Properties

Label 5292.2.x.a.881.3
Level $5292$
Weight $2$
Character 5292.881
Analytic conductor $42.257$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 5292 = 2^{2} \cdot 3^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5292.x (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(42.2568327497\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \(x^{16} - 2 x^{15} + 5 x^{14} - 17 x^{13} + 22 x^{12} - 31 x^{11} + 62 x^{10} - 52 x^{9} + 52 x^{8} - 156 x^{7} + 558 x^{6} - 837 x^{5} + 1782 x^{4} - 4131 x^{3} + 3645 x^{2} - 4374 x + 6561\)
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 3^{6} \)
Twist minimal: no (minimal twist has level 252)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 881.3
Root \(-1.61108 - 0.635951i\) of defining polynomial
Character \(\chi\) \(=\) 5292.881
Dual form 5292.2.x.a.4409.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.09150 + 1.89054i) q^{5} +O(q^{10})\) \(q+(-1.09150 + 1.89054i) q^{5} +(-1.26889 + 0.732592i) q^{11} +(2.92752 + 1.69021i) q^{13} +2.64271 q^{17} -7.94221i q^{19} +(-3.47245 - 2.00482i) q^{23} +(0.117249 + 0.203081i) q^{25} +(6.71261 - 3.87553i) q^{29} +(0.612252 + 0.353484i) q^{31} -2.83477 q^{37} +(-3.74173 + 6.48086i) q^{41} +(-1.27112 - 2.20164i) q^{43} +(-6.27538 - 10.8693i) q^{47} +2.79062i q^{53} -3.19850i q^{55} +(6.71650 - 11.6333i) q^{59} +(6.75061 - 3.89747i) q^{61} +(-6.39079 + 3.68972i) q^{65} +(-2.92029 + 5.05809i) q^{67} +11.6854i q^{71} -4.57174i q^{73} +(-4.69189 - 8.12659i) q^{79} +(-1.70847 - 2.95917i) q^{83} +(-2.88452 + 4.99614i) q^{85} +9.23875 q^{89} +(15.0150 + 8.66894i) q^{95} +(6.38394 - 3.68577i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + O(q^{10}) \) \( 16 q - 6 q^{11} - 3 q^{13} + 18 q^{17} + 21 q^{23} - 8 q^{25} - 6 q^{29} + 6 q^{31} - 2 q^{37} + 6 q^{41} - 2 q^{43} - 18 q^{47} - 15 q^{59} + 3 q^{61} - 39 q^{65} - 7 q^{67} - q^{79} + 6 q^{85} + 42 q^{89} + 6 q^{95} - 3 q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/5292\mathbb{Z}\right)^\times\).

\(n\) \(785\) \(1081\) \(2647\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(-1\) \(1\)

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
\(5\) −1.09150 + 1.89054i −0.488134 + 0.845473i −0.999907 0.0136476i \(-0.995656\pi\)
0.511773 + 0.859121i \(0.328989\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −1.26889 + 0.732592i −0.382584 + 0.220885i −0.678942 0.734192i \(-0.737561\pi\)
0.296358 + 0.955077i \(0.404228\pi\)
\(12\) 0 0
\(13\) 2.92752 + 1.69021i 0.811948 + 0.468779i 0.847632 0.530585i \(-0.178028\pi\)
−0.0356837 + 0.999363i \(0.511361\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 2.64271 0.640952 0.320476 0.947257i \(-0.396157\pi\)
0.320476 + 0.947257i \(0.396157\pi\)
\(18\) 0 0
\(19\) 7.94221i 1.82207i −0.412331 0.911034i \(-0.635285\pi\)
0.412331 0.911034i \(-0.364715\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −3.47245 2.00482i −0.724056 0.418034i 0.0921879 0.995742i \(-0.470614\pi\)
−0.816244 + 0.577708i \(0.803947\pi\)
\(24\) 0 0
\(25\) 0.117249 + 0.203081i 0.0234498 + 0.0406163i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 6.71261 3.87553i 1.24650 0.719667i 0.276091 0.961132i \(-0.410961\pi\)
0.970410 + 0.241464i \(0.0776276\pi\)
\(30\) 0 0
\(31\) 0.612252 + 0.353484i 0.109964 + 0.0634876i 0.553973 0.832534i \(-0.313111\pi\)
−0.444009 + 0.896022i \(0.646444\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −2.83477 −0.466033 −0.233016 0.972473i \(-0.574860\pi\)
−0.233016 + 0.972473i \(0.574860\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −3.74173 + 6.48086i −0.584360 + 1.01214i 0.410595 + 0.911818i \(0.365321\pi\)
−0.994955 + 0.100323i \(0.968012\pi\)
\(42\) 0 0
\(43\) −1.27112 2.20164i −0.193844 0.335748i 0.752677 0.658390i \(-0.228762\pi\)
−0.946521 + 0.322642i \(0.895429\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −6.27538 10.8693i −0.915358 1.58545i −0.806376 0.591403i \(-0.798574\pi\)
−0.108983 0.994044i \(-0.534759\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 2.79062i 0.383321i 0.981461 + 0.191661i \(0.0613873\pi\)
−0.981461 + 0.191661i \(0.938613\pi\)
\(54\) 0 0
\(55\) 3.19850i 0.431286i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 6.71650 11.6333i 0.874414 1.51453i 0.0170287 0.999855i \(-0.494579\pi\)
0.857385 0.514675i \(-0.172087\pi\)
\(60\) 0 0
\(61\) 6.75061 3.89747i 0.864327 0.499020i −0.00113176 0.999999i \(-0.500360\pi\)
0.865459 + 0.500980i \(0.167027\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −6.39079 + 3.68972i −0.792680 + 0.457654i
\(66\) 0 0
\(67\) −2.92029 + 5.05809i −0.356770 + 0.617945i −0.987419 0.158124i \(-0.949455\pi\)
0.630649 + 0.776068i \(0.282789\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 11.6854i 1.38680i 0.720554 + 0.693398i \(0.243887\pi\)
−0.720554 + 0.693398i \(0.756113\pi\)
\(72\) 0 0
\(73\) 4.57174i 0.535082i −0.963547 0.267541i \(-0.913789\pi\)
0.963547 0.267541i \(-0.0862110\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) −4.69189 8.12659i −0.527879 0.914312i −0.999472 0.0324963i \(-0.989654\pi\)
0.471593 0.881816i \(-0.343679\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −1.70847 2.95917i −0.187529 0.324811i 0.756896 0.653535i \(-0.226715\pi\)
−0.944426 + 0.328724i \(0.893381\pi\)
\(84\) 0 0
\(85\) −2.88452 + 4.99614i −0.312871 + 0.541908i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 9.23875 0.979306 0.489653 0.871918i \(-0.337124\pi\)
0.489653 + 0.871918i \(0.337124\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 15.0150 + 8.66894i 1.54051 + 0.889414i
\(96\) 0 0
\(97\) 6.38394 3.68577i 0.648191 0.374233i −0.139572 0.990212i \(-0.544573\pi\)
0.787763 + 0.615979i \(0.211239\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −3.96357 6.86510i −0.394390 0.683103i 0.598633 0.801023i \(-0.295711\pi\)
−0.993023 + 0.117920i \(0.962377\pi\)
\(102\) 0 0
\(103\) 3.26825 + 1.88693i 0.322031 + 0.185924i 0.652297 0.757963i \(-0.273805\pi\)
−0.330267 + 0.943888i \(0.607139\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 7.94712i 0.768277i −0.923275 0.384138i \(-0.874499\pi\)
0.923275 0.384138i \(-0.125501\pi\)
\(108\) 0 0
\(109\) −1.01028 −0.0967677 −0.0483838 0.998829i \(-0.515407\pi\)
−0.0483838 + 0.998829i \(0.515407\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 10.5557 + 6.09431i 0.992992 + 0.573304i 0.906167 0.422919i \(-0.138995\pi\)
0.0868250 + 0.996224i \(0.472328\pi\)
\(114\) 0 0
\(115\) 7.58037 4.37653i 0.706873 0.408113i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −4.42662 + 7.66713i −0.402420 + 0.697012i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −11.4269 −1.02206
\(126\) 0 0
\(127\) 6.79350 0.602826 0.301413 0.953494i \(-0.402542\pi\)
0.301413 + 0.953494i \(0.402542\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −6.86790 + 11.8956i −0.600051 + 1.03932i 0.392761 + 0.919640i \(0.371520\pi\)
−0.992813 + 0.119679i \(0.961813\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 17.4028 10.0475i 1.48682 0.858416i 0.486933 0.873439i \(-0.338116\pi\)
0.999887 + 0.0150235i \(0.00478229\pi\)
\(138\) 0 0
\(139\) 8.51403 + 4.91558i 0.722151 + 0.416934i 0.815544 0.578695i \(-0.196438\pi\)
−0.0933930 + 0.995629i \(0.529771\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −4.95292 −0.414184
\(144\) 0 0
\(145\) 16.9206i 1.40518i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 17.3512 + 10.0177i 1.42146 + 0.820682i 0.996424 0.0844939i \(-0.0269274\pi\)
0.425038 + 0.905175i \(0.360261\pi\)
\(150\) 0 0
\(151\) 11.1168 + 19.2549i 0.904675 + 1.56694i 0.821353 + 0.570420i \(0.193220\pi\)
0.0833218 + 0.996523i \(0.473447\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −1.33655 + 0.771657i −0.107354 + 0.0619810i
\(156\) 0 0
\(157\) 6.95305 + 4.01435i 0.554914 + 0.320380i 0.751102 0.660187i \(-0.229523\pi\)
−0.196188 + 0.980566i \(0.562856\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 12.4521 0.975323 0.487661 0.873033i \(-0.337850\pi\)
0.487661 + 0.873033i \(0.337850\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 9.85984 17.0777i 0.762978 1.32152i −0.178332 0.983970i \(-0.557070\pi\)
0.941309 0.337546i \(-0.109597\pi\)
\(168\) 0 0
\(169\) −0.786412 1.36211i −0.0604933 0.104777i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 0.913733 + 1.58263i 0.0694699 + 0.120325i 0.898668 0.438629i \(-0.144536\pi\)
−0.829198 + 0.558955i \(0.811203\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 13.9929i 1.04588i −0.852370 0.522939i \(-0.824836\pi\)
0.852370 0.522939i \(-0.175164\pi\)
\(180\) 0 0
\(181\) 16.3594i 1.21599i −0.793942 0.607994i \(-0.791975\pi\)
0.793942 0.607994i \(-0.208025\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 3.09415 5.35923i 0.227486 0.394018i
\(186\) 0 0
\(187\) −3.35330 + 1.93603i −0.245218 + 0.141577i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −11.8326 + 6.83153i −0.856173 + 0.494312i −0.862729 0.505667i \(-0.831247\pi\)
0.00655557 + 0.999979i \(0.497913\pi\)
\(192\) 0 0
\(193\) 2.18885 3.79119i 0.157557 0.272896i −0.776430 0.630203i \(-0.782972\pi\)
0.933987 + 0.357307i \(0.116305\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 1.00603i 0.0716767i −0.999358 0.0358384i \(-0.988590\pi\)
0.999358 0.0358384i \(-0.0114101\pi\)
\(198\) 0 0
\(199\) 6.55453i 0.464638i −0.972640 0.232319i \(-0.925369\pi\)
0.972640 0.232319i \(-0.0746313\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) −8.16820 14.1477i −0.570492 0.988121i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 5.81840 + 10.0778i 0.402467 + 0.697094i
\(210\) 0 0
\(211\) −9.11202 + 15.7825i −0.627297 + 1.08651i 0.360794 + 0.932645i \(0.382506\pi\)
−0.988092 + 0.153866i \(0.950828\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 5.54972 0.378487
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 7.73660 + 4.46673i 0.520420 + 0.300464i
\(222\) 0 0
\(223\) −8.71705 + 5.03279i −0.583737 + 0.337021i −0.762617 0.646850i \(-0.776086\pi\)
0.178880 + 0.983871i \(0.442753\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −9.94372 17.2230i −0.659988 1.14313i −0.980618 0.195928i \(-0.937228\pi\)
0.320630 0.947204i \(-0.396105\pi\)
\(228\) 0 0
\(229\) 15.3854 + 8.88275i 1.01669 + 0.586988i 0.913145 0.407636i \(-0.133647\pi\)
0.103549 + 0.994624i \(0.466980\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 16.0592i 1.05208i −0.850461 0.526038i \(-0.823677\pi\)
0.850461 0.526038i \(-0.176323\pi\)
\(234\) 0 0
\(235\) 27.3983 1.78727
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 7.11117 + 4.10564i 0.459983 + 0.265572i 0.712037 0.702142i \(-0.247773\pi\)
−0.252054 + 0.967713i \(0.581106\pi\)
\(240\) 0 0
\(241\) 24.6614 14.2382i 1.58858 0.917166i 0.595037 0.803698i \(-0.297137\pi\)
0.993542 0.113468i \(-0.0361959\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 13.4240 23.2510i 0.854147 1.47943i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −0.656343 −0.0414280 −0.0207140 0.999785i \(-0.506594\pi\)
−0.0207140 + 0.999785i \(0.506594\pi\)
\(252\) 0 0
\(253\) 5.87486 0.369349
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 3.82042 6.61716i 0.238311 0.412767i −0.721918 0.691978i \(-0.756739\pi\)
0.960230 + 0.279211i \(0.0900728\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −5.73888 + 3.31334i −0.353874 + 0.204310i −0.666390 0.745603i \(-0.732162\pi\)
0.312516 + 0.949913i \(0.398828\pi\)
\(264\) 0 0
\(265\) −5.27577 3.04597i −0.324088 0.187112i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 8.76693 0.534529 0.267265 0.963623i \(-0.413880\pi\)
0.267265 + 0.963623i \(0.413880\pi\)
\(270\) 0 0
\(271\) 16.4669i 1.00029i −0.865941 0.500147i \(-0.833279\pi\)
0.865941 0.500147i \(-0.166721\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −0.297551 0.171791i −0.0179430 0.0103594i
\(276\) 0 0
\(277\) 8.88732 + 15.3933i 0.533987 + 0.924893i 0.999212 + 0.0397001i \(0.0126402\pi\)
−0.465225 + 0.885193i \(0.654026\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 14.0252 8.09748i 0.836676 0.483055i −0.0194568 0.999811i \(-0.506194\pi\)
0.856133 + 0.516755i \(0.172860\pi\)
\(282\) 0 0
\(283\) 24.5717 + 14.1865i 1.46063 + 0.843298i 0.999041 0.0437937i \(-0.0139444\pi\)
0.461594 + 0.887091i \(0.347278\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −10.0161 −0.589181
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 4.38260 7.59088i 0.256034 0.443464i −0.709142 0.705066i \(-0.750917\pi\)
0.965176 + 0.261602i \(0.0842507\pi\)
\(294\) 0 0
\(295\) 14.6621 + 25.3956i 0.853663 + 1.47859i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −6.77711 11.7383i −0.391931 0.678844i
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 17.0164i 0.974354i
\(306\) 0 0
\(307\) 12.8497i 0.733372i 0.930345 + 0.366686i \(0.119508\pi\)
−0.930345 + 0.366686i \(0.880492\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −3.29671 + 5.71007i −0.186939 + 0.323789i −0.944228 0.329291i \(-0.893190\pi\)
0.757289 + 0.653080i \(0.226523\pi\)
\(312\) 0 0
\(313\) −2.95711 + 1.70729i −0.167146 + 0.0965018i −0.581239 0.813733i \(-0.697432\pi\)
0.414093 + 0.910234i \(0.364099\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −27.8003 + 16.0505i −1.56142 + 0.901485i −0.564304 + 0.825567i \(0.690855\pi\)
−0.997114 + 0.0759182i \(0.975811\pi\)
\(318\) 0 0
\(319\) −5.67836 + 9.83521i −0.317927 + 0.550666i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 20.9890i 1.16786i
\(324\) 0 0
\(325\) 0.792700i 0.0439711i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 14.4416 + 25.0137i 0.793784 + 1.37487i 0.923608 + 0.383338i \(0.125225\pi\)
−0.129824 + 0.991537i \(0.541441\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −6.37501 11.0418i −0.348304 0.603280i
\(336\) 0 0
\(337\) 4.82568 8.35833i 0.262872 0.455307i −0.704132 0.710069i \(-0.748664\pi\)
0.967004 + 0.254762i \(0.0819971\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −1.03584 −0.0560938
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 10.6758 + 6.16367i 0.573106 + 0.330883i 0.758389 0.651802i \(-0.225987\pi\)
−0.185283 + 0.982685i \(0.559320\pi\)
\(348\) 0 0
\(349\) −10.2211 + 5.90115i −0.547123 + 0.315881i −0.747961 0.663743i \(-0.768967\pi\)
0.200838 + 0.979624i \(0.435634\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −6.59855 11.4290i −0.351205 0.608305i 0.635256 0.772302i \(-0.280895\pi\)
−0.986461 + 0.163997i \(0.947561\pi\)
\(354\) 0 0
\(355\) −22.0916 12.7546i −1.17250 0.676943i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 6.03311i 0.318416i −0.987245 0.159208i \(-0.949106\pi\)
0.987245 0.159208i \(-0.0508940\pi\)
\(360\) 0 0
\(361\) −44.0787 −2.31993
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 8.64304 + 4.99006i 0.452397 + 0.261192i
\(366\) 0 0
\(367\) −14.8755 + 8.58836i −0.776494 + 0.448309i −0.835186 0.549967i \(-0.814640\pi\)
0.0586924 + 0.998276i \(0.481307\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) −2.35902 + 4.08595i −0.122146 + 0.211562i −0.920614 0.390475i \(-0.872311\pi\)
0.798468 + 0.602037i \(0.205644\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 26.2017 1.34946
\(378\) 0 0
\(379\) 9.34015 0.479771 0.239886 0.970801i \(-0.422890\pi\)
0.239886 + 0.970801i \(0.422890\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −2.85036 + 4.93696i −0.145646 + 0.252267i −0.929614 0.368535i \(-0.879860\pi\)
0.783968 + 0.620802i \(0.213193\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 6.63671 3.83171i 0.336495 0.194275i −0.322226 0.946663i \(-0.604431\pi\)
0.658721 + 0.752387i \(0.271098\pi\)
\(390\) 0 0
\(391\) −9.17668 5.29816i −0.464085 0.267939i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 20.4848 1.03070
\(396\) 0 0
\(397\) 1.30262i 0.0653766i 0.999466 + 0.0326883i \(0.0104069\pi\)
−0.999466 + 0.0326883i \(0.989593\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −8.18778 4.72722i −0.408878 0.236066i 0.281429 0.959582i \(-0.409191\pi\)
−0.690308 + 0.723516i \(0.742525\pi\)
\(402\) 0 0
\(403\) 1.19492 + 2.06966i 0.0595233 + 0.103097i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 3.59700 2.07673i 0.178296 0.102940i
\(408\) 0 0
\(409\) −16.5182 9.53678i −0.816771 0.471563i 0.0325304 0.999471i \(-0.489643\pi\)
−0.849302 + 0.527908i \(0.822977\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 7.45921 0.366158
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 4.20003 7.27466i 0.205185 0.355390i −0.745007 0.667057i \(-0.767554\pi\)
0.950192 + 0.311666i \(0.100887\pi\)
\(420\) 0 0
\(421\) 19.7178 + 34.1522i 0.960985 + 1.66448i 0.720035 + 0.693938i \(0.244126\pi\)
0.240951 + 0.970537i \(0.422541\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 0.309855 + 0.536685i 0.0150302 + 0.0260331i
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 11.9327i 0.574777i −0.957814 0.287389i \(-0.907213\pi\)
0.957814 0.287389i \(-0.0927871\pi\)
\(432\) 0 0
\(433\) 12.2121i 0.586875i 0.955978 + 0.293437i \(0.0947992\pi\)
−0.955978 + 0.293437i \(0.905201\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −15.9227 + 27.5789i −0.761686 + 1.31928i
\(438\) 0 0
\(439\) 14.4639 8.35076i 0.690326 0.398560i −0.113408 0.993548i \(-0.536177\pi\)
0.803734 + 0.594989i \(0.202843\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 26.2403 15.1499i 1.24672 0.719791i 0.276262 0.961082i \(-0.410904\pi\)
0.970453 + 0.241291i \(0.0775708\pi\)
\(444\) 0 0
\(445\) −10.0841 + 17.4662i −0.478033 + 0.827977i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 30.1253i 1.42170i −0.703343 0.710851i \(-0.748310\pi\)
0.703343 0.710851i \(-0.251690\pi\)
\(450\) 0 0
\(451\) 10.9646i 0.516305i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −12.6159 21.8513i −0.590146 1.02216i −0.994212 0.107433i \(-0.965737\pi\)
0.404067 0.914730i \(-0.367596\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 12.3174 + 21.3344i 0.573680 + 0.993643i 0.996184 + 0.0872820i \(0.0278181\pi\)
−0.422503 + 0.906361i \(0.638849\pi\)
\(462\) 0 0
\(463\) −6.33215 + 10.9676i −0.294280 + 0.509708i −0.974817 0.223006i \(-0.928413\pi\)
0.680537 + 0.732713i \(0.261746\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 20.9445 0.969198 0.484599 0.874736i \(-0.338966\pi\)
0.484599 + 0.874736i \(0.338966\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 3.22581 + 1.86242i 0.148323 + 0.0856344i
\(474\) 0 0
\(475\) 1.61291 0.931217i 0.0740056 0.0427271i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −15.8852 27.5141i −0.725816 1.25715i −0.958637 0.284630i \(-0.908129\pi\)
0.232822 0.972519i \(-0.425204\pi\)
\(480\) 0 0
\(481\) −8.29884 4.79134i −0.378394 0.218466i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 16.0921i 0.730705i
\(486\) 0 0
\(487\) 35.5642 1.61157 0.805784 0.592210i \(-0.201744\pi\)
0.805784 + 0.592210i \(0.201744\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −2.75734 1.59195i −0.124437 0.0718437i 0.436490 0.899709i \(-0.356222\pi\)
−0.560926 + 0.827866i \(0.689555\pi\)
\(492\) 0 0
\(493\) 17.7395 10.2419i 0.798947 0.461272i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) −16.0214 + 27.7498i −0.717215 + 1.24225i 0.244884 + 0.969552i \(0.421250\pi\)
−0.962099 + 0.272700i \(0.912083\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −11.6608 −0.519930 −0.259965 0.965618i \(-0.583711\pi\)
−0.259965 + 0.965618i \(0.583711\pi\)
\(504\) 0 0
\(505\) 17.3050 0.770061
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 13.4427 23.2834i 0.595836 1.03202i −0.397592 0.917562i \(-0.630154\pi\)
0.993428 0.114457i \(-0.0365127\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −7.13461 + 4.11917i −0.314388 + 0.181512i
\(516\) 0 0
\(517\) 15.9255 + 9.19459i 0.700402 + 0.404378i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 34.0771 1.49294 0.746471 0.665418i \(-0.231746\pi\)
0.746471 + 0.665418i \(0.231746\pi\)
\(522\) 0 0
\(523\) 5.43867i 0.237816i −0.992905 0.118908i \(-0.962061\pi\)
0.992905 0.118908i \(-0.0379394\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 1.61801 + 0.934157i 0.0704815 + 0.0406925i
\(528\) 0 0
\(529\) −3.46140 5.99532i −0.150496 0.260666i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −21.9080 + 12.6486i −0.948940 + 0.547871i
\(534\) 0 0
\(535\) 15.0243 + 8.67429i 0.649558 + 0.375022i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) −23.6658 −1.01747 −0.508737 0.860922i \(-0.669887\pi\)
−0.508737 + 0.860922i \(0.669887\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 1.10273 1.90998i 0.0472356 0.0818145i
\(546\) 0 0
\(547\) −12.0824 20.9273i −0.516606 0.894788i −0.999814 0.0192822i \(-0.993862\pi\)
0.483208 0.875505i \(-0.339471\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −30.7803 53.3130i −1.31128 2.27121i
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 8.50223i 0.360251i 0.983644 + 0.180126i \(0.0576504\pi\)
−0.983644 + 0.180126i \(0.942350\pi\)
\(558\) 0 0
\(559\) 8.59381i 0.363480i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 0.473776 0.820605i 0.0199673 0.0345844i −0.855869 0.517192i \(-0.826977\pi\)
0.875836 + 0.482608i \(0.160310\pi\)
\(564\) 0 0
\(565\) −23.0430 + 13.3039i −0.969427 + 0.559699i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −15.7859 + 9.11401i −0.661781 + 0.382079i −0.792955 0.609280i \(-0.791458\pi\)
0.131175 + 0.991359i \(0.458125\pi\)
\(570\) 0 0
\(571\) 6.12121 10.6023i 0.256165 0.443691i −0.709046 0.705162i \(-0.750874\pi\)
0.965211 + 0.261471i \(0.0842077\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0.940253i 0.0392112i
\(576\) 0 0
\(577\) 11.8357i 0.492726i −0.969178 0.246363i \(-0.920764\pi\)
0.969178 0.246363i \(-0.0792355\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) −2.04439 3.54098i −0.0846699 0.146653i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −3.57681 6.19521i −0.147631 0.255704i 0.782721 0.622373i \(-0.213831\pi\)
−0.930351 + 0.366669i \(0.880498\pi\)
\(588\) 0 0
\(589\) 2.80745 4.86264i 0.115679 0.200362i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 26.9622 1.10721 0.553603 0.832781i \(-0.313252\pi\)
0.553603 + 0.832781i \(0.313252\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −30.5223 17.6221i −1.24711 0.720018i −0.276576 0.960992i \(-0.589200\pi\)
−0.970532 + 0.240974i \(0.922533\pi\)
\(600\) 0 0
\(601\) 3.39266 1.95875i 0.138389 0.0798991i −0.429207 0.903206i \(-0.641207\pi\)
0.567596 + 0.823307i \(0.307874\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −9.66332 16.7374i −0.392870 0.680470i
\(606\) 0 0
\(607\) 12.5377 + 7.23862i 0.508888 + 0.293807i 0.732376 0.680900i \(-0.238411\pi\)
−0.223488 + 0.974707i \(0.571744\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 42.4267i 1.71640i
\(612\) 0 0
\(613\) 13.0352 0.526488 0.263244 0.964729i \(-0.415208\pi\)
0.263244 + 0.964729i \(0.415208\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 3.14491 + 1.81571i 0.126609 + 0.0730979i 0.561967 0.827160i \(-0.310045\pi\)
−0.435358 + 0.900258i \(0.643378\pi\)
\(618\) 0 0
\(619\) 14.2737 8.24091i 0.573708 0.331230i −0.184921 0.982753i \(-0.559203\pi\)
0.758629 + 0.651523i \(0.225870\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 11.8863 20.5876i 0.475450 0.823504i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −7.49147 −0.298704
\(630\) 0 0
\(631\) −34.8383 −1.38689 −0.693446 0.720508i \(-0.743909\pi\)
−0.693446 + 0.720508i \(0.743909\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −7.41512 + 12.8434i −0.294260 + 0.509673i
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 7.25538 4.18889i 0.286570 0.165451i −0.349824 0.936815i \(-0.613759\pi\)
0.636394 + 0.771364i \(0.280425\pi\)
\(642\) 0 0
\(643\) −18.0021 10.3935i −0.709934 0.409881i 0.101103 0.994876i \(-0.467763\pi\)
−0.811037 + 0.584995i \(0.801096\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 9.49540 0.373303 0.186651 0.982426i \(-0.440237\pi\)
0.186651 + 0.982426i \(0.440237\pi\)
\(648\) 0 0
\(649\) 19.6818i 0.772579i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −6.64747 3.83792i −0.260136 0.150189i 0.364261 0.931297i \(-0.381322\pi\)
−0.624396 + 0.781108i \(0.714655\pi\)
\(654\) 0 0
\(655\) −14.9927 25.9680i −0.585811 1.01465i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −38.0493 + 21.9678i −1.48219 + 0.855743i −0.999796 0.0202102i \(-0.993566\pi\)
−0.482395 + 0.875954i \(0.660233\pi\)
\(660\) 0 0
\(661\) −22.1649 12.7969i −0.862115 0.497742i 0.00260513 0.999997i \(-0.499171\pi\)
−0.864720 + 0.502254i \(0.832504\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −31.0789 −1.20338
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −5.71051 + 9.89089i −0.220452 + 0.381834i
\(672\) 0 0
\(673\) −7.64671 13.2445i −0.294759 0.510538i 0.680170 0.733055i \(-0.261906\pi\)
−0.974929 + 0.222517i \(0.928573\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 22.6459 + 39.2238i 0.870352 + 1.50749i 0.861633 + 0.507532i \(0.169442\pi\)
0.00871898 + 0.999962i \(0.497225\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 27.8157i 1.06434i −0.846638 0.532169i \(-0.821377\pi\)
0.846638 0.532169i \(-0.178623\pi\)
\(684\) 0 0
\(685\) 43.8674i 1.67609i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −4.71672 + 8.16961i −0.179693 + 0.311237i
\(690\) 0 0
\(691\) 14.1115 8.14729i 0.536828 0.309938i −0.206965 0.978348i \(-0.566359\pi\)
0.743792 + 0.668411i \(0.233025\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −18.5862 + 10.7307i −0.705013 + 0.407040i
\(696\) 0 0
\(697\) −9.88831 + 17.1271i −0.374546 + 0.648733i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 0.393403i 0.0148586i 0.999972 + 0.00742932i \(0.00236485\pi\)
−0.999972 + 0.00742932i \(0.997635\pi\)
\(702\) 0 0
\(703\) 22.5143i 0.849143i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 16.3183 + 28.2641i 0.612846 + 1.06148i 0.990758 + 0.135639i \(0.0433087\pi\)
−0.377912 + 0.925841i \(0.623358\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −1.41734 2.45491i −0.0530799 0.0919372i
\(714\) 0 0
\(715\) 5.40612 9.36368i 0.202178 0.350182i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 0.213207 0.00795130 0.00397565 0.999992i \(-0.498735\pi\)
0.00397565 + 0.999992i \(0.498735\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 1.57409 + 0.908804i 0.0584604 + 0.0337521i
\(726\) 0 0
\(727\) 31.8208 18.3717i 1.18017 0.681370i 0.224114 0.974563i \(-0.428051\pi\)
0.956053 + 0.293193i \(0.0947180\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −3.35920 5.81831i −0.124245 0.215198i
\(732\) 0 0
\(733\) −9.41829 5.43765i −0.347873 0.200844i 0.315875 0.948801i \(-0.397702\pi\)
−0.663748 + 0.747956i \(0.731035\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 8.55753i 0.315221i
\(738\) 0 0
\(739\) −13.8256 −0.508584 −0.254292 0.967127i \(-0.581842\pi\)
−0.254292 + 0.967127i \(0.581842\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 15.8751 + 9.16552i 0.582403 + 0.336250i 0.762088 0.647474i \(-0.224175\pi\)
−0.179685 + 0.983724i \(0.557508\pi\)
\(744\) 0 0
\(745\) −37.8776 + 21.8687i −1.38773 + 0.801206i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 9.97084 17.2700i 0.363841 0.630191i −0.624748 0.780826i \(-0.714798\pi\)
0.988589 + 0.150635i \(0.0481318\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −48.5362 −1.76641
\(756\) 0 0
\(757\) −46.9292 −1.70567 −0.852836 0.522178i \(-0.825119\pi\)
−0.852836 + 0.522178i \(0.825119\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −26.7769 + 46.3789i −0.970661 + 1.68123i −0.277093 + 0.960843i \(0.589371\pi\)
−0.693568 + 0.720391i \(0.743962\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 39.3254 22.7045i 1.41996 0.819813i
\(768\) 0 0
\(769\) −34.7306 20.0517i −1.25242 0.723085i −0.280830 0.959758i \(-0.590610\pi\)
−0.971589 + 0.236673i \(0.923943\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −15.6475 −0.562801 −0.281401 0.959590i \(-0.590799\pi\)
−0.281401 + 0.959590i \(0.590799\pi\)
\(774\) 0 0
\(775\) 0.165783i 0.00595509i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 51.4724 + 29.7176i 1.84419 + 1.06474i
\(780\) 0 0
\(781\) −8.56060 14.8274i −0.306322 0.530566i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −15.1785 + 8.76333i −0.541745 + 0.312777i
\(786\) 0 0
\(787\) −39.9920 23.0894i −1.42556 0.823048i −0.428795 0.903402i \(-0.641062\pi\)
−0.996766 + 0.0803536i \(0.974395\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 26.3501 0.935719
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 16.9388 29.3388i 0.600002 1.03923i −0.392818 0.919616i \(-0.628500\pi\)
0.992820 0.119618i \(-0.0381669\pi\)
\(798\) 0 0
\(799\) −16.5840 28.7244i −0.586701 1.01620i
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 3.34922 + 5.80102i 0.118191 + 0.204714i
\(804\) 0 0
\(805\) 0 0
\(806\)