Properties

Label 6026.2.a.h.1.9
Level 6026
Weight 2
Character 6026.1
Self dual Yes
Analytic conductor 48.118
Analytic rank 1
Dimension 24
CM No

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Newspace parameters

Level: \( N \) = \( 6026 = 2 \cdot 23 \cdot 131 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6026.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.117852258\)
Analytic rank: \(1\)
Dimension: \(24\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.9
Character \(\chi\) = 6026.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{2}\) \(-0.985760 q^{3}\) \(+1.00000 q^{4}\) \(-1.64046 q^{5}\) \(+0.985760 q^{6}\) \(-3.55255 q^{7}\) \(-1.00000 q^{8}\) \(-2.02828 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{2}\) \(-0.985760 q^{3}\) \(+1.00000 q^{4}\) \(-1.64046 q^{5}\) \(+0.985760 q^{6}\) \(-3.55255 q^{7}\) \(-1.00000 q^{8}\) \(-2.02828 q^{9}\) \(+1.64046 q^{10}\) \(-5.13279 q^{11}\) \(-0.985760 q^{12}\) \(+6.08548 q^{13}\) \(+3.55255 q^{14}\) \(+1.61710 q^{15}\) \(+1.00000 q^{16}\) \(+2.28811 q^{17}\) \(+2.02828 q^{18}\) \(-2.08371 q^{19}\) \(-1.64046 q^{20}\) \(+3.50196 q^{21}\) \(+5.13279 q^{22}\) \(-1.00000 q^{23}\) \(+0.985760 q^{24}\) \(-2.30888 q^{25}\) \(-6.08548 q^{26}\) \(+4.95667 q^{27}\) \(-3.55255 q^{28}\) \(+4.26613 q^{29}\) \(-1.61710 q^{30}\) \(+7.60003 q^{31}\) \(-1.00000 q^{32}\) \(+5.05970 q^{33}\) \(-2.28811 q^{34}\) \(+5.82782 q^{35}\) \(-2.02828 q^{36}\) \(-10.6134 q^{37}\) \(+2.08371 q^{38}\) \(-5.99882 q^{39}\) \(+1.64046 q^{40}\) \(-3.54572 q^{41}\) \(-3.50196 q^{42}\) \(-1.68228 q^{43}\) \(-5.13279 q^{44}\) \(+3.32731 q^{45}\) \(+1.00000 q^{46}\) \(+3.20533 q^{47}\) \(-0.985760 q^{48}\) \(+5.62058 q^{49}\) \(+2.30888 q^{50}\) \(-2.25552 q^{51}\) \(+6.08548 q^{52}\) \(+6.59122 q^{53}\) \(-4.95667 q^{54}\) \(+8.42015 q^{55}\) \(+3.55255 q^{56}\) \(+2.05403 q^{57}\) \(-4.26613 q^{58}\) \(+6.75387 q^{59}\) \(+1.61710 q^{60}\) \(-0.344834 q^{61}\) \(-7.60003 q^{62}\) \(+7.20555 q^{63}\) \(+1.00000 q^{64}\) \(-9.98300 q^{65}\) \(-5.05970 q^{66}\) \(-0.234329 q^{67}\) \(+2.28811 q^{68}\) \(+0.985760 q^{69}\) \(-5.82782 q^{70}\) \(+14.0464 q^{71}\) \(+2.02828 q^{72}\) \(+9.01126 q^{73}\) \(+10.6134 q^{74}\) \(+2.27600 q^{75}\) \(-2.08371 q^{76}\) \(+18.2345 q^{77}\) \(+5.99882 q^{78}\) \(+0.193537 q^{79}\) \(-1.64046 q^{80}\) \(+1.19874 q^{81}\) \(+3.54572 q^{82}\) \(-4.78759 q^{83}\) \(+3.50196 q^{84}\) \(-3.75356 q^{85}\) \(+1.68228 q^{86}\) \(-4.20538 q^{87}\) \(+5.13279 q^{88}\) \(+10.7210 q^{89}\) \(-3.32731 q^{90}\) \(-21.6189 q^{91}\) \(-1.00000 q^{92}\) \(-7.49181 q^{93}\) \(-3.20533 q^{94}\) \(+3.41824 q^{95}\) \(+0.985760 q^{96}\) \(-7.40863 q^{97}\) \(-5.62058 q^{98}\) \(+10.4107 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(24q \) \(\mathstrut -\mathstrut 24q^{2} \) \(\mathstrut -\mathstrut q^{3} \) \(\mathstrut +\mathstrut 24q^{4} \) \(\mathstrut -\mathstrut q^{5} \) \(\mathstrut +\mathstrut q^{6} \) \(\mathstrut -\mathstrut 7q^{7} \) \(\mathstrut -\mathstrut 24q^{8} \) \(\mathstrut +\mathstrut 27q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(24q \) \(\mathstrut -\mathstrut 24q^{2} \) \(\mathstrut -\mathstrut q^{3} \) \(\mathstrut +\mathstrut 24q^{4} \) \(\mathstrut -\mathstrut q^{5} \) \(\mathstrut +\mathstrut q^{6} \) \(\mathstrut -\mathstrut 7q^{7} \) \(\mathstrut -\mathstrut 24q^{8} \) \(\mathstrut +\mathstrut 27q^{9} \) \(\mathstrut +\mathstrut q^{10} \) \(\mathstrut -\mathstrut 4q^{11} \) \(\mathstrut -\mathstrut q^{12} \) \(\mathstrut -\mathstrut 5q^{13} \) \(\mathstrut +\mathstrut 7q^{14} \) \(\mathstrut -\mathstrut 6q^{15} \) \(\mathstrut +\mathstrut 24q^{16} \) \(\mathstrut +\mathstrut 5q^{17} \) \(\mathstrut -\mathstrut 27q^{18} \) \(\mathstrut -\mathstrut 20q^{19} \) \(\mathstrut -\mathstrut q^{20} \) \(\mathstrut +\mathstrut 4q^{22} \) \(\mathstrut -\mathstrut 24q^{23} \) \(\mathstrut +\mathstrut q^{24} \) \(\mathstrut +\mathstrut q^{25} \) \(\mathstrut +\mathstrut 5q^{26} \) \(\mathstrut -\mathstrut q^{27} \) \(\mathstrut -\mathstrut 7q^{28} \) \(\mathstrut -\mathstrut 6q^{29} \) \(\mathstrut +\mathstrut 6q^{30} \) \(\mathstrut -\mathstrut 23q^{31} \) \(\mathstrut -\mathstrut 24q^{32} \) \(\mathstrut -\mathstrut 6q^{33} \) \(\mathstrut -\mathstrut 5q^{34} \) \(\mathstrut +\mathstrut 5q^{35} \) \(\mathstrut +\mathstrut 27q^{36} \) \(\mathstrut -\mathstrut 6q^{37} \) \(\mathstrut +\mathstrut 20q^{38} \) \(\mathstrut -\mathstrut 39q^{39} \) \(\mathstrut +\mathstrut q^{40} \) \(\mathstrut -\mathstrut q^{41} \) \(\mathstrut -\mathstrut 44q^{43} \) \(\mathstrut -\mathstrut 4q^{44} \) \(\mathstrut -\mathstrut 13q^{45} \) \(\mathstrut +\mathstrut 24q^{46} \) \(\mathstrut +\mathstrut 32q^{47} \) \(\mathstrut -\mathstrut q^{48} \) \(\mathstrut -\mathstrut 13q^{49} \) \(\mathstrut -\mathstrut q^{50} \) \(\mathstrut -\mathstrut 44q^{51} \) \(\mathstrut -\mathstrut 5q^{52} \) \(\mathstrut +\mathstrut 21q^{53} \) \(\mathstrut +\mathstrut q^{54} \) \(\mathstrut -\mathstrut 13q^{55} \) \(\mathstrut +\mathstrut 7q^{56} \) \(\mathstrut +\mathstrut 10q^{57} \) \(\mathstrut +\mathstrut 6q^{58} \) \(\mathstrut -\mathstrut 24q^{59} \) \(\mathstrut -\mathstrut 6q^{60} \) \(\mathstrut -\mathstrut 40q^{61} \) \(\mathstrut +\mathstrut 23q^{62} \) \(\mathstrut -\mathstrut 54q^{63} \) \(\mathstrut +\mathstrut 24q^{64} \) \(\mathstrut -\mathstrut 29q^{65} \) \(\mathstrut +\mathstrut 6q^{66} \) \(\mathstrut -\mathstrut 17q^{67} \) \(\mathstrut +\mathstrut 5q^{68} \) \(\mathstrut +\mathstrut q^{69} \) \(\mathstrut -\mathstrut 5q^{70} \) \(\mathstrut +\mathstrut 4q^{71} \) \(\mathstrut -\mathstrut 27q^{72} \) \(\mathstrut -\mathstrut 16q^{73} \) \(\mathstrut +\mathstrut 6q^{74} \) \(\mathstrut -\mathstrut 36q^{75} \) \(\mathstrut -\mathstrut 20q^{76} \) \(\mathstrut +\mathstrut 24q^{77} \) \(\mathstrut +\mathstrut 39q^{78} \) \(\mathstrut -\mathstrut 53q^{79} \) \(\mathstrut -\mathstrut q^{80} \) \(\mathstrut +\mathstrut 24q^{81} \) \(\mathstrut +\mathstrut q^{82} \) \(\mathstrut -\mathstrut 9q^{83} \) \(\mathstrut -\mathstrut 37q^{85} \) \(\mathstrut +\mathstrut 44q^{86} \) \(\mathstrut +\mathstrut 7q^{87} \) \(\mathstrut +\mathstrut 4q^{88} \) \(\mathstrut -\mathstrut 46q^{89} \) \(\mathstrut +\mathstrut 13q^{90} \) \(\mathstrut -\mathstrut 44q^{91} \) \(\mathstrut -\mathstrut 24q^{92} \) \(\mathstrut +\mathstrut 23q^{93} \) \(\mathstrut -\mathstrut 32q^{94} \) \(\mathstrut +\mathstrut 28q^{95} \) \(\mathstrut +\mathstrut q^{96} \) \(\mathstrut -\mathstrut 20q^{97} \) \(\mathstrut +\mathstrut 13q^{98} \) \(\mathstrut -\mathstrut 78q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) −0.985760 −0.569129 −0.284564 0.958657i \(-0.591849\pi\)
−0.284564 + 0.958657i \(0.591849\pi\)
\(4\) 1.00000 0.500000
\(5\) −1.64046 −0.733637 −0.366819 0.930292i \(-0.619553\pi\)
−0.366819 + 0.930292i \(0.619553\pi\)
\(6\) 0.985760 0.402435
\(7\) −3.55255 −1.34274 −0.671368 0.741124i \(-0.734293\pi\)
−0.671368 + 0.741124i \(0.734293\pi\)
\(8\) −1.00000 −0.353553
\(9\) −2.02828 −0.676093
\(10\) 1.64046 0.518760
\(11\) −5.13279 −1.54759 −0.773797 0.633433i \(-0.781645\pi\)
−0.773797 + 0.633433i \(0.781645\pi\)
\(12\) −0.985760 −0.284564
\(13\) 6.08548 1.68781 0.843904 0.536495i \(-0.180252\pi\)
0.843904 + 0.536495i \(0.180252\pi\)
\(14\) 3.55255 0.949458
\(15\) 1.61710 0.417534
\(16\) 1.00000 0.250000
\(17\) 2.28811 0.554948 0.277474 0.960733i \(-0.410503\pi\)
0.277474 + 0.960733i \(0.410503\pi\)
\(18\) 2.02828 0.478070
\(19\) −2.08371 −0.478035 −0.239017 0.971015i \(-0.576825\pi\)
−0.239017 + 0.971015i \(0.576825\pi\)
\(20\) −1.64046 −0.366819
\(21\) 3.50196 0.764190
\(22\) 5.13279 1.09431
\(23\) −1.00000 −0.208514
\(24\) 0.985760 0.201217
\(25\) −2.30888 −0.461776
\(26\) −6.08548 −1.19346
\(27\) 4.95667 0.953912
\(28\) −3.55255 −0.671368
\(29\) 4.26613 0.792201 0.396100 0.918207i \(-0.370363\pi\)
0.396100 + 0.918207i \(0.370363\pi\)
\(30\) −1.61710 −0.295241
\(31\) 7.60003 1.36501 0.682503 0.730883i \(-0.260891\pi\)
0.682503 + 0.730883i \(0.260891\pi\)
\(32\) −1.00000 −0.176777
\(33\) 5.05970 0.880781
\(34\) −2.28811 −0.392407
\(35\) 5.82782 0.985081
\(36\) −2.02828 −0.338046
\(37\) −10.6134 −1.74484 −0.872419 0.488759i \(-0.837450\pi\)
−0.872419 + 0.488759i \(0.837450\pi\)
\(38\) 2.08371 0.338022
\(39\) −5.99882 −0.960580
\(40\) 1.64046 0.259380
\(41\) −3.54572 −0.553748 −0.276874 0.960906i \(-0.589298\pi\)
−0.276874 + 0.960906i \(0.589298\pi\)
\(42\) −3.50196 −0.540364
\(43\) −1.68228 −0.256546 −0.128273 0.991739i \(-0.540943\pi\)
−0.128273 + 0.991739i \(0.540943\pi\)
\(44\) −5.13279 −0.773797
\(45\) 3.32731 0.496007
\(46\) 1.00000 0.147442
\(47\) 3.20533 0.467545 0.233773 0.972291i \(-0.424893\pi\)
0.233773 + 0.972291i \(0.424893\pi\)
\(48\) −0.985760 −0.142282
\(49\) 5.62058 0.802941
\(50\) 2.30888 0.326525
\(51\) −2.25552 −0.315837
\(52\) 6.08548 0.843904
\(53\) 6.59122 0.905374 0.452687 0.891669i \(-0.350465\pi\)
0.452687 + 0.891669i \(0.350465\pi\)
\(54\) −4.95667 −0.674518
\(55\) 8.42015 1.13537
\(56\) 3.55255 0.474729
\(57\) 2.05403 0.272063
\(58\) −4.26613 −0.560170
\(59\) 6.75387 0.879278 0.439639 0.898174i \(-0.355106\pi\)
0.439639 + 0.898174i \(0.355106\pi\)
\(60\) 1.61710 0.208767
\(61\) −0.344834 −0.0441514 −0.0220757 0.999756i \(-0.507027\pi\)
−0.0220757 + 0.999756i \(0.507027\pi\)
\(62\) −7.60003 −0.965205
\(63\) 7.20555 0.907814
\(64\) 1.00000 0.125000
\(65\) −9.98300 −1.23824
\(66\) −5.05970 −0.622806
\(67\) −0.234329 −0.0286278 −0.0143139 0.999898i \(-0.504556\pi\)
−0.0143139 + 0.999898i \(0.504556\pi\)
\(68\) 2.28811 0.277474
\(69\) 0.985760 0.118672
\(70\) −5.82782 −0.696558
\(71\) 14.0464 1.66700 0.833502 0.552517i \(-0.186332\pi\)
0.833502 + 0.552517i \(0.186332\pi\)
\(72\) 2.02828 0.239035
\(73\) 9.01126 1.05469 0.527344 0.849652i \(-0.323188\pi\)
0.527344 + 0.849652i \(0.323188\pi\)
\(74\) 10.6134 1.23379
\(75\) 2.27600 0.262810
\(76\) −2.08371 −0.239017
\(77\) 18.2345 2.07801
\(78\) 5.99882 0.679232
\(79\) 0.193537 0.0217746 0.0108873 0.999941i \(-0.496534\pi\)
0.0108873 + 0.999941i \(0.496534\pi\)
\(80\) −1.64046 −0.183409
\(81\) 1.19874 0.133194
\(82\) 3.54572 0.391559
\(83\) −4.78759 −0.525506 −0.262753 0.964863i \(-0.584630\pi\)
−0.262753 + 0.964863i \(0.584630\pi\)
\(84\) 3.50196 0.382095
\(85\) −3.75356 −0.407130
\(86\) 1.68228 0.181405
\(87\) −4.20538 −0.450864
\(88\) 5.13279 0.547157
\(89\) 10.7210 1.13643 0.568214 0.822881i \(-0.307635\pi\)
0.568214 + 0.822881i \(0.307635\pi\)
\(90\) −3.32731 −0.350730
\(91\) −21.6189 −2.26628
\(92\) −1.00000 −0.104257
\(93\) −7.49181 −0.776864
\(94\) −3.20533 −0.330604
\(95\) 3.41824 0.350704
\(96\) 0.985760 0.100609
\(97\) −7.40863 −0.752232 −0.376116 0.926573i \(-0.622741\pi\)
−0.376116 + 0.926573i \(0.622741\pi\)
\(98\) −5.62058 −0.567765
\(99\) 10.4107 1.04632
\(100\) −2.30888 −0.230888
\(101\) 0.881706 0.0877330 0.0438665 0.999037i \(-0.486032\pi\)
0.0438665 + 0.999037i \(0.486032\pi\)
\(102\) 2.25552 0.223330
\(103\) −10.8662 −1.07068 −0.535338 0.844638i \(-0.679816\pi\)
−0.535338 + 0.844638i \(0.679816\pi\)
\(104\) −6.08548 −0.596730
\(105\) −5.74483 −0.560638
\(106\) −6.59122 −0.640196
\(107\) 8.93158 0.863448 0.431724 0.902006i \(-0.357905\pi\)
0.431724 + 0.902006i \(0.357905\pi\)
\(108\) 4.95667 0.476956
\(109\) 4.23098 0.405255 0.202627 0.979256i \(-0.435052\pi\)
0.202627 + 0.979256i \(0.435052\pi\)
\(110\) −8.42015 −0.802830
\(111\) 10.4623 0.993037
\(112\) −3.55255 −0.335684
\(113\) 18.5824 1.74808 0.874041 0.485852i \(-0.161491\pi\)
0.874041 + 0.485852i \(0.161491\pi\)
\(114\) −2.05403 −0.192378
\(115\) 1.64046 0.152974
\(116\) 4.26613 0.396100
\(117\) −12.3430 −1.14111
\(118\) −6.75387 −0.621744
\(119\) −8.12861 −0.745148
\(120\) −1.61710 −0.147621
\(121\) 15.3455 1.39505
\(122\) 0.344834 0.0312198
\(123\) 3.49523 0.315154
\(124\) 7.60003 0.682503
\(125\) 11.9899 1.07241
\(126\) −7.20555 −0.641921
\(127\) −0.0874655 −0.00776131 −0.00388066 0.999992i \(-0.501235\pi\)
−0.00388066 + 0.999992i \(0.501235\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 1.65833 0.146008
\(130\) 9.98300 0.875567
\(131\) −1.00000 −0.0873704
\(132\) 5.05970 0.440390
\(133\) 7.40246 0.641875
\(134\) 0.234329 0.0202429
\(135\) −8.13124 −0.699826
\(136\) −2.28811 −0.196204
\(137\) −10.5557 −0.901835 −0.450918 0.892566i \(-0.648903\pi\)
−0.450918 + 0.892566i \(0.648903\pi\)
\(138\) −0.985760 −0.0839134
\(139\) −12.4274 −1.05407 −0.527037 0.849842i \(-0.676697\pi\)
−0.527037 + 0.849842i \(0.676697\pi\)
\(140\) 5.82782 0.492541
\(141\) −3.15968 −0.266093
\(142\) −14.0464 −1.17875
\(143\) −31.2355 −2.61204
\(144\) −2.02828 −0.169023
\(145\) −6.99843 −0.581188
\(146\) −9.01126 −0.745777
\(147\) −5.54055 −0.456977
\(148\) −10.6134 −0.872419
\(149\) 1.72873 0.141623 0.0708116 0.997490i \(-0.477441\pi\)
0.0708116 + 0.997490i \(0.477441\pi\)
\(150\) −2.27600 −0.185835
\(151\) −24.3176 −1.97894 −0.989469 0.144745i \(-0.953764\pi\)
−0.989469 + 0.144745i \(0.953764\pi\)
\(152\) 2.08371 0.169011
\(153\) −4.64092 −0.375196
\(154\) −18.2345 −1.46938
\(155\) −12.4676 −1.00142
\(156\) −5.99882 −0.480290
\(157\) −3.82661 −0.305397 −0.152698 0.988273i \(-0.548796\pi\)
−0.152698 + 0.988273i \(0.548796\pi\)
\(158\) −0.193537 −0.0153970
\(159\) −6.49736 −0.515274
\(160\) 1.64046 0.129690
\(161\) 3.55255 0.279980
\(162\) −1.19874 −0.0941821
\(163\) −14.1496 −1.10828 −0.554140 0.832424i \(-0.686953\pi\)
−0.554140 + 0.832424i \(0.686953\pi\)
\(164\) −3.54572 −0.276874
\(165\) −8.30025 −0.646173
\(166\) 4.78759 0.371589
\(167\) 6.10216 0.472199 0.236100 0.971729i \(-0.424131\pi\)
0.236100 + 0.971729i \(0.424131\pi\)
\(168\) −3.50196 −0.270182
\(169\) 24.0330 1.84869
\(170\) 3.75356 0.287885
\(171\) 4.22633 0.323196
\(172\) −1.68228 −0.128273
\(173\) −7.87980 −0.599090 −0.299545 0.954082i \(-0.596835\pi\)
−0.299545 + 0.954082i \(0.596835\pi\)
\(174\) 4.20538 0.318809
\(175\) 8.20241 0.620044
\(176\) −5.13279 −0.386899
\(177\) −6.65769 −0.500423
\(178\) −10.7210 −0.803576
\(179\) 25.4501 1.90223 0.951115 0.308838i \(-0.0999401\pi\)
0.951115 + 0.308838i \(0.0999401\pi\)
\(180\) 3.32731 0.248003
\(181\) −14.3388 −1.06580 −0.532899 0.846179i \(-0.678897\pi\)
−0.532899 + 0.846179i \(0.678897\pi\)
\(182\) 21.6189 1.60250
\(183\) 0.339923 0.0251278
\(184\) 1.00000 0.0737210
\(185\) 17.4109 1.28008
\(186\) 7.49181 0.549326
\(187\) −11.7444 −0.858834
\(188\) 3.20533 0.233773
\(189\) −17.6088 −1.28085
\(190\) −3.41824 −0.247985
\(191\) −15.0122 −1.08624 −0.543122 0.839654i \(-0.682758\pi\)
−0.543122 + 0.839654i \(0.682758\pi\)
\(192\) −0.985760 −0.0711411
\(193\) 16.1288 1.16098 0.580489 0.814268i \(-0.302861\pi\)
0.580489 + 0.814268i \(0.302861\pi\)
\(194\) 7.40863 0.531908
\(195\) 9.84084 0.704717
\(196\) 5.62058 0.401470
\(197\) 12.3743 0.881629 0.440815 0.897598i \(-0.354690\pi\)
0.440815 + 0.897598i \(0.354690\pi\)
\(198\) −10.4107 −0.739858
\(199\) −6.41266 −0.454581 −0.227291 0.973827i \(-0.572987\pi\)
−0.227291 + 0.973827i \(0.572987\pi\)
\(200\) 2.30888 0.163263
\(201\) 0.230992 0.0162929
\(202\) −0.881706 −0.0620366
\(203\) −15.1556 −1.06372
\(204\) −2.25552 −0.157918
\(205\) 5.81662 0.406250
\(206\) 10.8662 0.757082
\(207\) 2.02828 0.140975
\(208\) 6.08548 0.421952
\(209\) 10.6952 0.739804
\(210\) 5.74483 0.396431
\(211\) 23.4824 1.61660 0.808298 0.588773i \(-0.200389\pi\)
0.808298 + 0.588773i \(0.200389\pi\)
\(212\) 6.59122 0.452687
\(213\) −13.8464 −0.948740
\(214\) −8.93158 −0.610550
\(215\) 2.75973 0.188212
\(216\) −4.95667 −0.337259
\(217\) −26.9995 −1.83284
\(218\) −4.23098 −0.286558
\(219\) −8.88294 −0.600254
\(220\) 8.42015 0.567687
\(221\) 13.9242 0.936645
\(222\) −10.4623 −0.702183
\(223\) −20.7187 −1.38743 −0.693713 0.720251i \(-0.744026\pi\)
−0.693713 + 0.720251i \(0.744026\pi\)
\(224\) 3.55255 0.237364
\(225\) 4.68305 0.312204
\(226\) −18.5824 −1.23608
\(227\) −19.2788 −1.27958 −0.639790 0.768550i \(-0.720979\pi\)
−0.639790 + 0.768550i \(0.720979\pi\)
\(228\) 2.05403 0.136032
\(229\) −17.7188 −1.17089 −0.585447 0.810711i \(-0.699081\pi\)
−0.585447 + 0.810711i \(0.699081\pi\)
\(230\) −1.64046 −0.108169
\(231\) −17.9748 −1.18266
\(232\) −4.26613 −0.280085
\(233\) −11.6904 −0.765863 −0.382931 0.923777i \(-0.625085\pi\)
−0.382931 + 0.923777i \(0.625085\pi\)
\(234\) 12.3430 0.806889
\(235\) −5.25822 −0.343009
\(236\) 6.75387 0.439639
\(237\) −0.190781 −0.0123926
\(238\) 8.12861 0.526899
\(239\) −21.1698 −1.36936 −0.684680 0.728844i \(-0.740058\pi\)
−0.684680 + 0.728844i \(0.740058\pi\)
\(240\) 1.61710 0.104384
\(241\) 26.1252 1.68287 0.841435 0.540358i \(-0.181711\pi\)
0.841435 + 0.540358i \(0.181711\pi\)
\(242\) −15.3455 −0.986449
\(243\) −16.0517 −1.02972
\(244\) −0.344834 −0.0220757
\(245\) −9.22036 −0.589067
\(246\) −3.49523 −0.222847
\(247\) −12.6803 −0.806831
\(248\) −7.60003 −0.482603
\(249\) 4.71941 0.299081
\(250\) −11.9899 −0.758311
\(251\) −24.3231 −1.53526 −0.767630 0.640893i \(-0.778564\pi\)
−0.767630 + 0.640893i \(0.778564\pi\)
\(252\) 7.20555 0.453907
\(253\) 5.13279 0.322696
\(254\) 0.0874655 0.00548808
\(255\) 3.70010 0.231709
\(256\) 1.00000 0.0625000
\(257\) 20.3447 1.26907 0.634534 0.772895i \(-0.281192\pi\)
0.634534 + 0.772895i \(0.281192\pi\)
\(258\) −1.65833 −0.103243
\(259\) 37.7047 2.34286
\(260\) −9.98300 −0.619119
\(261\) −8.65290 −0.535601
\(262\) 1.00000 0.0617802
\(263\) −12.0050 −0.740258 −0.370129 0.928980i \(-0.620686\pi\)
−0.370129 + 0.928980i \(0.620686\pi\)
\(264\) −5.05970 −0.311403
\(265\) −10.8127 −0.664216
\(266\) −7.40246 −0.453874
\(267\) −10.5684 −0.646773
\(268\) −0.234329 −0.0143139
\(269\) 29.4419 1.79510 0.897551 0.440911i \(-0.145345\pi\)
0.897551 + 0.440911i \(0.145345\pi\)
\(270\) 8.13124 0.494851
\(271\) −22.0660 −1.34041 −0.670206 0.742175i \(-0.733794\pi\)
−0.670206 + 0.742175i \(0.733794\pi\)
\(272\) 2.28811 0.138737
\(273\) 21.3111 1.28981
\(274\) 10.5557 0.637694
\(275\) 11.8510 0.714643
\(276\) 0.985760 0.0593358
\(277\) −22.2051 −1.33418 −0.667088 0.744979i \(-0.732460\pi\)
−0.667088 + 0.744979i \(0.732460\pi\)
\(278\) 12.4274 0.745343
\(279\) −15.4150 −0.922870
\(280\) −5.82782 −0.348279
\(281\) −19.5238 −1.16469 −0.582346 0.812941i \(-0.697865\pi\)
−0.582346 + 0.812941i \(0.697865\pi\)
\(282\) 3.15968 0.188156
\(283\) −4.11990 −0.244903 −0.122451 0.992475i \(-0.539076\pi\)
−0.122451 + 0.992475i \(0.539076\pi\)
\(284\) 14.0464 0.833502
\(285\) −3.36957 −0.199596
\(286\) 31.2355 1.84699
\(287\) 12.5963 0.743537
\(288\) 2.02828 0.119517
\(289\) −11.7646 −0.692033
\(290\) 6.99843 0.410962
\(291\) 7.30313 0.428117
\(292\) 9.01126 0.527344
\(293\) 8.91211 0.520651 0.260325 0.965521i \(-0.416170\pi\)
0.260325 + 0.965521i \(0.416170\pi\)
\(294\) 5.54055 0.323131
\(295\) −11.0795 −0.645071
\(296\) 10.6134 0.616893
\(297\) −25.4416 −1.47627
\(298\) −1.72873 −0.100143
\(299\) −6.08548 −0.351932
\(300\) 2.27600 0.131405
\(301\) 5.97639 0.344474
\(302\) 24.3176 1.39932
\(303\) −0.869150 −0.0499314
\(304\) −2.08371 −0.119509
\(305\) 0.565687 0.0323911
\(306\) 4.64092 0.265304
\(307\) 21.3669 1.21948 0.609738 0.792603i \(-0.291275\pi\)
0.609738 + 0.792603i \(0.291275\pi\)
\(308\) 18.2345 1.03901
\(309\) 10.7114 0.609353
\(310\) 12.4676 0.708110
\(311\) 7.96552 0.451683 0.225841 0.974164i \(-0.427487\pi\)
0.225841 + 0.974164i \(0.427487\pi\)
\(312\) 5.99882 0.339616
\(313\) 23.7098 1.34016 0.670078 0.742290i \(-0.266261\pi\)
0.670078 + 0.742290i \(0.266261\pi\)
\(314\) 3.82661 0.215948
\(315\) −11.8204 −0.666006
\(316\) 0.193537 0.0108873
\(317\) −14.1143 −0.792739 −0.396370 0.918091i \(-0.629730\pi\)
−0.396370 + 0.918091i \(0.629730\pi\)
\(318\) 6.49736 0.364354
\(319\) −21.8972 −1.22601
\(320\) −1.64046 −0.0917047
\(321\) −8.80439 −0.491413
\(322\) −3.55255 −0.197976
\(323\) −4.76774 −0.265284
\(324\) 1.19874 0.0665968
\(325\) −14.0506 −0.779390
\(326\) 14.1496 0.783672
\(327\) −4.17073 −0.230642
\(328\) 3.54572 0.195779
\(329\) −11.3871 −0.627790
\(330\) 8.30025 0.456914
\(331\) −18.0011 −0.989430 −0.494715 0.869055i \(-0.664728\pi\)
−0.494715 + 0.869055i \(0.664728\pi\)
\(332\) −4.78759 −0.262753
\(333\) 21.5270 1.17967
\(334\) −6.10216 −0.333895
\(335\) 0.384408 0.0210024
\(336\) 3.50196 0.191047
\(337\) 31.5337 1.71775 0.858875 0.512186i \(-0.171164\pi\)
0.858875 + 0.512186i \(0.171164\pi\)
\(338\) −24.0330 −1.30722
\(339\) −18.3178 −0.994884
\(340\) −3.75356 −0.203565
\(341\) −39.0094 −2.11248
\(342\) −4.22633 −0.228534
\(343\) 4.90044 0.264599
\(344\) 1.68228 0.0907027
\(345\) −1.61710 −0.0870619
\(346\) 7.87980 0.423620
\(347\) 24.4268 1.31130 0.655650 0.755065i \(-0.272395\pi\)
0.655650 + 0.755065i \(0.272395\pi\)
\(348\) −4.20538 −0.225432
\(349\) −16.3111 −0.873113 −0.436557 0.899677i \(-0.643802\pi\)
−0.436557 + 0.899677i \(0.643802\pi\)
\(350\) −8.20241 −0.438437
\(351\) 30.1637 1.61002
\(352\) 5.13279 0.273579
\(353\) −15.4915 −0.824528 −0.412264 0.911064i \(-0.635262\pi\)
−0.412264 + 0.911064i \(0.635262\pi\)
\(354\) 6.65769 0.353852
\(355\) −23.0426 −1.22298
\(356\) 10.7210 0.568214
\(357\) 8.01285 0.424085
\(358\) −25.4501 −1.34508
\(359\) 3.84703 0.203038 0.101519 0.994834i \(-0.467630\pi\)
0.101519 + 0.994834i \(0.467630\pi\)
\(360\) −3.32731 −0.175365
\(361\) −14.6582 −0.771483
\(362\) 14.3388 0.753633
\(363\) −15.1270 −0.793962
\(364\) −21.6189 −1.13314
\(365\) −14.7826 −0.773759
\(366\) −0.339923 −0.0177681
\(367\) −24.9848 −1.30419 −0.652097 0.758135i \(-0.726111\pi\)
−0.652097 + 0.758135i \(0.726111\pi\)
\(368\) −1.00000 −0.0521286
\(369\) 7.19170 0.374385
\(370\) −17.4109 −0.905152
\(371\) −23.4156 −1.21568
\(372\) −7.49181 −0.388432
\(373\) 6.33796 0.328167 0.164084 0.986446i \(-0.447533\pi\)
0.164084 + 0.986446i \(0.447533\pi\)
\(374\) 11.7444 0.607287
\(375\) −11.8192 −0.610341
\(376\) −3.20533 −0.165302
\(377\) 25.9614 1.33708
\(378\) 17.6088 0.905700
\(379\) 16.8692 0.866513 0.433256 0.901271i \(-0.357364\pi\)
0.433256 + 0.901271i \(0.357364\pi\)
\(380\) 3.41824 0.175352
\(381\) 0.0862200 0.00441719
\(382\) 15.0122 0.768091
\(383\) 16.0096 0.818051 0.409025 0.912523i \(-0.365869\pi\)
0.409025 + 0.912523i \(0.365869\pi\)
\(384\) 0.985760 0.0503043
\(385\) −29.9130 −1.52451
\(386\) −16.1288 −0.820935
\(387\) 3.41214 0.173449
\(388\) −7.40863 −0.376116
\(389\) 18.0492 0.915130 0.457565 0.889176i \(-0.348722\pi\)
0.457565 + 0.889176i \(0.348722\pi\)
\(390\) −9.84084 −0.498310
\(391\) −2.28811 −0.115715
\(392\) −5.62058 −0.283882
\(393\) 0.985760 0.0497250
\(394\) −12.3743 −0.623406
\(395\) −0.317491 −0.0159747
\(396\) 10.4107 0.523159
\(397\) 37.7833 1.89629 0.948146 0.317836i \(-0.102956\pi\)
0.948146 + 0.317836i \(0.102956\pi\)
\(398\) 6.41266 0.321438
\(399\) −7.29705 −0.365309
\(400\) −2.30888 −0.115444
\(401\) −6.36284 −0.317745 −0.158872 0.987299i \(-0.550786\pi\)
−0.158872 + 0.987299i \(0.550786\pi\)
\(402\) −0.230992 −0.0115208
\(403\) 46.2498 2.30387
\(404\) 0.881706 0.0438665
\(405\) −1.96649 −0.0977158
\(406\) 15.1556 0.752161
\(407\) 54.4765 2.70030
\(408\) 2.25552 0.111665
\(409\) −5.68752 −0.281230 −0.140615 0.990064i \(-0.544908\pi\)
−0.140615 + 0.990064i \(0.544908\pi\)
\(410\) −5.81662 −0.287262
\(411\) 10.4054 0.513260
\(412\) −10.8662 −0.535338
\(413\) −23.9934 −1.18064
\(414\) −2.02828 −0.0996844
\(415\) 7.85386 0.385531
\(416\) −6.08548 −0.298365
\(417\) 12.2504 0.599904
\(418\) −10.6952 −0.523121
\(419\) −33.4220 −1.63277 −0.816385 0.577508i \(-0.804025\pi\)
−0.816385 + 0.577508i \(0.804025\pi\)
\(420\) −5.74483 −0.280319
\(421\) 12.4592 0.607226 0.303613 0.952795i \(-0.401807\pi\)
0.303613 + 0.952795i \(0.401807\pi\)
\(422\) −23.4824 −1.14311
\(423\) −6.50129 −0.316104
\(424\) −6.59122 −0.320098
\(425\) −5.28297 −0.256262
\(426\) 13.8464 0.670860
\(427\) 1.22504 0.0592837
\(428\) 8.93158 0.431724
\(429\) 30.7907 1.48659
\(430\) −2.75973 −0.133086
\(431\) −23.5076 −1.13232 −0.566162 0.824294i \(-0.691572\pi\)
−0.566162 + 0.824294i \(0.691572\pi\)
\(432\) 4.95667 0.238478
\(433\) 20.3601 0.978445 0.489222 0.872159i \(-0.337281\pi\)
0.489222 + 0.872159i \(0.337281\pi\)
\(434\) 26.9995 1.29602
\(435\) 6.89877 0.330771
\(436\) 4.23098 0.202627
\(437\) 2.08371 0.0996772
\(438\) 8.88294 0.424443
\(439\) 5.62864 0.268640 0.134320 0.990938i \(-0.457115\pi\)
0.134320 + 0.990938i \(0.457115\pi\)
\(440\) −8.42015 −0.401415
\(441\) −11.4001 −0.542862
\(442\) −13.9242 −0.662308
\(443\) 5.63390 0.267675 0.133837 0.991003i \(-0.457270\pi\)
0.133837 + 0.991003i \(0.457270\pi\)
\(444\) 10.4623 0.496519
\(445\) −17.5875 −0.833726
\(446\) 20.7187 0.981058
\(447\) −1.70412 −0.0806019
\(448\) −3.55255 −0.167842
\(449\) −19.0253 −0.897858 −0.448929 0.893567i \(-0.648194\pi\)
−0.448929 + 0.893567i \(0.648194\pi\)
\(450\) −4.68305 −0.220761
\(451\) 18.1994 0.856977
\(452\) 18.5824 0.874041
\(453\) 23.9713 1.12627
\(454\) 19.2788 0.904800
\(455\) 35.4651 1.66263
\(456\) −2.05403 −0.0961889
\(457\) −2.64264 −0.123617 −0.0618087 0.998088i \(-0.519687\pi\)
−0.0618087 + 0.998088i \(0.519687\pi\)
\(458\) 17.7188 0.827947
\(459\) 11.3414 0.529371
\(460\) 1.64046 0.0764870
\(461\) 21.7083 1.01106 0.505529 0.862810i \(-0.331297\pi\)
0.505529 + 0.862810i \(0.331297\pi\)
\(462\) 17.9748 0.836264
\(463\) −2.85097 −0.132496 −0.0662478 0.997803i \(-0.521103\pi\)
−0.0662478 + 0.997803i \(0.521103\pi\)
\(464\) 4.26613 0.198050
\(465\) 12.2900 0.569937
\(466\) 11.6904 0.541547
\(467\) −22.7892 −1.05456 −0.527280 0.849692i \(-0.676788\pi\)
−0.527280 + 0.849692i \(0.676788\pi\)
\(468\) −12.3430 −0.570557
\(469\) 0.832464 0.0384396
\(470\) 5.25822 0.242544
\(471\) 3.77212 0.173810
\(472\) −6.75387 −0.310872
\(473\) 8.63481 0.397029
\(474\) 0.190781 0.00876287
\(475\) 4.81103 0.220745
\(476\) −8.12861 −0.372574
\(477\) −13.3688 −0.612117
\(478\) 21.1698 0.968284
\(479\) −21.3814 −0.976943 −0.488472 0.872580i \(-0.662445\pi\)
−0.488472 + 0.872580i \(0.662445\pi\)
\(480\) −1.61710 −0.0738103
\(481\) −64.5878 −2.94495
\(482\) −26.1252 −1.18997
\(483\) −3.50196 −0.159345
\(484\) 15.3455 0.697524
\(485\) 12.1536 0.551865
\(486\) 16.0517 0.728120
\(487\) 16.1368 0.731229 0.365615 0.930766i \(-0.380859\pi\)
0.365615 + 0.930766i \(0.380859\pi\)
\(488\) 0.344834 0.0156099
\(489\) 13.9481 0.630754
\(490\) 9.22036 0.416533
\(491\) −18.9922 −0.857108 −0.428554 0.903516i \(-0.640977\pi\)
−0.428554 + 0.903516i \(0.640977\pi\)
\(492\) 3.49523 0.157577
\(493\) 9.76137 0.439630
\(494\) 12.6803 0.570516
\(495\) −17.0784 −0.767617
\(496\) 7.60003 0.341252
\(497\) −49.9006 −2.23835
\(498\) −4.71941 −0.211482
\(499\) −38.0897 −1.70513 −0.852565 0.522622i \(-0.824954\pi\)
−0.852565 + 0.522622i \(0.824954\pi\)
\(500\) 11.9899 0.536207
\(501\) −6.01526 −0.268742
\(502\) 24.3231 1.08559
\(503\) −21.4949 −0.958410 −0.479205 0.877703i \(-0.659075\pi\)
−0.479205 + 0.877703i \(0.659075\pi\)
\(504\) −7.20555 −0.320961
\(505\) −1.44641 −0.0643642
\(506\) −5.13279 −0.228180
\(507\) −23.6908 −1.05214
\(508\) −0.0874655 −0.00388066
\(509\) −2.44766 −0.108491 −0.0542453 0.998528i \(-0.517275\pi\)
−0.0542453 + 0.998528i \(0.517275\pi\)
\(510\) −3.70010 −0.163843
\(511\) −32.0129 −1.41617
\(512\) −1.00000 −0.0441942
\(513\) −10.3283 −0.456003
\(514\) −20.3447 −0.897366
\(515\) 17.8256 0.785488
\(516\) 1.65833 0.0730038
\(517\) −16.4523 −0.723570
\(518\) −37.7047 −1.65665
\(519\) 7.76759 0.340959
\(520\) 9.98300 0.437783
\(521\) 35.8666 1.57134 0.785671 0.618644i \(-0.212318\pi\)
0.785671 + 0.618644i \(0.212318\pi\)
\(522\) 8.65290 0.378727
\(523\) 5.49231 0.240162 0.120081 0.992764i \(-0.461685\pi\)
0.120081 + 0.992764i \(0.461685\pi\)
\(524\) −1.00000 −0.0436852
\(525\) −8.08561 −0.352885
\(526\) 12.0050 0.523441
\(527\) 17.3897 0.757507
\(528\) 5.05970 0.220195
\(529\) 1.00000 0.0434783
\(530\) 10.8127 0.469672
\(531\) −13.6987 −0.594474
\(532\) 7.40246 0.320937
\(533\) −21.5774 −0.934620
\(534\) 10.5684 0.457338
\(535\) −14.6519 −0.633458
\(536\) 0.234329 0.0101215
\(537\) −25.0877 −1.08261
\(538\) −29.4419 −1.26933
\(539\) −28.8493 −1.24263
\(540\) −8.13124 −0.349913
\(541\) −40.6653 −1.74834 −0.874168 0.485623i \(-0.838593\pi\)
−0.874168 + 0.485623i \(0.838593\pi\)
\(542\) 22.0660 0.947815
\(543\) 14.1347 0.606576
\(544\) −2.28811 −0.0981018
\(545\) −6.94077 −0.297310
\(546\) −21.3111 −0.912030
\(547\) −5.95639 −0.254677 −0.127339 0.991859i \(-0.540643\pi\)
−0.127339 + 0.991859i \(0.540643\pi\)
\(548\) −10.5557 −0.450918
\(549\) 0.699418 0.0298504
\(550\) −11.8510 −0.505329
\(551\) −8.88936 −0.378700
\(552\) −0.985760 −0.0419567
\(553\) −0.687550 −0.0292376
\(554\) 22.2051 0.943405
\(555\) −17.1630 −0.728529
\(556\) −12.4274 −0.527037
\(557\) −4.62002 −0.195757 −0.0978783 0.995198i \(-0.531206\pi\)
−0.0978783 + 0.995198i \(0.531206\pi\)
\(558\) 15.4150 0.652568
\(559\) −10.2375 −0.433000
\(560\) 5.82782 0.246270
\(561\) 11.5771 0.488787
\(562\) 19.5238 0.823561
\(563\) 6.22721 0.262445 0.131223 0.991353i \(-0.458110\pi\)
0.131223 + 0.991353i \(0.458110\pi\)
\(564\) −3.15968 −0.133047
\(565\) −30.4837 −1.28246
\(566\) 4.11990 0.173172
\(567\) −4.25859 −0.178844
\(568\) −14.0464 −0.589375
\(569\) 14.5551 0.610182 0.305091 0.952323i \(-0.401313\pi\)
0.305091 + 0.952323i \(0.401313\pi\)
\(570\) 3.36957 0.141136
\(571\) 7.89802 0.330522 0.165261 0.986250i \(-0.447153\pi\)
0.165261 + 0.986250i \(0.447153\pi\)
\(572\) −31.2355 −1.30602
\(573\) 14.7984 0.618213
\(574\) −12.5963 −0.525760
\(575\) 2.30888 0.0962870
\(576\) −2.02828 −0.0845116
\(577\) −25.7040 −1.07007 −0.535037 0.844829i \(-0.679702\pi\)
−0.535037 + 0.844829i \(0.679702\pi\)
\(578\) 11.7646 0.489341
\(579\) −15.8991 −0.660746
\(580\) −6.99843 −0.290594
\(581\) 17.0081 0.705616
\(582\) −7.30313 −0.302724
\(583\) −33.8314 −1.40115
\(584\) −9.01126 −0.372889
\(585\) 20.2483 0.837164
\(586\) −8.91211 −0.368156
\(587\) −8.42235 −0.347627 −0.173814 0.984779i \(-0.555609\pi\)
−0.173814 + 0.984779i \(0.555609\pi\)
\(588\) −5.54055 −0.228488
\(589\) −15.8362 −0.652521
\(590\) 11.0795 0.456134
\(591\) −12.1980 −0.501761
\(592\) −10.6134 −0.436209
\(593\) 9.69390 0.398081 0.199040 0.979991i \(-0.436218\pi\)
0.199040 + 0.979991i \(0.436218\pi\)
\(594\) 25.4416 1.04388
\(595\) 13.3347 0.546668
\(596\) 1.72873 0.0708116
\(597\) 6.32134 0.258715
\(598\) 6.08548 0.248854
\(599\) 11.4666 0.468511 0.234256 0.972175i \(-0.424735\pi\)
0.234256 + 0.972175i \(0.424735\pi\)
\(600\) −2.27600 −0.0929174
\(601\) −43.9080 −1.79105 −0.895523 0.445015i \(-0.853198\pi\)
−0.895523 + 0.445015i \(0.853198\pi\)
\(602\) −5.97639 −0.243580
\(603\) 0.475284 0.0193551
\(604\) −24.3176 −0.989469
\(605\) −25.1738 −1.02346
\(606\) 0.869150 0.0353068
\(607\) −43.3596 −1.75991 −0.879957 0.475053i \(-0.842429\pi\)
−0.879957 + 0.475053i \(0.842429\pi\)
\(608\) 2.08371 0.0845054
\(609\) 14.9398 0.605392
\(610\) −0.565687 −0.0229040
\(611\) 19.5059 0.789126
\(612\) −4.64092 −0.187598
\(613\) 15.0969 0.609757 0.304878 0.952391i \(-0.401384\pi\)
0.304878 + 0.952391i \(0.401384\pi\)
\(614\) −21.3669 −0.862300
\(615\) −5.73379 −0.231209
\(616\) −18.2345 −0.734688
\(617\) −9.96338 −0.401110 −0.200555 0.979682i \(-0.564275\pi\)
−0.200555 + 0.979682i \(0.564275\pi\)
\(618\) −10.7114 −0.430877
\(619\) −36.5213 −1.46791 −0.733957 0.679196i \(-0.762329\pi\)
−0.733957 + 0.679196i \(0.762329\pi\)
\(620\) −12.4676 −0.500710
\(621\) −4.95667 −0.198904
\(622\) −7.96552 −0.319388
\(623\) −38.0870 −1.52592
\(624\) −5.99882 −0.240145
\(625\) −8.12466 −0.324986
\(626\) −23.7098 −0.947634
\(627\) −10.5429 −0.421044
\(628\) −3.82661 −0.152698
\(629\) −24.2847 −0.968293
\(630\) 11.8204 0.470937
\(631\) 46.3173 1.84386 0.921932 0.387352i \(-0.126610\pi\)
0.921932 + 0.387352i \(0.126610\pi\)
\(632\) −0.193537 −0.00769849
\(633\) −23.1480 −0.920051
\(634\) 14.1143 0.560551
\(635\) 0.143484 0.00569399
\(636\) −6.49736 −0.257637
\(637\) 34.2039 1.35521
\(638\) 21.8972 0.866917
\(639\) −28.4900 −1.12705
\(640\) 1.64046 0.0648450
\(641\) 32.5598 1.28604 0.643018 0.765851i \(-0.277682\pi\)
0.643018 + 0.765851i \(0.277682\pi\)
\(642\) 8.80439 0.347482
\(643\) −5.15697 −0.203371 −0.101685 0.994817i \(-0.532424\pi\)
−0.101685 + 0.994817i \(0.532424\pi\)
\(644\) 3.55255 0.139990
\(645\) −2.72043 −0.107117
\(646\) 4.76774 0.187584
\(647\) 27.1466 1.06724 0.533622 0.845723i \(-0.320831\pi\)
0.533622 + 0.845723i \(0.320831\pi\)
\(648\) −1.19874 −0.0470911
\(649\) −34.6662 −1.36077
\(650\) 14.0506 0.551112
\(651\) 26.6150 1.04312
\(652\) −14.1496 −0.554140
\(653\) 11.5809 0.453196 0.226598 0.973988i \(-0.427240\pi\)
0.226598 + 0.973988i \(0.427240\pi\)
\(654\) 4.17073 0.163089
\(655\) 1.64046 0.0640982
\(656\) −3.54572 −0.138437
\(657\) −18.2773 −0.713067
\(658\) 11.3871 0.443914
\(659\) 9.86372 0.384236 0.192118 0.981372i \(-0.438464\pi\)
0.192118 + 0.981372i \(0.438464\pi\)
\(660\) −8.30025 −0.323087
\(661\) −36.1062 −1.40437 −0.702184 0.711996i \(-0.747792\pi\)
−0.702184 + 0.711996i \(0.747792\pi\)
\(662\) 18.0011 0.699633
\(663\) −13.7259 −0.533071
\(664\) 4.78759 0.185794
\(665\) −12.1435 −0.470903
\(666\) −21.5270 −0.834154
\(667\) −4.26613 −0.165185
\(668\) 6.10216 0.236100
\(669\) 20.4237 0.789624
\(670\) −0.384408 −0.0148510
\(671\) 1.76996 0.0683285
\(672\) −3.50196 −0.135091
\(673\) −43.2743 −1.66810 −0.834052 0.551686i \(-0.813985\pi\)
−0.834052 + 0.551686i \(0.813985\pi\)
\(674\) −31.5337 −1.21463
\(675\) −11.4444 −0.440494
\(676\) 24.0330 0.924347
\(677\) −6.12452 −0.235384 −0.117692 0.993050i \(-0.537550\pi\)
−0.117692 + 0.993050i \(0.537550\pi\)
\(678\) 18.3178 0.703489
\(679\) 26.3195 1.01005
\(680\) 3.75356 0.143942
\(681\) 19.0043 0.728246
\(682\) 39.0094 1.49375
\(683\) −4.93016 −0.188647 −0.0943237 0.995542i \(-0.530069\pi\)
−0.0943237 + 0.995542i \(0.530069\pi\)
\(684\) 4.22633 0.161598
\(685\) 17.3162 0.661620
\(686\) −4.90044 −0.187100
\(687\) 17.4665 0.666389
\(688\) −1.68228 −0.0641365
\(689\) 40.1107 1.52810
\(690\) 1.61710 0.0615620
\(691\) 1.95568 0.0743977 0.0371989 0.999308i \(-0.488156\pi\)
0.0371989 + 0.999308i \(0.488156\pi\)
\(692\) −7.87980 −0.299545
\(693\) −36.9846 −1.40493
\(694\) −24.4268 −0.927229
\(695\) 20.3866 0.773309
\(696\) 4.20538 0.159405
\(697\) −8.11298 −0.307301
\(698\) 16.3111 0.617384
\(699\) 11.5239 0.435875
\(700\) 8.20241 0.310022
\(701\) −27.7314 −1.04740 −0.523701 0.851902i \(-0.675449\pi\)
−0.523701 + 0.851902i \(0.675449\pi\)
\(702\) −30.1637 −1.13846
\(703\) 22.1153 0.834093
\(704\) −5.13279 −0.193449
\(705\) 5.18334 0.195216
\(706\) 15.4915 0.583030
\(707\) −3.13230 −0.117802
\(708\) −6.65769 −0.250211
\(709\) 42.6173 1.60053 0.800263 0.599649i \(-0.204693\pi\)
0.800263 + 0.599649i \(0.204693\pi\)
\(710\) 23.0426 0.864775
\(711\) −0.392547 −0.0147217
\(712\) −10.7210 −0.401788
\(713\) −7.60003 −0.284623
\(714\) −8.01285 −0.299874
\(715\) 51.2406 1.91629
\(716\) 25.4501 0.951115
\(717\) 20.8683 0.779342
\(718\) −3.84703 −0.143570
\(719\) 0.139679 0.00520916 0.00260458 0.999997i \(-0.499171\pi\)
0.00260458 + 0.999997i \(0.499171\pi\)
\(720\) 3.32731 0.124002
\(721\) 38.6026 1.43764
\(722\) 14.6582 0.545521
\(723\) −25.7532 −0.957770
\(724\) −14.3388 −0.532899
\(725\) −9.84999 −0.365820
\(726\) 15.1270 0.561416
\(727\) 4.07709 0.151211 0.0756055 0.997138i \(-0.475911\pi\)
0.0756055 + 0.997138i \(0.475911\pi\)
\(728\) 21.6189 0.801251
\(729\) 12.2269 0.452848
\(730\) 14.7826 0.547130
\(731\) −3.84925 −0.142370
\(732\) 0.339923 0.0125639
\(733\) 16.0534 0.592946 0.296473 0.955041i \(-0.404189\pi\)
0.296473 + 0.955041i \(0.404189\pi\)
\(734\) 24.9848 0.922205
\(735\) 9.08906 0.335255
\(736\) 1.00000 0.0368605
\(737\) 1.20276 0.0443043
\(738\) −7.19170 −0.264730
\(739\) 37.7983 1.39043 0.695217 0.718800i \(-0.255308\pi\)
0.695217 + 0.718800i \(0.255308\pi\)
\(740\) 17.4109 0.640039
\(741\) 12.4998 0.459191
\(742\) 23.4156 0.859615
\(743\) 18.1861 0.667184 0.333592 0.942718i \(-0.391739\pi\)
0.333592 + 0.942718i \(0.391739\pi\)
\(744\) 7.49181 0.274663
\(745\) −2.83592 −0.103900
\(746\) −6.33796 −0.232049
\(747\) 9.71056 0.355291
\(748\) −11.7444 −0.429417
\(749\) −31.7298 −1.15938
\(750\) 11.8192 0.431577
\(751\) −21.2332 −0.774811 −0.387406 0.921909i \(-0.626629\pi\)
−0.387406 + 0.921909i \(0.626629\pi\)
\(752\) 3.20533 0.116886
\(753\) 23.9767 0.873761
\(754\) −25.9614 −0.945460
\(755\) 39.8921 1.45182
\(756\) −17.6088 −0.640426
\(757\) 14.2379 0.517484 0.258742 0.965947i \(-0.416692\pi\)
0.258742 + 0.965947i \(0.416692\pi\)
\(758\) −16.8692 −0.612717
\(759\) −5.05970 −0.183655
\(760\) −3.41824 −0.123993
\(761\) −28.5909 −1.03642 −0.518210 0.855253i \(-0.673402\pi\)
−0.518210 + 0.855253i \(0.673402\pi\)
\(762\) −0.0862200 −0.00312342
\(763\) −15.0308 −0.544150
\(764\) −15.0122 −0.543122
\(765\) 7.61325 0.275258
\(766\) −16.0096 −0.578449
\(767\) 41.1005 1.48405
\(768\) −0.985760 −0.0355705
\(769\) −6.15523 −0.221963 −0.110982 0.993822i \(-0.535399\pi\)
−0.110982 + 0.993822i \(0.535399\pi\)
\(770\) 29.9130 1.07799
\(771\) −20.0550 −0.722263
\(772\) 16.1288 0.580489
\(773\) −29.3274 −1.05483 −0.527416 0.849607i \(-0.676839\pi\)
−0.527416 + 0.849607i \(0.676839\pi\)
\(774\) −3.41214 −0.122647
\(775\) −17.5476 −0.630328
\(776\) 7.40863 0.265954
\(777\) −37.1678 −1.33339
\(778\) −18.0492 −0.647095
\(779\) 7.38823 0.264711
\(780\) 9.84084 0.352359
\(781\) −72.0973 −2.57985
\(782\) 2.28811 0.0818226
\(783\) 21.1458 0.755690
\(784\) 5.62058 0.200735
\(785\) 6.27741 0.224051
\(786\) −0.985760 −0.0351609
\(787\) 12.1983 0.434821 0.217410 0.976080i \(-0.430239\pi\)
0.217410 + 0.976080i \(0.430239\pi\)
\(788\) 12.3743 0.440815
\(789\) 11.8340 0.421302
\(790\) 0.317491 0.0112958
\(791\) −66.0147 −2.34721
\(792\) −10.4107 −0.369929
\(793\) −2.09848 −0.0745191
\(794\) −37.7833 −1.34088
\(795\) 10.6587 0.378024
\(796\) −6.41266 −0.227291
\(797\) −15.1707 −0.537373 −0.268687 0.963228i \(-0.586590\pi\)
−0.268687 + 0.963228i \(0.586590\pi\)
\(798\) 7.29705 0.258313
\(799\) 7.33413 0.259463
\(800\) 2.30888 0.0816313
\(801\) −21.7452 −0.768330
\(802\) 6.36284 0.224680
\(803\) −46.2529 −1.63223
\(804\) 0.230992 0.00814646
\(805\) −5.82782 −0.205404
\(806\) −46.2498 −1.62908
\(807\) −29.0226 −1.02164
\(808\) −0.881706 −0.0310183
\(809\) −0.206083 −0.00724550 −0.00362275 0.999993i \(-0.501153\pi\)
−0.00362275 + 0.999993i \(0.501153\pi\)
\(810\) 1.96649 0.0690955
\(811\) 1.19234 0.0418687 0.0209343 0.999781i \(-0.493336\pi\)
0.0209343 + 0.999781i \(0.493336\pi\)
\(812\) −15.1556 −0.531858
\(813\) 21.7518 0.762867
\(814\) −54.4765 −1.90940
\(815\) 23.2118 0.813075
\(816\) −2.25552 −0.0789591
\(817\) 3.50539 0.122638
\(818\) 5.68752 0.198860
\(819\) 43.8492 1.53222
\(820\) 5.81662 0.203125
\(821\) 26.7231 0.932643 0.466322 0.884615i \(-0.345579\pi\)
0.466322 + 0.884615i \(0.345579\pi\)
\(822\) −10.4054 −0.362930
\(823\) 27.3042 0.951765 0.475883 0.879509i \(-0.342129\pi\)
0.475883 + 0.879509i \(0.342129\pi\)
\(824\) 10.8662 0.378541
\(825\) −11.6822 −0.406724
\(826\) 23.9934 0.834838
\(827\) −31.2743 −1.08751 −0.543757 0.839243i \(-0.682999\pi\)
−0.543757 + 0.839243i \(0.682999\pi\)
\(828\) 2.02828 0.0704875
\(829\) 5.28700 0.183625 0.0918125 0.995776i \(-0.470734\pi\)
0.0918125 + 0.995776i \(0.470734\pi\)
\(830\) −7.85386 −0.272611
\(831\) 21.8889 0.759318
\(832\) 6.08548 0.210976
\(833\) 12.8605 0.445590
\(834\) −12.2504 −0.424196
\(835\) −10.0104 −0.346423
\(836\) 10.6952 0.369902
\(837\) 37.6709 1.30210
\(838\) 33.4220 1.15454
\(839\) 8.70014 0.300362 0.150181 0.988659i \(-0.452014\pi\)
0.150181 + 0.988659i \(0.452014\pi\)
\(840\) 5.74483 0.198215
\(841\) −10.8001 −0.372418
\(842\) −12.4592 −0.429373
\(843\) 19.2458 0.662859
\(844\) 23.4824 0.808298
\(845\) −39.4253 −1.35627
\(846\) 6.50129 0.223519
\(847\) −54.5157 −1.87318
\(848\) 6.59122 0.226344
\(849\) 4.06123 0.139381
\(850\) 5.28297 0.181204
\(851\) 10.6134 0.363824
\(852\) −13.8464 −0.474370
\(853\) 19.1939 0.657188 0.328594 0.944471i \(-0.393425\pi\)
0.328594 + 0.944471i \(0.393425\pi\)
\(854\) −1.22504 −0.0419199
\(855\) −6.93314 −0.237108
\(856\) −8.93158 −0.305275
\(857\) −29.0971 −0.993938 −0.496969 0.867768i \(-0.665554\pi\)
−0.496969 + 0.867768i \(0.665554\pi\)
\(858\) −30.7907 −1.05118
\(859\) 43.4661 1.48305 0.741523 0.670928i \(-0.234104\pi\)
0.741523 + 0.670928i \(0.234104\pi\)
\(860\) 2.75973 0.0941059
\(861\) −12.4169 −0.423168
\(862\) 23.5076 0.800674
\(863\) 13.9001 0.473166 0.236583 0.971611i \(-0.423973\pi\)
0.236583 + 0.971611i \(0.423973\pi\)
\(864\) −4.95667 −0.168629
\(865\) 12.9265 0.439515
\(866\) −20.3601 −0.691865
\(867\) 11.5970 0.393856
\(868\) −26.9995 −0.916422
\(869\) −0.993386 −0.0336983
\(870\) −6.89877 −0.233890
\(871\) −1.42600 −0.0483183
\(872\) −4.23098 −0.143279
\(873\) 15.0267 0.508578
\(874\) −2.08371 −0.0704824
\(875\) −42.5948 −1.43997
\(876\) −8.88294 −0.300127
\(877\) 26.4408 0.892842 0.446421 0.894823i \(-0.352698\pi\)
0.446421 + 0.894823i \(0.352698\pi\)
\(878\) −5.62864 −0.189957
\(879\) −8.78520 −0.296317
\(880\) 8.42015 0.283843
\(881\) 8.32507 0.280479 0.140239 0.990118i \(-0.455213\pi\)
0.140239 + 0.990118i \(0.455213\pi\)
\(882\) 11.4001 0.383862
\(883\) 2.99178 0.100681 0.0503406 0.998732i \(-0.483969\pi\)
0.0503406 + 0.998732i \(0.483969\pi\)
\(884\) 13.9242 0.468322
\(885\) 10.9217 0.367129
\(886\) −5.63390 −0.189275
\(887\) 32.6609 1.09665 0.548323 0.836266i \(-0.315266\pi\)
0.548323 + 0.836266i \(0.315266\pi\)
\(888\) −10.4623 −0.351092
\(889\) 0.310725 0.0104214
\(890\) 17.5875 0.589533
\(891\) −6.15289 −0.206130
\(892\) −20.7187 −0.693713
\(893\) −6.67896 −0.223503
\(894\) 1.70412 0.0569941
\(895\) −41.7499 −1.39555
\(896\) 3.55255 0.118682
\(897\) 5.99882 0.200295
\(898\) 19.0253 0.634881
\(899\) 32.4227 1.08136
\(900\) 4.68305 0.156102
\(901\) 15.0814 0.502435
\(902\) −18.1994 −0.605974
\(903\) −5.89129 −0.196050
\(904\) −18.5824 −0.618040
\(905\) 23.5223 0.781909
\(906\) −23.9713 −0.796393
\(907\) 55.3303 1.83721 0.918607 0.395173i \(-0.129315\pi\)
0.918607 + 0.395173i \(0.129315\pi\)
\(908\) −19.2788 −0.639790
\(909\) −1.78834 −0.0593156
\(910\) −35.4651 −1.17566
\(911\) −41.5621 −1.37701 −0.688506 0.725230i \(-0.741733\pi\)
−0.688506 + 0.725230i \(0.741733\pi\)
\(912\) 2.05403 0.0680158
\(913\) 24.5737 0.813270
\(914\) 2.64264 0.0874107
\(915\) −0.557631 −0.0184347
\(916\) −17.7188 −0.585447
\(917\) 3.55255 0.117315
\(918\) −11.3414 −0.374322
\(919\) 21.2579 0.701233 0.350617 0.936519i \(-0.385972\pi\)
0.350617 + 0.936519i \(0.385972\pi\)
\(920\) −1.64046 −0.0540845
\(921\) −21.0627 −0.694039
\(922\) −21.7083 −0.714926
\(923\) 85.4792 2.81358
\(924\) −17.9748 −0.591328
\(925\) 24.5052 0.805725
\(926\) 2.85097 0.0936885
\(927\) 22.0396 0.723876
\(928\) −4.26613 −0.140043
\(929\) 27.1619 0.891153 0.445576 0.895244i \(-0.352999\pi\)
0.445576 + 0.895244i \(0.352999\pi\)
\(930\) −12.2900 −0.403006
\(931\) −11.7116 −0.383834
\(932\) −11.6904 −0.382931
\(933\) −7.85209 −0.257066
\(934\) 22.7892 0.745686
\(935\) 19.2662 0.630073
\(936\) 12.3430 0.403445
\(937\) 10.7504 0.351199 0.175599 0.984462i \(-0.443814\pi\)
0.175599 + 0.984462i \(0.443814\pi\)
\(938\) −0.832464 −0.0271809
\(939\) −23.3722 −0.762722
\(940\) −5.25822 −0.171504
\(941\) −33.4873 −1.09165 −0.545827 0.837898i \(-0.683785\pi\)
−0.545827 + 0.837898i \(0.683785\pi\)
\(942\) −3.77212 −0.122902
\(943\) 3.54572 0.115464
\(944\) 6.75387 0.219820
\(945\) 28.8866 0.939681
\(946\) −8.63481 −0.280742
\(947\) −42.1163 −1.36859 −0.684297 0.729203i \(-0.739891\pi\)
−0.684297 + 0.729203i \(0.739891\pi\)
\(948\) −0.190781 −0.00619628
\(949\) 54.8378 1.78011
\(950\) −4.81103 −0.156090
\(951\) 13.9133 0.451171
\(952\) 8.12861 0.263450
\(953\) 19.0994 0.618691 0.309345 0.950950i \(-0.399890\pi\)
0.309345 + 0.950950i \(0.399890\pi\)
\(954\) 13.3688 0.432832
\(955\) 24.6270 0.796910
\(956\) −21.1698 −0.684680
\(957\) 21.5853 0.697755
\(958\) 21.3814 0.690803
\(959\) 37.4996 1.21093
\(960\) 1.61710 0.0521918
\(961\) 26.7605 0.863242
\(962\) 64.5878 2.08239
\(963\) −18.1157 −0.583771
\(964\) 26.1252 0.841435
\(965\) −26.4587 −0.851737
\(966\) 3.50196 0.112674
\(967\) 50.0205 1.60855 0.804275 0.594257i \(-0.202554\pi\)
0.804275 + 0.594257i \(0.202554\pi\)
\(968\) −15.3455 −0.493224
\(969\) 4.69985 0.150981
\(970\) −12.1536 −0.390228
\(971\) −48.1804 −1.54618 −0.773092 0.634294i \(-0.781291\pi\)
−0.773092 + 0.634294i \(0.781291\pi\)
\(972\) −16.0517 −0.514858
\(973\) 44.1488 1.41534
\(974\) −16.1368 −0.517057
\(975\) 13.8506 0.443573
\(976\) −0.344834 −0.0110379
\(977\) 15.0717 0.482187 0.241094 0.970502i \(-0.422494\pi\)
0.241094 + 0.970502i \(0.422494\pi\)
\(978\) −13.9481 −0.446010
\(979\) −55.0288 −1.75873
\(980\) −9.22036 −0.294534
\(981\) −8.58161 −0.273990
\(982\) 18.9922 0.606067
\(983\) −16.8907 −0.538729 −0.269365 0.963038i \(-0.586814\pi\)
−0.269365 + 0.963038i \(0.586814\pi\)
\(984\) −3.49523 −0.111424
\(985\) −20.2995 −0.646796
\(986\) −9.76137 −0.310865
\(987\) 11.2249 0.357293
\(988\) −12.6803 −0.403415
\(989\) 1.68228 0.0534935
\(990\) 17.0784 0.542787
\(991\) −50.9252 −1.61769 −0.808847 0.588019i \(-0.799908\pi\)
−0.808847 + 0.588019i \(0.799908\pi\)
\(992\) −7.60003 −0.241301
\(993\) 17.7448 0.563113
\(994\) 49.9006 1.58275
\(995\) 10.5197 0.333498
\(996\) 4.71941 0.149540
\(997\) −41.7289 −1.32157 −0.660784 0.750577i \(-0.729776\pi\)
−0.660784 + 0.750577i \(0.729776\pi\)
\(998\) 38.0897 1.20571
\(999\) −52.6073 −1.66442
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 \(a_p\))