Properties

Label 8002.2.a.e.1.11
Level 8002
Weight 2
Character 8002.1
Self dual Yes
Analytic conductor 63.896
Analytic rank 0
Dimension 77
CM No

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Newspace parameters

Level: \( N \) = \( 8002 = 2 \cdot 4001 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8002.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.8962916974\)
Analytic rank: \(0\)
Dimension: \(77\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.11
Character \(\chi\) = 8002.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} -2.42114 q^{3} +1.00000 q^{4} -1.19106 q^{5} +2.42114 q^{6} -3.77401 q^{7} -1.00000 q^{8} +2.86190 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -2.42114 q^{3} +1.00000 q^{4} -1.19106 q^{5} +2.42114 q^{6} -3.77401 q^{7} -1.00000 q^{8} +2.86190 q^{9} +1.19106 q^{10} -4.05323 q^{11} -2.42114 q^{12} +4.55675 q^{13} +3.77401 q^{14} +2.88372 q^{15} +1.00000 q^{16} -1.21373 q^{17} -2.86190 q^{18} +3.72235 q^{19} -1.19106 q^{20} +9.13739 q^{21} +4.05323 q^{22} +5.44972 q^{23} +2.42114 q^{24} -3.58137 q^{25} -4.55675 q^{26} +0.334365 q^{27} -3.77401 q^{28} -4.71760 q^{29} -2.88372 q^{30} +4.49242 q^{31} -1.00000 q^{32} +9.81341 q^{33} +1.21373 q^{34} +4.49508 q^{35} +2.86190 q^{36} -3.22114 q^{37} -3.72235 q^{38} -11.0325 q^{39} +1.19106 q^{40} +2.91252 q^{41} -9.13739 q^{42} -0.507770 q^{43} -4.05323 q^{44} -3.40870 q^{45} -5.44972 q^{46} +1.10085 q^{47} -2.42114 q^{48} +7.24314 q^{49} +3.58137 q^{50} +2.93862 q^{51} +4.55675 q^{52} +0.544770 q^{53} -0.334365 q^{54} +4.82764 q^{55} +3.77401 q^{56} -9.01232 q^{57} +4.71760 q^{58} -1.10577 q^{59} +2.88372 q^{60} -14.8634 q^{61} -4.49242 q^{62} -10.8008 q^{63} +1.00000 q^{64} -5.42737 q^{65} -9.81341 q^{66} -3.02571 q^{67} -1.21373 q^{68} -13.1945 q^{69} -4.49508 q^{70} +15.7675 q^{71} -2.86190 q^{72} -6.91652 q^{73} +3.22114 q^{74} +8.67099 q^{75} +3.72235 q^{76} +15.2969 q^{77} +11.0325 q^{78} -9.08476 q^{79} -1.19106 q^{80} -9.39524 q^{81} -2.91252 q^{82} -2.39658 q^{83} +9.13739 q^{84} +1.44563 q^{85} +0.507770 q^{86} +11.4220 q^{87} +4.05323 q^{88} -13.5949 q^{89} +3.40870 q^{90} -17.1972 q^{91} +5.44972 q^{92} -10.8768 q^{93} -1.10085 q^{94} -4.43355 q^{95} +2.42114 q^{96} -6.06191 q^{97} -7.24314 q^{98} -11.5999 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 77q - 77q^{2} + 10q^{3} + 77q^{4} + 18q^{5} - 10q^{6} + 21q^{7} - 77q^{8} + 71q^{9} + O(q^{10}) \) \( 77q - 77q^{2} + 10q^{3} + 77q^{4} + 18q^{5} - 10q^{6} + 21q^{7} - 77q^{8} + 71q^{9} - 18q^{10} + 30q^{11} + 10q^{12} - 2q^{13} - 21q^{14} + 21q^{15} + 77q^{16} + 60q^{17} - 71q^{18} - 3q^{19} + 18q^{20} + 10q^{21} - 30q^{22} + 53q^{23} - 10q^{24} + 59q^{25} + 2q^{26} + 43q^{27} + 21q^{28} + 30q^{29} - 21q^{30} + 22q^{31} - 77q^{32} + 31q^{33} - 60q^{34} + 41q^{35} + 71q^{36} - 3q^{37} + 3q^{38} + 44q^{39} - 18q^{40} + 48q^{41} - 10q^{42} + 21q^{43} + 30q^{44} + 33q^{45} - 53q^{46} + 107q^{47} + 10q^{48} + 24q^{49} - 59q^{50} + 18q^{51} - 2q^{52} + 42q^{53} - 43q^{54} + 49q^{55} - 21q^{56} + 32q^{57} - 30q^{58} + 42q^{59} + 21q^{60} - 31q^{61} - 22q^{62} + 109q^{63} + 77q^{64} + 39q^{65} - 31q^{66} - q^{67} + 60q^{68} - 33q^{69} - 41q^{70} + 58q^{71} - 71q^{72} + 35q^{73} + 3q^{74} + 34q^{75} - 3q^{76} + 86q^{77} - 44q^{78} + 25q^{79} + 18q^{80} + 53q^{81} - 48q^{82} + 107q^{83} + 10q^{84} + 21q^{85} - 21q^{86} + 100q^{87} - 30q^{88} + 34q^{89} - 33q^{90} - 51q^{91} + 53q^{92} + 48q^{93} - 107q^{94} + 118q^{95} - 10q^{96} - 13q^{97} - 24q^{98} + 63q^{99} + O(q^{100}) \)

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
\(3\) −2.42114 −1.39784 −0.698922 0.715198i \(-0.746336\pi\)
−0.698922 + 0.715198i \(0.746336\pi\)
\(4\) 1.00000 0.500000
\(5\) −1.19106 −0.532659 −0.266330 0.963882i \(-0.585811\pi\)
−0.266330 + 0.963882i \(0.585811\pi\)
\(6\) 2.42114 0.988424
\(7\) −3.77401 −1.42644 −0.713220 0.700940i \(-0.752764\pi\)
−0.713220 + 0.700940i \(0.752764\pi\)
\(8\) −1.00000 −0.353553
\(9\) 2.86190 0.953966
\(10\) 1.19106 0.376647
\(11\) −4.05323 −1.22209 −0.611047 0.791595i \(-0.709251\pi\)
−0.611047 + 0.791595i \(0.709251\pi\)
\(12\) −2.42114 −0.698922
\(13\) 4.55675 1.26381 0.631907 0.775044i \(-0.282272\pi\)
0.631907 + 0.775044i \(0.282272\pi\)
\(14\) 3.77401 1.00865
\(15\) 2.88372 0.744574
\(16\) 1.00000 0.250000
\(17\) −1.21373 −0.294374 −0.147187 0.989109i \(-0.547022\pi\)
−0.147187 + 0.989109i \(0.547022\pi\)
\(18\) −2.86190 −0.674556
\(19\) 3.72235 0.853966 0.426983 0.904260i \(-0.359576\pi\)
0.426983 + 0.904260i \(0.359576\pi\)
\(20\) −1.19106 −0.266330
\(21\) 9.13739 1.99394
\(22\) 4.05323 0.864150
\(23\) 5.44972 1.13635 0.568173 0.822909i \(-0.307651\pi\)
0.568173 + 0.822909i \(0.307651\pi\)
\(24\) 2.42114 0.494212
\(25\) −3.58137 −0.716274
\(26\) −4.55675 −0.893652
\(27\) 0.334365 0.0643485
\(28\) −3.77401 −0.713220
\(29\) −4.71760 −0.876036 −0.438018 0.898966i \(-0.644319\pi\)
−0.438018 + 0.898966i \(0.644319\pi\)
\(30\) −2.88372 −0.526493
\(31\) 4.49242 0.806863 0.403431 0.915010i \(-0.367817\pi\)
0.403431 + 0.915010i \(0.367817\pi\)
\(32\) −1.00000 −0.176777
\(33\) 9.81341 1.70829
\(34\) 1.21373 0.208154
\(35\) 4.49508 0.759807
\(36\) 2.86190 0.476983
\(37\) −3.22114 −0.529551 −0.264776 0.964310i \(-0.585298\pi\)
−0.264776 + 0.964310i \(0.585298\pi\)
\(38\) −3.72235 −0.603845
\(39\) −11.0325 −1.76661
\(40\) 1.19106 0.188323
\(41\) 2.91252 0.454859 0.227430 0.973794i \(-0.426968\pi\)
0.227430 + 0.973794i \(0.426968\pi\)
\(42\) −9.13739 −1.40993
\(43\) −0.507770 −0.0774342 −0.0387171 0.999250i \(-0.512327\pi\)
−0.0387171 + 0.999250i \(0.512327\pi\)
\(44\) −4.05323 −0.611047
\(45\) −3.40870 −0.508139
\(46\) −5.44972 −0.803517
\(47\) 1.10085 0.160575 0.0802874 0.996772i \(-0.474416\pi\)
0.0802874 + 0.996772i \(0.474416\pi\)
\(48\) −2.42114 −0.349461
\(49\) 7.24314 1.03473
\(50\) 3.58137 0.506482
\(51\) 2.93862 0.411488
\(52\) 4.55675 0.631907
\(53\) 0.544770 0.0748299 0.0374149 0.999300i \(-0.488088\pi\)
0.0374149 + 0.999300i \(0.488088\pi\)
\(54\) −0.334365 −0.0455013
\(55\) 4.82764 0.650959
\(56\) 3.77401 0.504323
\(57\) −9.01232 −1.19371
\(58\) 4.71760 0.619451
\(59\) −1.10577 −0.143959 −0.0719797 0.997406i \(-0.522932\pi\)
−0.0719797 + 0.997406i \(0.522932\pi\)
\(60\) 2.88372 0.372287
\(61\) −14.8634 −1.90306 −0.951532 0.307549i \(-0.900491\pi\)
−0.951532 + 0.307549i \(0.900491\pi\)
\(62\) −4.49242 −0.570538
\(63\) −10.8008 −1.36078
\(64\) 1.00000 0.125000
\(65\) −5.42737 −0.673182
\(66\) −9.81341 −1.20795
\(67\) −3.02571 −0.369649 −0.184825 0.982772i \(-0.559172\pi\)
−0.184825 + 0.982772i \(0.559172\pi\)
\(68\) −1.21373 −0.147187
\(69\) −13.1945 −1.58843
\(70\) −4.49508 −0.537265
\(71\) 15.7675 1.87126 0.935631 0.352979i \(-0.114831\pi\)
0.935631 + 0.352979i \(0.114831\pi\)
\(72\) −2.86190 −0.337278
\(73\) −6.91652 −0.809517 −0.404759 0.914424i \(-0.632644\pi\)
−0.404759 + 0.914424i \(0.632644\pi\)
\(74\) 3.22114 0.374449
\(75\) 8.67099 1.00124
\(76\) 3.72235 0.426983
\(77\) 15.2969 1.74324
\(78\) 11.0325 1.24919
\(79\) −9.08476 −1.02212 −0.511058 0.859546i \(-0.670746\pi\)
−0.511058 + 0.859546i \(0.670746\pi\)
\(80\) −1.19106 −0.133165
\(81\) −9.39524 −1.04392
\(82\) −2.91252 −0.321634
\(83\) −2.39658 −0.263058 −0.131529 0.991312i \(-0.541989\pi\)
−0.131529 + 0.991312i \(0.541989\pi\)
\(84\) 9.13739 0.996970
\(85\) 1.44563 0.156801
\(86\) 0.507770 0.0547542
\(87\) 11.4220 1.22456
\(88\) 4.05323 0.432075
\(89\) −13.5949 −1.44106 −0.720530 0.693424i \(-0.756101\pi\)
−0.720530 + 0.693424i \(0.756101\pi\)
\(90\) 3.40870 0.359308
\(91\) −17.1972 −1.80276
\(92\) 5.44972 0.568173
\(93\) −10.8768 −1.12787
\(94\) −1.10085 −0.113544
\(95\) −4.43355 −0.454873
\(96\) 2.42114 0.247106
\(97\) −6.06191 −0.615493 −0.307747 0.951468i \(-0.599575\pi\)
−0.307747 + 0.951468i \(0.599575\pi\)
\(98\) −7.24314 −0.731667
\(99\) −11.5999 −1.16584
\(100\) −3.58137 −0.358137
\(101\) −10.1678 −1.01173 −0.505866 0.862612i \(-0.668827\pi\)
−0.505866 + 0.862612i \(0.668827\pi\)
\(102\) −2.93862 −0.290966
\(103\) −13.0078 −1.28170 −0.640849 0.767667i \(-0.721418\pi\)
−0.640849 + 0.767667i \(0.721418\pi\)
\(104\) −4.55675 −0.446826
\(105\) −10.8832 −1.06209
\(106\) −0.544770 −0.0529127
\(107\) −4.76857 −0.460995 −0.230498 0.973073i \(-0.574035\pi\)
−0.230498 + 0.973073i \(0.574035\pi\)
\(108\) 0.334365 0.0321743
\(109\) −8.45849 −0.810176 −0.405088 0.914278i \(-0.632759\pi\)
−0.405088 + 0.914278i \(0.632759\pi\)
\(110\) −4.82764 −0.460298
\(111\) 7.79881 0.740230
\(112\) −3.77401 −0.356610
\(113\) 18.4306 1.73380 0.866901 0.498481i \(-0.166109\pi\)
0.866901 + 0.498481i \(0.166109\pi\)
\(114\) 9.01232 0.844081
\(115\) −6.49096 −0.605285
\(116\) −4.71760 −0.438018
\(117\) 13.0409 1.20564
\(118\) 1.10577 0.101795
\(119\) 4.58064 0.419907
\(120\) −2.88372 −0.263247
\(121\) 5.42863 0.493512
\(122\) 14.8634 1.34567
\(123\) −7.05161 −0.635822
\(124\) 4.49242 0.403431
\(125\) 10.2209 0.914189
\(126\) 10.8008 0.962214
\(127\) 3.20094 0.284037 0.142019 0.989864i \(-0.454641\pi\)
0.142019 + 0.989864i \(0.454641\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 1.22938 0.108241
\(130\) 5.42737 0.476012
\(131\) 19.0299 1.66265 0.831324 0.555789i \(-0.187584\pi\)
0.831324 + 0.555789i \(0.187584\pi\)
\(132\) 9.81341 0.854147
\(133\) −14.0482 −1.21813
\(134\) 3.02571 0.261382
\(135\) −0.398249 −0.0342758
\(136\) 1.21373 0.104077
\(137\) −4.95703 −0.423508 −0.211754 0.977323i \(-0.567918\pi\)
−0.211754 + 0.977323i \(0.567918\pi\)
\(138\) 13.1945 1.12319
\(139\) −2.34546 −0.198939 −0.0994697 0.995041i \(-0.531715\pi\)
−0.0994697 + 0.995041i \(0.531715\pi\)
\(140\) 4.49508 0.379903
\(141\) −2.66530 −0.224458
\(142\) −15.7675 −1.32318
\(143\) −18.4695 −1.54450
\(144\) 2.86190 0.238491
\(145\) 5.61895 0.466629
\(146\) 6.91652 0.572415
\(147\) −17.5366 −1.44640
\(148\) −3.22114 −0.264776
\(149\) −9.26218 −0.758788 −0.379394 0.925235i \(-0.623867\pi\)
−0.379394 + 0.925235i \(0.623867\pi\)
\(150\) −8.67099 −0.707983
\(151\) −4.63025 −0.376805 −0.188402 0.982092i \(-0.560331\pi\)
−0.188402 + 0.982092i \(0.560331\pi\)
\(152\) −3.72235 −0.301923
\(153\) −3.47358 −0.280823
\(154\) −15.2969 −1.23266
\(155\) −5.35075 −0.429783
\(156\) −11.0325 −0.883307
\(157\) −14.6829 −1.17182 −0.585912 0.810375i \(-0.699264\pi\)
−0.585912 + 0.810375i \(0.699264\pi\)
\(158\) 9.08476 0.722745
\(159\) −1.31896 −0.104600
\(160\) 1.19106 0.0941617
\(161\) −20.5673 −1.62093
\(162\) 9.39524 0.738159
\(163\) −4.37158 −0.342408 −0.171204 0.985236i \(-0.554766\pi\)
−0.171204 + 0.985236i \(0.554766\pi\)
\(164\) 2.91252 0.227430
\(165\) −11.6884 −0.909939
\(166\) 2.39658 0.186010
\(167\) −5.25233 −0.406438 −0.203219 0.979133i \(-0.565140\pi\)
−0.203219 + 0.979133i \(0.565140\pi\)
\(168\) −9.13739 −0.704965
\(169\) 7.76396 0.597228
\(170\) −1.44563 −0.110875
\(171\) 10.6530 0.814655
\(172\) −0.507770 −0.0387171
\(173\) 11.0187 0.837740 0.418870 0.908046i \(-0.362426\pi\)
0.418870 + 0.908046i \(0.362426\pi\)
\(174\) −11.4220 −0.865896
\(175\) 13.5161 1.02172
\(176\) −4.05323 −0.305523
\(177\) 2.67723 0.201233
\(178\) 13.5949 1.01898
\(179\) −2.29122 −0.171254 −0.0856270 0.996327i \(-0.527289\pi\)
−0.0856270 + 0.996327i \(0.527289\pi\)
\(180\) −3.40870 −0.254069
\(181\) 8.46887 0.629486 0.314743 0.949177i \(-0.398082\pi\)
0.314743 + 0.949177i \(0.398082\pi\)
\(182\) 17.1972 1.27474
\(183\) 35.9863 2.66019
\(184\) −5.44972 −0.401759
\(185\) 3.83657 0.282070
\(186\) 10.8768 0.797523
\(187\) 4.91954 0.359752
\(188\) 1.10085 0.0802874
\(189\) −1.26190 −0.0917894
\(190\) 4.43355 0.321644
\(191\) 18.4418 1.33440 0.667200 0.744879i \(-0.267493\pi\)
0.667200 + 0.744879i \(0.267493\pi\)
\(192\) −2.42114 −0.174730
\(193\) 4.83354 0.347926 0.173963 0.984752i \(-0.444343\pi\)
0.173963 + 0.984752i \(0.444343\pi\)
\(194\) 6.06191 0.435220
\(195\) 13.1404 0.941004
\(196\) 7.24314 0.517367
\(197\) 19.4368 1.38482 0.692408 0.721506i \(-0.256550\pi\)
0.692408 + 0.721506i \(0.256550\pi\)
\(198\) 11.5999 0.824370
\(199\) 0.391267 0.0277362 0.0138681 0.999904i \(-0.495586\pi\)
0.0138681 + 0.999904i \(0.495586\pi\)
\(200\) 3.58137 0.253241
\(201\) 7.32566 0.516712
\(202\) 10.1678 0.715402
\(203\) 17.8043 1.24961
\(204\) 2.93862 0.205744
\(205\) −3.46899 −0.242285
\(206\) 13.0078 0.906298
\(207\) 15.5965 1.08403
\(208\) 4.55675 0.315954
\(209\) −15.0875 −1.04363
\(210\) 10.8832 0.751012
\(211\) −1.44290 −0.0993332 −0.0496666 0.998766i \(-0.515816\pi\)
−0.0496666 + 0.998766i \(0.515816\pi\)
\(212\) 0.544770 0.0374149
\(213\) −38.1754 −2.61573
\(214\) 4.76857 0.325973
\(215\) 0.604785 0.0412460
\(216\) −0.334365 −0.0227506
\(217\) −16.9544 −1.15094
\(218\) 8.45849 0.572881
\(219\) 16.7458 1.13158
\(220\) 4.82764 0.325480
\(221\) −5.53068 −0.372034
\(222\) −7.79881 −0.523422
\(223\) 0.155125 0.0103879 0.00519397 0.999987i \(-0.498347\pi\)
0.00519397 + 0.999987i \(0.498347\pi\)
\(224\) 3.77401 0.252162
\(225\) −10.2495 −0.683301
\(226\) −18.4306 −1.22598
\(227\) 12.9969 0.862636 0.431318 0.902200i \(-0.358049\pi\)
0.431318 + 0.902200i \(0.358049\pi\)
\(228\) −9.01232 −0.596856
\(229\) −21.8368 −1.44302 −0.721508 0.692406i \(-0.756551\pi\)
−0.721508 + 0.692406i \(0.756551\pi\)
\(230\) 6.49096 0.428001
\(231\) −37.0359 −2.43678
\(232\) 4.71760 0.309726
\(233\) 3.15738 0.206847 0.103423 0.994637i \(-0.467020\pi\)
0.103423 + 0.994637i \(0.467020\pi\)
\(234\) −13.0409 −0.852513
\(235\) −1.31118 −0.0855317
\(236\) −1.10577 −0.0719797
\(237\) 21.9954 1.42876
\(238\) −4.58064 −0.296919
\(239\) −12.5523 −0.811940 −0.405970 0.913886i \(-0.633066\pi\)
−0.405970 + 0.913886i \(0.633066\pi\)
\(240\) 2.88372 0.186144
\(241\) −13.2212 −0.851652 −0.425826 0.904805i \(-0.640016\pi\)
−0.425826 + 0.904805i \(0.640016\pi\)
\(242\) −5.42863 −0.348966
\(243\) 21.7440 1.39488
\(244\) −14.8634 −0.951532
\(245\) −8.62702 −0.551160
\(246\) 7.05161 0.449594
\(247\) 16.9618 1.07926
\(248\) −4.49242 −0.285269
\(249\) 5.80244 0.367715
\(250\) −10.2209 −0.646429
\(251\) −11.1448 −0.703456 −0.351728 0.936102i \(-0.614406\pi\)
−0.351728 + 0.936102i \(0.614406\pi\)
\(252\) −10.8008 −0.680388
\(253\) −22.0889 −1.38872
\(254\) −3.20094 −0.200845
\(255\) −3.50007 −0.219183
\(256\) 1.00000 0.0625000
\(257\) 15.9989 0.997985 0.498993 0.866606i \(-0.333703\pi\)
0.498993 + 0.866606i \(0.333703\pi\)
\(258\) −1.22938 −0.0765378
\(259\) 12.1566 0.755374
\(260\) −5.42737 −0.336591
\(261\) −13.5013 −0.835709
\(262\) −19.0299 −1.17567
\(263\) 5.52745 0.340837 0.170419 0.985372i \(-0.445488\pi\)
0.170419 + 0.985372i \(0.445488\pi\)
\(264\) −9.81341 −0.603973
\(265\) −0.648855 −0.0398588
\(266\) 14.0482 0.861350
\(267\) 32.9152 2.01438
\(268\) −3.02571 −0.184825
\(269\) −21.4404 −1.30724 −0.653622 0.756821i \(-0.726751\pi\)
−0.653622 + 0.756821i \(0.726751\pi\)
\(270\) 0.398249 0.0242367
\(271\) −2.64571 −0.160715 −0.0803576 0.996766i \(-0.525606\pi\)
−0.0803576 + 0.996766i \(0.525606\pi\)
\(272\) −1.21373 −0.0735935
\(273\) 41.6368 2.51997
\(274\) 4.95703 0.299465
\(275\) 14.5161 0.875354
\(276\) −13.1945 −0.794216
\(277\) 5.11141 0.307115 0.153558 0.988140i \(-0.450927\pi\)
0.153558 + 0.988140i \(0.450927\pi\)
\(278\) 2.34546 0.140671
\(279\) 12.8568 0.769719
\(280\) −4.49508 −0.268632
\(281\) −26.1082 −1.55749 −0.778744 0.627342i \(-0.784143\pi\)
−0.778744 + 0.627342i \(0.784143\pi\)
\(282\) 2.66530 0.158716
\(283\) −13.6087 −0.808952 −0.404476 0.914549i \(-0.632546\pi\)
−0.404476 + 0.914549i \(0.632546\pi\)
\(284\) 15.7675 0.935631
\(285\) 10.7342 0.635841
\(286\) 18.4695 1.09213
\(287\) −10.9919 −0.648830
\(288\) −2.86190 −0.168639
\(289\) −15.5268 −0.913344
\(290\) −5.61895 −0.329956
\(291\) 14.6767 0.860363
\(292\) −6.91652 −0.404759
\(293\) −7.31349 −0.427259 −0.213629 0.976915i \(-0.568528\pi\)
−0.213629 + 0.976915i \(0.568528\pi\)
\(294\) 17.5366 1.02276
\(295\) 1.31704 0.0766813
\(296\) 3.22114 0.187225
\(297\) −1.35526 −0.0786399
\(298\) 9.26218 0.536544
\(299\) 24.8330 1.43613
\(300\) 8.67099 0.500620
\(301\) 1.91633 0.110455
\(302\) 4.63025 0.266441
\(303\) 24.6176 1.41424
\(304\) 3.72235 0.213492
\(305\) 17.7032 1.01368
\(306\) 3.47358 0.198572
\(307\) 5.26143 0.300286 0.150143 0.988664i \(-0.452027\pi\)
0.150143 + 0.988664i \(0.452027\pi\)
\(308\) 15.2969 0.871622
\(309\) 31.4937 1.79161
\(310\) 5.35075 0.303902
\(311\) −1.31851 −0.0747659 −0.0373829 0.999301i \(-0.511902\pi\)
−0.0373829 + 0.999301i \(0.511902\pi\)
\(312\) 11.0325 0.624593
\(313\) −29.2825 −1.65514 −0.827572 0.561359i \(-0.810279\pi\)
−0.827572 + 0.561359i \(0.810279\pi\)
\(314\) 14.6829 0.828605
\(315\) 12.8645 0.724830
\(316\) −9.08476 −0.511058
\(317\) 12.9282 0.726121 0.363061 0.931766i \(-0.381732\pi\)
0.363061 + 0.931766i \(0.381732\pi\)
\(318\) 1.31896 0.0739637
\(319\) 19.1215 1.07060
\(320\) −1.19106 −0.0665824
\(321\) 11.5454 0.644399
\(322\) 20.5673 1.14617
\(323\) −4.51795 −0.251385
\(324\) −9.39524 −0.521958
\(325\) −16.3194 −0.905238
\(326\) 4.37158 0.242119
\(327\) 20.4791 1.13250
\(328\) −2.91252 −0.160817
\(329\) −4.15460 −0.229051
\(330\) 11.6884 0.643424
\(331\) 14.7764 0.812185 0.406092 0.913832i \(-0.366891\pi\)
0.406092 + 0.913832i \(0.366891\pi\)
\(332\) −2.39658 −0.131529
\(333\) −9.21856 −0.505174
\(334\) 5.25233 0.287395
\(335\) 3.60381 0.196897
\(336\) 9.13739 0.498485
\(337\) 20.2729 1.10434 0.552169 0.833732i \(-0.313800\pi\)
0.552169 + 0.833732i \(0.313800\pi\)
\(338\) −7.76396 −0.422304
\(339\) −44.6229 −2.42358
\(340\) 1.44563 0.0784005
\(341\) −18.2088 −0.986061
\(342\) −10.6530 −0.576048
\(343\) −0.917599 −0.0495457
\(344\) 0.507770 0.0273771
\(345\) 15.7155 0.846093
\(346\) −11.0187 −0.592371
\(347\) 12.0865 0.648838 0.324419 0.945914i \(-0.394831\pi\)
0.324419 + 0.945914i \(0.394831\pi\)
\(348\) 11.4220 0.612281
\(349\) −3.16619 −0.169482 −0.0847411 0.996403i \(-0.527006\pi\)
−0.0847411 + 0.996403i \(0.527006\pi\)
\(350\) −13.5161 −0.722467
\(351\) 1.52362 0.0813246
\(352\) 4.05323 0.216038
\(353\) 4.79538 0.255232 0.127616 0.991824i \(-0.459267\pi\)
0.127616 + 0.991824i \(0.459267\pi\)
\(354\) −2.67723 −0.142293
\(355\) −18.7801 −0.996745
\(356\) −13.5949 −0.720530
\(357\) −11.0904 −0.586964
\(358\) 2.29122 0.121095
\(359\) −17.5257 −0.924973 −0.462486 0.886626i \(-0.653043\pi\)
−0.462486 + 0.886626i \(0.653043\pi\)
\(360\) 3.40870 0.179654
\(361\) −5.14409 −0.270741
\(362\) −8.46887 −0.445114
\(363\) −13.1435 −0.689853
\(364\) −17.1972 −0.901379
\(365\) 8.23800 0.431197
\(366\) −35.9863 −1.88104
\(367\) 28.0392 1.46364 0.731818 0.681500i \(-0.238672\pi\)
0.731818 + 0.681500i \(0.238672\pi\)
\(368\) 5.44972 0.284086
\(369\) 8.33534 0.433920
\(370\) −3.83657 −0.199454
\(371\) −2.05597 −0.106740
\(372\) −10.8768 −0.563934
\(373\) −7.72894 −0.400189 −0.200095 0.979777i \(-0.564125\pi\)
−0.200095 + 0.979777i \(0.564125\pi\)
\(374\) −4.91954 −0.254383
\(375\) −24.7463 −1.27789
\(376\) −1.10085 −0.0567718
\(377\) −21.4969 −1.10715
\(378\) 1.26190 0.0649049
\(379\) 7.67069 0.394017 0.197008 0.980402i \(-0.436877\pi\)
0.197008 + 0.980402i \(0.436877\pi\)
\(380\) −4.43355 −0.227437
\(381\) −7.74990 −0.397040
\(382\) −18.4418 −0.943563
\(383\) −27.5071 −1.40555 −0.702774 0.711413i \(-0.748056\pi\)
−0.702774 + 0.711413i \(0.748056\pi\)
\(384\) 2.42114 0.123553
\(385\) −18.2196 −0.928555
\(386\) −4.83354 −0.246021
\(387\) −1.45318 −0.0738695
\(388\) −6.06191 −0.307747
\(389\) −10.8598 −0.550612 −0.275306 0.961357i \(-0.588779\pi\)
−0.275306 + 0.961357i \(0.588779\pi\)
\(390\) −13.1404 −0.665390
\(391\) −6.61451 −0.334510
\(392\) −7.24314 −0.365834
\(393\) −46.0739 −2.32412
\(394\) −19.4368 −0.979213
\(395\) 10.8205 0.544439
\(396\) −11.5999 −0.582918
\(397\) −14.0850 −0.706905 −0.353453 0.935452i \(-0.614992\pi\)
−0.353453 + 0.935452i \(0.614992\pi\)
\(398\) −0.391267 −0.0196124
\(399\) 34.0126 1.70276
\(400\) −3.58137 −0.179069
\(401\) 13.3483 0.666580 0.333290 0.942824i \(-0.391841\pi\)
0.333290 + 0.942824i \(0.391841\pi\)
\(402\) −7.32566 −0.365371
\(403\) 20.4708 1.01972
\(404\) −10.1678 −0.505866
\(405\) 11.1903 0.556051
\(406\) −17.8043 −0.883611
\(407\) 13.0560 0.647161
\(408\) −2.93862 −0.145483
\(409\) 14.6977 0.726757 0.363378 0.931642i \(-0.381623\pi\)
0.363378 + 0.931642i \(0.381623\pi\)
\(410\) 3.46899 0.171321
\(411\) 12.0016 0.591997
\(412\) −13.0078 −0.640849
\(413\) 4.17320 0.205350
\(414\) −15.5965 −0.766528
\(415\) 2.85447 0.140121
\(416\) −4.55675 −0.223413
\(417\) 5.67868 0.278086
\(418\) 15.0875 0.737955
\(419\) −21.4892 −1.04981 −0.524907 0.851160i \(-0.675900\pi\)
−0.524907 + 0.851160i \(0.675900\pi\)
\(420\) −10.8832 −0.531045
\(421\) 29.0308 1.41488 0.707438 0.706775i \(-0.249851\pi\)
0.707438 + 0.706775i \(0.249851\pi\)
\(422\) 1.44290 0.0702392
\(423\) 3.15051 0.153183
\(424\) −0.544770 −0.0264564
\(425\) 4.34683 0.210852
\(426\) 38.1754 1.84960
\(427\) 56.0946 2.71461
\(428\) −4.76857 −0.230498
\(429\) 44.7172 2.15897
\(430\) −0.604785 −0.0291653
\(431\) −24.4782 −1.17907 −0.589537 0.807741i \(-0.700690\pi\)
−0.589537 + 0.807741i \(0.700690\pi\)
\(432\) 0.334365 0.0160871
\(433\) −21.3135 −1.02426 −0.512131 0.858907i \(-0.671144\pi\)
−0.512131 + 0.858907i \(0.671144\pi\)
\(434\) 16.9544 0.813839
\(435\) −13.6043 −0.652274
\(436\) −8.45849 −0.405088
\(437\) 20.2858 0.970401
\(438\) −16.7458 −0.800147
\(439\) 29.8915 1.42664 0.713321 0.700837i \(-0.247190\pi\)
0.713321 + 0.700837i \(0.247190\pi\)
\(440\) −4.82764 −0.230149
\(441\) 20.7291 0.987101
\(442\) 5.53068 0.263068
\(443\) −35.0460 −1.66508 −0.832542 0.553962i \(-0.813115\pi\)
−0.832542 + 0.553962i \(0.813115\pi\)
\(444\) 7.79881 0.370115
\(445\) 16.1924 0.767594
\(446\) −0.155125 −0.00734539
\(447\) 22.4250 1.06067
\(448\) −3.77401 −0.178305
\(449\) 0.835529 0.0394310 0.0197155 0.999806i \(-0.493724\pi\)
0.0197155 + 0.999806i \(0.493724\pi\)
\(450\) 10.2495 0.483167
\(451\) −11.8051 −0.555881
\(452\) 18.4306 0.866901
\(453\) 11.2105 0.526714
\(454\) −12.9969 −0.609975
\(455\) 20.4829 0.960255
\(456\) 9.01232 0.422041
\(457\) 0.895256 0.0418783 0.0209392 0.999781i \(-0.493334\pi\)
0.0209392 + 0.999781i \(0.493334\pi\)
\(458\) 21.8368 1.02037
\(459\) −0.405830 −0.0189425
\(460\) −6.49096 −0.302642
\(461\) 25.1774 1.17263 0.586314 0.810084i \(-0.300579\pi\)
0.586314 + 0.810084i \(0.300579\pi\)
\(462\) 37.0359 1.72306
\(463\) 3.24013 0.150582 0.0752908 0.997162i \(-0.476012\pi\)
0.0752908 + 0.997162i \(0.476012\pi\)
\(464\) −4.71760 −0.219009
\(465\) 12.9549 0.600769
\(466\) −3.15738 −0.146263
\(467\) −2.58485 −0.119612 −0.0598062 0.998210i \(-0.519048\pi\)
−0.0598062 + 0.998210i \(0.519048\pi\)
\(468\) 13.0409 0.602818
\(469\) 11.4191 0.527283
\(470\) 1.31118 0.0604800
\(471\) 35.5493 1.63803
\(472\) 1.10577 0.0508973
\(473\) 2.05810 0.0946318
\(474\) −21.9954 −1.01028
\(475\) −13.3311 −0.611674
\(476\) 4.58064 0.209953
\(477\) 1.55908 0.0713852
\(478\) 12.5523 0.574128
\(479\) 1.56801 0.0716442 0.0358221 0.999358i \(-0.488595\pi\)
0.0358221 + 0.999358i \(0.488595\pi\)
\(480\) −2.88372 −0.131623
\(481\) −14.6779 −0.669255
\(482\) 13.2212 0.602209
\(483\) 49.7962 2.26581
\(484\) 5.42863 0.246756
\(485\) 7.22011 0.327848
\(486\) −21.7440 −0.986330
\(487\) 1.10775 0.0501969 0.0250985 0.999685i \(-0.492010\pi\)
0.0250985 + 0.999685i \(0.492010\pi\)
\(488\) 14.8634 0.672835
\(489\) 10.5842 0.478633
\(490\) 8.62702 0.389729
\(491\) 11.7817 0.531700 0.265850 0.964014i \(-0.414347\pi\)
0.265850 + 0.964014i \(0.414347\pi\)
\(492\) −7.05161 −0.317911
\(493\) 5.72591 0.257882
\(494\) −16.9618 −0.763149
\(495\) 13.8162 0.620993
\(496\) 4.49242 0.201716
\(497\) −59.5068 −2.66925
\(498\) −5.80244 −0.260013
\(499\) −30.6724 −1.37308 −0.686542 0.727090i \(-0.740872\pi\)
−0.686542 + 0.727090i \(0.740872\pi\)
\(500\) 10.2209 0.457095
\(501\) 12.7166 0.568136
\(502\) 11.1448 0.497418
\(503\) 4.79178 0.213655 0.106828 0.994278i \(-0.465931\pi\)
0.106828 + 0.994278i \(0.465931\pi\)
\(504\) 10.8008 0.481107
\(505\) 12.1104 0.538908
\(506\) 22.0889 0.981973
\(507\) −18.7976 −0.834831
\(508\) 3.20094 0.142019
\(509\) 30.4590 1.35007 0.675036 0.737785i \(-0.264128\pi\)
0.675036 + 0.737785i \(0.264128\pi\)
\(510\) 3.50007 0.154986
\(511\) 26.1030 1.15473
\(512\) −1.00000 −0.0441942
\(513\) 1.24462 0.0549515
\(514\) −15.9989 −0.705682
\(515\) 15.4931 0.682709
\(516\) 1.22938 0.0541204
\(517\) −4.46198 −0.196237
\(518\) −12.1566 −0.534130
\(519\) −26.6779 −1.17103
\(520\) 5.42737 0.238006
\(521\) 3.59477 0.157490 0.0787450 0.996895i \(-0.474909\pi\)
0.0787450 + 0.996895i \(0.474909\pi\)
\(522\) 13.5013 0.590935
\(523\) −16.6484 −0.727984 −0.363992 0.931402i \(-0.618586\pi\)
−0.363992 + 0.931402i \(0.618586\pi\)
\(524\) 19.0299 0.831324
\(525\) −32.7244 −1.42821
\(526\) −5.52745 −0.241008
\(527\) −5.45261 −0.237519
\(528\) 9.81341 0.427074
\(529\) 6.69946 0.291281
\(530\) 0.648855 0.0281844
\(531\) −3.16461 −0.137332
\(532\) −14.0482 −0.609066
\(533\) 13.2716 0.574858
\(534\) −32.9152 −1.42438
\(535\) 5.67967 0.245553
\(536\) 3.02571 0.130691
\(537\) 5.54736 0.239386
\(538\) 21.4404 0.924361
\(539\) −29.3581 −1.26454
\(540\) −0.398249 −0.0171379
\(541\) 9.29547 0.399643 0.199822 0.979832i \(-0.435964\pi\)
0.199822 + 0.979832i \(0.435964\pi\)
\(542\) 2.64571 0.113643
\(543\) −20.5043 −0.879923
\(544\) 1.21373 0.0520384
\(545\) 10.0746 0.431548
\(546\) −41.6368 −1.78189
\(547\) 20.1077 0.859743 0.429872 0.902890i \(-0.358559\pi\)
0.429872 + 0.902890i \(0.358559\pi\)
\(548\) −4.95703 −0.211754
\(549\) −42.5375 −1.81546
\(550\) −14.5161 −0.618969
\(551\) −17.5606 −0.748106
\(552\) 13.1945 0.561596
\(553\) 34.2860 1.45799
\(554\) −5.11141 −0.217163
\(555\) −9.28886 −0.394290
\(556\) −2.34546 −0.0994697
\(557\) 24.4631 1.03653 0.518267 0.855219i \(-0.326577\pi\)
0.518267 + 0.855219i \(0.326577\pi\)
\(558\) −12.8568 −0.544274
\(559\) −2.31378 −0.0978624
\(560\) 4.49508 0.189952
\(561\) −11.9109 −0.502877
\(562\) 26.1082 1.10131
\(563\) 34.1214 1.43805 0.719023 0.694986i \(-0.244589\pi\)
0.719023 + 0.694986i \(0.244589\pi\)
\(564\) −2.66530 −0.112229
\(565\) −21.9519 −0.923525
\(566\) 13.6087 0.572015
\(567\) 35.4577 1.48908
\(568\) −15.7675 −0.661591
\(569\) −5.33566 −0.223682 −0.111841 0.993726i \(-0.535675\pi\)
−0.111841 + 0.993726i \(0.535675\pi\)
\(570\) −10.7342 −0.449608
\(571\) 20.3701 0.852464 0.426232 0.904614i \(-0.359841\pi\)
0.426232 + 0.904614i \(0.359841\pi\)
\(572\) −18.4695 −0.772250
\(573\) −44.6500 −1.86528
\(574\) 10.9919 0.458792
\(575\) −19.5175 −0.813935
\(576\) 2.86190 0.119246
\(577\) −10.0639 −0.418965 −0.209483 0.977812i \(-0.567178\pi\)
−0.209483 + 0.977812i \(0.567178\pi\)
\(578\) 15.5268 0.645832
\(579\) −11.7027 −0.486346
\(580\) 5.61895 0.233314
\(581\) 9.04470 0.375237
\(582\) −14.6767 −0.608369
\(583\) −2.20807 −0.0914491
\(584\) 6.91652 0.286208
\(585\) −15.5326 −0.642193
\(586\) 7.31349 0.302118
\(587\) 30.7251 1.26816 0.634081 0.773267i \(-0.281379\pi\)
0.634081 + 0.773267i \(0.281379\pi\)
\(588\) −17.5366 −0.723198
\(589\) 16.7224 0.689034
\(590\) −1.31704 −0.0542219
\(591\) −47.0592 −1.93576
\(592\) −3.22114 −0.132388
\(593\) 6.18075 0.253813 0.126906 0.991915i \(-0.459495\pi\)
0.126906 + 0.991915i \(0.459495\pi\)
\(594\) 1.35526 0.0556068
\(595\) −5.45583 −0.223667
\(596\) −9.26218 −0.379394
\(597\) −0.947310 −0.0387708
\(598\) −24.8330 −1.01550
\(599\) 22.9386 0.937246 0.468623 0.883398i \(-0.344750\pi\)
0.468623 + 0.883398i \(0.344750\pi\)
\(600\) −8.67099 −0.353991
\(601\) 21.2860 0.868275 0.434137 0.900847i \(-0.357053\pi\)
0.434137 + 0.900847i \(0.357053\pi\)
\(602\) −1.91633 −0.0781037
\(603\) −8.65927 −0.352633
\(604\) −4.63025 −0.188402
\(605\) −6.46584 −0.262874
\(606\) −24.6176 −1.00002
\(607\) 25.6169 1.03976 0.519878 0.854240i \(-0.325977\pi\)
0.519878 + 0.854240i \(0.325977\pi\)
\(608\) −3.72235 −0.150961
\(609\) −43.1065 −1.74676
\(610\) −17.7032 −0.716783
\(611\) 5.01628 0.202937
\(612\) −3.47358 −0.140411
\(613\) 3.44936 0.139318 0.0696591 0.997571i \(-0.477809\pi\)
0.0696591 + 0.997571i \(0.477809\pi\)
\(614\) −5.26143 −0.212334
\(615\) 8.39890 0.338677
\(616\) −15.2969 −0.616330
\(617\) 13.5406 0.545125 0.272562 0.962138i \(-0.412129\pi\)
0.272562 + 0.962138i \(0.412129\pi\)
\(618\) −31.4937 −1.26686
\(619\) −6.48815 −0.260781 −0.130390 0.991463i \(-0.541623\pi\)
−0.130390 + 0.991463i \(0.541623\pi\)
\(620\) −5.35075 −0.214891
\(621\) 1.82220 0.0731222
\(622\) 1.31851 0.0528675
\(623\) 51.3074 2.05559
\(624\) −11.0325 −0.441654
\(625\) 5.73308 0.229323
\(626\) 29.2825 1.17036
\(627\) 36.5290 1.45883
\(628\) −14.6829 −0.585912
\(629\) 3.90960 0.155886
\(630\) −12.8645 −0.512532
\(631\) 12.2932 0.489386 0.244693 0.969601i \(-0.421313\pi\)
0.244693 + 0.969601i \(0.421313\pi\)
\(632\) 9.08476 0.361372
\(633\) 3.49345 0.138852
\(634\) −12.9282 −0.513445
\(635\) −3.81252 −0.151295
\(636\) −1.31896 −0.0523002
\(637\) 33.0052 1.30771
\(638\) −19.1215 −0.757027
\(639\) 45.1251 1.78512
\(640\) 1.19106 0.0470809
\(641\) 15.3514 0.606345 0.303172 0.952936i \(-0.401954\pi\)
0.303172 + 0.952936i \(0.401954\pi\)
\(642\) −11.5454 −0.455659
\(643\) 23.4730 0.925685 0.462843 0.886440i \(-0.346829\pi\)
0.462843 + 0.886440i \(0.346829\pi\)
\(644\) −20.5673 −0.810465
\(645\) −1.46427 −0.0576555
\(646\) 4.51795 0.177756
\(647\) 1.79563 0.0705934 0.0352967 0.999377i \(-0.488762\pi\)
0.0352967 + 0.999377i \(0.488762\pi\)
\(648\) 9.39524 0.369080
\(649\) 4.48195 0.175932
\(650\) 16.3194 0.640100
\(651\) 41.0490 1.60884
\(652\) −4.37158 −0.171204
\(653\) −18.8023 −0.735790 −0.367895 0.929867i \(-0.619921\pi\)
−0.367895 + 0.929867i \(0.619921\pi\)
\(654\) −20.4791 −0.800798
\(655\) −22.6658 −0.885624
\(656\) 2.91252 0.113715
\(657\) −19.7944 −0.772252
\(658\) 4.15460 0.161963
\(659\) −11.5759 −0.450932 −0.225466 0.974251i \(-0.572390\pi\)
−0.225466 + 0.974251i \(0.572390\pi\)
\(660\) −11.6884 −0.454969
\(661\) −31.2107 −1.21396 −0.606978 0.794719i \(-0.707618\pi\)
−0.606978 + 0.794719i \(0.707618\pi\)
\(662\) −14.7764 −0.574301
\(663\) 13.3905 0.520045
\(664\) 2.39658 0.0930052
\(665\) 16.7323 0.648850
\(666\) 9.21856 0.357212
\(667\) −25.7096 −0.995480
\(668\) −5.25233 −0.203219
\(669\) −0.375579 −0.0145207
\(670\) −3.60381 −0.139227
\(671\) 60.2447 2.32572
\(672\) −9.13739 −0.352482
\(673\) 5.66703 0.218448 0.109224 0.994017i \(-0.465163\pi\)
0.109224 + 0.994017i \(0.465163\pi\)
\(674\) −20.2729 −0.780884
\(675\) −1.19748 −0.0460912
\(676\) 7.76396 0.298614
\(677\) 27.1326 1.04279 0.521394 0.853316i \(-0.325412\pi\)
0.521394 + 0.853316i \(0.325412\pi\)
\(678\) 44.6229 1.71373
\(679\) 22.8777 0.877965
\(680\) −1.44563 −0.0554375
\(681\) −31.4673 −1.20583
\(682\) 18.2088 0.697251
\(683\) 36.2859 1.38844 0.694220 0.719763i \(-0.255749\pi\)
0.694220 + 0.719763i \(0.255749\pi\)
\(684\) 10.6530 0.407327
\(685\) 5.90413 0.225585
\(686\) 0.917599 0.0350341
\(687\) 52.8699 2.01711
\(688\) −0.507770 −0.0193585
\(689\) 2.48238 0.0945711
\(690\) −15.7155 −0.598278
\(691\) 4.91245 0.186878 0.0934391 0.995625i \(-0.470214\pi\)
0.0934391 + 0.995625i \(0.470214\pi\)
\(692\) 11.0187 0.418870
\(693\) 43.7782 1.66300
\(694\) −12.0865 −0.458797
\(695\) 2.79359 0.105967
\(696\) −11.4220 −0.432948
\(697\) −3.53503 −0.133899
\(698\) 3.16619 0.119842
\(699\) −7.64445 −0.289140
\(700\) 13.5161 0.510861
\(701\) −32.2635 −1.21858 −0.609288 0.792949i \(-0.708545\pi\)
−0.609288 + 0.792949i \(0.708545\pi\)
\(702\) −1.52362 −0.0575052
\(703\) −11.9902 −0.452219
\(704\) −4.05323 −0.152762
\(705\) 3.17453 0.119560
\(706\) −4.79538 −0.180476
\(707\) 38.3733 1.44317
\(708\) 2.67723 0.100616
\(709\) −6.54439 −0.245780 −0.122890 0.992420i \(-0.539216\pi\)
−0.122890 + 0.992420i \(0.539216\pi\)
\(710\) 18.7801 0.704805
\(711\) −25.9997 −0.975063
\(712\) 13.5949 0.509492
\(713\) 24.4824 0.916875
\(714\) 11.0904 0.415046
\(715\) 21.9984 0.822692
\(716\) −2.29122 −0.0856270
\(717\) 30.3908 1.13497
\(718\) 17.5257 0.654055
\(719\) −12.3867 −0.461947 −0.230974 0.972960i \(-0.574191\pi\)
−0.230974 + 0.972960i \(0.574191\pi\)
\(720\) −3.40870 −0.127035
\(721\) 49.0916 1.82827
\(722\) 5.14409 0.191443
\(723\) 32.0103 1.19048
\(724\) 8.46887 0.314743
\(725\) 16.8955 0.627482
\(726\) 13.1435 0.487799
\(727\) 25.9484 0.962373 0.481187 0.876618i \(-0.340206\pi\)
0.481187 + 0.876618i \(0.340206\pi\)
\(728\) 17.1972 0.637371
\(729\) −24.4596 −0.905910
\(730\) −8.23800 −0.304902
\(731\) 0.616298 0.0227946
\(732\) 35.9863 1.33009
\(733\) 15.1379 0.559132 0.279566 0.960126i \(-0.409809\pi\)
0.279566 + 0.960126i \(0.409809\pi\)
\(734\) −28.0392 −1.03495
\(735\) 20.8872 0.770436
\(736\) −5.44972 −0.200879
\(737\) 12.2639 0.451746
\(738\) −8.33534 −0.306828
\(739\) −48.8716 −1.79777 −0.898885 0.438185i \(-0.855622\pi\)
−0.898885 + 0.438185i \(0.855622\pi\)
\(740\) 3.83657 0.141035
\(741\) −41.0669 −1.50863
\(742\) 2.05597 0.0754769
\(743\) −1.38032 −0.0506390 −0.0253195 0.999679i \(-0.508060\pi\)
−0.0253195 + 0.999679i \(0.508060\pi\)
\(744\) 10.8768 0.398761
\(745\) 11.0318 0.404175
\(746\) 7.72894 0.282977
\(747\) −6.85876 −0.250949
\(748\) 4.91954 0.179876
\(749\) 17.9966 0.657583
\(750\) 24.7463 0.903607
\(751\) −45.0002 −1.64208 −0.821041 0.570869i \(-0.806606\pi\)
−0.821041 + 0.570869i \(0.806606\pi\)
\(752\) 1.10085 0.0401437
\(753\) 26.9832 0.983321
\(754\) 21.4969 0.782872
\(755\) 5.51492 0.200708
\(756\) −1.26190 −0.0458947
\(757\) −12.6466 −0.459647 −0.229824 0.973232i \(-0.573815\pi\)
−0.229824 + 0.973232i \(0.573815\pi\)
\(758\) −7.67069 −0.278612
\(759\) 53.4803 1.94121
\(760\) 4.43355 0.160822
\(761\) −21.2754 −0.771234 −0.385617 0.922659i \(-0.626011\pi\)
−0.385617 + 0.922659i \(0.626011\pi\)
\(762\) 7.74990 0.280749
\(763\) 31.9224 1.15567
\(764\) 18.4418 0.667200
\(765\) 4.13725 0.149583
\(766\) 27.5071 0.993873
\(767\) −5.03873 −0.181938
\(768\) −2.42114 −0.0873652
\(769\) 44.2214 1.59466 0.797332 0.603541i \(-0.206244\pi\)
0.797332 + 0.603541i \(0.206244\pi\)
\(770\) 18.2196 0.656587
\(771\) −38.7356 −1.39503
\(772\) 4.83354 0.173963
\(773\) −29.4341 −1.05867 −0.529335 0.848413i \(-0.677559\pi\)
−0.529335 + 0.848413i \(0.677559\pi\)
\(774\) 1.45318 0.0522337
\(775\) −16.0890 −0.577935
\(776\) 6.06191 0.217610
\(777\) −29.4328 −1.05589
\(778\) 10.8598 0.389342
\(779\) 10.8414 0.388435
\(780\) 13.1404 0.470502
\(781\) −63.9094 −2.28686
\(782\) 6.61451 0.236535
\(783\) −1.57740 −0.0563717
\(784\) 7.24314 0.258683
\(785\) 17.4883 0.624183
\(786\) 46.0739 1.64340
\(787\) 24.6186 0.877560 0.438780 0.898595i \(-0.355411\pi\)
0.438780 + 0.898595i \(0.355411\pi\)
\(788\) 19.4368 0.692408
\(789\) −13.3827 −0.476437
\(790\) −10.8205 −0.384977
\(791\) −69.5571 −2.47317
\(792\) 11.5999 0.412185
\(793\) −67.7288 −2.40512
\(794\) 14.0850 0.499857
\(795\) 1.57097 0.0557164
\(796\) 0.391267 0.0138681
\(797\) −42.1421 −1.49275 −0.746375 0.665525i \(-0.768208\pi\)
−0.746375 + 0.665525i \(0.768208\pi\)
\(798\) −34.0126 −1.20403
\(799\) −1.33613 −0.0472690
\(800\) 3.58137 0.126621
\(801\) −38.9073 −1.37472
\(802\) −13.3483 −0.471344
\(803\) 28.0342 0.989306
\(804\) 7.32566 0.258356
\(805\) 24.4969 0.863403
\(806\) −20.4708 −0.721054
\(807\) 51.9101 1.82732
\(808\) 10.1678 0.357701
\(809\) 26.6330 0.936366 0.468183 0.883632i \(-0.344909\pi\)
0.468183 + 0.883632i \(0.344909\pi\)
\(810\) −11.1903 −0.393187
\(811\) 27.0936 0.951384 0.475692 0.879612i \(-0.342198\pi\)
0.475692 + 0.879612i \(0.342198\pi\)
\(812\) 17.8043 0.624807
\(813\) 6.40561 0.224655
\(814\) −13.0560 −0.457612
\(815\) 5.20682 0.182387
\(816\) 2.93862 0.102872
\(817\) −1.89010 −0.0661262
\(818\) −14.6977 −0.513895
\(819\) −49.2166 −1.71977
\(820\) −3.46899 −0.121143
\(821\) −45.7306 −1.59601 −0.798004 0.602652i \(-0.794111\pi\)
−0.798004 + 0.602652i \(0.794111\pi\)
\(822\) −12.0016 −0.418605
\(823\) 6.76446 0.235794 0.117897 0.993026i \(-0.462385\pi\)
0.117897 + 0.993026i \(0.462385\pi\)
\(824\) 13.0078 0.453149
\(825\) −35.1455 −1.22361
\(826\) −4.17320 −0.145204
\(827\) 41.3750 1.43875 0.719375 0.694622i \(-0.244428\pi\)
0.719375 + 0.694622i \(0.244428\pi\)
\(828\) 15.5965 0.542017
\(829\) 32.6071 1.13249 0.566246 0.824236i \(-0.308395\pi\)
0.566246 + 0.824236i \(0.308395\pi\)
\(830\) −2.85447 −0.0990802
\(831\) −12.3754 −0.429299
\(832\) 4.55675 0.157977
\(833\) −8.79124 −0.304599
\(834\) −5.67868 −0.196636
\(835\) 6.25585 0.216493
\(836\) −15.0875 −0.521813
\(837\) 1.50211 0.0519204
\(838\) 21.4892 0.742331
\(839\) −8.47783 −0.292687 −0.146344 0.989234i \(-0.546750\pi\)
−0.146344 + 0.989234i \(0.546750\pi\)
\(840\) 10.8832 0.375506
\(841\) −6.74425 −0.232560
\(842\) −29.0308 −1.00047
\(843\) 63.2116 2.17712
\(844\) −1.44290 −0.0496666
\(845\) −9.24736 −0.318119
\(846\) −3.15051 −0.108317
\(847\) −20.4877 −0.703966
\(848\) 0.544770 0.0187075
\(849\) 32.9484 1.13079
\(850\) −4.34683 −0.149095
\(851\) −17.5543 −0.601753
\(852\) −38.1754 −1.30787
\(853\) −47.4072 −1.62319 −0.811596 0.584219i \(-0.801401\pi\)
−0.811596 + 0.584219i \(0.801401\pi\)
\(854\) −56.0946 −1.91952
\(855\) −12.6884 −0.433933
\(856\) 4.76857 0.162986
\(857\) 52.4303 1.79098 0.895492 0.445077i \(-0.146824\pi\)
0.895492 + 0.445077i \(0.146824\pi\)
\(858\) −44.7172 −1.52662
\(859\) −38.5493 −1.31529 −0.657643 0.753330i \(-0.728446\pi\)
−0.657643 + 0.753330i \(0.728446\pi\)
\(860\) 0.604785 0.0206230
\(861\) 26.6128 0.906963
\(862\) 24.4782 0.833731
\(863\) 23.7400 0.808120 0.404060 0.914732i \(-0.367599\pi\)
0.404060 + 0.914732i \(0.367599\pi\)
\(864\) −0.334365 −0.0113753
\(865\) −13.1240 −0.446230
\(866\) 21.3135 0.724263
\(867\) 37.5926 1.27671
\(868\) −16.9544 −0.575471
\(869\) 36.8226 1.24912
\(870\) 13.6043 0.461227
\(871\) −13.7874 −0.467168
\(872\) 8.45849 0.286440
\(873\) −17.3486 −0.587160
\(874\) −20.2858 −0.686177
\(875\) −38.5739 −1.30404
\(876\) 16.7458 0.565789
\(877\) 30.9822 1.04619 0.523097 0.852273i \(-0.324777\pi\)
0.523097 + 0.852273i \(0.324777\pi\)
\(878\) −29.8915 −1.00879
\(879\) 17.7070 0.597241
\(880\) 4.82764 0.162740
\(881\) 52.6496 1.77381 0.886906 0.461951i \(-0.152850\pi\)
0.886906 + 0.461951i \(0.152850\pi\)
\(882\) −20.7291 −0.697986
\(883\) −24.9835 −0.840761 −0.420381 0.907348i \(-0.638103\pi\)
−0.420381 + 0.907348i \(0.638103\pi\)
\(884\) −5.53068 −0.186017
\(885\) −3.18874 −0.107188
\(886\) 35.0460 1.17739
\(887\) −17.5402 −0.588942 −0.294471 0.955660i \(-0.595143\pi\)
−0.294471 + 0.955660i \(0.595143\pi\)
\(888\) −7.79881 −0.261711
\(889\) −12.0804 −0.405162
\(890\) −16.1924 −0.542771
\(891\) 38.0810 1.27576
\(892\) 0.155125 0.00519397
\(893\) 4.09774 0.137126
\(894\) −22.4250 −0.750004
\(895\) 2.72899 0.0912201
\(896\) 3.77401 0.126081
\(897\) −60.1241 −2.00748
\(898\) −0.835529 −0.0278820
\(899\) −21.1934 −0.706841
\(900\) −10.2495 −0.341651
\(901\) −0.661206 −0.0220280
\(902\) 11.8051 0.393067
\(903\) −4.63969 −0.154399
\(904\) −18.4306 −0.612991
\(905\) −10.0870 −0.335302
\(906\) −11.2105 −0.372443
\(907\) −32.7170 −1.08635 −0.543175 0.839620i \(-0.682778\pi\)
−0.543175 + 0.839620i \(0.682778\pi\)
\(908\) 12.9969 0.431318
\(909\) −29.0991 −0.965157
\(910\) −20.4829 −0.679003
\(911\) −4.25563 −0.140995 −0.0704977 0.997512i \(-0.522459\pi\)
−0.0704977 + 0.997512i \(0.522459\pi\)
\(912\) −9.01232 −0.298428
\(913\) 9.71387 0.321482
\(914\) −0.895256 −0.0296125
\(915\) −42.8619 −1.41697
\(916\) −21.8368 −0.721508
\(917\) −71.8189 −2.37167
\(918\) 0.405830 0.0133944
\(919\) 19.6378 0.647792 0.323896 0.946093i \(-0.395007\pi\)
0.323896 + 0.946093i \(0.395007\pi\)
\(920\) 6.49096 0.214000
\(921\) −12.7386 −0.419753
\(922\) −25.1774 −0.829173
\(923\) 71.8487 2.36493
\(924\) −37.0359 −1.21839
\(925\) 11.5361 0.379304
\(926\) −3.24013 −0.106477
\(927\) −37.2271 −1.22270
\(928\) 4.71760 0.154863
\(929\) −33.9022 −1.11229 −0.556147 0.831084i \(-0.687721\pi\)
−0.556147 + 0.831084i \(0.687721\pi\)
\(930\) −12.9549 −0.424808
\(931\) 26.9615 0.883628
\(932\) 3.15738 0.103423
\(933\) 3.19229 0.104511
\(934\) 2.58485 0.0845788
\(935\) −5.85948 −0.191625
\(936\) −13.0409 −0.426257
\(937\) 43.3772 1.41707 0.708536 0.705674i \(-0.249356\pi\)
0.708536 + 0.705674i \(0.249356\pi\)
\(938\) −11.4191 −0.372845
\(939\) 70.8969 2.31363
\(940\) −1.31118 −0.0427658
\(941\) −12.3451 −0.402437 −0.201219 0.979546i \(-0.564490\pi\)
−0.201219 + 0.979546i \(0.564490\pi\)
\(942\) −35.5493 −1.15826
\(943\) 15.8724 0.516877
\(944\) −1.10577 −0.0359899
\(945\) 1.50300 0.0488925
\(946\) −2.05810 −0.0669148
\(947\) 22.0054 0.715080 0.357540 0.933898i \(-0.383616\pi\)
0.357540 + 0.933898i \(0.383616\pi\)
\(948\) 21.9954 0.714379
\(949\) −31.5168 −1.02308
\(950\) 13.3311 0.432519
\(951\) −31.3010 −1.01500
\(952\) −4.58064 −0.148459
\(953\) 24.7244 0.800902 0.400451 0.916318i \(-0.368853\pi\)
0.400451 + 0.916318i \(0.368853\pi\)
\(954\) −1.55908 −0.0504769
\(955\) −21.9653 −0.710780
\(956\) −12.5523 −0.405970
\(957\) −46.2957 −1.49653
\(958\) −1.56801 −0.0506601
\(959\) 18.7079 0.604109
\(960\) 2.88372 0.0930718
\(961\) −10.8182 −0.348973
\(962\) 14.6779 0.473235
\(963\) −13.6472 −0.439774
\(964\) −13.2212 −0.425826
\(965\) −5.75705 −0.185326
\(966\) −49.7962 −1.60217
\(967\) 15.5679 0.500629 0.250314 0.968165i \(-0.419466\pi\)
0.250314 + 0.968165i \(0.419466\pi\)
\(968\) −5.42863 −0.174483
\(969\) 10.9386 0.351397
\(970\) −7.22011 −0.231824
\(971\) 2.49356 0.0800222 0.0400111 0.999199i \(-0.487261\pi\)
0.0400111 + 0.999199i \(0.487261\pi\)
\(972\) 21.7440 0.697441
\(973\) 8.85178 0.283775
\(974\) −1.10775 −0.0354946
\(975\) 39.5115 1.26538
\(976\) −14.8634 −0.475766
\(977\) 44.1235 1.41164 0.705818 0.708393i \(-0.250579\pi\)
0.705818 + 0.708393i \(0.250579\pi\)
\(978\) −10.5842 −0.338445
\(979\) 55.1033 1.76111
\(980\) −8.62702 −0.275580
\(981\) −24.2073 −0.772880
\(982\) −11.7817 −0.375968
\(983\) −26.0986 −0.832416 −0.416208 0.909269i \(-0.636641\pi\)
−0.416208 + 0.909269i \(0.636641\pi\)
\(984\) 7.05161 0.224797
\(985\) −23.1505 −0.737635
\(986\) −5.72591 −0.182350
\(987\) 10.0589 0.320177
\(988\) 16.9618 0.539628
\(989\) −2.76720 −0.0879919
\(990\) −13.8162 −0.439108
\(991\) −46.5745 −1.47949 −0.739743 0.672889i \(-0.765053\pi\)
−0.739743 + 0.672889i \(0.765053\pi\)
\(992\) −4.49242 −0.142634
\(993\) −35.7757 −1.13531
\(994\) 59.5068 1.88744
\(995\) −0.466023 −0.0147739
\(996\) 5.80244 0.183857
\(997\) 17.2731 0.547046 0.273523 0.961865i \(-0.411811\pi\)
0.273523 + 0.961865i \(0.411811\pi\)
\(998\) 30.6724 0.970918
\(999\) −1.07703 −0.0340759
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 \(a_p\))