Properties

Label 6008.2.a.e.1.39
Level 6008
Weight 2
Character 6008.1
Self dual Yes
Analytic conductor 47.974
Analytic rank 0
Dimension 50
CM No

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Newspace parameters

Level: \( N \) = \( 6008 = 2^{3} \cdot 751 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6008.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(47.9741215344\)
Analytic rank: \(0\)
Dimension: \(50\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.39
Character \(\chi\) = 6008.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.13242 q^{3} -1.12247 q^{5} -4.02550 q^{7} +1.54720 q^{9} +O(q^{10})\) \(q+2.13242 q^{3} -1.12247 q^{5} -4.02550 q^{7} +1.54720 q^{9} -5.57155 q^{11} +0.335534 q^{13} -2.39358 q^{15} +4.79184 q^{17} +1.73171 q^{19} -8.58404 q^{21} -3.07533 q^{23} -3.74005 q^{25} -3.09798 q^{27} +6.66349 q^{29} -3.51015 q^{31} -11.8809 q^{33} +4.51852 q^{35} +5.13640 q^{37} +0.715498 q^{39} +4.64579 q^{41} -9.81357 q^{43} -1.73669 q^{45} +11.9133 q^{47} +9.20464 q^{49} +10.2182 q^{51} +11.4349 q^{53} +6.25393 q^{55} +3.69273 q^{57} +2.35959 q^{59} +9.55165 q^{61} -6.22824 q^{63} -0.376628 q^{65} -2.78716 q^{67} -6.55787 q^{69} +7.12313 q^{71} +6.65412 q^{73} -7.97534 q^{75} +22.4283 q^{77} -8.62639 q^{79} -11.2478 q^{81} -1.96497 q^{83} -5.37873 q^{85} +14.2093 q^{87} +14.7566 q^{89} -1.35069 q^{91} -7.48510 q^{93} -1.94380 q^{95} +5.97150 q^{97} -8.62029 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 50q + 6q^{3} + 23q^{5} + 12q^{7} + 56q^{9} + O(q^{10}) \) \( 50q + 6q^{3} + 23q^{5} + 12q^{7} + 56q^{9} - 5q^{11} + 36q^{13} + 5q^{15} + 14q^{17} + 9q^{19} + 30q^{21} + 3q^{23} + 71q^{25} + 24q^{27} + 61q^{29} + 27q^{31} + 24q^{33} - 7q^{35} + 56q^{37} - 2q^{39} + 10q^{41} + 19q^{43} + 76q^{45} + 3q^{47} + 82q^{49} - q^{51} + 56q^{53} + 7q^{55} + 35q^{57} - q^{59} + 67q^{61} + 25q^{63} + 27q^{65} + 46q^{67} + 68q^{69} + 4q^{71} + 62q^{73} + 27q^{75} + 71q^{77} + 7q^{79} + 74q^{81} - q^{83} + 72q^{85} + 25q^{87} + 19q^{89} + 45q^{91} + 72q^{93} - 24q^{95} + 81q^{97} + 16q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 2.13242 1.23115 0.615576 0.788078i \(-0.288924\pi\)
0.615576 + 0.788078i \(0.288924\pi\)
\(4\) 0 0
\(5\) −1.12247 −0.501986 −0.250993 0.967989i \(-0.580757\pi\)
−0.250993 + 0.967989i \(0.580757\pi\)
\(6\) 0 0
\(7\) −4.02550 −1.52150 −0.760748 0.649048i \(-0.775168\pi\)
−0.760748 + 0.649048i \(0.775168\pi\)
\(8\) 0 0
\(9\) 1.54720 0.515733
\(10\) 0 0
\(11\) −5.57155 −1.67989 −0.839943 0.542675i \(-0.817412\pi\)
−0.839943 + 0.542675i \(0.817412\pi\)
\(12\) 0 0
\(13\) 0.335534 0.0930603 0.0465302 0.998917i \(-0.485184\pi\)
0.0465302 + 0.998917i \(0.485184\pi\)
\(14\) 0 0
\(15\) −2.39358 −0.618021
\(16\) 0 0
\(17\) 4.79184 1.16219 0.581097 0.813835i \(-0.302624\pi\)
0.581097 + 0.813835i \(0.302624\pi\)
\(18\) 0 0
\(19\) 1.73171 0.397282 0.198641 0.980072i \(-0.436347\pi\)
0.198641 + 0.980072i \(0.436347\pi\)
\(20\) 0 0
\(21\) −8.58404 −1.87319
\(22\) 0 0
\(23\) −3.07533 −0.641250 −0.320625 0.947206i \(-0.603893\pi\)
−0.320625 + 0.947206i \(0.603893\pi\)
\(24\) 0 0
\(25\) −3.74005 −0.748010
\(26\) 0 0
\(27\) −3.09798 −0.596206
\(28\) 0 0
\(29\) 6.66349 1.23738 0.618689 0.785636i \(-0.287664\pi\)
0.618689 + 0.785636i \(0.287664\pi\)
\(30\) 0 0
\(31\) −3.51015 −0.630442 −0.315221 0.949018i \(-0.602079\pi\)
−0.315221 + 0.949018i \(0.602079\pi\)
\(32\) 0 0
\(33\) −11.8809 −2.06819
\(34\) 0 0
\(35\) 4.51852 0.763769
\(36\) 0 0
\(37\) 5.13640 0.844418 0.422209 0.906498i \(-0.361255\pi\)
0.422209 + 0.906498i \(0.361255\pi\)
\(38\) 0 0
\(39\) 0.715498 0.114571
\(40\) 0 0
\(41\) 4.64579 0.725551 0.362775 0.931877i \(-0.381829\pi\)
0.362775 + 0.931877i \(0.381829\pi\)
\(42\) 0 0
\(43\) −9.81357 −1.49656 −0.748278 0.663386i \(-0.769119\pi\)
−0.748278 + 0.663386i \(0.769119\pi\)
\(44\) 0 0
\(45\) −1.73669 −0.258891
\(46\) 0 0
\(47\) 11.9133 1.73773 0.868864 0.495051i \(-0.164851\pi\)
0.868864 + 0.495051i \(0.164851\pi\)
\(48\) 0 0
\(49\) 9.20464 1.31495
\(50\) 0 0
\(51\) 10.2182 1.43084
\(52\) 0 0
\(53\) 11.4349 1.57070 0.785351 0.619050i \(-0.212482\pi\)
0.785351 + 0.619050i \(0.212482\pi\)
\(54\) 0 0
\(55\) 6.25393 0.843279
\(56\) 0 0
\(57\) 3.69273 0.489114
\(58\) 0 0
\(59\) 2.35959 0.307192 0.153596 0.988134i \(-0.450915\pi\)
0.153596 + 0.988134i \(0.450915\pi\)
\(60\) 0 0
\(61\) 9.55165 1.22296 0.611482 0.791259i \(-0.290574\pi\)
0.611482 + 0.791259i \(0.290574\pi\)
\(62\) 0 0
\(63\) −6.22824 −0.784685
\(64\) 0 0
\(65\) −0.376628 −0.0467150
\(66\) 0 0
\(67\) −2.78716 −0.340506 −0.170253 0.985400i \(-0.554458\pi\)
−0.170253 + 0.985400i \(0.554458\pi\)
\(68\) 0 0
\(69\) −6.55787 −0.789475
\(70\) 0 0
\(71\) 7.12313 0.845361 0.422680 0.906279i \(-0.361089\pi\)
0.422680 + 0.906279i \(0.361089\pi\)
\(72\) 0 0
\(73\) 6.65412 0.778806 0.389403 0.921067i \(-0.372681\pi\)
0.389403 + 0.921067i \(0.372681\pi\)
\(74\) 0 0
\(75\) −7.97534 −0.920913
\(76\) 0 0
\(77\) 22.4283 2.55594
\(78\) 0 0
\(79\) −8.62639 −0.970545 −0.485273 0.874363i \(-0.661280\pi\)
−0.485273 + 0.874363i \(0.661280\pi\)
\(80\) 0 0
\(81\) −11.2478 −1.24975
\(82\) 0 0
\(83\) −1.96497 −0.215684 −0.107842 0.994168i \(-0.534394\pi\)
−0.107842 + 0.994168i \(0.534394\pi\)
\(84\) 0 0
\(85\) −5.37873 −0.583405
\(86\) 0 0
\(87\) 14.2093 1.52340
\(88\) 0 0
\(89\) 14.7566 1.56420 0.782098 0.623156i \(-0.214150\pi\)
0.782098 + 0.623156i \(0.214150\pi\)
\(90\) 0 0
\(91\) −1.35069 −0.141591
\(92\) 0 0
\(93\) −7.48510 −0.776169
\(94\) 0 0
\(95\) −1.94380 −0.199430
\(96\) 0 0
\(97\) 5.97150 0.606313 0.303157 0.952941i \(-0.401959\pi\)
0.303157 + 0.952941i \(0.401959\pi\)
\(98\) 0 0
\(99\) −8.62029 −0.866372
\(100\) 0 0
\(101\) −3.40272 −0.338583 −0.169292 0.985566i \(-0.554148\pi\)
−0.169292 + 0.985566i \(0.554148\pi\)
\(102\) 0 0
\(103\) 1.65704 0.163273 0.0816363 0.996662i \(-0.473985\pi\)
0.0816363 + 0.996662i \(0.473985\pi\)
\(104\) 0 0
\(105\) 9.63537 0.940315
\(106\) 0 0
\(107\) −3.63844 −0.351741 −0.175870 0.984413i \(-0.556274\pi\)
−0.175870 + 0.984413i \(0.556274\pi\)
\(108\) 0 0
\(109\) −0.535565 −0.0512978 −0.0256489 0.999671i \(-0.508165\pi\)
−0.0256489 + 0.999671i \(0.508165\pi\)
\(110\) 0 0
\(111\) 10.9529 1.03961
\(112\) 0 0
\(113\) −16.9182 −1.59153 −0.795765 0.605606i \(-0.792931\pi\)
−0.795765 + 0.605606i \(0.792931\pi\)
\(114\) 0 0
\(115\) 3.45198 0.321898
\(116\) 0 0
\(117\) 0.519137 0.0479943
\(118\) 0 0
\(119\) −19.2896 −1.76827
\(120\) 0 0
\(121\) 20.0422 1.82202
\(122\) 0 0
\(123\) 9.90676 0.893262
\(124\) 0 0
\(125\) 9.81049 0.877477
\(126\) 0 0
\(127\) 9.05841 0.803804 0.401902 0.915683i \(-0.368349\pi\)
0.401902 + 0.915683i \(0.368349\pi\)
\(128\) 0 0
\(129\) −20.9266 −1.84249
\(130\) 0 0
\(131\) 10.6997 0.934835 0.467418 0.884037i \(-0.345184\pi\)
0.467418 + 0.884037i \(0.345184\pi\)
\(132\) 0 0
\(133\) −6.97101 −0.604463
\(134\) 0 0
\(135\) 3.47740 0.299287
\(136\) 0 0
\(137\) −6.52914 −0.557822 −0.278911 0.960317i \(-0.589973\pi\)
−0.278911 + 0.960317i \(0.589973\pi\)
\(138\) 0 0
\(139\) −13.6873 −1.16094 −0.580472 0.814280i \(-0.697132\pi\)
−0.580472 + 0.814280i \(0.697132\pi\)
\(140\) 0 0
\(141\) 25.4040 2.13941
\(142\) 0 0
\(143\) −1.86944 −0.156331
\(144\) 0 0
\(145\) −7.47960 −0.621147
\(146\) 0 0
\(147\) 19.6281 1.61890
\(148\) 0 0
\(149\) −15.7650 −1.29152 −0.645758 0.763542i \(-0.723459\pi\)
−0.645758 + 0.763542i \(0.723459\pi\)
\(150\) 0 0
\(151\) 8.93828 0.727387 0.363694 0.931519i \(-0.381516\pi\)
0.363694 + 0.931519i \(0.381516\pi\)
\(152\) 0 0
\(153\) 7.41393 0.599381
\(154\) 0 0
\(155\) 3.94006 0.316473
\(156\) 0 0
\(157\) 0.790479 0.0630871 0.0315435 0.999502i \(-0.489958\pi\)
0.0315435 + 0.999502i \(0.489958\pi\)
\(158\) 0 0
\(159\) 24.3839 1.93377
\(160\) 0 0
\(161\) 12.3797 0.975659
\(162\) 0 0
\(163\) 23.8021 1.86433 0.932164 0.362036i \(-0.117918\pi\)
0.932164 + 0.362036i \(0.117918\pi\)
\(164\) 0 0
\(165\) 13.3360 1.03820
\(166\) 0 0
\(167\) −12.9128 −0.999223 −0.499611 0.866250i \(-0.666524\pi\)
−0.499611 + 0.866250i \(0.666524\pi\)
\(168\) 0 0
\(169\) −12.8874 −0.991340
\(170\) 0 0
\(171\) 2.67930 0.204891
\(172\) 0 0
\(173\) 13.0712 0.993782 0.496891 0.867813i \(-0.334475\pi\)
0.496891 + 0.867813i \(0.334475\pi\)
\(174\) 0 0
\(175\) 15.0556 1.13809
\(176\) 0 0
\(177\) 5.03162 0.378200
\(178\) 0 0
\(179\) 9.20320 0.687880 0.343940 0.938992i \(-0.388238\pi\)
0.343940 + 0.938992i \(0.388238\pi\)
\(180\) 0 0
\(181\) 0.613750 0.0456197 0.0228098 0.999740i \(-0.492739\pi\)
0.0228098 + 0.999740i \(0.492739\pi\)
\(182\) 0 0
\(183\) 20.3681 1.50565
\(184\) 0 0
\(185\) −5.76548 −0.423886
\(186\) 0 0
\(187\) −26.6980 −1.95235
\(188\) 0 0
\(189\) 12.4709 0.907125
\(190\) 0 0
\(191\) 6.31450 0.456901 0.228451 0.973556i \(-0.426634\pi\)
0.228451 + 0.973556i \(0.426634\pi\)
\(192\) 0 0
\(193\) 10.8091 0.778052 0.389026 0.921227i \(-0.372812\pi\)
0.389026 + 0.921227i \(0.372812\pi\)
\(194\) 0 0
\(195\) −0.803128 −0.0575132
\(196\) 0 0
\(197\) 20.9045 1.48938 0.744692 0.667409i \(-0.232597\pi\)
0.744692 + 0.667409i \(0.232597\pi\)
\(198\) 0 0
\(199\) 14.3645 1.01828 0.509138 0.860685i \(-0.329964\pi\)
0.509138 + 0.860685i \(0.329964\pi\)
\(200\) 0 0
\(201\) −5.94338 −0.419214
\(202\) 0 0
\(203\) −26.8239 −1.88267
\(204\) 0 0
\(205\) −5.21478 −0.364216
\(206\) 0 0
\(207\) −4.75814 −0.330714
\(208\) 0 0
\(209\) −9.64833 −0.667389
\(210\) 0 0
\(211\) 16.9552 1.16724 0.583622 0.812025i \(-0.301635\pi\)
0.583622 + 0.812025i \(0.301635\pi\)
\(212\) 0 0
\(213\) 15.1895 1.04077
\(214\) 0 0
\(215\) 11.0155 0.751250
\(216\) 0 0
\(217\) 14.1301 0.959214
\(218\) 0 0
\(219\) 14.1894 0.958828
\(220\) 0 0
\(221\) 1.60783 0.108154
\(222\) 0 0
\(223\) 22.9004 1.53352 0.766762 0.641932i \(-0.221867\pi\)
0.766762 + 0.641932i \(0.221867\pi\)
\(224\) 0 0
\(225\) −5.78660 −0.385773
\(226\) 0 0
\(227\) −19.1925 −1.27385 −0.636924 0.770926i \(-0.719794\pi\)
−0.636924 + 0.770926i \(0.719794\pi\)
\(228\) 0 0
\(229\) −4.16542 −0.275258 −0.137629 0.990484i \(-0.543948\pi\)
−0.137629 + 0.990484i \(0.543948\pi\)
\(230\) 0 0
\(231\) 47.8264 3.14675
\(232\) 0 0
\(233\) −24.3789 −1.59711 −0.798557 0.601920i \(-0.794403\pi\)
−0.798557 + 0.601920i \(0.794403\pi\)
\(234\) 0 0
\(235\) −13.3723 −0.872315
\(236\) 0 0
\(237\) −18.3951 −1.19489
\(238\) 0 0
\(239\) 8.48871 0.549089 0.274545 0.961574i \(-0.411473\pi\)
0.274545 + 0.961574i \(0.411473\pi\)
\(240\) 0 0
\(241\) −14.4061 −0.927978 −0.463989 0.885841i \(-0.653582\pi\)
−0.463989 + 0.885841i \(0.653582\pi\)
\(242\) 0 0
\(243\) −14.6910 −0.942428
\(244\) 0 0
\(245\) −10.3320 −0.660086
\(246\) 0 0
\(247\) 0.581048 0.0369712
\(248\) 0 0
\(249\) −4.19014 −0.265539
\(250\) 0 0
\(251\) −12.3277 −0.778118 −0.389059 0.921213i \(-0.627200\pi\)
−0.389059 + 0.921213i \(0.627200\pi\)
\(252\) 0 0
\(253\) 17.1343 1.07723
\(254\) 0 0
\(255\) −11.4697 −0.718259
\(256\) 0 0
\(257\) −21.1730 −1.32073 −0.660366 0.750944i \(-0.729599\pi\)
−0.660366 + 0.750944i \(0.729599\pi\)
\(258\) 0 0
\(259\) −20.6766 −1.28478
\(260\) 0 0
\(261\) 10.3097 0.638157
\(262\) 0 0
\(263\) 17.0142 1.04914 0.524570 0.851367i \(-0.324226\pi\)
0.524570 + 0.851367i \(0.324226\pi\)
\(264\) 0 0
\(265\) −12.8354 −0.788471
\(266\) 0 0
\(267\) 31.4672 1.92576
\(268\) 0 0
\(269\) −13.9957 −0.853334 −0.426667 0.904409i \(-0.640312\pi\)
−0.426667 + 0.904409i \(0.640312\pi\)
\(270\) 0 0
\(271\) −11.1835 −0.679351 −0.339675 0.940543i \(-0.610317\pi\)
−0.339675 + 0.940543i \(0.610317\pi\)
\(272\) 0 0
\(273\) −2.88023 −0.174320
\(274\) 0 0
\(275\) 20.8379 1.25657
\(276\) 0 0
\(277\) 12.3565 0.742431 0.371216 0.928547i \(-0.378941\pi\)
0.371216 + 0.928547i \(0.378941\pi\)
\(278\) 0 0
\(279\) −5.43090 −0.325140
\(280\) 0 0
\(281\) 7.82560 0.466836 0.233418 0.972376i \(-0.425009\pi\)
0.233418 + 0.972376i \(0.425009\pi\)
\(282\) 0 0
\(283\) 7.91901 0.470736 0.235368 0.971906i \(-0.424370\pi\)
0.235368 + 0.971906i \(0.424370\pi\)
\(284\) 0 0
\(285\) −4.14500 −0.245529
\(286\) 0 0
\(287\) −18.7016 −1.10392
\(288\) 0 0
\(289\) 5.96178 0.350693
\(290\) 0 0
\(291\) 12.7337 0.746463
\(292\) 0 0
\(293\) 5.56530 0.325128 0.162564 0.986698i \(-0.448024\pi\)
0.162564 + 0.986698i \(0.448024\pi\)
\(294\) 0 0
\(295\) −2.64858 −0.154206
\(296\) 0 0
\(297\) 17.2605 1.00156
\(298\) 0 0
\(299\) −1.03188 −0.0596749
\(300\) 0 0
\(301\) 39.5045 2.27700
\(302\) 0 0
\(303\) −7.25601 −0.416847
\(304\) 0 0
\(305\) −10.7215 −0.613910
\(306\) 0 0
\(307\) 1.54406 0.0881243 0.0440622 0.999029i \(-0.485970\pi\)
0.0440622 + 0.999029i \(0.485970\pi\)
\(308\) 0 0
\(309\) 3.53349 0.201013
\(310\) 0 0
\(311\) −25.6694 −1.45558 −0.727789 0.685801i \(-0.759452\pi\)
−0.727789 + 0.685801i \(0.759452\pi\)
\(312\) 0 0
\(313\) −19.0928 −1.07919 −0.539596 0.841924i \(-0.681423\pi\)
−0.539596 + 0.841924i \(0.681423\pi\)
\(314\) 0 0
\(315\) 6.99105 0.393901
\(316\) 0 0
\(317\) −19.9361 −1.11972 −0.559862 0.828586i \(-0.689146\pi\)
−0.559862 + 0.828586i \(0.689146\pi\)
\(318\) 0 0
\(319\) −37.1260 −2.07865
\(320\) 0 0
\(321\) −7.75866 −0.433046
\(322\) 0 0
\(323\) 8.29810 0.461719
\(324\) 0 0
\(325\) −1.25491 −0.0696101
\(326\) 0 0
\(327\) −1.14205 −0.0631553
\(328\) 0 0
\(329\) −47.9568 −2.64394
\(330\) 0 0
\(331\) 32.2130 1.77059 0.885293 0.465033i \(-0.153958\pi\)
0.885293 + 0.465033i \(0.153958\pi\)
\(332\) 0 0
\(333\) 7.94702 0.435494
\(334\) 0 0
\(335\) 3.12851 0.170929
\(336\) 0 0
\(337\) 30.0342 1.63606 0.818032 0.575172i \(-0.195065\pi\)
0.818032 + 0.575172i \(0.195065\pi\)
\(338\) 0 0
\(339\) −36.0766 −1.95941
\(340\) 0 0
\(341\) 19.5570 1.05907
\(342\) 0 0
\(343\) −8.87477 −0.479193
\(344\) 0 0
\(345\) 7.36105 0.396306
\(346\) 0 0
\(347\) 31.5880 1.69573 0.847866 0.530211i \(-0.177887\pi\)
0.847866 + 0.530211i \(0.177887\pi\)
\(348\) 0 0
\(349\) 2.95362 0.158103 0.0790517 0.996871i \(-0.474811\pi\)
0.0790517 + 0.996871i \(0.474811\pi\)
\(350\) 0 0
\(351\) −1.03948 −0.0554831
\(352\) 0 0
\(353\) 16.8619 0.897470 0.448735 0.893665i \(-0.351875\pi\)
0.448735 + 0.893665i \(0.351875\pi\)
\(354\) 0 0
\(355\) −7.99554 −0.424359
\(356\) 0 0
\(357\) −41.1334 −2.17701
\(358\) 0 0
\(359\) 15.0461 0.794105 0.397052 0.917796i \(-0.370033\pi\)
0.397052 + 0.917796i \(0.370033\pi\)
\(360\) 0 0
\(361\) −16.0012 −0.842167
\(362\) 0 0
\(363\) 42.7383 2.24318
\(364\) 0 0
\(365\) −7.46909 −0.390950
\(366\) 0 0
\(367\) −5.35745 −0.279657 −0.139828 0.990176i \(-0.544655\pi\)
−0.139828 + 0.990176i \(0.544655\pi\)
\(368\) 0 0
\(369\) 7.18796 0.374190
\(370\) 0 0
\(371\) −46.0311 −2.38982
\(372\) 0 0
\(373\) −25.7958 −1.33565 −0.667827 0.744316i \(-0.732776\pi\)
−0.667827 + 0.744316i \(0.732776\pi\)
\(374\) 0 0
\(375\) 20.9200 1.08031
\(376\) 0 0
\(377\) 2.23582 0.115151
\(378\) 0 0
\(379\) 5.57137 0.286182 0.143091 0.989710i \(-0.454296\pi\)
0.143091 + 0.989710i \(0.454296\pi\)
\(380\) 0 0
\(381\) 19.3163 0.989604
\(382\) 0 0
\(383\) 35.7960 1.82909 0.914545 0.404485i \(-0.132549\pi\)
0.914545 + 0.404485i \(0.132549\pi\)
\(384\) 0 0
\(385\) −25.1752 −1.28305
\(386\) 0 0
\(387\) −15.1835 −0.771823
\(388\) 0 0
\(389\) 11.5271 0.584448 0.292224 0.956350i \(-0.405605\pi\)
0.292224 + 0.956350i \(0.405605\pi\)
\(390\) 0 0
\(391\) −14.7365 −0.745256
\(392\) 0 0
\(393\) 22.8162 1.15092
\(394\) 0 0
\(395\) 9.68291 0.487200
\(396\) 0 0
\(397\) 23.3988 1.17435 0.587175 0.809460i \(-0.300240\pi\)
0.587175 + 0.809460i \(0.300240\pi\)
\(398\) 0 0
\(399\) −14.8651 −0.744185
\(400\) 0 0
\(401\) −9.59029 −0.478916 −0.239458 0.970907i \(-0.576970\pi\)
−0.239458 + 0.970907i \(0.576970\pi\)
\(402\) 0 0
\(403\) −1.17777 −0.0586691
\(404\) 0 0
\(405\) 12.6253 0.627358
\(406\) 0 0
\(407\) −28.6177 −1.41853
\(408\) 0 0
\(409\) 19.5036 0.964390 0.482195 0.876064i \(-0.339840\pi\)
0.482195 + 0.876064i \(0.339840\pi\)
\(410\) 0 0
\(411\) −13.9228 −0.686763
\(412\) 0 0
\(413\) −9.49852 −0.467391
\(414\) 0 0
\(415\) 2.20563 0.108270
\(416\) 0 0
\(417\) −29.1871 −1.42930
\(418\) 0 0
\(419\) −32.7536 −1.60012 −0.800060 0.599921i \(-0.795199\pi\)
−0.800060 + 0.599921i \(0.795199\pi\)
\(420\) 0 0
\(421\) −7.30658 −0.356101 −0.178051 0.984021i \(-0.556979\pi\)
−0.178051 + 0.984021i \(0.556979\pi\)
\(422\) 0 0
\(423\) 18.4322 0.896203
\(424\) 0 0
\(425\) −17.9217 −0.869332
\(426\) 0 0
\(427\) −38.4501 −1.86073
\(428\) 0 0
\(429\) −3.98643 −0.192467
\(430\) 0 0
\(431\) 13.3346 0.642307 0.321153 0.947027i \(-0.395929\pi\)
0.321153 + 0.947027i \(0.395929\pi\)
\(432\) 0 0
\(433\) −16.0887 −0.773175 −0.386587 0.922253i \(-0.626346\pi\)
−0.386587 + 0.922253i \(0.626346\pi\)
\(434\) 0 0
\(435\) −15.9496 −0.764725
\(436\) 0 0
\(437\) −5.32558 −0.254757
\(438\) 0 0
\(439\) 3.84338 0.183434 0.0917172 0.995785i \(-0.470764\pi\)
0.0917172 + 0.995785i \(0.470764\pi\)
\(440\) 0 0
\(441\) 14.2414 0.678162
\(442\) 0 0
\(443\) −14.4500 −0.686542 −0.343271 0.939236i \(-0.611535\pi\)
−0.343271 + 0.939236i \(0.611535\pi\)
\(444\) 0 0
\(445\) −16.5639 −0.785204
\(446\) 0 0
\(447\) −33.6175 −1.59005
\(448\) 0 0
\(449\) −9.12580 −0.430673 −0.215337 0.976540i \(-0.569085\pi\)
−0.215337 + 0.976540i \(0.569085\pi\)
\(450\) 0 0
\(451\) −25.8843 −1.21884
\(452\) 0 0
\(453\) 19.0601 0.895523
\(454\) 0 0
\(455\) 1.51612 0.0710766
\(456\) 0 0
\(457\) 0.218873 0.0102384 0.00511922 0.999987i \(-0.498370\pi\)
0.00511922 + 0.999987i \(0.498370\pi\)
\(458\) 0 0
\(459\) −14.8450 −0.692907
\(460\) 0 0
\(461\) −13.1822 −0.613955 −0.306978 0.951717i \(-0.599318\pi\)
−0.306978 + 0.951717i \(0.599318\pi\)
\(462\) 0 0
\(463\) −7.77002 −0.361104 −0.180552 0.983565i \(-0.557788\pi\)
−0.180552 + 0.983565i \(0.557788\pi\)
\(464\) 0 0
\(465\) 8.40184 0.389626
\(466\) 0 0
\(467\) −16.1107 −0.745515 −0.372758 0.927929i \(-0.621588\pi\)
−0.372758 + 0.927929i \(0.621588\pi\)
\(468\) 0 0
\(469\) 11.2197 0.518078
\(470\) 0 0
\(471\) 1.68563 0.0776697
\(472\) 0 0
\(473\) 54.6768 2.51404
\(474\) 0 0
\(475\) −6.47669 −0.297171
\(476\) 0 0
\(477\) 17.6920 0.810063
\(478\) 0 0
\(479\) −0.985380 −0.0450231 −0.0225116 0.999747i \(-0.507166\pi\)
−0.0225116 + 0.999747i \(0.507166\pi\)
\(480\) 0 0
\(481\) 1.72343 0.0785819
\(482\) 0 0
\(483\) 26.3987 1.20118
\(484\) 0 0
\(485\) −6.70285 −0.304361
\(486\) 0 0
\(487\) 12.8005 0.580045 0.290023 0.957020i \(-0.406337\pi\)
0.290023 + 0.957020i \(0.406337\pi\)
\(488\) 0 0
\(489\) 50.7561 2.29527
\(490\) 0 0
\(491\) −11.4113 −0.514985 −0.257492 0.966280i \(-0.582896\pi\)
−0.257492 + 0.966280i \(0.582896\pi\)
\(492\) 0 0
\(493\) 31.9304 1.43807
\(494\) 0 0
\(495\) 9.67606 0.434907
\(496\) 0 0
\(497\) −28.6742 −1.28621
\(498\) 0 0
\(499\) 1.85189 0.0829020 0.0414510 0.999141i \(-0.486802\pi\)
0.0414510 + 0.999141i \(0.486802\pi\)
\(500\) 0 0
\(501\) −27.5355 −1.23019
\(502\) 0 0
\(503\) 18.2301 0.812839 0.406419 0.913687i \(-0.366777\pi\)
0.406419 + 0.913687i \(0.366777\pi\)
\(504\) 0 0
\(505\) 3.81946 0.169964
\(506\) 0 0
\(507\) −27.4813 −1.22049
\(508\) 0 0
\(509\) 30.9539 1.37201 0.686003 0.727598i \(-0.259364\pi\)
0.686003 + 0.727598i \(0.259364\pi\)
\(510\) 0 0
\(511\) −26.7862 −1.18495
\(512\) 0 0
\(513\) −5.36481 −0.236862
\(514\) 0 0
\(515\) −1.85998 −0.0819605
\(516\) 0 0
\(517\) −66.3753 −2.91918
\(518\) 0 0
\(519\) 27.8732 1.22350
\(520\) 0 0
\(521\) 29.0190 1.27134 0.635672 0.771959i \(-0.280723\pi\)
0.635672 + 0.771959i \(0.280723\pi\)
\(522\) 0 0
\(523\) 10.2059 0.446273 0.223137 0.974787i \(-0.428370\pi\)
0.223137 + 0.974787i \(0.428370\pi\)
\(524\) 0 0
\(525\) 32.1047 1.40117
\(526\) 0 0
\(527\) −16.8201 −0.732695
\(528\) 0 0
\(529\) −13.5424 −0.588799
\(530\) 0 0
\(531\) 3.65075 0.158429
\(532\) 0 0
\(533\) 1.55882 0.0675200
\(534\) 0 0
\(535\) 4.08405 0.176569
\(536\) 0 0
\(537\) 19.6251 0.846884
\(538\) 0 0
\(539\) −51.2841 −2.20896
\(540\) 0 0
\(541\) 39.6458 1.70451 0.852253 0.523129i \(-0.175235\pi\)
0.852253 + 0.523129i \(0.175235\pi\)
\(542\) 0 0
\(543\) 1.30877 0.0561647
\(544\) 0 0
\(545\) 0.601158 0.0257508
\(546\) 0 0
\(547\) −18.0926 −0.773584 −0.386792 0.922167i \(-0.626417\pi\)
−0.386792 + 0.922167i \(0.626417\pi\)
\(548\) 0 0
\(549\) 14.7783 0.630722
\(550\) 0 0
\(551\) 11.5392 0.491588
\(552\) 0 0
\(553\) 34.7255 1.47668
\(554\) 0 0
\(555\) −12.2944 −0.521868
\(556\) 0 0
\(557\) −25.5133 −1.08103 −0.540516 0.841334i \(-0.681771\pi\)
−0.540516 + 0.841334i \(0.681771\pi\)
\(558\) 0 0
\(559\) −3.29278 −0.139270
\(560\) 0 0
\(561\) −56.9313 −2.40364
\(562\) 0 0
\(563\) −12.7379 −0.536837 −0.268419 0.963302i \(-0.586501\pi\)
−0.268419 + 0.963302i \(0.586501\pi\)
\(564\) 0 0
\(565\) 18.9902 0.798926
\(566\) 0 0
\(567\) 45.2779 1.90149
\(568\) 0 0
\(569\) 32.3406 1.35579 0.677894 0.735160i \(-0.262893\pi\)
0.677894 + 0.735160i \(0.262893\pi\)
\(570\) 0 0
\(571\) 31.3992 1.31401 0.657007 0.753884i \(-0.271822\pi\)
0.657007 + 0.753884i \(0.271822\pi\)
\(572\) 0 0
\(573\) 13.4651 0.562514
\(574\) 0 0
\(575\) 11.5019 0.479661
\(576\) 0 0
\(577\) 25.3641 1.05592 0.527960 0.849269i \(-0.322957\pi\)
0.527960 + 0.849269i \(0.322957\pi\)
\(578\) 0 0
\(579\) 23.0494 0.957900
\(580\) 0 0
\(581\) 7.91000 0.328162
\(582\) 0 0
\(583\) −63.7101 −2.63860
\(584\) 0 0
\(585\) −0.582719 −0.0240924
\(586\) 0 0
\(587\) −38.0082 −1.56877 −0.784383 0.620277i \(-0.787020\pi\)
−0.784383 + 0.620277i \(0.787020\pi\)
\(588\) 0 0
\(589\) −6.07858 −0.250463
\(590\) 0 0
\(591\) 44.5771 1.83366
\(592\) 0 0
\(593\) 28.7010 1.17861 0.589304 0.807911i \(-0.299402\pi\)
0.589304 + 0.807911i \(0.299402\pi\)
\(594\) 0 0
\(595\) 21.6521 0.887648
\(596\) 0 0
\(597\) 30.6312 1.25365
\(598\) 0 0
\(599\) −25.5053 −1.04212 −0.521059 0.853520i \(-0.674463\pi\)
−0.521059 + 0.853520i \(0.674463\pi\)
\(600\) 0 0
\(601\) 3.29859 0.134552 0.0672762 0.997734i \(-0.478569\pi\)
0.0672762 + 0.997734i \(0.478569\pi\)
\(602\) 0 0
\(603\) −4.31229 −0.175610
\(604\) 0 0
\(605\) −22.4968 −0.914627
\(606\) 0 0
\(607\) −6.84359 −0.277773 −0.138886 0.990308i \(-0.544352\pi\)
−0.138886 + 0.990308i \(0.544352\pi\)
\(608\) 0 0
\(609\) −57.1996 −2.31785
\(610\) 0 0
\(611\) 3.99730 0.161714
\(612\) 0 0
\(613\) −33.1661 −1.33957 −0.669784 0.742556i \(-0.733613\pi\)
−0.669784 + 0.742556i \(0.733613\pi\)
\(614\) 0 0
\(615\) −11.1201 −0.448405
\(616\) 0 0
\(617\) 21.2071 0.853766 0.426883 0.904307i \(-0.359612\pi\)
0.426883 + 0.904307i \(0.359612\pi\)
\(618\) 0 0
\(619\) 34.1470 1.37249 0.686243 0.727373i \(-0.259259\pi\)
0.686243 + 0.727373i \(0.259259\pi\)
\(620\) 0 0
\(621\) 9.52729 0.382317
\(622\) 0 0
\(623\) −59.4026 −2.37992
\(624\) 0 0
\(625\) 7.68823 0.307529
\(626\) 0 0
\(627\) −20.5742 −0.821656
\(628\) 0 0
\(629\) 24.6128 0.981377
\(630\) 0 0
\(631\) −1.70207 −0.0677584 −0.0338792 0.999426i \(-0.510786\pi\)
−0.0338792 + 0.999426i \(0.510786\pi\)
\(632\) 0 0
\(633\) 36.1556 1.43705
\(634\) 0 0
\(635\) −10.1678 −0.403498
\(636\) 0 0
\(637\) 3.08847 0.122370
\(638\) 0 0
\(639\) 11.0209 0.435980
\(640\) 0 0
\(641\) 12.0794 0.477107 0.238553 0.971129i \(-0.423327\pi\)
0.238553 + 0.971129i \(0.423327\pi\)
\(642\) 0 0
\(643\) −43.9208 −1.73207 −0.866033 0.499987i \(-0.833338\pi\)
−0.866033 + 0.499987i \(0.833338\pi\)
\(644\) 0 0
\(645\) 23.4896 0.924902
\(646\) 0 0
\(647\) −30.1591 −1.18567 −0.592837 0.805322i \(-0.701992\pi\)
−0.592837 + 0.805322i \(0.701992\pi\)
\(648\) 0 0
\(649\) −13.1466 −0.516048
\(650\) 0 0
\(651\) 30.1313 1.18094
\(652\) 0 0
\(653\) −50.5228 −1.97711 −0.988555 0.150862i \(-0.951795\pi\)
−0.988555 + 0.150862i \(0.951795\pi\)
\(654\) 0 0
\(655\) −12.0101 −0.469274
\(656\) 0 0
\(657\) 10.2953 0.401656
\(658\) 0 0
\(659\) 43.4812 1.69379 0.846893 0.531763i \(-0.178470\pi\)
0.846893 + 0.531763i \(0.178470\pi\)
\(660\) 0 0
\(661\) 14.3401 0.557765 0.278883 0.960325i \(-0.410036\pi\)
0.278883 + 0.960325i \(0.410036\pi\)
\(662\) 0 0
\(663\) 3.42855 0.133154
\(664\) 0 0
\(665\) 7.82478 0.303432
\(666\) 0 0
\(667\) −20.4924 −0.793469
\(668\) 0 0
\(669\) 48.8331 1.88800
\(670\) 0 0
\(671\) −53.2175 −2.05444
\(672\) 0 0
\(673\) −22.0505 −0.849982 −0.424991 0.905197i \(-0.639723\pi\)
−0.424991 + 0.905197i \(0.639723\pi\)
\(674\) 0 0
\(675\) 11.5866 0.445968
\(676\) 0 0
\(677\) −27.6304 −1.06192 −0.530960 0.847397i \(-0.678169\pi\)
−0.530960 + 0.847397i \(0.678169\pi\)
\(678\) 0 0
\(679\) −24.0382 −0.922503
\(680\) 0 0
\(681\) −40.9263 −1.56830
\(682\) 0 0
\(683\) −6.39771 −0.244802 −0.122401 0.992481i \(-0.539059\pi\)
−0.122401 + 0.992481i \(0.539059\pi\)
\(684\) 0 0
\(685\) 7.32879 0.280019
\(686\) 0 0
\(687\) −8.88240 −0.338885
\(688\) 0 0
\(689\) 3.83679 0.146170
\(690\) 0 0
\(691\) 37.0289 1.40865 0.704324 0.709879i \(-0.251250\pi\)
0.704324 + 0.709879i \(0.251250\pi\)
\(692\) 0 0
\(693\) 34.7010 1.31818
\(694\) 0 0
\(695\) 15.3637 0.582778
\(696\) 0 0
\(697\) 22.2619 0.843230
\(698\) 0 0
\(699\) −51.9859 −1.96629
\(700\) 0 0
\(701\) −23.8442 −0.900584 −0.450292 0.892881i \(-0.648680\pi\)
−0.450292 + 0.892881i \(0.648680\pi\)
\(702\) 0 0
\(703\) 8.89476 0.335472
\(704\) 0 0
\(705\) −28.5154 −1.07395
\(706\) 0 0
\(707\) 13.6976 0.515153
\(708\) 0 0
\(709\) 3.10748 0.116704 0.0583519 0.998296i \(-0.481415\pi\)
0.0583519 + 0.998296i \(0.481415\pi\)
\(710\) 0 0
\(711\) −13.3467 −0.500542
\(712\) 0 0
\(713\) 10.7949 0.404271
\(714\) 0 0
\(715\) 2.09840 0.0784758
\(716\) 0 0
\(717\) 18.1015 0.676012
\(718\) 0 0
\(719\) 15.6524 0.583736 0.291868 0.956459i \(-0.405723\pi\)
0.291868 + 0.956459i \(0.405723\pi\)
\(720\) 0 0
\(721\) −6.67039 −0.248418
\(722\) 0 0
\(723\) −30.7198 −1.14248
\(724\) 0 0
\(725\) −24.9218 −0.925571
\(726\) 0 0
\(727\) 12.9463 0.480152 0.240076 0.970754i \(-0.422828\pi\)
0.240076 + 0.970754i \(0.422828\pi\)
\(728\) 0 0
\(729\) 2.41600 0.0894813
\(730\) 0 0
\(731\) −47.0251 −1.73929
\(732\) 0 0
\(733\) −29.5007 −1.08963 −0.544817 0.838555i \(-0.683401\pi\)
−0.544817 + 0.838555i \(0.683401\pi\)
\(734\) 0 0
\(735\) −22.0321 −0.812665
\(736\) 0 0
\(737\) 15.5288 0.572010
\(738\) 0 0
\(739\) −41.9176 −1.54196 −0.770982 0.636857i \(-0.780234\pi\)
−0.770982 + 0.636857i \(0.780234\pi\)
\(740\) 0 0
\(741\) 1.23904 0.0455171
\(742\) 0 0
\(743\) 20.1143 0.737923 0.368961 0.929445i \(-0.379713\pi\)
0.368961 + 0.929445i \(0.379713\pi\)
\(744\) 0 0
\(745\) 17.6958 0.648323
\(746\) 0 0
\(747\) −3.04020 −0.111235
\(748\) 0 0
\(749\) 14.6465 0.535172
\(750\) 0 0
\(751\) −1.00000 −0.0364905
\(752\) 0 0
\(753\) −26.2878 −0.957980
\(754\) 0 0
\(755\) −10.0330 −0.365138
\(756\) 0 0
\(757\) 26.2904 0.955539 0.477770 0.878485i \(-0.341445\pi\)
0.477770 + 0.878485i \(0.341445\pi\)
\(758\) 0 0
\(759\) 36.5375 1.32623
\(760\) 0 0
\(761\) −39.0399 −1.41520 −0.707598 0.706615i \(-0.750221\pi\)
−0.707598 + 0.706615i \(0.750221\pi\)
\(762\) 0 0
\(763\) 2.15591 0.0780493
\(764\) 0 0
\(765\) −8.32195 −0.300881
\(766\) 0 0
\(767\) 0.791721 0.0285874
\(768\) 0 0
\(769\) 27.5522 0.993559 0.496779 0.867877i \(-0.334516\pi\)
0.496779 + 0.867877i \(0.334516\pi\)
\(770\) 0 0
\(771\) −45.1496 −1.62602
\(772\) 0 0
\(773\) 7.14155 0.256864 0.128432 0.991718i \(-0.459006\pi\)
0.128432 + 0.991718i \(0.459006\pi\)
\(774\) 0 0
\(775\) 13.1281 0.471577
\(776\) 0 0
\(777\) −44.0910 −1.58176
\(778\) 0 0
\(779\) 8.04517 0.288248
\(780\) 0 0
\(781\) −39.6869 −1.42011
\(782\) 0 0
\(783\) −20.6433 −0.737732
\(784\) 0 0
\(785\) −0.887293 −0.0316688
\(786\) 0 0
\(787\) 23.1663 0.825788 0.412894 0.910779i \(-0.364518\pi\)
0.412894 + 0.910779i \(0.364518\pi\)
\(788\) 0 0
\(789\) 36.2814 1.29165
\(790\) 0 0
\(791\) 68.1042 2.42151
\(792\) 0 0
\(793\) 3.20490 0.113809
\(794\) 0 0
\(795\) −27.3704 −0.970727
\(796\) 0 0
\(797\) 1.70129 0.0602629 0.0301315 0.999546i \(-0.490407\pi\)
0.0301315 + 0.999546i \(0.490407\pi\)
\(798\) 0 0
\(799\) 57.0865 2.01957
\(800\) 0 0
\(801\) 22.8314 0.806707
\(802\) 0 0
\(803\) −37.0738 −1.30831
\(804\) 0 0
\(805\) −13.8959 −0.489767
\(806\) 0 0
\(807\) −29.8447 −1.05058
\(808\) 0 0
\(809\) 38.5226 1.35438 0.677192 0.735807i \(-0.263197\pi\)
0.677192 + 0.735807i \(0.263197\pi\)
\(810\) 0 0
\(811\) −8.20547 −0.288133 −0.144067 0.989568i \(-0.546018\pi\)
−0.144067 + 0.989568i \(0.546018\pi\)
\(812\) 0 0
\(813\) −23.8479 −0.836383
\(814\) 0 0
\(815\) −26.7173 −0.935867
\(816\) 0 0
\(817\) −16.9943 −0.594555
\(818\) 0 0
\(819\) −2.08979 −0.0730231
\(820\) 0 0
\(821\) 15.1611 0.529125 0.264562 0.964369i \(-0.414772\pi\)
0.264562 + 0.964369i \(0.414772\pi\)
\(822\) 0 0
\(823\) −28.7968 −1.00379 −0.501896 0.864928i \(-0.667364\pi\)
−0.501896 + 0.864928i \(0.667364\pi\)
\(824\) 0 0
\(825\) 44.4350 1.54703
\(826\) 0 0
\(827\) −35.8128 −1.24533 −0.622666 0.782488i \(-0.713950\pi\)
−0.622666 + 0.782488i \(0.713950\pi\)
\(828\) 0 0
\(829\) −51.0514 −1.77309 −0.886544 0.462645i \(-0.846900\pi\)
−0.886544 + 0.462645i \(0.846900\pi\)
\(830\) 0 0
\(831\) 26.3492 0.914045
\(832\) 0 0
\(833\) 44.1072 1.52822
\(834\) 0 0
\(835\) 14.4943 0.501596
\(836\) 0 0
\(837\) 10.8744 0.375873
\(838\) 0 0
\(839\) 27.5439 0.950920 0.475460 0.879737i \(-0.342282\pi\)
0.475460 + 0.879737i \(0.342282\pi\)
\(840\) 0 0
\(841\) 15.4021 0.531105
\(842\) 0 0
\(843\) 16.6874 0.574746
\(844\) 0 0
\(845\) 14.4658 0.497639
\(846\) 0 0
\(847\) −80.6798 −2.77219
\(848\) 0 0
\(849\) 16.8866 0.579548
\(850\) 0 0
\(851\) −15.7961 −0.541483
\(852\) 0 0
\(853\) 52.7334 1.80556 0.902778 0.430107i \(-0.141524\pi\)
0.902778 + 0.430107i \(0.141524\pi\)
\(854\) 0 0
\(855\) −3.00745 −0.102853
\(856\) 0 0
\(857\) 20.2839 0.692885 0.346443 0.938071i \(-0.387390\pi\)
0.346443 + 0.938071i \(0.387390\pi\)
\(858\) 0 0
\(859\) 8.72502 0.297694 0.148847 0.988860i \(-0.452444\pi\)
0.148847 + 0.988860i \(0.452444\pi\)
\(860\) 0 0
\(861\) −39.8796 −1.35909
\(862\) 0 0
\(863\) −20.7641 −0.706817 −0.353408 0.935469i \(-0.614977\pi\)
−0.353408 + 0.935469i \(0.614977\pi\)
\(864\) 0 0
\(865\) −14.6721 −0.498865
\(866\) 0 0
\(867\) 12.7130 0.431756
\(868\) 0 0
\(869\) 48.0624 1.63041
\(870\) 0 0
\(871\) −0.935186 −0.0316876
\(872\) 0 0
\(873\) 9.23909 0.312696
\(874\) 0 0
\(875\) −39.4921 −1.33508
\(876\) 0 0
\(877\) 45.9513 1.55167 0.775833 0.630939i \(-0.217330\pi\)
0.775833 + 0.630939i \(0.217330\pi\)
\(878\) 0 0
\(879\) 11.8675 0.400282
\(880\) 0 0
\(881\) −44.3695 −1.49485 −0.747423 0.664349i \(-0.768709\pi\)
−0.747423 + 0.664349i \(0.768709\pi\)
\(882\) 0 0
\(883\) 34.4308 1.15869 0.579345 0.815083i \(-0.303309\pi\)
0.579345 + 0.815083i \(0.303309\pi\)
\(884\) 0 0
\(885\) −5.64787 −0.189851
\(886\) 0 0
\(887\) 9.46631 0.317848 0.158924 0.987291i \(-0.449198\pi\)
0.158924 + 0.987291i \(0.449198\pi\)
\(888\) 0 0
\(889\) −36.4646 −1.22298
\(890\) 0 0
\(891\) 62.6675 2.09944
\(892\) 0 0
\(893\) 20.6303 0.690368
\(894\) 0 0
\(895\) −10.3304 −0.345306
\(896\) 0 0
\(897\) −2.20039 −0.0734688
\(898\) 0 0
\(899\) −23.3898 −0.780095
\(900\) 0 0
\(901\) 54.7942 1.82546
\(902\) 0 0
\(903\) 84.2401 2.80333
\(904\) 0 0
\(905\) −0.688919 −0.0229004
\(906\) 0 0
\(907\) 49.1029 1.63043 0.815217 0.579156i \(-0.196618\pi\)
0.815217 + 0.579156i \(0.196618\pi\)
\(908\) 0 0
\(909\) −5.26468 −0.174618
\(910\) 0 0
\(911\) 17.8459 0.591260 0.295630 0.955302i \(-0.404470\pi\)
0.295630 + 0.955302i \(0.404470\pi\)
\(912\) 0 0
\(913\) 10.9479 0.362324
\(914\) 0 0
\(915\) −22.8627 −0.755816
\(916\) 0 0
\(917\) −43.0715 −1.42235
\(918\) 0 0
\(919\) −51.0203 −1.68300 −0.841501 0.540255i \(-0.818328\pi\)
−0.841501 + 0.540255i \(0.818328\pi\)
\(920\) 0 0
\(921\) 3.29258 0.108494
\(922\) 0 0
\(923\) 2.39005 0.0786695
\(924\) 0 0
\(925\) −19.2104 −0.631633
\(926\) 0 0
\(927\) 2.56376 0.0842050
\(928\) 0 0
\(929\) 31.6458 1.03827 0.519133 0.854693i \(-0.326255\pi\)
0.519133 + 0.854693i \(0.326255\pi\)
\(930\) 0 0
\(931\) 15.9398 0.522406
\(932\) 0 0
\(933\) −54.7379 −1.79204
\(934\) 0 0
\(935\) 29.9678 0.980053
\(936\) 0 0
\(937\) 3.25942 0.106481 0.0532404 0.998582i \(-0.483045\pi\)
0.0532404 + 0.998582i \(0.483045\pi\)
\(938\) 0 0
\(939\) −40.7139 −1.32865
\(940\) 0 0
\(941\) 17.3811 0.566608 0.283304 0.959030i \(-0.408570\pi\)
0.283304 + 0.959030i \(0.408570\pi\)
\(942\) 0 0
\(943\) −14.2873 −0.465259
\(944\) 0 0
\(945\) −13.9983 −0.455364
\(946\) 0 0
\(947\) 45.8162 1.48883 0.744413 0.667719i \(-0.232729\pi\)
0.744413 + 0.667719i \(0.232729\pi\)
\(948\) 0 0
\(949\) 2.23268 0.0724760
\(950\) 0 0
\(951\) −42.5121 −1.37855
\(952\) 0 0
\(953\) 36.8662 1.19421 0.597107 0.802162i \(-0.296317\pi\)
0.597107 + 0.802162i \(0.296317\pi\)
\(954\) 0 0
\(955\) −7.08787 −0.229358
\(956\) 0 0
\(957\) −79.1680 −2.55914
\(958\) 0 0
\(959\) 26.2830 0.848723
\(960\) 0 0
\(961\) −18.6788 −0.602543
\(962\) 0 0
\(963\) −5.62938 −0.181404
\(964\) 0 0
\(965\) −12.1329 −0.390571
\(966\) 0 0
\(967\) 10.7123 0.344485 0.172243 0.985055i \(-0.444899\pi\)
0.172243 + 0.985055i \(0.444899\pi\)
\(968\) 0 0
\(969\) 17.6950 0.568445
\(970\) 0 0
\(971\) 32.4423 1.04112 0.520561 0.853824i \(-0.325723\pi\)
0.520561 + 0.853824i \(0.325723\pi\)
\(972\) 0 0
\(973\) 55.0984 1.76637
\(974\) 0 0
\(975\) −2.67600 −0.0857005
\(976\) 0 0
\(977\) −17.8203 −0.570121 −0.285060 0.958510i \(-0.592014\pi\)
−0.285060 + 0.958510i \(0.592014\pi\)
\(978\) 0 0
\(979\) −82.2171 −2.62767
\(980\) 0 0
\(981\) −0.828625 −0.0264559
\(982\) 0 0
\(983\) −2.06406 −0.0658333 −0.0329166 0.999458i \(-0.510480\pi\)
−0.0329166 + 0.999458i \(0.510480\pi\)
\(984\) 0 0
\(985\) −23.4648 −0.747649
\(986\) 0 0
\(987\) −102.264 −3.25510
\(988\) 0 0
\(989\) 30.1799 0.959666
\(990\) 0 0
\(991\) 31.7175 1.00754 0.503770 0.863838i \(-0.331946\pi\)
0.503770 + 0.863838i \(0.331946\pi\)
\(992\) 0 0
\(993\) 68.6915 2.17986
\(994\) 0 0
\(995\) −16.1238 −0.511160
\(996\) 0 0
\(997\) −53.5470 −1.69585 −0.847925 0.530116i \(-0.822148\pi\)
−0.847925 + 0.530116i \(0.822148\pi\)
\(998\) 0 0
\(999\) −15.9124 −0.503447
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 \(a_p\))