Properties

Label 8041.2.a.g.1.19
Level 8041
Weight 2
Character 8041.1
Self dual Yes
Analytic conductor 64.208
Analytic rank 1
Dimension 69
CM No

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Newspace parameters

Level: \( N \) = \( 8041 = 11 \cdot 17 \cdot 43 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8041.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2077082653\)
Analytic rank: \(1\)
Dimension: \(69\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.19
Character \(\chi\) = 8041.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.67732 q^{2} -1.15146 q^{3} +0.813414 q^{4} +0.864739 q^{5} +1.93138 q^{6} +4.27290 q^{7} +1.99029 q^{8} -1.67413 q^{9} +O(q^{10})\) \(q-1.67732 q^{2} -1.15146 q^{3} +0.813414 q^{4} +0.864739 q^{5} +1.93138 q^{6} +4.27290 q^{7} +1.99029 q^{8} -1.67413 q^{9} -1.45045 q^{10} -1.00000 q^{11} -0.936615 q^{12} -3.63737 q^{13} -7.16704 q^{14} -0.995715 q^{15} -4.96519 q^{16} +1.00000 q^{17} +2.80806 q^{18} -5.18808 q^{19} +0.703391 q^{20} -4.92009 q^{21} +1.67732 q^{22} +6.08938 q^{23} -2.29174 q^{24} -4.25223 q^{25} +6.10105 q^{26} +5.38209 q^{27} +3.47564 q^{28} +6.16986 q^{29} +1.67014 q^{30} -8.85311 q^{31} +4.34764 q^{32} +1.15146 q^{33} -1.67732 q^{34} +3.69495 q^{35} -1.36176 q^{36} +3.85625 q^{37} +8.70209 q^{38} +4.18830 q^{39} +1.72108 q^{40} +5.22332 q^{41} +8.25258 q^{42} +1.00000 q^{43} -0.813414 q^{44} -1.44769 q^{45} -10.2139 q^{46} +2.34464 q^{47} +5.71723 q^{48} +11.2577 q^{49} +7.13236 q^{50} -1.15146 q^{51} -2.95869 q^{52} -11.6657 q^{53} -9.02751 q^{54} -0.864739 q^{55} +8.50431 q^{56} +5.97389 q^{57} -10.3488 q^{58} -5.41617 q^{59} -0.809928 q^{60} +8.78057 q^{61} +14.8495 q^{62} -7.15341 q^{63} +2.63797 q^{64} -3.14538 q^{65} -1.93138 q^{66} +4.24084 q^{67} +0.813414 q^{68} -7.01170 q^{69} -6.19762 q^{70} +9.07897 q^{71} -3.33201 q^{72} -9.81684 q^{73} -6.46817 q^{74} +4.89628 q^{75} -4.22006 q^{76} -4.27290 q^{77} -7.02513 q^{78} -12.8691 q^{79} -4.29359 q^{80} -1.17487 q^{81} -8.76120 q^{82} +11.8943 q^{83} -4.00207 q^{84} +0.864739 q^{85} -1.67732 q^{86} -7.10436 q^{87} -1.99029 q^{88} +0.950347 q^{89} +2.42824 q^{90} -15.5421 q^{91} +4.95319 q^{92} +10.1940 q^{93} -3.93272 q^{94} -4.48634 q^{95} -5.00615 q^{96} +4.39615 q^{97} -18.8828 q^{98} +1.67413 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 69q - 11q^{2} - 3q^{3} + 65q^{4} - 6q^{5} - 10q^{6} - 11q^{7} - 33q^{8} + 56q^{9} + O(q^{10}) \) \( 69q - 11q^{2} - 3q^{3} + 65q^{4} - 6q^{5} - 10q^{6} - 11q^{7} - 33q^{8} + 56q^{9} - q^{10} - 69q^{11} - 3q^{12} - 28q^{13} - 15q^{14} - 45q^{15} + 53q^{16} + 69q^{17} - 17q^{18} - 32q^{19} - 21q^{20} - 38q^{21} + 11q^{22} - 41q^{23} - 11q^{24} + 67q^{25} - 6q^{26} - 3q^{27} - 21q^{28} - 22q^{29} - 22q^{30} - 27q^{31} - 87q^{32} + 3q^{33} - 11q^{34} - 44q^{35} + 59q^{36} + 24q^{37} - 22q^{38} - 59q^{39} + q^{40} - 43q^{41} - 15q^{42} + 69q^{43} - 65q^{44} - 12q^{45} - 21q^{46} - 99q^{47} + 2q^{48} + 64q^{49} - 78q^{50} - 3q^{51} - 57q^{52} - 50q^{53} + 20q^{54} + 6q^{55} - 59q^{56} - 15q^{57} + 22q^{58} - 82q^{59} - 86q^{60} - 24q^{61} + 15q^{62} - 63q^{63} + 63q^{64} - 23q^{65} + 10q^{66} - 54q^{67} + 65q^{68} + 36q^{69} + 9q^{70} - 128q^{71} - 69q^{72} + 2q^{73} - 58q^{74} - 31q^{75} - 76q^{76} + 11q^{77} - 19q^{78} - 43q^{79} - 19q^{80} + 49q^{81} - 2q^{82} - 62q^{83} - 82q^{84} - 6q^{85} - 11q^{86} - 62q^{87} + 33q^{88} - 49q^{89} - 37q^{90} - 2q^{91} - 96q^{92} - 29q^{93} - 75q^{94} - 133q^{95} - 86q^{96} + 5q^{97} - 72q^{98} - 56q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.67732 −1.18605 −0.593023 0.805185i \(-0.702066\pi\)
−0.593023 + 0.805185i \(0.702066\pi\)
\(3\) −1.15146 −0.664797 −0.332399 0.943139i \(-0.607858\pi\)
−0.332399 + 0.943139i \(0.607858\pi\)
\(4\) 0.813414 0.406707
\(5\) 0.864739 0.386723 0.193362 0.981128i \(-0.438061\pi\)
0.193362 + 0.981128i \(0.438061\pi\)
\(6\) 1.93138 0.788481
\(7\) 4.27290 1.61501 0.807503 0.589864i \(-0.200819\pi\)
0.807503 + 0.589864i \(0.200819\pi\)
\(8\) 1.99029 0.703673
\(9\) −1.67413 −0.558045
\(10\) −1.45045 −0.458672
\(11\) −1.00000 −0.301511
\(12\) −0.936615 −0.270378
\(13\) −3.63737 −1.00883 −0.504413 0.863463i \(-0.668291\pi\)
−0.504413 + 0.863463i \(0.668291\pi\)
\(14\) −7.16704 −1.91547
\(15\) −0.995715 −0.257092
\(16\) −4.96519 −1.24130
\(17\) 1.00000 0.242536
\(18\) 2.80806 0.661867
\(19\) −5.18808 −1.19023 −0.595114 0.803641i \(-0.702893\pi\)
−0.595114 + 0.803641i \(0.702893\pi\)
\(20\) 0.703391 0.157283
\(21\) −4.92009 −1.07365
\(22\) 1.67732 0.357607
\(23\) 6.08938 1.26972 0.634862 0.772625i \(-0.281057\pi\)
0.634862 + 0.772625i \(0.281057\pi\)
\(24\) −2.29174 −0.467800
\(25\) −4.25223 −0.850445
\(26\) 6.10105 1.19651
\(27\) 5.38209 1.03578
\(28\) 3.47564 0.656834
\(29\) 6.16986 1.14571 0.572857 0.819655i \(-0.305835\pi\)
0.572857 + 0.819655i \(0.305835\pi\)
\(30\) 1.67014 0.304924
\(31\) −8.85311 −1.59007 −0.795033 0.606566i \(-0.792547\pi\)
−0.795033 + 0.606566i \(0.792547\pi\)
\(32\) 4.34764 0.768562
\(33\) 1.15146 0.200444
\(34\) −1.67732 −0.287659
\(35\) 3.69495 0.624560
\(36\) −1.36176 −0.226961
\(37\) 3.85625 0.633963 0.316981 0.948432i \(-0.397331\pi\)
0.316981 + 0.948432i \(0.397331\pi\)
\(38\) 8.70209 1.41167
\(39\) 4.18830 0.670665
\(40\) 1.72108 0.272127
\(41\) 5.22332 0.815746 0.407873 0.913039i \(-0.366271\pi\)
0.407873 + 0.913039i \(0.366271\pi\)
\(42\) 8.25258 1.27340
\(43\) 1.00000 0.152499
\(44\) −0.813414 −0.122627
\(45\) −1.44769 −0.215809
\(46\) −10.2139 −1.50595
\(47\) 2.34464 0.342001 0.171000 0.985271i \(-0.445300\pi\)
0.171000 + 0.985271i \(0.445300\pi\)
\(48\) 5.71723 0.825210
\(49\) 11.2577 1.60824
\(50\) 7.13236 1.00867
\(51\) −1.15146 −0.161237
\(52\) −2.95869 −0.410296
\(53\) −11.6657 −1.60241 −0.801205 0.598391i \(-0.795807\pi\)
−0.801205 + 0.598391i \(0.795807\pi\)
\(54\) −9.02751 −1.22849
\(55\) −0.864739 −0.116601
\(56\) 8.50431 1.13644
\(57\) 5.97389 0.791260
\(58\) −10.3488 −1.35887
\(59\) −5.41617 −0.705125 −0.352562 0.935788i \(-0.614690\pi\)
−0.352562 + 0.935788i \(0.614690\pi\)
\(60\) −0.809928 −0.104561
\(61\) 8.78057 1.12424 0.562118 0.827057i \(-0.309987\pi\)
0.562118 + 0.827057i \(0.309987\pi\)
\(62\) 14.8495 1.88589
\(63\) −7.15341 −0.901245
\(64\) 2.63797 0.329746
\(65\) −3.14538 −0.390136
\(66\) −1.93138 −0.237736
\(67\) 4.24084 0.518101 0.259050 0.965864i \(-0.416590\pi\)
0.259050 + 0.965864i \(0.416590\pi\)
\(68\) 0.813414 0.0986409
\(69\) −7.01170 −0.844109
\(70\) −6.19762 −0.740757
\(71\) 9.07897 1.07747 0.538737 0.842474i \(-0.318901\pi\)
0.538737 + 0.842474i \(0.318901\pi\)
\(72\) −3.33201 −0.392681
\(73\) −9.81684 −1.14897 −0.574487 0.818514i \(-0.694798\pi\)
−0.574487 + 0.818514i \(0.694798\pi\)
\(74\) −6.46817 −0.751910
\(75\) 4.89628 0.565374
\(76\) −4.22006 −0.484074
\(77\) −4.27290 −0.486942
\(78\) −7.02513 −0.795440
\(79\) −12.8691 −1.44789 −0.723946 0.689857i \(-0.757673\pi\)
−0.723946 + 0.689857i \(0.757673\pi\)
\(80\) −4.29359 −0.480038
\(81\) −1.17487 −0.130542
\(82\) −8.76120 −0.967513
\(83\) 11.8943 1.30557 0.652784 0.757544i \(-0.273601\pi\)
0.652784 + 0.757544i \(0.273601\pi\)
\(84\) −4.00207 −0.436661
\(85\) 0.864739 0.0937941
\(86\) −1.67732 −0.180870
\(87\) −7.10436 −0.761667
\(88\) −1.99029 −0.212166
\(89\) 0.950347 0.100737 0.0503683 0.998731i \(-0.483960\pi\)
0.0503683 + 0.998731i \(0.483960\pi\)
\(90\) 2.42824 0.255959
\(91\) −15.5421 −1.62926
\(92\) 4.95319 0.516405
\(93\) 10.1940 1.05707
\(94\) −3.93272 −0.405629
\(95\) −4.48634 −0.460289
\(96\) −5.00615 −0.510938
\(97\) 4.39615 0.446362 0.223181 0.974777i \(-0.428356\pi\)
0.223181 + 0.974777i \(0.428356\pi\)
\(98\) −18.8828 −1.90745
\(99\) 1.67413 0.168257
\(100\) −3.45882 −0.345882
\(101\) 7.01478 0.697997 0.348998 0.937123i \(-0.386522\pi\)
0.348998 + 0.937123i \(0.386522\pi\)
\(102\) 1.93138 0.191235
\(103\) −15.2667 −1.50427 −0.752137 0.659007i \(-0.770977\pi\)
−0.752137 + 0.659007i \(0.770977\pi\)
\(104\) −7.23943 −0.709884
\(105\) −4.25459 −0.415206
\(106\) 19.5672 1.90053
\(107\) −11.1033 −1.07340 −0.536700 0.843773i \(-0.680329\pi\)
−0.536700 + 0.843773i \(0.680329\pi\)
\(108\) 4.37787 0.421260
\(109\) 15.3496 1.47023 0.735113 0.677944i \(-0.237129\pi\)
0.735113 + 0.677944i \(0.237129\pi\)
\(110\) 1.45045 0.138295
\(111\) −4.44032 −0.421457
\(112\) −21.2158 −2.00470
\(113\) −6.36107 −0.598399 −0.299199 0.954191i \(-0.596720\pi\)
−0.299199 + 0.954191i \(0.596720\pi\)
\(114\) −10.0201 −0.938472
\(115\) 5.26573 0.491032
\(116\) 5.01865 0.465970
\(117\) 6.08945 0.562970
\(118\) 9.08466 0.836311
\(119\) 4.27290 0.391696
\(120\) −1.98176 −0.180909
\(121\) 1.00000 0.0909091
\(122\) −14.7278 −1.33340
\(123\) −6.01446 −0.542306
\(124\) −7.20124 −0.646691
\(125\) −8.00076 −0.715610
\(126\) 11.9986 1.06892
\(127\) −17.3234 −1.53720 −0.768602 0.639728i \(-0.779047\pi\)
−0.768602 + 0.639728i \(0.779047\pi\)
\(128\) −13.1200 −1.15966
\(129\) −1.15146 −0.101381
\(130\) 5.27582 0.462720
\(131\) −14.0079 −1.22388 −0.611939 0.790905i \(-0.709610\pi\)
−0.611939 + 0.790905i \(0.709610\pi\)
\(132\) 0.936615 0.0815219
\(133\) −22.1682 −1.92222
\(134\) −7.11325 −0.614492
\(135\) 4.65410 0.400562
\(136\) 1.99029 0.170666
\(137\) −5.28457 −0.451491 −0.225745 0.974186i \(-0.572482\pi\)
−0.225745 + 0.974186i \(0.572482\pi\)
\(138\) 11.7609 1.00115
\(139\) 6.72632 0.570519 0.285259 0.958450i \(-0.407920\pi\)
0.285259 + 0.958450i \(0.407920\pi\)
\(140\) 3.00552 0.254013
\(141\) −2.69976 −0.227361
\(142\) −15.2284 −1.27794
\(143\) 3.63737 0.304172
\(144\) 8.31238 0.692699
\(145\) 5.33532 0.443074
\(146\) 16.4660 1.36274
\(147\) −12.9628 −1.06915
\(148\) 3.13672 0.257837
\(149\) −13.4692 −1.10344 −0.551720 0.834030i \(-0.686028\pi\)
−0.551720 + 0.834030i \(0.686028\pi\)
\(150\) −8.21264 −0.670560
\(151\) 10.8352 0.881754 0.440877 0.897567i \(-0.354667\pi\)
0.440877 + 0.897567i \(0.354667\pi\)
\(152\) −10.3258 −0.837532
\(153\) −1.67413 −0.135346
\(154\) 7.16704 0.577536
\(155\) −7.65563 −0.614915
\(156\) 3.40682 0.272764
\(157\) −18.8229 −1.50223 −0.751115 0.660172i \(-0.770484\pi\)
−0.751115 + 0.660172i \(0.770484\pi\)
\(158\) 21.5857 1.71727
\(159\) 13.4326 1.06528
\(160\) 3.75958 0.297221
\(161\) 26.0193 2.05061
\(162\) 1.97064 0.154828
\(163\) 11.1814 0.875796 0.437898 0.899025i \(-0.355723\pi\)
0.437898 + 0.899025i \(0.355723\pi\)
\(164\) 4.24872 0.331769
\(165\) 0.995715 0.0775163
\(166\) −19.9506 −1.54846
\(167\) 17.5563 1.35855 0.679274 0.733884i \(-0.262295\pi\)
0.679274 + 0.733884i \(0.262295\pi\)
\(168\) −9.79240 −0.755500
\(169\) 0.230488 0.0177298
\(170\) −1.45045 −0.111244
\(171\) 8.68555 0.664200
\(172\) 0.813414 0.0620222
\(173\) −9.34971 −0.710845 −0.355423 0.934706i \(-0.615663\pi\)
−0.355423 + 0.934706i \(0.615663\pi\)
\(174\) 11.9163 0.903373
\(175\) −18.1693 −1.37347
\(176\) 4.96519 0.374265
\(177\) 6.23651 0.468765
\(178\) −1.59404 −0.119478
\(179\) −13.3130 −0.995059 −0.497529 0.867447i \(-0.665759\pi\)
−0.497529 + 0.867447i \(0.665759\pi\)
\(180\) −1.17757 −0.0877709
\(181\) 1.56808 0.116554 0.0582772 0.998300i \(-0.481439\pi\)
0.0582772 + 0.998300i \(0.481439\pi\)
\(182\) 26.0692 1.93238
\(183\) −10.1105 −0.747389
\(184\) 12.1196 0.893471
\(185\) 3.33465 0.245168
\(186\) −17.0987 −1.25374
\(187\) −1.00000 −0.0731272
\(188\) 1.90716 0.139094
\(189\) 22.9971 1.67280
\(190\) 7.52504 0.545924
\(191\) 14.1536 1.02412 0.512059 0.858950i \(-0.328883\pi\)
0.512059 + 0.858950i \(0.328883\pi\)
\(192\) −3.03752 −0.219214
\(193\) 0.170964 0.0123062 0.00615311 0.999981i \(-0.498041\pi\)
0.00615311 + 0.999981i \(0.498041\pi\)
\(194\) −7.37377 −0.529406
\(195\) 3.62179 0.259362
\(196\) 9.15716 0.654083
\(197\) 9.57856 0.682444 0.341222 0.939983i \(-0.389159\pi\)
0.341222 + 0.939983i \(0.389159\pi\)
\(198\) −2.80806 −0.199560
\(199\) −9.03919 −0.640771 −0.320386 0.947287i \(-0.603813\pi\)
−0.320386 + 0.947287i \(0.603813\pi\)
\(200\) −8.46316 −0.598436
\(201\) −4.88316 −0.344432
\(202\) −11.7661 −0.827857
\(203\) 26.3632 1.85033
\(204\) −0.936615 −0.0655762
\(205\) 4.51681 0.315468
\(206\) 25.6072 1.78414
\(207\) −10.1944 −0.708563
\(208\) 18.0602 1.25225
\(209\) 5.18808 0.358867
\(210\) 7.13633 0.492453
\(211\) 24.8770 1.71260 0.856302 0.516475i \(-0.172756\pi\)
0.856302 + 0.516475i \(0.172756\pi\)
\(212\) −9.48905 −0.651711
\(213\) −10.4541 −0.716302
\(214\) 18.6239 1.27310
\(215\) 0.864739 0.0589747
\(216\) 10.7119 0.728854
\(217\) −37.8285 −2.56797
\(218\) −25.7463 −1.74376
\(219\) 11.3037 0.763835
\(220\) −0.703391 −0.0474226
\(221\) −3.63737 −0.244676
\(222\) 7.44786 0.499867
\(223\) −7.15198 −0.478932 −0.239466 0.970905i \(-0.576972\pi\)
−0.239466 + 0.970905i \(0.576972\pi\)
\(224\) 18.5771 1.24123
\(225\) 7.11880 0.474586
\(226\) 10.6696 0.709729
\(227\) −5.08228 −0.337323 −0.168661 0.985674i \(-0.553944\pi\)
−0.168661 + 0.985674i \(0.553944\pi\)
\(228\) 4.85924 0.321811
\(229\) −21.0669 −1.39214 −0.696071 0.717973i \(-0.745070\pi\)
−0.696071 + 0.717973i \(0.745070\pi\)
\(230\) −8.83233 −0.582387
\(231\) 4.92009 0.323718
\(232\) 12.2798 0.806208
\(233\) −9.41555 −0.616833 −0.308417 0.951251i \(-0.599799\pi\)
−0.308417 + 0.951251i \(0.599799\pi\)
\(234\) −10.2140 −0.667709
\(235\) 2.02750 0.132260
\(236\) −4.40558 −0.286779
\(237\) 14.8183 0.962554
\(238\) −7.16704 −0.464570
\(239\) −9.63432 −0.623192 −0.311596 0.950215i \(-0.600864\pi\)
−0.311596 + 0.950215i \(0.600864\pi\)
\(240\) 4.94391 0.319128
\(241\) 13.6007 0.876100 0.438050 0.898951i \(-0.355669\pi\)
0.438050 + 0.898951i \(0.355669\pi\)
\(242\) −1.67732 −0.107822
\(243\) −14.7934 −0.949000
\(244\) 7.14223 0.457234
\(245\) 9.73497 0.621944
\(246\) 10.0882 0.643200
\(247\) 18.8710 1.20073
\(248\) −17.6203 −1.11889
\(249\) −13.6958 −0.867937
\(250\) 13.4199 0.848747
\(251\) 16.9772 1.07159 0.535796 0.844348i \(-0.320012\pi\)
0.535796 + 0.844348i \(0.320012\pi\)
\(252\) −5.81868 −0.366542
\(253\) −6.08938 −0.382836
\(254\) 29.0569 1.82319
\(255\) −0.995715 −0.0623541
\(256\) 16.7306 1.04566
\(257\) −20.9979 −1.30981 −0.654907 0.755710i \(-0.727292\pi\)
−0.654907 + 0.755710i \(0.727292\pi\)
\(258\) 1.93138 0.120242
\(259\) 16.4774 1.02385
\(260\) −2.55849 −0.158671
\(261\) −10.3292 −0.639359
\(262\) 23.4958 1.45158
\(263\) 1.58540 0.0977598 0.0488799 0.998805i \(-0.484435\pi\)
0.0488799 + 0.998805i \(0.484435\pi\)
\(264\) 2.29174 0.141047
\(265\) −10.0878 −0.619689
\(266\) 37.1832 2.27985
\(267\) −1.09429 −0.0669694
\(268\) 3.44955 0.210715
\(269\) −5.84899 −0.356619 −0.178310 0.983974i \(-0.557063\pi\)
−0.178310 + 0.983974i \(0.557063\pi\)
\(270\) −7.80644 −0.475085
\(271\) 29.8039 1.81046 0.905229 0.424923i \(-0.139699\pi\)
0.905229 + 0.424923i \(0.139699\pi\)
\(272\) −4.96519 −0.301059
\(273\) 17.8962 1.08313
\(274\) 8.86393 0.535489
\(275\) 4.25223 0.256419
\(276\) −5.70341 −0.343305
\(277\) −16.4703 −0.989604 −0.494802 0.869006i \(-0.664759\pi\)
−0.494802 + 0.869006i \(0.664759\pi\)
\(278\) −11.2822 −0.676662
\(279\) 14.8213 0.887328
\(280\) 7.35401 0.439486
\(281\) −11.8918 −0.709403 −0.354702 0.934980i \(-0.615418\pi\)
−0.354702 + 0.934980i \(0.615418\pi\)
\(282\) 4.52838 0.269661
\(283\) 19.3990 1.15315 0.576576 0.817044i \(-0.304388\pi\)
0.576576 + 0.817044i \(0.304388\pi\)
\(284\) 7.38495 0.438216
\(285\) 5.16585 0.305999
\(286\) −6.10105 −0.360763
\(287\) 22.3187 1.31743
\(288\) −7.27854 −0.428892
\(289\) 1.00000 0.0588235
\(290\) −8.94905 −0.525506
\(291\) −5.06201 −0.296740
\(292\) −7.98515 −0.467295
\(293\) 0.229983 0.0134357 0.00671787 0.999977i \(-0.497862\pi\)
0.00671787 + 0.999977i \(0.497862\pi\)
\(294\) 21.7428 1.26807
\(295\) −4.68357 −0.272688
\(296\) 7.67505 0.446103
\(297\) −5.38209 −0.312301
\(298\) 22.5922 1.30873
\(299\) −22.1494 −1.28093
\(300\) 3.98270 0.229941
\(301\) 4.27290 0.246286
\(302\) −18.1741 −1.04580
\(303\) −8.07726 −0.464026
\(304\) 25.7598 1.47743
\(305\) 7.59290 0.434768
\(306\) 2.80806 0.160526
\(307\) 31.5765 1.80217 0.901083 0.433648i \(-0.142774\pi\)
0.901083 + 0.433648i \(0.142774\pi\)
\(308\) −3.47564 −0.198043
\(309\) 17.5790 1.00004
\(310\) 12.8410 0.729318
\(311\) −14.9980 −0.850459 −0.425230 0.905086i \(-0.639807\pi\)
−0.425230 + 0.905086i \(0.639807\pi\)
\(312\) 8.33593 0.471929
\(313\) −8.09259 −0.457420 −0.228710 0.973495i \(-0.573451\pi\)
−0.228710 + 0.973495i \(0.573451\pi\)
\(314\) 31.5721 1.78171
\(315\) −6.18583 −0.348532
\(316\) −10.4679 −0.588867
\(317\) −18.3538 −1.03085 −0.515425 0.856935i \(-0.672366\pi\)
−0.515425 + 0.856935i \(0.672366\pi\)
\(318\) −22.5309 −1.26347
\(319\) −6.16986 −0.345446
\(320\) 2.28115 0.127520
\(321\) 12.7851 0.713593
\(322\) −43.6428 −2.43212
\(323\) −5.18808 −0.288673
\(324\) −0.955659 −0.0530922
\(325\) 15.4669 0.857951
\(326\) −18.7548 −1.03873
\(327\) −17.6745 −0.977402
\(328\) 10.3959 0.574019
\(329\) 10.0184 0.552333
\(330\) −1.67014 −0.0919379
\(331\) 20.9775 1.15303 0.576514 0.817088i \(-0.304413\pi\)
0.576514 + 0.817088i \(0.304413\pi\)
\(332\) 9.67497 0.530983
\(333\) −6.45587 −0.353780
\(334\) −29.4476 −1.61130
\(335\) 3.66722 0.200361
\(336\) 24.4291 1.33272
\(337\) 6.12489 0.333644 0.166822 0.985987i \(-0.446649\pi\)
0.166822 + 0.985987i \(0.446649\pi\)
\(338\) −0.386603 −0.0210284
\(339\) 7.32453 0.397814
\(340\) 0.703391 0.0381467
\(341\) 8.85311 0.479423
\(342\) −14.5685 −0.787773
\(343\) 18.1927 0.982314
\(344\) 1.99029 0.107309
\(345\) −6.06329 −0.326437
\(346\) 15.6825 0.843096
\(347\) 2.02113 0.108500 0.0542499 0.998527i \(-0.482723\pi\)
0.0542499 + 0.998527i \(0.482723\pi\)
\(348\) −5.77878 −0.309775
\(349\) 21.1727 1.13335 0.566675 0.823941i \(-0.308229\pi\)
0.566675 + 0.823941i \(0.308229\pi\)
\(350\) 30.4759 1.62900
\(351\) −19.5767 −1.04493
\(352\) −4.34764 −0.231730
\(353\) 31.0972 1.65514 0.827568 0.561365i \(-0.189724\pi\)
0.827568 + 0.561365i \(0.189724\pi\)
\(354\) −10.4606 −0.555977
\(355\) 7.85094 0.416684
\(356\) 0.773025 0.0409703
\(357\) −4.92009 −0.260399
\(358\) 22.3302 1.18019
\(359\) −11.8162 −0.623635 −0.311818 0.950142i \(-0.600938\pi\)
−0.311818 + 0.950142i \(0.600938\pi\)
\(360\) −2.88132 −0.151859
\(361\) 7.91622 0.416643
\(362\) −2.63018 −0.138239
\(363\) −1.15146 −0.0604361
\(364\) −12.6422 −0.662631
\(365\) −8.48900 −0.444335
\(366\) 16.9586 0.886439
\(367\) −3.77522 −0.197065 −0.0985325 0.995134i \(-0.531415\pi\)
−0.0985325 + 0.995134i \(0.531415\pi\)
\(368\) −30.2349 −1.57610
\(369\) −8.74454 −0.455223
\(370\) −5.59328 −0.290781
\(371\) −49.8465 −2.58790
\(372\) 8.29196 0.429918
\(373\) 3.50210 0.181332 0.0906658 0.995881i \(-0.471100\pi\)
0.0906658 + 0.995881i \(0.471100\pi\)
\(374\) 1.67732 0.0867323
\(375\) 9.21258 0.475736
\(376\) 4.66651 0.240657
\(377\) −22.4421 −1.15583
\(378\) −38.5736 −1.98401
\(379\) −3.67954 −0.189005 −0.0945026 0.995525i \(-0.530126\pi\)
−0.0945026 + 0.995525i \(0.530126\pi\)
\(380\) −3.64925 −0.187203
\(381\) 19.9472 1.02193
\(382\) −23.7401 −1.21465
\(383\) −16.7645 −0.856626 −0.428313 0.903631i \(-0.640892\pi\)
−0.428313 + 0.903631i \(0.640892\pi\)
\(384\) 15.1072 0.770936
\(385\) −3.69495 −0.188312
\(386\) −0.286761 −0.0145958
\(387\) −1.67413 −0.0851010
\(388\) 3.57589 0.181538
\(389\) −30.4907 −1.54594 −0.772970 0.634442i \(-0.781230\pi\)
−0.772970 + 0.634442i \(0.781230\pi\)
\(390\) −6.07491 −0.307615
\(391\) 6.08938 0.307953
\(392\) 22.4061 1.13168
\(393\) 16.1296 0.813631
\(394\) −16.0663 −0.809411
\(395\) −11.1285 −0.559933
\(396\) 1.36176 0.0684312
\(397\) 8.46300 0.424746 0.212373 0.977189i \(-0.431881\pi\)
0.212373 + 0.977189i \(0.431881\pi\)
\(398\) 15.1616 0.759985
\(399\) 25.5258 1.27789
\(400\) 21.1131 1.05565
\(401\) −26.6014 −1.32841 −0.664205 0.747550i \(-0.731230\pi\)
−0.664205 + 0.747550i \(0.731230\pi\)
\(402\) 8.19065 0.408512
\(403\) 32.2021 1.60410
\(404\) 5.70592 0.283880
\(405\) −1.01596 −0.0504835
\(406\) −44.2196 −2.19458
\(407\) −3.85625 −0.191147
\(408\) −2.29174 −0.113458
\(409\) −3.42813 −0.169510 −0.0847551 0.996402i \(-0.527011\pi\)
−0.0847551 + 0.996402i \(0.527011\pi\)
\(410\) −7.57615 −0.374160
\(411\) 6.08498 0.300150
\(412\) −12.4181 −0.611798
\(413\) −23.1428 −1.13878
\(414\) 17.0994 0.840388
\(415\) 10.2855 0.504893
\(416\) −15.8140 −0.775345
\(417\) −7.74510 −0.379279
\(418\) −8.70209 −0.425633
\(419\) −26.7252 −1.30561 −0.652806 0.757525i \(-0.726408\pi\)
−0.652806 + 0.757525i \(0.726408\pi\)
\(420\) −3.46074 −0.168867
\(421\) 16.6101 0.809525 0.404762 0.914422i \(-0.367354\pi\)
0.404762 + 0.914422i \(0.367354\pi\)
\(422\) −41.7268 −2.03123
\(423\) −3.92524 −0.190852
\(424\) −23.2181 −1.12757
\(425\) −4.25223 −0.206263
\(426\) 17.5349 0.849568
\(427\) 37.5185 1.81565
\(428\) −9.03160 −0.436559
\(429\) −4.18830 −0.202213
\(430\) −1.45045 −0.0699468
\(431\) 1.36297 0.0656517 0.0328259 0.999461i \(-0.489549\pi\)
0.0328259 + 0.999461i \(0.489549\pi\)
\(432\) −26.7231 −1.28571
\(433\) −31.6453 −1.52078 −0.760389 0.649468i \(-0.774992\pi\)
−0.760389 + 0.649468i \(0.774992\pi\)
\(434\) 63.4506 3.04573
\(435\) −6.14342 −0.294554
\(436\) 12.4856 0.597951
\(437\) −31.5922 −1.51126
\(438\) −18.9600 −0.905944
\(439\) −6.83218 −0.326082 −0.163041 0.986619i \(-0.552130\pi\)
−0.163041 + 0.986619i \(0.552130\pi\)
\(440\) −1.72108 −0.0820493
\(441\) −18.8469 −0.897471
\(442\) 6.10105 0.290197
\(443\) 20.0838 0.954208 0.477104 0.878847i \(-0.341686\pi\)
0.477104 + 0.878847i \(0.341686\pi\)
\(444\) −3.61182 −0.171409
\(445\) 0.821803 0.0389572
\(446\) 11.9962 0.568035
\(447\) 15.5093 0.733564
\(448\) 11.2718 0.532542
\(449\) 0.204759 0.00966317 0.00483158 0.999988i \(-0.498462\pi\)
0.00483158 + 0.999988i \(0.498462\pi\)
\(450\) −11.9405 −0.562882
\(451\) −5.22332 −0.245957
\(452\) −5.17418 −0.243373
\(453\) −12.4763 −0.586188
\(454\) 8.52462 0.400080
\(455\) −13.4399 −0.630072
\(456\) 11.8898 0.556789
\(457\) −0.622232 −0.0291068 −0.0145534 0.999894i \(-0.504633\pi\)
−0.0145534 + 0.999894i \(0.504633\pi\)
\(458\) 35.3361 1.65115
\(459\) 5.38209 0.251214
\(460\) 4.28321 0.199706
\(461\) −24.2058 −1.12738 −0.563689 0.825987i \(-0.690618\pi\)
−0.563689 + 0.825987i \(0.690618\pi\)
\(462\) −8.25258 −0.383945
\(463\) 2.35716 0.109547 0.0547733 0.998499i \(-0.482556\pi\)
0.0547733 + 0.998499i \(0.482556\pi\)
\(464\) −30.6345 −1.42217
\(465\) 8.81518 0.408794
\(466\) 15.7929 0.731593
\(467\) 7.43362 0.343987 0.171993 0.985098i \(-0.444979\pi\)
0.171993 + 0.985098i \(0.444979\pi\)
\(468\) 4.95324 0.228964
\(469\) 18.1207 0.836735
\(470\) −3.40078 −0.156866
\(471\) 21.6738 0.998678
\(472\) −10.7797 −0.496178
\(473\) −1.00000 −0.0459800
\(474\) −24.8551 −1.14163
\(475\) 22.0609 1.01222
\(476\) 3.47564 0.159306
\(477\) 19.5300 0.894216
\(478\) 16.1599 0.739135
\(479\) −34.7011 −1.58553 −0.792767 0.609525i \(-0.791360\pi\)
−0.792767 + 0.609525i \(0.791360\pi\)
\(480\) −4.32901 −0.197591
\(481\) −14.0266 −0.639558
\(482\) −22.8128 −1.03910
\(483\) −29.9603 −1.36324
\(484\) 0.813414 0.0369733
\(485\) 3.80153 0.172618
\(486\) 24.8134 1.12556
\(487\) 14.0865 0.638320 0.319160 0.947701i \(-0.396599\pi\)
0.319160 + 0.947701i \(0.396599\pi\)
\(488\) 17.4759 0.791095
\(489\) −12.8750 −0.582227
\(490\) −16.3287 −0.737655
\(491\) −29.6256 −1.33699 −0.668493 0.743719i \(-0.733060\pi\)
−0.668493 + 0.743719i \(0.733060\pi\)
\(492\) −4.89224 −0.220559
\(493\) 6.16986 0.277876
\(494\) −31.6528 −1.42413
\(495\) 1.44769 0.0650688
\(496\) 43.9574 1.97374
\(497\) 38.7935 1.74013
\(498\) 22.9723 1.02941
\(499\) −31.1634 −1.39506 −0.697532 0.716554i \(-0.745718\pi\)
−0.697532 + 0.716554i \(0.745718\pi\)
\(500\) −6.50793 −0.291043
\(501\) −20.2154 −0.903160
\(502\) −28.4762 −1.27096
\(503\) 8.86786 0.395398 0.197699 0.980263i \(-0.436653\pi\)
0.197699 + 0.980263i \(0.436653\pi\)
\(504\) −14.2374 −0.634182
\(505\) 6.06596 0.269932
\(506\) 10.2139 0.454062
\(507\) −0.265398 −0.0117867
\(508\) −14.0911 −0.625191
\(509\) −24.8705 −1.10236 −0.551182 0.834385i \(-0.685823\pi\)
−0.551182 + 0.834385i \(0.685823\pi\)
\(510\) 1.67014 0.0739549
\(511\) −41.9464 −1.85560
\(512\) −1.82254 −0.0805458
\(513\) −27.9227 −1.23282
\(514\) 35.2203 1.55350
\(515\) −13.2017 −0.581737
\(516\) −0.936615 −0.0412322
\(517\) −2.34464 −0.103117
\(518\) −27.6379 −1.21434
\(519\) 10.7658 0.472568
\(520\) −6.26022 −0.274529
\(521\) −2.89692 −0.126916 −0.0634582 0.997984i \(-0.520213\pi\)
−0.0634582 + 0.997984i \(0.520213\pi\)
\(522\) 17.3254 0.758310
\(523\) −31.1372 −1.36154 −0.680768 0.732499i \(-0.738354\pi\)
−0.680768 + 0.732499i \(0.738354\pi\)
\(524\) −11.3942 −0.497760
\(525\) 20.9213 0.913081
\(526\) −2.65922 −0.115948
\(527\) −8.85311 −0.385648
\(528\) −5.71723 −0.248810
\(529\) 14.0806 0.612200
\(530\) 16.9205 0.734980
\(531\) 9.06739 0.393491
\(532\) −18.0319 −0.781782
\(533\) −18.9992 −0.822946
\(534\) 1.83548 0.0794289
\(535\) −9.60148 −0.415108
\(536\) 8.44049 0.364574
\(537\) 15.3294 0.661512
\(538\) 9.81065 0.422967
\(539\) −11.2577 −0.484903
\(540\) 3.78571 0.162911
\(541\) −45.2449 −1.94523 −0.972616 0.232417i \(-0.925336\pi\)
−0.972616 + 0.232417i \(0.925336\pi\)
\(542\) −49.9908 −2.14729
\(543\) −1.80558 −0.0774851
\(544\) 4.34764 0.186404
\(545\) 13.2734 0.568571
\(546\) −30.0177 −1.28464
\(547\) −27.0170 −1.15516 −0.577582 0.816332i \(-0.696004\pi\)
−0.577582 + 0.816332i \(0.696004\pi\)
\(548\) −4.29854 −0.183624
\(549\) −14.6998 −0.627374
\(550\) −7.13236 −0.304125
\(551\) −32.0097 −1.36366
\(552\) −13.9553 −0.593977
\(553\) −54.9886 −2.33835
\(554\) 27.6260 1.17372
\(555\) −3.83972 −0.162987
\(556\) 5.47128 0.232034
\(557\) −0.490211 −0.0207709 −0.0103855 0.999946i \(-0.503306\pi\)
−0.0103855 + 0.999946i \(0.503306\pi\)
\(558\) −24.8601 −1.05241
\(559\) −3.63737 −0.153845
\(560\) −18.3461 −0.775264
\(561\) 1.15146 0.0486148
\(562\) 19.9463 0.841385
\(563\) −16.8842 −0.711586 −0.355793 0.934565i \(-0.615789\pi\)
−0.355793 + 0.934565i \(0.615789\pi\)
\(564\) −2.19602 −0.0924693
\(565\) −5.50066 −0.231415
\(566\) −32.5384 −1.36769
\(567\) −5.02012 −0.210825
\(568\) 18.0698 0.758191
\(569\) −1.70745 −0.0715800 −0.0357900 0.999359i \(-0.511395\pi\)
−0.0357900 + 0.999359i \(0.511395\pi\)
\(570\) −8.66481 −0.362929
\(571\) 0.331367 0.0138673 0.00693365 0.999976i \(-0.497793\pi\)
0.00693365 + 0.999976i \(0.497793\pi\)
\(572\) 2.95869 0.123709
\(573\) −16.2973 −0.680831
\(574\) −37.4357 −1.56254
\(575\) −25.8934 −1.07983
\(576\) −4.41631 −0.184013
\(577\) 0.506196 0.0210732 0.0105366 0.999944i \(-0.496646\pi\)
0.0105366 + 0.999944i \(0.496646\pi\)
\(578\) −1.67732 −0.0697675
\(579\) −0.196858 −0.00818115
\(580\) 4.33982 0.180201
\(581\) 50.8231 2.10850
\(582\) 8.49062 0.351948
\(583\) 11.6657 0.483144
\(584\) −19.5383 −0.808502
\(585\) 5.26579 0.217713
\(586\) −0.385755 −0.0159354
\(587\) 11.9171 0.491872 0.245936 0.969286i \(-0.420905\pi\)
0.245936 + 0.969286i \(0.420905\pi\)
\(588\) −10.5441 −0.434833
\(589\) 45.9307 1.89254
\(590\) 7.85586 0.323421
\(591\) −11.0294 −0.453687
\(592\) −19.1470 −0.786936
\(593\) 43.7935 1.79838 0.899192 0.437555i \(-0.144156\pi\)
0.899192 + 0.437555i \(0.144156\pi\)
\(594\) 9.02751 0.370403
\(595\) 3.69495 0.151478
\(596\) −10.9560 −0.448776
\(597\) 10.4083 0.425983
\(598\) 37.1516 1.51924
\(599\) 12.3121 0.503058 0.251529 0.967850i \(-0.419067\pi\)
0.251529 + 0.967850i \(0.419067\pi\)
\(600\) 9.74501 0.397838
\(601\) −31.1109 −1.26904 −0.634520 0.772906i \(-0.718802\pi\)
−0.634520 + 0.772906i \(0.718802\pi\)
\(602\) −7.16704 −0.292107
\(603\) −7.09973 −0.289123
\(604\) 8.81348 0.358616
\(605\) 0.864739 0.0351566
\(606\) 13.5482 0.550357
\(607\) −19.2929 −0.783077 −0.391538 0.920162i \(-0.628057\pi\)
−0.391538 + 0.920162i \(0.628057\pi\)
\(608\) −22.5559 −0.914764
\(609\) −30.3562 −1.23010
\(610\) −12.7357 −0.515655
\(611\) −8.52833 −0.345019
\(612\) −1.36176 −0.0550460
\(613\) −40.0560 −1.61785 −0.808923 0.587914i \(-0.799949\pi\)
−0.808923 + 0.587914i \(0.799949\pi\)
\(614\) −52.9640 −2.13745
\(615\) −5.20094 −0.209722
\(616\) −8.50431 −0.342648
\(617\) 2.64543 0.106501 0.0532505 0.998581i \(-0.483042\pi\)
0.0532505 + 0.998581i \(0.483042\pi\)
\(618\) −29.4857 −1.18609
\(619\) −19.5240 −0.784734 −0.392367 0.919809i \(-0.628344\pi\)
−0.392367 + 0.919809i \(0.628344\pi\)
\(620\) −6.22720 −0.250090
\(621\) 32.7736 1.31516
\(622\) 25.1565 1.00868
\(623\) 4.06074 0.162690
\(624\) −20.7957 −0.832494
\(625\) 14.3426 0.573702
\(626\) 13.5739 0.542522
\(627\) −5.97389 −0.238574
\(628\) −15.3108 −0.610967
\(629\) 3.85625 0.153759
\(630\) 10.3756 0.413376
\(631\) −35.7479 −1.42310 −0.711551 0.702634i \(-0.752007\pi\)
−0.711551 + 0.702634i \(0.752007\pi\)
\(632\) −25.6133 −1.01884
\(633\) −28.6450 −1.13853
\(634\) 30.7852 1.22264
\(635\) −14.9802 −0.594472
\(636\) 10.9263 0.433255
\(637\) −40.9484 −1.62244
\(638\) 10.3488 0.409715
\(639\) −15.1994 −0.601279
\(640\) −11.3454 −0.448466
\(641\) 21.0910 0.833044 0.416522 0.909126i \(-0.363249\pi\)
0.416522 + 0.909126i \(0.363249\pi\)
\(642\) −21.4447 −0.846355
\(643\) −18.2420 −0.719396 −0.359698 0.933069i \(-0.617120\pi\)
−0.359698 + 0.933069i \(0.617120\pi\)
\(644\) 21.1645 0.833997
\(645\) −0.995715 −0.0392062
\(646\) 8.70209 0.342379
\(647\) 21.5489 0.847176 0.423588 0.905855i \(-0.360770\pi\)
0.423588 + 0.905855i \(0.360770\pi\)
\(648\) −2.33834 −0.0918587
\(649\) 5.41617 0.212603
\(650\) −25.9431 −1.01757
\(651\) 43.5581 1.70718
\(652\) 9.09511 0.356192
\(653\) −7.69137 −0.300987 −0.150493 0.988611i \(-0.548086\pi\)
−0.150493 + 0.988611i \(0.548086\pi\)
\(654\) 29.6459 1.15924
\(655\) −12.1132 −0.473302
\(656\) −25.9348 −1.01258
\(657\) 16.4347 0.641179
\(658\) −16.8041 −0.655093
\(659\) −16.0265 −0.624304 −0.312152 0.950032i \(-0.601050\pi\)
−0.312152 + 0.950032i \(0.601050\pi\)
\(660\) 0.809928 0.0315264
\(661\) 24.9762 0.971461 0.485730 0.874109i \(-0.338554\pi\)
0.485730 + 0.874109i \(0.338554\pi\)
\(662\) −35.1860 −1.36754
\(663\) 4.18830 0.162660
\(664\) 23.6731 0.918693
\(665\) −19.1697 −0.743369
\(666\) 10.8286 0.419599
\(667\) 37.5706 1.45474
\(668\) 14.2805 0.552531
\(669\) 8.23523 0.318393
\(670\) −6.15111 −0.237638
\(671\) −8.78057 −0.338970
\(672\) −21.3908 −0.825167
\(673\) −43.1325 −1.66264 −0.831319 0.555796i \(-0.812414\pi\)
−0.831319 + 0.555796i \(0.812414\pi\)
\(674\) −10.2734 −0.395718
\(675\) −22.8859 −0.880877
\(676\) 0.187482 0.00721084
\(677\) 45.8118 1.76069 0.880345 0.474334i \(-0.157311\pi\)
0.880345 + 0.474334i \(0.157311\pi\)
\(678\) −12.2856 −0.471826
\(679\) 18.7843 0.720877
\(680\) 1.72108 0.0660004
\(681\) 5.85205 0.224251
\(682\) −14.8495 −0.568618
\(683\) 4.62756 0.177069 0.0885344 0.996073i \(-0.471782\pi\)
0.0885344 + 0.996073i \(0.471782\pi\)
\(684\) 7.06494 0.270135
\(685\) −4.56977 −0.174602
\(686\) −30.5151 −1.16507
\(687\) 24.2578 0.925493
\(688\) −4.96519 −0.189296
\(689\) 42.4326 1.61655
\(690\) 10.1701 0.387169
\(691\) −38.8612 −1.47835 −0.739174 0.673514i \(-0.764784\pi\)
−0.739174 + 0.673514i \(0.764784\pi\)
\(692\) −7.60518 −0.289106
\(693\) 7.15341 0.271736
\(694\) −3.39008 −0.128686
\(695\) 5.81651 0.220633
\(696\) −14.1397 −0.535965
\(697\) 5.22332 0.197847
\(698\) −35.5135 −1.34421
\(699\) 10.8417 0.410069
\(700\) −14.7792 −0.558601
\(701\) −17.3203 −0.654181 −0.327090 0.944993i \(-0.606068\pi\)
−0.327090 + 0.944993i \(0.606068\pi\)
\(702\) 32.8364 1.23933
\(703\) −20.0065 −0.754561
\(704\) −2.63797 −0.0994222
\(705\) −2.33459 −0.0879258
\(706\) −52.1601 −1.96307
\(707\) 29.9735 1.12727
\(708\) 5.07286 0.190650
\(709\) 37.6808 1.41513 0.707567 0.706646i \(-0.249793\pi\)
0.707567 + 0.706646i \(0.249793\pi\)
\(710\) −13.1686 −0.494207
\(711\) 21.5447 0.807988
\(712\) 1.89147 0.0708857
\(713\) −53.9100 −2.01895
\(714\) 8.25258 0.308845
\(715\) 3.14538 0.117631
\(716\) −10.8290 −0.404697
\(717\) 11.0936 0.414297
\(718\) 19.8196 0.739661
\(719\) −14.5962 −0.544347 −0.272173 0.962248i \(-0.587742\pi\)
−0.272173 + 0.962248i \(0.587742\pi\)
\(720\) 7.18805 0.267883
\(721\) −65.2332 −2.42941
\(722\) −13.2781 −0.494158
\(723\) −15.6607 −0.582429
\(724\) 1.27550 0.0474035
\(725\) −26.2356 −0.974367
\(726\) 1.93138 0.0716801
\(727\) −17.1624 −0.636518 −0.318259 0.948004i \(-0.603098\pi\)
−0.318259 + 0.948004i \(0.603098\pi\)
\(728\) −30.9334 −1.14647
\(729\) 20.5587 0.761434
\(730\) 14.2388 0.527002
\(731\) 1.00000 0.0369863
\(732\) −8.22401 −0.303968
\(733\) 38.8930 1.43655 0.718273 0.695761i \(-0.244933\pi\)
0.718273 + 0.695761i \(0.244933\pi\)
\(734\) 6.33227 0.233728
\(735\) −11.2095 −0.413467
\(736\) 26.4745 0.975862
\(737\) −4.24084 −0.156213
\(738\) 14.6674 0.539915
\(739\) 23.5168 0.865079 0.432539 0.901615i \(-0.357618\pi\)
0.432539 + 0.901615i \(0.357618\pi\)
\(740\) 2.71245 0.0997115
\(741\) −21.7293 −0.798244
\(742\) 83.6086 3.06937
\(743\) −47.7068 −1.75019 −0.875096 0.483950i \(-0.839202\pi\)
−0.875096 + 0.483950i \(0.839202\pi\)
\(744\) 20.2891 0.743833
\(745\) −11.6473 −0.426726
\(746\) −5.87415 −0.215068
\(747\) −19.9126 −0.728565
\(748\) −0.813414 −0.0297413
\(749\) −47.4434 −1.73355
\(750\) −15.4525 −0.564245
\(751\) −35.1586 −1.28296 −0.641478 0.767141i \(-0.721678\pi\)
−0.641478 + 0.767141i \(0.721678\pi\)
\(752\) −11.6416 −0.424524
\(753\) −19.5486 −0.712391
\(754\) 37.6426 1.37086
\(755\) 9.36961 0.340995
\(756\) 18.7062 0.680338
\(757\) 17.0524 0.619781 0.309890 0.950772i \(-0.399708\pi\)
0.309890 + 0.950772i \(0.399708\pi\)
\(758\) 6.17178 0.224169
\(759\) 7.01170 0.254508
\(760\) −8.92911 −0.323893
\(761\) 16.2250 0.588155 0.294077 0.955782i \(-0.404988\pi\)
0.294077 + 0.955782i \(0.404988\pi\)
\(762\) −33.4580 −1.21205
\(763\) 65.5874 2.37442
\(764\) 11.5127 0.416516
\(765\) −1.44769 −0.0523413
\(766\) 28.1195 1.01600
\(767\) 19.7006 0.711348
\(768\) −19.2646 −0.695152
\(769\) 17.4922 0.630784 0.315392 0.948962i \(-0.397864\pi\)
0.315392 + 0.948962i \(0.397864\pi\)
\(770\) 6.19762 0.223347
\(771\) 24.1783 0.870760
\(772\) 0.139064 0.00500503
\(773\) 44.6653 1.60650 0.803249 0.595643i \(-0.203103\pi\)
0.803249 + 0.595643i \(0.203103\pi\)
\(774\) 2.80806 0.100934
\(775\) 37.6454 1.35226
\(776\) 8.74962 0.314093
\(777\) −18.9731 −0.680655
\(778\) 51.1428 1.83356
\(779\) −27.0990 −0.970924
\(780\) 2.94601 0.105484
\(781\) −9.07897 −0.324871
\(782\) −10.2139 −0.365247
\(783\) 33.2067 1.18671
\(784\) −55.8965 −1.99630
\(785\) −16.2769 −0.580947
\(786\) −27.0546 −0.965005
\(787\) −25.7516 −0.917947 −0.458973 0.888450i \(-0.651783\pi\)
−0.458973 + 0.888450i \(0.651783\pi\)
\(788\) 7.79133 0.277555
\(789\) −1.82553 −0.0649905
\(790\) 18.6660 0.664107
\(791\) −27.1802 −0.966417
\(792\) 3.33201 0.118398
\(793\) −31.9382 −1.13416
\(794\) −14.1952 −0.503768
\(795\) 11.6157 0.411967
\(796\) −7.35260 −0.260606
\(797\) 14.5972 0.517061 0.258530 0.966003i \(-0.416762\pi\)
0.258530 + 0.966003i \(0.416762\pi\)
\(798\) −42.8151 −1.51564
\(799\) 2.34464 0.0829474
\(800\) −18.4872 −0.653620
\(801\) −1.59101 −0.0562155
\(802\) 44.6191 1.57556
\(803\) 9.81684 0.346429
\(804\) −3.97203 −0.140083
\(805\) 22.4999 0.793019
\(806\) −54.0133 −1.90254
\(807\) 6.73489 0.237079
\(808\) 13.9614 0.491162
\(809\) 25.6232 0.900865 0.450432 0.892811i \(-0.351270\pi\)
0.450432 + 0.892811i \(0.351270\pi\)
\(810\) 1.70409 0.0598757
\(811\) −4.82738 −0.169512 −0.0847562 0.996402i \(-0.527011\pi\)
−0.0847562 + 0.996402i \(0.527011\pi\)
\(812\) 21.4442 0.752543
\(813\) −34.3181 −1.20359
\(814\) 6.46817 0.226709
\(815\) 9.66901 0.338691
\(816\) 5.71723 0.200143
\(817\) −5.18808 −0.181508
\(818\) 5.75009 0.201047
\(819\) 26.0196 0.909199
\(820\) 3.67404 0.128303
\(821\) 0.259077 0.00904187 0.00452093 0.999990i \(-0.498561\pi\)
0.00452093 + 0.999990i \(0.498561\pi\)
\(822\) −10.2065 −0.355992
\(823\) −3.15977 −0.110143 −0.0550713 0.998482i \(-0.517539\pi\)
−0.0550713 + 0.998482i \(0.517539\pi\)
\(824\) −30.3852 −1.05852
\(825\) −4.89628 −0.170467
\(826\) 38.8179 1.35065
\(827\) 10.2275 0.355646 0.177823 0.984062i \(-0.443095\pi\)
0.177823 + 0.984062i \(0.443095\pi\)
\(828\) −8.29230 −0.288177
\(829\) −13.5436 −0.470387 −0.235194 0.971949i \(-0.575572\pi\)
−0.235194 + 0.971949i \(0.575572\pi\)
\(830\) −17.2520 −0.598827
\(831\) 18.9649 0.657886
\(832\) −9.59528 −0.332656
\(833\) 11.2577 0.390056
\(834\) 12.9910 0.449843
\(835\) 15.1816 0.525382
\(836\) 4.22006 0.145954
\(837\) −47.6483 −1.64696
\(838\) 44.8268 1.54852
\(839\) 8.04702 0.277814 0.138907 0.990305i \(-0.455641\pi\)
0.138907 + 0.990305i \(0.455641\pi\)
\(840\) −8.46787 −0.292169
\(841\) 9.06714 0.312660
\(842\) −27.8604 −0.960134
\(843\) 13.6929 0.471609
\(844\) 20.2353 0.696528
\(845\) 0.199312 0.00685654
\(846\) 6.58390 0.226359
\(847\) 4.27290 0.146819
\(848\) 57.9224 1.98906
\(849\) −22.3372 −0.766612
\(850\) 7.13236 0.244638
\(851\) 23.4822 0.804958
\(852\) −8.50350 −0.291325
\(853\) 27.8307 0.952903 0.476452 0.879201i \(-0.341923\pi\)
0.476452 + 0.879201i \(0.341923\pi\)
\(854\) −62.9307 −2.15344
\(855\) 7.51073 0.256862
\(856\) −22.0988 −0.755323
\(857\) 50.1440 1.71289 0.856444 0.516241i \(-0.172669\pi\)
0.856444 + 0.516241i \(0.172669\pi\)
\(858\) 7.02513 0.239834
\(859\) 52.1920 1.78077 0.890384 0.455210i \(-0.150436\pi\)
0.890384 + 0.455210i \(0.150436\pi\)
\(860\) 0.703391 0.0239854
\(861\) −25.6992 −0.875826
\(862\) −2.28613 −0.0778660
\(863\) −51.2681 −1.74519 −0.872593 0.488448i \(-0.837563\pi\)
−0.872593 + 0.488448i \(0.837563\pi\)
\(864\) 23.3994 0.796064
\(865\) −8.08506 −0.274900
\(866\) 53.0795 1.80371
\(867\) −1.15146 −0.0391057
\(868\) −30.7702 −1.04441
\(869\) 12.8691 0.436556
\(870\) 10.3045 0.349355
\(871\) −15.4255 −0.522673
\(872\) 30.5502 1.03456
\(873\) −7.35975 −0.249090
\(874\) 52.9904 1.79243
\(875\) −34.1865 −1.15571
\(876\) 9.19460 0.310657
\(877\) −9.60183 −0.324231 −0.162115 0.986772i \(-0.551832\pi\)
−0.162115 + 0.986772i \(0.551832\pi\)
\(878\) 11.4598 0.386749
\(879\) −0.264816 −0.00893204
\(880\) 4.29359 0.144737
\(881\) −9.41947 −0.317350 −0.158675 0.987331i \(-0.550722\pi\)
−0.158675 + 0.987331i \(0.550722\pi\)
\(882\) 31.6123 1.06444
\(883\) −5.21504 −0.175500 −0.0877500 0.996143i \(-0.527968\pi\)
−0.0877500 + 0.996143i \(0.527968\pi\)
\(884\) −2.95869 −0.0995115
\(885\) 5.39296 0.181282
\(886\) −33.6870 −1.13174
\(887\) −32.9155 −1.10520 −0.552598 0.833448i \(-0.686363\pi\)
−0.552598 + 0.833448i \(0.686363\pi\)
\(888\) −8.83753 −0.296568
\(889\) −74.0212 −2.48259
\(890\) −1.37843 −0.0462050
\(891\) 1.17487 0.0393598
\(892\) −5.81751 −0.194785
\(893\) −12.1642 −0.407059
\(894\) −26.0141 −0.870041
\(895\) −11.5123 −0.384812
\(896\) −56.0605 −1.87285
\(897\) 25.5042 0.851559
\(898\) −0.343447 −0.0114610
\(899\) −54.6225 −1.82176
\(900\) 5.79052 0.193017
\(901\) −11.6657 −0.388641
\(902\) 8.76120 0.291716
\(903\) −4.92009 −0.163730
\(904\) −12.6604 −0.421077
\(905\) 1.35598 0.0450743
\(906\) 20.9268 0.695246
\(907\) −32.0727 −1.06496 −0.532479 0.846443i \(-0.678739\pi\)
−0.532479 + 0.846443i \(0.678739\pi\)
\(908\) −4.13399 −0.137191
\(909\) −11.7437 −0.389513
\(910\) 22.5431 0.747295
\(911\) −42.7210 −1.41541 −0.707705 0.706508i \(-0.750269\pi\)
−0.707705 + 0.706508i \(0.750269\pi\)
\(912\) −29.6614 −0.982189
\(913\) −11.8943 −0.393643
\(914\) 1.04369 0.0345220
\(915\) −8.74294 −0.289033
\(916\) −17.1361 −0.566194
\(917\) −59.8545 −1.97657
\(918\) −9.02751 −0.297952
\(919\) 45.2298 1.49199 0.745997 0.665950i \(-0.231974\pi\)
0.745997 + 0.665950i \(0.231974\pi\)
\(920\) 10.4803 0.345526
\(921\) −36.3591 −1.19807
\(922\) 40.6010 1.33712
\(923\) −33.0236 −1.08698
\(924\) 4.00207 0.131658
\(925\) −16.3976 −0.539151
\(926\) −3.95373 −0.129927
\(927\) 25.5585 0.839452
\(928\) 26.8243 0.880552
\(929\) 44.2355 1.45132 0.725659 0.688054i \(-0.241535\pi\)
0.725659 + 0.688054i \(0.241535\pi\)
\(930\) −14.7859 −0.484849
\(931\) −58.4059 −1.91417
\(932\) −7.65873 −0.250870
\(933\) 17.2696 0.565383
\(934\) −12.4686 −0.407984
\(935\) −0.864739 −0.0282800
\(936\) 12.1198 0.396147
\(937\) 3.74517 0.122349 0.0611747 0.998127i \(-0.480515\pi\)
0.0611747 + 0.998127i \(0.480515\pi\)
\(938\) −30.3942 −0.992407
\(939\) 9.31832 0.304092
\(940\) 1.64920 0.0537909
\(941\) 36.3145 1.18382 0.591909 0.806005i \(-0.298374\pi\)
0.591909 + 0.806005i \(0.298374\pi\)
\(942\) −36.3541 −1.18448
\(943\) 31.8068 1.03577
\(944\) 26.8923 0.875269
\(945\) 19.8865 0.646909
\(946\) 1.67732 0.0545345
\(947\) 42.9674 1.39625 0.698126 0.715975i \(-0.254017\pi\)
0.698126 + 0.715975i \(0.254017\pi\)
\(948\) 12.0534 0.391477
\(949\) 35.7075 1.15911
\(950\) −37.0033 −1.20054
\(951\) 21.1337 0.685306
\(952\) 8.50431 0.275626
\(953\) −53.7341 −1.74062 −0.870310 0.492505i \(-0.836081\pi\)
−0.870310 + 0.492505i \(0.836081\pi\)
\(954\) −32.7581 −1.06058
\(955\) 12.2392 0.396050
\(956\) −7.83669 −0.253457
\(957\) 7.10436 0.229651
\(958\) 58.2050 1.88052
\(959\) −22.5804 −0.729160
\(960\) −2.62666 −0.0847752
\(961\) 47.3776 1.52831
\(962\) 23.5272 0.758546
\(963\) 18.5885 0.599005
\(964\) 11.0630 0.356316
\(965\) 0.147839 0.00475910
\(966\) 50.2531 1.61687
\(967\) −27.3361 −0.879071 −0.439535 0.898225i \(-0.644857\pi\)
−0.439535 + 0.898225i \(0.644857\pi\)
\(968\) 1.99029 0.0639703
\(969\) 5.97389 0.191909
\(970\) −6.37639 −0.204734
\(971\) 12.0804 0.387677 0.193839 0.981033i \(-0.437906\pi\)
0.193839 + 0.981033i \(0.437906\pi\)
\(972\) −12.0332 −0.385965
\(973\) 28.7409 0.921391
\(974\) −23.6276 −0.757077
\(975\) −17.8096 −0.570364
\(976\) −43.5971 −1.39551
\(977\) 15.7842 0.504982 0.252491 0.967599i \(-0.418750\pi\)
0.252491 + 0.967599i \(0.418750\pi\)
\(978\) 21.5955 0.690548
\(979\) −0.950347 −0.0303732
\(980\) 7.91856 0.252949
\(981\) −25.6973 −0.820452
\(982\) 49.6917 1.58573
\(983\) −51.0876 −1.62944 −0.814721 0.579854i \(-0.803110\pi\)
−0.814721 + 0.579854i \(0.803110\pi\)
\(984\) −11.9705 −0.381606
\(985\) 8.28296 0.263917
\(986\) −10.3488 −0.329574
\(987\) −11.5358 −0.367189
\(988\) 15.3499 0.488346
\(989\) 6.08938 0.193631
\(990\) −2.42824 −0.0771746
\(991\) 38.4437 1.22120 0.610602 0.791938i \(-0.290928\pi\)
0.610602 + 0.791938i \(0.290928\pi\)
\(992\) −38.4902 −1.22206
\(993\) −24.1548 −0.766529
\(994\) −65.0693 −2.06387
\(995\) −7.81654 −0.247801
\(996\) −11.1404 −0.352996
\(997\) −40.8881 −1.29494 −0.647469 0.762092i \(-0.724172\pi\)
−0.647469 + 0.762092i \(0.724172\pi\)
\(998\) 52.2710 1.65461
\(999\) 20.7547 0.656649
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 \(a_p\))