Properties

Label 4003.2.a.b.1.16
Level 4003
Weight 2
Character 4003.1
Self dual Yes
Analytic conductor 31.964
Analytic rank 1
Dimension 152
CM No

Related objects

Downloads

Learn more about

Newspace parameters

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

Newform invariants

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

Embedding invariants

Embedding label 1.16
Character \(\chi\) = 4003.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.42958 q^{2} -1.44088 q^{3} +3.90288 q^{4} +0.473210 q^{5} +3.50074 q^{6} -4.22120 q^{7} -4.62321 q^{8} -0.923870 q^{9} +O(q^{10})\) \(q-2.42958 q^{2} -1.44088 q^{3} +3.90288 q^{4} +0.473210 q^{5} +3.50074 q^{6} -4.22120 q^{7} -4.62321 q^{8} -0.923870 q^{9} -1.14970 q^{10} +2.71553 q^{11} -5.62358 q^{12} -6.52831 q^{13} +10.2558 q^{14} -0.681838 q^{15} +3.42672 q^{16} -2.95637 q^{17} +2.24462 q^{18} +2.50601 q^{19} +1.84688 q^{20} +6.08223 q^{21} -6.59761 q^{22} +0.352460 q^{23} +6.66148 q^{24} -4.77607 q^{25} +15.8611 q^{26} +5.65382 q^{27} -16.4748 q^{28} +5.98074 q^{29} +1.65658 q^{30} -0.0270305 q^{31} +0.920923 q^{32} -3.91275 q^{33} +7.18276 q^{34} -1.99751 q^{35} -3.60575 q^{36} +7.65604 q^{37} -6.08857 q^{38} +9.40650 q^{39} -2.18775 q^{40} +6.98781 q^{41} -14.7773 q^{42} -9.53851 q^{43} +10.5984 q^{44} -0.437185 q^{45} -0.856332 q^{46} +6.18705 q^{47} -4.93748 q^{48} +10.8185 q^{49} +11.6039 q^{50} +4.25978 q^{51} -25.4792 q^{52} +8.86731 q^{53} -13.7364 q^{54} +1.28502 q^{55} +19.5155 q^{56} -3.61086 q^{57} -14.5307 q^{58} -7.83611 q^{59} -2.66113 q^{60} +9.95309 q^{61} +0.0656729 q^{62} +3.89984 q^{63} -9.09089 q^{64} -3.08926 q^{65} +9.50635 q^{66} +1.86101 q^{67} -11.5384 q^{68} -0.507852 q^{69} +4.85313 q^{70} -13.0373 q^{71} +4.27124 q^{72} +8.64784 q^{73} -18.6010 q^{74} +6.88174 q^{75} +9.78068 q^{76} -11.4628 q^{77} -22.8539 q^{78} +7.74098 q^{79} +1.62156 q^{80} -5.37485 q^{81} -16.9775 q^{82} +7.49076 q^{83} +23.7382 q^{84} -1.39899 q^{85} +23.1746 q^{86} -8.61751 q^{87} -12.5545 q^{88} -12.0652 q^{89} +1.06218 q^{90} +27.5573 q^{91} +1.37561 q^{92} +0.0389477 q^{93} -15.0320 q^{94} +1.18587 q^{95} -1.32694 q^{96} -6.42719 q^{97} -26.2845 q^{98} -2.50880 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 152q - 22q^{2} - 18q^{3} + 138q^{4} - 59q^{5} - 17q^{6} - 19q^{7} - 66q^{8} + 106q^{9} + O(q^{10}) \) \( 152q - 22q^{2} - 18q^{3} + 138q^{4} - 59q^{5} - 17q^{6} - 19q^{7} - 66q^{8} + 106q^{9} - 15q^{10} - 40q^{11} - 53q^{12} - 59q^{13} - 36q^{14} - 40q^{15} + 118q^{16} - 93q^{17} - 59q^{18} - 16q^{19} - 108q^{20} - 62q^{21} - 37q^{22} - 107q^{23} - 31q^{24} + 101q^{25} - 64q^{26} - 63q^{27} - 53q^{28} - 124q^{29} - 68q^{30} - 15q^{31} - 129q^{32} - 49q^{33} - 76q^{35} + 45q^{36} - 98q^{37} - 125q^{38} - 47q^{39} - 7q^{40} - 56q^{41} - 84q^{42} - 62q^{43} - 114q^{44} - 142q^{45} - 3q^{46} - 111q^{47} - 92q^{48} + 117q^{49} - 64q^{50} - 21q^{51} - 85q^{52} - 347q^{53} + 3q^{54} - 16q^{55} - 73q^{56} - 115q^{57} - 29q^{58} - 50q^{59} - 54q^{60} - 62q^{61} - 55q^{62} - 70q^{63} + 64q^{64} - 147q^{65} + 34q^{66} - 86q^{67} - 174q^{68} - 104q^{69} - 7q^{70} - 86q^{71} - 139q^{72} - 27q^{73} - 52q^{74} - 49q^{75} - 11q^{76} - 346q^{77} - 59q^{78} - 17q^{79} - 149q^{80} - 8q^{81} - 31q^{82} - 106q^{83} - 51q^{84} - 69q^{85} - 85q^{86} - 32q^{87} - 113q^{88} - 59q^{89} + 10q^{90} - 9q^{91} - 314q^{92} - 230q^{93} + 7q^{94} - 74q^{95} - 54q^{96} - 60q^{97} - 77q^{98} - 96q^{99} + O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.42958 −1.71798 −0.858988 0.511996i \(-0.828906\pi\)
−0.858988 + 0.511996i \(0.828906\pi\)
\(3\) −1.44088 −0.831891 −0.415946 0.909389i \(-0.636549\pi\)
−0.415946 + 0.909389i \(0.636549\pi\)
\(4\) 3.90288 1.95144
\(5\) 0.473210 0.211626 0.105813 0.994386i \(-0.466255\pi\)
0.105813 + 0.994386i \(0.466255\pi\)
\(6\) 3.50074 1.42917
\(7\) −4.22120 −1.59546 −0.797731 0.603013i \(-0.793967\pi\)
−0.797731 + 0.603013i \(0.793967\pi\)
\(8\) −4.62321 −1.63455
\(9\) −0.923870 −0.307957
\(10\) −1.14970 −0.363568
\(11\) 2.71553 0.818763 0.409381 0.912363i \(-0.365745\pi\)
0.409381 + 0.912363i \(0.365745\pi\)
\(12\) −5.62358 −1.62339
\(13\) −6.52831 −1.81063 −0.905313 0.424744i \(-0.860364\pi\)
−0.905313 + 0.424744i \(0.860364\pi\)
\(14\) 10.2558 2.74097
\(15\) −0.681838 −0.176050
\(16\) 3.42672 0.856679
\(17\) −2.95637 −0.717026 −0.358513 0.933525i \(-0.616716\pi\)
−0.358513 + 0.933525i \(0.616716\pi\)
\(18\) 2.24462 0.529062
\(19\) 2.50601 0.574919 0.287460 0.957793i \(-0.407189\pi\)
0.287460 + 0.957793i \(0.407189\pi\)
\(20\) 1.84688 0.412976
\(21\) 6.08223 1.32725
\(22\) −6.59761 −1.40661
\(23\) 0.352460 0.0734930 0.0367465 0.999325i \(-0.488301\pi\)
0.0367465 + 0.999325i \(0.488301\pi\)
\(24\) 6.66148 1.35977
\(25\) −4.77607 −0.955214
\(26\) 15.8611 3.11061
\(27\) 5.65382 1.08808
\(28\) −16.4748 −3.11345
\(29\) 5.98074 1.11060 0.555298 0.831652i \(-0.312604\pi\)
0.555298 + 0.831652i \(0.312604\pi\)
\(30\) 1.65658 0.302449
\(31\) −0.0270305 −0.00485483 −0.00242741 0.999997i \(-0.500773\pi\)
−0.00242741 + 0.999997i \(0.500773\pi\)
\(32\) 0.920923 0.162798
\(33\) −3.91275 −0.681122
\(34\) 7.18276 1.23183
\(35\) −1.99751 −0.337641
\(36\) −3.60575 −0.600959
\(37\) 7.65604 1.25865 0.629323 0.777144i \(-0.283332\pi\)
0.629323 + 0.777144i \(0.283332\pi\)
\(38\) −6.08857 −0.987697
\(39\) 9.40650 1.50625
\(40\) −2.18775 −0.345914
\(41\) 6.98781 1.09131 0.545656 0.838009i \(-0.316281\pi\)
0.545656 + 0.838009i \(0.316281\pi\)
\(42\) −14.7773 −2.28019
\(43\) −9.53851 −1.45461 −0.727304 0.686315i \(-0.759227\pi\)
−0.727304 + 0.686315i \(0.759227\pi\)
\(44\) 10.5984 1.59777
\(45\) −0.437185 −0.0651717
\(46\) −0.856332 −0.126259
\(47\) 6.18705 0.902473 0.451237 0.892404i \(-0.350983\pi\)
0.451237 + 0.892404i \(0.350983\pi\)
\(48\) −4.93748 −0.712664
\(49\) 10.8185 1.54550
\(50\) 11.6039 1.64104
\(51\) 4.25978 0.596488
\(52\) −25.4792 −3.53333
\(53\) 8.86731 1.21802 0.609010 0.793163i \(-0.291567\pi\)
0.609010 + 0.793163i \(0.291567\pi\)
\(54\) −13.7364 −1.86929
\(55\) 1.28502 0.173272
\(56\) 19.5155 2.60787
\(57\) −3.61086 −0.478270
\(58\) −14.5307 −1.90798
\(59\) −7.83611 −1.02017 −0.510087 0.860123i \(-0.670387\pi\)
−0.510087 + 0.860123i \(0.670387\pi\)
\(60\) −2.66113 −0.343551
\(61\) 9.95309 1.27436 0.637181 0.770714i \(-0.280100\pi\)
0.637181 + 0.770714i \(0.280100\pi\)
\(62\) 0.0656729 0.00834047
\(63\) 3.89984 0.491333
\(64\) −9.09089 −1.13636
\(65\) −3.08926 −0.383176
\(66\) 9.50635 1.17015
\(67\) 1.86101 0.227359 0.113679 0.993517i \(-0.463736\pi\)
0.113679 + 0.993517i \(0.463736\pi\)
\(68\) −11.5384 −1.39923
\(69\) −0.507852 −0.0611382
\(70\) 4.85313 0.580060
\(71\) −13.0373 −1.54724 −0.773619 0.633651i \(-0.781556\pi\)
−0.773619 + 0.633651i \(0.781556\pi\)
\(72\) 4.27124 0.503371
\(73\) 8.64784 1.01215 0.506077 0.862488i \(-0.331095\pi\)
0.506077 + 0.862488i \(0.331095\pi\)
\(74\) −18.6010 −2.16232
\(75\) 6.88174 0.794635
\(76\) 9.78068 1.12192
\(77\) −11.4628 −1.30631
\(78\) −22.8539 −2.58769
\(79\) 7.74098 0.870929 0.435464 0.900206i \(-0.356584\pi\)
0.435464 + 0.900206i \(0.356584\pi\)
\(80\) 1.62156 0.181296
\(81\) −5.37485 −0.597206
\(82\) −16.9775 −1.87485
\(83\) 7.49076 0.822218 0.411109 0.911586i \(-0.365142\pi\)
0.411109 + 0.911586i \(0.365142\pi\)
\(84\) 23.7382 2.59005
\(85\) −1.39899 −0.151741
\(86\) 23.1746 2.49898
\(87\) −8.61751 −0.923895
\(88\) −12.5545 −1.33831
\(89\) −12.0652 −1.27891 −0.639455 0.768829i \(-0.720840\pi\)
−0.639455 + 0.768829i \(0.720840\pi\)
\(90\) 1.06218 0.111963
\(91\) 27.5573 2.88879
\(92\) 1.37561 0.143417
\(93\) 0.0389477 0.00403869
\(94\) −15.0320 −1.55043
\(95\) 1.18587 0.121668
\(96\) −1.32694 −0.135430
\(97\) −6.42719 −0.652582 −0.326291 0.945269i \(-0.605799\pi\)
−0.326291 + 0.945269i \(0.605799\pi\)
\(98\) −26.2845 −2.65513
\(99\) −2.50880 −0.252143
\(100\) −18.6404 −1.86404
\(101\) 6.16354 0.613295 0.306648 0.951823i \(-0.400793\pi\)
0.306648 + 0.951823i \(0.400793\pi\)
\(102\) −10.3495 −1.02475
\(103\) −4.37926 −0.431501 −0.215750 0.976449i \(-0.569220\pi\)
−0.215750 + 0.976449i \(0.569220\pi\)
\(104\) 30.1817 2.95956
\(105\) 2.87817 0.280881
\(106\) −21.5439 −2.09253
\(107\) 1.17057 0.113163 0.0565816 0.998398i \(-0.481980\pi\)
0.0565816 + 0.998398i \(0.481980\pi\)
\(108\) 22.0662 2.12332
\(109\) −1.72583 −0.165304 −0.0826521 0.996578i \(-0.526339\pi\)
−0.0826521 + 0.996578i \(0.526339\pi\)
\(110\) −3.12206 −0.297676
\(111\) −11.0314 −1.04706
\(112\) −14.4648 −1.36680
\(113\) −6.87121 −0.646389 −0.323194 0.946333i \(-0.604757\pi\)
−0.323194 + 0.946333i \(0.604757\pi\)
\(114\) 8.77289 0.821657
\(115\) 0.166788 0.0155530
\(116\) 23.3421 2.16726
\(117\) 6.03131 0.557595
\(118\) 19.0385 1.75264
\(119\) 12.4794 1.14399
\(120\) 3.15228 0.287763
\(121\) −3.62590 −0.329627
\(122\) −24.1819 −2.18932
\(123\) −10.0686 −0.907853
\(124\) −0.105497 −0.00947390
\(125\) −4.62614 −0.413774
\(126\) −9.47499 −0.844099
\(127\) −17.7077 −1.57131 −0.785654 0.618667i \(-0.787673\pi\)
−0.785654 + 0.618667i \(0.787673\pi\)
\(128\) 20.2452 1.78944
\(129\) 13.7438 1.21008
\(130\) 7.50562 0.658287
\(131\) 5.88021 0.513756 0.256878 0.966444i \(-0.417306\pi\)
0.256878 + 0.966444i \(0.417306\pi\)
\(132\) −15.2710 −1.32917
\(133\) −10.5784 −0.917262
\(134\) −4.52149 −0.390597
\(135\) 2.67545 0.230266
\(136\) 13.6679 1.17202
\(137\) −14.8661 −1.27009 −0.635047 0.772474i \(-0.719019\pi\)
−0.635047 + 0.772474i \(0.719019\pi\)
\(138\) 1.23387 0.105034
\(139\) 11.1701 0.947434 0.473717 0.880677i \(-0.342912\pi\)
0.473717 + 0.880677i \(0.342912\pi\)
\(140\) −7.79606 −0.658887
\(141\) −8.91478 −0.750760
\(142\) 31.6751 2.65812
\(143\) −17.7278 −1.48247
\(144\) −3.16584 −0.263820
\(145\) 2.83015 0.235031
\(146\) −21.0107 −1.73886
\(147\) −15.5882 −1.28569
\(148\) 29.8806 2.45617
\(149\) −7.96345 −0.652392 −0.326196 0.945302i \(-0.605767\pi\)
−0.326196 + 0.945302i \(0.605767\pi\)
\(150\) −16.7198 −1.36516
\(151\) 15.5499 1.26543 0.632716 0.774384i \(-0.281940\pi\)
0.632716 + 0.774384i \(0.281940\pi\)
\(152\) −11.5858 −0.939735
\(153\) 2.73131 0.220813
\(154\) 27.8498 2.24420
\(155\) −0.0127911 −0.00102741
\(156\) 36.7124 2.93935
\(157\) 19.9856 1.59502 0.797510 0.603305i \(-0.206150\pi\)
0.797510 + 0.603305i \(0.206150\pi\)
\(158\) −18.8074 −1.49623
\(159\) −12.7767 −1.01326
\(160\) 0.435790 0.0344522
\(161\) −1.48780 −0.117255
\(162\) 13.0587 1.02599
\(163\) 14.7854 1.15808 0.579039 0.815300i \(-0.303428\pi\)
0.579039 + 0.815300i \(0.303428\pi\)
\(164\) 27.2726 2.12963
\(165\) −1.85155 −0.144143
\(166\) −18.1994 −1.41255
\(167\) −9.67370 −0.748573 −0.374287 0.927313i \(-0.622112\pi\)
−0.374287 + 0.927313i \(0.622112\pi\)
\(168\) −28.1194 −2.16946
\(169\) 29.6188 2.27837
\(170\) 3.39896 0.260688
\(171\) −2.31523 −0.177050
\(172\) −37.2277 −2.83858
\(173\) 10.1770 0.773742 0.386871 0.922134i \(-0.373556\pi\)
0.386871 + 0.922134i \(0.373556\pi\)
\(174\) 20.9370 1.58723
\(175\) 20.1607 1.52401
\(176\) 9.30535 0.701417
\(177\) 11.2909 0.848675
\(178\) 29.3134 2.19714
\(179\) 22.8065 1.70463 0.852317 0.523025i \(-0.175197\pi\)
0.852317 + 0.523025i \(0.175197\pi\)
\(180\) −1.70628 −0.127179
\(181\) −12.7603 −0.948468 −0.474234 0.880399i \(-0.657275\pi\)
−0.474234 + 0.880399i \(0.657275\pi\)
\(182\) −66.9527 −4.96287
\(183\) −14.3412 −1.06013
\(184\) −1.62950 −0.120128
\(185\) 3.62292 0.266362
\(186\) −0.0946267 −0.00693837
\(187\) −8.02812 −0.587074
\(188\) 24.1473 1.76112
\(189\) −23.8659 −1.73599
\(190\) −2.88118 −0.209022
\(191\) −5.83263 −0.422035 −0.211017 0.977482i \(-0.567678\pi\)
−0.211017 + 0.977482i \(0.567678\pi\)
\(192\) 13.0989 0.945329
\(193\) −1.90949 −0.137448 −0.0687239 0.997636i \(-0.521893\pi\)
−0.0687239 + 0.997636i \(0.521893\pi\)
\(194\) 15.6154 1.12112
\(195\) 4.45125 0.318761
\(196\) 42.2234 3.01595
\(197\) −17.6728 −1.25914 −0.629568 0.776945i \(-0.716768\pi\)
−0.629568 + 0.776945i \(0.716768\pi\)
\(198\) 6.09533 0.433176
\(199\) 11.7783 0.834944 0.417472 0.908690i \(-0.362916\pi\)
0.417472 + 0.908690i \(0.362916\pi\)
\(200\) 22.0808 1.56135
\(201\) −2.68149 −0.189138
\(202\) −14.9748 −1.05363
\(203\) −25.2459 −1.77191
\(204\) 16.6254 1.16401
\(205\) 3.30670 0.230950
\(206\) 10.6398 0.741308
\(207\) −0.325627 −0.0226327
\(208\) −22.3707 −1.55113
\(209\) 6.80516 0.470722
\(210\) −6.99277 −0.482547
\(211\) 14.2399 0.980317 0.490159 0.871633i \(-0.336939\pi\)
0.490159 + 0.871633i \(0.336939\pi\)
\(212\) 34.6081 2.37689
\(213\) 18.7851 1.28713
\(214\) −2.84400 −0.194412
\(215\) −4.51372 −0.307833
\(216\) −26.1388 −1.77852
\(217\) 0.114101 0.00774569
\(218\) 4.19304 0.283989
\(219\) −12.4605 −0.842002
\(220\) 5.01527 0.338129
\(221\) 19.3001 1.29827
\(222\) 26.8018 1.79882
\(223\) 6.97758 0.467253 0.233627 0.972326i \(-0.424941\pi\)
0.233627 + 0.972326i \(0.424941\pi\)
\(224\) −3.88740 −0.259738
\(225\) 4.41247 0.294165
\(226\) 16.6942 1.11048
\(227\) −2.30847 −0.153219 −0.0766093 0.997061i \(-0.524409\pi\)
−0.0766093 + 0.997061i \(0.524409\pi\)
\(228\) −14.0928 −0.933316
\(229\) −9.93102 −0.656260 −0.328130 0.944633i \(-0.606418\pi\)
−0.328130 + 0.944633i \(0.606418\pi\)
\(230\) −0.405225 −0.0267197
\(231\) 16.5165 1.08670
\(232\) −27.6502 −1.81532
\(233\) 3.82809 0.250786 0.125393 0.992107i \(-0.459981\pi\)
0.125393 + 0.992107i \(0.459981\pi\)
\(234\) −14.6536 −0.957934
\(235\) 2.92777 0.190987
\(236\) −30.5834 −1.99081
\(237\) −11.1538 −0.724518
\(238\) −30.3199 −1.96534
\(239\) 29.2213 1.89017 0.945083 0.326830i \(-0.105981\pi\)
0.945083 + 0.326830i \(0.105981\pi\)
\(240\) −2.33647 −0.150818
\(241\) −30.0754 −1.93733 −0.968663 0.248377i \(-0.920103\pi\)
−0.968663 + 0.248377i \(0.920103\pi\)
\(242\) 8.80943 0.566292
\(243\) −9.21695 −0.591267
\(244\) 38.8457 2.48684
\(245\) 5.11943 0.327068
\(246\) 24.4625 1.55967
\(247\) −16.3600 −1.04096
\(248\) 0.124968 0.00793546
\(249\) −10.7933 −0.683996
\(250\) 11.2396 0.710854
\(251\) −0.407155 −0.0256994 −0.0128497 0.999917i \(-0.504090\pi\)
−0.0128497 + 0.999917i \(0.504090\pi\)
\(252\) 15.2206 0.958808
\(253\) 0.957116 0.0601734
\(254\) 43.0224 2.69947
\(255\) 2.01577 0.126232
\(256\) −31.0057 −1.93786
\(257\) −14.6781 −0.915594 −0.457797 0.889057i \(-0.651361\pi\)
−0.457797 + 0.889057i \(0.651361\pi\)
\(258\) −33.3918 −2.07888
\(259\) −32.3177 −2.00812
\(260\) −12.0570 −0.747745
\(261\) −5.52542 −0.342015
\(262\) −14.2865 −0.882621
\(263\) −3.42094 −0.210944 −0.105472 0.994422i \(-0.533635\pi\)
−0.105472 + 0.994422i \(0.533635\pi\)
\(264\) 18.0894 1.11333
\(265\) 4.19610 0.257765
\(266\) 25.7011 1.57583
\(267\) 17.3845 1.06391
\(268\) 7.26331 0.443677
\(269\) −14.3900 −0.877372 −0.438686 0.898640i \(-0.644556\pi\)
−0.438686 + 0.898640i \(0.644556\pi\)
\(270\) −6.50022 −0.395591
\(271\) −4.07265 −0.247396 −0.123698 0.992320i \(-0.539475\pi\)
−0.123698 + 0.992320i \(0.539475\pi\)
\(272\) −10.1307 −0.614261
\(273\) −39.7067 −2.40316
\(274\) 36.1184 2.18199
\(275\) −12.9696 −0.782094
\(276\) −1.98209 −0.119308
\(277\) 24.0712 1.44630 0.723148 0.690693i \(-0.242695\pi\)
0.723148 + 0.690693i \(0.242695\pi\)
\(278\) −27.1387 −1.62767
\(279\) 0.0249727 0.00149508
\(280\) 9.23493 0.551892
\(281\) 7.83799 0.467576 0.233788 0.972288i \(-0.424888\pi\)
0.233788 + 0.972288i \(0.424888\pi\)
\(282\) 21.6592 1.28979
\(283\) −24.1881 −1.43784 −0.718918 0.695095i \(-0.755362\pi\)
−0.718918 + 0.695095i \(0.755362\pi\)
\(284\) −50.8829 −3.01934
\(285\) −1.70870 −0.101214
\(286\) 43.0712 2.54685
\(287\) −29.4969 −1.74115
\(288\) −0.850813 −0.0501346
\(289\) −8.25985 −0.485874
\(290\) −6.87608 −0.403777
\(291\) 9.26080 0.542877
\(292\) 33.7515 1.97516
\(293\) 14.7265 0.860329 0.430165 0.902751i \(-0.358456\pi\)
0.430165 + 0.902751i \(0.358456\pi\)
\(294\) 37.8727 2.20878
\(295\) −3.70813 −0.215896
\(296\) −35.3955 −2.05732
\(297\) 15.3531 0.890878
\(298\) 19.3479 1.12079
\(299\) −2.30097 −0.133068
\(300\) 26.8586 1.55068
\(301\) 40.2639 2.32077
\(302\) −37.7798 −2.17398
\(303\) −8.88091 −0.510195
\(304\) 8.58740 0.492521
\(305\) 4.70990 0.269688
\(306\) −6.63594 −0.379351
\(307\) 17.6980 1.01008 0.505040 0.863096i \(-0.331478\pi\)
0.505040 + 0.863096i \(0.331478\pi\)
\(308\) −44.7379 −2.54918
\(309\) 6.30997 0.358962
\(310\) 0.0310771 0.00176506
\(311\) −3.34765 −0.189828 −0.0949139 0.995485i \(-0.530258\pi\)
−0.0949139 + 0.995485i \(0.530258\pi\)
\(312\) −43.4882 −2.46203
\(313\) 4.56242 0.257883 0.128942 0.991652i \(-0.458842\pi\)
0.128942 + 0.991652i \(0.458842\pi\)
\(314\) −48.5566 −2.74021
\(315\) 1.84544 0.103979
\(316\) 30.2121 1.69957
\(317\) −2.62279 −0.147310 −0.0736552 0.997284i \(-0.523466\pi\)
−0.0736552 + 0.997284i \(0.523466\pi\)
\(318\) 31.0421 1.74076
\(319\) 16.2409 0.909314
\(320\) −4.30190 −0.240484
\(321\) −1.68665 −0.0941396
\(322\) 3.61475 0.201442
\(323\) −7.40872 −0.412232
\(324\) −20.9774 −1.16541
\(325\) 31.1797 1.72954
\(326\) −35.9223 −1.98955
\(327\) 2.48671 0.137515
\(328\) −32.3061 −1.78381
\(329\) −26.1167 −1.43986
\(330\) 4.49850 0.247634
\(331\) 7.11368 0.391003 0.195502 0.980703i \(-0.437367\pi\)
0.195502 + 0.980703i \(0.437367\pi\)
\(332\) 29.2355 1.60451
\(333\) −7.07319 −0.387608
\(334\) 23.5031 1.28603
\(335\) 0.880651 0.0481151
\(336\) 20.8421 1.13703
\(337\) −4.64050 −0.252784 −0.126392 0.991980i \(-0.540340\pi\)
−0.126392 + 0.991980i \(0.540340\pi\)
\(338\) −71.9614 −3.91418
\(339\) 9.90057 0.537725
\(340\) −5.46008 −0.296114
\(341\) −0.0734022 −0.00397495
\(342\) 5.62505 0.304168
\(343\) −16.1187 −0.870327
\(344\) 44.0985 2.37763
\(345\) −0.240321 −0.0129384
\(346\) −24.7259 −1.32927
\(347\) 8.86641 0.475974 0.237987 0.971268i \(-0.423512\pi\)
0.237987 + 0.971268i \(0.423512\pi\)
\(348\) −33.6331 −1.80292
\(349\) −17.0538 −0.912867 −0.456434 0.889757i \(-0.650873\pi\)
−0.456434 + 0.889757i \(0.650873\pi\)
\(350\) −48.9822 −2.61821
\(351\) −36.9099 −1.97010
\(352\) 2.50079 0.133293
\(353\) −7.62697 −0.405943 −0.202971 0.979185i \(-0.565060\pi\)
−0.202971 + 0.979185i \(0.565060\pi\)
\(354\) −27.4321 −1.45800
\(355\) −6.16937 −0.327436
\(356\) −47.0891 −2.49572
\(357\) −17.9814 −0.951674
\(358\) −55.4102 −2.92852
\(359\) −2.68468 −0.141692 −0.0708460 0.997487i \(-0.522570\pi\)
−0.0708460 + 0.997487i \(0.522570\pi\)
\(360\) 2.02120 0.106526
\(361\) −12.7199 −0.669468
\(362\) 31.0023 1.62944
\(363\) 5.22448 0.274214
\(364\) 107.553 5.63730
\(365\) 4.09225 0.214198
\(366\) 34.8431 1.82128
\(367\) −5.68366 −0.296685 −0.148342 0.988936i \(-0.547394\pi\)
−0.148342 + 0.988936i \(0.547394\pi\)
\(368\) 1.20778 0.0629599
\(369\) −6.45582 −0.336077
\(370\) −8.80219 −0.457604
\(371\) −37.4307 −1.94330
\(372\) 0.152008 0.00788126
\(373\) −9.19869 −0.476290 −0.238145 0.971230i \(-0.576539\pi\)
−0.238145 + 0.971230i \(0.576539\pi\)
\(374\) 19.5050 1.00858
\(375\) 6.66570 0.344215
\(376\) −28.6040 −1.47514
\(377\) −39.0441 −2.01087
\(378\) 57.9842 2.98238
\(379\) −33.5670 −1.72422 −0.862110 0.506722i \(-0.830857\pi\)
−0.862110 + 0.506722i \(0.830857\pi\)
\(380\) 4.62832 0.237428
\(381\) 25.5147 1.30716
\(382\) 14.1709 0.725045
\(383\) −14.6642 −0.749304 −0.374652 0.927166i \(-0.622238\pi\)
−0.374652 + 0.927166i \(0.622238\pi\)
\(384\) −29.1709 −1.48862
\(385\) −5.42431 −0.276448
\(386\) 4.63926 0.236132
\(387\) 8.81234 0.447956
\(388\) −25.0845 −1.27347
\(389\) −15.3825 −0.779924 −0.389962 0.920831i \(-0.627512\pi\)
−0.389962 + 0.920831i \(0.627512\pi\)
\(390\) −10.8147 −0.547623
\(391\) −1.04200 −0.0526964
\(392\) −50.0162 −2.52620
\(393\) −8.47266 −0.427389
\(394\) 42.9376 2.16317
\(395\) 3.66311 0.184311
\(396\) −9.79153 −0.492043
\(397\) 19.0189 0.954532 0.477266 0.878759i \(-0.341628\pi\)
0.477266 + 0.878759i \(0.341628\pi\)
\(398\) −28.6164 −1.43441
\(399\) 15.2422 0.763062
\(400\) −16.3662 −0.818312
\(401\) −12.4188 −0.620166 −0.310083 0.950709i \(-0.600357\pi\)
−0.310083 + 0.950709i \(0.600357\pi\)
\(402\) 6.51492 0.324934
\(403\) 0.176464 0.00879028
\(404\) 24.0556 1.19681
\(405\) −2.54344 −0.126384
\(406\) 61.3370 3.04410
\(407\) 20.7902 1.03053
\(408\) −19.6938 −0.974990
\(409\) −30.0625 −1.48650 −0.743248 0.669016i \(-0.766716\pi\)
−0.743248 + 0.669016i \(0.766716\pi\)
\(410\) −8.03391 −0.396767
\(411\) 21.4202 1.05658
\(412\) −17.0917 −0.842048
\(413\) 33.0778 1.62765
\(414\) 0.791139 0.0388824
\(415\) 3.54470 0.174003
\(416\) −6.01207 −0.294766
\(417\) −16.0947 −0.788162
\(418\) −16.5337 −0.808690
\(419\) 8.09742 0.395585 0.197793 0.980244i \(-0.436623\pi\)
0.197793 + 0.980244i \(0.436623\pi\)
\(420\) 11.2332 0.548123
\(421\) 9.13851 0.445384 0.222692 0.974889i \(-0.428516\pi\)
0.222692 + 0.974889i \(0.428516\pi\)
\(422\) −34.5971 −1.68416
\(423\) −5.71603 −0.277923
\(424\) −40.9954 −1.99091
\(425\) 14.1199 0.684914
\(426\) −45.6400 −2.21127
\(427\) −42.0139 −2.03320
\(428\) 4.56859 0.220831
\(429\) 25.5436 1.23326
\(430\) 10.9665 0.528850
\(431\) −0.568045 −0.0273618 −0.0136809 0.999906i \(-0.504355\pi\)
−0.0136809 + 0.999906i \(0.504355\pi\)
\(432\) 19.3740 0.932133
\(433\) −18.8326 −0.905035 −0.452517 0.891756i \(-0.649474\pi\)
−0.452517 + 0.891756i \(0.649474\pi\)
\(434\) −0.277218 −0.0133069
\(435\) −4.07790 −0.195520
\(436\) −6.73570 −0.322581
\(437\) 0.883270 0.0422525
\(438\) 30.2738 1.44654
\(439\) 0.531438 0.0253642 0.0126821 0.999920i \(-0.495963\pi\)
0.0126821 + 0.999920i \(0.495963\pi\)
\(440\) −5.94090 −0.283221
\(441\) −9.99490 −0.475947
\(442\) −46.8913 −2.23039
\(443\) −27.7046 −1.31628 −0.658141 0.752894i \(-0.728657\pi\)
−0.658141 + 0.752894i \(0.728657\pi\)
\(444\) −43.0543 −2.04327
\(445\) −5.70938 −0.270651
\(446\) −16.9526 −0.802730
\(447\) 11.4744 0.542719
\(448\) 38.3745 1.81302
\(449\) −34.8489 −1.64462 −0.822310 0.569040i \(-0.807315\pi\)
−0.822310 + 0.569040i \(0.807315\pi\)
\(450\) −10.7205 −0.505368
\(451\) 18.9756 0.893526
\(452\) −26.8175 −1.26139
\(453\) −22.4055 −1.05270
\(454\) 5.60863 0.263226
\(455\) 13.0404 0.611343
\(456\) 16.6938 0.781757
\(457\) 26.6961 1.24879 0.624395 0.781109i \(-0.285346\pi\)
0.624395 + 0.781109i \(0.285346\pi\)
\(458\) 24.1282 1.12744
\(459\) −16.7148 −0.780180
\(460\) 0.650953 0.0303508
\(461\) −3.83211 −0.178479 −0.0892397 0.996010i \(-0.528444\pi\)
−0.0892397 + 0.996010i \(0.528444\pi\)
\(462\) −40.1282 −1.86693
\(463\) −1.51711 −0.0705061 −0.0352530 0.999378i \(-0.511224\pi\)
−0.0352530 + 0.999378i \(0.511224\pi\)
\(464\) 20.4943 0.951423
\(465\) 0.0184304 0.000854692 0
\(466\) −9.30067 −0.430845
\(467\) −21.6294 −1.00089 −0.500445 0.865768i \(-0.666830\pi\)
−0.500445 + 0.865768i \(0.666830\pi\)
\(468\) 23.5395 1.08811
\(469\) −7.85571 −0.362743
\(470\) −7.11327 −0.328111
\(471\) −28.7967 −1.32688
\(472\) 36.2280 1.66753
\(473\) −25.9021 −1.19098
\(474\) 27.0991 1.24470
\(475\) −11.9689 −0.549171
\(476\) 48.7058 2.23243
\(477\) −8.19224 −0.375097
\(478\) −70.9955 −3.24726
\(479\) −34.0595 −1.55622 −0.778109 0.628129i \(-0.783821\pi\)
−0.778109 + 0.628129i \(0.783821\pi\)
\(480\) −0.627921 −0.0286605
\(481\) −49.9810 −2.27894
\(482\) 73.0707 3.32828
\(483\) 2.14374 0.0975438
\(484\) −14.1515 −0.643248
\(485\) −3.04141 −0.138103
\(486\) 22.3933 1.01578
\(487\) −27.4575 −1.24422 −0.622108 0.782931i \(-0.713724\pi\)
−0.622108 + 0.782931i \(0.713724\pi\)
\(488\) −46.0152 −2.08301
\(489\) −21.3039 −0.963395
\(490\) −12.4381 −0.561895
\(491\) 27.8544 1.25705 0.628525 0.777789i \(-0.283659\pi\)
0.628525 + 0.777789i \(0.283659\pi\)
\(492\) −39.2965 −1.77162
\(493\) −17.6813 −0.796326
\(494\) 39.7481 1.78835
\(495\) −1.18719 −0.0533601
\(496\) −0.0926259 −0.00415903
\(497\) 55.0329 2.46856
\(498\) 26.2232 1.17509
\(499\) 0.535608 0.0239771 0.0119886 0.999928i \(-0.496184\pi\)
0.0119886 + 0.999928i \(0.496184\pi\)
\(500\) −18.0553 −0.807456
\(501\) 13.9386 0.622732
\(502\) 0.989216 0.0441509
\(503\) 8.06094 0.359419 0.179710 0.983720i \(-0.442484\pi\)
0.179710 + 0.983720i \(0.442484\pi\)
\(504\) −18.0298 −0.803110
\(505\) 2.91665 0.129789
\(506\) −2.32539 −0.103376
\(507\) −42.6771 −1.89536
\(508\) −69.1112 −3.06631
\(509\) −2.22821 −0.0987636 −0.0493818 0.998780i \(-0.515725\pi\)
−0.0493818 + 0.998780i \(0.515725\pi\)
\(510\) −4.89748 −0.216864
\(511\) −36.5043 −1.61485
\(512\) 34.8406 1.53975
\(513\) 14.1686 0.625557
\(514\) 35.6617 1.57297
\(515\) −2.07231 −0.0913168
\(516\) 53.6405 2.36139
\(517\) 16.8011 0.738912
\(518\) 78.5185 3.44991
\(519\) −14.6638 −0.643670
\(520\) 14.2823 0.626321
\(521\) −4.16539 −0.182489 −0.0912445 0.995829i \(-0.529084\pi\)
−0.0912445 + 0.995829i \(0.529084\pi\)
\(522\) 13.4245 0.587574
\(523\) −10.4545 −0.457145 −0.228573 0.973527i \(-0.573406\pi\)
−0.228573 + 0.973527i \(0.573406\pi\)
\(524\) 22.9498 1.00256
\(525\) −29.0492 −1.26781
\(526\) 8.31147 0.362397
\(527\) 0.0799123 0.00348104
\(528\) −13.4079 −0.583503
\(529\) −22.8758 −0.994599
\(530\) −10.1948 −0.442833
\(531\) 7.23955 0.314170
\(532\) −41.2862 −1.78998
\(533\) −45.6185 −1.97596
\(534\) −42.2371 −1.82778
\(535\) 0.553926 0.0239483
\(536\) −8.60385 −0.371630
\(537\) −32.8613 −1.41807
\(538\) 34.9617 1.50730
\(539\) 29.3780 1.26540
\(540\) 10.4419 0.449350
\(541\) −40.8896 −1.75798 −0.878992 0.476837i \(-0.841783\pi\)
−0.878992 + 0.476837i \(0.841783\pi\)
\(542\) 9.89484 0.425020
\(543\) 18.3861 0.789022
\(544\) −2.72259 −0.116730
\(545\) −0.816679 −0.0349827
\(546\) 96.4707 4.12857
\(547\) 25.5833 1.09386 0.546931 0.837178i \(-0.315796\pi\)
0.546931 + 0.837178i \(0.315796\pi\)
\(548\) −58.0205 −2.47851
\(549\) −9.19536 −0.392448
\(550\) 31.5107 1.34362
\(551\) 14.9878 0.638502
\(552\) 2.34791 0.0999336
\(553\) −32.6762 −1.38953
\(554\) −58.4829 −2.48470
\(555\) −5.22018 −0.221584
\(556\) 43.5955 1.84886
\(557\) −16.6364 −0.704905 −0.352453 0.935830i \(-0.614652\pi\)
−0.352453 + 0.935830i \(0.614652\pi\)
\(558\) −0.0606733 −0.00256850
\(559\) 62.2703 2.63375
\(560\) −6.84491 −0.289250
\(561\) 11.5675 0.488382
\(562\) −19.0431 −0.803283
\(563\) 13.0087 0.548250 0.274125 0.961694i \(-0.411612\pi\)
0.274125 + 0.961694i \(0.411612\pi\)
\(564\) −34.7933 −1.46506
\(565\) −3.25152 −0.136793
\(566\) 58.7671 2.47017
\(567\) 22.6883 0.952820
\(568\) 60.2740 2.52904
\(569\) 16.8064 0.704563 0.352281 0.935894i \(-0.385406\pi\)
0.352281 + 0.935894i \(0.385406\pi\)
\(570\) 4.15142 0.173884
\(571\) −0.106134 −0.00444158 −0.00222079 0.999998i \(-0.500707\pi\)
−0.00222079 + 0.999998i \(0.500707\pi\)
\(572\) −69.1895 −2.89296
\(573\) 8.40412 0.351087
\(574\) 71.6652 2.99125
\(575\) −1.68338 −0.0702016
\(576\) 8.39880 0.349950
\(577\) 32.3438 1.34649 0.673244 0.739420i \(-0.264900\pi\)
0.673244 + 0.739420i \(0.264900\pi\)
\(578\) 20.0680 0.834719
\(579\) 2.75134 0.114342
\(580\) 11.0457 0.458649
\(581\) −31.6200 −1.31182
\(582\) −22.4999 −0.932650
\(583\) 24.0794 0.997269
\(584\) −39.9808 −1.65442
\(585\) 2.85408 0.118002
\(586\) −35.7792 −1.47802
\(587\) 35.2976 1.45689 0.728444 0.685106i \(-0.240244\pi\)
0.728444 + 0.685106i \(0.240244\pi\)
\(588\) −60.8387 −2.50895
\(589\) −0.0677389 −0.00279113
\(590\) 9.00921 0.370903
\(591\) 25.4644 1.04746
\(592\) 26.2351 1.07826
\(593\) 27.6475 1.13535 0.567674 0.823254i \(-0.307844\pi\)
0.567674 + 0.823254i \(0.307844\pi\)
\(594\) −37.3017 −1.53051
\(595\) 5.90540 0.242098
\(596\) −31.0804 −1.27310
\(597\) −16.9711 −0.694582
\(598\) 5.59040 0.228608
\(599\) 5.45353 0.222825 0.111413 0.993774i \(-0.464462\pi\)
0.111413 + 0.993774i \(0.464462\pi\)
\(600\) −31.8157 −1.29887
\(601\) −29.1888 −1.19063 −0.595317 0.803491i \(-0.702974\pi\)
−0.595317 + 0.803491i \(0.702974\pi\)
\(602\) −97.8246 −3.98703
\(603\) −1.71933 −0.0700167
\(604\) 60.6894 2.46942
\(605\) −1.71581 −0.0697577
\(606\) 21.5769 0.876503
\(607\) 24.0021 0.974216 0.487108 0.873342i \(-0.338052\pi\)
0.487108 + 0.873342i \(0.338052\pi\)
\(608\) 2.30785 0.0935955
\(609\) 36.3762 1.47404
\(610\) −11.4431 −0.463318
\(611\) −40.3909 −1.63404
\(612\) 10.6600 0.430903
\(613\) −1.10290 −0.0445458 −0.0222729 0.999752i \(-0.507090\pi\)
−0.0222729 + 0.999752i \(0.507090\pi\)
\(614\) −42.9989 −1.73529
\(615\) −4.76455 −0.192125
\(616\) 52.9949 2.13522
\(617\) 23.1467 0.931852 0.465926 0.884824i \(-0.345721\pi\)
0.465926 + 0.884824i \(0.345721\pi\)
\(618\) −15.3306 −0.616688
\(619\) 8.60339 0.345799 0.172900 0.984939i \(-0.444686\pi\)
0.172900 + 0.984939i \(0.444686\pi\)
\(620\) −0.0499222 −0.00200492
\(621\) 1.99275 0.0799661
\(622\) 8.13340 0.326120
\(623\) 50.9296 2.04045
\(624\) 32.2334 1.29037
\(625\) 21.6912 0.867649
\(626\) −11.0848 −0.443037
\(627\) −9.80540 −0.391590
\(628\) 78.0012 3.11259
\(629\) −22.6341 −0.902482
\(630\) −4.48366 −0.178633
\(631\) −25.2963 −1.00703 −0.503515 0.863986i \(-0.667960\pi\)
−0.503515 + 0.863986i \(0.667960\pi\)
\(632\) −35.7882 −1.42358
\(633\) −20.5180 −0.815517
\(634\) 6.37228 0.253076
\(635\) −8.37948 −0.332530
\(636\) −49.8660 −1.97732
\(637\) −70.6266 −2.79833
\(638\) −39.4586 −1.56218
\(639\) 12.0447 0.476482
\(640\) 9.58026 0.378693
\(641\) 17.4396 0.688823 0.344412 0.938819i \(-0.388078\pi\)
0.344412 + 0.938819i \(0.388078\pi\)
\(642\) 4.09786 0.161729
\(643\) 43.5893 1.71900 0.859498 0.511139i \(-0.170776\pi\)
0.859498 + 0.511139i \(0.170776\pi\)
\(644\) −5.80672 −0.228817
\(645\) 6.50372 0.256084
\(646\) 18.0001 0.708205
\(647\) −9.02345 −0.354749 −0.177374 0.984143i \(-0.556760\pi\)
−0.177374 + 0.984143i \(0.556760\pi\)
\(648\) 24.8491 0.976164
\(649\) −21.2792 −0.835281
\(650\) −75.7536 −2.97130
\(651\) −0.164406 −0.00644358
\(652\) 57.7055 2.25992
\(653\) −21.5540 −0.843475 −0.421737 0.906718i \(-0.638580\pi\)
−0.421737 + 0.906718i \(0.638580\pi\)
\(654\) −6.04166 −0.236248
\(655\) 2.78258 0.108724
\(656\) 23.9452 0.934904
\(657\) −7.98948 −0.311699
\(658\) 63.4528 2.47365
\(659\) 33.5681 1.30763 0.653813 0.756656i \(-0.273168\pi\)
0.653813 + 0.756656i \(0.273168\pi\)
\(660\) −7.22639 −0.281287
\(661\) 17.0629 0.663670 0.331835 0.943337i \(-0.392332\pi\)
0.331835 + 0.943337i \(0.392332\pi\)
\(662\) −17.2833 −0.671734
\(663\) −27.8091 −1.08002
\(664\) −34.6313 −1.34396
\(665\) −5.00580 −0.194117
\(666\) 17.1849 0.665902
\(667\) 2.10797 0.0816210
\(668\) −37.7553 −1.46080
\(669\) −10.0538 −0.388704
\(670\) −2.13962 −0.0826605
\(671\) 27.0279 1.04340
\(672\) 5.60127 0.216074
\(673\) −9.33152 −0.359704 −0.179852 0.983694i \(-0.557562\pi\)
−0.179852 + 0.983694i \(0.557562\pi\)
\(674\) 11.2745 0.434277
\(675\) −27.0030 −1.03935
\(676\) 115.599 4.44610
\(677\) 29.7028 1.14157 0.570786 0.821099i \(-0.306639\pi\)
0.570786 + 0.821099i \(0.306639\pi\)
\(678\) −24.0543 −0.923799
\(679\) 27.1304 1.04117
\(680\) 6.46781 0.248029
\(681\) 3.32623 0.127461
\(682\) 0.178337 0.00682887
\(683\) −3.86612 −0.147933 −0.0739664 0.997261i \(-0.523566\pi\)
−0.0739664 + 0.997261i \(0.523566\pi\)
\(684\) −9.03607 −0.345503
\(685\) −7.03477 −0.268785
\(686\) 39.1617 1.49520
\(687\) 14.3094 0.545937
\(688\) −32.6857 −1.24613
\(689\) −57.8886 −2.20538
\(690\) 0.583880 0.0222279
\(691\) 27.7296 1.05488 0.527442 0.849591i \(-0.323151\pi\)
0.527442 + 0.849591i \(0.323151\pi\)
\(692\) 39.7196 1.50991
\(693\) 10.5901 0.402286
\(694\) −21.5417 −0.817711
\(695\) 5.28580 0.200502
\(696\) 39.8406 1.51015
\(697\) −20.6586 −0.782499
\(698\) 41.4336 1.56828
\(699\) −5.51581 −0.208627
\(700\) 78.6850 2.97401
\(701\) −16.2452 −0.613572 −0.306786 0.951779i \(-0.599254\pi\)
−0.306786 + 0.951779i \(0.599254\pi\)
\(702\) 89.6757 3.38459
\(703\) 19.1862 0.723620
\(704\) −24.6866 −0.930411
\(705\) −4.21857 −0.158880
\(706\) 18.5304 0.697399
\(707\) −26.0175 −0.978490
\(708\) 44.0670 1.65614
\(709\) −37.5708 −1.41100 −0.705500 0.708710i \(-0.749277\pi\)
−0.705500 + 0.708710i \(0.749277\pi\)
\(710\) 14.9890 0.562527
\(711\) −7.15166 −0.268208
\(712\) 55.7800 2.09044
\(713\) −0.00952718 −0.000356796 0
\(714\) 43.6872 1.63495
\(715\) −8.38898 −0.313730
\(716\) 89.0109 3.32649
\(717\) −42.1043 −1.57241
\(718\) 6.52266 0.243423
\(719\) −27.4001 −1.02185 −0.510926 0.859625i \(-0.670697\pi\)
−0.510926 + 0.859625i \(0.670697\pi\)
\(720\) −1.49811 −0.0558312
\(721\) 18.4857 0.688444
\(722\) 30.9041 1.15013
\(723\) 43.3350 1.61165
\(724\) −49.8020 −1.85088
\(725\) −28.5644 −1.06086
\(726\) −12.6933 −0.471093
\(727\) −9.36260 −0.347240 −0.173620 0.984813i \(-0.555546\pi\)
−0.173620 + 0.984813i \(0.555546\pi\)
\(728\) −127.403 −4.72187
\(729\) 29.4051 1.08908
\(730\) −9.94246 −0.367987
\(731\) 28.1994 1.04299
\(732\) −55.9719 −2.06878
\(733\) −26.6562 −0.984568 −0.492284 0.870435i \(-0.663838\pi\)
−0.492284 + 0.870435i \(0.663838\pi\)
\(734\) 13.8089 0.509697
\(735\) −7.37647 −0.272085
\(736\) 0.324589 0.0119645
\(737\) 5.05364 0.186153
\(738\) 15.6850 0.577372
\(739\) 4.58031 0.168489 0.0842446 0.996445i \(-0.473152\pi\)
0.0842446 + 0.996445i \(0.473152\pi\)
\(740\) 14.1398 0.519790
\(741\) 23.5728 0.865969
\(742\) 90.9410 3.33855
\(743\) 19.4743 0.714443 0.357222 0.934020i \(-0.383724\pi\)
0.357222 + 0.934020i \(0.383724\pi\)
\(744\) −0.180063 −0.00660144
\(745\) −3.76839 −0.138063
\(746\) 22.3490 0.818255
\(747\) −6.92049 −0.253207
\(748\) −31.3328 −1.14564
\(749\) −4.94121 −0.180548
\(750\) −16.1949 −0.591354
\(751\) 5.94272 0.216853 0.108426 0.994104i \(-0.465419\pi\)
0.108426 + 0.994104i \(0.465419\pi\)
\(752\) 21.2012 0.773130
\(753\) 0.586660 0.0213791
\(754\) 94.8609 3.45463
\(755\) 7.35837 0.267799
\(756\) −93.1457 −3.38768
\(757\) 35.6732 1.29656 0.648282 0.761400i \(-0.275488\pi\)
0.648282 + 0.761400i \(0.275488\pi\)
\(758\) 81.5538 2.96217
\(759\) −1.37909 −0.0500577
\(760\) −5.48253 −0.198872
\(761\) −28.0282 −1.01602 −0.508011 0.861351i \(-0.669619\pi\)
−0.508011 + 0.861351i \(0.669619\pi\)
\(762\) −61.9901 −2.24566
\(763\) 7.28506 0.263737
\(764\) −22.7641 −0.823575
\(765\) 1.29248 0.0467298
\(766\) 35.6278 1.28729
\(767\) 51.1565 1.84716
\(768\) 44.6755 1.61209
\(769\) 44.4412 1.60259 0.801295 0.598269i \(-0.204145\pi\)
0.801295 + 0.598269i \(0.204145\pi\)
\(770\) 13.1788 0.474931
\(771\) 21.1493 0.761675
\(772\) −7.45249 −0.268221
\(773\) −46.4098 −1.66924 −0.834622 0.550823i \(-0.814314\pi\)
−0.834622 + 0.550823i \(0.814314\pi\)
\(774\) −21.4103 −0.769578
\(775\) 0.129100 0.00463740
\(776\) 29.7142 1.06668
\(777\) 46.5658 1.67054
\(778\) 37.3731 1.33989
\(779\) 17.5115 0.627416
\(780\) 17.3727 0.622042
\(781\) −35.4031 −1.26682
\(782\) 2.53164 0.0905312
\(783\) 33.8140 1.20841
\(784\) 37.0720 1.32400
\(785\) 9.45737 0.337548
\(786\) 20.5851 0.734245
\(787\) 17.1169 0.610152 0.305076 0.952328i \(-0.401318\pi\)
0.305076 + 0.952328i \(0.401318\pi\)
\(788\) −68.9749 −2.45713
\(789\) 4.92916 0.175483
\(790\) −8.89984 −0.316642
\(791\) 29.0047 1.03129
\(792\) 11.5987 0.412141
\(793\) −64.9768 −2.30739
\(794\) −46.2081 −1.63986
\(795\) −6.04607 −0.214432
\(796\) 45.9694 1.62934
\(797\) −8.29473 −0.293815 −0.146907 0.989150i \(-0.546932\pi\)
−0.146907 + 0.989150i \(0.546932\pi\)
\(798\) −37.0321 −1.31092
\(799\) −18.2912 −0.647097
\(800\) −4.39839 −0.155507
\(801\) 11.1467 0.393849
\(802\) 30.1726 1.06543
\(803\) 23.4835 0.828714
\(804\) −10.4656 −0.369092
\(805\) −0.704044 −0.0248143
\(806\) −0.428733 −0.0151015
\(807\) 20.7342 0.729879
\(808\) −28.4953 −1.00246
\(809\) −30.1774 −1.06098 −0.530491 0.847691i \(-0.677992\pi\)
−0.530491 + 0.847691i \(0.677992\pi\)
\(810\) 6.17949 0.217125
\(811\) 43.0654 1.51223 0.756116 0.654438i \(-0.227095\pi\)
0.756116 + 0.654438i \(0.227095\pi\)
\(812\) −98.5316 −3.45778
\(813\) 5.86819 0.205806
\(814\) −50.5116 −1.77043
\(815\) 6.99658 0.245080
\(816\) 14.5970 0.510999
\(817\) −23.9036 −0.836282
\(818\) 73.0394 2.55376
\(819\) −25.4593 −0.889621
\(820\) 12.9057 0.450685
\(821\) −33.4416 −1.16712 −0.583559 0.812071i \(-0.698340\pi\)
−0.583559 + 0.812071i \(0.698340\pi\)
\(822\) −52.0422 −1.81518
\(823\) −52.0514 −1.81440 −0.907198 0.420703i \(-0.861783\pi\)
−0.907198 + 0.420703i \(0.861783\pi\)
\(824\) 20.2462 0.705310
\(825\) 18.6876 0.650617
\(826\) −80.3652 −2.79626
\(827\) −29.1481 −1.01358 −0.506790 0.862069i \(-0.669168\pi\)
−0.506790 + 0.862069i \(0.669168\pi\)
\(828\) −1.27088 −0.0441663
\(829\) 20.1273 0.699052 0.349526 0.936927i \(-0.386343\pi\)
0.349526 + 0.936927i \(0.386343\pi\)
\(830\) −8.61216 −0.298932
\(831\) −34.6836 −1.20316
\(832\) 59.3481 2.05753
\(833\) −31.9836 −1.10816
\(834\) 39.1035 1.35404
\(835\) −4.57769 −0.158418
\(836\) 26.5597 0.918587
\(837\) −0.152826 −0.00528243
\(838\) −19.6734 −0.679606
\(839\) −29.4120 −1.01541 −0.507707 0.861530i \(-0.669507\pi\)
−0.507707 + 0.861530i \(0.669507\pi\)
\(840\) −13.3064 −0.459114
\(841\) 6.76922 0.233421
\(842\) −22.2028 −0.765159
\(843\) −11.2936 −0.388972
\(844\) 55.5767 1.91303
\(845\) 14.0159 0.482162
\(846\) 13.8876 0.477464
\(847\) 15.3056 0.525908
\(848\) 30.3858 1.04345
\(849\) 34.8522 1.19612
\(850\) −34.3054 −1.17666
\(851\) 2.69845 0.0925017
\(852\) 73.3160 2.51177
\(853\) 24.4616 0.837548 0.418774 0.908091i \(-0.362460\pi\)
0.418774 + 0.908091i \(0.362460\pi\)
\(854\) 102.076 3.49298
\(855\) −1.09559 −0.0374684
\(856\) −5.41179 −0.184971
\(857\) −10.2946 −0.351658 −0.175829 0.984421i \(-0.556261\pi\)
−0.175829 + 0.984421i \(0.556261\pi\)
\(858\) −62.0604 −2.11871
\(859\) 24.6948 0.842576 0.421288 0.906927i \(-0.361578\pi\)
0.421288 + 0.906927i \(0.361578\pi\)
\(860\) −17.6165 −0.600718
\(861\) 42.5015 1.44845
\(862\) 1.38011 0.0470068
\(863\) −43.5613 −1.48284 −0.741421 0.671040i \(-0.765848\pi\)
−0.741421 + 0.671040i \(0.765848\pi\)
\(864\) 5.20673 0.177137
\(865\) 4.81586 0.163744
\(866\) 45.7553 1.55483
\(867\) 11.9014 0.404194
\(868\) 0.445323 0.0151153
\(869\) 21.0209 0.713084
\(870\) 9.90759 0.335899
\(871\) −12.1493 −0.411662
\(872\) 7.97886 0.270198
\(873\) 5.93789 0.200967
\(874\) −2.14598 −0.0725889
\(875\) 19.5278 0.660162
\(876\) −48.6318 −1.64312
\(877\) 57.5742 1.94414 0.972070 0.234689i \(-0.0754072\pi\)
0.972070 + 0.234689i \(0.0754072\pi\)
\(878\) −1.29117 −0.0435750
\(879\) −21.2190 −0.715700
\(880\) 4.40339 0.148438
\(881\) −20.0579 −0.675767 −0.337883 0.941188i \(-0.609711\pi\)
−0.337883 + 0.941188i \(0.609711\pi\)
\(882\) 24.2834 0.817666
\(883\) 12.5227 0.421423 0.210711 0.977548i \(-0.432422\pi\)
0.210711 + 0.977548i \(0.432422\pi\)
\(884\) 75.3261 2.53349
\(885\) 5.34296 0.179602
\(886\) 67.3105 2.26134
\(887\) −47.6108 −1.59862 −0.799308 0.600922i \(-0.794800\pi\)
−0.799308 + 0.600922i \(0.794800\pi\)
\(888\) 51.0006 1.71147
\(889\) 74.7478 2.50696
\(890\) 13.8714 0.464971
\(891\) −14.5956 −0.488970
\(892\) 27.2327 0.911817
\(893\) 15.5048 0.518849
\(894\) −27.8779 −0.932378
\(895\) 10.7922 0.360745
\(896\) −85.4592 −2.85499
\(897\) 3.31542 0.110699
\(898\) 84.6683 2.82542
\(899\) −0.161662 −0.00539174
\(900\) 17.2213 0.574045
\(901\) −26.2151 −0.873352
\(902\) −46.1028 −1.53506
\(903\) −58.0154 −1.93063
\(904\) 31.7670 1.05656
\(905\) −6.03832 −0.200720
\(906\) 54.4361 1.80852
\(907\) 22.5698 0.749417 0.374709 0.927143i \(-0.377743\pi\)
0.374709 + 0.927143i \(0.377743\pi\)
\(908\) −9.00969 −0.298997
\(909\) −5.69431 −0.188868
\(910\) −31.6827 −1.05027
\(911\) 36.2098 1.19968 0.599842 0.800118i \(-0.295230\pi\)
0.599842 + 0.800118i \(0.295230\pi\)
\(912\) −12.3734 −0.409724
\(913\) 20.3414 0.673201
\(914\) −64.8604 −2.14539
\(915\) −6.78640 −0.224351
\(916\) −38.7596 −1.28065
\(917\) −24.8215 −0.819679
\(918\) 40.6100 1.34033
\(919\) −46.3987 −1.53055 −0.765276 0.643702i \(-0.777398\pi\)
−0.765276 + 0.643702i \(0.777398\pi\)
\(920\) −0.771095 −0.0254222
\(921\) −25.5007 −0.840278
\(922\) 9.31044 0.306623
\(923\) 85.1113 2.80147
\(924\) 64.4618 2.12064
\(925\) −36.5658 −1.20228
\(926\) 3.68595 0.121128
\(927\) 4.04586 0.132884
\(928\) 5.50780 0.180802
\(929\) −31.8139 −1.04378 −0.521890 0.853013i \(-0.674773\pi\)
−0.521890 + 0.853013i \(0.674773\pi\)
\(930\) −0.0447783 −0.00146834
\(931\) 27.1113 0.888538
\(932\) 14.9406 0.489395
\(933\) 4.82356 0.157916
\(934\) 52.5505 1.71951
\(935\) −3.79899 −0.124240
\(936\) −27.8840 −0.911417
\(937\) −8.62905 −0.281899 −0.140949 0.990017i \(-0.545015\pi\)
−0.140949 + 0.990017i \(0.545015\pi\)
\(938\) 19.0861 0.623183
\(939\) −6.57389 −0.214531
\(940\) 11.4268 0.372700
\(941\) 34.7944 1.13426 0.567132 0.823627i \(-0.308053\pi\)
0.567132 + 0.823627i \(0.308053\pi\)
\(942\) 69.9641 2.27955
\(943\) 2.46292 0.0802038
\(944\) −26.8521 −0.873962
\(945\) −11.2936 −0.367380
\(946\) 62.9313 2.04607
\(947\) 31.7042 1.03025 0.515124 0.857116i \(-0.327746\pi\)
0.515124 + 0.857116i \(0.327746\pi\)
\(948\) −43.5320 −1.41385
\(949\) −56.4558 −1.83263
\(950\) 29.0795 0.943462
\(951\) 3.77912 0.122546
\(952\) −57.6951 −1.86991
\(953\) −19.2582 −0.623834 −0.311917 0.950109i \(-0.600971\pi\)
−0.311917 + 0.950109i \(0.600971\pi\)
\(954\) 19.9038 0.644408
\(955\) −2.76006 −0.0893135
\(956\) 114.047 3.68855
\(957\) −23.4011 −0.756451
\(958\) 82.7505 2.67355
\(959\) 62.7526 2.02639
\(960\) 6.19852 0.200056
\(961\) −30.9993 −0.999976
\(962\) 121.433 3.91516
\(963\) −1.08145 −0.0348494
\(964\) −117.381 −3.78058
\(965\) −0.903588 −0.0290875
\(966\) −5.20841 −0.167578
\(967\) 24.5965 0.790972 0.395486 0.918472i \(-0.370576\pi\)
0.395486 + 0.918472i \(0.370576\pi\)
\(968\) 16.7633 0.538793
\(969\) 10.6751 0.342932
\(970\) 7.38937 0.237258
\(971\) 52.8165 1.69496 0.847480 0.530827i \(-0.178118\pi\)
0.847480 + 0.530827i \(0.178118\pi\)
\(972\) −35.9726 −1.15382
\(973\) −47.1511 −1.51160
\(974\) 66.7102 2.13753
\(975\) −44.9261 −1.43879
\(976\) 34.1064 1.09172
\(977\) −14.6001 −0.467099 −0.233550 0.972345i \(-0.575034\pi\)
−0.233550 + 0.972345i \(0.575034\pi\)
\(978\) 51.7596 1.65509
\(979\) −32.7634 −1.04712
\(980\) 19.9805 0.638254
\(981\) 1.59444 0.0509065
\(982\) −67.6745 −2.15958
\(983\) −45.2811 −1.44424 −0.722122 0.691766i \(-0.756833\pi\)
−0.722122 + 0.691766i \(0.756833\pi\)
\(984\) 46.5491 1.48393
\(985\) −8.36296 −0.266466
\(986\) 42.9582 1.36807
\(987\) 37.6310 1.19781
\(988\) −63.8513 −2.03138
\(989\) −3.36194 −0.106904
\(990\) 2.88437 0.0916714
\(991\) 6.48047 0.205859 0.102930 0.994689i \(-0.467178\pi\)
0.102930 + 0.994689i \(0.467178\pi\)
\(992\) −0.0248930 −0.000790355 0
\(993\) −10.2499 −0.325272
\(994\) −133.707 −4.24093
\(995\) 5.57363 0.176696
\(996\) −42.1248 −1.33478
\(997\) 42.3298 1.34060 0.670298 0.742092i \(-0.266166\pi\)
0.670298 + 0.742092i \(0.266166\pi\)
\(998\) −1.30130 −0.0411921
\(999\) 43.2859 1.36950
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 \(a_p\))