Properties

Label 8043.2.a.t.1.9
Level 8043
Weight 2
Character 8043.1
Self dual Yes
Analytic conductor 64.224
Analytic rank 0
Dimension 52
CM No

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Newspace parameters

Level: \( N \) = \( 8043 = 3 \cdot 7 \cdot 383 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8043.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2236783457\)
Analytic rank: \(0\)
Dimension: \(52\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.9
Character \(\chi\) = 8043.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.95089 q^{2} -1.00000 q^{3} +1.80596 q^{4} +3.26605 q^{5} +1.95089 q^{6} +1.00000 q^{7} +0.378554 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.95089 q^{2} -1.00000 q^{3} +1.80596 q^{4} +3.26605 q^{5} +1.95089 q^{6} +1.00000 q^{7} +0.378554 q^{8} +1.00000 q^{9} -6.37169 q^{10} -1.43949 q^{11} -1.80596 q^{12} -3.48899 q^{13} -1.95089 q^{14} -3.26605 q^{15} -4.35043 q^{16} +3.01314 q^{17} -1.95089 q^{18} +6.60909 q^{19} +5.89834 q^{20} -1.00000 q^{21} +2.80827 q^{22} +7.49534 q^{23} -0.378554 q^{24} +5.66707 q^{25} +6.80662 q^{26} -1.00000 q^{27} +1.80596 q^{28} +1.76528 q^{29} +6.37169 q^{30} -1.14437 q^{31} +7.73009 q^{32} +1.43949 q^{33} -5.87830 q^{34} +3.26605 q^{35} +1.80596 q^{36} +2.00710 q^{37} -12.8936 q^{38} +3.48899 q^{39} +1.23638 q^{40} +1.48767 q^{41} +1.95089 q^{42} -10.3216 q^{43} -2.59965 q^{44} +3.26605 q^{45} -14.6226 q^{46} +5.79854 q^{47} +4.35043 q^{48} +1.00000 q^{49} -11.0558 q^{50} -3.01314 q^{51} -6.30096 q^{52} -0.0536793 q^{53} +1.95089 q^{54} -4.70143 q^{55} +0.378554 q^{56} -6.60909 q^{57} -3.44386 q^{58} +0.935462 q^{59} -5.89834 q^{60} +3.12556 q^{61} +2.23254 q^{62} +1.00000 q^{63} -6.37966 q^{64} -11.3952 q^{65} -2.80827 q^{66} +8.90697 q^{67} +5.44161 q^{68} -7.49534 q^{69} -6.37169 q^{70} -5.37319 q^{71} +0.378554 q^{72} -5.95082 q^{73} -3.91562 q^{74} -5.66707 q^{75} +11.9357 q^{76} -1.43949 q^{77} -6.80662 q^{78} +5.79667 q^{79} -14.2087 q^{80} +1.00000 q^{81} -2.90228 q^{82} -9.06967 q^{83} -1.80596 q^{84} +9.84107 q^{85} +20.1362 q^{86} -1.76528 q^{87} -0.544923 q^{88} +3.30982 q^{89} -6.37169 q^{90} -3.48899 q^{91} +13.5363 q^{92} +1.14437 q^{93} -11.3123 q^{94} +21.5856 q^{95} -7.73009 q^{96} +5.46972 q^{97} -1.95089 q^{98} -1.43949 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 52q + 3q^{2} - 52q^{3} + 61q^{4} - 7q^{5} - 3q^{6} + 52q^{7} + 24q^{8} + 52q^{9} + O(q^{10}) \) \( 52q + 3q^{2} - 52q^{3} + 61q^{4} - 7q^{5} - 3q^{6} + 52q^{7} + 24q^{8} + 52q^{9} - 2q^{10} + 9q^{11} - 61q^{12} + 44q^{13} + 3q^{14} + 7q^{15} + 95q^{16} - 6q^{17} + 3q^{18} + 7q^{19} - 21q^{20} - 52q^{21} + 19q^{22} - 4q^{23} - 24q^{24} + 83q^{25} - 5q^{26} - 52q^{27} + 61q^{28} + 31q^{29} + 2q^{30} + 11q^{31} + 71q^{32} - 9q^{33} + 17q^{34} - 7q^{35} + 61q^{36} + 71q^{37} - 8q^{38} - 44q^{39} + 20q^{40} - 25q^{41} - 3q^{42} + 75q^{43} + 14q^{44} - 7q^{45} + 36q^{46} - 20q^{47} - 95q^{48} + 52q^{49} + 26q^{50} + 6q^{51} + 88q^{52} + 70q^{53} - 3q^{54} + 12q^{55} + 24q^{56} - 7q^{57} + 48q^{58} - 27q^{59} + 21q^{60} + 59q^{61} - 23q^{62} + 52q^{63} + 138q^{64} + 44q^{65} - 19q^{66} + 65q^{67} - 8q^{68} + 4q^{69} - 2q^{70} - 11q^{71} + 24q^{72} + 34q^{73} + 38q^{74} - 83q^{75} + 31q^{76} + 9q^{77} + 5q^{78} + 74q^{79} - 5q^{80} + 52q^{81} + 51q^{82} - 30q^{83} - 61q^{84} + 70q^{85} + 29q^{86} - 31q^{87} + 90q^{88} - q^{89} - 2q^{90} + 44q^{91} + 34q^{92} - 11q^{93} + 27q^{94} + 9q^{95} - 71q^{96} + 73q^{97} + 3q^{98} + 9q^{99} + O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.95089 −1.37949 −0.689743 0.724055i \(-0.742276\pi\)
−0.689743 + 0.724055i \(0.742276\pi\)
\(3\) −1.00000 −0.577350
\(4\) 1.80596 0.902979
\(5\) 3.26605 1.46062 0.730310 0.683115i \(-0.239375\pi\)
0.730310 + 0.683115i \(0.239375\pi\)
\(6\) 1.95089 0.796446
\(7\) 1.00000 0.377964
\(8\) 0.378554 0.133839
\(9\) 1.00000 0.333333
\(10\) −6.37169 −2.01490
\(11\) −1.43949 −0.434021 −0.217011 0.976169i \(-0.569631\pi\)
−0.217011 + 0.976169i \(0.569631\pi\)
\(12\) −1.80596 −0.521335
\(13\) −3.48899 −0.967671 −0.483835 0.875159i \(-0.660757\pi\)
−0.483835 + 0.875159i \(0.660757\pi\)
\(14\) −1.95089 −0.521396
\(15\) −3.26605 −0.843290
\(16\) −4.35043 −1.08761
\(17\) 3.01314 0.730795 0.365397 0.930852i \(-0.380933\pi\)
0.365397 + 0.930852i \(0.380933\pi\)
\(18\) −1.95089 −0.459828
\(19\) 6.60909 1.51623 0.758115 0.652121i \(-0.226121\pi\)
0.758115 + 0.652121i \(0.226121\pi\)
\(20\) 5.89834 1.31891
\(21\) −1.00000 −0.218218
\(22\) 2.80827 0.598726
\(23\) 7.49534 1.56289 0.781444 0.623976i \(-0.214484\pi\)
0.781444 + 0.623976i \(0.214484\pi\)
\(24\) −0.378554 −0.0772721
\(25\) 5.66707 1.13341
\(26\) 6.80662 1.33489
\(27\) −1.00000 −0.192450
\(28\) 1.80596 0.341294
\(29\) 1.76528 0.327804 0.163902 0.986477i \(-0.447592\pi\)
0.163902 + 0.986477i \(0.447592\pi\)
\(30\) 6.37169 1.16331
\(31\) −1.14437 −0.205535 −0.102768 0.994705i \(-0.532770\pi\)
−0.102768 + 0.994705i \(0.532770\pi\)
\(32\) 7.73009 1.36650
\(33\) 1.43949 0.250582
\(34\) −5.87830 −1.00812
\(35\) 3.26605 0.552063
\(36\) 1.80596 0.300993
\(37\) 2.00710 0.329965 0.164982 0.986297i \(-0.447243\pi\)
0.164982 + 0.986297i \(0.447243\pi\)
\(38\) −12.8936 −2.09162
\(39\) 3.48899 0.558685
\(40\) 1.23638 0.195488
\(41\) 1.48767 0.232336 0.116168 0.993230i \(-0.462939\pi\)
0.116168 + 0.993230i \(0.462939\pi\)
\(42\) 1.95089 0.301028
\(43\) −10.3216 −1.57402 −0.787012 0.616937i \(-0.788373\pi\)
−0.787012 + 0.616937i \(0.788373\pi\)
\(44\) −2.59965 −0.391912
\(45\) 3.26605 0.486874
\(46\) −14.6226 −2.15598
\(47\) 5.79854 0.845804 0.422902 0.906175i \(-0.361011\pi\)
0.422902 + 0.906175i \(0.361011\pi\)
\(48\) 4.35043 0.627931
\(49\) 1.00000 0.142857
\(50\) −11.0558 −1.56353
\(51\) −3.01314 −0.421925
\(52\) −6.30096 −0.873786
\(53\) −0.0536793 −0.00737341 −0.00368671 0.999993i \(-0.501174\pi\)
−0.00368671 + 0.999993i \(0.501174\pi\)
\(54\) 1.95089 0.265482
\(55\) −4.70143 −0.633940
\(56\) 0.378554 0.0505865
\(57\) −6.60909 −0.875396
\(58\) −3.44386 −0.452201
\(59\) 0.935462 0.121787 0.0608934 0.998144i \(-0.480605\pi\)
0.0608934 + 0.998144i \(0.480605\pi\)
\(60\) −5.89834 −0.761473
\(61\) 3.12556 0.400186 0.200093 0.979777i \(-0.435876\pi\)
0.200093 + 0.979777i \(0.435876\pi\)
\(62\) 2.23254 0.283533
\(63\) 1.00000 0.125988
\(64\) −6.37966 −0.797458
\(65\) −11.3952 −1.41340
\(66\) −2.80827 −0.345674
\(67\) 8.90697 1.08816 0.544080 0.839033i \(-0.316879\pi\)
0.544080 + 0.839033i \(0.316879\pi\)
\(68\) 5.44161 0.659892
\(69\) −7.49534 −0.902333
\(70\) −6.37169 −0.761562
\(71\) −5.37319 −0.637680 −0.318840 0.947809i \(-0.603293\pi\)
−0.318840 + 0.947809i \(0.603293\pi\)
\(72\) 0.378554 0.0446131
\(73\) −5.95082 −0.696491 −0.348245 0.937403i \(-0.613222\pi\)
−0.348245 + 0.937403i \(0.613222\pi\)
\(74\) −3.91562 −0.455182
\(75\) −5.66707 −0.654376
\(76\) 11.9357 1.36912
\(77\) −1.43949 −0.164045
\(78\) −6.80662 −0.770698
\(79\) 5.79667 0.652176 0.326088 0.945339i \(-0.394269\pi\)
0.326088 + 0.945339i \(0.394269\pi\)
\(80\) −14.2087 −1.58858
\(81\) 1.00000 0.111111
\(82\) −2.90228 −0.320504
\(83\) −9.06967 −0.995525 −0.497763 0.867313i \(-0.665845\pi\)
−0.497763 + 0.867313i \(0.665845\pi\)
\(84\) −1.80596 −0.197046
\(85\) 9.84107 1.06741
\(86\) 20.1362 2.17134
\(87\) −1.76528 −0.189258
\(88\) −0.544923 −0.0580890
\(89\) 3.30982 0.350840 0.175420 0.984494i \(-0.443872\pi\)
0.175420 + 0.984494i \(0.443872\pi\)
\(90\) −6.37169 −0.671635
\(91\) −3.48899 −0.365745
\(92\) 13.5363 1.41125
\(93\) 1.14437 0.118666
\(94\) −11.3123 −1.16677
\(95\) 21.5856 2.21464
\(96\) −7.73009 −0.788949
\(97\) 5.46972 0.555365 0.277683 0.960673i \(-0.410434\pi\)
0.277683 + 0.960673i \(0.410434\pi\)
\(98\) −1.95089 −0.197069
\(99\) −1.43949 −0.144674
\(100\) 10.2345 1.02345
\(101\) −2.98367 −0.296887 −0.148443 0.988921i \(-0.547426\pi\)
−0.148443 + 0.988921i \(0.547426\pi\)
\(102\) 5.87830 0.582039
\(103\) 8.91168 0.878094 0.439047 0.898464i \(-0.355316\pi\)
0.439047 + 0.898464i \(0.355316\pi\)
\(104\) −1.32077 −0.129512
\(105\) −3.26605 −0.318734
\(106\) 0.104722 0.0101715
\(107\) −9.32518 −0.901499 −0.450749 0.892651i \(-0.648843\pi\)
−0.450749 + 0.892651i \(0.648843\pi\)
\(108\) −1.80596 −0.173778
\(109\) 1.79471 0.171902 0.0859509 0.996299i \(-0.472607\pi\)
0.0859509 + 0.996299i \(0.472607\pi\)
\(110\) 9.17195 0.874511
\(111\) −2.00710 −0.190505
\(112\) −4.35043 −0.411077
\(113\) 18.3322 1.72455 0.862276 0.506439i \(-0.169039\pi\)
0.862276 + 0.506439i \(0.169039\pi\)
\(114\) 12.8936 1.20760
\(115\) 24.4802 2.28279
\(116\) 3.18802 0.296000
\(117\) −3.48899 −0.322557
\(118\) −1.82498 −0.168003
\(119\) 3.01314 0.276215
\(120\) −1.23638 −0.112865
\(121\) −8.92788 −0.811626
\(122\) −6.09760 −0.552051
\(123\) −1.48767 −0.134139
\(124\) −2.06669 −0.185594
\(125\) 2.17867 0.194866
\(126\) −1.95089 −0.173799
\(127\) −2.02704 −0.179871 −0.0899355 0.995948i \(-0.528666\pi\)
−0.0899355 + 0.995948i \(0.528666\pi\)
\(128\) −3.01418 −0.266419
\(129\) 10.3216 0.908764
\(130\) 22.2307 1.94976
\(131\) 9.38551 0.820015 0.410008 0.912082i \(-0.365526\pi\)
0.410008 + 0.912082i \(0.365526\pi\)
\(132\) 2.59965 0.226270
\(133\) 6.60909 0.573081
\(134\) −17.3765 −1.50110
\(135\) −3.26605 −0.281097
\(136\) 1.14064 0.0978090
\(137\) 7.35628 0.628489 0.314245 0.949342i \(-0.398249\pi\)
0.314245 + 0.949342i \(0.398249\pi\)
\(138\) 14.6226 1.24476
\(139\) 5.67058 0.480972 0.240486 0.970653i \(-0.422693\pi\)
0.240486 + 0.970653i \(0.422693\pi\)
\(140\) 5.89834 0.498501
\(141\) −5.79854 −0.488325
\(142\) 10.4825 0.879670
\(143\) 5.02234 0.419990
\(144\) −4.35043 −0.362536
\(145\) 5.76549 0.478798
\(146\) 11.6094 0.960799
\(147\) −1.00000 −0.0824786
\(148\) 3.62473 0.297951
\(149\) 4.34367 0.355847 0.177924 0.984044i \(-0.443062\pi\)
0.177924 + 0.984044i \(0.443062\pi\)
\(150\) 11.0558 0.902703
\(151\) 3.02545 0.246207 0.123104 0.992394i \(-0.460715\pi\)
0.123104 + 0.992394i \(0.460715\pi\)
\(152\) 2.50190 0.202931
\(153\) 3.01314 0.243598
\(154\) 2.80827 0.226297
\(155\) −3.73757 −0.300209
\(156\) 6.30096 0.504481
\(157\) 9.49801 0.758024 0.379012 0.925392i \(-0.376264\pi\)
0.379012 + 0.925392i \(0.376264\pi\)
\(158\) −11.3086 −0.899667
\(159\) 0.0536793 0.00425704
\(160\) 25.2468 1.99594
\(161\) 7.49534 0.590716
\(162\) −1.95089 −0.153276
\(163\) 0.407358 0.0319067 0.0159534 0.999873i \(-0.494922\pi\)
0.0159534 + 0.999873i \(0.494922\pi\)
\(164\) 2.68668 0.209794
\(165\) 4.70143 0.366006
\(166\) 17.6939 1.37331
\(167\) −5.70345 −0.441346 −0.220673 0.975348i \(-0.570825\pi\)
−0.220673 + 0.975348i \(0.570825\pi\)
\(168\) −0.378554 −0.0292061
\(169\) −0.826971 −0.0636132
\(170\) −19.1988 −1.47248
\(171\) 6.60909 0.505410
\(172\) −18.6403 −1.42131
\(173\) −1.94055 −0.147537 −0.0737685 0.997275i \(-0.523503\pi\)
−0.0737685 + 0.997275i \(0.523503\pi\)
\(174\) 3.44386 0.261078
\(175\) 5.66707 0.428390
\(176\) 6.26238 0.472045
\(177\) −0.935462 −0.0703136
\(178\) −6.45709 −0.483979
\(179\) −6.33176 −0.473258 −0.236629 0.971600i \(-0.576043\pi\)
−0.236629 + 0.971600i \(0.576043\pi\)
\(180\) 5.89834 0.439637
\(181\) 18.4468 1.37114 0.685570 0.728007i \(-0.259553\pi\)
0.685570 + 0.728007i \(0.259553\pi\)
\(182\) 6.80662 0.504540
\(183\) −3.12556 −0.231048
\(184\) 2.83740 0.209176
\(185\) 6.55528 0.481954
\(186\) −2.23254 −0.163698
\(187\) −4.33738 −0.317180
\(188\) 10.4719 0.763743
\(189\) −1.00000 −0.0727393
\(190\) −42.1111 −3.05506
\(191\) 6.18650 0.447640 0.223820 0.974631i \(-0.428147\pi\)
0.223820 + 0.974631i \(0.428147\pi\)
\(192\) 6.37966 0.460413
\(193\) −10.9880 −0.790936 −0.395468 0.918480i \(-0.629418\pi\)
−0.395468 + 0.918480i \(0.629418\pi\)
\(194\) −10.6708 −0.766118
\(195\) 11.3952 0.816027
\(196\) 1.80596 0.128997
\(197\) 11.8638 0.845264 0.422632 0.906301i \(-0.361106\pi\)
0.422632 + 0.906301i \(0.361106\pi\)
\(198\) 2.80827 0.199575
\(199\) −8.54030 −0.605406 −0.302703 0.953085i \(-0.597889\pi\)
−0.302703 + 0.953085i \(0.597889\pi\)
\(200\) 2.14529 0.151695
\(201\) −8.90697 −0.628250
\(202\) 5.82081 0.409551
\(203\) 1.76528 0.123898
\(204\) −5.44161 −0.380989
\(205\) 4.85881 0.339354
\(206\) −17.3857 −1.21132
\(207\) 7.49534 0.520962
\(208\) 15.1786 1.05245
\(209\) −9.51369 −0.658076
\(210\) 6.37169 0.439688
\(211\) 9.42075 0.648551 0.324276 0.945963i \(-0.394879\pi\)
0.324276 + 0.945963i \(0.394879\pi\)
\(212\) −0.0969425 −0.00665804
\(213\) 5.37319 0.368165
\(214\) 18.1924 1.24360
\(215\) −33.7107 −2.29905
\(216\) −0.378554 −0.0257574
\(217\) −1.14437 −0.0776850
\(218\) −3.50127 −0.237136
\(219\) 5.95082 0.402119
\(220\) −8.49058 −0.572435
\(221\) −10.5128 −0.707169
\(222\) 3.91562 0.262799
\(223\) −12.1252 −0.811967 −0.405983 0.913880i \(-0.633071\pi\)
−0.405983 + 0.913880i \(0.633071\pi\)
\(224\) 7.73009 0.516488
\(225\) 5.66707 0.377804
\(226\) −35.7641 −2.37899
\(227\) 7.43302 0.493347 0.246673 0.969099i \(-0.420663\pi\)
0.246673 + 0.969099i \(0.420663\pi\)
\(228\) −11.9357 −0.790464
\(229\) −9.16552 −0.605675 −0.302837 0.953042i \(-0.597934\pi\)
−0.302837 + 0.953042i \(0.597934\pi\)
\(230\) −47.7580 −3.14907
\(231\) 1.43949 0.0947112
\(232\) 0.668254 0.0438730
\(233\) −19.5291 −1.27939 −0.639697 0.768627i \(-0.720940\pi\)
−0.639697 + 0.768627i \(0.720940\pi\)
\(234\) 6.80662 0.444962
\(235\) 18.9383 1.23540
\(236\) 1.68940 0.109971
\(237\) −5.79667 −0.376534
\(238\) −5.87830 −0.381034
\(239\) −3.26265 −0.211043 −0.105522 0.994417i \(-0.533651\pi\)
−0.105522 + 0.994417i \(0.533651\pi\)
\(240\) 14.2087 0.917169
\(241\) 26.5215 1.70840 0.854199 0.519946i \(-0.174048\pi\)
0.854199 + 0.519946i \(0.174048\pi\)
\(242\) 17.4173 1.11963
\(243\) −1.00000 −0.0641500
\(244\) 5.64462 0.361360
\(245\) 3.26605 0.208660
\(246\) 2.90228 0.185043
\(247\) −23.0590 −1.46721
\(248\) −0.433207 −0.0275086
\(249\) 9.06967 0.574767
\(250\) −4.25034 −0.268815
\(251\) 10.6804 0.674138 0.337069 0.941480i \(-0.390564\pi\)
0.337069 + 0.941480i \(0.390564\pi\)
\(252\) 1.80596 0.113765
\(253\) −10.7894 −0.678326
\(254\) 3.95453 0.248129
\(255\) −9.84107 −0.616272
\(256\) 18.6397 1.16498
\(257\) 0.319850 0.0199517 0.00997585 0.999950i \(-0.496825\pi\)
0.00997585 + 0.999950i \(0.496825\pi\)
\(258\) −20.1362 −1.25363
\(259\) 2.00710 0.124715
\(260\) −20.5792 −1.27627
\(261\) 1.76528 0.109268
\(262\) −18.3101 −1.13120
\(263\) −13.7882 −0.850219 −0.425109 0.905142i \(-0.639764\pi\)
−0.425109 + 0.905142i \(0.639764\pi\)
\(264\) 0.544923 0.0335377
\(265\) −0.175319 −0.0107698
\(266\) −12.8936 −0.790557
\(267\) −3.30982 −0.202558
\(268\) 16.0856 0.982586
\(269\) −12.4605 −0.759731 −0.379866 0.925042i \(-0.624030\pi\)
−0.379866 + 0.925042i \(0.624030\pi\)
\(270\) 6.37169 0.387769
\(271\) −3.46189 −0.210295 −0.105147 0.994457i \(-0.533531\pi\)
−0.105147 + 0.994457i \(0.533531\pi\)
\(272\) −13.1085 −0.794818
\(273\) 3.48899 0.211163
\(274\) −14.3513 −0.866992
\(275\) −8.15766 −0.491925
\(276\) −13.5363 −0.814788
\(277\) 25.8641 1.55402 0.777011 0.629487i \(-0.216735\pi\)
0.777011 + 0.629487i \(0.216735\pi\)
\(278\) −11.0627 −0.663494
\(279\) −1.14437 −0.0685117
\(280\) 1.23638 0.0738876
\(281\) −13.0980 −0.781363 −0.390682 0.920526i \(-0.627761\pi\)
−0.390682 + 0.920526i \(0.627761\pi\)
\(282\) 11.3123 0.673637
\(283\) −11.8955 −0.707116 −0.353558 0.935413i \(-0.615028\pi\)
−0.353558 + 0.935413i \(0.615028\pi\)
\(284\) −9.70375 −0.575812
\(285\) −21.5856 −1.27862
\(286\) −9.79802 −0.579369
\(287\) 1.48767 0.0878146
\(288\) 7.73009 0.455500
\(289\) −7.92096 −0.465939
\(290\) −11.2478 −0.660494
\(291\) −5.46972 −0.320640
\(292\) −10.7469 −0.628917
\(293\) −16.4343 −0.960100 −0.480050 0.877241i \(-0.659381\pi\)
−0.480050 + 0.877241i \(0.659381\pi\)
\(294\) 1.95089 0.113778
\(295\) 3.05526 0.177884
\(296\) 0.759796 0.0441622
\(297\) 1.43949 0.0835274
\(298\) −8.47400 −0.490886
\(299\) −26.1512 −1.51236
\(300\) −10.2345 −0.590888
\(301\) −10.3216 −0.594925
\(302\) −5.90230 −0.339639
\(303\) 2.98367 0.171408
\(304\) −28.7524 −1.64906
\(305\) 10.2082 0.584521
\(306\) −5.87830 −0.336040
\(307\) 5.36031 0.305929 0.152965 0.988232i \(-0.451118\pi\)
0.152965 + 0.988232i \(0.451118\pi\)
\(308\) −2.59965 −0.148129
\(309\) −8.91168 −0.506968
\(310\) 7.29157 0.414134
\(311\) −32.1402 −1.82250 −0.911252 0.411848i \(-0.864883\pi\)
−0.911252 + 0.411848i \(0.864883\pi\)
\(312\) 1.32077 0.0747739
\(313\) −3.45816 −0.195467 −0.0977333 0.995213i \(-0.531159\pi\)
−0.0977333 + 0.995213i \(0.531159\pi\)
\(314\) −18.5295 −1.04568
\(315\) 3.26605 0.184021
\(316\) 10.4685 0.588901
\(317\) 30.5235 1.71437 0.857186 0.515006i \(-0.172210\pi\)
0.857186 + 0.515006i \(0.172210\pi\)
\(318\) −0.104722 −0.00587253
\(319\) −2.54109 −0.142274
\(320\) −20.8363 −1.16478
\(321\) 9.32518 0.520481
\(322\) −14.6226 −0.814884
\(323\) 19.9142 1.10805
\(324\) 1.80596 0.100331
\(325\) −19.7723 −1.09677
\(326\) −0.794708 −0.0440148
\(327\) −1.79471 −0.0992476
\(328\) 0.563165 0.0310956
\(329\) 5.79854 0.319684
\(330\) −9.17195 −0.504899
\(331\) −21.7793 −1.19710 −0.598550 0.801086i \(-0.704256\pi\)
−0.598550 + 0.801086i \(0.704256\pi\)
\(332\) −16.3794 −0.898938
\(333\) 2.00710 0.109988
\(334\) 11.1268 0.608830
\(335\) 29.0906 1.58939
\(336\) 4.35043 0.237336
\(337\) −27.2936 −1.48678 −0.743388 0.668861i \(-0.766782\pi\)
−0.743388 + 0.668861i \(0.766782\pi\)
\(338\) 1.61333 0.0877534
\(339\) −18.3322 −0.995670
\(340\) 17.7726 0.963853
\(341\) 1.64731 0.0892066
\(342\) −12.8936 −0.697205
\(343\) 1.00000 0.0539949
\(344\) −3.90727 −0.210666
\(345\) −24.4802 −1.31797
\(346\) 3.78579 0.203525
\(347\) 23.4078 1.25660 0.628298 0.777973i \(-0.283752\pi\)
0.628298 + 0.777973i \(0.283752\pi\)
\(348\) −3.18802 −0.170896
\(349\) −7.10331 −0.380232 −0.190116 0.981762i \(-0.560886\pi\)
−0.190116 + 0.981762i \(0.560886\pi\)
\(350\) −11.0558 −0.590958
\(351\) 3.48899 0.186228
\(352\) −11.1273 −0.593090
\(353\) −13.9706 −0.743581 −0.371790 0.928317i \(-0.621256\pi\)
−0.371790 + 0.928317i \(0.621256\pi\)
\(354\) 1.82498 0.0969966
\(355\) −17.5491 −0.931409
\(356\) 5.97740 0.316801
\(357\) −3.01314 −0.159473
\(358\) 12.3525 0.652852
\(359\) −25.6347 −1.35295 −0.676475 0.736466i \(-0.736493\pi\)
−0.676475 + 0.736466i \(0.736493\pi\)
\(360\) 1.23638 0.0651628
\(361\) 24.6801 1.29895
\(362\) −35.9876 −1.89147
\(363\) 8.92788 0.468592
\(364\) −6.30096 −0.330260
\(365\) −19.4357 −1.01731
\(366\) 6.09760 0.318727
\(367\) −5.04974 −0.263595 −0.131797 0.991277i \(-0.542075\pi\)
−0.131797 + 0.991277i \(0.542075\pi\)
\(368\) −32.6080 −1.69981
\(369\) 1.48767 0.0774452
\(370\) −12.7886 −0.664848
\(371\) −0.0536793 −0.00278689
\(372\) 2.06669 0.107153
\(373\) 16.0478 0.830923 0.415462 0.909611i \(-0.363620\pi\)
0.415462 + 0.909611i \(0.363620\pi\)
\(374\) 8.46173 0.437546
\(375\) −2.17867 −0.112506
\(376\) 2.19506 0.113202
\(377\) −6.15904 −0.317207
\(378\) 1.95089 0.100343
\(379\) 4.61899 0.237261 0.118631 0.992938i \(-0.462150\pi\)
0.118631 + 0.992938i \(0.462150\pi\)
\(380\) 38.9827 1.99977
\(381\) 2.02704 0.103849
\(382\) −12.0692 −0.617512
\(383\) −1.00000 −0.0510976
\(384\) 3.01418 0.153817
\(385\) −4.70143 −0.239607
\(386\) 21.4364 1.09108
\(387\) −10.3216 −0.524675
\(388\) 9.87807 0.501483
\(389\) 10.3376 0.524136 0.262068 0.965049i \(-0.415596\pi\)
0.262068 + 0.965049i \(0.415596\pi\)
\(390\) −22.2307 −1.12570
\(391\) 22.5846 1.14215
\(392\) 0.378554 0.0191199
\(393\) −9.38551 −0.473436
\(394\) −23.1450 −1.16603
\(395\) 18.9322 0.952582
\(396\) −2.59965 −0.130637
\(397\) 29.8353 1.49739 0.748694 0.662916i \(-0.230681\pi\)
0.748694 + 0.662916i \(0.230681\pi\)
\(398\) 16.6612 0.835148
\(399\) −6.60909 −0.330868
\(400\) −24.6542 −1.23271
\(401\) 14.5231 0.725251 0.362626 0.931935i \(-0.381880\pi\)
0.362626 + 0.931935i \(0.381880\pi\)
\(402\) 17.3765 0.866661
\(403\) 3.99270 0.198890
\(404\) −5.38839 −0.268082
\(405\) 3.26605 0.162291
\(406\) −3.44386 −0.170916
\(407\) −2.88919 −0.143212
\(408\) −1.14064 −0.0564700
\(409\) 23.8252 1.17808 0.589040 0.808104i \(-0.299506\pi\)
0.589040 + 0.808104i \(0.299506\pi\)
\(410\) −9.47899 −0.468134
\(411\) −7.35628 −0.362859
\(412\) 16.0941 0.792900
\(413\) 0.935462 0.0460311
\(414\) −14.6226 −0.718660
\(415\) −29.6220 −1.45409
\(416\) −26.9702 −1.32232
\(417\) −5.67058 −0.277689
\(418\) 18.5601 0.907805
\(419\) 10.3552 0.505885 0.252942 0.967481i \(-0.418602\pi\)
0.252942 + 0.967481i \(0.418602\pi\)
\(420\) −5.89834 −0.287810
\(421\) −7.78179 −0.379261 −0.189631 0.981855i \(-0.560729\pi\)
−0.189631 + 0.981855i \(0.560729\pi\)
\(422\) −18.3788 −0.894667
\(423\) 5.79854 0.281935
\(424\) −0.0203205 −0.000986852 0
\(425\) 17.0757 0.828293
\(426\) −10.4825 −0.507878
\(427\) 3.12556 0.151256
\(428\) −16.8409 −0.814034
\(429\) −5.02234 −0.242481
\(430\) 65.7658 3.17151
\(431\) −26.2215 −1.26304 −0.631522 0.775358i \(-0.717570\pi\)
−0.631522 + 0.775358i \(0.717570\pi\)
\(432\) 4.35043 0.209310
\(433\) 29.5550 1.42032 0.710161 0.704039i \(-0.248622\pi\)
0.710161 + 0.704039i \(0.248622\pi\)
\(434\) 2.23254 0.107165
\(435\) −5.76549 −0.276434
\(436\) 3.24117 0.155224
\(437\) 49.5374 2.36970
\(438\) −11.6094 −0.554717
\(439\) 30.1094 1.43704 0.718522 0.695504i \(-0.244819\pi\)
0.718522 + 0.695504i \(0.244819\pi\)
\(440\) −1.77975 −0.0848460
\(441\) 1.00000 0.0476190
\(442\) 20.5093 0.975529
\(443\) −39.7065 −1.88651 −0.943257 0.332064i \(-0.892255\pi\)
−0.943257 + 0.332064i \(0.892255\pi\)
\(444\) −3.62473 −0.172022
\(445\) 10.8100 0.512445
\(446\) 23.6550 1.12010
\(447\) −4.34367 −0.205448
\(448\) −6.37966 −0.301411
\(449\) −13.2739 −0.626433 −0.313217 0.949682i \(-0.601407\pi\)
−0.313217 + 0.949682i \(0.601407\pi\)
\(450\) −11.0558 −0.521176
\(451\) −2.14148 −0.100839
\(452\) 33.1072 1.55723
\(453\) −3.02545 −0.142148
\(454\) −14.5010 −0.680564
\(455\) −11.3952 −0.534215
\(456\) −2.50190 −0.117162
\(457\) 31.3746 1.46764 0.733821 0.679343i \(-0.237735\pi\)
0.733821 + 0.679343i \(0.237735\pi\)
\(458\) 17.8809 0.835519
\(459\) −3.01314 −0.140642
\(460\) 44.2101 2.06131
\(461\) −21.9267 −1.02123 −0.510615 0.859809i \(-0.670582\pi\)
−0.510615 + 0.859809i \(0.670582\pi\)
\(462\) −2.80827 −0.130653
\(463\) 21.8616 1.01600 0.507998 0.861358i \(-0.330386\pi\)
0.507998 + 0.861358i \(0.330386\pi\)
\(464\) −7.67973 −0.356522
\(465\) 3.73757 0.173326
\(466\) 38.0991 1.76490
\(467\) −3.97210 −0.183807 −0.0919034 0.995768i \(-0.529295\pi\)
−0.0919034 + 0.995768i \(0.529295\pi\)
\(468\) −6.30096 −0.291262
\(469\) 8.90697 0.411286
\(470\) −36.9465 −1.70421
\(471\) −9.49801 −0.437645
\(472\) 0.354123 0.0162998
\(473\) 14.8577 0.683160
\(474\) 11.3086 0.519423
\(475\) 37.4542 1.71851
\(476\) 5.44161 0.249416
\(477\) −0.0536793 −0.00245780
\(478\) 6.36506 0.291131
\(479\) −18.4711 −0.843965 −0.421982 0.906604i \(-0.638666\pi\)
−0.421982 + 0.906604i \(0.638666\pi\)
\(480\) −25.2468 −1.15236
\(481\) −7.00274 −0.319297
\(482\) −51.7404 −2.35671
\(483\) −7.49534 −0.341050
\(484\) −16.1234 −0.732881
\(485\) 17.8643 0.811178
\(486\) 1.95089 0.0884940
\(487\) 16.8317 0.762716 0.381358 0.924427i \(-0.375457\pi\)
0.381358 + 0.924427i \(0.375457\pi\)
\(488\) 1.18319 0.0535606
\(489\) −0.407358 −0.0184213
\(490\) −6.37169 −0.287844
\(491\) 17.7431 0.800734 0.400367 0.916355i \(-0.368883\pi\)
0.400367 + 0.916355i \(0.368883\pi\)
\(492\) −2.68668 −0.121125
\(493\) 5.31904 0.239558
\(494\) 44.9856 2.02400
\(495\) −4.70143 −0.211313
\(496\) 4.97851 0.223542
\(497\) −5.37319 −0.241020
\(498\) −17.6939 −0.792882
\(499\) −22.0430 −0.986780 −0.493390 0.869808i \(-0.664242\pi\)
−0.493390 + 0.869808i \(0.664242\pi\)
\(500\) 3.93459 0.175960
\(501\) 5.70345 0.254811
\(502\) −20.8362 −0.929963
\(503\) −9.40324 −0.419270 −0.209635 0.977780i \(-0.567228\pi\)
−0.209635 + 0.977780i \(0.567228\pi\)
\(504\) 0.378554 0.0168622
\(505\) −9.74482 −0.433639
\(506\) 21.0490 0.935741
\(507\) 0.826971 0.0367271
\(508\) −3.66076 −0.162420
\(509\) −3.42550 −0.151832 −0.0759162 0.997114i \(-0.524188\pi\)
−0.0759162 + 0.997114i \(0.524188\pi\)
\(510\) 19.1988 0.850138
\(511\) −5.95082 −0.263249
\(512\) −30.3355 −1.34065
\(513\) −6.60909 −0.291799
\(514\) −0.623991 −0.0275231
\(515\) 29.1060 1.28256
\(516\) 18.6403 0.820594
\(517\) −8.34691 −0.367097
\(518\) −3.91562 −0.172042
\(519\) 1.94055 0.0851805
\(520\) −4.31370 −0.189168
\(521\) 36.4021 1.59481 0.797403 0.603447i \(-0.206206\pi\)
0.797403 + 0.603447i \(0.206206\pi\)
\(522\) −3.44386 −0.150734
\(523\) 24.6066 1.07597 0.537985 0.842954i \(-0.319186\pi\)
0.537985 + 0.842954i \(0.319186\pi\)
\(524\) 16.9498 0.740457
\(525\) −5.66707 −0.247331
\(526\) 26.8993 1.17286
\(527\) −3.44816 −0.150204
\(528\) −6.26238 −0.272535
\(529\) 33.1802 1.44262
\(530\) 0.342028 0.0148567
\(531\) 0.935462 0.0405956
\(532\) 11.9357 0.517480
\(533\) −5.19047 −0.224824
\(534\) 6.45709 0.279425
\(535\) −30.4565 −1.31675
\(536\) 3.37177 0.145638
\(537\) 6.33176 0.273236
\(538\) 24.3091 1.04804
\(539\) −1.43949 −0.0620030
\(540\) −5.89834 −0.253824
\(541\) −12.6112 −0.542197 −0.271099 0.962552i \(-0.587387\pi\)
−0.271099 + 0.962552i \(0.587387\pi\)
\(542\) 6.75375 0.290098
\(543\) −18.4468 −0.791628
\(544\) 23.2919 0.998631
\(545\) 5.86160 0.251083
\(546\) −6.80662 −0.291296
\(547\) 40.0386 1.71193 0.855963 0.517036i \(-0.172965\pi\)
0.855963 + 0.517036i \(0.172965\pi\)
\(548\) 13.2851 0.567513
\(549\) 3.12556 0.133395
\(550\) 15.9147 0.678604
\(551\) 11.6669 0.497026
\(552\) −2.83740 −0.120768
\(553\) 5.79667 0.246499
\(554\) −50.4579 −2.14375
\(555\) −6.55528 −0.278256
\(556\) 10.2408 0.434308
\(557\) −15.1818 −0.643274 −0.321637 0.946863i \(-0.604233\pi\)
−0.321637 + 0.946863i \(0.604233\pi\)
\(558\) 2.23254 0.0945109
\(559\) 36.0118 1.52314
\(560\) −14.2087 −0.600428
\(561\) 4.33738 0.183124
\(562\) 25.5528 1.07788
\(563\) −36.1211 −1.52232 −0.761161 0.648563i \(-0.775370\pi\)
−0.761161 + 0.648563i \(0.775370\pi\)
\(564\) −10.4719 −0.440947
\(565\) 59.8739 2.51892
\(566\) 23.2068 0.975456
\(567\) 1.00000 0.0419961
\(568\) −2.03404 −0.0853466
\(569\) 2.63633 0.110521 0.0552603 0.998472i \(-0.482401\pi\)
0.0552603 + 0.998472i \(0.482401\pi\)
\(570\) 42.1111 1.76384
\(571\) 18.4600 0.772526 0.386263 0.922389i \(-0.373766\pi\)
0.386263 + 0.922389i \(0.373766\pi\)
\(572\) 9.07014 0.379242
\(573\) −6.18650 −0.258445
\(574\) −2.90228 −0.121139
\(575\) 42.4766 1.77140
\(576\) −6.37966 −0.265819
\(577\) 0.299121 0.0124526 0.00622629 0.999981i \(-0.498018\pi\)
0.00622629 + 0.999981i \(0.498018\pi\)
\(578\) 15.4529 0.642756
\(579\) 10.9880 0.456647
\(580\) 10.4122 0.432344
\(581\) −9.06967 −0.376273
\(582\) 10.6708 0.442319
\(583\) 0.0772705 0.00320022
\(584\) −2.25271 −0.0932178
\(585\) −11.3952 −0.471133
\(586\) 32.0614 1.32444
\(587\) 29.2904 1.20894 0.604472 0.796626i \(-0.293384\pi\)
0.604472 + 0.796626i \(0.293384\pi\)
\(588\) −1.80596 −0.0744764
\(589\) −7.56325 −0.311638
\(590\) −5.96047 −0.245389
\(591\) −11.8638 −0.488013
\(592\) −8.73174 −0.358872
\(593\) −20.1341 −0.826807 −0.413404 0.910548i \(-0.635660\pi\)
−0.413404 + 0.910548i \(0.635660\pi\)
\(594\) −2.80827 −0.115225
\(595\) 9.84107 0.403445
\(596\) 7.84448 0.321323
\(597\) 8.54030 0.349531
\(598\) 51.0179 2.08628
\(599\) −23.7233 −0.969306 −0.484653 0.874707i \(-0.661054\pi\)
−0.484653 + 0.874707i \(0.661054\pi\)
\(600\) −2.14529 −0.0875812
\(601\) −29.0331 −1.18428 −0.592142 0.805833i \(-0.701718\pi\)
−0.592142 + 0.805833i \(0.701718\pi\)
\(602\) 20.1362 0.820691
\(603\) 8.90697 0.362720
\(604\) 5.46383 0.222320
\(605\) −29.1589 −1.18548
\(606\) −5.82081 −0.236454
\(607\) 9.25204 0.375529 0.187764 0.982214i \(-0.439876\pi\)
0.187764 + 0.982214i \(0.439876\pi\)
\(608\) 51.0889 2.07193
\(609\) −1.76528 −0.0715327
\(610\) −19.9151 −0.806337
\(611\) −20.2310 −0.818460
\(612\) 5.44161 0.219964
\(613\) 29.0867 1.17480 0.587400 0.809297i \(-0.300152\pi\)
0.587400 + 0.809297i \(0.300152\pi\)
\(614\) −10.4574 −0.422025
\(615\) −4.85881 −0.195926
\(616\) −0.544923 −0.0219556
\(617\) 38.4668 1.54862 0.774308 0.632809i \(-0.218098\pi\)
0.774308 + 0.632809i \(0.218098\pi\)
\(618\) 17.3857 0.699354
\(619\) 2.72131 0.109379 0.0546893 0.998503i \(-0.482583\pi\)
0.0546893 + 0.998503i \(0.482583\pi\)
\(620\) −6.74989 −0.271082
\(621\) −7.49534 −0.300778
\(622\) 62.7019 2.51412
\(623\) 3.30982 0.132605
\(624\) −15.1786 −0.607630
\(625\) −21.2197 −0.848788
\(626\) 6.74647 0.269643
\(627\) 9.51369 0.379940
\(628\) 17.1530 0.684480
\(629\) 6.04768 0.241137
\(630\) −6.37169 −0.253854
\(631\) −32.6133 −1.29831 −0.649157 0.760654i \(-0.724878\pi\)
−0.649157 + 0.760654i \(0.724878\pi\)
\(632\) 2.19435 0.0872867
\(633\) −9.42075 −0.374441
\(634\) −59.5480 −2.36495
\(635\) −6.62042 −0.262723
\(636\) 0.0969425 0.00384402
\(637\) −3.48899 −0.138239
\(638\) 4.95738 0.196265
\(639\) −5.37319 −0.212560
\(640\) −9.84446 −0.389136
\(641\) −25.6089 −1.01149 −0.505745 0.862683i \(-0.668782\pi\)
−0.505745 + 0.862683i \(0.668782\pi\)
\(642\) −18.1924 −0.717995
\(643\) 38.1923 1.50616 0.753079 0.657930i \(-0.228568\pi\)
0.753079 + 0.657930i \(0.228568\pi\)
\(644\) 13.5363 0.533404
\(645\) 33.7107 1.32736
\(646\) −38.8502 −1.52854
\(647\) 0.657378 0.0258442 0.0129221 0.999917i \(-0.495887\pi\)
0.0129221 + 0.999917i \(0.495887\pi\)
\(648\) 0.378554 0.0148710
\(649\) −1.34658 −0.0528580
\(650\) 38.5735 1.51298
\(651\) 1.14437 0.0448514
\(652\) 0.735671 0.0288111
\(653\) −7.18768 −0.281276 −0.140638 0.990061i \(-0.544915\pi\)
−0.140638 + 0.990061i \(0.544915\pi\)
\(654\) 3.50127 0.136911
\(655\) 30.6535 1.19773
\(656\) −6.47202 −0.252690
\(657\) −5.95082 −0.232164
\(658\) −11.3123 −0.440999
\(659\) 10.8833 0.423954 0.211977 0.977275i \(-0.432010\pi\)
0.211977 + 0.977275i \(0.432010\pi\)
\(660\) 8.49058 0.330495
\(661\) 1.13832 0.0442757 0.0221378 0.999755i \(-0.492953\pi\)
0.0221378 + 0.999755i \(0.492953\pi\)
\(662\) 42.4890 1.65138
\(663\) 10.5128 0.408284
\(664\) −3.43336 −0.133240
\(665\) 21.5856 0.837054
\(666\) −3.91562 −0.151727
\(667\) 13.2314 0.512321
\(668\) −10.3002 −0.398526
\(669\) 12.1252 0.468789
\(670\) −56.7525 −2.19254
\(671\) −4.49919 −0.173689
\(672\) −7.73009 −0.298195
\(673\) −15.3130 −0.590273 −0.295136 0.955455i \(-0.595365\pi\)
−0.295136 + 0.955455i \(0.595365\pi\)
\(674\) 53.2466 2.05098
\(675\) −5.66707 −0.218125
\(676\) −1.49348 −0.0574414
\(677\) 12.5657 0.482939 0.241469 0.970408i \(-0.422371\pi\)
0.241469 + 0.970408i \(0.422371\pi\)
\(678\) 35.7641 1.37351
\(679\) 5.46972 0.209908
\(680\) 3.72538 0.142862
\(681\) −7.43302 −0.284834
\(682\) −3.21370 −0.123059
\(683\) 16.2412 0.621453 0.310726 0.950499i \(-0.399428\pi\)
0.310726 + 0.950499i \(0.399428\pi\)
\(684\) 11.9357 0.456374
\(685\) 24.0260 0.917985
\(686\) −1.95089 −0.0744852
\(687\) 9.16552 0.349686
\(688\) 44.9033 1.71192
\(689\) 0.187286 0.00713504
\(690\) 47.7580 1.81812
\(691\) 3.40255 0.129439 0.0647196 0.997903i \(-0.479385\pi\)
0.0647196 + 0.997903i \(0.479385\pi\)
\(692\) −3.50455 −0.133223
\(693\) −1.43949 −0.0546815
\(694\) −45.6659 −1.73345
\(695\) 18.5204 0.702518
\(696\) −0.668254 −0.0253301
\(697\) 4.48258 0.169790
\(698\) 13.8578 0.524524
\(699\) 19.5291 0.738658
\(700\) 10.2345 0.386827
\(701\) −1.92672 −0.0727712 −0.0363856 0.999338i \(-0.511584\pi\)
−0.0363856 + 0.999338i \(0.511584\pi\)
\(702\) −6.80662 −0.256899
\(703\) 13.2651 0.500303
\(704\) 9.18343 0.346114
\(705\) −18.9383 −0.713258
\(706\) 27.2551 1.02576
\(707\) −2.98367 −0.112213
\(708\) −1.68940 −0.0634917
\(709\) 8.65456 0.325029 0.162514 0.986706i \(-0.448040\pi\)
0.162514 + 0.986706i \(0.448040\pi\)
\(710\) 34.2363 1.28486
\(711\) 5.79667 0.217392
\(712\) 1.25295 0.0469562
\(713\) −8.57746 −0.321228
\(714\) 5.87830 0.219990
\(715\) 16.4032 0.613445
\(716\) −11.4349 −0.427342
\(717\) 3.26265 0.121846
\(718\) 50.0105 1.86637
\(719\) −33.3635 −1.24425 −0.622125 0.782918i \(-0.713730\pi\)
−0.622125 + 0.782918i \(0.713730\pi\)
\(720\) −14.2087 −0.529528
\(721\) 8.91168 0.331888
\(722\) −48.1481 −1.79189
\(723\) −26.5215 −0.986344
\(724\) 33.3142 1.23811
\(725\) 10.0040 0.371538
\(726\) −17.4173 −0.646416
\(727\) −37.5605 −1.39304 −0.696521 0.717536i \(-0.745270\pi\)
−0.696521 + 0.717536i \(0.745270\pi\)
\(728\) −1.32077 −0.0489510
\(729\) 1.00000 0.0370370
\(730\) 37.9168 1.40336
\(731\) −31.1004 −1.15029
\(732\) −5.64462 −0.208631
\(733\) 27.5679 1.01824 0.509122 0.860695i \(-0.329970\pi\)
0.509122 + 0.860695i \(0.329970\pi\)
\(734\) 9.85148 0.363625
\(735\) −3.26605 −0.120470
\(736\) 57.9397 2.13569
\(737\) −12.8215 −0.472284
\(738\) −2.90228 −0.106835
\(739\) −19.9805 −0.734996 −0.367498 0.930024i \(-0.619786\pi\)
−0.367498 + 0.930024i \(0.619786\pi\)
\(740\) 11.8386 0.435194
\(741\) 23.0590 0.847095
\(742\) 0.104722 0.00384447
\(743\) 9.09988 0.333842 0.166921 0.985970i \(-0.446617\pi\)
0.166921 + 0.985970i \(0.446617\pi\)
\(744\) 0.433207 0.0158821
\(745\) 14.1866 0.519758
\(746\) −31.3074 −1.14625
\(747\) −9.06967 −0.331842
\(748\) −7.83312 −0.286407
\(749\) −9.32518 −0.340735
\(750\) 4.25034 0.155200
\(751\) −14.9832 −0.546747 −0.273373 0.961908i \(-0.588139\pi\)
−0.273373 + 0.961908i \(0.588139\pi\)
\(752\) −25.2262 −0.919903
\(753\) −10.6804 −0.389214
\(754\) 12.0156 0.437582
\(755\) 9.88125 0.359615
\(756\) −1.80596 −0.0656820
\(757\) 0.597449 0.0217147 0.0108573 0.999941i \(-0.496544\pi\)
0.0108573 + 0.999941i \(0.496544\pi\)
\(758\) −9.01112 −0.327299
\(759\) 10.7894 0.391632
\(760\) 8.17133 0.296405
\(761\) 6.37245 0.231001 0.115501 0.993307i \(-0.463153\pi\)
0.115501 + 0.993307i \(0.463153\pi\)
\(762\) −3.95453 −0.143258
\(763\) 1.79471 0.0649728
\(764\) 11.1726 0.404209
\(765\) 9.84107 0.355805
\(766\) 1.95089 0.0704884
\(767\) −3.26381 −0.117850
\(768\) −18.6397 −0.672601
\(769\) 40.5672 1.46289 0.731446 0.681900i \(-0.238846\pi\)
0.731446 + 0.681900i \(0.238846\pi\)
\(770\) 9.17195 0.330534
\(771\) −0.319850 −0.0115191
\(772\) −19.8439 −0.714199
\(773\) −6.72389 −0.241842 −0.120921 0.992662i \(-0.538585\pi\)
−0.120921 + 0.992662i \(0.538585\pi\)
\(774\) 20.1362 0.723781
\(775\) −6.48523 −0.232956
\(776\) 2.07058 0.0743297
\(777\) −2.00710 −0.0720042
\(778\) −20.1674 −0.723037
\(779\) 9.83217 0.352274
\(780\) 20.5792 0.736855
\(781\) 7.73462 0.276767
\(782\) −44.0599 −1.57558
\(783\) −1.76528 −0.0630859
\(784\) −4.35043 −0.155373
\(785\) 31.0210 1.10719
\(786\) 18.3101 0.653098
\(787\) −25.7925 −0.919403 −0.459701 0.888074i \(-0.652044\pi\)
−0.459701 + 0.888074i \(0.652044\pi\)
\(788\) 21.4256 0.763255
\(789\) 13.7882 0.490874
\(790\) −36.9345 −1.31407
\(791\) 18.3322 0.651819
\(792\) −0.544923 −0.0193630
\(793\) −10.9050 −0.387249
\(794\) −58.2052 −2.06562
\(795\) 0.175319 0.00621793
\(796\) −15.4234 −0.546669
\(797\) 12.2224 0.432940 0.216470 0.976289i \(-0.430546\pi\)
0.216470 + 0.976289i \(0.430546\pi\)
\(798\) 12.8936 0.456428
\(799\) 17.4718 0.618109
\(800\) 43.8069 1.54881
\(801\) 3.30982 0.116947
\(802\) −28.3330 −1.00047
\(803\) 8.56612 0.302292
\(804\) −16.0856 −0.567296
\(805\) 24.4802 0.862812
\(806\) −7.78930 −0.274366
\(807\) 12.4605 0.438631
\(808\) −1.12948 −0.0397351
\(809\) 38.9864 1.37069 0.685345 0.728218i \(-0.259651\pi\)
0.685345 + 0.728218i \(0.259651\pi\)
\(810\) −6.37169 −0.223878
\(811\) 20.8289 0.731400 0.365700 0.930733i \(-0.380830\pi\)
0.365700 + 0.930733i \(0.380830\pi\)
\(812\) 3.18802 0.111878
\(813\) 3.46189 0.121414
\(814\) 5.63648 0.197558
\(815\) 1.33045 0.0466036
\(816\) 13.1085 0.458889
\(817\) −68.2162 −2.38658
\(818\) −46.4803 −1.62514
\(819\) −3.48899 −0.121915
\(820\) 8.77481 0.306430
\(821\) −12.6952 −0.443066 −0.221533 0.975153i \(-0.571106\pi\)
−0.221533 + 0.975153i \(0.571106\pi\)
\(822\) 14.3513 0.500558
\(823\) 34.1746 1.19125 0.595626 0.803262i \(-0.296904\pi\)
0.595626 + 0.803262i \(0.296904\pi\)
\(824\) 3.37356 0.117523
\(825\) 8.15766 0.284013
\(826\) −1.82498 −0.0634992
\(827\) −27.2931 −0.949075 −0.474537 0.880235i \(-0.657385\pi\)
−0.474537 + 0.880235i \(0.657385\pi\)
\(828\) 13.5363 0.470418
\(829\) 10.0320 0.348426 0.174213 0.984708i \(-0.444262\pi\)
0.174213 + 0.984708i \(0.444262\pi\)
\(830\) 57.7891 2.00589
\(831\) −25.8641 −0.897215
\(832\) 22.2586 0.771677
\(833\) 3.01314 0.104399
\(834\) 11.0627 0.383068
\(835\) −18.6277 −0.644639
\(836\) −17.1813 −0.594228
\(837\) 1.14437 0.0395552
\(838\) −20.2018 −0.697860
\(839\) −20.5503 −0.709475 −0.354738 0.934966i \(-0.615430\pi\)
−0.354738 + 0.934966i \(0.615430\pi\)
\(840\) −1.23638 −0.0426590
\(841\) −25.8838 −0.892544
\(842\) 15.1814 0.523185
\(843\) 13.0980 0.451120
\(844\) 17.0135 0.585628
\(845\) −2.70093 −0.0929147
\(846\) −11.3123 −0.388925
\(847\) −8.92788 −0.306766
\(848\) 0.233528 0.00801938
\(849\) 11.8955 0.408254
\(850\) −33.3127 −1.14262
\(851\) 15.0439 0.515698
\(852\) 9.70375 0.332445
\(853\) 32.9954 1.12974 0.564871 0.825179i \(-0.308926\pi\)
0.564871 + 0.825179i \(0.308926\pi\)
\(854\) −6.09760 −0.208656
\(855\) 21.5856 0.738212
\(856\) −3.53009 −0.120656
\(857\) −13.2235 −0.451706 −0.225853 0.974161i \(-0.572517\pi\)
−0.225853 + 0.974161i \(0.572517\pi\)
\(858\) 9.79802 0.334499
\(859\) 48.7649 1.66384 0.831919 0.554898i \(-0.187243\pi\)
0.831919 + 0.554898i \(0.187243\pi\)
\(860\) −60.8802 −2.07600
\(861\) −1.48767 −0.0506998
\(862\) 51.1551 1.74235
\(863\) 33.4688 1.13929 0.569646 0.821890i \(-0.307080\pi\)
0.569646 + 0.821890i \(0.307080\pi\)
\(864\) −7.73009 −0.262983
\(865\) −6.33792 −0.215496
\(866\) −57.6584 −1.95931
\(867\) 7.92096 0.269010
\(868\) −2.06669 −0.0701479
\(869\) −8.34421 −0.283058
\(870\) 11.2478 0.381336
\(871\) −31.0763 −1.05298
\(872\) 0.679394 0.0230072
\(873\) 5.46972 0.185122
\(874\) −96.6419 −3.26896
\(875\) 2.17867 0.0736525
\(876\) 10.7469 0.363105
\(877\) −19.6138 −0.662309 −0.331155 0.943576i \(-0.607438\pi\)
−0.331155 + 0.943576i \(0.607438\pi\)
\(878\) −58.7400 −1.98238
\(879\) 16.4343 0.554314
\(880\) 20.4532 0.689478
\(881\) 20.9543 0.705967 0.352984 0.935630i \(-0.385167\pi\)
0.352984 + 0.935630i \(0.385167\pi\)
\(882\) −1.95089 −0.0656898
\(883\) −52.3519 −1.76178 −0.880890 0.473321i \(-0.843055\pi\)
−0.880890 + 0.473321i \(0.843055\pi\)
\(884\) −18.9857 −0.638559
\(885\) −3.05526 −0.102702
\(886\) 77.4629 2.60242
\(887\) −30.2470 −1.01560 −0.507798 0.861476i \(-0.669540\pi\)
−0.507798 + 0.861476i \(0.669540\pi\)
\(888\) −0.759796 −0.0254971
\(889\) −2.02704 −0.0679849
\(890\) −21.0891 −0.706910
\(891\) −1.43949 −0.0482246
\(892\) −21.8977 −0.733189
\(893\) 38.3231 1.28243
\(894\) 8.47400 0.283413
\(895\) −20.6798 −0.691251
\(896\) −3.01418 −0.100697
\(897\) 26.1512 0.873162
\(898\) 25.8958 0.864156
\(899\) −2.02013 −0.0673753
\(900\) 10.2345 0.341149
\(901\) −0.161743 −0.00538845
\(902\) 4.17779 0.139105
\(903\) 10.3216 0.343480
\(904\) 6.93975 0.230812
\(905\) 60.2482 2.00272
\(906\) 5.90230 0.196091
\(907\) 40.4922 1.34452 0.672261 0.740314i \(-0.265323\pi\)
0.672261 + 0.740314i \(0.265323\pi\)
\(908\) 13.4237 0.445482
\(909\) −2.98367 −0.0989622
\(910\) 22.2307 0.736942
\(911\) 42.0951 1.39467 0.697336 0.716744i \(-0.254369\pi\)
0.697336 + 0.716744i \(0.254369\pi\)
\(912\) 28.7524 0.952087
\(913\) 13.0557 0.432079
\(914\) −61.2083 −2.02459
\(915\) −10.2082 −0.337473
\(916\) −16.5525 −0.546911
\(917\) 9.38551 0.309937
\(918\) 5.87830 0.194013
\(919\) −10.8169 −0.356818 −0.178409 0.983956i \(-0.557095\pi\)
−0.178409 + 0.983956i \(0.557095\pi\)
\(920\) 9.26707 0.305526
\(921\) −5.36031 −0.176628
\(922\) 42.7766 1.40877
\(923\) 18.7470 0.617064
\(924\) 2.59965 0.0855222
\(925\) 11.3744 0.373987
\(926\) −42.6495 −1.40155
\(927\) 8.91168 0.292698
\(928\) 13.6458 0.447944
\(929\) 11.5229 0.378055 0.189027 0.981972i \(-0.439466\pi\)
0.189027 + 0.981972i \(0.439466\pi\)
\(930\) −7.29157 −0.239100
\(931\) 6.60909 0.216604
\(932\) −35.2687 −1.15527
\(933\) 32.1402 1.05222
\(934\) 7.74911 0.253559
\(935\) −14.1661 −0.463280
\(936\) −1.32077 −0.0431708
\(937\) −17.2530 −0.563632 −0.281816 0.959469i \(-0.590937\pi\)
−0.281816 + 0.959469i \(0.590937\pi\)
\(938\) −17.3765 −0.567363
\(939\) 3.45816 0.112853
\(940\) 34.2018 1.11554
\(941\) 5.51735 0.179860 0.0899302 0.995948i \(-0.471336\pi\)
0.0899302 + 0.995948i \(0.471336\pi\)
\(942\) 18.5295 0.603725
\(943\) 11.1506 0.363114
\(944\) −4.06966 −0.132456
\(945\) −3.26605 −0.106245
\(946\) −28.9858 −0.942409
\(947\) 11.7776 0.382721 0.191361 0.981520i \(-0.438710\pi\)
0.191361 + 0.981520i \(0.438710\pi\)
\(948\) −10.4685 −0.340002
\(949\) 20.7623 0.673974
\(950\) −73.0688 −2.37067
\(951\) −30.5235 −0.989794
\(952\) 1.14064 0.0369683
\(953\) 40.5645 1.31401 0.657006 0.753885i \(-0.271823\pi\)
0.657006 + 0.753885i \(0.271823\pi\)
\(954\) 0.104722 0.00339051
\(955\) 20.2054 0.653832
\(956\) −5.89220 −0.190567
\(957\) 2.54109 0.0821419
\(958\) 36.0350 1.16424
\(959\) 7.35628 0.237547
\(960\) 20.8363 0.672488
\(961\) −29.6904 −0.957755
\(962\) 13.6615 0.440466
\(963\) −9.32518 −0.300500
\(964\) 47.8967 1.54265
\(965\) −35.8875 −1.15526
\(966\) 14.6226 0.470473
\(967\) −23.3498 −0.750879 −0.375440 0.926847i \(-0.622508\pi\)
−0.375440 + 0.926847i \(0.622508\pi\)
\(968\) −3.37969 −0.108627
\(969\) −19.9142 −0.639735
\(970\) −34.8513 −1.11901
\(971\) −40.7007 −1.30615 −0.653074 0.757294i \(-0.726521\pi\)
−0.653074 + 0.757294i \(0.726521\pi\)
\(972\) −1.80596 −0.0579261
\(973\) 5.67058 0.181790
\(974\) −32.8367 −1.05216
\(975\) 19.7723 0.633221
\(976\) −13.5975 −0.435246
\(977\) 21.5843 0.690544 0.345272 0.938503i \(-0.387787\pi\)
0.345272 + 0.938503i \(0.387787\pi\)
\(978\) 0.794708 0.0254120
\(979\) −4.76444 −0.152272
\(980\) 5.89834 0.188416
\(981\) 1.79471 0.0573006
\(982\) −34.6147 −1.10460
\(983\) 36.3784 1.16029 0.580146 0.814513i \(-0.302996\pi\)
0.580146 + 0.814513i \(0.302996\pi\)
\(984\) −0.563165 −0.0179531
\(985\) 38.7479 1.23461
\(986\) −10.3768 −0.330466
\(987\) −5.79854 −0.184570
\(988\) −41.6436 −1.32486
\(989\) −77.3637 −2.46002
\(990\) 9.17195 0.291504
\(991\) −48.1578 −1.52978 −0.764891 0.644159i \(-0.777207\pi\)
−0.764891 + 0.644159i \(0.777207\pi\)
\(992\) −8.84609 −0.280864
\(993\) 21.7793 0.691145
\(994\) 10.4825 0.332484
\(995\) −27.8930 −0.884268
\(996\) 16.3794 0.519002
\(997\) 44.0746 1.39586 0.697928 0.716168i \(-0.254106\pi\)
0.697928 + 0.716168i \(0.254106\pi\)
\(998\) 43.0034 1.36125
\(999\) −2.00710 −0.0635018
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 \(a_p\))