Properties

Label 8018.2.a.j.1.15
Level 8018
Weight 2
Character 8018.1
Self dual Yes
Analytic conductor 64.024
Analytic rank 0
Dimension 47
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: \(0\)
Dimension: \(47\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.15
Character \(\chi\) = 8018.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{2}\) \(-1.14813 q^{3}\) \(+1.00000 q^{4}\) \(+2.89240 q^{5}\) \(-1.14813 q^{6}\) \(+3.60462 q^{7}\) \(+1.00000 q^{8}\) \(-1.68179 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{2}\) \(-1.14813 q^{3}\) \(+1.00000 q^{4}\) \(+2.89240 q^{5}\) \(-1.14813 q^{6}\) \(+3.60462 q^{7}\) \(+1.00000 q^{8}\) \(-1.68179 q^{9}\) \(+2.89240 q^{10}\) \(+3.08565 q^{11}\) \(-1.14813 q^{12}\) \(+1.07318 q^{13}\) \(+3.60462 q^{14}\) \(-3.32087 q^{15}\) \(+1.00000 q^{16}\) \(+2.58429 q^{17}\) \(-1.68179 q^{18}\) \(-1.00000 q^{19}\) \(+2.89240 q^{20}\) \(-4.13859 q^{21}\) \(+3.08565 q^{22}\) \(-1.16430 q^{23}\) \(-1.14813 q^{24}\) \(+3.36601 q^{25}\) \(+1.07318 q^{26}\) \(+5.37532 q^{27}\) \(+3.60462 q^{28}\) \(+5.13064 q^{29}\) \(-3.32087 q^{30}\) \(-0.677721 q^{31}\) \(+1.00000 q^{32}\) \(-3.54274 q^{33}\) \(+2.58429 q^{34}\) \(+10.4260 q^{35}\) \(-1.68179 q^{36}\) \(-2.27963 q^{37}\) \(-1.00000 q^{38}\) \(-1.23216 q^{39}\) \(+2.89240 q^{40}\) \(-3.80407 q^{41}\) \(-4.13859 q^{42}\) \(+1.52856 q^{43}\) \(+3.08565 q^{44}\) \(-4.86441 q^{45}\) \(-1.16430 q^{46}\) \(+1.09313 q^{47}\) \(-1.14813 q^{48}\) \(+5.99332 q^{49}\) \(+3.36601 q^{50}\) \(-2.96711 q^{51}\) \(+1.07318 q^{52}\) \(+11.0126 q^{53}\) \(+5.37532 q^{54}\) \(+8.92496 q^{55}\) \(+3.60462 q^{56}\) \(+1.14813 q^{57}\) \(+5.13064 q^{58}\) \(+7.21434 q^{59}\) \(-3.32087 q^{60}\) \(-11.7845 q^{61}\) \(-0.677721 q^{62}\) \(-6.06222 q^{63}\) \(+1.00000 q^{64}\) \(+3.10408 q^{65}\) \(-3.54274 q^{66}\) \(-14.8513 q^{67}\) \(+2.58429 q^{68}\) \(+1.33677 q^{69}\) \(+10.4260 q^{70}\) \(+8.91929 q^{71}\) \(-1.68179 q^{72}\) \(+3.33975 q^{73}\) \(-2.27963 q^{74}\) \(-3.86463 q^{75}\) \(-1.00000 q^{76}\) \(+11.1226 q^{77}\) \(-1.23216 q^{78}\) \(-10.6382 q^{79}\) \(+2.89240 q^{80}\) \(-1.12622 q^{81}\) \(-3.80407 q^{82}\) \(-4.72324 q^{83}\) \(-4.13859 q^{84}\) \(+7.47481 q^{85}\) \(+1.52856 q^{86}\) \(-5.89066 q^{87}\) \(+3.08565 q^{88}\) \(-0.242858 q^{89}\) \(-4.86441 q^{90}\) \(+3.86842 q^{91}\) \(-1.16430 q^{92}\) \(+0.778115 q^{93}\) \(+1.09313 q^{94}\) \(-2.89240 q^{95}\) \(-1.14813 q^{96}\) \(+0.265223 q^{97}\) \(+5.99332 q^{98}\) \(-5.18942 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(47q \) \(\mathstrut +\mathstrut 47q^{2} \) \(\mathstrut +\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 47q^{4} \) \(\mathstrut +\mathstrut 15q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut +\mathstrut 47q^{8} \) \(\mathstrut +\mathstrut 69q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(47q \) \(\mathstrut +\mathstrut 47q^{2} \) \(\mathstrut +\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 47q^{4} \) \(\mathstrut +\mathstrut 15q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut +\mathstrut 47q^{8} \) \(\mathstrut +\mathstrut 69q^{9} \) \(\mathstrut +\mathstrut 15q^{10} \) \(\mathstrut +\mathstrut 17q^{11} \) \(\mathstrut +\mathstrut 10q^{12} \) \(\mathstrut +\mathstrut 27q^{13} \) \(\mathstrut +\mathstrut 10q^{15} \) \(\mathstrut +\mathstrut 47q^{16} \) \(\mathstrut +\mathstrut 16q^{17} \) \(\mathstrut +\mathstrut 69q^{18} \) \(\mathstrut -\mathstrut 47q^{19} \) \(\mathstrut +\mathstrut 15q^{20} \) \(\mathstrut +\mathstrut 26q^{21} \) \(\mathstrut +\mathstrut 17q^{22} \) \(\mathstrut +\mathstrut 24q^{23} \) \(\mathstrut +\mathstrut 10q^{24} \) \(\mathstrut +\mathstrut 86q^{25} \) \(\mathstrut +\mathstrut 27q^{26} \) \(\mathstrut +\mathstrut 43q^{27} \) \(\mathstrut +\mathstrut 58q^{29} \) \(\mathstrut +\mathstrut 10q^{30} \) \(\mathstrut +\mathstrut 21q^{31} \) \(\mathstrut +\mathstrut 47q^{32} \) \(\mathstrut +\mathstrut 18q^{33} \) \(\mathstrut +\mathstrut 16q^{34} \) \(\mathstrut +\mathstrut 24q^{35} \) \(\mathstrut +\mathstrut 69q^{36} \) \(\mathstrut +\mathstrut 78q^{37} \) \(\mathstrut -\mathstrut 47q^{38} \) \(\mathstrut -\mathstrut 4q^{39} \) \(\mathstrut +\mathstrut 15q^{40} \) \(\mathstrut +\mathstrut 53q^{41} \) \(\mathstrut +\mathstrut 26q^{42} \) \(\mathstrut +\mathstrut 47q^{43} \) \(\mathstrut +\mathstrut 17q^{44} \) \(\mathstrut +\mathstrut 23q^{45} \) \(\mathstrut +\mathstrut 24q^{46} \) \(\mathstrut +\mathstrut 16q^{47} \) \(\mathstrut +\mathstrut 10q^{48} \) \(\mathstrut +\mathstrut 93q^{49} \) \(\mathstrut +\mathstrut 86q^{50} \) \(\mathstrut +\mathstrut 28q^{51} \) \(\mathstrut +\mathstrut 27q^{52} \) \(\mathstrut +\mathstrut 43q^{53} \) \(\mathstrut +\mathstrut 43q^{54} \) \(\mathstrut +\mathstrut 23q^{55} \) \(\mathstrut -\mathstrut 10q^{57} \) \(\mathstrut +\mathstrut 58q^{58} \) \(\mathstrut +\mathstrut 3q^{59} \) \(\mathstrut +\mathstrut 10q^{60} \) \(\mathstrut +\mathstrut 12q^{61} \) \(\mathstrut +\mathstrut 21q^{62} \) \(\mathstrut -\mathstrut 5q^{63} \) \(\mathstrut +\mathstrut 47q^{64} \) \(\mathstrut +\mathstrut 62q^{65} \) \(\mathstrut +\mathstrut 18q^{66} \) \(\mathstrut +\mathstrut 68q^{67} \) \(\mathstrut +\mathstrut 16q^{68} \) \(\mathstrut +\mathstrut 12q^{69} \) \(\mathstrut +\mathstrut 24q^{70} \) \(\mathstrut -\mathstrut 13q^{71} \) \(\mathstrut +\mathstrut 69q^{72} \) \(\mathstrut +\mathstrut 35q^{73} \) \(\mathstrut +\mathstrut 78q^{74} \) \(\mathstrut +\mathstrut 22q^{75} \) \(\mathstrut -\mathstrut 47q^{76} \) \(\mathstrut +\mathstrut 26q^{77} \) \(\mathstrut -\mathstrut 4q^{78} \) \(\mathstrut +\mathstrut 21q^{79} \) \(\mathstrut +\mathstrut 15q^{80} \) \(\mathstrut +\mathstrut 123q^{81} \) \(\mathstrut +\mathstrut 53q^{82} \) \(\mathstrut +\mathstrut 23q^{83} \) \(\mathstrut +\mathstrut 26q^{84} \) \(\mathstrut +\mathstrut 38q^{85} \) \(\mathstrut +\mathstrut 47q^{86} \) \(\mathstrut +\mathstrut 39q^{87} \) \(\mathstrut +\mathstrut 17q^{88} \) \(\mathstrut +\mathstrut 24q^{89} \) \(\mathstrut +\mathstrut 23q^{90} \) \(\mathstrut +\mathstrut 49q^{91} \) \(\mathstrut +\mathstrut 24q^{92} \) \(\mathstrut +\mathstrut 91q^{93} \) \(\mathstrut +\mathstrut 16q^{94} \) \(\mathstrut -\mathstrut 15q^{95} \) \(\mathstrut +\mathstrut 10q^{96} \) \(\mathstrut +\mathstrut 88q^{97} \) \(\mathstrut +\mathstrut 93q^{98} \) \(\mathstrut +\mathstrut 26q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) −1.14813 −0.662875 −0.331438 0.943477i \(-0.607534\pi\)
−0.331438 + 0.943477i \(0.607534\pi\)
\(4\) 1.00000 0.500000
\(5\) 2.89240 1.29352 0.646761 0.762692i \(-0.276123\pi\)
0.646761 + 0.762692i \(0.276123\pi\)
\(6\) −1.14813 −0.468724
\(7\) 3.60462 1.36242 0.681210 0.732088i \(-0.261454\pi\)
0.681210 + 0.732088i \(0.261454\pi\)
\(8\) 1.00000 0.353553
\(9\) −1.68179 −0.560596
\(10\) 2.89240 0.914659
\(11\) 3.08565 0.930360 0.465180 0.885216i \(-0.345990\pi\)
0.465180 + 0.885216i \(0.345990\pi\)
\(12\) −1.14813 −0.331438
\(13\) 1.07318 0.297647 0.148824 0.988864i \(-0.452451\pi\)
0.148824 + 0.988864i \(0.452451\pi\)
\(14\) 3.60462 0.963377
\(15\) −3.32087 −0.857444
\(16\) 1.00000 0.250000
\(17\) 2.58429 0.626782 0.313391 0.949624i \(-0.398535\pi\)
0.313391 + 0.949624i \(0.398535\pi\)
\(18\) −1.68179 −0.396401
\(19\) −1.00000 −0.229416
\(20\) 2.89240 0.646761
\(21\) −4.13859 −0.903115
\(22\) 3.08565 0.657864
\(23\) −1.16430 −0.242772 −0.121386 0.992605i \(-0.538734\pi\)
−0.121386 + 0.992605i \(0.538734\pi\)
\(24\) −1.14813 −0.234362
\(25\) 3.36601 0.673201
\(26\) 1.07318 0.210468
\(27\) 5.37532 1.03448
\(28\) 3.60462 0.681210
\(29\) 5.13064 0.952735 0.476368 0.879246i \(-0.341953\pi\)
0.476368 + 0.879246i \(0.341953\pi\)
\(30\) −3.32087 −0.606305
\(31\) −0.677721 −0.121722 −0.0608612 0.998146i \(-0.519385\pi\)
−0.0608612 + 0.998146i \(0.519385\pi\)
\(32\) 1.00000 0.176777
\(33\) −3.54274 −0.616712
\(34\) 2.58429 0.443202
\(35\) 10.4260 1.76232
\(36\) −1.68179 −0.280298
\(37\) −2.27963 −0.374768 −0.187384 0.982287i \(-0.560001\pi\)
−0.187384 + 0.982287i \(0.560001\pi\)
\(38\) −1.00000 −0.162221
\(39\) −1.23216 −0.197303
\(40\) 2.89240 0.457329
\(41\) −3.80407 −0.594096 −0.297048 0.954863i \(-0.596002\pi\)
−0.297048 + 0.954863i \(0.596002\pi\)
\(42\) −4.13859 −0.638599
\(43\) 1.52856 0.233103 0.116551 0.993185i \(-0.462816\pi\)
0.116551 + 0.993185i \(0.462816\pi\)
\(44\) 3.08565 0.465180
\(45\) −4.86441 −0.725144
\(46\) −1.16430 −0.171666
\(47\) 1.09313 0.159450 0.0797248 0.996817i \(-0.474596\pi\)
0.0797248 + 0.996817i \(0.474596\pi\)
\(48\) −1.14813 −0.165719
\(49\) 5.99332 0.856189
\(50\) 3.36601 0.476025
\(51\) −2.96711 −0.415478
\(52\) 1.07318 0.148824
\(53\) 11.0126 1.51270 0.756351 0.654166i \(-0.226980\pi\)
0.756351 + 0.654166i \(0.226980\pi\)
\(54\) 5.37532 0.731488
\(55\) 8.92496 1.20344
\(56\) 3.60462 0.481688
\(57\) 1.14813 0.152074
\(58\) 5.13064 0.673685
\(59\) 7.21434 0.939228 0.469614 0.882872i \(-0.344393\pi\)
0.469614 + 0.882872i \(0.344393\pi\)
\(60\) −3.32087 −0.428722
\(61\) −11.7845 −1.50885 −0.754426 0.656385i \(-0.772085\pi\)
−0.754426 + 0.656385i \(0.772085\pi\)
\(62\) −0.677721 −0.0860707
\(63\) −6.06222 −0.763768
\(64\) 1.00000 0.125000
\(65\) 3.10408 0.385013
\(66\) −3.54274 −0.436082
\(67\) −14.8513 −1.81437 −0.907185 0.420732i \(-0.861773\pi\)
−0.907185 + 0.420732i \(0.861773\pi\)
\(68\) 2.58429 0.313391
\(69\) 1.33677 0.160928
\(70\) 10.4260 1.24615
\(71\) 8.91929 1.05852 0.529262 0.848458i \(-0.322469\pi\)
0.529262 + 0.848458i \(0.322469\pi\)
\(72\) −1.68179 −0.198201
\(73\) 3.33975 0.390889 0.195444 0.980715i \(-0.437385\pi\)
0.195444 + 0.980715i \(0.437385\pi\)
\(74\) −2.27963 −0.265001
\(75\) −3.86463 −0.446248
\(76\) −1.00000 −0.114708
\(77\) 11.1226 1.26754
\(78\) −1.23216 −0.139514
\(79\) −10.6382 −1.19689 −0.598447 0.801162i \(-0.704215\pi\)
−0.598447 + 0.801162i \(0.704215\pi\)
\(80\) 2.89240 0.323381
\(81\) −1.12622 −0.125136
\(82\) −3.80407 −0.420089
\(83\) −4.72324 −0.518443 −0.259221 0.965818i \(-0.583466\pi\)
−0.259221 + 0.965818i \(0.583466\pi\)
\(84\) −4.13859 −0.451557
\(85\) 7.47481 0.810757
\(86\) 1.52856 0.164829
\(87\) −5.89066 −0.631545
\(88\) 3.08565 0.328932
\(89\) −0.242858 −0.0257429 −0.0128715 0.999917i \(-0.504097\pi\)
−0.0128715 + 0.999917i \(0.504097\pi\)
\(90\) −4.86441 −0.512754
\(91\) 3.86842 0.405520
\(92\) −1.16430 −0.121386
\(93\) 0.778115 0.0806868
\(94\) 1.09313 0.112748
\(95\) −2.89240 −0.296754
\(96\) −1.14813 −0.117181
\(97\) 0.265223 0.0269294 0.0134647 0.999909i \(-0.495714\pi\)
0.0134647 + 0.999909i \(0.495714\pi\)
\(98\) 5.99332 0.605417
\(99\) −5.18942 −0.521556
\(100\) 3.36601 0.336601
\(101\) 9.48072 0.943367 0.471683 0.881768i \(-0.343647\pi\)
0.471683 + 0.881768i \(0.343647\pi\)
\(102\) −2.96711 −0.293788
\(103\) 15.5020 1.52746 0.763728 0.645539i \(-0.223367\pi\)
0.763728 + 0.645539i \(0.223367\pi\)
\(104\) 1.07318 0.105234
\(105\) −11.9705 −1.16820
\(106\) 11.0126 1.06964
\(107\) 18.6332 1.80134 0.900670 0.434505i \(-0.143077\pi\)
0.900670 + 0.434505i \(0.143077\pi\)
\(108\) 5.37532 0.517240
\(109\) 3.82871 0.366724 0.183362 0.983045i \(-0.441302\pi\)
0.183362 + 0.983045i \(0.441302\pi\)
\(110\) 8.92496 0.850961
\(111\) 2.61732 0.248425
\(112\) 3.60462 0.340605
\(113\) 9.80817 0.922675 0.461337 0.887225i \(-0.347370\pi\)
0.461337 + 0.887225i \(0.347370\pi\)
\(114\) 1.14813 0.107533
\(115\) −3.36761 −0.314032
\(116\) 5.13064 0.476368
\(117\) −1.80486 −0.166860
\(118\) 7.21434 0.664134
\(119\) 9.31539 0.853940
\(120\) −3.32087 −0.303152
\(121\) −1.47874 −0.134431
\(122\) −11.7845 −1.06692
\(123\) 4.36758 0.393811
\(124\) −0.677721 −0.0608612
\(125\) −4.72617 −0.422722
\(126\) −6.06222 −0.540065
\(127\) −17.2883 −1.53409 −0.767043 0.641596i \(-0.778273\pi\)
−0.767043 + 0.641596i \(0.778273\pi\)
\(128\) 1.00000 0.0883883
\(129\) −1.75499 −0.154518
\(130\) 3.10408 0.272245
\(131\) −12.1046 −1.05759 −0.528794 0.848750i \(-0.677356\pi\)
−0.528794 + 0.848750i \(0.677356\pi\)
\(132\) −3.54274 −0.308356
\(133\) −3.60462 −0.312561
\(134\) −14.8513 −1.28295
\(135\) 15.5476 1.33812
\(136\) 2.58429 0.221601
\(137\) 0.462454 0.0395101 0.0197551 0.999805i \(-0.493711\pi\)
0.0197551 + 0.999805i \(0.493711\pi\)
\(138\) 1.33677 0.113793
\(139\) −8.83197 −0.749118 −0.374559 0.927203i \(-0.622206\pi\)
−0.374559 + 0.927203i \(0.622206\pi\)
\(140\) 10.4260 0.881161
\(141\) −1.25506 −0.105695
\(142\) 8.91929 0.748490
\(143\) 3.31147 0.276919
\(144\) −1.68179 −0.140149
\(145\) 14.8399 1.23238
\(146\) 3.33975 0.276400
\(147\) −6.88113 −0.567546
\(148\) −2.27963 −0.187384
\(149\) −4.05865 −0.332498 −0.166249 0.986084i \(-0.553166\pi\)
−0.166249 + 0.986084i \(0.553166\pi\)
\(150\) −3.86463 −0.315545
\(151\) 16.1335 1.31293 0.656465 0.754357i \(-0.272051\pi\)
0.656465 + 0.754357i \(0.272051\pi\)
\(152\) −1.00000 −0.0811107
\(153\) −4.34623 −0.351372
\(154\) 11.1226 0.896287
\(155\) −1.96024 −0.157451
\(156\) −1.23216 −0.0986514
\(157\) −17.7036 −1.41290 −0.706451 0.707762i \(-0.749705\pi\)
−0.706451 + 0.707762i \(0.749705\pi\)
\(158\) −10.6382 −0.846332
\(159\) −12.6440 −1.00273
\(160\) 2.89240 0.228665
\(161\) −4.19685 −0.330758
\(162\) −1.12622 −0.0884843
\(163\) −1.50056 −0.117533 −0.0587665 0.998272i \(-0.518717\pi\)
−0.0587665 + 0.998272i \(0.518717\pi\)
\(164\) −3.80407 −0.297048
\(165\) −10.2470 −0.797732
\(166\) −4.72324 −0.366594
\(167\) −12.3838 −0.958286 −0.479143 0.877737i \(-0.659053\pi\)
−0.479143 + 0.877737i \(0.659053\pi\)
\(168\) −4.13859 −0.319299
\(169\) −11.8483 −0.911406
\(170\) 7.47481 0.573292
\(171\) 1.68179 0.128610
\(172\) 1.52856 0.116551
\(173\) −13.4040 −1.01908 −0.509542 0.860446i \(-0.670185\pi\)
−0.509542 + 0.860446i \(0.670185\pi\)
\(174\) −5.89066 −0.446570
\(175\) 12.1332 0.917183
\(176\) 3.08565 0.232590
\(177\) −8.28303 −0.622591
\(178\) −0.242858 −0.0182030
\(179\) 11.7540 0.878535 0.439268 0.898356i \(-0.355238\pi\)
0.439268 + 0.898356i \(0.355238\pi\)
\(180\) −4.86441 −0.362572
\(181\) 15.2678 1.13485 0.567423 0.823426i \(-0.307940\pi\)
0.567423 + 0.823426i \(0.307940\pi\)
\(182\) 3.86842 0.286746
\(183\) 13.5302 1.00018
\(184\) −1.16430 −0.0858330
\(185\) −6.59360 −0.484771
\(186\) 0.778115 0.0570542
\(187\) 7.97422 0.583133
\(188\) 1.09313 0.0797248
\(189\) 19.3760 1.40940
\(190\) −2.89240 −0.209837
\(191\) 6.05520 0.438139 0.219070 0.975709i \(-0.429698\pi\)
0.219070 + 0.975709i \(0.429698\pi\)
\(192\) −1.14813 −0.0828594
\(193\) −8.50248 −0.612022 −0.306011 0.952028i \(-0.598994\pi\)
−0.306011 + 0.952028i \(0.598994\pi\)
\(194\) 0.265223 0.0190419
\(195\) −3.56389 −0.255216
\(196\) 5.99332 0.428094
\(197\) −1.75387 −0.124958 −0.0624791 0.998046i \(-0.519901\pi\)
−0.0624791 + 0.998046i \(0.519901\pi\)
\(198\) −5.18942 −0.368796
\(199\) 7.86507 0.557540 0.278770 0.960358i \(-0.410073\pi\)
0.278770 + 0.960358i \(0.410073\pi\)
\(200\) 3.36601 0.238013
\(201\) 17.0512 1.20270
\(202\) 9.48072 0.667061
\(203\) 18.4940 1.29803
\(204\) −2.96711 −0.207739
\(205\) −11.0029 −0.768476
\(206\) 15.5020 1.08007
\(207\) 1.95810 0.136097
\(208\) 1.07318 0.0744118
\(209\) −3.08565 −0.213439
\(210\) −11.9705 −0.826042
\(211\) −1.00000 −0.0688428
\(212\) 11.0126 0.756351
\(213\) −10.2405 −0.701670
\(214\) 18.6332 1.27374
\(215\) 4.42121 0.301524
\(216\) 5.37532 0.365744
\(217\) −2.44293 −0.165837
\(218\) 3.82871 0.259313
\(219\) −3.83448 −0.259110
\(220\) 8.92496 0.601721
\(221\) 2.77341 0.186560
\(222\) 2.61732 0.175663
\(223\) −5.48270 −0.367149 −0.183574 0.983006i \(-0.558767\pi\)
−0.183574 + 0.983006i \(0.558767\pi\)
\(224\) 3.60462 0.240844
\(225\) −5.66091 −0.377394
\(226\) 9.80817 0.652430
\(227\) −3.85510 −0.255872 −0.127936 0.991782i \(-0.540835\pi\)
−0.127936 + 0.991782i \(0.540835\pi\)
\(228\) 1.14813 0.0760370
\(229\) −21.4613 −1.41821 −0.709103 0.705105i \(-0.750900\pi\)
−0.709103 + 0.705105i \(0.750900\pi\)
\(230\) −3.36761 −0.222054
\(231\) −12.7703 −0.840222
\(232\) 5.13064 0.336843
\(233\) −12.9795 −0.850315 −0.425157 0.905119i \(-0.639781\pi\)
−0.425157 + 0.905119i \(0.639781\pi\)
\(234\) −1.80486 −0.117988
\(235\) 3.16178 0.206252
\(236\) 7.21434 0.469614
\(237\) 12.2141 0.793392
\(238\) 9.31539 0.603827
\(239\) −7.42290 −0.480148 −0.240074 0.970755i \(-0.577172\pi\)
−0.240074 + 0.970755i \(0.577172\pi\)
\(240\) −3.32087 −0.214361
\(241\) 26.4390 1.70308 0.851542 0.524286i \(-0.175668\pi\)
0.851542 + 0.524286i \(0.175668\pi\)
\(242\) −1.47874 −0.0950571
\(243\) −14.8329 −0.951531
\(244\) −11.7845 −0.754426
\(245\) 17.3351 1.10750
\(246\) 4.36758 0.278467
\(247\) −1.07318 −0.0682849
\(248\) −0.677721 −0.0430354
\(249\) 5.42291 0.343663
\(250\) −4.72617 −0.298909
\(251\) −18.0281 −1.13792 −0.568962 0.822364i \(-0.692655\pi\)
−0.568962 + 0.822364i \(0.692655\pi\)
\(252\) −6.06222 −0.381884
\(253\) −3.59261 −0.225866
\(254\) −17.2883 −1.08476
\(255\) −8.58208 −0.537431
\(256\) 1.00000 0.0625000
\(257\) −7.48343 −0.466804 −0.233402 0.972380i \(-0.574986\pi\)
−0.233402 + 0.972380i \(0.574986\pi\)
\(258\) −1.75499 −0.109261
\(259\) −8.21720 −0.510592
\(260\) 3.10408 0.192507
\(261\) −8.62864 −0.534100
\(262\) −12.1046 −0.747828
\(263\) −15.8610 −0.978030 −0.489015 0.872275i \(-0.662644\pi\)
−0.489015 + 0.872275i \(0.662644\pi\)
\(264\) −3.54274 −0.218041
\(265\) 31.8530 1.95671
\(266\) −3.60462 −0.221014
\(267\) 0.278834 0.0170644
\(268\) −14.8513 −0.907185
\(269\) 15.8287 0.965094 0.482547 0.875870i \(-0.339712\pi\)
0.482547 + 0.875870i \(0.339712\pi\)
\(270\) 15.5476 0.946197
\(271\) −3.22902 −0.196149 −0.0980744 0.995179i \(-0.531268\pi\)
−0.0980744 + 0.995179i \(0.531268\pi\)
\(272\) 2.58429 0.156696
\(273\) −4.44146 −0.268809
\(274\) 0.462454 0.0279379
\(275\) 10.3863 0.626319
\(276\) 1.33677 0.0804639
\(277\) −23.7207 −1.42524 −0.712620 0.701550i \(-0.752492\pi\)
−0.712620 + 0.701550i \(0.752492\pi\)
\(278\) −8.83197 −0.529706
\(279\) 1.13978 0.0682371
\(280\) 10.4260 0.623075
\(281\) −3.25297 −0.194056 −0.0970280 0.995282i \(-0.530934\pi\)
−0.0970280 + 0.995282i \(0.530934\pi\)
\(282\) −1.25506 −0.0747378
\(283\) −20.4911 −1.21807 −0.609034 0.793144i \(-0.708443\pi\)
−0.609034 + 0.793144i \(0.708443\pi\)
\(284\) 8.91929 0.529262
\(285\) 3.32087 0.196711
\(286\) 3.31147 0.195811
\(287\) −13.7122 −0.809408
\(288\) −1.68179 −0.0991003
\(289\) −10.3215 −0.607144
\(290\) 14.8399 0.871427
\(291\) −0.304512 −0.0178508
\(292\) 3.33975 0.195444
\(293\) 24.1342 1.40994 0.704969 0.709238i \(-0.250961\pi\)
0.704969 + 0.709238i \(0.250961\pi\)
\(294\) −6.88113 −0.401316
\(295\) 20.8668 1.21491
\(296\) −2.27963 −0.132501
\(297\) 16.5864 0.962439
\(298\) −4.05865 −0.235112
\(299\) −1.24950 −0.0722605
\(300\) −3.86463 −0.223124
\(301\) 5.50987 0.317584
\(302\) 16.1335 0.928381
\(303\) −10.8851 −0.625335
\(304\) −1.00000 −0.0573539
\(305\) −34.0856 −1.95173
\(306\) −4.34623 −0.248457
\(307\) 28.9899 1.65454 0.827272 0.561802i \(-0.189892\pi\)
0.827272 + 0.561802i \(0.189892\pi\)
\(308\) 11.1226 0.633770
\(309\) −17.7983 −1.01251
\(310\) −1.96024 −0.111334
\(311\) 20.6627 1.17168 0.585838 0.810428i \(-0.300765\pi\)
0.585838 + 0.810428i \(0.300765\pi\)
\(312\) −1.23216 −0.0697571
\(313\) 28.1894 1.59336 0.796678 0.604404i \(-0.206589\pi\)
0.796678 + 0.604404i \(0.206589\pi\)
\(314\) −17.7036 −0.999072
\(315\) −17.5344 −0.987951
\(316\) −10.6382 −0.598447
\(317\) −19.1312 −1.07452 −0.537258 0.843418i \(-0.680540\pi\)
−0.537258 + 0.843418i \(0.680540\pi\)
\(318\) −12.6440 −0.709039
\(319\) 15.8314 0.886386
\(320\) 2.89240 0.161690
\(321\) −21.3934 −1.19406
\(322\) −4.19685 −0.233881
\(323\) −2.58429 −0.143794
\(324\) −1.12622 −0.0625679
\(325\) 3.61234 0.200376
\(326\) −1.50056 −0.0831083
\(327\) −4.39587 −0.243092
\(328\) −3.80407 −0.210045
\(329\) 3.94033 0.217237
\(330\) −10.2470 −0.564081
\(331\) 11.9430 0.656446 0.328223 0.944600i \(-0.393550\pi\)
0.328223 + 0.944600i \(0.393550\pi\)
\(332\) −4.72324 −0.259221
\(333\) 3.83385 0.210094
\(334\) −12.3838 −0.677611
\(335\) −42.9558 −2.34693
\(336\) −4.13859 −0.225779
\(337\) 22.3523 1.21761 0.608804 0.793320i \(-0.291649\pi\)
0.608804 + 0.793320i \(0.291649\pi\)
\(338\) −11.8483 −0.644462
\(339\) −11.2611 −0.611618
\(340\) 7.47481 0.405378
\(341\) −2.09121 −0.113246
\(342\) 1.68179 0.0909407
\(343\) −3.62870 −0.195931
\(344\) 1.52856 0.0824143
\(345\) 3.86647 0.208164
\(346\) −13.4040 −0.720601
\(347\) 9.09589 0.488293 0.244146 0.969738i \(-0.421492\pi\)
0.244146 + 0.969738i \(0.421492\pi\)
\(348\) −5.89066 −0.315772
\(349\) −3.38526 −0.181209 −0.0906045 0.995887i \(-0.528880\pi\)
−0.0906045 + 0.995887i \(0.528880\pi\)
\(350\) 12.1332 0.648546
\(351\) 5.76869 0.307910
\(352\) 3.08565 0.164466
\(353\) 22.5913 1.20241 0.601207 0.799093i \(-0.294687\pi\)
0.601207 + 0.799093i \(0.294687\pi\)
\(354\) −8.28303 −0.440238
\(355\) 25.7982 1.36923
\(356\) −0.242858 −0.0128715
\(357\) −10.6953 −0.566056
\(358\) 11.7540 0.621218
\(359\) −2.77138 −0.146268 −0.0731338 0.997322i \(-0.523300\pi\)
−0.0731338 + 0.997322i \(0.523300\pi\)
\(360\) −4.86441 −0.256377
\(361\) 1.00000 0.0526316
\(362\) 15.2678 0.802457
\(363\) 1.69779 0.0891110
\(364\) 3.86842 0.202760
\(365\) 9.65992 0.505623
\(366\) 13.5302 0.707235
\(367\) −4.57543 −0.238836 −0.119418 0.992844i \(-0.538103\pi\)
−0.119418 + 0.992844i \(0.538103\pi\)
\(368\) −1.16430 −0.0606931
\(369\) 6.39764 0.333048
\(370\) −6.59360 −0.342785
\(371\) 39.6964 2.06094
\(372\) 0.778115 0.0403434
\(373\) −23.4072 −1.21198 −0.605990 0.795472i \(-0.707223\pi\)
−0.605990 + 0.795472i \(0.707223\pi\)
\(374\) 7.97422 0.412337
\(375\) 5.42628 0.280212
\(376\) 1.09313 0.0563739
\(377\) 5.50610 0.283579
\(378\) 19.3760 0.996595
\(379\) 6.81075 0.349845 0.174922 0.984582i \(-0.444033\pi\)
0.174922 + 0.984582i \(0.444033\pi\)
\(380\) −2.89240 −0.148377
\(381\) 19.8493 1.01691
\(382\) 6.05520 0.309811
\(383\) −31.2900 −1.59884 −0.799422 0.600769i \(-0.794861\pi\)
−0.799422 + 0.600769i \(0.794861\pi\)
\(384\) −1.14813 −0.0585905
\(385\) 32.1711 1.63959
\(386\) −8.50248 −0.432765
\(387\) −2.57071 −0.130677
\(388\) 0.265223 0.0134647
\(389\) 18.2539 0.925511 0.462755 0.886486i \(-0.346861\pi\)
0.462755 + 0.886486i \(0.346861\pi\)
\(390\) −3.56389 −0.180465
\(391\) −3.00887 −0.152165
\(392\) 5.99332 0.302708
\(393\) 13.8978 0.701049
\(394\) −1.75387 −0.0883587
\(395\) −30.7701 −1.54821
\(396\) −5.18942 −0.260778
\(397\) 38.3890 1.92669 0.963343 0.268272i \(-0.0864526\pi\)
0.963343 + 0.268272i \(0.0864526\pi\)
\(398\) 7.86507 0.394241
\(399\) 4.13859 0.207189
\(400\) 3.36601 0.168300
\(401\) 24.7296 1.23494 0.617468 0.786596i \(-0.288159\pi\)
0.617468 + 0.786596i \(0.288159\pi\)
\(402\) 17.0512 0.850438
\(403\) −0.727318 −0.0362303
\(404\) 9.48072 0.471683
\(405\) −3.25749 −0.161866
\(406\) 18.4940 0.917843
\(407\) −7.03414 −0.348669
\(408\) −2.96711 −0.146894
\(409\) −21.3875 −1.05754 −0.528772 0.848764i \(-0.677347\pi\)
−0.528772 + 0.848764i \(0.677347\pi\)
\(410\) −11.0029 −0.543395
\(411\) −0.530959 −0.0261903
\(412\) 15.5020 0.763728
\(413\) 26.0050 1.27962
\(414\) 1.95810 0.0962353
\(415\) −13.6615 −0.670617
\(416\) 1.07318 0.0526171
\(417\) 10.1403 0.496572
\(418\) −3.08565 −0.150924
\(419\) −16.4139 −0.801870 −0.400935 0.916107i \(-0.631315\pi\)
−0.400935 + 0.916107i \(0.631315\pi\)
\(420\) −11.9705 −0.584100
\(421\) 28.9547 1.41116 0.705582 0.708629i \(-0.250686\pi\)
0.705582 + 0.708629i \(0.250686\pi\)
\(422\) −1.00000 −0.0486792
\(423\) −1.83841 −0.0893868
\(424\) 11.0126 0.534821
\(425\) 8.69873 0.421950
\(426\) −10.2405 −0.496156
\(427\) −42.4788 −2.05569
\(428\) 18.6332 0.900670
\(429\) −3.80201 −0.183563
\(430\) 4.42121 0.213209
\(431\) 25.4238 1.22462 0.612311 0.790617i \(-0.290240\pi\)
0.612311 + 0.790617i \(0.290240\pi\)
\(432\) 5.37532 0.258620
\(433\) 14.1481 0.679916 0.339958 0.940441i \(-0.389587\pi\)
0.339958 + 0.940441i \(0.389587\pi\)
\(434\) −2.44293 −0.117264
\(435\) −17.0382 −0.816917
\(436\) 3.82871 0.183362
\(437\) 1.16430 0.0556958
\(438\) −3.83448 −0.183219
\(439\) −0.514582 −0.0245597 −0.0122798 0.999925i \(-0.503909\pi\)
−0.0122798 + 0.999925i \(0.503909\pi\)
\(440\) 8.92496 0.425481
\(441\) −10.0795 −0.479976
\(442\) 2.77341 0.131918
\(443\) 31.2539 1.48492 0.742459 0.669891i \(-0.233659\pi\)
0.742459 + 0.669891i \(0.233659\pi\)
\(444\) 2.61732 0.124212
\(445\) −0.702445 −0.0332991
\(446\) −5.48270 −0.259613
\(447\) 4.65988 0.220405
\(448\) 3.60462 0.170303
\(449\) 27.1541 1.28148 0.640740 0.767758i \(-0.278628\pi\)
0.640740 + 0.767758i \(0.278628\pi\)
\(450\) −5.66091 −0.266858
\(451\) −11.7380 −0.552723
\(452\) 9.80817 0.461337
\(453\) −18.5235 −0.870309
\(454\) −3.85510 −0.180929
\(455\) 11.1890 0.524550
\(456\) 1.14813 0.0537663
\(457\) 14.4320 0.675101 0.337551 0.941307i \(-0.390402\pi\)
0.337551 + 0.941307i \(0.390402\pi\)
\(458\) −21.4613 −1.00282
\(459\) 13.8914 0.648394
\(460\) −3.36761 −0.157016
\(461\) 21.3289 0.993386 0.496693 0.867926i \(-0.334548\pi\)
0.496693 + 0.867926i \(0.334548\pi\)
\(462\) −12.7703 −0.594126
\(463\) −33.5908 −1.56110 −0.780549 0.625094i \(-0.785061\pi\)
−0.780549 + 0.625094i \(0.785061\pi\)
\(464\) 5.13064 0.238184
\(465\) 2.25062 0.104370
\(466\) −12.9795 −0.601263
\(467\) −1.87156 −0.0866053 −0.0433027 0.999062i \(-0.513788\pi\)
−0.0433027 + 0.999062i \(0.513788\pi\)
\(468\) −1.80486 −0.0834299
\(469\) −53.5332 −2.47193
\(470\) 3.16178 0.145842
\(471\) 20.3261 0.936578
\(472\) 7.21434 0.332067
\(473\) 4.71660 0.216869
\(474\) 12.2141 0.561013
\(475\) −3.36601 −0.154443
\(476\) 9.31539 0.426970
\(477\) −18.5209 −0.848015
\(478\) −7.42290 −0.339516
\(479\) −12.3853 −0.565900 −0.282950 0.959135i \(-0.591313\pi\)
−0.282950 + 0.959135i \(0.591313\pi\)
\(480\) −3.32087 −0.151576
\(481\) −2.44645 −0.111549
\(482\) 26.4390 1.20426
\(483\) 4.81854 0.219251
\(484\) −1.47874 −0.0672155
\(485\) 0.767134 0.0348337
\(486\) −14.8329 −0.672834
\(487\) 29.3283 1.32899 0.664496 0.747292i \(-0.268646\pi\)
0.664496 + 0.747292i \(0.268646\pi\)
\(488\) −11.7845 −0.533460
\(489\) 1.72284 0.0779097
\(490\) 17.3351 0.783120
\(491\) −16.1721 −0.729834 −0.364917 0.931040i \(-0.618903\pi\)
−0.364917 + 0.931040i \(0.618903\pi\)
\(492\) 4.36758 0.196906
\(493\) 13.2590 0.597157
\(494\) −1.07318 −0.0482847
\(495\) −15.0099 −0.674645
\(496\) −0.677721 −0.0304306
\(497\) 32.1507 1.44216
\(498\) 5.42291 0.243006
\(499\) −9.16856 −0.410441 −0.205220 0.978716i \(-0.565791\pi\)
−0.205220 + 0.978716i \(0.565791\pi\)
\(500\) −4.72617 −0.211361
\(501\) 14.2182 0.635224
\(502\) −18.0281 −0.804634
\(503\) 9.02603 0.402451 0.201225 0.979545i \(-0.435508\pi\)
0.201225 + 0.979545i \(0.435508\pi\)
\(504\) −6.06222 −0.270033
\(505\) 27.4221 1.22027
\(506\) −3.59261 −0.159711
\(507\) 13.6034 0.604149
\(508\) −17.2883 −0.767043
\(509\) −39.3273 −1.74315 −0.871577 0.490259i \(-0.836902\pi\)
−0.871577 + 0.490259i \(0.836902\pi\)
\(510\) −8.58208 −0.380021
\(511\) 12.0386 0.532555
\(512\) 1.00000 0.0441942
\(513\) −5.37532 −0.237326
\(514\) −7.48343 −0.330080
\(515\) 44.8380 1.97580
\(516\) −1.75499 −0.0772590
\(517\) 3.37302 0.148345
\(518\) −8.21720 −0.361043
\(519\) 15.3895 0.675526
\(520\) 3.10408 0.136123
\(521\) 34.7695 1.52328 0.761640 0.648001i \(-0.224395\pi\)
0.761640 + 0.648001i \(0.224395\pi\)
\(522\) −8.62864 −0.377666
\(523\) −36.3544 −1.58967 −0.794834 0.606827i \(-0.792442\pi\)
−0.794834 + 0.606827i \(0.792442\pi\)
\(524\) −12.1046 −0.528794
\(525\) −13.9305 −0.607978
\(526\) −15.8610 −0.691572
\(527\) −1.75143 −0.0762934
\(528\) −3.54274 −0.154178
\(529\) −21.6444 −0.941062
\(530\) 31.8530 1.38361
\(531\) −12.1330 −0.526527
\(532\) −3.60462 −0.156280
\(533\) −4.08246 −0.176831
\(534\) 0.278834 0.0120663
\(535\) 53.8947 2.33007
\(536\) −14.8513 −0.641477
\(537\) −13.4952 −0.582360
\(538\) 15.8287 0.682424
\(539\) 18.4933 0.796563
\(540\) 15.5476 0.669062
\(541\) −5.54859 −0.238553 −0.119276 0.992861i \(-0.538057\pi\)
−0.119276 + 0.992861i \(0.538057\pi\)
\(542\) −3.22902 −0.138698
\(543\) −17.5295 −0.752262
\(544\) 2.58429 0.110800
\(545\) 11.0742 0.474366
\(546\) −4.44146 −0.190077
\(547\) 5.05168 0.215994 0.107997 0.994151i \(-0.465556\pi\)
0.107997 + 0.994151i \(0.465556\pi\)
\(548\) 0.462454 0.0197551
\(549\) 19.8191 0.845857
\(550\) 10.3863 0.442875
\(551\) −5.13064 −0.218572
\(552\) 1.33677 0.0568966
\(553\) −38.3468 −1.63067
\(554\) −23.7207 −1.00780
\(555\) 7.57034 0.321343
\(556\) −8.83197 −0.374559
\(557\) 6.42784 0.272356 0.136178 0.990684i \(-0.456518\pi\)
0.136178 + 0.990684i \(0.456518\pi\)
\(558\) 1.13978 0.0482509
\(559\) 1.64042 0.0693823
\(560\) 10.4260 0.440580
\(561\) −9.15547 −0.386544
\(562\) −3.25297 −0.137218
\(563\) −32.5159 −1.37038 −0.685190 0.728364i \(-0.740281\pi\)
−0.685190 + 0.728364i \(0.740281\pi\)
\(564\) −1.25506 −0.0528476
\(565\) 28.3692 1.19350
\(566\) −20.4911 −0.861304
\(567\) −4.05961 −0.170487
\(568\) 8.91929 0.374245
\(569\) 5.47372 0.229470 0.114735 0.993396i \(-0.463398\pi\)
0.114735 + 0.993396i \(0.463398\pi\)
\(570\) 3.32087 0.139096
\(571\) −17.7775 −0.743966 −0.371983 0.928240i \(-0.621322\pi\)
−0.371983 + 0.928240i \(0.621322\pi\)
\(572\) 3.31147 0.138459
\(573\) −6.95218 −0.290432
\(574\) −13.7122 −0.572338
\(575\) −3.91902 −0.163435
\(576\) −1.68179 −0.0700745
\(577\) 47.0623 1.95923 0.979614 0.200888i \(-0.0643827\pi\)
0.979614 + 0.200888i \(0.0643827\pi\)
\(578\) −10.3215 −0.429316
\(579\) 9.76199 0.405694
\(580\) 14.8399 0.616192
\(581\) −17.0255 −0.706337
\(582\) −0.304512 −0.0126224
\(583\) 33.9812 1.40736
\(584\) 3.33975 0.138200
\(585\) −5.22040 −0.215837
\(586\) 24.1342 0.996976
\(587\) 13.6260 0.562405 0.281203 0.959648i \(-0.409267\pi\)
0.281203 + 0.959648i \(0.409267\pi\)
\(588\) −6.88113 −0.283773
\(589\) 0.677721 0.0279250
\(590\) 20.8668 0.859073
\(591\) 2.01368 0.0828317
\(592\) −2.27963 −0.0936920
\(593\) −24.2196 −0.994580 −0.497290 0.867584i \(-0.665671\pi\)
−0.497290 + 0.867584i \(0.665671\pi\)
\(594\) 16.5864 0.680547
\(595\) 26.9439 1.10459
\(596\) −4.05865 −0.166249
\(597\) −9.03016 −0.369580
\(598\) −1.24950 −0.0510959
\(599\) −37.9391 −1.55015 −0.775074 0.631870i \(-0.782287\pi\)
−0.775074 + 0.631870i \(0.782287\pi\)
\(600\) −3.86463 −0.157773
\(601\) 23.0960 0.942104 0.471052 0.882106i \(-0.343874\pi\)
0.471052 + 0.882106i \(0.343874\pi\)
\(602\) 5.50987 0.224566
\(603\) 24.9767 1.01713
\(604\) 16.1335 0.656465
\(605\) −4.27712 −0.173890
\(606\) −10.8851 −0.442178
\(607\) 16.7339 0.679209 0.339604 0.940568i \(-0.389707\pi\)
0.339604 + 0.940568i \(0.389707\pi\)
\(608\) −1.00000 −0.0405554
\(609\) −21.2336 −0.860429
\(610\) −34.0856 −1.38008
\(611\) 1.17313 0.0474597
\(612\) −4.34623 −0.175686
\(613\) −25.7889 −1.04160 −0.520802 0.853678i \(-0.674367\pi\)
−0.520802 + 0.853678i \(0.674367\pi\)
\(614\) 28.9899 1.16994
\(615\) 12.6328 0.509404
\(616\) 11.1226 0.448143
\(617\) 9.86843 0.397288 0.198644 0.980072i \(-0.436346\pi\)
0.198644 + 0.980072i \(0.436346\pi\)
\(618\) −17.7983 −0.715955
\(619\) −8.02685 −0.322626 −0.161313 0.986903i \(-0.551573\pi\)
−0.161313 + 0.986903i \(0.551573\pi\)
\(620\) −1.96024 −0.0787253
\(621\) −6.25846 −0.251143
\(622\) 20.6627 0.828500
\(623\) −0.875414 −0.0350727
\(624\) −1.23216 −0.0493257
\(625\) −30.5000 −1.22000
\(626\) 28.1894 1.12667
\(627\) 3.54274 0.141484
\(628\) −17.7036 −0.706451
\(629\) −5.89121 −0.234898
\(630\) −17.5344 −0.698587
\(631\) 4.70063 0.187129 0.0935646 0.995613i \(-0.470174\pi\)
0.0935646 + 0.995613i \(0.470174\pi\)
\(632\) −10.6382 −0.423166
\(633\) 1.14813 0.0456342
\(634\) −19.1312 −0.759798
\(635\) −50.0047 −1.98438
\(636\) −12.6440 −0.501367
\(637\) 6.43192 0.254842
\(638\) 15.8314 0.626770
\(639\) −15.0004 −0.593405
\(640\) 2.89240 0.114332
\(641\) −43.4498 −1.71617 −0.858083 0.513511i \(-0.828344\pi\)
−0.858083 + 0.513511i \(0.828344\pi\)
\(642\) −21.3934 −0.844330
\(643\) −7.19718 −0.283829 −0.141914 0.989879i \(-0.545326\pi\)
−0.141914 + 0.989879i \(0.545326\pi\)
\(644\) −4.19685 −0.165379
\(645\) −5.07614 −0.199873
\(646\) −2.58429 −0.101677
\(647\) 13.0129 0.511589 0.255794 0.966731i \(-0.417663\pi\)
0.255794 + 0.966731i \(0.417663\pi\)
\(648\) −1.12622 −0.0442422
\(649\) 22.2610 0.873819
\(650\) 3.61234 0.141687
\(651\) 2.80481 0.109929
\(652\) −1.50056 −0.0587665
\(653\) 22.9873 0.899564 0.449782 0.893138i \(-0.351502\pi\)
0.449782 + 0.893138i \(0.351502\pi\)
\(654\) −4.39587 −0.171892
\(655\) −35.0115 −1.36801
\(656\) −3.80407 −0.148524
\(657\) −5.61676 −0.219131
\(658\) 3.94033 0.153610
\(659\) 3.50503 0.136537 0.0682684 0.997667i \(-0.478253\pi\)
0.0682684 + 0.997667i \(0.478253\pi\)
\(660\) −10.2470 −0.398866
\(661\) −28.9152 −1.12467 −0.562336 0.826909i \(-0.690097\pi\)
−0.562336 + 0.826909i \(0.690097\pi\)
\(662\) 11.9430 0.464178
\(663\) −3.18425 −0.123666
\(664\) −4.72324 −0.183297
\(665\) −10.4260 −0.404304
\(666\) 3.83385 0.148559
\(667\) −5.97357 −0.231298
\(668\) −12.3838 −0.479143
\(669\) 6.29488 0.243374
\(670\) −42.9558 −1.65953
\(671\) −36.3629 −1.40378
\(672\) −4.13859 −0.159650
\(673\) −3.99305 −0.153921 −0.0769603 0.997034i \(-0.524521\pi\)
−0.0769603 + 0.997034i \(0.524521\pi\)
\(674\) 22.3523 0.860979
\(675\) 18.0934 0.696414
\(676\) −11.8483 −0.455703
\(677\) −39.0687 −1.50153 −0.750766 0.660568i \(-0.770315\pi\)
−0.750766 + 0.660568i \(0.770315\pi\)
\(678\) −11.2611 −0.432480
\(679\) 0.956031 0.0366891
\(680\) 7.47481 0.286646
\(681\) 4.42618 0.169611
\(682\) −2.09121 −0.0800767
\(683\) −9.58891 −0.366909 −0.183455 0.983028i \(-0.558728\pi\)
−0.183455 + 0.983028i \(0.558728\pi\)
\(684\) 1.68179 0.0643048
\(685\) 1.33760 0.0511072
\(686\) −3.62870 −0.138544
\(687\) 24.6405 0.940093
\(688\) 1.52856 0.0582757
\(689\) 11.8186 0.450251
\(690\) 3.86647 0.147194
\(691\) −13.1465 −0.500116 −0.250058 0.968231i \(-0.580450\pi\)
−0.250058 + 0.968231i \(0.580450\pi\)
\(692\) −13.4040 −0.509542
\(693\) −18.7059 −0.710578
\(694\) 9.09589 0.345275
\(695\) −25.5456 −0.969001
\(696\) −5.89066 −0.223285
\(697\) −9.83081 −0.372369
\(698\) −3.38526 −0.128134
\(699\) 14.9022 0.563653
\(700\) 12.1332 0.458591
\(701\) 5.51304 0.208225 0.104112 0.994566i \(-0.466800\pi\)
0.104112 + 0.994566i \(0.466800\pi\)
\(702\) 5.76869 0.217725
\(703\) 2.27963 0.0859777
\(704\) 3.08565 0.116295
\(705\) −3.63014 −0.136719
\(706\) 22.5913 0.850236
\(707\) 34.1744 1.28526
\(708\) −8.28303 −0.311295
\(709\) 42.9535 1.61315 0.806575 0.591131i \(-0.201318\pi\)
0.806575 + 0.591131i \(0.201318\pi\)
\(710\) 25.7982 0.968189
\(711\) 17.8913 0.670975
\(712\) −0.242858 −0.00910151
\(713\) 0.789068 0.0295508
\(714\) −10.6953 −0.400262
\(715\) 9.57810 0.358201
\(716\) 11.7540 0.439268
\(717\) 8.52248 0.318278
\(718\) −2.77138 −0.103427
\(719\) −17.5295 −0.653741 −0.326871 0.945069i \(-0.605994\pi\)
−0.326871 + 0.945069i \(0.605994\pi\)
\(720\) −4.86441 −0.181286
\(721\) 55.8788 2.08104
\(722\) 1.00000 0.0372161
\(723\) −30.3555 −1.12893
\(724\) 15.2678 0.567423
\(725\) 17.2697 0.641382
\(726\) 1.69779 0.0630110
\(727\) −0.524755 −0.0194621 −0.00973105 0.999953i \(-0.503098\pi\)
−0.00973105 + 0.999953i \(0.503098\pi\)
\(728\) 3.86842 0.143373
\(729\) 20.4088 0.755883
\(730\) 9.65992 0.357530
\(731\) 3.95023 0.146105
\(732\) 13.5302 0.500091
\(733\) 37.6584 1.39095 0.695473 0.718552i \(-0.255195\pi\)
0.695473 + 0.718552i \(0.255195\pi\)
\(734\) −4.57543 −0.168882
\(735\) −19.9030 −0.734134
\(736\) −1.16430 −0.0429165
\(737\) −45.8258 −1.68802
\(738\) 6.39764 0.235500
\(739\) −17.3819 −0.639402 −0.319701 0.947518i \(-0.603583\pi\)
−0.319701 + 0.947518i \(0.603583\pi\)
\(740\) −6.59360 −0.242386
\(741\) 1.23216 0.0452644
\(742\) 39.6964 1.45730
\(743\) 33.2555 1.22003 0.610013 0.792391i \(-0.291164\pi\)
0.610013 + 0.792391i \(0.291164\pi\)
\(744\) 0.778115 0.0285271
\(745\) −11.7393 −0.430094
\(746\) −23.4072 −0.857000
\(747\) 7.94349 0.290637
\(748\) 7.97422 0.291566
\(749\) 67.1657 2.45418
\(750\) 5.42628 0.198140
\(751\) −31.0890 −1.13446 −0.567228 0.823561i \(-0.691984\pi\)
−0.567228 + 0.823561i \(0.691984\pi\)
\(752\) 1.09313 0.0398624
\(753\) 20.6987 0.754302
\(754\) 5.50610 0.200520
\(755\) 46.6647 1.69830
\(756\) 19.3760 0.704699
\(757\) 6.61706 0.240501 0.120251 0.992744i \(-0.461630\pi\)
0.120251 + 0.992744i \(0.461630\pi\)
\(758\) 6.81075 0.247378
\(759\) 4.12480 0.149721
\(760\) −2.89240 −0.104919
\(761\) −32.5345 −1.17937 −0.589687 0.807632i \(-0.700749\pi\)
−0.589687 + 0.807632i \(0.700749\pi\)
\(762\) 19.8493 0.719063
\(763\) 13.8011 0.499632
\(764\) 6.05520 0.219070
\(765\) −12.5710 −0.454507
\(766\) −31.2900 −1.13055
\(767\) 7.74230 0.279558
\(768\) −1.14813 −0.0414297
\(769\) 31.8448 1.14835 0.574177 0.818731i \(-0.305322\pi\)
0.574177 + 0.818731i \(0.305322\pi\)
\(770\) 32.1711 1.15937
\(771\) 8.59198 0.309433
\(772\) −8.50248 −0.306011
\(773\) 50.4131 1.81323 0.906616 0.421957i \(-0.138657\pi\)
0.906616 + 0.421957i \(0.138657\pi\)
\(774\) −2.57071 −0.0924023
\(775\) −2.28121 −0.0819436
\(776\) 0.265223 0.00952097
\(777\) 9.43444 0.338459
\(778\) 18.2539 0.654435
\(779\) 3.80407 0.136295
\(780\) −3.56389 −0.127608
\(781\) 27.5218 0.984808
\(782\) −3.00887 −0.107597
\(783\) 27.5788 0.985586
\(784\) 5.99332 0.214047
\(785\) −51.2060 −1.82762
\(786\) 13.8978 0.495717
\(787\) −35.4413 −1.26335 −0.631673 0.775235i \(-0.717631\pi\)
−0.631673 + 0.775235i \(0.717631\pi\)
\(788\) −1.75387 −0.0624791
\(789\) 18.2105 0.648312
\(790\) −30.7701 −1.09475
\(791\) 35.3548 1.25707
\(792\) −5.18942 −0.184398
\(793\) −12.6469 −0.449105
\(794\) 38.3890 1.36237
\(795\) −36.5715 −1.29706
\(796\) 7.86507 0.278770
\(797\) 22.0512 0.781095 0.390547 0.920583i \(-0.372286\pi\)
0.390547 + 0.920583i \(0.372286\pi\)
\(798\) 4.13859 0.146505
\(799\) 2.82497 0.0999401
\(800\) 3.36601 0.119006
\(801\) 0.408437 0.0144314
\(802\) 24.7296 0.873231
\(803\) 10.3053 0.363667
\(804\) 17.0512 0.601351
\(805\) −12.1390 −0.427843
\(806\) −0.727318 −0.0256187
\(807\) −18.1735 −0.639737
\(808\) 9.48072 0.333530
\(809\) −9.18925 −0.323077 −0.161538 0.986866i \(-0.551646\pi\)
−0.161538 + 0.986866i \(0.551646\pi\)
\(810\) −3.25749 −0.114456
\(811\) 9.37174 0.329086 0.164543 0.986370i \(-0.447385\pi\)
0.164543 + 0.986370i \(0.447385\pi\)
\(812\) 18.4940 0.649013
\(813\) 3.70734 0.130022
\(814\) −7.03414 −0.246546
\(815\) −4.34023 −0.152032
\(816\) −2.96711 −0.103870
\(817\) −1.52856 −0.0534774
\(818\) −21.3875 −0.747796
\(819\) −6.50586 −0.227333
\(820\) −11.0029 −0.384238
\(821\) −47.5802 −1.66056 −0.830280 0.557347i \(-0.811819\pi\)
−0.830280 + 0.557347i \(0.811819\pi\)
\(822\) −0.530959 −0.0185193
\(823\) −37.1208 −1.29395 −0.646975 0.762511i \(-0.723966\pi\)
−0.646975 + 0.762511i \(0.723966\pi\)
\(824\) 15.5020 0.540037
\(825\) −11.9249 −0.415172
\(826\) 26.0050 0.904830
\(827\) 14.2641 0.496011 0.248005 0.968759i \(-0.420225\pi\)
0.248005 + 0.968759i \(0.420225\pi\)
\(828\) 1.95810 0.0680486
\(829\) 40.2831 1.39909 0.699546 0.714588i \(-0.253386\pi\)
0.699546 + 0.714588i \(0.253386\pi\)
\(830\) −13.6615 −0.474198
\(831\) 27.2346 0.944757
\(832\) 1.07318 0.0372059
\(833\) 15.4885 0.536644
\(834\) 10.1403 0.351129
\(835\) −35.8189 −1.23957
\(836\) −3.08565 −0.106720
\(837\) −3.64297 −0.125919
\(838\) −16.4139 −0.567007
\(839\) −35.2303 −1.21629 −0.608143 0.793828i \(-0.708085\pi\)
−0.608143 + 0.793828i \(0.708085\pi\)
\(840\) −11.9705 −0.413021
\(841\) −2.67658 −0.0922958
\(842\) 28.9547 0.997843
\(843\) 3.73485 0.128635
\(844\) −1.00000 −0.0344214
\(845\) −34.2700 −1.17892
\(846\) −1.83841 −0.0632060
\(847\) −5.33031 −0.183152
\(848\) 11.0126 0.378176
\(849\) 23.5265 0.807427
\(850\) 8.69873 0.298364
\(851\) 2.65416 0.0909833
\(852\) −10.2405 −0.350835
\(853\) 1.99140 0.0681841 0.0340920 0.999419i \(-0.489146\pi\)
0.0340920 + 0.999419i \(0.489146\pi\)
\(854\) −42.4788 −1.45359
\(855\) 4.86441 0.166359
\(856\) 18.6332 0.636870
\(857\) −15.6461 −0.534462 −0.267231 0.963632i \(-0.586109\pi\)
−0.267231 + 0.963632i \(0.586109\pi\)
\(858\) −3.80201 −0.129798
\(859\) 28.4105 0.969355 0.484678 0.874693i \(-0.338937\pi\)
0.484678 + 0.874693i \(0.338937\pi\)
\(860\) 4.42121 0.150762
\(861\) 15.7435 0.536537
\(862\) 25.4238 0.865939
\(863\) −45.9406 −1.56384 −0.781919 0.623380i \(-0.785759\pi\)
−0.781919 + 0.623380i \(0.785759\pi\)
\(864\) 5.37532 0.182872
\(865\) −38.7697 −1.31821
\(866\) 14.1481 0.480773
\(867\) 11.8504 0.402461
\(868\) −2.44293 −0.0829185
\(869\) −32.8259 −1.11354
\(870\) −17.0382 −0.577648
\(871\) −15.9381 −0.540042
\(872\) 3.82871 0.129657
\(873\) −0.446050 −0.0150965
\(874\) 1.16430 0.0393829
\(875\) −17.0361 −0.575925
\(876\) −3.83448 −0.129555
\(877\) −50.8605 −1.71744 −0.858719 0.512447i \(-0.828739\pi\)
−0.858719 + 0.512447i \(0.828739\pi\)
\(878\) −0.514582 −0.0173663
\(879\) −27.7093 −0.934613
\(880\) 8.92496 0.300860
\(881\) 24.2179 0.815922 0.407961 0.912999i \(-0.366240\pi\)
0.407961 + 0.912999i \(0.366240\pi\)
\(882\) −10.0795 −0.339394
\(883\) −45.4004 −1.52784 −0.763922 0.645308i \(-0.776729\pi\)
−0.763922 + 0.645308i \(0.776729\pi\)
\(884\) 2.77341 0.0932799
\(885\) −23.9579 −0.805335
\(886\) 31.2539 1.05000
\(887\) −37.2388 −1.25036 −0.625179 0.780482i \(-0.714974\pi\)
−0.625179 + 0.780482i \(0.714974\pi\)
\(888\) 2.61732 0.0878314
\(889\) −62.3177 −2.09007
\(890\) −0.702445 −0.0235460
\(891\) −3.47513 −0.116421
\(892\) −5.48270 −0.183574
\(893\) −1.09313 −0.0365802
\(894\) 4.65988 0.155850
\(895\) 33.9973 1.13641
\(896\) 3.60462 0.120422
\(897\) 1.43459 0.0478997
\(898\) 27.1541 0.906143
\(899\) −3.47714 −0.115969
\(900\) −5.66091 −0.188697
\(901\) 28.4598 0.948135
\(902\) −11.7380 −0.390834
\(903\) −6.32607 −0.210519
\(904\) 9.80817 0.326215
\(905\) 44.1606 1.46795
\(906\) −18.5235 −0.615401
\(907\) −10.2174 −0.339263 −0.169632 0.985508i \(-0.554258\pi\)
−0.169632 + 0.985508i \(0.554258\pi\)
\(908\) −3.85510 −0.127936
\(909\) −15.9446 −0.528848
\(910\) 11.1890 0.370913
\(911\) −20.4904 −0.678876 −0.339438 0.940628i \(-0.610237\pi\)
−0.339438 + 0.940628i \(0.610237\pi\)
\(912\) 1.14813 0.0380185
\(913\) −14.5743 −0.482338
\(914\) 14.4320 0.477369
\(915\) 39.1348 1.29376
\(916\) −21.4613 −0.709103
\(917\) −43.6327 −1.44088
\(918\) 13.8914 0.458484
\(919\) 22.3104 0.735953 0.367977 0.929835i \(-0.380051\pi\)
0.367977 + 0.929835i \(0.380051\pi\)
\(920\) −3.36761 −0.111027
\(921\) −33.2843 −1.09676
\(922\) 21.3289 0.702430
\(923\) 9.57201 0.315067
\(924\) −12.7703 −0.420111
\(925\) −7.67323 −0.252294
\(926\) −33.5908 −1.10386
\(927\) −26.0711 −0.856286
\(928\) 5.13064 0.168421
\(929\) −3.86980 −0.126964 −0.0634820 0.997983i \(-0.520221\pi\)
−0.0634820 + 0.997983i \(0.520221\pi\)
\(930\) 2.25062 0.0738009
\(931\) −5.99332 −0.196423
\(932\) −12.9795 −0.425157
\(933\) −23.7236 −0.776675
\(934\) −1.87156 −0.0612392
\(935\) 23.0647 0.754295
\(936\) −1.80486 −0.0589938
\(937\) −24.6326 −0.804712 −0.402356 0.915483i \(-0.631809\pi\)
−0.402356 + 0.915483i \(0.631809\pi\)
\(938\) −53.5332 −1.74792
\(939\) −32.3652 −1.05620
\(940\) 3.16178 0.103126
\(941\) −41.7786 −1.36195 −0.680973 0.732309i \(-0.738443\pi\)
−0.680973 + 0.732309i \(0.738443\pi\)
\(942\) 20.3261 0.662260
\(943\) 4.42906 0.144230
\(944\) 7.21434 0.234807
\(945\) 56.0433 1.82309
\(946\) 4.71660 0.153350
\(947\) 46.1205 1.49872 0.749358 0.662165i \(-0.230362\pi\)
0.749358 + 0.662165i \(0.230362\pi\)
\(948\) 12.2141 0.396696
\(949\) 3.58416 0.116347
\(950\) −3.36601 −0.109208
\(951\) 21.9652 0.712271
\(952\) 9.31539 0.301914
\(953\) 24.6958 0.799975 0.399987 0.916521i \(-0.369014\pi\)
0.399987 + 0.916521i \(0.369014\pi\)
\(954\) −18.5209 −0.599637
\(955\) 17.5141 0.566743
\(956\) −7.42290 −0.240074
\(957\) −18.1765 −0.587564
\(958\) −12.3853 −0.400152
\(959\) 1.66697 0.0538294
\(960\) −3.32087 −0.107181
\(961\) −30.5407 −0.985184
\(962\) −2.44645 −0.0788768
\(963\) −31.3371 −1.00982
\(964\) 26.4390 0.851542
\(965\) −24.5926 −0.791664
\(966\) 4.81854 0.155034
\(967\) 44.0588 1.41683 0.708417 0.705794i \(-0.249410\pi\)
0.708417 + 0.705794i \(0.249410\pi\)
\(968\) −1.47874 −0.0475286
\(969\) 2.96711 0.0953173
\(970\) 0.767134 0.0246312
\(971\) 26.9373 0.864460 0.432230 0.901764i \(-0.357727\pi\)
0.432230 + 0.901764i \(0.357727\pi\)
\(972\) −14.8329 −0.475766
\(973\) −31.8359 −1.02061
\(974\) 29.3283 0.939739
\(975\) −4.14744 −0.132825
\(976\) −11.7845 −0.377213
\(977\) 32.3232 1.03411 0.517055 0.855952i \(-0.327028\pi\)
0.517055 + 0.855952i \(0.327028\pi\)
\(978\) 1.72284 0.0550905
\(979\) −0.749377 −0.0239502
\(980\) 17.3351 0.553750
\(981\) −6.43908 −0.205584
\(982\) −16.1721 −0.516071
\(983\) −28.6064 −0.912402 −0.456201 0.889877i \(-0.650790\pi\)
−0.456201 + 0.889877i \(0.650790\pi\)
\(984\) 4.36758 0.139233
\(985\) −5.07290 −0.161636
\(986\) 13.2590 0.422254
\(987\) −4.52402 −0.144001
\(988\) −1.07318 −0.0341425
\(989\) −1.77969 −0.0565909
\(990\) −15.0099 −0.477046
\(991\) −0.869027 −0.0276056 −0.0138028 0.999905i \(-0.504394\pi\)
−0.0138028 + 0.999905i \(0.504394\pi\)
\(992\) −0.677721 −0.0215177
\(993\) −13.7122 −0.435142
\(994\) 32.1507 1.01976
\(995\) 22.7490 0.721191
\(996\) 5.42291 0.171831
\(997\) 6.73255 0.213222 0.106611 0.994301i \(-0.466000\pi\)
0.106611 + 0.994301i \(0.466000\pi\)
\(998\) −9.16856 −0.290226
\(999\) −12.2537 −0.387691
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 \(a_p\))