Properties

Label 8042.2.a.c.1.9
Level 8042
Weight 2
Character 8042.1
Self dual Yes
Analytic conductor 64.216
Analytic rank 0
Dimension 86
CM No

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Newspace parameters

Level: \( N \) = \( 8042 = 2 \cdot 4021 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8042.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2156933055\)
Analytic rank: \(0\)
Dimension: \(86\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.9
Character \(\chi\) = 8042.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} -2.54862 q^{3} +1.00000 q^{4} -1.05969 q^{5} +2.54862 q^{6} -0.366146 q^{7} -1.00000 q^{8} +3.49545 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -2.54862 q^{3} +1.00000 q^{4} -1.05969 q^{5} +2.54862 q^{6} -0.366146 q^{7} -1.00000 q^{8} +3.49545 q^{9} +1.05969 q^{10} -0.330498 q^{11} -2.54862 q^{12} -2.15141 q^{13} +0.366146 q^{14} +2.70075 q^{15} +1.00000 q^{16} +2.98970 q^{17} -3.49545 q^{18} -8.00967 q^{19} -1.05969 q^{20} +0.933166 q^{21} +0.330498 q^{22} -7.06260 q^{23} +2.54862 q^{24} -3.87705 q^{25} +2.15141 q^{26} -1.26271 q^{27} -0.366146 q^{28} -2.43858 q^{29} -2.70075 q^{30} -8.65756 q^{31} -1.00000 q^{32} +0.842314 q^{33} -2.98970 q^{34} +0.388002 q^{35} +3.49545 q^{36} -6.23500 q^{37} +8.00967 q^{38} +5.48312 q^{39} +1.05969 q^{40} +5.24599 q^{41} -0.933166 q^{42} +8.94270 q^{43} -0.330498 q^{44} -3.70410 q^{45} +7.06260 q^{46} -2.67032 q^{47} -2.54862 q^{48} -6.86594 q^{49} +3.87705 q^{50} -7.61961 q^{51} -2.15141 q^{52} -9.83026 q^{53} +1.26271 q^{54} +0.350226 q^{55} +0.366146 q^{56} +20.4136 q^{57} +2.43858 q^{58} +8.95349 q^{59} +2.70075 q^{60} -3.72746 q^{61} +8.65756 q^{62} -1.27985 q^{63} +1.00000 q^{64} +2.27983 q^{65} -0.842314 q^{66} +13.8648 q^{67} +2.98970 q^{68} +17.9999 q^{69} -0.388002 q^{70} -6.95344 q^{71} -3.49545 q^{72} -15.4340 q^{73} +6.23500 q^{74} +9.88112 q^{75} -8.00967 q^{76} +0.121011 q^{77} -5.48312 q^{78} +5.74110 q^{79} -1.05969 q^{80} -7.26818 q^{81} -5.24599 q^{82} -4.36949 q^{83} +0.933166 q^{84} -3.16817 q^{85} -8.94270 q^{86} +6.21500 q^{87} +0.330498 q^{88} -0.774967 q^{89} +3.70410 q^{90} +0.787730 q^{91} -7.06260 q^{92} +22.0648 q^{93} +2.67032 q^{94} +8.48779 q^{95} +2.54862 q^{96} -6.51475 q^{97} +6.86594 q^{98} -1.15524 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 86q - 86q^{2} + 12q^{3} + 86q^{4} - 4q^{5} - 12q^{6} + 35q^{7} - 86q^{8} + 72q^{9} + O(q^{10}) \) \( 86q - 86q^{2} + 12q^{3} + 86q^{4} - 4q^{5} - 12q^{6} + 35q^{7} - 86q^{8} + 72q^{9} + 4q^{10} + 13q^{11} + 12q^{12} + 45q^{13} - 35q^{14} + 17q^{15} + 86q^{16} + 5q^{17} - 72q^{18} + 47q^{19} - 4q^{20} + 15q^{21} - 13q^{22} + 6q^{23} - 12q^{24} + 112q^{25} - 45q^{26} + 51q^{27} + 35q^{28} - 14q^{29} - 17q^{30} + 24q^{31} - 86q^{32} + 43q^{33} - 5q^{34} + 42q^{35} + 72q^{36} + 61q^{37} - 47q^{38} + 20q^{39} + 4q^{40} - 16q^{41} - 15q^{42} + 72q^{43} + 13q^{44} + 6q^{45} - 6q^{46} + 11q^{47} + 12q^{48} + 89q^{49} - 112q^{50} + 56q^{51} + 45q^{52} - 7q^{53} - 51q^{54} + 48q^{55} - 35q^{56} + 65q^{57} + 14q^{58} + 24q^{59} + 17q^{60} + 31q^{61} - 24q^{62} + 98q^{63} + 86q^{64} - 9q^{65} - 43q^{66} + 157q^{67} + 5q^{68} + q^{69} - 42q^{70} - 11q^{71} - 72q^{72} + 74q^{73} - 61q^{74} + 76q^{75} + 47q^{76} - 13q^{77} - 20q^{78} + 57q^{79} - 4q^{80} + 34q^{81} + 16q^{82} + 65q^{83} + 15q^{84} + 102q^{85} - 72q^{86} + 49q^{87} - 13q^{88} - 34q^{89} - 6q^{90} + 91q^{91} + 6q^{92} + 57q^{93} - 11q^{94} - 13q^{95} - 12q^{96} + 64q^{97} - 89q^{98} + 56q^{99} + O(q^{100}) \)

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
\(3\) −2.54862 −1.47144 −0.735722 0.677283i \(-0.763157\pi\)
−0.735722 + 0.677283i \(0.763157\pi\)
\(4\) 1.00000 0.500000
\(5\) −1.05969 −0.473909 −0.236954 0.971521i \(-0.576149\pi\)
−0.236954 + 0.971521i \(0.576149\pi\)
\(6\) 2.54862 1.04047
\(7\) −0.366146 −0.138390 −0.0691951 0.997603i \(-0.522043\pi\)
−0.0691951 + 0.997603i \(0.522043\pi\)
\(8\) −1.00000 −0.353553
\(9\) 3.49545 1.16515
\(10\) 1.05969 0.335104
\(11\) −0.330498 −0.0996490 −0.0498245 0.998758i \(-0.515866\pi\)
−0.0498245 + 0.998758i \(0.515866\pi\)
\(12\) −2.54862 −0.735722
\(13\) −2.15141 −0.596694 −0.298347 0.954458i \(-0.596435\pi\)
−0.298347 + 0.954458i \(0.596435\pi\)
\(14\) 0.366146 0.0978567
\(15\) 2.70075 0.697331
\(16\) 1.00000 0.250000
\(17\) 2.98970 0.725109 0.362555 0.931962i \(-0.381905\pi\)
0.362555 + 0.931962i \(0.381905\pi\)
\(18\) −3.49545 −0.823886
\(19\) −8.00967 −1.83754 −0.918772 0.394788i \(-0.870818\pi\)
−0.918772 + 0.394788i \(0.870818\pi\)
\(20\) −1.05969 −0.236954
\(21\) 0.933166 0.203634
\(22\) 0.330498 0.0704625
\(23\) −7.06260 −1.47265 −0.736327 0.676626i \(-0.763441\pi\)
−0.736327 + 0.676626i \(0.763441\pi\)
\(24\) 2.54862 0.520234
\(25\) −3.87705 −0.775410
\(26\) 2.15141 0.421926
\(27\) −1.26271 −0.243009
\(28\) −0.366146 −0.0691951
\(29\) −2.43858 −0.452832 −0.226416 0.974031i \(-0.572701\pi\)
−0.226416 + 0.974031i \(0.572701\pi\)
\(30\) −2.70075 −0.493087
\(31\) −8.65756 −1.55494 −0.777472 0.628917i \(-0.783498\pi\)
−0.777472 + 0.628917i \(0.783498\pi\)
\(32\) −1.00000 −0.176777
\(33\) 0.842314 0.146628
\(34\) −2.98970 −0.512730
\(35\) 0.388002 0.0655843
\(36\) 3.49545 0.582575
\(37\) −6.23500 −1.02503 −0.512514 0.858679i \(-0.671286\pi\)
−0.512514 + 0.858679i \(0.671286\pi\)
\(38\) 8.00967 1.29934
\(39\) 5.48312 0.878002
\(40\) 1.05969 0.167552
\(41\) 5.24599 0.819286 0.409643 0.912246i \(-0.365653\pi\)
0.409643 + 0.912246i \(0.365653\pi\)
\(42\) −0.933166 −0.143991
\(43\) 8.94270 1.36375 0.681874 0.731469i \(-0.261165\pi\)
0.681874 + 0.731469i \(0.261165\pi\)
\(44\) −0.330498 −0.0498245
\(45\) −3.70410 −0.552175
\(46\) 7.06260 1.04132
\(47\) −2.67032 −0.389506 −0.194753 0.980852i \(-0.562391\pi\)
−0.194753 + 0.980852i \(0.562391\pi\)
\(48\) −2.54862 −0.367861
\(49\) −6.86594 −0.980848
\(50\) 3.87705 0.548298
\(51\) −7.61961 −1.06696
\(52\) −2.15141 −0.298347
\(53\) −9.83026 −1.35029 −0.675145 0.737685i \(-0.735919\pi\)
−0.675145 + 0.737685i \(0.735919\pi\)
\(54\) 1.26271 0.171834
\(55\) 0.350226 0.0472245
\(56\) 0.366146 0.0489283
\(57\) 20.4136 2.70385
\(58\) 2.43858 0.320201
\(59\) 8.95349 1.16565 0.582823 0.812599i \(-0.301948\pi\)
0.582823 + 0.812599i \(0.301948\pi\)
\(60\) 2.70075 0.348665
\(61\) −3.72746 −0.477252 −0.238626 0.971112i \(-0.576697\pi\)
−0.238626 + 0.971112i \(0.576697\pi\)
\(62\) 8.65756 1.09951
\(63\) −1.27985 −0.161245
\(64\) 1.00000 0.125000
\(65\) 2.27983 0.282778
\(66\) −0.842314 −0.103682
\(67\) 13.8648 1.69385 0.846926 0.531711i \(-0.178451\pi\)
0.846926 + 0.531711i \(0.178451\pi\)
\(68\) 2.98970 0.362555
\(69\) 17.9999 2.16693
\(70\) −0.388002 −0.0463751
\(71\) −6.95344 −0.825221 −0.412610 0.910908i \(-0.635383\pi\)
−0.412610 + 0.910908i \(0.635383\pi\)
\(72\) −3.49545 −0.411943
\(73\) −15.4340 −1.80641 −0.903207 0.429205i \(-0.858794\pi\)
−0.903207 + 0.429205i \(0.858794\pi\)
\(74\) 6.23500 0.724804
\(75\) 9.88112 1.14097
\(76\) −8.00967 −0.918772
\(77\) 0.121011 0.0137904
\(78\) −5.48312 −0.620841
\(79\) 5.74110 0.645924 0.322962 0.946412i \(-0.395321\pi\)
0.322962 + 0.946412i \(0.395321\pi\)
\(80\) −1.05969 −0.118477
\(81\) −7.26818 −0.807575
\(82\) −5.24599 −0.579323
\(83\) −4.36949 −0.479614 −0.239807 0.970821i \(-0.577084\pi\)
−0.239807 + 0.970821i \(0.577084\pi\)
\(84\) 0.933166 0.101817
\(85\) −3.16817 −0.343636
\(86\) −8.94270 −0.964316
\(87\) 6.21500 0.666318
\(88\) 0.330498 0.0352312
\(89\) −0.774967 −0.0821464 −0.0410732 0.999156i \(-0.513078\pi\)
−0.0410732 + 0.999156i \(0.513078\pi\)
\(90\) 3.70410 0.390447
\(91\) 0.787730 0.0825766
\(92\) −7.06260 −0.736327
\(93\) 22.0648 2.28802
\(94\) 2.67032 0.275423
\(95\) 8.48779 0.870829
\(96\) 2.54862 0.260117
\(97\) −6.51475 −0.661473 −0.330736 0.943723i \(-0.607297\pi\)
−0.330736 + 0.943723i \(0.607297\pi\)
\(98\) 6.86594 0.693564
\(99\) −1.15524 −0.116106
\(100\) −3.87705 −0.387705
\(101\) −10.3298 −1.02786 −0.513929 0.857833i \(-0.671810\pi\)
−0.513929 + 0.857833i \(0.671810\pi\)
\(102\) 7.61961 0.754454
\(103\) 17.2839 1.70304 0.851518 0.524326i \(-0.175683\pi\)
0.851518 + 0.524326i \(0.175683\pi\)
\(104\) 2.15141 0.210963
\(105\) −0.988869 −0.0965037
\(106\) 9.83026 0.954800
\(107\) −8.50588 −0.822294 −0.411147 0.911569i \(-0.634872\pi\)
−0.411147 + 0.911569i \(0.634872\pi\)
\(108\) −1.26271 −0.121505
\(109\) −10.8442 −1.03869 −0.519345 0.854565i \(-0.673824\pi\)
−0.519345 + 0.854565i \(0.673824\pi\)
\(110\) −0.350226 −0.0333928
\(111\) 15.8906 1.50827
\(112\) −0.366146 −0.0345976
\(113\) −5.24240 −0.493163 −0.246582 0.969122i \(-0.579307\pi\)
−0.246582 + 0.969122i \(0.579307\pi\)
\(114\) −20.4136 −1.91191
\(115\) 7.48418 0.697904
\(116\) −2.43858 −0.226416
\(117\) −7.52015 −0.695238
\(118\) −8.95349 −0.824236
\(119\) −1.09467 −0.100348
\(120\) −2.70075 −0.246544
\(121\) −10.8908 −0.990070
\(122\) 3.72746 0.337468
\(123\) −13.3700 −1.20553
\(124\) −8.65756 −0.777472
\(125\) 9.40694 0.841383
\(126\) 1.27985 0.114018
\(127\) −17.7420 −1.57435 −0.787176 0.616729i \(-0.788458\pi\)
−0.787176 + 0.616729i \(0.788458\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −22.7915 −2.00668
\(130\) −2.27983 −0.199955
\(131\) −2.76252 −0.241362 −0.120681 0.992691i \(-0.538508\pi\)
−0.120681 + 0.992691i \(0.538508\pi\)
\(132\) 0.842314 0.0733140
\(133\) 2.93271 0.254298
\(134\) −13.8648 −1.19773
\(135\) 1.33809 0.115164
\(136\) −2.98970 −0.256365
\(137\) −3.43082 −0.293114 −0.146557 0.989202i \(-0.546819\pi\)
−0.146557 + 0.989202i \(0.546819\pi\)
\(138\) −17.9999 −1.53225
\(139\) 2.55804 0.216970 0.108485 0.994098i \(-0.465400\pi\)
0.108485 + 0.994098i \(0.465400\pi\)
\(140\) 0.388002 0.0327922
\(141\) 6.80563 0.573137
\(142\) 6.95344 0.583519
\(143\) 0.711037 0.0594599
\(144\) 3.49545 0.291288
\(145\) 2.58414 0.214601
\(146\) 15.4340 1.27733
\(147\) 17.4986 1.44326
\(148\) −6.23500 −0.512514
\(149\) −8.31160 −0.680913 −0.340456 0.940260i \(-0.610582\pi\)
−0.340456 + 0.940260i \(0.610582\pi\)
\(150\) −9.88112 −0.806790
\(151\) 14.9476 1.21642 0.608209 0.793777i \(-0.291888\pi\)
0.608209 + 0.793777i \(0.291888\pi\)
\(152\) 8.00967 0.649670
\(153\) 10.4504 0.844861
\(154\) −0.121011 −0.00975131
\(155\) 9.17436 0.736902
\(156\) 5.48312 0.439001
\(157\) −16.7138 −1.33390 −0.666952 0.745100i \(-0.732401\pi\)
−0.666952 + 0.745100i \(0.732401\pi\)
\(158\) −5.74110 −0.456738
\(159\) 25.0536 1.98688
\(160\) 1.05969 0.0837760
\(161\) 2.58594 0.203801
\(162\) 7.26818 0.571042
\(163\) 18.4268 1.44330 0.721649 0.692259i \(-0.243385\pi\)
0.721649 + 0.692259i \(0.243385\pi\)
\(164\) 5.24599 0.409643
\(165\) −0.892593 −0.0694883
\(166\) 4.36949 0.339138
\(167\) −20.2855 −1.56974 −0.784869 0.619662i \(-0.787270\pi\)
−0.784869 + 0.619662i \(0.787270\pi\)
\(168\) −0.933166 −0.0719953
\(169\) −8.37144 −0.643957
\(170\) 3.16817 0.242987
\(171\) −27.9974 −2.14102
\(172\) 8.94270 0.681874
\(173\) 13.6654 1.03896 0.519479 0.854483i \(-0.326126\pi\)
0.519479 + 0.854483i \(0.326126\pi\)
\(174\) −6.21500 −0.471158
\(175\) 1.41957 0.107309
\(176\) −0.330498 −0.0249122
\(177\) −22.8190 −1.71518
\(178\) 0.774967 0.0580862
\(179\) −22.8049 −1.70452 −0.852260 0.523118i \(-0.824769\pi\)
−0.852260 + 0.523118i \(0.824769\pi\)
\(180\) −3.70410 −0.276087
\(181\) −14.7165 −1.09387 −0.546935 0.837175i \(-0.684205\pi\)
−0.546935 + 0.837175i \(0.684205\pi\)
\(182\) −0.787730 −0.0583904
\(183\) 9.49986 0.702250
\(184\) 7.06260 0.520662
\(185\) 6.60718 0.485769
\(186\) −22.0648 −1.61787
\(187\) −0.988092 −0.0722564
\(188\) −2.67032 −0.194753
\(189\) 0.462338 0.0336301
\(190\) −8.48779 −0.615769
\(191\) 3.37278 0.244046 0.122023 0.992527i \(-0.461062\pi\)
0.122023 + 0.992527i \(0.461062\pi\)
\(192\) −2.54862 −0.183931
\(193\) −2.70698 −0.194853 −0.0974265 0.995243i \(-0.531061\pi\)
−0.0974265 + 0.995243i \(0.531061\pi\)
\(194\) 6.51475 0.467732
\(195\) −5.81042 −0.416093
\(196\) −6.86594 −0.490424
\(197\) −8.37524 −0.596711 −0.298356 0.954455i \(-0.596438\pi\)
−0.298356 + 0.954455i \(0.596438\pi\)
\(198\) 1.15524 0.0820993
\(199\) −17.8799 −1.26747 −0.633737 0.773549i \(-0.718480\pi\)
−0.633737 + 0.773549i \(0.718480\pi\)
\(200\) 3.87705 0.274149
\(201\) −35.3360 −2.49241
\(202\) 10.3298 0.726805
\(203\) 0.892875 0.0626676
\(204\) −7.61961 −0.533479
\(205\) −5.55913 −0.388267
\(206\) −17.2839 −1.20423
\(207\) −24.6870 −1.71586
\(208\) −2.15141 −0.149173
\(209\) 2.64718 0.183109
\(210\) 0.988869 0.0682385
\(211\) 12.1439 0.836019 0.418009 0.908443i \(-0.362728\pi\)
0.418009 + 0.908443i \(0.362728\pi\)
\(212\) −9.83026 −0.675145
\(213\) 17.7216 1.21427
\(214\) 8.50588 0.581450
\(215\) −9.47651 −0.646293
\(216\) 1.26271 0.0859168
\(217\) 3.16993 0.215189
\(218\) 10.8442 0.734464
\(219\) 39.3354 2.65804
\(220\) 0.350226 0.0236123
\(221\) −6.43208 −0.432668
\(222\) −15.8906 −1.06651
\(223\) −19.6029 −1.31271 −0.656355 0.754452i \(-0.727903\pi\)
−0.656355 + 0.754452i \(0.727903\pi\)
\(224\) 0.366146 0.0244642
\(225\) −13.5520 −0.903470
\(226\) 5.24240 0.348719
\(227\) −14.7189 −0.976925 −0.488463 0.872585i \(-0.662442\pi\)
−0.488463 + 0.872585i \(0.662442\pi\)
\(228\) 20.4136 1.35192
\(229\) 25.3893 1.67777 0.838887 0.544305i \(-0.183207\pi\)
0.838887 + 0.544305i \(0.183207\pi\)
\(230\) −7.48418 −0.493492
\(231\) −0.308410 −0.0202919
\(232\) 2.43858 0.160100
\(233\) 21.4986 1.40842 0.704210 0.709992i \(-0.251302\pi\)
0.704210 + 0.709992i \(0.251302\pi\)
\(234\) 7.52015 0.491607
\(235\) 2.82972 0.184590
\(236\) 8.95349 0.582823
\(237\) −14.6319 −0.950442
\(238\) 1.09467 0.0709568
\(239\) 14.2698 0.923034 0.461517 0.887131i \(-0.347305\pi\)
0.461517 + 0.887131i \(0.347305\pi\)
\(240\) 2.70075 0.174333
\(241\) −15.4480 −0.995093 −0.497547 0.867437i \(-0.665766\pi\)
−0.497547 + 0.867437i \(0.665766\pi\)
\(242\) 10.8908 0.700085
\(243\) 22.3119 1.43131
\(244\) −3.72746 −0.238626
\(245\) 7.27578 0.464833
\(246\) 13.3700 0.852441
\(247\) 17.2321 1.09645
\(248\) 8.65756 0.549756
\(249\) 11.1362 0.705726
\(250\) −9.40694 −0.594947
\(251\) −16.6366 −1.05009 −0.525047 0.851073i \(-0.675952\pi\)
−0.525047 + 0.851073i \(0.675952\pi\)
\(252\) −1.27985 −0.0806227
\(253\) 2.33418 0.146748
\(254\) 17.7420 1.11323
\(255\) 8.07444 0.505641
\(256\) 1.00000 0.0625000
\(257\) 1.42749 0.0890445 0.0445222 0.999008i \(-0.485823\pi\)
0.0445222 + 0.999008i \(0.485823\pi\)
\(258\) 22.7915 1.41894
\(259\) 2.28292 0.141854
\(260\) 2.27983 0.141389
\(261\) −8.52392 −0.527618
\(262\) 2.76252 0.170669
\(263\) 5.94040 0.366301 0.183150 0.983085i \(-0.441370\pi\)
0.183150 + 0.983085i \(0.441370\pi\)
\(264\) −0.842314 −0.0518408
\(265\) 10.4171 0.639915
\(266\) −2.93271 −0.179816
\(267\) 1.97509 0.120874
\(268\) 13.8648 0.846926
\(269\) −20.6741 −1.26052 −0.630260 0.776384i \(-0.717052\pi\)
−0.630260 + 0.776384i \(0.717052\pi\)
\(270\) −1.33809 −0.0814334
\(271\) −0.938906 −0.0570345 −0.0285172 0.999593i \(-0.509079\pi\)
−0.0285172 + 0.999593i \(0.509079\pi\)
\(272\) 2.98970 0.181277
\(273\) −2.00762 −0.121507
\(274\) 3.43082 0.207263
\(275\) 1.28136 0.0772688
\(276\) 17.9999 1.08346
\(277\) −12.3029 −0.739210 −0.369605 0.929189i \(-0.620507\pi\)
−0.369605 + 0.929189i \(0.620507\pi\)
\(278\) −2.55804 −0.153421
\(279\) −30.2621 −1.81174
\(280\) −0.388002 −0.0231876
\(281\) 5.33996 0.318555 0.159278 0.987234i \(-0.449083\pi\)
0.159278 + 0.987234i \(0.449083\pi\)
\(282\) −6.80563 −0.405269
\(283\) 13.5917 0.807943 0.403971 0.914772i \(-0.367630\pi\)
0.403971 + 0.914772i \(0.367630\pi\)
\(284\) −6.95344 −0.412610
\(285\) −21.6321 −1.28138
\(286\) −0.711037 −0.0420445
\(287\) −1.92080 −0.113381
\(288\) −3.49545 −0.205971
\(289\) −8.06168 −0.474216
\(290\) −2.58414 −0.151746
\(291\) 16.6036 0.973320
\(292\) −15.4340 −0.903207
\(293\) −25.0194 −1.46165 −0.730823 0.682567i \(-0.760864\pi\)
−0.730823 + 0.682567i \(0.760864\pi\)
\(294\) −17.4986 −1.02054
\(295\) −9.48795 −0.552410
\(296\) 6.23500 0.362402
\(297\) 0.417325 0.0242156
\(298\) 8.31160 0.481478
\(299\) 15.1945 0.878723
\(300\) 9.88112 0.570487
\(301\) −3.27433 −0.188729
\(302\) −14.9476 −0.860137
\(303\) 26.3268 1.51244
\(304\) −8.00967 −0.459386
\(305\) 3.94996 0.226174
\(306\) −10.4504 −0.597407
\(307\) 13.4626 0.768353 0.384177 0.923260i \(-0.374485\pi\)
0.384177 + 0.923260i \(0.374485\pi\)
\(308\) 0.121011 0.00689522
\(309\) −44.0501 −2.50592
\(310\) −9.17436 −0.521068
\(311\) −26.4013 −1.49708 −0.748541 0.663088i \(-0.769245\pi\)
−0.748541 + 0.663088i \(0.769245\pi\)
\(312\) −5.48312 −0.310421
\(313\) 22.3747 1.26469 0.632347 0.774686i \(-0.282092\pi\)
0.632347 + 0.774686i \(0.282092\pi\)
\(314\) 16.7138 0.943213
\(315\) 1.35624 0.0764156
\(316\) 5.74110 0.322962
\(317\) 20.0705 1.12727 0.563636 0.826023i \(-0.309402\pi\)
0.563636 + 0.826023i \(0.309402\pi\)
\(318\) −25.0536 −1.40493
\(319\) 0.805945 0.0451243
\(320\) −1.05969 −0.0592386
\(321\) 21.6782 1.20996
\(322\) −2.58594 −0.144109
\(323\) −23.9465 −1.33242
\(324\) −7.26818 −0.403788
\(325\) 8.34113 0.462682
\(326\) −18.4268 −1.02057
\(327\) 27.6378 1.52837
\(328\) −5.24599 −0.289661
\(329\) 0.977727 0.0539039
\(330\) 0.892593 0.0491356
\(331\) 1.67062 0.0918257 0.0459129 0.998945i \(-0.485380\pi\)
0.0459129 + 0.998945i \(0.485380\pi\)
\(332\) −4.36949 −0.239807
\(333\) −21.7941 −1.19431
\(334\) 20.2855 1.10997
\(335\) −14.6924 −0.802732
\(336\) 0.933166 0.0509084
\(337\) 7.19091 0.391714 0.195857 0.980633i \(-0.437251\pi\)
0.195857 + 0.980633i \(0.437251\pi\)
\(338\) 8.37144 0.455346
\(339\) 13.3609 0.725662
\(340\) −3.16817 −0.171818
\(341\) 2.86131 0.154949
\(342\) 27.9974 1.51393
\(343\) 5.07696 0.274130
\(344\) −8.94270 −0.482158
\(345\) −19.0743 −1.02693
\(346\) −13.6654 −0.734655
\(347\) −19.6921 −1.05713 −0.528565 0.848893i \(-0.677270\pi\)
−0.528565 + 0.848893i \(0.677270\pi\)
\(348\) 6.21500 0.333159
\(349\) 23.1445 1.23890 0.619448 0.785038i \(-0.287357\pi\)
0.619448 + 0.785038i \(0.287357\pi\)
\(350\) −1.41957 −0.0758791
\(351\) 2.71661 0.145002
\(352\) 0.330498 0.0176156
\(353\) −1.35810 −0.0722842 −0.0361421 0.999347i \(-0.511507\pi\)
−0.0361421 + 0.999347i \(0.511507\pi\)
\(354\) 22.8190 1.21282
\(355\) 7.36850 0.391080
\(356\) −0.774967 −0.0410732
\(357\) 2.78989 0.147657
\(358\) 22.8049 1.20528
\(359\) −10.7991 −0.569954 −0.284977 0.958534i \(-0.591986\pi\)
−0.284977 + 0.958534i \(0.591986\pi\)
\(360\) 3.70410 0.195223
\(361\) 45.1548 2.37657
\(362\) 14.7165 0.773482
\(363\) 27.7564 1.45683
\(364\) 0.787730 0.0412883
\(365\) 16.3553 0.856076
\(366\) −9.49986 −0.496566
\(367\) −11.8639 −0.619290 −0.309645 0.950852i \(-0.600210\pi\)
−0.309645 + 0.950852i \(0.600210\pi\)
\(368\) −7.06260 −0.368163
\(369\) 18.3371 0.954591
\(370\) −6.60718 −0.343491
\(371\) 3.59931 0.186867
\(372\) 22.0648 1.14401
\(373\) 6.60210 0.341844 0.170922 0.985285i \(-0.445325\pi\)
0.170922 + 0.985285i \(0.445325\pi\)
\(374\) 0.988092 0.0510930
\(375\) −23.9747 −1.23805
\(376\) 2.67032 0.137711
\(377\) 5.24638 0.270202
\(378\) −0.462338 −0.0237801
\(379\) 9.40309 0.483004 0.241502 0.970400i \(-0.422360\pi\)
0.241502 + 0.970400i \(0.422360\pi\)
\(380\) 8.48779 0.435414
\(381\) 45.2177 2.31657
\(382\) −3.37278 −0.172566
\(383\) −2.72237 −0.139106 −0.0695532 0.997578i \(-0.522157\pi\)
−0.0695532 + 0.997578i \(0.522157\pi\)
\(384\) 2.54862 0.130059
\(385\) −0.128234 −0.00653541
\(386\) 2.70698 0.137782
\(387\) 31.2588 1.58897
\(388\) −6.51475 −0.330736
\(389\) −15.1828 −0.769799 −0.384899 0.922959i \(-0.625764\pi\)
−0.384899 + 0.922959i \(0.625764\pi\)
\(390\) 5.81042 0.294222
\(391\) −21.1151 −1.06784
\(392\) 6.86594 0.346782
\(393\) 7.04060 0.355152
\(394\) 8.37524 0.421939
\(395\) −6.08380 −0.306109
\(396\) −1.15524 −0.0580530
\(397\) 3.09801 0.155485 0.0777424 0.996973i \(-0.475229\pi\)
0.0777424 + 0.996973i \(0.475229\pi\)
\(398\) 17.8799 0.896239
\(399\) −7.47436 −0.374186
\(400\) −3.87705 −0.193853
\(401\) 2.08597 0.104169 0.0520843 0.998643i \(-0.483414\pi\)
0.0520843 + 0.998643i \(0.483414\pi\)
\(402\) 35.3360 1.76240
\(403\) 18.6260 0.927825
\(404\) −10.3298 −0.513929
\(405\) 7.70203 0.382717
\(406\) −0.892875 −0.0443127
\(407\) 2.06066 0.102143
\(408\) 7.61961 0.377227
\(409\) −13.4996 −0.667514 −0.333757 0.942659i \(-0.608316\pi\)
−0.333757 + 0.942659i \(0.608316\pi\)
\(410\) 5.55913 0.274546
\(411\) 8.74384 0.431302
\(412\) 17.2839 0.851518
\(413\) −3.27829 −0.161314
\(414\) 24.6870 1.21330
\(415\) 4.63032 0.227293
\(416\) 2.15141 0.105482
\(417\) −6.51946 −0.319259
\(418\) −2.64718 −0.129478
\(419\) 12.6852 0.619714 0.309857 0.950783i \(-0.399719\pi\)
0.309857 + 0.950783i \(0.399719\pi\)
\(420\) −0.988869 −0.0482519
\(421\) −25.0748 −1.22207 −0.611035 0.791604i \(-0.709247\pi\)
−0.611035 + 0.791604i \(0.709247\pi\)
\(422\) −12.1439 −0.591155
\(423\) −9.33397 −0.453833
\(424\) 9.83026 0.477400
\(425\) −11.5912 −0.562257
\(426\) −17.7216 −0.858617
\(427\) 1.36479 0.0660470
\(428\) −8.50588 −0.411147
\(429\) −1.81216 −0.0874920
\(430\) 9.47651 0.456998
\(431\) −22.5872 −1.08799 −0.543993 0.839090i \(-0.683088\pi\)
−0.543993 + 0.839090i \(0.683088\pi\)
\(432\) −1.26271 −0.0607523
\(433\) 7.18379 0.345231 0.172615 0.984989i \(-0.444778\pi\)
0.172615 + 0.984989i \(0.444778\pi\)
\(434\) −3.16993 −0.152162
\(435\) −6.58599 −0.315774
\(436\) −10.8442 −0.519345
\(437\) 56.5691 2.70607
\(438\) −39.3354 −1.87952
\(439\) −15.5591 −0.742596 −0.371298 0.928514i \(-0.621087\pi\)
−0.371298 + 0.928514i \(0.621087\pi\)
\(440\) −0.350226 −0.0166964
\(441\) −23.9995 −1.14284
\(442\) 6.43208 0.305943
\(443\) 11.8115 0.561180 0.280590 0.959828i \(-0.409470\pi\)
0.280590 + 0.959828i \(0.409470\pi\)
\(444\) 15.8906 0.754136
\(445\) 0.821227 0.0389299
\(446\) 19.6029 0.928226
\(447\) 21.1831 1.00193
\(448\) −0.366146 −0.0172988
\(449\) −39.4386 −1.86122 −0.930611 0.366010i \(-0.880724\pi\)
−0.930611 + 0.366010i \(0.880724\pi\)
\(450\) 13.5520 0.638849
\(451\) −1.73379 −0.0816410
\(452\) −5.24240 −0.246582
\(453\) −38.0957 −1.78989
\(454\) 14.7189 0.690791
\(455\) −0.834752 −0.0391338
\(456\) −20.4136 −0.955954
\(457\) −8.03841 −0.376021 −0.188010 0.982167i \(-0.560204\pi\)
−0.188010 + 0.982167i \(0.560204\pi\)
\(458\) −25.3893 −1.18637
\(459\) −3.77514 −0.176208
\(460\) 7.48418 0.348952
\(461\) 1.68334 0.0784008 0.0392004 0.999231i \(-0.487519\pi\)
0.0392004 + 0.999231i \(0.487519\pi\)
\(462\) 0.308410 0.0143485
\(463\) 15.6386 0.726786 0.363393 0.931636i \(-0.381618\pi\)
0.363393 + 0.931636i \(0.381618\pi\)
\(464\) −2.43858 −0.113208
\(465\) −23.3819 −1.08431
\(466\) −21.4986 −0.995903
\(467\) 27.6720 1.28051 0.640255 0.768163i \(-0.278829\pi\)
0.640255 + 0.768163i \(0.278829\pi\)
\(468\) −7.52015 −0.347619
\(469\) −5.07653 −0.234413
\(470\) −2.82972 −0.130525
\(471\) 42.5970 1.96277
\(472\) −8.95349 −0.412118
\(473\) −2.95555 −0.135896
\(474\) 14.6319 0.672064
\(475\) 31.0539 1.42485
\(476\) −1.09467 −0.0501740
\(477\) −34.3612 −1.57329
\(478\) −14.2698 −0.652684
\(479\) −31.5909 −1.44342 −0.721712 0.692194i \(-0.756644\pi\)
−0.721712 + 0.692194i \(0.756644\pi\)
\(480\) −2.70075 −0.123272
\(481\) 13.4140 0.611627
\(482\) 15.4480 0.703637
\(483\) −6.59058 −0.299882
\(484\) −10.8908 −0.495035
\(485\) 6.90363 0.313478
\(486\) −22.3119 −1.01209
\(487\) −4.10339 −0.185942 −0.0929712 0.995669i \(-0.529636\pi\)
−0.0929712 + 0.995669i \(0.529636\pi\)
\(488\) 3.72746 0.168734
\(489\) −46.9628 −2.12373
\(490\) −7.27578 −0.328686
\(491\) −4.83659 −0.218272 −0.109136 0.994027i \(-0.534808\pi\)
−0.109136 + 0.994027i \(0.534808\pi\)
\(492\) −13.3700 −0.602767
\(493\) −7.29062 −0.328353
\(494\) −17.2321 −0.775308
\(495\) 1.22420 0.0550237
\(496\) −8.65756 −0.388736
\(497\) 2.54597 0.114202
\(498\) −11.1362 −0.499023
\(499\) 7.24316 0.324248 0.162124 0.986770i \(-0.448166\pi\)
0.162124 + 0.986770i \(0.448166\pi\)
\(500\) 9.40694 0.420691
\(501\) 51.6999 2.30978
\(502\) 16.6366 0.742529
\(503\) 7.47134 0.333130 0.166565 0.986030i \(-0.446732\pi\)
0.166565 + 0.986030i \(0.446732\pi\)
\(504\) 1.27985 0.0570088
\(505\) 10.9464 0.487111
\(506\) −2.33418 −0.103767
\(507\) 21.3356 0.947547
\(508\) −17.7420 −0.787176
\(509\) −43.1162 −1.91109 −0.955546 0.294844i \(-0.904732\pi\)
−0.955546 + 0.294844i \(0.904732\pi\)
\(510\) −8.07444 −0.357542
\(511\) 5.65110 0.249990
\(512\) −1.00000 −0.0441942
\(513\) 10.1139 0.446541
\(514\) −1.42749 −0.0629640
\(515\) −18.3156 −0.807084
\(516\) −22.7915 −1.00334
\(517\) 0.882536 0.0388139
\(518\) −2.28292 −0.100306
\(519\) −34.8278 −1.52877
\(520\) −2.27983 −0.0999773
\(521\) 30.9573 1.35626 0.678132 0.734940i \(-0.262790\pi\)
0.678132 + 0.734940i \(0.262790\pi\)
\(522\) 8.52392 0.373082
\(523\) 36.1888 1.58243 0.791213 0.611540i \(-0.209450\pi\)
0.791213 + 0.611540i \(0.209450\pi\)
\(524\) −2.76252 −0.120681
\(525\) −3.61793 −0.157900
\(526\) −5.94040 −0.259014
\(527\) −25.8835 −1.12750
\(528\) 0.842314 0.0366570
\(529\) 26.8803 1.16871
\(530\) −10.4171 −0.452488
\(531\) 31.2965 1.35815
\(532\) 2.93271 0.127149
\(533\) −11.2863 −0.488863
\(534\) −1.97509 −0.0854707
\(535\) 9.01361 0.389693
\(536\) −13.8648 −0.598867
\(537\) 58.1210 2.50811
\(538\) 20.6741 0.891322
\(539\) 2.26918 0.0977405
\(540\) 1.33809 0.0575821
\(541\) 34.8984 1.50040 0.750200 0.661211i \(-0.229957\pi\)
0.750200 + 0.661211i \(0.229957\pi\)
\(542\) 0.938906 0.0403295
\(543\) 37.5067 1.60957
\(544\) −2.98970 −0.128182
\(545\) 11.4916 0.492244
\(546\) 2.00762 0.0859183
\(547\) 34.3162 1.46725 0.733627 0.679553i \(-0.237826\pi\)
0.733627 + 0.679553i \(0.237826\pi\)
\(548\) −3.43082 −0.146557
\(549\) −13.0291 −0.556070
\(550\) −1.28136 −0.0546373
\(551\) 19.5322 0.832100
\(552\) −17.9999 −0.766125
\(553\) −2.10208 −0.0893896
\(554\) 12.3029 0.522700
\(555\) −16.8392 −0.714783
\(556\) 2.55804 0.108485
\(557\) −32.5766 −1.38031 −0.690157 0.723660i \(-0.742459\pi\)
−0.690157 + 0.723660i \(0.742459\pi\)
\(558\) 30.2621 1.28110
\(559\) −19.2394 −0.813740
\(560\) 0.388002 0.0163961
\(561\) 2.51827 0.106321
\(562\) −5.33996 −0.225253
\(563\) 38.8319 1.63657 0.818284 0.574814i \(-0.194925\pi\)
0.818284 + 0.574814i \(0.194925\pi\)
\(564\) 6.80563 0.286569
\(565\) 5.55533 0.233714
\(566\) −13.5917 −0.571302
\(567\) 2.66121 0.111761
\(568\) 6.95344 0.291760
\(569\) 6.29532 0.263913 0.131957 0.991255i \(-0.457874\pi\)
0.131957 + 0.991255i \(0.457874\pi\)
\(570\) 21.6321 0.906070
\(571\) −14.9014 −0.623606 −0.311803 0.950147i \(-0.600933\pi\)
−0.311803 + 0.950147i \(0.600933\pi\)
\(572\) 0.711037 0.0297300
\(573\) −8.59592 −0.359100
\(574\) 1.92080 0.0801726
\(575\) 27.3821 1.14191
\(576\) 3.49545 0.145644
\(577\) 4.65194 0.193663 0.0968315 0.995301i \(-0.469129\pi\)
0.0968315 + 0.995301i \(0.469129\pi\)
\(578\) 8.06168 0.335322
\(579\) 6.89907 0.286715
\(580\) 2.58414 0.107301
\(581\) 1.59987 0.0663739
\(582\) −16.6036 −0.688241
\(583\) 3.24888 0.134555
\(584\) 15.4340 0.638664
\(585\) 7.96904 0.329479
\(586\) 25.0194 1.03354
\(587\) 23.8958 0.986284 0.493142 0.869949i \(-0.335848\pi\)
0.493142 + 0.869949i \(0.335848\pi\)
\(588\) 17.4986 0.721632
\(589\) 69.3442 2.85728
\(590\) 9.48795 0.390613
\(591\) 21.3453 0.878028
\(592\) −6.23500 −0.256257
\(593\) 14.2096 0.583520 0.291760 0.956492i \(-0.405759\pi\)
0.291760 + 0.956492i \(0.405759\pi\)
\(594\) −0.417325 −0.0171230
\(595\) 1.16001 0.0475558
\(596\) −8.31160 −0.340456
\(597\) 45.5690 1.86502
\(598\) −15.1945 −0.621351
\(599\) −16.9127 −0.691035 −0.345517 0.938412i \(-0.612297\pi\)
−0.345517 + 0.938412i \(0.612297\pi\)
\(600\) −9.88112 −0.403395
\(601\) −23.6271 −0.963769 −0.481884 0.876235i \(-0.660048\pi\)
−0.481884 + 0.876235i \(0.660048\pi\)
\(602\) 3.27433 0.133452
\(603\) 48.4636 1.97359
\(604\) 14.9476 0.608209
\(605\) 11.5409 0.469203
\(606\) −26.3268 −1.06945
\(607\) −2.82393 −0.114620 −0.0573099 0.998356i \(-0.518252\pi\)
−0.0573099 + 0.998356i \(0.518252\pi\)
\(608\) 8.00967 0.324835
\(609\) −2.27560 −0.0922119
\(610\) −3.94996 −0.159929
\(611\) 5.74495 0.232416
\(612\) 10.4504 0.422431
\(613\) −21.5454 −0.870210 −0.435105 0.900380i \(-0.643289\pi\)
−0.435105 + 0.900380i \(0.643289\pi\)
\(614\) −13.4626 −0.543308
\(615\) 14.1681 0.571313
\(616\) −0.121011 −0.00487566
\(617\) 31.3867 1.26358 0.631791 0.775139i \(-0.282320\pi\)
0.631791 + 0.775139i \(0.282320\pi\)
\(618\) 44.0501 1.77196
\(619\) 21.5477 0.866075 0.433038 0.901376i \(-0.357442\pi\)
0.433038 + 0.901376i \(0.357442\pi\)
\(620\) 9.17436 0.368451
\(621\) 8.91804 0.357869
\(622\) 26.4013 1.05860
\(623\) 0.283751 0.0113683
\(624\) 5.48312 0.219500
\(625\) 9.41679 0.376672
\(626\) −22.3747 −0.894273
\(627\) −6.74665 −0.269435
\(628\) −16.7138 −0.666952
\(629\) −18.6408 −0.743257
\(630\) −1.35624 −0.0540340
\(631\) 29.5610 1.17680 0.588402 0.808568i \(-0.299757\pi\)
0.588402 + 0.808568i \(0.299757\pi\)
\(632\) −5.74110 −0.228369
\(633\) −30.9501 −1.23016
\(634\) −20.0705 −0.797101
\(635\) 18.8011 0.746099
\(636\) 25.0536 0.993439
\(637\) 14.7714 0.585266
\(638\) −0.805945 −0.0319077
\(639\) −24.3054 −0.961506
\(640\) 1.05969 0.0418880
\(641\) −3.11296 −0.122955 −0.0614774 0.998108i \(-0.519581\pi\)
−0.0614774 + 0.998108i \(0.519581\pi\)
\(642\) −21.6782 −0.855571
\(643\) −29.9587 −1.18146 −0.590728 0.806871i \(-0.701159\pi\)
−0.590728 + 0.806871i \(0.701159\pi\)
\(644\) 2.58594 0.101900
\(645\) 24.1520 0.950984
\(646\) 23.9465 0.942164
\(647\) −48.0370 −1.88853 −0.944265 0.329188i \(-0.893225\pi\)
−0.944265 + 0.329188i \(0.893225\pi\)
\(648\) 7.26818 0.285521
\(649\) −2.95911 −0.116155
\(650\) −8.34113 −0.327166
\(651\) −8.07895 −0.316639
\(652\) 18.4268 0.721649
\(653\) 46.6806 1.82675 0.913376 0.407118i \(-0.133466\pi\)
0.913376 + 0.407118i \(0.133466\pi\)
\(654\) −27.6378 −1.08072
\(655\) 2.92742 0.114384
\(656\) 5.24599 0.204821
\(657\) −53.9488 −2.10474
\(658\) −0.977727 −0.0381158
\(659\) −13.1787 −0.513370 −0.256685 0.966495i \(-0.582630\pi\)
−0.256685 + 0.966495i \(0.582630\pi\)
\(660\) −0.892593 −0.0347441
\(661\) 15.8645 0.617057 0.308528 0.951215i \(-0.400164\pi\)
0.308528 + 0.951215i \(0.400164\pi\)
\(662\) −1.67062 −0.0649306
\(663\) 16.3929 0.636647
\(664\) 4.36949 0.169569
\(665\) −3.10777 −0.120514
\(666\) 21.7941 0.844505
\(667\) 17.2227 0.666865
\(668\) −20.2855 −0.784869
\(669\) 49.9604 1.93158
\(670\) 14.6924 0.567617
\(671\) 1.23192 0.0475577
\(672\) −0.933166 −0.0359977
\(673\) 16.8205 0.648384 0.324192 0.945991i \(-0.394908\pi\)
0.324192 + 0.945991i \(0.394908\pi\)
\(674\) −7.19091 −0.276983
\(675\) 4.89561 0.188432
\(676\) −8.37144 −0.321978
\(677\) −24.3155 −0.934519 −0.467260 0.884120i \(-0.654759\pi\)
−0.467260 + 0.884120i \(0.654759\pi\)
\(678\) −13.3609 −0.513121
\(679\) 2.38535 0.0915413
\(680\) 3.16817 0.121494
\(681\) 37.5128 1.43749
\(682\) −2.86131 −0.109565
\(683\) 36.1274 1.38238 0.691188 0.722675i \(-0.257087\pi\)
0.691188 + 0.722675i \(0.257087\pi\)
\(684\) −27.9974 −1.07051
\(685\) 3.63561 0.138909
\(686\) −5.07696 −0.193839
\(687\) −64.7077 −2.46875
\(688\) 8.94270 0.340937
\(689\) 21.1489 0.805710
\(690\) 19.0743 0.726147
\(691\) 8.41715 0.320204 0.160102 0.987101i \(-0.448818\pi\)
0.160102 + 0.987101i \(0.448818\pi\)
\(692\) 13.6654 0.519479
\(693\) 0.422987 0.0160679
\(694\) 19.6921 0.747504
\(695\) −2.71073 −0.102824
\(696\) −6.21500 −0.235579
\(697\) 15.6839 0.594072
\(698\) −23.1445 −0.876031
\(699\) −54.7917 −2.07241
\(700\) 1.41957 0.0536546
\(701\) −33.3448 −1.25942 −0.629708 0.776832i \(-0.716825\pi\)
−0.629708 + 0.776832i \(0.716825\pi\)
\(702\) −2.71661 −0.102532
\(703\) 49.9403 1.88353
\(704\) −0.330498 −0.0124561
\(705\) −7.21187 −0.271615
\(706\) 1.35810 0.0511126
\(707\) 3.78223 0.142245
\(708\) −22.8190 −0.857592
\(709\) 38.4715 1.44483 0.722413 0.691462i \(-0.243033\pi\)
0.722413 + 0.691462i \(0.243033\pi\)
\(710\) −7.36850 −0.276535
\(711\) 20.0677 0.752599
\(712\) 0.774967 0.0290431
\(713\) 61.1449 2.28989
\(714\) −2.78989 −0.104409
\(715\) −0.753481 −0.0281786
\(716\) −22.8049 −0.852260
\(717\) −36.3682 −1.35819
\(718\) 10.7991 0.403018
\(719\) 20.5776 0.767416 0.383708 0.923454i \(-0.374647\pi\)
0.383708 + 0.923454i \(0.374647\pi\)
\(720\) −3.70410 −0.138044
\(721\) −6.32844 −0.235683
\(722\) −45.1548 −1.68049
\(723\) 39.3710 1.46422
\(724\) −14.7165 −0.546935
\(725\) 9.45449 0.351131
\(726\) −27.7564 −1.03014
\(727\) −9.44500 −0.350296 −0.175148 0.984542i \(-0.556040\pi\)
−0.175148 + 0.984542i \(0.556040\pi\)
\(728\) −0.787730 −0.0291952
\(729\) −35.0601 −1.29852
\(730\) −16.3553 −0.605337
\(731\) 26.7360 0.988867
\(732\) 9.49986 0.351125
\(733\) 8.98357 0.331816 0.165908 0.986141i \(-0.446945\pi\)
0.165908 + 0.986141i \(0.446945\pi\)
\(734\) 11.8639 0.437905
\(735\) −18.5432 −0.683976
\(736\) 7.06260 0.260331
\(737\) −4.58228 −0.168791
\(738\) −18.3371 −0.674998
\(739\) −12.5226 −0.460651 −0.230326 0.973114i \(-0.573979\pi\)
−0.230326 + 0.973114i \(0.573979\pi\)
\(740\) 6.60718 0.242885
\(741\) −43.9180 −1.61337
\(742\) −3.59931 −0.132135
\(743\) 31.5382 1.15703 0.578513 0.815674i \(-0.303633\pi\)
0.578513 + 0.815674i \(0.303633\pi\)
\(744\) −22.0648 −0.808936
\(745\) 8.80774 0.322691
\(746\) −6.60210 −0.241720
\(747\) −15.2733 −0.558822
\(748\) −0.988092 −0.0361282
\(749\) 3.11439 0.113797
\(750\) 23.9747 0.875432
\(751\) −29.9161 −1.09165 −0.545826 0.837898i \(-0.683784\pi\)
−0.545826 + 0.837898i \(0.683784\pi\)
\(752\) −2.67032 −0.0973766
\(753\) 42.4004 1.54516
\(754\) −5.24638 −0.191062
\(755\) −15.8399 −0.576471
\(756\) 0.462338 0.0168151
\(757\) 51.6813 1.87839 0.939195 0.343385i \(-0.111573\pi\)
0.939195 + 0.343385i \(0.111573\pi\)
\(758\) −9.40309 −0.341536
\(759\) −5.94892 −0.215932
\(760\) −8.48779 −0.307884
\(761\) −17.0393 −0.617673 −0.308837 0.951115i \(-0.599940\pi\)
−0.308837 + 0.951115i \(0.599940\pi\)
\(762\) −45.2177 −1.63806
\(763\) 3.97057 0.143744
\(764\) 3.37278 0.122023
\(765\) −11.0742 −0.400387
\(766\) 2.72237 0.0983631
\(767\) −19.2626 −0.695533
\(768\) −2.54862 −0.0919653
\(769\) 9.90111 0.357043 0.178522 0.983936i \(-0.442869\pi\)
0.178522 + 0.983936i \(0.442869\pi\)
\(770\) 0.128234 0.00462123
\(771\) −3.63813 −0.131024
\(772\) −2.70698 −0.0974265
\(773\) −2.81430 −0.101224 −0.0506118 0.998718i \(-0.516117\pi\)
−0.0506118 + 0.998718i \(0.516117\pi\)
\(774\) −31.2588 −1.12357
\(775\) 33.5658 1.20572
\(776\) 6.51475 0.233866
\(777\) −5.81829 −0.208730
\(778\) 15.1828 0.544330
\(779\) −42.0186 −1.50547
\(780\) −5.81042 −0.208046
\(781\) 2.29810 0.0822324
\(782\) 21.1151 0.755073
\(783\) 3.07922 0.110043
\(784\) −6.86594 −0.245212
\(785\) 17.7115 0.632149
\(786\) −7.04060 −0.251130
\(787\) 15.1718 0.540815 0.270408 0.962746i \(-0.412842\pi\)
0.270408 + 0.962746i \(0.412842\pi\)
\(788\) −8.37524 −0.298356
\(789\) −15.1398 −0.538991
\(790\) 6.08380 0.216452
\(791\) 1.91948 0.0682490
\(792\) 1.15524 0.0410497
\(793\) 8.01929 0.284773
\(794\) −3.09801 −0.109944
\(795\) −26.5491 −0.941599
\(796\) −17.8799 −0.633737
\(797\) 41.2589 1.46146 0.730732 0.682664i \(-0.239179\pi\)
0.730732 + 0.682664i \(0.239179\pi\)
\(798\) 7.47436 0.264589
\(799\) −7.98347 −0.282435
\(800\) 3.87705 0.137074
\(801\) −2.70886 −0.0957128
\(802\) −2.08597 −0.0736583
\(803\) 5.10091 0.180007
\(804\) −35.3360 −1.24621
\(805\) −2.74030 −0.0965830
\(806\) −18.6260 −0.656072
\(807\) 52.6903 1.85479
\(808\) 10.3298 0.363402
\(809\) 28.6529 1.00738 0.503691 0.863884i \(-0.331975\pi\)
0.503691 + 0.863884i \(0.331975\pi\)
\(810\) −7.70203 −0.270622
\(811\) 24.5042 0.860457 0.430229 0.902720i \(-0.358433\pi\)
0.430229 + 0.902720i \(0.358433\pi\)
\(812\) 0.892875 0.0313338
\(813\) 2.39291 0.0839231
\(814\) −2.06066 −0.0722259
\(815\) −19.5267 −0.683992
\(816\) −7.61961 −0.266740
\(817\) −71.6281 −2.50595
\(818\) 13.4996 0.472003
\(819\) 2.75347 0.0962141
\(820\) −5.55913 −0.194133
\(821\) 11.0710 0.386381 0.193191 0.981161i \(-0.438116\pi\)
0.193191 + 0.981161i \(0.438116\pi\)
\(822\) −8.74384 −0.304976
\(823\) −36.2138 −1.26233 −0.631167 0.775647i \(-0.717424\pi\)
−0.631167 + 0.775647i \(0.717424\pi\)
\(824\) −17.2839 −0.602114
\(825\) −3.26569 −0.113697
\(826\) 3.27829 0.114066
\(827\) −34.5386 −1.20103 −0.600513 0.799615i \(-0.705037\pi\)
−0.600513 + 0.799615i \(0.705037\pi\)
\(828\) −24.6870 −0.857931
\(829\) 25.0908 0.871439 0.435720 0.900082i \(-0.356494\pi\)
0.435720 + 0.900082i \(0.356494\pi\)
\(830\) −4.63032 −0.160721
\(831\) 31.3554 1.08771
\(832\) −2.15141 −0.0745867
\(833\) −20.5271 −0.711222
\(834\) 6.51946 0.225750
\(835\) 21.4964 0.743913
\(836\) 2.64718 0.0915547
\(837\) 10.9320 0.377866
\(838\) −12.6852 −0.438204
\(839\) −22.6697 −0.782645 −0.391323 0.920254i \(-0.627982\pi\)
−0.391323 + 0.920254i \(0.627982\pi\)
\(840\) 0.988869 0.0341192
\(841\) −23.0533 −0.794943
\(842\) 25.0748 0.864134
\(843\) −13.6095 −0.468737
\(844\) 12.1439 0.418009
\(845\) 8.87115 0.305177
\(846\) 9.33397 0.320909
\(847\) 3.98761 0.137016
\(848\) −9.83026 −0.337573
\(849\) −34.6400 −1.18884
\(850\) 11.5912 0.397576
\(851\) 44.0353 1.50951
\(852\) 17.7216 0.607134
\(853\) −26.4036 −0.904042 −0.452021 0.892007i \(-0.649297\pi\)
−0.452021 + 0.892007i \(0.649297\pi\)
\(854\) −1.36479 −0.0467023
\(855\) 29.6686 1.01465
\(856\) 8.50588 0.290725
\(857\) −43.9697 −1.50198 −0.750988 0.660316i \(-0.770423\pi\)
−0.750988 + 0.660316i \(0.770423\pi\)
\(858\) 1.81216 0.0618662
\(859\) −42.2380 −1.44114 −0.720571 0.693381i \(-0.756120\pi\)
−0.720571 + 0.693381i \(0.756120\pi\)
\(860\) −9.47651 −0.323146
\(861\) 4.89538 0.166834
\(862\) 22.5872 0.769322
\(863\) 43.1074 1.46739 0.733696 0.679477i \(-0.237793\pi\)
0.733696 + 0.679477i \(0.237793\pi\)
\(864\) 1.26271 0.0429584
\(865\) −14.4811 −0.492372
\(866\) −7.18379 −0.244115
\(867\) 20.5461 0.697783
\(868\) 3.16993 0.107595
\(869\) −1.89742 −0.0643657
\(870\) 6.58599 0.223286
\(871\) −29.8288 −1.01071
\(872\) 10.8442 0.367232
\(873\) −22.7720 −0.770715
\(874\) −56.5691 −1.91348
\(875\) −3.44432 −0.116439
\(876\) 39.3354 1.32902
\(877\) 27.8161 0.939284 0.469642 0.882857i \(-0.344383\pi\)
0.469642 + 0.882857i \(0.344383\pi\)
\(878\) 15.5591 0.525095
\(879\) 63.7648 2.15073
\(880\) 0.350226 0.0118061
\(881\) −24.6494 −0.830460 −0.415230 0.909716i \(-0.636299\pi\)
−0.415230 + 0.909716i \(0.636299\pi\)
\(882\) 23.9995 0.808107
\(883\) 58.3109 1.96232 0.981159 0.193204i \(-0.0618880\pi\)
0.981159 + 0.193204i \(0.0618880\pi\)
\(884\) −6.43208 −0.216334
\(885\) 24.1811 0.812840
\(886\) −11.8115 −0.396814
\(887\) 13.8987 0.466672 0.233336 0.972396i \(-0.425036\pi\)
0.233336 + 0.972396i \(0.425036\pi\)
\(888\) −15.8906 −0.533254
\(889\) 6.49618 0.217875
\(890\) −0.821227 −0.0275276
\(891\) 2.40212 0.0804740
\(892\) −19.6029 −0.656355
\(893\) 21.3884 0.715735
\(894\) −21.1831 −0.708468
\(895\) 24.1662 0.807787
\(896\) 0.366146 0.0122321
\(897\) −38.7251 −1.29299
\(898\) 39.4386 1.31608
\(899\) 21.1121 0.704129
\(900\) −13.5520 −0.451735
\(901\) −29.3896 −0.979108
\(902\) 1.73379 0.0577289
\(903\) 8.34502 0.277705
\(904\) 5.24240 0.174360
\(905\) 15.5950 0.518394
\(906\) 38.0957 1.26564
\(907\) −27.5844 −0.915924 −0.457962 0.888972i \(-0.651420\pi\)
−0.457962 + 0.888972i \(0.651420\pi\)
\(908\) −14.7189 −0.488463
\(909\) −36.1074 −1.19761
\(910\) 0.834752 0.0276717
\(911\) 35.3576 1.17145 0.585725 0.810510i \(-0.300810\pi\)
0.585725 + 0.810510i \(0.300810\pi\)
\(912\) 20.4136 0.675961
\(913\) 1.44411 0.0477930
\(914\) 8.03841 0.265887
\(915\) −10.0669 −0.332803
\(916\) 25.3893 0.838887
\(917\) 1.01149 0.0334022
\(918\) 3.77514 0.124598
\(919\) 18.8639 0.622262 0.311131 0.950367i \(-0.399292\pi\)
0.311131 + 0.950367i \(0.399292\pi\)
\(920\) −7.48418 −0.246746
\(921\) −34.3111 −1.13059
\(922\) −1.68334 −0.0554377
\(923\) 14.9597 0.492404
\(924\) −0.308410 −0.0101459
\(925\) 24.1734 0.794817
\(926\) −15.6386 −0.513915
\(927\) 60.4151 1.98429
\(928\) 2.43858 0.0800502
\(929\) −46.8990 −1.53871 −0.769353 0.638824i \(-0.779421\pi\)
−0.769353 + 0.638824i \(0.779421\pi\)
\(930\) 23.3819 0.766723
\(931\) 54.9939 1.80235
\(932\) 21.4986 0.704210
\(933\) 67.2869 2.20287
\(934\) −27.6720 −0.905457
\(935\) 1.04707 0.0342430
\(936\) 7.52015 0.245804
\(937\) −39.5010 −1.29044 −0.645221 0.763996i \(-0.723235\pi\)
−0.645221 + 0.763996i \(0.723235\pi\)
\(938\) 5.07653 0.165755
\(939\) −57.0246 −1.86093
\(940\) 2.82972 0.0922952
\(941\) −2.64668 −0.0862791 −0.0431396 0.999069i \(-0.513736\pi\)
−0.0431396 + 0.999069i \(0.513736\pi\)
\(942\) −42.5970 −1.38789
\(943\) −37.0503 −1.20652
\(944\) 8.95349 0.291411
\(945\) −0.489936 −0.0159376
\(946\) 2.95555 0.0960931
\(947\) 3.22084 0.104663 0.0523316 0.998630i \(-0.483335\pi\)
0.0523316 + 0.998630i \(0.483335\pi\)
\(948\) −14.6319 −0.475221
\(949\) 33.2049 1.07788
\(950\) −31.0539 −1.00752
\(951\) −51.1520 −1.65872
\(952\) 1.09467 0.0354784
\(953\) 9.36133 0.303243 0.151622 0.988439i \(-0.451550\pi\)
0.151622 + 0.988439i \(0.451550\pi\)
\(954\) 34.3612 1.11248
\(955\) −3.57411 −0.115655
\(956\) 14.2698 0.461517
\(957\) −2.05405 −0.0663979
\(958\) 31.5909 1.02065
\(959\) 1.25618 0.0405642
\(960\) 2.70075 0.0871663
\(961\) 43.9534 1.41785
\(962\) −13.4140 −0.432486
\(963\) −29.7319 −0.958096
\(964\) −15.4480 −0.497547
\(965\) 2.86857 0.0923426
\(966\) 6.59058 0.212048
\(967\) 19.8715 0.639025 0.319512 0.947582i \(-0.396481\pi\)
0.319512 + 0.947582i \(0.396481\pi\)
\(968\) 10.8908 0.350043
\(969\) 61.0306 1.96058
\(970\) −6.90363 −0.221662
\(971\) 12.4048 0.398090 0.199045 0.979990i \(-0.436216\pi\)
0.199045 + 0.979990i \(0.436216\pi\)
\(972\) 22.3119 0.715656
\(973\) −0.936616 −0.0300265
\(974\) 4.10339 0.131481
\(975\) −21.2583 −0.680812
\(976\) −3.72746 −0.119313
\(977\) 28.0136 0.896235 0.448117 0.893975i \(-0.352095\pi\)
0.448117 + 0.893975i \(0.352095\pi\)
\(978\) 46.9628 1.50171
\(979\) 0.256125 0.00818580
\(980\) 7.27578 0.232416
\(981\) −37.9055 −1.21023
\(982\) 4.83659 0.154342
\(983\) −58.1407 −1.85440 −0.927200 0.374568i \(-0.877791\pi\)
−0.927200 + 0.374568i \(0.877791\pi\)
\(984\) 13.3700 0.426221
\(985\) 8.87518 0.282787
\(986\) 7.29062 0.232181
\(987\) −2.49185 −0.0793166
\(988\) 17.2321 0.548226
\(989\) −63.1587 −2.00833
\(990\) −1.22420 −0.0389076
\(991\) −37.1599 −1.18042 −0.590212 0.807249i \(-0.700956\pi\)
−0.590212 + 0.807249i \(0.700956\pi\)
\(992\) 8.65756 0.274878
\(993\) −4.25778 −0.135116
\(994\) −2.54597 −0.0807534
\(995\) 18.9472 0.600667
\(996\) 11.1362 0.352863
\(997\) 53.1299 1.68264 0.841321 0.540537i \(-0.181779\pi\)
0.841321 + 0.540537i \(0.181779\pi\)
\(998\) −7.24316 −0.229278
\(999\) 7.87302 0.249091
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 \(a_p\))