Properties

Label 6004.2.a.g.1.24
Level 6004
Weight 2
Character 6004.1
Self dual Yes
Analytic conductor 47.942
Analytic rank 1
Dimension 27
CM No

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Newspace parameters

Level: \( N \) = \( 6004 = 2^{2} \cdot 19 \cdot 79 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6004.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(47.9421813736\)
Analytic rank: \(1\)
Dimension: \(27\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.24
Character \(\chi\) = 6004.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.46349 q^{3} -2.98290 q^{5} +1.48454 q^{7} +3.06877 q^{9} +O(q^{10})\) \(q+2.46349 q^{3} -2.98290 q^{5} +1.48454 q^{7} +3.06877 q^{9} +3.74396 q^{11} -5.67303 q^{13} -7.34834 q^{15} +0.776015 q^{17} +1.00000 q^{19} +3.65715 q^{21} -4.98298 q^{23} +3.89772 q^{25} +0.169406 q^{27} -1.20223 q^{29} -6.15818 q^{31} +9.22319 q^{33} -4.42824 q^{35} -4.57336 q^{37} -13.9754 q^{39} -6.38928 q^{41} +7.04640 q^{43} -9.15384 q^{45} +4.91092 q^{47} -4.79614 q^{49} +1.91170 q^{51} -12.3950 q^{53} -11.1679 q^{55} +2.46349 q^{57} +12.5803 q^{59} -8.82838 q^{61} +4.55571 q^{63} +16.9221 q^{65} +2.66800 q^{67} -12.2755 q^{69} +0.725716 q^{71} +5.70371 q^{73} +9.60197 q^{75} +5.55806 q^{77} -1.00000 q^{79} -8.78897 q^{81} -6.75282 q^{83} -2.31478 q^{85} -2.96169 q^{87} -2.60908 q^{89} -8.42184 q^{91} -15.1706 q^{93} -2.98290 q^{95} +0.185948 q^{97} +11.4893 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 27q - 4q^{3} - 10q^{5} - 8q^{7} + 19q^{9} + O(q^{10}) \) \( 27q - 4q^{3} - 10q^{5} - 8q^{7} + 19q^{9} + 3q^{11} - 5q^{13} - 11q^{15} - 17q^{17} + 27q^{19} - 28q^{21} - 11q^{23} + 13q^{25} - 7q^{27} - 39q^{29} - 27q^{31} - 18q^{33} - 5q^{35} - q^{37} - 22q^{39} - 36q^{41} - 2q^{43} - 18q^{45} - 12q^{47} + 15q^{49} + 4q^{51} - 28q^{53} + 5q^{55} - 4q^{57} - 30q^{59} - 6q^{61} - 4q^{63} - 32q^{65} + 13q^{67} - 27q^{69} - 59q^{71} - 30q^{73} - 21q^{75} - 39q^{77} - 27q^{79} - 5q^{81} + 4q^{83} - 3q^{85} + 22q^{87} - 56q^{89} - 8q^{91} - 38q^{93} - 10q^{95} - 30q^{97} + 31q^{99} + O(q^{100}) \)

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
\(3\) 2.46349 1.42229 0.711147 0.703043i \(-0.248176\pi\)
0.711147 + 0.703043i \(0.248176\pi\)
\(4\) 0 0
\(5\) −2.98290 −1.33400 −0.666998 0.745060i \(-0.732421\pi\)
−0.666998 + 0.745060i \(0.732421\pi\)
\(6\) 0 0
\(7\) 1.48454 0.561104 0.280552 0.959839i \(-0.409483\pi\)
0.280552 + 0.959839i \(0.409483\pi\)
\(8\) 0 0
\(9\) 3.06877 1.02292
\(10\) 0 0
\(11\) 3.74396 1.12885 0.564423 0.825486i \(-0.309099\pi\)
0.564423 + 0.825486i \(0.309099\pi\)
\(12\) 0 0
\(13\) −5.67303 −1.57342 −0.786708 0.617326i \(-0.788216\pi\)
−0.786708 + 0.617326i \(0.788216\pi\)
\(14\) 0 0
\(15\) −7.34834 −1.89733
\(16\) 0 0
\(17\) 0.776015 0.188211 0.0941056 0.995562i \(-0.470001\pi\)
0.0941056 + 0.995562i \(0.470001\pi\)
\(18\) 0 0
\(19\) 1.00000 0.229416
\(20\) 0 0
\(21\) 3.65715 0.798055
\(22\) 0 0
\(23\) −4.98298 −1.03902 −0.519511 0.854464i \(-0.673886\pi\)
−0.519511 + 0.854464i \(0.673886\pi\)
\(24\) 0 0
\(25\) 3.89772 0.779543
\(26\) 0 0
\(27\) 0.169406 0.0326022
\(28\) 0 0
\(29\) −1.20223 −0.223249 −0.111625 0.993750i \(-0.535605\pi\)
−0.111625 + 0.993750i \(0.535605\pi\)
\(30\) 0 0
\(31\) −6.15818 −1.10604 −0.553021 0.833168i \(-0.686525\pi\)
−0.553021 + 0.833168i \(0.686525\pi\)
\(32\) 0 0
\(33\) 9.22319 1.60555
\(34\) 0 0
\(35\) −4.42824 −0.748509
\(36\) 0 0
\(37\) −4.57336 −0.751856 −0.375928 0.926649i \(-0.622676\pi\)
−0.375928 + 0.926649i \(0.622676\pi\)
\(38\) 0 0
\(39\) −13.9754 −2.23786
\(40\) 0 0
\(41\) −6.38928 −0.997838 −0.498919 0.866649i \(-0.666270\pi\)
−0.498919 + 0.866649i \(0.666270\pi\)
\(42\) 0 0
\(43\) 7.04640 1.07457 0.537283 0.843402i \(-0.319451\pi\)
0.537283 + 0.843402i \(0.319451\pi\)
\(44\) 0 0
\(45\) −9.15384 −1.36457
\(46\) 0 0
\(47\) 4.91092 0.716331 0.358165 0.933658i \(-0.383402\pi\)
0.358165 + 0.933658i \(0.383402\pi\)
\(48\) 0 0
\(49\) −4.79614 −0.685163
\(50\) 0 0
\(51\) 1.91170 0.267692
\(52\) 0 0
\(53\) −12.3950 −1.70258 −0.851292 0.524693i \(-0.824180\pi\)
−0.851292 + 0.524693i \(0.824180\pi\)
\(54\) 0 0
\(55\) −11.1679 −1.50587
\(56\) 0 0
\(57\) 2.46349 0.326297
\(58\) 0 0
\(59\) 12.5803 1.63782 0.818910 0.573922i \(-0.194579\pi\)
0.818910 + 0.573922i \(0.194579\pi\)
\(60\) 0 0
\(61\) −8.82838 −1.13036 −0.565179 0.824968i \(-0.691193\pi\)
−0.565179 + 0.824968i \(0.691193\pi\)
\(62\) 0 0
\(63\) 4.55571 0.573965
\(64\) 0 0
\(65\) 16.9221 2.09893
\(66\) 0 0
\(67\) 2.66800 0.325948 0.162974 0.986630i \(-0.447891\pi\)
0.162974 + 0.986630i \(0.447891\pi\)
\(68\) 0 0
\(69\) −12.2755 −1.47780
\(70\) 0 0
\(71\) 0.725716 0.0861266 0.0430633 0.999072i \(-0.486288\pi\)
0.0430633 + 0.999072i \(0.486288\pi\)
\(72\) 0 0
\(73\) 5.70371 0.667569 0.333785 0.942649i \(-0.391674\pi\)
0.333785 + 0.942649i \(0.391674\pi\)
\(74\) 0 0
\(75\) 9.60197 1.10874
\(76\) 0 0
\(77\) 5.55806 0.633399
\(78\) 0 0
\(79\) −1.00000 −0.112509
\(80\) 0 0
\(81\) −8.78897 −0.976552
\(82\) 0 0
\(83\) −6.75282 −0.741218 −0.370609 0.928789i \(-0.620851\pi\)
−0.370609 + 0.928789i \(0.620851\pi\)
\(84\) 0 0
\(85\) −2.31478 −0.251073
\(86\) 0 0
\(87\) −2.96169 −0.317526
\(88\) 0 0
\(89\) −2.60908 −0.276562 −0.138281 0.990393i \(-0.544158\pi\)
−0.138281 + 0.990393i \(0.544158\pi\)
\(90\) 0 0
\(91\) −8.42184 −0.882849
\(92\) 0 0
\(93\) −15.1706 −1.57312
\(94\) 0 0
\(95\) −2.98290 −0.306039
\(96\) 0 0
\(97\) 0.185948 0.0188801 0.00944007 0.999955i \(-0.496995\pi\)
0.00944007 + 0.999955i \(0.496995\pi\)
\(98\) 0 0
\(99\) 11.4893 1.15472
\(100\) 0 0
\(101\) 14.2079 1.41374 0.706871 0.707342i \(-0.250106\pi\)
0.706871 + 0.707342i \(0.250106\pi\)
\(102\) 0 0
\(103\) 0.703536 0.0693214 0.0346607 0.999399i \(-0.488965\pi\)
0.0346607 + 0.999399i \(0.488965\pi\)
\(104\) 0 0
\(105\) −10.9089 −1.06460
\(106\) 0 0
\(107\) −15.0528 −1.45521 −0.727607 0.685994i \(-0.759367\pi\)
−0.727607 + 0.685994i \(0.759367\pi\)
\(108\) 0 0
\(109\) 9.51819 0.911678 0.455839 0.890062i \(-0.349339\pi\)
0.455839 + 0.890062i \(0.349339\pi\)
\(110\) 0 0
\(111\) −11.2664 −1.06936
\(112\) 0 0
\(113\) −8.72901 −0.821156 −0.410578 0.911826i \(-0.634673\pi\)
−0.410578 + 0.911826i \(0.634673\pi\)
\(114\) 0 0
\(115\) 14.8637 1.38605
\(116\) 0 0
\(117\) −17.4092 −1.60948
\(118\) 0 0
\(119\) 1.15203 0.105606
\(120\) 0 0
\(121\) 3.01722 0.274293
\(122\) 0 0
\(123\) −15.7399 −1.41922
\(124\) 0 0
\(125\) 3.28801 0.294088
\(126\) 0 0
\(127\) −10.5745 −0.938334 −0.469167 0.883109i \(-0.655446\pi\)
−0.469167 + 0.883109i \(0.655446\pi\)
\(128\) 0 0
\(129\) 17.3587 1.52835
\(130\) 0 0
\(131\) −11.1678 −0.975738 −0.487869 0.872917i \(-0.662226\pi\)
−0.487869 + 0.872917i \(0.662226\pi\)
\(132\) 0 0
\(133\) 1.48454 0.128726
\(134\) 0 0
\(135\) −0.505322 −0.0434912
\(136\) 0 0
\(137\) 3.83691 0.327809 0.163905 0.986476i \(-0.447591\pi\)
0.163905 + 0.986476i \(0.447591\pi\)
\(138\) 0 0
\(139\) −15.6172 −1.32463 −0.662317 0.749224i \(-0.730427\pi\)
−0.662317 + 0.749224i \(0.730427\pi\)
\(140\) 0 0
\(141\) 12.0980 1.01883
\(142\) 0 0
\(143\) −21.2396 −1.77614
\(144\) 0 0
\(145\) 3.58615 0.297813
\(146\) 0 0
\(147\) −11.8152 −0.974503
\(148\) 0 0
\(149\) −17.1279 −1.40317 −0.701587 0.712584i \(-0.747525\pi\)
−0.701587 + 0.712584i \(0.747525\pi\)
\(150\) 0 0
\(151\) 0.632870 0.0515023 0.0257511 0.999668i \(-0.491802\pi\)
0.0257511 + 0.999668i \(0.491802\pi\)
\(152\) 0 0
\(153\) 2.38141 0.192525
\(154\) 0 0
\(155\) 18.3693 1.47545
\(156\) 0 0
\(157\) −2.24077 −0.178833 −0.0894164 0.995994i \(-0.528500\pi\)
−0.0894164 + 0.995994i \(0.528500\pi\)
\(158\) 0 0
\(159\) −30.5349 −2.42158
\(160\) 0 0
\(161\) −7.39743 −0.582999
\(162\) 0 0
\(163\) 9.01895 0.706419 0.353209 0.935544i \(-0.385090\pi\)
0.353209 + 0.935544i \(0.385090\pi\)
\(164\) 0 0
\(165\) −27.5119 −2.14180
\(166\) 0 0
\(167\) −12.1361 −0.939122 −0.469561 0.882900i \(-0.655588\pi\)
−0.469561 + 0.882900i \(0.655588\pi\)
\(168\) 0 0
\(169\) 19.1833 1.47563
\(170\) 0 0
\(171\) 3.06877 0.234674
\(172\) 0 0
\(173\) 22.4693 1.70831 0.854154 0.520020i \(-0.174076\pi\)
0.854154 + 0.520020i \(0.174076\pi\)
\(174\) 0 0
\(175\) 5.78632 0.437404
\(176\) 0 0
\(177\) 30.9915 2.32946
\(178\) 0 0
\(179\) −2.20412 −0.164744 −0.0823719 0.996602i \(-0.526250\pi\)
−0.0823719 + 0.996602i \(0.526250\pi\)
\(180\) 0 0
\(181\) −3.82843 −0.284565 −0.142282 0.989826i \(-0.545444\pi\)
−0.142282 + 0.989826i \(0.545444\pi\)
\(182\) 0 0
\(183\) −21.7486 −1.60770
\(184\) 0 0
\(185\) 13.6419 1.00297
\(186\) 0 0
\(187\) 2.90537 0.212461
\(188\) 0 0
\(189\) 0.251490 0.0182932
\(190\) 0 0
\(191\) −13.4697 −0.974634 −0.487317 0.873225i \(-0.662024\pi\)
−0.487317 + 0.873225i \(0.662024\pi\)
\(192\) 0 0
\(193\) 20.7367 1.49266 0.746330 0.665577i \(-0.231814\pi\)
0.746330 + 0.665577i \(0.231814\pi\)
\(194\) 0 0
\(195\) 41.6874 2.98529
\(196\) 0 0
\(197\) −3.92353 −0.279540 −0.139770 0.990184i \(-0.544636\pi\)
−0.139770 + 0.990184i \(0.544636\pi\)
\(198\) 0 0
\(199\) 14.8646 1.05373 0.526863 0.849950i \(-0.323368\pi\)
0.526863 + 0.849950i \(0.323368\pi\)
\(200\) 0 0
\(201\) 6.57258 0.463594
\(202\) 0 0
\(203\) −1.78477 −0.125266
\(204\) 0 0
\(205\) 19.0586 1.33111
\(206\) 0 0
\(207\) −15.2916 −1.06284
\(208\) 0 0
\(209\) 3.74396 0.258975
\(210\) 0 0
\(211\) −21.6197 −1.48836 −0.744182 0.667977i \(-0.767161\pi\)
−0.744182 + 0.667977i \(0.767161\pi\)
\(212\) 0 0
\(213\) 1.78779 0.122497
\(214\) 0 0
\(215\) −21.0187 −1.43347
\(216\) 0 0
\(217\) −9.14206 −0.620604
\(218\) 0 0
\(219\) 14.0510 0.949480
\(220\) 0 0
\(221\) −4.40235 −0.296134
\(222\) 0 0
\(223\) −2.85875 −0.191436 −0.0957181 0.995408i \(-0.530515\pi\)
−0.0957181 + 0.995408i \(0.530515\pi\)
\(224\) 0 0
\(225\) 11.9612 0.797412
\(226\) 0 0
\(227\) −10.5941 −0.703157 −0.351578 0.936158i \(-0.614355\pi\)
−0.351578 + 0.936158i \(0.614355\pi\)
\(228\) 0 0
\(229\) 6.38561 0.421973 0.210986 0.977489i \(-0.432332\pi\)
0.210986 + 0.977489i \(0.432332\pi\)
\(230\) 0 0
\(231\) 13.6922 0.900881
\(232\) 0 0
\(233\) 0.114938 0.00752986 0.00376493 0.999993i \(-0.498802\pi\)
0.00376493 + 0.999993i \(0.498802\pi\)
\(234\) 0 0
\(235\) −14.6488 −0.955582
\(236\) 0 0
\(237\) −2.46349 −0.160021
\(238\) 0 0
\(239\) 3.40065 0.219970 0.109985 0.993933i \(-0.464920\pi\)
0.109985 + 0.993933i \(0.464920\pi\)
\(240\) 0 0
\(241\) 14.1156 0.909269 0.454634 0.890678i \(-0.349770\pi\)
0.454634 + 0.890678i \(0.349770\pi\)
\(242\) 0 0
\(243\) −22.1597 −1.42155
\(244\) 0 0
\(245\) 14.3064 0.914004
\(246\) 0 0
\(247\) −5.67303 −0.360966
\(248\) 0 0
\(249\) −16.6355 −1.05423
\(250\) 0 0
\(251\) −8.58849 −0.542101 −0.271050 0.962565i \(-0.587371\pi\)
−0.271050 + 0.962565i \(0.587371\pi\)
\(252\) 0 0
\(253\) −18.6561 −1.17290
\(254\) 0 0
\(255\) −5.70242 −0.357100
\(256\) 0 0
\(257\) −11.7806 −0.734851 −0.367425 0.930053i \(-0.619761\pi\)
−0.367425 + 0.930053i \(0.619761\pi\)
\(258\) 0 0
\(259\) −6.78934 −0.421869
\(260\) 0 0
\(261\) −3.68938 −0.228367
\(262\) 0 0
\(263\) −8.90377 −0.549030 −0.274515 0.961583i \(-0.588517\pi\)
−0.274515 + 0.961583i \(0.588517\pi\)
\(264\) 0 0
\(265\) 36.9731 2.27124
\(266\) 0 0
\(267\) −6.42744 −0.393353
\(268\) 0 0
\(269\) 4.78700 0.291869 0.145934 0.989294i \(-0.453381\pi\)
0.145934 + 0.989294i \(0.453381\pi\)
\(270\) 0 0
\(271\) −4.49157 −0.272843 −0.136422 0.990651i \(-0.543560\pi\)
−0.136422 + 0.990651i \(0.543560\pi\)
\(272\) 0 0
\(273\) −20.7471 −1.25567
\(274\) 0 0
\(275\) 14.5929 0.879984
\(276\) 0 0
\(277\) −5.27428 −0.316901 −0.158450 0.987367i \(-0.550650\pi\)
−0.158450 + 0.987367i \(0.550650\pi\)
\(278\) 0 0
\(279\) −18.8980 −1.13139
\(280\) 0 0
\(281\) 9.47780 0.565398 0.282699 0.959209i \(-0.408770\pi\)
0.282699 + 0.959209i \(0.408770\pi\)
\(282\) 0 0
\(283\) 14.7428 0.876366 0.438183 0.898886i \(-0.355622\pi\)
0.438183 + 0.898886i \(0.355622\pi\)
\(284\) 0 0
\(285\) −7.34834 −0.435278
\(286\) 0 0
\(287\) −9.48515 −0.559891
\(288\) 0 0
\(289\) −16.3978 −0.964577
\(290\) 0 0
\(291\) 0.458080 0.0268531
\(292\) 0 0
\(293\) −30.5973 −1.78752 −0.893758 0.448550i \(-0.851941\pi\)
−0.893758 + 0.448550i \(0.851941\pi\)
\(294\) 0 0
\(295\) −37.5259 −2.18484
\(296\) 0 0
\(297\) 0.634249 0.0368029
\(298\) 0 0
\(299\) 28.2686 1.63481
\(300\) 0 0
\(301\) 10.4607 0.602943
\(302\) 0 0
\(303\) 35.0011 2.01076
\(304\) 0 0
\(305\) 26.3342 1.50789
\(306\) 0 0
\(307\) −14.4944 −0.827238 −0.413619 0.910450i \(-0.635736\pi\)
−0.413619 + 0.910450i \(0.635736\pi\)
\(308\) 0 0
\(309\) 1.73315 0.0985955
\(310\) 0 0
\(311\) −9.85849 −0.559024 −0.279512 0.960142i \(-0.590173\pi\)
−0.279512 + 0.960142i \(0.590173\pi\)
\(312\) 0 0
\(313\) 4.13440 0.233690 0.116845 0.993150i \(-0.462722\pi\)
0.116845 + 0.993150i \(0.462722\pi\)
\(314\) 0 0
\(315\) −13.5892 −0.765667
\(316\) 0 0
\(317\) −15.3790 −0.863771 −0.431885 0.901929i \(-0.642151\pi\)
−0.431885 + 0.901929i \(0.642151\pi\)
\(318\) 0 0
\(319\) −4.50111 −0.252014
\(320\) 0 0
\(321\) −37.0825 −2.06974
\(322\) 0 0
\(323\) 0.776015 0.0431786
\(324\) 0 0
\(325\) −22.1119 −1.22654
\(326\) 0 0
\(327\) 23.4479 1.29667
\(328\) 0 0
\(329\) 7.29045 0.401936
\(330\) 0 0
\(331\) −1.77868 −0.0977653 −0.0488827 0.998805i \(-0.515566\pi\)
−0.0488827 + 0.998805i \(0.515566\pi\)
\(332\) 0 0
\(333\) −14.0346 −0.769090
\(334\) 0 0
\(335\) −7.95838 −0.434813
\(336\) 0 0
\(337\) −4.32898 −0.235815 −0.117907 0.993025i \(-0.537619\pi\)
−0.117907 + 0.993025i \(0.537619\pi\)
\(338\) 0 0
\(339\) −21.5038 −1.16793
\(340\) 0 0
\(341\) −23.0560 −1.24855
\(342\) 0 0
\(343\) −17.5118 −0.945551
\(344\) 0 0
\(345\) 36.6166 1.97137
\(346\) 0 0
\(347\) 9.06369 0.486564 0.243282 0.969956i \(-0.421776\pi\)
0.243282 + 0.969956i \(0.421776\pi\)
\(348\) 0 0
\(349\) −8.21345 −0.439656 −0.219828 0.975539i \(-0.570550\pi\)
−0.219828 + 0.975539i \(0.570550\pi\)
\(350\) 0 0
\(351\) −0.961045 −0.0512968
\(352\) 0 0
\(353\) 16.5443 0.880563 0.440282 0.897860i \(-0.354879\pi\)
0.440282 + 0.897860i \(0.354879\pi\)
\(354\) 0 0
\(355\) −2.16474 −0.114892
\(356\) 0 0
\(357\) 2.83800 0.150203
\(358\) 0 0
\(359\) 1.62100 0.0855532 0.0427766 0.999085i \(-0.486380\pi\)
0.0427766 + 0.999085i \(0.486380\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 0 0
\(363\) 7.43288 0.390125
\(364\) 0 0
\(365\) −17.0136 −0.890534
\(366\) 0 0
\(367\) 19.4015 1.01275 0.506375 0.862313i \(-0.330985\pi\)
0.506375 + 0.862313i \(0.330985\pi\)
\(368\) 0 0
\(369\) −19.6072 −1.02071
\(370\) 0 0
\(371\) −18.4009 −0.955326
\(372\) 0 0
\(373\) 34.3133 1.77668 0.888338 0.459190i \(-0.151860\pi\)
0.888338 + 0.459190i \(0.151860\pi\)
\(374\) 0 0
\(375\) 8.09996 0.418280
\(376\) 0 0
\(377\) 6.82031 0.351264
\(378\) 0 0
\(379\) −33.7077 −1.73145 −0.865725 0.500521i \(-0.833142\pi\)
−0.865725 + 0.500521i \(0.833142\pi\)
\(380\) 0 0
\(381\) −26.0501 −1.33459
\(382\) 0 0
\(383\) −32.0475 −1.63755 −0.818776 0.574113i \(-0.805347\pi\)
−0.818776 + 0.574113i \(0.805347\pi\)
\(384\) 0 0
\(385\) −16.5791 −0.844952
\(386\) 0 0
\(387\) 21.6238 1.09920
\(388\) 0 0
\(389\) 25.7408 1.30511 0.652556 0.757741i \(-0.273697\pi\)
0.652556 + 0.757741i \(0.273697\pi\)
\(390\) 0 0
\(391\) −3.86686 −0.195556
\(392\) 0 0
\(393\) −27.5118 −1.38779
\(394\) 0 0
\(395\) 2.98290 0.150086
\(396\) 0 0
\(397\) 8.27193 0.415156 0.207578 0.978218i \(-0.433442\pi\)
0.207578 + 0.978218i \(0.433442\pi\)
\(398\) 0 0
\(399\) 3.65715 0.183086
\(400\) 0 0
\(401\) −32.1487 −1.60543 −0.802715 0.596363i \(-0.796612\pi\)
−0.802715 + 0.596363i \(0.796612\pi\)
\(402\) 0 0
\(403\) 34.9355 1.74026
\(404\) 0 0
\(405\) 26.2167 1.30272
\(406\) 0 0
\(407\) −17.1225 −0.848729
\(408\) 0 0
\(409\) −6.54609 −0.323683 −0.161842 0.986817i \(-0.551743\pi\)
−0.161842 + 0.986817i \(0.551743\pi\)
\(410\) 0 0
\(411\) 9.45217 0.466241
\(412\) 0 0
\(413\) 18.6760 0.918986
\(414\) 0 0
\(415\) 20.1430 0.988782
\(416\) 0 0
\(417\) −38.4728 −1.88402
\(418\) 0 0
\(419\) 12.4824 0.609807 0.304903 0.952383i \(-0.401376\pi\)
0.304903 + 0.952383i \(0.401376\pi\)
\(420\) 0 0
\(421\) 8.45980 0.412306 0.206153 0.978520i \(-0.433906\pi\)
0.206153 + 0.978520i \(0.433906\pi\)
\(422\) 0 0
\(423\) 15.0705 0.732751
\(424\) 0 0
\(425\) 3.02468 0.146719
\(426\) 0 0
\(427\) −13.1061 −0.634248
\(428\) 0 0
\(429\) −52.3234 −2.52620
\(430\) 0 0
\(431\) 6.66995 0.321280 0.160640 0.987013i \(-0.448644\pi\)
0.160640 + 0.987013i \(0.448644\pi\)
\(432\) 0 0
\(433\) −9.79831 −0.470877 −0.235438 0.971889i \(-0.575653\pi\)
−0.235438 + 0.971889i \(0.575653\pi\)
\(434\) 0 0
\(435\) 8.83443 0.423578
\(436\) 0 0
\(437\) −4.98298 −0.238368
\(438\) 0 0
\(439\) 1.97553 0.0942869 0.0471434 0.998888i \(-0.484988\pi\)
0.0471434 + 0.998888i \(0.484988\pi\)
\(440\) 0 0
\(441\) −14.7182 −0.700868
\(442\) 0 0
\(443\) −5.84638 −0.277770 −0.138885 0.990309i \(-0.544352\pi\)
−0.138885 + 0.990309i \(0.544352\pi\)
\(444\) 0 0
\(445\) 7.78264 0.368933
\(446\) 0 0
\(447\) −42.1944 −1.99573
\(448\) 0 0
\(449\) −31.2095 −1.47287 −0.736434 0.676510i \(-0.763492\pi\)
−0.736434 + 0.676510i \(0.763492\pi\)
\(450\) 0 0
\(451\) −23.9212 −1.12641
\(452\) 0 0
\(453\) 1.55907 0.0732514
\(454\) 0 0
\(455\) 25.1215 1.17772
\(456\) 0 0
\(457\) −10.5289 −0.492522 −0.246261 0.969204i \(-0.579202\pi\)
−0.246261 + 0.969204i \(0.579202\pi\)
\(458\) 0 0
\(459\) 0.131462 0.00613610
\(460\) 0 0
\(461\) 6.27172 0.292103 0.146052 0.989277i \(-0.453343\pi\)
0.146052 + 0.989277i \(0.453343\pi\)
\(462\) 0 0
\(463\) 1.37514 0.0639080 0.0319540 0.999489i \(-0.489827\pi\)
0.0319540 + 0.999489i \(0.489827\pi\)
\(464\) 0 0
\(465\) 45.2524 2.09853
\(466\) 0 0
\(467\) 3.63683 0.168292 0.0841462 0.996453i \(-0.473184\pi\)
0.0841462 + 0.996453i \(0.473184\pi\)
\(468\) 0 0
\(469\) 3.96075 0.182891
\(470\) 0 0
\(471\) −5.52010 −0.254353
\(472\) 0 0
\(473\) 26.3814 1.21302
\(474\) 0 0
\(475\) 3.89772 0.178839
\(476\) 0 0
\(477\) −38.0374 −1.74161
\(478\) 0 0
\(479\) 39.3195 1.79655 0.898277 0.439429i \(-0.144819\pi\)
0.898277 + 0.439429i \(0.144819\pi\)
\(480\) 0 0
\(481\) 25.9448 1.18298
\(482\) 0 0
\(483\) −18.2235 −0.829197
\(484\) 0 0
\(485\) −0.554665 −0.0251860
\(486\) 0 0
\(487\) 32.9332 1.49235 0.746173 0.665752i \(-0.231889\pi\)
0.746173 + 0.665752i \(0.231889\pi\)
\(488\) 0 0
\(489\) 22.2181 1.00474
\(490\) 0 0
\(491\) 21.6766 0.978252 0.489126 0.872213i \(-0.337316\pi\)
0.489126 + 0.872213i \(0.337316\pi\)
\(492\) 0 0
\(493\) −0.932951 −0.0420180
\(494\) 0 0
\(495\) −34.2716 −1.54039
\(496\) 0 0
\(497\) 1.07735 0.0483259
\(498\) 0 0
\(499\) −18.2967 −0.819072 −0.409536 0.912294i \(-0.634309\pi\)
−0.409536 + 0.912294i \(0.634309\pi\)
\(500\) 0 0
\(501\) −29.8972 −1.33571
\(502\) 0 0
\(503\) 30.4652 1.35838 0.679188 0.733964i \(-0.262332\pi\)
0.679188 + 0.733964i \(0.262332\pi\)
\(504\) 0 0
\(505\) −42.3809 −1.88593
\(506\) 0 0
\(507\) 47.2577 2.09879
\(508\) 0 0
\(509\) −1.24658 −0.0552539 −0.0276269 0.999618i \(-0.508795\pi\)
−0.0276269 + 0.999618i \(0.508795\pi\)
\(510\) 0 0
\(511\) 8.46740 0.374576
\(512\) 0 0
\(513\) 0.169406 0.00747946
\(514\) 0 0
\(515\) −2.09858 −0.0924744
\(516\) 0 0
\(517\) 18.3863 0.808627
\(518\) 0 0
\(519\) 55.3528 2.42972
\(520\) 0 0
\(521\) 1.93057 0.0845796 0.0422898 0.999105i \(-0.486535\pi\)
0.0422898 + 0.999105i \(0.486535\pi\)
\(522\) 0 0
\(523\) 43.4590 1.90033 0.950165 0.311747i \(-0.100914\pi\)
0.950165 + 0.311747i \(0.100914\pi\)
\(524\) 0 0
\(525\) 14.2545 0.622118
\(526\) 0 0
\(527\) −4.77884 −0.208169
\(528\) 0 0
\(529\) 1.83006 0.0795677
\(530\) 0 0
\(531\) 38.6061 1.67536
\(532\) 0 0
\(533\) 36.2466 1.57001
\(534\) 0 0
\(535\) 44.9012 1.94125
\(536\) 0 0
\(537\) −5.42982 −0.234314
\(538\) 0 0
\(539\) −17.9565 −0.773443
\(540\) 0 0
\(541\) 22.9603 0.987141 0.493571 0.869706i \(-0.335691\pi\)
0.493571 + 0.869706i \(0.335691\pi\)
\(542\) 0 0
\(543\) −9.43128 −0.404735
\(544\) 0 0
\(545\) −28.3919 −1.21617
\(546\) 0 0
\(547\) 30.2577 1.29373 0.646864 0.762606i \(-0.276080\pi\)
0.646864 + 0.762606i \(0.276080\pi\)
\(548\) 0 0
\(549\) −27.0922 −1.15627
\(550\) 0 0
\(551\) −1.20223 −0.0512169
\(552\) 0 0
\(553\) −1.48454 −0.0631291
\(554\) 0 0
\(555\) 33.6066 1.42652
\(556\) 0 0
\(557\) 23.0051 0.974756 0.487378 0.873191i \(-0.337953\pi\)
0.487378 + 0.873191i \(0.337953\pi\)
\(558\) 0 0
\(559\) −39.9744 −1.69074
\(560\) 0 0
\(561\) 7.15733 0.302183
\(562\) 0 0
\(563\) 19.7496 0.832348 0.416174 0.909285i \(-0.363371\pi\)
0.416174 + 0.909285i \(0.363371\pi\)
\(564\) 0 0
\(565\) 26.0378 1.09542
\(566\) 0 0
\(567\) −13.0476 −0.547947
\(568\) 0 0
\(569\) −29.6645 −1.24360 −0.621801 0.783175i \(-0.713599\pi\)
−0.621801 + 0.783175i \(0.713599\pi\)
\(570\) 0 0
\(571\) −9.09131 −0.380460 −0.190230 0.981740i \(-0.560923\pi\)
−0.190230 + 0.981740i \(0.560923\pi\)
\(572\) 0 0
\(573\) −33.1825 −1.38622
\(574\) 0 0
\(575\) −19.4222 −0.809963
\(576\) 0 0
\(577\) 5.04236 0.209916 0.104958 0.994477i \(-0.466529\pi\)
0.104958 + 0.994477i \(0.466529\pi\)
\(578\) 0 0
\(579\) 51.0845 2.12300
\(580\) 0 0
\(581\) −10.0248 −0.415900
\(582\) 0 0
\(583\) −46.4063 −1.92195
\(584\) 0 0
\(585\) 51.9300 2.14704
\(586\) 0 0
\(587\) −14.0026 −0.577950 −0.288975 0.957337i \(-0.593314\pi\)
−0.288975 + 0.957337i \(0.593314\pi\)
\(588\) 0 0
\(589\) −6.15818 −0.253743
\(590\) 0 0
\(591\) −9.66556 −0.397588
\(592\) 0 0
\(593\) 33.9610 1.39461 0.697306 0.716774i \(-0.254382\pi\)
0.697306 + 0.716774i \(0.254382\pi\)
\(594\) 0 0
\(595\) −3.43638 −0.140878
\(596\) 0 0
\(597\) 36.6188 1.49871
\(598\) 0 0
\(599\) 36.6212 1.49630 0.748150 0.663529i \(-0.230942\pi\)
0.748150 + 0.663529i \(0.230942\pi\)
\(600\) 0 0
\(601\) 17.5665 0.716553 0.358277 0.933615i \(-0.383364\pi\)
0.358277 + 0.933615i \(0.383364\pi\)
\(602\) 0 0
\(603\) 8.18747 0.333419
\(604\) 0 0
\(605\) −9.00007 −0.365905
\(606\) 0 0
\(607\) −2.70273 −0.109701 −0.0548503 0.998495i \(-0.517468\pi\)
−0.0548503 + 0.998495i \(0.517468\pi\)
\(608\) 0 0
\(609\) −4.39674 −0.178165
\(610\) 0 0
\(611\) −27.8598 −1.12709
\(612\) 0 0
\(613\) 48.2519 1.94888 0.974439 0.224654i \(-0.0721252\pi\)
0.974439 + 0.224654i \(0.0721252\pi\)
\(614\) 0 0
\(615\) 46.9506 1.89323
\(616\) 0 0
\(617\) 5.58414 0.224809 0.112405 0.993663i \(-0.464145\pi\)
0.112405 + 0.993663i \(0.464145\pi\)
\(618\) 0 0
\(619\) −36.1367 −1.45245 −0.726227 0.687455i \(-0.758728\pi\)
−0.726227 + 0.687455i \(0.758728\pi\)
\(620\) 0 0
\(621\) −0.844146 −0.0338744
\(622\) 0 0
\(623\) −3.87329 −0.155180
\(624\) 0 0
\(625\) −29.2964 −1.17186
\(626\) 0 0
\(627\) 9.22319 0.368339
\(628\) 0 0
\(629\) −3.54899 −0.141508
\(630\) 0 0
\(631\) 29.9727 1.19319 0.596596 0.802541i \(-0.296519\pi\)
0.596596 + 0.802541i \(0.296519\pi\)
\(632\) 0 0
\(633\) −53.2599 −2.11689
\(634\) 0 0
\(635\) 31.5427 1.25173
\(636\) 0 0
\(637\) 27.2086 1.07805
\(638\) 0 0
\(639\) 2.22705 0.0881008
\(640\) 0 0
\(641\) −8.49150 −0.335394 −0.167697 0.985839i \(-0.553633\pi\)
−0.167697 + 0.985839i \(0.553633\pi\)
\(642\) 0 0
\(643\) 26.3439 1.03890 0.519451 0.854500i \(-0.326136\pi\)
0.519451 + 0.854500i \(0.326136\pi\)
\(644\) 0 0
\(645\) −51.7794 −2.03881
\(646\) 0 0
\(647\) −19.3732 −0.761638 −0.380819 0.924650i \(-0.624358\pi\)
−0.380819 + 0.924650i \(0.624358\pi\)
\(648\) 0 0
\(649\) 47.1002 1.84885
\(650\) 0 0
\(651\) −22.5214 −0.882681
\(652\) 0 0
\(653\) −1.14545 −0.0448249 −0.0224125 0.999749i \(-0.507135\pi\)
−0.0224125 + 0.999749i \(0.507135\pi\)
\(654\) 0 0
\(655\) 33.3126 1.30163
\(656\) 0 0
\(657\) 17.5034 0.682872
\(658\) 0 0
\(659\) −29.3942 −1.14504 −0.572519 0.819892i \(-0.694034\pi\)
−0.572519 + 0.819892i \(0.694034\pi\)
\(660\) 0 0
\(661\) 33.0247 1.28451 0.642256 0.766490i \(-0.277999\pi\)
0.642256 + 0.766490i \(0.277999\pi\)
\(662\) 0 0
\(663\) −10.8451 −0.421190
\(664\) 0 0
\(665\) −4.42824 −0.171720
\(666\) 0 0
\(667\) 5.99070 0.231961
\(668\) 0 0
\(669\) −7.04250 −0.272279
\(670\) 0 0
\(671\) −33.0531 −1.27600
\(672\) 0 0
\(673\) 24.5562 0.946572 0.473286 0.880909i \(-0.343068\pi\)
0.473286 + 0.880909i \(0.343068\pi\)
\(674\) 0 0
\(675\) 0.660297 0.0254148
\(676\) 0 0
\(677\) 29.1017 1.11847 0.559234 0.829010i \(-0.311095\pi\)
0.559234 + 0.829010i \(0.311095\pi\)
\(678\) 0 0
\(679\) 0.276047 0.0105937
\(680\) 0 0
\(681\) −26.0985 −1.00010
\(682\) 0 0
\(683\) −32.1310 −1.22946 −0.614730 0.788738i \(-0.710735\pi\)
−0.614730 + 0.788738i \(0.710735\pi\)
\(684\) 0 0
\(685\) −11.4451 −0.437296
\(686\) 0 0
\(687\) 15.7309 0.600170
\(688\) 0 0
\(689\) 70.3172 2.67887
\(690\) 0 0
\(691\) −9.21024 −0.350374 −0.175187 0.984535i \(-0.556053\pi\)
−0.175187 + 0.984535i \(0.556053\pi\)
\(692\) 0 0
\(693\) 17.0564 0.647918
\(694\) 0 0
\(695\) 46.5846 1.76705
\(696\) 0 0
\(697\) −4.95818 −0.187804
\(698\) 0 0
\(699\) 0.283149 0.0107097
\(700\) 0 0
\(701\) −38.8819 −1.46855 −0.734274 0.678853i \(-0.762477\pi\)
−0.734274 + 0.678853i \(0.762477\pi\)
\(702\) 0 0
\(703\) −4.57336 −0.172488
\(704\) 0 0
\(705\) −36.0871 −1.35912
\(706\) 0 0
\(707\) 21.0923 0.793256
\(708\) 0 0
\(709\) 22.6080 0.849062 0.424531 0.905413i \(-0.360439\pi\)
0.424531 + 0.905413i \(0.360439\pi\)
\(710\) 0 0
\(711\) −3.06877 −0.115088
\(712\) 0 0
\(713\) 30.6861 1.14920
\(714\) 0 0
\(715\) 63.3556 2.36937
\(716\) 0 0
\(717\) 8.37745 0.312862
\(718\) 0 0
\(719\) −28.0851 −1.04740 −0.523698 0.851904i \(-0.675448\pi\)
−0.523698 + 0.851904i \(0.675448\pi\)
\(720\) 0 0
\(721\) 1.04443 0.0388965
\(722\) 0 0
\(723\) 34.7737 1.29325
\(724\) 0 0
\(725\) −4.68597 −0.174032
\(726\) 0 0
\(727\) 42.7897 1.58698 0.793491 0.608581i \(-0.208261\pi\)
0.793491 + 0.608581i \(0.208261\pi\)
\(728\) 0 0
\(729\) −28.2233 −1.04531
\(730\) 0 0
\(731\) 5.46811 0.202245
\(732\) 0 0
\(733\) 24.7829 0.915377 0.457688 0.889113i \(-0.348678\pi\)
0.457688 + 0.889113i \(0.348678\pi\)
\(734\) 0 0
\(735\) 35.2437 1.29998
\(736\) 0 0
\(737\) 9.98888 0.367945
\(738\) 0 0
\(739\) 36.0333 1.32551 0.662753 0.748838i \(-0.269388\pi\)
0.662753 + 0.748838i \(0.269388\pi\)
\(740\) 0 0
\(741\) −13.9754 −0.513400
\(742\) 0 0
\(743\) −28.9124 −1.06069 −0.530347 0.847781i \(-0.677938\pi\)
−0.530347 + 0.847781i \(0.677938\pi\)
\(744\) 0 0
\(745\) 51.0909 1.87183
\(746\) 0 0
\(747\) −20.7228 −0.758209
\(748\) 0 0
\(749\) −22.3466 −0.816526
\(750\) 0 0
\(751\) −4.50606 −0.164428 −0.0822142 0.996615i \(-0.526199\pi\)
−0.0822142 + 0.996615i \(0.526199\pi\)
\(752\) 0 0
\(753\) −21.1576 −0.771027
\(754\) 0 0
\(755\) −1.88779 −0.0687038
\(756\) 0 0
\(757\) 30.6921 1.11552 0.557761 0.830002i \(-0.311661\pi\)
0.557761 + 0.830002i \(0.311661\pi\)
\(758\) 0 0
\(759\) −45.9589 −1.66820
\(760\) 0 0
\(761\) −16.5641 −0.600446 −0.300223 0.953869i \(-0.597061\pi\)
−0.300223 + 0.953869i \(0.597061\pi\)
\(762\) 0 0
\(763\) 14.1301 0.511546
\(764\) 0 0
\(765\) −7.10351 −0.256828
\(766\) 0 0
\(767\) −71.3686 −2.57697
\(768\) 0 0
\(769\) −6.64468 −0.239613 −0.119807 0.992797i \(-0.538227\pi\)
−0.119807 + 0.992797i \(0.538227\pi\)
\(770\) 0 0
\(771\) −29.0212 −1.04517
\(772\) 0 0
\(773\) −21.3328 −0.767286 −0.383643 0.923481i \(-0.625331\pi\)
−0.383643 + 0.923481i \(0.625331\pi\)
\(774\) 0 0
\(775\) −24.0028 −0.862207
\(776\) 0 0
\(777\) −16.7254 −0.600022
\(778\) 0 0
\(779\) −6.38928 −0.228920
\(780\) 0 0
\(781\) 2.71705 0.0972236
\(782\) 0 0
\(783\) −0.203666 −0.00727842
\(784\) 0 0
\(785\) 6.68400 0.238562
\(786\) 0 0
\(787\) 0.238950 0.00851765 0.00425882 0.999991i \(-0.498644\pi\)
0.00425882 + 0.999991i \(0.498644\pi\)
\(788\) 0 0
\(789\) −21.9343 −0.780883
\(790\) 0 0
\(791\) −12.9586 −0.460753
\(792\) 0 0
\(793\) 50.0837 1.77852
\(794\) 0 0
\(795\) 91.0827 3.23037
\(796\) 0 0
\(797\) 40.6092 1.43845 0.719226 0.694777i \(-0.244497\pi\)
0.719226 + 0.694777i \(0.244497\pi\)
\(798\) 0 0
\(799\) 3.81094 0.134821
\(800\) 0 0
\(801\) −8.00667 −0.282902
\(802\) 0 0
\(803\) 21.3545 0.753583
\(804\) 0 0
\(805\) 22.0658 0.777718
\(806\) 0 0
\(807\) 11.7927 0.415124
\(808\) 0 0
\(809\) 52.3709 1.84126 0.920632 0.390431i \(-0.127674\pi\)
0.920632 + 0.390431i \(0.127674\pi\)
\(810\) 0 0
\(811\) −19.0170 −0.667776 −0.333888 0.942613i \(-0.608361\pi\)
−0.333888 + 0.942613i \(0.608361\pi\)
\(812\) 0 0
\(813\) −11.0649 −0.388063
\(814\) 0 0
\(815\) −26.9027 −0.942359
\(816\) 0 0
\(817\) 7.04640 0.246522
\(818\) 0 0
\(819\) −25.8447 −0.903086
\(820\) 0 0
\(821\) −29.4288 −1.02707 −0.513535 0.858068i \(-0.671664\pi\)
−0.513535 + 0.858068i \(0.671664\pi\)
\(822\) 0 0
\(823\) −24.1108 −0.840449 −0.420225 0.907420i \(-0.638049\pi\)
−0.420225 + 0.907420i \(0.638049\pi\)
\(824\) 0 0
\(825\) 35.9494 1.25160
\(826\) 0 0
\(827\) −2.38960 −0.0830944 −0.0415472 0.999137i \(-0.513229\pi\)
−0.0415472 + 0.999137i \(0.513229\pi\)
\(828\) 0 0
\(829\) −44.2534 −1.53698 −0.768492 0.639860i \(-0.778992\pi\)
−0.768492 + 0.639860i \(0.778992\pi\)
\(830\) 0 0
\(831\) −12.9931 −0.450726
\(832\) 0 0
\(833\) −3.72187 −0.128955
\(834\) 0 0
\(835\) 36.2009 1.25278
\(836\) 0 0
\(837\) −1.04323 −0.0360594
\(838\) 0 0
\(839\) −46.7820 −1.61509 −0.807547 0.589803i \(-0.799206\pi\)
−0.807547 + 0.589803i \(0.799206\pi\)
\(840\) 0 0
\(841\) −27.5546 −0.950160
\(842\) 0 0
\(843\) 23.3484 0.804163
\(844\) 0 0
\(845\) −57.2218 −1.96849
\(846\) 0 0
\(847\) 4.47918 0.153907
\(848\) 0 0
\(849\) 36.3186 1.24645
\(850\) 0 0
\(851\) 22.7889 0.781195
\(852\) 0 0
\(853\) −21.2185 −0.726509 −0.363255 0.931690i \(-0.618334\pi\)
−0.363255 + 0.931690i \(0.618334\pi\)
\(854\) 0 0
\(855\) −9.15384 −0.313055
\(856\) 0 0
\(857\) −54.2612 −1.85353 −0.926763 0.375645i \(-0.877421\pi\)
−0.926763 + 0.375645i \(0.877421\pi\)
\(858\) 0 0
\(859\) 2.93585 0.100170 0.0500850 0.998745i \(-0.484051\pi\)
0.0500850 + 0.998745i \(0.484051\pi\)
\(860\) 0 0
\(861\) −23.3665 −0.796329
\(862\) 0 0
\(863\) −9.75145 −0.331943 −0.165972 0.986131i \(-0.553076\pi\)
−0.165972 + 0.986131i \(0.553076\pi\)
\(864\) 0 0
\(865\) −67.0237 −2.27887
\(866\) 0 0
\(867\) −40.3958 −1.37191
\(868\) 0 0
\(869\) −3.74396 −0.127005
\(870\) 0 0
\(871\) −15.1356 −0.512851
\(872\) 0 0
\(873\) 0.570631 0.0193129
\(874\) 0 0
\(875\) 4.88118 0.165014
\(876\) 0 0
\(877\) 17.8712 0.603467 0.301734 0.953392i \(-0.402435\pi\)
0.301734 + 0.953392i \(0.402435\pi\)
\(878\) 0 0
\(879\) −75.3761 −2.54237
\(880\) 0 0
\(881\) 0.816355 0.0275037 0.0137519 0.999905i \(-0.495623\pi\)
0.0137519 + 0.999905i \(0.495623\pi\)
\(882\) 0 0
\(883\) 28.2581 0.950960 0.475480 0.879726i \(-0.342274\pi\)
0.475480 + 0.879726i \(0.342274\pi\)
\(884\) 0 0
\(885\) −92.4446 −3.10749
\(886\) 0 0
\(887\) 0.805723 0.0270535 0.0135268 0.999909i \(-0.495694\pi\)
0.0135268 + 0.999909i \(0.495694\pi\)
\(888\) 0 0
\(889\) −15.6983 −0.526503
\(890\) 0 0
\(891\) −32.9055 −1.10238
\(892\) 0 0
\(893\) 4.91092 0.164338
\(894\) 0 0
\(895\) 6.57468 0.219767
\(896\) 0 0
\(897\) 69.6392 2.32519
\(898\) 0 0
\(899\) 7.40357 0.246923
\(900\) 0 0
\(901\) −9.61870 −0.320445
\(902\) 0 0
\(903\) 25.7697 0.857562
\(904\) 0 0
\(905\) 11.4198 0.379608
\(906\) 0 0
\(907\) 54.3897 1.80598 0.902991 0.429659i \(-0.141366\pi\)
0.902991 + 0.429659i \(0.141366\pi\)
\(908\) 0 0
\(909\) 43.6008 1.44615
\(910\) 0 0
\(911\) 47.0649 1.55933 0.779665 0.626196i \(-0.215389\pi\)
0.779665 + 0.626196i \(0.215389\pi\)
\(912\) 0 0
\(913\) −25.2823 −0.836721
\(914\) 0 0
\(915\) 64.8740 2.14467
\(916\) 0 0
\(917\) −16.5791 −0.547490
\(918\) 0 0
\(919\) −23.6447 −0.779967 −0.389983 0.920822i \(-0.627519\pi\)
−0.389983 + 0.920822i \(0.627519\pi\)
\(920\) 0 0
\(921\) −35.7067 −1.17658
\(922\) 0 0
\(923\) −4.11701 −0.135513
\(924\) 0 0
\(925\) −17.8257 −0.586104
\(926\) 0 0
\(927\) 2.15899 0.0709104
\(928\) 0 0
\(929\) −56.1042 −1.84072 −0.920360 0.391072i \(-0.872104\pi\)
−0.920360 + 0.391072i \(0.872104\pi\)
\(930\) 0 0
\(931\) −4.79614 −0.157187
\(932\) 0 0
\(933\) −24.2863 −0.795096
\(934\) 0 0
\(935\) −8.66643 −0.283423
\(936\) 0 0
\(937\) 28.9436 0.945545 0.472772 0.881185i \(-0.343253\pi\)
0.472772 + 0.881185i \(0.343253\pi\)
\(938\) 0 0
\(939\) 10.1850 0.332376
\(940\) 0 0
\(941\) −23.9849 −0.781885 −0.390942 0.920415i \(-0.627851\pi\)
−0.390942 + 0.920415i \(0.627851\pi\)
\(942\) 0 0
\(943\) 31.8376 1.03678
\(944\) 0 0
\(945\) −0.750171 −0.0244031
\(946\) 0 0
\(947\) 0.0634084 0.00206050 0.00103025 0.999999i \(-0.499672\pi\)
0.00103025 + 0.999999i \(0.499672\pi\)
\(948\) 0 0
\(949\) −32.3573 −1.05036
\(950\) 0 0
\(951\) −37.8860 −1.22854
\(952\) 0 0
\(953\) 0.789685 0.0255804 0.0127902 0.999918i \(-0.495929\pi\)
0.0127902 + 0.999918i \(0.495929\pi\)
\(954\) 0 0
\(955\) 40.1789 1.30016
\(956\) 0 0
\(957\) −11.0884 −0.358438
\(958\) 0 0
\(959\) 5.69604 0.183935
\(960\) 0 0
\(961\) 6.92315 0.223327
\(962\) 0 0
\(963\) −46.1937 −1.48857
\(964\) 0 0
\(965\) −61.8555 −1.99120
\(966\) 0 0
\(967\) −24.2811 −0.780828 −0.390414 0.920639i \(-0.627668\pi\)
−0.390414 + 0.920639i \(0.627668\pi\)
\(968\) 0 0
\(969\) 1.91170 0.0614127
\(970\) 0 0
\(971\) 38.9003 1.24837 0.624185 0.781276i \(-0.285431\pi\)
0.624185 + 0.781276i \(0.285431\pi\)
\(972\) 0 0
\(973\) −23.1844 −0.743256
\(974\) 0 0
\(975\) −54.4723 −1.74451
\(976\) 0 0
\(977\) −53.6926 −1.71778 −0.858889 0.512162i \(-0.828845\pi\)
−0.858889 + 0.512162i \(0.828845\pi\)
\(978\) 0 0
\(979\) −9.76829 −0.312196
\(980\) 0 0
\(981\) 29.2091 0.932575
\(982\) 0 0
\(983\) −25.9429 −0.827448 −0.413724 0.910402i \(-0.635772\pi\)
−0.413724 + 0.910402i \(0.635772\pi\)
\(984\) 0 0
\(985\) 11.7035 0.372905
\(986\) 0 0
\(987\) 17.9599 0.571671
\(988\) 0 0
\(989\) −35.1120 −1.11650
\(990\) 0 0
\(991\) 25.3334 0.804743 0.402372 0.915476i \(-0.368186\pi\)
0.402372 + 0.915476i \(0.368186\pi\)
\(992\) 0 0
\(993\) −4.38177 −0.139051
\(994\) 0 0
\(995\) −44.3397 −1.40566
\(996\) 0 0
\(997\) 0.0487709 0.00154459 0.000772294 1.00000i \(-0.499754\pi\)
0.000772294 1.00000i \(0.499754\pi\)
\(998\) 0 0
\(999\) −0.774755 −0.0245122
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 \(a_p\))