Properties

Label 8018.2.a.d.1.2
Level 8018
Weight 2
Character 8018.1
Self dual Yes
Analytic conductor 64.024
Analytic rank 1
Dimension 30
CM No

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Newspace parameters

Level: \( N \) = \( 8018 = 2 \cdot 19 \cdot 211 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8018.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0240523407\)
Analytic rank: \(1\)
Dimension: \(30\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Character \(\chi\) = 8018.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} -3.09428 q^{3} +1.00000 q^{4} +2.68879 q^{5} -3.09428 q^{6} +2.69798 q^{7} +1.00000 q^{8} +6.57455 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -3.09428 q^{3} +1.00000 q^{4} +2.68879 q^{5} -3.09428 q^{6} +2.69798 q^{7} +1.00000 q^{8} +6.57455 q^{9} +2.68879 q^{10} -5.80467 q^{11} -3.09428 q^{12} -1.02008 q^{13} +2.69798 q^{14} -8.31986 q^{15} +1.00000 q^{16} -5.21133 q^{17} +6.57455 q^{18} +1.00000 q^{19} +2.68879 q^{20} -8.34831 q^{21} -5.80467 q^{22} +4.91566 q^{23} -3.09428 q^{24} +2.22960 q^{25} -1.02008 q^{26} -11.0607 q^{27} +2.69798 q^{28} +3.23208 q^{29} -8.31986 q^{30} +6.99206 q^{31} +1.00000 q^{32} +17.9613 q^{33} -5.21133 q^{34} +7.25432 q^{35} +6.57455 q^{36} -9.62772 q^{37} +1.00000 q^{38} +3.15640 q^{39} +2.68879 q^{40} -5.63748 q^{41} -8.34831 q^{42} -4.61898 q^{43} -5.80467 q^{44} +17.6776 q^{45} +4.91566 q^{46} -2.14466 q^{47} -3.09428 q^{48} +0.279119 q^{49} +2.22960 q^{50} +16.1253 q^{51} -1.02008 q^{52} -10.0456 q^{53} -11.0607 q^{54} -15.6075 q^{55} +2.69798 q^{56} -3.09428 q^{57} +3.23208 q^{58} +5.68410 q^{59} -8.31986 q^{60} -8.48789 q^{61} +6.99206 q^{62} +17.7380 q^{63} +1.00000 q^{64} -2.74277 q^{65} +17.9613 q^{66} -4.70299 q^{67} -5.21133 q^{68} -15.2104 q^{69} +7.25432 q^{70} +6.37379 q^{71} +6.57455 q^{72} -12.3353 q^{73} -9.62772 q^{74} -6.89899 q^{75} +1.00000 q^{76} -15.6609 q^{77} +3.15640 q^{78} +2.49251 q^{79} +2.68879 q^{80} +14.5011 q^{81} -5.63748 q^{82} -6.10451 q^{83} -8.34831 q^{84} -14.0122 q^{85} -4.61898 q^{86} -10.0009 q^{87} -5.80467 q^{88} -2.99680 q^{89} +17.6776 q^{90} -2.75215 q^{91} +4.91566 q^{92} -21.6354 q^{93} -2.14466 q^{94} +2.68879 q^{95} -3.09428 q^{96} +4.49014 q^{97} +0.279119 q^{98} -38.1631 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 30q + 30q^{2} - 10q^{3} + 30q^{4} - 12q^{5} - 10q^{6} - 15q^{7} + 30q^{8} + 10q^{9} + O(q^{10}) \) \( 30q + 30q^{2} - 10q^{3} + 30q^{4} - 12q^{5} - 10q^{6} - 15q^{7} + 30q^{8} + 10q^{9} - 12q^{10} - 17q^{11} - 10q^{12} - 19q^{13} - 15q^{14} - 8q^{15} + 30q^{16} - 18q^{17} + 10q^{18} + 30q^{19} - 12q^{20} - 14q^{21} - 17q^{22} - 15q^{23} - 10q^{24} - 4q^{25} - 19q^{26} - 37q^{27} - 15q^{28} - 37q^{29} - 8q^{30} - 11q^{31} + 30q^{32} + 6q^{33} - 18q^{34} - 4q^{35} + 10q^{36} - 46q^{37} + 30q^{38} - 12q^{40} - 28q^{41} - 14q^{42} - 61q^{43} - 17q^{44} - 14q^{45} - 15q^{46} - 4q^{47} - 10q^{48} - q^{49} - 4q^{50} - 8q^{51} - 19q^{52} - 19q^{53} - 37q^{54} - 17q^{55} - 15q^{56} - 10q^{57} - 37q^{58} - 6q^{59} - 8q^{60} - 32q^{61} - 11q^{62} - 24q^{63} + 30q^{64} - 24q^{65} + 6q^{66} - 44q^{67} - 18q^{68} - 2q^{69} - 4q^{70} + 10q^{71} + 10q^{72} - 58q^{73} - 46q^{74} - 42q^{75} + 30q^{76} - 32q^{77} - 42q^{79} - 12q^{80} - 38q^{81} - 28q^{82} - 25q^{83} - 14q^{84} - 48q^{85} - 61q^{86} - 15q^{87} - 17q^{88} - 39q^{89} - 14q^{90} - 21q^{91} - 15q^{92} - 45q^{93} - 4q^{94} - 12q^{95} - 10q^{96} - 33q^{97} - q^{98} - 38q^{99} + O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) −3.09428 −1.78648 −0.893241 0.449578i \(-0.851574\pi\)
−0.893241 + 0.449578i \(0.851574\pi\)
\(4\) 1.00000 0.500000
\(5\) 2.68879 1.20246 0.601232 0.799075i \(-0.294677\pi\)
0.601232 + 0.799075i \(0.294677\pi\)
\(6\) −3.09428 −1.26323
\(7\) 2.69798 1.01974 0.509871 0.860251i \(-0.329693\pi\)
0.509871 + 0.860251i \(0.329693\pi\)
\(8\) 1.00000 0.353553
\(9\) 6.57455 2.19152
\(10\) 2.68879 0.850270
\(11\) −5.80467 −1.75017 −0.875087 0.483965i \(-0.839196\pi\)
−0.875087 + 0.483965i \(0.839196\pi\)
\(12\) −3.09428 −0.893241
\(13\) −1.02008 −0.282918 −0.141459 0.989944i \(-0.545179\pi\)
−0.141459 + 0.989944i \(0.545179\pi\)
\(14\) 2.69798 0.721067
\(15\) −8.31986 −2.14818
\(16\) 1.00000 0.250000
\(17\) −5.21133 −1.26393 −0.631967 0.774996i \(-0.717752\pi\)
−0.631967 + 0.774996i \(0.717752\pi\)
\(18\) 6.57455 1.54964
\(19\) 1.00000 0.229416
\(20\) 2.68879 0.601232
\(21\) −8.34831 −1.82175
\(22\) −5.80467 −1.23756
\(23\) 4.91566 1.02499 0.512493 0.858691i \(-0.328722\pi\)
0.512493 + 0.858691i \(0.328722\pi\)
\(24\) −3.09428 −0.631617
\(25\) 2.22960 0.445919
\(26\) −1.02008 −0.200054
\(27\) −11.0607 −2.12862
\(28\) 2.69798 0.509871
\(29\) 3.23208 0.600182 0.300091 0.953911i \(-0.402983\pi\)
0.300091 + 0.953911i \(0.402983\pi\)
\(30\) −8.31986 −1.51899
\(31\) 6.99206 1.25581 0.627905 0.778290i \(-0.283913\pi\)
0.627905 + 0.778290i \(0.283913\pi\)
\(32\) 1.00000 0.176777
\(33\) 17.9613 3.12666
\(34\) −5.21133 −0.893736
\(35\) 7.25432 1.22620
\(36\) 6.57455 1.09576
\(37\) −9.62772 −1.58279 −0.791394 0.611307i \(-0.790644\pi\)
−0.791394 + 0.611307i \(0.790644\pi\)
\(38\) 1.00000 0.162221
\(39\) 3.15640 0.505429
\(40\) 2.68879 0.425135
\(41\) −5.63748 −0.880427 −0.440214 0.897893i \(-0.645097\pi\)
−0.440214 + 0.897893i \(0.645097\pi\)
\(42\) −8.34831 −1.28817
\(43\) −4.61898 −0.704388 −0.352194 0.935927i \(-0.614564\pi\)
−0.352194 + 0.935927i \(0.614564\pi\)
\(44\) −5.80467 −0.875087
\(45\) 17.6776 2.63522
\(46\) 4.91566 0.724775
\(47\) −2.14466 −0.312831 −0.156416 0.987691i \(-0.549994\pi\)
−0.156416 + 0.987691i \(0.549994\pi\)
\(48\) −3.09428 −0.446620
\(49\) 0.279119 0.0398741
\(50\) 2.22960 0.315312
\(51\) 16.1253 2.25799
\(52\) −1.02008 −0.141459
\(53\) −10.0456 −1.37986 −0.689932 0.723874i \(-0.742360\pi\)
−0.689932 + 0.723874i \(0.742360\pi\)
\(54\) −11.0607 −1.50516
\(55\) −15.6075 −2.10452
\(56\) 2.69798 0.360533
\(57\) −3.09428 −0.409847
\(58\) 3.23208 0.424393
\(59\) 5.68410 0.740007 0.370003 0.929030i \(-0.379357\pi\)
0.370003 + 0.929030i \(0.379357\pi\)
\(60\) −8.31986 −1.07409
\(61\) −8.48789 −1.08676 −0.543381 0.839486i \(-0.682856\pi\)
−0.543381 + 0.839486i \(0.682856\pi\)
\(62\) 6.99206 0.887992
\(63\) 17.7380 2.23478
\(64\) 1.00000 0.125000
\(65\) −2.74277 −0.340199
\(66\) 17.9613 2.21088
\(67\) −4.70299 −0.574562 −0.287281 0.957846i \(-0.592751\pi\)
−0.287281 + 0.957846i \(0.592751\pi\)
\(68\) −5.21133 −0.631967
\(69\) −15.2104 −1.83112
\(70\) 7.25432 0.867056
\(71\) 6.37379 0.756430 0.378215 0.925718i \(-0.376538\pi\)
0.378215 + 0.925718i \(0.376538\pi\)
\(72\) 6.57455 0.774818
\(73\) −12.3353 −1.44374 −0.721868 0.692031i \(-0.756716\pi\)
−0.721868 + 0.692031i \(0.756716\pi\)
\(74\) −9.62772 −1.11920
\(75\) −6.89899 −0.796627
\(76\) 1.00000 0.114708
\(77\) −15.6609 −1.78473
\(78\) 3.15640 0.357392
\(79\) 2.49251 0.280429 0.140214 0.990121i \(-0.455221\pi\)
0.140214 + 0.990121i \(0.455221\pi\)
\(80\) 2.68879 0.300616
\(81\) 14.5011 1.61123
\(82\) −5.63748 −0.622556
\(83\) −6.10451 −0.670057 −0.335028 0.942208i \(-0.608746\pi\)
−0.335028 + 0.942208i \(0.608746\pi\)
\(84\) −8.34831 −0.910875
\(85\) −14.0122 −1.51983
\(86\) −4.61898 −0.498078
\(87\) −10.0009 −1.07221
\(88\) −5.80467 −0.618780
\(89\) −2.99680 −0.317660 −0.158830 0.987306i \(-0.550772\pi\)
−0.158830 + 0.987306i \(0.550772\pi\)
\(90\) 17.6776 1.86338
\(91\) −2.75215 −0.288504
\(92\) 4.91566 0.512493
\(93\) −21.6354 −2.24348
\(94\) −2.14466 −0.221205
\(95\) 2.68879 0.275864
\(96\) −3.09428 −0.315808
\(97\) 4.49014 0.455904 0.227952 0.973672i \(-0.426797\pi\)
0.227952 + 0.973672i \(0.426797\pi\)
\(98\) 0.279119 0.0281953
\(99\) −38.1631 −3.83554
\(100\) 2.22960 0.222960
\(101\) 6.09662 0.606637 0.303318 0.952889i \(-0.401905\pi\)
0.303318 + 0.952889i \(0.401905\pi\)
\(102\) 16.1253 1.59664
\(103\) 2.01258 0.198306 0.0991529 0.995072i \(-0.468387\pi\)
0.0991529 + 0.995072i \(0.468387\pi\)
\(104\) −1.02008 −0.100027
\(105\) −22.4469 −2.19059
\(106\) −10.0456 −0.975711
\(107\) 2.95811 0.285971 0.142985 0.989725i \(-0.454330\pi\)
0.142985 + 0.989725i \(0.454330\pi\)
\(108\) −11.0607 −1.06431
\(109\) 12.9724 1.24253 0.621264 0.783601i \(-0.286619\pi\)
0.621264 + 0.783601i \(0.286619\pi\)
\(110\) −15.6075 −1.48812
\(111\) 29.7908 2.82762
\(112\) 2.69798 0.254936
\(113\) −11.0538 −1.03985 −0.519927 0.854211i \(-0.674041\pi\)
−0.519927 + 0.854211i \(0.674041\pi\)
\(114\) −3.09428 −0.289806
\(115\) 13.2172 1.23251
\(116\) 3.23208 0.300091
\(117\) −6.70655 −0.620021
\(118\) 5.68410 0.523264
\(119\) −14.0601 −1.28889
\(120\) −8.31986 −0.759496
\(121\) 22.6942 2.06311
\(122\) −8.48789 −0.768457
\(123\) 17.4439 1.57287
\(124\) 6.99206 0.627905
\(125\) −7.44904 −0.666262
\(126\) 17.7380 1.58023
\(127\) −6.99251 −0.620485 −0.310243 0.950657i \(-0.600410\pi\)
−0.310243 + 0.950657i \(0.600410\pi\)
\(128\) 1.00000 0.0883883
\(129\) 14.2924 1.25838
\(130\) −2.74277 −0.240557
\(131\) −21.2407 −1.85581 −0.927903 0.372821i \(-0.878391\pi\)
−0.927903 + 0.372821i \(0.878391\pi\)
\(132\) 17.9613 1.56333
\(133\) 2.69798 0.233945
\(134\) −4.70299 −0.406277
\(135\) −29.7398 −2.55959
\(136\) −5.21133 −0.446868
\(137\) 16.9283 1.44629 0.723143 0.690699i \(-0.242697\pi\)
0.723143 + 0.690699i \(0.242697\pi\)
\(138\) −15.2104 −1.29480
\(139\) 0.538672 0.0456896 0.0228448 0.999739i \(-0.492728\pi\)
0.0228448 + 0.999739i \(0.492728\pi\)
\(140\) 7.25432 0.613102
\(141\) 6.63618 0.558867
\(142\) 6.37379 0.534877
\(143\) 5.92121 0.495157
\(144\) 6.57455 0.547879
\(145\) 8.69038 0.721697
\(146\) −12.3353 −1.02088
\(147\) −0.863671 −0.0712344
\(148\) −9.62772 −0.791394
\(149\) −22.0651 −1.80764 −0.903821 0.427910i \(-0.859250\pi\)
−0.903821 + 0.427910i \(0.859250\pi\)
\(150\) −6.89899 −0.563300
\(151\) 11.2101 0.912263 0.456131 0.889912i \(-0.349235\pi\)
0.456131 + 0.889912i \(0.349235\pi\)
\(152\) 1.00000 0.0811107
\(153\) −34.2622 −2.76993
\(154\) −15.6609 −1.26199
\(155\) 18.8002 1.51007
\(156\) 3.15640 0.252714
\(157\) −3.27420 −0.261309 −0.130655 0.991428i \(-0.541708\pi\)
−0.130655 + 0.991428i \(0.541708\pi\)
\(158\) 2.49251 0.198293
\(159\) 31.0838 2.46510
\(160\) 2.68879 0.212568
\(161\) 13.2624 1.04522
\(162\) 14.5011 1.13931
\(163\) −21.6594 −1.69649 −0.848247 0.529601i \(-0.822342\pi\)
−0.848247 + 0.529601i \(0.822342\pi\)
\(164\) −5.63748 −0.440214
\(165\) 48.2941 3.75969
\(166\) −6.10451 −0.473802
\(167\) 18.4021 1.42400 0.711998 0.702181i \(-0.247790\pi\)
0.711998 + 0.702181i \(0.247790\pi\)
\(168\) −8.34831 −0.644086
\(169\) −11.9594 −0.919957
\(170\) −14.0122 −1.07468
\(171\) 6.57455 0.502769
\(172\) −4.61898 −0.352194
\(173\) 24.7440 1.88125 0.940625 0.339448i \(-0.110240\pi\)
0.940625 + 0.339448i \(0.110240\pi\)
\(174\) −10.0009 −0.758170
\(175\) 6.01541 0.454723
\(176\) −5.80467 −0.437544
\(177\) −17.5882 −1.32201
\(178\) −2.99680 −0.224620
\(179\) −23.0901 −1.72584 −0.862918 0.505343i \(-0.831366\pi\)
−0.862918 + 0.505343i \(0.831366\pi\)
\(180\) 17.6776 1.31761
\(181\) 5.37021 0.399165 0.199582 0.979881i \(-0.436041\pi\)
0.199582 + 0.979881i \(0.436041\pi\)
\(182\) −2.75215 −0.204003
\(183\) 26.2639 1.94148
\(184\) 4.91566 0.362387
\(185\) −25.8869 −1.90324
\(186\) −21.6354 −1.58638
\(187\) 30.2501 2.21210
\(188\) −2.14466 −0.156416
\(189\) −29.8415 −2.17065
\(190\) 2.68879 0.195065
\(191\) 3.26272 0.236082 0.118041 0.993009i \(-0.462339\pi\)
0.118041 + 0.993009i \(0.462339\pi\)
\(192\) −3.09428 −0.223310
\(193\) 5.16392 0.371707 0.185853 0.982577i \(-0.440495\pi\)
0.185853 + 0.982577i \(0.440495\pi\)
\(194\) 4.49014 0.322373
\(195\) 8.48690 0.607760
\(196\) 0.279119 0.0199371
\(197\) −1.77258 −0.126291 −0.0631455 0.998004i \(-0.520113\pi\)
−0.0631455 + 0.998004i \(0.520113\pi\)
\(198\) −38.1631 −2.71213
\(199\) 3.95646 0.280466 0.140233 0.990119i \(-0.455215\pi\)
0.140233 + 0.990119i \(0.455215\pi\)
\(200\) 2.22960 0.157656
\(201\) 14.5524 1.02644
\(202\) 6.09662 0.428957
\(203\) 8.72009 0.612031
\(204\) 16.1253 1.12900
\(205\) −15.1580 −1.05868
\(206\) 2.01258 0.140223
\(207\) 32.3183 2.24627
\(208\) −1.02008 −0.0707296
\(209\) −5.80467 −0.401518
\(210\) −22.4469 −1.54898
\(211\) −1.00000 −0.0688428
\(212\) −10.0456 −0.689932
\(213\) −19.7223 −1.35135
\(214\) 2.95811 0.202212
\(215\) −12.4195 −0.847001
\(216\) −11.0607 −0.752582
\(217\) 18.8645 1.28060
\(218\) 12.9724 0.878600
\(219\) 38.1688 2.57921
\(220\) −15.6075 −1.05226
\(221\) 5.31596 0.357590
\(222\) 29.7908 1.99943
\(223\) −11.7745 −0.788478 −0.394239 0.919008i \(-0.628992\pi\)
−0.394239 + 0.919008i \(0.628992\pi\)
\(224\) 2.69798 0.180267
\(225\) 14.6586 0.977240
\(226\) −11.0538 −0.735287
\(227\) 20.7359 1.37629 0.688145 0.725573i \(-0.258425\pi\)
0.688145 + 0.725573i \(0.258425\pi\)
\(228\) −3.09428 −0.204924
\(229\) −7.70226 −0.508979 −0.254490 0.967075i \(-0.581907\pi\)
−0.254490 + 0.967075i \(0.581907\pi\)
\(230\) 13.2172 0.871515
\(231\) 48.4592 3.18838
\(232\) 3.23208 0.212196
\(233\) −13.0991 −0.858148 −0.429074 0.903269i \(-0.641160\pi\)
−0.429074 + 0.903269i \(0.641160\pi\)
\(234\) −6.70655 −0.438421
\(235\) −5.76655 −0.376168
\(236\) 5.68410 0.370003
\(237\) −7.71250 −0.500981
\(238\) −14.0601 −0.911380
\(239\) 3.58986 0.232209 0.116104 0.993237i \(-0.462959\pi\)
0.116104 + 0.993237i \(0.462959\pi\)
\(240\) −8.31986 −0.537045
\(241\) −20.7327 −1.33551 −0.667756 0.744380i \(-0.732745\pi\)
−0.667756 + 0.744380i \(0.732745\pi\)
\(242\) 22.6942 1.45884
\(243\) −11.6884 −0.749811
\(244\) −8.48789 −0.543381
\(245\) 0.750492 0.0479472
\(246\) 17.4439 1.11219
\(247\) −1.02008 −0.0649059
\(248\) 6.99206 0.443996
\(249\) 18.8890 1.19704
\(250\) −7.44904 −0.471118
\(251\) 20.0261 1.26404 0.632018 0.774953i \(-0.282227\pi\)
0.632018 + 0.774953i \(0.282227\pi\)
\(252\) 17.7380 1.11739
\(253\) −28.5338 −1.79390
\(254\) −6.99251 −0.438749
\(255\) 43.3576 2.71516
\(256\) 1.00000 0.0625000
\(257\) −20.5611 −1.28257 −0.641283 0.767304i \(-0.721598\pi\)
−0.641283 + 0.767304i \(0.721598\pi\)
\(258\) 14.2924 0.889807
\(259\) −25.9754 −1.61403
\(260\) −2.74277 −0.170100
\(261\) 21.2495 1.31531
\(262\) −21.2407 −1.31225
\(263\) 18.8516 1.16244 0.581219 0.813747i \(-0.302576\pi\)
0.581219 + 0.813747i \(0.302576\pi\)
\(264\) 17.9613 1.10544
\(265\) −27.0104 −1.65924
\(266\) 2.69798 0.165424
\(267\) 9.27294 0.567495
\(268\) −4.70299 −0.287281
\(269\) 12.3597 0.753585 0.376792 0.926298i \(-0.377027\pi\)
0.376792 + 0.926298i \(0.377027\pi\)
\(270\) −29.7398 −1.80991
\(271\) −9.97986 −0.606233 −0.303117 0.952953i \(-0.598027\pi\)
−0.303117 + 0.952953i \(0.598027\pi\)
\(272\) −5.21133 −0.315983
\(273\) 8.51592 0.515407
\(274\) 16.9283 1.02268
\(275\) −12.9421 −0.780436
\(276\) −15.2104 −0.915560
\(277\) −16.2948 −0.979059 −0.489530 0.871987i \(-0.662832\pi\)
−0.489530 + 0.871987i \(0.662832\pi\)
\(278\) 0.538672 0.0323074
\(279\) 45.9696 2.75213
\(280\) 7.25432 0.433528
\(281\) 7.82076 0.466547 0.233274 0.972411i \(-0.425056\pi\)
0.233274 + 0.972411i \(0.425056\pi\)
\(282\) 6.63618 0.395179
\(283\) −16.2700 −0.967153 −0.483577 0.875302i \(-0.660663\pi\)
−0.483577 + 0.875302i \(0.660663\pi\)
\(284\) 6.37379 0.378215
\(285\) −8.31986 −0.492826
\(286\) 5.92121 0.350129
\(287\) −15.2098 −0.897809
\(288\) 6.57455 0.387409
\(289\) 10.1580 0.597527
\(290\) 8.69038 0.510317
\(291\) −13.8937 −0.814465
\(292\) −12.3353 −0.721868
\(293\) 4.48833 0.262211 0.131106 0.991368i \(-0.458147\pi\)
0.131106 + 0.991368i \(0.458147\pi\)
\(294\) −0.863671 −0.0503703
\(295\) 15.2834 0.889831
\(296\) −9.62772 −0.559600
\(297\) 64.2035 3.72546
\(298\) −22.0651 −1.27820
\(299\) −5.01435 −0.289987
\(300\) −6.89899 −0.398313
\(301\) −12.4619 −0.718294
\(302\) 11.2101 0.645067
\(303\) −18.8646 −1.08375
\(304\) 1.00000 0.0573539
\(305\) −22.8222 −1.30679
\(306\) −34.2622 −1.95864
\(307\) 11.5583 0.659666 0.329833 0.944039i \(-0.393008\pi\)
0.329833 + 0.944039i \(0.393008\pi\)
\(308\) −15.6609 −0.892363
\(309\) −6.22749 −0.354270
\(310\) 18.8002 1.06778
\(311\) 11.3152 0.641629 0.320814 0.947142i \(-0.396043\pi\)
0.320814 + 0.947142i \(0.396043\pi\)
\(312\) 3.15640 0.178696
\(313\) −22.1917 −1.25435 −0.627174 0.778879i \(-0.715789\pi\)
−0.627174 + 0.778879i \(0.715789\pi\)
\(314\) −3.27420 −0.184774
\(315\) 47.6939 2.68725
\(316\) 2.49251 0.140214
\(317\) 10.0320 0.563453 0.281726 0.959495i \(-0.409093\pi\)
0.281726 + 0.959495i \(0.409093\pi\)
\(318\) 31.0838 1.74309
\(319\) −18.7612 −1.05042
\(320\) 2.68879 0.150308
\(321\) −9.15320 −0.510882
\(322\) 13.2624 0.739083
\(323\) −5.21133 −0.289966
\(324\) 14.5011 0.805616
\(325\) −2.27436 −0.126159
\(326\) −21.6594 −1.19960
\(327\) −40.1401 −2.21975
\(328\) −5.63748 −0.311278
\(329\) −5.78627 −0.319007
\(330\) 48.2941 2.65850
\(331\) 6.12083 0.336431 0.168216 0.985750i \(-0.446200\pi\)
0.168216 + 0.985750i \(0.446200\pi\)
\(332\) −6.10451 −0.335028
\(333\) −63.2979 −3.46871
\(334\) 18.4021 1.00692
\(335\) −12.6454 −0.690890
\(336\) −8.34831 −0.455438
\(337\) −30.1681 −1.64336 −0.821681 0.569948i \(-0.806963\pi\)
−0.821681 + 0.569948i \(0.806963\pi\)
\(338\) −11.9594 −0.650508
\(339\) 34.2035 1.85768
\(340\) −14.0122 −0.759917
\(341\) −40.5866 −2.19789
\(342\) 6.57455 0.355511
\(343\) −18.1328 −0.979081
\(344\) −4.61898 −0.249039
\(345\) −40.8976 −2.20185
\(346\) 24.7440 1.33024
\(347\) −6.59271 −0.353915 −0.176958 0.984218i \(-0.556626\pi\)
−0.176958 + 0.984218i \(0.556626\pi\)
\(348\) −10.0009 −0.536107
\(349\) −8.52462 −0.456312 −0.228156 0.973625i \(-0.573270\pi\)
−0.228156 + 0.973625i \(0.573270\pi\)
\(350\) 6.01541 0.321537
\(351\) 11.2827 0.602227
\(352\) −5.80467 −0.309390
\(353\) −10.3889 −0.552947 −0.276474 0.961021i \(-0.589166\pi\)
−0.276474 + 0.961021i \(0.589166\pi\)
\(354\) −17.5882 −0.934801
\(355\) 17.1378 0.909579
\(356\) −2.99680 −0.158830
\(357\) 43.5058 2.30257
\(358\) −23.0901 −1.22035
\(359\) 25.3768 1.33933 0.669667 0.742661i \(-0.266437\pi\)
0.669667 + 0.742661i \(0.266437\pi\)
\(360\) 17.6776 0.931691
\(361\) 1.00000 0.0526316
\(362\) 5.37021 0.282252
\(363\) −70.2222 −3.68571
\(364\) −2.75215 −0.144252
\(365\) −33.1670 −1.73604
\(366\) 26.2639 1.37283
\(367\) 14.9400 0.779864 0.389932 0.920844i \(-0.372499\pi\)
0.389932 + 0.920844i \(0.372499\pi\)
\(368\) 4.91566 0.256247
\(369\) −37.0639 −1.92947
\(370\) −25.8869 −1.34580
\(371\) −27.1028 −1.40711
\(372\) −21.6354 −1.12174
\(373\) −18.2635 −0.945650 −0.472825 0.881156i \(-0.656766\pi\)
−0.472825 + 0.881156i \(0.656766\pi\)
\(374\) 30.2501 1.56419
\(375\) 23.0494 1.19027
\(376\) −2.14466 −0.110603
\(377\) −3.29697 −0.169802
\(378\) −29.8415 −1.53488
\(379\) −15.4863 −0.795477 −0.397738 0.917499i \(-0.630205\pi\)
−0.397738 + 0.917499i \(0.630205\pi\)
\(380\) 2.68879 0.137932
\(381\) 21.6368 1.10849
\(382\) 3.26272 0.166935
\(383\) 8.99696 0.459723 0.229862 0.973223i \(-0.426173\pi\)
0.229862 + 0.973223i \(0.426173\pi\)
\(384\) −3.09428 −0.157904
\(385\) −42.1089 −2.14607
\(386\) 5.16392 0.262836
\(387\) −30.3677 −1.54368
\(388\) 4.49014 0.227952
\(389\) 22.4887 1.14022 0.570112 0.821567i \(-0.306900\pi\)
0.570112 + 0.821567i \(0.306900\pi\)
\(390\) 8.48690 0.429751
\(391\) −25.6171 −1.29551
\(392\) 0.279119 0.0140976
\(393\) 65.7246 3.31537
\(394\) −1.77258 −0.0893013
\(395\) 6.70183 0.337205
\(396\) −38.1631 −1.91777
\(397\) 13.8583 0.695526 0.347763 0.937582i \(-0.386941\pi\)
0.347763 + 0.937582i \(0.386941\pi\)
\(398\) 3.95646 0.198319
\(399\) −8.34831 −0.417938
\(400\) 2.22960 0.111480
\(401\) −16.8575 −0.841824 −0.420912 0.907101i \(-0.638290\pi\)
−0.420912 + 0.907101i \(0.638290\pi\)
\(402\) 14.5524 0.725806
\(403\) −7.13243 −0.355292
\(404\) 6.09662 0.303318
\(405\) 38.9904 1.93745
\(406\) 8.72009 0.432771
\(407\) 55.8858 2.77015
\(408\) 16.1253 0.798321
\(409\) 10.9497 0.541430 0.270715 0.962660i \(-0.412740\pi\)
0.270715 + 0.962660i \(0.412740\pi\)
\(410\) −15.1580 −0.748601
\(411\) −52.3810 −2.58376
\(412\) 2.01258 0.0991529
\(413\) 15.3356 0.754616
\(414\) 32.3183 1.58836
\(415\) −16.4137 −0.805719
\(416\) −1.02008 −0.0500134
\(417\) −1.66680 −0.0816236
\(418\) −5.80467 −0.283916
\(419\) 10.0233 0.489668 0.244834 0.969565i \(-0.421266\pi\)
0.244834 + 0.969565i \(0.421266\pi\)
\(420\) −22.4469 −1.09529
\(421\) 10.6602 0.519548 0.259774 0.965669i \(-0.416352\pi\)
0.259774 + 0.965669i \(0.416352\pi\)
\(422\) −1.00000 −0.0486792
\(423\) −14.1002 −0.685575
\(424\) −10.0456 −0.487856
\(425\) −11.6192 −0.563612
\(426\) −19.7223 −0.955547
\(427\) −22.9002 −1.10822
\(428\) 2.95811 0.142985
\(429\) −18.3219 −0.884588
\(430\) −12.4195 −0.598920
\(431\) 29.9005 1.44025 0.720127 0.693842i \(-0.244084\pi\)
0.720127 + 0.693842i \(0.244084\pi\)
\(432\) −11.0607 −0.532156
\(433\) −2.10175 −0.101004 −0.0505018 0.998724i \(-0.516082\pi\)
−0.0505018 + 0.998724i \(0.516082\pi\)
\(434\) 18.8645 0.905523
\(435\) −26.8904 −1.28930
\(436\) 12.9724 0.621264
\(437\) 4.91566 0.235148
\(438\) 38.1688 1.82377
\(439\) −29.7140 −1.41817 −0.709086 0.705122i \(-0.750892\pi\)
−0.709086 + 0.705122i \(0.750892\pi\)
\(440\) −15.6075 −0.744061
\(441\) 1.83508 0.0873848
\(442\) 5.31596 0.252854
\(443\) −29.1694 −1.38588 −0.692941 0.720994i \(-0.743685\pi\)
−0.692941 + 0.720994i \(0.743685\pi\)
\(444\) 29.7908 1.41381
\(445\) −8.05778 −0.381975
\(446\) −11.7745 −0.557538
\(447\) 68.2755 3.22932
\(448\) 2.69798 0.127468
\(449\) −21.3994 −1.00990 −0.504950 0.863148i \(-0.668489\pi\)
−0.504950 + 0.863148i \(0.668489\pi\)
\(450\) 14.6586 0.691013
\(451\) 32.7238 1.54090
\(452\) −11.0538 −0.519927
\(453\) −34.6871 −1.62974
\(454\) 20.7359 0.973184
\(455\) −7.39996 −0.346915
\(456\) −3.09428 −0.144903
\(457\) 25.2187 1.17968 0.589841 0.807519i \(-0.299190\pi\)
0.589841 + 0.807519i \(0.299190\pi\)
\(458\) −7.70226 −0.359903
\(459\) 57.6407 2.69044
\(460\) 13.2172 0.616254
\(461\) −18.4586 −0.859703 −0.429852 0.902900i \(-0.641434\pi\)
−0.429852 + 0.902900i \(0.641434\pi\)
\(462\) 48.4592 2.25453
\(463\) −30.6189 −1.42298 −0.711491 0.702695i \(-0.751980\pi\)
−0.711491 + 0.702695i \(0.751980\pi\)
\(464\) 3.23208 0.150045
\(465\) −58.1730 −2.69771
\(466\) −13.0991 −0.606803
\(467\) −20.9490 −0.969403 −0.484701 0.874680i \(-0.661072\pi\)
−0.484701 + 0.874680i \(0.661072\pi\)
\(468\) −6.70655 −0.310010
\(469\) −12.6886 −0.585905
\(470\) −5.76655 −0.265991
\(471\) 10.1313 0.466824
\(472\) 5.68410 0.261632
\(473\) 26.8117 1.23280
\(474\) −7.71250 −0.354247
\(475\) 2.22960 0.102301
\(476\) −14.0601 −0.644443
\(477\) −66.0451 −3.02400
\(478\) 3.58986 0.164196
\(479\) −18.1492 −0.829258 −0.414629 0.909990i \(-0.636089\pi\)
−0.414629 + 0.909990i \(0.636089\pi\)
\(480\) −8.31986 −0.379748
\(481\) 9.82101 0.447800
\(482\) −20.7327 −0.944350
\(483\) −41.0375 −1.86727
\(484\) 22.6942 1.03156
\(485\) 12.0730 0.548208
\(486\) −11.6884 −0.530196
\(487\) −12.2598 −0.555546 −0.277773 0.960647i \(-0.589596\pi\)
−0.277773 + 0.960647i \(0.589596\pi\)
\(488\) −8.48789 −0.384229
\(489\) 67.0201 3.03076
\(490\) 0.750492 0.0339038
\(491\) 0.409512 0.0184810 0.00924052 0.999957i \(-0.497059\pi\)
0.00924052 + 0.999957i \(0.497059\pi\)
\(492\) 17.4439 0.786434
\(493\) −16.8434 −0.758590
\(494\) −1.02008 −0.0458954
\(495\) −102.613 −4.61210
\(496\) 6.99206 0.313953
\(497\) 17.1964 0.771363
\(498\) 18.8890 0.846438
\(499\) 19.8019 0.886453 0.443227 0.896410i \(-0.353834\pi\)
0.443227 + 0.896410i \(0.353834\pi\)
\(500\) −7.44904 −0.333131
\(501\) −56.9412 −2.54394
\(502\) 20.0261 0.893809
\(503\) −8.25561 −0.368100 −0.184050 0.982917i \(-0.558921\pi\)
−0.184050 + 0.982917i \(0.558921\pi\)
\(504\) 17.7380 0.790115
\(505\) 16.3925 0.729459
\(506\) −28.5338 −1.26848
\(507\) 37.0058 1.64349
\(508\) −6.99251 −0.310243
\(509\) −15.8574 −0.702867 −0.351433 0.936213i \(-0.614306\pi\)
−0.351433 + 0.936213i \(0.614306\pi\)
\(510\) 43.3576 1.91990
\(511\) −33.2804 −1.47224
\(512\) 1.00000 0.0441942
\(513\) −11.0607 −0.488340
\(514\) −20.5611 −0.906911
\(515\) 5.41142 0.238456
\(516\) 14.2924 0.629188
\(517\) 12.4491 0.547509
\(518\) −25.9754 −1.14129
\(519\) −76.5647 −3.36082
\(520\) −2.74277 −0.120279
\(521\) 15.9390 0.698302 0.349151 0.937067i \(-0.386470\pi\)
0.349151 + 0.937067i \(0.386470\pi\)
\(522\) 21.2495 0.930064
\(523\) 4.73045 0.206848 0.103424 0.994637i \(-0.467020\pi\)
0.103424 + 0.994637i \(0.467020\pi\)
\(524\) −21.2407 −0.927903
\(525\) −18.6134 −0.812354
\(526\) 18.8516 0.821968
\(527\) −36.4379 −1.58726
\(528\) 17.9613 0.781664
\(529\) 1.16372 0.0505965
\(530\) −27.0104 −1.17326
\(531\) 37.3704 1.62174
\(532\) 2.69798 0.116972
\(533\) 5.75067 0.249089
\(534\) 9.27294 0.401279
\(535\) 7.95373 0.343870
\(536\) −4.70299 −0.203138
\(537\) 71.4472 3.08318
\(538\) 12.3597 0.532865
\(539\) −1.62019 −0.0697867
\(540\) −29.7398 −1.27980
\(541\) −28.9967 −1.24666 −0.623332 0.781957i \(-0.714221\pi\)
−0.623332 + 0.781957i \(0.714221\pi\)
\(542\) −9.97986 −0.428672
\(543\) −16.6169 −0.713100
\(544\) −5.21133 −0.223434
\(545\) 34.8800 1.49410
\(546\) 8.51592 0.364448
\(547\) −28.4124 −1.21483 −0.607414 0.794385i \(-0.707793\pi\)
−0.607414 + 0.794385i \(0.707793\pi\)
\(548\) 16.9283 0.723143
\(549\) −55.8040 −2.38166
\(550\) −12.9421 −0.551852
\(551\) 3.23208 0.137691
\(552\) −15.2104 −0.647398
\(553\) 6.72474 0.285965
\(554\) −16.2948 −0.692300
\(555\) 80.1013 3.40011
\(556\) 0.538672 0.0228448
\(557\) 34.4257 1.45866 0.729331 0.684161i \(-0.239831\pi\)
0.729331 + 0.684161i \(0.239831\pi\)
\(558\) 45.9696 1.94605
\(559\) 4.71172 0.199284
\(560\) 7.25432 0.306551
\(561\) −93.6021 −3.95188
\(562\) 7.82076 0.329899
\(563\) −6.20147 −0.261361 −0.130680 0.991425i \(-0.541716\pi\)
−0.130680 + 0.991425i \(0.541716\pi\)
\(564\) 6.63618 0.279434
\(565\) −29.7213 −1.25039
\(566\) −16.2700 −0.683881
\(567\) 39.1237 1.64304
\(568\) 6.37379 0.267438
\(569\) −42.3188 −1.77410 −0.887049 0.461675i \(-0.847248\pi\)
−0.887049 + 0.461675i \(0.847248\pi\)
\(570\) −8.31986 −0.348481
\(571\) −6.92442 −0.289778 −0.144889 0.989448i \(-0.546282\pi\)
−0.144889 + 0.989448i \(0.546282\pi\)
\(572\) 5.92121 0.247578
\(573\) −10.0958 −0.421756
\(574\) −15.2098 −0.634847
\(575\) 10.9599 0.457061
\(576\) 6.57455 0.273940
\(577\) −11.0193 −0.458741 −0.229370 0.973339i \(-0.573667\pi\)
−0.229370 + 0.973339i \(0.573667\pi\)
\(578\) 10.1580 0.422515
\(579\) −15.9786 −0.664048
\(580\) 8.69038 0.360848
\(581\) −16.4699 −0.683285
\(582\) −13.8937 −0.575913
\(583\) 58.3112 2.41500
\(584\) −12.3353 −0.510438
\(585\) −18.0325 −0.745552
\(586\) 4.48833 0.185411
\(587\) −28.6989 −1.18453 −0.592265 0.805743i \(-0.701766\pi\)
−0.592265 + 0.805743i \(0.701766\pi\)
\(588\) −0.863671 −0.0356172
\(589\) 6.99206 0.288103
\(590\) 15.2834 0.629206
\(591\) 5.48485 0.225617
\(592\) −9.62772 −0.395697
\(593\) −47.1414 −1.93586 −0.967932 0.251211i \(-0.919171\pi\)
−0.967932 + 0.251211i \(0.919171\pi\)
\(594\) 64.2035 2.63430
\(595\) −37.8046 −1.54984
\(596\) −22.0651 −0.903821
\(597\) −12.2424 −0.501047
\(598\) −5.01435 −0.205052
\(599\) −12.8321 −0.524304 −0.262152 0.965027i \(-0.584432\pi\)
−0.262152 + 0.965027i \(0.584432\pi\)
\(600\) −6.89899 −0.281650
\(601\) 30.4272 1.24115 0.620577 0.784146i \(-0.286899\pi\)
0.620577 + 0.784146i \(0.286899\pi\)
\(602\) −12.4619 −0.507911
\(603\) −30.9201 −1.25916
\(604\) 11.2101 0.456131
\(605\) 61.0200 2.48082
\(606\) −18.8646 −0.766324
\(607\) −3.64491 −0.147942 −0.0739712 0.997260i \(-0.523567\pi\)
−0.0739712 + 0.997260i \(0.523567\pi\)
\(608\) 1.00000 0.0405554
\(609\) −26.9824 −1.09338
\(610\) −22.8222 −0.924042
\(611\) 2.18772 0.0885057
\(612\) −34.2622 −1.38497
\(613\) 18.6551 0.753473 0.376736 0.926321i \(-0.377046\pi\)
0.376736 + 0.926321i \(0.377046\pi\)
\(614\) 11.5583 0.466455
\(615\) 46.9031 1.89132
\(616\) −15.6609 −0.630996
\(617\) 14.6266 0.588843 0.294422 0.955676i \(-0.404873\pi\)
0.294422 + 0.955676i \(0.404873\pi\)
\(618\) −6.22749 −0.250507
\(619\) 1.44896 0.0582387 0.0291194 0.999576i \(-0.490730\pi\)
0.0291194 + 0.999576i \(0.490730\pi\)
\(620\) 18.8002 0.755033
\(621\) −54.3704 −2.18181
\(622\) 11.3152 0.453700
\(623\) −8.08533 −0.323932
\(624\) 3.15640 0.126357
\(625\) −31.1769 −1.24708
\(626\) −22.1917 −0.886958
\(627\) 17.9613 0.717304
\(628\) −3.27420 −0.130655
\(629\) 50.1732 2.00054
\(630\) 47.6939 1.90017
\(631\) −17.2479 −0.686629 −0.343315 0.939220i \(-0.611550\pi\)
−0.343315 + 0.939220i \(0.611550\pi\)
\(632\) 2.49251 0.0991465
\(633\) 3.09428 0.122986
\(634\) 10.0320 0.398421
\(635\) −18.8014 −0.746111
\(636\) 31.0838 1.23255
\(637\) −0.284723 −0.0112811
\(638\) −18.7612 −0.742761
\(639\) 41.9048 1.65773
\(640\) 2.68879 0.106284
\(641\) 23.3046 0.920477 0.460238 0.887795i \(-0.347764\pi\)
0.460238 + 0.887795i \(0.347764\pi\)
\(642\) −9.15320 −0.361248
\(643\) −29.2777 −1.15460 −0.577300 0.816532i \(-0.695894\pi\)
−0.577300 + 0.816532i \(0.695894\pi\)
\(644\) 13.2624 0.522611
\(645\) 38.4293 1.51315
\(646\) −5.21133 −0.205037
\(647\) 24.3443 0.957074 0.478537 0.878067i \(-0.341167\pi\)
0.478537 + 0.878067i \(0.341167\pi\)
\(648\) 14.5011 0.569656
\(649\) −32.9943 −1.29514
\(650\) −2.27436 −0.0892077
\(651\) −58.3719 −2.28777
\(652\) −21.6594 −0.848247
\(653\) −20.2614 −0.792891 −0.396445 0.918058i \(-0.629756\pi\)
−0.396445 + 0.918058i \(0.629756\pi\)
\(654\) −40.1401 −1.56960
\(655\) −57.1117 −2.23154
\(656\) −5.63748 −0.220107
\(657\) −81.0989 −3.16397
\(658\) −5.78627 −0.225572
\(659\) −46.0440 −1.79362 −0.896809 0.442418i \(-0.854121\pi\)
−0.896809 + 0.442418i \(0.854121\pi\)
\(660\) 48.2941 1.87984
\(661\) 0.200679 0.00780551 0.00390276 0.999992i \(-0.498758\pi\)
0.00390276 + 0.999992i \(0.498758\pi\)
\(662\) 6.12083 0.237893
\(663\) −16.4490 −0.638828
\(664\) −6.10451 −0.236901
\(665\) 7.25432 0.281310
\(666\) −63.2979 −2.45275
\(667\) 15.8878 0.615178
\(668\) 18.4021 0.711998
\(669\) 36.4335 1.40860
\(670\) −12.6454 −0.488533
\(671\) 49.2694 1.90202
\(672\) −8.34831 −0.322043
\(673\) −10.8814 −0.419448 −0.209724 0.977761i \(-0.567257\pi\)
−0.209724 + 0.977761i \(0.567257\pi\)
\(674\) −30.1681 −1.16203
\(675\) −24.6608 −0.949194
\(676\) −11.9594 −0.459979
\(677\) −16.8531 −0.647718 −0.323859 0.946105i \(-0.604980\pi\)
−0.323859 + 0.946105i \(0.604980\pi\)
\(678\) 34.2035 1.31358
\(679\) 12.1143 0.464905
\(680\) −14.0122 −0.537342
\(681\) −64.1626 −2.45872
\(682\) −40.5866 −1.55414
\(683\) 3.36580 0.128789 0.0643944 0.997925i \(-0.479488\pi\)
0.0643944 + 0.997925i \(0.479488\pi\)
\(684\) 6.57455 0.251384
\(685\) 45.5168 1.73911
\(686\) −18.1328 −0.692315
\(687\) 23.8329 0.909282
\(688\) −4.61898 −0.176097
\(689\) 10.2472 0.390389
\(690\) −40.8976 −1.55695
\(691\) 13.1189 0.499068 0.249534 0.968366i \(-0.419723\pi\)
0.249534 + 0.968366i \(0.419723\pi\)
\(692\) 24.7440 0.940625
\(693\) −102.963 −3.91126
\(694\) −6.59271 −0.250256
\(695\) 1.44838 0.0549401
\(696\) −10.0009 −0.379085
\(697\) 29.3788 1.11280
\(698\) −8.52462 −0.322662
\(699\) 40.5322 1.53307
\(700\) 6.01541 0.227361
\(701\) −15.8741 −0.599557 −0.299779 0.954009i \(-0.596913\pi\)
−0.299779 + 0.954009i \(0.596913\pi\)
\(702\) 11.2827 0.425839
\(703\) −9.62772 −0.363116
\(704\) −5.80467 −0.218772
\(705\) 17.8433 0.672018
\(706\) −10.3889 −0.390993
\(707\) 16.4486 0.618613
\(708\) −17.5882 −0.661004
\(709\) −1.40514 −0.0527710 −0.0263855 0.999652i \(-0.508400\pi\)
−0.0263855 + 0.999652i \(0.508400\pi\)
\(710\) 17.1378 0.643170
\(711\) 16.3871 0.614565
\(712\) −2.99680 −0.112310
\(713\) 34.3706 1.28719
\(714\) 43.5058 1.62816
\(715\) 15.9209 0.595408
\(716\) −23.0901 −0.862918
\(717\) −11.1080 −0.414836
\(718\) 25.3768 0.947052
\(719\) 50.1743 1.87119 0.935593 0.353081i \(-0.114866\pi\)
0.935593 + 0.353081i \(0.114866\pi\)
\(720\) 17.6776 0.658805
\(721\) 5.42992 0.202221
\(722\) 1.00000 0.0372161
\(723\) 64.1528 2.38587
\(724\) 5.37021 0.199582
\(725\) 7.20623 0.267633
\(726\) −70.2222 −2.60619
\(727\) −7.84044 −0.290786 −0.145393 0.989374i \(-0.546445\pi\)
−0.145393 + 0.989374i \(0.546445\pi\)
\(728\) −2.75215 −0.102001
\(729\) −7.33610 −0.271708
\(730\) −33.1670 −1.22757
\(731\) 24.0710 0.890299
\(732\) 26.2639 0.970741
\(733\) −19.6031 −0.724056 −0.362028 0.932167i \(-0.617916\pi\)
−0.362028 + 0.932167i \(0.617916\pi\)
\(734\) 14.9400 0.551447
\(735\) −2.32223 −0.0856568
\(736\) 4.91566 0.181194
\(737\) 27.2993 1.00558
\(738\) −37.0639 −1.36434
\(739\) 38.6814 1.42292 0.711459 0.702728i \(-0.248035\pi\)
0.711459 + 0.702728i \(0.248035\pi\)
\(740\) −25.8869 −0.951622
\(741\) 3.15640 0.115953
\(742\) −27.1028 −0.994974
\(743\) 35.4939 1.30214 0.651072 0.759016i \(-0.274320\pi\)
0.651072 + 0.759016i \(0.274320\pi\)
\(744\) −21.6354 −0.793191
\(745\) −59.3284 −2.17362
\(746\) −18.2635 −0.668676
\(747\) −40.1344 −1.46844
\(748\) 30.2501 1.10605
\(749\) 7.98092 0.291617
\(750\) 23.0494 0.841645
\(751\) 3.42607 0.125019 0.0625095 0.998044i \(-0.480090\pi\)
0.0625095 + 0.998044i \(0.480090\pi\)
\(752\) −2.14466 −0.0782078
\(753\) −61.9663 −2.25818
\(754\) −3.29697 −0.120068
\(755\) 30.1415 1.09696
\(756\) −29.8415 −1.08532
\(757\) 47.2149 1.71605 0.858027 0.513604i \(-0.171690\pi\)
0.858027 + 0.513604i \(0.171690\pi\)
\(758\) −15.4863 −0.562487
\(759\) 88.2915 3.20478
\(760\) 2.68879 0.0975327
\(761\) 18.0283 0.653524 0.326762 0.945107i \(-0.394042\pi\)
0.326762 + 0.945107i \(0.394042\pi\)
\(762\) 21.6368 0.783818
\(763\) 34.9993 1.26706
\(764\) 3.26272 0.118041
\(765\) −92.1238 −3.33074
\(766\) 8.99696 0.325073
\(767\) −5.79822 −0.209361
\(768\) −3.09428 −0.111655
\(769\) 12.5508 0.452595 0.226298 0.974058i \(-0.427338\pi\)
0.226298 + 0.974058i \(0.427338\pi\)
\(770\) −42.1089 −1.51750
\(771\) 63.6218 2.29128
\(772\) 5.16392 0.185853
\(773\) −17.9794 −0.646676 −0.323338 0.946284i \(-0.604805\pi\)
−0.323338 + 0.946284i \(0.604805\pi\)
\(774\) −30.3677 −1.09155
\(775\) 15.5895 0.559990
\(776\) 4.49014 0.161186
\(777\) 80.3752 2.88344
\(778\) 22.4887 0.806261
\(779\) −5.63748 −0.201984
\(780\) 8.48690 0.303880
\(781\) −36.9978 −1.32388
\(782\) −25.6171 −0.916067
\(783\) −35.7489 −1.27756
\(784\) 0.279119 0.00996853
\(785\) −8.80363 −0.314215
\(786\) 65.7246 2.34432
\(787\) −48.5559 −1.73083 −0.865416 0.501054i \(-0.832946\pi\)
−0.865416 + 0.501054i \(0.832946\pi\)
\(788\) −1.77258 −0.0631455
\(789\) −58.3320 −2.07668
\(790\) 6.70183 0.238440
\(791\) −29.8230 −1.06038
\(792\) −38.1631 −1.35607
\(793\) 8.65829 0.307465
\(794\) 13.8583 0.491811
\(795\) 83.5777 2.96420
\(796\) 3.95646 0.140233
\(797\) 48.3845 1.71387 0.856934 0.515426i \(-0.172366\pi\)
0.856934 + 0.515426i \(0.172366\pi\)
\(798\) −8.34831 −0.295527
\(799\) 11.1765 0.395398
\(800\) 2.22960 0.0788281
\(801\) −19.7026 −0.696158
\(802\) −16.8575 −0.595260
\(803\) 71.6023 2.52679
\(804\) 14.5524 0.513222
\(805\) 35.6598 1.25684
\(806\) −7.13243 −0.251229
\(807\) −38.2444 −1.34627
\(808\) 6.09662 0.214479
\(809\) −2.93682 −0.103253 −0.0516266 0.998666i \(-0.516441\pi\)
−0.0516266 + 0.998666i \(0.516441\pi\)
\(810\) 38.9904 1.36998
\(811\) 30.0317 1.05456 0.527278 0.849693i \(-0.323213\pi\)
0.527278 + 0.849693i \(0.323213\pi\)
\(812\) 8.72009 0.306015
\(813\) 30.8804 1.08302
\(814\) 55.8858 1.95879
\(815\) −58.2376 −2.03997
\(816\) 16.1253 0.564498
\(817\) −4.61898 −0.161598
\(818\) 10.9497 0.382849
\(819\) −18.0942 −0.632261
\(820\) −15.1580 −0.529341
\(821\) −46.8286 −1.63433 −0.817164 0.576405i \(-0.804455\pi\)
−0.817164 + 0.576405i \(0.804455\pi\)
\(822\) −52.3810 −1.82700
\(823\) −40.0217 −1.39507 −0.697535 0.716551i \(-0.745720\pi\)
−0.697535 + 0.716551i \(0.745720\pi\)
\(824\) 2.01258 0.0701117
\(825\) 40.0464 1.39424
\(826\) 15.3356 0.533594
\(827\) 31.9683 1.11165 0.555823 0.831301i \(-0.312403\pi\)
0.555823 + 0.831301i \(0.312403\pi\)
\(828\) 32.3183 1.12314
\(829\) 28.3019 0.982965 0.491482 0.870887i \(-0.336455\pi\)
0.491482 + 0.870887i \(0.336455\pi\)
\(830\) −16.4137 −0.569729
\(831\) 50.4206 1.74907
\(832\) −1.02008 −0.0353648
\(833\) −1.45458 −0.0503982
\(834\) −1.66680 −0.0577166
\(835\) 49.4794 1.71230
\(836\) −5.80467 −0.200759
\(837\) −77.3367 −2.67315
\(838\) 10.0233 0.346248
\(839\) −18.3322 −0.632897 −0.316448 0.948610i \(-0.602490\pi\)
−0.316448 + 0.948610i \(0.602490\pi\)
\(840\) −22.4469 −0.774490
\(841\) −18.5537 −0.639782
\(842\) 10.6602 0.367376
\(843\) −24.1996 −0.833478
\(844\) −1.00000 −0.0344214
\(845\) −32.1564 −1.10622
\(846\) −14.1002 −0.484775
\(847\) 61.2287 2.10384
\(848\) −10.0456 −0.344966
\(849\) 50.3440 1.72780
\(850\) −11.6192 −0.398534
\(851\) −47.3266 −1.62233
\(852\) −19.7223 −0.675674
\(853\) 2.64013 0.0903964 0.0451982 0.998978i \(-0.485608\pi\)
0.0451982 + 0.998978i \(0.485608\pi\)
\(854\) −22.9002 −0.783628
\(855\) 17.6776 0.604561
\(856\) 2.95811 0.101106
\(857\) 51.8234 1.77025 0.885127 0.465349i \(-0.154071\pi\)
0.885127 + 0.465349i \(0.154071\pi\)
\(858\) −18.3219 −0.625498
\(859\) −10.1640 −0.346790 −0.173395 0.984852i \(-0.555474\pi\)
−0.173395 + 0.984852i \(0.555474\pi\)
\(860\) −12.4195 −0.423501
\(861\) 47.0635 1.60392
\(862\) 29.9005 1.01841
\(863\) 5.69497 0.193859 0.0969296 0.995291i \(-0.469098\pi\)
0.0969296 + 0.995291i \(0.469098\pi\)
\(864\) −11.0607 −0.376291
\(865\) 66.5314 2.26213
\(866\) −2.10175 −0.0714204
\(867\) −31.4315 −1.06747
\(868\) 18.8645 0.640302
\(869\) −14.4682 −0.490799
\(870\) −26.8904 −0.911672
\(871\) 4.79741 0.162554
\(872\) 12.9724 0.439300
\(873\) 29.5206 0.999122
\(874\) 4.91566 0.166275
\(875\) −20.0974 −0.679416
\(876\) 38.1688 1.28960
\(877\) 33.4559 1.12973 0.564863 0.825185i \(-0.308929\pi\)
0.564863 + 0.825185i \(0.308929\pi\)
\(878\) −29.7140 −1.00280
\(879\) −13.8881 −0.468436
\(880\) −15.6075 −0.526130
\(881\) −10.5076 −0.354009 −0.177004 0.984210i \(-0.556641\pi\)
−0.177004 + 0.984210i \(0.556641\pi\)
\(882\) 1.83508 0.0617904
\(883\) 8.18920 0.275589 0.137794 0.990461i \(-0.455999\pi\)
0.137794 + 0.990461i \(0.455999\pi\)
\(884\) 5.31596 0.178795
\(885\) −47.2909 −1.58967
\(886\) −29.1694 −0.979966
\(887\) 0.0122459 0.000411177 0 0.000205589 1.00000i \(-0.499935\pi\)
0.000205589 1.00000i \(0.499935\pi\)
\(888\) 29.7908 0.999715
\(889\) −18.8657 −0.632735
\(890\) −8.05778 −0.270097
\(891\) −84.1740 −2.81994
\(892\) −11.7745 −0.394239
\(893\) −2.14466 −0.0717684
\(894\) 68.2755 2.28347
\(895\) −62.0845 −2.07526
\(896\) 2.69798 0.0901333
\(897\) 15.5158 0.518057
\(898\) −21.3994 −0.714107
\(899\) 22.5989 0.753715
\(900\) 14.6586 0.488620
\(901\) 52.3507 1.74406
\(902\) 32.7238 1.08958
\(903\) 38.5607 1.28322
\(904\) −11.0538 −0.367644
\(905\) 14.4394 0.479981
\(906\) −34.6871 −1.15240
\(907\) −39.5002 −1.31158 −0.655791 0.754943i \(-0.727665\pi\)
−0.655791 + 0.754943i \(0.727665\pi\)
\(908\) 20.7359 0.688145
\(909\) 40.0826 1.32946
\(910\) −7.39996 −0.245306
\(911\) −7.57559 −0.250991 −0.125495 0.992094i \(-0.540052\pi\)
−0.125495 + 0.992094i \(0.540052\pi\)
\(912\) −3.09428 −0.102462
\(913\) 35.4347 1.17272
\(914\) 25.2187 0.834161
\(915\) 70.6181 2.33456
\(916\) −7.70226 −0.254490
\(917\) −57.3070 −1.89244
\(918\) 57.6407 1.90243
\(919\) 58.2143 1.92031 0.960157 0.279463i \(-0.0901563\pi\)
0.960157 + 0.279463i \(0.0901563\pi\)
\(920\) 13.2172 0.435758
\(921\) −35.7645 −1.17848
\(922\) −18.4586 −0.607902
\(923\) −6.50175 −0.214008
\(924\) 48.4592 1.59419
\(925\) −21.4659 −0.705795
\(926\) −30.6189 −1.00620
\(927\) 13.2318 0.434591
\(928\) 3.23208 0.106098
\(929\) 51.2285 1.68075 0.840376 0.542004i \(-0.182334\pi\)
0.840376 + 0.542004i \(0.182334\pi\)
\(930\) −58.1730 −1.90757
\(931\) 0.279119 0.00914775
\(932\) −13.0991 −0.429074
\(933\) −35.0125 −1.14626
\(934\) −20.9490 −0.685471
\(935\) 81.3361 2.65997
\(936\) −6.70655 −0.219210
\(937\) 10.3375 0.337712 0.168856 0.985641i \(-0.445993\pi\)
0.168856 + 0.985641i \(0.445993\pi\)
\(938\) −12.6886 −0.414298
\(939\) 68.6673 2.24087
\(940\) −5.76655 −0.188084
\(941\) 35.7453 1.16526 0.582632 0.812736i \(-0.302023\pi\)
0.582632 + 0.812736i \(0.302023\pi\)
\(942\) 10.1313 0.330095
\(943\) −27.7120 −0.902426
\(944\) 5.68410 0.185002
\(945\) −80.2375 −2.61013
\(946\) 26.8117 0.871723
\(947\) −6.11275 −0.198638 −0.0993189 0.995056i \(-0.531666\pi\)
−0.0993189 + 0.995056i \(0.531666\pi\)
\(948\) −7.71250 −0.250490
\(949\) 12.5829 0.408459
\(950\) 2.22960 0.0723376
\(951\) −31.0418 −1.00660
\(952\) −14.0601 −0.455690
\(953\) 6.85567 0.222077 0.111038 0.993816i \(-0.464582\pi\)
0.111038 + 0.993816i \(0.464582\pi\)
\(954\) −66.0451 −2.13829
\(955\) 8.77277 0.283880
\(956\) 3.58986 0.116104
\(957\) 58.0522 1.87656
\(958\) −18.1492 −0.586374
\(959\) 45.6724 1.47484
\(960\) −8.31986 −0.268522
\(961\) 17.8889 0.577060
\(962\) 9.82101 0.316642
\(963\) 19.4482 0.626710
\(964\) −20.7327 −0.667756
\(965\) 13.8847 0.446964
\(966\) −41.0375 −1.32036
\(967\) 49.1958 1.58203 0.791015 0.611796i \(-0.209553\pi\)
0.791015 + 0.611796i \(0.209553\pi\)
\(968\) 22.6942 0.729420
\(969\) 16.1253 0.518019
\(970\) 12.0730 0.387642
\(971\) 22.2753 0.714850 0.357425 0.933942i \(-0.383655\pi\)
0.357425 + 0.933942i \(0.383655\pi\)
\(972\) −11.6884 −0.374905
\(973\) 1.45333 0.0465916
\(974\) −12.2598 −0.392830
\(975\) 7.03750 0.225380
\(976\) −8.48789 −0.271691
\(977\) 54.6672 1.74896 0.874479 0.485063i \(-0.161204\pi\)
0.874479 + 0.485063i \(0.161204\pi\)
\(978\) 67.0201 2.14307
\(979\) 17.3955 0.555961
\(980\) 0.750492 0.0239736
\(981\) 85.2876 2.72302
\(982\) 0.409512 0.0130681
\(983\) −20.5308 −0.654832 −0.327416 0.944880i \(-0.606178\pi\)
−0.327416 + 0.944880i \(0.606178\pi\)
\(984\) 17.4439 0.556093
\(985\) −4.76610 −0.151860
\(986\) −16.8434 −0.536404
\(987\) 17.9043 0.569901
\(988\) −1.02008 −0.0324530
\(989\) −22.7053 −0.721988
\(990\) −102.613 −3.26124
\(991\) −33.6003 −1.06735 −0.533675 0.845690i \(-0.679189\pi\)
−0.533675 + 0.845690i \(0.679189\pi\)
\(992\) 6.99206 0.221998
\(993\) −18.9395 −0.601028
\(994\) 17.1964 0.545436
\(995\) 10.6381 0.337250
\(996\) 18.8890 0.598522
\(997\) 33.3144 1.05508 0.527538 0.849531i \(-0.323115\pi\)
0.527538 + 0.849531i \(0.323115\pi\)
\(998\) 19.8019 0.626817
\(999\) 106.489 3.36916
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 \(a_p\))