Properties

Label 8007.2.a.e.1.7
Level 8007
Weight 2
Character 8007.1
Self dual Yes
Analytic conductor 63.936
Analytic rank 1
Dimension 46
CM No

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Newspace parameters

Level: \( N \) = \( 8007 = 3 \cdot 17 \cdot 157 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8007.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.9362168984\)
Analytic rank: \(1\)
Dimension: \(46\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.7
Character \(\chi\) = 8007.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.18789 q^{2} +1.00000 q^{3} +2.78687 q^{4} +1.88275 q^{5} -2.18789 q^{6} -4.23490 q^{7} -1.72159 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-2.18789 q^{2} +1.00000 q^{3} +2.78687 q^{4} +1.88275 q^{5} -2.18789 q^{6} -4.23490 q^{7} -1.72159 q^{8} +1.00000 q^{9} -4.11926 q^{10} -2.82858 q^{11} +2.78687 q^{12} -3.44968 q^{13} +9.26549 q^{14} +1.88275 q^{15} -1.80709 q^{16} -1.00000 q^{17} -2.18789 q^{18} +4.03133 q^{19} +5.24699 q^{20} -4.23490 q^{21} +6.18863 q^{22} +7.09312 q^{23} -1.72159 q^{24} -1.45524 q^{25} +7.54753 q^{26} +1.00000 q^{27} -11.8021 q^{28} +4.45240 q^{29} -4.11926 q^{30} -6.06536 q^{31} +7.39690 q^{32} -2.82858 q^{33} +2.18789 q^{34} -7.97327 q^{35} +2.78687 q^{36} +0.948127 q^{37} -8.82011 q^{38} -3.44968 q^{39} -3.24133 q^{40} -1.88245 q^{41} +9.26549 q^{42} +2.93590 q^{43} -7.88289 q^{44} +1.88275 q^{45} -15.5190 q^{46} +7.81020 q^{47} -1.80709 q^{48} +10.9343 q^{49} +3.18390 q^{50} -1.00000 q^{51} -9.61381 q^{52} -3.16643 q^{53} -2.18789 q^{54} -5.32553 q^{55} +7.29075 q^{56} +4.03133 q^{57} -9.74138 q^{58} -1.33133 q^{59} +5.24699 q^{60} +2.15231 q^{61} +13.2704 q^{62} -4.23490 q^{63} -12.5694 q^{64} -6.49490 q^{65} +6.18863 q^{66} -4.67577 q^{67} -2.78687 q^{68} +7.09312 q^{69} +17.4447 q^{70} +1.47881 q^{71} -1.72159 q^{72} +3.77361 q^{73} -2.07440 q^{74} -1.45524 q^{75} +11.2348 q^{76} +11.9788 q^{77} +7.54753 q^{78} +13.2228 q^{79} -3.40231 q^{80} +1.00000 q^{81} +4.11860 q^{82} +6.59385 q^{83} -11.8021 q^{84} -1.88275 q^{85} -6.42343 q^{86} +4.45240 q^{87} +4.86965 q^{88} -16.0826 q^{89} -4.11926 q^{90} +14.6090 q^{91} +19.7676 q^{92} -6.06536 q^{93} -17.0879 q^{94} +7.59000 q^{95} +7.39690 q^{96} +7.74922 q^{97} -23.9232 q^{98} -2.82858 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 46q - 5q^{2} + 46q^{3} + 43q^{4} - 19q^{5} - 5q^{6} + q^{7} - 18q^{8} + 46q^{9} + O(q^{10}) \) \( 46q - 5q^{2} + 46q^{3} + 43q^{4} - 19q^{5} - 5q^{6} + q^{7} - 18q^{8} + 46q^{9} - 10q^{10} - 25q^{11} + 43q^{12} - 8q^{13} - 28q^{14} - 19q^{15} + 33q^{16} - 46q^{17} - 5q^{18} - 2q^{19} - 56q^{20} + q^{21} - 19q^{22} - 64q^{23} - 18q^{24} + 11q^{25} - 13q^{26} + 46q^{27} - 38q^{28} - 51q^{29} - 10q^{30} - 19q^{31} - 61q^{32} - 25q^{33} + 5q^{34} - 39q^{35} + 43q^{36} - 46q^{37} - 48q^{38} - 8q^{39} - 10q^{40} - 53q^{41} - 28q^{42} - 33q^{43} - 62q^{44} - 19q^{45} + 2q^{46} - 45q^{47} + 33q^{48} + 21q^{49} - 60q^{50} - 46q^{51} - 63q^{52} - 47q^{53} - 5q^{54} + 5q^{55} - 82q^{56} - 2q^{57} - 21q^{58} - 65q^{59} - 56q^{60} - 37q^{61} - 46q^{62} + q^{63} + 74q^{64} - 85q^{65} - 19q^{66} - 52q^{67} - 43q^{68} - 64q^{69} - 20q^{70} - 48q^{71} - 18q^{72} - 39q^{73} - 16q^{74} + 11q^{75} + 42q^{76} - 78q^{77} - 13q^{78} - 26q^{79} - 78q^{80} + 46q^{81} + 3q^{82} - 47q^{83} - 38q^{84} + 19q^{85} - 6q^{86} - 51q^{87} - 58q^{88} - 58q^{89} - 10q^{90} - 43q^{91} - 68q^{92} - 19q^{93} - 78q^{95} - 61q^{96} - 44q^{97} - 4q^{98} - 25q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.18789 −1.54707 −0.773537 0.633752i \(-0.781514\pi\)
−0.773537 + 0.633752i \(0.781514\pi\)
\(3\) 1.00000 0.577350
\(4\) 2.78687 1.39344
\(5\) 1.88275 0.841993 0.420997 0.907062i \(-0.361680\pi\)
0.420997 + 0.907062i \(0.361680\pi\)
\(6\) −2.18789 −0.893203
\(7\) −4.23490 −1.60064 −0.800320 0.599573i \(-0.795337\pi\)
−0.800320 + 0.599573i \(0.795337\pi\)
\(8\) −1.72159 −0.608673
\(9\) 1.00000 0.333333
\(10\) −4.11926 −1.30263
\(11\) −2.82858 −0.852850 −0.426425 0.904523i \(-0.640227\pi\)
−0.426425 + 0.904523i \(0.640227\pi\)
\(12\) 2.78687 0.804500
\(13\) −3.44968 −0.956769 −0.478385 0.878150i \(-0.658777\pi\)
−0.478385 + 0.878150i \(0.658777\pi\)
\(14\) 9.26549 2.47631
\(15\) 1.88275 0.486125
\(16\) −1.80709 −0.451773
\(17\) −1.00000 −0.242536
\(18\) −2.18789 −0.515691
\(19\) 4.03133 0.924850 0.462425 0.886658i \(-0.346979\pi\)
0.462425 + 0.886658i \(0.346979\pi\)
\(20\) 5.24699 1.17326
\(21\) −4.23490 −0.924130
\(22\) 6.18863 1.31942
\(23\) 7.09312 1.47902 0.739509 0.673147i \(-0.235058\pi\)
0.739509 + 0.673147i \(0.235058\pi\)
\(24\) −1.72159 −0.351418
\(25\) −1.45524 −0.291047
\(26\) 7.54753 1.48019
\(27\) 1.00000 0.192450
\(28\) −11.8021 −2.23039
\(29\) 4.45240 0.826791 0.413395 0.910552i \(-0.364343\pi\)
0.413395 + 0.910552i \(0.364343\pi\)
\(30\) −4.11926 −0.752071
\(31\) −6.06536 −1.08937 −0.544686 0.838640i \(-0.683351\pi\)
−0.544686 + 0.838640i \(0.683351\pi\)
\(32\) 7.39690 1.30760
\(33\) −2.82858 −0.492393
\(34\) 2.18789 0.375220
\(35\) −7.97327 −1.34773
\(36\) 2.78687 0.464478
\(37\) 0.948127 0.155871 0.0779356 0.996958i \(-0.475167\pi\)
0.0779356 + 0.996958i \(0.475167\pi\)
\(38\) −8.82011 −1.43081
\(39\) −3.44968 −0.552391
\(40\) −3.24133 −0.512499
\(41\) −1.88245 −0.293989 −0.146995 0.989137i \(-0.546960\pi\)
−0.146995 + 0.989137i \(0.546960\pi\)
\(42\) 9.26549 1.42970
\(43\) 2.93590 0.447720 0.223860 0.974621i \(-0.428134\pi\)
0.223860 + 0.974621i \(0.428134\pi\)
\(44\) −7.88289 −1.18839
\(45\) 1.88275 0.280664
\(46\) −15.5190 −2.28815
\(47\) 7.81020 1.13923 0.569617 0.821910i \(-0.307091\pi\)
0.569617 + 0.821910i \(0.307091\pi\)
\(48\) −1.80709 −0.260831
\(49\) 10.9343 1.56205
\(50\) 3.18390 0.450271
\(51\) −1.00000 −0.140028
\(52\) −9.61381 −1.33320
\(53\) −3.16643 −0.434943 −0.217472 0.976067i \(-0.569781\pi\)
−0.217472 + 0.976067i \(0.569781\pi\)
\(54\) −2.18789 −0.297734
\(55\) −5.32553 −0.718094
\(56\) 7.29075 0.974267
\(57\) 4.03133 0.533963
\(58\) −9.74138 −1.27911
\(59\) −1.33133 −0.173325 −0.0866623 0.996238i \(-0.527620\pi\)
−0.0866623 + 0.996238i \(0.527620\pi\)
\(60\) 5.24699 0.677384
\(61\) 2.15231 0.275575 0.137788 0.990462i \(-0.456001\pi\)
0.137788 + 0.990462i \(0.456001\pi\)
\(62\) 13.2704 1.68534
\(63\) −4.23490 −0.533547
\(64\) −12.5694 −1.57118
\(65\) −6.49490 −0.805593
\(66\) 6.18863 0.761768
\(67\) −4.67577 −0.571237 −0.285618 0.958343i \(-0.592199\pi\)
−0.285618 + 0.958343i \(0.592199\pi\)
\(68\) −2.78687 −0.337958
\(69\) 7.09312 0.853912
\(70\) 17.4447 2.08503
\(71\) 1.47881 0.175502 0.0877511 0.996142i \(-0.472032\pi\)
0.0877511 + 0.996142i \(0.472032\pi\)
\(72\) −1.72159 −0.202891
\(73\) 3.77361 0.441667 0.220834 0.975312i \(-0.429122\pi\)
0.220834 + 0.975312i \(0.429122\pi\)
\(74\) −2.07440 −0.241144
\(75\) −1.45524 −0.168036
\(76\) 11.2348 1.28872
\(77\) 11.9788 1.36511
\(78\) 7.54753 0.854589
\(79\) 13.2228 1.48768 0.743840 0.668358i \(-0.233003\pi\)
0.743840 + 0.668358i \(0.233003\pi\)
\(80\) −3.40231 −0.380390
\(81\) 1.00000 0.111111
\(82\) 4.11860 0.454823
\(83\) 6.59385 0.723769 0.361884 0.932223i \(-0.382133\pi\)
0.361884 + 0.932223i \(0.382133\pi\)
\(84\) −11.8021 −1.28772
\(85\) −1.88275 −0.204213
\(86\) −6.42343 −0.692656
\(87\) 4.45240 0.477348
\(88\) 4.86965 0.519107
\(89\) −16.0826 −1.70476 −0.852379 0.522925i \(-0.824841\pi\)
−0.852379 + 0.522925i \(0.824841\pi\)
\(90\) −4.11926 −0.434208
\(91\) 14.6090 1.53144
\(92\) 19.7676 2.06092
\(93\) −6.06536 −0.628949
\(94\) −17.0879 −1.76248
\(95\) 7.59000 0.778718
\(96\) 7.39690 0.754943
\(97\) 7.74922 0.786814 0.393407 0.919364i \(-0.371296\pi\)
0.393407 + 0.919364i \(0.371296\pi\)
\(98\) −23.9232 −2.41660
\(99\) −2.82858 −0.284283
\(100\) −4.05555 −0.405555
\(101\) 16.0824 1.60026 0.800128 0.599829i \(-0.204765\pi\)
0.800128 + 0.599829i \(0.204765\pi\)
\(102\) 2.18789 0.216634
\(103\) −14.0991 −1.38923 −0.694615 0.719382i \(-0.744425\pi\)
−0.694615 + 0.719382i \(0.744425\pi\)
\(104\) 5.93893 0.582360
\(105\) −7.97327 −0.778111
\(106\) 6.92782 0.672889
\(107\) −8.60245 −0.831630 −0.415815 0.909449i \(-0.636504\pi\)
−0.415815 + 0.909449i \(0.636504\pi\)
\(108\) 2.78687 0.268167
\(109\) 4.25026 0.407101 0.203550 0.979064i \(-0.434752\pi\)
0.203550 + 0.979064i \(0.434752\pi\)
\(110\) 11.6517 1.11094
\(111\) 0.948127 0.0899922
\(112\) 7.65285 0.723127
\(113\) 2.34468 0.220569 0.110284 0.993900i \(-0.464824\pi\)
0.110284 + 0.993900i \(0.464824\pi\)
\(114\) −8.82011 −0.826079
\(115\) 13.3546 1.24532
\(116\) 12.4083 1.15208
\(117\) −3.44968 −0.318923
\(118\) 2.91281 0.268146
\(119\) 4.23490 0.388212
\(120\) −3.24133 −0.295891
\(121\) −2.99912 −0.272647
\(122\) −4.70902 −0.426335
\(123\) −1.88245 −0.169735
\(124\) −16.9034 −1.51797
\(125\) −12.1536 −1.08705
\(126\) 9.26549 0.825436
\(127\) −6.49424 −0.576271 −0.288135 0.957590i \(-0.593035\pi\)
−0.288135 + 0.957590i \(0.593035\pi\)
\(128\) 12.7068 1.12313
\(129\) 2.93590 0.258492
\(130\) 14.2101 1.24631
\(131\) −16.2039 −1.41574 −0.707869 0.706344i \(-0.750343\pi\)
−0.707869 + 0.706344i \(0.750343\pi\)
\(132\) −7.88289 −0.686118
\(133\) −17.0723 −1.48035
\(134\) 10.2301 0.883745
\(135\) 1.88275 0.162042
\(136\) 1.72159 0.147625
\(137\) 3.74290 0.319778 0.159889 0.987135i \(-0.448886\pi\)
0.159889 + 0.987135i \(0.448886\pi\)
\(138\) −15.5190 −1.32106
\(139\) 7.95250 0.674522 0.337261 0.941411i \(-0.390499\pi\)
0.337261 + 0.941411i \(0.390499\pi\)
\(140\) −22.2205 −1.87797
\(141\) 7.81020 0.657738
\(142\) −3.23547 −0.271515
\(143\) 9.75771 0.815980
\(144\) −1.80709 −0.150591
\(145\) 8.38278 0.696152
\(146\) −8.25624 −0.683291
\(147\) 10.9343 0.901849
\(148\) 2.64231 0.217196
\(149\) 19.5879 1.60471 0.802353 0.596850i \(-0.203581\pi\)
0.802353 + 0.596850i \(0.203581\pi\)
\(150\) 3.18390 0.259964
\(151\) 6.22240 0.506372 0.253186 0.967418i \(-0.418522\pi\)
0.253186 + 0.967418i \(0.418522\pi\)
\(152\) −6.94029 −0.562932
\(153\) −1.00000 −0.0808452
\(154\) −26.2082 −2.11192
\(155\) −11.4196 −0.917243
\(156\) −9.61381 −0.769721
\(157\) 1.00000 0.0798087
\(158\) −28.9300 −2.30155
\(159\) −3.16643 −0.251115
\(160\) 13.9265 1.10099
\(161\) −30.0386 −2.36738
\(162\) −2.18789 −0.171897
\(163\) −7.51333 −0.588489 −0.294245 0.955730i \(-0.595068\pi\)
−0.294245 + 0.955730i \(0.595068\pi\)
\(164\) −5.24614 −0.409655
\(165\) −5.32553 −0.414592
\(166\) −14.4266 −1.11972
\(167\) 2.04948 0.158594 0.0792968 0.996851i \(-0.474733\pi\)
0.0792968 + 0.996851i \(0.474733\pi\)
\(168\) 7.29075 0.562493
\(169\) −1.09971 −0.0845928
\(170\) 4.11926 0.315933
\(171\) 4.03133 0.308283
\(172\) 8.18197 0.623869
\(173\) −23.5641 −1.79154 −0.895772 0.444513i \(-0.853377\pi\)
−0.895772 + 0.444513i \(0.853377\pi\)
\(174\) −9.74138 −0.738492
\(175\) 6.16277 0.465862
\(176\) 5.11151 0.385295
\(177\) −1.33133 −0.100069
\(178\) 35.1871 2.63738
\(179\) 1.12270 0.0839144 0.0419572 0.999119i \(-0.486641\pi\)
0.0419572 + 0.999119i \(0.486641\pi\)
\(180\) 5.24699 0.391088
\(181\) −21.1199 −1.56983 −0.784914 0.619605i \(-0.787293\pi\)
−0.784914 + 0.619605i \(0.787293\pi\)
\(182\) −31.9630 −2.36925
\(183\) 2.15231 0.159103
\(184\) −12.2114 −0.900239
\(185\) 1.78509 0.131242
\(186\) 13.2704 0.973030
\(187\) 2.82858 0.206846
\(188\) 21.7660 1.58745
\(189\) −4.23490 −0.308043
\(190\) −16.6061 −1.20473
\(191\) −22.4112 −1.62162 −0.810809 0.585310i \(-0.800973\pi\)
−0.810809 + 0.585310i \(0.800973\pi\)
\(192\) −12.5694 −0.907121
\(193\) −4.52019 −0.325371 −0.162685 0.986678i \(-0.552016\pi\)
−0.162685 + 0.986678i \(0.552016\pi\)
\(194\) −16.9544 −1.21726
\(195\) −6.49490 −0.465110
\(196\) 30.4726 2.17661
\(197\) −24.5880 −1.75182 −0.875912 0.482471i \(-0.839739\pi\)
−0.875912 + 0.482471i \(0.839739\pi\)
\(198\) 6.18863 0.439807
\(199\) −8.69617 −0.616455 −0.308227 0.951313i \(-0.599736\pi\)
−0.308227 + 0.951313i \(0.599736\pi\)
\(200\) 2.50532 0.177153
\(201\) −4.67577 −0.329804
\(202\) −35.1865 −2.47571
\(203\) −18.8555 −1.32339
\(204\) −2.78687 −0.195120
\(205\) −3.54419 −0.247537
\(206\) 30.8474 2.14924
\(207\) 7.09312 0.493006
\(208\) 6.23389 0.432243
\(209\) −11.4029 −0.788758
\(210\) 17.4447 1.20380
\(211\) 11.8238 0.813986 0.406993 0.913431i \(-0.366577\pi\)
0.406993 + 0.913431i \(0.366577\pi\)
\(212\) −8.82444 −0.606065
\(213\) 1.47881 0.101326
\(214\) 18.8212 1.28659
\(215\) 5.52758 0.376978
\(216\) −1.72159 −0.117139
\(217\) 25.6862 1.74369
\(218\) −9.29910 −0.629815
\(219\) 3.77361 0.254997
\(220\) −14.8416 −1.00062
\(221\) 3.44968 0.232051
\(222\) −2.07440 −0.139225
\(223\) −17.4177 −1.16638 −0.583189 0.812336i \(-0.698195\pi\)
−0.583189 + 0.812336i \(0.698195\pi\)
\(224\) −31.3251 −2.09300
\(225\) −1.45524 −0.0970157
\(226\) −5.12991 −0.341236
\(227\) 21.8626 1.45107 0.725536 0.688185i \(-0.241592\pi\)
0.725536 + 0.688185i \(0.241592\pi\)
\(228\) 11.2348 0.744042
\(229\) −23.9910 −1.58537 −0.792686 0.609630i \(-0.791318\pi\)
−0.792686 + 0.609630i \(0.791318\pi\)
\(230\) −29.2184 −1.92661
\(231\) 11.9788 0.788144
\(232\) −7.66520 −0.503245
\(233\) −23.3784 −1.53157 −0.765786 0.643095i \(-0.777650\pi\)
−0.765786 + 0.643095i \(0.777650\pi\)
\(234\) 7.54753 0.493397
\(235\) 14.7047 0.959228
\(236\) −3.71025 −0.241517
\(237\) 13.2228 0.858912
\(238\) −9.26549 −0.600593
\(239\) −20.9874 −1.35756 −0.678781 0.734340i \(-0.737492\pi\)
−0.678781 + 0.734340i \(0.737492\pi\)
\(240\) −3.40231 −0.219618
\(241\) 11.9185 0.767737 0.383868 0.923388i \(-0.374592\pi\)
0.383868 + 0.923388i \(0.374592\pi\)
\(242\) 6.56175 0.421805
\(243\) 1.00000 0.0641500
\(244\) 5.99821 0.383996
\(245\) 20.5867 1.31524
\(246\) 4.11860 0.262592
\(247\) −13.9068 −0.884868
\(248\) 10.4421 0.663071
\(249\) 6.59385 0.417868
\(250\) 26.5908 1.68175
\(251\) −21.9973 −1.38846 −0.694230 0.719753i \(-0.744255\pi\)
−0.694230 + 0.719753i \(0.744255\pi\)
\(252\) −11.8021 −0.743463
\(253\) −20.0635 −1.26138
\(254\) 14.2087 0.891533
\(255\) −1.88275 −0.117903
\(256\) −2.66214 −0.166384
\(257\) 1.98422 0.123772 0.0618861 0.998083i \(-0.480288\pi\)
0.0618861 + 0.998083i \(0.480288\pi\)
\(258\) −6.42343 −0.399905
\(259\) −4.01522 −0.249494
\(260\) −18.1005 −1.12254
\(261\) 4.45240 0.275597
\(262\) 35.4523 2.19025
\(263\) −15.1935 −0.936874 −0.468437 0.883497i \(-0.655183\pi\)
−0.468437 + 0.883497i \(0.655183\pi\)
\(264\) 4.86965 0.299706
\(265\) −5.96162 −0.366219
\(266\) 37.3523 2.29021
\(267\) −16.0826 −0.984242
\(268\) −13.0308 −0.795981
\(269\) −11.1681 −0.680929 −0.340465 0.940257i \(-0.610584\pi\)
−0.340465 + 0.940257i \(0.610584\pi\)
\(270\) −4.11926 −0.250690
\(271\) 29.3218 1.78118 0.890588 0.454812i \(-0.150293\pi\)
0.890588 + 0.454812i \(0.150293\pi\)
\(272\) 1.80709 0.109571
\(273\) 14.6090 0.884179
\(274\) −8.18906 −0.494719
\(275\) 4.11625 0.248219
\(276\) 19.7676 1.18987
\(277\) −9.78287 −0.587796 −0.293898 0.955837i \(-0.594953\pi\)
−0.293898 + 0.955837i \(0.594953\pi\)
\(278\) −17.3992 −1.04354
\(279\) −6.06536 −0.363124
\(280\) 13.7267 0.820326
\(281\) 18.6134 1.11038 0.555191 0.831723i \(-0.312645\pi\)
0.555191 + 0.831723i \(0.312645\pi\)
\(282\) −17.0879 −1.01757
\(283\) 1.36808 0.0813237 0.0406618 0.999173i \(-0.487053\pi\)
0.0406618 + 0.999173i \(0.487053\pi\)
\(284\) 4.12125 0.244551
\(285\) 7.59000 0.449593
\(286\) −21.3488 −1.26238
\(287\) 7.97198 0.470571
\(288\) 7.39690 0.435867
\(289\) 1.00000 0.0588235
\(290\) −18.3406 −1.07700
\(291\) 7.74922 0.454267
\(292\) 10.5165 0.615435
\(293\) −0.159950 −0.00934437 −0.00467219 0.999989i \(-0.501487\pi\)
−0.00467219 + 0.999989i \(0.501487\pi\)
\(294\) −23.9232 −1.39523
\(295\) −2.50657 −0.145938
\(296\) −1.63228 −0.0948746
\(297\) −2.82858 −0.164131
\(298\) −42.8563 −2.48260
\(299\) −24.4690 −1.41508
\(300\) −4.05555 −0.234147
\(301\) −12.4332 −0.716639
\(302\) −13.6139 −0.783394
\(303\) 16.0824 0.923909
\(304\) −7.28499 −0.417823
\(305\) 4.05227 0.232033
\(306\) 2.18789 0.125073
\(307\) −2.25214 −0.128536 −0.0642682 0.997933i \(-0.520471\pi\)
−0.0642682 + 0.997933i \(0.520471\pi\)
\(308\) 33.3832 1.90219
\(309\) −14.0991 −0.802072
\(310\) 24.9848 1.41904
\(311\) −16.9471 −0.960983 −0.480491 0.876999i \(-0.659542\pi\)
−0.480491 + 0.876999i \(0.659542\pi\)
\(312\) 5.93893 0.336226
\(313\) 6.77575 0.382988 0.191494 0.981494i \(-0.438667\pi\)
0.191494 + 0.981494i \(0.438667\pi\)
\(314\) −2.18789 −0.123470
\(315\) −7.97327 −0.449243
\(316\) 36.8502 2.07298
\(317\) 0.868483 0.0487789 0.0243894 0.999703i \(-0.492236\pi\)
0.0243894 + 0.999703i \(0.492236\pi\)
\(318\) 6.92782 0.388493
\(319\) −12.5940 −0.705128
\(320\) −23.6652 −1.32292
\(321\) −8.60245 −0.480142
\(322\) 65.7213 3.66250
\(323\) −4.03133 −0.224309
\(324\) 2.78687 0.154826
\(325\) 5.02010 0.278465
\(326\) 16.4383 0.910436
\(327\) 4.25026 0.235040
\(328\) 3.24080 0.178943
\(329\) −33.0754 −1.82350
\(330\) 11.6517 0.641404
\(331\) 4.68586 0.257558 0.128779 0.991673i \(-0.458894\pi\)
0.128779 + 0.991673i \(0.458894\pi\)
\(332\) 18.3762 1.00853
\(333\) 0.948127 0.0519570
\(334\) −4.48404 −0.245356
\(335\) −8.80333 −0.480977
\(336\) 7.65285 0.417497
\(337\) −29.3330 −1.59787 −0.798934 0.601419i \(-0.794602\pi\)
−0.798934 + 0.601419i \(0.794602\pi\)
\(338\) 2.40604 0.130871
\(339\) 2.34468 0.127346
\(340\) −5.24699 −0.284558
\(341\) 17.1564 0.929070
\(342\) −8.82011 −0.476937
\(343\) −16.6615 −0.899638
\(344\) −5.05441 −0.272515
\(345\) 13.3546 0.718988
\(346\) 51.5557 2.77165
\(347\) −26.5955 −1.42772 −0.713860 0.700288i \(-0.753055\pi\)
−0.713860 + 0.700288i \(0.753055\pi\)
\(348\) 12.4083 0.665153
\(349\) −5.64738 −0.302297 −0.151149 0.988511i \(-0.548297\pi\)
−0.151149 + 0.988511i \(0.548297\pi\)
\(350\) −13.4835 −0.720722
\(351\) −3.44968 −0.184130
\(352\) −20.9227 −1.11519
\(353\) 17.6895 0.941516 0.470758 0.882262i \(-0.343980\pi\)
0.470758 + 0.882262i \(0.343980\pi\)
\(354\) 2.91281 0.154814
\(355\) 2.78423 0.147772
\(356\) −44.8203 −2.37547
\(357\) 4.23490 0.224134
\(358\) −2.45634 −0.129822
\(359\) 16.3229 0.861489 0.430744 0.902474i \(-0.358251\pi\)
0.430744 + 0.902474i \(0.358251\pi\)
\(360\) −3.24133 −0.170833
\(361\) −2.74838 −0.144652
\(362\) 46.2080 2.42864
\(363\) −2.99912 −0.157413
\(364\) 40.7135 2.13397
\(365\) 7.10477 0.371881
\(366\) −4.70902 −0.246145
\(367\) −4.92235 −0.256945 −0.128472 0.991713i \(-0.541007\pi\)
−0.128472 + 0.991713i \(0.541007\pi\)
\(368\) −12.8179 −0.668181
\(369\) −1.88245 −0.0979964
\(370\) −3.90558 −0.203042
\(371\) 13.4095 0.696188
\(372\) −16.9034 −0.876399
\(373\) −0.443592 −0.0229683 −0.0114842 0.999934i \(-0.503656\pi\)
−0.0114842 + 0.999934i \(0.503656\pi\)
\(374\) −6.18863 −0.320007
\(375\) −12.1536 −0.627610
\(376\) −13.4459 −0.693422
\(377\) −15.3594 −0.791048
\(378\) 9.26549 0.476566
\(379\) 13.7476 0.706165 0.353083 0.935592i \(-0.385133\pi\)
0.353083 + 0.935592i \(0.385133\pi\)
\(380\) 21.1524 1.08509
\(381\) −6.49424 −0.332710
\(382\) 49.0333 2.50876
\(383\) −32.9438 −1.68335 −0.841675 0.539985i \(-0.818430\pi\)
−0.841675 + 0.539985i \(0.818430\pi\)
\(384\) 12.7068 0.648439
\(385\) 22.5531 1.14941
\(386\) 9.88969 0.503372
\(387\) 2.93590 0.149240
\(388\) 21.5961 1.09637
\(389\) −7.31894 −0.371085 −0.185543 0.982636i \(-0.559404\pi\)
−0.185543 + 0.982636i \(0.559404\pi\)
\(390\) 14.2101 0.719559
\(391\) −7.09312 −0.358715
\(392\) −18.8244 −0.950777
\(393\) −16.2039 −0.817377
\(394\) 53.7959 2.71020
\(395\) 24.8953 1.25262
\(396\) −7.88289 −0.396130
\(397\) 9.70448 0.487054 0.243527 0.969894i \(-0.421696\pi\)
0.243527 + 0.969894i \(0.421696\pi\)
\(398\) 19.0263 0.953701
\(399\) −17.0723 −0.854682
\(400\) 2.62975 0.131487
\(401\) −14.1843 −0.708331 −0.354165 0.935183i \(-0.615235\pi\)
−0.354165 + 0.935183i \(0.615235\pi\)
\(402\) 10.2301 0.510230
\(403\) 20.9236 1.04228
\(404\) 44.8195 2.22985
\(405\) 1.88275 0.0935548
\(406\) 41.2537 2.04739
\(407\) −2.68186 −0.132935
\(408\) 1.72159 0.0852313
\(409\) −9.36389 −0.463014 −0.231507 0.972833i \(-0.574366\pi\)
−0.231507 + 0.972833i \(0.574366\pi\)
\(410\) 7.75431 0.382958
\(411\) 3.74290 0.184624
\(412\) −39.2925 −1.93580
\(413\) 5.63805 0.277430
\(414\) −15.5190 −0.762716
\(415\) 12.4146 0.609409
\(416\) −25.5169 −1.25107
\(417\) 7.95250 0.389436
\(418\) 24.9484 1.22027
\(419\) 14.3834 0.702675 0.351338 0.936249i \(-0.385727\pi\)
0.351338 + 0.936249i \(0.385727\pi\)
\(420\) −22.2205 −1.08425
\(421\) 30.7115 1.49678 0.748392 0.663256i \(-0.230826\pi\)
0.748392 + 0.663256i \(0.230826\pi\)
\(422\) −25.8693 −1.25930
\(423\) 7.81020 0.379745
\(424\) 5.45130 0.264738
\(425\) 1.45524 0.0705893
\(426\) −3.23547 −0.156759
\(427\) −9.11481 −0.441097
\(428\) −23.9739 −1.15882
\(429\) 9.75771 0.471106
\(430\) −12.0937 −0.583212
\(431\) −16.6451 −0.801765 −0.400883 0.916129i \(-0.631296\pi\)
−0.400883 + 0.916129i \(0.631296\pi\)
\(432\) −1.80709 −0.0869438
\(433\) 14.7178 0.707291 0.353646 0.935379i \(-0.384942\pi\)
0.353646 + 0.935379i \(0.384942\pi\)
\(434\) −56.1986 −2.69762
\(435\) 8.38278 0.401924
\(436\) 11.8449 0.567268
\(437\) 28.5947 1.36787
\(438\) −8.25624 −0.394498
\(439\) −12.2352 −0.583954 −0.291977 0.956425i \(-0.594313\pi\)
−0.291977 + 0.956425i \(0.594313\pi\)
\(440\) 9.16836 0.437085
\(441\) 10.9343 0.520683
\(442\) −7.54753 −0.358999
\(443\) −32.6376 −1.55066 −0.775330 0.631556i \(-0.782417\pi\)
−0.775330 + 0.631556i \(0.782417\pi\)
\(444\) 2.64231 0.125398
\(445\) −30.2797 −1.43539
\(446\) 38.1081 1.80447
\(447\) 19.5879 0.926477
\(448\) 53.2302 2.51489
\(449\) 13.4223 0.633435 0.316718 0.948520i \(-0.397419\pi\)
0.316718 + 0.948520i \(0.397419\pi\)
\(450\) 3.18390 0.150090
\(451\) 5.32466 0.250729
\(452\) 6.53432 0.307349
\(453\) 6.22240 0.292354
\(454\) −47.8330 −2.24491
\(455\) 27.5052 1.28947
\(456\) −6.94029 −0.325009
\(457\) −10.9402 −0.511760 −0.255880 0.966708i \(-0.582365\pi\)
−0.255880 + 0.966708i \(0.582365\pi\)
\(458\) 52.4898 2.45269
\(459\) −1.00000 −0.0466760
\(460\) 37.2176 1.73528
\(461\) −29.6276 −1.37989 −0.689946 0.723860i \(-0.742366\pi\)
−0.689946 + 0.723860i \(0.742366\pi\)
\(462\) −26.2082 −1.21932
\(463\) −0.622749 −0.0289416 −0.0144708 0.999895i \(-0.504606\pi\)
−0.0144708 + 0.999895i \(0.504606\pi\)
\(464\) −8.04591 −0.373522
\(465\) −11.4196 −0.529571
\(466\) 51.1495 2.36945
\(467\) −25.0738 −1.16028 −0.580138 0.814518i \(-0.697002\pi\)
−0.580138 + 0.814518i \(0.697002\pi\)
\(468\) −9.61381 −0.444399
\(469\) 19.8014 0.914344
\(470\) −32.1723 −1.48400
\(471\) 1.00000 0.0460776
\(472\) 2.29200 0.105498
\(473\) −8.30443 −0.381838
\(474\) −28.9300 −1.32880
\(475\) −5.86653 −0.269175
\(476\) 11.8021 0.540949
\(477\) −3.16643 −0.144981
\(478\) 45.9182 2.10025
\(479\) 41.7998 1.90988 0.954940 0.296798i \(-0.0959188\pi\)
0.954940 + 0.296798i \(0.0959188\pi\)
\(480\) 13.9265 0.635657
\(481\) −3.27073 −0.149133
\(482\) −26.0763 −1.18775
\(483\) −30.0386 −1.36681
\(484\) −8.35816 −0.379916
\(485\) 14.5899 0.662492
\(486\) −2.18789 −0.0992448
\(487\) 17.3991 0.788430 0.394215 0.919018i \(-0.371017\pi\)
0.394215 + 0.919018i \(0.371017\pi\)
\(488\) −3.70539 −0.167735
\(489\) −7.51333 −0.339764
\(490\) −45.0414 −2.03476
\(491\) 28.1789 1.27170 0.635849 0.771814i \(-0.280650\pi\)
0.635849 + 0.771814i \(0.280650\pi\)
\(492\) −5.24614 −0.236514
\(493\) −4.45240 −0.200526
\(494\) 30.4266 1.36896
\(495\) −5.32553 −0.239365
\(496\) 10.9607 0.492149
\(497\) −6.26260 −0.280916
\(498\) −14.4266 −0.646473
\(499\) 18.3741 0.822539 0.411269 0.911514i \(-0.365086\pi\)
0.411269 + 0.911514i \(0.365086\pi\)
\(500\) −33.8706 −1.51474
\(501\) 2.04948 0.0915640
\(502\) 48.1278 2.14805
\(503\) −23.5000 −1.04781 −0.523906 0.851776i \(-0.675526\pi\)
−0.523906 + 0.851776i \(0.675526\pi\)
\(504\) 7.29075 0.324756
\(505\) 30.2792 1.34741
\(506\) 43.8967 1.95145
\(507\) −1.09971 −0.0488396
\(508\) −18.0986 −0.802996
\(509\) −3.80681 −0.168734 −0.0843669 0.996435i \(-0.526887\pi\)
−0.0843669 + 0.996435i \(0.526887\pi\)
\(510\) 4.11926 0.182404
\(511\) −15.9808 −0.706950
\(512\) −19.5890 −0.865721
\(513\) 4.03133 0.177988
\(514\) −4.34126 −0.191485
\(515\) −26.5452 −1.16972
\(516\) 8.18197 0.360191
\(517\) −22.0918 −0.971596
\(518\) 8.78486 0.385985
\(519\) −23.5641 −1.03435
\(520\) 11.1815 0.490343
\(521\) −3.09103 −0.135420 −0.0677102 0.997705i \(-0.521569\pi\)
−0.0677102 + 0.997705i \(0.521569\pi\)
\(522\) −9.74138 −0.426369
\(523\) −21.7874 −0.952695 −0.476347 0.879257i \(-0.658040\pi\)
−0.476347 + 0.879257i \(0.658040\pi\)
\(524\) −45.1581 −1.97274
\(525\) 6.16277 0.268965
\(526\) 33.2418 1.44941
\(527\) 6.06536 0.264211
\(528\) 5.11151 0.222450
\(529\) 27.3124 1.18750
\(530\) 13.0434 0.566568
\(531\) −1.33133 −0.0577749
\(532\) −47.5782 −2.06278
\(533\) 6.49385 0.281280
\(534\) 35.1871 1.52269
\(535\) −16.1963 −0.700227
\(536\) 8.04975 0.347696
\(537\) 1.12270 0.0484480
\(538\) 24.4345 1.05345
\(539\) −30.9287 −1.33219
\(540\) 5.24699 0.225795
\(541\) 16.9903 0.730472 0.365236 0.930915i \(-0.380988\pi\)
0.365236 + 0.930915i \(0.380988\pi\)
\(542\) −64.1530 −2.75561
\(543\) −21.1199 −0.906341
\(544\) −7.39690 −0.317139
\(545\) 8.00219 0.342776
\(546\) −31.9630 −1.36789
\(547\) 1.92712 0.0823978 0.0411989 0.999151i \(-0.486882\pi\)
0.0411989 + 0.999151i \(0.486882\pi\)
\(548\) 10.4310 0.445590
\(549\) 2.15231 0.0918584
\(550\) −9.00592 −0.384014
\(551\) 17.9491 0.764658
\(552\) −12.2114 −0.519753
\(553\) −55.9971 −2.38124
\(554\) 21.4039 0.909363
\(555\) 1.78509 0.0757729
\(556\) 22.1626 0.939903
\(557\) −15.4813 −0.655964 −0.327982 0.944684i \(-0.606369\pi\)
−0.327982 + 0.944684i \(0.606369\pi\)
\(558\) 13.2704 0.561779
\(559\) −10.1279 −0.428365
\(560\) 14.4084 0.608868
\(561\) 2.82858 0.119423
\(562\) −40.7241 −1.71784
\(563\) 23.2434 0.979593 0.489797 0.871837i \(-0.337071\pi\)
0.489797 + 0.871837i \(0.337071\pi\)
\(564\) 21.7660 0.916515
\(565\) 4.41446 0.185718
\(566\) −2.99320 −0.125814
\(567\) −4.23490 −0.177849
\(568\) −2.54590 −0.106823
\(569\) −8.55499 −0.358644 −0.179322 0.983790i \(-0.557390\pi\)
−0.179322 + 0.983790i \(0.557390\pi\)
\(570\) −16.6061 −0.695553
\(571\) 16.8806 0.706433 0.353216 0.935542i \(-0.385088\pi\)
0.353216 + 0.935542i \(0.385088\pi\)
\(572\) 27.1935 1.13702
\(573\) −22.4112 −0.936242
\(574\) −17.4418 −0.728008
\(575\) −10.3222 −0.430464
\(576\) −12.5694 −0.523726
\(577\) −15.3905 −0.640713 −0.320357 0.947297i \(-0.603803\pi\)
−0.320357 + 0.947297i \(0.603803\pi\)
\(578\) −2.18789 −0.0910043
\(579\) −4.52019 −0.187853
\(580\) 23.3617 0.970043
\(581\) −27.9243 −1.15849
\(582\) −16.9544 −0.702785
\(583\) 8.95652 0.370941
\(584\) −6.49659 −0.268831
\(585\) −6.49490 −0.268531
\(586\) 0.349953 0.0144564
\(587\) 17.2247 0.710939 0.355470 0.934688i \(-0.384321\pi\)
0.355470 + 0.934688i \(0.384321\pi\)
\(588\) 30.4726 1.25667
\(589\) −24.4515 −1.00751
\(590\) 5.48411 0.225777
\(591\) −24.5880 −1.01142
\(592\) −1.71335 −0.0704184
\(593\) 17.8936 0.734804 0.367402 0.930062i \(-0.380247\pi\)
0.367402 + 0.930062i \(0.380247\pi\)
\(594\) 6.18863 0.253923
\(595\) 7.97327 0.326872
\(596\) 54.5890 2.23605
\(597\) −8.69617 −0.355910
\(598\) 53.5355 2.18923
\(599\) 27.5913 1.12735 0.563675 0.825997i \(-0.309387\pi\)
0.563675 + 0.825997i \(0.309387\pi\)
\(600\) 2.50532 0.102279
\(601\) 21.4736 0.875926 0.437963 0.898993i \(-0.355700\pi\)
0.437963 + 0.898993i \(0.355700\pi\)
\(602\) 27.2026 1.10869
\(603\) −4.67577 −0.190412
\(604\) 17.3410 0.705596
\(605\) −5.64661 −0.229567
\(606\) −35.1865 −1.42935
\(607\) 1.40781 0.0571412 0.0285706 0.999592i \(-0.490904\pi\)
0.0285706 + 0.999592i \(0.490904\pi\)
\(608\) 29.8193 1.20933
\(609\) −18.8555 −0.764062
\(610\) −8.86594 −0.358971
\(611\) −26.9427 −1.08998
\(612\) −2.78687 −0.112653
\(613\) −9.77917 −0.394977 −0.197488 0.980305i \(-0.563278\pi\)
−0.197488 + 0.980305i \(0.563278\pi\)
\(614\) 4.92744 0.198855
\(615\) −3.54419 −0.142916
\(616\) −20.6225 −0.830903
\(617\) 4.27814 0.172231 0.0861157 0.996285i \(-0.472555\pi\)
0.0861157 + 0.996285i \(0.472555\pi\)
\(618\) 30.8474 1.24086
\(619\) 24.4177 0.981428 0.490714 0.871321i \(-0.336736\pi\)
0.490714 + 0.871321i \(0.336736\pi\)
\(620\) −31.8249 −1.27812
\(621\) 7.09312 0.284637
\(622\) 37.0785 1.48671
\(623\) 68.1083 2.72870
\(624\) 6.23389 0.249556
\(625\) −15.6061 −0.624245
\(626\) −14.8246 −0.592511
\(627\) −11.4029 −0.455390
\(628\) 2.78687 0.111208
\(629\) −0.948127 −0.0378043
\(630\) 17.4447 0.695012
\(631\) 6.96315 0.277199 0.138599 0.990349i \(-0.455740\pi\)
0.138599 + 0.990349i \(0.455740\pi\)
\(632\) −22.7642 −0.905510
\(633\) 11.8238 0.469955
\(634\) −1.90015 −0.0754645
\(635\) −12.2271 −0.485216
\(636\) −8.82444 −0.349912
\(637\) −37.7200 −1.49452
\(638\) 27.5543 1.09089
\(639\) 1.47881 0.0585007
\(640\) 23.9237 0.945667
\(641\) 41.3401 1.63284 0.816418 0.577461i \(-0.195957\pi\)
0.816418 + 0.577461i \(0.195957\pi\)
\(642\) 18.8212 0.742814
\(643\) −25.3084 −0.998064 −0.499032 0.866583i \(-0.666311\pi\)
−0.499032 + 0.866583i \(0.666311\pi\)
\(644\) −83.7138 −3.29879
\(645\) 5.52758 0.217648
\(646\) 8.82011 0.347023
\(647\) 11.1879 0.439841 0.219920 0.975518i \(-0.429420\pi\)
0.219920 + 0.975518i \(0.429420\pi\)
\(648\) −1.72159 −0.0676304
\(649\) 3.76578 0.147820
\(650\) −10.9834 −0.430805
\(651\) 25.6862 1.00672
\(652\) −20.9387 −0.820022
\(653\) −10.4168 −0.407639 −0.203820 0.979008i \(-0.565336\pi\)
−0.203820 + 0.979008i \(0.565336\pi\)
\(654\) −9.29910 −0.363624
\(655\) −30.5079 −1.19204
\(656\) 3.40176 0.132817
\(657\) 3.77361 0.147222
\(658\) 72.3654 2.82110
\(659\) −23.2041 −0.903902 −0.451951 0.892043i \(-0.649272\pi\)
−0.451951 + 0.892043i \(0.649272\pi\)
\(660\) −14.8416 −0.577707
\(661\) 15.3483 0.596981 0.298490 0.954413i \(-0.403517\pi\)
0.298490 + 0.954413i \(0.403517\pi\)
\(662\) −10.2521 −0.398461
\(663\) 3.44968 0.133974
\(664\) −11.3519 −0.440539
\(665\) −32.1429 −1.24645
\(666\) −2.07440 −0.0803813
\(667\) 31.5814 1.22284
\(668\) 5.71164 0.220990
\(669\) −17.4177 −0.673409
\(670\) 19.2607 0.744107
\(671\) −6.08799 −0.235024
\(672\) −31.3251 −1.20839
\(673\) −10.3906 −0.400527 −0.200263 0.979742i \(-0.564180\pi\)
−0.200263 + 0.979742i \(0.564180\pi\)
\(674\) 64.1773 2.47202
\(675\) −1.45524 −0.0560120
\(676\) −3.06474 −0.117875
\(677\) −36.5723 −1.40559 −0.702794 0.711394i \(-0.748064\pi\)
−0.702794 + 0.711394i \(0.748064\pi\)
\(678\) −5.12991 −0.197013
\(679\) −32.8171 −1.25941
\(680\) 3.24133 0.124299
\(681\) 21.8626 0.837776
\(682\) −37.5363 −1.43734
\(683\) 3.65663 0.139917 0.0699585 0.997550i \(-0.477713\pi\)
0.0699585 + 0.997550i \(0.477713\pi\)
\(684\) 11.2348 0.429573
\(685\) 7.04697 0.269251
\(686\) 36.4536 1.39181
\(687\) −23.9910 −0.915315
\(688\) −5.30544 −0.202268
\(689\) 10.9232 0.416140
\(690\) −29.2184 −1.11233
\(691\) 25.6964 0.977536 0.488768 0.872414i \(-0.337446\pi\)
0.488768 + 0.872414i \(0.337446\pi\)
\(692\) −65.6701 −2.49640
\(693\) 11.9788 0.455035
\(694\) 58.1880 2.20879
\(695\) 14.9726 0.567943
\(696\) −7.66520 −0.290549
\(697\) 1.88245 0.0713029
\(698\) 12.3559 0.467676
\(699\) −23.3784 −0.884254
\(700\) 17.1748 0.649148
\(701\) 44.1837 1.66879 0.834397 0.551164i \(-0.185816\pi\)
0.834397 + 0.551164i \(0.185816\pi\)
\(702\) 7.54753 0.284863
\(703\) 3.82221 0.144157
\(704\) 35.5537 1.33998
\(705\) 14.7047 0.553811
\(706\) −38.7027 −1.45659
\(707\) −68.1072 −2.56144
\(708\) −3.71025 −0.139440
\(709\) −37.1353 −1.39465 −0.697323 0.716757i \(-0.745626\pi\)
−0.697323 + 0.716757i \(0.745626\pi\)
\(710\) −6.09160 −0.228614
\(711\) 13.2228 0.495893
\(712\) 27.6877 1.03764
\(713\) −43.0224 −1.61120
\(714\) −9.26549 −0.346752
\(715\) 18.3714 0.687050
\(716\) 3.12881 0.116929
\(717\) −20.9874 −0.783789
\(718\) −35.7127 −1.33279
\(719\) 10.7049 0.399227 0.199613 0.979875i \(-0.436031\pi\)
0.199613 + 0.979875i \(0.436031\pi\)
\(720\) −3.40231 −0.126797
\(721\) 59.7084 2.22366
\(722\) 6.01316 0.223787
\(723\) 11.9185 0.443253
\(724\) −58.8584 −2.18745
\(725\) −6.47929 −0.240635
\(726\) 6.56175 0.243529
\(727\) −27.7585 −1.02950 −0.514752 0.857339i \(-0.672116\pi\)
−0.514752 + 0.857339i \(0.672116\pi\)
\(728\) −25.1507 −0.932148
\(729\) 1.00000 0.0370370
\(730\) −15.5445 −0.575327
\(731\) −2.93590 −0.108588
\(732\) 5.99821 0.221700
\(733\) −20.8522 −0.770193 −0.385097 0.922876i \(-0.625832\pi\)
−0.385097 + 0.922876i \(0.625832\pi\)
\(734\) 10.7696 0.397512
\(735\) 20.5867 0.759351
\(736\) 52.4671 1.93396
\(737\) 13.2258 0.487179
\(738\) 4.11860 0.151608
\(739\) 3.23412 0.118969 0.0594846 0.998229i \(-0.481054\pi\)
0.0594846 + 0.998229i \(0.481054\pi\)
\(740\) 4.97482 0.182878
\(741\) −13.9068 −0.510879
\(742\) −29.3386 −1.07705
\(743\) 30.4522 1.11718 0.558591 0.829444i \(-0.311342\pi\)
0.558591 + 0.829444i \(0.311342\pi\)
\(744\) 10.4421 0.382824
\(745\) 36.8793 1.35115
\(746\) 0.970532 0.0355337
\(747\) 6.59385 0.241256
\(748\) 7.88289 0.288227
\(749\) 36.4305 1.33114
\(750\) 26.5908 0.970959
\(751\) 10.2312 0.373341 0.186671 0.982423i \(-0.440230\pi\)
0.186671 + 0.982423i \(0.440230\pi\)
\(752\) −14.1138 −0.514676
\(753\) −21.9973 −0.801628
\(754\) 33.6046 1.22381
\(755\) 11.7153 0.426362
\(756\) −11.8021 −0.429238
\(757\) −33.3454 −1.21196 −0.605979 0.795481i \(-0.707219\pi\)
−0.605979 + 0.795481i \(0.707219\pi\)
\(758\) −30.0782 −1.09249
\(759\) −20.0635 −0.728258
\(760\) −13.0669 −0.473985
\(761\) −30.9441 −1.12172 −0.560862 0.827909i \(-0.689530\pi\)
−0.560862 + 0.827909i \(0.689530\pi\)
\(762\) 14.2087 0.514727
\(763\) −17.9994 −0.651622
\(764\) −62.4572 −2.25962
\(765\) −1.88275 −0.0680711
\(766\) 72.0775 2.60426
\(767\) 4.59267 0.165832
\(768\) −2.66214 −0.0960618
\(769\) −3.45199 −0.124482 −0.0622410 0.998061i \(-0.519825\pi\)
−0.0622410 + 0.998061i \(0.519825\pi\)
\(770\) −49.3436 −1.77822
\(771\) 1.98422 0.0714599
\(772\) −12.5972 −0.453383
\(773\) −28.3895 −1.02110 −0.510549 0.859849i \(-0.670558\pi\)
−0.510549 + 0.859849i \(0.670558\pi\)
\(774\) −6.42343 −0.230885
\(775\) 8.82653 0.317058
\(776\) −13.3410 −0.478912
\(777\) −4.01522 −0.144045
\(778\) 16.0131 0.574096
\(779\) −7.58878 −0.271896
\(780\) −18.1005 −0.648100
\(781\) −4.18293 −0.149677
\(782\) 15.5190 0.554958
\(783\) 4.45240 0.159116
\(784\) −19.7594 −0.705692
\(785\) 1.88275 0.0671984
\(786\) 35.4523 1.26454
\(787\) −0.202310 −0.00721158 −0.00360579 0.999993i \(-0.501148\pi\)
−0.00360579 + 0.999993i \(0.501148\pi\)
\(788\) −68.5236 −2.44105
\(789\) −15.1935 −0.540905
\(790\) −54.4681 −1.93789
\(791\) −9.92948 −0.353052
\(792\) 4.86965 0.173036
\(793\) −7.42479 −0.263662
\(794\) −21.2324 −0.753508
\(795\) −5.96162 −0.211437
\(796\) −24.2351 −0.858990
\(797\) −27.3207 −0.967750 −0.483875 0.875137i \(-0.660771\pi\)
−0.483875 + 0.875137i \(0.660771\pi\)
\(798\) 37.3523 1.32226
\(799\) −7.81020 −0.276305
\(800\) −10.7642 −0.380573
\(801\) −16.0826 −0.568252
\(802\) 31.0337 1.09584
\(803\) −10.6740 −0.376676
\(804\) −13.0308 −0.459560
\(805\) −56.5554 −1.99332
\(806\) −45.7785 −1.61248
\(807\) −11.1681 −0.393135
\(808\) −27.6872 −0.974033
\(809\) −23.9304 −0.841347 −0.420674 0.907212i \(-0.638206\pi\)
−0.420674 + 0.907212i \(0.638206\pi\)
\(810\) −4.11926 −0.144736
\(811\) 7.40361 0.259976 0.129988 0.991516i \(-0.458506\pi\)
0.129988 + 0.991516i \(0.458506\pi\)
\(812\) −52.5477 −1.84406
\(813\) 29.3218 1.02836
\(814\) 5.86761 0.205660
\(815\) −14.1458 −0.495504
\(816\) 1.80709 0.0632609
\(817\) 11.8356 0.414074
\(818\) 20.4872 0.716317
\(819\) 14.6090 0.510481
\(820\) −9.87720 −0.344927
\(821\) −16.6659 −0.581644 −0.290822 0.956777i \(-0.593929\pi\)
−0.290822 + 0.956777i \(0.593929\pi\)
\(822\) −8.18906 −0.285626
\(823\) −0.0710389 −0.00247626 −0.00123813 0.999999i \(-0.500394\pi\)
−0.00123813 + 0.999999i \(0.500394\pi\)
\(824\) 24.2729 0.845587
\(825\) 4.11625 0.143310
\(826\) −12.3354 −0.429205
\(827\) 15.7587 0.547984 0.273992 0.961732i \(-0.411656\pi\)
0.273992 + 0.961732i \(0.411656\pi\)
\(828\) 19.7676 0.686972
\(829\) 24.7596 0.859938 0.429969 0.902844i \(-0.358525\pi\)
0.429969 + 0.902844i \(0.358525\pi\)
\(830\) −27.1618 −0.942800
\(831\) −9.78287 −0.339364
\(832\) 43.3605 1.50326
\(833\) −10.9343 −0.378853
\(834\) −17.3992 −0.602485
\(835\) 3.85867 0.133535
\(836\) −31.7785 −1.09908
\(837\) −6.06536 −0.209650
\(838\) −31.4693 −1.08709
\(839\) −52.0084 −1.79553 −0.897764 0.440477i \(-0.854809\pi\)
−0.897764 + 0.440477i \(0.854809\pi\)
\(840\) 13.7267 0.473616
\(841\) −9.17610 −0.316417
\(842\) −67.1933 −2.31564
\(843\) 18.6134 0.641079
\(844\) 32.9515 1.13424
\(845\) −2.07048 −0.0712265
\(846\) −17.0879 −0.587493
\(847\) 12.7010 0.436410
\(848\) 5.72204 0.196496
\(849\) 1.36808 0.0469522
\(850\) −3.18390 −0.109207
\(851\) 6.72518 0.230536
\(852\) 4.12125 0.141192
\(853\) 31.2454 1.06982 0.534910 0.844909i \(-0.320345\pi\)
0.534910 + 0.844909i \(0.320345\pi\)
\(854\) 19.9422 0.682409
\(855\) 7.59000 0.259573
\(856\) 14.8099 0.506191
\(857\) −0.229233 −0.00783046 −0.00391523 0.999992i \(-0.501246\pi\)
−0.00391523 + 0.999992i \(0.501246\pi\)
\(858\) −21.3488 −0.728836
\(859\) 31.4090 1.07166 0.535831 0.844326i \(-0.319999\pi\)
0.535831 + 0.844326i \(0.319999\pi\)
\(860\) 15.4046 0.525294
\(861\) 7.97198 0.271684
\(862\) 36.4176 1.24039
\(863\) 8.20297 0.279232 0.139616 0.990206i \(-0.455413\pi\)
0.139616 + 0.990206i \(0.455413\pi\)
\(864\) 7.39690 0.251648
\(865\) −44.3654 −1.50847
\(866\) −32.2009 −1.09423
\(867\) 1.00000 0.0339618
\(868\) 71.5841 2.42972
\(869\) −37.4017 −1.26877
\(870\) −18.3406 −0.621805
\(871\) 16.1299 0.546542
\(872\) −7.31719 −0.247791
\(873\) 7.74922 0.262271
\(874\) −62.5621 −2.11620
\(875\) 51.4693 1.73998
\(876\) 10.5165 0.355321
\(877\) 23.1390 0.781349 0.390675 0.920529i \(-0.372242\pi\)
0.390675 + 0.920529i \(0.372242\pi\)
\(878\) 26.7693 0.903419
\(879\) −0.159950 −0.00539498
\(880\) 9.62372 0.324416
\(881\) −33.7002 −1.13539 −0.567694 0.823239i \(-0.692164\pi\)
−0.567694 + 0.823239i \(0.692164\pi\)
\(882\) −23.9232 −0.805535
\(883\) −41.1042 −1.38327 −0.691633 0.722249i \(-0.743108\pi\)
−0.691633 + 0.722249i \(0.743108\pi\)
\(884\) 9.61381 0.323348
\(885\) −2.50657 −0.0842575
\(886\) 71.4076 2.39899
\(887\) 26.1015 0.876402 0.438201 0.898877i \(-0.355616\pi\)
0.438201 + 0.898877i \(0.355616\pi\)
\(888\) −1.63228 −0.0547759
\(889\) 27.5024 0.922402
\(890\) 66.2487 2.22066
\(891\) −2.82858 −0.0947611
\(892\) −48.5410 −1.62527
\(893\) 31.4855 1.05362
\(894\) −42.8563 −1.43333
\(895\) 2.11376 0.0706554
\(896\) −53.8118 −1.79773
\(897\) −24.4690 −0.816996
\(898\) −29.3664 −0.979971
\(899\) −27.0054 −0.900682
\(900\) −4.05555 −0.135185
\(901\) 3.16643 0.105489
\(902\) −11.6498 −0.387896
\(903\) −12.4332 −0.413752
\(904\) −4.03657 −0.134254
\(905\) −39.7635 −1.32178
\(906\) −13.6139 −0.452293
\(907\) −39.5256 −1.31242 −0.656212 0.754576i \(-0.727842\pi\)
−0.656212 + 0.754576i \(0.727842\pi\)
\(908\) 60.9282 2.02197
\(909\) 16.0824 0.533419
\(910\) −60.1785 −1.99490
\(911\) 23.3071 0.772199 0.386100 0.922457i \(-0.373822\pi\)
0.386100 + 0.922457i \(0.373822\pi\)
\(912\) −7.28499 −0.241230
\(913\) −18.6512 −0.617266
\(914\) 23.9360 0.791731
\(915\) 4.05227 0.133964
\(916\) −66.8599 −2.20911
\(917\) 68.6217 2.26609
\(918\) 2.18789 0.0722112
\(919\) −20.9166 −0.689975 −0.344988 0.938607i \(-0.612117\pi\)
−0.344988 + 0.938607i \(0.612117\pi\)
\(920\) −22.9911 −0.757995
\(921\) −2.25214 −0.0742105
\(922\) 64.8219 2.13480
\(923\) −5.10141 −0.167915
\(924\) 33.3832 1.09823
\(925\) −1.37975 −0.0453658
\(926\) 1.36251 0.0447747
\(927\) −14.0991 −0.463077
\(928\) 32.9340 1.08111
\(929\) −30.3691 −0.996376 −0.498188 0.867069i \(-0.666001\pi\)
−0.498188 + 0.867069i \(0.666001\pi\)
\(930\) 24.9848 0.819285
\(931\) 44.0799 1.44466
\(932\) −65.1527 −2.13415
\(933\) −16.9471 −0.554824
\(934\) 54.8588 1.79503
\(935\) 5.32553 0.174163
\(936\) 5.93893 0.194120
\(937\) 29.9322 0.977841 0.488920 0.872328i \(-0.337391\pi\)
0.488920 + 0.872328i \(0.337391\pi\)
\(938\) −43.3233 −1.41456
\(939\) 6.77575 0.221118
\(940\) 40.9801 1.33662
\(941\) −6.32722 −0.206262 −0.103131 0.994668i \(-0.532886\pi\)
−0.103131 + 0.994668i \(0.532886\pi\)
\(942\) −2.18789 −0.0712854
\(943\) −13.3524 −0.434815
\(944\) 2.40584 0.0783035
\(945\) −7.97327 −0.259370
\(946\) 18.1692 0.590732
\(947\) −54.3355 −1.76567 −0.882833 0.469686i \(-0.844367\pi\)
−0.882833 + 0.469686i \(0.844367\pi\)
\(948\) 36.8502 1.19684
\(949\) −13.0177 −0.422573
\(950\) 12.8353 0.416433
\(951\) 0.868483 0.0281625
\(952\) −7.29075 −0.236294
\(953\) −30.2246 −0.979072 −0.489536 0.871983i \(-0.662834\pi\)
−0.489536 + 0.871983i \(0.662834\pi\)
\(954\) 6.92782 0.224296
\(955\) −42.1948 −1.36539
\(956\) −58.4892 −1.89168
\(957\) −12.5940 −0.407106
\(958\) −91.4534 −2.95472
\(959\) −15.8508 −0.511849
\(960\) −23.6652 −0.763790
\(961\) 5.78862 0.186730
\(962\) 7.15601 0.230719
\(963\) −8.60245 −0.277210
\(964\) 33.2153 1.06979
\(965\) −8.51041 −0.273960
\(966\) 65.7213 2.11455
\(967\) 31.8242 1.02340 0.511699 0.859165i \(-0.329016\pi\)
0.511699 + 0.859165i \(0.329016\pi\)
\(968\) 5.16325 0.165953
\(969\) −4.03133 −0.129505
\(970\) −31.9211 −1.02492
\(971\) −22.4909 −0.721769 −0.360884 0.932611i \(-0.617525\pi\)
−0.360884 + 0.932611i \(0.617525\pi\)
\(972\) 2.78687 0.0893889
\(973\) −33.6780 −1.07967
\(974\) −38.0674 −1.21976
\(975\) 5.02010 0.160772
\(976\) −3.88943 −0.124498
\(977\) −39.7919 −1.27306 −0.636528 0.771254i \(-0.719630\pi\)
−0.636528 + 0.771254i \(0.719630\pi\)
\(978\) 16.4383 0.525640
\(979\) 45.4911 1.45390
\(980\) 57.3724 1.83269
\(981\) 4.25026 0.135700
\(982\) −61.6524 −1.96741
\(983\) 38.3590 1.22346 0.611730 0.791066i \(-0.290474\pi\)
0.611730 + 0.791066i \(0.290474\pi\)
\(984\) 3.24080 0.103313
\(985\) −46.2932 −1.47502
\(986\) 9.74138 0.310229
\(987\) −33.0754 −1.05280
\(988\) −38.7564 −1.23301
\(989\) 20.8247 0.662187
\(990\) 11.6517 0.370315
\(991\) −48.6123 −1.54422 −0.772111 0.635488i \(-0.780799\pi\)
−0.772111 + 0.635488i \(0.780799\pi\)
\(992\) −44.8649 −1.42446
\(993\) 4.68586 0.148701
\(994\) 13.7019 0.434597
\(995\) −16.3727 −0.519051
\(996\) 18.3762 0.582272
\(997\) 34.2859 1.08585 0.542923 0.839783i \(-0.317318\pi\)
0.542923 + 0.839783i \(0.317318\pi\)
\(998\) −40.2006 −1.27253
\(999\) 0.948127 0.0299974
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 \(a_p\))