Properties

Label 8018.2.a.f.1.7
Level 8018
Weight 2
Character 8018.1
Self dual Yes
Analytic conductor 64.024
Analytic rank 1
Dimension 34
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: \(34\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.7
Character \(\chi\) = 8018.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{2}\) \(-2.46365 q^{3}\) \(+1.00000 q^{4}\) \(-0.0638040 q^{5}\) \(+2.46365 q^{6}\) \(+3.24244 q^{7}\) \(-1.00000 q^{8}\) \(+3.06956 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{2}\) \(-2.46365 q^{3}\) \(+1.00000 q^{4}\) \(-0.0638040 q^{5}\) \(+2.46365 q^{6}\) \(+3.24244 q^{7}\) \(-1.00000 q^{8}\) \(+3.06956 q^{9}\) \(+0.0638040 q^{10}\) \(+1.81445 q^{11}\) \(-2.46365 q^{12}\) \(-6.18473 q^{13}\) \(-3.24244 q^{14}\) \(+0.157191 q^{15}\) \(+1.00000 q^{16}\) \(+2.99383 q^{17}\) \(-3.06956 q^{18}\) \(-1.00000 q^{19}\) \(-0.0638040 q^{20}\) \(-7.98822 q^{21}\) \(-1.81445 q^{22}\) \(-0.142289 q^{23}\) \(+2.46365 q^{24}\) \(-4.99593 q^{25}\) \(+6.18473 q^{26}\) \(-0.171366 q^{27}\) \(+3.24244 q^{28}\) \(+1.88437 q^{29}\) \(-0.157191 q^{30}\) \(+8.38673 q^{31}\) \(-1.00000 q^{32}\) \(-4.47016 q^{33}\) \(-2.99383 q^{34}\) \(-0.206880 q^{35}\) \(+3.06956 q^{36}\) \(-0.447694 q^{37}\) \(+1.00000 q^{38}\) \(+15.2370 q^{39}\) \(+0.0638040 q^{40}\) \(-10.3628 q^{41}\) \(+7.98822 q^{42}\) \(+9.43065 q^{43}\) \(+1.81445 q^{44}\) \(-0.195850 q^{45}\) \(+0.142289 q^{46}\) \(-4.96054 q^{47}\) \(-2.46365 q^{48}\) \(+3.51340 q^{49}\) \(+4.99593 q^{50}\) \(-7.37575 q^{51}\) \(-6.18473 q^{52}\) \(+3.48668 q^{53}\) \(+0.171366 q^{54}\) \(-0.115769 q^{55}\) \(-3.24244 q^{56}\) \(+2.46365 q^{57}\) \(-1.88437 q^{58}\) \(+2.98972 q^{59}\) \(+0.157191 q^{60}\) \(+4.57273 q^{61}\) \(-8.38673 q^{62}\) \(+9.95285 q^{63}\) \(+1.00000 q^{64}\) \(+0.394610 q^{65}\) \(+4.47016 q^{66}\) \(-6.70410 q^{67}\) \(+2.99383 q^{68}\) \(+0.350551 q^{69}\) \(+0.206880 q^{70}\) \(-13.2336 q^{71}\) \(-3.06956 q^{72}\) \(-11.2113 q^{73}\) \(+0.447694 q^{74}\) \(+12.3082 q^{75}\) \(-1.00000 q^{76}\) \(+5.88323 q^{77}\) \(-15.2370 q^{78}\) \(-3.92645 q^{79}\) \(-0.0638040 q^{80}\) \(-8.78649 q^{81}\) \(+10.3628 q^{82}\) \(+4.00145 q^{83}\) \(-7.98822 q^{84}\) \(-0.191018 q^{85}\) \(-9.43065 q^{86}\) \(-4.64242 q^{87}\) \(-1.81445 q^{88}\) \(-8.86710 q^{89}\) \(+0.195850 q^{90}\) \(-20.0536 q^{91}\) \(-0.142289 q^{92}\) \(-20.6619 q^{93}\) \(+4.96054 q^{94}\) \(+0.0638040 q^{95}\) \(+2.46365 q^{96}\) \(+2.20408 q^{97}\) \(-3.51340 q^{98}\) \(+5.56955 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(34q \) \(\mathstrut -\mathstrut 34q^{2} \) \(\mathstrut -\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 34q^{4} \) \(\mathstrut +\mathstrut 7q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut -\mathstrut 6q^{7} \) \(\mathstrut -\mathstrut 34q^{8} \) \(\mathstrut +\mathstrut 38q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(34q \) \(\mathstrut -\mathstrut 34q^{2} \) \(\mathstrut -\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 34q^{4} \) \(\mathstrut +\mathstrut 7q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut -\mathstrut 6q^{7} \) \(\mathstrut -\mathstrut 34q^{8} \) \(\mathstrut +\mathstrut 38q^{9} \) \(\mathstrut -\mathstrut 7q^{10} \) \(\mathstrut +\mathstrut 4q^{11} \) \(\mathstrut -\mathstrut 10q^{12} \) \(\mathstrut -\mathstrut 5q^{13} \) \(\mathstrut +\mathstrut 6q^{14} \) \(\mathstrut -\mathstrut 17q^{15} \) \(\mathstrut +\mathstrut 34q^{16} \) \(\mathstrut +\mathstrut 8q^{17} \) \(\mathstrut -\mathstrut 38q^{18} \) \(\mathstrut -\mathstrut 34q^{19} \) \(\mathstrut +\mathstrut 7q^{20} \) \(\mathstrut -\mathstrut 4q^{22} \) \(\mathstrut -\mathstrut 24q^{23} \) \(\mathstrut +\mathstrut 10q^{24} \) \(\mathstrut +\mathstrut 5q^{25} \) \(\mathstrut +\mathstrut 5q^{26} \) \(\mathstrut -\mathstrut 31q^{27} \) \(\mathstrut -\mathstrut 6q^{28} \) \(\mathstrut +\mathstrut 24q^{29} \) \(\mathstrut +\mathstrut 17q^{30} \) \(\mathstrut -\mathstrut 28q^{31} \) \(\mathstrut -\mathstrut 34q^{32} \) \(\mathstrut -\mathstrut 16q^{33} \) \(\mathstrut -\mathstrut 8q^{34} \) \(\mathstrut +\mathstrut 2q^{35} \) \(\mathstrut +\mathstrut 38q^{36} \) \(\mathstrut -\mathstrut 36q^{37} \) \(\mathstrut +\mathstrut 34q^{38} \) \(\mathstrut -\mathstrut 9q^{39} \) \(\mathstrut -\mathstrut 7q^{40} \) \(\mathstrut +\mathstrut 9q^{41} \) \(\mathstrut -\mathstrut 24q^{43} \) \(\mathstrut +\mathstrut 4q^{44} \) \(\mathstrut +\mathstrut 22q^{45} \) \(\mathstrut +\mathstrut 24q^{46} \) \(\mathstrut -\mathstrut 29q^{47} \) \(\mathstrut -\mathstrut 10q^{48} \) \(\mathstrut +\mathstrut 22q^{49} \) \(\mathstrut -\mathstrut 5q^{50} \) \(\mathstrut -\mathstrut 21q^{51} \) \(\mathstrut -\mathstrut 5q^{52} \) \(\mathstrut -\mathstrut 9q^{53} \) \(\mathstrut +\mathstrut 31q^{54} \) \(\mathstrut -\mathstrut 28q^{55} \) \(\mathstrut +\mathstrut 6q^{56} \) \(\mathstrut +\mathstrut 10q^{57} \) \(\mathstrut -\mathstrut 24q^{58} \) \(\mathstrut -\mathstrut 28q^{59} \) \(\mathstrut -\mathstrut 17q^{60} \) \(\mathstrut +\mathstrut 23q^{61} \) \(\mathstrut +\mathstrut 28q^{62} \) \(\mathstrut -\mathstrut 27q^{63} \) \(\mathstrut +\mathstrut 34q^{64} \) \(\mathstrut -\mathstrut 6q^{65} \) \(\mathstrut +\mathstrut 16q^{66} \) \(\mathstrut -\mathstrut 51q^{67} \) \(\mathstrut +\mathstrut 8q^{68} \) \(\mathstrut -\mathstrut 17q^{69} \) \(\mathstrut -\mathstrut 2q^{70} \) \(\mathstrut -\mathstrut 31q^{71} \) \(\mathstrut -\mathstrut 38q^{72} \) \(\mathstrut -\mathstrut 26q^{73} \) \(\mathstrut +\mathstrut 36q^{74} \) \(\mathstrut -\mathstrut 109q^{75} \) \(\mathstrut -\mathstrut 34q^{76} \) \(\mathstrut -\mathstrut 28q^{77} \) \(\mathstrut +\mathstrut 9q^{78} \) \(\mathstrut -\mathstrut 36q^{79} \) \(\mathstrut +\mathstrut 7q^{80} \) \(\mathstrut +\mathstrut 6q^{81} \) \(\mathstrut -\mathstrut 9q^{82} \) \(\mathstrut -\mathstrut 10q^{83} \) \(\mathstrut -\mathstrut 32q^{85} \) \(\mathstrut +\mathstrut 24q^{86} \) \(\mathstrut -\mathstrut 8q^{87} \) \(\mathstrut -\mathstrut 4q^{88} \) \(\mathstrut -\mathstrut 34q^{89} \) \(\mathstrut -\mathstrut 22q^{90} \) \(\mathstrut -\mathstrut 41q^{91} \) \(\mathstrut -\mathstrut 24q^{92} \) \(\mathstrut -\mathstrut 33q^{93} \) \(\mathstrut +\mathstrut 29q^{94} \) \(\mathstrut -\mathstrut 7q^{95} \) \(\mathstrut +\mathstrut 10q^{96} \) \(\mathstrut -\mathstrut 56q^{97} \) \(\mathstrut -\mathstrut 22q^{98} \) \(\mathstrut -\mathstrut 28q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) −2.46365 −1.42239 −0.711194 0.702996i \(-0.751845\pi\)
−0.711194 + 0.702996i \(0.751845\pi\)
\(4\) 1.00000 0.500000
\(5\) −0.0638040 −0.0285340 −0.0142670 0.999898i \(-0.504541\pi\)
−0.0142670 + 0.999898i \(0.504541\pi\)
\(6\) 2.46365 1.00578
\(7\) 3.24244 1.22553 0.612763 0.790267i \(-0.290058\pi\)
0.612763 + 0.790267i \(0.290058\pi\)
\(8\) −1.00000 −0.353553
\(9\) 3.06956 1.02319
\(10\) 0.0638040 0.0201766
\(11\) 1.81445 0.547076 0.273538 0.961861i \(-0.411806\pi\)
0.273538 + 0.961861i \(0.411806\pi\)
\(12\) −2.46365 −0.711194
\(13\) −6.18473 −1.71533 −0.857667 0.514205i \(-0.828087\pi\)
−0.857667 + 0.514205i \(0.828087\pi\)
\(14\) −3.24244 −0.866578
\(15\) 0.157191 0.0405864
\(16\) 1.00000 0.250000
\(17\) 2.99383 0.726111 0.363055 0.931768i \(-0.381734\pi\)
0.363055 + 0.931768i \(0.381734\pi\)
\(18\) −3.06956 −0.723502
\(19\) −1.00000 −0.229416
\(20\) −0.0638040 −0.0142670
\(21\) −7.98822 −1.74317
\(22\) −1.81445 −0.386841
\(23\) −0.142289 −0.0296694 −0.0148347 0.999890i \(-0.504722\pi\)
−0.0148347 + 0.999890i \(0.504722\pi\)
\(24\) 2.46365 0.502890
\(25\) −4.99593 −0.999186
\(26\) 6.18473 1.21292
\(27\) −0.171366 −0.0329794
\(28\) 3.24244 0.612763
\(29\) 1.88437 0.349918 0.174959 0.984576i \(-0.444021\pi\)
0.174959 + 0.984576i \(0.444021\pi\)
\(30\) −0.157191 −0.0286989
\(31\) 8.38673 1.50630 0.753150 0.657849i \(-0.228533\pi\)
0.753150 + 0.657849i \(0.228533\pi\)
\(32\) −1.00000 −0.176777
\(33\) −4.47016 −0.778154
\(34\) −2.99383 −0.513438
\(35\) −0.206880 −0.0349692
\(36\) 3.06956 0.511593
\(37\) −0.447694 −0.0736005 −0.0368003 0.999323i \(-0.511717\pi\)
−0.0368003 + 0.999323i \(0.511717\pi\)
\(38\) 1.00000 0.162221
\(39\) 15.2370 2.43987
\(40\) 0.0638040 0.0100883
\(41\) −10.3628 −1.61840 −0.809198 0.587536i \(-0.800098\pi\)
−0.809198 + 0.587536i \(0.800098\pi\)
\(42\) 7.98822 1.23261
\(43\) 9.43065 1.43816 0.719080 0.694927i \(-0.244563\pi\)
0.719080 + 0.694927i \(0.244563\pi\)
\(44\) 1.81445 0.273538
\(45\) −0.195850 −0.0291956
\(46\) 0.142289 0.0209794
\(47\) −4.96054 −0.723569 −0.361785 0.932262i \(-0.617832\pi\)
−0.361785 + 0.932262i \(0.617832\pi\)
\(48\) −2.46365 −0.355597
\(49\) 3.51340 0.501915
\(50\) 4.99593 0.706531
\(51\) −7.37575 −1.03281
\(52\) −6.18473 −0.857667
\(53\) 3.48668 0.478933 0.239466 0.970905i \(-0.423028\pi\)
0.239466 + 0.970905i \(0.423028\pi\)
\(54\) 0.171366 0.0233199
\(55\) −0.115769 −0.0156103
\(56\) −3.24244 −0.433289
\(57\) 2.46365 0.326318
\(58\) −1.88437 −0.247430
\(59\) 2.98972 0.389228 0.194614 0.980880i \(-0.437655\pi\)
0.194614 + 0.980880i \(0.437655\pi\)
\(60\) 0.157191 0.0202932
\(61\) 4.57273 0.585478 0.292739 0.956192i \(-0.405433\pi\)
0.292739 + 0.956192i \(0.405433\pi\)
\(62\) −8.38673 −1.06512
\(63\) 9.95285 1.25394
\(64\) 1.00000 0.125000
\(65\) 0.394610 0.0489454
\(66\) 4.47016 0.550238
\(67\) −6.70410 −0.819036 −0.409518 0.912302i \(-0.634303\pi\)
−0.409518 + 0.912302i \(0.634303\pi\)
\(68\) 2.99383 0.363055
\(69\) 0.350551 0.0422014
\(70\) 0.206880 0.0247269
\(71\) −13.2336 −1.57054 −0.785272 0.619151i \(-0.787477\pi\)
−0.785272 + 0.619151i \(0.787477\pi\)
\(72\) −3.06956 −0.361751
\(73\) −11.2113 −1.31219 −0.656094 0.754679i \(-0.727792\pi\)
−0.656094 + 0.754679i \(0.727792\pi\)
\(74\) 0.447694 0.0520434
\(75\) 12.3082 1.42123
\(76\) −1.00000 −0.114708
\(77\) 5.88323 0.670456
\(78\) −15.2370 −1.72525
\(79\) −3.92645 −0.441761 −0.220880 0.975301i \(-0.570893\pi\)
−0.220880 + 0.975301i \(0.570893\pi\)
\(80\) −0.0638040 −0.00713350
\(81\) −8.78649 −0.976276
\(82\) 10.3628 1.14438
\(83\) 4.00145 0.439216 0.219608 0.975588i \(-0.429522\pi\)
0.219608 + 0.975588i \(0.429522\pi\)
\(84\) −7.98822 −0.871587
\(85\) −0.191018 −0.0207189
\(86\) −9.43065 −1.01693
\(87\) −4.64242 −0.497719
\(88\) −1.81445 −0.193421
\(89\) −8.86710 −0.939911 −0.469955 0.882690i \(-0.655730\pi\)
−0.469955 + 0.882690i \(0.655730\pi\)
\(90\) 0.195850 0.0206444
\(91\) −20.0536 −2.10219
\(92\) −0.142289 −0.0148347
\(93\) −20.6619 −2.14254
\(94\) 4.96054 0.511641
\(95\) 0.0638040 0.00654615
\(96\) 2.46365 0.251445
\(97\) 2.20408 0.223791 0.111895 0.993720i \(-0.464308\pi\)
0.111895 + 0.993720i \(0.464308\pi\)
\(98\) −3.51340 −0.354907
\(99\) 5.56955 0.559761
\(100\) −4.99593 −0.499593
\(101\) 7.66406 0.762603 0.381301 0.924451i \(-0.375476\pi\)
0.381301 + 0.924451i \(0.375476\pi\)
\(102\) 7.37575 0.730308
\(103\) 12.0826 1.19053 0.595265 0.803530i \(-0.297047\pi\)
0.595265 + 0.803530i \(0.297047\pi\)
\(104\) 6.18473 0.606462
\(105\) 0.509681 0.0497397
\(106\) −3.48668 −0.338657
\(107\) −1.02906 −0.0994830 −0.0497415 0.998762i \(-0.515840\pi\)
−0.0497415 + 0.998762i \(0.515840\pi\)
\(108\) −0.171366 −0.0164897
\(109\) −7.65541 −0.733256 −0.366628 0.930368i \(-0.619488\pi\)
−0.366628 + 0.930368i \(0.619488\pi\)
\(110\) 0.115769 0.0110381
\(111\) 1.10296 0.104688
\(112\) 3.24244 0.306382
\(113\) −7.16054 −0.673607 −0.336804 0.941575i \(-0.609346\pi\)
−0.336804 + 0.941575i \(0.609346\pi\)
\(114\) −2.46365 −0.230742
\(115\) 0.00907864 0.000846587 0
\(116\) 1.88437 0.174959
\(117\) −18.9844 −1.75511
\(118\) −2.98972 −0.275226
\(119\) 9.70731 0.889868
\(120\) −0.157191 −0.0143495
\(121\) −7.70778 −0.700708
\(122\) −4.57273 −0.413996
\(123\) 25.5303 2.30199
\(124\) 8.38673 0.753150
\(125\) 0.637780 0.0570448
\(126\) −9.95285 −0.886670
\(127\) −10.2450 −0.909095 −0.454548 0.890722i \(-0.650199\pi\)
−0.454548 + 0.890722i \(0.650199\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −23.2338 −2.04562
\(130\) −0.394610 −0.0346096
\(131\) 10.3789 0.906806 0.453403 0.891306i \(-0.350210\pi\)
0.453403 + 0.891306i \(0.350210\pi\)
\(132\) −4.47016 −0.389077
\(133\) −3.24244 −0.281155
\(134\) 6.70410 0.579146
\(135\) 0.0109338 0.000941034 0
\(136\) −2.99383 −0.256719
\(137\) 17.5839 1.50230 0.751148 0.660134i \(-0.229501\pi\)
0.751148 + 0.660134i \(0.229501\pi\)
\(138\) −0.350551 −0.0298409
\(139\) −12.0072 −1.01844 −0.509218 0.860638i \(-0.670065\pi\)
−0.509218 + 0.860638i \(0.670065\pi\)
\(140\) −0.206880 −0.0174846
\(141\) 12.2210 1.02920
\(142\) 13.2336 1.11054
\(143\) −11.2219 −0.938419
\(144\) 3.06956 0.255796
\(145\) −0.120230 −0.00998458
\(146\) 11.2113 0.927857
\(147\) −8.65578 −0.713917
\(148\) −0.447694 −0.0368003
\(149\) 16.8503 1.38043 0.690216 0.723604i \(-0.257516\pi\)
0.690216 + 0.723604i \(0.257516\pi\)
\(150\) −12.3082 −1.00496
\(151\) 14.3539 1.16811 0.584053 0.811715i \(-0.301466\pi\)
0.584053 + 0.811715i \(0.301466\pi\)
\(152\) 1.00000 0.0811107
\(153\) 9.18974 0.742946
\(154\) −5.88323 −0.474084
\(155\) −0.535107 −0.0429808
\(156\) 15.2370 1.21994
\(157\) −17.1541 −1.36905 −0.684523 0.728992i \(-0.739989\pi\)
−0.684523 + 0.728992i \(0.739989\pi\)
\(158\) 3.92645 0.312372
\(159\) −8.58996 −0.681228
\(160\) 0.0638040 0.00504415
\(161\) −0.461365 −0.0363606
\(162\) 8.78649 0.690332
\(163\) −15.4266 −1.20831 −0.604154 0.796868i \(-0.706489\pi\)
−0.604154 + 0.796868i \(0.706489\pi\)
\(164\) −10.3628 −0.809198
\(165\) 0.285214 0.0222039
\(166\) −4.00145 −0.310573
\(167\) −0.0738214 −0.00571247 −0.00285624 0.999996i \(-0.500909\pi\)
−0.00285624 + 0.999996i \(0.500909\pi\)
\(168\) 7.98822 0.616305
\(169\) 25.2509 1.94237
\(170\) 0.191018 0.0146504
\(171\) −3.06956 −0.234735
\(172\) 9.43065 0.719080
\(173\) 9.65770 0.734261 0.367131 0.930169i \(-0.380340\pi\)
0.367131 + 0.930169i \(0.380340\pi\)
\(174\) 4.64242 0.351941
\(175\) −16.1990 −1.22453
\(176\) 1.81445 0.136769
\(177\) −7.36561 −0.553633
\(178\) 8.86710 0.664617
\(179\) 12.5121 0.935196 0.467598 0.883941i \(-0.345119\pi\)
0.467598 + 0.883941i \(0.345119\pi\)
\(180\) −0.195850 −0.0145978
\(181\) 12.3961 0.921396 0.460698 0.887557i \(-0.347599\pi\)
0.460698 + 0.887557i \(0.347599\pi\)
\(182\) 20.0536 1.48647
\(183\) −11.2656 −0.832777
\(184\) 0.142289 0.0104897
\(185\) 0.0285647 0.00210012
\(186\) 20.6619 1.51501
\(187\) 5.43215 0.397238
\(188\) −4.96054 −0.361785
\(189\) −0.555643 −0.0404171
\(190\) −0.0638040 −0.00462883
\(191\) −14.0475 −1.01644 −0.508220 0.861227i \(-0.669696\pi\)
−0.508220 + 0.861227i \(0.669696\pi\)
\(192\) −2.46365 −0.177798
\(193\) −5.38469 −0.387598 −0.193799 0.981041i \(-0.562081\pi\)
−0.193799 + 0.981041i \(0.562081\pi\)
\(194\) −2.20408 −0.158244
\(195\) −0.972181 −0.0696193
\(196\) 3.51340 0.250957
\(197\) −12.8316 −0.914213 −0.457107 0.889412i \(-0.651114\pi\)
−0.457107 + 0.889412i \(0.651114\pi\)
\(198\) −5.56955 −0.395811
\(199\) 21.8427 1.54838 0.774192 0.632950i \(-0.218156\pi\)
0.774192 + 0.632950i \(0.218156\pi\)
\(200\) 4.99593 0.353266
\(201\) 16.5165 1.16499
\(202\) −7.66406 −0.539241
\(203\) 6.10995 0.428834
\(204\) −7.37575 −0.516405
\(205\) 0.661188 0.0461794
\(206\) −12.0826 −0.841831
\(207\) −0.436766 −0.0303573
\(208\) −6.18473 −0.428834
\(209\) −1.81445 −0.125508
\(210\) −0.509681 −0.0351713
\(211\) −1.00000 −0.0688428
\(212\) 3.48668 0.239466
\(213\) 32.6030 2.23392
\(214\) 1.02906 0.0703451
\(215\) −0.601713 −0.0410365
\(216\) 0.171366 0.0116600
\(217\) 27.1934 1.84601
\(218\) 7.65541 0.518490
\(219\) 27.6208 1.86644
\(220\) −0.115769 −0.00780514
\(221\) −18.5160 −1.24552
\(222\) −1.10296 −0.0740259
\(223\) −1.42620 −0.0955052 −0.0477526 0.998859i \(-0.515206\pi\)
−0.0477526 + 0.998859i \(0.515206\pi\)
\(224\) −3.24244 −0.216644
\(225\) −15.3353 −1.02235
\(226\) 7.16054 0.476312
\(227\) −18.0578 −1.19854 −0.599269 0.800548i \(-0.704542\pi\)
−0.599269 + 0.800548i \(0.704542\pi\)
\(228\) 2.46365 0.163159
\(229\) 13.0825 0.864515 0.432257 0.901750i \(-0.357717\pi\)
0.432257 + 0.901750i \(0.357717\pi\)
\(230\) −0.00907864 −0.000598627 0
\(231\) −14.4942 −0.953649
\(232\) −1.88437 −0.123715
\(233\) −23.6783 −1.55122 −0.775609 0.631214i \(-0.782557\pi\)
−0.775609 + 0.631214i \(0.782557\pi\)
\(234\) 18.9844 1.24105
\(235\) 0.316502 0.0206463
\(236\) 2.98972 0.194614
\(237\) 9.67340 0.628355
\(238\) −9.70731 −0.629232
\(239\) 22.0557 1.42666 0.713332 0.700827i \(-0.247185\pi\)
0.713332 + 0.700827i \(0.247185\pi\)
\(240\) 0.157191 0.0101466
\(241\) −11.3034 −0.728115 −0.364057 0.931376i \(-0.618609\pi\)
−0.364057 + 0.931376i \(0.618609\pi\)
\(242\) 7.70778 0.495475
\(243\) 22.1609 1.42162
\(244\) 4.57273 0.292739
\(245\) −0.224169 −0.0143216
\(246\) −25.5303 −1.62775
\(247\) 6.18473 0.393525
\(248\) −8.38673 −0.532558
\(249\) −9.85817 −0.624736
\(250\) −0.637780 −0.0403368
\(251\) −14.5250 −0.916808 −0.458404 0.888744i \(-0.651579\pi\)
−0.458404 + 0.888744i \(0.651579\pi\)
\(252\) 9.95285 0.626971
\(253\) −0.258177 −0.0162314
\(254\) 10.2450 0.642827
\(255\) 0.470602 0.0294702
\(256\) 1.00000 0.0625000
\(257\) −13.9317 −0.869036 −0.434518 0.900663i \(-0.643081\pi\)
−0.434518 + 0.900663i \(0.643081\pi\)
\(258\) 23.2338 1.44647
\(259\) −1.45162 −0.0901994
\(260\) 0.394610 0.0244727
\(261\) 5.78418 0.358032
\(262\) −10.3789 −0.641209
\(263\) 25.6929 1.58429 0.792145 0.610333i \(-0.208965\pi\)
0.792145 + 0.610333i \(0.208965\pi\)
\(264\) 4.47016 0.275119
\(265\) −0.222464 −0.0136659
\(266\) 3.24244 0.198807
\(267\) 21.8454 1.33692
\(268\) −6.70410 −0.409518
\(269\) 24.9095 1.51876 0.759379 0.650649i \(-0.225503\pi\)
0.759379 + 0.650649i \(0.225503\pi\)
\(270\) −0.0109338 −0.000665412 0
\(271\) 5.15392 0.313078 0.156539 0.987672i \(-0.449966\pi\)
0.156539 + 0.987672i \(0.449966\pi\)
\(272\) 2.99383 0.181528
\(273\) 49.4050 2.99013
\(274\) −17.5839 −1.06228
\(275\) −9.06485 −0.546631
\(276\) 0.350551 0.0211007
\(277\) 9.12431 0.548227 0.274113 0.961697i \(-0.411616\pi\)
0.274113 + 0.961697i \(0.411616\pi\)
\(278\) 12.0072 0.720143
\(279\) 25.7435 1.54123
\(280\) 0.206880 0.0123635
\(281\) 9.08087 0.541719 0.270860 0.962619i \(-0.412692\pi\)
0.270860 + 0.962619i \(0.412692\pi\)
\(282\) −12.2210 −0.727751
\(283\) 8.03240 0.477477 0.238738 0.971084i \(-0.423266\pi\)
0.238738 + 0.971084i \(0.423266\pi\)
\(284\) −13.2336 −0.785272
\(285\) −0.157191 −0.00931116
\(286\) 11.2219 0.663562
\(287\) −33.6007 −1.98339
\(288\) −3.06956 −0.180875
\(289\) −8.03697 −0.472763
\(290\) 0.120230 0.00706016
\(291\) −5.43008 −0.318317
\(292\) −11.2113 −0.656094
\(293\) −4.55557 −0.266139 −0.133070 0.991107i \(-0.542483\pi\)
−0.133070 + 0.991107i \(0.542483\pi\)
\(294\) 8.65578 0.504816
\(295\) −0.190756 −0.0111062
\(296\) 0.447694 0.0260217
\(297\) −0.310934 −0.0180422
\(298\) −16.8503 −0.976112
\(299\) 0.880021 0.0508930
\(300\) 12.3082 0.710615
\(301\) 30.5783 1.76250
\(302\) −14.3539 −0.825976
\(303\) −18.8815 −1.08472
\(304\) −1.00000 −0.0573539
\(305\) −0.291758 −0.0167060
\(306\) −9.18974 −0.525342
\(307\) −7.55740 −0.431324 −0.215662 0.976468i \(-0.569191\pi\)
−0.215662 + 0.976468i \(0.569191\pi\)
\(308\) 5.88323 0.335228
\(309\) −29.7672 −1.69339
\(310\) 0.535107 0.0303920
\(311\) 27.8873 1.58134 0.790672 0.612240i \(-0.209731\pi\)
0.790672 + 0.612240i \(0.209731\pi\)
\(312\) −15.2370 −0.862625
\(313\) −18.8074 −1.06306 −0.531528 0.847041i \(-0.678382\pi\)
−0.531528 + 0.847041i \(0.678382\pi\)
\(314\) 17.1541 0.968061
\(315\) −0.635032 −0.0357800
\(316\) −3.92645 −0.220880
\(317\) −32.9643 −1.85146 −0.925731 0.378183i \(-0.876549\pi\)
−0.925731 + 0.378183i \(0.876549\pi\)
\(318\) 8.58996 0.481701
\(319\) 3.41909 0.191432
\(320\) −0.0638040 −0.00356675
\(321\) 2.53524 0.141503
\(322\) 0.461365 0.0257108
\(323\) −2.99383 −0.166581
\(324\) −8.78649 −0.488138
\(325\) 30.8985 1.71394
\(326\) 15.4266 0.854403
\(327\) 18.8602 1.04297
\(328\) 10.3628 0.572190
\(329\) −16.0842 −0.886753
\(330\) −0.285214 −0.0157005
\(331\) 3.39601 0.186662 0.0933308 0.995635i \(-0.470249\pi\)
0.0933308 + 0.995635i \(0.470249\pi\)
\(332\) 4.00145 0.219608
\(333\) −1.37422 −0.0753070
\(334\) 0.0738214 0.00403933
\(335\) 0.427748 0.0233704
\(336\) −7.98822 −0.435793
\(337\) 10.6295 0.579028 0.289514 0.957174i \(-0.406506\pi\)
0.289514 + 0.957174i \(0.406506\pi\)
\(338\) −25.2509 −1.37347
\(339\) 17.6410 0.958130
\(340\) −0.191018 −0.0103594
\(341\) 15.2173 0.824061
\(342\) 3.06956 0.165983
\(343\) −11.3051 −0.610417
\(344\) −9.43065 −0.508467
\(345\) −0.0223666 −0.00120417
\(346\) −9.65770 −0.519201
\(347\) −18.6487 −1.00112 −0.500559 0.865703i \(-0.666872\pi\)
−0.500559 + 0.865703i \(0.666872\pi\)
\(348\) −4.64242 −0.248860
\(349\) 27.0351 1.44716 0.723578 0.690242i \(-0.242496\pi\)
0.723578 + 0.690242i \(0.242496\pi\)
\(350\) 16.1990 0.865872
\(351\) 1.05985 0.0565707
\(352\) −1.81445 −0.0967103
\(353\) −14.6637 −0.780472 −0.390236 0.920715i \(-0.627606\pi\)
−0.390236 + 0.920715i \(0.627606\pi\)
\(354\) 7.36561 0.391478
\(355\) 0.844359 0.0448139
\(356\) −8.86710 −0.469955
\(357\) −23.9154 −1.26574
\(358\) −12.5121 −0.661284
\(359\) −25.2586 −1.33310 −0.666550 0.745461i \(-0.732230\pi\)
−0.666550 + 0.745461i \(0.732230\pi\)
\(360\) 0.195850 0.0103222
\(361\) 1.00000 0.0526316
\(362\) −12.3961 −0.651525
\(363\) 18.9893 0.996678
\(364\) −20.0536 −1.05109
\(365\) 0.715328 0.0374420
\(366\) 11.2656 0.588862
\(367\) −30.8463 −1.61017 −0.805083 0.593163i \(-0.797879\pi\)
−0.805083 + 0.593163i \(0.797879\pi\)
\(368\) −0.142289 −0.00741735
\(369\) −31.8092 −1.65592
\(370\) −0.0285647 −0.00148501
\(371\) 11.3054 0.586945
\(372\) −20.6619 −1.07127
\(373\) −16.2752 −0.842696 −0.421348 0.906899i \(-0.638443\pi\)
−0.421348 + 0.906899i \(0.638443\pi\)
\(374\) −5.43215 −0.280890
\(375\) −1.57127 −0.0811398
\(376\) 4.96054 0.255820
\(377\) −11.6543 −0.600227
\(378\) 0.555643 0.0285792
\(379\) −30.2278 −1.55270 −0.776349 0.630304i \(-0.782930\pi\)
−0.776349 + 0.630304i \(0.782930\pi\)
\(380\) 0.0638040 0.00327308
\(381\) 25.2400 1.29309
\(382\) 14.0475 0.718732
\(383\) 26.1709 1.33727 0.668634 0.743592i \(-0.266879\pi\)
0.668634 + 0.743592i \(0.266879\pi\)
\(384\) 2.46365 0.125722
\(385\) −0.375374 −0.0191308
\(386\) 5.38469 0.274073
\(387\) 28.9479 1.47151
\(388\) 2.20408 0.111895
\(389\) 23.2243 1.17752 0.588759 0.808308i \(-0.299617\pi\)
0.588759 + 0.808308i \(0.299617\pi\)
\(390\) 0.972181 0.0492283
\(391\) −0.425991 −0.0215433
\(392\) −3.51340 −0.177454
\(393\) −25.5699 −1.28983
\(394\) 12.8316 0.646446
\(395\) 0.250523 0.0126052
\(396\) 5.56955 0.279880
\(397\) −16.8631 −0.846337 −0.423168 0.906051i \(-0.639082\pi\)
−0.423168 + 0.906051i \(0.639082\pi\)
\(398\) −21.8427 −1.09487
\(399\) 7.98822 0.399911
\(400\) −4.99593 −0.249796
\(401\) −15.8367 −0.790845 −0.395422 0.918499i \(-0.629402\pi\)
−0.395422 + 0.918499i \(0.629402\pi\)
\(402\) −16.5165 −0.823770
\(403\) −51.8696 −2.58381
\(404\) 7.66406 0.381301
\(405\) 0.560613 0.0278571
\(406\) −6.10995 −0.303232
\(407\) −0.812318 −0.0402651
\(408\) 7.37575 0.365154
\(409\) −8.83200 −0.436714 −0.218357 0.975869i \(-0.570070\pi\)
−0.218357 + 0.975869i \(0.570070\pi\)
\(410\) −0.661188 −0.0326537
\(411\) −43.3206 −2.13685
\(412\) 12.0826 0.595265
\(413\) 9.69397 0.477009
\(414\) 0.436766 0.0214659
\(415\) −0.255309 −0.0125326
\(416\) 6.18473 0.303231
\(417\) 29.5815 1.44861
\(418\) 1.81445 0.0887475
\(419\) 9.05400 0.442317 0.221159 0.975238i \(-0.429016\pi\)
0.221159 + 0.975238i \(0.429016\pi\)
\(420\) 0.509681 0.0248699
\(421\) 12.1882 0.594018 0.297009 0.954875i \(-0.404011\pi\)
0.297009 + 0.954875i \(0.404011\pi\)
\(422\) 1.00000 0.0486792
\(423\) −15.2267 −0.740346
\(424\) −3.48668 −0.169328
\(425\) −14.9570 −0.725520
\(426\) −32.6030 −1.57962
\(427\) 14.8268 0.717519
\(428\) −1.02906 −0.0497415
\(429\) 27.6467 1.33480
\(430\) 0.601713 0.0290172
\(431\) −32.3186 −1.55673 −0.778365 0.627812i \(-0.783951\pi\)
−0.778365 + 0.627812i \(0.783951\pi\)
\(432\) −0.171366 −0.00824485
\(433\) 19.3512 0.929961 0.464980 0.885321i \(-0.346061\pi\)
0.464980 + 0.885321i \(0.346061\pi\)
\(434\) −27.1934 −1.30533
\(435\) 0.296205 0.0142019
\(436\) −7.65541 −0.366628
\(437\) 0.142289 0.00680663
\(438\) −27.6208 −1.31977
\(439\) −35.6457 −1.70128 −0.850638 0.525752i \(-0.823784\pi\)
−0.850638 + 0.525752i \(0.823784\pi\)
\(440\) 0.115769 0.00551907
\(441\) 10.7846 0.513552
\(442\) 18.5160 0.880718
\(443\) 13.3557 0.634551 0.317275 0.948333i \(-0.397232\pi\)
0.317275 + 0.948333i \(0.397232\pi\)
\(444\) 1.10296 0.0523442
\(445\) 0.565756 0.0268194
\(446\) 1.42620 0.0675324
\(447\) −41.5132 −1.96351
\(448\) 3.24244 0.153191
\(449\) 16.6425 0.785408 0.392704 0.919665i \(-0.371540\pi\)
0.392704 + 0.919665i \(0.371540\pi\)
\(450\) 15.3353 0.722913
\(451\) −18.8027 −0.885386
\(452\) −7.16054 −0.336804
\(453\) −35.3630 −1.66150
\(454\) 18.0578 0.847494
\(455\) 1.27950 0.0599839
\(456\) −2.46365 −0.115371
\(457\) 17.7077 0.828332 0.414166 0.910201i \(-0.364073\pi\)
0.414166 + 0.910201i \(0.364073\pi\)
\(458\) −13.0825 −0.611304
\(459\) −0.513041 −0.0239467
\(460\) 0.00907864 0.000423294 0
\(461\) 33.5594 1.56302 0.781509 0.623893i \(-0.214450\pi\)
0.781509 + 0.623893i \(0.214450\pi\)
\(462\) 14.4942 0.674331
\(463\) −41.6369 −1.93503 −0.967514 0.252816i \(-0.918643\pi\)
−0.967514 + 0.252816i \(0.918643\pi\)
\(464\) 1.88437 0.0874796
\(465\) 1.31831 0.0611354
\(466\) 23.6783 1.09688
\(467\) 24.9248 1.15338 0.576692 0.816962i \(-0.304343\pi\)
0.576692 + 0.816962i \(0.304343\pi\)
\(468\) −18.9844 −0.877553
\(469\) −21.7376 −1.00375
\(470\) −0.316502 −0.0145992
\(471\) 42.2616 1.94731
\(472\) −2.98972 −0.137613
\(473\) 17.1114 0.786783
\(474\) −9.67340 −0.444314
\(475\) 4.99593 0.229229
\(476\) 9.70731 0.444934
\(477\) 10.7026 0.490037
\(478\) −22.0557 −1.00880
\(479\) 22.1305 1.01117 0.505583 0.862778i \(-0.331277\pi\)
0.505583 + 0.862778i \(0.331277\pi\)
\(480\) −0.157191 −0.00717473
\(481\) 2.76887 0.126250
\(482\) 11.3034 0.514855
\(483\) 1.13664 0.0517189
\(484\) −7.70778 −0.350354
\(485\) −0.140629 −0.00638565
\(486\) −22.1609 −1.00524
\(487\) 3.16629 0.143478 0.0717391 0.997423i \(-0.477145\pi\)
0.0717391 + 0.997423i \(0.477145\pi\)
\(488\) −4.57273 −0.206998
\(489\) 38.0058 1.71868
\(490\) 0.224169 0.0101269
\(491\) −21.5232 −0.971327 −0.485664 0.874146i \(-0.661422\pi\)
−0.485664 + 0.874146i \(0.661422\pi\)
\(492\) 25.5303 1.15099
\(493\) 5.64148 0.254080
\(494\) −6.18473 −0.278264
\(495\) −0.355359 −0.0159722
\(496\) 8.38673 0.376575
\(497\) −42.9092 −1.92474
\(498\) 9.85817 0.441755
\(499\) 24.0079 1.07474 0.537370 0.843347i \(-0.319418\pi\)
0.537370 + 0.843347i \(0.319418\pi\)
\(500\) 0.637780 0.0285224
\(501\) 0.181870 0.00812535
\(502\) 14.5250 0.648281
\(503\) −18.2537 −0.813893 −0.406947 0.913452i \(-0.633407\pi\)
−0.406947 + 0.913452i \(0.633407\pi\)
\(504\) −9.95285 −0.443335
\(505\) −0.488998 −0.0217601
\(506\) 0.258177 0.0114773
\(507\) −62.2092 −2.76281
\(508\) −10.2450 −0.454548
\(509\) −17.4821 −0.774880 −0.387440 0.921895i \(-0.626641\pi\)
−0.387440 + 0.921895i \(0.626641\pi\)
\(510\) −0.470602 −0.0208386
\(511\) −36.3521 −1.60812
\(512\) −1.00000 −0.0441942
\(513\) 0.171366 0.00756599
\(514\) 13.9317 0.614501
\(515\) −0.770915 −0.0339706
\(516\) −23.2338 −1.02281
\(517\) −9.00064 −0.395848
\(518\) 1.45162 0.0637806
\(519\) −23.7932 −1.04440
\(520\) −0.394610 −0.0173048
\(521\) 30.2143 1.32371 0.661857 0.749630i \(-0.269769\pi\)
0.661857 + 0.749630i \(0.269769\pi\)
\(522\) −5.78418 −0.253167
\(523\) −36.8934 −1.61324 −0.806618 0.591073i \(-0.798705\pi\)
−0.806618 + 0.591073i \(0.798705\pi\)
\(524\) 10.3789 0.453403
\(525\) 39.9086 1.74175
\(526\) −25.6929 −1.12026
\(527\) 25.1084 1.09374
\(528\) −4.47016 −0.194539
\(529\) −22.9798 −0.999120
\(530\) 0.222464 0.00966323
\(531\) 9.17711 0.398253
\(532\) −3.24244 −0.140578
\(533\) 64.0911 2.77609
\(534\) −21.8454 −0.945343
\(535\) 0.0656582 0.00283865
\(536\) 6.70410 0.289573
\(537\) −30.8253 −1.33021
\(538\) −24.9095 −1.07392
\(539\) 6.37488 0.274586
\(540\) 0.0109338 0.000470517 0
\(541\) −30.0123 −1.29033 −0.645164 0.764044i \(-0.723211\pi\)
−0.645164 + 0.764044i \(0.723211\pi\)
\(542\) −5.15392 −0.221380
\(543\) −30.5397 −1.31058
\(544\) −2.99383 −0.128359
\(545\) 0.488446 0.0209227
\(546\) −49.4050 −2.11434
\(547\) −25.8116 −1.10362 −0.551812 0.833969i \(-0.686063\pi\)
−0.551812 + 0.833969i \(0.686063\pi\)
\(548\) 17.5839 0.751148
\(549\) 14.0363 0.599053
\(550\) 9.06485 0.386526
\(551\) −1.88437 −0.0802768
\(552\) −0.350551 −0.0149204
\(553\) −12.7313 −0.541389
\(554\) −9.12431 −0.387655
\(555\) −0.0703733 −0.00298718
\(556\) −12.0072 −0.509218
\(557\) −13.7354 −0.581986 −0.290993 0.956725i \(-0.593986\pi\)
−0.290993 + 0.956725i \(0.593986\pi\)
\(558\) −25.7435 −1.08981
\(559\) −58.3260 −2.46693
\(560\) −0.206880 −0.00874230
\(561\) −13.3829 −0.565026
\(562\) −9.08087 −0.383053
\(563\) 22.2159 0.936287 0.468144 0.883652i \(-0.344923\pi\)
0.468144 + 0.883652i \(0.344923\pi\)
\(564\) 12.2210 0.514598
\(565\) 0.456871 0.0192207
\(566\) −8.03240 −0.337627
\(567\) −28.4896 −1.19645
\(568\) 13.2336 0.555271
\(569\) −28.6945 −1.20294 −0.601469 0.798896i \(-0.705418\pi\)
−0.601469 + 0.798896i \(0.705418\pi\)
\(570\) 0.157191 0.00658399
\(571\) −35.7563 −1.49636 −0.748178 0.663498i \(-0.769071\pi\)
−0.748178 + 0.663498i \(0.769071\pi\)
\(572\) −11.2219 −0.469209
\(573\) 34.6081 1.44577
\(574\) 33.6007 1.40247
\(575\) 0.710868 0.0296452
\(576\) 3.06956 0.127898
\(577\) −13.5398 −0.563670 −0.281835 0.959463i \(-0.590943\pi\)
−0.281835 + 0.959463i \(0.590943\pi\)
\(578\) 8.03697 0.334294
\(579\) 13.2660 0.551315
\(580\) −0.120230 −0.00499229
\(581\) 12.9745 0.538271
\(582\) 5.43008 0.225084
\(583\) 6.32640 0.262013
\(584\) 11.2113 0.463928
\(585\) 1.21128 0.0500802
\(586\) 4.55557 0.188189
\(587\) −37.7131 −1.55658 −0.778292 0.627902i \(-0.783914\pi\)
−0.778292 + 0.627902i \(0.783914\pi\)
\(588\) −8.65578 −0.356959
\(589\) −8.38673 −0.345569
\(590\) 0.190756 0.00785329
\(591\) 31.6125 1.30037
\(592\) −0.447694 −0.0184001
\(593\) 21.9626 0.901896 0.450948 0.892550i \(-0.351086\pi\)
0.450948 + 0.892550i \(0.351086\pi\)
\(594\) 0.310934 0.0127578
\(595\) −0.619365 −0.0253915
\(596\) 16.8503 0.690216
\(597\) −53.8126 −2.20240
\(598\) −0.880021 −0.0359868
\(599\) −26.4084 −1.07902 −0.539510 0.841979i \(-0.681390\pi\)
−0.539510 + 0.841979i \(0.681390\pi\)
\(600\) −12.3082 −0.502480
\(601\) −18.2337 −0.743770 −0.371885 0.928279i \(-0.621288\pi\)
−0.371885 + 0.928279i \(0.621288\pi\)
\(602\) −30.5783 −1.24628
\(603\) −20.5786 −0.838026
\(604\) 14.3539 0.584053
\(605\) 0.491787 0.0199940
\(606\) 18.8815 0.767010
\(607\) −45.3963 −1.84258 −0.921289 0.388879i \(-0.872862\pi\)
−0.921289 + 0.388879i \(0.872862\pi\)
\(608\) 1.00000 0.0405554
\(609\) −15.0528 −0.609968
\(610\) 0.291758 0.0118130
\(611\) 30.6796 1.24116
\(612\) 9.18974 0.371473
\(613\) 37.2161 1.50314 0.751571 0.659652i \(-0.229296\pi\)
0.751571 + 0.659652i \(0.229296\pi\)
\(614\) 7.55740 0.304992
\(615\) −1.62893 −0.0656849
\(616\) −5.88323 −0.237042
\(617\) 9.05290 0.364456 0.182228 0.983256i \(-0.441669\pi\)
0.182228 + 0.983256i \(0.441669\pi\)
\(618\) 29.7672 1.19741
\(619\) 9.99067 0.401559 0.200779 0.979636i \(-0.435653\pi\)
0.200779 + 0.979636i \(0.435653\pi\)
\(620\) −0.535107 −0.0214904
\(621\) 0.0243836 0.000978479 0
\(622\) −27.8873 −1.11818
\(623\) −28.7510 −1.15189
\(624\) 15.2370 0.609968
\(625\) 24.9390 0.997558
\(626\) 18.8074 0.751694
\(627\) 4.47016 0.178521
\(628\) −17.1541 −0.684523
\(629\) −1.34032 −0.0534421
\(630\) 0.635032 0.0253003
\(631\) −42.0381 −1.67351 −0.836755 0.547577i \(-0.815550\pi\)
−0.836755 + 0.547577i \(0.815550\pi\)
\(632\) 3.92645 0.156186
\(633\) 2.46365 0.0979212
\(634\) 32.9643 1.30918
\(635\) 0.653671 0.0259401
\(636\) −8.58996 −0.340614
\(637\) −21.7294 −0.860952
\(638\) −3.41909 −0.135363
\(639\) −40.6214 −1.60696
\(640\) 0.0638040 0.00252207
\(641\) 4.12200 0.162809 0.0814046 0.996681i \(-0.474059\pi\)
0.0814046 + 0.996681i \(0.474059\pi\)
\(642\) −2.53524 −0.100058
\(643\) 6.22845 0.245626 0.122813 0.992430i \(-0.460808\pi\)
0.122813 + 0.992430i \(0.460808\pi\)
\(644\) −0.461365 −0.0181803
\(645\) 1.48241 0.0583698
\(646\) 2.99383 0.117791
\(647\) −34.7613 −1.36661 −0.683304 0.730134i \(-0.739458\pi\)
−0.683304 + 0.730134i \(0.739458\pi\)
\(648\) 8.78649 0.345166
\(649\) 5.42468 0.212937
\(650\) −30.8985 −1.21194
\(651\) −66.9950 −2.62574
\(652\) −15.4266 −0.604154
\(653\) −24.6032 −0.962796 −0.481398 0.876502i \(-0.659871\pi\)
−0.481398 + 0.876502i \(0.659871\pi\)
\(654\) −18.8602 −0.737494
\(655\) −0.662213 −0.0258748
\(656\) −10.3628 −0.404599
\(657\) −34.4138 −1.34261
\(658\) 16.0842 0.627029
\(659\) −10.2206 −0.398137 −0.199069 0.979986i \(-0.563792\pi\)
−0.199069 + 0.979986i \(0.563792\pi\)
\(660\) 0.285214 0.0111019
\(661\) 2.64938 0.103049 0.0515244 0.998672i \(-0.483592\pi\)
0.0515244 + 0.998672i \(0.483592\pi\)
\(662\) −3.39601 −0.131990
\(663\) 45.6170 1.77162
\(664\) −4.00145 −0.155286
\(665\) 0.206880 0.00802248
\(666\) 1.37422 0.0532501
\(667\) −0.268126 −0.0103819
\(668\) −0.0738214 −0.00285624
\(669\) 3.51365 0.135845
\(670\) −0.427748 −0.0165254
\(671\) 8.29697 0.320301
\(672\) 7.98822 0.308152
\(673\) −11.0373 −0.425456 −0.212728 0.977111i \(-0.568235\pi\)
−0.212728 + 0.977111i \(0.568235\pi\)
\(674\) −10.6295 −0.409435
\(675\) 0.856132 0.0329525
\(676\) 25.2509 0.971187
\(677\) 38.1764 1.46724 0.733620 0.679560i \(-0.237829\pi\)
0.733620 + 0.679560i \(0.237829\pi\)
\(678\) −17.6410 −0.677500
\(679\) 7.14660 0.274261
\(680\) 0.191018 0.00732522
\(681\) 44.4880 1.70478
\(682\) −15.2173 −0.582699
\(683\) −9.12638 −0.349211 −0.174606 0.984638i \(-0.555865\pi\)
−0.174606 + 0.984638i \(0.555865\pi\)
\(684\) −3.06956 −0.117367
\(685\) −1.12192 −0.0428665
\(686\) 11.3051 0.431630
\(687\) −32.2306 −1.22967
\(688\) 9.43065 0.359540
\(689\) −21.5642 −0.821530
\(690\) 0.0223666 0.000851480 0
\(691\) −49.9686 −1.90089 −0.950447 0.310887i \(-0.899374\pi\)
−0.950447 + 0.310887i \(0.899374\pi\)
\(692\) 9.65770 0.367131
\(693\) 18.0589 0.686001
\(694\) 18.6487 0.707897
\(695\) 0.766106 0.0290601
\(696\) 4.64242 0.175970
\(697\) −31.0245 −1.17514
\(698\) −27.0351 −1.02329
\(699\) 58.3350 2.20643
\(700\) −16.1990 −0.612264
\(701\) 43.9046 1.65825 0.829127 0.559060i \(-0.188838\pi\)
0.829127 + 0.559060i \(0.188838\pi\)
\(702\) −1.05985 −0.0400015
\(703\) 0.447694 0.0168851
\(704\) 1.81445 0.0683845
\(705\) −0.779750 −0.0293671
\(706\) 14.6637 0.551877
\(707\) 24.8502 0.934589
\(708\) −7.36561 −0.276816
\(709\) −21.6353 −0.812532 −0.406266 0.913755i \(-0.633169\pi\)
−0.406266 + 0.913755i \(0.633169\pi\)
\(710\) −0.844359 −0.0316882
\(711\) −12.0525 −0.452003
\(712\) 8.86710 0.332309
\(713\) −1.19334 −0.0446910
\(714\) 23.9154 0.895011
\(715\) 0.715999 0.0267769
\(716\) 12.5121 0.467598
\(717\) −54.3374 −2.02927
\(718\) 25.2586 0.942643
\(719\) −9.59982 −0.358013 −0.179006 0.983848i \(-0.557288\pi\)
−0.179006 + 0.983848i \(0.557288\pi\)
\(720\) −0.195850 −0.00729890
\(721\) 39.1769 1.45903
\(722\) −1.00000 −0.0372161
\(723\) 27.8476 1.03566
\(724\) 12.3961 0.460698
\(725\) −9.41417 −0.349633
\(726\) −18.9893 −0.704758
\(727\) −36.2426 −1.34417 −0.672083 0.740476i \(-0.734600\pi\)
−0.672083 + 0.740476i \(0.734600\pi\)
\(728\) 20.0536 0.743236
\(729\) −28.2372 −1.04582
\(730\) −0.715328 −0.0264755
\(731\) 28.2338 1.04426
\(732\) −11.2656 −0.416388
\(733\) 44.5708 1.64626 0.823129 0.567854i \(-0.192226\pi\)
0.823129 + 0.567854i \(0.192226\pi\)
\(734\) 30.8463 1.13856
\(735\) 0.552274 0.0203709
\(736\) 0.142289 0.00524486
\(737\) −12.1642 −0.448075
\(738\) 31.8092 1.17091
\(739\) 27.0437 0.994818 0.497409 0.867516i \(-0.334285\pi\)
0.497409 + 0.867516i \(0.334285\pi\)
\(740\) 0.0285647 0.00105006
\(741\) −15.2370 −0.559745
\(742\) −11.3054 −0.415033
\(743\) −41.3944 −1.51861 −0.759307 0.650732i \(-0.774462\pi\)
−0.759307 + 0.650732i \(0.774462\pi\)
\(744\) 20.6619 0.757503
\(745\) −1.07512 −0.0393893
\(746\) 16.2752 0.595876
\(747\) 12.2827 0.449400
\(748\) 5.43215 0.198619
\(749\) −3.33666 −0.121919
\(750\) 1.57127 0.0573745
\(751\) 54.2407 1.97927 0.989635 0.143605i \(-0.0458696\pi\)
0.989635 + 0.143605i \(0.0458696\pi\)
\(752\) −4.96054 −0.180892
\(753\) 35.7844 1.30406
\(754\) 11.6543 0.424425
\(755\) −0.915838 −0.0333308
\(756\) −0.555643 −0.0202086
\(757\) −50.0049 −1.81746 −0.908730 0.417385i \(-0.862947\pi\)
−0.908730 + 0.417385i \(0.862947\pi\)
\(758\) 30.2278 1.09792
\(759\) 0.636056 0.0230874
\(760\) −0.0638040 −0.00231441
\(761\) −3.29367 −0.119395 −0.0596977 0.998217i \(-0.519014\pi\)
−0.0596977 + 0.998217i \(0.519014\pi\)
\(762\) −25.2400 −0.914350
\(763\) −24.8222 −0.898624
\(764\) −14.0475 −0.508220
\(765\) −0.586342 −0.0211992
\(766\) −26.1709 −0.945591
\(767\) −18.4906 −0.667656
\(768\) −2.46365 −0.0888992
\(769\) −37.2546 −1.34343 −0.671717 0.740808i \(-0.734443\pi\)
−0.671717 + 0.740808i \(0.734443\pi\)
\(770\) 0.375374 0.0135275
\(771\) 34.3228 1.23611
\(772\) −5.38469 −0.193799
\(773\) 9.87091 0.355032 0.177516 0.984118i \(-0.443194\pi\)
0.177516 + 0.984118i \(0.443194\pi\)
\(774\) −28.9479 −1.04051
\(775\) −41.8995 −1.50507
\(776\) −2.20408 −0.0791220
\(777\) 3.57628 0.128298
\(778\) −23.2243 −0.832632
\(779\) 10.3628 0.371286
\(780\) −0.972181 −0.0348097
\(781\) −24.0117 −0.859207
\(782\) 0.425991 0.0152334
\(783\) −0.322916 −0.0115401
\(784\) 3.51340 0.125479
\(785\) 1.09450 0.0390644
\(786\) 25.5699 0.912047
\(787\) −19.8196 −0.706491 −0.353246 0.935531i \(-0.614922\pi\)
−0.353246 + 0.935531i \(0.614922\pi\)
\(788\) −12.8316 −0.457107
\(789\) −63.2981 −2.25347
\(790\) −0.250523 −0.00891322
\(791\) −23.2176 −0.825523
\(792\) −5.56955 −0.197905
\(793\) −28.2811 −1.00429
\(794\) 16.8631 0.598451
\(795\) 0.548074 0.0194382
\(796\) 21.8427 0.774192
\(797\) −18.8434 −0.667469 −0.333734 0.942667i \(-0.608309\pi\)
−0.333734 + 0.942667i \(0.608309\pi\)
\(798\) −7.98822 −0.282780
\(799\) −14.8510 −0.525391
\(800\) 4.99593 0.176633
\(801\) −27.2181 −0.961703
\(802\) 15.8367 0.559212
\(803\) −20.3424 −0.717867
\(804\) 16.5165 0.582493
\(805\) 0.0294369 0.00103751
\(806\) 51.8696 1.82703
\(807\) −61.3682 −2.16026
\(808\) −7.66406 −0.269621
\(809\) 11.7855 0.414355 0.207178 0.978303i \(-0.433572\pi\)
0.207178 + 0.978303i \(0.433572\pi\)
\(810\) −0.560613 −0.0196979
\(811\) 1.58032 0.0554927 0.0277463 0.999615i \(-0.491167\pi\)
0.0277463 + 0.999615i \(0.491167\pi\)
\(812\) 6.10995 0.214417
\(813\) −12.6974 −0.445318
\(814\) 0.812318 0.0284717
\(815\) 0.984282 0.0344779
\(816\) −7.37575 −0.258203
\(817\) −9.43065 −0.329937
\(818\) 8.83200 0.308804
\(819\) −61.5557 −2.15093
\(820\) 0.661188 0.0230897
\(821\) −16.6072 −0.579596 −0.289798 0.957088i \(-0.593588\pi\)
−0.289798 + 0.957088i \(0.593588\pi\)
\(822\) 43.3206 1.51098
\(823\) 37.3627 1.30238 0.651191 0.758913i \(-0.274269\pi\)
0.651191 + 0.758913i \(0.274269\pi\)
\(824\) −12.0826 −0.420916
\(825\) 22.3326 0.777521
\(826\) −9.69397 −0.337296
\(827\) 47.4718 1.65076 0.825378 0.564581i \(-0.190962\pi\)
0.825378 + 0.564581i \(0.190962\pi\)
\(828\) −0.436766 −0.0151787
\(829\) −34.9343 −1.21332 −0.606659 0.794962i \(-0.707491\pi\)
−0.606659 + 0.794962i \(0.707491\pi\)
\(830\) 0.255309 0.00886189
\(831\) −22.4791 −0.779791
\(832\) −6.18473 −0.214417
\(833\) 10.5185 0.364446
\(834\) −29.5815 −1.02432
\(835\) 0.00471010 0.000163000 0
\(836\) −1.81445 −0.0627539
\(837\) −1.43720 −0.0496769
\(838\) −9.05400 −0.312765
\(839\) 22.9026 0.790685 0.395342 0.918534i \(-0.370626\pi\)
0.395342 + 0.918534i \(0.370626\pi\)
\(840\) −0.509681 −0.0175857
\(841\) −25.4492 −0.877557
\(842\) −12.1882 −0.420034
\(843\) −22.3721 −0.770534
\(844\) −1.00000 −0.0344214
\(845\) −1.61111 −0.0554237
\(846\) 15.2267 0.523504
\(847\) −24.9920 −0.858736
\(848\) 3.48668 0.119733
\(849\) −19.7890 −0.679157
\(850\) 14.9570 0.513020
\(851\) 0.0637022 0.00218368
\(852\) 32.6030 1.11696
\(853\) 16.3848 0.561006 0.280503 0.959853i \(-0.409499\pi\)
0.280503 + 0.959853i \(0.409499\pi\)
\(854\) −14.8268 −0.507362
\(855\) 0.195850 0.00669793
\(856\) 1.02906 0.0351726
\(857\) −37.8599 −1.29327 −0.646635 0.762800i \(-0.723824\pi\)
−0.646635 + 0.762800i \(0.723824\pi\)
\(858\) −27.6467 −0.943843
\(859\) 45.8994 1.56607 0.783034 0.621979i \(-0.213671\pi\)
0.783034 + 0.621979i \(0.213671\pi\)
\(860\) −0.601713 −0.0205182
\(861\) 82.7803 2.82115
\(862\) 32.3186 1.10077
\(863\) 56.8778 1.93614 0.968071 0.250677i \(-0.0806532\pi\)
0.968071 + 0.250677i \(0.0806532\pi\)
\(864\) 0.171366 0.00582999
\(865\) −0.616200 −0.0209514
\(866\) −19.3512 −0.657582
\(867\) 19.8003 0.672452
\(868\) 27.1934 0.923005
\(869\) −7.12434 −0.241677
\(870\) −0.296205 −0.0100423
\(871\) 41.4630 1.40492
\(872\) 7.65541 0.259245
\(873\) 6.76556 0.228979
\(874\) −0.142289 −0.00481301
\(875\) 2.06796 0.0699099
\(876\) 27.6208 0.933220
\(877\) −47.1899 −1.59349 −0.796746 0.604315i \(-0.793447\pi\)
−0.796746 + 0.604315i \(0.793447\pi\)
\(878\) 35.6457 1.20298
\(879\) 11.2233 0.378553
\(880\) −0.115769 −0.00390257
\(881\) 18.5342 0.624431 0.312216 0.950011i \(-0.398929\pi\)
0.312216 + 0.950011i \(0.398929\pi\)
\(882\) −10.7846 −0.363136
\(883\) 25.4821 0.857542 0.428771 0.903413i \(-0.358947\pi\)
0.428771 + 0.903413i \(0.358947\pi\)
\(884\) −18.5160 −0.622762
\(885\) 0.469955 0.0157974
\(886\) −13.3557 −0.448695
\(887\) −10.0908 −0.338817 −0.169409 0.985546i \(-0.554186\pi\)
−0.169409 + 0.985546i \(0.554186\pi\)
\(888\) −1.10296 −0.0370130
\(889\) −33.2187 −1.11412
\(890\) −0.565756 −0.0189642
\(891\) −15.9426 −0.534098
\(892\) −1.42620 −0.0477526
\(893\) 4.96054 0.165998
\(894\) 41.5132 1.38841
\(895\) −0.798320 −0.0266849
\(896\) −3.24244 −0.108322
\(897\) −2.16806 −0.0723895
\(898\) −16.6425 −0.555367
\(899\) 15.8037 0.527082
\(900\) −15.3353 −0.511176
\(901\) 10.4385 0.347758
\(902\) 18.8027 0.626063
\(903\) −75.3341 −2.50696
\(904\) 7.16054 0.238156
\(905\) −0.790922 −0.0262911
\(906\) 35.3630 1.17486
\(907\) 17.2445 0.572593 0.286296 0.958141i \(-0.407576\pi\)
0.286296 + 0.958141i \(0.407576\pi\)
\(908\) −18.0578 −0.599269
\(909\) 23.5253 0.780284
\(910\) −1.27950 −0.0424150
\(911\) −32.0433 −1.06164 −0.530821 0.847484i \(-0.678116\pi\)
−0.530821 + 0.847484i \(0.678116\pi\)
\(912\) 2.46365 0.0815795
\(913\) 7.26042 0.240285
\(914\) −17.7077 −0.585719
\(915\) 0.718790 0.0237625
\(916\) 13.0825 0.432257
\(917\) 33.6528 1.11131
\(918\) 0.513041 0.0169329
\(919\) −23.3239 −0.769384 −0.384692 0.923045i \(-0.625692\pi\)
−0.384692 + 0.923045i \(0.625692\pi\)
\(920\) −0.00907864 −0.000299314 0
\(921\) 18.6188 0.613509
\(922\) −33.5594 −1.10522
\(923\) 81.8464 2.69401
\(924\) −14.4942 −0.476824
\(925\) 2.23665 0.0735406
\(926\) 41.6369 1.36827
\(927\) 37.0881 1.21813
\(928\) −1.88437 −0.0618574
\(929\) −29.3269 −0.962185 −0.481093 0.876670i \(-0.659760\pi\)
−0.481093 + 0.876670i \(0.659760\pi\)
\(930\) −1.31831 −0.0432292
\(931\) −3.51340 −0.115147
\(932\) −23.6783 −0.775609
\(933\) −68.7045 −2.24928
\(934\) −24.9248 −0.815565
\(935\) −0.346593 −0.0113348
\(936\) 18.9844 0.620524
\(937\) −35.8742 −1.17196 −0.585979 0.810326i \(-0.699290\pi\)
−0.585979 + 0.810326i \(0.699290\pi\)
\(938\) 21.7376 0.709758
\(939\) 46.3348 1.51208
\(940\) 0.316502 0.0103232
\(941\) 25.4859 0.830816 0.415408 0.909635i \(-0.363639\pi\)
0.415408 + 0.909635i \(0.363639\pi\)
\(942\) −42.2616 −1.37696
\(943\) 1.47452 0.0480169
\(944\) 2.98972 0.0973070
\(945\) 0.0354523 0.00115326
\(946\) −17.1114 −0.556340
\(947\) 18.5929 0.604188 0.302094 0.953278i \(-0.402314\pi\)
0.302094 + 0.953278i \(0.402314\pi\)
\(948\) 9.67340 0.314177
\(949\) 69.3391 2.25084
\(950\) −4.99593 −0.162089
\(951\) 81.2125 2.63350
\(952\) −9.70731 −0.314616
\(953\) −35.4636 −1.14878 −0.574389 0.818582i \(-0.694760\pi\)
−0.574389 + 0.818582i \(0.694760\pi\)
\(954\) −10.7026 −0.346509
\(955\) 0.896286 0.0290031
\(956\) 22.0557 0.713332
\(957\) −8.42342 −0.272291
\(958\) −22.1305 −0.715003
\(959\) 57.0148 1.84110
\(960\) 0.157191 0.00507330
\(961\) 39.3372 1.26894
\(962\) −2.76887 −0.0892719
\(963\) −3.15876 −0.101790
\(964\) −11.3034 −0.364057
\(965\) 0.343565 0.0110597
\(966\) −1.13664 −0.0365708
\(967\) −16.4220 −0.528097 −0.264048 0.964509i \(-0.585058\pi\)
−0.264048 + 0.964509i \(0.585058\pi\)
\(968\) 7.70778 0.247738
\(969\) 7.37575 0.236943
\(970\) 0.140629 0.00451533
\(971\) −18.9869 −0.609317 −0.304659 0.952462i \(-0.598542\pi\)
−0.304659 + 0.952462i \(0.598542\pi\)
\(972\) 22.1609 0.710811
\(973\) −38.9325 −1.24812
\(974\) −3.16629 −0.101454
\(975\) −76.1229 −2.43788
\(976\) 4.57273 0.146370
\(977\) −19.6897 −0.629929 −0.314964 0.949104i \(-0.601993\pi\)
−0.314964 + 0.949104i \(0.601993\pi\)
\(978\) −38.0058 −1.21529
\(979\) −16.0889 −0.514203
\(980\) −0.224169 −0.00716082
\(981\) −23.4987 −0.750257
\(982\) 21.5232 0.686832
\(983\) 38.7750 1.23673 0.618366 0.785891i \(-0.287795\pi\)
0.618366 + 0.785891i \(0.287795\pi\)
\(984\) −25.5303 −0.813875
\(985\) 0.818707 0.0260862
\(986\) −5.64148 −0.179661
\(987\) 39.6259 1.26131
\(988\) 6.18473 0.196762
\(989\) −1.34188 −0.0426694
\(990\) 0.355359 0.0112941
\(991\) −31.1071 −0.988150 −0.494075 0.869419i \(-0.664493\pi\)
−0.494075 + 0.869419i \(0.664493\pi\)
\(992\) −8.38673 −0.266279
\(993\) −8.36657 −0.265505
\(994\) 42.9092 1.36100
\(995\) −1.39365 −0.0441816
\(996\) −9.85817 −0.312368
\(997\) −60.2155 −1.90704 −0.953522 0.301322i \(-0.902572\pi\)
−0.953522 + 0.301322i \(0.902572\pi\)
\(998\) −24.0079 −0.759956
\(999\) 0.0767196 0.00242730
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 \(a_p\))