Properties

Label 8047.2.a.b.1.14
Level 8047
Weight 2
Character 8047.1
Self dual Yes
Analytic conductor 64.256
Analytic rank 1
Dimension 142
CM No

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Newspace parameters

Level: \( N \) = \( 8047 = 13 \cdot 619 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8047.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2556185065\)
Analytic rank: \(1\)
Dimension: \(142\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.14
Character \(\chi\) = 8047.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.45771 q^{2} +2.98686 q^{3} +4.04034 q^{4} -1.52748 q^{5} -7.34083 q^{6} +5.18217 q^{7} -5.01456 q^{8} +5.92132 q^{9} +O(q^{10})\) \(q-2.45771 q^{2} +2.98686 q^{3} +4.04034 q^{4} -1.52748 q^{5} -7.34083 q^{6} +5.18217 q^{7} -5.01456 q^{8} +5.92132 q^{9} +3.75410 q^{10} -3.38966 q^{11} +12.0679 q^{12} +1.00000 q^{13} -12.7363 q^{14} -4.56236 q^{15} +4.24365 q^{16} -6.38035 q^{17} -14.5529 q^{18} -0.342245 q^{19} -6.17152 q^{20} +15.4784 q^{21} +8.33080 q^{22} -2.04112 q^{23} -14.9778 q^{24} -2.66681 q^{25} -2.45771 q^{26} +8.72558 q^{27} +20.9377 q^{28} -10.3843 q^{29} +11.2130 q^{30} +0.408753 q^{31} -0.400547 q^{32} -10.1244 q^{33} +15.6810 q^{34} -7.91565 q^{35} +23.9241 q^{36} -6.11794 q^{37} +0.841139 q^{38} +2.98686 q^{39} +7.65962 q^{40} +7.78956 q^{41} -38.0415 q^{42} -5.88168 q^{43} -13.6954 q^{44} -9.04469 q^{45} +5.01647 q^{46} -7.49849 q^{47} +12.6752 q^{48} +19.8549 q^{49} +6.55425 q^{50} -19.0572 q^{51} +4.04034 q^{52} +5.42105 q^{53} -21.4449 q^{54} +5.17763 q^{55} -25.9863 q^{56} -1.02224 q^{57} +25.5216 q^{58} -11.6026 q^{59} -18.4335 q^{60} -3.06923 q^{61} -1.00460 q^{62} +30.6853 q^{63} -7.50287 q^{64} -1.52748 q^{65} +24.8829 q^{66} +12.7491 q^{67} -25.7788 q^{68} -6.09652 q^{69} +19.4544 q^{70} +4.94261 q^{71} -29.6928 q^{72} -5.49144 q^{73} +15.0361 q^{74} -7.96539 q^{75} -1.38279 q^{76} -17.5658 q^{77} -7.34083 q^{78} +3.51488 q^{79} -6.48208 q^{80} +8.29811 q^{81} -19.1445 q^{82} +10.9590 q^{83} +62.5380 q^{84} +9.74584 q^{85} +14.4555 q^{86} -31.0165 q^{87} +16.9976 q^{88} -7.93955 q^{89} +22.2292 q^{90} +5.18217 q^{91} -8.24679 q^{92} +1.22089 q^{93} +18.4291 q^{94} +0.522772 q^{95} -1.19638 q^{96} -14.5818 q^{97} -48.7976 q^{98} -20.0713 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 142q - 13q^{2} - 26q^{3} + 129q^{4} - 37q^{5} - 15q^{6} - 14q^{7} - 39q^{8} + 98q^{9} + O(q^{10}) \) \( 142q - 13q^{2} - 26q^{3} + 129q^{4} - 37q^{5} - 15q^{6} - 14q^{7} - 39q^{8} + 98q^{9} - 25q^{10} - 25q^{11} - 62q^{12} + 142q^{13} - 57q^{14} - 14q^{15} + 111q^{16} - 141q^{17} - 29q^{18} - 3q^{19} - 87q^{20} - 19q^{21} - 24q^{22} - 69q^{23} - 40q^{24} + 87q^{25} - 13q^{26} - 95q^{27} - 34q^{28} - 147q^{29} - 2q^{30} - 21q^{31} - 66q^{32} - 62q^{33} - 6q^{34} - 59q^{35} + 74q^{36} - 37q^{37} - 76q^{38} - 26q^{39} - 61q^{40} - 97q^{41} - 29q^{42} - 33q^{43} - 57q^{44} - 86q^{45} - q^{46} - 102q^{47} - 141q^{48} + 70q^{49} - 28q^{50} - 13q^{51} + 129q^{52} - 137q^{53} - 29q^{54} - 24q^{55} - 130q^{56} - 65q^{57} - 15q^{58} - 56q^{59} + 11q^{60} - 77q^{61} - 150q^{62} - 32q^{63} + 73q^{64} - 37q^{65} - 32q^{66} - 9q^{67} - 226q^{68} - 113q^{69} + 6q^{70} - 18q^{71} - 82q^{72} - 117q^{73} - 70q^{74} - 83q^{75} + 40q^{76} - 214q^{77} - 15q^{78} - 52q^{79} - 161q^{80} - 10q^{81} - 36q^{82} - 74q^{83} + 53q^{84} + 2q^{85} + 17q^{86} - 49q^{87} - 29q^{88} - 171q^{89} - 57q^{90} - 14q^{91} - 187q^{92} - 39q^{93} + 13q^{94} - 150q^{95} - 47q^{96} - 126q^{97} - 85q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.45771 −1.73786 −0.868932 0.494932i \(-0.835193\pi\)
−0.868932 + 0.494932i \(0.835193\pi\)
\(3\) 2.98686 1.72446 0.862232 0.506514i \(-0.169066\pi\)
0.862232 + 0.506514i \(0.169066\pi\)
\(4\) 4.04034 2.02017
\(5\) −1.52748 −0.683109 −0.341554 0.939862i \(-0.610953\pi\)
−0.341554 + 0.939862i \(0.610953\pi\)
\(6\) −7.34083 −2.99688
\(7\) 5.18217 1.95868 0.979339 0.202227i \(-0.0648178\pi\)
0.979339 + 0.202227i \(0.0648178\pi\)
\(8\) −5.01456 −1.77291
\(9\) 5.92132 1.97377
\(10\) 3.75410 1.18715
\(11\) −3.38966 −1.02202 −0.511010 0.859575i \(-0.670729\pi\)
−0.511010 + 0.859575i \(0.670729\pi\)
\(12\) 12.0679 3.48371
\(13\) 1.00000 0.277350
\(14\) −12.7363 −3.40391
\(15\) −4.56236 −1.17800
\(16\) 4.24365 1.06091
\(17\) −6.38035 −1.54746 −0.773731 0.633514i \(-0.781612\pi\)
−0.773731 + 0.633514i \(0.781612\pi\)
\(18\) −14.5529 −3.43015
\(19\) −0.342245 −0.0785164 −0.0392582 0.999229i \(-0.512499\pi\)
−0.0392582 + 0.999229i \(0.512499\pi\)
\(20\) −6.17152 −1.37999
\(21\) 15.4784 3.37767
\(22\) 8.33080 1.77613
\(23\) −2.04112 −0.425602 −0.212801 0.977096i \(-0.568259\pi\)
−0.212801 + 0.977096i \(0.568259\pi\)
\(24\) −14.9778 −3.05732
\(25\) −2.66681 −0.533362
\(26\) −2.45771 −0.481997
\(27\) 8.72558 1.67924
\(28\) 20.9377 3.95686
\(29\) −10.3843 −1.92832 −0.964159 0.265325i \(-0.914521\pi\)
−0.964159 + 0.265325i \(0.914521\pi\)
\(30\) 11.2130 2.04720
\(31\) 0.408753 0.0734142 0.0367071 0.999326i \(-0.488313\pi\)
0.0367071 + 0.999326i \(0.488313\pi\)
\(32\) −0.400547 −0.0708073
\(33\) −10.1244 −1.76244
\(34\) 15.6810 2.68928
\(35\) −7.91565 −1.33799
\(36\) 23.9241 3.98736
\(37\) −6.11794 −1.00578 −0.502891 0.864350i \(-0.667730\pi\)
−0.502891 + 0.864350i \(0.667730\pi\)
\(38\) 0.841139 0.136451
\(39\) 2.98686 0.478280
\(40\) 7.65962 1.21109
\(41\) 7.78956 1.21652 0.608262 0.793736i \(-0.291867\pi\)
0.608262 + 0.793736i \(0.291867\pi\)
\(42\) −38.0415 −5.86992
\(43\) −5.88168 −0.896947 −0.448474 0.893796i \(-0.648032\pi\)
−0.448474 + 0.893796i \(0.648032\pi\)
\(44\) −13.6954 −2.06465
\(45\) −9.04469 −1.34830
\(46\) 5.01647 0.739638
\(47\) −7.49849 −1.09377 −0.546883 0.837209i \(-0.684186\pi\)
−0.546883 + 0.837209i \(0.684186\pi\)
\(48\) 12.6752 1.82950
\(49\) 19.8549 2.83642
\(50\) 6.55425 0.926911
\(51\) −19.0572 −2.66854
\(52\) 4.04034 0.560294
\(53\) 5.42105 0.744638 0.372319 0.928105i \(-0.378563\pi\)
0.372319 + 0.928105i \(0.378563\pi\)
\(54\) −21.4449 −2.91829
\(55\) 5.17763 0.698151
\(56\) −25.9863 −3.47257
\(57\) −1.02224 −0.135399
\(58\) 25.5216 3.35115
\(59\) −11.6026 −1.51053 −0.755267 0.655417i \(-0.772493\pi\)
−0.755267 + 0.655417i \(0.772493\pi\)
\(60\) −18.4335 −2.37975
\(61\) −3.06923 −0.392974 −0.196487 0.980506i \(-0.562953\pi\)
−0.196487 + 0.980506i \(0.562953\pi\)
\(62\) −1.00460 −0.127584
\(63\) 30.6853 3.86599
\(64\) −7.50287 −0.937859
\(65\) −1.52748 −0.189460
\(66\) 24.8829 3.06287
\(67\) 12.7491 1.55755 0.778777 0.627301i \(-0.215840\pi\)
0.778777 + 0.627301i \(0.215840\pi\)
\(68\) −25.7788 −3.12613
\(69\) −6.09652 −0.733935
\(70\) 19.4544 2.32524
\(71\) 4.94261 0.586580 0.293290 0.956023i \(-0.405250\pi\)
0.293290 + 0.956023i \(0.405250\pi\)
\(72\) −29.6928 −3.49933
\(73\) −5.49144 −0.642724 −0.321362 0.946956i \(-0.604141\pi\)
−0.321362 + 0.946956i \(0.604141\pi\)
\(74\) 15.0361 1.74791
\(75\) −7.96539 −0.919764
\(76\) −1.38279 −0.158616
\(77\) −17.5658 −2.00181
\(78\) −7.34083 −0.831185
\(79\) 3.51488 0.395455 0.197728 0.980257i \(-0.436644\pi\)
0.197728 + 0.980257i \(0.436644\pi\)
\(80\) −6.48208 −0.724719
\(81\) 8.29811 0.922012
\(82\) −19.1445 −2.11415
\(83\) 10.9590 1.20290 0.601452 0.798909i \(-0.294589\pi\)
0.601452 + 0.798909i \(0.294589\pi\)
\(84\) 62.5380 6.82346
\(85\) 9.74584 1.05708
\(86\) 14.4555 1.55877
\(87\) −31.0165 −3.32531
\(88\) 16.9976 1.81195
\(89\) −7.93955 −0.841591 −0.420795 0.907156i \(-0.638249\pi\)
−0.420795 + 0.907156i \(0.638249\pi\)
\(90\) 22.2292 2.34317
\(91\) 5.18217 0.543239
\(92\) −8.24679 −0.859788
\(93\) 1.22089 0.126600
\(94\) 18.4291 1.90082
\(95\) 0.522772 0.0536352
\(96\) −1.19638 −0.122105
\(97\) −14.5818 −1.48056 −0.740278 0.672301i \(-0.765306\pi\)
−0.740278 + 0.672301i \(0.765306\pi\)
\(98\) −48.7976 −4.92931
\(99\) −20.0713 −2.01724
\(100\) −10.7748 −1.07748
\(101\) −4.97015 −0.494548 −0.247274 0.968946i \(-0.579535\pi\)
−0.247274 + 0.968946i \(0.579535\pi\)
\(102\) 46.8371 4.63756
\(103\) −3.95903 −0.390095 −0.195047 0.980794i \(-0.562486\pi\)
−0.195047 + 0.980794i \(0.562486\pi\)
\(104\) −5.01456 −0.491718
\(105\) −23.6429 −2.30731
\(106\) −13.3234 −1.29408
\(107\) −8.86480 −0.856993 −0.428496 0.903544i \(-0.640957\pi\)
−0.428496 + 0.903544i \(0.640957\pi\)
\(108\) 35.2543 3.39235
\(109\) −2.94574 −0.282151 −0.141075 0.989999i \(-0.545056\pi\)
−0.141075 + 0.989999i \(0.545056\pi\)
\(110\) −12.7251 −1.21329
\(111\) −18.2734 −1.73444
\(112\) 21.9913 2.07799
\(113\) −0.152845 −0.0143784 −0.00718922 0.999974i \(-0.502288\pi\)
−0.00718922 + 0.999974i \(0.502288\pi\)
\(114\) 2.51236 0.235304
\(115\) 3.11776 0.290732
\(116\) −41.9561 −3.89553
\(117\) 5.92132 0.547427
\(118\) 28.5159 2.62510
\(119\) −33.0641 −3.03098
\(120\) 22.8782 2.08849
\(121\) 0.489785 0.0445259
\(122\) 7.54327 0.682936
\(123\) 23.2663 2.09785
\(124\) 1.65150 0.148309
\(125\) 11.7109 1.04745
\(126\) −75.4156 −6.71856
\(127\) −10.9358 −0.970395 −0.485198 0.874405i \(-0.661252\pi\)
−0.485198 + 0.874405i \(0.661252\pi\)
\(128\) 19.2410 1.70068
\(129\) −17.5677 −1.54675
\(130\) 3.75410 0.329256
\(131\) −2.20261 −0.192443 −0.0962217 0.995360i \(-0.530676\pi\)
−0.0962217 + 0.995360i \(0.530676\pi\)
\(132\) −40.9061 −3.56042
\(133\) −1.77357 −0.153788
\(134\) −31.3337 −2.70682
\(135\) −13.3281 −1.14710
\(136\) 31.9946 2.74352
\(137\) 12.0345 1.02817 0.514087 0.857738i \(-0.328131\pi\)
0.514087 + 0.857738i \(0.328131\pi\)
\(138\) 14.9835 1.27548
\(139\) −17.2365 −1.46198 −0.730991 0.682387i \(-0.760942\pi\)
−0.730991 + 0.682387i \(0.760942\pi\)
\(140\) −31.9819 −2.70296
\(141\) −22.3969 −1.88616
\(142\) −12.1475 −1.01940
\(143\) −3.38966 −0.283457
\(144\) 25.1280 2.09400
\(145\) 15.8618 1.31725
\(146\) 13.4964 1.11697
\(147\) 59.3038 4.89130
\(148\) −24.7185 −2.03185
\(149\) −0.979981 −0.0802832 −0.0401416 0.999194i \(-0.512781\pi\)
−0.0401416 + 0.999194i \(0.512781\pi\)
\(150\) 19.5766 1.59842
\(151\) 17.6666 1.43769 0.718844 0.695171i \(-0.244672\pi\)
0.718844 + 0.695171i \(0.244672\pi\)
\(152\) 1.71621 0.139203
\(153\) −37.7801 −3.05434
\(154\) 43.1716 3.47887
\(155\) −0.624361 −0.0501499
\(156\) 12.0679 0.966207
\(157\) −21.5511 −1.71996 −0.859982 0.510324i \(-0.829525\pi\)
−0.859982 + 0.510324i \(0.829525\pi\)
\(158\) −8.63856 −0.687247
\(159\) 16.1919 1.28410
\(160\) 0.611826 0.0483691
\(161\) −10.5774 −0.833617
\(162\) −20.3943 −1.60233
\(163\) −17.7714 −1.39196 −0.695980 0.718061i \(-0.745030\pi\)
−0.695980 + 0.718061i \(0.745030\pi\)
\(164\) 31.4724 2.45759
\(165\) 15.4648 1.20394
\(166\) −26.9340 −2.09048
\(167\) −9.21042 −0.712724 −0.356362 0.934348i \(-0.615983\pi\)
−0.356362 + 0.934348i \(0.615983\pi\)
\(168\) −77.6174 −5.98831
\(169\) 1.00000 0.0769231
\(170\) −23.9525 −1.83707
\(171\) −2.02654 −0.154974
\(172\) −23.7640 −1.81198
\(173\) 13.5281 1.02852 0.514262 0.857633i \(-0.328066\pi\)
0.514262 + 0.857633i \(0.328066\pi\)
\(174\) 76.2295 5.77894
\(175\) −13.8199 −1.04468
\(176\) −14.3845 −1.08427
\(177\) −34.6554 −2.60486
\(178\) 19.5131 1.46257
\(179\) −3.82914 −0.286204 −0.143102 0.989708i \(-0.545708\pi\)
−0.143102 + 0.989708i \(0.545708\pi\)
\(180\) −36.5436 −2.72380
\(181\) −17.0122 −1.26451 −0.632253 0.774762i \(-0.717870\pi\)
−0.632253 + 0.774762i \(0.717870\pi\)
\(182\) −12.7363 −0.944076
\(183\) −9.16735 −0.677670
\(184\) 10.2353 0.754555
\(185\) 9.34501 0.687059
\(186\) −3.00059 −0.220014
\(187\) 21.6272 1.58154
\(188\) −30.2964 −2.20959
\(189\) 45.2175 3.28909
\(190\) −1.28482 −0.0932107
\(191\) 20.3595 1.47316 0.736582 0.676348i \(-0.236438\pi\)
0.736582 + 0.676348i \(0.236438\pi\)
\(192\) −22.4100 −1.61730
\(193\) −14.7942 −1.06491 −0.532456 0.846458i \(-0.678731\pi\)
−0.532456 + 0.846458i \(0.678731\pi\)
\(194\) 35.8378 2.57300
\(195\) −4.56236 −0.326717
\(196\) 80.2206 5.73004
\(197\) 15.9375 1.13550 0.567749 0.823202i \(-0.307814\pi\)
0.567749 + 0.823202i \(0.307814\pi\)
\(198\) 49.3293 3.50568
\(199\) 12.9588 0.918628 0.459314 0.888274i \(-0.348095\pi\)
0.459314 + 0.888274i \(0.348095\pi\)
\(200\) 13.3729 0.945605
\(201\) 38.0798 2.68595
\(202\) 12.2152 0.859457
\(203\) −53.8133 −3.77695
\(204\) −76.9975 −5.39091
\(205\) −11.8984 −0.831019
\(206\) 9.73014 0.677931
\(207\) −12.0861 −0.840042
\(208\) 4.24365 0.294244
\(209\) 1.16009 0.0802454
\(210\) 58.1075 4.00980
\(211\) 9.28866 0.639458 0.319729 0.947509i \(-0.396408\pi\)
0.319729 + 0.947509i \(0.396408\pi\)
\(212\) 21.9029 1.50429
\(213\) 14.7629 1.01154
\(214\) 21.7871 1.48934
\(215\) 8.98413 0.612713
\(216\) −43.7549 −2.97715
\(217\) 2.11823 0.143795
\(218\) 7.23977 0.490339
\(219\) −16.4021 −1.10835
\(220\) 20.9194 1.41038
\(221\) −6.38035 −0.429189
\(222\) 44.9108 3.01421
\(223\) 16.0288 1.07337 0.536685 0.843783i \(-0.319676\pi\)
0.536685 + 0.843783i \(0.319676\pi\)
\(224\) −2.07570 −0.138689
\(225\) −15.7911 −1.05274
\(226\) 0.375648 0.0249878
\(227\) 16.1569 1.07237 0.536185 0.844101i \(-0.319865\pi\)
0.536185 + 0.844101i \(0.319865\pi\)
\(228\) −4.13018 −0.273528
\(229\) 16.6606 1.10096 0.550482 0.834847i \(-0.314444\pi\)
0.550482 + 0.834847i \(0.314444\pi\)
\(230\) −7.66254 −0.505253
\(231\) −52.4666 −3.45205
\(232\) 52.0727 3.41874
\(233\) 3.65358 0.239354 0.119677 0.992813i \(-0.461814\pi\)
0.119677 + 0.992813i \(0.461814\pi\)
\(234\) −14.5529 −0.951353
\(235\) 11.4538 0.747162
\(236\) −46.8786 −3.05153
\(237\) 10.4985 0.681948
\(238\) 81.2619 5.26743
\(239\) −14.6949 −0.950532 −0.475266 0.879842i \(-0.657648\pi\)
−0.475266 + 0.879842i \(0.657648\pi\)
\(240\) −19.3611 −1.24975
\(241\) −9.73367 −0.627000 −0.313500 0.949588i \(-0.601502\pi\)
−0.313500 + 0.949588i \(0.601502\pi\)
\(242\) −1.20375 −0.0773800
\(243\) −1.39147 −0.0892629
\(244\) −12.4007 −0.793875
\(245\) −30.3279 −1.93758
\(246\) −57.1818 −3.64578
\(247\) −0.342245 −0.0217765
\(248\) −2.04972 −0.130157
\(249\) 32.7329 2.07436
\(250\) −28.7820 −1.82033
\(251\) 11.9580 0.754782 0.377391 0.926054i \(-0.376821\pi\)
0.377391 + 0.926054i \(0.376821\pi\)
\(252\) 123.979 7.80995
\(253\) 6.91868 0.434974
\(254\) 26.8770 1.68641
\(255\) 29.1095 1.82290
\(256\) −32.2830 −2.01769
\(257\) −8.02412 −0.500531 −0.250265 0.968177i \(-0.580518\pi\)
−0.250265 + 0.968177i \(0.580518\pi\)
\(258\) 43.1764 2.68805
\(259\) −31.7042 −1.97000
\(260\) −6.17152 −0.382742
\(261\) −61.4889 −3.80607
\(262\) 5.41339 0.334440
\(263\) −24.6066 −1.51731 −0.758655 0.651493i \(-0.774143\pi\)
−0.758655 + 0.651493i \(0.774143\pi\)
\(264\) 50.7695 3.12465
\(265\) −8.28053 −0.508669
\(266\) 4.35893 0.267263
\(267\) −23.7143 −1.45129
\(268\) 51.5108 3.14652
\(269\) 4.39893 0.268207 0.134104 0.990967i \(-0.457184\pi\)
0.134104 + 0.990967i \(0.457184\pi\)
\(270\) 32.7567 1.99351
\(271\) −21.8040 −1.32450 −0.662249 0.749284i \(-0.730398\pi\)
−0.662249 + 0.749284i \(0.730398\pi\)
\(272\) −27.0760 −1.64172
\(273\) 15.4784 0.936797
\(274\) −29.5772 −1.78682
\(275\) 9.03958 0.545107
\(276\) −24.6320 −1.48267
\(277\) −15.6534 −0.940522 −0.470261 0.882527i \(-0.655840\pi\)
−0.470261 + 0.882527i \(0.655840\pi\)
\(278\) 42.3623 2.54072
\(279\) 2.42036 0.144903
\(280\) 39.6935 2.37214
\(281\) 23.6332 1.40984 0.704920 0.709287i \(-0.250983\pi\)
0.704920 + 0.709287i \(0.250983\pi\)
\(282\) 55.0451 3.27789
\(283\) −6.48779 −0.385659 −0.192830 0.981232i \(-0.561766\pi\)
−0.192830 + 0.981232i \(0.561766\pi\)
\(284\) 19.9698 1.18499
\(285\) 1.56144 0.0924920
\(286\) 8.33080 0.492610
\(287\) 40.3669 2.38278
\(288\) −2.37177 −0.139758
\(289\) 23.7089 1.39464
\(290\) −38.9837 −2.28920
\(291\) −43.5537 −2.55317
\(292\) −22.1873 −1.29841
\(293\) −0.736764 −0.0430422 −0.0215211 0.999768i \(-0.506851\pi\)
−0.0215211 + 0.999768i \(0.506851\pi\)
\(294\) −145.752 −8.50041
\(295\) 17.7228 1.03186
\(296\) 30.6788 1.78317
\(297\) −29.5767 −1.71622
\(298\) 2.40851 0.139521
\(299\) −2.04112 −0.118041
\(300\) −32.1829 −1.85808
\(301\) −30.4799 −1.75683
\(302\) −43.4194 −2.49851
\(303\) −14.8451 −0.852830
\(304\) −1.45237 −0.0832990
\(305\) 4.68818 0.268444
\(306\) 92.8526 5.30803
\(307\) 28.2791 1.61397 0.806986 0.590571i \(-0.201097\pi\)
0.806986 + 0.590571i \(0.201097\pi\)
\(308\) −70.9717 −4.04399
\(309\) −11.8251 −0.672704
\(310\) 1.53450 0.0871537
\(311\) −32.5481 −1.84563 −0.922817 0.385239i \(-0.874119\pi\)
−0.922817 + 0.385239i \(0.874119\pi\)
\(312\) −14.9778 −0.847949
\(313\) 4.91397 0.277754 0.138877 0.990310i \(-0.455651\pi\)
0.138877 + 0.990310i \(0.455651\pi\)
\(314\) 52.9663 2.98906
\(315\) −46.8712 −2.64089
\(316\) 14.2013 0.798886
\(317\) −16.3378 −0.917622 −0.458811 0.888534i \(-0.651725\pi\)
−0.458811 + 0.888534i \(0.651725\pi\)
\(318\) −39.7950 −2.23159
\(319\) 35.1993 1.97078
\(320\) 11.4605 0.640660
\(321\) −26.4779 −1.47785
\(322\) 25.9962 1.44871
\(323\) 2.18364 0.121501
\(324\) 33.5272 1.86262
\(325\) −2.66681 −0.147928
\(326\) 43.6768 2.41904
\(327\) −8.79851 −0.486559
\(328\) −39.0612 −2.15679
\(329\) −38.8585 −2.14234
\(330\) −38.0081 −2.09228
\(331\) 1.98972 0.109365 0.0546825 0.998504i \(-0.482585\pi\)
0.0546825 + 0.998504i \(0.482585\pi\)
\(332\) 44.2779 2.43007
\(333\) −36.2263 −1.98519
\(334\) 22.6365 1.23862
\(335\) −19.4740 −1.06398
\(336\) 65.6850 3.58341
\(337\) −21.7932 −1.18715 −0.593577 0.804777i \(-0.702285\pi\)
−0.593577 + 0.804777i \(0.702285\pi\)
\(338\) −2.45771 −0.133682
\(339\) −0.456526 −0.0247951
\(340\) 39.3765 2.13549
\(341\) −1.38553 −0.0750308
\(342\) 4.98066 0.269323
\(343\) 66.6164 3.59695
\(344\) 29.4940 1.59021
\(345\) 9.31230 0.501357
\(346\) −33.2482 −1.78743
\(347\) 30.1582 1.61898 0.809488 0.587136i \(-0.199745\pi\)
0.809488 + 0.587136i \(0.199745\pi\)
\(348\) −125.317 −6.71770
\(349\) 15.6396 0.837166 0.418583 0.908178i \(-0.362527\pi\)
0.418583 + 0.908178i \(0.362527\pi\)
\(350\) 33.9653 1.81552
\(351\) 8.72558 0.465737
\(352\) 1.35772 0.0723666
\(353\) −14.3140 −0.761855 −0.380928 0.924605i \(-0.624395\pi\)
−0.380928 + 0.924605i \(0.624395\pi\)
\(354\) 85.1730 4.52689
\(355\) −7.54973 −0.400698
\(356\) −32.0785 −1.70016
\(357\) −98.7577 −5.22681
\(358\) 9.41092 0.497383
\(359\) −25.7071 −1.35677 −0.678383 0.734708i \(-0.737319\pi\)
−0.678383 + 0.734708i \(0.737319\pi\)
\(360\) 45.3551 2.39042
\(361\) −18.8829 −0.993835
\(362\) 41.8110 2.19754
\(363\) 1.46292 0.0767833
\(364\) 20.9377 1.09744
\(365\) 8.38805 0.439051
\(366\) 22.5307 1.17770
\(367\) −4.35062 −0.227100 −0.113550 0.993532i \(-0.536222\pi\)
−0.113550 + 0.993532i \(0.536222\pi\)
\(368\) −8.66178 −0.451526
\(369\) 46.1245 2.40115
\(370\) −22.9673 −1.19401
\(371\) 28.0928 1.45851
\(372\) 4.93280 0.255754
\(373\) 14.6009 0.756003 0.378002 0.925805i \(-0.376611\pi\)
0.378002 + 0.925805i \(0.376611\pi\)
\(374\) −53.1534 −2.74850
\(375\) 34.9788 1.80630
\(376\) 37.6016 1.93915
\(377\) −10.3843 −0.534819
\(378\) −111.131 −5.71598
\(379\) 5.91846 0.304011 0.152005 0.988380i \(-0.451427\pi\)
0.152005 + 0.988380i \(0.451427\pi\)
\(380\) 2.11217 0.108352
\(381\) −32.6637 −1.67341
\(382\) −50.0378 −2.56016
\(383\) −35.6472 −1.82148 −0.910742 0.412975i \(-0.864490\pi\)
−0.910742 + 0.412975i \(0.864490\pi\)
\(384\) 57.4701 2.93276
\(385\) 26.8314 1.36745
\(386\) 36.3599 1.85067
\(387\) −34.8273 −1.77037
\(388\) −58.9153 −2.99097
\(389\) 10.4391 0.529286 0.264643 0.964347i \(-0.414746\pi\)
0.264643 + 0.964347i \(0.414746\pi\)
\(390\) 11.2130 0.567790
\(391\) 13.0230 0.658603
\(392\) −99.5636 −5.02872
\(393\) −6.57890 −0.331862
\(394\) −39.1697 −1.97334
\(395\) −5.36890 −0.270139
\(396\) −81.0947 −4.07516
\(397\) −3.04317 −0.152732 −0.0763661 0.997080i \(-0.524332\pi\)
−0.0763661 + 0.997080i \(0.524332\pi\)
\(398\) −31.8491 −1.59645
\(399\) −5.29741 −0.265202
\(400\) −11.3170 −0.565851
\(401\) 14.2306 0.710643 0.355321 0.934744i \(-0.384371\pi\)
0.355321 + 0.934744i \(0.384371\pi\)
\(402\) −93.5892 −4.66781
\(403\) 0.408753 0.0203614
\(404\) −20.0811 −0.999071
\(405\) −12.6752 −0.629834
\(406\) 132.257 6.56383
\(407\) 20.7377 1.02793
\(408\) 95.5634 4.73109
\(409\) −20.9710 −1.03695 −0.518475 0.855093i \(-0.673500\pi\)
−0.518475 + 0.855093i \(0.673500\pi\)
\(410\) 29.2428 1.44420
\(411\) 35.9452 1.77305
\(412\) −15.9958 −0.788057
\(413\) −60.1269 −2.95865
\(414\) 29.7041 1.45988
\(415\) −16.7396 −0.821714
\(416\) −0.400547 −0.0196384
\(417\) −51.4830 −2.52113
\(418\) −2.85117 −0.139455
\(419\) −19.5540 −0.955273 −0.477637 0.878558i \(-0.658506\pi\)
−0.477637 + 0.878558i \(0.658506\pi\)
\(420\) −95.5254 −4.66116
\(421\) 3.20576 0.156239 0.0781196 0.996944i \(-0.475108\pi\)
0.0781196 + 0.996944i \(0.475108\pi\)
\(422\) −22.8288 −1.11129
\(423\) −44.4010 −2.15885
\(424\) −27.1841 −1.32018
\(425\) 17.0152 0.825358
\(426\) −36.2829 −1.75791
\(427\) −15.9053 −0.769710
\(428\) −35.8168 −1.73127
\(429\) −10.1244 −0.488812
\(430\) −22.0804 −1.06481
\(431\) −8.66242 −0.417254 −0.208627 0.977995i \(-0.566899\pi\)
−0.208627 + 0.977995i \(0.566899\pi\)
\(432\) 37.0283 1.78153
\(433\) −25.1018 −1.20632 −0.603158 0.797622i \(-0.706091\pi\)
−0.603158 + 0.797622i \(0.706091\pi\)
\(434\) −5.20599 −0.249896
\(435\) 47.3770 2.27155
\(436\) −11.9018 −0.569992
\(437\) 0.698561 0.0334167
\(438\) 40.3117 1.92617
\(439\) −18.3193 −0.874333 −0.437167 0.899381i \(-0.644018\pi\)
−0.437167 + 0.899381i \(0.644018\pi\)
\(440\) −25.9635 −1.23776
\(441\) 117.567 5.59845
\(442\) 15.6810 0.745871
\(443\) 38.1649 1.81327 0.906636 0.421914i \(-0.138642\pi\)
0.906636 + 0.421914i \(0.138642\pi\)
\(444\) −73.8308 −3.50385
\(445\) 12.1275 0.574898
\(446\) −39.3942 −1.86537
\(447\) −2.92707 −0.138445
\(448\) −38.8812 −1.83696
\(449\) 5.16433 0.243720 0.121860 0.992547i \(-0.461114\pi\)
0.121860 + 0.992547i \(0.461114\pi\)
\(450\) 38.8098 1.82951
\(451\) −26.4039 −1.24331
\(452\) −0.617545 −0.0290469
\(453\) 52.7677 2.47924
\(454\) −39.7089 −1.86363
\(455\) −7.91565 −0.371092
\(456\) 5.12607 0.240050
\(457\) 27.3878 1.28115 0.640574 0.767896i \(-0.278696\pi\)
0.640574 + 0.767896i \(0.278696\pi\)
\(458\) −40.9470 −1.91333
\(459\) −55.6723 −2.59856
\(460\) 12.5968 0.587329
\(461\) 25.5838 1.19155 0.595777 0.803150i \(-0.296844\pi\)
0.595777 + 0.803150i \(0.296844\pi\)
\(462\) 128.948 5.99918
\(463\) 32.2289 1.49781 0.748903 0.662680i \(-0.230581\pi\)
0.748903 + 0.662680i \(0.230581\pi\)
\(464\) −44.0674 −2.04578
\(465\) −1.86488 −0.0864817
\(466\) −8.97943 −0.415964
\(467\) 27.7214 1.28279 0.641396 0.767210i \(-0.278356\pi\)
0.641396 + 0.767210i \(0.278356\pi\)
\(468\) 23.9241 1.10589
\(469\) 66.0682 3.05075
\(470\) −28.1500 −1.29846
\(471\) −64.3700 −2.96602
\(472\) 58.1821 2.67805
\(473\) 19.9369 0.916699
\(474\) −25.8022 −1.18513
\(475\) 0.912703 0.0418777
\(476\) −133.590 −6.12309
\(477\) 32.0998 1.46975
\(478\) 36.1157 1.65189
\(479\) 4.46868 0.204179 0.102090 0.994775i \(-0.467447\pi\)
0.102090 + 0.994775i \(0.467447\pi\)
\(480\) 1.82744 0.0834108
\(481\) −6.11794 −0.278954
\(482\) 23.9225 1.08964
\(483\) −31.5932 −1.43754
\(484\) 1.97890 0.0899499
\(485\) 22.2734 1.01138
\(486\) 3.41983 0.155127
\(487\) 39.7406 1.80082 0.900408 0.435046i \(-0.143268\pi\)
0.900408 + 0.435046i \(0.143268\pi\)
\(488\) 15.3908 0.696710
\(489\) −53.0805 −2.40038
\(490\) 74.5373 3.36725
\(491\) 30.1692 1.36152 0.680758 0.732509i \(-0.261651\pi\)
0.680758 + 0.732509i \(0.261651\pi\)
\(492\) 94.0038 4.23802
\(493\) 66.2555 2.98400
\(494\) 0.841139 0.0378446
\(495\) 30.6584 1.37799
\(496\) 1.73461 0.0778861
\(497\) 25.6135 1.14892
\(498\) −80.4480 −3.60496
\(499\) 22.9322 1.02658 0.513292 0.858214i \(-0.328426\pi\)
0.513292 + 0.858214i \(0.328426\pi\)
\(500\) 47.3159 2.11603
\(501\) −27.5102 −1.22907
\(502\) −29.3893 −1.31171
\(503\) −11.0690 −0.493542 −0.246771 0.969074i \(-0.579370\pi\)
−0.246771 + 0.969074i \(0.579370\pi\)
\(504\) −153.873 −6.85406
\(505\) 7.59179 0.337830
\(506\) −17.0041 −0.755925
\(507\) 2.98686 0.132651
\(508\) −44.1843 −1.96036
\(509\) −22.0427 −0.977026 −0.488513 0.872557i \(-0.662461\pi\)
−0.488513 + 0.872557i \(0.662461\pi\)
\(510\) −71.5426 −3.16796
\(511\) −28.4576 −1.25889
\(512\) 40.8603 1.80579
\(513\) −2.98629 −0.131848
\(514\) 19.7209 0.869854
\(515\) 6.04733 0.266477
\(516\) −70.9796 −3.12470
\(517\) 25.4173 1.11785
\(518\) 77.9198 3.42360
\(519\) 40.4066 1.77365
\(520\) 7.65962 0.335897
\(521\) −7.27689 −0.318806 −0.159403 0.987214i \(-0.550957\pi\)
−0.159403 + 0.987214i \(0.550957\pi\)
\(522\) 151.122 6.61442
\(523\) 13.0643 0.571261 0.285631 0.958340i \(-0.407797\pi\)
0.285631 + 0.958340i \(0.407797\pi\)
\(524\) −8.89931 −0.388768
\(525\) −41.2780 −1.80152
\(526\) 60.4759 2.63688
\(527\) −2.60799 −0.113606
\(528\) −42.9645 −1.86979
\(529\) −18.8338 −0.818863
\(530\) 20.3511 0.883997
\(531\) −68.7030 −2.98145
\(532\) −7.16583 −0.310678
\(533\) 7.78956 0.337403
\(534\) 58.2829 2.52215
\(535\) 13.5408 0.585419
\(536\) −63.9312 −2.76141
\(537\) −11.4371 −0.493548
\(538\) −10.8113 −0.466108
\(539\) −67.3014 −2.89888
\(540\) −53.8501 −2.31734
\(541\) 34.6307 1.48889 0.744446 0.667683i \(-0.232714\pi\)
0.744446 + 0.667683i \(0.232714\pi\)
\(542\) 53.5878 2.30179
\(543\) −50.8130 −2.18059
\(544\) 2.55563 0.109572
\(545\) 4.49955 0.192740
\(546\) −38.0415 −1.62802
\(547\) 31.6921 1.35506 0.677529 0.735496i \(-0.263051\pi\)
0.677529 + 0.735496i \(0.263051\pi\)
\(548\) 48.6233 2.07708
\(549\) −18.1739 −0.775643
\(550\) −22.2167 −0.947322
\(551\) 3.55398 0.151405
\(552\) 30.5714 1.30120
\(553\) 18.2147 0.774569
\(554\) 38.4715 1.63450
\(555\) 27.9122 1.18481
\(556\) −69.6413 −2.95345
\(557\) −17.6442 −0.747609 −0.373805 0.927507i \(-0.621947\pi\)
−0.373805 + 0.927507i \(0.621947\pi\)
\(558\) −5.94854 −0.251822
\(559\) −5.88168 −0.248768
\(560\) −33.5913 −1.41949
\(561\) 64.5974 2.72731
\(562\) −58.0836 −2.45011
\(563\) 42.5493 1.79324 0.896619 0.442804i \(-0.146016\pi\)
0.896619 + 0.442804i \(0.146016\pi\)
\(564\) −90.4911 −3.81036
\(565\) 0.233467 0.00982204
\(566\) 15.9451 0.670223
\(567\) 43.0022 1.80592
\(568\) −24.7850 −1.03996
\(569\) −0.473941 −0.0198686 −0.00993432 0.999951i \(-0.503162\pi\)
−0.00993432 + 0.999951i \(0.503162\pi\)
\(570\) −3.83758 −0.160738
\(571\) 0.385004 0.0161119 0.00805596 0.999968i \(-0.497436\pi\)
0.00805596 + 0.999968i \(0.497436\pi\)
\(572\) −13.6954 −0.572632
\(573\) 60.8111 2.54042
\(574\) −99.2100 −4.14095
\(575\) 5.44327 0.227000
\(576\) −44.4269 −1.85112
\(577\) 13.8601 0.577004 0.288502 0.957479i \(-0.406843\pi\)
0.288502 + 0.957479i \(0.406843\pi\)
\(578\) −58.2695 −2.42369
\(579\) −44.1883 −1.83640
\(580\) 64.0870 2.66107
\(581\) 56.7913 2.35610
\(582\) 107.042 4.43705
\(583\) −18.3755 −0.761035
\(584\) 27.5371 1.13949
\(585\) −9.04469 −0.373952
\(586\) 1.81075 0.0748015
\(587\) 43.1254 1.77998 0.889989 0.455983i \(-0.150712\pi\)
0.889989 + 0.455983i \(0.150712\pi\)
\(588\) 239.608 9.88125
\(589\) −0.139894 −0.00576422
\(590\) −43.5574 −1.79323
\(591\) 47.6030 1.95812
\(592\) −25.9624 −1.06705
\(593\) −6.34374 −0.260506 −0.130253 0.991481i \(-0.541579\pi\)
−0.130253 + 0.991481i \(0.541579\pi\)
\(594\) 72.6911 2.98255
\(595\) 50.5046 2.07049
\(596\) −3.95945 −0.162186
\(597\) 38.7062 1.58414
\(598\) 5.01647 0.205139
\(599\) −45.1339 −1.84412 −0.922060 0.387048i \(-0.873495\pi\)
−0.922060 + 0.387048i \(0.873495\pi\)
\(600\) 39.9429 1.63066
\(601\) −16.1640 −0.659342 −0.329671 0.944096i \(-0.606938\pi\)
−0.329671 + 0.944096i \(0.606938\pi\)
\(602\) 74.9107 3.05313
\(603\) 75.4917 3.07426
\(604\) 71.3791 2.90437
\(605\) −0.748136 −0.0304161
\(606\) 36.4850 1.48210
\(607\) −8.48631 −0.344449 −0.172224 0.985058i \(-0.555095\pi\)
−0.172224 + 0.985058i \(0.555095\pi\)
\(608\) 0.137085 0.00555954
\(609\) −160.733 −6.51322
\(610\) −11.5222 −0.466519
\(611\) −7.49849 −0.303356
\(612\) −152.644 −6.17029
\(613\) −28.3373 −1.14453 −0.572267 0.820068i \(-0.693936\pi\)
−0.572267 + 0.820068i \(0.693936\pi\)
\(614\) −69.5018 −2.80486
\(615\) −35.5388 −1.43306
\(616\) 88.0847 3.54903
\(617\) 11.1325 0.448177 0.224088 0.974569i \(-0.428060\pi\)
0.224088 + 0.974569i \(0.428060\pi\)
\(618\) 29.0626 1.16907
\(619\) 1.00000 0.0401934
\(620\) −2.52263 −0.101311
\(621\) −17.8099 −0.714687
\(622\) 79.9938 3.20746
\(623\) −41.1441 −1.64840
\(624\) 12.6752 0.507413
\(625\) −4.55405 −0.182162
\(626\) −12.0771 −0.482699
\(627\) 3.46504 0.138380
\(628\) −87.0737 −3.47462
\(629\) 39.0346 1.55641
\(630\) 115.196 4.58951
\(631\) −23.8515 −0.949512 −0.474756 0.880117i \(-0.657464\pi\)
−0.474756 + 0.880117i \(0.657464\pi\)
\(632\) −17.6256 −0.701108
\(633\) 27.7439 1.10272
\(634\) 40.1536 1.59470
\(635\) 16.7042 0.662885
\(636\) 65.4207 2.59410
\(637\) 19.8549 0.786681
\(638\) −86.5096 −3.42495
\(639\) 29.2668 1.15778
\(640\) −29.3902 −1.16175
\(641\) 24.7696 0.978341 0.489171 0.872188i \(-0.337300\pi\)
0.489171 + 0.872188i \(0.337300\pi\)
\(642\) 65.0750 2.56831
\(643\) −42.9256 −1.69282 −0.846411 0.532531i \(-0.821241\pi\)
−0.846411 + 0.532531i \(0.821241\pi\)
\(644\) −42.7363 −1.68405
\(645\) 26.8343 1.05660
\(646\) −5.36676 −0.211152
\(647\) 15.8630 0.623638 0.311819 0.950142i \(-0.399062\pi\)
0.311819 + 0.950142i \(0.399062\pi\)
\(648\) −41.6113 −1.63465
\(649\) 39.3290 1.54380
\(650\) 6.55425 0.257079
\(651\) 6.32685 0.247969
\(652\) −71.8023 −2.81199
\(653\) 43.4405 1.69996 0.849978 0.526818i \(-0.176615\pi\)
0.849978 + 0.526818i \(0.176615\pi\)
\(654\) 21.6242 0.845572
\(655\) 3.36444 0.131460
\(656\) 33.0562 1.29063
\(657\) −32.5166 −1.26859
\(658\) 95.5028 3.72309
\(659\) 0.240191 0.00935649 0.00467825 0.999989i \(-0.498511\pi\)
0.00467825 + 0.999989i \(0.498511\pi\)
\(660\) 62.4832 2.43215
\(661\) −34.8936 −1.35720 −0.678601 0.734507i \(-0.737413\pi\)
−0.678601 + 0.734507i \(0.737413\pi\)
\(662\) −4.89016 −0.190061
\(663\) −19.0572 −0.740120
\(664\) −54.9544 −2.13264
\(665\) 2.70909 0.105054
\(666\) 89.0337 3.44999
\(667\) 21.1956 0.820696
\(668\) −37.2132 −1.43982
\(669\) 47.8759 1.85099
\(670\) 47.8615 1.84905
\(671\) 10.4036 0.401628
\(672\) −6.19983 −0.239164
\(673\) −29.2862 −1.12890 −0.564449 0.825468i \(-0.690911\pi\)
−0.564449 + 0.825468i \(0.690911\pi\)
\(674\) 53.5615 2.06311
\(675\) −23.2695 −0.895643
\(676\) 4.04034 0.155398
\(677\) 48.2299 1.85363 0.926813 0.375523i \(-0.122537\pi\)
0.926813 + 0.375523i \(0.122537\pi\)
\(678\) 1.12201 0.0430905
\(679\) −75.5653 −2.89993
\(680\) −48.8711 −1.87412
\(681\) 48.2583 1.84926
\(682\) 3.40524 0.130393
\(683\) −30.3203 −1.16017 −0.580087 0.814554i \(-0.696982\pi\)
−0.580087 + 0.814554i \(0.696982\pi\)
\(684\) −8.18792 −0.313073
\(685\) −18.3824 −0.702354
\(686\) −163.724 −6.25100
\(687\) 49.7629 1.89857
\(688\) −24.9598 −0.951583
\(689\) 5.42105 0.206525
\(690\) −22.8869 −0.871291
\(691\) 5.73060 0.218002 0.109001 0.994042i \(-0.465235\pi\)
0.109001 + 0.994042i \(0.465235\pi\)
\(692\) 54.6581 2.07779
\(693\) −104.013 −3.95112
\(694\) −74.1201 −2.81356
\(695\) 26.3284 0.998693
\(696\) 155.534 5.89550
\(697\) −49.7001 −1.88253
\(698\) −38.4375 −1.45488
\(699\) 10.9127 0.412757
\(700\) −55.8370 −2.11044
\(701\) 10.1621 0.383817 0.191909 0.981413i \(-0.438532\pi\)
0.191909 + 0.981413i \(0.438532\pi\)
\(702\) −21.4449 −0.809387
\(703\) 2.09383 0.0789704
\(704\) 25.4322 0.958511
\(705\) 34.2108 1.28845
\(706\) 35.1796 1.32400
\(707\) −25.7562 −0.968660
\(708\) −140.020 −5.26226
\(709\) −0.120200 −0.00451421 −0.00225710 0.999997i \(-0.500718\pi\)
−0.00225710 + 0.999997i \(0.500718\pi\)
\(710\) 18.5551 0.696359
\(711\) 20.8128 0.780539
\(712\) 39.8133 1.49207
\(713\) −0.834312 −0.0312452
\(714\) 242.718 9.08349
\(715\) 5.17763 0.193632
\(716\) −15.4710 −0.578180
\(717\) −43.8915 −1.63916
\(718\) 63.1805 2.35787
\(719\) −16.6608 −0.621345 −0.310672 0.950517i \(-0.600554\pi\)
−0.310672 + 0.950517i \(0.600554\pi\)
\(720\) −38.3825 −1.43043
\(721\) −20.5164 −0.764070
\(722\) 46.4086 1.72715
\(723\) −29.0731 −1.08124
\(724\) −68.7350 −2.55452
\(725\) 27.6930 1.02849
\(726\) −3.59543 −0.133439
\(727\) −28.7802 −1.06740 −0.533699 0.845674i \(-0.679198\pi\)
−0.533699 + 0.845674i \(0.679198\pi\)
\(728\) −25.9863 −0.963116
\(729\) −29.0505 −1.07594
\(730\) −20.6154 −0.763010
\(731\) 37.5272 1.38799
\(732\) −37.0392 −1.36901
\(733\) −18.6476 −0.688764 −0.344382 0.938830i \(-0.611912\pi\)
−0.344382 + 0.938830i \(0.611912\pi\)
\(734\) 10.6926 0.394669
\(735\) −90.5853 −3.34129
\(736\) 0.817562 0.0301357
\(737\) −43.2152 −1.59185
\(738\) −113.361 −4.17286
\(739\) −13.7404 −0.505448 −0.252724 0.967538i \(-0.581326\pi\)
−0.252724 + 0.967538i \(0.581326\pi\)
\(740\) 37.7570 1.38798
\(741\) −1.02224 −0.0375528
\(742\) −69.0440 −2.53468
\(743\) −4.89938 −0.179741 −0.0898704 0.995953i \(-0.528645\pi\)
−0.0898704 + 0.995953i \(0.528645\pi\)
\(744\) −6.12221 −0.224451
\(745\) 1.49690 0.0548422
\(746\) −35.8847 −1.31383
\(747\) 64.8916 2.37426
\(748\) 87.3812 3.19497
\(749\) −45.9389 −1.67857
\(750\) −85.9676 −3.13909
\(751\) −28.2207 −1.02979 −0.514893 0.857254i \(-0.672168\pi\)
−0.514893 + 0.857254i \(0.672168\pi\)
\(752\) −31.8210 −1.16039
\(753\) 35.7169 1.30159
\(754\) 25.5216 0.929443
\(755\) −26.9853 −0.982097
\(756\) 182.694 6.64451
\(757\) 36.4334 1.32419 0.662097 0.749418i \(-0.269667\pi\)
0.662097 + 0.749418i \(0.269667\pi\)
\(758\) −14.5459 −0.528329
\(759\) 20.6651 0.750097
\(760\) −2.62147 −0.0950906
\(761\) −0.411195 −0.0149058 −0.00745291 0.999972i \(-0.502372\pi\)
−0.00745291 + 0.999972i \(0.502372\pi\)
\(762\) 80.2778 2.90816
\(763\) −15.2653 −0.552642
\(764\) 82.2594 2.97604
\(765\) 57.7083 2.08645
\(766\) 87.6104 3.16549
\(767\) −11.6026 −0.418947
\(768\) −96.4247 −3.47943
\(769\) −4.19905 −0.151422 −0.0757109 0.997130i \(-0.524123\pi\)
−0.0757109 + 0.997130i \(0.524123\pi\)
\(770\) −65.9437 −2.37645
\(771\) −23.9669 −0.863147
\(772\) −59.7737 −2.15130
\(773\) 26.5578 0.955217 0.477608 0.878573i \(-0.341504\pi\)
0.477608 + 0.878573i \(0.341504\pi\)
\(774\) 85.5954 3.07666
\(775\) −1.09007 −0.0391564
\(776\) 73.1212 2.62490
\(777\) −94.6960 −3.39720
\(778\) −25.6564 −0.919826
\(779\) −2.66594 −0.0955171
\(780\) −18.4335 −0.660024
\(781\) −16.7538 −0.599497
\(782\) −32.0068 −1.14456
\(783\) −90.6092 −3.23811
\(784\) 84.2573 3.00919
\(785\) 32.9188 1.17492
\(786\) 16.1690 0.576730
\(787\) 26.9943 0.962241 0.481121 0.876654i \(-0.340230\pi\)
0.481121 + 0.876654i \(0.340230\pi\)
\(788\) 64.3928 2.29390
\(789\) −73.4965 −2.61655
\(790\) 13.1952 0.469464
\(791\) −0.792069 −0.0281627
\(792\) 100.649 3.57639
\(793\) −3.06923 −0.108991
\(794\) 7.47922 0.265428
\(795\) −24.7328 −0.877181
\(796\) 52.3581 1.85578
\(797\) 6.12022 0.216789 0.108395 0.994108i \(-0.465429\pi\)
0.108395 + 0.994108i \(0.465429\pi\)
\(798\) 13.0195 0.460885
\(799\) 47.8430 1.69256
\(800\) 1.06818 0.0377660
\(801\) −47.0127 −1.66111
\(802\) −34.9747 −1.23500
\(803\) 18.6141 0.656877
\(804\) 153.855 5.42606
\(805\) 16.1568 0.569451
\(806\) −1.00460 −0.0353854
\(807\) 13.1390 0.462514
\(808\) 24.9231 0.876791
\(809\) −33.7005 −1.18485 −0.592423 0.805627i \(-0.701828\pi\)
−0.592423 + 0.805627i \(0.701828\pi\)
\(810\) 31.1519 1.09457
\(811\) 34.5015 1.21151 0.605756 0.795651i \(-0.292871\pi\)
0.605756 + 0.795651i \(0.292871\pi\)
\(812\) −217.424 −7.63008
\(813\) −65.1254 −2.28405
\(814\) −50.9673 −1.78640
\(815\) 27.1453 0.950860
\(816\) −80.8721 −2.83109
\(817\) 2.01297 0.0704251
\(818\) 51.5407 1.80208
\(819\) 30.6853 1.07223
\(820\) −48.0735 −1.67880
\(821\) −34.6963 −1.21091 −0.605454 0.795880i \(-0.707008\pi\)
−0.605454 + 0.795880i \(0.707008\pi\)
\(822\) −88.3429 −3.08131
\(823\) 6.51841 0.227217 0.113609 0.993526i \(-0.463759\pi\)
0.113609 + 0.993526i \(0.463759\pi\)
\(824\) 19.8528 0.691604
\(825\) 27.0000 0.940018
\(826\) 147.774 5.14173
\(827\) 12.7726 0.444147 0.222074 0.975030i \(-0.428717\pi\)
0.222074 + 0.975030i \(0.428717\pi\)
\(828\) −48.8319 −1.69703
\(829\) −7.22018 −0.250767 −0.125384 0.992108i \(-0.540016\pi\)
−0.125384 + 0.992108i \(0.540016\pi\)
\(830\) 41.1410 1.42803
\(831\) −46.7545 −1.62190
\(832\) −7.50287 −0.260115
\(833\) −126.681 −4.38925
\(834\) 126.530 4.38139
\(835\) 14.0687 0.486868
\(836\) 4.68717 0.162109
\(837\) 3.56661 0.123280
\(838\) 48.0579 1.66013
\(839\) −48.0940 −1.66039 −0.830195 0.557473i \(-0.811771\pi\)
−0.830195 + 0.557473i \(0.811771\pi\)
\(840\) 118.559 4.09067
\(841\) 78.8339 2.71841
\(842\) −7.87883 −0.271522
\(843\) 70.5891 2.43122
\(844\) 37.5293 1.29181
\(845\) −1.52748 −0.0525468
\(846\) 109.125 3.75178
\(847\) 2.53815 0.0872119
\(848\) 23.0050 0.789996
\(849\) −19.3781 −0.665055
\(850\) −41.8184 −1.43436
\(851\) 12.4874 0.428063
\(852\) 59.6471 2.04347
\(853\) 9.47360 0.324370 0.162185 0.986760i \(-0.448146\pi\)
0.162185 + 0.986760i \(0.448146\pi\)
\(854\) 39.0905 1.33765
\(855\) 3.09550 0.105864
\(856\) 44.4530 1.51937
\(857\) 34.7861 1.18827 0.594136 0.804365i \(-0.297494\pi\)
0.594136 + 0.804365i \(0.297494\pi\)
\(858\) 24.8829 0.849489
\(859\) −0.201976 −0.00689133 −0.00344567 0.999994i \(-0.501097\pi\)
−0.00344567 + 0.999994i \(0.501097\pi\)
\(860\) 36.2989 1.23778
\(861\) 120.570 4.10902
\(862\) 21.2897 0.725131
\(863\) 34.9891 1.19104 0.595522 0.803339i \(-0.296945\pi\)
0.595522 + 0.803339i \(0.296945\pi\)
\(864\) −3.49500 −0.118902
\(865\) −20.6639 −0.702593
\(866\) 61.6929 2.09641
\(867\) 70.8150 2.40500
\(868\) 8.55836 0.290490
\(869\) −11.9143 −0.404163
\(870\) −116.439 −3.94765
\(871\) 12.7491 0.431988
\(872\) 14.7716 0.500229
\(873\) −86.3435 −2.92228
\(874\) −1.71686 −0.0580737
\(875\) 60.6878 2.05162
\(876\) −66.2702 −2.23906
\(877\) −19.0414 −0.642981 −0.321491 0.946913i \(-0.604184\pi\)
−0.321491 + 0.946913i \(0.604184\pi\)
\(878\) 45.0236 1.51947
\(879\) −2.20061 −0.0742248
\(880\) 21.9720 0.740677
\(881\) −37.6093 −1.26709 −0.633544 0.773707i \(-0.718400\pi\)
−0.633544 + 0.773707i \(0.718400\pi\)
\(882\) −288.947 −9.72934
\(883\) −3.78623 −0.127417 −0.0637084 0.997969i \(-0.520293\pi\)
−0.0637084 + 0.997969i \(0.520293\pi\)
\(884\) −25.7788 −0.867034
\(885\) 52.9354 1.77940
\(886\) −93.7984 −3.15122
\(887\) −34.9355 −1.17302 −0.586510 0.809942i \(-0.699498\pi\)
−0.586510 + 0.809942i \(0.699498\pi\)
\(888\) 91.6331 3.07501
\(889\) −56.6712 −1.90069
\(890\) −29.8058 −0.999094
\(891\) −28.1278 −0.942315
\(892\) 64.7619 2.16839
\(893\) 2.56632 0.0858786
\(894\) 7.19388 0.240599
\(895\) 5.84893 0.195508
\(896\) 99.7101 3.33108
\(897\) −6.09652 −0.203557
\(898\) −12.6924 −0.423552
\(899\) −4.24462 −0.141566
\(900\) −63.8012 −2.12671
\(901\) −34.5882 −1.15230
\(902\) 64.8932 2.16071
\(903\) −91.0391 −3.02959
\(904\) 0.766449 0.0254917
\(905\) 25.9857 0.863795
\(906\) −129.688 −4.30858
\(907\) −16.9678 −0.563405 −0.281703 0.959502i \(-0.590899\pi\)
−0.281703 + 0.959502i \(0.590899\pi\)
\(908\) 65.2793 2.16637
\(909\) −29.4299 −0.976127
\(910\) 19.4544 0.644906
\(911\) −4.74641 −0.157255 −0.0786277 0.996904i \(-0.525054\pi\)
−0.0786277 + 0.996904i \(0.525054\pi\)
\(912\) −4.33802 −0.143646
\(913\) −37.1472 −1.22939
\(914\) −67.3113 −2.22646
\(915\) 14.0029 0.462922
\(916\) 67.3145 2.22413
\(917\) −11.4143 −0.376934
\(918\) 136.826 4.51594
\(919\) 23.7505 0.783455 0.391728 0.920081i \(-0.371878\pi\)
0.391728 + 0.920081i \(0.371878\pi\)
\(920\) −15.6342 −0.515443
\(921\) 84.4656 2.78324
\(922\) −62.8775 −2.07076
\(923\) 4.94261 0.162688
\(924\) −211.983 −6.97371
\(925\) 16.3154 0.536447
\(926\) −79.2094 −2.60298
\(927\) −23.4427 −0.769959
\(928\) 4.15940 0.136539
\(929\) −39.6588 −1.30116 −0.650581 0.759437i \(-0.725475\pi\)
−0.650581 + 0.759437i \(0.725475\pi\)
\(930\) 4.58333 0.150293
\(931\) −6.79525 −0.222705
\(932\) 14.7617 0.483535
\(933\) −97.2166 −3.18273
\(934\) −68.1311 −2.22932
\(935\) −33.0351 −1.08036
\(936\) −29.6928 −0.970540
\(937\) −3.41241 −0.111479 −0.0557393 0.998445i \(-0.517752\pi\)
−0.0557393 + 0.998445i \(0.517752\pi\)
\(938\) −162.376 −5.30178
\(939\) 14.6773 0.478977
\(940\) 46.2771 1.50939
\(941\) 4.98237 0.162421 0.0812103 0.996697i \(-0.474121\pi\)
0.0812103 + 0.996697i \(0.474121\pi\)
\(942\) 158.203 5.15453
\(943\) −15.8994 −0.517755
\(944\) −49.2375 −1.60254
\(945\) −69.0687 −2.24680
\(946\) −48.9991 −1.59310
\(947\) −29.4914 −0.958340 −0.479170 0.877722i \(-0.659062\pi\)
−0.479170 + 0.877722i \(0.659062\pi\)
\(948\) 42.4173 1.37765
\(949\) −5.49144 −0.178260
\(950\) −2.24316 −0.0727777
\(951\) −48.7987 −1.58241
\(952\) 165.802 5.37366
\(953\) 45.8479 1.48516 0.742579 0.669758i \(-0.233602\pi\)
0.742579 + 0.669758i \(0.233602\pi\)
\(954\) −78.8919 −2.55422
\(955\) −31.0987 −1.00633
\(956\) −59.3722 −1.92023
\(957\) 105.135 3.39854
\(958\) −10.9827 −0.354836
\(959\) 62.3647 2.01386
\(960\) 34.2308 1.10479
\(961\) −30.8329 −0.994610
\(962\) 15.0361 0.484784
\(963\) −52.4914 −1.69151
\(964\) −39.3273 −1.26665
\(965\) 22.5978 0.727450
\(966\) 77.6470 2.49825
\(967\) 12.7421 0.409760 0.204880 0.978787i \(-0.434320\pi\)
0.204880 + 0.978787i \(0.434320\pi\)
\(968\) −2.45606 −0.0789406
\(969\) 6.52223 0.209524
\(970\) −54.7414 −1.75764
\(971\) −7.61524 −0.244385 −0.122192 0.992506i \(-0.538992\pi\)
−0.122192 + 0.992506i \(0.538992\pi\)
\(972\) −5.62201 −0.180326
\(973\) −89.3226 −2.86355
\(974\) −97.6707 −3.12957
\(975\) −7.96539 −0.255097
\(976\) −13.0247 −0.416911
\(977\) −24.6855 −0.789759 −0.394880 0.918733i \(-0.629214\pi\)
−0.394880 + 0.918733i \(0.629214\pi\)
\(978\) 130.457 4.17154
\(979\) 26.9124 0.860123
\(980\) −122.535 −3.91424
\(981\) −17.4427 −0.556902
\(982\) −74.1471 −2.36613
\(983\) −25.3886 −0.809771 −0.404886 0.914367i \(-0.632689\pi\)
−0.404886 + 0.914367i \(0.632689\pi\)
\(984\) −116.670 −3.71931
\(985\) −24.3441 −0.775668
\(986\) −162.837 −5.18578
\(987\) −116.065 −3.69438
\(988\) −1.38279 −0.0439923
\(989\) 12.0052 0.381743
\(990\) −75.3495 −2.39476
\(991\) 56.7807 1.80370 0.901849 0.432051i \(-0.142210\pi\)
0.901849 + 0.432051i \(0.142210\pi\)
\(992\) −0.163725 −0.00519827
\(993\) 5.94302 0.188596
\(994\) −62.9505 −1.99667
\(995\) −19.7943 −0.627523
\(996\) 132.252 4.19056
\(997\) 2.70596 0.0856986 0.0428493 0.999082i \(-0.486356\pi\)
0.0428493 + 0.999082i \(0.486356\pi\)
\(998\) −56.3606 −1.78406
\(999\) −53.3826 −1.68895
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 \(a_p\))