Properties

Label 5077.2.a.c.1.1
Level 5077
Weight 2
Character 5077.1
Self dual Yes
Analytic conductor 40.540
Analytic rank 0
Dimension 216
CM No

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Newspace parameters

Level: \( N \) = \( 5077 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 5077.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(40.5400491062\)
Analytic rank: \(0\)
Dimension: \(216\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) = 5077.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.74765 q^{2} +1.79689 q^{3} +5.54960 q^{4} -1.53731 q^{5} -4.93723 q^{6} -2.66154 q^{7} -9.75307 q^{8} +0.228810 q^{9} +O(q^{10})\) \(q-2.74765 q^{2} +1.79689 q^{3} +5.54960 q^{4} -1.53731 q^{5} -4.93723 q^{6} -2.66154 q^{7} -9.75307 q^{8} +0.228810 q^{9} +4.22399 q^{10} +6.00651 q^{11} +9.97201 q^{12} +2.63805 q^{13} +7.31298 q^{14} -2.76237 q^{15} +15.6988 q^{16} -2.14393 q^{17} -0.628690 q^{18} -5.68526 q^{19} -8.53145 q^{20} -4.78248 q^{21} -16.5038 q^{22} +5.77175 q^{23} -17.5252 q^{24} -2.63668 q^{25} -7.24846 q^{26} -4.97952 q^{27} -14.7705 q^{28} -5.82907 q^{29} +7.59004 q^{30} -1.12302 q^{31} -23.6289 q^{32} +10.7930 q^{33} +5.89077 q^{34} +4.09160 q^{35} +1.26980 q^{36} -0.852256 q^{37} +15.6211 q^{38} +4.74029 q^{39} +14.9935 q^{40} -7.11031 q^{41} +13.1406 q^{42} +6.82774 q^{43} +33.3337 q^{44} -0.351751 q^{45} -15.8588 q^{46} +11.9169 q^{47} +28.2091 q^{48} +0.0837686 q^{49} +7.24469 q^{50} -3.85240 q^{51} +14.6401 q^{52} +4.95543 q^{53} +13.6820 q^{54} -9.23386 q^{55} +25.9581 q^{56} -10.2158 q^{57} +16.0163 q^{58} +12.5895 q^{59} -15.3301 q^{60} -6.82849 q^{61} +3.08567 q^{62} -0.608986 q^{63} +33.5262 q^{64} -4.05550 q^{65} -29.6555 q^{66} +3.64999 q^{67} -11.8979 q^{68} +10.3712 q^{69} -11.2423 q^{70} -1.60799 q^{71} -2.23160 q^{72} +13.2649 q^{73} +2.34170 q^{74} -4.73783 q^{75} -31.5509 q^{76} -15.9865 q^{77} -13.0247 q^{78} -0.221411 q^{79} -24.1340 q^{80} -9.63408 q^{81} +19.5367 q^{82} -10.5305 q^{83} -26.5409 q^{84} +3.29588 q^{85} -18.7603 q^{86} -10.4742 q^{87} -58.5819 q^{88} +12.2722 q^{89} +0.966491 q^{90} -7.02127 q^{91} +32.0309 q^{92} -2.01794 q^{93} -32.7436 q^{94} +8.73999 q^{95} -42.4584 q^{96} +13.4558 q^{97} -0.230167 q^{98} +1.37435 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 216q + 25q^{2} + 62q^{3} + 223q^{4} + 46q^{5} + 26q^{6} + 30q^{7} + 75q^{8} + 234q^{9} + O(q^{10}) \) \( 216q + 25q^{2} + 62q^{3} + 223q^{4} + 46q^{5} + 26q^{6} + 30q^{7} + 75q^{8} + 234q^{9} + 24q^{10} + 89q^{11} + 114q^{12} + 34q^{13} + 53q^{14} + 61q^{15} + 229q^{16} + 76q^{17} + 57q^{18} + 54q^{19} + 118q^{20} + 25q^{21} + 26q^{22} + 109q^{23} + 65q^{24} + 232q^{25} + 58q^{26} + 236q^{27} + 57q^{28} + 54q^{29} + 6q^{30} + 77q^{31} + 155q^{32} + 80q^{33} + 28q^{34} + 137q^{35} + 257q^{36} + 42q^{37} + 104q^{38} + 46q^{39} + 47q^{40} + 109q^{41} + 27q^{42} + 68q^{43} + 145q^{44} + 109q^{45} - 7q^{46} + 264q^{47} + 198q^{48} + 222q^{49} + 86q^{50} + 57q^{51} + 68q^{52} + 95q^{53} + 79q^{54} + 50q^{55} + 108q^{56} + 55q^{57} + 38q^{58} + 292q^{59} + 91q^{60} + 16q^{61} + 91q^{62} + 113q^{63} + 231q^{64} + 68q^{65} - 15q^{66} + 152q^{67} + 199q^{68} + 83q^{69} + 24q^{70} + 131q^{71} + 162q^{72} + 71q^{73} + 10q^{74} + 232q^{75} + 60q^{76} + 131q^{77} + 102q^{78} + 10q^{79} + 236q^{80} + 268q^{81} + 54q^{82} + 299q^{83} - 9q^{85} + 35q^{86} + 103q^{87} + 45q^{88} + 134q^{89} + 8q^{90} + 79q^{91} + 206q^{92} + 95q^{93} + 18q^{94} + 119q^{95} + 77q^{96} + 129q^{97} + 150q^{98} + 221q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.74765 −1.94288 −0.971442 0.237277i \(-0.923745\pi\)
−0.971442 + 0.237277i \(0.923745\pi\)
\(3\) 1.79689 1.03743 0.518717 0.854946i \(-0.326410\pi\)
0.518717 + 0.854946i \(0.326410\pi\)
\(4\) 5.54960 2.77480
\(5\) −1.53731 −0.687505 −0.343753 0.939060i \(-0.611698\pi\)
−0.343753 + 0.939060i \(0.611698\pi\)
\(6\) −4.93723 −2.01561
\(7\) −2.66154 −1.00597 −0.502983 0.864296i \(-0.667764\pi\)
−0.502983 + 0.864296i \(0.667764\pi\)
\(8\) −9.75307 −3.44823
\(9\) 0.228810 0.0762700
\(10\) 4.22399 1.33574
\(11\) 6.00651 1.81103 0.905516 0.424312i \(-0.139484\pi\)
0.905516 + 0.424312i \(0.139484\pi\)
\(12\) 9.97201 2.87867
\(13\) 2.63805 0.731664 0.365832 0.930681i \(-0.380784\pi\)
0.365832 + 0.930681i \(0.380784\pi\)
\(14\) 7.31298 1.95447
\(15\) −2.76237 −0.713242
\(16\) 15.6988 3.92471
\(17\) −2.14393 −0.519979 −0.259989 0.965612i \(-0.583719\pi\)
−0.259989 + 0.965612i \(0.583719\pi\)
\(18\) −0.628690 −0.148184
\(19\) −5.68526 −1.30429 −0.652144 0.758095i \(-0.726130\pi\)
−0.652144 + 0.758095i \(0.726130\pi\)
\(20\) −8.53145 −1.90769
\(21\) −4.78248 −1.04362
\(22\) −16.5038 −3.51863
\(23\) 5.77175 1.20349 0.601746 0.798687i \(-0.294472\pi\)
0.601746 + 0.798687i \(0.294472\pi\)
\(24\) −17.5252 −3.57731
\(25\) −2.63668 −0.527337
\(26\) −7.24846 −1.42154
\(27\) −4.97952 −0.958309
\(28\) −14.7705 −2.79135
\(29\) −5.82907 −1.08243 −0.541215 0.840884i \(-0.682036\pi\)
−0.541215 + 0.840884i \(0.682036\pi\)
\(30\) 7.59004 1.38575
\(31\) −1.12302 −0.201700 −0.100850 0.994902i \(-0.532156\pi\)
−0.100850 + 0.994902i \(0.532156\pi\)
\(32\) −23.6289 −4.17703
\(33\) 10.7930 1.87883
\(34\) 5.89077 1.01026
\(35\) 4.09160 0.691607
\(36\) 1.26980 0.211634
\(37\) −0.852256 −0.140110 −0.0700550 0.997543i \(-0.522317\pi\)
−0.0700550 + 0.997543i \(0.522317\pi\)
\(38\) 15.6211 2.53408
\(39\) 4.74029 0.759054
\(40\) 14.9935 2.37068
\(41\) −7.11031 −1.11044 −0.555222 0.831702i \(-0.687367\pi\)
−0.555222 + 0.831702i \(0.687367\pi\)
\(42\) 13.1406 2.02764
\(43\) 6.82774 1.04122 0.520610 0.853794i \(-0.325704\pi\)
0.520610 + 0.853794i \(0.325704\pi\)
\(44\) 33.3337 5.02525
\(45\) −0.351751 −0.0524360
\(46\) −15.8588 −2.33825
\(47\) 11.9169 1.73826 0.869132 0.494581i \(-0.164678\pi\)
0.869132 + 0.494581i \(0.164678\pi\)
\(48\) 28.2091 4.07163
\(49\) 0.0837686 0.0119669
\(50\) 7.24469 1.02455
\(51\) −3.85240 −0.539444
\(52\) 14.6401 2.03022
\(53\) 4.95543 0.680681 0.340340 0.940302i \(-0.389458\pi\)
0.340340 + 0.940302i \(0.389458\pi\)
\(54\) 13.6820 1.86188
\(55\) −9.23386 −1.24509
\(56\) 25.9581 3.46880
\(57\) −10.2158 −1.35311
\(58\) 16.0163 2.10304
\(59\) 12.5895 1.63901 0.819505 0.573072i \(-0.194248\pi\)
0.819505 + 0.573072i \(0.194248\pi\)
\(60\) −15.3301 −1.97910
\(61\) −6.82849 −0.874298 −0.437149 0.899389i \(-0.644012\pi\)
−0.437149 + 0.899389i \(0.644012\pi\)
\(62\) 3.08567 0.391880
\(63\) −0.608986 −0.0767250
\(64\) 33.5262 4.19078
\(65\) −4.05550 −0.503023
\(66\) −29.6555 −3.65034
\(67\) 3.64999 0.445917 0.222959 0.974828i \(-0.428429\pi\)
0.222959 + 0.974828i \(0.428429\pi\)
\(68\) −11.8979 −1.44284
\(69\) 10.3712 1.24854
\(70\) −11.2423 −1.34371
\(71\) −1.60799 −0.190833 −0.0954165 0.995437i \(-0.530418\pi\)
−0.0954165 + 0.995437i \(0.530418\pi\)
\(72\) −2.23160 −0.262996
\(73\) 13.2649 1.55254 0.776270 0.630401i \(-0.217109\pi\)
0.776270 + 0.630401i \(0.217109\pi\)
\(74\) 2.34170 0.272218
\(75\) −4.73783 −0.547077
\(76\) −31.5509 −3.61914
\(77\) −15.9865 −1.82184
\(78\) −13.0247 −1.47475
\(79\) −0.221411 −0.0249107 −0.0124554 0.999922i \(-0.503965\pi\)
−0.0124554 + 0.999922i \(0.503965\pi\)
\(80\) −24.1340 −2.69826
\(81\) −9.63408 −1.07045
\(82\) 19.5367 2.15746
\(83\) −10.5305 −1.15588 −0.577938 0.816081i \(-0.696142\pi\)
−0.577938 + 0.816081i \(0.696142\pi\)
\(84\) −26.5409 −2.89585
\(85\) 3.29588 0.357488
\(86\) −18.7603 −2.02297
\(87\) −10.4742 −1.12295
\(88\) −58.5819 −6.24485
\(89\) 12.2722 1.30085 0.650427 0.759569i \(-0.274590\pi\)
0.650427 + 0.759569i \(0.274590\pi\)
\(90\) 0.966491 0.101877
\(91\) −7.02127 −0.736029
\(92\) 32.0309 3.33945
\(93\) −2.01794 −0.209251
\(94\) −32.7436 −3.37724
\(95\) 8.73999 0.896704
\(96\) −42.4584 −4.33340
\(97\) 13.4558 1.36623 0.683113 0.730313i \(-0.260626\pi\)
0.683113 + 0.730313i \(0.260626\pi\)
\(98\) −0.230167 −0.0232504
\(99\) 1.37435 0.138127
\(100\) −14.6325 −1.46325
\(101\) 6.44246 0.641049 0.320524 0.947240i \(-0.396141\pi\)
0.320524 + 0.947240i \(0.396141\pi\)
\(102\) 10.5851 1.04808
\(103\) −7.61928 −0.750750 −0.375375 0.926873i \(-0.622486\pi\)
−0.375375 + 0.926873i \(0.622486\pi\)
\(104\) −25.7291 −2.52295
\(105\) 7.35215 0.717497
\(106\) −13.6158 −1.32248
\(107\) −11.8935 −1.14979 −0.574894 0.818228i \(-0.694957\pi\)
−0.574894 + 0.818228i \(0.694957\pi\)
\(108\) −27.6343 −2.65912
\(109\) 16.6514 1.59492 0.797458 0.603374i \(-0.206177\pi\)
0.797458 + 0.603374i \(0.206177\pi\)
\(110\) 25.3715 2.41907
\(111\) −1.53141 −0.145355
\(112\) −41.7830 −3.94813
\(113\) −2.48707 −0.233964 −0.116982 0.993134i \(-0.537322\pi\)
−0.116982 + 0.993134i \(0.537322\pi\)
\(114\) 28.0694 2.62894
\(115\) −8.87295 −0.827407
\(116\) −32.3490 −3.00353
\(117\) 0.603613 0.0558040
\(118\) −34.5915 −3.18441
\(119\) 5.70614 0.523081
\(120\) 26.9416 2.45942
\(121\) 25.0782 2.27984
\(122\) 18.7623 1.69866
\(123\) −12.7764 −1.15201
\(124\) −6.23231 −0.559678
\(125\) 11.7399 1.05005
\(126\) 1.67328 0.149068
\(127\) −15.9885 −1.41875 −0.709373 0.704833i \(-0.751022\pi\)
−0.709373 + 0.704833i \(0.751022\pi\)
\(128\) −44.8607 −3.96516
\(129\) 12.2687 1.08020
\(130\) 11.1431 0.977316
\(131\) 5.53406 0.483513 0.241756 0.970337i \(-0.422276\pi\)
0.241756 + 0.970337i \(0.422276\pi\)
\(132\) 59.8970 5.21337
\(133\) 15.1315 1.31207
\(134\) −10.0289 −0.866366
\(135\) 7.65506 0.658843
\(136\) 20.9099 1.79301
\(137\) 5.30114 0.452907 0.226453 0.974022i \(-0.427287\pi\)
0.226453 + 0.974022i \(0.427287\pi\)
\(138\) −28.4964 −2.42578
\(139\) −3.68073 −0.312196 −0.156098 0.987742i \(-0.549892\pi\)
−0.156098 + 0.987742i \(0.549892\pi\)
\(140\) 22.7067 1.91907
\(141\) 21.4134 1.80333
\(142\) 4.41819 0.370766
\(143\) 15.8455 1.32507
\(144\) 3.59205 0.299338
\(145\) 8.96107 0.744177
\(146\) −36.4474 −3.01640
\(147\) 0.150523 0.0124149
\(148\) −4.72968 −0.388777
\(149\) 0.816180 0.0668641 0.0334320 0.999441i \(-0.489356\pi\)
0.0334320 + 0.999441i \(0.489356\pi\)
\(150\) 13.0179 1.06291
\(151\) −16.8816 −1.37380 −0.686901 0.726751i \(-0.741029\pi\)
−0.686901 + 0.726751i \(0.741029\pi\)
\(152\) 55.4487 4.49748
\(153\) −0.490552 −0.0396588
\(154\) 43.9255 3.53962
\(155\) 1.72643 0.138670
\(156\) 26.3067 2.10622
\(157\) −11.9217 −0.951454 −0.475727 0.879593i \(-0.657815\pi\)
−0.475727 + 0.879593i \(0.657815\pi\)
\(158\) 0.608362 0.0483987
\(159\) 8.90436 0.706161
\(160\) 36.3248 2.87173
\(161\) −15.3617 −1.21067
\(162\) 26.4711 2.07977
\(163\) −7.80839 −0.611600 −0.305800 0.952096i \(-0.598924\pi\)
−0.305800 + 0.952096i \(0.598924\pi\)
\(164\) −39.4593 −3.08126
\(165\) −16.5922 −1.29170
\(166\) 28.9342 2.24573
\(167\) 7.73195 0.598316 0.299158 0.954204i \(-0.403294\pi\)
0.299158 + 0.954204i \(0.403294\pi\)
\(168\) 46.6439 3.59865
\(169\) −6.04068 −0.464667
\(170\) −9.05593 −0.694558
\(171\) −1.30084 −0.0994780
\(172\) 37.8912 2.88918
\(173\) 18.7775 1.42763 0.713813 0.700336i \(-0.246967\pi\)
0.713813 + 0.700336i \(0.246967\pi\)
\(174\) 28.7794 2.18176
\(175\) 7.01762 0.530482
\(176\) 94.2953 7.10778
\(177\) 22.6219 1.70037
\(178\) −33.7198 −2.52741
\(179\) 7.70770 0.576101 0.288050 0.957615i \(-0.406993\pi\)
0.288050 + 0.957615i \(0.406993\pi\)
\(180\) −1.95208 −0.145499
\(181\) −16.2930 −1.21105 −0.605526 0.795825i \(-0.707037\pi\)
−0.605526 + 0.795825i \(0.707037\pi\)
\(182\) 19.2920 1.43002
\(183\) −12.2700 −0.907027
\(184\) −56.2922 −4.14992
\(185\) 1.31018 0.0963264
\(186\) 5.54461 0.406550
\(187\) −12.8775 −0.941698
\(188\) 66.1342 4.82333
\(189\) 13.2532 0.964026
\(190\) −24.0145 −1.74219
\(191\) 5.01655 0.362985 0.181493 0.983392i \(-0.441907\pi\)
0.181493 + 0.983392i \(0.441907\pi\)
\(192\) 60.2429 4.34766
\(193\) −6.14579 −0.442384 −0.221192 0.975230i \(-0.570995\pi\)
−0.221192 + 0.975230i \(0.570995\pi\)
\(194\) −36.9718 −2.65442
\(195\) −7.28729 −0.521853
\(196\) 0.464882 0.0332059
\(197\) 19.7033 1.40380 0.701902 0.712274i \(-0.252335\pi\)
0.701902 + 0.712274i \(0.252335\pi\)
\(198\) −3.77624 −0.268365
\(199\) −16.7423 −1.18683 −0.593415 0.804896i \(-0.702221\pi\)
−0.593415 + 0.804896i \(0.702221\pi\)
\(200\) 25.7157 1.81838
\(201\) 6.55863 0.462610
\(202\) −17.7016 −1.24548
\(203\) 15.5143 1.08889
\(204\) −21.3793 −1.49685
\(205\) 10.9307 0.763436
\(206\) 20.9351 1.45862
\(207\) 1.32063 0.0917903
\(208\) 41.4144 2.87157
\(209\) −34.1486 −2.36211
\(210\) −20.2012 −1.39401
\(211\) −2.20807 −0.152010 −0.0760048 0.997107i \(-0.524216\pi\)
−0.0760048 + 0.997107i \(0.524216\pi\)
\(212\) 27.5006 1.88875
\(213\) −2.88938 −0.197977
\(214\) 32.6792 2.23391
\(215\) −10.4963 −0.715845
\(216\) 48.5656 3.30447
\(217\) 2.98896 0.202904
\(218\) −45.7523 −3.09874
\(219\) 23.8356 1.61066
\(220\) −51.2442 −3.45489
\(221\) −5.65579 −0.380450
\(222\) 4.20778 0.282408
\(223\) 11.2610 0.754094 0.377047 0.926194i \(-0.376939\pi\)
0.377047 + 0.926194i \(0.376939\pi\)
\(224\) 62.8890 4.20195
\(225\) −0.603299 −0.0402199
\(226\) 6.83360 0.454565
\(227\) 22.0937 1.46641 0.733204 0.680008i \(-0.238024\pi\)
0.733204 + 0.680008i \(0.238024\pi\)
\(228\) −56.6935 −3.75462
\(229\) −3.92434 −0.259328 −0.129664 0.991558i \(-0.541390\pi\)
−0.129664 + 0.991558i \(0.541390\pi\)
\(230\) 24.3798 1.60756
\(231\) −28.7260 −1.89003
\(232\) 56.8513 3.73247
\(233\) 22.8343 1.49593 0.747963 0.663740i \(-0.231032\pi\)
0.747963 + 0.663740i \(0.231032\pi\)
\(234\) −1.65852 −0.108421
\(235\) −18.3200 −1.19507
\(236\) 69.8665 4.54792
\(237\) −0.397852 −0.0258432
\(238\) −15.6785 −1.01628
\(239\) 27.2646 1.76360 0.881800 0.471624i \(-0.156332\pi\)
0.881800 + 0.471624i \(0.156332\pi\)
\(240\) −43.3661 −2.79927
\(241\) −24.9771 −1.60891 −0.804457 0.594011i \(-0.797543\pi\)
−0.804457 + 0.594011i \(0.797543\pi\)
\(242\) −68.9062 −4.42946
\(243\) −2.37280 −0.152215
\(244\) −37.8954 −2.42600
\(245\) −0.128778 −0.00822733
\(246\) 35.1052 2.23823
\(247\) −14.9980 −0.954300
\(248\) 10.9529 0.695509
\(249\) −18.9222 −1.19915
\(250\) −32.2573 −2.04013
\(251\) 19.6007 1.23719 0.618593 0.785711i \(-0.287703\pi\)
0.618593 + 0.785711i \(0.287703\pi\)
\(252\) −3.37963 −0.212896
\(253\) 34.6681 2.17956
\(254\) 43.9307 2.75646
\(255\) 5.92232 0.370870
\(256\) 56.2092 3.51308
\(257\) −1.96280 −0.122436 −0.0612179 0.998124i \(-0.519498\pi\)
−0.0612179 + 0.998124i \(0.519498\pi\)
\(258\) −33.7101 −2.09870
\(259\) 2.26831 0.140946
\(260\) −22.5064 −1.39579
\(261\) −1.33375 −0.0825569
\(262\) −15.2057 −0.939410
\(263\) −21.0955 −1.30080 −0.650401 0.759591i \(-0.725399\pi\)
−0.650401 + 0.759591i \(0.725399\pi\)
\(264\) −105.265 −6.47863
\(265\) −7.61802 −0.467971
\(266\) −41.5761 −2.54920
\(267\) 22.0518 1.34955
\(268\) 20.2560 1.23733
\(269\) 19.3251 1.17827 0.589135 0.808034i \(-0.299469\pi\)
0.589135 + 0.808034i \(0.299469\pi\)
\(270\) −21.0335 −1.28006
\(271\) 12.3351 0.749305 0.374652 0.927165i \(-0.377762\pi\)
0.374652 + 0.927165i \(0.377762\pi\)
\(272\) −33.6572 −2.04077
\(273\) −12.6164 −0.763582
\(274\) −14.5657 −0.879946
\(275\) −15.8373 −0.955023
\(276\) 57.5559 3.46446
\(277\) −5.99215 −0.360034 −0.180017 0.983664i \(-0.557615\pi\)
−0.180017 + 0.983664i \(0.557615\pi\)
\(278\) 10.1134 0.606560
\(279\) −0.256958 −0.0153837
\(280\) −39.9057 −2.38482
\(281\) −8.17397 −0.487618 −0.243809 0.969823i \(-0.578397\pi\)
−0.243809 + 0.969823i \(0.578397\pi\)
\(282\) −58.8366 −3.50367
\(283\) −16.1185 −0.958144 −0.479072 0.877776i \(-0.659027\pi\)
−0.479072 + 0.877776i \(0.659027\pi\)
\(284\) −8.92369 −0.529523
\(285\) 15.7048 0.930272
\(286\) −43.5379 −2.57445
\(287\) 18.9243 1.11707
\(288\) −5.40652 −0.318582
\(289\) −12.4036 −0.729622
\(290\) −24.6219 −1.44585
\(291\) 24.1785 1.41737
\(292\) 73.6149 4.30799
\(293\) 18.4366 1.07708 0.538540 0.842600i \(-0.318976\pi\)
0.538540 + 0.842600i \(0.318976\pi\)
\(294\) −0.413585 −0.0241207
\(295\) −19.3539 −1.12683
\(296\) 8.31211 0.483131
\(297\) −29.9096 −1.73553
\(298\) −2.24258 −0.129909
\(299\) 15.2262 0.880552
\(300\) −26.2930 −1.51803
\(301\) −18.1723 −1.04743
\(302\) 46.3847 2.66914
\(303\) 11.5764 0.665046
\(304\) −89.2520 −5.11895
\(305\) 10.4975 0.601085
\(306\) 1.34787 0.0770524
\(307\) 19.0580 1.08770 0.543848 0.839184i \(-0.316967\pi\)
0.543848 + 0.839184i \(0.316967\pi\)
\(308\) −88.7189 −5.05523
\(309\) −13.6910 −0.778853
\(310\) −4.74363 −0.269420
\(311\) −27.6210 −1.56624 −0.783120 0.621870i \(-0.786373\pi\)
−0.783120 + 0.621870i \(0.786373\pi\)
\(312\) −46.2323 −2.61739
\(313\) 31.9583 1.80639 0.903196 0.429229i \(-0.141215\pi\)
0.903196 + 0.429229i \(0.141215\pi\)
\(314\) 32.7567 1.84857
\(315\) 0.936199 0.0527488
\(316\) −1.22874 −0.0691223
\(317\) −26.2116 −1.47219 −0.736094 0.676880i \(-0.763332\pi\)
−0.736094 + 0.676880i \(0.763332\pi\)
\(318\) −24.4661 −1.37199
\(319\) −35.0124 −1.96032
\(320\) −51.5401 −2.88118
\(321\) −21.3713 −1.19283
\(322\) 42.2086 2.35220
\(323\) 12.1888 0.678201
\(324\) −53.4653 −2.97029
\(325\) −6.95571 −0.385833
\(326\) 21.4548 1.18827
\(327\) 29.9207 1.65462
\(328\) 69.3473 3.82906
\(329\) −31.7173 −1.74863
\(330\) 45.5897 2.50963
\(331\) 23.5932 1.29680 0.648400 0.761300i \(-0.275438\pi\)
0.648400 + 0.761300i \(0.275438\pi\)
\(332\) −58.4402 −3.20732
\(333\) −0.195005 −0.0106862
\(334\) −21.2447 −1.16246
\(335\) −5.61116 −0.306570
\(336\) −75.0795 −4.09592
\(337\) 23.8780 1.30072 0.650360 0.759626i \(-0.274618\pi\)
0.650360 + 0.759626i \(0.274618\pi\)
\(338\) 16.5977 0.902795
\(339\) −4.46899 −0.242722
\(340\) 18.2908 0.991957
\(341\) −6.74543 −0.365286
\(342\) 3.57427 0.193274
\(343\) 18.4078 0.993927
\(344\) −66.5914 −3.59037
\(345\) −15.9437 −0.858381
\(346\) −51.5940 −2.77371
\(347\) 17.6057 0.945124 0.472562 0.881297i \(-0.343329\pi\)
0.472562 + 0.881297i \(0.343329\pi\)
\(348\) −58.1275 −3.11596
\(349\) 12.5489 0.671725 0.335862 0.941911i \(-0.390972\pi\)
0.335862 + 0.941911i \(0.390972\pi\)
\(350\) −19.2820 −1.03067
\(351\) −13.1362 −0.701161
\(352\) −141.927 −7.56474
\(353\) 11.8941 0.633059 0.316529 0.948583i \(-0.397482\pi\)
0.316529 + 0.948583i \(0.397482\pi\)
\(354\) −62.1571 −3.30361
\(355\) 2.47197 0.131199
\(356\) 68.1060 3.60961
\(357\) 10.2533 0.542662
\(358\) −21.1781 −1.11930
\(359\) −25.0803 −1.32369 −0.661844 0.749642i \(-0.730226\pi\)
−0.661844 + 0.749642i \(0.730226\pi\)
\(360\) 3.43066 0.180811
\(361\) 13.3221 0.701165
\(362\) 44.7676 2.35294
\(363\) 45.0627 2.36518
\(364\) −38.9652 −2.04233
\(365\) −20.3922 −1.06738
\(366\) 33.7138 1.76225
\(367\) 10.8592 0.566844 0.283422 0.958995i \(-0.408530\pi\)
0.283422 + 0.958995i \(0.408530\pi\)
\(368\) 90.6098 4.72336
\(369\) −1.62691 −0.0846935
\(370\) −3.59992 −0.187151
\(371\) −13.1890 −0.684741
\(372\) −11.1988 −0.580629
\(373\) 22.7268 1.17675 0.588375 0.808588i \(-0.299768\pi\)
0.588375 + 0.808588i \(0.299768\pi\)
\(374\) 35.3830 1.82961
\(375\) 21.0954 1.08936
\(376\) −116.227 −5.99393
\(377\) −15.3774 −0.791976
\(378\) −36.4151 −1.87299
\(379\) 15.4174 0.791938 0.395969 0.918264i \(-0.370409\pi\)
0.395969 + 0.918264i \(0.370409\pi\)
\(380\) 48.5035 2.48817
\(381\) −28.7295 −1.47186
\(382\) −13.7838 −0.705238
\(383\) 16.0382 0.819512 0.409756 0.912195i \(-0.365614\pi\)
0.409756 + 0.912195i \(0.365614\pi\)
\(384\) −80.6097 −4.11360
\(385\) 24.5763 1.25252
\(386\) 16.8865 0.859500
\(387\) 1.56225 0.0794139
\(388\) 74.6741 3.79100
\(389\) −8.86877 −0.449664 −0.224832 0.974398i \(-0.572183\pi\)
−0.224832 + 0.974398i \(0.572183\pi\)
\(390\) 20.0229 1.01390
\(391\) −12.3742 −0.625790
\(392\) −0.817000 −0.0412648
\(393\) 9.94409 0.501613
\(394\) −54.1379 −2.72743
\(395\) 0.340378 0.0171263
\(396\) 7.62709 0.383276
\(397\) −5.93564 −0.297901 −0.148951 0.988845i \(-0.547590\pi\)
−0.148951 + 0.988845i \(0.547590\pi\)
\(398\) 46.0021 2.30587
\(399\) 27.1896 1.36118
\(400\) −41.3929 −2.06964
\(401\) −5.73143 −0.286214 −0.143107 0.989707i \(-0.545709\pi\)
−0.143107 + 0.989707i \(0.545709\pi\)
\(402\) −18.0208 −0.898798
\(403\) −2.96259 −0.147577
\(404\) 35.7531 1.77878
\(405\) 14.8105 0.735942
\(406\) −42.6278 −2.11558
\(407\) −5.11909 −0.253744
\(408\) 37.5727 1.86013
\(409\) 28.4758 1.40804 0.704018 0.710182i \(-0.251388\pi\)
0.704018 + 0.710182i \(0.251388\pi\)
\(410\) −30.0339 −1.48327
\(411\) 9.52556 0.469861
\(412\) −42.2839 −2.08318
\(413\) −33.5073 −1.64879
\(414\) −3.62864 −0.178338
\(415\) 16.1887 0.794671
\(416\) −62.3342 −3.05618
\(417\) −6.61387 −0.323883
\(418\) 93.8284 4.58930
\(419\) −0.262449 −0.0128215 −0.00641073 0.999979i \(-0.502041\pi\)
−0.00641073 + 0.999979i \(0.502041\pi\)
\(420\) 40.8015 1.99091
\(421\) 2.33993 0.114041 0.0570205 0.998373i \(-0.481840\pi\)
0.0570205 + 0.998373i \(0.481840\pi\)
\(422\) 6.06700 0.295337
\(423\) 2.72671 0.132577
\(424\) −48.3306 −2.34714
\(425\) 5.65285 0.274204
\(426\) 7.93900 0.384646
\(427\) 18.1743 0.879514
\(428\) −66.0042 −3.19043
\(429\) 28.4726 1.37467
\(430\) 28.8403 1.39080
\(431\) 31.6224 1.52320 0.761599 0.648049i \(-0.224415\pi\)
0.761599 + 0.648049i \(0.224415\pi\)
\(432\) −78.1727 −3.76109
\(433\) 36.3318 1.74599 0.872997 0.487725i \(-0.162173\pi\)
0.872997 + 0.487725i \(0.162173\pi\)
\(434\) −8.21262 −0.394218
\(435\) 16.1021 0.772034
\(436\) 92.4087 4.42557
\(437\) −32.8139 −1.56970
\(438\) −65.4919 −3.12932
\(439\) −4.87129 −0.232494 −0.116247 0.993220i \(-0.537086\pi\)
−0.116247 + 0.993220i \(0.537086\pi\)
\(440\) 90.0585 4.29337
\(441\) 0.0191671 0.000912718 0
\(442\) 15.5402 0.739170
\(443\) 28.8189 1.36923 0.684613 0.728907i \(-0.259971\pi\)
0.684613 + 0.728907i \(0.259971\pi\)
\(444\) −8.49871 −0.403331
\(445\) −18.8662 −0.894344
\(446\) −30.9414 −1.46512
\(447\) 1.46658 0.0693671
\(448\) −89.2312 −4.21578
\(449\) 38.6122 1.82222 0.911112 0.412159i \(-0.135225\pi\)
0.911112 + 0.412159i \(0.135225\pi\)
\(450\) 1.65766 0.0781427
\(451\) −42.7081 −2.01105
\(452\) −13.8022 −0.649203
\(453\) −30.3343 −1.42523
\(454\) −60.7058 −2.84906
\(455\) 10.7939 0.506024
\(456\) 99.6351 4.66584
\(457\) 19.9686 0.934091 0.467046 0.884233i \(-0.345318\pi\)
0.467046 + 0.884233i \(0.345318\pi\)
\(458\) 10.7827 0.503844
\(459\) 10.6757 0.498300
\(460\) −49.2413 −2.29589
\(461\) −31.6643 −1.47475 −0.737377 0.675481i \(-0.763936\pi\)
−0.737377 + 0.675481i \(0.763936\pi\)
\(462\) 78.9292 3.67212
\(463\) −5.32366 −0.247411 −0.123706 0.992319i \(-0.539478\pi\)
−0.123706 + 0.992319i \(0.539478\pi\)
\(464\) −91.5096 −4.24823
\(465\) 3.10220 0.143861
\(466\) −62.7408 −2.90641
\(467\) 35.1204 1.62518 0.812589 0.582837i \(-0.198057\pi\)
0.812589 + 0.582837i \(0.198057\pi\)
\(468\) 3.34981 0.154845
\(469\) −9.71458 −0.448577
\(470\) 50.3370 2.32187
\(471\) −21.4219 −0.987071
\(472\) −122.786 −5.65168
\(473\) 41.0109 1.88568
\(474\) 1.09316 0.0502104
\(475\) 14.9902 0.687798
\(476\) 31.6668 1.45144
\(477\) 1.13385 0.0519155
\(478\) −74.9136 −3.42647
\(479\) −15.4434 −0.705625 −0.352813 0.935694i \(-0.614775\pi\)
−0.352813 + 0.935694i \(0.614775\pi\)
\(480\) 65.2717 2.97923
\(481\) −2.24830 −0.102513
\(482\) 68.6283 3.12593
\(483\) −27.6033 −1.25599
\(484\) 139.174 6.32609
\(485\) −20.6857 −0.939288
\(486\) 6.51964 0.295737
\(487\) 36.2029 1.64051 0.820255 0.571998i \(-0.193831\pi\)
0.820255 + 0.571998i \(0.193831\pi\)
\(488\) 66.5987 3.01478
\(489\) −14.0308 −0.634495
\(490\) 0.353838 0.0159848
\(491\) 28.9409 1.30608 0.653042 0.757322i \(-0.273493\pi\)
0.653042 + 0.757322i \(0.273493\pi\)
\(492\) −70.9041 −3.19660
\(493\) 12.4971 0.562841
\(494\) 41.2093 1.85410
\(495\) −2.11280 −0.0949633
\(496\) −17.6301 −0.791616
\(497\) 4.27972 0.191971
\(498\) 51.9916 2.32980
\(499\) −1.67147 −0.0748251 −0.0374126 0.999300i \(-0.511912\pi\)
−0.0374126 + 0.999300i \(0.511912\pi\)
\(500\) 65.1519 2.91368
\(501\) 13.8935 0.620714
\(502\) −53.8560 −2.40371
\(503\) −14.5452 −0.648537 −0.324268 0.945965i \(-0.605118\pi\)
−0.324268 + 0.945965i \(0.605118\pi\)
\(504\) 5.93948 0.264565
\(505\) −9.90405 −0.440724
\(506\) −95.2558 −4.23464
\(507\) −10.8544 −0.482062
\(508\) −88.7295 −3.93674
\(509\) 19.5158 0.865024 0.432512 0.901628i \(-0.357627\pi\)
0.432512 + 0.901628i \(0.357627\pi\)
\(510\) −16.2725 −0.720558
\(511\) −35.3050 −1.56180
\(512\) −64.7220 −2.86034
\(513\) 28.3099 1.24991
\(514\) 5.39308 0.237879
\(515\) 11.7132 0.516144
\(516\) 68.0863 2.99733
\(517\) 71.5792 3.14805
\(518\) −6.23253 −0.273841
\(519\) 33.7411 1.48107
\(520\) 39.5536 1.73454
\(521\) 10.0222 0.439080 0.219540 0.975604i \(-0.429544\pi\)
0.219540 + 0.975604i \(0.429544\pi\)
\(522\) 3.66468 0.160399
\(523\) −10.3345 −0.451896 −0.225948 0.974139i \(-0.572548\pi\)
−0.225948 + 0.974139i \(0.572548\pi\)
\(524\) 30.7118 1.34165
\(525\) 12.6099 0.550341
\(526\) 57.9630 2.52731
\(527\) 2.40767 0.104880
\(528\) 169.438 7.37385
\(529\) 10.3130 0.448393
\(530\) 20.9317 0.909214
\(531\) 2.88060 0.125007
\(532\) 83.9738 3.64073
\(533\) −18.7574 −0.812472
\(534\) −60.5908 −2.62202
\(535\) 18.2840 0.790486
\(536\) −35.5986 −1.53763
\(537\) 13.8499 0.597667
\(538\) −53.0986 −2.28924
\(539\) 0.503157 0.0216725
\(540\) 42.4825 1.82816
\(541\) −23.3728 −1.00488 −0.502439 0.864613i \(-0.667564\pi\)
−0.502439 + 0.864613i \(0.667564\pi\)
\(542\) −33.8926 −1.45581
\(543\) −29.2768 −1.25639
\(544\) 50.6585 2.17197
\(545\) −25.5984 −1.09651
\(546\) 34.6656 1.48355
\(547\) 10.1669 0.434706 0.217353 0.976093i \(-0.430258\pi\)
0.217353 + 0.976093i \(0.430258\pi\)
\(548\) 29.4192 1.25673
\(549\) −1.56243 −0.0666827
\(550\) 43.5153 1.85550
\(551\) 33.1397 1.41180
\(552\) −101.151 −4.30527
\(553\) 0.589294 0.0250593
\(554\) 16.4644 0.699503
\(555\) 2.35425 0.0999323
\(556\) −20.4266 −0.866280
\(557\) 20.5719 0.871658 0.435829 0.900030i \(-0.356455\pi\)
0.435829 + 0.900030i \(0.356455\pi\)
\(558\) 0.706032 0.0298887
\(559\) 18.0119 0.761824
\(560\) 64.2334 2.71436
\(561\) −23.1395 −0.976949
\(562\) 22.4592 0.947386
\(563\) −17.5320 −0.738886 −0.369443 0.929253i \(-0.620452\pi\)
−0.369443 + 0.929253i \(0.620452\pi\)
\(564\) 118.836 5.00389
\(565\) 3.82339 0.160851
\(566\) 44.2880 1.86156
\(567\) 25.6414 1.07684
\(568\) 15.6828 0.658036
\(569\) 7.49755 0.314314 0.157157 0.987574i \(-0.449767\pi\)
0.157157 + 0.987574i \(0.449767\pi\)
\(570\) −43.1513 −1.80741
\(571\) −5.90334 −0.247047 −0.123524 0.992342i \(-0.539419\pi\)
−0.123524 + 0.992342i \(0.539419\pi\)
\(572\) 87.9362 3.67680
\(573\) 9.01419 0.376573
\(574\) −51.9975 −2.17033
\(575\) −15.2183 −0.634645
\(576\) 7.67113 0.319630
\(577\) −27.6448 −1.15087 −0.575433 0.817849i \(-0.695167\pi\)
−0.575433 + 0.817849i \(0.695167\pi\)
\(578\) 34.0807 1.41757
\(579\) −11.0433 −0.458944
\(580\) 49.7304 2.06494
\(581\) 28.0274 1.16277
\(582\) −66.4342 −2.75379
\(583\) 29.7648 1.23273
\(584\) −129.373 −5.35351
\(585\) −0.927939 −0.0383656
\(586\) −50.6575 −2.09264
\(587\) −46.3180 −1.91175 −0.955875 0.293773i \(-0.905089\pi\)
−0.955875 + 0.293773i \(0.905089\pi\)
\(588\) 0.835341 0.0344489
\(589\) 6.38466 0.263075
\(590\) 53.1778 2.18930
\(591\) 35.4047 1.45635
\(592\) −13.3794 −0.549891
\(593\) 30.9064 1.26917 0.634587 0.772852i \(-0.281170\pi\)
0.634587 + 0.772852i \(0.281170\pi\)
\(594\) 82.1811 3.37193
\(595\) −8.77209 −0.359621
\(596\) 4.52947 0.185534
\(597\) −30.0841 −1.23126
\(598\) −41.8362 −1.71081
\(599\) −10.3533 −0.423024 −0.211512 0.977375i \(-0.567839\pi\)
−0.211512 + 0.977375i \(0.567839\pi\)
\(600\) 46.2083 1.88645
\(601\) −15.9140 −0.649145 −0.324572 0.945861i \(-0.605220\pi\)
−0.324572 + 0.945861i \(0.605220\pi\)
\(602\) 49.9311 2.03504
\(603\) 0.835154 0.0340101
\(604\) −93.6858 −3.81202
\(605\) −38.5529 −1.56740
\(606\) −31.8079 −1.29211
\(607\) 30.0623 1.22019 0.610096 0.792327i \(-0.291131\pi\)
0.610096 + 0.792327i \(0.291131\pi\)
\(608\) 134.336 5.44805
\(609\) 27.8774 1.12965
\(610\) −28.8435 −1.16784
\(611\) 31.4375 1.27183
\(612\) −2.72236 −0.110045
\(613\) −7.40276 −0.298994 −0.149497 0.988762i \(-0.547766\pi\)
−0.149497 + 0.988762i \(0.547766\pi\)
\(614\) −52.3647 −2.11327
\(615\) 19.6413 0.792014
\(616\) 155.918 6.28211
\(617\) −0.862925 −0.0347401 −0.0173700 0.999849i \(-0.505529\pi\)
−0.0173700 + 0.999849i \(0.505529\pi\)
\(618\) 37.6181 1.51322
\(619\) 11.0332 0.443462 0.221731 0.975108i \(-0.428829\pi\)
0.221731 + 0.975108i \(0.428829\pi\)
\(620\) 9.58098 0.384782
\(621\) −28.7405 −1.15332
\(622\) 75.8928 3.04302
\(623\) −32.6630 −1.30861
\(624\) 74.4171 2.97907
\(625\) −4.86449 −0.194580
\(626\) −87.8104 −3.50961
\(627\) −61.3612 −2.45053
\(628\) −66.1606 −2.64009
\(629\) 1.82717 0.0728542
\(630\) −2.57235 −0.102485
\(631\) 19.7789 0.787386 0.393693 0.919242i \(-0.371197\pi\)
0.393693 + 0.919242i \(0.371197\pi\)
\(632\) 2.15944 0.0858979
\(633\) −3.96765 −0.157700
\(634\) 72.0203 2.86029
\(635\) 24.5792 0.975396
\(636\) 49.4156 1.95946
\(637\) 0.220986 0.00875578
\(638\) 96.2018 3.80867
\(639\) −0.367924 −0.0145548
\(640\) 68.9647 2.72607
\(641\) −13.4011 −0.529312 −0.264656 0.964343i \(-0.585258\pi\)
−0.264656 + 0.964343i \(0.585258\pi\)
\(642\) 58.7210 2.31753
\(643\) 2.51171 0.0990523 0.0495262 0.998773i \(-0.484229\pi\)
0.0495262 + 0.998773i \(0.484229\pi\)
\(644\) −85.2513 −3.35937
\(645\) −18.8608 −0.742642
\(646\) −33.4905 −1.31767
\(647\) −38.0294 −1.49509 −0.747545 0.664211i \(-0.768768\pi\)
−0.747545 + 0.664211i \(0.768768\pi\)
\(648\) 93.9618 3.69117
\(649\) 75.6188 2.96830
\(650\) 19.1119 0.749629
\(651\) 5.37082 0.210499
\(652\) −43.3334 −1.69707
\(653\) −20.6623 −0.808579 −0.404290 0.914631i \(-0.632481\pi\)
−0.404290 + 0.914631i \(0.632481\pi\)
\(654\) −82.2118 −3.21474
\(655\) −8.50755 −0.332418
\(656\) −111.624 −4.35817
\(657\) 3.03514 0.118412
\(658\) 87.1482 3.39739
\(659\) −38.0504 −1.48224 −0.741118 0.671375i \(-0.765704\pi\)
−0.741118 + 0.671375i \(0.765704\pi\)
\(660\) −92.0802 −3.58422
\(661\) 39.9475 1.55378 0.776889 0.629637i \(-0.216796\pi\)
0.776889 + 0.629637i \(0.216796\pi\)
\(662\) −64.8260 −2.51953
\(663\) −10.1628 −0.394692
\(664\) 102.705 3.98573
\(665\) −23.2618 −0.902054
\(666\) 0.535805 0.0207620
\(667\) −33.6439 −1.30270
\(668\) 42.9092 1.66021
\(669\) 20.2348 0.782323
\(670\) 15.4175 0.595631
\(671\) −41.0154 −1.58338
\(672\) 113.005 4.35925
\(673\) 45.4721 1.75282 0.876410 0.481565i \(-0.159931\pi\)
0.876410 + 0.481565i \(0.159931\pi\)
\(674\) −65.6086 −2.52715
\(675\) 13.1294 0.505351
\(676\) −33.5233 −1.28936
\(677\) 13.8720 0.533145 0.266573 0.963815i \(-0.414109\pi\)
0.266573 + 0.963815i \(0.414109\pi\)
\(678\) 12.2792 0.471581
\(679\) −35.8130 −1.37438
\(680\) −32.1449 −1.23270
\(681\) 39.6999 1.52130
\(682\) 18.5341 0.709708
\(683\) 9.88924 0.378401 0.189201 0.981938i \(-0.439410\pi\)
0.189201 + 0.981938i \(0.439410\pi\)
\(684\) −7.21916 −0.276031
\(685\) −8.14949 −0.311376
\(686\) −50.5782 −1.93109
\(687\) −7.05161 −0.269036
\(688\) 107.188 4.08649
\(689\) 13.0727 0.498030
\(690\) 43.8078 1.66773
\(691\) −42.2294 −1.60648 −0.803241 0.595655i \(-0.796893\pi\)
−0.803241 + 0.595655i \(0.796893\pi\)
\(692\) 104.208 3.96138
\(693\) −3.65788 −0.138951
\(694\) −48.3744 −1.83627
\(695\) 5.65842 0.214636
\(696\) 102.155 3.87219
\(697\) 15.2440 0.577407
\(698\) −34.4799 −1.30508
\(699\) 41.0307 1.55192
\(700\) 38.9450 1.47198
\(701\) 18.5998 0.702505 0.351253 0.936281i \(-0.385756\pi\)
0.351253 + 0.936281i \(0.385756\pi\)
\(702\) 36.0938 1.36227
\(703\) 4.84529 0.182744
\(704\) 201.376 7.58963
\(705\) −32.9190 −1.23980
\(706\) −32.6809 −1.22996
\(707\) −17.1468 −0.644873
\(708\) 125.542 4.71817
\(709\) −30.6046 −1.14938 −0.574690 0.818371i \(-0.694877\pi\)
−0.574690 + 0.818371i \(0.694877\pi\)
\(710\) −6.79213 −0.254904
\(711\) −0.0506611 −0.00189994
\(712\) −119.692 −4.48564
\(713\) −6.48179 −0.242745
\(714\) −28.1725 −1.05433
\(715\) −24.3594 −0.910991
\(716\) 42.7746 1.59856
\(717\) 48.9914 1.82962
\(718\) 68.9120 2.57177
\(719\) −29.2485 −1.09079 −0.545393 0.838181i \(-0.683619\pi\)
−0.545393 + 0.838181i \(0.683619\pi\)
\(720\) −5.52209 −0.205796
\(721\) 20.2790 0.755228
\(722\) −36.6046 −1.36228
\(723\) −44.8810 −1.66914
\(724\) −90.4199 −3.36043
\(725\) 15.3694 0.570805
\(726\) −123.817 −4.59527
\(727\) −12.0050 −0.445239 −0.222620 0.974905i \(-0.571461\pi\)
−0.222620 + 0.974905i \(0.571461\pi\)
\(728\) 68.4789 2.53800
\(729\) 24.6386 0.912539
\(730\) 56.0308 2.07379
\(731\) −14.6382 −0.541412
\(732\) −68.0938 −2.51682
\(733\) 14.5821 0.538604 0.269302 0.963056i \(-0.413207\pi\)
0.269302 + 0.963056i \(0.413207\pi\)
\(734\) −29.8372 −1.10131
\(735\) −0.231400 −0.00853532
\(736\) −136.380 −5.02702
\(737\) 21.9237 0.807570
\(738\) 4.47018 0.164550
\(739\) −13.4481 −0.494698 −0.247349 0.968926i \(-0.579559\pi\)
−0.247349 + 0.968926i \(0.579559\pi\)
\(740\) 7.27097 0.267286
\(741\) −26.9498 −0.990024
\(742\) 36.2389 1.33037
\(743\) −35.5887 −1.30562 −0.652812 0.757520i \(-0.726411\pi\)
−0.652812 + 0.757520i \(0.726411\pi\)
\(744\) 19.6811 0.721545
\(745\) −1.25472 −0.0459694
\(746\) −62.4454 −2.28629
\(747\) −2.40949 −0.0881586
\(748\) −71.4651 −2.61302
\(749\) 31.6550 1.15665
\(750\) −57.9627 −2.11650
\(751\) 48.3330 1.76370 0.881848 0.471534i \(-0.156300\pi\)
0.881848 + 0.471534i \(0.156300\pi\)
\(752\) 187.082 6.82218
\(753\) 35.2203 1.28350
\(754\) 42.2517 1.53872
\(755\) 25.9522 0.944496
\(756\) 73.5498 2.67498
\(757\) 21.6110 0.785465 0.392733 0.919653i \(-0.371530\pi\)
0.392733 + 0.919653i \(0.371530\pi\)
\(758\) −42.3617 −1.53864
\(759\) 62.2947 2.26115
\(760\) −85.2417 −3.09204
\(761\) −40.2274 −1.45824 −0.729121 0.684385i \(-0.760071\pi\)
−0.729121 + 0.684385i \(0.760071\pi\)
\(762\) 78.9387 2.85965
\(763\) −44.3183 −1.60443
\(764\) 27.8399 1.00721
\(765\) 0.754129 0.0272656
\(766\) −44.0673 −1.59222
\(767\) 33.2117 1.19921
\(768\) 101.002 3.64459
\(769\) 5.16990 0.186432 0.0932158 0.995646i \(-0.470285\pi\)
0.0932158 + 0.995646i \(0.470285\pi\)
\(770\) −67.5270 −2.43350
\(771\) −3.52693 −0.127019
\(772\) −34.1067 −1.22753
\(773\) −21.8922 −0.787407 −0.393703 0.919237i \(-0.628806\pi\)
−0.393703 + 0.919237i \(0.628806\pi\)
\(774\) −4.29253 −0.154292
\(775\) 2.96105 0.106364
\(776\) −131.235 −4.71106
\(777\) 4.07590 0.146222
\(778\) 24.3683 0.873646
\(779\) 40.4239 1.44834
\(780\) −40.4415 −1.44804
\(781\) −9.65840 −0.345605
\(782\) 34.0000 1.21584
\(783\) 29.0260 1.03730
\(784\) 1.31507 0.0469668
\(785\) 18.3273 0.654130
\(786\) −27.3229 −0.974576
\(787\) −32.4625 −1.15716 −0.578582 0.815625i \(-0.696394\pi\)
−0.578582 + 0.815625i \(0.696394\pi\)
\(788\) 109.346 3.89527
\(789\) −37.9062 −1.34950
\(790\) −0.935240 −0.0332743
\(791\) 6.61942 0.235360
\(792\) −13.4041 −0.476295
\(793\) −18.0139 −0.639693
\(794\) 16.3091 0.578788
\(795\) −13.6887 −0.485490
\(796\) −92.9131 −3.29322
\(797\) −11.2539 −0.398634 −0.199317 0.979935i \(-0.563872\pi\)
−0.199317 + 0.979935i \(0.563872\pi\)
\(798\) −74.7077 −2.64462
\(799\) −25.5490 −0.903860
\(800\) 62.3018 2.20270
\(801\) 2.80801 0.0992161
\(802\) 15.7480 0.556080
\(803\) 79.6758 2.81170
\(804\) 36.3977 1.28365
\(805\) 23.6157 0.832343
\(806\) 8.14016 0.286725
\(807\) 34.7250 1.22238
\(808\) −62.8337 −2.21048
\(809\) 12.3184 0.433092 0.216546 0.976272i \(-0.430521\pi\)
0.216546 + 0.976272i \(0.430521\pi\)
\(810\) −40.6942 −1.42985
\(811\) 28.7023 1.00788 0.503938 0.863740i \(-0.331884\pi\)
0.503938 + 0.863740i \(0.331884\pi\)
\(812\) 86.0979 3.02145
\(813\) 22.1648 0.777354
\(814\) 14.0655 0.492995
\(815\) 12.0039 0.420478
\(816\) −60.4782 −2.11716
\(817\) −38.8175 −1.35805
\(818\) −78.2415 −2.73565
\(819\) −1.60654 −0.0561369
\(820\) 60.6612 2.11838
\(821\) −11.8770 −0.414509 −0.207255 0.978287i \(-0.566453\pi\)
−0.207255 + 0.978287i \(0.566453\pi\)
\(822\) −26.1729 −0.912886
\(823\) 8.67871 0.302521 0.151260 0.988494i \(-0.451667\pi\)
0.151260 + 0.988494i \(0.451667\pi\)
\(824\) 74.3113 2.58876
\(825\) −28.4578 −0.990774
\(826\) 92.0665 3.20340
\(827\) −30.6964 −1.06742 −0.533709 0.845668i \(-0.679202\pi\)
−0.533709 + 0.845668i \(0.679202\pi\)
\(828\) 7.32898 0.254700
\(829\) 8.66405 0.300915 0.150458 0.988616i \(-0.451925\pi\)
0.150458 + 0.988616i \(0.451925\pi\)
\(830\) −44.4809 −1.54395
\(831\) −10.7672 −0.373511
\(832\) 88.4439 3.06624
\(833\) −0.179594 −0.00622255
\(834\) 18.1726 0.629266
\(835\) −11.8864 −0.411345
\(836\) −189.511 −6.55437
\(837\) 5.59210 0.193291
\(838\) 0.721118 0.0249106
\(839\) −37.6271 −1.29903 −0.649516 0.760348i \(-0.725029\pi\)
−0.649516 + 0.760348i \(0.725029\pi\)
\(840\) −71.7060 −2.47409
\(841\) 4.97801 0.171656
\(842\) −6.42930 −0.221568
\(843\) −14.6877 −0.505872
\(844\) −12.2539 −0.421796
\(845\) 9.28638 0.319461
\(846\) −7.49206 −0.257582
\(847\) −66.7465 −2.29344
\(848\) 77.7945 2.67147
\(849\) −28.9631 −0.994011
\(850\) −15.5321 −0.532746
\(851\) −4.91900 −0.168621
\(852\) −16.0349 −0.549346
\(853\) 43.1768 1.47834 0.739172 0.673517i \(-0.235217\pi\)
0.739172 + 0.673517i \(0.235217\pi\)
\(854\) −49.9366 −1.70879
\(855\) 1.99980 0.0683916
\(856\) 115.998 3.96474
\(857\) 0.907335 0.0309940 0.0154970 0.999880i \(-0.495067\pi\)
0.0154970 + 0.999880i \(0.495067\pi\)
\(858\) −78.2328 −2.67083
\(859\) 6.25521 0.213425 0.106712 0.994290i \(-0.465968\pi\)
0.106712 + 0.994290i \(0.465968\pi\)
\(860\) −58.2505 −1.98633
\(861\) 34.0049 1.15888
\(862\) −86.8874 −2.95940
\(863\) 19.0895 0.649813 0.324906 0.945746i \(-0.394667\pi\)
0.324906 + 0.945746i \(0.394667\pi\)
\(864\) 117.660 4.00289
\(865\) −28.8668 −0.981500
\(866\) −99.8271 −3.39226
\(867\) −22.2879 −0.756935
\(868\) 16.5875 0.563017
\(869\) −1.32991 −0.0451141
\(870\) −44.2429 −1.49997
\(871\) 9.62887 0.326262
\(872\) −162.402 −5.49964
\(873\) 3.07881 0.104202
\(874\) 90.1611 3.04974
\(875\) −31.2463 −1.05632
\(876\) 132.278 4.46925
\(877\) −9.38810 −0.317014 −0.158507 0.987358i \(-0.550668\pi\)
−0.158507 + 0.987358i \(0.550668\pi\)
\(878\) 13.3846 0.451709
\(879\) 33.1286 1.11740
\(880\) −144.961 −4.88663
\(881\) 11.4529 0.385858 0.192929 0.981213i \(-0.438201\pi\)
0.192929 + 0.981213i \(0.438201\pi\)
\(882\) −0.0526645 −0.00177331
\(883\) 5.60765 0.188712 0.0943562 0.995538i \(-0.469921\pi\)
0.0943562 + 0.995538i \(0.469921\pi\)
\(884\) −31.3874 −1.05567
\(885\) −34.7768 −1.16901
\(886\) −79.1843 −2.66025
\(887\) 38.2123 1.28304 0.641522 0.767105i \(-0.278303\pi\)
0.641522 + 0.767105i \(0.278303\pi\)
\(888\) 14.9359 0.501217
\(889\) 42.5538 1.42721
\(890\) 51.8378 1.73761
\(891\) −57.8672 −1.93862
\(892\) 62.4942 2.09246
\(893\) −67.7508 −2.26719
\(894\) −4.02967 −0.134772
\(895\) −11.8491 −0.396072
\(896\) 119.398 3.98882
\(897\) 27.3597 0.913515
\(898\) −106.093 −3.54037
\(899\) 6.54616 0.218327
\(900\) −3.34807 −0.111602
\(901\) −10.6241 −0.353939
\(902\) 117.347 3.90723
\(903\) −32.6536 −1.08664
\(904\) 24.2566 0.806761
\(905\) 25.0474 0.832605
\(906\) 83.3481 2.76905
\(907\) −4.23550 −0.140637 −0.0703187 0.997525i \(-0.522402\pi\)
−0.0703187 + 0.997525i \(0.522402\pi\)
\(908\) 122.611 4.06899
\(909\) 1.47410 0.0488928
\(910\) −29.6578 −0.983146
\(911\) 44.3546 1.46953 0.734767 0.678320i \(-0.237292\pi\)
0.734767 + 0.678320i \(0.237292\pi\)
\(912\) −160.376 −5.31058
\(913\) −63.2518 −2.09333
\(914\) −54.8668 −1.81483
\(915\) 18.8628 0.623586
\(916\) −21.7785 −0.719583
\(917\) −14.7291 −0.486397
\(918\) −29.3332 −0.968140
\(919\) −6.53978 −0.215728 −0.107864 0.994166i \(-0.534401\pi\)
−0.107864 + 0.994166i \(0.534401\pi\)
\(920\) 86.5385 2.85309
\(921\) 34.2450 1.12841
\(922\) 87.0026 2.86528
\(923\) −4.24196 −0.139626
\(924\) −159.418 −5.24447
\(925\) 2.24713 0.0738851
\(926\) 14.6276 0.480692
\(927\) −1.74337 −0.0572597
\(928\) 137.734 4.52135
\(929\) 12.6105 0.413738 0.206869 0.978369i \(-0.433673\pi\)
0.206869 + 0.978369i \(0.433673\pi\)
\(930\) −8.52377 −0.279505
\(931\) −0.476246 −0.0156083
\(932\) 126.721 4.15089
\(933\) −49.6318 −1.62487
\(934\) −96.4987 −3.15753
\(935\) 19.7967 0.647422
\(936\) −5.88708 −0.192425
\(937\) −3.84677 −0.125669 −0.0628343 0.998024i \(-0.520014\pi\)
−0.0628343 + 0.998024i \(0.520014\pi\)
\(938\) 26.6923 0.871534
\(939\) 57.4256 1.87401
\(940\) −101.669 −3.31607
\(941\) −7.15469 −0.233236 −0.116618 0.993177i \(-0.537205\pi\)
−0.116618 + 0.993177i \(0.537205\pi\)
\(942\) 58.8601 1.91777
\(943\) −41.0389 −1.33641
\(944\) 197.640 6.43264
\(945\) −20.3742 −0.662773
\(946\) −112.684 −3.66367
\(947\) 38.7238 1.25835 0.629177 0.777262i \(-0.283392\pi\)
0.629177 + 0.777262i \(0.283392\pi\)
\(948\) −2.20792 −0.0717098
\(949\) 34.9935 1.13594
\(950\) −41.1879 −1.33631
\(951\) −47.0993 −1.52730
\(952\) −55.6523 −1.80370
\(953\) −46.0828 −1.49277 −0.746384 0.665516i \(-0.768212\pi\)
−0.746384 + 0.665516i \(0.768212\pi\)
\(954\) −3.11543 −0.100866
\(955\) −7.71199 −0.249554
\(956\) 151.308 4.89364
\(957\) −62.9133 −2.03370
\(958\) 42.4330 1.37095
\(959\) −14.1092 −0.455609
\(960\) −92.6119 −2.98904
\(961\) −29.7388 −0.959317
\(962\) 6.17754 0.199172
\(963\) −2.72135 −0.0876944
\(964\) −138.613 −4.46441
\(965\) 9.44798 0.304141
\(966\) 75.8442 2.44025
\(967\) −17.4409 −0.560863 −0.280432 0.959874i \(-0.590478\pi\)
−0.280432 + 0.959874i \(0.590478\pi\)
\(968\) −244.589 −7.86140
\(969\) 21.9019 0.703589
\(970\) 56.8370 1.82493
\(971\) −18.9143 −0.606987 −0.303494 0.952833i \(-0.598153\pi\)
−0.303494 + 0.952833i \(0.598153\pi\)
\(972\) −13.1681 −0.422367
\(973\) 9.79640 0.314058
\(974\) −99.4731 −3.18732
\(975\) −12.4986 −0.400277
\(976\) −107.199 −3.43137
\(977\) 39.3981 1.26046 0.630229 0.776410i \(-0.282961\pi\)
0.630229 + 0.776410i \(0.282961\pi\)
\(978\) 38.5518 1.23275
\(979\) 73.7133 2.35589
\(980\) −0.714667 −0.0228292
\(981\) 3.81001 0.121644
\(982\) −79.5195 −2.53757
\(983\) −10.5169 −0.335437 −0.167718 0.985835i \(-0.553640\pi\)
−0.167718 + 0.985835i \(0.553640\pi\)
\(984\) 124.609 3.97240
\(985\) −30.2901 −0.965122
\(986\) −34.3377 −1.09353
\(987\) −56.9925 −1.81409
\(988\) −83.2329 −2.64799
\(989\) 39.4080 1.25310
\(990\) 5.80524 0.184503
\(991\) 1.91125 0.0607128 0.0303564 0.999539i \(-0.490336\pi\)
0.0303564 + 0.999539i \(0.490336\pi\)
\(992\) 26.5357 0.842509
\(993\) 42.3944 1.34534
\(994\) −11.7592 −0.372978
\(995\) 25.7381 0.815952
\(996\) −105.011 −3.32739
\(997\) 34.4346 1.09055 0.545277 0.838256i \(-0.316425\pi\)
0.545277 + 0.838256i \(0.316425\pi\)
\(998\) 4.59261 0.145377
\(999\) 4.24383 0.134269
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 \(a_p\))