Properties

Label 1440.2.d.e.1009.1
Level 1440
Weight 2
Character 1440.1009
Analytic conductor 11.498
Analytic rank 0
Dimension 6
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 1440 = 2^{5} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1440.d (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(11.4984578911\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: 6.0.839056.1
Defining polynomial: \(x^{6} + 6 x^{4} + 8 x^{2} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{5} \)
Twist minimal: no (minimal twist has level 120)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 1009.1
Root \(-2.02852i\) of defining polynomial
Character \(\chi\) \(=\) 1440.1009
Dual form 1440.2.d.e.1009.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.11491 - 0.726062i) q^{5} +4.05705i q^{7} +O(q^{10})\) \(q+(-2.11491 - 0.726062i) q^{5} +4.05705i q^{7} +0.985939i q^{11} -4.94567 q^{13} -4.52323i q^{17} -2.60492i q^{19} -3.53729i q^{23} +(3.94567 + 3.07111i) q^{25} -7.59434i q^{29} +3.28415 q^{31} +(2.94567 - 8.58028i) q^{35} +0.945668 q^{37} -0.568295 q^{41} +8.45963 q^{43} +2.60492i q^{47} -9.45963 q^{49} +0.229815 q^{53} +(0.715853 - 2.08517i) q^{55} -9.10003i q^{59} -11.0183i q^{61} +(10.4596 + 3.59086i) q^{65} -8.45963 q^{67} +1.43171 q^{71} -11.9507i q^{73} -4.00000 q^{77} -3.28415 q^{79} -9.89134 q^{83} +(-3.28415 + 9.56622i) q^{85} -12.3510 q^{89} -20.0648i q^{91} +(-1.89134 + 5.50917i) q^{95} -3.23797i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q + O(q^{10}) \) \( 6q - 8q^{13} + 2q^{25} + 16q^{31} - 4q^{35} - 16q^{37} + 4q^{41} - 6q^{49} - 24q^{53} + 8q^{55} + 12q^{65} + 16q^{71} - 24q^{77} - 16q^{79} - 16q^{83} - 16q^{85} + 20q^{89} + 32q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1440\mathbb{Z}\right)^\times\).

\(n\) \(577\) \(641\) \(901\) \(991\)
\(\chi(n)\) \(-1\) \(1\) \(-1\) \(1\)

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
\(5\) −2.11491 0.726062i −0.945815 0.324705i
\(6\) 0 0
\(7\) 4.05705i 1.53342i 0.641994 + 0.766710i \(0.278107\pi\)
−0.641994 + 0.766710i \(0.721893\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 0.985939i 0.297272i 0.988892 + 0.148636i \(0.0474882\pi\)
−0.988892 + 0.148636i \(0.952512\pi\)
\(12\) 0 0
\(13\) −4.94567 −1.37168 −0.685841 0.727752i \(-0.740565\pi\)
−0.685841 + 0.727752i \(0.740565\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 4.52323i 1.09704i −0.836136 0.548522i \(-0.815191\pi\)
0.836136 0.548522i \(-0.184809\pi\)
\(18\) 0 0
\(19\) 2.60492i 0.597610i −0.954314 0.298805i \(-0.903412\pi\)
0.954314 0.298805i \(-0.0965881\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 3.53729i 0.737577i −0.929513 0.368788i \(-0.879773\pi\)
0.929513 0.368788i \(-0.120227\pi\)
\(24\) 0 0
\(25\) 3.94567 + 3.07111i 0.789134 + 0.614222i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 7.59434i 1.41023i −0.709091 0.705117i \(-0.750895\pi\)
0.709091 0.705117i \(-0.249105\pi\)
\(30\) 0 0
\(31\) 3.28415 0.589850 0.294925 0.955520i \(-0.404705\pi\)
0.294925 + 0.955520i \(0.404705\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 2.94567 8.58028i 0.497909 1.45033i
\(36\) 0 0
\(37\) 0.945668 0.155467 0.0777334 0.996974i \(-0.475232\pi\)
0.0777334 + 0.996974i \(0.475232\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −0.568295 −0.0887527 −0.0443763 0.999015i \(-0.514130\pi\)
−0.0443763 + 0.999015i \(0.514130\pi\)
\(42\) 0 0
\(43\) 8.45963 1.29008 0.645041 0.764148i \(-0.276840\pi\)
0.645041 + 0.764148i \(0.276840\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 2.60492i 0.379967i 0.981787 + 0.189984i \(0.0608435\pi\)
−0.981787 + 0.189984i \(0.939157\pi\)
\(48\) 0 0
\(49\) −9.45963 −1.35138
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 0.229815 0.0315675 0.0157838 0.999875i \(-0.494976\pi\)
0.0157838 + 0.999875i \(0.494976\pi\)
\(54\) 0 0
\(55\) 0.715853 2.08517i 0.0965256 0.281164i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 9.10003i 1.18472i −0.805672 0.592362i \(-0.798196\pi\)
0.805672 0.592362i \(-0.201804\pi\)
\(60\) 0 0
\(61\) 11.0183i 1.41075i −0.708832 0.705377i \(-0.750778\pi\)
0.708832 0.705377i \(-0.249222\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 10.4596 + 3.59086i 1.29736 + 0.445392i
\(66\) 0 0
\(67\) −8.45963 −1.03351 −0.516754 0.856134i \(-0.672860\pi\)
−0.516754 + 0.856134i \(0.672860\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 1.43171 0.169912 0.0849561 0.996385i \(-0.472925\pi\)
0.0849561 + 0.996385i \(0.472925\pi\)
\(72\) 0 0
\(73\) 11.9507i 1.39873i −0.714767 0.699363i \(-0.753467\pi\)
0.714767 0.699363i \(-0.246533\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −4.00000 −0.455842
\(78\) 0 0
\(79\) −3.28415 −0.369495 −0.184748 0.982786i \(-0.559147\pi\)
−0.184748 + 0.982786i \(0.559147\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −9.89134 −1.08572 −0.542858 0.839825i \(-0.682658\pi\)
−0.542858 + 0.839825i \(0.682658\pi\)
\(84\) 0 0
\(85\) −3.28415 + 9.56622i −0.356216 + 1.03760i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −12.3510 −1.30920 −0.654600 0.755976i \(-0.727163\pi\)
−0.654600 + 0.755976i \(0.727163\pi\)
\(90\) 0 0
\(91\) 20.0648i 2.10336i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −1.89134 + 5.50917i −0.194047 + 0.565229i
\(96\) 0 0
\(97\) 3.23797i 0.328766i −0.986397 0.164383i \(-0.947437\pi\)
0.986397 0.164383i \(-0.0525633\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 4.35637i 0.433475i 0.976230 + 0.216738i \(0.0695416\pi\)
−0.976230 + 0.216738i \(0.930458\pi\)
\(102\) 0 0
\(103\) 15.0754i 1.48542i −0.669612 0.742711i \(-0.733540\pi\)
0.669612 0.742711i \(-0.266460\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −4.00000 −0.386695 −0.193347 0.981130i \(-0.561934\pi\)
−0.193347 + 0.981130i \(0.561934\pi\)
\(108\) 0 0
\(109\) 4.17034i 0.399446i −0.979852 0.199723i \(-0.935996\pi\)
0.979852 0.199723i \(-0.0640042\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 1.28526i 0.120907i −0.998171 0.0604537i \(-0.980745\pi\)
0.998171 0.0604537i \(-0.0192548\pi\)
\(114\) 0 0
\(115\) −2.56829 + 7.48105i −0.239495 + 0.697611i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 18.3510 1.68223
\(120\) 0 0
\(121\) 10.0279 0.911630
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −6.11491 9.35991i −0.546934 0.837176i
\(126\) 0 0
\(127\) 1.15280i 0.102294i 0.998691 + 0.0511472i \(0.0162878\pi\)
−0.998691 + 0.0511472i \(0.983712\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 3.89019i 0.339887i 0.985454 + 0.169944i \(0.0543586\pi\)
−0.985454 + 0.169944i \(0.945641\pi\)
\(132\) 0 0
\(133\) 10.5683 0.916387
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 17.5135i 1.49628i 0.663544 + 0.748138i \(0.269052\pi\)
−0.663544 + 0.748138i \(0.730948\pi\)
\(138\) 0 0
\(139\) 16.8612i 1.43015i 0.699047 + 0.715076i \(0.253608\pi\)
−0.699047 + 0.715076i \(0.746392\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 4.87613i 0.407762i
\(144\) 0 0
\(145\) −5.51396 + 16.0613i −0.457910 + 1.33382i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 10.4986i 0.860078i −0.902810 0.430039i \(-0.858500\pi\)
0.902810 0.430039i \(-0.141500\pi\)
\(150\) 0 0
\(151\) −4.71585 −0.383771 −0.191885 0.981417i \(-0.561460\pi\)
−0.191885 + 0.981417i \(0.561460\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −6.94567 2.38449i −0.557889 0.191527i
\(156\) 0 0
\(157\) 8.94567 0.713942 0.356971 0.934115i \(-0.383809\pi\)
0.356971 + 0.934115i \(0.383809\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 14.3510 1.13101
\(162\) 0 0
\(163\) −15.7827 −1.23619 −0.618097 0.786102i \(-0.712096\pi\)
−0.618097 + 0.786102i \(0.712096\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 5.50917i 0.426312i 0.977018 + 0.213156i \(0.0683743\pi\)
−0.977018 + 0.213156i \(0.931626\pi\)
\(168\) 0 0
\(169\) 11.4596 0.881510
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 10.3385 0.786020 0.393010 0.919534i \(-0.371434\pi\)
0.393010 + 0.919534i \(0.371434\pi\)
\(174\) 0 0
\(175\) −12.4596 + 16.0078i −0.941860 + 1.21007i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 16.1746i 1.20895i 0.796625 + 0.604474i \(0.206617\pi\)
−0.796625 + 0.604474i \(0.793383\pi\)
\(180\) 0 0
\(181\) 8.11409i 0.603116i −0.953448 0.301558i \(-0.902493\pi\)
0.953448 0.301558i \(-0.0975067\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −2.00000 0.686614i −0.147043 0.0504808i
\(186\) 0 0
\(187\) 4.45963 0.326120
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −24.9193 −1.80309 −0.901547 0.432681i \(-0.857568\pi\)
−0.901547 + 0.432681i \(0.857568\pi\)
\(192\) 0 0
\(193\) 1.03951i 0.0748254i −0.999300 0.0374127i \(-0.988088\pi\)
0.999300 0.0374127i \(-0.0119116\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 9.66152 0.688355 0.344177 0.938905i \(-0.388158\pi\)
0.344177 + 0.938905i \(0.388158\pi\)
\(198\) 0 0
\(199\) 23.0668 1.63516 0.817582 0.575813i \(-0.195314\pi\)
0.817582 + 0.575813i \(0.195314\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 30.8106 2.16248
\(204\) 0 0
\(205\) 1.20189 + 0.412617i 0.0839437 + 0.0288184i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 2.56829 0.177653
\(210\) 0 0
\(211\) 6.44154i 0.443454i 0.975109 + 0.221727i \(0.0711694\pi\)
−0.975109 + 0.221727i \(0.928831\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −17.8913 6.14222i −1.22018 0.418896i
\(216\) 0 0
\(217\) 13.3239i 0.904488i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 22.3704i 1.50480i
\(222\) 0 0
\(223\) 17.9796i 1.20401i −0.798494 0.602003i \(-0.794370\pi\)
0.798494 0.602003i \(-0.205630\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −7.02792 −0.466460 −0.233230 0.972422i \(-0.574929\pi\)
−0.233230 + 0.972422i \(0.574929\pi\)
\(228\) 0 0
\(229\) 4.17034i 0.275584i 0.990461 + 0.137792i \(0.0440005\pi\)
−0.990461 + 0.137792i \(0.955999\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 23.9894i 1.57160i −0.618483 0.785799i \(-0.712252\pi\)
0.618483 0.785799i \(-0.287748\pi\)
\(234\) 0 0
\(235\) 1.89134 5.50917i 0.123377 0.359379i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 8.91926 0.576939 0.288469 0.957489i \(-0.406854\pi\)
0.288469 + 0.957489i \(0.406854\pi\)
\(240\) 0 0
\(241\) −16.3510 −1.05326 −0.526629 0.850095i \(-0.676544\pi\)
−0.526629 + 0.850095i \(0.676544\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 20.0062 + 6.86828i 1.27815 + 0.438798i
\(246\) 0 0
\(247\) 12.8831i 0.819731i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 4.22391i 0.266611i 0.991075 + 0.133305i \(0.0425591\pi\)
−0.991075 + 0.133305i \(0.957441\pi\)
\(252\) 0 0
\(253\) 3.48755 0.219261
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 24.6952i 1.54044i −0.637777 0.770221i \(-0.720146\pi\)
0.637777 0.770221i \(-0.279854\pi\)
\(258\) 0 0
\(259\) 3.83662i 0.238396i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 14.6628i 0.904145i −0.891981 0.452073i \(-0.850685\pi\)
0.891981 0.452073i \(-0.149315\pi\)
\(264\) 0 0
\(265\) −0.486038 0.166860i −0.0298571 0.0102501i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 11.5381i 0.703490i 0.936096 + 0.351745i \(0.114412\pi\)
−0.936096 + 0.351745i \(0.885588\pi\)
\(270\) 0 0
\(271\) −5.63511 −0.342309 −0.171154 0.985244i \(-0.554750\pi\)
−0.171154 + 0.985244i \(0.554750\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −3.02792 + 3.89019i −0.182591 + 0.234587i
\(276\) 0 0
\(277\) −17.4053 −1.04578 −0.522892 0.852399i \(-0.675147\pi\)
−0.522892 + 0.852399i \(0.675147\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −21.7827 −1.29945 −0.649723 0.760171i \(-0.725115\pi\)
−0.649723 + 0.760171i \(0.725115\pi\)
\(282\) 0 0
\(283\) 21.5962 1.28376 0.641881 0.766804i \(-0.278154\pi\)
0.641881 + 0.766804i \(0.278154\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 2.30560i 0.136095i
\(288\) 0 0
\(289\) −3.45963 −0.203508
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −32.0125 −1.87019 −0.935095 0.354398i \(-0.884686\pi\)
−0.935095 + 0.354398i \(0.884686\pi\)
\(294\) 0 0
\(295\) −6.60719 + 19.2457i −0.384685 + 1.12053i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 17.4943i 1.01172i
\(300\) 0 0
\(301\) 34.3211i 1.97824i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −8.00000 + 23.3028i −0.458079 + 1.33431i
\(306\) 0 0
\(307\) −1.13659 −0.0648686 −0.0324343 0.999474i \(-0.510326\pi\)
−0.0324343 + 0.999474i \(0.510326\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 5.13659 0.291269 0.145635 0.989338i \(-0.453478\pi\)
0.145635 + 0.989338i \(0.453478\pi\)
\(312\) 0 0
\(313\) 23.0762i 1.30434i −0.758071 0.652172i \(-0.773858\pi\)
0.758071 0.652172i \(-0.226142\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 1.66152 0.0933203 0.0466601 0.998911i \(-0.485142\pi\)
0.0466601 + 0.998911i \(0.485142\pi\)
\(318\) 0 0
\(319\) 7.48755 0.419223
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −11.7827 −0.655605
\(324\) 0 0
\(325\) −19.5140 15.1887i −1.08244 0.842516i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −10.5683 −0.582649
\(330\) 0 0
\(331\) 25.9077i 1.42402i 0.702171 + 0.712008i \(0.252214\pi\)
−0.702171 + 0.712008i \(0.747786\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 17.8913 + 6.14222i 0.977508 + 0.335585i
\(336\) 0 0
\(337\) 8.00696i 0.436167i 0.975930 + 0.218083i \(0.0699805\pi\)
−0.975930 + 0.218083i \(0.930020\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 3.23797i 0.175346i
\(342\) 0 0
\(343\) 9.97884i 0.538806i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 23.0279 1.23620 0.618102 0.786098i \(-0.287902\pi\)
0.618102 + 0.786098i \(0.287902\pi\)
\(348\) 0 0
\(349\) 21.4380i 1.14755i 0.819012 + 0.573776i \(0.194522\pi\)
−0.819012 + 0.573776i \(0.805478\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 4.52323i 0.240747i −0.992729 0.120374i \(-0.961591\pi\)
0.992729 0.120374i \(-0.0384093\pi\)
\(354\) 0 0
\(355\) −3.02792 1.03951i −0.160706 0.0551713i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −10.3510 −0.546303 −0.273152 0.961971i \(-0.588066\pi\)
−0.273152 + 0.961971i \(0.588066\pi\)
\(360\) 0 0
\(361\) 12.2144 0.642862
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −8.67696 + 25.2747i −0.454173 + 1.32294i
\(366\) 0 0
\(367\) 0.485359i 0.0253355i 0.999920 + 0.0126678i \(0.00403238\pi\)
−0.999920 + 0.0126678i \(0.995968\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 0.932371i 0.0484063i
\(372\) 0 0
\(373\) 30.0823 1.55760 0.778800 0.627272i \(-0.215829\pi\)
0.778800 + 0.627272i \(0.215829\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 37.5591i 1.93439i
\(378\) 0 0
\(379\) 33.6881i 1.73044i −0.501392 0.865220i \(-0.667179\pi\)
0.501392 0.865220i \(-0.332821\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 5.17545i 0.264453i 0.991220 + 0.132227i \(0.0422127\pi\)
−0.991220 + 0.132227i \(0.957787\pi\)
\(384\) 0 0
\(385\) 8.45963 + 2.90425i 0.431143 + 0.148014i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 16.6408i 0.843722i 0.906660 + 0.421861i \(0.138623\pi\)
−0.906660 + 0.421861i \(0.861377\pi\)
\(390\) 0 0
\(391\) −16.0000 −0.809155
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 6.94567 + 2.38449i 0.349474 + 0.119977i
\(396\) 0 0
\(397\) −20.4332 −1.02551 −0.512757 0.858534i \(-0.671376\pi\)
−0.512757 + 0.858534i \(0.671376\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 4.56829 0.228130 0.114065 0.993473i \(-0.463613\pi\)
0.114065 + 0.993473i \(0.463613\pi\)
\(402\) 0 0
\(403\) −16.2423 −0.809087
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0.932371i 0.0462159i
\(408\) 0 0
\(409\) −19.8913 −0.983563 −0.491782 0.870719i \(-0.663654\pi\)
−0.491782 + 0.870719i \(0.663654\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 36.9193 1.81668
\(414\) 0 0
\(415\) 20.9193 + 7.18172i 1.02689 + 0.352537i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 0.387288i 0.0189203i −0.999955 0.00946013i \(-0.996989\pi\)
0.999955 0.00946013i \(-0.00301130\pi\)
\(420\) 0 0
\(421\) 12.0578i 0.587664i 0.955857 + 0.293832i \(0.0949306\pi\)
−0.955857 + 0.293832i \(0.905069\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 13.8913 17.8472i 0.673829 0.865715i
\(426\) 0 0
\(427\) 44.7019 2.16328
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 40.4068 1.94633 0.973164 0.230113i \(-0.0739096\pi\)
0.973164 + 0.230113i \(0.0739096\pi\)
\(432\) 0 0
\(433\) 36.1859i 1.73898i −0.493949 0.869491i \(-0.664447\pi\)
0.493949 0.869491i \(-0.335553\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −9.21438 −0.440783
\(438\) 0 0
\(439\) −25.4178 −1.21312 −0.606562 0.795036i \(-0.707452\pi\)
−0.606562 + 0.795036i \(0.707452\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 7.02792 0.333907 0.166953 0.985965i \(-0.446607\pi\)
0.166953 + 0.985965i \(0.446607\pi\)
\(444\) 0 0
\(445\) 26.1212 + 8.96757i 1.23826 + 0.425103i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −2.00000 −0.0943858 −0.0471929 0.998886i \(-0.515028\pi\)
−0.0471929 + 0.998886i \(0.515028\pi\)
\(450\) 0 0
\(451\) 0.560304i 0.0263837i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −14.5683 + 42.4352i −0.682972 + 1.98939i
\(456\) 0 0
\(457\) 25.2747i 1.18230i 0.806562 + 0.591149i \(0.201326\pi\)
−0.806562 + 0.591149i \(0.798674\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 41.0902i 1.91376i −0.290479 0.956881i \(-0.593815\pi\)
0.290479 0.956881i \(-0.406185\pi\)
\(462\) 0 0
\(463\) 13.2106i 0.613951i −0.951717 0.306975i \(-0.900683\pi\)
0.951717 0.306975i \(-0.0993169\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 1.89134 0.0875206 0.0437603 0.999042i \(-0.486066\pi\)
0.0437603 + 0.999042i \(0.486066\pi\)
\(468\) 0 0
\(469\) 34.3211i 1.58480i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 8.34068i 0.383505i
\(474\) 0 0
\(475\) 8.00000 10.2782i 0.367065 0.471594i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −31.4876 −1.43870 −0.719352 0.694646i \(-0.755561\pi\)
−0.719352 + 0.694646i \(0.755561\pi\)
\(480\) 0 0
\(481\) −4.67696 −0.213251
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −2.35097 + 6.84800i −0.106752 + 0.310952i
\(486\) 0 0
\(487\) 12.9964i 0.588922i −0.955664 0.294461i \(-0.904860\pi\)
0.955664 0.294461i \(-0.0951401\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 14.9085i 0.672812i −0.941717 0.336406i \(-0.890788\pi\)
0.941717 0.336406i \(-0.109212\pi\)
\(492\) 0 0
\(493\) −34.3510 −1.54709
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 5.80850i 0.260547i
\(498\) 0 0
\(499\) 35.6599i 1.59636i 0.602420 + 0.798179i \(0.294203\pi\)
−0.602420 + 0.798179i \(0.705797\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 25.3090i 1.12847i 0.825613 + 0.564237i \(0.190830\pi\)
−0.825613 + 0.564237i \(0.809170\pi\)
\(504\) 0 0
\(505\) 3.16300 9.21332i 0.140751 0.409988i
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 13.7366i 0.608862i 0.952534 + 0.304431i \(0.0984663\pi\)
−0.952534 + 0.304431i \(0.901534\pi\)
\(510\) 0 0
\(511\) 48.4846 2.14483
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −10.9457 + 31.8831i −0.482324 + 1.40494i
\(516\) 0 0
\(517\) −2.56829 −0.112953
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 30.9193 1.35460 0.677299 0.735708i \(-0.263150\pi\)
0.677299 + 0.735708i \(0.263150\pi\)
\(522\) 0 0
\(523\) 21.8385 0.954932 0.477466 0.878650i \(-0.341555\pi\)
0.477466 + 0.878650i \(0.341555\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 14.8550i 0.647092i
\(528\) 0 0
\(529\) 10.4876 0.455981
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 2.81060 0.121740
\(534\) 0 0
\(535\) 8.45963 + 2.90425i 0.365742 + 0.125562i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 9.32662i 0.401726i
\(540\) 0 0
\(541\) 24.3423i 1.04656i −0.852162 0.523278i \(-0.824709\pi\)
0.852162 0.523278i \(-0.175291\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −3.02792 + 8.81988i −0.129702 + 0.377802i
\(546\) 0 0
\(547\) −33.3789 −1.42718 −0.713589 0.700564i \(-0.752932\pi\)
−0.713589 + 0.700564i \(0.752932\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −19.7827 −0.842770
\(552\) 0 0
\(553\) 13.3239i 0.566592i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −30.5808 −1.29575 −0.647875 0.761747i \(-0.724342\pi\)
−0.647875 + 0.761747i \(0.724342\pi\)
\(558\) 0 0
\(559\) −41.8385 −1.76958
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −7.02792 −0.296192 −0.148096 0.988973i \(-0.547314\pi\)
−0.148096 + 0.988973i \(0.547314\pi\)
\(564\) 0 0
\(565\) −0.933181 + 2.71821i −0.0392592 + 0.114356i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 24.3510 1.02085 0.510423 0.859924i \(-0.329489\pi\)
0.510423 + 0.859924i \(0.329489\pi\)
\(570\) 0 0
\(571\) 20.0992i 0.841125i 0.907263 + 0.420563i \(0.138167\pi\)
−0.907263 + 0.420563i \(0.861833\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 10.8634 13.9570i 0.453036 0.582047i
\(576\) 0 0
\(577\) 4.76899i 0.198536i −0.995061 0.0992678i \(-0.968350\pi\)
0.995061 0.0992678i \(-0.0316501\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 40.1296i 1.66486i
\(582\) 0 0
\(583\) 0.226584i 0.00938413i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −8.21733 −0.339165 −0.169583 0.985516i \(-0.554242\pi\)
−0.169583 + 0.985516i \(0.554242\pi\)
\(588\) 0 0
\(589\) 8.55495i 0.352501i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 7.76120i 0.318714i −0.987221 0.159357i \(-0.949058\pi\)
0.987221 0.159357i \(-0.0509421\pi\)
\(594\) 0 0
\(595\) −38.8106 13.3239i −1.59108 0.546228i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 5.64903 0.230813 0.115407 0.993318i \(-0.463183\pi\)
0.115407 + 0.993318i \(0.463183\pi\)
\(600\) 0 0
\(601\) −37.7299 −1.53903 −0.769516 0.638627i \(-0.779503\pi\)
−0.769516 + 0.638627i \(0.779503\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −21.2081 7.28090i −0.862233 0.296010i
\(606\) 0 0
\(607\) 0.113292i 0.00459837i 0.999997 + 0.00229919i \(0.000731854\pi\)
−0.999997 + 0.00229919i \(0.999268\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 12.8831i 0.521194i
\(612\) 0 0
\(613\) 0.703366 0.0284087 0.0142044 0.999899i \(-0.495478\pi\)
0.0142044 + 0.999899i \(0.495478\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 24.4809i 0.985564i −0.870153 0.492782i \(-0.835980\pi\)
0.870153 0.492782i \(-0.164020\pi\)
\(618\) 0 0
\(619\) 39.4966i 1.58750i −0.608243 0.793751i \(-0.708126\pi\)
0.608243 0.793751i \(-0.291874\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 50.1084i 2.00755i
\(624\) 0 0
\(625\) 6.13659 + 24.2351i 0.245464 + 0.969406i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 4.27748i 0.170554i
\(630\) 0 0
\(631\) −17.3400 −0.690294 −0.345147 0.938549i \(-0.612171\pi\)
−0.345147 + 0.938549i \(0.612171\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 0.837003 2.43806i 0.0332155 0.0967516i
\(636\) 0 0
\(637\) 46.7842 1.85366
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −38.7019 −1.52863 −0.764317 0.644840i \(-0.776924\pi\)
−0.764317 + 0.644840i \(0.776924\pi\)
\(642\) 0 0
\(643\) −1.13659 −0.0448227 −0.0224113 0.999749i \(-0.507134\pi\)
−0.0224113 + 0.999749i \(0.507134\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 6.54868i 0.257455i 0.991680 + 0.128728i \(0.0410893\pi\)
−0.991680 + 0.128728i \(0.958911\pi\)
\(648\) 0 0
\(649\) 8.97208 0.352185
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 8.74226 0.342111 0.171056 0.985261i \(-0.445282\pi\)
0.171056 + 0.985261i \(0.445282\pi\)
\(654\) 0 0
\(655\) 2.82452 8.22739i 0.110363 0.321471i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 35.5336i 1.38419i −0.721804 0.692097i \(-0.756687\pi\)
0.721804 0.692097i \(-0.243313\pi\)
\(660\) 0 0
\(661\) 23.3028i 0.906373i 0.891416 + 0.453186i \(0.149713\pi\)
−0.891416 + 0.453186i \(0.850287\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −22.3510 7.67324i −0.866733 0.297555i
\(666\) 0 0
\(667\) −26.8634 −1.04016
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 10.8634 0.419377
\(672\) 0 0
\(673\) 14.3634i 0.553670i 0.960917 + 0.276835i \(0.0892856\pi\)
−0.960917 + 0.276835i \(0.910714\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 24.3076 0.934217 0.467109 0.884200i \(-0.345296\pi\)
0.467109 + 0.884200i \(0.345296\pi\)
\(678\) 0 0
\(679\) 13.1366 0.504136
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −38.5933 −1.47673 −0.738365 0.674401i \(-0.764402\pi\)
−0.738365 + 0.674401i \(0.764402\pi\)
\(684\) 0 0
\(685\) 12.7159 37.0393i 0.485848 1.41520i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −1.13659 −0.0433006
\(690\) 0 0
\(691\) 13.4090i 0.510102i 0.966928 + 0.255051i \(0.0820923\pi\)
−0.966928 + 0.255051i \(0.917908\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 12.2423 35.6599i 0.464377 1.35266i
\(696\) 0 0
\(697\) 2.57053i 0.0973657i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 15.6013i 0.589253i −0.955613 0.294626i \(-0.904805\pi\)
0.955613 0.294626i \(-0.0951952\pi\)
\(702\) 0 0
\(703\) 2.46339i 0.0929086i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −17.6740 −0.664699
\(708\) 0 0
\(709\) 15.7873i 0.592906i 0.955047 + 0.296453i \(0.0958038\pi\)
−0.955047 + 0.296453i \(0.904196\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 11.6170i 0.435060i
\(714\) 0 0
\(715\) −3.54037 + 10.3126i −0.132402 + 0.385668i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −22.5683 −0.841655 −0.420828 0.907141i \(-0.638260\pi\)
−0.420828 + 0.907141i \(0.638260\pi\)
\(720\) 0 0
\(721\) 61.1616 2.27778
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 23.3230 29.9647i 0.866196 1.11286i
\(726\) 0 0
\(727\) 2.79096i 0.103511i −0.998660 0.0517554i \(-0.983518\pi\)
0.998660 0.0517554i \(-0.0164816\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 38.2649i 1.41528i
\(732\) 0 0
\(733\) −16.4860 −0.608926 −0.304463 0.952524i \(-0.598477\pi\)
−0.304463 + 0.952524i \(0.598477\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 8.34068i 0.307233i
\(738\) 0 0
\(739\) 14.8894i 0.547714i −0.961770 0.273857i \(-0.911701\pi\)
0.961770 0.273857i \(-0.0882995\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 41.4301i 1.51992i −0.649968 0.759961i \(-0.725218\pi\)
0.649968 0.759961i \(-0.274782\pi\)
\(744\) 0 0
\(745\) −7.62263 + 22.2035i −0.279271 + 0.813475i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 16.2282i 0.592965i
\(750\) 0 0
\(751\) −30.5544 −1.11494 −0.557472 0.830195i \(-0.688229\pi\)
−0.557472 + 0.830195i \(0.688229\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 9.97359 + 3.42400i 0.362976 + 0.124612i
\(756\) 0 0
\(757\) 0.433223 0.0157457 0.00787287 0.999969i \(-0.497494\pi\)
0.00787287 + 0.999969i \(0.497494\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 14.9193 0.540823 0.270411 0.962745i \(-0.412840\pi\)
0.270411 + 0.962745i \(0.412840\pi\)
\(762\) 0 0
\(763\) 16.9193 0.612518
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 45.0057i 1.62506i
\(768\) 0 0
\(769\) 31.3789 1.13155 0.565776 0.824559i \(-0.308577\pi\)
0.565776 + 0.824559i \(0.308577\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −13.4192 −0.482656 −0.241328 0.970444i \(-0.577583\pi\)
−0.241328 + 0.970444i \(0.577583\pi\)
\(774\) 0 0
\(775\) 12.9582 + 10.0860i 0.465471 + 0.362299i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 1.48036i 0.0530395i
\(780\) 0 0
\(781\) 1.41157i 0.0505101i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −18.9193 6.49511i −0.675257 0.231820i
\(786\) 0 0
\(787\) −36.4846 −1.30054 −0.650268 0.759705i \(-0.725343\pi\)
−0.650268 + 0.759705i \(0.725343\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 5.21438 0.185402
\(792\) 0 0
\(793\) 54.4931i 1.93511i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 26.0683 0.923388 0.461694 0.887039i \(-0.347242\pi\)
0.461694 + 0.887039i \(0.347242\pi\)
\(798\) 0 0
\(799\) 11.7827 0.416841
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 11.7827 0.415801
\(804\) 0 0
\(805\) −30.3510 10.4197i −1.06973 0.367246i
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 35.6212 1.25237 0.626187 0.779673i \(-0.284615\pi\)
0.626187 + 0.779673i \(0.284615\pi\)
\(810\) 0 0
\(811\) 43.8935i 1.54131i −0.637253 0.770654i \(-0.719929\pi\)
0.637253 0.770654i \(-0.280071\pi\)