Properties

Label 5292.2.x.a.4409.7
Level $5292$
Weight $2$
Character 5292.4409
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 4409.7
Root \(1.68042 + 0.419752i\) of defining polynomial
Character \(\chi\) \(=\) 5292.4409
Dual form 5292.2.x.a.881.7

$q$-expansion

\(f(q)\) \(=\) \(q+(1.48494 + 2.57199i) q^{5} +O(q^{10})\) \(q+(1.48494 + 2.57199i) q^{5} +(-4.09466 - 2.36406i) q^{11} +(-3.54045 + 2.04408i) q^{13} -1.67056 q^{17} -4.91183i q^{19} +(4.25297 - 2.45545i) q^{23} +(-1.91009 + 3.30837i) q^{25} +(-0.238557 - 0.137731i) q^{29} +(-1.38847 + 0.801636i) q^{31} +3.39362 q^{37} +(3.55632 + 6.15972i) q^{41} +(5.22930 - 9.05742i) q^{43} +(-5.49885 + 9.52430i) q^{47} +0.816814i q^{53} -14.0419i q^{55} +(1.37428 + 2.38032i) q^{59} +(-6.23807 - 3.60155i) q^{61} +(-10.5147 - 6.07067i) q^{65} +(-5.80513 - 10.0548i) q^{67} -10.4406i q^{71} -15.7608i q^{73} +(6.15163 - 10.6549i) q^{79} +(4.03981 - 6.99715i) q^{83} +(-2.48067 - 4.29665i) q^{85} +9.21744 q^{89} +(12.6332 - 7.29377i) q^{95} +(7.00772 + 4.04591i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + O(q^{10}) \) \( 16 q - 6 q^{11} - 3 q^{13} + 18 q^{17} + 21 q^{23} - 8 q^{25} - 6 q^{29} + 6 q^{31} - 2 q^{37} + 6 q^{41} - 2 q^{43} - 18 q^{47} - 15 q^{59} + 3 q^{61} - 39 q^{65} - 7 q^{67} - q^{79} + 6 q^{85} + 42 q^{89} + 6 q^{95} - 3 q^{97} + O(q^{100}) \)

Character values

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

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

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
\(5\) 1.48494 + 2.57199i 0.664085 + 1.15023i 0.979532 + 0.201286i \(0.0645121\pi\)
−0.315447 + 0.948943i \(0.602155\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −4.09466 2.36406i −1.23459 0.712790i −0.266605 0.963806i \(-0.585902\pi\)
−0.967983 + 0.251016i \(0.919235\pi\)
\(12\) 0 0
\(13\) −3.54045 + 2.04408i −0.981945 + 0.566926i −0.902857 0.429942i \(-0.858534\pi\)
−0.0790880 + 0.996868i \(0.525201\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −1.67056 −0.405169 −0.202585 0.979265i \(-0.564934\pi\)
−0.202585 + 0.979265i \(0.564934\pi\)
\(18\) 0 0
\(19\) 4.91183i 1.12685i −0.826167 0.563426i \(-0.809483\pi\)
0.826167 0.563426i \(-0.190517\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 4.25297 2.45545i 0.886805 0.511997i 0.0139086 0.999903i \(-0.495573\pi\)
0.872896 + 0.487906i \(0.162239\pi\)
\(24\) 0 0
\(25\) −1.91009 + 3.30837i −0.382018 + 0.661675i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −0.238557 0.137731i −0.0442989 0.0255760i 0.477687 0.878530i \(-0.341475\pi\)
−0.521986 + 0.852954i \(0.674809\pi\)
\(30\) 0 0
\(31\) −1.38847 + 0.801636i −0.249377 + 0.143978i −0.619479 0.785013i \(-0.712656\pi\)
0.370102 + 0.928991i \(0.379323\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 3.39362 0.557907 0.278954 0.960305i \(-0.410012\pi\)
0.278954 + 0.960305i \(0.410012\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 3.55632 + 6.15972i 0.555404 + 0.961987i 0.997872 + 0.0652031i \(0.0207695\pi\)
−0.442468 + 0.896784i \(0.645897\pi\)
\(42\) 0 0
\(43\) 5.22930 9.05742i 0.797461 1.38124i −0.123804 0.992307i \(-0.539509\pi\)
0.921265 0.388936i \(-0.127157\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −5.49885 + 9.52430i −0.802090 + 1.38926i 0.116148 + 0.993232i \(0.462945\pi\)
−0.918238 + 0.396029i \(0.870388\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 0.816814i 0.112198i 0.998425 + 0.0560990i \(0.0178662\pi\)
−0.998425 + 0.0560990i \(0.982134\pi\)
\(54\) 0 0
\(55\) 14.0419i 1.89341i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 1.37428 + 2.38032i 0.178916 + 0.309891i 0.941509 0.336986i \(-0.109408\pi\)
−0.762594 + 0.646878i \(0.776074\pi\)
\(60\) 0 0
\(61\) −6.23807 3.60155i −0.798703 0.461131i 0.0443147 0.999018i \(-0.485890\pi\)
−0.843017 + 0.537886i \(0.819223\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −10.5147 6.07067i −1.30419 0.752974i
\(66\) 0 0
\(67\) −5.80513 10.0548i −0.709210 1.22839i −0.965151 0.261695i \(-0.915719\pi\)
0.255941 0.966692i \(-0.417615\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 10.4406i 1.23907i −0.784968 0.619537i \(-0.787320\pi\)
0.784968 0.619537i \(-0.212680\pi\)
\(72\) 0 0
\(73\) 15.7608i 1.84467i −0.386395 0.922334i \(-0.626280\pi\)
0.386395 0.922334i \(-0.373720\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 6.15163 10.6549i 0.692112 1.19877i −0.279032 0.960282i \(-0.590014\pi\)
0.971145 0.238492i \(-0.0766530\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 4.03981 6.99715i 0.443426 0.768037i −0.554515 0.832174i \(-0.687096\pi\)
0.997941 + 0.0641368i \(0.0204294\pi\)
\(84\) 0 0
\(85\) −2.48067 4.29665i −0.269067 0.466037i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 9.21744 0.977047 0.488523 0.872551i \(-0.337536\pi\)
0.488523 + 0.872551i \(0.337536\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 12.6332 7.29377i 1.29614 0.748325i
\(96\) 0 0
\(97\) 7.00772 + 4.04591i 0.711527 + 0.410800i 0.811626 0.584177i \(-0.198583\pi\)
−0.100099 + 0.994977i \(0.531916\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 3.65365 6.32831i 0.363552 0.629690i −0.624991 0.780632i \(-0.714897\pi\)
0.988543 + 0.150942i \(0.0482307\pi\)
\(102\) 0 0
\(103\) 6.08409 3.51265i 0.599483 0.346112i −0.169355 0.985555i \(-0.554168\pi\)
0.768838 + 0.639443i \(0.220835\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 14.1588i 1.36878i 0.729117 + 0.684389i \(0.239931\pi\)
−0.729117 + 0.684389i \(0.760069\pi\)
\(108\) 0 0
\(109\) 5.64405 0.540602 0.270301 0.962776i \(-0.412877\pi\)
0.270301 + 0.962776i \(0.412877\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −11.6411 + 6.72099i −1.09510 + 0.632258i −0.934930 0.354831i \(-0.884538\pi\)
−0.160172 + 0.987089i \(0.551205\pi\)
\(114\) 0 0
\(115\) 12.6308 + 7.29239i 1.17783 + 0.680019i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 5.67752 + 9.83375i 0.516138 + 0.893977i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 3.50392 0.313400
\(126\) 0 0
\(127\) −12.7730 −1.13342 −0.566712 0.823916i \(-0.691785\pi\)
−0.566712 + 0.823916i \(0.691785\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −6.70890 11.6202i −0.586159 1.01526i −0.994730 0.102531i \(-0.967306\pi\)
0.408570 0.912727i \(-0.366027\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −7.79449 4.50015i −0.665928 0.384474i 0.128604 0.991696i \(-0.458950\pi\)
−0.794532 + 0.607222i \(0.792284\pi\)
\(138\) 0 0
\(139\) 1.54902 0.894326i 0.131386 0.0758557i −0.432866 0.901458i \(-0.642498\pi\)
0.564252 + 0.825602i \(0.309164\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 19.3293 1.61640
\(144\) 0 0
\(145\) 0.818088i 0.0679385i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −11.1779 + 6.45358i −0.915732 + 0.528698i −0.882271 0.470742i \(-0.843986\pi\)
−0.0334609 + 0.999440i \(0.510653\pi\)
\(150\) 0 0
\(151\) 6.48364 11.2300i 0.527631 0.913884i −0.471850 0.881679i \(-0.656414\pi\)
0.999481 0.0322054i \(-0.0102531\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −4.12360 2.38076i −0.331216 0.191227i
\(156\) 0 0
\(157\) 14.8720 8.58638i 1.18692 0.685268i 0.229314 0.973353i \(-0.426352\pi\)
0.957605 + 0.288085i \(0.0930185\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) −5.06214 −0.396497 −0.198249 0.980152i \(-0.563525\pi\)
−0.198249 + 0.980152i \(0.563525\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 5.79673 + 10.0402i 0.448564 + 0.776936i 0.998293 0.0584072i \(-0.0186022\pi\)
−0.549729 + 0.835343i \(0.685269\pi\)
\(168\) 0 0
\(169\) 1.85653 3.21561i 0.142810 0.247354i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 3.13346 5.42730i 0.238232 0.412630i −0.721975 0.691919i \(-0.756765\pi\)
0.960207 + 0.279289i \(0.0900987\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 14.7418i 1.10185i −0.834554 0.550927i \(-0.814274\pi\)
0.834554 0.550927i \(-0.185726\pi\)
\(180\) 0 0
\(181\) 0.0833642i 0.00619641i 0.999995 + 0.00309821i \(0.000986191\pi\)
−0.999995 + 0.00309821i \(0.999014\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 5.03932 + 8.72835i 0.370498 + 0.641721i
\(186\) 0 0
\(187\) 6.84036 + 3.94929i 0.500217 + 0.288800i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 13.3672 + 7.71754i 0.967214 + 0.558421i 0.898386 0.439207i \(-0.144741\pi\)
0.0688282 + 0.997629i \(0.478074\pi\)
\(192\) 0 0
\(193\) −10.7779 18.6678i −0.775808 1.34374i −0.934339 0.356385i \(-0.884009\pi\)
0.158532 0.987354i \(-0.449324\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 9.88306i 0.704139i −0.935974 0.352069i \(-0.885478\pi\)
0.935974 0.352069i \(-0.114522\pi\)
\(198\) 0 0
\(199\) 10.5612i 0.748660i 0.927295 + 0.374330i \(0.122127\pi\)
−0.927295 + 0.374330i \(0.877873\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) −10.5618 + 18.2936i −0.737670 + 1.27768i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −11.6118 + 20.1123i −0.803208 + 1.39120i
\(210\) 0 0
\(211\) 6.08453 + 10.5387i 0.418876 + 0.725514i 0.995827 0.0912645i \(-0.0290909\pi\)
−0.576951 + 0.816779i \(0.695758\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 31.0608 2.11833
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 5.91452 3.41475i 0.397854 0.229701i
\(222\) 0 0
\(223\) 0.714485 + 0.412508i 0.0478455 + 0.0276236i 0.523732 0.851883i \(-0.324539\pi\)
−0.475886 + 0.879507i \(0.657873\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −0.166778 + 0.288869i −0.0110695 + 0.0191729i −0.871507 0.490383i \(-0.836857\pi\)
0.860438 + 0.509556i \(0.170190\pi\)
\(228\) 0 0
\(229\) −12.4893 + 7.21072i −0.825319 + 0.476498i −0.852247 0.523139i \(-0.824761\pi\)
0.0269285 + 0.999637i \(0.491427\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 14.7748i 0.967927i 0.875088 + 0.483964i \(0.160803\pi\)
−0.875088 + 0.483964i \(0.839197\pi\)
\(234\) 0 0
\(235\) −32.6619 −2.13063
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 22.5339 13.0100i 1.45760 0.841545i 0.458707 0.888588i \(-0.348313\pi\)
0.998893 + 0.0470423i \(0.0149795\pi\)
\(240\) 0 0
\(241\) −1.66295 0.960105i −0.107120 0.0618458i 0.445483 0.895290i \(-0.353032\pi\)
−0.552603 + 0.833445i \(0.686365\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 10.0402 + 17.3901i 0.638841 + 1.10651i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −9.97663 −0.629719 −0.314860 0.949138i \(-0.601957\pi\)
−0.314860 + 0.949138i \(0.601957\pi\)
\(252\) 0 0
\(253\) −23.2193 −1.45978
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −7.50364 12.9967i −0.468064 0.810711i 0.531270 0.847203i \(-0.321715\pi\)
−0.999334 + 0.0364915i \(0.988382\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 6.11010 + 3.52767i 0.376765 + 0.217525i 0.676410 0.736525i \(-0.263535\pi\)
−0.299645 + 0.954051i \(0.596868\pi\)
\(264\) 0 0
\(265\) −2.10084 + 1.21292i −0.129053 + 0.0745090i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 29.7795 1.81569 0.907844 0.419308i \(-0.137727\pi\)
0.907844 + 0.419308i \(0.137727\pi\)
\(270\) 0 0
\(271\) 2.78816i 0.169369i −0.996408 0.0846843i \(-0.973012\pi\)
0.996408 0.0846843i \(-0.0269882\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 15.6424 9.03112i 0.943270 0.544597i
\(276\) 0 0
\(277\) −6.79074 + 11.7619i −0.408016 + 0.706705i −0.994667 0.103135i \(-0.967113\pi\)
0.586651 + 0.809840i \(0.300446\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 3.95777 + 2.28502i 0.236101 + 0.136313i 0.613383 0.789785i \(-0.289808\pi\)
−0.377283 + 0.926098i \(0.623141\pi\)
\(282\) 0 0
\(283\) 17.6685 10.2009i 1.05029 0.606383i 0.127556 0.991831i \(-0.459287\pi\)
0.922729 + 0.385449i \(0.125953\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −14.2092 −0.835838
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −6.41037 11.1031i −0.374498 0.648649i 0.615754 0.787939i \(-0.288852\pi\)
−0.990252 + 0.139289i \(0.955518\pi\)
\(294\) 0 0
\(295\) −4.08144 + 7.06926i −0.237631 + 0.411589i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −10.0383 + 17.3868i −0.580529 + 1.00551i
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 21.3923i 1.22492i
\(306\) 0 0
\(307\) 1.93411i 0.110386i 0.998476 + 0.0551928i \(0.0175773\pi\)
−0.998476 + 0.0551928i \(0.982423\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 1.04458 + 1.80926i 0.0592326 + 0.102594i 0.894121 0.447825i \(-0.147801\pi\)
−0.834889 + 0.550419i \(0.814468\pi\)
\(312\) 0 0
\(313\) 19.4066 + 11.2044i 1.09692 + 0.633309i 0.935411 0.353562i \(-0.115030\pi\)
0.161512 + 0.986871i \(0.448363\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −3.01788 1.74237i −0.169501 0.0978614i 0.412850 0.910799i \(-0.364534\pi\)
−0.582350 + 0.812938i \(0.697867\pi\)
\(318\) 0 0
\(319\) 0.651207 + 1.12792i 0.0364606 + 0.0631516i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 8.20549i 0.456565i
\(324\) 0 0
\(325\) 15.6175i 0.866304i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 2.28857 3.96392i 0.125791 0.217877i −0.796251 0.604967i \(-0.793186\pi\)
0.922042 + 0.387090i \(0.126520\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 17.2405 29.8615i 0.941951 1.63151i
\(336\) 0 0
\(337\) −14.7062 25.4720i −0.801100 1.38755i −0.918893 0.394508i \(-0.870915\pi\)
0.117793 0.993038i \(-0.462418\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 7.58045 0.410504
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 17.0245 9.82911i 0.913924 0.527654i 0.0322323 0.999480i \(-0.489738\pi\)
0.881692 + 0.471826i \(0.156405\pi\)
\(348\) 0 0
\(349\) −8.47286 4.89181i −0.453542 0.261852i 0.255783 0.966734i \(-0.417667\pi\)
−0.709325 + 0.704882i \(0.751000\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −12.5322 + 21.7065i −0.667023 + 1.15532i 0.311709 + 0.950178i \(0.399099\pi\)
−0.978733 + 0.205141i \(0.934235\pi\)
\(354\) 0 0
\(355\) 26.8532 15.5037i 1.42522 0.822850i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 9.35147i 0.493552i 0.969073 + 0.246776i \(0.0793712\pi\)
−0.969073 + 0.246776i \(0.920629\pi\)
\(360\) 0 0
\(361\) −5.12609 −0.269794
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 40.5367 23.4039i 2.12179 1.22502i
\(366\) 0 0
\(367\) −18.9530 10.9425i −0.989337 0.571194i −0.0842608 0.996444i \(-0.526853\pi\)
−0.905076 + 0.425250i \(0.860186\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) −2.30822 3.99795i −0.119515 0.207006i 0.800061 0.599919i \(-0.204801\pi\)
−0.919576 + 0.392913i \(0.871467\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 1.12613 0.0579988
\(378\) 0 0
\(379\) −6.22396 −0.319703 −0.159852 0.987141i \(-0.551102\pi\)
−0.159852 + 0.987141i \(0.551102\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 10.9989 + 19.0506i 0.562015 + 0.973439i 0.997321 + 0.0731560i \(0.0233071\pi\)
−0.435305 + 0.900283i \(0.643360\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −8.51109 4.91388i −0.431529 0.249144i 0.268469 0.963288i \(-0.413482\pi\)
−0.699998 + 0.714145i \(0.746816\pi\)
\(390\) 0 0
\(391\) −7.10481 + 4.10197i −0.359306 + 0.207445i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 36.5392 1.83849
\(396\) 0 0
\(397\) 5.25762i 0.263873i 0.991258 + 0.131936i \(0.0421194\pi\)
−0.991258 + 0.131936i \(0.957881\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 14.7847 8.53594i 0.738312 0.426265i −0.0831432 0.996538i \(-0.526496\pi\)
0.821455 + 0.570273i \(0.193163\pi\)
\(402\) 0 0
\(403\) 3.27722 5.67631i 0.163250 0.282757i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −13.8957 8.02270i −0.688786 0.397671i
\(408\) 0 0
\(409\) 16.9484 9.78516i 0.838044 0.483845i −0.0185546 0.999828i \(-0.505906\pi\)
0.856599 + 0.515983i \(0.172573\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 23.9955 1.17789
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −10.3073 17.8529i −0.503547 0.872169i −0.999992 0.00410056i \(-0.998695\pi\)
0.496445 0.868068i \(-0.334639\pi\)
\(420\) 0 0
\(421\) 0.704748 1.22066i 0.0343473 0.0594913i −0.848341 0.529451i \(-0.822398\pi\)
0.882688 + 0.469959i \(0.155731\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 3.19091 5.52682i 0.154782 0.268090i
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 13.4714i 0.648894i 0.945904 + 0.324447i \(0.105178\pi\)
−0.945904 + 0.324447i \(0.894822\pi\)
\(432\) 0 0
\(433\) 12.9356i 0.621646i 0.950468 + 0.310823i \(0.100605\pi\)
−0.950468 + 0.310823i \(0.899395\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −12.0608 20.8899i −0.576944 0.999297i
\(438\) 0 0
\(439\) 8.75023 + 5.05195i 0.417626 + 0.241116i 0.694061 0.719916i \(-0.255820\pi\)
−0.276435 + 0.961033i \(0.589153\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −25.1220 14.5042i −1.19358 0.689115i −0.234466 0.972124i \(-0.575334\pi\)
−0.959117 + 0.283009i \(0.908667\pi\)
\(444\) 0 0
\(445\) 13.6873 + 23.7072i 0.648842 + 1.12383i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 7.94881i 0.375127i −0.982252 0.187564i \(-0.939941\pi\)
0.982252 0.187564i \(-0.0600591\pi\)
\(450\) 0 0
\(451\) 33.6293i 1.58354i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 6.98084 12.0912i 0.326550 0.565601i −0.655275 0.755391i \(-0.727447\pi\)
0.981825 + 0.189789i \(0.0607805\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 16.4030 28.4108i 0.763964 1.32322i −0.176829 0.984242i \(-0.556584\pi\)
0.940793 0.338983i \(-0.110083\pi\)
\(462\) 0 0
\(463\) −13.8812 24.0429i −0.645112 1.11737i −0.984276 0.176640i \(-0.943477\pi\)
0.339163 0.940727i \(-0.389856\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −22.8621 −1.05793 −0.528966 0.848643i \(-0.677420\pi\)
−0.528966 + 0.848643i \(0.677420\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −42.8245 + 24.7247i −1.96907 + 1.13684i
\(474\) 0 0
\(475\) 16.2502 + 9.38204i 0.745609 + 0.430478i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −1.21212 + 2.09946i −0.0553834 + 0.0959269i −0.892388 0.451269i \(-0.850971\pi\)
0.837004 + 0.547196i \(0.184305\pi\)
\(480\) 0 0
\(481\) −12.0149 + 6.93683i −0.547834 + 0.316292i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 24.0317i 1.09122i
\(486\) 0 0
\(487\) −10.3930 −0.470952 −0.235476 0.971880i \(-0.575665\pi\)
−0.235476 + 0.971880i \(0.575665\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 2.93014 1.69172i 0.132235 0.0763462i −0.432423 0.901671i \(-0.642341\pi\)
0.564658 + 0.825325i \(0.309008\pi\)
\(492\) 0 0
\(493\) 0.398522 + 0.230087i 0.0179485 + 0.0103626i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) −19.7801 34.2602i −0.885481 1.53370i −0.845162 0.534511i \(-0.820496\pi\)
−0.0403188 0.999187i \(-0.512837\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −14.5476 −0.648645 −0.324323 0.945947i \(-0.605136\pi\)
−0.324323 + 0.945947i \(0.605136\pi\)
\(504\) 0 0
\(505\) 21.7018 0.965717
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −10.1958 17.6596i −0.451921 0.782750i 0.546585 0.837404i \(-0.315928\pi\)
−0.998505 + 0.0546542i \(0.982594\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 18.0690 + 10.4322i 0.796216 + 0.459696i
\(516\) 0 0
\(517\) 45.0319 25.9992i 1.98050 1.14344i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −15.5024 −0.679175 −0.339587 0.940575i \(-0.610287\pi\)
−0.339587 + 0.940575i \(0.610287\pi\)
\(522\) 0 0
\(523\) 10.8079i 0.472595i 0.971681 + 0.236298i \(0.0759340\pi\)
−0.971681 + 0.236298i \(0.924066\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 2.31952 1.33918i 0.101040 0.0583355i
\(528\) 0 0
\(529\) 0.558476 0.967309i 0.0242816 0.0420569i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −25.1819 14.5388i −1.09075 0.629745i
\(534\) 0 0
\(535\) −36.4162 + 21.0249i −1.57441 + 0.908986i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) 17.5871 0.756130 0.378065 0.925779i \(-0.376590\pi\)
0.378065 + 0.925779i \(0.376590\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 8.38108 + 14.5165i 0.359006 + 0.621817i
\(546\) 0 0
\(547\) −5.72451 + 9.91513i −0.244762 + 0.423940i −0.962065 0.272821i \(-0.912043\pi\)
0.717303 + 0.696762i \(0.245377\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −0.676511 + 1.17175i −0.0288203 + 0.0499183i
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 38.0080i 1.61045i −0.592968 0.805226i \(-0.702044\pi\)
0.592968 0.805226i \(-0.297956\pi\)
\(558\) 0 0
\(559\) 42.7565i 1.80841i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −8.88438 15.3882i −0.374432 0.648535i 0.615810 0.787895i \(-0.288829\pi\)
−0.990242 + 0.139360i \(0.955496\pi\)
\(564\) 0 0
\(565\) −34.5727 19.9605i −1.45448 0.839746i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −33.7404 19.4801i −1.41447 0.816646i −0.418667 0.908140i \(-0.637503\pi\)
−0.995806 + 0.0914936i \(0.970836\pi\)
\(570\) 0 0
\(571\) −8.45245 14.6401i −0.353724 0.612668i 0.633175 0.774009i \(-0.281752\pi\)
−0.986899 + 0.161341i \(0.948418\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 18.7605i 0.782368i
\(576\) 0 0
\(577\) 47.2653i 1.96768i 0.179050 + 0.983840i \(0.442698\pi\)
−0.179050 + 0.983840i \(0.557302\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 1.93099 3.34458i 0.0799736 0.138518i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −11.6343 + 20.1513i −0.480200 + 0.831731i −0.999742 0.0227138i \(-0.992769\pi\)
0.519542 + 0.854445i \(0.326103\pi\)
\(588\) 0 0
\(589\) 3.93750 + 6.81995i 0.162242 + 0.281011i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −37.1924 −1.52731 −0.763654 0.645626i \(-0.776596\pi\)
−0.763654 + 0.645626i \(0.776596\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 27.9591 16.1422i 1.14238 0.659552i 0.195359 0.980732i \(-0.437413\pi\)
0.947018 + 0.321180i \(0.104079\pi\)
\(600\) 0 0
\(601\) −14.7559 8.51933i −0.601906 0.347511i 0.167885 0.985807i \(-0.446306\pi\)
−0.769791 + 0.638296i \(0.779640\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −16.8615 + 29.2051i −0.685519 + 1.18735i
\(606\) 0 0
\(607\) −8.44393 + 4.87510i −0.342728 + 0.197874i −0.661478 0.749965i \(-0.730070\pi\)
0.318749 + 0.947839i \(0.396737\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 44.9604i 1.81890i
\(612\) 0 0
\(613\) 13.7266 0.554414 0.277207 0.960810i \(-0.410591\pi\)
0.277207 + 0.960810i \(0.410591\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 2.84301 1.64141i 0.114455 0.0660807i −0.441680 0.897173i \(-0.645617\pi\)
0.556135 + 0.831092i \(0.312284\pi\)
\(618\) 0 0
\(619\) 14.9907 + 8.65490i 0.602528 + 0.347870i 0.770036 0.638001i \(-0.220238\pi\)
−0.167507 + 0.985871i \(0.553572\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 14.7536 + 25.5539i 0.590142 + 1.02216i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −5.66923 −0.226047
\(630\) 0 0
\(631\) −6.27821 −0.249932 −0.124966 0.992161i \(-0.539882\pi\)
−0.124966 + 0.992161i \(0.539882\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −18.9672 32.8522i −0.752691 1.30370i
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −17.9788 10.3801i −0.710120 0.409988i 0.100986 0.994888i \(-0.467800\pi\)
−0.811105 + 0.584900i \(0.801134\pi\)
\(642\) 0 0
\(643\) −17.2553 + 9.96236i −0.680483 + 0.392877i −0.800037 0.599950i \(-0.795187\pi\)
0.119554 + 0.992828i \(0.461854\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −29.5340 −1.16110 −0.580551 0.814224i \(-0.697163\pi\)
−0.580551 + 0.814224i \(0.697163\pi\)
\(648\) 0 0
\(649\) 12.9955i 0.510118i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 13.7914 7.96249i 0.539701 0.311596i −0.205257 0.978708i \(-0.565803\pi\)
0.744958 + 0.667112i \(0.232470\pi\)
\(654\) 0 0
\(655\) 19.9246 34.5105i 0.778520 1.34844i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −2.80283 1.61822i −0.109183 0.0630368i 0.444414 0.895821i \(-0.353412\pi\)
−0.553597 + 0.832785i \(0.686745\pi\)
\(660\) 0 0
\(661\) 7.71194 4.45249i 0.299960 0.173182i −0.342465 0.939531i \(-0.611262\pi\)
0.642425 + 0.766349i \(0.277928\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −1.35277 −0.0523793
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 17.0285 + 29.4943i 0.657379 + 1.13861i
\(672\) 0 0
\(673\) −13.2311 + 22.9169i −0.510021 + 0.883382i 0.489912 + 0.871772i \(0.337029\pi\)
−0.999933 + 0.0116101i \(0.996304\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 4.46424 7.73229i 0.171575 0.297176i −0.767396 0.641174i \(-0.778448\pi\)
0.938971 + 0.343997i \(0.111781\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 37.8628i 1.44878i 0.689390 + 0.724390i \(0.257879\pi\)
−0.689390 + 0.724390i \(0.742121\pi\)
\(684\) 0 0
\(685\) 26.7298i 1.02129i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −1.66963 2.89189i −0.0636080 0.110172i
\(690\) 0 0
\(691\) −4.94211 2.85333i −0.188007 0.108546i 0.403042 0.915181i \(-0.367953\pi\)
−0.591049 + 0.806636i \(0.701286\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 4.60039 + 2.65604i 0.174503 + 0.100749i
\(696\) 0 0
\(697\) −5.94103 10.2902i −0.225032 0.389768i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 8.19949i 0.309690i 0.987939 + 0.154845i \(0.0494879\pi\)
−0.987939 + 0.154845i \(0.950512\pi\)
\(702\) 0 0
\(703\) 16.6689i 0.628679i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) −10.0757 + 17.4517i −0.378402 + 0.655412i −0.990830 0.135115i \(-0.956860\pi\)
0.612428 + 0.790527i \(0.290193\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −3.93676 + 6.81866i −0.147433 + 0.255361i
\(714\) 0 0
\(715\) 28.7028 + 49.7147i 1.07342 + 1.85923i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 51.1991 1.90940 0.954702 0.297563i \(-0.0961739\pi\)
0.954702 + 0.297563i \(0.0961739\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 0.911330 0.526157i 0.0338460 0.0195410i
\(726\) 0 0
\(727\) 13.7848 + 7.95865i 0.511249 + 0.295170i 0.733347 0.679854i \(-0.237957\pi\)
−0.222098 + 0.975024i \(0.571290\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −8.73584 + 15.1309i −0.323107 + 0.559637i
\(732\) 0 0
\(733\) −3.67216 + 2.12012i −0.135634 + 0.0783086i −0.566282 0.824212i \(-0.691619\pi\)
0.430647 + 0.902520i \(0.358285\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 54.8946i 2.02207i
\(738\) 0 0
\(739\) 28.3669 1.04349 0.521747 0.853100i \(-0.325280\pi\)
0.521747 + 0.853100i \(0.325280\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −21.8850 + 12.6353i −0.802884 + 0.463545i −0.844479 0.535589i \(-0.820090\pi\)
0.0415945 + 0.999135i \(0.486756\pi\)
\(744\) 0 0
\(745\) −33.1971 19.1664i −1.21625 0.702201i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −23.7730 41.1761i −0.867490 1.50254i −0.864554 0.502540i \(-0.832399\pi\)
−0.00293597 0.999996i \(-0.500935\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 38.5113 1.40157
\(756\) 0 0
\(757\) 37.3922 1.35904 0.679521 0.733656i \(-0.262188\pi\)
0.679521 + 0.733656i \(0.262188\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 4.12142 + 7.13850i 0.149401 + 0.258770i 0.931006 0.365003i \(-0.118932\pi\)
−0.781605 + 0.623774i \(0.785599\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −9.73114 5.61827i −0.351371 0.202864i
\(768\) 0 0
\(769\) −20.2182 + 11.6730i −0.729086 + 0.420938i −0.818088 0.575094i \(-0.804966\pi\)
0.0890020 + 0.996031i \(0.471632\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 34.4402 1.23873 0.619364 0.785104i \(-0.287391\pi\)
0.619364 + 0.785104i \(0.287391\pi\)
\(774\) 0 0
\(775\) 6.12479i 0.220009i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 30.2555 17.4680i 1.08402 0.625857i
\(780\) 0 0
\(781\) −24.6822 + 42.7508i −0.883199 + 1.52975i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 44.1682 + 25.5005i 1.57643 + 0.910152i
\(786\) 0 0
\(787\) −7.19975 + 4.15678i −0.256643 + 0.148173i −0.622802 0.782379i \(-0.714006\pi\)
0.366159 + 0.930552i \(0.380673\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 29.4474 1.04571
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 0.426036 + 0.737916i 0.0150910 + 0.0261383i 0.873472 0.486874i \(-0.161863\pi\)
−0.858381 + 0.513012i \(0.828530\pi\)
\(798\) 0 0
\(799\) 9.18614 15.9109i 0.324982 0.562886i
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −37.2595 + 64.5354i −1.31486 + 2.27740i
\(804\) 0 0
\(805\) 0 0
\(806\)