Properties

Label 8018.2.a.f.1.14
Level 8018
Weight 2
Character 8018.1
Self dual Yes
Analytic conductor 64.024
Analytic rank 1
Dimension 34
CM No

Related objects

Downloads

Learn more about

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: \(34\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.14
Character \(\chi\) = 8018.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} -1.11253 q^{3} +1.00000 q^{4} -2.63739 q^{5} +1.11253 q^{6} -4.04134 q^{7} -1.00000 q^{8} -1.76228 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -1.11253 q^{3} +1.00000 q^{4} -2.63739 q^{5} +1.11253 q^{6} -4.04134 q^{7} -1.00000 q^{8} -1.76228 q^{9} +2.63739 q^{10} -0.240117 q^{11} -1.11253 q^{12} -4.90150 q^{13} +4.04134 q^{14} +2.93417 q^{15} +1.00000 q^{16} -2.68375 q^{17} +1.76228 q^{18} -1.00000 q^{19} -2.63739 q^{20} +4.49610 q^{21} +0.240117 q^{22} +4.56012 q^{23} +1.11253 q^{24} +1.95582 q^{25} +4.90150 q^{26} +5.29817 q^{27} -4.04134 q^{28} -3.19444 q^{29} -2.93417 q^{30} +4.37170 q^{31} -1.00000 q^{32} +0.267137 q^{33} +2.68375 q^{34} +10.6586 q^{35} -1.76228 q^{36} -9.88907 q^{37} +1.00000 q^{38} +5.45305 q^{39} +2.63739 q^{40} -0.240486 q^{41} -4.49610 q^{42} +11.1937 q^{43} -0.240117 q^{44} +4.64783 q^{45} -4.56012 q^{46} +5.99061 q^{47} -1.11253 q^{48} +9.33245 q^{49} -1.95582 q^{50} +2.98575 q^{51} -4.90150 q^{52} -11.9229 q^{53} -5.29817 q^{54} +0.633283 q^{55} +4.04134 q^{56} +1.11253 q^{57} +3.19444 q^{58} -3.67352 q^{59} +2.93417 q^{60} +4.10473 q^{61} -4.37170 q^{62} +7.12199 q^{63} +1.00000 q^{64} +12.9272 q^{65} -0.267137 q^{66} +13.1464 q^{67} -2.68375 q^{68} -5.07326 q^{69} -10.6586 q^{70} +6.19117 q^{71} +1.76228 q^{72} +0.320560 q^{73} +9.88907 q^{74} -2.17591 q^{75} -1.00000 q^{76} +0.970397 q^{77} -5.45305 q^{78} +3.48112 q^{79} -2.63739 q^{80} -0.607511 q^{81} +0.240486 q^{82} +1.60709 q^{83} +4.49610 q^{84} +7.07809 q^{85} -11.1937 q^{86} +3.55390 q^{87} +0.240117 q^{88} +1.30673 q^{89} -4.64783 q^{90} +19.8086 q^{91} +4.56012 q^{92} -4.86364 q^{93} -5.99061 q^{94} +2.63739 q^{95} +1.11253 q^{96} -15.2653 q^{97} -9.33245 q^{98} +0.423155 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 34q - 34q^{2} - 10q^{3} + 34q^{4} + 7q^{5} + 10q^{6} - 6q^{7} - 34q^{8} + 38q^{9} + O(q^{10}) \) \( 34q - 34q^{2} - 10q^{3} + 34q^{4} + 7q^{5} + 10q^{6} - 6q^{7} - 34q^{8} + 38q^{9} - 7q^{10} + 4q^{11} - 10q^{12} - 5q^{13} + 6q^{14} - 17q^{15} + 34q^{16} + 8q^{17} - 38q^{18} - 34q^{19} + 7q^{20} - 4q^{22} - 24q^{23} + 10q^{24} + 5q^{25} + 5q^{26} - 31q^{27} - 6q^{28} + 24q^{29} + 17q^{30} - 28q^{31} - 34q^{32} - 16q^{33} - 8q^{34} + 2q^{35} + 38q^{36} - 36q^{37} + 34q^{38} - 9q^{39} - 7q^{40} + 9q^{41} - 24q^{43} + 4q^{44} + 22q^{45} + 24q^{46} - 29q^{47} - 10q^{48} + 22q^{49} - 5q^{50} - 21q^{51} - 5q^{52} - 9q^{53} + 31q^{54} - 28q^{55} + 6q^{56} + 10q^{57} - 24q^{58} - 28q^{59} - 17q^{60} + 23q^{61} + 28q^{62} - 27q^{63} + 34q^{64} - 6q^{65} + 16q^{66} - 51q^{67} + 8q^{68} - 17q^{69} - 2q^{70} - 31q^{71} - 38q^{72} - 26q^{73} + 36q^{74} - 109q^{75} - 34q^{76} - 28q^{77} + 9q^{78} - 36q^{79} + 7q^{80} + 6q^{81} - 9q^{82} - 10q^{83} - 32q^{85} + 24q^{86} - 8q^{87} - 4q^{88} - 34q^{89} - 22q^{90} - 41q^{91} - 24q^{92} - 33q^{93} + 29q^{94} - 7q^{95} + 10q^{96} - 56q^{97} - 22q^{98} - 28q^{99} + O(q^{100}) \)

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
\(3\) −1.11253 −0.642318 −0.321159 0.947025i \(-0.604072\pi\)
−0.321159 + 0.947025i \(0.604072\pi\)
\(4\) 1.00000 0.500000
\(5\) −2.63739 −1.17948 −0.589738 0.807594i \(-0.700769\pi\)
−0.589738 + 0.807594i \(0.700769\pi\)
\(6\) 1.11253 0.454187
\(7\) −4.04134 −1.52748 −0.763742 0.645522i \(-0.776640\pi\)
−0.763742 + 0.645522i \(0.776640\pi\)
\(8\) −1.00000 −0.353553
\(9\) −1.76228 −0.587428
\(10\) 2.63739 0.834016
\(11\) −0.240117 −0.0723981 −0.0361991 0.999345i \(-0.511525\pi\)
−0.0361991 + 0.999345i \(0.511525\pi\)
\(12\) −1.11253 −0.321159
\(13\) −4.90150 −1.35943 −0.679716 0.733476i \(-0.737897\pi\)
−0.679716 + 0.733476i \(0.737897\pi\)
\(14\) 4.04134 1.08009
\(15\) 2.93417 0.757599
\(16\) 1.00000 0.250000
\(17\) −2.68375 −0.650905 −0.325453 0.945558i \(-0.605517\pi\)
−0.325453 + 0.945558i \(0.605517\pi\)
\(18\) 1.76228 0.415374
\(19\) −1.00000 −0.229416
\(20\) −2.63739 −0.589738
\(21\) 4.49610 0.981130
\(22\) 0.240117 0.0511932
\(23\) 4.56012 0.950850 0.475425 0.879756i \(-0.342294\pi\)
0.475425 + 0.879756i \(0.342294\pi\)
\(24\) 1.11253 0.227094
\(25\) 1.95582 0.391165
\(26\) 4.90150 0.961263
\(27\) 5.29817 1.01963
\(28\) −4.04134 −0.763742
\(29\) −3.19444 −0.593193 −0.296597 0.955003i \(-0.595852\pi\)
−0.296597 + 0.955003i \(0.595852\pi\)
\(30\) −2.93417 −0.535703
\(31\) 4.37170 0.785180 0.392590 0.919714i \(-0.371579\pi\)
0.392590 + 0.919714i \(0.371579\pi\)
\(32\) −1.00000 −0.176777
\(33\) 0.267137 0.0465026
\(34\) 2.68375 0.460259
\(35\) 10.6586 1.80163
\(36\) −1.76228 −0.293714
\(37\) −9.88907 −1.62575 −0.812877 0.582436i \(-0.802100\pi\)
−0.812877 + 0.582436i \(0.802100\pi\)
\(38\) 1.00000 0.162221
\(39\) 5.45305 0.873187
\(40\) 2.63739 0.417008
\(41\) −0.240486 −0.0375575 −0.0187788 0.999824i \(-0.505978\pi\)
−0.0187788 + 0.999824i \(0.505978\pi\)
\(42\) −4.49610 −0.693764
\(43\) 11.1937 1.70702 0.853508 0.521080i \(-0.174471\pi\)
0.853508 + 0.521080i \(0.174471\pi\)
\(44\) −0.240117 −0.0361991
\(45\) 4.64783 0.692857
\(46\) −4.56012 −0.672353
\(47\) 5.99061 0.873821 0.436910 0.899505i \(-0.356073\pi\)
0.436910 + 0.899505i \(0.356073\pi\)
\(48\) −1.11253 −0.160580
\(49\) 9.33245 1.33321
\(50\) −1.95582 −0.276595
\(51\) 2.98575 0.418088
\(52\) −4.90150 −0.679716
\(53\) −11.9229 −1.63773 −0.818867 0.573983i \(-0.805398\pi\)
−0.818867 + 0.573983i \(0.805398\pi\)
\(54\) −5.29817 −0.720990
\(55\) 0.633283 0.0853919
\(56\) 4.04134 0.540047
\(57\) 1.11253 0.147358
\(58\) 3.19444 0.419451
\(59\) −3.67352 −0.478251 −0.239126 0.970989i \(-0.576861\pi\)
−0.239126 + 0.970989i \(0.576861\pi\)
\(60\) 2.93417 0.378799
\(61\) 4.10473 0.525557 0.262779 0.964856i \(-0.415361\pi\)
0.262779 + 0.964856i \(0.415361\pi\)
\(62\) −4.37170 −0.555206
\(63\) 7.12199 0.897286
\(64\) 1.00000 0.125000
\(65\) 12.9272 1.60342
\(66\) −0.267137 −0.0328823
\(67\) 13.1464 1.60608 0.803042 0.595922i \(-0.203213\pi\)
0.803042 + 0.595922i \(0.203213\pi\)
\(68\) −2.68375 −0.325453
\(69\) −5.07326 −0.610748
\(70\) −10.6586 −1.27395
\(71\) 6.19117 0.734757 0.367379 0.930071i \(-0.380255\pi\)
0.367379 + 0.930071i \(0.380255\pi\)
\(72\) 1.76228 0.207687
\(73\) 0.320560 0.0375187 0.0187594 0.999824i \(-0.494028\pi\)
0.0187594 + 0.999824i \(0.494028\pi\)
\(74\) 9.88907 1.14958
\(75\) −2.17591 −0.251252
\(76\) −1.00000 −0.114708
\(77\) 0.970397 0.110587
\(78\) −5.45305 −0.617437
\(79\) 3.48112 0.391656 0.195828 0.980638i \(-0.437261\pi\)
0.195828 + 0.980638i \(0.437261\pi\)
\(80\) −2.63739 −0.294869
\(81\) −0.607511 −0.0675013
\(82\) 0.240486 0.0265572
\(83\) 1.60709 0.176401 0.0882005 0.996103i \(-0.471888\pi\)
0.0882005 + 0.996103i \(0.471888\pi\)
\(84\) 4.49610 0.490565
\(85\) 7.07809 0.767727
\(86\) −11.1937 −1.20704
\(87\) 3.55390 0.381019
\(88\) 0.240117 0.0255966
\(89\) 1.30673 0.138513 0.0692565 0.997599i \(-0.477937\pi\)
0.0692565 + 0.997599i \(0.477937\pi\)
\(90\) −4.64783 −0.489924
\(91\) 19.8086 2.07651
\(92\) 4.56012 0.475425
\(93\) −4.86364 −0.504335
\(94\) −5.99061 −0.617885
\(95\) 2.63739 0.270590
\(96\) 1.11253 0.113547
\(97\) −15.2653 −1.54996 −0.774978 0.631988i \(-0.782239\pi\)
−0.774978 + 0.631988i \(0.782239\pi\)
\(98\) −9.33245 −0.942720
\(99\) 0.423155 0.0425287
\(100\) 1.95582 0.195582
\(101\) 9.93722 0.988790 0.494395 0.869237i \(-0.335390\pi\)
0.494395 + 0.869237i \(0.335390\pi\)
\(102\) −2.98575 −0.295633
\(103\) 4.46964 0.440407 0.220204 0.975454i \(-0.429328\pi\)
0.220204 + 0.975454i \(0.429328\pi\)
\(104\) 4.90150 0.480632
\(105\) −11.8580 −1.15722
\(106\) 11.9229 1.15805
\(107\) 3.94388 0.381269 0.190635 0.981661i \(-0.438945\pi\)
0.190635 + 0.981661i \(0.438945\pi\)
\(108\) 5.29817 0.509817
\(109\) 8.89273 0.851769 0.425885 0.904778i \(-0.359963\pi\)
0.425885 + 0.904778i \(0.359963\pi\)
\(110\) −0.633283 −0.0603812
\(111\) 11.0019 1.04425
\(112\) −4.04134 −0.381871
\(113\) −16.3838 −1.54126 −0.770628 0.637286i \(-0.780057\pi\)
−0.770628 + 0.637286i \(0.780057\pi\)
\(114\) −1.11253 −0.104198
\(115\) −12.0268 −1.12151
\(116\) −3.19444 −0.296597
\(117\) 8.63783 0.798568
\(118\) 3.67352 0.338175
\(119\) 10.8460 0.994247
\(120\) −2.93417 −0.267852
\(121\) −10.9423 −0.994759
\(122\) −4.10473 −0.371625
\(123\) 0.267547 0.0241239
\(124\) 4.37170 0.392590
\(125\) 8.02868 0.718107
\(126\) −7.12199 −0.634477
\(127\) −0.665924 −0.0590912 −0.0295456 0.999563i \(-0.509406\pi\)
−0.0295456 + 0.999563i \(0.509406\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −12.4532 −1.09645
\(130\) −12.9272 −1.13379
\(131\) 10.6208 0.927947 0.463973 0.885849i \(-0.346423\pi\)
0.463973 + 0.885849i \(0.346423\pi\)
\(132\) 0.267137 0.0232513
\(133\) 4.04134 0.350429
\(134\) −13.1464 −1.13567
\(135\) −13.9733 −1.20263
\(136\) 2.68375 0.230130
\(137\) 11.3837 0.972574 0.486287 0.873799i \(-0.338351\pi\)
0.486287 + 0.873799i \(0.338351\pi\)
\(138\) 5.07326 0.431864
\(139\) −3.41808 −0.289918 −0.144959 0.989438i \(-0.546305\pi\)
−0.144959 + 0.989438i \(0.546305\pi\)
\(140\) 10.6586 0.900816
\(141\) −6.66472 −0.561271
\(142\) −6.19117 −0.519552
\(143\) 1.17694 0.0984203
\(144\) −1.76228 −0.146857
\(145\) 8.42499 0.699657
\(146\) −0.320560 −0.0265298
\(147\) −10.3826 −0.856343
\(148\) −9.88907 −0.812877
\(149\) 0.185320 0.0151820 0.00759101 0.999971i \(-0.497584\pi\)
0.00759101 + 0.999971i \(0.497584\pi\)
\(150\) 2.17591 0.177662
\(151\) 0.925829 0.0753429 0.0376714 0.999290i \(-0.488006\pi\)
0.0376714 + 0.999290i \(0.488006\pi\)
\(152\) 1.00000 0.0811107
\(153\) 4.72953 0.382360
\(154\) −0.970397 −0.0781968
\(155\) −11.5299 −0.926102
\(156\) 5.45305 0.436594
\(157\) 1.64724 0.131464 0.0657318 0.997837i \(-0.479062\pi\)
0.0657318 + 0.997837i \(0.479062\pi\)
\(158\) −3.48112 −0.276943
\(159\) 13.2645 1.05195
\(160\) 2.63739 0.208504
\(161\) −18.4290 −1.45241
\(162\) 0.607511 0.0477306
\(163\) −20.6772 −1.61956 −0.809781 0.586733i \(-0.800414\pi\)
−0.809781 + 0.586733i \(0.800414\pi\)
\(164\) −0.240486 −0.0187788
\(165\) −0.704545 −0.0548487
\(166\) −1.60709 −0.124734
\(167\) −20.6628 −1.59894 −0.799469 0.600708i \(-0.794885\pi\)
−0.799469 + 0.600708i \(0.794885\pi\)
\(168\) −4.49610 −0.346882
\(169\) 11.0247 0.848054
\(170\) −7.07809 −0.542865
\(171\) 1.76228 0.134765
\(172\) 11.1937 0.853508
\(173\) 4.07508 0.309823 0.154911 0.987928i \(-0.450491\pi\)
0.154911 + 0.987928i \(0.450491\pi\)
\(174\) −3.55390 −0.269421
\(175\) −7.90415 −0.597498
\(176\) −0.240117 −0.0180995
\(177\) 4.08689 0.307190
\(178\) −1.30673 −0.0979434
\(179\) 8.87378 0.663258 0.331629 0.943410i \(-0.392402\pi\)
0.331629 + 0.943410i \(0.392402\pi\)
\(180\) 4.64783 0.346428
\(181\) 21.5901 1.60478 0.802391 0.596799i \(-0.203561\pi\)
0.802391 + 0.596799i \(0.203561\pi\)
\(182\) −19.8086 −1.46831
\(183\) −4.56663 −0.337575
\(184\) −4.56012 −0.336176
\(185\) 26.0813 1.91754
\(186\) 4.86364 0.356619
\(187\) 0.644415 0.0471243
\(188\) 5.99061 0.436910
\(189\) −21.4117 −1.55747
\(190\) −2.63739 −0.191336
\(191\) −1.66451 −0.120440 −0.0602200 0.998185i \(-0.519180\pi\)
−0.0602200 + 0.998185i \(0.519180\pi\)
\(192\) −1.11253 −0.0802898
\(193\) −6.70278 −0.482476 −0.241238 0.970466i \(-0.577553\pi\)
−0.241238 + 0.970466i \(0.577553\pi\)
\(194\) 15.2653 1.09598
\(195\) −14.3818 −1.02990
\(196\) 9.33245 0.666604
\(197\) 14.5377 1.03577 0.517885 0.855451i \(-0.326720\pi\)
0.517885 + 0.855451i \(0.326720\pi\)
\(198\) −0.423155 −0.0300723
\(199\) −5.89512 −0.417894 −0.208947 0.977927i \(-0.567004\pi\)
−0.208947 + 0.977927i \(0.567004\pi\)
\(200\) −1.95582 −0.138298
\(201\) −14.6257 −1.03162
\(202\) −9.93722 −0.699180
\(203\) 12.9098 0.906093
\(204\) 2.98575 0.209044
\(205\) 0.634254 0.0442982
\(206\) −4.46964 −0.311415
\(207\) −8.03622 −0.558556
\(208\) −4.90150 −0.339858
\(209\) 0.240117 0.0166093
\(210\) 11.8580 0.818278
\(211\) −1.00000 −0.0688428
\(212\) −11.9229 −0.818867
\(213\) −6.88785 −0.471948
\(214\) −3.94388 −0.269598
\(215\) −29.5220 −2.01339
\(216\) −5.29817 −0.360495
\(217\) −17.6675 −1.19935
\(218\) −8.89273 −0.602292
\(219\) −0.356632 −0.0240990
\(220\) 0.633283 0.0426959
\(221\) 13.1544 0.884861
\(222\) −11.0019 −0.738397
\(223\) 10.7285 0.718431 0.359216 0.933255i \(-0.383044\pi\)
0.359216 + 0.933255i \(0.383044\pi\)
\(224\) 4.04134 0.270024
\(225\) −3.44671 −0.229781
\(226\) 16.3838 1.08983
\(227\) 2.86126 0.189909 0.0949543 0.995482i \(-0.469730\pi\)
0.0949543 + 0.995482i \(0.469730\pi\)
\(228\) 1.11253 0.0736789
\(229\) −6.49370 −0.429116 −0.214558 0.976711i \(-0.568831\pi\)
−0.214558 + 0.976711i \(0.568831\pi\)
\(230\) 12.0268 0.793024
\(231\) −1.07959 −0.0710320
\(232\) 3.19444 0.209725
\(233\) −16.1920 −1.06077 −0.530387 0.847756i \(-0.677953\pi\)
−0.530387 + 0.847756i \(0.677953\pi\)
\(234\) −8.63783 −0.564673
\(235\) −15.7996 −1.03065
\(236\) −3.67352 −0.239126
\(237\) −3.87284 −0.251568
\(238\) −10.8460 −0.703039
\(239\) −7.58705 −0.490765 −0.245383 0.969426i \(-0.578914\pi\)
−0.245383 + 0.969426i \(0.578914\pi\)
\(240\) 2.93417 0.189400
\(241\) 20.2339 1.30338 0.651689 0.758486i \(-0.274061\pi\)
0.651689 + 0.758486i \(0.274061\pi\)
\(242\) 10.9423 0.703400
\(243\) −15.2186 −0.976276
\(244\) 4.10473 0.262779
\(245\) −24.6133 −1.57249
\(246\) −0.267547 −0.0170582
\(247\) 4.90150 0.311875
\(248\) −4.37170 −0.277603
\(249\) −1.78793 −0.113306
\(250\) −8.02868 −0.507778
\(251\) −7.07907 −0.446827 −0.223414 0.974724i \(-0.571720\pi\)
−0.223414 + 0.974724i \(0.571720\pi\)
\(252\) 7.12199 0.448643
\(253\) −1.09496 −0.0688398
\(254\) 0.665924 0.0417838
\(255\) −7.87457 −0.493125
\(256\) 1.00000 0.0625000
\(257\) 17.7435 1.10681 0.553403 0.832913i \(-0.313329\pi\)
0.553403 + 0.832913i \(0.313329\pi\)
\(258\) 12.4532 0.775305
\(259\) 39.9651 2.48331
\(260\) 12.9272 0.801709
\(261\) 5.62951 0.348458
\(262\) −10.6208 −0.656158
\(263\) −0.728201 −0.0449028 −0.0224514 0.999748i \(-0.507147\pi\)
−0.0224514 + 0.999748i \(0.507147\pi\)
\(264\) −0.267137 −0.0164412
\(265\) 31.4453 1.93167
\(266\) −4.04134 −0.247791
\(267\) −1.45377 −0.0889694
\(268\) 13.1464 0.803042
\(269\) −22.3864 −1.36492 −0.682461 0.730922i \(-0.739090\pi\)
−0.682461 + 0.730922i \(0.739090\pi\)
\(270\) 13.9733 0.850390
\(271\) −4.48730 −0.272584 −0.136292 0.990669i \(-0.543519\pi\)
−0.136292 + 0.990669i \(0.543519\pi\)
\(272\) −2.68375 −0.162726
\(273\) −22.0377 −1.33378
\(274\) −11.3837 −0.687714
\(275\) −0.469627 −0.0283196
\(276\) −5.07326 −0.305374
\(277\) −4.33567 −0.260505 −0.130253 0.991481i \(-0.541579\pi\)
−0.130253 + 0.991481i \(0.541579\pi\)
\(278\) 3.41808 0.205003
\(279\) −7.70417 −0.461237
\(280\) −10.6586 −0.636973
\(281\) 7.06389 0.421396 0.210698 0.977551i \(-0.432426\pi\)
0.210698 + 0.977551i \(0.432426\pi\)
\(282\) 6.66472 0.396878
\(283\) −16.6476 −0.989596 −0.494798 0.869008i \(-0.664758\pi\)
−0.494798 + 0.869008i \(0.664758\pi\)
\(284\) 6.19117 0.367379
\(285\) −2.93417 −0.173805
\(286\) −1.17694 −0.0695937
\(287\) 0.971884 0.0573685
\(288\) 1.76228 0.103844
\(289\) −9.79748 −0.576323
\(290\) −8.42499 −0.494732
\(291\) 16.9831 0.995565
\(292\) 0.320560 0.0187594
\(293\) 31.9214 1.86487 0.932435 0.361339i \(-0.117680\pi\)
0.932435 + 0.361339i \(0.117680\pi\)
\(294\) 10.3826 0.605526
\(295\) 9.68850 0.564086
\(296\) 9.88907 0.574791
\(297\) −1.27218 −0.0738196
\(298\) −0.185320 −0.0107353
\(299\) −22.3514 −1.29262
\(300\) −2.17591 −0.125626
\(301\) −45.2374 −2.60744
\(302\) −0.925829 −0.0532755
\(303\) −11.0554 −0.635118
\(304\) −1.00000 −0.0573539
\(305\) −10.8258 −0.619882
\(306\) −4.72953 −0.270369
\(307\) 4.25202 0.242676 0.121338 0.992611i \(-0.461282\pi\)
0.121338 + 0.992611i \(0.461282\pi\)
\(308\) 0.970397 0.0552935
\(309\) −4.97260 −0.282881
\(310\) 11.5299 0.654853
\(311\) −19.7674 −1.12091 −0.560454 0.828185i \(-0.689373\pi\)
−0.560454 + 0.828185i \(0.689373\pi\)
\(312\) −5.45305 −0.308718
\(313\) 4.71903 0.266735 0.133368 0.991067i \(-0.457421\pi\)
0.133368 + 0.991067i \(0.457421\pi\)
\(314\) −1.64724 −0.0929589
\(315\) −18.7835 −1.05833
\(316\) 3.48112 0.195828
\(317\) −4.74019 −0.266236 −0.133118 0.991100i \(-0.542499\pi\)
−0.133118 + 0.991100i \(0.542499\pi\)
\(318\) −13.2645 −0.743838
\(319\) 0.767041 0.0429461
\(320\) −2.63739 −0.147435
\(321\) −4.38768 −0.244896
\(322\) 18.4290 1.02701
\(323\) 2.68375 0.149328
\(324\) −0.607511 −0.0337506
\(325\) −9.58647 −0.531761
\(326\) 20.6772 1.14520
\(327\) −9.89341 −0.547107
\(328\) 0.240486 0.0132786
\(329\) −24.2101 −1.33475
\(330\) 0.704545 0.0387839
\(331\) 16.5217 0.908116 0.454058 0.890972i \(-0.349976\pi\)
0.454058 + 0.890972i \(0.349976\pi\)
\(332\) 1.60709 0.0882005
\(333\) 17.4273 0.955012
\(334\) 20.6628 1.13062
\(335\) −34.6721 −1.89434
\(336\) 4.49610 0.245283
\(337\) −1.01955 −0.0555382 −0.0277691 0.999614i \(-0.508840\pi\)
−0.0277691 + 0.999614i \(0.508840\pi\)
\(338\) −11.0247 −0.599665
\(339\) 18.2274 0.989976
\(340\) 7.07809 0.383864
\(341\) −1.04972 −0.0568456
\(342\) −1.76228 −0.0952933
\(343\) −9.42624 −0.508969
\(344\) −11.1937 −0.603521
\(345\) 13.3802 0.720363
\(346\) −4.07508 −0.219078
\(347\) 24.1571 1.29682 0.648411 0.761291i \(-0.275434\pi\)
0.648411 + 0.761291i \(0.275434\pi\)
\(348\) 3.55390 0.190509
\(349\) −18.5645 −0.993736 −0.496868 0.867826i \(-0.665517\pi\)
−0.496868 + 0.867826i \(0.665517\pi\)
\(350\) 7.90415 0.422495
\(351\) −25.9690 −1.38612
\(352\) 0.240117 0.0127983
\(353\) 1.94911 0.103741 0.0518704 0.998654i \(-0.483482\pi\)
0.0518704 + 0.998654i \(0.483482\pi\)
\(354\) −4.08689 −0.217216
\(355\) −16.3285 −0.866629
\(356\) 1.30673 0.0692565
\(357\) −12.0664 −0.638623
\(358\) −8.87378 −0.468994
\(359\) 10.9179 0.576225 0.288112 0.957597i \(-0.406972\pi\)
0.288112 + 0.957597i \(0.406972\pi\)
\(360\) −4.64783 −0.244962
\(361\) 1.00000 0.0526316
\(362\) −21.5901 −1.13475
\(363\) 12.1737 0.638951
\(364\) 19.8086 1.03825
\(365\) −0.845442 −0.0442525
\(366\) 4.56663 0.238701
\(367\) −9.96585 −0.520213 −0.260107 0.965580i \(-0.583758\pi\)
−0.260107 + 0.965580i \(0.583758\pi\)
\(368\) 4.56012 0.237713
\(369\) 0.423803 0.0220623
\(370\) −26.0813 −1.35590
\(371\) 48.1845 2.50161
\(372\) −4.86364 −0.252168
\(373\) −21.0215 −1.08845 −0.544225 0.838939i \(-0.683176\pi\)
−0.544225 + 0.838939i \(0.683176\pi\)
\(374\) −0.644415 −0.0333219
\(375\) −8.93213 −0.461253
\(376\) −5.99061 −0.308942
\(377\) 15.6576 0.806405
\(378\) 21.4117 1.10130
\(379\) 16.0239 0.823090 0.411545 0.911389i \(-0.364989\pi\)
0.411545 + 0.911389i \(0.364989\pi\)
\(380\) 2.63739 0.135295
\(381\) 0.740858 0.0379553
\(382\) 1.66451 0.0851640
\(383\) −9.09873 −0.464923 −0.232462 0.972606i \(-0.574678\pi\)
−0.232462 + 0.972606i \(0.574678\pi\)
\(384\) 1.11253 0.0567734
\(385\) −2.55931 −0.130435
\(386\) 6.70278 0.341162
\(387\) −19.7264 −1.00275
\(388\) −15.2653 −0.774978
\(389\) −7.90064 −0.400578 −0.200289 0.979737i \(-0.564188\pi\)
−0.200289 + 0.979737i \(0.564188\pi\)
\(390\) 14.3818 0.728252
\(391\) −12.2382 −0.618913
\(392\) −9.33245 −0.471360
\(393\) −11.8160 −0.596037
\(394\) −14.5377 −0.732399
\(395\) −9.18106 −0.461949
\(396\) 0.423155 0.0212643
\(397\) 23.4712 1.17798 0.588992 0.808139i \(-0.299525\pi\)
0.588992 + 0.808139i \(0.299525\pi\)
\(398\) 5.89512 0.295496
\(399\) −4.49610 −0.225087
\(400\) 1.95582 0.0977911
\(401\) 39.4713 1.97110 0.985552 0.169374i \(-0.0541745\pi\)
0.985552 + 0.169374i \(0.0541745\pi\)
\(402\) 14.6257 0.729463
\(403\) −21.4279 −1.06740
\(404\) 9.93722 0.494395
\(405\) 1.60224 0.0796162
\(406\) −12.9098 −0.640704
\(407\) 2.37454 0.117701
\(408\) −2.98575 −0.147816
\(409\) 26.1666 1.29385 0.646927 0.762552i \(-0.276054\pi\)
0.646927 + 0.762552i \(0.276054\pi\)
\(410\) −0.634254 −0.0313236
\(411\) −12.6647 −0.624702
\(412\) 4.46964 0.220204
\(413\) 14.8459 0.730521
\(414\) 8.03622 0.394959
\(415\) −4.23852 −0.208061
\(416\) 4.90150 0.240316
\(417\) 3.80271 0.186219
\(418\) −0.240117 −0.0117445
\(419\) 39.0719 1.90879 0.954393 0.298553i \(-0.0965039\pi\)
0.954393 + 0.298553i \(0.0965039\pi\)
\(420\) −11.8580 −0.578610
\(421\) −38.6123 −1.88185 −0.940923 0.338620i \(-0.890040\pi\)
−0.940923 + 0.338620i \(0.890040\pi\)
\(422\) 1.00000 0.0486792
\(423\) −10.5572 −0.513306
\(424\) 11.9229 0.579027
\(425\) −5.24894 −0.254611
\(426\) 6.88785 0.333717
\(427\) −16.5886 −0.802780
\(428\) 3.94388 0.190635
\(429\) −1.30937 −0.0632171
\(430\) 29.5220 1.42368
\(431\) −3.77651 −0.181908 −0.0909540 0.995855i \(-0.528992\pi\)
−0.0909540 + 0.995855i \(0.528992\pi\)
\(432\) 5.29817 0.254908
\(433\) −28.8779 −1.38778 −0.693891 0.720080i \(-0.744105\pi\)
−0.693891 + 0.720080i \(0.744105\pi\)
\(434\) 17.6675 0.848069
\(435\) −9.37303 −0.449402
\(436\) 8.89273 0.425885
\(437\) −4.56012 −0.218140
\(438\) 0.356632 0.0170405
\(439\) −22.3702 −1.06767 −0.533836 0.845588i \(-0.679250\pi\)
−0.533836 + 0.845588i \(0.679250\pi\)
\(440\) −0.633283 −0.0301906
\(441\) −16.4464 −0.783163
\(442\) −13.1544 −0.625691
\(443\) −25.0821 −1.19169 −0.595844 0.803100i \(-0.703182\pi\)
−0.595844 + 0.803100i \(0.703182\pi\)
\(444\) 11.0019 0.522125
\(445\) −3.44635 −0.163373
\(446\) −10.7285 −0.508008
\(447\) −0.206174 −0.00975169
\(448\) −4.04134 −0.190935
\(449\) −0.763087 −0.0360123 −0.0180062 0.999838i \(-0.505732\pi\)
−0.0180062 + 0.999838i \(0.505732\pi\)
\(450\) 3.44671 0.162480
\(451\) 0.0577448 0.00271910
\(452\) −16.3838 −0.770628
\(453\) −1.03001 −0.0483941
\(454\) −2.86126 −0.134286
\(455\) −52.2431 −2.44919
\(456\) −1.11253 −0.0520989
\(457\) 3.10779 0.145376 0.0726882 0.997355i \(-0.476842\pi\)
0.0726882 + 0.997355i \(0.476842\pi\)
\(458\) 6.49370 0.303431
\(459\) −14.2190 −0.663685
\(460\) −12.0268 −0.560753
\(461\) −4.63610 −0.215925 −0.107962 0.994155i \(-0.534433\pi\)
−0.107962 + 0.994155i \(0.534433\pi\)
\(462\) 1.07959 0.0502272
\(463\) 0.137750 0.00640177 0.00320089 0.999995i \(-0.498981\pi\)
0.00320089 + 0.999995i \(0.498981\pi\)
\(464\) −3.19444 −0.148298
\(465\) 12.8273 0.594852
\(466\) 16.1920 0.750081
\(467\) 32.7027 1.51330 0.756649 0.653821i \(-0.226835\pi\)
0.756649 + 0.653821i \(0.226835\pi\)
\(468\) 8.63783 0.399284
\(469\) −53.1290 −2.45327
\(470\) 15.7996 0.728780
\(471\) −1.83259 −0.0844415
\(472\) 3.67352 0.169087
\(473\) −2.68779 −0.123585
\(474\) 3.87284 0.177885
\(475\) −1.95582 −0.0897393
\(476\) 10.8460 0.497124
\(477\) 21.0115 0.962050
\(478\) 7.58705 0.347023
\(479\) 16.5721 0.757198 0.378599 0.925561i \(-0.376406\pi\)
0.378599 + 0.925561i \(0.376406\pi\)
\(480\) −2.93417 −0.133926
\(481\) 48.4713 2.21010
\(482\) −20.2339 −0.921627
\(483\) 20.5028 0.932908
\(484\) −10.9423 −0.497379
\(485\) 40.2605 1.82814
\(486\) 15.2186 0.690331
\(487\) 1.90081 0.0861341 0.0430671 0.999072i \(-0.486287\pi\)
0.0430671 + 0.999072i \(0.486287\pi\)
\(488\) −4.10473 −0.185813
\(489\) 23.0039 1.04027
\(490\) 24.6133 1.11192
\(491\) 14.8056 0.668170 0.334085 0.942543i \(-0.391573\pi\)
0.334085 + 0.942543i \(0.391573\pi\)
\(492\) 0.267547 0.0120619
\(493\) 8.57309 0.386112
\(494\) −4.90150 −0.220529
\(495\) −1.11602 −0.0501616
\(496\) 4.37170 0.196295
\(497\) −25.0207 −1.12233
\(498\) 1.78793 0.0801191
\(499\) 5.92541 0.265258 0.132629 0.991166i \(-0.457658\pi\)
0.132629 + 0.991166i \(0.457658\pi\)
\(500\) 8.02868 0.359054
\(501\) 22.9880 1.02703
\(502\) 7.07907 0.315955
\(503\) −21.3962 −0.954010 −0.477005 0.878901i \(-0.658278\pi\)
−0.477005 + 0.878901i \(0.658278\pi\)
\(504\) −7.12199 −0.317239
\(505\) −26.2083 −1.16625
\(506\) 1.09496 0.0486771
\(507\) −12.2653 −0.544720
\(508\) −0.665924 −0.0295456
\(509\) −2.77983 −0.123214 −0.0616068 0.998100i \(-0.519622\pi\)
−0.0616068 + 0.998100i \(0.519622\pi\)
\(510\) 7.87457 0.348692
\(511\) −1.29549 −0.0573093
\(512\) −1.00000 −0.0441942
\(513\) −5.29817 −0.233920
\(514\) −17.7435 −0.782630
\(515\) −11.7882 −0.519450
\(516\) −12.4532 −0.548224
\(517\) −1.43845 −0.0632630
\(518\) −39.9651 −1.75597
\(519\) −4.53364 −0.199005
\(520\) −12.9272 −0.566894
\(521\) 24.1864 1.05962 0.529812 0.848115i \(-0.322262\pi\)
0.529812 + 0.848115i \(0.322262\pi\)
\(522\) −5.62951 −0.246397
\(523\) −16.0536 −0.701976 −0.350988 0.936380i \(-0.614154\pi\)
−0.350988 + 0.936380i \(0.614154\pi\)
\(524\) 10.6208 0.463973
\(525\) 8.79358 0.383783
\(526\) 0.728201 0.0317511
\(527\) −11.7325 −0.511078
\(528\) 0.267137 0.0116257
\(529\) −2.20532 −0.0958834
\(530\) −31.4453 −1.36590
\(531\) 6.47378 0.280938
\(532\) 4.04134 0.175214
\(533\) 1.17874 0.0510569
\(534\) 1.45377 0.0629108
\(535\) −10.4016 −0.449698
\(536\) −13.1464 −0.567837
\(537\) −9.87233 −0.426022
\(538\) 22.3864 0.965145
\(539\) −2.24088 −0.0965217
\(540\) −13.9733 −0.601317
\(541\) 14.4094 0.619511 0.309755 0.950816i \(-0.399753\pi\)
0.309755 + 0.950816i \(0.399753\pi\)
\(542\) 4.48730 0.192746
\(543\) −24.0196 −1.03078
\(544\) 2.68375 0.115065
\(545\) −23.4536 −1.00464
\(546\) 22.0377 0.943125
\(547\) −15.3359 −0.655715 −0.327857 0.944727i \(-0.606327\pi\)
−0.327857 + 0.944727i \(0.606327\pi\)
\(548\) 11.3837 0.486287
\(549\) −7.23370 −0.308727
\(550\) 0.469627 0.0200250
\(551\) 3.19444 0.136088
\(552\) 5.07326 0.215932
\(553\) −14.0684 −0.598249
\(554\) 4.33567 0.184205
\(555\) −29.0162 −1.23167
\(556\) −3.41808 −0.144959
\(557\) −3.09288 −0.131050 −0.0655248 0.997851i \(-0.520872\pi\)
−0.0655248 + 0.997851i \(0.520872\pi\)
\(558\) 7.70417 0.326144
\(559\) −54.8657 −2.32057
\(560\) 10.6586 0.450408
\(561\) −0.716930 −0.0302688
\(562\) −7.06389 −0.297972
\(563\) −1.88851 −0.0795913 −0.0397957 0.999208i \(-0.512671\pi\)
−0.0397957 + 0.999208i \(0.512671\pi\)
\(564\) −6.66472 −0.280635
\(565\) 43.2104 1.81787
\(566\) 16.6476 0.699750
\(567\) 2.45516 0.103107
\(568\) −6.19117 −0.259776
\(569\) −2.89516 −0.121372 −0.0606858 0.998157i \(-0.519329\pi\)
−0.0606858 + 0.998157i \(0.519329\pi\)
\(570\) 2.93417 0.122899
\(571\) 4.16620 0.174350 0.0871751 0.996193i \(-0.472216\pi\)
0.0871751 + 0.996193i \(0.472216\pi\)
\(572\) 1.17694 0.0492102
\(573\) 1.85182 0.0773608
\(574\) −0.971884 −0.0405657
\(575\) 8.91878 0.371939
\(576\) −1.76228 −0.0734284
\(577\) −8.66978 −0.360928 −0.180464 0.983582i \(-0.557760\pi\)
−0.180464 + 0.983582i \(0.557760\pi\)
\(578\) 9.79748 0.407522
\(579\) 7.45702 0.309903
\(580\) 8.42499 0.349829
\(581\) −6.49480 −0.269450
\(582\) −16.9831 −0.703971
\(583\) 2.86289 0.118569
\(584\) −0.320560 −0.0132649
\(585\) −22.7813 −0.941892
\(586\) −31.9214 −1.31866
\(587\) 47.3551 1.95455 0.977276 0.211970i \(-0.0679879\pi\)
0.977276 + 0.211970i \(0.0679879\pi\)
\(588\) −10.3826 −0.428172
\(589\) −4.37170 −0.180133
\(590\) −9.68850 −0.398869
\(591\) −16.1736 −0.665293
\(592\) −9.88907 −0.406438
\(593\) 30.7889 1.26435 0.632174 0.774827i \(-0.282163\pi\)
0.632174 + 0.774827i \(0.282163\pi\)
\(594\) 1.27218 0.0521983
\(595\) −28.6050 −1.17269
\(596\) 0.185320 0.00759101
\(597\) 6.55848 0.268421
\(598\) 22.3514 0.914018
\(599\) −44.1625 −1.80443 −0.902215 0.431286i \(-0.858060\pi\)
−0.902215 + 0.431286i \(0.858060\pi\)
\(600\) 2.17591 0.0888310
\(601\) 16.0161 0.653311 0.326656 0.945143i \(-0.394078\pi\)
0.326656 + 0.945143i \(0.394078\pi\)
\(602\) 45.2374 1.84374
\(603\) −23.1676 −0.943458
\(604\) 0.925829 0.0376714
\(605\) 28.8592 1.17329
\(606\) 11.0554 0.449096
\(607\) −35.2017 −1.42879 −0.714397 0.699741i \(-0.753299\pi\)
−0.714397 + 0.699741i \(0.753299\pi\)
\(608\) 1.00000 0.0405554
\(609\) −14.3625 −0.582000
\(610\) 10.8258 0.438323
\(611\) −29.3630 −1.18790
\(612\) 4.72953 0.191180
\(613\) −29.7543 −1.20177 −0.600883 0.799337i \(-0.705184\pi\)
−0.600883 + 0.799337i \(0.705184\pi\)
\(614\) −4.25202 −0.171598
\(615\) −0.705625 −0.0284535
\(616\) −0.970397 −0.0390984
\(617\) −8.71022 −0.350660 −0.175330 0.984510i \(-0.556099\pi\)
−0.175330 + 0.984510i \(0.556099\pi\)
\(618\) 4.97260 0.200027
\(619\) 6.02889 0.242322 0.121161 0.992633i \(-0.461338\pi\)
0.121161 + 0.992633i \(0.461338\pi\)
\(620\) −11.5299 −0.463051
\(621\) 24.1603 0.969519
\(622\) 19.7674 0.792602
\(623\) −5.28094 −0.211576
\(624\) 5.45305 0.218297
\(625\) −30.9539 −1.23815
\(626\) −4.71903 −0.188610
\(627\) −0.267137 −0.0106684
\(628\) 1.64724 0.0657318
\(629\) 26.5398 1.05821
\(630\) 18.7835 0.748351
\(631\) 6.91748 0.275381 0.137690 0.990475i \(-0.456032\pi\)
0.137690 + 0.990475i \(0.456032\pi\)
\(632\) −3.48112 −0.138471
\(633\) 1.11253 0.0442190
\(634\) 4.74019 0.188257
\(635\) 1.75630 0.0696967
\(636\) 13.2645 0.525973
\(637\) −45.7430 −1.81240
\(638\) −0.767041 −0.0303675
\(639\) −10.9106 −0.431617
\(640\) 2.63739 0.104252
\(641\) 20.0416 0.791595 0.395798 0.918338i \(-0.370468\pi\)
0.395798 + 0.918338i \(0.370468\pi\)
\(642\) 4.38768 0.173168
\(643\) −3.64402 −0.143706 −0.0718531 0.997415i \(-0.522891\pi\)
−0.0718531 + 0.997415i \(0.522891\pi\)
\(644\) −18.4290 −0.726204
\(645\) 32.8441 1.29323
\(646\) −2.68375 −0.105591
\(647\) 29.5775 1.16281 0.581406 0.813614i \(-0.302503\pi\)
0.581406 + 0.813614i \(0.302503\pi\)
\(648\) 0.607511 0.0238653
\(649\) 0.882076 0.0346245
\(650\) 9.58647 0.376012
\(651\) 19.6556 0.770364
\(652\) −20.6772 −0.809781
\(653\) −17.3919 −0.680596 −0.340298 0.940318i \(-0.610528\pi\)
−0.340298 + 0.940318i \(0.610528\pi\)
\(654\) 9.89341 0.386863
\(655\) −28.0113 −1.09449
\(656\) −0.240486 −0.00938938
\(657\) −0.564918 −0.0220395
\(658\) 24.2101 0.943809
\(659\) −17.3694 −0.676615 −0.338308 0.941036i \(-0.609854\pi\)
−0.338308 + 0.941036i \(0.609854\pi\)
\(660\) −0.704545 −0.0274244
\(661\) −20.0851 −0.781220 −0.390610 0.920556i \(-0.627736\pi\)
−0.390610 + 0.920556i \(0.627736\pi\)
\(662\) −16.5217 −0.642135
\(663\) −14.6346 −0.568362
\(664\) −1.60709 −0.0623672
\(665\) −10.6586 −0.413323
\(666\) −17.4273 −0.675296
\(667\) −14.5670 −0.564038
\(668\) −20.6628 −0.799469
\(669\) −11.9357 −0.461461
\(670\) 34.6721 1.33950
\(671\) −0.985618 −0.0380494
\(672\) −4.49610 −0.173441
\(673\) 2.17284 0.0837568 0.0418784 0.999123i \(-0.486666\pi\)
0.0418784 + 0.999123i \(0.486666\pi\)
\(674\) 1.01955 0.0392714
\(675\) 10.3623 0.398844
\(676\) 11.0247 0.424027
\(677\) −9.56754 −0.367710 −0.183855 0.982953i \(-0.558858\pi\)
−0.183855 + 0.982953i \(0.558858\pi\)
\(678\) −18.2274 −0.700019
\(679\) 61.6923 2.36753
\(680\) −7.07809 −0.271433
\(681\) −3.18323 −0.121982
\(682\) 1.04972 0.0401959
\(683\) 24.9655 0.955280 0.477640 0.878556i \(-0.341492\pi\)
0.477640 + 0.878556i \(0.341492\pi\)
\(684\) 1.76228 0.0673826
\(685\) −30.0232 −1.14713
\(686\) 9.42624 0.359895
\(687\) 7.22442 0.275629
\(688\) 11.1937 0.426754
\(689\) 58.4400 2.22639
\(690\) −13.3802 −0.509374
\(691\) 44.3186 1.68596 0.842980 0.537945i \(-0.180799\pi\)
0.842980 + 0.537945i \(0.180799\pi\)
\(692\) 4.07508 0.154911
\(693\) −1.71011 −0.0649618
\(694\) −24.1571 −0.916991
\(695\) 9.01481 0.341951
\(696\) −3.55390 −0.134710
\(697\) 0.645403 0.0244464
\(698\) 18.5645 0.702677
\(699\) 18.0141 0.681355
\(700\) −7.90415 −0.298749
\(701\) 26.5774 1.00381 0.501907 0.864921i \(-0.332632\pi\)
0.501907 + 0.864921i \(0.332632\pi\)
\(702\) 25.9690 0.980136
\(703\) 9.88907 0.372973
\(704\) −0.240117 −0.00904977
\(705\) 17.5775 0.662006
\(706\) −1.94911 −0.0733558
\(707\) −40.1597 −1.51036
\(708\) 4.08689 0.153595
\(709\) 37.6406 1.41362 0.706812 0.707402i \(-0.250133\pi\)
0.706812 + 0.707402i \(0.250133\pi\)
\(710\) 16.3285 0.612799
\(711\) −6.13471 −0.230070
\(712\) −1.30673 −0.0489717
\(713\) 19.9355 0.746589
\(714\) 12.0664 0.451575
\(715\) −3.10404 −0.116084
\(716\) 8.87378 0.331629
\(717\) 8.44080 0.315227
\(718\) −10.9179 −0.407452
\(719\) 34.4837 1.28603 0.643013 0.765856i \(-0.277684\pi\)
0.643013 + 0.765856i \(0.277684\pi\)
\(720\) 4.64783 0.173214
\(721\) −18.0634 −0.672715
\(722\) −1.00000 −0.0372161
\(723\) −22.5107 −0.837183
\(724\) 21.5901 0.802391
\(725\) −6.24776 −0.232036
\(726\) −12.1737 −0.451807
\(727\) −25.4792 −0.944969 −0.472485 0.881339i \(-0.656643\pi\)
−0.472485 + 0.881339i \(0.656643\pi\)
\(728\) −19.8086 −0.734157
\(729\) 18.7537 0.694581
\(730\) 0.845442 0.0312912
\(731\) −30.0410 −1.11111
\(732\) −4.56663 −0.168787
\(733\) −27.0738 −0.999995 −0.499998 0.866027i \(-0.666666\pi\)
−0.499998 + 0.866027i \(0.666666\pi\)
\(734\) 9.96585 0.367846
\(735\) 27.3830 1.01004
\(736\) −4.56012 −0.168088
\(737\) −3.15667 −0.116278
\(738\) −0.423803 −0.0156004
\(739\) 24.6132 0.905411 0.452705 0.891660i \(-0.350459\pi\)
0.452705 + 0.891660i \(0.350459\pi\)
\(740\) 26.0813 0.958769
\(741\) −5.45305 −0.200323
\(742\) −48.1845 −1.76891
\(743\) −14.1354 −0.518579 −0.259289 0.965800i \(-0.583488\pi\)
−0.259289 + 0.965800i \(0.583488\pi\)
\(744\) 4.86364 0.178310
\(745\) −0.488762 −0.0179068
\(746\) 21.0215 0.769651
\(747\) −2.83215 −0.103623
\(748\) 0.644415 0.0235622
\(749\) −15.9386 −0.582383
\(750\) 8.93213 0.326155
\(751\) −40.5619 −1.48013 −0.740063 0.672538i \(-0.765204\pi\)
−0.740063 + 0.672538i \(0.765204\pi\)
\(752\) 5.99061 0.218455
\(753\) 7.87566 0.287005
\(754\) −15.6576 −0.570215
\(755\) −2.44177 −0.0888651
\(756\) −21.4117 −0.778737
\(757\) −37.4358 −1.36063 −0.680313 0.732922i \(-0.738156\pi\)
−0.680313 + 0.732922i \(0.738156\pi\)
\(758\) −16.0239 −0.582013
\(759\) 1.21818 0.0442170
\(760\) −2.63739 −0.0956682
\(761\) 29.8262 1.08120 0.540600 0.841280i \(-0.318197\pi\)
0.540600 + 0.841280i \(0.318197\pi\)
\(762\) −0.740858 −0.0268385
\(763\) −35.9386 −1.30106
\(764\) −1.66451 −0.0602200
\(765\) −12.4736 −0.450984
\(766\) 9.09873 0.328750
\(767\) 18.0058 0.650150
\(768\) −1.11253 −0.0401449
\(769\) 19.9827 0.720593 0.360296 0.932838i \(-0.382676\pi\)
0.360296 + 0.932838i \(0.382676\pi\)
\(770\) 2.55931 0.0922313
\(771\) −19.7401 −0.710922
\(772\) −6.70278 −0.241238
\(773\) −7.02999 −0.252851 −0.126426 0.991976i \(-0.540350\pi\)
−0.126426 + 0.991976i \(0.540350\pi\)
\(774\) 19.7264 0.709050
\(775\) 8.55027 0.307135
\(776\) 15.2653 0.547992
\(777\) −44.4623 −1.59508
\(778\) 7.90064 0.283252
\(779\) 0.240486 0.00861629
\(780\) −14.3818 −0.514952
\(781\) −1.48661 −0.0531950
\(782\) 12.2382 0.437638
\(783\) −16.9247 −0.604839
\(784\) 9.33245 0.333302
\(785\) −4.34440 −0.155058
\(786\) 11.8160 0.421462
\(787\) 42.4992 1.51493 0.757466 0.652874i \(-0.226437\pi\)
0.757466 + 0.652874i \(0.226437\pi\)
\(788\) 14.5377 0.517885
\(789\) 0.810144 0.0288419
\(790\) 9.18106 0.326648
\(791\) 66.2124 2.35424
\(792\) −0.423155 −0.0150362
\(793\) −20.1194 −0.714459
\(794\) −23.4712 −0.832960
\(795\) −34.9838 −1.24075
\(796\) −5.89512 −0.208947
\(797\) 21.6865 0.768174 0.384087 0.923297i \(-0.374516\pi\)
0.384087 + 0.923297i \(0.374516\pi\)
\(798\) 4.49610 0.159160
\(799\) −16.0773 −0.568774
\(800\) −1.95582 −0.0691488
\(801\) −2.30282 −0.0813663
\(802\) −39.4713 −1.39378
\(803\) −0.0769721 −0.00271629
\(804\) −14.6257 −0.515809
\(805\) 48.6045 1.71308
\(806\) 21.4279 0.754765
\(807\) 24.9055 0.876714
\(808\) −9.93722 −0.349590
\(809\) 7.52737 0.264648 0.132324 0.991206i \(-0.457756\pi\)
0.132324 + 0.991206i \(0.457756\pi\)
\(810\) −1.60224 −0.0562971
\(811\) −17.3928 −0.610745 −0.305373 0.952233i \(-0.598781\pi\)
−0.305373 + 0.952233i \(0.598781\pi\)
\(812\) 12.9098 0.453046
\(813\) 4.99224 0.175086
\(814\) −2.37454 −0.0832275
\(815\) 54.5338 1.91023
\(816\) 2.98575 0.104522
\(817\) −11.1937 −0.391616
\(818\) −26.1666 −0.914893
\(819\) −34.9084 −1.21980
\(820\) 0.634254 0.0221491
\(821\) −12.9496 −0.451944 −0.225972 0.974134i \(-0.572556\pi\)
−0.225972 + 0.974134i \(0.572556\pi\)
\(822\) 12.6647 0.441731
\(823\) 37.5911 1.31034 0.655172 0.755480i \(-0.272596\pi\)
0.655172 + 0.755480i \(0.272596\pi\)
\(824\) −4.46964 −0.155707
\(825\) 0.522473 0.0181902
\(826\) −14.8459 −0.516557
\(827\) −5.78087 −0.201020 −0.100510 0.994936i \(-0.532048\pi\)
−0.100510 + 0.994936i \(0.532048\pi\)
\(828\) −8.03622 −0.279278
\(829\) 22.6678 0.787285 0.393642 0.919264i \(-0.371215\pi\)
0.393642 + 0.919264i \(0.371215\pi\)
\(830\) 4.23852 0.147121
\(831\) 4.82355 0.167327
\(832\) −4.90150 −0.169929
\(833\) −25.0460 −0.867791
\(834\) −3.80271 −0.131677
\(835\) 54.4959 1.88591
\(836\) 0.240117 0.00830464
\(837\) 23.1620 0.800596
\(838\) −39.0719 −1.34972
\(839\) −38.5355 −1.33039 −0.665197 0.746668i \(-0.731652\pi\)
−0.665197 + 0.746668i \(0.731652\pi\)
\(840\) 11.8580 0.409139
\(841\) −18.7955 −0.648122
\(842\) 38.6123 1.33067
\(843\) −7.85877 −0.270670
\(844\) −1.00000 −0.0344214
\(845\) −29.0764 −1.00026
\(846\) 10.5572 0.362962
\(847\) 44.2218 1.51948
\(848\) −11.9229 −0.409434
\(849\) 18.5209 0.635635
\(850\) 5.24894 0.180037
\(851\) −45.0953 −1.54585
\(852\) −6.88785 −0.235974
\(853\) −18.9154 −0.647649 −0.323825 0.946117i \(-0.604969\pi\)
−0.323825 + 0.946117i \(0.604969\pi\)
\(854\) 16.5886 0.567651
\(855\) −4.64783 −0.158952
\(856\) −3.94388 −0.134799
\(857\) −52.2864 −1.78607 −0.893034 0.449989i \(-0.851428\pi\)
−0.893034 + 0.449989i \(0.851428\pi\)
\(858\) 1.30937 0.0447013
\(859\) 9.19712 0.313802 0.156901 0.987614i \(-0.449850\pi\)
0.156901 + 0.987614i \(0.449850\pi\)
\(860\) −29.5220 −1.00669
\(861\) −1.08125 −0.0368488
\(862\) 3.77651 0.128628
\(863\) 35.6821 1.21463 0.607316 0.794460i \(-0.292246\pi\)
0.607316 + 0.794460i \(0.292246\pi\)
\(864\) −5.29817 −0.180247
\(865\) −10.7476 −0.365429
\(866\) 28.8779 0.981311
\(867\) 10.9000 0.370182
\(868\) −17.6675 −0.599675
\(869\) −0.835877 −0.0283552
\(870\) 9.37303 0.317776
\(871\) −64.4369 −2.18336
\(872\) −8.89273 −0.301146
\(873\) 26.9018 0.910487
\(874\) 4.56012 0.154248
\(875\) −32.4467 −1.09690
\(876\) −0.356632 −0.0120495
\(877\) −44.1936 −1.49231 −0.746156 0.665771i \(-0.768103\pi\)
−0.746156 + 0.665771i \(0.768103\pi\)
\(878\) 22.3702 0.754958
\(879\) −35.5135 −1.19784
\(880\) 0.633283 0.0213480
\(881\) −9.54827 −0.321689 −0.160845 0.986980i \(-0.551422\pi\)
−0.160845 + 0.986980i \(0.551422\pi\)
\(882\) 16.4464 0.553780
\(883\) −36.6577 −1.23363 −0.616815 0.787108i \(-0.711577\pi\)
−0.616815 + 0.787108i \(0.711577\pi\)
\(884\) 13.1544 0.442430
\(885\) −10.7787 −0.362323
\(886\) 25.0821 0.842651
\(887\) −29.1701 −0.979435 −0.489718 0.871881i \(-0.662900\pi\)
−0.489718 + 0.871881i \(0.662900\pi\)
\(888\) −11.0019 −0.369198
\(889\) 2.69123 0.0902608
\(890\) 3.44635 0.115522
\(891\) 0.145874 0.00488697
\(892\) 10.7285 0.359216
\(893\) −5.99061 −0.200468
\(894\) 0.206174 0.00689548
\(895\) −23.4036 −0.782297
\(896\) 4.04134 0.135012
\(897\) 24.8666 0.830271
\(898\) 0.763087 0.0254646
\(899\) −13.9651 −0.465764
\(900\) −3.44671 −0.114890
\(901\) 31.9981 1.06601
\(902\) −0.0577448 −0.00192269
\(903\) 50.3278 1.67481
\(904\) 16.3838 0.544916
\(905\) −56.9416 −1.89280
\(906\) 1.03001 0.0342198
\(907\) 13.6328 0.452669 0.226335 0.974050i \(-0.427326\pi\)
0.226335 + 0.974050i \(0.427326\pi\)
\(908\) 2.86126 0.0949543
\(909\) −17.5122 −0.580842
\(910\) 52.2431 1.73184
\(911\) 43.8365 1.45237 0.726184 0.687501i \(-0.241292\pi\)
0.726184 + 0.687501i \(0.241292\pi\)
\(912\) 1.11253 0.0368395
\(913\) −0.385890 −0.0127711
\(914\) −3.10779 −0.102797
\(915\) 12.0440 0.398162
\(916\) −6.49370 −0.214558
\(917\) −42.9225 −1.41742
\(918\) 14.2190 0.469296
\(919\) 31.7893 1.04863 0.524317 0.851523i \(-0.324321\pi\)
0.524317 + 0.851523i \(0.324321\pi\)
\(920\) 12.0268 0.396512
\(921\) −4.73049 −0.155875
\(922\) 4.63610 0.152682
\(923\) −30.3460 −0.998852
\(924\) −1.07959 −0.0355160
\(925\) −19.3413 −0.635937
\(926\) −0.137750 −0.00452674
\(927\) −7.87678 −0.258707
\(928\) 3.19444 0.104863
\(929\) −16.1920 −0.531241 −0.265620 0.964078i \(-0.585577\pi\)
−0.265620 + 0.964078i \(0.585577\pi\)
\(930\) −12.8273 −0.420624
\(931\) −9.33245 −0.305859
\(932\) −16.1920 −0.530387
\(933\) 21.9918 0.719980
\(934\) −32.7027 −1.07006
\(935\) −1.69957 −0.0555820
\(936\) −8.63783 −0.282336
\(937\) −46.1222 −1.50675 −0.753373 0.657594i \(-0.771574\pi\)
−0.753373 + 0.657594i \(0.771574\pi\)
\(938\) 53.1290 1.73472
\(939\) −5.25005 −0.171329
\(940\) −15.7996 −0.515325
\(941\) 3.47118 0.113157 0.0565787 0.998398i \(-0.481981\pi\)
0.0565787 + 0.998398i \(0.481981\pi\)
\(942\) 1.83259 0.0597092
\(943\) −1.09664 −0.0357116
\(944\) −3.67352 −0.119563
\(945\) 56.4710 1.83700
\(946\) 2.68779 0.0873876
\(947\) 46.7599 1.51949 0.759747 0.650219i \(-0.225323\pi\)
0.759747 + 0.650219i \(0.225323\pi\)
\(948\) −3.87284 −0.125784
\(949\) −1.57123 −0.0510042
\(950\) 1.95582 0.0634553
\(951\) 5.27359 0.171008
\(952\) −10.8460 −0.351519
\(953\) −34.4097 −1.11464 −0.557319 0.830298i \(-0.688170\pi\)
−0.557319 + 0.830298i \(0.688170\pi\)
\(954\) −21.0115 −0.680272
\(955\) 4.38997 0.142056
\(956\) −7.58705 −0.245383
\(957\) −0.853355 −0.0275850
\(958\) −16.5721 −0.535420
\(959\) −46.0054 −1.48559
\(960\) 2.93417 0.0946999
\(961\) −11.8882 −0.383492
\(962\) −48.4713 −1.56278
\(963\) −6.95024 −0.223968
\(964\) 20.2339 0.651689
\(965\) 17.6778 0.569069
\(966\) −20.5028 −0.659666
\(967\) −2.41118 −0.0775383 −0.0387692 0.999248i \(-0.512344\pi\)
−0.0387692 + 0.999248i \(0.512344\pi\)
\(968\) 10.9423 0.351700
\(969\) −2.98575 −0.0959160
\(970\) −40.2605 −1.29269
\(971\) −15.0196 −0.482001 −0.241000 0.970525i \(-0.577476\pi\)
−0.241000 + 0.970525i \(0.577476\pi\)
\(972\) −15.2186 −0.488138
\(973\) 13.8136 0.442845
\(974\) −1.90081 −0.0609060
\(975\) 10.6652 0.341560
\(976\) 4.10473 0.131389
\(977\) −8.09269 −0.258908 −0.129454 0.991585i \(-0.541322\pi\)
−0.129454 + 0.991585i \(0.541322\pi\)
\(978\) −23.0039 −0.735584
\(979\) −0.313768 −0.0100281
\(980\) −24.6133 −0.786243
\(981\) −15.6715 −0.500353
\(982\) −14.8056 −0.472467
\(983\) −54.2942 −1.73172 −0.865858 0.500289i \(-0.833227\pi\)
−0.865858 + 0.500289i \(0.833227\pi\)
\(984\) −0.267547 −0.00852908
\(985\) −38.3416 −1.22167
\(986\) −8.57309 −0.273023
\(987\) 26.9344 0.857332
\(988\) 4.90150 0.155937
\(989\) 51.0444 1.62312
\(990\) 1.11602 0.0354696
\(991\) −24.7944 −0.787619 −0.393809 0.919192i \(-0.628843\pi\)
−0.393809 + 0.919192i \(0.628843\pi\)
\(992\) −4.37170 −0.138802
\(993\) −18.3809 −0.583300
\(994\) 25.0207 0.793607
\(995\) 15.5477 0.492896
\(996\) −1.78793 −0.0566528
\(997\) −51.1748 −1.62072 −0.810361 0.585931i \(-0.800729\pi\)
−0.810361 + 0.585931i \(0.800729\pi\)
\(998\) −5.92541 −0.187566
\(999\) −52.3940 −1.65767
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 \(a_p\))