Properties

Label 4003.2.a.b.1.3
Level 4003
Weight 2
Character 4003.1
Self dual Yes
Analytic conductor 31.964
Analytic rank 1
Dimension 152
CM No

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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 1.3
Character \(\chi\) = 4003.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.74603 q^{2} -0.470182 q^{3} +5.54067 q^{4} -1.60967 q^{5} +1.29113 q^{6} -2.65994 q^{7} -9.72280 q^{8} -2.77893 q^{9} +O(q^{10})\) \(q-2.74603 q^{2} -0.470182 q^{3} +5.54067 q^{4} -1.60967 q^{5} +1.29113 q^{6} -2.65994 q^{7} -9.72280 q^{8} -2.77893 q^{9} +4.42020 q^{10} -4.89664 q^{11} -2.60512 q^{12} +4.07842 q^{13} +7.30426 q^{14} +0.756837 q^{15} +15.6177 q^{16} -1.69505 q^{17} +7.63102 q^{18} +2.50475 q^{19} -8.91866 q^{20} +1.25065 q^{21} +13.4463 q^{22} -5.52567 q^{23} +4.57148 q^{24} -2.40896 q^{25} -11.1995 q^{26} +2.71715 q^{27} -14.7378 q^{28} -0.190228 q^{29} -2.07830 q^{30} +5.82448 q^{31} -23.4411 q^{32} +2.30231 q^{33} +4.65467 q^{34} +4.28162 q^{35} -15.3971 q^{36} +6.76398 q^{37} -6.87812 q^{38} -1.91760 q^{39} +15.6505 q^{40} +6.84648 q^{41} -3.43433 q^{42} +3.96451 q^{43} -27.1307 q^{44} +4.47316 q^{45} +15.1736 q^{46} +6.99841 q^{47} -7.34317 q^{48} +0.0752656 q^{49} +6.61507 q^{50} +0.796983 q^{51} +22.5972 q^{52} +0.426551 q^{53} -7.46136 q^{54} +7.88198 q^{55} +25.8620 q^{56} -1.17769 q^{57} +0.522372 q^{58} +10.7234 q^{59} +4.19339 q^{60} +11.5904 q^{61} -15.9942 q^{62} +7.39178 q^{63} +33.1346 q^{64} -6.56492 q^{65} -6.32221 q^{66} -9.73873 q^{67} -9.39174 q^{68} +2.59807 q^{69} -11.7575 q^{70} +11.1732 q^{71} +27.0190 q^{72} -3.34920 q^{73} -18.5741 q^{74} +1.13265 q^{75} +13.8780 q^{76} +13.0248 q^{77} +5.26578 q^{78} -8.54360 q^{79} -25.1394 q^{80} +7.05924 q^{81} -18.8006 q^{82} -9.08513 q^{83} +6.92946 q^{84} +2.72848 q^{85} -10.8867 q^{86} +0.0894418 q^{87} +47.6090 q^{88} -11.6083 q^{89} -12.2834 q^{90} -10.8483 q^{91} -30.6159 q^{92} -2.73856 q^{93} -19.2178 q^{94} -4.03182 q^{95} +11.0216 q^{96} -11.2327 q^{97} -0.206681 q^{98} +13.6074 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 152q - 22q^{2} - 18q^{3} + 138q^{4} - 59q^{5} - 17q^{6} - 19q^{7} - 66q^{8} + 106q^{9} + O(q^{10}) \) \( 152q - 22q^{2} - 18q^{3} + 138q^{4} - 59q^{5} - 17q^{6} - 19q^{7} - 66q^{8} + 106q^{9} - 15q^{10} - 40q^{11} - 53q^{12} - 59q^{13} - 36q^{14} - 40q^{15} + 118q^{16} - 93q^{17} - 59q^{18} - 16q^{19} - 108q^{20} - 62q^{21} - 37q^{22} - 107q^{23} - 31q^{24} + 101q^{25} - 64q^{26} - 63q^{27} - 53q^{28} - 124q^{29} - 68q^{30} - 15q^{31} - 129q^{32} - 49q^{33} - 76q^{35} + 45q^{36} - 98q^{37} - 125q^{38} - 47q^{39} - 7q^{40} - 56q^{41} - 84q^{42} - 62q^{43} - 114q^{44} - 142q^{45} - 3q^{46} - 111q^{47} - 92q^{48} + 117q^{49} - 64q^{50} - 21q^{51} - 85q^{52} - 347q^{53} + 3q^{54} - 16q^{55} - 73q^{56} - 115q^{57} - 29q^{58} - 50q^{59} - 54q^{60} - 62q^{61} - 55q^{62} - 70q^{63} + 64q^{64} - 147q^{65} + 34q^{66} - 86q^{67} - 174q^{68} - 104q^{69} - 7q^{70} - 86q^{71} - 139q^{72} - 27q^{73} - 52q^{74} - 49q^{75} - 11q^{76} - 346q^{77} - 59q^{78} - 17q^{79} - 149q^{80} - 8q^{81} - 31q^{82} - 106q^{83} - 51q^{84} - 69q^{85} - 85q^{86} - 32q^{87} - 113q^{88} - 59q^{89} + 10q^{90} - 9q^{91} - 314q^{92} - 230q^{93} + 7q^{94} - 74q^{95} - 54q^{96} - 60q^{97} - 77q^{98} - 96q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.74603 −1.94174 −0.970868 0.239616i \(-0.922979\pi\)
−0.970868 + 0.239616i \(0.922979\pi\)
\(3\) −0.470182 −0.271459 −0.135730 0.990746i \(-0.543338\pi\)
−0.135730 + 0.990746i \(0.543338\pi\)
\(4\) 5.54067 2.77034
\(5\) −1.60967 −0.719867 −0.359933 0.932978i \(-0.617201\pi\)
−0.359933 + 0.932978i \(0.617201\pi\)
\(6\) 1.29113 0.527102
\(7\) −2.65994 −1.00536 −0.502681 0.864472i \(-0.667653\pi\)
−0.502681 + 0.864472i \(0.667653\pi\)
\(8\) −9.72280 −3.43753
\(9\) −2.77893 −0.926310
\(10\) 4.42020 1.39779
\(11\) −4.89664 −1.47639 −0.738196 0.674586i \(-0.764322\pi\)
−0.738196 + 0.674586i \(0.764322\pi\)
\(12\) −2.60512 −0.752034
\(13\) 4.07842 1.13115 0.565575 0.824697i \(-0.308654\pi\)
0.565575 + 0.824697i \(0.308654\pi\)
\(14\) 7.30426 1.95215
\(15\) 0.756837 0.195415
\(16\) 15.6177 3.90443
\(17\) −1.69505 −0.411111 −0.205555 0.978645i \(-0.565900\pi\)
−0.205555 + 0.978645i \(0.565900\pi\)
\(18\) 7.63102 1.79865
\(19\) 2.50475 0.574629 0.287315 0.957836i \(-0.407237\pi\)
0.287315 + 0.957836i \(0.407237\pi\)
\(20\) −8.91866 −1.99427
\(21\) 1.25065 0.272915
\(22\) 13.4463 2.86676
\(23\) −5.52567 −1.15218 −0.576091 0.817386i \(-0.695422\pi\)
−0.576091 + 0.817386i \(0.695422\pi\)
\(24\) 4.57148 0.933149
\(25\) −2.40896 −0.481792
\(26\) −11.1995 −2.19640
\(27\) 2.71715 0.522915
\(28\) −14.7378 −2.78519
\(29\) −0.190228 −0.0353245 −0.0176622 0.999844i \(-0.505622\pi\)
−0.0176622 + 0.999844i \(0.505622\pi\)
\(30\) −2.07830 −0.379443
\(31\) 5.82448 1.04611 0.523053 0.852300i \(-0.324793\pi\)
0.523053 + 0.852300i \(0.324793\pi\)
\(32\) −23.4411 −4.14385
\(33\) 2.30231 0.400781
\(34\) 4.65467 0.798268
\(35\) 4.28162 0.723726
\(36\) −15.3971 −2.56619
\(37\) 6.76398 1.11199 0.555996 0.831185i \(-0.312337\pi\)
0.555996 + 0.831185i \(0.312337\pi\)
\(38\) −6.87812 −1.11578
\(39\) −1.91760 −0.307062
\(40\) 15.6505 2.47456
\(41\) 6.84648 1.06924 0.534620 0.845092i \(-0.320455\pi\)
0.534620 + 0.845092i \(0.320455\pi\)
\(42\) −3.43433 −0.529929
\(43\) 3.96451 0.604583 0.302291 0.953216i \(-0.402248\pi\)
0.302291 + 0.953216i \(0.402248\pi\)
\(44\) −27.1307 −4.09010
\(45\) 4.47316 0.666819
\(46\) 15.1736 2.23723
\(47\) 6.99841 1.02082 0.510412 0.859930i \(-0.329493\pi\)
0.510412 + 0.859930i \(0.329493\pi\)
\(48\) −7.34317 −1.05989
\(49\) 0.0752656 0.0107522
\(50\) 6.61507 0.935513
\(51\) 0.796983 0.111600
\(52\) 22.5972 3.13367
\(53\) 0.426551 0.0585913 0.0292956 0.999571i \(-0.490674\pi\)
0.0292956 + 0.999571i \(0.490674\pi\)
\(54\) −7.46136 −1.01536
\(55\) 7.88198 1.06281
\(56\) 25.8620 3.45596
\(57\) −1.17769 −0.155988
\(58\) 0.522372 0.0685908
\(59\) 10.7234 1.39606 0.698031 0.716068i \(-0.254060\pi\)
0.698031 + 0.716068i \(0.254060\pi\)
\(60\) 4.19339 0.541364
\(61\) 11.5904 1.48400 0.742001 0.670399i \(-0.233877\pi\)
0.742001 + 0.670399i \(0.233877\pi\)
\(62\) −15.9942 −2.03126
\(63\) 7.39178 0.931276
\(64\) 33.1346 4.14182
\(65\) −6.56492 −0.814278
\(66\) −6.32221 −0.778210
\(67\) −9.73873 −1.18978 −0.594888 0.803809i \(-0.702803\pi\)
−0.594888 + 0.803809i \(0.702803\pi\)
\(68\) −9.39174 −1.13892
\(69\) 2.59807 0.312770
\(70\) −11.7575 −1.40529
\(71\) 11.1732 1.32601 0.663007 0.748614i \(-0.269280\pi\)
0.663007 + 0.748614i \(0.269280\pi\)
\(72\) 27.0190 3.18422
\(73\) −3.34920 −0.391994 −0.195997 0.980604i \(-0.562794\pi\)
−0.195997 + 0.980604i \(0.562794\pi\)
\(74\) −18.5741 −2.15919
\(75\) 1.13265 0.130787
\(76\) 13.8780 1.59192
\(77\) 13.0248 1.48431
\(78\) 5.26578 0.596232
\(79\) −8.54360 −0.961230 −0.480615 0.876932i \(-0.659587\pi\)
−0.480615 + 0.876932i \(0.659587\pi\)
\(80\) −25.1394 −2.81067
\(81\) 7.05924 0.784360
\(82\) −18.8006 −2.07618
\(83\) −9.08513 −0.997222 −0.498611 0.866826i \(-0.666156\pi\)
−0.498611 + 0.866826i \(0.666156\pi\)
\(84\) 6.92946 0.756066
\(85\) 2.72848 0.295945
\(86\) −10.8867 −1.17394
\(87\) 0.0894418 0.00958917
\(88\) 47.6090 5.07514
\(89\) −11.6083 −1.23048 −0.615241 0.788339i \(-0.710941\pi\)
−0.615241 + 0.788339i \(0.710941\pi\)
\(90\) −12.2834 −1.29479
\(91\) −10.8483 −1.13722
\(92\) −30.6159 −3.19193
\(93\) −2.73856 −0.283976
\(94\) −19.2178 −1.98217
\(95\) −4.03182 −0.413656
\(96\) 11.0216 1.12489
\(97\) −11.2327 −1.14050 −0.570252 0.821470i \(-0.693154\pi\)
−0.570252 + 0.821470i \(0.693154\pi\)
\(98\) −0.206681 −0.0208780
\(99\) 13.6074 1.36760
\(100\) −13.3473 −1.33473
\(101\) −6.24174 −0.621076 −0.310538 0.950561i \(-0.600509\pi\)
−0.310538 + 0.950561i \(0.600509\pi\)
\(102\) −2.18854 −0.216697
\(103\) 4.94761 0.487502 0.243751 0.969838i \(-0.421622\pi\)
0.243751 + 0.969838i \(0.421622\pi\)
\(104\) −39.6537 −3.88836
\(105\) −2.01314 −0.196462
\(106\) −1.17132 −0.113769
\(107\) 17.5616 1.69774 0.848872 0.528599i \(-0.177282\pi\)
0.848872 + 0.528599i \(0.177282\pi\)
\(108\) 15.0548 1.44865
\(109\) −12.5718 −1.20416 −0.602079 0.798436i \(-0.705661\pi\)
−0.602079 + 0.798436i \(0.705661\pi\)
\(110\) −21.6441 −2.06369
\(111\) −3.18030 −0.301861
\(112\) −41.5422 −3.92537
\(113\) 3.48385 0.327733 0.163867 0.986482i \(-0.447603\pi\)
0.163867 + 0.986482i \(0.447603\pi\)
\(114\) 3.23396 0.302888
\(115\) 8.89450 0.829417
\(116\) −1.05399 −0.0978608
\(117\) −11.3336 −1.04780
\(118\) −29.4466 −2.71078
\(119\) 4.50873 0.413315
\(120\) −7.35858 −0.671743
\(121\) 12.9771 1.17973
\(122\) −31.8276 −2.88154
\(123\) −3.21909 −0.290255
\(124\) 32.2715 2.89807
\(125\) 11.9260 1.06669
\(126\) −20.2980 −1.80829
\(127\) −14.8041 −1.31365 −0.656827 0.754041i \(-0.728102\pi\)
−0.656827 + 0.754041i \(0.728102\pi\)
\(128\) −44.1063 −3.89848
\(129\) −1.86404 −0.164120
\(130\) 18.0275 1.58111
\(131\) −6.14475 −0.536869 −0.268435 0.963298i \(-0.586506\pi\)
−0.268435 + 0.963298i \(0.586506\pi\)
\(132\) 12.7563 1.11030
\(133\) −6.66248 −0.577710
\(134\) 26.7428 2.31023
\(135\) −4.37371 −0.376429
\(136\) 16.4807 1.41320
\(137\) −5.66736 −0.484195 −0.242097 0.970252i \(-0.577835\pi\)
−0.242097 + 0.970252i \(0.577835\pi\)
\(138\) −7.13436 −0.607317
\(139\) 14.0764 1.19394 0.596971 0.802263i \(-0.296371\pi\)
0.596971 + 0.802263i \(0.296371\pi\)
\(140\) 23.7231 2.00497
\(141\) −3.29052 −0.277112
\(142\) −30.6819 −2.57477
\(143\) −19.9706 −1.67002
\(144\) −43.4006 −3.61671
\(145\) 0.306205 0.0254289
\(146\) 9.19700 0.761149
\(147\) −0.0353885 −0.00291879
\(148\) 37.4770 3.08059
\(149\) 9.59049 0.785684 0.392842 0.919606i \(-0.371492\pi\)
0.392842 + 0.919606i \(0.371492\pi\)
\(150\) −3.11029 −0.253954
\(151\) 13.8690 1.12865 0.564323 0.825554i \(-0.309137\pi\)
0.564323 + 0.825554i \(0.309137\pi\)
\(152\) −24.3532 −1.97530
\(153\) 4.71043 0.380816
\(154\) −35.7663 −2.88213
\(155\) −9.37549 −0.753057
\(156\) −10.6248 −0.850664
\(157\) −4.79420 −0.382619 −0.191310 0.981530i \(-0.561273\pi\)
−0.191310 + 0.981530i \(0.561273\pi\)
\(158\) 23.4610 1.86646
\(159\) −0.200556 −0.0159052
\(160\) 37.7325 2.98302
\(161\) 14.6979 1.15836
\(162\) −19.3849 −1.52302
\(163\) −5.56014 −0.435504 −0.217752 0.976004i \(-0.569872\pi\)
−0.217752 + 0.976004i \(0.569872\pi\)
\(164\) 37.9341 2.96216
\(165\) −3.70596 −0.288509
\(166\) 24.9480 1.93634
\(167\) 10.3760 0.802920 0.401460 0.915876i \(-0.368503\pi\)
0.401460 + 0.915876i \(0.368503\pi\)
\(168\) −12.1598 −0.938152
\(169\) 3.63353 0.279502
\(170\) −7.49248 −0.574647
\(171\) −6.96052 −0.532285
\(172\) 21.9661 1.67490
\(173\) −21.1798 −1.61027 −0.805134 0.593093i \(-0.797906\pi\)
−0.805134 + 0.593093i \(0.797906\pi\)
\(174\) −0.245610 −0.0186196
\(175\) 6.40768 0.484375
\(176\) −76.4744 −5.76447
\(177\) −5.04192 −0.378974
\(178\) 31.8768 2.38927
\(179\) 13.7086 1.02463 0.512314 0.858798i \(-0.328788\pi\)
0.512314 + 0.858798i \(0.328788\pi\)
\(180\) 24.7843 1.84731
\(181\) −18.1284 −1.34747 −0.673736 0.738973i \(-0.735311\pi\)
−0.673736 + 0.738973i \(0.735311\pi\)
\(182\) 29.7899 2.20817
\(183\) −5.44960 −0.402846
\(184\) 53.7249 3.96065
\(185\) −10.8878 −0.800486
\(186\) 7.52017 0.551405
\(187\) 8.30006 0.606961
\(188\) 38.7759 2.82802
\(189\) −7.22744 −0.525719
\(190\) 11.0715 0.803211
\(191\) 1.02485 0.0741558 0.0370779 0.999312i \(-0.488195\pi\)
0.0370779 + 0.999312i \(0.488195\pi\)
\(192\) −15.5793 −1.12434
\(193\) −4.00182 −0.288057 −0.144029 0.989574i \(-0.546006\pi\)
−0.144029 + 0.989574i \(0.546006\pi\)
\(194\) 30.8452 2.21456
\(195\) 3.08670 0.221043
\(196\) 0.417022 0.0297873
\(197\) 14.8251 1.05624 0.528122 0.849168i \(-0.322896\pi\)
0.528122 + 0.849168i \(0.322896\pi\)
\(198\) −37.3663 −2.65551
\(199\) −7.26216 −0.514801 −0.257400 0.966305i \(-0.582866\pi\)
−0.257400 + 0.966305i \(0.582866\pi\)
\(200\) 23.4218 1.65617
\(201\) 4.57897 0.322976
\(202\) 17.1400 1.20597
\(203\) 0.505995 0.0355139
\(204\) 4.41582 0.309169
\(205\) −11.0206 −0.769711
\(206\) −13.5863 −0.946601
\(207\) 15.3554 1.06728
\(208\) 63.6957 4.41650
\(209\) −12.2649 −0.848378
\(210\) 5.52814 0.381478
\(211\) −4.01457 −0.276375 −0.138187 0.990406i \(-0.544128\pi\)
−0.138187 + 0.990406i \(0.544128\pi\)
\(212\) 2.36338 0.162318
\(213\) −5.25342 −0.359959
\(214\) −48.2247 −3.29657
\(215\) −6.38156 −0.435219
\(216\) −26.4183 −1.79753
\(217\) −15.4927 −1.05172
\(218\) 34.5225 2.33816
\(219\) 1.57473 0.106411
\(220\) 43.6715 2.94433
\(221\) −6.91314 −0.465028
\(222\) 8.73319 0.586133
\(223\) 0.161528 0.0108167 0.00540835 0.999985i \(-0.498278\pi\)
0.00540835 + 0.999985i \(0.498278\pi\)
\(224\) 62.3520 4.16607
\(225\) 6.69433 0.446289
\(226\) −9.56676 −0.636372
\(227\) −6.79610 −0.451073 −0.225536 0.974235i \(-0.572413\pi\)
−0.225536 + 0.974235i \(0.572413\pi\)
\(228\) −6.52518 −0.432141
\(229\) 11.9247 0.788004 0.394002 0.919110i \(-0.371090\pi\)
0.394002 + 0.919110i \(0.371090\pi\)
\(230\) −24.4246 −1.61051
\(231\) −6.12400 −0.402929
\(232\) 1.84955 0.121429
\(233\) −13.3036 −0.871549 −0.435774 0.900056i \(-0.643525\pi\)
−0.435774 + 0.900056i \(0.643525\pi\)
\(234\) 31.1225 2.03454
\(235\) −11.2651 −0.734857
\(236\) 59.4146 3.86756
\(237\) 4.01704 0.260935
\(238\) −12.3811 −0.802549
\(239\) 7.62197 0.493024 0.246512 0.969140i \(-0.420715\pi\)
0.246512 + 0.969140i \(0.420715\pi\)
\(240\) 11.8201 0.762983
\(241\) −21.2907 −1.37146 −0.685728 0.727858i \(-0.740516\pi\)
−0.685728 + 0.727858i \(0.740516\pi\)
\(242\) −35.6354 −2.29073
\(243\) −11.4706 −0.735837
\(244\) 64.2187 4.11118
\(245\) −0.121153 −0.00774017
\(246\) 8.83971 0.563599
\(247\) 10.2154 0.649992
\(248\) −56.6302 −3.59602
\(249\) 4.27166 0.270705
\(250\) −32.7491 −2.07124
\(251\) −2.29506 −0.144863 −0.0724315 0.997373i \(-0.523076\pi\)
−0.0724315 + 0.997373i \(0.523076\pi\)
\(252\) 40.9554 2.57995
\(253\) 27.0572 1.70107
\(254\) 40.6526 2.55077
\(255\) −1.28288 −0.0803370
\(256\) 54.8479 3.42800
\(257\) 23.0571 1.43826 0.719130 0.694876i \(-0.244541\pi\)
0.719130 + 0.694876i \(0.244541\pi\)
\(258\) 5.11871 0.318677
\(259\) −17.9918 −1.11795
\(260\) −36.3741 −2.25582
\(261\) 0.528631 0.0327214
\(262\) 16.8737 1.04246
\(263\) −15.2074 −0.937727 −0.468864 0.883271i \(-0.655336\pi\)
−0.468864 + 0.883271i \(0.655336\pi\)
\(264\) −22.3849 −1.37769
\(265\) −0.686607 −0.0421779
\(266\) 18.2954 1.12176
\(267\) 5.45802 0.334026
\(268\) −53.9591 −3.29608
\(269\) 30.0857 1.83435 0.917177 0.398479i \(-0.130462\pi\)
0.917177 + 0.398479i \(0.130462\pi\)
\(270\) 12.0103 0.730926
\(271\) 1.70814 0.103762 0.0518810 0.998653i \(-0.483478\pi\)
0.0518810 + 0.998653i \(0.483478\pi\)
\(272\) −26.4729 −1.60515
\(273\) 5.10069 0.308708
\(274\) 15.5627 0.940178
\(275\) 11.7958 0.711314
\(276\) 14.3950 0.866480
\(277\) 16.1307 0.969202 0.484601 0.874735i \(-0.338965\pi\)
0.484601 + 0.874735i \(0.338965\pi\)
\(278\) −38.6541 −2.31832
\(279\) −16.1858 −0.969019
\(280\) −41.6293 −2.48783
\(281\) −22.1067 −1.31878 −0.659388 0.751803i \(-0.729184\pi\)
−0.659388 + 0.751803i \(0.729184\pi\)
\(282\) 9.03587 0.538078
\(283\) 9.10027 0.540955 0.270478 0.962726i \(-0.412818\pi\)
0.270478 + 0.962726i \(0.412818\pi\)
\(284\) 61.9070 3.67350
\(285\) 1.89569 0.112291
\(286\) 54.8397 3.24274
\(287\) −18.2112 −1.07497
\(288\) 65.1413 3.83849
\(289\) −14.1268 −0.830988
\(290\) −0.840847 −0.0493762
\(291\) 5.28139 0.309601
\(292\) −18.5568 −1.08596
\(293\) 5.55305 0.324413 0.162206 0.986757i \(-0.448139\pi\)
0.162206 + 0.986757i \(0.448139\pi\)
\(294\) 0.0971778 0.00566752
\(295\) −17.2611 −1.00498
\(296\) −65.7648 −3.82250
\(297\) −13.3049 −0.772027
\(298\) −26.3358 −1.52559
\(299\) −22.5360 −1.30329
\(300\) 6.27564 0.362324
\(301\) −10.5454 −0.607824
\(302\) −38.0848 −2.19153
\(303\) 2.93475 0.168597
\(304\) 39.1185 2.24360
\(305\) −18.6568 −1.06828
\(306\) −12.9350 −0.739444
\(307\) −2.10232 −0.119986 −0.0599929 0.998199i \(-0.519108\pi\)
−0.0599929 + 0.998199i \(0.519108\pi\)
\(308\) 72.1659 4.11203
\(309\) −2.32627 −0.132337
\(310\) 25.7454 1.46224
\(311\) 7.69815 0.436522 0.218261 0.975890i \(-0.429962\pi\)
0.218261 + 0.975890i \(0.429962\pi\)
\(312\) 18.6444 1.05553
\(313\) −15.8785 −0.897508 −0.448754 0.893655i \(-0.648132\pi\)
−0.448754 + 0.893655i \(0.648132\pi\)
\(314\) 13.1650 0.742945
\(315\) −11.8983 −0.670395
\(316\) −47.3373 −2.66293
\(317\) −9.55406 −0.536610 −0.268305 0.963334i \(-0.586463\pi\)
−0.268305 + 0.963334i \(0.586463\pi\)
\(318\) 0.550734 0.0308836
\(319\) 0.931479 0.0521528
\(320\) −53.3358 −2.98156
\(321\) −8.25714 −0.460868
\(322\) −40.3609 −2.24923
\(323\) −4.24568 −0.236236
\(324\) 39.1129 2.17294
\(325\) −9.82476 −0.544979
\(326\) 15.2683 0.845634
\(327\) 5.91102 0.326880
\(328\) −66.5669 −3.67554
\(329\) −18.6153 −1.02630
\(330\) 10.1767 0.560207
\(331\) 27.6748 1.52114 0.760572 0.649254i \(-0.224919\pi\)
0.760572 + 0.649254i \(0.224919\pi\)
\(332\) −50.3377 −2.76264
\(333\) −18.7966 −1.03005
\(334\) −28.4928 −1.55906
\(335\) 15.6761 0.856479
\(336\) 19.5324 1.06558
\(337\) −10.6232 −0.578680 −0.289340 0.957226i \(-0.593436\pi\)
−0.289340 + 0.957226i \(0.593436\pi\)
\(338\) −9.97777 −0.542719
\(339\) −1.63804 −0.0889663
\(340\) 15.1176 0.819867
\(341\) −28.5204 −1.54446
\(342\) 19.1138 1.03356
\(343\) 18.4194 0.994552
\(344\) −38.5462 −2.07827
\(345\) −4.18203 −0.225153
\(346\) 58.1602 3.12671
\(347\) −18.7687 −1.00756 −0.503778 0.863833i \(-0.668057\pi\)
−0.503778 + 0.863833i \(0.668057\pi\)
\(348\) 0.495568 0.0265652
\(349\) 24.7753 1.32619 0.663096 0.748534i \(-0.269242\pi\)
0.663096 + 0.748534i \(0.269242\pi\)
\(350\) −17.5957 −0.940529
\(351\) 11.0817 0.591496
\(352\) 114.783 6.11794
\(353\) −10.7918 −0.574390 −0.287195 0.957872i \(-0.592723\pi\)
−0.287195 + 0.957872i \(0.592723\pi\)
\(354\) 13.8453 0.735868
\(355\) −17.9851 −0.954553
\(356\) −64.3180 −3.40885
\(357\) −2.11992 −0.112198
\(358\) −37.6442 −1.98956
\(359\) 23.0128 1.21457 0.607284 0.794485i \(-0.292259\pi\)
0.607284 + 0.794485i \(0.292259\pi\)
\(360\) −43.4916 −2.29221
\(361\) −12.7262 −0.669801
\(362\) 49.7810 2.61643
\(363\) −6.10158 −0.320250
\(364\) −60.1072 −3.15047
\(365\) 5.39111 0.282184
\(366\) 14.9648 0.782221
\(367\) −37.0853 −1.93584 −0.967920 0.251260i \(-0.919155\pi\)
−0.967920 + 0.251260i \(0.919155\pi\)
\(368\) −86.2984 −4.49861
\(369\) −19.0259 −0.990448
\(370\) 29.8982 1.55433
\(371\) −1.13460 −0.0589054
\(372\) −15.1735 −0.786708
\(373\) −8.65496 −0.448137 −0.224068 0.974573i \(-0.571934\pi\)
−0.224068 + 0.974573i \(0.571934\pi\)
\(374\) −22.7922 −1.17856
\(375\) −5.60738 −0.289564
\(376\) −68.0441 −3.50911
\(377\) −0.775831 −0.0399573
\(378\) 19.8468 1.02081
\(379\) 27.2552 1.40000 0.700002 0.714141i \(-0.253182\pi\)
0.700002 + 0.714141i \(0.253182\pi\)
\(380\) −22.3390 −1.14597
\(381\) 6.96063 0.356604
\(382\) −2.81428 −0.143991
\(383\) 20.2303 1.03372 0.516860 0.856070i \(-0.327101\pi\)
0.516860 + 0.856070i \(0.327101\pi\)
\(384\) 20.7380 1.05828
\(385\) −20.9656 −1.06850
\(386\) 10.9891 0.559331
\(387\) −11.0171 −0.560031
\(388\) −62.2365 −3.15958
\(389\) 7.56961 0.383795 0.191897 0.981415i \(-0.438536\pi\)
0.191897 + 0.981415i \(0.438536\pi\)
\(390\) −8.47617 −0.429208
\(391\) 9.36630 0.473674
\(392\) −0.731792 −0.0369611
\(393\) 2.88915 0.145738
\(394\) −40.7102 −2.05095
\(395\) 13.7524 0.691958
\(396\) 75.3943 3.78870
\(397\) 8.45853 0.424522 0.212261 0.977213i \(-0.431917\pi\)
0.212261 + 0.977213i \(0.431917\pi\)
\(398\) 19.9421 0.999607
\(399\) 3.13257 0.156825
\(400\) −37.6225 −1.88112
\(401\) −0.861583 −0.0430254 −0.0215127 0.999769i \(-0.506848\pi\)
−0.0215127 + 0.999769i \(0.506848\pi\)
\(402\) −12.5740 −0.627133
\(403\) 23.7547 1.18330
\(404\) −34.5835 −1.72059
\(405\) −11.3630 −0.564634
\(406\) −1.38948 −0.0689586
\(407\) −33.1208 −1.64174
\(408\) −7.74890 −0.383628
\(409\) 21.7678 1.07635 0.538173 0.842834i \(-0.319115\pi\)
0.538173 + 0.842834i \(0.319115\pi\)
\(410\) 30.2628 1.49457
\(411\) 2.66469 0.131439
\(412\) 27.4131 1.35055
\(413\) −28.5234 −1.40355
\(414\) −42.1665 −2.07237
\(415\) 14.6241 0.717867
\(416\) −95.6029 −4.68732
\(417\) −6.61845 −0.324107
\(418\) 33.6797 1.64733
\(419\) −2.74815 −0.134256 −0.0671280 0.997744i \(-0.521384\pi\)
−0.0671280 + 0.997744i \(0.521384\pi\)
\(420\) −11.1542 −0.544267
\(421\) 7.34156 0.357806 0.178903 0.983867i \(-0.442745\pi\)
0.178903 + 0.983867i \(0.442745\pi\)
\(422\) 11.0241 0.536647
\(423\) −19.4481 −0.945599
\(424\) −4.14727 −0.201409
\(425\) 4.08332 0.198070
\(426\) 14.4261 0.698945
\(427\) −30.8298 −1.49196
\(428\) 97.3031 4.70332
\(429\) 9.38979 0.453343
\(430\) 17.5240 0.845080
\(431\) −7.41589 −0.357211 −0.178605 0.983921i \(-0.557159\pi\)
−0.178605 + 0.983921i \(0.557159\pi\)
\(432\) 42.4356 2.04169
\(433\) −34.7396 −1.66948 −0.834739 0.550645i \(-0.814382\pi\)
−0.834739 + 0.550645i \(0.814382\pi\)
\(434\) 42.5435 2.04215
\(435\) −0.143972 −0.00690292
\(436\) −69.6562 −3.33593
\(437\) −13.8404 −0.662077
\(438\) −4.32426 −0.206621
\(439\) 3.29480 0.157252 0.0786262 0.996904i \(-0.474947\pi\)
0.0786262 + 0.996904i \(0.474947\pi\)
\(440\) −76.6348 −3.65342
\(441\) −0.209158 −0.00995989
\(442\) 18.9837 0.902962
\(443\) 5.38213 0.255713 0.127856 0.991793i \(-0.459190\pi\)
0.127856 + 0.991793i \(0.459190\pi\)
\(444\) −17.6210 −0.836256
\(445\) 18.6856 0.885782
\(446\) −0.443560 −0.0210032
\(447\) −4.50927 −0.213281
\(448\) −88.1359 −4.16403
\(449\) −11.3022 −0.533386 −0.266693 0.963782i \(-0.585931\pi\)
−0.266693 + 0.963782i \(0.585931\pi\)
\(450\) −18.3828 −0.866575
\(451\) −33.5247 −1.57862
\(452\) 19.3029 0.907932
\(453\) −6.52096 −0.306381
\(454\) 18.6623 0.875864
\(455\) 17.4623 0.818644
\(456\) 11.4504 0.536215
\(457\) 1.49305 0.0698421 0.0349211 0.999390i \(-0.488882\pi\)
0.0349211 + 0.999390i \(0.488882\pi\)
\(458\) −32.7455 −1.53010
\(459\) −4.60571 −0.214976
\(460\) 49.2815 2.29776
\(461\) 5.75443 0.268010 0.134005 0.990981i \(-0.457216\pi\)
0.134005 + 0.990981i \(0.457216\pi\)
\(462\) 16.8167 0.782382
\(463\) −21.1701 −0.983860 −0.491930 0.870635i \(-0.663708\pi\)
−0.491930 + 0.870635i \(0.663708\pi\)
\(464\) −2.97093 −0.137922
\(465\) 4.40818 0.204425
\(466\) 36.5321 1.69232
\(467\) −16.4039 −0.759081 −0.379540 0.925175i \(-0.623918\pi\)
−0.379540 + 0.925175i \(0.623918\pi\)
\(468\) −62.7961 −2.90275
\(469\) 25.9044 1.19615
\(470\) 30.9344 1.42690
\(471\) 2.25415 0.103866
\(472\) −104.261 −4.79900
\(473\) −19.4128 −0.892601
\(474\) −11.0309 −0.506667
\(475\) −6.03384 −0.276852
\(476\) 24.9814 1.14502
\(477\) −1.18536 −0.0542737
\(478\) −20.9302 −0.957323
\(479\) 9.35845 0.427598 0.213799 0.976878i \(-0.431416\pi\)
0.213799 + 0.976878i \(0.431416\pi\)
\(480\) −17.7411 −0.809768
\(481\) 27.5864 1.25783
\(482\) 58.4650 2.66301
\(483\) −6.91069 −0.314447
\(484\) 71.9017 3.26826
\(485\) 18.0809 0.821011
\(486\) 31.4985 1.42880
\(487\) 22.6800 1.02773 0.513864 0.857872i \(-0.328214\pi\)
0.513864 + 0.857872i \(0.328214\pi\)
\(488\) −112.691 −5.10129
\(489\) 2.61428 0.118222
\(490\) 0.332689 0.0150294
\(491\) 16.9729 0.765977 0.382989 0.923753i \(-0.374895\pi\)
0.382989 + 0.923753i \(0.374895\pi\)
\(492\) −17.8359 −0.804105
\(493\) 0.322447 0.0145223
\(494\) −28.0519 −1.26211
\(495\) −21.9035 −0.984487
\(496\) 90.9651 4.08445
\(497\) −29.7200 −1.33312
\(498\) −11.7301 −0.525638
\(499\) 28.3413 1.26873 0.634366 0.773033i \(-0.281261\pi\)
0.634366 + 0.773033i \(0.281261\pi\)
\(500\) 66.0780 2.95510
\(501\) −4.87861 −0.217960
\(502\) 6.30230 0.281286
\(503\) −3.42434 −0.152684 −0.0763418 0.997082i \(-0.524324\pi\)
−0.0763418 + 0.997082i \(0.524324\pi\)
\(504\) −71.8687 −3.20129
\(505\) 10.0471 0.447092
\(506\) −74.2998 −3.30303
\(507\) −1.70842 −0.0758735
\(508\) −82.0248 −3.63926
\(509\) −14.1239 −0.626031 −0.313015 0.949748i \(-0.601339\pi\)
−0.313015 + 0.949748i \(0.601339\pi\)
\(510\) 3.52282 0.155993
\(511\) 8.90866 0.394096
\(512\) −62.4014 −2.75778
\(513\) 6.80577 0.300482
\(514\) −63.3154 −2.79272
\(515\) −7.96402 −0.350937
\(516\) −10.3280 −0.454667
\(517\) −34.2687 −1.50714
\(518\) 49.4059 2.17077
\(519\) 9.95833 0.437122
\(520\) 63.8293 2.79910
\(521\) −22.7648 −0.997344 −0.498672 0.866791i \(-0.666179\pi\)
−0.498672 + 0.866791i \(0.666179\pi\)
\(522\) −1.45164 −0.0635363
\(523\) −27.9751 −1.22327 −0.611633 0.791142i \(-0.709487\pi\)
−0.611633 + 0.791142i \(0.709487\pi\)
\(524\) −34.0461 −1.48731
\(525\) −3.01277 −0.131488
\(526\) 41.7599 1.82082
\(527\) −9.87280 −0.430066
\(528\) 35.9568 1.56482
\(529\) 7.53299 0.327521
\(530\) 1.88544 0.0818984
\(531\) −29.7994 −1.29319
\(532\) −36.9146 −1.60045
\(533\) 27.9228 1.20947
\(534\) −14.9879 −0.648590
\(535\) −28.2684 −1.22215
\(536\) 94.6877 4.08989
\(537\) −6.44553 −0.278145
\(538\) −82.6161 −3.56183
\(539\) −0.368548 −0.0158745
\(540\) −24.2333 −1.04284
\(541\) 24.0526 1.03410 0.517052 0.855954i \(-0.327030\pi\)
0.517052 + 0.855954i \(0.327030\pi\)
\(542\) −4.69060 −0.201478
\(543\) 8.52362 0.365784
\(544\) 39.7340 1.70358
\(545\) 20.2364 0.866833
\(546\) −14.0066 −0.599429
\(547\) 38.0708 1.62779 0.813895 0.581011i \(-0.197343\pi\)
0.813895 + 0.581011i \(0.197343\pi\)
\(548\) −31.4010 −1.34138
\(549\) −32.2090 −1.37464
\(550\) −32.3916 −1.38118
\(551\) −0.476474 −0.0202985
\(552\) −25.2605 −1.07516
\(553\) 22.7254 0.966384
\(554\) −44.2955 −1.88193
\(555\) 5.11923 0.217299
\(556\) 77.9926 3.30762
\(557\) −30.8288 −1.30626 −0.653129 0.757246i \(-0.726544\pi\)
−0.653129 + 0.757246i \(0.726544\pi\)
\(558\) 44.4467 1.88158
\(559\) 16.1690 0.683874
\(560\) 66.8692 2.82574
\(561\) −3.90254 −0.164765
\(562\) 60.7056 2.56071
\(563\) −31.0356 −1.30799 −0.653997 0.756497i \(-0.726909\pi\)
−0.653997 + 0.756497i \(0.726909\pi\)
\(564\) −18.2317 −0.767694
\(565\) −5.60786 −0.235924
\(566\) −24.9896 −1.05039
\(567\) −18.7771 −0.788565
\(568\) −108.635 −4.55821
\(569\) −10.8245 −0.453786 −0.226893 0.973920i \(-0.572857\pi\)
−0.226893 + 0.973920i \(0.572857\pi\)
\(570\) −5.20562 −0.218039
\(571\) −3.08269 −0.129007 −0.0645033 0.997917i \(-0.520546\pi\)
−0.0645033 + 0.997917i \(0.520546\pi\)
\(572\) −110.650 −4.62652
\(573\) −0.481867 −0.0201303
\(574\) 50.0085 2.08731
\(575\) 13.3111 0.555112
\(576\) −92.0787 −3.83661
\(577\) −32.6341 −1.35857 −0.679287 0.733873i \(-0.737711\pi\)
−0.679287 + 0.733873i \(0.737711\pi\)
\(578\) 38.7926 1.61356
\(579\) 1.88158 0.0781958
\(580\) 1.69658 0.0704467
\(581\) 24.1659 1.00257
\(582\) −14.5029 −0.601162
\(583\) −2.08867 −0.0865037
\(584\) 32.5636 1.34749
\(585\) 18.2434 0.754273
\(586\) −15.2488 −0.629924
\(587\) −0.246729 −0.0101836 −0.00509180 0.999987i \(-0.501621\pi\)
−0.00509180 + 0.999987i \(0.501621\pi\)
\(588\) −0.196076 −0.00808604
\(589\) 14.5889 0.601123
\(590\) 47.3994 1.95140
\(591\) −6.97049 −0.286728
\(592\) 105.638 4.34170
\(593\) −24.1964 −0.993627 −0.496813 0.867857i \(-0.665497\pi\)
−0.496813 + 0.867857i \(0.665497\pi\)
\(594\) 36.5356 1.49907
\(595\) −7.25758 −0.297532
\(596\) 53.1378 2.17661
\(597\) 3.41453 0.139747
\(598\) 61.8845 2.53065
\(599\) −44.7347 −1.82781 −0.913906 0.405927i \(-0.866949\pi\)
−0.913906 + 0.405927i \(0.866949\pi\)
\(600\) −11.0125 −0.449584
\(601\) 34.4612 1.40570 0.702850 0.711338i \(-0.251910\pi\)
0.702850 + 0.711338i \(0.251910\pi\)
\(602\) 28.9579 1.18023
\(603\) 27.0632 1.10210
\(604\) 76.8438 3.12673
\(605\) −20.8888 −0.849251
\(606\) −8.05891 −0.327371
\(607\) −14.3095 −0.580805 −0.290403 0.956905i \(-0.593789\pi\)
−0.290403 + 0.956905i \(0.593789\pi\)
\(608\) −58.7142 −2.38118
\(609\) −0.237910 −0.00964058
\(610\) 51.2320 2.07432
\(611\) 28.5425 1.15470
\(612\) 26.0990 1.05499
\(613\) 42.8703 1.73151 0.865757 0.500465i \(-0.166838\pi\)
0.865757 + 0.500465i \(0.166838\pi\)
\(614\) 5.77303 0.232981
\(615\) 5.18167 0.208945
\(616\) −126.637 −5.10235
\(617\) 2.19462 0.0883521 0.0441761 0.999024i \(-0.485934\pi\)
0.0441761 + 0.999024i \(0.485934\pi\)
\(618\) 6.38802 0.256964
\(619\) −10.2708 −0.412818 −0.206409 0.978466i \(-0.566178\pi\)
−0.206409 + 0.978466i \(0.566178\pi\)
\(620\) −51.9465 −2.08622
\(621\) −15.0140 −0.602493
\(622\) −21.1393 −0.847610
\(623\) 30.8774 1.23708
\(624\) −29.9485 −1.19890
\(625\) −7.15211 −0.286084
\(626\) 43.6029 1.74272
\(627\) 5.76671 0.230300
\(628\) −26.5631 −1.05998
\(629\) −11.4653 −0.457152
\(630\) 32.6732 1.30173
\(631\) −34.0423 −1.35520 −0.677601 0.735430i \(-0.736980\pi\)
−0.677601 + 0.735430i \(0.736980\pi\)
\(632\) 83.0677 3.30426
\(633\) 1.88758 0.0750245
\(634\) 26.2357 1.04195
\(635\) 23.8298 0.945655
\(636\) −1.11122 −0.0440626
\(637\) 0.306965 0.0121624
\(638\) −2.55787 −0.101267
\(639\) −31.0495 −1.22830
\(640\) 70.9966 2.80639
\(641\) −25.3312 −1.00052 −0.500262 0.865874i \(-0.666763\pi\)
−0.500262 + 0.865874i \(0.666763\pi\)
\(642\) 22.6743 0.894885
\(643\) −22.6069 −0.891528 −0.445764 0.895151i \(-0.647068\pi\)
−0.445764 + 0.895151i \(0.647068\pi\)
\(644\) 81.4364 3.20904
\(645\) 3.00049 0.118144
\(646\) 11.6588 0.458708
\(647\) 38.5836 1.51688 0.758438 0.651745i \(-0.225963\pi\)
0.758438 + 0.651745i \(0.225963\pi\)
\(648\) −68.6355 −2.69626
\(649\) −52.5084 −2.06113
\(650\) 26.9791 1.05821
\(651\) 7.28440 0.285498
\(652\) −30.8069 −1.20649
\(653\) 30.6649 1.20001 0.600006 0.799996i \(-0.295165\pi\)
0.600006 + 0.799996i \(0.295165\pi\)
\(654\) −16.2318 −0.634715
\(655\) 9.89103 0.386474
\(656\) 106.926 4.17478
\(657\) 9.30719 0.363108
\(658\) 51.1182 1.99280
\(659\) 26.1911 1.02026 0.510129 0.860098i \(-0.329598\pi\)
0.510129 + 0.860098i \(0.329598\pi\)
\(660\) −20.5335 −0.799266
\(661\) −28.8131 −1.12070 −0.560349 0.828257i \(-0.689333\pi\)
−0.560349 + 0.828257i \(0.689333\pi\)
\(662\) −75.9958 −2.95366
\(663\) 3.25043 0.126236
\(664\) 88.3328 3.42798
\(665\) 10.7244 0.415874
\(666\) 51.6161 2.00008
\(667\) 1.05114 0.0407002
\(668\) 57.4901 2.22436
\(669\) −0.0759474 −0.00293629
\(670\) −43.0472 −1.66306
\(671\) −56.7541 −2.19097
\(672\) −29.3167 −1.13092
\(673\) 14.7278 0.567716 0.283858 0.958866i \(-0.408386\pi\)
0.283858 + 0.958866i \(0.408386\pi\)
\(674\) 29.1715 1.12364
\(675\) −6.54550 −0.251936
\(676\) 20.1322 0.774315
\(677\) −28.3284 −1.08875 −0.544375 0.838842i \(-0.683233\pi\)
−0.544375 + 0.838842i \(0.683233\pi\)
\(678\) 4.49812 0.172749
\(679\) 29.8782 1.14662
\(680\) −26.5284 −1.01732
\(681\) 3.19540 0.122448
\(682\) 78.3177 2.99894
\(683\) −32.4897 −1.24318 −0.621591 0.783342i \(-0.713513\pi\)
−0.621591 + 0.783342i \(0.713513\pi\)
\(684\) −38.5660 −1.47461
\(685\) 9.12258 0.348556
\(686\) −50.5801 −1.93116
\(687\) −5.60676 −0.213911
\(688\) 61.9167 2.36055
\(689\) 1.73965 0.0662756
\(690\) 11.4840 0.437188
\(691\) −47.5626 −1.80937 −0.904684 0.426084i \(-0.859893\pi\)
−0.904684 + 0.426084i \(0.859893\pi\)
\(692\) −117.350 −4.46098
\(693\) −36.1949 −1.37493
\(694\) 51.5393 1.95641
\(695\) −22.6583 −0.859479
\(696\) −0.869624 −0.0329630
\(697\) −11.6051 −0.439576
\(698\) −68.0338 −2.57512
\(699\) 6.25511 0.236590
\(700\) 35.5029 1.34188
\(701\) −26.3336 −0.994605 −0.497303 0.867577i \(-0.665676\pi\)
−0.497303 + 0.867577i \(0.665676\pi\)
\(702\) −30.4306 −1.14853
\(703\) 16.9421 0.638983
\(704\) −162.248 −6.11496
\(705\) 5.29666 0.199484
\(706\) 29.6346 1.11531
\(707\) 16.6026 0.624406
\(708\) −27.9357 −1.04989
\(709\) −21.2688 −0.798766 −0.399383 0.916784i \(-0.630776\pi\)
−0.399383 + 0.916784i \(0.630776\pi\)
\(710\) 49.3877 1.85349
\(711\) 23.7421 0.890397
\(712\) 112.865 4.22981
\(713\) −32.1841 −1.20530
\(714\) 5.82137 0.217859
\(715\) 32.1460 1.20219
\(716\) 75.9549 2.83857
\(717\) −3.58371 −0.133836
\(718\) −63.1937 −2.35837
\(719\) 28.8499 1.07592 0.537960 0.842970i \(-0.319195\pi\)
0.537960 + 0.842970i \(0.319195\pi\)
\(720\) 69.8606 2.60355
\(721\) −13.1603 −0.490116
\(722\) 34.9466 1.30058
\(723\) 10.0105 0.372295
\(724\) −100.443 −3.73295
\(725\) 0.458252 0.0170191
\(726\) 16.7551 0.621840
\(727\) 0.900002 0.0333792 0.0166896 0.999861i \(-0.494687\pi\)
0.0166896 + 0.999861i \(0.494687\pi\)
\(728\) 105.476 3.90921
\(729\) −15.7845 −0.584610
\(730\) −14.8041 −0.547926
\(731\) −6.72006 −0.248551
\(732\) −30.1945 −1.11602
\(733\) 5.03562 0.185995 0.0929974 0.995666i \(-0.470355\pi\)
0.0929974 + 0.995666i \(0.470355\pi\)
\(734\) 101.837 3.75889
\(735\) 0.0569638 0.00210114
\(736\) 129.528 4.77446
\(737\) 47.6870 1.75657
\(738\) 52.2456 1.92319
\(739\) 17.6396 0.648884 0.324442 0.945906i \(-0.394823\pi\)
0.324442 + 0.945906i \(0.394823\pi\)
\(740\) −60.3257 −2.21762
\(741\) −4.80311 −0.176446
\(742\) 3.11564 0.114379
\(743\) −41.9569 −1.53925 −0.769625 0.638497i \(-0.779557\pi\)
−0.769625 + 0.638497i \(0.779557\pi\)
\(744\) 26.6265 0.976174
\(745\) −15.4375 −0.565587
\(746\) 23.7668 0.870163
\(747\) 25.2469 0.923737
\(748\) 45.9880 1.68149
\(749\) −46.7127 −1.70685
\(750\) 15.3980 0.562256
\(751\) −38.5387 −1.40630 −0.703148 0.711043i \(-0.748223\pi\)
−0.703148 + 0.711043i \(0.748223\pi\)
\(752\) 109.299 3.98573
\(753\) 1.07910 0.0393244
\(754\) 2.13045 0.0775866
\(755\) −22.3246 −0.812474
\(756\) −40.0449 −1.45642
\(757\) −41.5869 −1.51150 −0.755750 0.654860i \(-0.772728\pi\)
−0.755750 + 0.654860i \(0.772728\pi\)
\(758\) −74.8435 −2.71844
\(759\) −12.7218 −0.461772
\(760\) 39.2006 1.42195
\(761\) −45.5773 −1.65218 −0.826088 0.563541i \(-0.809439\pi\)
−0.826088 + 0.563541i \(0.809439\pi\)
\(762\) −19.1141 −0.692430
\(763\) 33.4402 1.21061
\(764\) 5.67838 0.205437
\(765\) −7.58225 −0.274137
\(766\) −55.5530 −2.00721
\(767\) 43.7344 1.57916
\(768\) −25.7885 −0.930562
\(769\) 3.56591 0.128590 0.0642950 0.997931i \(-0.479520\pi\)
0.0642950 + 0.997931i \(0.479520\pi\)
\(770\) 57.5720 2.07475
\(771\) −10.8410 −0.390429
\(772\) −22.1728 −0.798015
\(773\) −36.8221 −1.32440 −0.662200 0.749328i \(-0.730377\pi\)
−0.662200 + 0.749328i \(0.730377\pi\)
\(774\) 30.2533 1.08743
\(775\) −14.0309 −0.504006
\(776\) 109.213 3.92051
\(777\) 8.45939 0.303479
\(778\) −20.7864 −0.745228
\(779\) 17.1487 0.614417
\(780\) 17.1024 0.612365
\(781\) −54.7110 −1.95772
\(782\) −25.7201 −0.919750
\(783\) −0.516878 −0.0184717
\(784\) 1.17548 0.0419813
\(785\) 7.71709 0.275435
\(786\) −7.93369 −0.282985
\(787\) −29.7462 −1.06034 −0.530168 0.847892i \(-0.677871\pi\)
−0.530168 + 0.847892i \(0.677871\pi\)
\(788\) 82.1411 2.92615
\(789\) 7.15023 0.254555
\(790\) −37.7645 −1.34360
\(791\) −9.26683 −0.329491
\(792\) −132.302 −4.70115
\(793\) 47.2706 1.67863
\(794\) −23.2274 −0.824309
\(795\) 0.322830 0.0114496
\(796\) −40.2373 −1.42617
\(797\) 18.0581 0.639652 0.319826 0.947476i \(-0.396376\pi\)
0.319826 + 0.947476i \(0.396376\pi\)
\(798\) −8.60214 −0.304512
\(799\) −11.8627 −0.419671
\(800\) 56.4688 1.99647
\(801\) 32.2587 1.13981
\(802\) 2.36593 0.0835440
\(803\) 16.3998 0.578737
\(804\) 25.3706 0.894752
\(805\) −23.6588 −0.833864
\(806\) −65.2310 −2.29766
\(807\) −14.1457 −0.497953
\(808\) 60.6872 2.13497
\(809\) −36.1766 −1.27190 −0.635951 0.771729i \(-0.719392\pi\)
−0.635951 + 0.771729i \(0.719392\pi\)
\(810\) 31.2033 1.09637
\(811\) −3.75195 −0.131749 −0.0658744 0.997828i \(-0.520984\pi\)
−0.0658744 + 0.997828i \(0.520984\pi\)
\(812\) 2.80355 0.0983855
\(813\) −0.803135 −0.0281672
\(814\) 90.9506 3.18782
\(815\) 8.95000 0.313505
\(816\) 12.4471 0.435734
\(817\) 9.93012 0.347411
\(818\) −59.7749 −2.08998
\(819\) 30.1468 1.05341
\(820\) −61.0614 −2.13236
\(821\) 43.5031 1.51827 0.759134 0.650935i \(-0.225623\pi\)
0.759134 + 0.650935i \(0.225623\pi\)
\(822\) −7.31730 −0.255220
\(823\) 51.9001 1.80913 0.904563 0.426341i \(-0.140198\pi\)
0.904563 + 0.426341i \(0.140198\pi\)
\(824\) −48.1046 −1.67580
\(825\) −5.54617 −0.193093
\(826\) 78.3262 2.72532
\(827\) −34.7769 −1.20931 −0.604655 0.796487i \(-0.706689\pi\)
−0.604655 + 0.796487i \(0.706689\pi\)
\(828\) 85.0795 2.95672
\(829\) −50.2100 −1.74387 −0.871933 0.489625i \(-0.837134\pi\)
−0.871933 + 0.489625i \(0.837134\pi\)
\(830\) −40.1581 −1.39391
\(831\) −7.58437 −0.263099
\(832\) 135.137 4.68503
\(833\) −0.127579 −0.00442036
\(834\) 18.1745 0.629330
\(835\) −16.7020 −0.577996
\(836\) −67.9556 −2.35029
\(837\) 15.8260 0.547025
\(838\) 7.54650 0.260689
\(839\) 46.5277 1.60632 0.803158 0.595766i \(-0.203152\pi\)
0.803158 + 0.595766i \(0.203152\pi\)
\(840\) 19.5733 0.675345
\(841\) −28.9638 −0.998752
\(842\) −20.1601 −0.694764
\(843\) 10.3942 0.357994
\(844\) −22.2435 −0.765651
\(845\) −5.84878 −0.201204
\(846\) 53.4050 1.83610
\(847\) −34.5182 −1.18606
\(848\) 6.66176 0.228766
\(849\) −4.27878 −0.146847
\(850\) −11.2129 −0.384599
\(851\) −37.3755 −1.28122
\(852\) −29.1075 −0.997207
\(853\) 29.3807 1.00597 0.502987 0.864294i \(-0.332234\pi\)
0.502987 + 0.864294i \(0.332234\pi\)
\(854\) 84.6595 2.89699
\(855\) 11.2042 0.383174
\(856\) −170.748 −5.83604
\(857\) 13.9617 0.476924 0.238462 0.971152i \(-0.423357\pi\)
0.238462 + 0.971152i \(0.423357\pi\)
\(858\) −25.7846 −0.880273
\(859\) −3.16770 −0.108081 −0.0540403 0.998539i \(-0.517210\pi\)
−0.0540403 + 0.998539i \(0.517210\pi\)
\(860\) −35.3582 −1.20570
\(861\) 8.56257 0.291812
\(862\) 20.3643 0.693609
\(863\) −9.71500 −0.330703 −0.165351 0.986235i \(-0.552876\pi\)
−0.165351 + 0.986235i \(0.552876\pi\)
\(864\) −63.6930 −2.16688
\(865\) 34.0924 1.15918
\(866\) 95.3959 3.24169
\(867\) 6.64216 0.225579
\(868\) −85.8402 −2.91361
\(869\) 41.8349 1.41915
\(870\) 0.395351 0.0134036
\(871\) −39.7187 −1.34582
\(872\) 122.233 4.13933
\(873\) 31.2148 1.05646
\(874\) 38.0062 1.28558
\(875\) −31.7224 −1.07241
\(876\) 8.72508 0.294793
\(877\) 47.7665 1.61296 0.806480 0.591261i \(-0.201370\pi\)
0.806480 + 0.591261i \(0.201370\pi\)
\(878\) −9.04763 −0.305343
\(879\) −2.61094 −0.0880649
\(880\) 123.099 4.14965
\(881\) 29.7879 1.00358 0.501790 0.864989i \(-0.332675\pi\)
0.501790 + 0.864989i \(0.332675\pi\)
\(882\) 0.574353 0.0193395
\(883\) 33.4635 1.12613 0.563067 0.826411i \(-0.309621\pi\)
0.563067 + 0.826411i \(0.309621\pi\)
\(884\) −38.3035 −1.28829
\(885\) 8.11584 0.272811
\(886\) −14.7795 −0.496526
\(887\) 26.8872 0.902783 0.451391 0.892326i \(-0.350928\pi\)
0.451391 + 0.892326i \(0.350928\pi\)
\(888\) 30.9214 1.03765
\(889\) 39.3780 1.32070
\(890\) −51.3112 −1.71996
\(891\) −34.5665 −1.15802
\(892\) 0.894973 0.0299659
\(893\) 17.5293 0.586595
\(894\) 12.3826 0.414136
\(895\) −22.0663 −0.737596
\(896\) 117.320 3.91938
\(897\) 10.5960 0.353790
\(898\) 31.0363 1.03569
\(899\) −1.10798 −0.0369532
\(900\) 37.0911 1.23637
\(901\) −0.723027 −0.0240875
\(902\) 92.0599 3.06526
\(903\) 4.95823 0.165000
\(904\) −33.8728 −1.12659
\(905\) 29.1807 0.969999
\(906\) 17.9067 0.594912
\(907\) −31.3165 −1.03985 −0.519923 0.854213i \(-0.674040\pi\)
−0.519923 + 0.854213i \(0.674040\pi\)
\(908\) −37.6550 −1.24962
\(909\) 17.3454 0.575309
\(910\) −47.9519 −1.58959
\(911\) −5.68168 −0.188243 −0.0941213 0.995561i \(-0.530004\pi\)
−0.0941213 + 0.995561i \(0.530004\pi\)
\(912\) −18.3928 −0.609046
\(913\) 44.4866 1.47229
\(914\) −4.09997 −0.135615
\(915\) 8.77206 0.289995
\(916\) 66.0707 2.18304
\(917\) 16.3447 0.539748
\(918\) 12.6474 0.417427
\(919\) −12.5936 −0.415426 −0.207713 0.978190i \(-0.566602\pi\)
−0.207713 + 0.978190i \(0.566602\pi\)
\(920\) −86.4794 −2.85114
\(921\) 0.988473 0.0325713
\(922\) −15.8018 −0.520406
\(923\) 45.5690 1.49992
\(924\) −33.9311 −1.11625
\(925\) −16.2942 −0.535749
\(926\) 58.1338 1.91040
\(927\) −13.7491 −0.451578
\(928\) 4.45917 0.146379
\(929\) 7.31497 0.239996 0.119998 0.992774i \(-0.461711\pi\)
0.119998 + 0.992774i \(0.461711\pi\)
\(930\) −12.1050 −0.396938
\(931\) 0.188521 0.00617854
\(932\) −73.7110 −2.41448
\(933\) −3.61953 −0.118498
\(934\) 45.0455 1.47393
\(935\) −13.3604 −0.436931
\(936\) 110.195 3.60183
\(937\) 58.1266 1.89891 0.949456 0.313899i \(-0.101635\pi\)
0.949456 + 0.313899i \(0.101635\pi\)
\(938\) −71.1343 −2.32262
\(939\) 7.46580 0.243637
\(940\) −62.4165 −2.03580
\(941\) −18.5988 −0.606304 −0.303152 0.952942i \(-0.598039\pi\)
−0.303152 + 0.952942i \(0.598039\pi\)
\(942\) −6.18995 −0.201679
\(943\) −37.8314 −1.23196
\(944\) 167.474 5.45083
\(945\) 11.6338 0.378447
\(946\) 53.3081 1.73320
\(947\) 56.7319 1.84354 0.921770 0.387738i \(-0.126743\pi\)
0.921770 + 0.387738i \(0.126743\pi\)
\(948\) 22.2571 0.722878
\(949\) −13.6595 −0.443405
\(950\) 16.5691 0.537573
\(951\) 4.49214 0.145668
\(952\) −43.8375 −1.42078
\(953\) 19.3861 0.627979 0.313989 0.949427i \(-0.398334\pi\)
0.313989 + 0.949427i \(0.398334\pi\)
\(954\) 3.25502 0.105385
\(955\) −1.64968 −0.0533823
\(956\) 42.2309 1.36584
\(957\) −0.437964 −0.0141574
\(958\) −25.6986 −0.830283
\(959\) 15.0748 0.486791
\(960\) 25.0775 0.809373
\(961\) 2.92453 0.0943396
\(962\) −75.7530 −2.44237
\(963\) −48.8024 −1.57264
\(964\) −117.965 −3.79940
\(965\) 6.44161 0.207363
\(966\) 18.9770 0.610574
\(967\) 41.0883 1.32131 0.660655 0.750689i \(-0.270279\pi\)
0.660655 + 0.750689i \(0.270279\pi\)
\(968\) −126.173 −4.05537
\(969\) 1.99624 0.0641285
\(970\) −49.6506 −1.59419
\(971\) −36.8027 −1.18105 −0.590527 0.807018i \(-0.701080\pi\)
−0.590527 + 0.807018i \(0.701080\pi\)
\(972\) −63.5546 −2.03852
\(973\) −37.4423 −1.20034
\(974\) −62.2798 −1.99557
\(975\) 4.61942 0.147940
\(976\) 181.016 5.79418
\(977\) −5.25283 −0.168053 −0.0840264 0.996464i \(-0.526778\pi\)
−0.0840264 + 0.996464i \(0.526778\pi\)
\(978\) −7.17888 −0.229555
\(979\) 56.8418 1.81667
\(980\) −0.671268 −0.0214429
\(981\) 34.9361 1.11542
\(982\) −46.6081 −1.48733
\(983\) −6.69589 −0.213566 −0.106783 0.994282i \(-0.534055\pi\)
−0.106783 + 0.994282i \(0.534055\pi\)
\(984\) 31.2985 0.997761
\(985\) −23.8635 −0.760355
\(986\) −0.885449 −0.0281984
\(987\) 8.75259 0.278598
\(988\) 56.6004 1.80070
\(989\) −21.9066 −0.696589
\(990\) 60.1475 1.91161
\(991\) 34.1011 1.08326 0.541628 0.840618i \(-0.317808\pi\)
0.541628 + 0.840618i \(0.317808\pi\)
\(992\) −136.532 −4.33491
\(993\) −13.0122 −0.412929
\(994\) 81.6119 2.58857
\(995\) 11.6897 0.370588
\(996\) 23.6679 0.749945
\(997\) −6.02981 −0.190966 −0.0954830 0.995431i \(-0.530440\pi\)
−0.0954830 + 0.995431i \(0.530440\pi\)
\(998\) −77.8261 −2.46354
\(999\) 18.3787 0.581477
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 \(a_p\))