Properties

Label 4032.2.c.k.2017.3
Level 4032
Weight 2
Character 4032.2017
Analytic conductor 32.196
Analytic rank 0
Dimension 4
CM No
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 4032 = 2^{6} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4032.c (of order \(2\) and degree \(1\))

Newform invariants

Self dual: No
Analytic conductor: \(32.195682095\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{12})\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{5} \)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 2017.3
Root \(0.866025 - 0.500000i\)
Character \(\chi\) = 4032.2017
Dual form 4032.2.c.k.2017.2

$q$-expansion

\(f(q)\) \(=\) \(q+0.732051i q^{5} -1.00000 q^{7} +O(q^{10})\) \(q+0.732051i q^{5} -1.00000 q^{7} +1.46410i q^{11} -3.26795i q^{13} -2.00000 q^{17} -4.73205i q^{19} +3.46410 q^{23} +4.46410 q^{25} +5.46410i q^{29} -4.00000 q^{31} -0.732051i q^{35} +5.46410i q^{37} +2.00000 q^{41} -1.46410i q^{43} -10.9282 q^{47} +1.00000 q^{49} -12.0000i q^{53} -1.07180 q^{55} -7.66025i q^{59} -13.1244i q^{61} +2.39230 q^{65} +8.00000i q^{67} -10.9282 q^{71} -0.928203 q^{73} -1.46410i q^{77} -2.92820 q^{79} -11.6603i q^{83} -1.46410i q^{85} +15.8564 q^{89} +3.26795i q^{91} +3.46410 q^{95} -4.92820 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 4q^{7} + O(q^{10}) \) \( 4q - 4q^{7} - 8q^{17} + 4q^{25} - 16q^{31} + 8q^{41} - 16q^{47} + 4q^{49} - 32q^{55} - 32q^{65} - 16q^{71} + 24q^{73} + 16q^{79} + 8q^{89} + 8q^{97} + O(q^{100}) \)

Character Values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/4032\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(577\) \(1793\) \(3781\)
\(\chi(n)\) \(1\) \(1\) \(1\) \(-1\)

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
\(3\) 0 0
\(4\) 0 0
\(5\) 0.732051i 0.327383i 0.986512 + 0.163692i \(0.0523402\pi\)
−0.986512 + 0.163692i \(0.947660\pi\)
\(6\) 0 0
\(7\) −1.00000 −0.377964
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 1.46410i 0.441443i 0.975337 + 0.220722i \(0.0708412\pi\)
−0.975337 + 0.220722i \(0.929159\pi\)
\(12\) 0 0
\(13\) − 3.26795i − 0.906366i −0.891417 0.453183i \(-0.850288\pi\)
0.891417 0.453183i \(-0.149712\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −2.00000 −0.485071 −0.242536 0.970143i \(-0.577979\pi\)
−0.242536 + 0.970143i \(0.577979\pi\)
\(18\) 0 0
\(19\) − 4.73205i − 1.08561i −0.839860 0.542803i \(-0.817363\pi\)
0.839860 0.542803i \(-0.182637\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 3.46410 0.722315 0.361158 0.932505i \(-0.382382\pi\)
0.361158 + 0.932505i \(0.382382\pi\)
\(24\) 0 0
\(25\) 4.46410 0.892820
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 5.46410i 1.01466i 0.861752 + 0.507329i \(0.169367\pi\)
−0.861752 + 0.507329i \(0.830633\pi\)
\(30\) 0 0
\(31\) −4.00000 −0.718421 −0.359211 0.933257i \(-0.616954\pi\)
−0.359211 + 0.933257i \(0.616954\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) − 0.732051i − 0.123739i
\(36\) 0 0
\(37\) 5.46410i 0.898293i 0.893458 + 0.449146i \(0.148272\pi\)
−0.893458 + 0.449146i \(0.851728\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 2.00000 0.312348 0.156174 0.987730i \(-0.450084\pi\)
0.156174 + 0.987730i \(0.450084\pi\)
\(42\) 0 0
\(43\) − 1.46410i − 0.223273i −0.993749 0.111637i \(-0.964391\pi\)
0.993749 0.111637i \(-0.0356093\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −10.9282 −1.59404 −0.797021 0.603951i \(-0.793592\pi\)
−0.797021 + 0.603951i \(0.793592\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) − 12.0000i − 1.64833i −0.566352 0.824163i \(-0.691646\pi\)
0.566352 0.824163i \(-0.308354\pi\)
\(54\) 0 0
\(55\) −1.07180 −0.144521
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) − 7.66025i − 0.997280i −0.866809 0.498640i \(-0.833833\pi\)
0.866809 0.498640i \(-0.166167\pi\)
\(60\) 0 0
\(61\) − 13.1244i − 1.68040i −0.542275 0.840201i \(-0.682437\pi\)
0.542275 0.840201i \(-0.317563\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 2.39230 0.296729
\(66\) 0 0
\(67\) 8.00000i 0.977356i 0.872464 + 0.488678i \(0.162521\pi\)
−0.872464 + 0.488678i \(0.837479\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −10.9282 −1.29694 −0.648470 0.761241i \(-0.724591\pi\)
−0.648470 + 0.761241i \(0.724591\pi\)
\(72\) 0 0
\(73\) −0.928203 −0.108638 −0.0543190 0.998524i \(-0.517299\pi\)
−0.0543190 + 0.998524i \(0.517299\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) − 1.46410i − 0.166850i
\(78\) 0 0
\(79\) −2.92820 −0.329449 −0.164724 0.986340i \(-0.552673\pi\)
−0.164724 + 0.986340i \(0.552673\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) − 11.6603i − 1.27988i −0.768425 0.639940i \(-0.778959\pi\)
0.768425 0.639940i \(-0.221041\pi\)
\(84\) 0 0
\(85\) − 1.46410i − 0.158804i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 15.8564 1.68078 0.840388 0.541985i \(-0.182327\pi\)
0.840388 + 0.541985i \(0.182327\pi\)
\(90\) 0 0
\(91\) 3.26795i 0.342574i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 3.46410 0.355409
\(96\) 0 0
\(97\) −4.92820 −0.500383 −0.250192 0.968196i \(-0.580494\pi\)
−0.250192 + 0.968196i \(0.580494\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) − 15.6603i − 1.55825i −0.626866 0.779127i \(-0.715663\pi\)
0.626866 0.779127i \(-0.284337\pi\)
\(102\) 0 0
\(103\) 17.8564 1.75944 0.879722 0.475488i \(-0.157729\pi\)
0.879722 + 0.475488i \(0.157729\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) − 18.9282i − 1.82986i −0.403614 0.914929i \(-0.632246\pi\)
0.403614 0.914929i \(-0.367754\pi\)
\(108\) 0 0
\(109\) 8.39230i 0.803837i 0.915675 + 0.401919i \(0.131656\pi\)
−0.915675 + 0.401919i \(0.868344\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 13.4641 1.26660 0.633298 0.773908i \(-0.281701\pi\)
0.633298 + 0.773908i \(0.281701\pi\)
\(114\) 0 0
\(115\) 2.53590i 0.236474i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 2.00000 0.183340
\(120\) 0 0
\(121\) 8.85641 0.805128
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 6.92820i 0.619677i
\(126\) 0 0
\(127\) 4.53590 0.402496 0.201248 0.979540i \(-0.435500\pi\)
0.201248 + 0.979540i \(0.435500\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 7.26795i 0.635004i 0.948258 + 0.317502i \(0.102844\pi\)
−0.948258 + 0.317502i \(0.897156\pi\)
\(132\) 0 0
\(133\) 4.73205i 0.410321i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 7.85641 0.671218 0.335609 0.942001i \(-0.391058\pi\)
0.335609 + 0.942001i \(0.391058\pi\)
\(138\) 0 0
\(139\) − 12.7321i − 1.07992i −0.841691 0.539959i \(-0.818440\pi\)
0.841691 0.539959i \(-0.181560\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 4.78461 0.400109
\(144\) 0 0
\(145\) −4.00000 −0.332182
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) − 14.9282i − 1.22297i −0.791258 0.611483i \(-0.790573\pi\)
0.791258 0.611483i \(-0.209427\pi\)
\(150\) 0 0
\(151\) −18.3923 −1.49674 −0.748372 0.663279i \(-0.769164\pi\)
−0.748372 + 0.663279i \(0.769164\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) − 2.92820i − 0.235199i
\(156\) 0 0
\(157\) 1.80385i 0.143963i 0.997406 + 0.0719814i \(0.0229322\pi\)
−0.997406 + 0.0719814i \(0.977068\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −3.46410 −0.273009
\(162\) 0 0
\(163\) − 6.53590i − 0.511931i −0.966686 0.255966i \(-0.917607\pi\)
0.966686 0.255966i \(-0.0823934\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −18.9282 −1.46471 −0.732354 0.680924i \(-0.761578\pi\)
−0.732354 + 0.680924i \(0.761578\pi\)
\(168\) 0 0
\(169\) 2.32051 0.178501
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 14.1962i 1.07931i 0.841885 + 0.539657i \(0.181446\pi\)
−0.841885 + 0.539657i \(0.818554\pi\)
\(174\) 0 0
\(175\) −4.46410 −0.337454
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) − 10.9282i − 0.816812i −0.912800 0.408406i \(-0.866085\pi\)
0.912800 0.408406i \(-0.133915\pi\)
\(180\) 0 0
\(181\) − 7.26795i − 0.540222i −0.962829 0.270111i \(-0.912940\pi\)
0.962829 0.270111i \(-0.0870605\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −4.00000 −0.294086
\(186\) 0 0
\(187\) − 2.92820i − 0.214131i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 16.0000 1.15772 0.578860 0.815427i \(-0.303498\pi\)
0.578860 + 0.815427i \(0.303498\pi\)
\(192\) 0 0
\(193\) 13.4641 0.969167 0.484584 0.874745i \(-0.338971\pi\)
0.484584 + 0.874745i \(0.338971\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 1.85641i 0.132263i 0.997811 + 0.0661317i \(0.0210658\pi\)
−0.997811 + 0.0661317i \(0.978934\pi\)
\(198\) 0 0
\(199\) 4.00000 0.283552 0.141776 0.989899i \(-0.454719\pi\)
0.141776 + 0.989899i \(0.454719\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) − 5.46410i − 0.383505i
\(204\) 0 0
\(205\) 1.46410i 0.102257i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 6.92820 0.479234
\(210\) 0 0
\(211\) − 24.7846i − 1.70624i −0.521712 0.853121i \(-0.674707\pi\)
0.521712 0.853121i \(-0.325293\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 1.07180 0.0730959
\(216\) 0 0
\(217\) 4.00000 0.271538
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 6.53590i 0.439652i
\(222\) 0 0
\(223\) −6.92820 −0.463947 −0.231973 0.972722i \(-0.574518\pi\)
−0.231973 + 0.972722i \(0.574518\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) − 14.1962i − 0.942232i −0.882071 0.471116i \(-0.843851\pi\)
0.882071 0.471116i \(-0.156149\pi\)
\(228\) 0 0
\(229\) − 20.7321i − 1.37001i −0.728537 0.685006i \(-0.759799\pi\)
0.728537 0.685006i \(-0.240201\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −6.00000 −0.393073 −0.196537 0.980497i \(-0.562969\pi\)
−0.196537 + 0.980497i \(0.562969\pi\)
\(234\) 0 0
\(235\) − 8.00000i − 0.521862i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −19.4641 −1.25903 −0.629514 0.776989i \(-0.716746\pi\)
−0.629514 + 0.776989i \(0.716746\pi\)
\(240\) 0 0
\(241\) 22.7846 1.46769 0.733843 0.679319i \(-0.237725\pi\)
0.733843 + 0.679319i \(0.237725\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 0.732051i 0.0467690i
\(246\) 0 0
\(247\) −15.4641 −0.983957
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 26.1962i 1.65349i 0.562579 + 0.826743i \(0.309809\pi\)
−0.562579 + 0.826743i \(0.690191\pi\)
\(252\) 0 0
\(253\) 5.07180i 0.318861i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 6.00000 0.374270 0.187135 0.982334i \(-0.440080\pi\)
0.187135 + 0.982334i \(0.440080\pi\)
\(258\) 0 0
\(259\) − 5.46410i − 0.339523i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −2.92820 −0.180561 −0.0902804 0.995916i \(-0.528776\pi\)
−0.0902804 + 0.995916i \(0.528776\pi\)
\(264\) 0 0
\(265\) 8.78461 0.539634
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) − 18.5885i − 1.13336i −0.823939 0.566679i \(-0.808228\pi\)
0.823939 0.566679i \(-0.191772\pi\)
\(270\) 0 0
\(271\) −1.07180 −0.0651070 −0.0325535 0.999470i \(-0.510364\pi\)
−0.0325535 + 0.999470i \(0.510364\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 6.53590i 0.394130i
\(276\) 0 0
\(277\) − 4.00000i − 0.240337i −0.992754 0.120168i \(-0.961657\pi\)
0.992754 0.120168i \(-0.0383434\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −2.00000 −0.119310 −0.0596550 0.998219i \(-0.519000\pi\)
−0.0596550 + 0.998219i \(0.519000\pi\)
\(282\) 0 0
\(283\) − 14.5885i − 0.867194i −0.901107 0.433597i \(-0.857244\pi\)
0.901107 0.433597i \(-0.142756\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −2.00000 −0.118056
\(288\) 0 0
\(289\) −13.0000 −0.764706
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) − 1.80385i − 0.105382i −0.998611 0.0526910i \(-0.983220\pi\)
0.998611 0.0526910i \(-0.0167798\pi\)
\(294\) 0 0
\(295\) 5.60770 0.326493
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) − 11.3205i − 0.654682i
\(300\) 0 0
\(301\) 1.46410i 0.0843894i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 9.60770 0.550135
\(306\) 0 0
\(307\) 22.5885i 1.28919i 0.764524 + 0.644596i \(0.222974\pi\)
−0.764524 + 0.644596i \(0.777026\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 21.8564 1.23936 0.619682 0.784853i \(-0.287262\pi\)
0.619682 + 0.784853i \(0.287262\pi\)
\(312\) 0 0
\(313\) −7.85641 −0.444070 −0.222035 0.975039i \(-0.571270\pi\)
−0.222035 + 0.975039i \(0.571270\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) − 12.7846i − 0.718055i −0.933327 0.359028i \(-0.883108\pi\)
0.933327 0.359028i \(-0.116892\pi\)
\(318\) 0 0
\(319\) −8.00000 −0.447914
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 9.46410i 0.526597i
\(324\) 0 0
\(325\) − 14.5885i − 0.809222i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 10.9282 0.602491
\(330\) 0 0
\(331\) 4.39230i 0.241423i 0.992688 + 0.120711i \(0.0385176\pi\)
−0.992688 + 0.120711i \(0.961482\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −5.85641 −0.319970
\(336\) 0 0
\(337\) −4.39230 −0.239264 −0.119632 0.992818i \(-0.538171\pi\)
−0.119632 + 0.992818i \(0.538171\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) − 5.85641i − 0.317142i
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 0.679492i 0.0364770i 0.999834 + 0.0182385i \(0.00580582\pi\)
−0.999834 + 0.0182385i \(0.994194\pi\)
\(348\) 0 0
\(349\) 24.0526i 1.28750i 0.765234 + 0.643752i \(0.222623\pi\)
−0.765234 + 0.643752i \(0.777377\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 12.9282 0.688099 0.344049 0.938952i \(-0.388201\pi\)
0.344049 + 0.938952i \(0.388201\pi\)
\(354\) 0 0
\(355\) − 8.00000i − 0.424596i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −20.5359 −1.08384 −0.541922 0.840429i \(-0.682303\pi\)
−0.541922 + 0.840429i \(0.682303\pi\)
\(360\) 0 0
\(361\) −3.39230 −0.178542
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) − 0.679492i − 0.0355662i
\(366\) 0 0
\(367\) 20.7846 1.08495 0.542474 0.840073i \(-0.317488\pi\)
0.542474 + 0.840073i \(0.317488\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 12.0000i 0.623009i
\(372\) 0 0
\(373\) − 17.0718i − 0.883944i −0.897029 0.441972i \(-0.854279\pi\)
0.897029 0.441972i \(-0.145721\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 17.8564 0.919652
\(378\) 0 0
\(379\) 34.2487i 1.75924i 0.475679 + 0.879619i \(0.342202\pi\)
−0.475679 + 0.879619i \(0.657798\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 8.78461 0.448873 0.224436 0.974489i \(-0.427946\pi\)
0.224436 + 0.974489i \(0.427946\pi\)
\(384\) 0 0
\(385\) 1.07180 0.0546238
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 11.3205i 0.573973i 0.957935 + 0.286986i \(0.0926534\pi\)
−0.957935 + 0.286986i \(0.907347\pi\)
\(390\) 0 0
\(391\) −6.92820 −0.350374
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) − 2.14359i − 0.107856i
\(396\) 0 0
\(397\) 29.1244i 1.46171i 0.682533 + 0.730855i \(0.260878\pi\)
−0.682533 + 0.730855i \(0.739122\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −6.53590 −0.326387 −0.163194 0.986594i \(-0.552180\pi\)
−0.163194 + 0.986594i \(0.552180\pi\)
\(402\) 0 0
\(403\) 13.0718i 0.651153i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −8.00000 −0.396545
\(408\) 0 0
\(409\) −16.9282 −0.837046 −0.418523 0.908206i \(-0.637452\pi\)
−0.418523 + 0.908206i \(0.637452\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 7.66025i 0.376936i
\(414\) 0 0
\(415\) 8.53590 0.419011
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) − 34.1962i − 1.67059i −0.549801 0.835296i \(-0.685296\pi\)
0.549801 0.835296i \(-0.314704\pi\)
\(420\) 0 0
\(421\) 1.85641i 0.0904757i 0.998976 + 0.0452379i \(0.0144046\pi\)
−0.998976 + 0.0452379i \(0.985595\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −8.92820 −0.433081
\(426\) 0 0
\(427\) 13.1244i 0.635132i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −28.5359 −1.37453 −0.687263 0.726409i \(-0.741188\pi\)
−0.687263 + 0.726409i \(0.741188\pi\)
\(432\) 0 0
\(433\) −11.8564 −0.569783 −0.284891 0.958560i \(-0.591957\pi\)
−0.284891 + 0.958560i \(0.591957\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) − 16.3923i − 0.784150i
\(438\) 0 0
\(439\) −17.0718 −0.814792 −0.407396 0.913252i \(-0.633563\pi\)
−0.407396 + 0.913252i \(0.633563\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) − 24.0000i − 1.14027i −0.821549 0.570137i \(-0.806890\pi\)
0.821549 0.570137i \(-0.193110\pi\)
\(444\) 0 0
\(445\) 11.6077i 0.550258i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 2.00000 0.0943858 0.0471929 0.998886i \(-0.484972\pi\)
0.0471929 + 0.998886i \(0.484972\pi\)
\(450\) 0 0
\(451\) 2.92820i 0.137884i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −2.39230 −0.112153
\(456\) 0 0
\(457\) −19.3205 −0.903775 −0.451888 0.892075i \(-0.649249\pi\)
−0.451888 + 0.892075i \(0.649249\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 13.8038i 0.642909i 0.946925 + 0.321455i \(0.104172\pi\)
−0.946925 + 0.321455i \(0.895828\pi\)
\(462\) 0 0
\(463\) −16.0000 −0.743583 −0.371792 0.928316i \(-0.621256\pi\)
−0.371792 + 0.928316i \(0.621256\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) − 25.1244i − 1.16262i −0.813683 0.581308i \(-0.802541\pi\)
0.813683 0.581308i \(-0.197459\pi\)
\(468\) 0 0
\(469\) − 8.00000i − 0.369406i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 2.14359 0.0985625
\(474\) 0 0
\(475\) − 21.1244i − 0.969252i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 17.8564 0.815880 0.407940 0.913009i \(-0.366247\pi\)
0.407940 + 0.913009i \(0.366247\pi\)
\(480\) 0 0
\(481\) 17.8564 0.814182
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) − 3.60770i − 0.163817i
\(486\) 0 0
\(487\) 42.3923 1.92098 0.960489 0.278317i \(-0.0897765\pi\)
0.960489 + 0.278317i \(0.0897765\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 8.78461i 0.396444i 0.980157 + 0.198222i \(0.0635167\pi\)
−0.980157 + 0.198222i \(0.936483\pi\)
\(492\) 0 0
\(493\) − 10.9282i − 0.492182i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 10.9282 0.490197
\(498\) 0 0
\(499\) − 26.9282i − 1.20547i −0.797941 0.602736i \(-0.794077\pi\)
0.797941 0.602736i \(-0.205923\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 17.0718 0.761194 0.380597 0.924741i \(-0.375719\pi\)
0.380597 + 0.924741i \(0.375719\pi\)
\(504\) 0 0
\(505\) 11.4641 0.510146
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) − 21.1244i − 0.936321i −0.883644 0.468160i \(-0.844917\pi\)
0.883644 0.468160i \(-0.155083\pi\)
\(510\) 0 0
\(511\) 0.928203 0.0410613
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 13.0718i 0.576012i
\(516\) 0 0
\(517\) − 16.0000i − 0.703679i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −26.7846 −1.17346 −0.586728 0.809784i \(-0.699584\pi\)
−0.586728 + 0.809784i \(0.699584\pi\)
\(522\) 0 0
\(523\) 34.5885i 1.51245i 0.654313 + 0.756224i \(0.272958\pi\)
−0.654313 + 0.756224i \(0.727042\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 8.00000 0.348485
\(528\) 0 0
\(529\) −11.0000 −0.478261
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) − 6.53590i − 0.283101i
\(534\) 0 0
\(535\) 13.8564 0.599065
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 1.46410i 0.0630633i
\(540\) 0 0
\(541\) − 4.00000i − 0.171973i −0.996296 0.0859867i \(-0.972596\pi\)
0.996296 0.0859867i \(-0.0274043\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −6.14359 −0.263163
\(546\) 0 0
\(547\) 2.24871i 0.0961480i 0.998844 + 0.0480740i \(0.0153083\pi\)
−0.998844 + 0.0480740i \(0.984692\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 25.8564 1.10152
\(552\) 0 0
\(553\) 2.92820 0.124520
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 31.7128i 1.34372i 0.740680 + 0.671858i \(0.234503\pi\)
−0.740680 + 0.671858i \(0.765497\pi\)
\(558\) 0 0
\(559\) −4.78461 −0.202367
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 4.05256i 0.170795i 0.996347 + 0.0853975i \(0.0272160\pi\)
−0.996347 + 0.0853975i \(0.972784\pi\)
\(564\) 0 0
\(565\) 9.85641i 0.414662i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −1.46410 −0.0613783 −0.0306892 0.999529i \(-0.509770\pi\)
−0.0306892 + 0.999529i \(0.509770\pi\)
\(570\) 0 0
\(571\) − 37.1769i − 1.55581i −0.628385 0.777903i \(-0.716284\pi\)
0.628385 0.777903i \(-0.283716\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 15.4641 0.644898
\(576\) 0 0
\(577\) −44.9282 −1.87039 −0.935193 0.354139i \(-0.884774\pi\)
−0.935193 + 0.354139i \(0.884774\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 11.6603i 0.483749i
\(582\) 0 0
\(583\) 17.5692 0.727643
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 36.7321i 1.51609i 0.652200 + 0.758047i \(0.273846\pi\)
−0.652200 + 0.758047i \(0.726154\pi\)
\(588\) 0 0
\(589\) 18.9282i 0.779923i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −39.8564 −1.63671 −0.818353 0.574716i \(-0.805113\pi\)
−0.818353 + 0.574716i \(0.805113\pi\)
\(594\) 0 0
\(595\) 1.46410i 0.0600223i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −27.7128 −1.13231 −0.566157 0.824297i \(-0.691571\pi\)
−0.566157 + 0.824297i \(0.691571\pi\)
\(600\) 0 0
\(601\) 22.0000 0.897399 0.448699 0.893683i \(-0.351887\pi\)
0.448699 + 0.893683i \(0.351887\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 6.48334i 0.263585i
\(606\) 0 0
\(607\) −27.7128 −1.12483 −0.562414 0.826856i \(-0.690127\pi\)
−0.562414 + 0.826856i \(0.690127\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 35.7128i 1.44479i
\(612\) 0 0
\(613\) 4.67949i 0.189003i 0.995525 + 0.0945014i \(0.0301257\pi\)
−0.995525 + 0.0945014i \(0.969874\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 3.60770 0.145240 0.0726202 0.997360i \(-0.476864\pi\)
0.0726202 + 0.997360i \(0.476864\pi\)
\(618\) 0 0
\(619\) − 13.8038i − 0.554823i −0.960751 0.277412i \(-0.910523\pi\)
0.960751 0.277412i \(-0.0894766\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −15.8564 −0.635274
\(624\) 0 0
\(625\) 17.2487 0.689948
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) − 10.9282i − 0.435736i
\(630\) 0 0
\(631\) −33.5692 −1.33637 −0.668185 0.743995i \(-0.732928\pi\)
−0.668185 + 0.743995i \(0.732928\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 3.32051i 0.131770i
\(636\) 0 0
\(637\) − 3.26795i − 0.129481i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −26.2487 −1.03676 −0.518381 0.855150i \(-0.673465\pi\)
−0.518381 + 0.855150i \(0.673465\pi\)
\(642\) 0 0
\(643\) 31.6603i 1.24856i 0.781201 + 0.624279i \(0.214607\pi\)
−0.781201 + 0.624279i \(0.785393\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 25.8564 1.01652 0.508260 0.861204i \(-0.330289\pi\)
0.508260 + 0.861204i \(0.330289\pi\)
\(648\) 0 0
\(649\) 11.2154 0.440243
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 45.4641i 1.77915i 0.456791 + 0.889574i \(0.348999\pi\)
−0.456791 + 0.889574i \(0.651001\pi\)
\(654\) 0 0
\(655\) −5.32051 −0.207889
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 31.3205i 1.22007i 0.792373 + 0.610037i \(0.208845\pi\)
−0.792373 + 0.610037i \(0.791155\pi\)
\(660\) 0 0
\(661\) − 22.9808i − 0.893848i −0.894572 0.446924i \(-0.852519\pi\)
0.894572 0.446924i \(-0.147481\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −3.46410 −0.134332
\(666\) 0 0
\(667\) 18.9282i 0.732903i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 19.2154 0.741802
\(672\) 0 0
\(673\) 31.8564 1.22797 0.613987 0.789316i \(-0.289565\pi\)
0.613987 + 0.789316i \(0.289565\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) − 44.4449i − 1.70815i −0.520146 0.854077i \(-0.674122\pi\)
0.520146 0.854077i \(-0.325878\pi\)
\(678\) 0 0
\(679\) 4.92820 0.189127
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 38.6410i 1.47856i 0.673400 + 0.739279i \(0.264833\pi\)
−0.673400 + 0.739279i \(0.735167\pi\)
\(684\) 0 0
\(685\) 5.75129i 0.219745i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −39.2154 −1.49399
\(690\) 0 0
\(691\) − 13.1244i − 0.499274i −0.968339 0.249637i \(-0.919689\pi\)
0.968339 0.249637i \(-0.0803113\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 9.32051 0.353547
\(696\) 0 0
\(697\) −4.00000 −0.151511
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 40.3923i 1.52560i 0.646637 + 0.762798i \(0.276175\pi\)
−0.646637 + 0.762798i \(0.723825\pi\)
\(702\) 0 0
\(703\) 25.8564 0.975193
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 15.6603i 0.588964i
\(708\) 0 0
\(709\) − 28.1051i − 1.05551i −0.849397 0.527755i \(-0.823034\pi\)
0.849397 0.527755i \(-0.176966\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −13.8564 −0.518927
\(714\) 0 0
\(715\) 3.50258i 0.130989i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 34.9282 1.30260 0.651301 0.758819i \(-0.274223\pi\)
0.651301 + 0.758819i \(0.274223\pi\)
\(720\) 0 0
\(721\) −17.8564 −0.665007
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 24.3923i 0.905907i
\(726\) 0 0
\(727\) 2.92820 0.108601 0.0543005 0.998525i \(-0.482707\pi\)
0.0543005 + 0.998525i \(0.482707\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 2.92820i 0.108304i
\(732\) 0 0
\(733\) 3.66025i 0.135195i 0.997713 + 0.0675973i \(0.0215333\pi\)
−0.997713 + 0.0675973i \(0.978467\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −11.7128 −0.431447
\(738\) 0 0
\(739\) 31.3205i 1.15214i 0.817399 + 0.576072i \(0.195415\pi\)
−0.817399 + 0.576072i \(0.804585\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −16.2487 −0.596107 −0.298054 0.954549i \(-0.596337\pi\)
−0.298054 + 0.954549i \(0.596337\pi\)
\(744\) 0 0
\(745\) 10.9282 0.400378
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 18.9282i 0.691621i
\(750\) 0 0
\(751\) 24.2487 0.884848 0.442424 0.896806i \(-0.354119\pi\)
0.442424 + 0.896806i \(0.354119\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) − 13.4641i − 0.490009i
\(756\) 0 0
\(757\) 38.2487i 1.39017i 0.718926 + 0.695087i \(0.244634\pi\)
−0.718926 + 0.695087i \(0.755366\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −33.7128 −1.22209 −0.611044 0.791596i \(-0.709250\pi\)
−0.611044 + 0.791596i \(0.709250\pi\)
\(762\) 0 0
\(763\) − 8.39230i − 0.303822i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −25.0333 −0.903901
\(768\) 0 0
\(769\) 30.7846 1.11012 0.555061 0.831810i \(-0.312695\pi\)
0.555061 + 0.831810i \(0.312695\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) − 45.1244i − 1.62301i −0.584345 0.811505i \(-0.698649\pi\)
0.584345 0.811505i \(-0.301351\pi\)
\(774\) 0 0
\(775\) −17.8564 −0.641421
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) − 9.46410i − 0.339087i
\(780\) 0 0
\(781\) − 16.0000i − 0.572525i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −1.32051 −0.0471310
\(786\) 0 0
\(787\) − 10.5885i − 0.377438i −0.982031 0.188719i \(-0.939567\pi\)
0.982031 0.188719i \(-0.0604335\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −13.4641 −0.478728
\(792\) 0 0
\(793\) −42.8897 −1.52306
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 38.9808i 1.38077i 0.723442 + 0.690385i \(0.242559\pi\)
−0.723442 + 0.690385i \(0.757441\pi\)
\(798\) 0 0
\(799\) 21.8564 0.773224
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) − 1.35898i − 0.0479575i
\(804\) 0 0
\(805\) − 2.53590i − 0.0893787i
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 11.3205 0.398008 0.199004 0.979999i \(-0.436229\pi\)
0.199004 + 0.979999i \(0.436229\pi\)
\(810\) 0 0
\(811\) − 2.87564i − 0.100978i −0.998725 0.0504888i \(-0.983922\pi\)
0.998725 0.0504888i \(-0.0160779\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 4.78461 0.167598
\(816\) 0 0
\(817\) −6.92820 −0.242387
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) − 6.92820i − 0.241796i −0.992665 0.120898i \(-0.961423\pi\)
0.992665 0.120898i \(-0.0385774\pi\)
\(822\) 0 0
\(823\) −10.9282 −0.380933 −0.190467 0.981694i \(-0.561000\pi\)
−0.190467 + 0.981694i \(0.561000\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) − 13.8564i − 0.481834i −0.970546 0.240917i \(-0.922552\pi\)
0.970546 0.240917i \(-0.0774482\pi\)
\(828\) 0 0
\(829\) − 10.9808i − 0.381378i −0.981651 0.190689i \(-0.938928\pi\)
0.981651 0.190689i \(-0.0610721\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −2.00000 −0.0692959
\(834\) 0 0
\(835\) − 13.8564i − 0.479521i
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 15.7128 0.542467 0.271233 0.962514i \(-0.412569\pi\)
0.271233 + 0.962514i \(0.412569\pi\)
\(840\) 0 0
\(841\) −0.856406 −0.0295313
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 1.69873i 0.0584381i
\(846\) 0 0
\(847\) −8.85641 −0.304310
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 18.9282i 0.648850i
\(852\) 0 0
\(853\) 46.9808i 1.60859i 0.594230 + 0.804295i \(0.297457\pi\)
−0.594230 + 0.804295i \(0.702543\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −10.7846 −0.368395 −0.184198 0.982889i \(-0.558969\pi\)
−0.184198 + 0.982889i \(0.558969\pi\)
\(858\) 0 0
\(859\) 28.4449i 0.970526i 0.874368 + 0.485263i \(0.161276\pi\)
−0.874368 + 0.485263i \(0.838724\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 24.0000 0.816970 0.408485 0.912765i \(-0.366057\pi\)
0.408485 + 0.912765i \(0.366057\pi\)
\(864\) 0 0
\(865\) −10.3923 −0.353349
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) − 4.28719i − 0.145433i
\(870\) 0 0
\(871\) 26.1436 0.885842
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) − 6.92820i − 0.234216i
\(876\) 0 0
\(877\) − 0.392305i − 0.0132472i −0.999978 0.00662360i \(-0.997892\pi\)
0.999978 0.00662360i \(-0.00210837\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 9.21539 0.310474 0.155237 0.987877i \(-0.450386\pi\)
0.155237 + 0.987877i \(0.450386\pi\)
\(882\) 0 0
\(883\) 18.9282i 0.636985i 0.947925 + 0.318492i \(0.103177\pi\)
−0.947925 + 0.318492i \(0.896823\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 22.6410 0.760211 0.380105 0.924943i \(-0.375888\pi\)
0.380105 + 0.924943i \(0.375888\pi\)
\(888\) 0 0
\(889\) −4.53590 −0.152129
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 51.7128i 1.73050i
\(894\) 0 0
\(895\) 8.00000 0.267411
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) − 21.8564i − 0.728952i
\(900\) 0 0
\(901\) 24.0000i 0.799556i
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 5.32051 0.176860
\(906\) 0 0
\(907\) 11.7128i 0.388918i 0.980911 + 0.194459i \(0.0622951\pi\)
−0.980911 + 0.194459i \(0.937705\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −11.4641 −0.379823 −0.189911 0.981801i \(-0.560820\pi\)
−0.189911 + 0.981801i \(0.560820\pi\)
\(912\) 0 0
\(913\) 17.0718 0.564994
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) − 7.26795i − 0.240009i
\(918\) 0 0
\(919\) 48.7846 1.60926 0.804628 0.593779i \(-0.202365\pi\)
0.804628 + 0.593779i \(0.202365\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 35.7128i 1.17550i
\(924\) 0 0
\(925\) 24.3923i 0.802014i
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 17.7128 0.581139 0.290569 0.956854i \(-0.406155\pi\)
0.290569 + 0.956854i \(0.406155\pi\)
\(930\) 0 0
\(931\) − 4.73205i − 0.155087i
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 2.14359 0.0701030
\(936\) 0 0
\(937\) −60.6410 −1.98106 −0.990528 0.137312i \(-0.956154\pi\)
−0.990528 + 0.137312i \(0.956154\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) − 6.98076i − 0.227566i −0.993506 0.113783i \(-0.963703\pi\)
0.993506 0.113783i \(-0.0362969\pi\)
\(942\) 0 0
\(943\) 6.92820 0.225613
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 3.60770i 0.117234i 0.998281 + 0.0586172i \(0.0186691\pi\)
−0.998281 + 0.0586172i \(0.981331\pi\)
\(948\) 0 0
\(949\) 3.03332i 0.0984658i
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −7.85641 −0.254494 −0.127247 0.991871i \(-0.540614\pi\)
−0.127247 + 0.991871i \(0.540614\pi\)
\(954\) 0 0
\(955\) 11.7128i 0.379018i
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −7.85641 −0.253697
\(960\) 0 0
\(961\) −15.0000 −0.483871
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 9.85641i 0.317289i
\(966\) 0 0
\(967\) −47.1769 −1.51711 −0.758554 0.651611i \(-0.774094\pi\)
−0.758554 + 0.651611i \(0.774094\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 10.4833i 0.336426i 0.985751 + 0.168213i \(0.0537997\pi\)
−0.985751 + 0.168213i \(0.946200\pi\)
\(972\) 0 0
\(973\) 12.7321i 0.408171i
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 55.8564 1.78700 0.893502 0.449058i \(-0.148241\pi\)
0.893502 + 0.449058i \(0.148241\pi\)
\(978\) 0 0
\(979\) 23.2154i 0.741967i
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 7.71281 0.246001 0.123000 0.992407i \(-0.460748\pi\)
0.123000 + 0.992407i \(0.460748\pi\)
\(984\) 0 0
\(985\) −1.35898 −0.0433008
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) − 5.07180i − 0.161274i
\(990\) 0 0
\(991\) 16.7846 0.533181 0.266590 0.963810i \(-0.414103\pi\)
0.266590 + 0.963810i \(0.414103\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 2.92820i 0.0928303i
\(996\) 0 0
\(997\) − 8.73205i − 0.276547i −0.990394 0.138273i \(-0.955845\pi\)
0.990394 0.138273i \(-0.0441553\pi\)
\(998\) 0 0
\(999\) 0 0
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 \(a_p\))