Properties

Label 8036.2.a.t.1.3
Level 8036
Weight 2
Character 8036.1
Self dual Yes
Analytic conductor 64.168
Analytic rank 0
Dimension 20
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8036 = 2^{2} \cdot 7^{2} \cdot 41 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8036.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.1677830643\)
Analytic rank: \(0\)
Dimension: \(20\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{3} \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(-2.32542\)
Character \(\chi\) = 8036.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.32542 q^{3}\) \(+1.16439 q^{5}\) \(+2.40759 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.32542 q^{3}\) \(+1.16439 q^{5}\) \(+2.40759 q^{9}\) \(+0.577754 q^{11}\) \(+2.18295 q^{13}\) \(-2.70769 q^{15}\) \(+6.65536 q^{17}\) \(-2.12850 q^{19}\) \(+8.32156 q^{23}\) \(-3.64420 q^{25}\) \(+1.37760 q^{27}\) \(-6.30024 q^{29}\) \(-1.38664 q^{31}\) \(-1.34352 q^{33}\) \(+2.86577 q^{37}\) \(-5.07629 q^{39}\) \(-1.00000 q^{41}\) \(+6.21582 q^{43}\) \(+2.80337 q^{45}\) \(+12.3492 q^{47}\) \(-15.4765 q^{51}\) \(+13.0449 q^{53}\) \(+0.672730 q^{55}\) \(+4.94967 q^{57}\) \(-3.27380 q^{59}\) \(+5.15551 q^{61}\) \(+2.54180 q^{65}\) \(-5.35143 q^{67}\) \(-19.3511 q^{69}\) \(-14.3919 q^{71}\) \(+8.30995 q^{73}\) \(+8.47431 q^{75}\) \(-14.6782 q^{79}\) \(-10.4263 q^{81}\) \(-11.7691 q^{83}\) \(+7.74941 q^{85}\) \(+14.6507 q^{87}\) \(+6.56350 q^{89}\) \(+3.22452 q^{93}\) \(-2.47840 q^{95}\) \(-2.09480 q^{97}\) \(+1.39100 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(20q \) \(\mathstrut +\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 8q^{5} \) \(\mathstrut +\mathstrut 16q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(20q \) \(\mathstrut +\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 8q^{5} \) \(\mathstrut +\mathstrut 16q^{9} \) \(\mathstrut -\mathstrut 8q^{11} \) \(\mathstrut +\mathstrut 12q^{13} \) \(\mathstrut +\mathstrut 8q^{15} \) \(\mathstrut +\mathstrut 8q^{17} \) \(\mathstrut +\mathstrut 24q^{19} \) \(\mathstrut +\mathstrut 8q^{23} \) \(\mathstrut +\mathstrut 20q^{25} \) \(\mathstrut +\mathstrut 16q^{27} \) \(\mathstrut -\mathstrut 12q^{29} \) \(\mathstrut +\mathstrut 44q^{33} \) \(\mathstrut +\mathstrut 12q^{37} \) \(\mathstrut +\mathstrut 12q^{39} \) \(\mathstrut -\mathstrut 20q^{41} \) \(\mathstrut +\mathstrut 4q^{43} \) \(\mathstrut +\mathstrut 40q^{45} \) \(\mathstrut +\mathstrut 4q^{47} \) \(\mathstrut +\mathstrut 4q^{51} \) \(\mathstrut -\mathstrut 12q^{53} \) \(\mathstrut -\mathstrut 16q^{55} \) \(\mathstrut +\mathstrut 28q^{57} \) \(\mathstrut +\mathstrut 16q^{59} \) \(\mathstrut +\mathstrut 68q^{61} \) \(\mathstrut -\mathstrut 8q^{65} \) \(\mathstrut +\mathstrut 4q^{67} \) \(\mathstrut +\mathstrut 32q^{69} \) \(\mathstrut +\mathstrut 8q^{71} \) \(\mathstrut +\mathstrut 48q^{73} \) \(\mathstrut +\mathstrut 60q^{75} \) \(\mathstrut -\mathstrut 20q^{79} \) \(\mathstrut +\mathstrut 32q^{81} \) \(\mathstrut -\mathstrut 8q^{83} \) \(\mathstrut -\mathstrut 28q^{85} \) \(\mathstrut +\mathstrut 60q^{89} \) \(\mathstrut -\mathstrut 16q^{93} \) \(\mathstrut +\mathstrut 20q^{95} \) \(\mathstrut +\mathstrut 40q^{97} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −2.32542 −1.34258 −0.671292 0.741193i \(-0.734260\pi\)
−0.671292 + 0.741193i \(0.734260\pi\)
\(4\) 0 0
\(5\) 1.16439 0.520730 0.260365 0.965510i \(-0.416157\pi\)
0.260365 + 0.965510i \(0.416157\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) 2.40759 0.802531
\(10\) 0 0
\(11\) 0.577754 0.174199 0.0870997 0.996200i \(-0.472240\pi\)
0.0870997 + 0.996200i \(0.472240\pi\)
\(12\) 0 0
\(13\) 2.18295 0.605442 0.302721 0.953079i \(-0.402105\pi\)
0.302721 + 0.953079i \(0.402105\pi\)
\(14\) 0 0
\(15\) −2.70769 −0.699123
\(16\) 0 0
\(17\) 6.65536 1.61416 0.807081 0.590441i \(-0.201046\pi\)
0.807081 + 0.590441i \(0.201046\pi\)
\(18\) 0 0
\(19\) −2.12850 −0.488312 −0.244156 0.969736i \(-0.578511\pi\)
−0.244156 + 0.969736i \(0.578511\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 8.32156 1.73516 0.867582 0.497294i \(-0.165673\pi\)
0.867582 + 0.497294i \(0.165673\pi\)
\(24\) 0 0
\(25\) −3.64420 −0.728840
\(26\) 0 0
\(27\) 1.37760 0.265119
\(28\) 0 0
\(29\) −6.30024 −1.16993 −0.584963 0.811060i \(-0.698891\pi\)
−0.584963 + 0.811060i \(0.698891\pi\)
\(30\) 0 0
\(31\) −1.38664 −0.249047 −0.124524 0.992217i \(-0.539740\pi\)
−0.124524 + 0.992217i \(0.539740\pi\)
\(32\) 0 0
\(33\) −1.34352 −0.233877
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 2.86577 0.471130 0.235565 0.971859i \(-0.424306\pi\)
0.235565 + 0.971859i \(0.424306\pi\)
\(38\) 0 0
\(39\) −5.07629 −0.812856
\(40\) 0 0
\(41\) −1.00000 −0.156174
\(42\) 0 0
\(43\) 6.21582 0.947904 0.473952 0.880551i \(-0.342827\pi\)
0.473952 + 0.880551i \(0.342827\pi\)
\(44\) 0 0
\(45\) 2.80337 0.417902
\(46\) 0 0
\(47\) 12.3492 1.80132 0.900658 0.434528i \(-0.143085\pi\)
0.900658 + 0.434528i \(0.143085\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) −15.4765 −2.16715
\(52\) 0 0
\(53\) 13.0449 1.79185 0.895925 0.444204i \(-0.146514\pi\)
0.895925 + 0.444204i \(0.146514\pi\)
\(54\) 0 0
\(55\) 0.672730 0.0907109
\(56\) 0 0
\(57\) 4.94967 0.655600
\(58\) 0 0
\(59\) −3.27380 −0.426213 −0.213106 0.977029i \(-0.568358\pi\)
−0.213106 + 0.977029i \(0.568358\pi\)
\(60\) 0 0
\(61\) 5.15551 0.660095 0.330048 0.943964i \(-0.392935\pi\)
0.330048 + 0.943964i \(0.392935\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 2.54180 0.315272
\(66\) 0 0
\(67\) −5.35143 −0.653781 −0.326890 0.945062i \(-0.606001\pi\)
−0.326890 + 0.945062i \(0.606001\pi\)
\(68\) 0 0
\(69\) −19.3511 −2.32960
\(70\) 0 0
\(71\) −14.3919 −1.70801 −0.854004 0.520267i \(-0.825833\pi\)
−0.854004 + 0.520267i \(0.825833\pi\)
\(72\) 0 0
\(73\) 8.30995 0.972606 0.486303 0.873790i \(-0.338345\pi\)
0.486303 + 0.873790i \(0.338345\pi\)
\(74\) 0 0
\(75\) 8.47431 0.978529
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) −14.6782 −1.65143 −0.825716 0.564086i \(-0.809229\pi\)
−0.825716 + 0.564086i \(0.809229\pi\)
\(80\) 0 0
\(81\) −10.4263 −1.15848
\(82\) 0 0
\(83\) −11.7691 −1.29182 −0.645911 0.763413i \(-0.723522\pi\)
−0.645911 + 0.763413i \(0.723522\pi\)
\(84\) 0 0
\(85\) 7.74941 0.840542
\(86\) 0 0
\(87\) 14.6507 1.57072
\(88\) 0 0
\(89\) 6.56350 0.695730 0.347865 0.937545i \(-0.386907\pi\)
0.347865 + 0.937545i \(0.386907\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 3.22452 0.334367
\(94\) 0 0
\(95\) −2.47840 −0.254279
\(96\) 0 0
\(97\) −2.09480 −0.212695 −0.106347 0.994329i \(-0.533916\pi\)
−0.106347 + 0.994329i \(0.533916\pi\)
\(98\) 0 0
\(99\) 1.39100 0.139800
\(100\) 0 0
\(101\) 4.73209 0.470861 0.235430 0.971891i \(-0.424350\pi\)
0.235430 + 0.971891i \(0.424350\pi\)
\(102\) 0 0
\(103\) 15.6314 1.54021 0.770106 0.637916i \(-0.220204\pi\)
0.770106 + 0.637916i \(0.220204\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −4.34990 −0.420520 −0.210260 0.977645i \(-0.567431\pi\)
−0.210260 + 0.977645i \(0.567431\pi\)
\(108\) 0 0
\(109\) 14.7394 1.41178 0.705890 0.708321i \(-0.250547\pi\)
0.705890 + 0.708321i \(0.250547\pi\)
\(110\) 0 0
\(111\) −6.66413 −0.632531
\(112\) 0 0
\(113\) −1.29851 −0.122153 −0.0610766 0.998133i \(-0.519453\pi\)
−0.0610766 + 0.998133i \(0.519453\pi\)
\(114\) 0 0
\(115\) 9.68951 0.903552
\(116\) 0 0
\(117\) 5.25566 0.485886
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −10.6662 −0.969655
\(122\) 0 0
\(123\) 2.32542 0.209676
\(124\) 0 0
\(125\) −10.0652 −0.900259
\(126\) 0 0
\(127\) −16.6554 −1.47793 −0.738964 0.673745i \(-0.764685\pi\)
−0.738964 + 0.673745i \(0.764685\pi\)
\(128\) 0 0
\(129\) −14.4544 −1.27264
\(130\) 0 0
\(131\) 18.9750 1.65785 0.828926 0.559359i \(-0.188953\pi\)
0.828926 + 0.559359i \(0.188953\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 1.60406 0.138055
\(136\) 0 0
\(137\) −3.44151 −0.294028 −0.147014 0.989134i \(-0.546966\pi\)
−0.147014 + 0.989134i \(0.546966\pi\)
\(138\) 0 0
\(139\) −4.88501 −0.414341 −0.207171 0.978305i \(-0.566426\pi\)
−0.207171 + 0.978305i \(0.566426\pi\)
\(140\) 0 0
\(141\) −28.7171 −2.41842
\(142\) 0 0
\(143\) 1.26121 0.105468
\(144\) 0 0
\(145\) −7.33592 −0.609215
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 22.0258 1.80442 0.902210 0.431297i \(-0.141944\pi\)
0.902210 + 0.431297i \(0.141944\pi\)
\(150\) 0 0
\(151\) −9.59867 −0.781128 −0.390564 0.920576i \(-0.627720\pi\)
−0.390564 + 0.920576i \(0.627720\pi\)
\(152\) 0 0
\(153\) 16.0234 1.29541
\(154\) 0 0
\(155\) −1.61458 −0.129686
\(156\) 0 0
\(157\) 2.53129 0.202019 0.101010 0.994885i \(-0.467793\pi\)
0.101010 + 0.994885i \(0.467793\pi\)
\(158\) 0 0
\(159\) −30.3348 −2.40571
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) −18.9641 −1.48539 −0.742693 0.669632i \(-0.766452\pi\)
−0.742693 + 0.669632i \(0.766452\pi\)
\(164\) 0 0
\(165\) −1.56438 −0.121787
\(166\) 0 0
\(167\) −1.39051 −0.107601 −0.0538004 0.998552i \(-0.517133\pi\)
−0.0538004 + 0.998552i \(0.517133\pi\)
\(168\) 0 0
\(169\) −8.23472 −0.633440
\(170\) 0 0
\(171\) −5.12457 −0.391885
\(172\) 0 0
\(173\) 20.1903 1.53504 0.767518 0.641027i \(-0.221491\pi\)
0.767518 + 0.641027i \(0.221491\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 7.61298 0.572226
\(178\) 0 0
\(179\) 0.927522 0.0693262 0.0346631 0.999399i \(-0.488964\pi\)
0.0346631 + 0.999399i \(0.488964\pi\)
\(180\) 0 0
\(181\) −3.28822 −0.244412 −0.122206 0.992505i \(-0.538997\pi\)
−0.122206 + 0.992505i \(0.538997\pi\)
\(182\) 0 0
\(183\) −11.9887 −0.886233
\(184\) 0 0
\(185\) 3.33687 0.245331
\(186\) 0 0
\(187\) 3.84516 0.281186
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −14.1671 −1.02509 −0.512547 0.858659i \(-0.671298\pi\)
−0.512547 + 0.858659i \(0.671298\pi\)
\(192\) 0 0
\(193\) −20.1435 −1.44996 −0.724982 0.688768i \(-0.758152\pi\)
−0.724982 + 0.688768i \(0.758152\pi\)
\(194\) 0 0
\(195\) −5.91076 −0.423279
\(196\) 0 0
\(197\) 26.5834 1.89399 0.946996 0.321246i \(-0.104102\pi\)
0.946996 + 0.321246i \(0.104102\pi\)
\(198\) 0 0
\(199\) −14.9769 −1.06168 −0.530841 0.847471i \(-0.678124\pi\)
−0.530841 + 0.847471i \(0.678124\pi\)
\(200\) 0 0
\(201\) 12.4443 0.877755
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) −1.16439 −0.0813243
\(206\) 0 0
\(207\) 20.0349 1.39252
\(208\) 0 0
\(209\) −1.22975 −0.0850637
\(210\) 0 0
\(211\) 8.62894 0.594041 0.297020 0.954871i \(-0.404007\pi\)
0.297020 + 0.954871i \(0.404007\pi\)
\(212\) 0 0
\(213\) 33.4673 2.29314
\(214\) 0 0
\(215\) 7.23762 0.493602
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) −19.3242 −1.30581
\(220\) 0 0
\(221\) 14.5283 0.977281
\(222\) 0 0
\(223\) −1.53527 −0.102809 −0.0514045 0.998678i \(-0.516370\pi\)
−0.0514045 + 0.998678i \(0.516370\pi\)
\(224\) 0 0
\(225\) −8.77375 −0.584917
\(226\) 0 0
\(227\) 20.1904 1.34008 0.670042 0.742323i \(-0.266276\pi\)
0.670042 + 0.742323i \(0.266276\pi\)
\(228\) 0 0
\(229\) −5.96534 −0.394201 −0.197100 0.980383i \(-0.563153\pi\)
−0.197100 + 0.980383i \(0.563153\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −0.959514 −0.0628599 −0.0314299 0.999506i \(-0.510006\pi\)
−0.0314299 + 0.999506i \(0.510006\pi\)
\(234\) 0 0
\(235\) 14.3793 0.937999
\(236\) 0 0
\(237\) 34.1331 2.21719
\(238\) 0 0
\(239\) 6.77258 0.438082 0.219041 0.975716i \(-0.429707\pi\)
0.219041 + 0.975716i \(0.429707\pi\)
\(240\) 0 0
\(241\) 17.7945 1.14625 0.573123 0.819469i \(-0.305732\pi\)
0.573123 + 0.819469i \(0.305732\pi\)
\(242\) 0 0
\(243\) 20.1127 1.29023
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −4.64642 −0.295644
\(248\) 0 0
\(249\) 27.3680 1.73438
\(250\) 0 0
\(251\) −21.5340 −1.35922 −0.679608 0.733575i \(-0.737850\pi\)
−0.679608 + 0.733575i \(0.737850\pi\)
\(252\) 0 0
\(253\) 4.80781 0.302265
\(254\) 0 0
\(255\) −18.0207 −1.12850
\(256\) 0 0
\(257\) −22.1592 −1.38225 −0.691127 0.722733i \(-0.742885\pi\)
−0.691127 + 0.722733i \(0.742885\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) −15.1684 −0.938901
\(262\) 0 0
\(263\) 17.7048 1.09173 0.545863 0.837874i \(-0.316202\pi\)
0.545863 + 0.837874i \(0.316202\pi\)
\(264\) 0 0
\(265\) 15.1893 0.933070
\(266\) 0 0
\(267\) −15.2629 −0.934075
\(268\) 0 0
\(269\) 18.4884 1.12726 0.563628 0.826029i \(-0.309405\pi\)
0.563628 + 0.826029i \(0.309405\pi\)
\(270\) 0 0
\(271\) −14.1700 −0.860765 −0.430383 0.902647i \(-0.641621\pi\)
−0.430383 + 0.902647i \(0.641621\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −2.10545 −0.126964
\(276\) 0 0
\(277\) 15.7359 0.945481 0.472740 0.881202i \(-0.343265\pi\)
0.472740 + 0.881202i \(0.343265\pi\)
\(278\) 0 0
\(279\) −3.33846 −0.199868
\(280\) 0 0
\(281\) 26.1380 1.55926 0.779632 0.626237i \(-0.215406\pi\)
0.779632 + 0.626237i \(0.215406\pi\)
\(282\) 0 0
\(283\) −15.2769 −0.908119 −0.454059 0.890971i \(-0.650025\pi\)
−0.454059 + 0.890971i \(0.650025\pi\)
\(284\) 0 0
\(285\) 5.76333 0.341390
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 27.2938 1.60552
\(290\) 0 0
\(291\) 4.87130 0.285561
\(292\) 0 0
\(293\) 8.49926 0.496532 0.248266 0.968692i \(-0.420139\pi\)
0.248266 + 0.968692i \(0.420139\pi\)
\(294\) 0 0
\(295\) −3.81197 −0.221942
\(296\) 0 0
\(297\) 0.795913 0.0461836
\(298\) 0 0
\(299\) 18.1656 1.05054
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) −11.0041 −0.632170
\(304\) 0 0
\(305\) 6.00301 0.343731
\(306\) 0 0
\(307\) −9.03457 −0.515630 −0.257815 0.966194i \(-0.583002\pi\)
−0.257815 + 0.966194i \(0.583002\pi\)
\(308\) 0 0
\(309\) −36.3497 −2.06786
\(310\) 0 0
\(311\) −24.0195 −1.36202 −0.681010 0.732274i \(-0.738459\pi\)
−0.681010 + 0.732274i \(0.738459\pi\)
\(312\) 0 0
\(313\) 25.9450 1.46650 0.733249 0.679960i \(-0.238003\pi\)
0.733249 + 0.679960i \(0.238003\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −31.0716 −1.74515 −0.872576 0.488478i \(-0.837552\pi\)
−0.872576 + 0.488478i \(0.837552\pi\)
\(318\) 0 0
\(319\) −3.63999 −0.203800
\(320\) 0 0
\(321\) 10.1153 0.564584
\(322\) 0 0
\(323\) −14.1659 −0.788214
\(324\) 0 0
\(325\) −7.95512 −0.441270
\(326\) 0 0
\(327\) −34.2754 −1.89543
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 1.05839 0.0581746 0.0290873 0.999577i \(-0.490740\pi\)
0.0290873 + 0.999577i \(0.490740\pi\)
\(332\) 0 0
\(333\) 6.89961 0.378096
\(334\) 0 0
\(335\) −6.23113 −0.340443
\(336\) 0 0
\(337\) 22.0487 1.20107 0.600536 0.799598i \(-0.294954\pi\)
0.600536 + 0.799598i \(0.294954\pi\)
\(338\) 0 0
\(339\) 3.01958 0.164001
\(340\) 0 0
\(341\) −0.801135 −0.0433839
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) −22.5322 −1.21309
\(346\) 0 0
\(347\) −17.4946 −0.939161 −0.469581 0.882890i \(-0.655595\pi\)
−0.469581 + 0.882890i \(0.655595\pi\)
\(348\) 0 0
\(349\) −9.53548 −0.510423 −0.255211 0.966885i \(-0.582145\pi\)
−0.255211 + 0.966885i \(0.582145\pi\)
\(350\) 0 0
\(351\) 3.00723 0.160514
\(352\) 0 0
\(353\) 5.45842 0.290522 0.145261 0.989393i \(-0.453598\pi\)
0.145261 + 0.989393i \(0.453598\pi\)
\(354\) 0 0
\(355\) −16.7578 −0.889411
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 28.2188 1.48933 0.744665 0.667439i \(-0.232609\pi\)
0.744665 + 0.667439i \(0.232609\pi\)
\(360\) 0 0
\(361\) −14.4695 −0.761551
\(362\) 0 0
\(363\) 24.8034 1.30184
\(364\) 0 0
\(365\) 9.67600 0.506465
\(366\) 0 0
\(367\) 12.6548 0.660578 0.330289 0.943880i \(-0.392854\pi\)
0.330289 + 0.943880i \(0.392854\pi\)
\(368\) 0 0
\(369\) −2.40759 −0.125334
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 16.0610 0.831605 0.415803 0.909455i \(-0.363501\pi\)
0.415803 + 0.909455i \(0.363501\pi\)
\(374\) 0 0
\(375\) 23.4058 1.20867
\(376\) 0 0
\(377\) −13.7531 −0.708322
\(378\) 0 0
\(379\) −3.85863 −0.198205 −0.0991023 0.995077i \(-0.531597\pi\)
−0.0991023 + 0.995077i \(0.531597\pi\)
\(380\) 0 0
\(381\) 38.7308 1.98424
\(382\) 0 0
\(383\) 9.73227 0.497296 0.248648 0.968594i \(-0.420014\pi\)
0.248648 + 0.968594i \(0.420014\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 14.9652 0.760722
\(388\) 0 0
\(389\) 4.65923 0.236232 0.118116 0.993000i \(-0.462315\pi\)
0.118116 + 0.993000i \(0.462315\pi\)
\(390\) 0 0
\(391\) 55.3829 2.80084
\(392\) 0 0
\(393\) −44.1248 −2.22580
\(394\) 0 0
\(395\) −17.0912 −0.859950
\(396\) 0 0
\(397\) 23.7699 1.19298 0.596489 0.802622i \(-0.296562\pi\)
0.596489 + 0.802622i \(0.296562\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −16.1934 −0.808658 −0.404329 0.914614i \(-0.632495\pi\)
−0.404329 + 0.914614i \(0.632495\pi\)
\(402\) 0 0
\(403\) −3.02696 −0.150784
\(404\) 0 0
\(405\) −12.1402 −0.603253
\(406\) 0 0
\(407\) 1.65571 0.0820706
\(408\) 0 0
\(409\) 27.8628 1.37773 0.688863 0.724891i \(-0.258110\pi\)
0.688863 + 0.724891i \(0.258110\pi\)
\(410\) 0 0
\(411\) 8.00297 0.394758
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) −13.7037 −0.672690
\(416\) 0 0
\(417\) 11.3597 0.556288
\(418\) 0 0
\(419\) 16.5549 0.808759 0.404380 0.914591i \(-0.367487\pi\)
0.404380 + 0.914591i \(0.367487\pi\)
\(420\) 0 0
\(421\) −14.7753 −0.720104 −0.360052 0.932932i \(-0.617241\pi\)
−0.360052 + 0.932932i \(0.617241\pi\)
\(422\) 0 0
\(423\) 29.7319 1.44561
\(424\) 0 0
\(425\) −24.2535 −1.17647
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) −2.93285 −0.141599
\(430\) 0 0
\(431\) −11.4352 −0.550815 −0.275407 0.961328i \(-0.588813\pi\)
−0.275407 + 0.961328i \(0.588813\pi\)
\(432\) 0 0
\(433\) 0.174657 0.00839348 0.00419674 0.999991i \(-0.498664\pi\)
0.00419674 + 0.999991i \(0.498664\pi\)
\(434\) 0 0
\(435\) 17.0591 0.817922
\(436\) 0 0
\(437\) −17.7125 −0.847302
\(438\) 0 0
\(439\) 8.45595 0.403580 0.201790 0.979429i \(-0.435324\pi\)
0.201790 + 0.979429i \(0.435324\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 2.89323 0.137461 0.0687307 0.997635i \(-0.478105\pi\)
0.0687307 + 0.997635i \(0.478105\pi\)
\(444\) 0 0
\(445\) 7.64246 0.362287
\(446\) 0 0
\(447\) −51.2192 −2.42258
\(448\) 0 0
\(449\) −8.62766 −0.407164 −0.203582 0.979058i \(-0.565258\pi\)
−0.203582 + 0.979058i \(0.565258\pi\)
\(450\) 0 0
\(451\) −0.577754 −0.0272054
\(452\) 0 0
\(453\) 22.3210 1.04873
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 25.3212 1.18448 0.592238 0.805763i \(-0.298245\pi\)
0.592238 + 0.805763i \(0.298245\pi\)
\(458\) 0 0
\(459\) 9.16841 0.427945
\(460\) 0 0
\(461\) −13.1693 −0.613354 −0.306677 0.951814i \(-0.599217\pi\)
−0.306677 + 0.951814i \(0.599217\pi\)
\(462\) 0 0
\(463\) 21.7893 1.01264 0.506318 0.862347i \(-0.331006\pi\)
0.506318 + 0.862347i \(0.331006\pi\)
\(464\) 0 0
\(465\) 3.75459 0.174115
\(466\) 0 0
\(467\) 28.9339 1.33890 0.669451 0.742856i \(-0.266529\pi\)
0.669451 + 0.742856i \(0.266529\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) −5.88633 −0.271228
\(472\) 0 0
\(473\) 3.59122 0.165124
\(474\) 0 0
\(475\) 7.75669 0.355902
\(476\) 0 0
\(477\) 31.4067 1.43802
\(478\) 0 0
\(479\) 7.12399 0.325503 0.162752 0.986667i \(-0.447963\pi\)
0.162752 + 0.986667i \(0.447963\pi\)
\(480\) 0 0
\(481\) 6.25584 0.285242
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −2.43916 −0.110757
\(486\) 0 0
\(487\) 33.1983 1.50436 0.752179 0.658959i \(-0.229003\pi\)
0.752179 + 0.658959i \(0.229003\pi\)
\(488\) 0 0
\(489\) 44.0997 1.99426
\(490\) 0 0
\(491\) −0.0506885 −0.00228754 −0.00114377 0.999999i \(-0.500364\pi\)
−0.00114377 + 0.999999i \(0.500364\pi\)
\(492\) 0 0
\(493\) −41.9303 −1.88845
\(494\) 0 0
\(495\) 1.61966 0.0727983
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) −27.6020 −1.23563 −0.617817 0.786322i \(-0.711983\pi\)
−0.617817 + 0.786322i \(0.711983\pi\)
\(500\) 0 0
\(501\) 3.23352 0.144463
\(502\) 0 0
\(503\) 31.7270 1.41464 0.707318 0.706895i \(-0.249905\pi\)
0.707318 + 0.706895i \(0.249905\pi\)
\(504\) 0 0
\(505\) 5.50999 0.245191
\(506\) 0 0
\(507\) 19.1492 0.850446
\(508\) 0 0
\(509\) −5.24465 −0.232465 −0.116233 0.993222i \(-0.537082\pi\)
−0.116233 + 0.993222i \(0.537082\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) −2.93222 −0.129461
\(514\) 0 0
\(515\) 18.2010 0.802034
\(516\) 0 0
\(517\) 7.13481 0.313788
\(518\) 0 0
\(519\) −46.9509 −2.06092
\(520\) 0 0
\(521\) −7.11443 −0.311689 −0.155844 0.987782i \(-0.549810\pi\)
−0.155844 + 0.987782i \(0.549810\pi\)
\(522\) 0 0
\(523\) −7.45011 −0.325770 −0.162885 0.986645i \(-0.552080\pi\)
−0.162885 + 0.986645i \(0.552080\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −9.22856 −0.402003
\(528\) 0 0
\(529\) 46.2483 2.01080
\(530\) 0 0
\(531\) −7.88198 −0.342049
\(532\) 0 0
\(533\) −2.18295 −0.0945541
\(534\) 0 0
\(535\) −5.06496 −0.218977
\(536\) 0 0
\(537\) −2.15688 −0.0930762
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) −2.23267 −0.0959899 −0.0479949 0.998848i \(-0.515283\pi\)
−0.0479949 + 0.998848i \(0.515283\pi\)
\(542\) 0 0
\(543\) 7.64651 0.328143
\(544\) 0 0
\(545\) 17.1624 0.735156
\(546\) 0 0
\(547\) 20.7822 0.888582 0.444291 0.895882i \(-0.353456\pi\)
0.444291 + 0.895882i \(0.353456\pi\)
\(548\) 0 0
\(549\) 12.4124 0.529747
\(550\) 0 0
\(551\) 13.4101 0.571288
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) −7.75963 −0.329378
\(556\) 0 0
\(557\) −0.0133890 −0.000567310 0 −0.000283655 1.00000i \(-0.500090\pi\)
−0.000283655 1.00000i \(0.500090\pi\)
\(558\) 0 0
\(559\) 13.5688 0.573901
\(560\) 0 0
\(561\) −8.94163 −0.377516
\(562\) 0 0
\(563\) −17.7441 −0.747824 −0.373912 0.927464i \(-0.621984\pi\)
−0.373912 + 0.927464i \(0.621984\pi\)
\(564\) 0 0
\(565\) −1.51196 −0.0636088
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 34.4381 1.44372 0.721859 0.692040i \(-0.243288\pi\)
0.721859 + 0.692040i \(0.243288\pi\)
\(570\) 0 0
\(571\) −26.8148 −1.12216 −0.561081 0.827761i \(-0.689615\pi\)
−0.561081 + 0.827761i \(0.689615\pi\)
\(572\) 0 0
\(573\) 32.9444 1.37627
\(574\) 0 0
\(575\) −30.3254 −1.26466
\(576\) 0 0
\(577\) −2.11828 −0.0881853 −0.0440926 0.999027i \(-0.514040\pi\)
−0.0440926 + 0.999027i \(0.514040\pi\)
\(578\) 0 0
\(579\) 46.8422 1.94670
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 7.53673 0.312140
\(584\) 0 0
\(585\) 6.11962 0.253015
\(586\) 0 0
\(587\) 32.6369 1.34707 0.673534 0.739156i \(-0.264775\pi\)
0.673534 + 0.739156i \(0.264775\pi\)
\(588\) 0 0
\(589\) 2.95146 0.121613
\(590\) 0 0
\(591\) −61.8177 −2.54284
\(592\) 0 0
\(593\) −10.8698 −0.446371 −0.223186 0.974776i \(-0.571646\pi\)
−0.223186 + 0.974776i \(0.571646\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 34.8276 1.42540
\(598\) 0 0
\(599\) 13.0873 0.534731 0.267366 0.963595i \(-0.413847\pi\)
0.267366 + 0.963595i \(0.413847\pi\)
\(600\) 0 0
\(601\) −6.48319 −0.264455 −0.132227 0.991219i \(-0.542213\pi\)
−0.132227 + 0.991219i \(0.542213\pi\)
\(602\) 0 0
\(603\) −12.8841 −0.524679
\(604\) 0 0
\(605\) −12.4196 −0.504928
\(606\) 0 0
\(607\) 29.4411 1.19498 0.597488 0.801878i \(-0.296166\pi\)
0.597488 + 0.801878i \(0.296166\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 26.9577 1.09059
\(612\) 0 0
\(613\) −0.185150 −0.00747814 −0.00373907 0.999993i \(-0.501190\pi\)
−0.00373907 + 0.999993i \(0.501190\pi\)
\(614\) 0 0
\(615\) 2.70769 0.109185
\(616\) 0 0
\(617\) −37.6266 −1.51479 −0.757395 0.652957i \(-0.773528\pi\)
−0.757395 + 0.652957i \(0.773528\pi\)
\(618\) 0 0
\(619\) 34.9704 1.40558 0.702790 0.711397i \(-0.251937\pi\)
0.702790 + 0.711397i \(0.251937\pi\)
\(620\) 0 0
\(621\) 11.4638 0.460025
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 6.50122 0.260049
\(626\) 0 0
\(627\) 2.85969 0.114205
\(628\) 0 0
\(629\) 19.0727 0.760480
\(630\) 0 0
\(631\) 39.4821 1.57176 0.785878 0.618381i \(-0.212211\pi\)
0.785878 + 0.618381i \(0.212211\pi\)
\(632\) 0 0
\(633\) −20.0659 −0.797550
\(634\) 0 0
\(635\) −19.3933 −0.769601
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) −34.6499 −1.37073
\(640\) 0 0
\(641\) 26.1071 1.03117 0.515583 0.856839i \(-0.327575\pi\)
0.515583 + 0.856839i \(0.327575\pi\)
\(642\) 0 0
\(643\) 13.0439 0.514403 0.257201 0.966358i \(-0.417200\pi\)
0.257201 + 0.966358i \(0.417200\pi\)
\(644\) 0 0
\(645\) −16.8305 −0.662702
\(646\) 0 0
\(647\) 25.3524 0.996704 0.498352 0.866975i \(-0.333939\pi\)
0.498352 + 0.866975i \(0.333939\pi\)
\(648\) 0 0
\(649\) −1.89145 −0.0742461
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 32.7755 1.28260 0.641301 0.767289i \(-0.278395\pi\)
0.641301 + 0.767289i \(0.278395\pi\)
\(654\) 0 0
\(655\) 22.0942 0.863293
\(656\) 0 0
\(657\) 20.0070 0.780546
\(658\) 0 0
\(659\) 18.6120 0.725019 0.362509 0.931980i \(-0.381920\pi\)
0.362509 + 0.931980i \(0.381920\pi\)
\(660\) 0 0
\(661\) −21.6989 −0.843991 −0.421995 0.906598i \(-0.638670\pi\)
−0.421995 + 0.906598i \(0.638670\pi\)
\(662\) 0 0
\(663\) −33.7845 −1.31208
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −52.4278 −2.03001
\(668\) 0 0
\(669\) 3.57014 0.138030
\(670\) 0 0
\(671\) 2.97862 0.114988
\(672\) 0 0
\(673\) −4.48404 −0.172847 −0.0864235 0.996258i \(-0.527544\pi\)
−0.0864235 + 0.996258i \(0.527544\pi\)
\(674\) 0 0
\(675\) −5.02024 −0.193229
\(676\) 0 0
\(677\) −24.7715 −0.952047 −0.476023 0.879433i \(-0.657922\pi\)
−0.476023 + 0.879433i \(0.657922\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) −46.9512 −1.79917
\(682\) 0 0
\(683\) 34.2572 1.31082 0.655408 0.755275i \(-0.272497\pi\)
0.655408 + 0.755275i \(0.272497\pi\)
\(684\) 0 0
\(685\) −4.00725 −0.153109
\(686\) 0 0
\(687\) 13.8719 0.529248
\(688\) 0 0
\(689\) 28.4763 1.08486
\(690\) 0 0
\(691\) 50.4922 1.92081 0.960407 0.278600i \(-0.0898703\pi\)
0.960407 + 0.278600i \(0.0898703\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −5.68804 −0.215760
\(696\) 0 0
\(697\) −6.65536 −0.252090
\(698\) 0 0
\(699\) 2.23128 0.0843946
\(700\) 0 0
\(701\) 35.6345 1.34590 0.672948 0.739690i \(-0.265028\pi\)
0.672948 + 0.739690i \(0.265028\pi\)
\(702\) 0 0
\(703\) −6.09980 −0.230058
\(704\) 0 0
\(705\) −33.4379 −1.25934
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 4.63467 0.174059 0.0870294 0.996206i \(-0.472263\pi\)
0.0870294 + 0.996206i \(0.472263\pi\)
\(710\) 0 0
\(711\) −35.3392 −1.32533
\(712\) 0 0
\(713\) −11.5390 −0.432138
\(714\) 0 0
\(715\) 1.46854 0.0549202
\(716\) 0 0
\(717\) −15.7491 −0.588161
\(718\) 0 0
\(719\) −38.0114 −1.41759 −0.708794 0.705416i \(-0.750760\pi\)
−0.708794 + 0.705416i \(0.750760\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) −41.3798 −1.53893
\(724\) 0 0
\(725\) 22.9593 0.852689
\(726\) 0 0
\(727\) −8.03179 −0.297882 −0.148941 0.988846i \(-0.547587\pi\)
−0.148941 + 0.988846i \(0.547587\pi\)
\(728\) 0 0
\(729\) −15.4917 −0.573768
\(730\) 0 0
\(731\) 41.3685 1.53007
\(732\) 0 0
\(733\) −17.0042 −0.628063 −0.314032 0.949413i \(-0.601680\pi\)
−0.314032 + 0.949413i \(0.601680\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −3.09181 −0.113888
\(738\) 0 0
\(739\) 50.4482 1.85577 0.927883 0.372871i \(-0.121626\pi\)
0.927883 + 0.372871i \(0.121626\pi\)
\(740\) 0 0
\(741\) 10.8049 0.396927
\(742\) 0 0
\(743\) 49.1625 1.80360 0.901799 0.432156i \(-0.142247\pi\)
0.901799 + 0.432156i \(0.142247\pi\)
\(744\) 0 0
\(745\) 25.6465 0.939615
\(746\) 0 0
\(747\) −28.3351 −1.03673
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −0.812005 −0.0296305 −0.0148152 0.999890i \(-0.504716\pi\)
−0.0148152 + 0.999890i \(0.504716\pi\)
\(752\) 0 0
\(753\) 50.0758 1.82486
\(754\) 0 0
\(755\) −11.1766 −0.406757
\(756\) 0 0
\(757\) −6.57037 −0.238804 −0.119402 0.992846i \(-0.538098\pi\)
−0.119402 + 0.992846i \(0.538098\pi\)
\(758\) 0 0
\(759\) −11.1802 −0.405816
\(760\) 0 0
\(761\) 20.4663 0.741904 0.370952 0.928652i \(-0.379031\pi\)
0.370952 + 0.928652i \(0.379031\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 18.6574 0.674561
\(766\) 0 0
\(767\) −7.14655 −0.258047
\(768\) 0 0
\(769\) −12.6132 −0.454844 −0.227422 0.973796i \(-0.573030\pi\)
−0.227422 + 0.973796i \(0.573030\pi\)
\(770\) 0 0
\(771\) 51.5295 1.85579
\(772\) 0 0
\(773\) −46.2197 −1.66241 −0.831203 0.555969i \(-0.812347\pi\)
−0.831203 + 0.555969i \(0.812347\pi\)
\(774\) 0 0
\(775\) 5.05318 0.181516
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 2.12850 0.0762615
\(780\) 0 0
\(781\) −8.31500 −0.297534
\(782\) 0 0
\(783\) −8.67920 −0.310169
\(784\) 0 0
\(785\) 2.94741 0.105197
\(786\) 0 0
\(787\) −42.1247 −1.50158 −0.750791 0.660539i \(-0.770328\pi\)
−0.750791 + 0.660539i \(0.770328\pi\)
\(788\) 0 0
\(789\) −41.1712 −1.46573
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 11.2542 0.399649
\(794\) 0 0
\(795\) −35.3215 −1.25272
\(796\) 0 0
\(797\) −20.2562 −0.717510 −0.358755 0.933432i \(-0.616799\pi\)
−0.358755 + 0.933432i \(0.616799\pi\)
\(798\) 0 0
\(799\) 82.1884 2.90762
\(800\) 0 0
\(801\) 15.8022 0.558344
\(802\) 0 0
\(803\) 4.80111 0.169427
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) −42.9933 −1.51344
\(808\) 0 0
\(809\) −43.4001 −1.52587 −0.762934 0.646477i \(-0.776242\pi\)
−0.762934 + 0.646477i \(0.776242\pi\)
\(810\) 0 0
\(811\) −3.14538 −0.110449 −0.0552246 0.998474i \(-0.517587\pi\)
−0.0552246 + 0.998474i \(0.517587\pi\)
\(812\) 0 0
\(813\) 32.9512 1.15565
\(814\) 0 0
\(815\) −22.0816 −0.773485
\(816\) 0 0
\(817\) −13.2304 −0.462873
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 39.9800 1.39531 0.697656 0.716432i \(-0.254226\pi\)
0.697656 + 0.716432i \(0.254226\pi\)
\(822\) 0 0
\(823\) −38.4780 −1.34126 −0.670630 0.741792i \(-0.733976\pi\)
−0.670630 + 0.741792i \(0.733976\pi\)
\(824\) 0 0
\(825\) 4.89607 0.170459
\(826\) 0 0
\(827\) 23.8196 0.828289 0.414145 0.910211i \(-0.364081\pi\)
0.414145 + 0.910211i \(0.364081\pi\)
\(828\) 0 0
\(829\) 25.5478 0.887311 0.443655 0.896197i \(-0.353681\pi\)
0.443655 + 0.896197i \(0.353681\pi\)
\(830\) 0 0
\(831\) −36.5927 −1.26939
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) −1.61909 −0.0560310
\(836\) 0 0
\(837\) −1.91023 −0.0660271
\(838\) 0 0
\(839\) −35.2200 −1.21593 −0.607966 0.793963i \(-0.708014\pi\)
−0.607966 + 0.793963i \(0.708014\pi\)
\(840\) 0 0
\(841\) 10.6930 0.368725
\(842\) 0 0
\(843\) −60.7820 −2.09344
\(844\) 0 0
\(845\) −9.58841 −0.329851
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) 35.5253 1.21923
\(850\) 0 0
\(851\) 23.8477 0.817488
\(852\) 0 0
\(853\) −23.5636 −0.806803 −0.403401 0.915023i \(-0.632172\pi\)
−0.403401 + 0.915023i \(0.632172\pi\)
\(854\) 0 0
\(855\) −5.96698 −0.204066
\(856\) 0 0
\(857\) −13.1481 −0.449131 −0.224565 0.974459i \(-0.572096\pi\)
−0.224565 + 0.974459i \(0.572096\pi\)
\(858\) 0 0
\(859\) 41.6355 1.42058 0.710292 0.703907i \(-0.248563\pi\)
0.710292 + 0.703907i \(0.248563\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −36.6615 −1.24797 −0.623986 0.781435i \(-0.714488\pi\)
−0.623986 + 0.781435i \(0.714488\pi\)
\(864\) 0 0
\(865\) 23.5093 0.799339
\(866\) 0 0
\(867\) −63.4696 −2.15554
\(868\) 0 0
\(869\) −8.48042 −0.287679
\(870\) 0 0
\(871\) −11.6819 −0.395826
\(872\) 0 0
\(873\) −5.04343 −0.170694
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 23.3610 0.788844 0.394422 0.918929i \(-0.370945\pi\)
0.394422 + 0.918929i \(0.370945\pi\)
\(878\) 0 0
\(879\) −19.7644 −0.666636
\(880\) 0 0
\(881\) 34.3795 1.15827 0.579137 0.815230i \(-0.303389\pi\)
0.579137 + 0.815230i \(0.303389\pi\)
\(882\) 0 0
\(883\) 6.66499 0.224295 0.112147 0.993692i \(-0.464227\pi\)
0.112147 + 0.993692i \(0.464227\pi\)
\(884\) 0 0
\(885\) 8.86445 0.297975
\(886\) 0 0
\(887\) 12.1283 0.407229 0.203615 0.979051i \(-0.434731\pi\)
0.203615 + 0.979051i \(0.434731\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) −6.02383 −0.201806
\(892\) 0 0
\(893\) −26.2853 −0.879604
\(894\) 0 0
\(895\) 1.07999 0.0361002
\(896\) 0 0
\(897\) −42.2426 −1.41044
\(898\) 0 0
\(899\) 8.73614 0.291367
\(900\) 0 0
\(901\) 86.8183 2.89234
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −3.82876 −0.127272
\(906\) 0 0
\(907\) 8.69194 0.288611 0.144306 0.989533i \(-0.453905\pi\)
0.144306 + 0.989533i \(0.453905\pi\)
\(908\) 0 0
\(909\) 11.3929 0.377880
\(910\) 0 0
\(911\) −10.6870 −0.354076 −0.177038 0.984204i \(-0.556652\pi\)
−0.177038 + 0.984204i \(0.556652\pi\)
\(912\) 0 0
\(913\) −6.79963 −0.225035
\(914\) 0 0
\(915\) −13.9595 −0.461488
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) 37.0944 1.22363 0.611815 0.791001i \(-0.290440\pi\)
0.611815 + 0.791001i \(0.290440\pi\)
\(920\) 0 0
\(921\) 21.0092 0.692276
\(922\) 0 0
\(923\) −31.4169 −1.03410
\(924\) 0 0
\(925\) −10.4435 −0.343379
\(926\) 0 0
\(927\) 37.6341 1.23607
\(928\) 0 0
\(929\) −13.7333 −0.450574 −0.225287 0.974292i \(-0.572332\pi\)
−0.225287 + 0.974292i \(0.572332\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) 55.8555 1.82863
\(934\) 0 0
\(935\) 4.47726 0.146422
\(936\) 0 0
\(937\) −14.5987 −0.476920 −0.238460 0.971152i \(-0.576643\pi\)
−0.238460 + 0.971152i \(0.576643\pi\)
\(938\) 0 0
\(939\) −60.3331 −1.96890
\(940\) 0 0
\(941\) −10.5934 −0.345334 −0.172667 0.984980i \(-0.555238\pi\)
−0.172667 + 0.984980i \(0.555238\pi\)
\(942\) 0 0
\(943\) −8.32156 −0.270987
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 8.15610 0.265038 0.132519 0.991180i \(-0.457693\pi\)
0.132519 + 0.991180i \(0.457693\pi\)
\(948\) 0 0
\(949\) 18.1402 0.588856
\(950\) 0 0
\(951\) 72.2545 2.34301
\(952\) 0 0
\(953\) −58.9994 −1.91118 −0.955589 0.294703i \(-0.904779\pi\)
−0.955589 + 0.294703i \(0.904779\pi\)
\(954\) 0 0
\(955\) −16.4960 −0.533797
\(956\) 0 0
\(957\) 8.46452 0.273619
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) −29.0772 −0.937975
\(962\) 0 0
\(963\) −10.4728 −0.337480
\(964\) 0 0
\(965\) −23.4549 −0.755039
\(966\) 0 0
\(967\) −22.9767 −0.738880 −0.369440 0.929255i \(-0.620450\pi\)
−0.369440 + 0.929255i \(0.620450\pi\)
\(968\) 0 0
\(969\) 32.9418 1.05824
\(970\) 0 0
\(971\) −53.3603 −1.71241 −0.856206 0.516634i \(-0.827185\pi\)
−0.856206 + 0.516634i \(0.827185\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) 18.4990 0.592443
\(976\) 0 0
\(977\) 14.6210 0.467769 0.233884 0.972264i \(-0.424856\pi\)
0.233884 + 0.972264i \(0.424856\pi\)
\(978\) 0 0
\(979\) 3.79209 0.121196
\(980\) 0 0
\(981\) 35.4865 1.13300
\(982\) 0 0
\(983\) 21.9944 0.701512 0.350756 0.936467i \(-0.385925\pi\)
0.350756 + 0.936467i \(0.385925\pi\)
\(984\) 0 0
\(985\) 30.9534 0.986258
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 51.7253 1.64477
\(990\) 0 0
\(991\) −28.0746 −0.891820 −0.445910 0.895078i \(-0.647120\pi\)
−0.445910 + 0.895078i \(0.647120\pi\)
\(992\) 0 0
\(993\) −2.46122 −0.0781043
\(994\) 0 0
\(995\) −17.4389 −0.552850
\(996\) 0 0
\(997\) 28.3418 0.897593 0.448797 0.893634i \(-0.351853\pi\)
0.448797 + 0.893634i \(0.351853\pi\)
\(998\) 0 0
\(999\) 3.94788 0.124905
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 \(a_p\))