Properties

Label 1440.2.d.e.1009.5
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 1009.5
Root \(-0.373087i\) of defining polynomial
Character \(\chi\) \(=\) 1440.1009
Dual form 1440.2.d.e.1009.6

$q$-expansion

\(f(q)\) \(=\) \(q+(1.86081 - 1.23992i) q^{5} +0.746175i q^{7} +O(q^{10})\) \(q+(1.86081 - 1.23992i) q^{5} +0.746175i q^{7} +5.36068i q^{11} -2.92520 q^{13} +2.13466i q^{17} +1.73367i q^{19} +7.49534i q^{23} +(1.92520 - 4.61450i) q^{25} +6.74916i q^{29} -2.64681 q^{31} +(0.925197 + 1.38849i) q^{35} -1.07480 q^{37} +11.2936 q^{41} -7.44322 q^{43} -1.73367i q^{47} +6.44322 q^{49} -7.72161 q^{53} +(6.64681 + 9.97518i) q^{55} -6.85302i q^{59} -6.45203i q^{61} +(-5.44322 + 3.62701i) q^{65} +7.44322 q^{67} +13.2936 q^{71} -0.690358i q^{73} -4.00000 q^{77} +2.64681 q^{79} -5.85039 q^{83} +(2.64681 + 3.97219i) q^{85} +7.59283 q^{89} -2.18271i q^{91} +(2.14961 + 3.22601i) q^{95} +14.1887i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q + O(q^{10}) \) \( 6q - 8q^{13} + 2q^{25} + 16q^{31} - 4q^{35} - 16q^{37} + 4q^{41} - 6q^{49} - 24q^{53} + 8q^{55} + 12q^{65} + 16q^{71} - 24q^{77} - 16q^{79} - 16q^{83} - 16q^{85} + 20q^{89} + 32q^{95} + O(q^{100}) \)

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
\(5\) 1.86081 1.23992i 0.832178 0.554509i
\(6\) 0 0
\(7\) 0.746175i 0.282028i 0.990008 + 0.141014i \(0.0450362\pi\)
−0.990008 + 0.141014i \(0.954964\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 5.36068i 1.61630i 0.588974 + 0.808152i \(0.299532\pi\)
−0.588974 + 0.808152i \(0.700468\pi\)
\(12\) 0 0
\(13\) −2.92520 −0.811304 −0.405652 0.914028i \(-0.632955\pi\)
−0.405652 + 0.914028i \(0.632955\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 2.13466i 0.517731i 0.965913 + 0.258866i \(0.0833487\pi\)
−0.965913 + 0.258866i \(0.916651\pi\)
\(18\) 0 0
\(19\) 1.73367i 0.397730i 0.980027 + 0.198865i \(0.0637255\pi\)
−0.980027 + 0.198865i \(0.936274\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 7.49534i 1.56289i 0.623977 + 0.781443i \(0.285516\pi\)
−0.623977 + 0.781443i \(0.714484\pi\)
\(24\) 0 0
\(25\) 1.92520 4.61450i 0.385039 0.922900i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 6.74916i 1.25329i 0.779306 + 0.626644i \(0.215572\pi\)
−0.779306 + 0.626644i \(0.784428\pi\)
\(30\) 0 0
\(31\) −2.64681 −0.475381 −0.237690 0.971341i \(-0.576390\pi\)
−0.237690 + 0.971341i \(0.576390\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 0.925197 + 1.38849i 0.156387 + 0.234697i
\(36\) 0 0
\(37\) −1.07480 −0.176697 −0.0883483 0.996090i \(-0.528159\pi\)
−0.0883483 + 0.996090i \(0.528159\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 11.2936 1.76377 0.881883 0.471468i \(-0.156276\pi\)
0.881883 + 0.471468i \(0.156276\pi\)
\(42\) 0 0
\(43\) −7.44322 −1.13508 −0.567540 0.823346i \(-0.692105\pi\)
−0.567540 + 0.823346i \(0.692105\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 1.73367i 0.252881i −0.991974 0.126441i \(-0.959645\pi\)
0.991974 0.126441i \(-0.0403553\pi\)
\(48\) 0 0
\(49\) 6.44322 0.920460
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −7.72161 −1.06064 −0.530322 0.847796i \(-0.677929\pi\)
−0.530322 + 0.847796i \(0.677929\pi\)
\(54\) 0 0
\(55\) 6.64681 + 9.97518i 0.896255 + 1.34505i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 6.85302i 0.892188i −0.894986 0.446094i \(-0.852815\pi\)
0.894986 0.446094i \(-0.147185\pi\)
\(60\) 0 0
\(61\) 6.45203i 0.826098i −0.910709 0.413049i \(-0.864464\pi\)
0.910709 0.413049i \(-0.135536\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −5.44322 + 3.62701i −0.675149 + 0.449875i
\(66\) 0 0
\(67\) 7.44322 0.909334 0.454667 0.890661i \(-0.349758\pi\)
0.454667 + 0.890661i \(0.349758\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 13.2936 1.57766 0.788831 0.614610i \(-0.210687\pi\)
0.788831 + 0.614610i \(0.210687\pi\)
\(72\) 0 0
\(73\) 0.690358i 0.0808003i −0.999184 0.0404002i \(-0.987137\pi\)
0.999184 0.0404002i \(-0.0128633\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −4.00000 −0.455842
\(78\) 0 0
\(79\) 2.64681 0.297789 0.148895 0.988853i \(-0.452428\pi\)
0.148895 + 0.988853i \(0.452428\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −5.85039 −0.642164 −0.321082 0.947051i \(-0.604047\pi\)
−0.321082 + 0.947051i \(0.604047\pi\)
\(84\) 0 0
\(85\) 2.64681 + 3.97219i 0.287087 + 0.430844i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 7.59283 0.804838 0.402419 0.915456i \(-0.368169\pi\)
0.402419 + 0.915456i \(0.368169\pi\)
\(90\) 0 0
\(91\) 2.18271i 0.228810i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 2.14961 + 3.22601i 0.220545 + 0.330982i
\(96\) 0 0
\(97\) 14.1887i 1.44064i 0.693641 + 0.720321i \(0.256006\pi\)
−0.693641 + 0.720321i \(0.743994\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 7.43952i 0.740260i 0.928980 + 0.370130i \(0.120687\pi\)
−0.928980 + 0.370130i \(0.879313\pi\)
\(102\) 0 0
\(103\) 7.19820i 0.709260i −0.935007 0.354630i \(-0.884607\pi\)
0.935007 0.354630i \(-0.115393\pi\)
\(104\) 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
\(109\) 19.9504i 1.91090i 0.295158 + 0.955449i \(0.404628\pi\)
−0.295158 + 0.955449i \(0.595372\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 12.0540i 1.13395i −0.823736 0.566973i \(-0.808114\pi\)
0.823736 0.566973i \(-0.191886\pi\)
\(114\) 0 0
\(115\) 9.29362 + 13.9474i 0.866634 + 1.30060i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −1.59283 −0.146014
\(120\) 0 0
\(121\) −17.7368 −1.61244
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −2.13919 10.9738i −0.191335 0.981525i
\(126\) 0 0
\(127\) 4.21351i 0.373888i −0.982371 0.186944i \(-0.940142\pi\)
0.982371 0.186944i \(-0.0598583\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 10.3204i 0.901694i 0.892601 + 0.450847i \(0.148878\pi\)
−0.892601 + 0.450847i \(0.851122\pi\)
\(132\) 0 0
\(133\) −1.29362 −0.112171
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 15.0387i 1.28484i 0.766351 + 0.642422i \(0.222070\pi\)
−0.766351 + 0.642422i \(0.777930\pi\)
\(138\) 0 0
\(139\) 9.47032i 0.803262i −0.915802 0.401631i \(-0.868443\pi\)
0.915802 0.401631i \(-0.131557\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 15.6810i 1.31131i
\(144\) 0 0
\(145\) 8.36842 + 12.5589i 0.694959 + 1.04296i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 1.78948i 0.146600i 0.997310 + 0.0733000i \(0.0233531\pi\)
−0.997310 + 0.0733000i \(0.976647\pi\)
\(150\) 0 0
\(151\) −10.6468 −0.866425 −0.433212 0.901292i \(-0.642620\pi\)
−0.433212 + 0.901292i \(0.642620\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −4.92520 + 3.28183i −0.395601 + 0.263603i
\(156\) 0 0
\(157\) 6.92520 0.552691 0.276345 0.961058i \(-0.410877\pi\)
0.276345 + 0.961058i \(0.410877\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −5.59283 −0.440777
\(162\) 0 0
\(163\) −7.70079 −0.603172 −0.301586 0.953439i \(-0.597516\pi\)
−0.301586 + 0.953439i \(0.597516\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 3.22601i 0.249637i 0.992180 + 0.124818i \(0.0398348\pi\)
−0.992180 + 0.124818i \(0.960165\pi\)
\(168\) 0 0
\(169\) −4.44322 −0.341786
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 6.42799 0.488711 0.244356 0.969686i \(-0.421424\pi\)
0.244356 + 0.969686i \(0.421424\pi\)
\(174\) 0 0
\(175\) 3.44322 + 1.43653i 0.260283 + 0.108592i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 8.13765i 0.608236i −0.952634 0.304118i \(-0.901638\pi\)
0.952634 0.304118i \(-0.0983618\pi\)
\(180\) 0 0
\(181\) 1.49235i 0.110925i −0.998461 0.0554627i \(-0.982337\pi\)
0.998461 0.0554627i \(-0.0176634\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −2.00000 + 1.33267i −0.147043 + 0.0979798i
\(186\) 0 0
\(187\) −11.4432 −0.836811
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 6.88645 0.498286 0.249143 0.968467i \(-0.419851\pi\)
0.249143 + 0.968467i \(0.419851\pi\)
\(192\) 0 0
\(193\) 16.4830i 1.18647i −0.805028 0.593237i \(-0.797850\pi\)
0.805028 0.593237i \(-0.202150\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 13.5720 0.966965 0.483483 0.875354i \(-0.339372\pi\)
0.483483 + 0.875354i \(0.339372\pi\)
\(198\) 0 0
\(199\) 9.05398 0.641820 0.320910 0.947110i \(-0.396011\pi\)
0.320910 + 0.947110i \(0.396011\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −5.03605 −0.353462
\(204\) 0 0
\(205\) 21.0152 14.0032i 1.46777 0.978025i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −9.29362 −0.642853
\(210\) 0 0
\(211\) 2.53566i 0.174562i −0.996184 0.0872809i \(-0.972182\pi\)
0.996184 0.0872809i \(-0.0278178\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −13.8504 + 9.22900i −0.944589 + 0.629413i
\(216\) 0 0
\(217\) 1.97498i 0.134070i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 6.24430i 0.420037i
\(222\) 0 0
\(223\) 12.1579i 0.814152i −0.913394 0.407076i \(-0.866548\pi\)
0.913394 0.407076i \(-0.133452\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 20.7368 1.37635 0.688176 0.725544i \(-0.258412\pi\)
0.688176 + 0.725544i \(0.258412\pi\)
\(228\) 0 0
\(229\) 19.9504i 1.31836i −0.751987 0.659178i \(-0.770904\pi\)
0.751987 0.659178i \(-0.229096\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 13.3386i 0.873844i 0.899499 + 0.436922i \(0.143931\pi\)
−0.899499 + 0.436922i \(0.856069\pi\)
\(234\) 0 0
\(235\) −2.14961 3.22601i −0.140225 0.210442i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −22.8864 −1.48040 −0.740201 0.672386i \(-0.765269\pi\)
−0.740201 + 0.672386i \(0.765269\pi\)
\(240\) 0 0
\(241\) 3.59283 0.231435 0.115717 0.993282i \(-0.463083\pi\)
0.115717 + 0.993282i \(0.463083\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 11.9896 7.98908i 0.765987 0.510404i
\(246\) 0 0
\(247\) 5.07131i 0.322680i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 8.82801i 0.557219i −0.960404 0.278609i \(-0.910127\pi\)
0.960404 0.278609i \(-0.0898735\pi\)
\(252\) 0 0
\(253\) −40.1801 −2.52610
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 22.2927i 1.39058i −0.718728 0.695291i \(-0.755275\pi\)
0.718728 0.695291i \(-0.244725\pi\)
\(258\) 0 0
\(259\) 0.801991i 0.0498333i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 21.2014i 1.30733i −0.756783 0.653667i \(-0.773230\pi\)
0.756783 0.653667i \(-0.226770\pi\)
\(264\) 0 0
\(265\) −14.3684 + 9.57418i −0.882645 + 0.588137i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 14.6935i 0.895881i 0.894063 + 0.447940i \(0.147842\pi\)
−0.894063 + 0.447940i \(0.852158\pi\)
\(270\) 0 0
\(271\) 20.2396 1.22947 0.614735 0.788734i \(-0.289263\pi\)
0.614735 + 0.788734i \(0.289263\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 24.7368 + 10.3204i 1.49169 + 0.622341i
\(276\) 0 0
\(277\) 0.518027 0.0311252 0.0155626 0.999879i \(-0.495046\pi\)
0.0155626 + 0.999879i \(0.495046\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −13.7008 −0.817320 −0.408660 0.912687i \(-0.634004\pi\)
−0.408660 + 0.912687i \(0.634004\pi\)
\(282\) 0 0
\(283\) −18.0305 −1.07180 −0.535900 0.844282i \(-0.680027\pi\)
−0.535900 + 0.844282i \(0.680027\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 8.42701i 0.497431i
\(288\) 0 0
\(289\) 12.4432 0.731954
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −15.9792 −0.933513 −0.466757 0.884386i \(-0.654578\pi\)
−0.466757 + 0.884386i \(0.654578\pi\)
\(294\) 0 0
\(295\) −8.49720 12.7521i −0.494726 0.742459i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 21.9253i 1.26797i
\(300\) 0 0
\(301\) 5.55394i 0.320124i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −8.00000 12.0060i −0.458079 0.687460i
\(306\) 0 0
\(307\) 22.5872 1.28912 0.644561 0.764553i \(-0.277040\pi\)
0.644561 + 0.764553i \(0.277040\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −18.5872 −1.05399 −0.526993 0.849870i \(-0.676680\pi\)
−0.526993 + 0.849870i \(0.676680\pi\)
\(312\) 0 0
\(313\) 29.3871i 1.66106i −0.556977 0.830528i \(-0.688039\pi\)
0.556977 0.830528i \(-0.311961\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 5.57201 0.312955 0.156478 0.987682i \(-0.449986\pi\)
0.156478 + 0.987682i \(0.449986\pi\)
\(318\) 0 0
\(319\) −36.1801 −2.02569
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −3.70079 −0.205917
\(324\) 0 0
\(325\) −5.63158 + 13.4983i −0.312384 + 0.748752i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 1.29362 0.0713194
\(330\) 0 0
\(331\) 13.7396i 0.755199i −0.925969 0.377599i \(-0.876750\pi\)
0.925969 0.377599i \(-0.123250\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 13.8504 9.22900i 0.756728 0.504234i
\(336\) 0 0
\(337\) 20.7523i 1.13045i −0.824936 0.565226i \(-0.808789\pi\)
0.824936 0.565226i \(-0.191211\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 14.1887i 0.768360i
\(342\) 0 0
\(343\) 10.0310i 0.541623i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −4.73684 −0.254287 −0.127143 0.991884i \(-0.540581\pi\)
−0.127143 + 0.991884i \(0.540581\pi\)
\(348\) 0 0
\(349\) 0.482632i 0.0258347i −0.999917 0.0129174i \(-0.995888\pi\)
0.999917 0.0129174i \(-0.00411184\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 2.13466i 0.113617i 0.998385 + 0.0568083i \(0.0180924\pi\)
−0.998385 + 0.0568083i \(0.981908\pi\)
\(354\) 0 0
\(355\) 24.7368 16.4830i 1.31290 0.874828i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 9.59283 0.506290 0.253145 0.967428i \(-0.418535\pi\)
0.253145 + 0.967428i \(0.418535\pi\)
\(360\) 0 0
\(361\) 15.9944 0.841811
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −0.855989 1.28462i −0.0448045 0.0672402i
\(366\) 0 0
\(367\) 34.0832i 1.77913i 0.456809 + 0.889565i \(0.348992\pi\)
−0.456809 + 0.889565i \(0.651008\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 5.76167i 0.299131i
\(372\) 0 0
\(373\) 4.33796 0.224611 0.112306 0.993674i \(-0.464176\pi\)
0.112306 + 0.993674i \(0.464176\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 19.7426i 1.01680i
\(378\) 0 0
\(379\) 6.90107i 0.354484i −0.984167 0.177242i \(-0.943282\pi\)
0.984167 0.177242i \(-0.0567176\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 22.3744i 1.14328i 0.820506 + 0.571639i \(0.193692\pi\)
−0.820506 + 0.571639i \(0.806308\pi\)
\(384\) 0 0
\(385\) −7.44322 + 4.95968i −0.379342 + 0.252769i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 11.0185i 0.558659i −0.960195 0.279330i \(-0.909888\pi\)
0.960195 0.279330i \(-0.0901122\pi\)
\(390\) 0 0
\(391\) −16.0000 −0.809155
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 4.92520 3.28183i 0.247814 0.165127i
\(396\) 0 0
\(397\) 25.2549 1.26751 0.633753 0.773536i \(-0.281514\pi\)
0.633753 + 0.773536i \(0.281514\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −7.29362 −0.364226 −0.182113 0.983278i \(-0.558294\pi\)
−0.182113 + 0.983278i \(0.558294\pi\)
\(402\) 0 0
\(403\) 7.74244 0.385678
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 5.76167i 0.285595i
\(408\) 0 0
\(409\) −15.8504 −0.783752 −0.391876 0.920018i \(-0.628174\pi\)
−0.391876 + 0.920018i \(0.628174\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 5.11355 0.251622
\(414\) 0 0
\(415\) −10.8864 + 7.25402i −0.534395 + 0.356086i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 8.02602i 0.392097i 0.980594 + 0.196048i \(0.0628109\pi\)
−0.980594 + 0.196048i \(0.937189\pi\)
\(420\) 0 0
\(421\) 22.9351i 1.11779i 0.829240 + 0.558893i \(0.188774\pi\)
−0.829240 + 0.558893i \(0.811226\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 9.85039 + 4.10964i 0.477814 + 0.199347i
\(426\) 0 0
\(427\) 4.81434 0.232982
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −35.0665 −1.68909 −0.844547 0.535481i \(-0.820130\pi\)
−0.844547 + 0.535481i \(0.820130\pi\)
\(432\) 0 0
\(433\) 17.0773i 0.820682i 0.911932 + 0.410341i \(0.134590\pi\)
−0.911932 + 0.410341i \(0.865410\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −12.9944 −0.621607
\(438\) 0 0
\(439\) 8.53885 0.407537 0.203769 0.979019i \(-0.434681\pi\)
0.203769 + 0.979019i \(0.434681\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −20.7368 −0.985237 −0.492619 0.870245i \(-0.663960\pi\)
−0.492619 + 0.870245i \(0.663960\pi\)
\(444\) 0 0
\(445\) 14.1288 9.41450i 0.669769 0.446290i
\(446\) 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
\(451\) 60.5414i 2.85078i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −2.70638 4.06160i −0.126877 0.190411i
\(456\) 0 0
\(457\) 1.28462i 0.0600921i −0.999549 0.0300461i \(-0.990435\pi\)
0.999549 0.0300461i \(-0.00956540\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 15.7033i 0.731374i −0.930738 0.365687i \(-0.880834\pi\)
0.930738 0.365687i \(-0.119166\pi\)
\(462\) 0 0
\(463\) 18.7215i 0.870064i −0.900415 0.435032i \(-0.856737\pi\)
0.900415 0.435032i \(-0.143263\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −2.14961 −0.0994719 −0.0497360 0.998762i \(-0.515838\pi\)
−0.0497360 + 0.998762i \(0.515838\pi\)
\(468\) 0 0
\(469\) 5.55394i 0.256457i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 39.9007i 1.83464i
\(474\) 0 0
\(475\) 8.00000 + 3.33765i 0.367065 + 0.153142i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 12.1801 0.556521 0.278261 0.960506i \(-0.410242\pi\)
0.278261 + 0.960506i \(0.410242\pi\)
\(480\) 0 0
\(481\) 3.14401 0.143355
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 17.5928 + 26.4024i 0.798849 + 1.19887i
\(486\) 0 0
\(487\) 25.7678i 1.16765i 0.811879 + 0.583826i \(0.198445\pi\)
−0.811879 + 0.583826i \(0.801555\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 16.7724i 0.756927i −0.925616 0.378464i \(-0.876453\pi\)
0.925616 0.378464i \(-0.123547\pi\)
\(492\) 0 0
\(493\) −14.4072 −0.648866
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 9.91936i 0.444944i
\(498\) 0 0
\(499\) 17.6224i 0.788888i 0.918920 + 0.394444i \(0.129063\pi\)
−0.918920 + 0.394444i \(0.870937\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 27.1263i 1.20950i −0.796414 0.604752i \(-0.793272\pi\)
0.796414 0.604752i \(-0.206728\pi\)
\(504\) 0 0
\(505\) 9.22441 + 13.8435i 0.410481 + 0.616028i
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 15.9782i 0.708220i −0.935204 0.354110i \(-0.884784\pi\)
0.935204 0.354110i \(-0.115216\pi\)
\(510\) 0 0
\(511\) 0.515128 0.0227879
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −8.92520 13.3945i −0.393291 0.590230i
\(516\) 0 0
\(517\) 9.29362 0.408733
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −0.886447 −0.0388359 −0.0194180 0.999811i \(-0.506181\pi\)
−0.0194180 + 0.999811i \(0.506181\pi\)
\(522\) 0 0
\(523\) −41.7729 −1.82660 −0.913301 0.407286i \(-0.866475\pi\)
−0.913301 + 0.407286i \(0.866475\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 5.65004i 0.246120i
\(528\) 0 0
\(529\) −33.1801 −1.44261
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −33.0361 −1.43095
\(534\) 0 0
\(535\) −7.44322 + 4.95968i −0.321799 + 0.214426i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 34.5400i 1.48774i
\(540\) 0 0
\(541\) 4.47705i 0.192483i −0.995358 0.0962417i \(-0.969318\pi\)
0.995358 0.0962417i \(-0.0306822\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 24.7368 + 37.1237i 1.05961 + 1.59021i
\(546\) 0 0
\(547\) 14.3297 0.612692 0.306346 0.951920i \(-0.400893\pi\)
0.306346 + 0.951920i \(0.400893\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −11.7008 −0.498470
\(552\) 0 0
\(553\) 1.97498i 0.0839848i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −2.68556 −0.113791 −0.0568954 0.998380i \(-0.518120\pi\)
−0.0568954 + 0.998380i \(0.518120\pi\)
\(558\) 0 0
\(559\) 21.7729 0.920895
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 20.7368 0.873954 0.436977 0.899473i \(-0.356049\pi\)
0.436977 + 0.899473i \(0.356049\pi\)
\(564\) 0 0
\(565\) −14.9460 22.4302i −0.628784 0.943645i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 4.40717 0.184758 0.0923791 0.995724i \(-0.470553\pi\)
0.0923791 + 0.995724i \(0.470553\pi\)
\(570\) 0 0
\(571\) 23.6590i 0.990098i −0.868865 0.495049i \(-0.835150\pi\)
0.868865 0.495049i \(-0.164850\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 34.5872 + 14.4300i 1.44239 + 0.601772i
\(576\) 0 0
\(577\) 6.56366i 0.273249i 0.990623 + 0.136624i \(0.0436253\pi\)
−0.990623 + 0.136624i \(0.956375\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 4.36542i 0.181108i
\(582\) 0 0
\(583\) 41.3931i 1.71433i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −16.2992 −0.672741 −0.336370 0.941730i \(-0.609199\pi\)
−0.336370 + 0.941730i \(0.609199\pi\)
\(588\) 0 0
\(589\) 4.58868i 0.189073i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 16.3233i 0.670319i 0.942161 + 0.335160i \(0.108790\pi\)
−0.942161 + 0.335160i \(0.891210\pi\)
\(594\) 0 0
\(595\) −2.96395 + 1.97498i −0.121510 + 0.0809663i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 25.5928 1.04569 0.522847 0.852426i \(-0.324870\pi\)
0.522847 + 0.852426i \(0.324870\pi\)
\(600\) 0 0
\(601\) 29.9225 1.22056 0.610282 0.792184i \(-0.291056\pi\)
0.610282 + 0.792184i \(0.291056\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −33.0048 + 21.9923i −1.34184 + 0.894113i
\(606\) 0 0
\(607\) 20.6965i 0.840046i −0.907513 0.420023i \(-0.862022\pi\)
0.907513 0.420023i \(-0.137978\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 5.07131i 0.205163i
\(612\) 0 0
\(613\) 22.6676 0.915537 0.457769 0.889071i \(-0.348649\pi\)
0.457769 + 0.889071i \(0.348649\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 22.1966i 0.893603i 0.894633 + 0.446802i \(0.147437\pi\)
−0.894633 + 0.446802i \(0.852563\pi\)
\(618\) 0 0
\(619\) 16.8204i 0.676070i −0.941133 0.338035i \(-0.890238\pi\)
0.941133 0.338035i \(-0.109762\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 5.66558i 0.226987i
\(624\) 0 0
\(625\) −17.5872 17.7676i −0.703489 0.710706i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 2.29434i 0.0914813i
\(630\) 0 0
\(631\) 44.1205 1.75641 0.878204 0.478285i \(-0.158742\pi\)
0.878204 + 0.478285i \(0.158742\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −5.22441 7.84052i −0.207324 0.311141i
\(636\) 0 0
\(637\) −18.8477 −0.746773
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 1.18566 0.0468307 0.0234154 0.999726i \(-0.492546\pi\)
0.0234154 + 0.999726i \(0.492546\pi\)
\(642\) 0 0
\(643\) 22.5872 0.890754 0.445377 0.895343i \(-0.353070\pi\)
0.445377 + 0.895343i \(0.353070\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 19.7090i 0.774842i 0.921903 + 0.387421i \(0.126634\pi\)
−0.921903 + 0.387421i \(0.873366\pi\)
\(648\) 0 0
\(649\) 36.7368 1.44205
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 44.4585 1.73979 0.869897 0.493234i \(-0.164185\pi\)
0.869897 + 0.493234i \(0.164185\pi\)
\(654\) 0 0
\(655\) 12.7964 + 19.2042i 0.499997 + 0.750369i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 41.5863i 1.61997i 0.586448 + 0.809987i \(0.300526\pi\)
−0.586448 + 0.809987i \(0.699474\pi\)
\(660\) 0 0
\(661\) 12.0060i 0.466978i −0.972359 0.233489i \(-0.924986\pi\)
0.972359 0.233489i \(-0.0750143\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −2.40717 + 1.60398i −0.0933461 + 0.0621997i
\(666\) 0 0
\(667\) −50.5872 −1.95875
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 34.5872 1.33523
\(672\) 0 0
\(673\) 14.5080i 0.559244i 0.960110 + 0.279622i \(0.0902091\pi\)
−0.960110 + 0.279622i \(0.909791\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 43.8600 1.68568 0.842839 0.538166i \(-0.180883\pi\)
0.842839 + 0.538166i \(0.180883\pi\)
\(678\) 0 0
\(679\) −10.5872 −0.406301
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 5.33527 0.204148 0.102074 0.994777i \(-0.467452\pi\)
0.102074 + 0.994777i \(0.467452\pi\)
\(684\) 0 0
\(685\) 18.6468 + 27.9841i 0.712458 + 1.06922i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 22.5872 0.860505
\(690\) 0 0
\(691\) 39.7710i 1.51296i −0.654016 0.756480i \(-0.726917\pi\)
0.654016 0.756480i \(-0.273083\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −11.7424 17.6224i −0.445416 0.668457i
\(696\) 0 0
\(697\) 24.1080i 0.913157i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 27.5015i 1.03872i 0.854556 + 0.519359i \(0.173829\pi\)
−0.854556 + 0.519359i \(0.826171\pi\)
\(702\) 0 0
\(703\) 1.86335i 0.0702775i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −5.55118 −0.208774
\(708\) 0 0
\(709\) 0.111632i 0.00419244i −0.999998 0.00209622i \(-0.999333\pi\)
0.999998 0.00209622i \(-0.000667249\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 19.8387i 0.742966i
\(714\) 0 0
\(715\) −19.4432 29.1794i −0.727135 1.09125i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −10.7064 −0.399281 −0.199640 0.979869i \(-0.563977\pi\)
−0.199640 + 0.979869i \(0.563977\pi\)
\(720\) 0 0
\(721\) 5.37112 0.200031
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 31.1440 + 12.9935i 1.15666 + 0.482565i
\(726\) 0 0
\(727\) 25.6562i 0.951536i −0.879571 0.475768i \(-0.842170\pi\)
0.879571 0.475768i \(-0.157830\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 15.8888i 0.587667i
\(732\) 0 0
\(733\) −30.3684 −1.12168 −0.560842 0.827923i \(-0.689522\pi\)
−0.560842 + 0.827923i \(0.689522\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 39.9007i 1.46976i
\(738\) 0 0
\(739\) 20.1917i 0.742763i 0.928480 + 0.371381i \(0.121116\pi\)
−0.928480 + 0.371381i \(0.878884\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 46.3863i 1.70175i 0.525369 + 0.850875i \(0.323927\pi\)
−0.525369 + 0.850875i \(0.676073\pi\)
\(744\) 0 0
\(745\) 2.21881 + 3.32988i 0.0812911 + 0.121997i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 2.98470i 0.109059i
\(750\) 0 0
\(751\) 27.1261 0.989845 0.494922 0.868937i \(-0.335196\pi\)
0.494922 + 0.868937i \(0.335196\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −19.8116 + 13.2012i −0.721020 + 0.480441i
\(756\) 0 0
\(757\) −45.2549 −1.64482 −0.822408 0.568898i \(-0.807370\pi\)
−0.822408 + 0.568898i \(0.807370\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −16.8864 −0.612133 −0.306067 0.952010i \(-0.599013\pi\)
−0.306067 + 0.952010i \(0.599013\pi\)
\(762\) 0 0
\(763\) −14.8864 −0.538926
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 20.0464i 0.723835i
\(768\) 0 0
\(769\) −16.3297 −0.588863 −0.294431 0.955673i \(-0.595130\pi\)
−0.294431 + 0.955673i \(0.595130\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −41.3144 −1.48598 −0.742989 0.669304i \(-0.766592\pi\)
−0.742989 + 0.669304i \(0.766592\pi\)
\(774\) 0 0
\(775\) −5.09563 + 12.2137i −0.183040 + 0.438729i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 19.5794i 0.701503i
\(780\) 0 0
\(781\) 71.2628i 2.54998i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 12.8864 8.58669i 0.459937 0.306472i
\(786\) 0 0
\(787\) 11.4849 0.409391 0.204696 0.978826i \(-0.434380\pi\)
0.204696 + 0.978826i \(0.434380\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 8.99440 0.319804
\(792\) 0 0
\(793\) 18.8735i 0.670216i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −45.4945 −1.61150 −0.805749 0.592257i \(-0.798237\pi\)
−0.805749 + 0.592257i \(0.798237\pi\)
\(798\) 0 0
\(799\) 3.70079 0.130924
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 3.70079 0.130598
\(804\) 0 0
\(805\) −10.4072 + 6.93466i −0.366805 + 0.244415i
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −36.0721 −1.26823 −0.634114 0.773240i \(-0.718635\pi\)
−0.634114 + 0.773240i \(0.718635\pi\)
\(810\) 0 0
\(811\) 44.5230i 1.56341i 0.623646 + 0.781707i \(0.285651\pi\)
−0.623646 + 0.781707i \(0.714349\pi\)