Properties

Label 8007.2.a.e.1.13
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 1.13
Character \(\chi\) = 8007.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.50188 q^{2}\) \(+1.00000 q^{3}\) \(+0.255640 q^{4}\) \(-0.915140 q^{5}\) \(-1.50188 q^{6}\) \(-3.11181 q^{7}\) \(+2.61982 q^{8}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.50188 q^{2}\) \(+1.00000 q^{3}\) \(+0.255640 q^{4}\) \(-0.915140 q^{5}\) \(-1.50188 q^{6}\) \(-3.11181 q^{7}\) \(+2.61982 q^{8}\) \(+1.00000 q^{9}\) \(+1.37443 q^{10}\) \(+1.83124 q^{11}\) \(+0.255640 q^{12}\) \(-4.69886 q^{13}\) \(+4.67357 q^{14}\) \(-0.915140 q^{15}\) \(-4.44593 q^{16}\) \(-1.00000 q^{17}\) \(-1.50188 q^{18}\) \(+4.81296 q^{19}\) \(-0.233947 q^{20}\) \(-3.11181 q^{21}\) \(-2.75030 q^{22}\) \(-2.49596 q^{23}\) \(+2.61982 q^{24}\) \(-4.16252 q^{25}\) \(+7.05712 q^{26}\) \(+1.00000 q^{27}\) \(-0.795505 q^{28}\) \(+4.17081 q^{29}\) \(+1.37443 q^{30}\) \(+7.38733 q^{31}\) \(+1.43761 q^{32}\) \(+1.83124 q^{33}\) \(+1.50188 q^{34}\) \(+2.84775 q^{35}\) \(+0.255640 q^{36}\) \(-5.82140 q^{37}\) \(-7.22848 q^{38}\) \(-4.69886 q^{39}\) \(-2.39750 q^{40}\) \(+3.73781 q^{41}\) \(+4.67357 q^{42}\) \(-3.88336 q^{43}\) \(+0.468138 q^{44}\) \(-0.915140 q^{45}\) \(+3.74863 q^{46}\) \(+3.13382 q^{47}\) \(-4.44593 q^{48}\) \(+2.68339 q^{49}\) \(+6.25160 q^{50}\) \(-1.00000 q^{51}\) \(-1.20122 q^{52}\) \(+12.4806 q^{53}\) \(-1.50188 q^{54}\) \(-1.67584 q^{55}\) \(-8.15239 q^{56}\) \(+4.81296 q^{57}\) \(-6.26405 q^{58}\) \(+3.86590 q^{59}\) \(-0.233947 q^{60}\) \(+4.04555 q^{61}\) \(-11.0949 q^{62}\) \(-3.11181 q^{63}\) \(+6.73274 q^{64}\) \(+4.30011 q^{65}\) \(-2.75030 q^{66}\) \(-10.2633 q^{67}\) \(-0.255640 q^{68}\) \(-2.49596 q^{69}\) \(-4.27697 q^{70}\) \(+4.17445 q^{71}\) \(+2.61982 q^{72}\) \(+3.90172 q^{73}\) \(+8.74304 q^{74}\) \(-4.16252 q^{75}\) \(+1.23039 q^{76}\) \(-5.69847 q^{77}\) \(+7.05712 q^{78}\) \(-1.84040 q^{79}\) \(+4.06865 q^{80}\) \(+1.00000 q^{81}\) \(-5.61374 q^{82}\) \(-2.87241 q^{83}\) \(-0.795505 q^{84}\) \(+0.915140 q^{85}\) \(+5.83233 q^{86}\) \(+4.17081 q^{87}\) \(+4.79751 q^{88}\) \(-10.5142 q^{89}\) \(+1.37443 q^{90}\) \(+14.6220 q^{91}\) \(-0.638067 q^{92}\) \(+7.38733 q^{93}\) \(-4.70661 q^{94}\) \(-4.40453 q^{95}\) \(+1.43761 q^{96}\) \(+5.66576 q^{97}\) \(-4.03013 q^{98}\) \(+1.83124 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(46q \) \(\mathstrut -\mathstrut 5q^{2} \) \(\mathstrut +\mathstrut 46q^{3} \) \(\mathstrut +\mathstrut 43q^{4} \) \(\mathstrut -\mathstrut 19q^{5} \) \(\mathstrut -\mathstrut 5q^{6} \) \(\mathstrut +\mathstrut q^{7} \) \(\mathstrut -\mathstrut 18q^{8} \) \(\mathstrut +\mathstrut 46q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(46q \) \(\mathstrut -\mathstrut 5q^{2} \) \(\mathstrut +\mathstrut 46q^{3} \) \(\mathstrut +\mathstrut 43q^{4} \) \(\mathstrut -\mathstrut 19q^{5} \) \(\mathstrut -\mathstrut 5q^{6} \) \(\mathstrut +\mathstrut q^{7} \) \(\mathstrut -\mathstrut 18q^{8} \) \(\mathstrut +\mathstrut 46q^{9} \) \(\mathstrut -\mathstrut 10q^{10} \) \(\mathstrut -\mathstrut 25q^{11} \) \(\mathstrut +\mathstrut 43q^{12} \) \(\mathstrut -\mathstrut 8q^{13} \) \(\mathstrut -\mathstrut 28q^{14} \) \(\mathstrut -\mathstrut 19q^{15} \) \(\mathstrut +\mathstrut 33q^{16} \) \(\mathstrut -\mathstrut 46q^{17} \) \(\mathstrut -\mathstrut 5q^{18} \) \(\mathstrut -\mathstrut 2q^{19} \) \(\mathstrut -\mathstrut 56q^{20} \) \(\mathstrut +\mathstrut q^{21} \) \(\mathstrut -\mathstrut 19q^{22} \) \(\mathstrut -\mathstrut 64q^{23} \) \(\mathstrut -\mathstrut 18q^{24} \) \(\mathstrut +\mathstrut 11q^{25} \) \(\mathstrut -\mathstrut 13q^{26} \) \(\mathstrut +\mathstrut 46q^{27} \) \(\mathstrut -\mathstrut 38q^{28} \) \(\mathstrut -\mathstrut 51q^{29} \) \(\mathstrut -\mathstrut 10q^{30} \) \(\mathstrut -\mathstrut 19q^{31} \) \(\mathstrut -\mathstrut 61q^{32} \) \(\mathstrut -\mathstrut 25q^{33} \) \(\mathstrut +\mathstrut 5q^{34} \) \(\mathstrut -\mathstrut 39q^{35} \) \(\mathstrut +\mathstrut 43q^{36} \) \(\mathstrut -\mathstrut 46q^{37} \) \(\mathstrut -\mathstrut 48q^{38} \) \(\mathstrut -\mathstrut 8q^{39} \) \(\mathstrut -\mathstrut 10q^{40} \) \(\mathstrut -\mathstrut 53q^{41} \) \(\mathstrut -\mathstrut 28q^{42} \) \(\mathstrut -\mathstrut 33q^{43} \) \(\mathstrut -\mathstrut 62q^{44} \) \(\mathstrut -\mathstrut 19q^{45} \) \(\mathstrut +\mathstrut 2q^{46} \) \(\mathstrut -\mathstrut 45q^{47} \) \(\mathstrut +\mathstrut 33q^{48} \) \(\mathstrut +\mathstrut 21q^{49} \) \(\mathstrut -\mathstrut 60q^{50} \) \(\mathstrut -\mathstrut 46q^{51} \) \(\mathstrut -\mathstrut 63q^{52} \) \(\mathstrut -\mathstrut 47q^{53} \) \(\mathstrut -\mathstrut 5q^{54} \) \(\mathstrut +\mathstrut 5q^{55} \) \(\mathstrut -\mathstrut 82q^{56} \) \(\mathstrut -\mathstrut 2q^{57} \) \(\mathstrut -\mathstrut 21q^{58} \) \(\mathstrut -\mathstrut 65q^{59} \) \(\mathstrut -\mathstrut 56q^{60} \) \(\mathstrut -\mathstrut 37q^{61} \) \(\mathstrut -\mathstrut 46q^{62} \) \(\mathstrut +\mathstrut q^{63} \) \(\mathstrut +\mathstrut 74q^{64} \) \(\mathstrut -\mathstrut 85q^{65} \) \(\mathstrut -\mathstrut 19q^{66} \) \(\mathstrut -\mathstrut 52q^{67} \) \(\mathstrut -\mathstrut 43q^{68} \) \(\mathstrut -\mathstrut 64q^{69} \) \(\mathstrut -\mathstrut 20q^{70} \) \(\mathstrut -\mathstrut 48q^{71} \) \(\mathstrut -\mathstrut 18q^{72} \) \(\mathstrut -\mathstrut 39q^{73} \) \(\mathstrut -\mathstrut 16q^{74} \) \(\mathstrut +\mathstrut 11q^{75} \) \(\mathstrut +\mathstrut 42q^{76} \) \(\mathstrut -\mathstrut 78q^{77} \) \(\mathstrut -\mathstrut 13q^{78} \) \(\mathstrut -\mathstrut 26q^{79} \) \(\mathstrut -\mathstrut 78q^{80} \) \(\mathstrut +\mathstrut 46q^{81} \) \(\mathstrut +\mathstrut 3q^{82} \) \(\mathstrut -\mathstrut 47q^{83} \) \(\mathstrut -\mathstrut 38q^{84} \) \(\mathstrut +\mathstrut 19q^{85} \) \(\mathstrut -\mathstrut 6q^{86} \) \(\mathstrut -\mathstrut 51q^{87} \) \(\mathstrut -\mathstrut 58q^{88} \) \(\mathstrut -\mathstrut 58q^{89} \) \(\mathstrut -\mathstrut 10q^{90} \) \(\mathstrut -\mathstrut 43q^{91} \) \(\mathstrut -\mathstrut 68q^{92} \) \(\mathstrut -\mathstrut 19q^{93} \) \(\mathstrut -\mathstrut 78q^{95} \) \(\mathstrut -\mathstrut 61q^{96} \) \(\mathstrut -\mathstrut 44q^{97} \) \(\mathstrut -\mathstrut 4q^{98} \) \(\mathstrut -\mathstrut 25q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.50188 −1.06199 −0.530994 0.847375i \(-0.678181\pi\)
−0.530994 + 0.847375i \(0.678181\pi\)
\(3\) 1.00000 0.577350
\(4\) 0.255640 0.127820
\(5\) −0.915140 −0.409263 −0.204632 0.978839i \(-0.565600\pi\)
−0.204632 + 0.978839i \(0.565600\pi\)
\(6\) −1.50188 −0.613139
\(7\) −3.11181 −1.17616 −0.588078 0.808804i \(-0.700115\pi\)
−0.588078 + 0.808804i \(0.700115\pi\)
\(8\) 2.61982 0.926245
\(9\) 1.00000 0.333333
\(10\) 1.37443 0.434633
\(11\) 1.83124 0.552139 0.276069 0.961138i \(-0.410968\pi\)
0.276069 + 0.961138i \(0.410968\pi\)
\(12\) 0.255640 0.0737970
\(13\) −4.69886 −1.30323 −0.651614 0.758550i \(-0.725908\pi\)
−0.651614 + 0.758550i \(0.725908\pi\)
\(14\) 4.67357 1.24906
\(15\) −0.915140 −0.236288
\(16\) −4.44593 −1.11148
\(17\) −1.00000 −0.242536
\(18\) −1.50188 −0.353996
\(19\) 4.81296 1.10417 0.552084 0.833789i \(-0.313833\pi\)
0.552084 + 0.833789i \(0.313833\pi\)
\(20\) −0.233947 −0.0523120
\(21\) −3.11181 −0.679054
\(22\) −2.75030 −0.586365
\(23\) −2.49596 −0.520443 −0.260222 0.965549i \(-0.583796\pi\)
−0.260222 + 0.965549i \(0.583796\pi\)
\(24\) 2.61982 0.534768
\(25\) −4.16252 −0.832504
\(26\) 7.05712 1.38401
\(27\) 1.00000 0.192450
\(28\) −0.795505 −0.150336
\(29\) 4.17081 0.774500 0.387250 0.921975i \(-0.373425\pi\)
0.387250 + 0.921975i \(0.373425\pi\)
\(30\) 1.37443 0.250935
\(31\) 7.38733 1.32680 0.663402 0.748264i \(-0.269112\pi\)
0.663402 + 0.748264i \(0.269112\pi\)
\(32\) 1.43761 0.254136
\(33\) 1.83124 0.318777
\(34\) 1.50188 0.257570
\(35\) 2.84775 0.481357
\(36\) 0.255640 0.0426067
\(37\) −5.82140 −0.957032 −0.478516 0.878079i \(-0.658825\pi\)
−0.478516 + 0.878079i \(0.658825\pi\)
\(38\) −7.22848 −1.17261
\(39\) −4.69886 −0.752420
\(40\) −2.39750 −0.379078
\(41\) 3.73781 0.583748 0.291874 0.956457i \(-0.405721\pi\)
0.291874 + 0.956457i \(0.405721\pi\)
\(42\) 4.67357 0.721147
\(43\) −3.88336 −0.592206 −0.296103 0.955156i \(-0.595687\pi\)
−0.296103 + 0.955156i \(0.595687\pi\)
\(44\) 0.468138 0.0705744
\(45\) −0.915140 −0.136421
\(46\) 3.74863 0.552705
\(47\) 3.13382 0.457114 0.228557 0.973530i \(-0.426599\pi\)
0.228557 + 0.973530i \(0.426599\pi\)
\(48\) −4.44593 −0.641715
\(49\) 2.68339 0.383342
\(50\) 6.25160 0.884110
\(51\) −1.00000 −0.140028
\(52\) −1.20122 −0.166579
\(53\) 12.4806 1.71434 0.857172 0.515030i \(-0.172219\pi\)
0.857172 + 0.515030i \(0.172219\pi\)
\(54\) −1.50188 −0.204380
\(55\) −1.67584 −0.225970
\(56\) −8.15239 −1.08941
\(57\) 4.81296 0.637492
\(58\) −6.26405 −0.822511
\(59\) 3.86590 0.503297 0.251648 0.967819i \(-0.419027\pi\)
0.251648 + 0.967819i \(0.419027\pi\)
\(60\) −0.233947 −0.0302024
\(61\) 4.04555 0.517980 0.258990 0.965880i \(-0.416610\pi\)
0.258990 + 0.965880i \(0.416610\pi\)
\(62\) −11.0949 −1.40905
\(63\) −3.11181 −0.392052
\(64\) 6.73274 0.841592
\(65\) 4.30011 0.533363
\(66\) −2.75030 −0.338538
\(67\) −10.2633 −1.25386 −0.626928 0.779077i \(-0.715688\pi\)
−0.626928 + 0.779077i \(0.715688\pi\)
\(68\) −0.255640 −0.0310009
\(69\) −2.49596 −0.300478
\(70\) −4.27697 −0.511196
\(71\) 4.17445 0.495416 0.247708 0.968835i \(-0.420323\pi\)
0.247708 + 0.968835i \(0.420323\pi\)
\(72\) 2.61982 0.308748
\(73\) 3.90172 0.456662 0.228331 0.973584i \(-0.426673\pi\)
0.228331 + 0.973584i \(0.426673\pi\)
\(74\) 8.74304 1.01636
\(75\) −4.16252 −0.480646
\(76\) 1.23039 0.141135
\(77\) −5.69847 −0.649401
\(78\) 7.05712 0.799061
\(79\) −1.84040 −0.207061 −0.103530 0.994626i \(-0.533014\pi\)
−0.103530 + 0.994626i \(0.533014\pi\)
\(80\) 4.06865 0.454889
\(81\) 1.00000 0.111111
\(82\) −5.61374 −0.619934
\(83\) −2.87241 −0.315288 −0.157644 0.987496i \(-0.550390\pi\)
−0.157644 + 0.987496i \(0.550390\pi\)
\(84\) −0.795505 −0.0867967
\(85\) 0.915140 0.0992609
\(86\) 5.83233 0.628917
\(87\) 4.17081 0.447158
\(88\) 4.79751 0.511416
\(89\) −10.5142 −1.11451 −0.557253 0.830343i \(-0.688145\pi\)
−0.557253 + 0.830343i \(0.688145\pi\)
\(90\) 1.37443 0.144878
\(91\) 14.6220 1.53280
\(92\) −0.638067 −0.0665231
\(93\) 7.38733 0.766030
\(94\) −4.70661 −0.485450
\(95\) −4.40453 −0.451895
\(96\) 1.43761 0.146726
\(97\) 5.66576 0.575271 0.287635 0.957740i \(-0.407131\pi\)
0.287635 + 0.957740i \(0.407131\pi\)
\(98\) −4.03013 −0.407104
\(99\) 1.83124 0.184046
\(100\) −1.06411 −0.106411
\(101\) −15.9150 −1.58361 −0.791803 0.610777i \(-0.790857\pi\)
−0.791803 + 0.610777i \(0.790857\pi\)
\(102\) 1.50188 0.148708
\(103\) −16.7480 −1.65023 −0.825114 0.564967i \(-0.808889\pi\)
−0.825114 + 0.564967i \(0.808889\pi\)
\(104\) −12.3101 −1.20711
\(105\) 2.84775 0.277912
\(106\) −18.7444 −1.82061
\(107\) 10.0590 0.972438 0.486219 0.873837i \(-0.338376\pi\)
0.486219 + 0.873837i \(0.338376\pi\)
\(108\) 0.255640 0.0245990
\(109\) 10.6498 1.02007 0.510033 0.860155i \(-0.329633\pi\)
0.510033 + 0.860155i \(0.329633\pi\)
\(110\) 2.51691 0.239978
\(111\) −5.82140 −0.552543
\(112\) 13.8349 1.30728
\(113\) 10.9013 1.02550 0.512752 0.858537i \(-0.328626\pi\)
0.512752 + 0.858537i \(0.328626\pi\)
\(114\) −7.22848 −0.677009
\(115\) 2.28415 0.212998
\(116\) 1.06623 0.0989967
\(117\) −4.69886 −0.434410
\(118\) −5.80611 −0.534496
\(119\) 3.11181 0.285260
\(120\) −2.39750 −0.218861
\(121\) −7.64657 −0.695143
\(122\) −6.07593 −0.550089
\(123\) 3.73781 0.337027
\(124\) 1.88850 0.169592
\(125\) 8.38499 0.749976
\(126\) 4.67357 0.416355
\(127\) 18.9120 1.67817 0.839084 0.544001i \(-0.183091\pi\)
0.839084 + 0.544001i \(0.183091\pi\)
\(128\) −12.9870 −1.14790
\(129\) −3.88336 −0.341911
\(130\) −6.45825 −0.566426
\(131\) 15.5951 1.36255 0.681276 0.732026i \(-0.261425\pi\)
0.681276 + 0.732026i \(0.261425\pi\)
\(132\) 0.468138 0.0407462
\(133\) −14.9770 −1.29867
\(134\) 15.4142 1.33158
\(135\) −0.915140 −0.0787627
\(136\) −2.61982 −0.224647
\(137\) −14.0854 −1.20340 −0.601698 0.798724i \(-0.705509\pi\)
−0.601698 + 0.798724i \(0.705509\pi\)
\(138\) 3.74863 0.319104
\(139\) −18.8607 −1.59974 −0.799871 0.600172i \(-0.795099\pi\)
−0.799871 + 0.600172i \(0.795099\pi\)
\(140\) 0.727998 0.0615271
\(141\) 3.13382 0.263915
\(142\) −6.26952 −0.526126
\(143\) −8.60472 −0.719563
\(144\) −4.44593 −0.370494
\(145\) −3.81688 −0.316974
\(146\) −5.85991 −0.484970
\(147\) 2.68339 0.221322
\(148\) −1.48818 −0.122328
\(149\) −4.02889 −0.330059 −0.165030 0.986289i \(-0.552772\pi\)
−0.165030 + 0.986289i \(0.552772\pi\)
\(150\) 6.25160 0.510441
\(151\) 8.06088 0.655985 0.327993 0.944680i \(-0.393628\pi\)
0.327993 + 0.944680i \(0.393628\pi\)
\(152\) 12.6091 1.02273
\(153\) −1.00000 −0.0808452
\(154\) 8.55841 0.689657
\(155\) −6.76044 −0.543011
\(156\) −1.20122 −0.0961743
\(157\) 1.00000 0.0798087
\(158\) 2.76405 0.219896
\(159\) 12.4806 0.989777
\(160\) −1.31562 −0.104009
\(161\) 7.76696 0.612122
\(162\) −1.50188 −0.117999
\(163\) −18.2135 −1.42659 −0.713297 0.700861i \(-0.752799\pi\)
−0.713297 + 0.700861i \(0.752799\pi\)
\(164\) 0.955535 0.0746147
\(165\) −1.67584 −0.130464
\(166\) 4.31401 0.334832
\(167\) −18.6021 −1.43947 −0.719735 0.694248i \(-0.755737\pi\)
−0.719735 + 0.694248i \(0.755737\pi\)
\(168\) −8.15239 −0.628970
\(169\) 9.07927 0.698405
\(170\) −1.37443 −0.105414
\(171\) 4.81296 0.368056
\(172\) −0.992742 −0.0756959
\(173\) 3.81136 0.289773 0.144886 0.989448i \(-0.453718\pi\)
0.144886 + 0.989448i \(0.453718\pi\)
\(174\) −6.26405 −0.474877
\(175\) 12.9530 0.979154
\(176\) −8.14155 −0.613692
\(177\) 3.86590 0.290579
\(178\) 15.7911 1.18359
\(179\) −21.3262 −1.59400 −0.796998 0.603982i \(-0.793580\pi\)
−0.796998 + 0.603982i \(0.793580\pi\)
\(180\) −0.233947 −0.0174373
\(181\) 17.5474 1.30429 0.652145 0.758094i \(-0.273869\pi\)
0.652145 + 0.758094i \(0.273869\pi\)
\(182\) −21.9604 −1.62782
\(183\) 4.04555 0.299056
\(184\) −6.53896 −0.482058
\(185\) 5.32740 0.391678
\(186\) −11.0949 −0.813515
\(187\) −1.83124 −0.133913
\(188\) 0.801130 0.0584284
\(189\) −3.11181 −0.226351
\(190\) 6.61507 0.479907
\(191\) 22.2002 1.60635 0.803175 0.595744i \(-0.203143\pi\)
0.803175 + 0.595744i \(0.203143\pi\)
\(192\) 6.73274 0.485894
\(193\) 11.2600 0.810515 0.405258 0.914202i \(-0.367182\pi\)
0.405258 + 0.914202i \(0.367182\pi\)
\(194\) −8.50929 −0.610931
\(195\) 4.30011 0.307938
\(196\) 0.685983 0.0489988
\(197\) −11.4265 −0.814104 −0.407052 0.913405i \(-0.633443\pi\)
−0.407052 + 0.913405i \(0.633443\pi\)
\(198\) −2.75030 −0.195455
\(199\) −9.58517 −0.679475 −0.339737 0.940520i \(-0.610338\pi\)
−0.339737 + 0.940520i \(0.610338\pi\)
\(200\) −10.9050 −0.771103
\(201\) −10.2633 −0.723914
\(202\) 23.9025 1.68177
\(203\) −12.9788 −0.910933
\(204\) −0.255640 −0.0178984
\(205\) −3.42062 −0.238906
\(206\) 25.1534 1.75252
\(207\) −2.49596 −0.173481
\(208\) 20.8908 1.44852
\(209\) 8.81366 0.609654
\(210\) −4.27697 −0.295139
\(211\) 15.8365 1.09023 0.545116 0.838360i \(-0.316485\pi\)
0.545116 + 0.838360i \(0.316485\pi\)
\(212\) 3.19055 0.219128
\(213\) 4.17445 0.286029
\(214\) −15.1074 −1.03272
\(215\) 3.55382 0.242368
\(216\) 2.61982 0.178256
\(217\) −22.9880 −1.56053
\(218\) −15.9947 −1.08330
\(219\) 3.90172 0.263654
\(220\) −0.428412 −0.0288835
\(221\) 4.69886 0.316079
\(222\) 8.74304 0.586794
\(223\) 7.95027 0.532389 0.266195 0.963919i \(-0.414234\pi\)
0.266195 + 0.963919i \(0.414234\pi\)
\(224\) −4.47358 −0.298904
\(225\) −4.16252 −0.277501
\(226\) −16.3724 −1.08907
\(227\) −16.8738 −1.11996 −0.559978 0.828508i \(-0.689190\pi\)
−0.559978 + 0.828508i \(0.689190\pi\)
\(228\) 1.23039 0.0814842
\(229\) 17.6968 1.16944 0.584719 0.811236i \(-0.301205\pi\)
0.584719 + 0.811236i \(0.301205\pi\)
\(230\) −3.43052 −0.226202
\(231\) −5.69847 −0.374932
\(232\) 10.9268 0.717377
\(233\) −3.99403 −0.261658 −0.130829 0.991405i \(-0.541764\pi\)
−0.130829 + 0.991405i \(0.541764\pi\)
\(234\) 7.05712 0.461338
\(235\) −2.86788 −0.187080
\(236\) 0.988278 0.0643314
\(237\) −1.84040 −0.119547
\(238\) −4.67357 −0.302942
\(239\) 12.5749 0.813401 0.406701 0.913562i \(-0.366679\pi\)
0.406701 + 0.913562i \(0.366679\pi\)
\(240\) 4.06865 0.262630
\(241\) 0.414955 0.0267296 0.0133648 0.999911i \(-0.495746\pi\)
0.0133648 + 0.999911i \(0.495746\pi\)
\(242\) 11.4842 0.738234
\(243\) 1.00000 0.0641500
\(244\) 1.03421 0.0662083
\(245\) −2.45568 −0.156888
\(246\) −5.61374 −0.357919
\(247\) −22.6154 −1.43898
\(248\) 19.3534 1.22895
\(249\) −2.87241 −0.182032
\(250\) −12.5932 −0.796466
\(251\) 7.38317 0.466022 0.233011 0.972474i \(-0.425142\pi\)
0.233011 + 0.972474i \(0.425142\pi\)
\(252\) −0.795505 −0.0501121
\(253\) −4.57069 −0.287357
\(254\) −28.4035 −1.78220
\(255\) 0.915140 0.0573083
\(256\) 6.03940 0.377462
\(257\) 2.48429 0.154966 0.0774828 0.996994i \(-0.475312\pi\)
0.0774828 + 0.996994i \(0.475312\pi\)
\(258\) 5.83233 0.363105
\(259\) 18.1151 1.12562
\(260\) 1.09928 0.0681746
\(261\) 4.17081 0.258167
\(262\) −23.4220 −1.44702
\(263\) −14.0861 −0.868583 −0.434292 0.900772i \(-0.643001\pi\)
−0.434292 + 0.900772i \(0.643001\pi\)
\(264\) 4.79751 0.295266
\(265\) −11.4215 −0.701618
\(266\) 22.4937 1.37918
\(267\) −10.5142 −0.643460
\(268\) −2.62370 −0.160268
\(269\) 26.1809 1.59628 0.798138 0.602475i \(-0.205819\pi\)
0.798138 + 0.602475i \(0.205819\pi\)
\(270\) 1.37443 0.0836451
\(271\) −1.66508 −0.101147 −0.0505733 0.998720i \(-0.516105\pi\)
−0.0505733 + 0.998720i \(0.516105\pi\)
\(272\) 4.44593 0.269574
\(273\) 14.6220 0.884962
\(274\) 21.1546 1.27799
\(275\) −7.62256 −0.459658
\(276\) −0.638067 −0.0384071
\(277\) 5.21404 0.313282 0.156641 0.987656i \(-0.449934\pi\)
0.156641 + 0.987656i \(0.449934\pi\)
\(278\) 28.3265 1.69891
\(279\) 7.38733 0.442268
\(280\) 7.46057 0.445855
\(281\) −21.5851 −1.28766 −0.643830 0.765168i \(-0.722656\pi\)
−0.643830 + 0.765168i \(0.722656\pi\)
\(282\) −4.70661 −0.280275
\(283\) −19.8556 −1.18029 −0.590145 0.807297i \(-0.700930\pi\)
−0.590145 + 0.807297i \(0.700930\pi\)
\(284\) 1.06716 0.0633241
\(285\) −4.40453 −0.260902
\(286\) 12.9233 0.764168
\(287\) −11.6314 −0.686578
\(288\) 1.43761 0.0847121
\(289\) 1.00000 0.0588235
\(290\) 5.73249 0.336623
\(291\) 5.66576 0.332133
\(292\) 0.997437 0.0583706
\(293\) −30.9786 −1.80979 −0.904894 0.425638i \(-0.860050\pi\)
−0.904894 + 0.425638i \(0.860050\pi\)
\(294\) −4.03013 −0.235042
\(295\) −3.53784 −0.205981
\(296\) −15.2510 −0.886447
\(297\) 1.83124 0.106259
\(298\) 6.05090 0.350519
\(299\) 11.7282 0.678257
\(300\) −1.06411 −0.0614363
\(301\) 12.0843 0.696527
\(302\) −12.1065 −0.696649
\(303\) −15.9150 −0.914295
\(304\) −21.3981 −1.22726
\(305\) −3.70225 −0.211990
\(306\) 1.50188 0.0858567
\(307\) −31.1940 −1.78034 −0.890169 0.455631i \(-0.849414\pi\)
−0.890169 + 0.455631i \(0.849414\pi\)
\(308\) −1.45676 −0.0830065
\(309\) −16.7480 −0.952759
\(310\) 10.1534 0.576672
\(311\) −19.7758 −1.12138 −0.560691 0.828025i \(-0.689464\pi\)
−0.560691 + 0.828025i \(0.689464\pi\)
\(312\) −12.3101 −0.696925
\(313\) −14.9782 −0.846618 −0.423309 0.905985i \(-0.639132\pi\)
−0.423309 + 0.905985i \(0.639132\pi\)
\(314\) −1.50188 −0.0847559
\(315\) 2.84775 0.160452
\(316\) −0.470480 −0.0264665
\(317\) 9.00178 0.505590 0.252795 0.967520i \(-0.418650\pi\)
0.252795 + 0.967520i \(0.418650\pi\)
\(318\) −18.7444 −1.05113
\(319\) 7.63774 0.427632
\(320\) −6.16140 −0.344433
\(321\) 10.0590 0.561437
\(322\) −11.6650 −0.650067
\(323\) −4.81296 −0.267800
\(324\) 0.255640 0.0142022
\(325\) 19.5591 1.08494
\(326\) 27.3545 1.51503
\(327\) 10.6498 0.588935
\(328\) 9.79238 0.540694
\(329\) −9.75186 −0.537637
\(330\) 2.51691 0.138551
\(331\) 13.0512 0.717359 0.358680 0.933461i \(-0.383227\pi\)
0.358680 + 0.933461i \(0.383227\pi\)
\(332\) −0.734304 −0.0403002
\(333\) −5.82140 −0.319011
\(334\) 27.9380 1.52870
\(335\) 9.39231 0.513157
\(336\) 13.8349 0.754756
\(337\) −28.5224 −1.55372 −0.776858 0.629676i \(-0.783188\pi\)
−0.776858 + 0.629676i \(0.783188\pi\)
\(338\) −13.6360 −0.741699
\(339\) 10.9013 0.592075
\(340\) 0.233947 0.0126875
\(341\) 13.5279 0.732579
\(342\) −7.22848 −0.390871
\(343\) 13.4325 0.725286
\(344\) −10.1737 −0.548528
\(345\) 2.28415 0.122975
\(346\) −5.72421 −0.307735
\(347\) −31.2471 −1.67743 −0.838715 0.544570i \(-0.816693\pi\)
−0.838715 + 0.544570i \(0.816693\pi\)
\(348\) 1.06623 0.0571558
\(349\) 28.3573 1.51793 0.758967 0.651129i \(-0.225704\pi\)
0.758967 + 0.651129i \(0.225704\pi\)
\(350\) −19.4538 −1.03985
\(351\) −4.69886 −0.250807
\(352\) 2.63261 0.140318
\(353\) −19.4903 −1.03736 −0.518682 0.854968i \(-0.673577\pi\)
−0.518682 + 0.854968i \(0.673577\pi\)
\(354\) −5.80611 −0.308591
\(355\) −3.82021 −0.202755
\(356\) −2.68786 −0.142456
\(357\) 3.11181 0.164695
\(358\) 32.0294 1.69281
\(359\) −31.8602 −1.68151 −0.840757 0.541412i \(-0.817890\pi\)
−0.840757 + 0.541412i \(0.817890\pi\)
\(360\) −2.39750 −0.126359
\(361\) 4.16454 0.219186
\(362\) −26.3541 −1.38514
\(363\) −7.64657 −0.401341
\(364\) 3.73797 0.195923
\(365\) −3.57062 −0.186895
\(366\) −6.07593 −0.317594
\(367\) 35.3160 1.84348 0.921741 0.387805i \(-0.126767\pi\)
0.921741 + 0.387805i \(0.126767\pi\)
\(368\) 11.0969 0.578463
\(369\) 3.73781 0.194583
\(370\) −8.00110 −0.415958
\(371\) −38.8374 −2.01634
\(372\) 1.88850 0.0979141
\(373\) 3.36495 0.174231 0.0871153 0.996198i \(-0.472235\pi\)
0.0871153 + 0.996198i \(0.472235\pi\)
\(374\) 2.75030 0.142214
\(375\) 8.38499 0.432999
\(376\) 8.21003 0.423400
\(377\) −19.5981 −1.00935
\(378\) 4.67357 0.240382
\(379\) 12.8544 0.660288 0.330144 0.943931i \(-0.392903\pi\)
0.330144 + 0.943931i \(0.392903\pi\)
\(380\) −1.12597 −0.0577613
\(381\) 18.9120 0.968891
\(382\) −33.3420 −1.70592
\(383\) 6.75149 0.344985 0.172492 0.985011i \(-0.444818\pi\)
0.172492 + 0.985011i \(0.444818\pi\)
\(384\) −12.9870 −0.662739
\(385\) 5.21490 0.265776
\(386\) −16.9112 −0.860758
\(387\) −3.88336 −0.197402
\(388\) 1.44840 0.0735312
\(389\) −10.0817 −0.511162 −0.255581 0.966788i \(-0.582267\pi\)
−0.255581 + 0.966788i \(0.582267\pi\)
\(390\) −6.45825 −0.327026
\(391\) 2.49596 0.126226
\(392\) 7.02999 0.355068
\(393\) 15.5951 0.786670
\(394\) 17.1612 0.864569
\(395\) 1.68422 0.0847424
\(396\) 0.468138 0.0235248
\(397\) −2.78465 −0.139758 −0.0698789 0.997555i \(-0.522261\pi\)
−0.0698789 + 0.997555i \(0.522261\pi\)
\(398\) 14.3958 0.721595
\(399\) −14.9770 −0.749789
\(400\) 18.5063 0.925313
\(401\) 0.965042 0.0481919 0.0240959 0.999710i \(-0.492329\pi\)
0.0240959 + 0.999710i \(0.492329\pi\)
\(402\) 15.4142 0.768789
\(403\) −34.7120 −1.72913
\(404\) −4.06852 −0.202417
\(405\) −0.915140 −0.0454737
\(406\) 19.4926 0.967400
\(407\) −10.6604 −0.528415
\(408\) −2.61982 −0.129700
\(409\) −35.9049 −1.77538 −0.887692 0.460437i \(-0.847693\pi\)
−0.887692 + 0.460437i \(0.847693\pi\)
\(410\) 5.13736 0.253716
\(411\) −14.0854 −0.694781
\(412\) −4.28146 −0.210932
\(413\) −12.0300 −0.591955
\(414\) 3.74863 0.184235
\(415\) 2.62866 0.129036
\(416\) −6.75514 −0.331198
\(417\) −18.8607 −0.923611
\(418\) −13.2371 −0.647445
\(419\) −5.08050 −0.248199 −0.124099 0.992270i \(-0.539604\pi\)
−0.124099 + 0.992270i \(0.539604\pi\)
\(420\) 0.727998 0.0355227
\(421\) −10.7271 −0.522807 −0.261403 0.965230i \(-0.584185\pi\)
−0.261403 + 0.965230i \(0.584185\pi\)
\(422\) −23.7846 −1.15782
\(423\) 3.13382 0.152371
\(424\) 32.6969 1.58790
\(425\) 4.16252 0.201912
\(426\) −6.26952 −0.303759
\(427\) −12.5890 −0.609225
\(428\) 2.57148 0.124297
\(429\) −8.60472 −0.415440
\(430\) −5.33740 −0.257392
\(431\) −8.95163 −0.431185 −0.215593 0.976483i \(-0.569168\pi\)
−0.215593 + 0.976483i \(0.569168\pi\)
\(432\) −4.44593 −0.213905
\(433\) 18.8978 0.908172 0.454086 0.890958i \(-0.349966\pi\)
0.454086 + 0.890958i \(0.349966\pi\)
\(434\) 34.5252 1.65726
\(435\) −3.81688 −0.183005
\(436\) 2.72252 0.130385
\(437\) −12.0129 −0.574657
\(438\) −5.85991 −0.279997
\(439\) −36.3004 −1.73253 −0.866263 0.499589i \(-0.833484\pi\)
−0.866263 + 0.499589i \(0.833484\pi\)
\(440\) −4.39039 −0.209304
\(441\) 2.68339 0.127781
\(442\) −7.05712 −0.335673
\(443\) −33.2829 −1.58132 −0.790660 0.612256i \(-0.790262\pi\)
−0.790660 + 0.612256i \(0.790262\pi\)
\(444\) −1.48818 −0.0706261
\(445\) 9.62199 0.456126
\(446\) −11.9403 −0.565392
\(447\) −4.02889 −0.190560
\(448\) −20.9510 −0.989843
\(449\) −33.2779 −1.57048 −0.785241 0.619190i \(-0.787461\pi\)
−0.785241 + 0.619190i \(0.787461\pi\)
\(450\) 6.25160 0.294703
\(451\) 6.84482 0.322310
\(452\) 2.78680 0.131080
\(453\) 8.06088 0.378733
\(454\) 25.3425 1.18938
\(455\) −13.3812 −0.627318
\(456\) 12.6091 0.590473
\(457\) 5.36358 0.250898 0.125449 0.992100i \(-0.459963\pi\)
0.125449 + 0.992100i \(0.459963\pi\)
\(458\) −26.5785 −1.24193
\(459\) −1.00000 −0.0466760
\(460\) 0.583921 0.0272255
\(461\) 15.4815 0.721047 0.360523 0.932750i \(-0.382598\pi\)
0.360523 + 0.932750i \(0.382598\pi\)
\(462\) 8.55841 0.398173
\(463\) 11.1458 0.517988 0.258994 0.965879i \(-0.416609\pi\)
0.258994 + 0.965879i \(0.416609\pi\)
\(464\) −18.5431 −0.860843
\(465\) −6.76044 −0.313508
\(466\) 5.99856 0.277878
\(467\) −24.9412 −1.15414 −0.577072 0.816693i \(-0.695805\pi\)
−0.577072 + 0.816693i \(0.695805\pi\)
\(468\) −1.20122 −0.0555263
\(469\) 31.9373 1.47473
\(470\) 4.30721 0.198677
\(471\) 1.00000 0.0460776
\(472\) 10.1279 0.466176
\(473\) −7.11135 −0.326980
\(474\) 2.76405 0.126957
\(475\) −20.0340 −0.919224
\(476\) 0.795505 0.0364619
\(477\) 12.4806 0.571448
\(478\) −18.8859 −0.863823
\(479\) −4.34821 −0.198675 −0.0993375 0.995054i \(-0.531672\pi\)
−0.0993375 + 0.995054i \(0.531672\pi\)
\(480\) −1.31562 −0.0600494
\(481\) 27.3539 1.24723
\(482\) −0.623212 −0.0283865
\(483\) 7.76696 0.353409
\(484\) −1.95477 −0.0888532
\(485\) −5.18496 −0.235437
\(486\) −1.50188 −0.0681266
\(487\) −27.3229 −1.23812 −0.619060 0.785344i \(-0.712486\pi\)
−0.619060 + 0.785344i \(0.712486\pi\)
\(488\) 10.5986 0.479776
\(489\) −18.2135 −0.823645
\(490\) 3.68813 0.166613
\(491\) −4.23577 −0.191158 −0.0955788 0.995422i \(-0.530470\pi\)
−0.0955788 + 0.995422i \(0.530470\pi\)
\(492\) 0.955535 0.0430788
\(493\) −4.17081 −0.187844
\(494\) 33.9656 1.52818
\(495\) −1.67584 −0.0753233
\(496\) −32.8435 −1.47472
\(497\) −12.9901 −0.582686
\(498\) 4.31401 0.193316
\(499\) −19.6122 −0.877961 −0.438981 0.898496i \(-0.644660\pi\)
−0.438981 + 0.898496i \(0.644660\pi\)
\(500\) 2.14354 0.0958620
\(501\) −18.6021 −0.831079
\(502\) −11.0886 −0.494910
\(503\) 7.71947 0.344194 0.172097 0.985080i \(-0.444946\pi\)
0.172097 + 0.985080i \(0.444946\pi\)
\(504\) −8.15239 −0.363136
\(505\) 14.5645 0.648111
\(506\) 6.86463 0.305170
\(507\) 9.07927 0.403225
\(508\) 4.83467 0.214504
\(509\) −29.3330 −1.30016 −0.650081 0.759865i \(-0.725265\pi\)
−0.650081 + 0.759865i \(0.725265\pi\)
\(510\) −1.37443 −0.0608608
\(511\) −12.1414 −0.537105
\(512\) 16.9035 0.747037
\(513\) 4.81296 0.212497
\(514\) −3.73110 −0.164572
\(515\) 15.3267 0.675377
\(516\) −0.992742 −0.0437030
\(517\) 5.73876 0.252391
\(518\) −27.2067 −1.19539
\(519\) 3.81136 0.167300
\(520\) 11.2655 0.494025
\(521\) 24.6332 1.07920 0.539600 0.841921i \(-0.318575\pi\)
0.539600 + 0.841921i \(0.318575\pi\)
\(522\) −6.26405 −0.274170
\(523\) −14.4385 −0.631351 −0.315675 0.948867i \(-0.602231\pi\)
−0.315675 + 0.948867i \(0.602231\pi\)
\(524\) 3.98674 0.174162
\(525\) 12.9530 0.565315
\(526\) 21.1555 0.922426
\(527\) −7.38733 −0.321797
\(528\) −8.14155 −0.354315
\(529\) −16.7702 −0.729139
\(530\) 17.1537 0.745110
\(531\) 3.86590 0.167766
\(532\) −3.82873 −0.165997
\(533\) −17.5634 −0.760757
\(534\) 15.7911 0.683347
\(535\) −9.20537 −0.397983
\(536\) −26.8878 −1.16138
\(537\) −21.3262 −0.920294
\(538\) −39.3205 −1.69523
\(539\) 4.91393 0.211658
\(540\) −0.233947 −0.0100675
\(541\) −13.8201 −0.594173 −0.297086 0.954851i \(-0.596015\pi\)
−0.297086 + 0.954851i \(0.596015\pi\)
\(542\) 2.50075 0.107416
\(543\) 17.5474 0.753032
\(544\) −1.43761 −0.0616371
\(545\) −9.74605 −0.417475
\(546\) −21.9604 −0.939820
\(547\) 41.3531 1.76813 0.884065 0.467364i \(-0.154796\pi\)
0.884065 + 0.467364i \(0.154796\pi\)
\(548\) −3.60079 −0.153818
\(549\) 4.04555 0.172660
\(550\) 11.4482 0.488151
\(551\) 20.0739 0.855178
\(552\) −6.53896 −0.278316
\(553\) 5.72698 0.243536
\(554\) −7.83086 −0.332701
\(555\) 5.32740 0.226135
\(556\) −4.82155 −0.204479
\(557\) 8.36064 0.354252 0.177126 0.984188i \(-0.443320\pi\)
0.177126 + 0.984188i \(0.443320\pi\)
\(558\) −11.0949 −0.469683
\(559\) 18.2473 0.771780
\(560\) −12.6609 −0.535020
\(561\) −1.83124 −0.0773149
\(562\) 32.4182 1.36748
\(563\) 15.6157 0.658124 0.329062 0.944308i \(-0.393268\pi\)
0.329062 + 0.944308i \(0.393268\pi\)
\(564\) 0.801130 0.0337337
\(565\) −9.97618 −0.419701
\(566\) 29.8207 1.25346
\(567\) −3.11181 −0.130684
\(568\) 10.9363 0.458877
\(569\) −21.5052 −0.901546 −0.450773 0.892639i \(-0.648852\pi\)
−0.450773 + 0.892639i \(0.648852\pi\)
\(570\) 6.61507 0.277075
\(571\) 22.6781 0.949049 0.474524 0.880242i \(-0.342620\pi\)
0.474524 + 0.880242i \(0.342620\pi\)
\(572\) −2.19971 −0.0919746
\(573\) 22.2002 0.927426
\(574\) 17.4689 0.729138
\(575\) 10.3895 0.433271
\(576\) 6.73274 0.280531
\(577\) 14.4168 0.600178 0.300089 0.953911i \(-0.402984\pi\)
0.300089 + 0.953911i \(0.402984\pi\)
\(578\) −1.50188 −0.0624699
\(579\) 11.2600 0.467951
\(580\) −0.975747 −0.0405157
\(581\) 8.93841 0.370828
\(582\) −8.50929 −0.352721
\(583\) 22.8550 0.946556
\(584\) 10.2218 0.422981
\(585\) 4.30011 0.177788
\(586\) 46.5261 1.92197
\(587\) −26.2285 −1.08257 −0.541283 0.840840i \(-0.682061\pi\)
−0.541283 + 0.840840i \(0.682061\pi\)
\(588\) 0.685983 0.0282895
\(589\) 35.5549 1.46501
\(590\) 5.31340 0.218749
\(591\) −11.4265 −0.470023
\(592\) 25.8815 1.06372
\(593\) 37.7746 1.55122 0.775608 0.631215i \(-0.217444\pi\)
0.775608 + 0.631215i \(0.217444\pi\)
\(594\) −2.75030 −0.112846
\(595\) −2.84775 −0.116746
\(596\) −1.02995 −0.0421882
\(597\) −9.58517 −0.392295
\(598\) −17.6143 −0.720301
\(599\) −27.8240 −1.13686 −0.568429 0.822733i \(-0.692448\pi\)
−0.568429 + 0.822733i \(0.692448\pi\)
\(600\) −10.9050 −0.445196
\(601\) 11.0182 0.449443 0.224722 0.974423i \(-0.427853\pi\)
0.224722 + 0.974423i \(0.427853\pi\)
\(602\) −18.1491 −0.739704
\(603\) −10.2633 −0.417952
\(604\) 2.06069 0.0838481
\(605\) 6.99768 0.284496
\(606\) 23.9025 0.970971
\(607\) 2.12634 0.0863055 0.0431527 0.999068i \(-0.486260\pi\)
0.0431527 + 0.999068i \(0.486260\pi\)
\(608\) 6.91916 0.280609
\(609\) −12.9788 −0.525927
\(610\) 5.56033 0.225131
\(611\) −14.7254 −0.595725
\(612\) −0.255640 −0.0103336
\(613\) 23.4373 0.946625 0.473312 0.880895i \(-0.343058\pi\)
0.473312 + 0.880895i \(0.343058\pi\)
\(614\) 46.8497 1.89070
\(615\) −3.42062 −0.137933
\(616\) −14.9290 −0.601505
\(617\) 20.3337 0.818606 0.409303 0.912399i \(-0.365772\pi\)
0.409303 + 0.912399i \(0.365772\pi\)
\(618\) 25.1534 1.01182
\(619\) 11.5193 0.463000 0.231500 0.972835i \(-0.425637\pi\)
0.231500 + 0.972835i \(0.425637\pi\)
\(620\) −1.72824 −0.0694078
\(621\) −2.49596 −0.100159
\(622\) 29.7008 1.19089
\(623\) 32.7183 1.31083
\(624\) 20.8908 0.836301
\(625\) 13.1392 0.525566
\(626\) 22.4955 0.899099
\(627\) 8.81366 0.351984
\(628\) 0.255640 0.0102012
\(629\) 5.82140 0.232114
\(630\) −4.27697 −0.170399
\(631\) 3.62641 0.144365 0.0721826 0.997391i \(-0.477004\pi\)
0.0721826 + 0.997391i \(0.477004\pi\)
\(632\) −4.82150 −0.191789
\(633\) 15.8365 0.629446
\(634\) −13.5196 −0.536931
\(635\) −17.3071 −0.686813
\(636\) 3.19055 0.126513
\(637\) −12.6089 −0.499582
\(638\) −11.4710 −0.454140
\(639\) 4.17445 0.165139
\(640\) 11.8849 0.469792
\(641\) −13.0015 −0.513530 −0.256765 0.966474i \(-0.582657\pi\)
−0.256765 + 0.966474i \(0.582657\pi\)
\(642\) −15.1074 −0.596240
\(643\) −32.0750 −1.26491 −0.632457 0.774595i \(-0.717953\pi\)
−0.632457 + 0.774595i \(0.717953\pi\)
\(644\) 1.98555 0.0782415
\(645\) 3.55382 0.139931
\(646\) 7.22848 0.284401
\(647\) 30.9965 1.21860 0.609299 0.792940i \(-0.291451\pi\)
0.609299 + 0.792940i \(0.291451\pi\)
\(648\) 2.61982 0.102916
\(649\) 7.07937 0.277890
\(650\) −29.3754 −1.15220
\(651\) −22.9880 −0.900970
\(652\) −4.65611 −0.182348
\(653\) −2.30916 −0.0903646 −0.0451823 0.998979i \(-0.514387\pi\)
−0.0451823 + 0.998979i \(0.514387\pi\)
\(654\) −15.9947 −0.625442
\(655\) −14.2717 −0.557642
\(656\) −16.6180 −0.648825
\(657\) 3.90172 0.152221
\(658\) 14.6461 0.570965
\(659\) −6.79254 −0.264600 −0.132300 0.991210i \(-0.542236\pi\)
−0.132300 + 0.991210i \(0.542236\pi\)
\(660\) −0.428412 −0.0166759
\(661\) −31.4243 −1.22226 −0.611132 0.791529i \(-0.709286\pi\)
−0.611132 + 0.791529i \(0.709286\pi\)
\(662\) −19.6013 −0.761827
\(663\) 4.69886 0.182489
\(664\) −7.52519 −0.292034
\(665\) 13.7061 0.531499
\(666\) 8.74304 0.338786
\(667\) −10.4102 −0.403084
\(668\) −4.75544 −0.183993
\(669\) 7.95027 0.307375
\(670\) −14.1061 −0.544967
\(671\) 7.40837 0.285997
\(672\) −4.47358 −0.172572
\(673\) 30.1465 1.16206 0.581032 0.813881i \(-0.302649\pi\)
0.581032 + 0.813881i \(0.302649\pi\)
\(674\) 42.8372 1.65003
\(675\) −4.16252 −0.160215
\(676\) 2.32103 0.0892703
\(677\) 1.85605 0.0713339 0.0356670 0.999364i \(-0.488644\pi\)
0.0356670 + 0.999364i \(0.488644\pi\)
\(678\) −16.3724 −0.628778
\(679\) −17.6308 −0.676608
\(680\) 2.39750 0.0919399
\(681\) −16.8738 −0.646607
\(682\) −20.3173 −0.777991
\(683\) −42.0446 −1.60879 −0.804395 0.594094i \(-0.797511\pi\)
−0.804395 + 0.594094i \(0.797511\pi\)
\(684\) 1.23039 0.0470449
\(685\) 12.8901 0.492506
\(686\) −20.1740 −0.770246
\(687\) 17.6968 0.675175
\(688\) 17.2651 0.658227
\(689\) −58.6446 −2.23418
\(690\) −3.43052 −0.130598
\(691\) −20.4108 −0.776463 −0.388232 0.921562i \(-0.626914\pi\)
−0.388232 + 0.921562i \(0.626914\pi\)
\(692\) 0.974338 0.0370388
\(693\) −5.69847 −0.216467
\(694\) 46.9293 1.78141
\(695\) 17.2602 0.654715
\(696\) 10.9268 0.414178
\(697\) −3.73781 −0.141580
\(698\) −42.5893 −1.61203
\(699\) −3.99403 −0.151068
\(700\) 3.31130 0.125156
\(701\) −28.4942 −1.07621 −0.538106 0.842877i \(-0.680860\pi\)
−0.538106 + 0.842877i \(0.680860\pi\)
\(702\) 7.05712 0.266354
\(703\) −28.0181 −1.05672
\(704\) 12.3292 0.464676
\(705\) −2.86788 −0.108011
\(706\) 29.2720 1.10167
\(707\) 49.5246 1.86257
\(708\) 0.988278 0.0371418
\(709\) 23.1444 0.869207 0.434604 0.900622i \(-0.356889\pi\)
0.434604 + 0.900622i \(0.356889\pi\)
\(710\) 5.73749 0.215324
\(711\) −1.84040 −0.0690203
\(712\) −27.5453 −1.03231
\(713\) −18.4385 −0.690526
\(714\) −4.67357 −0.174904
\(715\) 7.87453 0.294491
\(716\) −5.45184 −0.203745
\(717\) 12.5749 0.469617
\(718\) 47.8501 1.78575
\(719\) −19.1557 −0.714387 −0.357194 0.934030i \(-0.616266\pi\)
−0.357194 + 0.934030i \(0.616266\pi\)
\(720\) 4.06865 0.151630
\(721\) 52.1166 1.94092
\(722\) −6.25464 −0.232773
\(723\) 0.414955 0.0154323
\(724\) 4.48583 0.166714
\(725\) −17.3611 −0.644774
\(726\) 11.4842 0.426219
\(727\) −12.6329 −0.468527 −0.234264 0.972173i \(-0.575268\pi\)
−0.234264 + 0.972173i \(0.575268\pi\)
\(728\) 38.3069 1.41975
\(729\) 1.00000 0.0370370
\(730\) 5.36264 0.198480
\(731\) 3.88336 0.143631
\(732\) 1.03421 0.0382254
\(733\) 31.6526 1.16911 0.584557 0.811352i \(-0.301268\pi\)
0.584557 + 0.811352i \(0.301268\pi\)
\(734\) −53.0404 −1.95776
\(735\) −2.45568 −0.0905791
\(736\) −3.58822 −0.132264
\(737\) −18.7945 −0.692302
\(738\) −5.61374 −0.206645
\(739\) −16.3722 −0.602262 −0.301131 0.953583i \(-0.597364\pi\)
−0.301131 + 0.953583i \(0.597364\pi\)
\(740\) 1.36190 0.0500643
\(741\) −22.6154 −0.830797
\(742\) 58.3290 2.14133
\(743\) −27.4874 −1.00841 −0.504207 0.863583i \(-0.668215\pi\)
−0.504207 + 0.863583i \(0.668215\pi\)
\(744\) 19.3534 0.709532
\(745\) 3.68700 0.135081
\(746\) −5.05375 −0.185031
\(747\) −2.87241 −0.105096
\(748\) −0.468138 −0.0171168
\(749\) −31.3017 −1.14374
\(750\) −12.5932 −0.459840
\(751\) 18.2375 0.665495 0.332748 0.943016i \(-0.392024\pi\)
0.332748 + 0.943016i \(0.392024\pi\)
\(752\) −13.9327 −0.508074
\(753\) 7.38317 0.269058
\(754\) 29.4339 1.07192
\(755\) −7.37684 −0.268471
\(756\) −0.795505 −0.0289322
\(757\) −44.7603 −1.62684 −0.813420 0.581677i \(-0.802397\pi\)
−0.813420 + 0.581677i \(0.802397\pi\)
\(758\) −19.3058 −0.701219
\(759\) −4.57069 −0.165906
\(760\) −11.5391 −0.418566
\(761\) 38.5692 1.39813 0.699066 0.715057i \(-0.253599\pi\)
0.699066 + 0.715057i \(0.253599\pi\)
\(762\) −28.4035 −1.02895
\(763\) −33.1402 −1.19976
\(764\) 5.67526 0.205324
\(765\) 0.915140 0.0330870
\(766\) −10.1399 −0.366370
\(767\) −18.1653 −0.655911
\(768\) 6.03940 0.217928
\(769\) −24.0629 −0.867729 −0.433864 0.900978i \(-0.642850\pi\)
−0.433864 + 0.900978i \(0.642850\pi\)
\(770\) −7.83215 −0.282251
\(771\) 2.48429 0.0894694
\(772\) 2.87852 0.103600
\(773\) −0.696648 −0.0250567 −0.0125283 0.999922i \(-0.503988\pi\)
−0.0125283 + 0.999922i \(0.503988\pi\)
\(774\) 5.83233 0.209639
\(775\) −30.7499 −1.10457
\(776\) 14.8433 0.532842
\(777\) 18.1151 0.649876
\(778\) 15.1415 0.542848
\(779\) 17.9899 0.644556
\(780\) 1.09928 0.0393606
\(781\) 7.64441 0.273538
\(782\) −3.74863 −0.134051
\(783\) 4.17081 0.149053
\(784\) −11.9302 −0.426077
\(785\) −0.915140 −0.0326627
\(786\) −23.4220 −0.835435
\(787\) −27.7211 −0.988150 −0.494075 0.869419i \(-0.664493\pi\)
−0.494075 + 0.869419i \(0.664493\pi\)
\(788\) −2.92107 −0.104059
\(789\) −14.0861 −0.501477
\(790\) −2.52950 −0.0899954
\(791\) −33.9227 −1.20615
\(792\) 4.79751 0.170472
\(793\) −19.0095 −0.675046
\(794\) 4.18221 0.148421
\(795\) −11.4215 −0.405079
\(796\) −2.45036 −0.0868506
\(797\) 28.8795 1.02297 0.511483 0.859294i \(-0.329096\pi\)
0.511483 + 0.859294i \(0.329096\pi\)
\(798\) 22.4937 0.796268
\(799\) −3.13382 −0.110867
\(800\) −5.98409 −0.211569
\(801\) −10.5142 −0.371502
\(802\) −1.44938 −0.0511792
\(803\) 7.14498 0.252141
\(804\) −2.62370 −0.0925308
\(805\) −7.10786 −0.250519
\(806\) 52.1332 1.83631
\(807\) 26.1809 0.921610
\(808\) −41.6945 −1.46681
\(809\) 30.5648 1.07460 0.537300 0.843391i \(-0.319444\pi\)
0.537300 + 0.843391i \(0.319444\pi\)
\(810\) 1.37443 0.0482925
\(811\) 17.1111 0.600853 0.300426 0.953805i \(-0.402871\pi\)
0.300426 + 0.953805i \(0.402871\pi\)
\(812\) −3.31790 −0.116436
\(813\) −1.66508 −0.0583970
\(814\) 16.0106 0.561170
\(815\) 16.6679 0.583853
\(816\) 4.44593 0.155639
\(817\) −18.6904 −0.653895
\(818\) 53.9249 1.88544
\(819\) 14.6220 0.510933
\(820\) −0.874448 −0.0305370
\(821\) −18.0481 −0.629884 −0.314942 0.949111i \(-0.601985\pi\)
−0.314942 + 0.949111i \(0.601985\pi\)
\(822\) 21.1546 0.737850
\(823\) −19.5413 −0.681167 −0.340583 0.940214i \(-0.610625\pi\)
−0.340583 + 0.940214i \(0.610625\pi\)
\(824\) −43.8766 −1.52851
\(825\) −7.62256 −0.265383
\(826\) 18.0675 0.628650
\(827\) 43.2662 1.50451 0.752257 0.658870i \(-0.228965\pi\)
0.752257 + 0.658870i \(0.228965\pi\)
\(828\) −0.638067 −0.0221744
\(829\) −39.0073 −1.35478 −0.677389 0.735625i \(-0.736889\pi\)
−0.677389 + 0.735625i \(0.736889\pi\)
\(830\) −3.94793 −0.137035
\(831\) 5.21404 0.180873
\(832\) −31.6362 −1.09679
\(833\) −2.68339 −0.0929740
\(834\) 28.3265 0.980865
\(835\) 17.0235 0.589122
\(836\) 2.25313 0.0779260
\(837\) 7.38733 0.255343
\(838\) 7.63030 0.263584
\(839\) −48.1734 −1.66313 −0.831566 0.555426i \(-0.812555\pi\)
−0.831566 + 0.555426i \(0.812555\pi\)
\(840\) 7.46057 0.257414
\(841\) −11.6043 −0.400149
\(842\) 16.1108 0.555215
\(843\) −21.5851 −0.743431
\(844\) 4.04846 0.139354
\(845\) −8.30880 −0.285832
\(846\) −4.70661 −0.161817
\(847\) 23.7947 0.817596
\(848\) −55.4879 −1.90546
\(849\) −19.8556 −0.681441
\(850\) −6.25160 −0.214428
\(851\) 14.5300 0.498081
\(852\) 1.06716 0.0365602
\(853\) −47.2449 −1.61763 −0.808817 0.588061i \(-0.799892\pi\)
−0.808817 + 0.588061i \(0.799892\pi\)
\(854\) 18.9072 0.646990
\(855\) −4.40453 −0.150632
\(856\) 26.3527 0.900716
\(857\) −44.4208 −1.51738 −0.758692 0.651449i \(-0.774161\pi\)
−0.758692 + 0.651449i \(0.774161\pi\)
\(858\) 12.9233 0.441193
\(859\) 10.6719 0.364121 0.182060 0.983287i \(-0.441723\pi\)
0.182060 + 0.983287i \(0.441723\pi\)
\(860\) 0.908498 0.0309795
\(861\) −11.6314 −0.396396
\(862\) 13.4443 0.457914
\(863\) 46.3561 1.57798 0.788990 0.614406i \(-0.210604\pi\)
0.788990 + 0.614406i \(0.210604\pi\)
\(864\) 1.43761 0.0489086
\(865\) −3.48793 −0.118593
\(866\) −28.3822 −0.964468
\(867\) 1.00000 0.0339618
\(868\) −5.87666 −0.199467
\(869\) −3.37020 −0.114326
\(870\) 5.73249 0.194349
\(871\) 48.2256 1.63406
\(872\) 27.9005 0.944830
\(873\) 5.66576 0.191757
\(874\) 18.0420 0.610279
\(875\) −26.0925 −0.882088
\(876\) 0.997437 0.0337003
\(877\) −29.8111 −1.00665 −0.503325 0.864097i \(-0.667890\pi\)
−0.503325 + 0.864097i \(0.667890\pi\)
\(878\) 54.5189 1.83992
\(879\) −30.9786 −1.04488
\(880\) 7.45066 0.251162
\(881\) −29.5075 −0.994132 −0.497066 0.867713i \(-0.665589\pi\)
−0.497066 + 0.867713i \(0.665589\pi\)
\(882\) −4.03013 −0.135701
\(883\) −4.60611 −0.155008 −0.0775040 0.996992i \(-0.524695\pi\)
−0.0775040 + 0.996992i \(0.524695\pi\)
\(884\) 1.20122 0.0404013
\(885\) −3.53784 −0.118923
\(886\) 49.9869 1.67934
\(887\) 23.1898 0.778636 0.389318 0.921103i \(-0.372711\pi\)
0.389318 + 0.921103i \(0.372711\pi\)
\(888\) −15.2510 −0.511790
\(889\) −58.8507 −1.97379
\(890\) −14.4511 −0.484401
\(891\) 1.83124 0.0613488
\(892\) 2.03241 0.0680501
\(893\) 15.0829 0.504731
\(894\) 6.05090 0.202372
\(895\) 19.5165 0.652364
\(896\) 40.4131 1.35011
\(897\) 11.7282 0.391592
\(898\) 49.9794 1.66783
\(899\) 30.8111 1.02761
\(900\) −1.06411 −0.0354702
\(901\) −12.4806 −0.415790
\(902\) −10.2801 −0.342289
\(903\) 12.0843 0.402140
\(904\) 28.5593 0.949869
\(905\) −16.0584 −0.533798
\(906\) −12.1065 −0.402211
\(907\) −28.1937 −0.936157 −0.468078 0.883687i \(-0.655054\pi\)
−0.468078 + 0.883687i \(0.655054\pi\)
\(908\) −4.31363 −0.143153
\(909\) −15.9150 −0.527868
\(910\) 20.0969 0.666205
\(911\) −28.1315 −0.932038 −0.466019 0.884775i \(-0.654312\pi\)
−0.466019 + 0.884775i \(0.654312\pi\)
\(912\) −21.3981 −0.708560
\(913\) −5.26007 −0.174083
\(914\) −8.05545 −0.266450
\(915\) −3.70225 −0.122393
\(916\) 4.52402 0.149478
\(917\) −48.5291 −1.60257
\(918\) 1.50188 0.0495694
\(919\) −5.37789 −0.177400 −0.0887001 0.996058i \(-0.528271\pi\)
−0.0887001 + 0.996058i \(0.528271\pi\)
\(920\) 5.98406 0.197289
\(921\) −31.1940 −1.02788
\(922\) −23.2514 −0.765744
\(923\) −19.6151 −0.645640
\(924\) −1.45676 −0.0479238
\(925\) 24.2317 0.796733
\(926\) −16.7396 −0.550097
\(927\) −16.7480 −0.550076
\(928\) 5.99601 0.196829
\(929\) −7.80116 −0.255948 −0.127974 0.991778i \(-0.540847\pi\)
−0.127974 + 0.991778i \(0.540847\pi\)
\(930\) 10.1534 0.332942
\(931\) 12.9150 0.423273
\(932\) −1.02104 −0.0334451
\(933\) −19.7758 −0.647430
\(934\) 37.4587 1.22569
\(935\) 1.67584 0.0548058
\(936\) −12.3101 −0.402370
\(937\) −36.3746 −1.18831 −0.594154 0.804352i \(-0.702513\pi\)
−0.594154 + 0.804352i \(0.702513\pi\)
\(938\) −47.9660 −1.56615
\(939\) −14.9782 −0.488795
\(940\) −0.733146 −0.0239126
\(941\) −60.4168 −1.96953 −0.984766 0.173887i \(-0.944367\pi\)
−0.984766 + 0.173887i \(0.944367\pi\)
\(942\) −1.50188 −0.0489339
\(943\) −9.32942 −0.303808
\(944\) −17.1875 −0.559405
\(945\) 2.84775 0.0926372
\(946\) 10.6804 0.347249
\(947\) −38.6064 −1.25454 −0.627270 0.778802i \(-0.715828\pi\)
−0.627270 + 0.778802i \(0.715828\pi\)
\(948\) −0.470480 −0.0152805
\(949\) −18.3336 −0.595135
\(950\) 30.0887 0.976205
\(951\) 9.00178 0.291903
\(952\) 8.15239 0.264220
\(953\) 34.3529 1.11280 0.556400 0.830915i \(-0.312182\pi\)
0.556400 + 0.830915i \(0.312182\pi\)
\(954\) −18.7444 −0.606871
\(955\) −20.3163 −0.657419
\(956\) 3.21464 0.103969
\(957\) 7.63774 0.246893
\(958\) 6.53049 0.210991
\(959\) 43.8311 1.41538
\(960\) −6.16140 −0.198858
\(961\) 23.5726 0.760406
\(962\) −41.0823 −1.32455
\(963\) 10.0590 0.324146
\(964\) 0.106079 0.00341658
\(965\) −10.3045 −0.331714
\(966\) −11.6650 −0.375316
\(967\) −4.19285 −0.134833 −0.0674165 0.997725i \(-0.521476\pi\)
−0.0674165 + 0.997725i \(0.521476\pi\)
\(968\) −20.0326 −0.643873
\(969\) −4.81296 −0.154614
\(970\) 7.78719 0.250032
\(971\) 11.3531 0.364339 0.182169 0.983267i \(-0.441688\pi\)
0.182169 + 0.983267i \(0.441688\pi\)
\(972\) 0.255640 0.00819966
\(973\) 58.6909 1.88155
\(974\) 41.0357 1.31487
\(975\) 19.5591 0.626392
\(976\) −17.9862 −0.575725
\(977\) 9.32622 0.298372 0.149186 0.988809i \(-0.452335\pi\)
0.149186 + 0.988809i \(0.452335\pi\)
\(978\) 27.3545 0.874702
\(979\) −19.2540 −0.615362
\(980\) −0.627770 −0.0200534
\(981\) 10.6498 0.340022
\(982\) 6.36161 0.203007
\(983\) 7.93673 0.253142 0.126571 0.991958i \(-0.459603\pi\)
0.126571 + 0.991958i \(0.459603\pi\)
\(984\) 9.79238 0.312170
\(985\) 10.4568 0.333183
\(986\) 6.26405 0.199488
\(987\) −9.75186 −0.310405
\(988\) −5.78141 −0.183931
\(989\) 9.69270 0.308210
\(990\) 2.51691 0.0799925
\(991\) −31.3797 −0.996809 −0.498404 0.866945i \(-0.666080\pi\)
−0.498404 + 0.866945i \(0.666080\pi\)
\(992\) 10.6201 0.337189
\(993\) 13.0512 0.414167
\(994\) 19.5096 0.618806
\(995\) 8.77178 0.278084
\(996\) −0.734304 −0.0232673
\(997\) −12.8996 −0.408533 −0.204266 0.978915i \(-0.565481\pi\)
−0.204266 + 0.978915i \(0.565481\pi\)
\(998\) 29.4551 0.932385
\(999\) −5.82140 −0.184181
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 \(a_p\))