pi\)
\(620\) 41.8796 1.68192
\(621\) 13.5327 0.543047
\(622\) 82.4217 3.30481
\(623\) −14.7571 −0.591231
\(624\) 1.27492 0.0510378
\(625\) −18.5667 −0.742669
\(626\) −24.3245 −0.972204
\(627\) 46.6509 1.86306
\(628\) 0.916684 0.0365797
\(629\) 1.32959 0.0530144
\(630\) −104.899 −4.17929
\(631\) −6.97152 −0.277532 −0.138766 0.990325i \(-0.544314\pi\)
−0.138766 + 0.990325i \(0.544314\pi\)
\(632\) −33.0361 −1.31410
\(633\) −74.1657 −2.94782
\(634\) 29.4623 1.17010
\(635\) −40.0054 −1.58757
\(636\) 179.048 7.09972
\(637\) −0.572220 −0.0226722
\(638\) 134.735 5.33419
\(639\) 58.3917 2.30994
\(640\) 59.9027 2.36786
\(641\) −6.22642 −0.245929 −0.122964 0.992411i \(-0.539240\pi\)
−0.122964 + 0.992411i \(0.539240\pi\)
\(642\) −111.590 −4.40412
\(643\) 24.6830 0.973401 0.486701 0.873569i \(-0.338200\pi\)
0.486701 + 0.873569i \(0.338200\pi\)
\(644\) 132.886 5.23643
\(645\) 41.0369 1.61582
\(646\) 36.2670 1.42691
\(647\) 20.1731 0.793088 0.396544 0.918016i \(-0.370209\pi\)
0.396544 + 0.918016i \(0.370209\pi\)
\(648\) 45.4425 1.78515
\(649\) −8.21377 −0.322419
\(650\) −0.0988622 −0.00387770
\(651\) −50.6648 −1.98571
\(652\) 15.7875 0.618287
\(653\) −26.2964 −1.02906 −0.514529 0.857473i \(-0.672033\pi\)
−0.514529 + 0.857473i \(0.672033\pi\)
\(654\) 62.0932 2.42804
\(655\) −28.7889 −1.12488
\(656\) 32.6342 1.27415
\(657\) −38.6194 −1.50669
\(658\) −50.6879 −1.97602
\(659\) −33.5966 −1.30874 −0.654369 0.756176i \(-0.727066\pi\)
−0.654369 + 0.756176i \(0.727066\pi\)
\(660\) 133.763 5.20672
\(661\) 43.8683 1.70628 0.853140 0.521683i \(-0.174695\pi\)
0.853140 + 0.521683i \(0.174695\pi\)
\(662\) −75.4291 −2.93164
\(663\) 0.327137 0.0127049
\(664\) −108.639 −4.21601
\(665\) −35.8384 −1.38975
\(666\) −4.01161 −0.155447
\(667\) 53.2543 2.06201
\(668\) 90.6858 3.50874
\(669\) 45.6159 1.76361
\(670\) 50.7682 1.96135
\(671\) 12.4636 0.481151
\(672\) −255.317 −9.84905
\(673\) 28.8287 1.11126 0.555631 0.831429i \(-0.312477\pi\)
0.555631 + 0.831429i \(0.312477\pi\)
\(674\) −14.1230 −0.543998
\(675\) 2.81997 0.108541
\(676\) −69.7092 −2.68112
\(677\) −0.337843 −0.0129844 −0.00649218 0.999979i \(-0.502067\pi\)
−0.00649218 + 0.999979i \(0.502067\pi\)
\(678\) −46.2673 −1.77689
\(679\) −88.4792 −3.39552
\(680\) 65.2070 2.50057
\(681\) −7.84057 −0.300451
\(682\) 50.7070 1.94167
\(683\) −7.15032 −0.273600 −0.136800 0.990599i \(-0.543682\pi\)
−0.136800 + 0.990599i \(0.543682\pi\)
\(684\) −79.6999 −3.04740
\(685\) 21.4130 0.818147
\(686\) 127.644 4.87347
\(687\) −19.0953 −0.728531
\(688\) 109.646 4.18022
\(689\) 0.433073 0.0164988
\(690\) 72.5880 2.76338
\(691\) −41.9893 −1.59735 −0.798674 0.601764i \(-0.794465\pi\)
−0.798674 + 0.601764i \(0.794465\pi\)
\(692\) 104.469 3.97131
\(693\) −92.5094 −3.51414
\(694\) −51.7299 −1.96364
\(695\) −9.45195 −0.358533
\(696\) −252.486 −9.57045
\(697\) 8.37372 0.317177
\(698\) −70.3550 −2.66297
\(699\) −29.3021 −1.10831
\(700\) 27.6910 1.04662
\(701\) 22.9393 0.866407 0.433203 0.901296i \(-0.357383\pi\)
0.433203 + 0.901296i \(0.357383\pi\)
\(702\) −0.247486 −0.00934077
\(703\) −1.37055 −0.0516911
\(704\) 122.239 4.60706
\(705\) −20.1669 −0.759528
\(706\) 32.7506 1.23258
\(707\) 77.2072 2.90368
\(708\) 24.5468 0.922524
\(709\) −20.3350 −0.763697 −0.381849 0.924225i \(-0.624712\pi\)
−0.381849 + 0.924225i \(0.624712\pi\)
\(710\) 78.5336 2.94732
\(711\) 14.4966 0.543664
\(712\) −27.6772 −1.03725
\(713\) 20.0421 0.750583
\(714\) −125.803 −4.70807
\(715\) 0.323540 0.0120997
\(716\) −31.9294 −1.19326
\(717\) −24.7047 −0.922614
\(718\) 57.6479 2.15140
\(719\) −0.890809 −0.0332216 −0.0166108 0.999862i \(-0.505288\pi\)
−0.0166108 + 0.999862i \(0.505288\pi\)
\(720\) −111.513 −4.15585
\(721\) −42.8112 −1.59437
\(722\) 14.1712 0.527399
\(723\) 30.4235 1.13146
\(724\) 25.2864 0.939763
\(725\) 11.0972 0.412142
\(726\) 82.9659 3.07915
\(727\) −10.1021 −0.374666 −0.187333 0.982296i \(-0.559984\pi\)
−0.187333 + 0.982296i \(0.559984\pi\)
\(728\) −1.52389 −0.0564790
\(729\) −41.0354 −1.51983
\(730\) −51.9410 −1.92242
\(731\) 28.1344 1.04059
\(732\) −37.2472 −1.37670
\(733\) 3.04749 0.112561 0.0562807 0.998415i \(-0.482076\pi\)
0.0562807 + 0.998415i \(0.482076\pi\)
\(734\) 23.9837 0.885255
\(735\) 87.5505 3.22935
\(736\) 100.999 3.72287
\(737\) 44.7718 1.64919
\(738\) −25.2649 −0.930014
\(739\) 21.4491 0.789019 0.394510 0.918892i \(-0.370914\pi\)
0.394510 + 0.918892i \(0.370914\pi\)
\(740\) −3.92979 −0.144462
\(741\) −0.337213 −0.0123878
\(742\) −166.542 −6.11394
\(743\) −28.0663 −1.02965 −0.514826 0.857295i \(-0.672143\pi\)
−0.514826 + 0.857295i \(0.672143\pi\)
\(744\) −95.0225 −3.48369
\(745\) 36.8184 1.34892
\(746\) 22.2298 0.813891
\(747\) 47.6719 1.74422
\(748\) 91.7067 3.35313
\(749\) 75.6009 2.76240
\(750\) 86.3842 3.15430
\(751\) −27.7716 −1.01340 −0.506700 0.862122i \(-0.669135\pi\)
−0.506700 + 0.862122i \(0.669135\pi\)
\(752\) −53.8837 −1.96494
\(753\) −15.0925 −0.550002
\(754\) −0.973918 −0.0354680
\(755\) −29.0985 −1.05900
\(756\) 69.3203 2.52115
\(757\) −6.74776 −0.245251 −0.122626 0.992453i \(-0.539131\pi\)
−0.122626 + 0.992453i \(0.539131\pi\)
\(758\) 2.93346 0.106548
\(759\) 64.0144 2.32358
\(760\) −67.2153 −2.43816
\(761\) 32.2845 1.17031 0.585156 0.810920i \(-0.301033\pi\)
0.585156 + 0.810920i \(0.301033\pi\)
\(762\) 144.756 5.24396
\(763\) −42.0673 −1.52294
\(764\) −12.2604 −0.443564
\(765\) −28.6135 −1.03452
\(766\) −91.6144 −3.31016
\(767\) 0.0593726 0.00214382
\(768\) −80.5122 −2.90523
\(769\) 41.6877 1.50330 0.751649 0.659563i \(-0.229259\pi\)
0.751649 + 0.659563i \(0.229259\pi\)
\(770\) −124.420 −4.48378
\(771\) −2.36054 −0.0850128
\(772\) −11.4518 −0.412158
\(773\) −14.6025 −0.525217 −0.262608 0.964903i \(-0.584583\pi\)
−0.262608 + 0.964903i \(0.584583\pi\)
\(774\) −84.8862 −3.05117
\(775\) 4.17643 0.150022
\(776\) −165.944 −5.95704
\(777\) 4.75415 0.170554
\(778\) −35.0789 −1.25764
\(779\) −8.63163 −0.309260
\(780\) −0.966897 −0.0346204
\(781\) 69.2578 2.47824
\(782\) 49.7656 1.77961
\(783\) 27.7803 0.992786
\(784\) 233.926 8.35449
\(785\) −0.339240 −0.0121080
\(786\) 104.170 3.71562
\(787\) 42.2699 1.50676 0.753379 0.657587i \(-0.228423\pi\)
0.753379 + 0.657587i \(0.228423\pi\)
\(788\) 18.2519 0.650197
\(789\) 39.8322 1.41806
\(790\) 19.4971 0.693675
\(791\) 31.3455 1.11452
\(792\) −173.503 −6.16515
\(793\) −0.0900919 −0.00319926
\(794\) −79.5845 −2.82435
\(795\) −66.2609 −2.35003
\(796\) −91.9235 −3.25814
\(797\) −33.8714 −1.19979 −0.599894 0.800080i \(-0.704791\pi\)
−0.599894 + 0.800080i \(0.704791\pi\)
\(798\) 129.678 4.59055
\(799\) −13.8262 −0.489136
\(800\) 21.0464 0.744103
\(801\) 12.1450 0.429123
\(802\) 45.0783 1.59177
\(803\) −45.8061 −1.61646
\(804\) −133.800 −4.71876
\(805\) −49.1774 −1.73328
\(806\) −0.366532 −0.0129105
\(807\) −0.352099 −0.0123945
\(808\) 144.803 5.09416
\(809\) −27.9630 −0.983128 −0.491564 0.870842i \(-0.663575\pi\)
−0.491564 + 0.870842i \(0.663575\pi\)
\(810\) −26.8191 −0.942325
\(811\) −40.0624 −1.40678 −0.703390 0.710804i \(-0.748331\pi\)
−0.703390 + 0.710804i \(0.748331\pi\)
\(812\) 272.792 9.57312
\(813\) −28.8965 −1.01344
\(814\) −4.75812 −0.166772
\(815\) −5.84253 −0.204655
\(816\) −133.735 −4.68165
\(817\) −29.0010 −1.01462
\(818\) 15.8853 0.555417
\(819\) 0.668697 0.0233661
\(820\) −24.7496 −0.864295
\(821\) 53.0461 1.85132 0.925661 0.378353i \(-0.123510\pi\)
0.925661 + 0.378353i \(0.123510\pi\)
\(822\) −77.4809 −2.70246
\(823\) −13.2914 −0.463308 −0.231654 0.972798i \(-0.574414\pi\)
−0.231654 + 0.972798i \(0.574414\pi\)
\(824\) −80.2929 −2.79714
\(825\) 13.3395 0.464421
\(826\) −22.8322 −0.794434
\(827\) 38.3575 1.33382 0.666910 0.745138i \(-0.267616\pi\)
0.666910 + 0.745138i \(0.267616\pi\)
\(828\) −109.364 −3.80067
\(829\) −39.3863 −1.36794 −0.683972 0.729509i \(-0.739749\pi\)
−0.683972 + 0.729509i \(0.739749\pi\)
\(830\) 64.1161 2.22550
\(831\) −33.4135 −1.15910
\(832\) −0.883595 −0.0306332
\(833\) 60.0237 2.07970
\(834\) 34.2010 1.18428
\(835\) −33.5604 −1.16140
\(836\) −94.5312 −3.26943
\(837\) 10.4550 0.361379
\(838\) −30.1386 −1.04112
\(839\) 43.9661 1.51788 0.758939 0.651162i \(-0.225718\pi\)
0.758939 + 0.651162i \(0.225718\pi\)
\(840\) 233.157 8.04467
\(841\) 80.3219 2.76972
\(842\) −1.99153 −0.0686327
\(843\) −30.6718 −1.05639
\(844\) 150.286 5.17305
\(845\) 25.7975 0.887460
\(846\) 41.7159 1.43422
\(847\) −56.2083 −1.93134
\(848\) −177.042 −6.07965
\(849\) 67.6051 2.32020
\(850\) 10.3703 0.355698
\(851\) −1.88066 −0.0644683
\(852\) −206.976 −7.09089
\(853\) 19.5038 0.667798 0.333899 0.942609i \(-0.391636\pi\)
0.333899 + 0.942609i \(0.391636\pi\)
\(854\) 34.6456 1.18555
\(855\) 29.4948 1.00870
\(856\) 141.791 4.84630
\(857\) −1.14295 −0.0390423 −0.0195211 0.999809i \(-0.506214\pi\)
−0.0195211 + 0.999809i \(0.506214\pi\)
\(858\) −1.17070 −0.0399671
\(859\) −41.5952 −1.41921 −0.709605 0.704599i \(-0.751127\pi\)
−0.709605 + 0.704599i \(0.751127\pi\)
\(860\) −83.1551 −2.83556
\(861\) 29.9414 1.02040
\(862\) −59.8239 −2.03761
\(863\) −0.738241 −0.0251300 −0.0125650 0.999921i \(-0.504000\pi\)
−0.0125650 + 0.999921i \(0.504000\pi\)
\(864\) 52.6864 1.79243
\(865\) −38.6610 −1.31452
\(866\) −48.0236 −1.63191
\(867\) 10.6750 0.362542
\(868\) 102.665 3.48466
\(869\) 17.1942 0.583274
\(870\) 149.011 5.05194
\(871\) −0.323629 −0.0109658
\(872\) −78.8978 −2.67182
\(873\) 72.8179 2.46451
\(874\) −51.2984 −1.73519
\(875\) −58.5241 −1.97848
\(876\) 136.891 4.62512
\(877\) −51.8481 −1.75079 −0.875393 0.483413i \(-0.839397\pi\)
−0.875393 + 0.483413i \(0.839397\pi\)
\(878\) −52.3357 −1.76624
\(879\) 4.55682 0.153698
\(880\) −132.264 −4.45863
\(881\) −56.1590 −1.89204 −0.946022 0.324103i \(-0.894938\pi\)
−0.946022 + 0.324103i \(0.894938\pi\)
\(882\) −181.101 −6.09800
\(883\) −36.9204 −1.24247 −0.621236 0.783624i \(-0.713369\pi\)
−0.621236 + 0.783624i \(0.713369\pi\)
\(884\) −0.662894 −0.0222956
\(885\) −9.08409 −0.305358
\(886\) 57.1344 1.91947
\(887\) 29.7015 0.997277 0.498639 0.866810i \(-0.333833\pi\)
0.498639 + 0.866810i \(0.333833\pi\)
\(888\) 8.91648 0.299218
\(889\) −98.0702 −3.28917
\(890\) 16.3344 0.547530
\(891\) −23.6514 −0.792351
\(892\) −92.4337 −3.09491
\(893\) 14.2520 0.476926
\(894\) −133.224 −4.45568
\(895\) 11.8162 0.394972
\(896\) 146.847 4.90581
\(897\) −0.462723 −0.0154499
\(898\) 16.0441 0.535398
\(899\) 41.1431 1.37220
\(900\) −22.7896 −0.759653
\(901\) −45.4278 −1.51342
\(902\) −29.9664 −0.997772
\(903\) 100.599 3.34771
\(904\) 58.7889 1.95529
\(905\) −9.35782 −0.311064
\(906\) 105.290 3.49803
\(907\) −34.3483 −1.14052 −0.570259 0.821465i \(-0.693157\pi\)
−0.570259 + 0.821465i \(0.693157\pi\)
\(908\) 15.8877 0.527253
\(909\) −63.5411 −2.10752
\(910\) 0.899360 0.0298135
\(911\) −47.1301 −1.56149 −0.780745 0.624850i \(-0.785160\pi\)
−0.780745 + 0.624850i \(0.785160\pi\)
\(912\) 137.854 4.56480
\(913\) 56.5431 1.87130
\(914\) 17.0512 0.564004
\(915\) 13.7842 0.455691
\(916\) 38.6937 1.27848
\(917\) −70.5738 −2.33055
\(918\) 25.9604 0.856821
\(919\) −16.1997 −0.534380 −0.267190 0.963644i \(-0.586095\pi\)
−0.267190 + 0.963644i \(0.586095\pi\)
\(920\) −92.2329 −3.04083
\(921\) 39.6445 1.30633
\(922\) 41.4810 1.36610
\(923\) −0.500625 −0.0164783
\(924\) 327.910 10.7875
\(925\) −0.391897 −0.0128855
\(926\) 27.5817 0.906390
\(927\) 35.2333 1.15721
\(928\) 207.334 6.80606
\(929\) 39.8133 1.30623 0.653117 0.757257i \(-0.273461\pi\)
0.653117 + 0.757257i \(0.273461\pi\)
\(930\) 56.0799 1.83893
\(931\) −61.8725 −2.02779
\(932\) 59.3763 1.94494
\(933\) 80.3884 2.63180
\(934\) −28.1941 −0.922539
\(935\) −33.9381 −1.10990
\(936\) 1.25415 0.0409932
\(937\) 29.4900 0.963397 0.481699 0.876337i \(-0.340020\pi\)
0.481699 + 0.876337i \(0.340020\pi\)
\(938\) 124.454 4.06357
\(939\) −23.7245 −0.774219
\(940\) 40.8651 1.33287
\(941\) −52.2897 −1.70459 −0.852297 0.523058i \(-0.824791\pi\)
−0.852297 + 0.523058i \(0.824791\pi\)
\(942\) 1.22751 0.0399944
\(943\) −11.8443 −0.385704
\(944\) −24.2717 −0.789978
\(945\) −25.6536 −0.834510
\(946\) −100.683 −3.27347
\(947\) 26.2321 0.852429 0.426215 0.904622i \(-0.359847\pi\)
0.426215 + 0.904622i \(0.359847\pi\)
\(948\) −51.3847 −1.66890
\(949\) 0.331106 0.0107481
\(950\) −10.6897 −0.346819
\(951\) 28.7355 0.931811
\(952\) 159.850 5.18077
\(953\) −21.9584 −0.711302 −0.355651 0.934619i \(-0.615741\pi\)
−0.355651 + 0.934619i \(0.615741\pi\)
\(954\) 137.063 4.43758
\(955\) 4.53723 0.146821
\(956\) 50.0604 1.61907
\(957\) 131.411 4.24791
\(958\) 100.463 3.24580
\(959\) 52.4922 1.69506
\(960\) 135.191 4.36328
\(961\) −15.5159 −0.500513
\(962\) 0.0343937 0.00110890
\(963\) −62.2191 −2.00498
\(964\) −61.6486 −1.98557
\(965\) 4.23798 0.136426
\(966\) 177.944 5.72525
\(967\) −36.9220 −1.18733 −0.593665 0.804712i \(-0.702320\pi\)
−0.593665 + 0.804712i \(0.702320\pi\)
\(968\) −105.419 −3.38831
\(969\) 35.3723 1.13632
\(970\) 97.9360 3.14453
\(971\) −19.5418 −0.627127 −0.313564 0.949567i \(-0.601523\pi\)
−0.313564 + 0.949567i \(0.601523\pi\)
\(972\) 113.427 3.63818
\(973\) −23.1707 −0.742819
\(974\) 82.3694 2.63929
\(975\) −0.0964234 −0.00308802
\(976\) 36.8299 1.17890
\(977\) −20.2680 −0.648429 −0.324215 0.945984i \(-0.605100\pi\)
−0.324215 + 0.945984i \(0.605100\pi\)
\(978\) 21.1407 0.676004
\(979\) 14.4051 0.460388
\(980\) −177.408 −5.66709
\(981\) 34.6211 1.10537
\(982\) 104.149 3.32354
\(983\) 53.4834 1.70586 0.852928 0.522028i \(-0.174825\pi\)
0.852928 + 0.522028i \(0.174825\pi\)
\(984\) 56.1556 1.79017
\(985\) −6.75453 −0.215217
\(986\) 102.160 3.25345
\(987\) −49.4375 −1.57361
\(988\) 0.683311 0.0217390
\(989\) −39.7951 −1.26541
\(990\) 102.397 3.25439
\(991\) 34.3746 1.09194 0.545972 0.837803i \(-0.316160\pi\)
0.545972 + 0.837803i \(0.316160\pi\)
\(992\) 78.0296 2.47744
\(993\) −73.5684 −2.33462
\(994\) 192.519 6.10634
\(995\) 34.0184 1.07846
\(996\) −168.979 −5.35429
\(997\) −16.2246 −0.513838 −0.256919 0.966433i \(-0.582707\pi\)
−0.256919 + 0.966433i \(0.582707\pi\)
\(998\) −44.8614 −1.42006
\(999\) −0.981054 −0.0310392
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 \(a_p\))