Properties

Label 8007.2.a.e.1.4
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 1.4
Character \(\chi\) = 8007.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.58291 q^{2}\) \(+1.00000 q^{3}\) \(+4.67145 q^{4}\) \(+2.37262 q^{5}\) \(-2.58291 q^{6}\) \(-1.51271 q^{7}\) \(-6.90012 q^{8}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.58291 q^{2}\) \(+1.00000 q^{3}\) \(+4.67145 q^{4}\) \(+2.37262 q^{5}\) \(-2.58291 q^{6}\) \(-1.51271 q^{7}\) \(-6.90012 q^{8}\) \(+1.00000 q^{9}\) \(-6.12828 q^{10}\) \(+0.0286762 q^{11}\) \(+4.67145 q^{12}\) \(-2.28200 q^{13}\) \(+3.90720 q^{14}\) \(+2.37262 q^{15}\) \(+8.47952 q^{16}\) \(-1.00000 q^{17}\) \(-2.58291 q^{18}\) \(+3.73826 q^{19}\) \(+11.0836 q^{20}\) \(-1.51271 q^{21}\) \(-0.0740682 q^{22}\) \(+0.0338407 q^{23}\) \(-6.90012 q^{24}\) \(+0.629343 q^{25}\) \(+5.89421 q^{26}\) \(+1.00000 q^{27}\) \(-7.06654 q^{28}\) \(-5.28971 q^{29}\) \(-6.12828 q^{30}\) \(+5.40462 q^{31}\) \(-8.10165 q^{32}\) \(+0.0286762 q^{33}\) \(+2.58291 q^{34}\) \(-3.58909 q^{35}\) \(+4.67145 q^{36}\) \(-4.32358 q^{37}\) \(-9.65561 q^{38}\) \(-2.28200 q^{39}\) \(-16.3714 q^{40}\) \(+9.63055 q^{41}\) \(+3.90720 q^{42}\) \(-6.66478 q^{43}\) \(+0.133959 q^{44}\) \(+2.37262 q^{45}\) \(-0.0874076 q^{46}\) \(-7.80572 q^{47}\) \(+8.47952 q^{48}\) \(-4.71171 q^{49}\) \(-1.62554 q^{50}\) \(-1.00000 q^{51}\) \(-10.6602 q^{52}\) \(-4.66126 q^{53}\) \(-2.58291 q^{54}\) \(+0.0680378 q^{55}\) \(+10.4379 q^{56}\) \(+3.73826 q^{57}\) \(+13.6629 q^{58}\) \(-6.95607 q^{59}\) \(+11.0836 q^{60}\) \(+12.0288 q^{61}\) \(-13.9597 q^{62}\) \(-1.51271 q^{63}\) \(+3.96681 q^{64}\) \(-5.41433 q^{65}\) \(-0.0740682 q^{66}\) \(-10.8834 q^{67}\) \(-4.67145 q^{68}\) \(+0.0338407 q^{69}\) \(+9.27031 q^{70}\) \(-14.3426 q^{71}\) \(-6.90012 q^{72}\) \(+6.50034 q^{73}\) \(+11.1674 q^{74}\) \(+0.629343 q^{75}\) \(+17.4631 q^{76}\) \(-0.0433788 q^{77}\) \(+5.89421 q^{78}\) \(+7.88568 q^{79}\) \(+20.1187 q^{80}\) \(+1.00000 q^{81}\) \(-24.8749 q^{82}\) \(-6.05338 q^{83}\) \(-7.06654 q^{84}\) \(-2.37262 q^{85}\) \(+17.2145 q^{86}\) \(-5.28971 q^{87}\) \(-0.197869 q^{88}\) \(+14.4772 q^{89}\) \(-6.12828 q^{90}\) \(+3.45200 q^{91}\) \(+0.158085 q^{92}\) \(+5.40462 q^{93}\) \(+20.1615 q^{94}\) \(+8.86949 q^{95}\) \(-8.10165 q^{96}\) \(-17.9042 q^{97}\) \(+12.1699 q^{98}\) \(+0.0286762 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(46q \) \(\mathstrut -\mathstrut 5q^{2} \) \(\mathstrut +\mathstrut 46q^{3} \) \(\mathstrut +\mathstrut 43q^{4} \) \(\mathstrut -\mathstrut 19q^{5} \) \(\mathstrut -\mathstrut 5q^{6} \) \(\mathstrut +\mathstrut q^{7} \) \(\mathstrut -\mathstrut 18q^{8} \) \(\mathstrut +\mathstrut 46q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(46q \) \(\mathstrut -\mathstrut 5q^{2} \) \(\mathstrut +\mathstrut 46q^{3} \) \(\mathstrut +\mathstrut 43q^{4} \) \(\mathstrut -\mathstrut 19q^{5} \) \(\mathstrut -\mathstrut 5q^{6} \) \(\mathstrut +\mathstrut q^{7} \) \(\mathstrut -\mathstrut 18q^{8} \) \(\mathstrut +\mathstrut 46q^{9} \) \(\mathstrut -\mathstrut 10q^{10} \) \(\mathstrut -\mathstrut 25q^{11} \) \(\mathstrut +\mathstrut 43q^{12} \) \(\mathstrut -\mathstrut 8q^{13} \) \(\mathstrut -\mathstrut 28q^{14} \) \(\mathstrut -\mathstrut 19q^{15} \) \(\mathstrut +\mathstrut 33q^{16} \) \(\mathstrut -\mathstrut 46q^{17} \) \(\mathstrut -\mathstrut 5q^{18} \) \(\mathstrut -\mathstrut 2q^{19} \) \(\mathstrut -\mathstrut 56q^{20} \) \(\mathstrut +\mathstrut q^{21} \) \(\mathstrut -\mathstrut 19q^{22} \) \(\mathstrut -\mathstrut 64q^{23} \) \(\mathstrut -\mathstrut 18q^{24} \) \(\mathstrut +\mathstrut 11q^{25} \) \(\mathstrut -\mathstrut 13q^{26} \) \(\mathstrut +\mathstrut 46q^{27} \) \(\mathstrut -\mathstrut 38q^{28} \) \(\mathstrut -\mathstrut 51q^{29} \) \(\mathstrut -\mathstrut 10q^{30} \) \(\mathstrut -\mathstrut 19q^{31} \) \(\mathstrut -\mathstrut 61q^{32} \) \(\mathstrut -\mathstrut 25q^{33} \) \(\mathstrut +\mathstrut 5q^{34} \) \(\mathstrut -\mathstrut 39q^{35} \) \(\mathstrut +\mathstrut 43q^{36} \) \(\mathstrut -\mathstrut 46q^{37} \) \(\mathstrut -\mathstrut 48q^{38} \) \(\mathstrut -\mathstrut 8q^{39} \) \(\mathstrut -\mathstrut 10q^{40} \) \(\mathstrut -\mathstrut 53q^{41} \) \(\mathstrut -\mathstrut 28q^{42} \) \(\mathstrut -\mathstrut 33q^{43} \) \(\mathstrut -\mathstrut 62q^{44} \) \(\mathstrut -\mathstrut 19q^{45} \) \(\mathstrut +\mathstrut 2q^{46} \) \(\mathstrut -\mathstrut 45q^{47} \) \(\mathstrut +\mathstrut 33q^{48} \) \(\mathstrut +\mathstrut 21q^{49} \) \(\mathstrut -\mathstrut 60q^{50} \) \(\mathstrut -\mathstrut 46q^{51} \) \(\mathstrut -\mathstrut 63q^{52} \) \(\mathstrut -\mathstrut 47q^{53} \) \(\mathstrut -\mathstrut 5q^{54} \) \(\mathstrut +\mathstrut 5q^{55} \) \(\mathstrut -\mathstrut 82q^{56} \) \(\mathstrut -\mathstrut 2q^{57} \) \(\mathstrut -\mathstrut 21q^{58} \) \(\mathstrut -\mathstrut 65q^{59} \) \(\mathstrut -\mathstrut 56q^{60} \) \(\mathstrut -\mathstrut 37q^{61} \) \(\mathstrut -\mathstrut 46q^{62} \) \(\mathstrut +\mathstrut q^{63} \) \(\mathstrut +\mathstrut 74q^{64} \) \(\mathstrut -\mathstrut 85q^{65} \) \(\mathstrut -\mathstrut 19q^{66} \) \(\mathstrut -\mathstrut 52q^{67} \) \(\mathstrut -\mathstrut 43q^{68} \) \(\mathstrut -\mathstrut 64q^{69} \) \(\mathstrut -\mathstrut 20q^{70} \) \(\mathstrut -\mathstrut 48q^{71} \) \(\mathstrut -\mathstrut 18q^{72} \) \(\mathstrut -\mathstrut 39q^{73} \) \(\mathstrut -\mathstrut 16q^{74} \) \(\mathstrut +\mathstrut 11q^{75} \) \(\mathstrut +\mathstrut 42q^{76} \) \(\mathstrut -\mathstrut 78q^{77} \) \(\mathstrut -\mathstrut 13q^{78} \) \(\mathstrut -\mathstrut 26q^{79} \) \(\mathstrut -\mathstrut 78q^{80} \) \(\mathstrut +\mathstrut 46q^{81} \) \(\mathstrut +\mathstrut 3q^{82} \) \(\mathstrut -\mathstrut 47q^{83} \) \(\mathstrut -\mathstrut 38q^{84} \) \(\mathstrut +\mathstrut 19q^{85} \) \(\mathstrut -\mathstrut 6q^{86} \) \(\mathstrut -\mathstrut 51q^{87} \) \(\mathstrut -\mathstrut 58q^{88} \) \(\mathstrut -\mathstrut 58q^{89} \) \(\mathstrut -\mathstrut 10q^{90} \) \(\mathstrut -\mathstrut 43q^{91} \) \(\mathstrut -\mathstrut 68q^{92} \) \(\mathstrut -\mathstrut 19q^{93} \) \(\mathstrut -\mathstrut 78q^{95} \) \(\mathstrut -\mathstrut 61q^{96} \) \(\mathstrut -\mathstrut 44q^{97} \) \(\mathstrut -\mathstrut 4q^{98} \) \(\mathstrut -\mathstrut 25q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.58291 −1.82640 −0.913198 0.407516i \(-0.866395\pi\)
−0.913198 + 0.407516i \(0.866395\pi\)
\(3\) 1.00000 0.577350
\(4\) 4.67145 2.33572
\(5\) 2.37262 1.06107 0.530535 0.847663i \(-0.321991\pi\)
0.530535 + 0.847663i \(0.321991\pi\)
\(6\) −2.58291 −1.05447
\(7\) −1.51271 −0.571750 −0.285875 0.958267i \(-0.592284\pi\)
−0.285875 + 0.958267i \(0.592284\pi\)
\(8\) −6.90012 −2.43956
\(9\) 1.00000 0.333333
\(10\) −6.12828 −1.93793
\(11\) 0.0286762 0.00864620 0.00432310 0.999991i \(-0.498624\pi\)
0.00432310 + 0.999991i \(0.498624\pi\)
\(12\) 4.67145 1.34853
\(13\) −2.28200 −0.632913 −0.316457 0.948607i \(-0.602493\pi\)
−0.316457 + 0.948607i \(0.602493\pi\)
\(14\) 3.90720 1.04424
\(15\) 2.37262 0.612609
\(16\) 8.47952 2.11988
\(17\) −1.00000 −0.242536
\(18\) −2.58291 −0.608799
\(19\) 3.73826 0.857616 0.428808 0.903396i \(-0.358934\pi\)
0.428808 + 0.903396i \(0.358934\pi\)
\(20\) 11.0836 2.47837
\(21\) −1.51271 −0.330100
\(22\) −0.0740682 −0.0157914
\(23\) 0.0338407 0.00705627 0.00352814 0.999994i \(-0.498877\pi\)
0.00352814 + 0.999994i \(0.498877\pi\)
\(24\) −6.90012 −1.40848
\(25\) 0.629343 0.125869
\(26\) 5.89421 1.15595
\(27\) 1.00000 0.192450
\(28\) −7.06654 −1.33545
\(29\) −5.28971 −0.982275 −0.491138 0.871082i \(-0.663419\pi\)
−0.491138 + 0.871082i \(0.663419\pi\)
\(30\) −6.12828 −1.11887
\(31\) 5.40462 0.970699 0.485350 0.874320i \(-0.338692\pi\)
0.485350 + 0.874320i \(0.338692\pi\)
\(32\) −8.10165 −1.43218
\(33\) 0.0286762 0.00499189
\(34\) 2.58291 0.442966
\(35\) −3.58909 −0.606667
\(36\) 4.67145 0.778575
\(37\) −4.32358 −0.710791 −0.355396 0.934716i \(-0.615654\pi\)
−0.355396 + 0.934716i \(0.615654\pi\)
\(38\) −9.65561 −1.56635
\(39\) −2.28200 −0.365413
\(40\) −16.3714 −2.58854
\(41\) 9.63055 1.50404 0.752020 0.659140i \(-0.229080\pi\)
0.752020 + 0.659140i \(0.229080\pi\)
\(42\) 3.90720 0.602894
\(43\) −6.66478 −1.01637 −0.508184 0.861248i \(-0.669683\pi\)
−0.508184 + 0.861248i \(0.669683\pi\)
\(44\) 0.133959 0.0201951
\(45\) 2.37262 0.353690
\(46\) −0.0874076 −0.0128876
\(47\) −7.80572 −1.13858 −0.569291 0.822136i \(-0.692782\pi\)
−0.569291 + 0.822136i \(0.692782\pi\)
\(48\) 8.47952 1.22391
\(49\) −4.71171 −0.673102
\(50\) −1.62554 −0.229886
\(51\) −1.00000 −0.140028
\(52\) −10.6602 −1.47831
\(53\) −4.66126 −0.640273 −0.320137 0.947371i \(-0.603729\pi\)
−0.320137 + 0.947371i \(0.603729\pi\)
\(54\) −2.58291 −0.351490
\(55\) 0.0680378 0.00917422
\(56\) 10.4379 1.39482
\(57\) 3.73826 0.495145
\(58\) 13.6629 1.79402
\(59\) −6.95607 −0.905603 −0.452802 0.891611i \(-0.649575\pi\)
−0.452802 + 0.891611i \(0.649575\pi\)
\(60\) 11.0836 1.43088
\(61\) 12.0288 1.54013 0.770066 0.637964i \(-0.220223\pi\)
0.770066 + 0.637964i \(0.220223\pi\)
\(62\) −13.9597 −1.77288
\(63\) −1.51271 −0.190583
\(64\) 3.96681 0.495851
\(65\) −5.41433 −0.671565
\(66\) −0.0740682 −0.00911716
\(67\) −10.8834 −1.32962 −0.664811 0.747012i \(-0.731488\pi\)
−0.664811 + 0.747012i \(0.731488\pi\)
\(68\) −4.67145 −0.566496
\(69\) 0.0338407 0.00407394
\(70\) 9.27031 1.10801
\(71\) −14.3426 −1.70215 −0.851076 0.525043i \(-0.824049\pi\)
−0.851076 + 0.525043i \(0.824049\pi\)
\(72\) −6.90012 −0.813187
\(73\) 6.50034 0.760807 0.380404 0.924821i \(-0.375785\pi\)
0.380404 + 0.924821i \(0.375785\pi\)
\(74\) 11.1674 1.29819
\(75\) 0.629343 0.0726702
\(76\) 17.4631 2.00315
\(77\) −0.0433788 −0.00494347
\(78\) 5.89421 0.667388
\(79\) 7.88568 0.887209 0.443604 0.896223i \(-0.353700\pi\)
0.443604 + 0.896223i \(0.353700\pi\)
\(80\) 20.1187 2.24934
\(81\) 1.00000 0.111111
\(82\) −24.8749 −2.74697
\(83\) −6.05338 −0.664445 −0.332222 0.943201i \(-0.607798\pi\)
−0.332222 + 0.943201i \(0.607798\pi\)
\(84\) −7.06654 −0.771023
\(85\) −2.37262 −0.257347
\(86\) 17.2145 1.85629
\(87\) −5.28971 −0.567117
\(88\) −0.197869 −0.0210929
\(89\) 14.4772 1.53458 0.767291 0.641299i \(-0.221604\pi\)
0.767291 + 0.641299i \(0.221604\pi\)
\(90\) −6.12828 −0.645978
\(91\) 3.45200 0.361868
\(92\) 0.158085 0.0164815
\(93\) 5.40462 0.560433
\(94\) 20.1615 2.07950
\(95\) 8.86949 0.909990
\(96\) −8.10165 −0.826871
\(97\) −17.9042 −1.81790 −0.908951 0.416904i \(-0.863115\pi\)
−0.908951 + 0.416904i \(0.863115\pi\)
\(98\) 12.1699 1.22935
\(99\) 0.0286762 0.00288207
\(100\) 2.93994 0.293994
\(101\) 3.95845 0.393881 0.196940 0.980415i \(-0.436899\pi\)
0.196940 + 0.980415i \(0.436899\pi\)
\(102\) 2.58291 0.255747
\(103\) 7.76336 0.764947 0.382473 0.923967i \(-0.375072\pi\)
0.382473 + 0.923967i \(0.375072\pi\)
\(104\) 15.7461 1.54403
\(105\) −3.58909 −0.350259
\(106\) 12.0396 1.16939
\(107\) 1.85870 0.179687 0.0898436 0.995956i \(-0.471363\pi\)
0.0898436 + 0.995956i \(0.471363\pi\)
\(108\) 4.67145 0.449510
\(109\) 9.08366 0.870057 0.435028 0.900417i \(-0.356738\pi\)
0.435028 + 0.900417i \(0.356738\pi\)
\(110\) −0.175736 −0.0167558
\(111\) −4.32358 −0.410376
\(112\) −12.8271 −1.21204
\(113\) −14.5043 −1.36445 −0.682224 0.731143i \(-0.738987\pi\)
−0.682224 + 0.731143i \(0.738987\pi\)
\(114\) −9.65561 −0.904331
\(115\) 0.0802912 0.00748720
\(116\) −24.7106 −2.29432
\(117\) −2.28200 −0.210971
\(118\) 17.9669 1.65399
\(119\) 1.51271 0.138670
\(120\) −16.3714 −1.49450
\(121\) −10.9992 −0.999925
\(122\) −31.0694 −2.81289
\(123\) 9.63055 0.868358
\(124\) 25.2474 2.26728
\(125\) −10.3699 −0.927514
\(126\) 3.90720 0.348081
\(127\) 8.52240 0.756241 0.378120 0.925756i \(-0.376571\pi\)
0.378120 + 0.925756i \(0.376571\pi\)
\(128\) 5.95736 0.526561
\(129\) −6.66478 −0.586801
\(130\) 13.9848 1.22654
\(131\) 3.65276 0.319143 0.159572 0.987186i \(-0.448989\pi\)
0.159572 + 0.987186i \(0.448989\pi\)
\(132\) 0.133959 0.0116597
\(133\) −5.65490 −0.490342
\(134\) 28.1110 2.42842
\(135\) 2.37262 0.204203
\(136\) 6.90012 0.591680
\(137\) 4.43424 0.378842 0.189421 0.981896i \(-0.439339\pi\)
0.189421 + 0.981896i \(0.439339\pi\)
\(138\) −0.0874076 −0.00744063
\(139\) 15.4863 1.31353 0.656766 0.754094i \(-0.271924\pi\)
0.656766 + 0.754094i \(0.271924\pi\)
\(140\) −16.7662 −1.41701
\(141\) −7.80572 −0.657360
\(142\) 37.0457 3.10880
\(143\) −0.0654391 −0.00547230
\(144\) 8.47952 0.706627
\(145\) −12.5505 −1.04226
\(146\) −16.7898 −1.38954
\(147\) −4.71171 −0.388615
\(148\) −20.1974 −1.66021
\(149\) −24.1740 −1.98041 −0.990207 0.139605i \(-0.955417\pi\)
−0.990207 + 0.139605i \(0.955417\pi\)
\(150\) −1.62554 −0.132725
\(151\) −8.74504 −0.711662 −0.355831 0.934550i \(-0.615802\pi\)
−0.355831 + 0.934550i \(0.615802\pi\)
\(152\) −25.7944 −2.09221
\(153\) −1.00000 −0.0808452
\(154\) 0.112044 0.00902873
\(155\) 12.8231 1.02998
\(156\) −10.6602 −0.853503
\(157\) 1.00000 0.0798087
\(158\) −20.3680 −1.62039
\(159\) −4.66126 −0.369662
\(160\) −19.2222 −1.51964
\(161\) −0.0511911 −0.00403443
\(162\) −2.58291 −0.202933
\(163\) 8.83357 0.691898 0.345949 0.938253i \(-0.387557\pi\)
0.345949 + 0.938253i \(0.387557\pi\)
\(164\) 44.9886 3.51302
\(165\) 0.0680378 0.00529674
\(166\) 15.6354 1.21354
\(167\) 0.442060 0.0342077 0.0171038 0.999854i \(-0.494555\pi\)
0.0171038 + 0.999854i \(0.494555\pi\)
\(168\) 10.4379 0.805299
\(169\) −7.79247 −0.599421
\(170\) 6.12828 0.470018
\(171\) 3.73826 0.285872
\(172\) −31.1341 −2.37396
\(173\) −20.4052 −1.55138 −0.775688 0.631117i \(-0.782597\pi\)
−0.775688 + 0.631117i \(0.782597\pi\)
\(174\) 13.6629 1.03578
\(175\) −0.952012 −0.0719654
\(176\) 0.243161 0.0183289
\(177\) −6.95607 −0.522850
\(178\) −37.3934 −2.80275
\(179\) −7.46180 −0.557721 −0.278860 0.960332i \(-0.589957\pi\)
−0.278860 + 0.960332i \(0.589957\pi\)
\(180\) 11.0836 0.826122
\(181\) 12.9590 0.963237 0.481619 0.876381i \(-0.340049\pi\)
0.481619 + 0.876381i \(0.340049\pi\)
\(182\) −8.91623 −0.660915
\(183\) 12.0288 0.889196
\(184\) −0.233505 −0.0172142
\(185\) −10.2582 −0.754199
\(186\) −13.9597 −1.02357
\(187\) −0.0286762 −0.00209701
\(188\) −36.4640 −2.65941
\(189\) −1.51271 −0.110033
\(190\) −22.9091 −1.66200
\(191\) 11.3965 0.824624 0.412312 0.911043i \(-0.364721\pi\)
0.412312 + 0.911043i \(0.364721\pi\)
\(192\) 3.96681 0.286280
\(193\) 20.0172 1.44087 0.720435 0.693523i \(-0.243942\pi\)
0.720435 + 0.693523i \(0.243942\pi\)
\(194\) 46.2451 3.32021
\(195\) −5.41433 −0.387728
\(196\) −22.0105 −1.57218
\(197\) −22.2550 −1.58560 −0.792801 0.609480i \(-0.791378\pi\)
−0.792801 + 0.609480i \(0.791378\pi\)
\(198\) −0.0740682 −0.00526380
\(199\) 0.846276 0.0599909 0.0299955 0.999550i \(-0.490451\pi\)
0.0299955 + 0.999550i \(0.490451\pi\)
\(200\) −4.34254 −0.307064
\(201\) −10.8834 −0.767658
\(202\) −10.2243 −0.719382
\(203\) 8.00180 0.561616
\(204\) −4.67145 −0.327067
\(205\) 22.8497 1.59589
\(206\) −20.0521 −1.39710
\(207\) 0.0338407 0.00235209
\(208\) −19.3503 −1.34170
\(209\) 0.107199 0.00741512
\(210\) 9.27031 0.639712
\(211\) −25.3900 −1.74792 −0.873961 0.485996i \(-0.838457\pi\)
−0.873961 + 0.485996i \(0.838457\pi\)
\(212\) −21.7748 −1.49550
\(213\) −14.3426 −0.982738
\(214\) −4.80086 −0.328180
\(215\) −15.8130 −1.07844
\(216\) −6.90012 −0.469494
\(217\) −8.17562 −0.554998
\(218\) −23.4623 −1.58907
\(219\) 6.50034 0.439252
\(220\) 0.317835 0.0214284
\(221\) 2.28200 0.153504
\(222\) 11.1674 0.749508
\(223\) 2.62729 0.175936 0.0879682 0.996123i \(-0.471963\pi\)
0.0879682 + 0.996123i \(0.471963\pi\)
\(224\) 12.2554 0.818850
\(225\) 0.629343 0.0419562
\(226\) 37.4633 2.49202
\(227\) 14.8856 0.987990 0.493995 0.869465i \(-0.335536\pi\)
0.493995 + 0.869465i \(0.335536\pi\)
\(228\) 17.4631 1.15652
\(229\) −13.0204 −0.860413 −0.430206 0.902731i \(-0.641559\pi\)
−0.430206 + 0.902731i \(0.641559\pi\)
\(230\) −0.207385 −0.0136746
\(231\) −0.0433788 −0.00285411
\(232\) 36.4997 2.39632
\(233\) −21.9985 −1.44117 −0.720583 0.693368i \(-0.756126\pi\)
−0.720583 + 0.693368i \(0.756126\pi\)
\(234\) 5.89421 0.385317
\(235\) −18.5200 −1.20811
\(236\) −32.4949 −2.11524
\(237\) 7.88568 0.512230
\(238\) −3.90720 −0.253266
\(239\) −11.3861 −0.736505 −0.368253 0.929726i \(-0.620044\pi\)
−0.368253 + 0.929726i \(0.620044\pi\)
\(240\) 20.1187 1.29866
\(241\) 4.02368 0.259188 0.129594 0.991567i \(-0.458633\pi\)
0.129594 + 0.991567i \(0.458633\pi\)
\(242\) 28.4099 1.82626
\(243\) 1.00000 0.0641500
\(244\) 56.1920 3.59732
\(245\) −11.1791 −0.714208
\(246\) −24.8749 −1.58597
\(247\) −8.53072 −0.542797
\(248\) −37.2926 −2.36808
\(249\) −6.05338 −0.383617
\(250\) 26.7846 1.69401
\(251\) −19.8345 −1.25194 −0.625971 0.779847i \(-0.715297\pi\)
−0.625971 + 0.779847i \(0.715297\pi\)
\(252\) −7.06654 −0.445150
\(253\) 0.000970423 0 6.10100e−5 0
\(254\) −22.0126 −1.38120
\(255\) −2.37262 −0.148579
\(256\) −23.3210 −1.45756
\(257\) −22.4275 −1.39899 −0.699495 0.714637i \(-0.746592\pi\)
−0.699495 + 0.714637i \(0.746592\pi\)
\(258\) 17.2145 1.07173
\(259\) 6.54031 0.406395
\(260\) −25.2928 −1.56859
\(261\) −5.28971 −0.327425
\(262\) −9.43478 −0.582882
\(263\) −16.1298 −0.994607 −0.497304 0.867577i \(-0.665677\pi\)
−0.497304 + 0.867577i \(0.665677\pi\)
\(264\) −0.197869 −0.0121780
\(265\) −11.0594 −0.679374
\(266\) 14.6061 0.895559
\(267\) 14.4772 0.885991
\(268\) −50.8413 −3.10563
\(269\) −16.2546 −0.991062 −0.495531 0.868590i \(-0.665026\pi\)
−0.495531 + 0.868590i \(0.665026\pi\)
\(270\) −6.12828 −0.372955
\(271\) −21.3796 −1.29872 −0.649360 0.760481i \(-0.724963\pi\)
−0.649360 + 0.760481i \(0.724963\pi\)
\(272\) −8.47952 −0.514147
\(273\) 3.45200 0.208925
\(274\) −11.4533 −0.691917
\(275\) 0.0180472 0.00108828
\(276\) 0.158085 0.00951560
\(277\) 21.3761 1.28436 0.642182 0.766552i \(-0.278029\pi\)
0.642182 + 0.766552i \(0.278029\pi\)
\(278\) −39.9999 −2.39903
\(279\) 5.40462 0.323566
\(280\) 24.7651 1.48000
\(281\) −11.0237 −0.657620 −0.328810 0.944396i \(-0.606648\pi\)
−0.328810 + 0.944396i \(0.606648\pi\)
\(282\) 20.1615 1.20060
\(283\) 11.1859 0.664931 0.332466 0.943115i \(-0.392119\pi\)
0.332466 + 0.943115i \(0.392119\pi\)
\(284\) −67.0006 −3.97576
\(285\) 8.86949 0.525383
\(286\) 0.169024 0.00999458
\(287\) −14.5682 −0.859935
\(288\) −8.10165 −0.477394
\(289\) 1.00000 0.0588235
\(290\) 32.4169 1.90358
\(291\) −17.9042 −1.04957
\(292\) 30.3660 1.77704
\(293\) −14.6330 −0.854870 −0.427435 0.904046i \(-0.640583\pi\)
−0.427435 + 0.904046i \(0.640583\pi\)
\(294\) 12.1699 0.709766
\(295\) −16.5041 −0.960908
\(296\) 29.8332 1.73402
\(297\) 0.0286762 0.00166396
\(298\) 62.4395 3.61702
\(299\) −0.0772245 −0.00446601
\(300\) 2.93994 0.169738
\(301\) 10.0819 0.581109
\(302\) 22.5877 1.29978
\(303\) 3.95845 0.227407
\(304\) 31.6987 1.81804
\(305\) 28.5399 1.63419
\(306\) 2.58291 0.147655
\(307\) −17.6730 −1.00865 −0.504327 0.863513i \(-0.668259\pi\)
−0.504327 + 0.863513i \(0.668259\pi\)
\(308\) −0.202642 −0.0115466
\(309\) 7.76336 0.441642
\(310\) −33.1211 −1.88115
\(311\) 11.9994 0.680421 0.340210 0.940349i \(-0.389502\pi\)
0.340210 + 0.940349i \(0.389502\pi\)
\(312\) 15.7461 0.891446
\(313\) 23.4022 1.32277 0.661384 0.750047i \(-0.269969\pi\)
0.661384 + 0.750047i \(0.269969\pi\)
\(314\) −2.58291 −0.145762
\(315\) −3.58909 −0.202222
\(316\) 36.8376 2.07227
\(317\) 30.6745 1.72285 0.861427 0.507882i \(-0.169571\pi\)
0.861427 + 0.507882i \(0.169571\pi\)
\(318\) 12.0396 0.675149
\(319\) −0.151689 −0.00849295
\(320\) 9.41175 0.526133
\(321\) 1.85870 0.103742
\(322\) 0.132222 0.00736846
\(323\) −3.73826 −0.208002
\(324\) 4.67145 0.259525
\(325\) −1.43616 −0.0796639
\(326\) −22.8163 −1.26368
\(327\) 9.08366 0.502328
\(328\) −66.4520 −3.66920
\(329\) 11.8078 0.650984
\(330\) −0.175736 −0.00967394
\(331\) −5.21080 −0.286412 −0.143206 0.989693i \(-0.545741\pi\)
−0.143206 + 0.989693i \(0.545741\pi\)
\(332\) −28.2780 −1.55196
\(333\) −4.32358 −0.236930
\(334\) −1.14180 −0.0624768
\(335\) −25.8223 −1.41082
\(336\) −12.8271 −0.699773
\(337\) 30.7138 1.67309 0.836544 0.547900i \(-0.184573\pi\)
0.836544 + 0.547900i \(0.184573\pi\)
\(338\) 20.1273 1.09478
\(339\) −14.5043 −0.787765
\(340\) −11.0836 −0.601092
\(341\) 0.154984 0.00839286
\(342\) −9.65561 −0.522115
\(343\) 17.7164 0.956596
\(344\) 45.9877 2.47949
\(345\) 0.0802912 0.00432274
\(346\) 52.7048 2.83343
\(347\) 22.9647 1.23281 0.616406 0.787429i \(-0.288588\pi\)
0.616406 + 0.787429i \(0.288588\pi\)
\(348\) −24.7106 −1.32463
\(349\) −17.6342 −0.943935 −0.471968 0.881616i \(-0.656456\pi\)
−0.471968 + 0.881616i \(0.656456\pi\)
\(350\) 2.45897 0.131437
\(351\) −2.28200 −0.121804
\(352\) −0.232324 −0.0123829
\(353\) −18.5631 −0.988012 −0.494006 0.869459i \(-0.664468\pi\)
−0.494006 + 0.869459i \(0.664468\pi\)
\(354\) 17.9669 0.954932
\(355\) −34.0296 −1.80610
\(356\) 67.6295 3.58436
\(357\) 1.51271 0.0800610
\(358\) 19.2732 1.01862
\(359\) −22.1744 −1.17032 −0.585160 0.810918i \(-0.698968\pi\)
−0.585160 + 0.810918i \(0.698968\pi\)
\(360\) −16.3714 −0.862848
\(361\) −5.02541 −0.264495
\(362\) −33.4721 −1.75925
\(363\) −10.9992 −0.577307
\(364\) 16.1259 0.845224
\(365\) 15.4229 0.807270
\(366\) −31.0694 −1.62402
\(367\) 36.6906 1.91524 0.957618 0.288043i \(-0.0930045\pi\)
0.957618 + 0.288043i \(0.0930045\pi\)
\(368\) 0.286953 0.0149585
\(369\) 9.63055 0.501347
\(370\) 26.4961 1.37747
\(371\) 7.05113 0.366076
\(372\) 25.2474 1.30902
\(373\) −18.7946 −0.973148 −0.486574 0.873639i \(-0.661754\pi\)
−0.486574 + 0.873639i \(0.661754\pi\)
\(374\) 0.0740682 0.00382997
\(375\) −10.3699 −0.535501
\(376\) 53.8604 2.77764
\(377\) 12.0711 0.621695
\(378\) 3.90720 0.200965
\(379\) −19.8808 −1.02121 −0.510605 0.859816i \(-0.670578\pi\)
−0.510605 + 0.859816i \(0.670578\pi\)
\(380\) 41.4333 2.12549
\(381\) 8.52240 0.436616
\(382\) −29.4363 −1.50609
\(383\) 20.6523 1.05528 0.527642 0.849467i \(-0.323076\pi\)
0.527642 + 0.849467i \(0.323076\pi\)
\(384\) 5.95736 0.304010
\(385\) −0.102921 −0.00524536
\(386\) −51.7027 −2.63160
\(387\) −6.66478 −0.338790
\(388\) −83.6388 −4.24611
\(389\) 18.9814 0.962397 0.481199 0.876612i \(-0.340202\pi\)
0.481199 + 0.876612i \(0.340202\pi\)
\(390\) 13.9848 0.708145
\(391\) −0.0338407 −0.00171140
\(392\) 32.5114 1.64207
\(393\) 3.65276 0.184258
\(394\) 57.4828 2.89594
\(395\) 18.7098 0.941390
\(396\) 0.133959 0.00673171
\(397\) −9.79340 −0.491517 −0.245758 0.969331i \(-0.579037\pi\)
−0.245758 + 0.969331i \(0.579037\pi\)
\(398\) −2.18586 −0.109567
\(399\) −5.65490 −0.283099
\(400\) 5.33653 0.266826
\(401\) −0.655997 −0.0327589 −0.0163795 0.999866i \(-0.505214\pi\)
−0.0163795 + 0.999866i \(0.505214\pi\)
\(402\) 28.1110 1.40205
\(403\) −12.3334 −0.614368
\(404\) 18.4917 0.919997
\(405\) 2.37262 0.117897
\(406\) −20.6680 −1.02573
\(407\) −0.123984 −0.00614565
\(408\) 6.90012 0.341607
\(409\) 35.9707 1.77864 0.889319 0.457287i \(-0.151179\pi\)
0.889319 + 0.457287i \(0.151179\pi\)
\(410\) −59.0188 −2.91473
\(411\) 4.43424 0.218725
\(412\) 36.2661 1.78670
\(413\) 10.5225 0.517779
\(414\) −0.0874076 −0.00429585
\(415\) −14.3624 −0.705022
\(416\) 18.4880 0.906447
\(417\) 15.4863 0.758369
\(418\) −0.276886 −0.0135429
\(419\) 6.54048 0.319523 0.159762 0.987156i \(-0.448927\pi\)
0.159762 + 0.987156i \(0.448927\pi\)
\(420\) −16.7662 −0.818109
\(421\) 1.25924 0.0613718 0.0306859 0.999529i \(-0.490231\pi\)
0.0306859 + 0.999529i \(0.490231\pi\)
\(422\) 65.5803 3.19240
\(423\) −7.80572 −0.379527
\(424\) 32.1632 1.56199
\(425\) −0.629343 −0.0305276
\(426\) 37.0457 1.79487
\(427\) −18.1961 −0.880571
\(428\) 8.68281 0.419700
\(429\) −0.0654391 −0.00315943
\(430\) 40.8436 1.96965
\(431\) 35.8060 1.72471 0.862357 0.506301i \(-0.168988\pi\)
0.862357 + 0.506301i \(0.168988\pi\)
\(432\) 8.47952 0.407971
\(433\) −20.8729 −1.00309 −0.501545 0.865132i \(-0.667235\pi\)
−0.501545 + 0.865132i \(0.667235\pi\)
\(434\) 21.1169 1.01365
\(435\) −12.5505 −0.601750
\(436\) 42.4338 2.03221
\(437\) 0.126505 0.00605157
\(438\) −16.7898 −0.802249
\(439\) −36.6084 −1.74722 −0.873612 0.486622i \(-0.838229\pi\)
−0.873612 + 0.486622i \(0.838229\pi\)
\(440\) −0.469469 −0.0223811
\(441\) −4.71171 −0.224367
\(442\) −5.89421 −0.280359
\(443\) 12.2761 0.583257 0.291629 0.956532i \(-0.405803\pi\)
0.291629 + 0.956532i \(0.405803\pi\)
\(444\) −20.1974 −0.958524
\(445\) 34.3490 1.62830
\(446\) −6.78607 −0.321330
\(447\) −24.1740 −1.14339
\(448\) −6.00063 −0.283503
\(449\) −41.6897 −1.96746 −0.983730 0.179651i \(-0.942503\pi\)
−0.983730 + 0.179651i \(0.942503\pi\)
\(450\) −1.62554 −0.0766286
\(451\) 0.276168 0.0130042
\(452\) −67.7560 −3.18698
\(453\) −8.74504 −0.410878
\(454\) −38.4482 −1.80446
\(455\) 8.19031 0.383967
\(456\) −25.7944 −1.20794
\(457\) 25.6731 1.20094 0.600468 0.799649i \(-0.294981\pi\)
0.600468 + 0.799649i \(0.294981\pi\)
\(458\) 33.6306 1.57145
\(459\) −1.00000 −0.0466760
\(460\) 0.375076 0.0174880
\(461\) 27.7166 1.29089 0.645446 0.763806i \(-0.276671\pi\)
0.645446 + 0.763806i \(0.276671\pi\)
\(462\) 0.112044 0.00521274
\(463\) −0.997341 −0.0463504 −0.0231752 0.999731i \(-0.507378\pi\)
−0.0231752 + 0.999731i \(0.507378\pi\)
\(464\) −44.8543 −2.08231
\(465\) 12.8231 0.594659
\(466\) 56.8201 2.63214
\(467\) −41.6728 −1.92839 −0.964194 0.265199i \(-0.914562\pi\)
−0.964194 + 0.265199i \(0.914562\pi\)
\(468\) −10.6602 −0.492770
\(469\) 16.4635 0.760212
\(470\) 47.8357 2.20649
\(471\) 1.00000 0.0460776
\(472\) 47.9977 2.20927
\(473\) −0.191120 −0.00878773
\(474\) −20.3680 −0.935535
\(475\) 2.35265 0.107947
\(476\) 7.06654 0.323894
\(477\) −4.66126 −0.213424
\(478\) 29.4093 1.34515
\(479\) 4.86314 0.222202 0.111101 0.993809i \(-0.464562\pi\)
0.111101 + 0.993809i \(0.464562\pi\)
\(480\) −19.2222 −0.877367
\(481\) 9.86641 0.449869
\(482\) −10.3928 −0.473380
\(483\) −0.0511911 −0.00232928
\(484\) −51.3821 −2.33555
\(485\) −42.4800 −1.92892
\(486\) −2.58291 −0.117163
\(487\) −20.0544 −0.908753 −0.454376 0.890810i \(-0.650138\pi\)
−0.454376 + 0.890810i \(0.650138\pi\)
\(488\) −83.0003 −3.75725
\(489\) 8.83357 0.399468
\(490\) 28.8747 1.30443
\(491\) −7.57996 −0.342079 −0.171039 0.985264i \(-0.554713\pi\)
−0.171039 + 0.985264i \(0.554713\pi\)
\(492\) 44.9886 2.02824
\(493\) 5.28971 0.238237
\(494\) 22.0341 0.991362
\(495\) 0.0680378 0.00305807
\(496\) 45.8286 2.05777
\(497\) 21.6962 0.973206
\(498\) 15.6354 0.700637
\(499\) −21.0943 −0.944311 −0.472155 0.881515i \(-0.656524\pi\)
−0.472155 + 0.881515i \(0.656524\pi\)
\(500\) −48.4426 −2.16642
\(501\) 0.442060 0.0197498
\(502\) 51.2308 2.28654
\(503\) −20.9533 −0.934260 −0.467130 0.884189i \(-0.654712\pi\)
−0.467130 + 0.884189i \(0.654712\pi\)
\(504\) 10.4379 0.464940
\(505\) 9.39192 0.417935
\(506\) −0.00250652 −0.000111428 0
\(507\) −7.79247 −0.346076
\(508\) 39.8119 1.76637
\(509\) 28.6678 1.27068 0.635339 0.772233i \(-0.280860\pi\)
0.635339 + 0.772233i \(0.280860\pi\)
\(510\) 6.12828 0.271365
\(511\) −9.83312 −0.434992
\(512\) 48.3214 2.13552
\(513\) 3.73826 0.165048
\(514\) 57.9284 2.55511
\(515\) 18.4195 0.811662
\(516\) −31.1341 −1.37060
\(517\) −0.223838 −0.00984440
\(518\) −16.8931 −0.742239
\(519\) −20.4052 −0.895687
\(520\) 37.3595 1.63832
\(521\) −27.3387 −1.19773 −0.598864 0.800851i \(-0.704381\pi\)
−0.598864 + 0.800851i \(0.704381\pi\)
\(522\) 13.6629 0.598008
\(523\) 41.8747 1.83105 0.915526 0.402260i \(-0.131775\pi\)
0.915526 + 0.402260i \(0.131775\pi\)
\(524\) 17.0637 0.745431
\(525\) −0.952012 −0.0415492
\(526\) 41.6619 1.81655
\(527\) −5.40462 −0.235429
\(528\) 0.243161 0.0105822
\(529\) −22.9989 −0.999950
\(530\) 28.5655 1.24081
\(531\) −6.95607 −0.301868
\(532\) −26.4166 −1.14530
\(533\) −21.9769 −0.951927
\(534\) −37.3934 −1.61817
\(535\) 4.40999 0.190661
\(536\) 75.0969 3.24369
\(537\) −7.46180 −0.322000
\(538\) 41.9843 1.81007
\(539\) −0.135114 −0.00581977
\(540\) 11.0836 0.476962
\(541\) 24.8749 1.06945 0.534727 0.845025i \(-0.320414\pi\)
0.534727 + 0.845025i \(0.320414\pi\)
\(542\) 55.2218 2.37198
\(543\) 12.9590 0.556125
\(544\) 8.10165 0.347355
\(545\) 21.5521 0.923191
\(546\) −8.91623 −0.381579
\(547\) −3.06881 −0.131213 −0.0656063 0.997846i \(-0.520898\pi\)
−0.0656063 + 0.997846i \(0.520898\pi\)
\(548\) 20.7143 0.884871
\(549\) 12.0288 0.513377
\(550\) −0.0466143 −0.00198764
\(551\) −19.7743 −0.842415
\(552\) −0.233505 −0.00993863
\(553\) −11.9287 −0.507262
\(554\) −55.2126 −2.34576
\(555\) −10.2582 −0.435437
\(556\) 72.3435 3.06805
\(557\) −4.80336 −0.203525 −0.101762 0.994809i \(-0.532448\pi\)
−0.101762 + 0.994809i \(0.532448\pi\)
\(558\) −13.9597 −0.590960
\(559\) 15.2090 0.643273
\(560\) −30.4338 −1.28606
\(561\) −0.0286762 −0.00121071
\(562\) 28.4733 1.20107
\(563\) −16.8888 −0.711776 −0.355888 0.934529i \(-0.615822\pi\)
−0.355888 + 0.934529i \(0.615822\pi\)
\(564\) −36.4640 −1.53541
\(565\) −34.4132 −1.44777
\(566\) −28.8922 −1.21443
\(567\) −1.51271 −0.0635278
\(568\) 98.9656 4.15250
\(569\) 19.9842 0.837780 0.418890 0.908037i \(-0.362419\pi\)
0.418890 + 0.908037i \(0.362419\pi\)
\(570\) −22.9091 −0.959558
\(571\) 8.52893 0.356925 0.178462 0.983947i \(-0.442888\pi\)
0.178462 + 0.983947i \(0.442888\pi\)
\(572\) −0.305695 −0.0127818
\(573\) 11.3965 0.476097
\(574\) 37.6285 1.57058
\(575\) 0.0212974 0.000888163 0
\(576\) 3.96681 0.165284
\(577\) −18.7931 −0.782366 −0.391183 0.920313i \(-0.627934\pi\)
−0.391183 + 0.920313i \(0.627934\pi\)
\(578\) −2.58291 −0.107435
\(579\) 20.0172 0.831886
\(580\) −58.6290 −2.43444
\(581\) 9.15700 0.379896
\(582\) 46.2451 1.91692
\(583\) −0.133667 −0.00553593
\(584\) −44.8531 −1.85604
\(585\) −5.41433 −0.223855
\(586\) 37.7958 1.56133
\(587\) 5.70930 0.235648 0.117824 0.993034i \(-0.462408\pi\)
0.117824 + 0.993034i \(0.462408\pi\)
\(588\) −22.0105 −0.907698
\(589\) 20.2039 0.832487
\(590\) 42.6288 1.75500
\(591\) −22.2550 −0.915448
\(592\) −36.6619 −1.50679
\(593\) −31.6183 −1.29841 −0.649204 0.760614i \(-0.724898\pi\)
−0.649204 + 0.760614i \(0.724898\pi\)
\(594\) −0.0740682 −0.00303905
\(595\) 3.58909 0.147138
\(596\) −112.928 −4.62570
\(597\) 0.846276 0.0346358
\(598\) 0.199464 0.00815670
\(599\) −27.0048 −1.10339 −0.551693 0.834048i \(-0.686018\pi\)
−0.551693 + 0.834048i \(0.686018\pi\)
\(600\) −4.34254 −0.177283
\(601\) −4.78688 −0.195261 −0.0976304 0.995223i \(-0.531126\pi\)
−0.0976304 + 0.995223i \(0.531126\pi\)
\(602\) −26.0406 −1.06134
\(603\) −10.8834 −0.443207
\(604\) −40.8520 −1.66224
\(605\) −26.0969 −1.06099
\(606\) −10.2243 −0.415336
\(607\) −28.2056 −1.14483 −0.572415 0.819964i \(-0.693993\pi\)
−0.572415 + 0.819964i \(0.693993\pi\)
\(608\) −30.2861 −1.22826
\(609\) 8.00180 0.324249
\(610\) −73.7160 −2.98467
\(611\) 17.8127 0.720623
\(612\) −4.67145 −0.188832
\(613\) 4.49092 0.181387 0.0906933 0.995879i \(-0.471092\pi\)
0.0906933 + 0.995879i \(0.471092\pi\)
\(614\) 45.6479 1.84220
\(615\) 22.8497 0.921388
\(616\) 0.299319 0.0120599
\(617\) −15.9359 −0.641557 −0.320778 0.947154i \(-0.603945\pi\)
−0.320778 + 0.947154i \(0.603945\pi\)
\(618\) −20.0521 −0.806614
\(619\) 47.2496 1.89912 0.949560 0.313585i \(-0.101530\pi\)
0.949560 + 0.313585i \(0.101530\pi\)
\(620\) 59.9026 2.40575
\(621\) 0.0338407 0.00135798
\(622\) −30.9933 −1.24272
\(623\) −21.8998 −0.877397
\(624\) −19.3503 −0.774631
\(625\) −27.7506 −1.11003
\(626\) −60.4458 −2.41590
\(627\) 0.107199 0.00428112
\(628\) 4.67145 0.186411
\(629\) 4.32358 0.172392
\(630\) 9.27031 0.369338
\(631\) 43.4005 1.72775 0.863874 0.503709i \(-0.168032\pi\)
0.863874 + 0.503709i \(0.168032\pi\)
\(632\) −54.4122 −2.16440
\(633\) −25.3900 −1.00916
\(634\) −79.2297 −3.14661
\(635\) 20.2205 0.802424
\(636\) −21.7748 −0.863428
\(637\) 10.7521 0.426015
\(638\) 0.391799 0.0155115
\(639\) −14.3426 −0.567384
\(640\) 14.1346 0.558718
\(641\) 43.2254 1.70730 0.853650 0.520847i \(-0.174384\pi\)
0.853650 + 0.520847i \(0.174384\pi\)
\(642\) −4.80086 −0.189475
\(643\) −31.2128 −1.23091 −0.615457 0.788170i \(-0.711029\pi\)
−0.615457 + 0.788170i \(0.711029\pi\)
\(644\) −0.239137 −0.00942330
\(645\) −15.8130 −0.622636
\(646\) 9.65561 0.379895
\(647\) −29.6126 −1.16419 −0.582096 0.813120i \(-0.697767\pi\)
−0.582096 + 0.813120i \(0.697767\pi\)
\(648\) −6.90012 −0.271062
\(649\) −0.199474 −0.00783003
\(650\) 3.70948 0.145498
\(651\) −8.17562 −0.320428
\(652\) 41.2655 1.61608
\(653\) 19.9254 0.779743 0.389871 0.920869i \(-0.372519\pi\)
0.389871 + 0.920869i \(0.372519\pi\)
\(654\) −23.4623 −0.917449
\(655\) 8.66663 0.338633
\(656\) 81.6625 3.18839
\(657\) 6.50034 0.253602
\(658\) −30.4985 −1.18895
\(659\) 22.6520 0.882395 0.441197 0.897410i \(-0.354554\pi\)
0.441197 + 0.897410i \(0.354554\pi\)
\(660\) 0.317835 0.0123717
\(661\) 9.50529 0.369713 0.184857 0.982766i \(-0.440818\pi\)
0.184857 + 0.982766i \(0.440818\pi\)
\(662\) 13.4591 0.523101
\(663\) 2.28200 0.0886256
\(664\) 41.7690 1.62095
\(665\) −13.4170 −0.520287
\(666\) 11.1674 0.432729
\(667\) −0.179008 −0.00693120
\(668\) 2.06506 0.0798997
\(669\) 2.62729 0.101577
\(670\) 66.6967 2.57672
\(671\) 0.344941 0.0133163
\(672\) 12.2554 0.472764
\(673\) −39.6317 −1.52769 −0.763846 0.645399i \(-0.776691\pi\)
−0.763846 + 0.645399i \(0.776691\pi\)
\(674\) −79.3311 −3.05572
\(675\) 0.629343 0.0242234
\(676\) −36.4021 −1.40008
\(677\) 14.6513 0.563096 0.281548 0.959547i \(-0.409152\pi\)
0.281548 + 0.959547i \(0.409152\pi\)
\(678\) 37.4633 1.43877
\(679\) 27.0839 1.03939
\(680\) 16.3714 0.627814
\(681\) 14.8856 0.570417
\(682\) −0.400311 −0.0153287
\(683\) 23.4988 0.899157 0.449579 0.893241i \(-0.351574\pi\)
0.449579 + 0.893241i \(0.351574\pi\)
\(684\) 17.4631 0.667718
\(685\) 10.5208 0.401978
\(686\) −45.7600 −1.74712
\(687\) −13.0204 −0.496760
\(688\) −56.5141 −2.15458
\(689\) 10.6370 0.405237
\(690\) −0.207385 −0.00789503
\(691\) 15.5103 0.590041 0.295020 0.955491i \(-0.404674\pi\)
0.295020 + 0.955491i \(0.404674\pi\)
\(692\) −95.3216 −3.62358
\(693\) −0.0433788 −0.00164782
\(694\) −59.3159 −2.25160
\(695\) 36.7432 1.39375
\(696\) 36.4997 1.38352
\(697\) −9.63055 −0.364783
\(698\) 45.5475 1.72400
\(699\) −21.9985 −0.832058
\(700\) −4.44728 −0.168091
\(701\) 0.516175 0.0194957 0.00974783 0.999952i \(-0.496897\pi\)
0.00974783 + 0.999952i \(0.496897\pi\)
\(702\) 5.89421 0.222463
\(703\) −16.1627 −0.609586
\(704\) 0.113753 0.00428723
\(705\) −18.5200 −0.697505
\(706\) 47.9468 1.80450
\(707\) −5.98799 −0.225201
\(708\) −32.4949 −1.22123
\(709\) 40.0680 1.50478 0.752392 0.658715i \(-0.228900\pi\)
0.752392 + 0.658715i \(0.228900\pi\)
\(710\) 87.8954 3.29866
\(711\) 7.88568 0.295736
\(712\) −99.8945 −3.74370
\(713\) 0.182896 0.00684952
\(714\) −3.90720 −0.146223
\(715\) −0.155262 −0.00580649
\(716\) −34.8574 −1.30268
\(717\) −11.3861 −0.425222
\(718\) 57.2745 2.13747
\(719\) −36.8765 −1.37526 −0.687631 0.726060i \(-0.741349\pi\)
−0.687631 + 0.726060i \(0.741349\pi\)
\(720\) 20.1187 0.749780
\(721\) −11.7437 −0.437358
\(722\) 12.9802 0.483073
\(723\) 4.02368 0.149642
\(724\) 60.5374 2.24986
\(725\) −3.32904 −0.123638
\(726\) 28.4099 1.05439
\(727\) −30.7527 −1.14056 −0.570278 0.821452i \(-0.693164\pi\)
−0.570278 + 0.821452i \(0.693164\pi\)
\(728\) −23.8192 −0.882800
\(729\) 1.00000 0.0370370
\(730\) −39.8359 −1.47439
\(731\) 6.66478 0.246506
\(732\) 56.1920 2.07692
\(733\) −24.1240 −0.891042 −0.445521 0.895271i \(-0.646982\pi\)
−0.445521 + 0.895271i \(0.646982\pi\)
\(734\) −94.7688 −3.49798
\(735\) −11.1791 −0.412348
\(736\) −0.274165 −0.0101059
\(737\) −0.312095 −0.0114962
\(738\) −24.8749 −0.915658
\(739\) −30.5703 −1.12455 −0.562273 0.826951i \(-0.690073\pi\)
−0.562273 + 0.826951i \(0.690073\pi\)
\(740\) −47.9207 −1.76160
\(741\) −8.53072 −0.313384
\(742\) −18.2125 −0.668601
\(743\) 21.5567 0.790840 0.395420 0.918500i \(-0.370599\pi\)
0.395420 + 0.918500i \(0.370599\pi\)
\(744\) −37.2926 −1.36721
\(745\) −57.3559 −2.10136
\(746\) 48.5449 1.77735
\(747\) −6.05338 −0.221482
\(748\) −0.133959 −0.00489804
\(749\) −2.81167 −0.102736
\(750\) 26.7846 0.978036
\(751\) 34.4229 1.25611 0.628054 0.778170i \(-0.283852\pi\)
0.628054 + 0.778170i \(0.283852\pi\)
\(752\) −66.1888 −2.41366
\(753\) −19.8345 −0.722809
\(754\) −31.1787 −1.13546
\(755\) −20.7487 −0.755122
\(756\) −7.06654 −0.257008
\(757\) −33.0431 −1.20097 −0.600486 0.799635i \(-0.705026\pi\)
−0.600486 + 0.799635i \(0.705026\pi\)
\(758\) 51.3505 1.86513
\(759\) 0.000970423 0 3.52241e−5 0
\(760\) −61.2005 −2.21998
\(761\) −13.5002 −0.489382 −0.244691 0.969601i \(-0.578687\pi\)
−0.244691 + 0.969601i \(0.578687\pi\)
\(762\) −22.0126 −0.797434
\(763\) −13.7409 −0.497455
\(764\) 53.2383 1.92609
\(765\) −2.37262 −0.0857824
\(766\) −53.3432 −1.92737
\(767\) 15.8738 0.573168
\(768\) −23.3210 −0.841523
\(769\) 38.0526 1.37221 0.686106 0.727502i \(-0.259319\pi\)
0.686106 + 0.727502i \(0.259319\pi\)
\(770\) 0.265837 0.00958011
\(771\) −22.4275 −0.807708
\(772\) 93.5093 3.36547
\(773\) −5.98815 −0.215379 −0.107689 0.994185i \(-0.534345\pi\)
−0.107689 + 0.994185i \(0.534345\pi\)
\(774\) 17.2145 0.618764
\(775\) 3.40136 0.122180
\(776\) 123.541 4.43488
\(777\) 6.54031 0.234632
\(778\) −49.0274 −1.75772
\(779\) 36.0015 1.28989
\(780\) −25.2928 −0.905626
\(781\) −0.411291 −0.0147171
\(782\) 0.0874076 0.00312569
\(783\) −5.28971 −0.189039
\(784\) −39.9531 −1.42690
\(785\) 2.37262 0.0846826
\(786\) −9.43478 −0.336527
\(787\) 32.4237 1.15578 0.577890 0.816115i \(-0.303876\pi\)
0.577890 + 0.816115i \(0.303876\pi\)
\(788\) −103.963 −3.70353
\(789\) −16.1298 −0.574237
\(790\) −48.3257 −1.71935
\(791\) 21.9408 0.780124
\(792\) −0.197869 −0.00703098
\(793\) −27.4498 −0.974770
\(794\) 25.2955 0.897705
\(795\) −11.0594 −0.392237
\(796\) 3.95333 0.140122
\(797\) 9.29495 0.329244 0.164622 0.986357i \(-0.447360\pi\)
0.164622 + 0.986357i \(0.447360\pi\)
\(798\) 14.6061 0.517051
\(799\) 7.80572 0.276146
\(800\) −5.09871 −0.180267
\(801\) 14.4772 0.511527
\(802\) 1.69438 0.0598308
\(803\) 0.186405 0.00657809
\(804\) −50.8413 −1.79304
\(805\) −0.121457 −0.00428081
\(806\) 31.8560 1.12208
\(807\) −16.2546 −0.572190
\(808\) −27.3138 −0.960896
\(809\) −47.0654 −1.65473 −0.827366 0.561663i \(-0.810162\pi\)
−0.827366 + 0.561663i \(0.810162\pi\)
\(810\) −6.12828 −0.215326
\(811\) −49.1822 −1.72702 −0.863510 0.504331i \(-0.831739\pi\)
−0.863510 + 0.504331i \(0.831739\pi\)
\(812\) 37.3800 1.31178
\(813\) −21.3796 −0.749817
\(814\) 0.320239 0.0112244
\(815\) 20.9587 0.734152
\(816\) −8.47952 −0.296843
\(817\) −24.9147 −0.871654
\(818\) −92.9093 −3.24850
\(819\) 3.45200 0.120623
\(820\) 106.741 3.72756
\(821\) 8.57676 0.299331 0.149666 0.988737i \(-0.452180\pi\)
0.149666 + 0.988737i \(0.452180\pi\)
\(822\) −11.4533 −0.399478
\(823\) 1.25206 0.0436442 0.0218221 0.999762i \(-0.493053\pi\)
0.0218221 + 0.999762i \(0.493053\pi\)
\(824\) −53.5681 −1.86613
\(825\) 0.0180472 0.000628321 0
\(826\) −27.1787 −0.945669
\(827\) 38.9584 1.35472 0.677358 0.735654i \(-0.263125\pi\)
0.677358 + 0.735654i \(0.263125\pi\)
\(828\) 0.158085 0.00549383
\(829\) 10.3655 0.360008 0.180004 0.983666i \(-0.442389\pi\)
0.180004 + 0.983666i \(0.442389\pi\)
\(830\) 37.0968 1.28765
\(831\) 21.3761 0.741528
\(832\) −9.05226 −0.313831
\(833\) 4.71171 0.163251
\(834\) −39.9999 −1.38508
\(835\) 1.04884 0.0362967
\(836\) 0.500775 0.0173197
\(837\) 5.40462 0.186811
\(838\) −16.8935 −0.583576
\(839\) −16.4567 −0.568147 −0.284073 0.958803i \(-0.591686\pi\)
−0.284073 + 0.958803i \(0.591686\pi\)
\(840\) 24.7651 0.854479
\(841\) −1.01893 −0.0351355
\(842\) −3.25252 −0.112089
\(843\) −11.0237 −0.379677
\(844\) −118.608 −4.08266
\(845\) −18.4886 −0.636027
\(846\) 20.1615 0.693167
\(847\) 16.6386 0.571708
\(848\) −39.5253 −1.35730
\(849\) 11.1859 0.383898
\(850\) 1.62554 0.0557555
\(851\) −0.146313 −0.00501554
\(852\) −67.0006 −2.29540
\(853\) −14.1523 −0.484566 −0.242283 0.970206i \(-0.577896\pi\)
−0.242283 + 0.970206i \(0.577896\pi\)
\(854\) 46.9990 1.60827
\(855\) 8.86949 0.303330
\(856\) −12.8252 −0.438358
\(857\) −35.3956 −1.20909 −0.604545 0.796571i \(-0.706645\pi\)
−0.604545 + 0.796571i \(0.706645\pi\)
\(858\) 0.169024 0.00577037
\(859\) −7.80266 −0.266223 −0.133112 0.991101i \(-0.542497\pi\)
−0.133112 + 0.991101i \(0.542497\pi\)
\(860\) −73.8696 −2.51893
\(861\) −14.5682 −0.496484
\(862\) −92.4838 −3.15001
\(863\) −43.0230 −1.46452 −0.732260 0.681026i \(-0.761534\pi\)
−0.732260 + 0.681026i \(0.761534\pi\)
\(864\) −8.10165 −0.275624
\(865\) −48.4138 −1.64612
\(866\) 53.9130 1.83204
\(867\) 1.00000 0.0339618
\(868\) −38.1920 −1.29632
\(869\) 0.226131 0.00767098
\(870\) 32.4169 1.09903
\(871\) 24.8360 0.841536
\(872\) −62.6783 −2.12256
\(873\) −17.9042 −0.605967
\(874\) −0.326753 −0.0110526
\(875\) 15.6867 0.530307
\(876\) 30.3660 1.02597
\(877\) −11.9359 −0.403048 −0.201524 0.979484i \(-0.564589\pi\)
−0.201524 + 0.979484i \(0.564589\pi\)
\(878\) 94.5564 3.19113
\(879\) −14.6330 −0.493559
\(880\) 0.576928 0.0194483
\(881\) −57.4822 −1.93662 −0.968312 0.249742i \(-0.919654\pi\)
−0.968312 + 0.249742i \(0.919654\pi\)
\(882\) 12.1699 0.409783
\(883\) 3.38181 0.113807 0.0569035 0.998380i \(-0.481877\pi\)
0.0569035 + 0.998380i \(0.481877\pi\)
\(884\) 10.6602 0.358543
\(885\) −16.5041 −0.554780
\(886\) −31.7082 −1.06526
\(887\) −21.2891 −0.714818 −0.357409 0.933948i \(-0.616340\pi\)
−0.357409 + 0.933948i \(0.616340\pi\)
\(888\) 29.8332 1.00114
\(889\) −12.8919 −0.432381
\(890\) −88.7205 −2.97392
\(891\) 0.0286762 0.000960689 0
\(892\) 12.2733 0.410939
\(893\) −29.1798 −0.976465
\(894\) 62.4395 2.08829
\(895\) −17.7040 −0.591781
\(896\) −9.01175 −0.301062
\(897\) −0.0772245 −0.00257845
\(898\) 107.681 3.59336
\(899\) −28.5889 −0.953494
\(900\) 2.93994 0.0979980
\(901\) 4.66126 0.155289
\(902\) −0.713318 −0.0237509
\(903\) 10.0819 0.335503
\(904\) 100.081 3.32866
\(905\) 30.7469 1.02206
\(906\) 22.5877 0.750426
\(907\) −5.16508 −0.171504 −0.0857518 0.996317i \(-0.527329\pi\)
−0.0857518 + 0.996317i \(0.527329\pi\)
\(908\) 69.5372 2.30767
\(909\) 3.95845 0.131294
\(910\) −21.1549 −0.701277
\(911\) 26.6273 0.882203 0.441101 0.897457i \(-0.354588\pi\)
0.441101 + 0.897457i \(0.354588\pi\)
\(912\) 31.6987 1.04965
\(913\) −0.173588 −0.00574492
\(914\) −66.3113 −2.19338
\(915\) 28.5399 0.943499
\(916\) −60.8241 −2.00969
\(917\) −5.52557 −0.182470
\(918\) 2.58291 0.0852489
\(919\) 16.5329 0.545372 0.272686 0.962103i \(-0.412088\pi\)
0.272686 + 0.962103i \(0.412088\pi\)
\(920\) −0.554019 −0.0182655
\(921\) −17.6730 −0.582346
\(922\) −71.5897 −2.35768
\(923\) 32.7298 1.07731
\(924\) −0.202642 −0.00666642
\(925\) −2.72101 −0.0894663
\(926\) 2.57605 0.0846542
\(927\) 7.76336 0.254982
\(928\) 42.8554 1.40680
\(929\) −27.5828 −0.904963 −0.452481 0.891774i \(-0.649461\pi\)
−0.452481 + 0.891774i \(0.649461\pi\)
\(930\) −33.1211 −1.08608
\(931\) −17.6136 −0.577263
\(932\) −102.765 −3.36617
\(933\) 11.9994 0.392841
\(934\) 107.637 3.52200
\(935\) −0.0680378 −0.00222508
\(936\) 15.7461 0.514677
\(937\) 16.6308 0.543304 0.271652 0.962396i \(-0.412430\pi\)
0.271652 + 0.962396i \(0.412430\pi\)
\(938\) −42.5237 −1.38845
\(939\) 23.4022 0.763701
\(940\) −86.5153 −2.82182
\(941\) −36.7704 −1.19868 −0.599341 0.800494i \(-0.704571\pi\)
−0.599341 + 0.800494i \(0.704571\pi\)
\(942\) −2.58291 −0.0841559
\(943\) 0.325905 0.0106129
\(944\) −58.9842 −1.91977
\(945\) −3.58909 −0.116753
\(946\) 0.493648 0.0160499
\(947\) 48.1935 1.56608 0.783039 0.621972i \(-0.213668\pi\)
0.783039 + 0.621972i \(0.213668\pi\)
\(948\) 36.8376 1.19643
\(949\) −14.8338 −0.481525
\(950\) −6.07669 −0.197154
\(951\) 30.6745 0.994690
\(952\) −10.4379 −0.338293
\(953\) 21.7547 0.704704 0.352352 0.935868i \(-0.385382\pi\)
0.352352 + 0.935868i \(0.385382\pi\)
\(954\) 12.0396 0.389798
\(955\) 27.0397 0.874983
\(956\) −53.1896 −1.72027
\(957\) −0.151689 −0.00490341
\(958\) −12.5611 −0.405830
\(959\) −6.70771 −0.216603
\(960\) 9.41175 0.303763
\(961\) −1.79004 −0.0577431
\(962\) −25.4841 −0.821640
\(963\) 1.85870 0.0598957
\(964\) 18.7964 0.605392
\(965\) 47.4933 1.52886
\(966\) 0.132222 0.00425418
\(967\) −17.3147 −0.556805 −0.278402 0.960465i \(-0.589805\pi\)
−0.278402 + 0.960465i \(0.589805\pi\)
\(968\) 75.8956 2.43938
\(969\) −3.73826 −0.120090
\(970\) 109.722 3.52297
\(971\) 9.92492 0.318506 0.159253 0.987238i \(-0.449091\pi\)
0.159253 + 0.987238i \(0.449091\pi\)
\(972\) 4.67145 0.149837
\(973\) −23.4263 −0.751013
\(974\) 51.7989 1.65974
\(975\) −1.43616 −0.0459940
\(976\) 101.999 3.26490
\(977\) 13.8017 0.441556 0.220778 0.975324i \(-0.429140\pi\)
0.220778 + 0.975324i \(0.429140\pi\)
\(978\) −22.8163 −0.729586
\(979\) 0.415152 0.0132683
\(980\) −52.2227 −1.66819
\(981\) 9.08366 0.290019
\(982\) 19.5784 0.624772
\(983\) 28.3122 0.903018 0.451509 0.892267i \(-0.350886\pi\)
0.451509 + 0.892267i \(0.350886\pi\)
\(984\) −66.4520 −2.11841
\(985\) −52.8027 −1.68243
\(986\) −13.6629 −0.435115
\(987\) 11.8078 0.375846
\(988\) −39.8508 −1.26782
\(989\) −0.225541 −0.00717178
\(990\) −0.175736 −0.00558525
\(991\) 20.1767 0.640933 0.320467 0.947260i \(-0.396160\pi\)
0.320467 + 0.947260i \(0.396160\pi\)
\(992\) −43.7863 −1.39022
\(993\) −5.21080 −0.165360
\(994\) −56.0393 −1.77746
\(995\) 2.00789 0.0636545
\(996\) −28.2780 −0.896024
\(997\) −33.4910 −1.06067 −0.530335 0.847788i \(-0.677934\pi\)
−0.530335 + 0.847788i \(0.677934\pi\)
\(998\) 54.4848 1.72469
\(999\) −4.32358 −0.136792
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 \(a_p\))