Properties

Label 3024.2.q.g.2881.2
Level 3024
Weight 2
Character 3024.2881
Analytic conductor 24.147
Analytic rank 0
Dimension 6
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3024.q (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(24.1467615712\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.309123.1
Defining polynomial: \(x^{6} - 3 x^{5} + 10 x^{4} - 15 x^{3} + 19 x^{2} - 12 x + 3\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 126)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 2881.2
Root \(0.500000 - 2.05195i\) of defining polynomial
Character \(\chi\) \(=\) 3024.2881
Dual form 3024.2.q.g.2305.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.296790 - 0.514055i) q^{5} +(-2.32383 + 1.26483i) q^{7} +O(q^{10})\) \(q+(0.296790 - 0.514055i) q^{5} +(-2.32383 + 1.26483i) q^{7} +(0.296790 + 0.514055i) q^{11} +(-1.25729 - 2.17770i) q^{13} +(-1.46050 + 2.52967i) q^{17} +(-2.69076 - 4.66053i) q^{19} +(-2.23025 + 3.86291i) q^{23} +(2.32383 + 4.02499i) q^{25} +(3.09718 - 5.36447i) q^{29} +7.86693 q^{31} +(-0.0394951 + 1.56997i) q^{35} +(0.500000 + 0.866025i) q^{37} +(0.136673 + 0.236725i) q^{41} +(5.58113 - 9.66679i) q^{43} +12.1623 q^{47} +(3.80039 - 5.87852i) q^{49} +(-4.02704 + 6.97504i) q^{53} +0.352336 q^{55} +8.64766 q^{59} -6.64766 q^{61} -1.49261 q^{65} +1.91381 q^{67} -14.4107 q^{71} +(3.95691 - 6.85356i) q^{73} +(-1.33988 - 0.819187i) q^{77} +9.24844 q^{79} +(3.85087 - 6.66991i) q^{83} +(0.866926 + 1.50156i) q^{85} +(6.21780 + 10.7695i) q^{89} +(5.67617 + 3.47033i) q^{91} -3.19436 q^{95} +(5.86693 - 10.1618i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q - q^{5} - 2q^{7} + O(q^{10}) \) \( 6q - q^{5} - 2q^{7} - q^{11} + 8q^{13} + 4q^{17} + 3q^{19} - 7q^{23} + 2q^{25} + 5q^{29} + 40q^{31} - 13q^{35} + 3q^{37} + 6q^{43} + 18q^{47} + 12q^{49} - 15q^{53} + 26q^{55} + 28q^{59} - 16q^{61} - 24q^{65} + 2q^{67} + 14q^{71} + 19q^{73} - 10q^{77} + 10q^{79} + 2q^{83} - 2q^{85} + 9q^{89} + 46q^{91} + 8q^{95} + 28q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3024\mathbb{Z}\right)^\times\).

\(n\) \(757\) \(785\) \(1135\) \(2593\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0 0
\(4\) 0 0
\(5\) 0.296790 0.514055i 0.132728 0.229892i −0.791999 0.610522i \(-0.790960\pi\)
0.924727 + 0.380630i \(0.124293\pi\)
\(6\) 0 0
\(7\) −2.32383 + 1.26483i −0.878326 + 0.478062i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 0.296790 + 0.514055i 0.0894855 + 0.154993i 0.907294 0.420497i \(-0.138144\pi\)
−0.817808 + 0.575491i \(0.804811\pi\)
\(12\) 0 0
\(13\) −1.25729 2.17770i −0.348711 0.603985i 0.637310 0.770608i \(-0.280047\pi\)
−0.986021 + 0.166623i \(0.946714\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −1.46050 + 2.52967i −0.354224 + 0.613535i −0.986985 0.160813i \(-0.948588\pi\)
0.632760 + 0.774348i \(0.281922\pi\)
\(18\) 0 0
\(19\) −2.69076 4.66053i −0.617302 1.06920i −0.989976 0.141236i \(-0.954892\pi\)
0.372674 0.927962i \(-0.378441\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −2.23025 + 3.86291i −0.465040 + 0.805473i −0.999203 0.0399086i \(-0.987293\pi\)
0.534164 + 0.845381i \(0.320627\pi\)
\(24\) 0 0
\(25\) 2.32383 + 4.02499i 0.464766 + 0.804999i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 3.09718 5.36447i 0.575132 0.996157i −0.420896 0.907109i \(-0.638284\pi\)
0.996027 0.0890480i \(-0.0283825\pi\)
\(30\) 0 0
\(31\) 7.86693 1.41294 0.706471 0.707742i \(-0.250286\pi\)
0.706471 + 0.707742i \(0.250286\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −0.0394951 + 1.56997i −0.00667590 + 0.265373i
\(36\) 0 0
\(37\) 0.500000 + 0.866025i 0.0821995 + 0.142374i 0.904194 0.427121i \(-0.140472\pi\)
−0.821995 + 0.569495i \(0.807139\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 0.136673 + 0.236725i 0.0213448 + 0.0369702i 0.876500 0.481401i \(-0.159872\pi\)
−0.855156 + 0.518371i \(0.826539\pi\)
\(42\) 0 0
\(43\) 5.58113 9.66679i 0.851114 1.47417i −0.0290902 0.999577i \(-0.509261\pi\)
0.880204 0.474596i \(-0.157406\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 12.1623 1.77405 0.887023 0.461724i \(-0.152769\pi\)
0.887023 + 0.461724i \(0.152769\pi\)
\(48\) 0 0
\(49\) 3.80039 5.87852i 0.542913 0.839789i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −4.02704 + 6.97504i −0.553157 + 0.958096i 0.444888 + 0.895586i \(0.353244\pi\)
−0.998044 + 0.0625092i \(0.980090\pi\)
\(54\) 0 0
\(55\) 0.352336 0.0475090
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 8.64766 1.12583 0.562915 0.826515i \(-0.309680\pi\)
0.562915 + 0.826515i \(0.309680\pi\)
\(60\) 0 0
\(61\) −6.64766 −0.851146 −0.425573 0.904924i \(-0.639927\pi\)
−0.425573 + 0.904924i \(0.639927\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −1.49261 −0.185135
\(66\) 0 0
\(67\) 1.91381 0.233809 0.116905 0.993143i \(-0.462703\pi\)
0.116905 + 0.993143i \(0.462703\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −14.4107 −1.71023 −0.855117 0.518435i \(-0.826515\pi\)
−0.855117 + 0.518435i \(0.826515\pi\)
\(72\) 0 0
\(73\) 3.95691 6.85356i 0.463121 0.802149i −0.535994 0.844222i \(-0.680063\pi\)
0.999115 + 0.0420732i \(0.0133963\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −1.33988 0.819187i −0.152694 0.0933550i
\(78\) 0 0
\(79\) 9.24844 1.04053 0.520265 0.854005i \(-0.325833\pi\)
0.520265 + 0.854005i \(0.325833\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 3.85087 6.66991i 0.422688 0.732118i −0.573513 0.819196i \(-0.694420\pi\)
0.996201 + 0.0870787i \(0.0277532\pi\)
\(84\) 0 0
\(85\) 0.866926 + 1.50156i 0.0940313 + 0.162867i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 6.21780 + 10.7695i 0.659085 + 1.14157i 0.980853 + 0.194751i \(0.0623898\pi\)
−0.321767 + 0.946819i \(0.604277\pi\)
\(90\) 0 0
\(91\) 5.67617 + 3.47033i 0.595024 + 0.363790i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −3.19436 −0.327734
\(96\) 0 0
\(97\) 5.86693 10.1618i 0.595696 1.03178i −0.397752 0.917493i \(-0.630210\pi\)
0.993448 0.114283i \(-0.0364570\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −0.811379 1.40535i −0.0807352 0.139837i 0.822831 0.568287i \(-0.192393\pi\)
−0.903566 + 0.428449i \(0.859060\pi\)
\(102\) 0 0
\(103\) 3.19076 5.52655i 0.314395 0.544548i −0.664914 0.746920i \(-0.731532\pi\)
0.979309 + 0.202372i \(0.0648651\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 9.35447 + 16.2024i 0.904331 + 1.56635i 0.821813 + 0.569758i \(0.192963\pi\)
0.0825182 + 0.996590i \(0.473704\pi\)
\(108\) 0 0
\(109\) −1.43346 + 2.48283i −0.137301 + 0.237812i −0.926474 0.376359i \(-0.877176\pi\)
0.789173 + 0.614171i \(0.210509\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 6.16012 + 10.6696i 0.579495 + 1.00371i 0.995537 + 0.0943695i \(0.0300835\pi\)
−0.416042 + 0.909345i \(0.636583\pi\)
\(114\) 0 0
\(115\) 1.32383 + 2.29294i 0.123448 + 0.213818i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 0.194356 7.72582i 0.0178166 0.708225i
\(120\) 0 0
\(121\) 5.32383 9.22115i 0.483985 0.838286i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 5.72665 0.512207
\(126\) 0 0
\(127\) −12.3346 −1.09452 −0.547261 0.836962i \(-0.684329\pi\)
−0.547261 + 0.836962i \(0.684329\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 0.593579 1.02811i 0.0518613 0.0898264i −0.838929 0.544240i \(-0.816818\pi\)
0.890791 + 0.454414i \(0.150151\pi\)
\(132\) 0 0
\(133\) 12.1477 + 7.42692i 1.05334 + 0.643996i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 1.26089 + 2.18393i 0.107725 + 0.186586i 0.914848 0.403797i \(-0.132310\pi\)
−0.807123 + 0.590383i \(0.798977\pi\)
\(138\) 0 0
\(139\) −2.45691 4.25549i −0.208392 0.360946i 0.742816 0.669496i \(-0.233490\pi\)
−0.951208 + 0.308550i \(0.900156\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0.746304 1.29264i 0.0624091 0.108096i
\(144\) 0 0
\(145\) −1.83842 3.18424i −0.152673 0.264437i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 9.02558 15.6328i 0.739404 1.28069i −0.213360 0.976974i \(-0.568441\pi\)
0.952764 0.303712i \(-0.0982261\pi\)
\(150\) 0 0
\(151\) 0.823832 + 1.42692i 0.0670425 + 0.116121i 0.897598 0.440815i \(-0.145310\pi\)
−0.830556 + 0.556936i \(0.811977\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 2.33482 4.04403i 0.187537 0.324824i
\(156\) 0 0
\(157\) −6.60078 −0.526799 −0.263400 0.964687i \(-0.584844\pi\)
−0.263400 + 0.964687i \(0.584844\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0.296790 11.7977i 0.0233903 0.929785i
\(162\) 0 0
\(163\) 2.99115 + 5.18082i 0.234285 + 0.405793i 0.959065 0.283188i \(-0.0913919\pi\)
−0.724780 + 0.688980i \(0.758059\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 3.73025 + 6.46099i 0.288656 + 0.499966i 0.973489 0.228733i \(-0.0734584\pi\)
−0.684833 + 0.728700i \(0.740125\pi\)
\(168\) 0 0
\(169\) 3.33842 5.78231i 0.256802 0.444793i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 25.6591 1.95083 0.975414 0.220381i \(-0.0707301\pi\)
0.975414 + 0.220381i \(0.0707301\pi\)
\(174\) 0 0
\(175\) −10.4911 6.41415i −0.793056 0.484864i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 7.51819 13.0219i 0.561936 0.973301i −0.435392 0.900241i \(-0.643390\pi\)
0.997328 0.0730602i \(-0.0232765\pi\)
\(180\) 0 0
\(181\) −0.0861875 −0.00640627 −0.00320313 0.999995i \(-0.501020\pi\)
−0.00320313 + 0.999995i \(0.501020\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0.593579 0.0436408
\(186\) 0 0
\(187\) −1.73385 −0.126792
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 3.98229 0.288148 0.144074 0.989567i \(-0.453980\pi\)
0.144074 + 0.989567i \(0.453980\pi\)
\(192\) 0 0
\(193\) 6.78074 0.488088 0.244044 0.969764i \(-0.421526\pi\)
0.244044 + 0.969764i \(0.421526\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −11.0584 −0.787875 −0.393938 0.919137i \(-0.628887\pi\)
−0.393938 + 0.919137i \(0.628887\pi\)
\(198\) 0 0
\(199\) −2.80924 + 4.86575i −0.199142 + 0.344924i −0.948250 0.317523i \(-0.897149\pi\)
0.749109 + 0.662447i \(0.230482\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −0.412155 + 16.3835i −0.0289276 + 1.14990i
\(204\) 0 0
\(205\) 0.162253 0.0113322
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 1.59718 2.76639i 0.110479 0.191355i
\(210\) 0 0
\(211\) −9.66225 16.7355i −0.665177 1.15212i −0.979237 0.202717i \(-0.935023\pi\)
0.314060 0.949403i \(-0.398311\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −3.31284 5.73801i −0.225934 0.391329i
\(216\) 0 0
\(217\) −18.2814 + 9.95036i −1.24102 + 0.675474i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 7.34514 0.494088
\(222\) 0 0
\(223\) −12.6623 + 21.9317i −0.847927 + 1.46865i 0.0351275 + 0.999383i \(0.488816\pi\)
−0.883055 + 0.469270i \(0.844517\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −2.40856 4.17174i −0.159862 0.276888i 0.774957 0.632014i \(-0.217771\pi\)
−0.934819 + 0.355126i \(0.884438\pi\)
\(228\) 0 0
\(229\) 4.64766 8.04999i 0.307126 0.531958i −0.670606 0.741814i \(-0.733966\pi\)
0.977732 + 0.209855i \(0.0672993\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −0.0971780 0.168317i −0.00636634 0.0110268i 0.862825 0.505503i \(-0.168693\pi\)
−0.869191 + 0.494476i \(0.835360\pi\)
\(234\) 0 0
\(235\) 3.60963 6.25206i 0.235466 0.407840i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −6.82743 11.8255i −0.441630 0.764925i 0.556181 0.831061i \(-0.312266\pi\)
−0.997811 + 0.0661361i \(0.978933\pi\)
\(240\) 0 0
\(241\) 6.50000 + 11.2583i 0.418702 + 0.725213i 0.995809 0.0914555i \(-0.0291519\pi\)
−0.577107 + 0.816668i \(0.695819\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −1.89397 3.69829i −0.121001 0.236275i
\(246\) 0 0
\(247\) −6.76615 + 11.7193i −0.430520 + 0.745682i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −19.5438 −1.23359 −0.616796 0.787123i \(-0.711570\pi\)
−0.616796 + 0.787123i \(0.711570\pi\)
\(252\) 0 0
\(253\) −2.64766 −0.166457
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 4.16372 7.21177i 0.259725 0.449858i −0.706443 0.707770i \(-0.749701\pi\)
0.966168 + 0.257912i \(0.0830346\pi\)
\(258\) 0 0
\(259\) −2.25729 1.38008i −0.140261 0.0857540i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 8.54523 + 14.8008i 0.526921 + 0.912655i 0.999508 + 0.0313704i \(0.00998713\pi\)
−0.472586 + 0.881284i \(0.656680\pi\)
\(264\) 0 0
\(265\) 2.39037 + 4.14024i 0.146839 + 0.254333i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 5.00720 8.67272i 0.305294 0.528785i −0.672033 0.740522i \(-0.734579\pi\)
0.977327 + 0.211737i \(0.0679119\pi\)
\(270\) 0 0
\(271\) −5.10457 8.84137i −0.310081 0.537075i 0.668299 0.743893i \(-0.267023\pi\)
−0.978380 + 0.206818i \(0.933689\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −1.37938 + 2.38915i −0.0831797 + 0.144071i
\(276\) 0 0
\(277\) −9.67111 16.7508i −0.581081 1.00646i −0.995352 0.0963074i \(-0.969297\pi\)
0.414271 0.910154i \(-0.364037\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 6.40136 11.0875i 0.381873 0.661424i −0.609457 0.792819i \(-0.708612\pi\)
0.991330 + 0.131396i \(0.0419458\pi\)
\(282\) 0 0
\(283\) 16.3523 0.972046 0.486023 0.873946i \(-0.338447\pi\)
0.486023 + 0.873946i \(0.338447\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −0.617023 0.377240i −0.0364217 0.0222678i
\(288\) 0 0
\(289\) 4.23385 + 7.33325i 0.249050 + 0.431367i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 10.3889 + 17.9941i 0.606926 + 1.05123i 0.991744 + 0.128235i \(0.0409311\pi\)
−0.384817 + 0.922993i \(0.625736\pi\)
\(294\) 0 0
\(295\) 2.56654 4.44537i 0.149430 0.258820i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 11.2163 0.648658
\(300\) 0 0
\(301\) −0.742705 + 29.5232i −0.0428088 + 1.70169i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −1.97296 + 3.41726i −0.112971 + 0.195672i
\(306\) 0 0
\(307\) 22.6768 1.29424 0.647118 0.762390i \(-0.275974\pi\)
0.647118 + 0.762390i \(0.275974\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −6.51459 −0.369408 −0.184704 0.982794i \(-0.559133\pi\)
−0.184704 + 0.982794i \(0.559133\pi\)
\(312\) 0 0
\(313\) 0.266149 0.0150436 0.00752181 0.999972i \(-0.497606\pi\)
0.00752181 + 0.999972i \(0.497606\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −15.7237 −0.883133 −0.441566 0.897229i \(-0.645577\pi\)
−0.441566 + 0.897229i \(0.645577\pi\)
\(318\) 0 0
\(319\) 3.67684 0.205864
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 15.7195 0.874654
\(324\) 0 0
\(325\) 5.84348 10.1212i 0.324138 0.561424i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −28.2630 + 15.3832i −1.55819 + 0.848105i
\(330\) 0 0
\(331\) 25.1623 1.38304 0.691521 0.722356i \(-0.256941\pi\)
0.691521 + 0.722356i \(0.256941\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 0.568000 0.983804i 0.0310331 0.0537510i
\(336\) 0 0
\(337\) −9.36693 16.2240i −0.510249 0.883777i −0.999929 0.0118752i \(-0.996220\pi\)
0.489681 0.871902i \(-0.337113\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 2.33482 + 4.04403i 0.126438 + 0.218997i
\(342\) 0 0
\(343\) −1.39610 + 18.4676i −0.0753825 + 0.997155i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 22.5438 1.21021 0.605106 0.796145i \(-0.293131\pi\)
0.605106 + 0.796145i \(0.293131\pi\)
\(348\) 0 0
\(349\) 1.89543 3.28298i 0.101460 0.175734i −0.810826 0.585287i \(-0.800982\pi\)
0.912286 + 0.409553i \(0.134315\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 3.41741 + 5.91913i 0.181890 + 0.315043i 0.942524 0.334138i \(-0.108445\pi\)
−0.760634 + 0.649181i \(0.775112\pi\)
\(354\) 0 0
\(355\) −4.27694 + 7.40789i −0.226997 + 0.393170i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −6.32237 10.9507i −0.333682 0.577954i 0.649549 0.760320i \(-0.274958\pi\)
−0.983231 + 0.182366i \(0.941624\pi\)
\(360\) 0 0
\(361\) −4.98035 + 8.62622i −0.262124 + 0.454012i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −2.34874 4.06813i −0.122939 0.212936i
\(366\) 0 0
\(367\) 3.27188 + 5.66707i 0.170791 + 0.295819i 0.938697 0.344744i \(-0.112034\pi\)
−0.767906 + 0.640563i \(0.778701\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 0.535897 21.3024i 0.0278224 1.10596i
\(372\) 0 0
\(373\) −4.71420 + 8.16524i −0.244092 + 0.422780i −0.961876 0.273486i \(-0.911823\pi\)
0.717784 + 0.696266i \(0.245157\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −15.5763 −0.802218
\(378\) 0 0
\(379\) 7.27762 0.373826 0.186913 0.982376i \(-0.440152\pi\)
0.186913 + 0.982376i \(0.440152\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 12.0416 20.8567i 0.615299 1.06573i −0.375033 0.927011i \(-0.622369\pi\)
0.990332 0.138717i \(-0.0442979\pi\)
\(384\) 0 0
\(385\) −0.818771 + 0.445647i −0.0417284 + 0.0227123i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −8.14913 14.1147i −0.413177 0.715644i 0.582058 0.813147i \(-0.302248\pi\)
−0.995235 + 0.0975035i \(0.968914\pi\)
\(390\) 0 0
\(391\) −6.51459 11.2836i −0.329457 0.570636i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 2.74484 4.75420i 0.138108 0.239210i
\(396\) 0 0
\(397\) −6.08619 10.5416i −0.305457 0.529067i 0.671906 0.740636i \(-0.265476\pi\)
−0.977363 + 0.211569i \(0.932143\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −16.6804 + 28.8914i −0.832981 + 1.44277i 0.0626819 + 0.998034i \(0.480035\pi\)
−0.895663 + 0.444733i \(0.853299\pi\)
\(402\) 0 0
\(403\) −9.89104 17.1318i −0.492708 0.853395i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −0.296790 + 0.514055i −0.0147113 + 0.0254808i
\(408\) 0 0
\(409\) −5.78074 −0.285839 −0.142920 0.989734i \(-0.545649\pi\)
−0.142920 + 0.989734i \(0.545649\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −20.0957 + 10.9379i −0.988846 + 0.538217i
\(414\) 0 0
\(415\) −2.28580 3.95912i −0.112205 0.194346i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 15.4356 + 26.7352i 0.754078 + 1.30610i 0.945831 + 0.324659i \(0.105249\pi\)
−0.191753 + 0.981443i \(0.561417\pi\)
\(420\) 0 0
\(421\) −1.86693 + 3.23361i −0.0909884 + 0.157597i −0.907927 0.419128i \(-0.862336\pi\)
0.816939 + 0.576724i \(0.195669\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −13.5759 −0.658526
\(426\) 0 0
\(427\) 15.4481 8.40819i 0.747584 0.406901i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −14.0979 + 24.4182i −0.679070 + 1.17618i 0.296192 + 0.955128i \(0.404283\pi\)
−0.975261 + 0.221055i \(0.929050\pi\)
\(432\) 0 0
\(433\) 12.5438 0.602815 0.301407 0.953495i \(-0.402544\pi\)
0.301407 + 0.953495i \(0.402544\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 24.0043 1.14828
\(438\) 0 0
\(439\) −26.0406 −1.24285 −0.621426 0.783473i \(-0.713446\pi\)
−0.621426 + 0.783473i \(0.713446\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −23.5729 −1.11998 −0.559992 0.828498i \(-0.689196\pi\)
−0.559992 + 0.828498i \(0.689196\pi\)
\(444\) 0 0
\(445\) 7.38151 0.349917
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −13.6870 −0.645928 −0.322964 0.946411i \(-0.604679\pi\)
−0.322964 + 0.946411i \(0.604679\pi\)
\(450\) 0 0
\(451\) −0.0811263 + 0.140515i −0.00382009 + 0.00661659i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 3.46857 1.88790i 0.162609 0.0885062i
\(456\) 0 0
\(457\) −22.3523 −1.04560 −0.522799 0.852456i \(-0.675112\pi\)
−0.522799 + 0.852456i \(0.675112\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 3.98755 6.90663i 0.185719 0.321674i −0.758100 0.652138i \(-0.773872\pi\)
0.943818 + 0.330464i \(0.107205\pi\)
\(462\) 0 0
\(463\) 14.3676 + 24.8854i 0.667719 + 1.15652i 0.978540 + 0.206055i \(0.0660625\pi\)
−0.310821 + 0.950468i \(0.600604\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 16.7829 + 29.0688i 0.776619 + 1.34514i 0.933880 + 0.357586i \(0.116400\pi\)
−0.157261 + 0.987557i \(0.550267\pi\)
\(468\) 0 0
\(469\) −4.44738 + 2.42066i −0.205361 + 0.111775i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 6.62568 0.304649
\(474\) 0 0
\(475\) 12.5057 21.6606i 0.573802 0.993855i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −0.183560 0.317935i −0.00838707 0.0145268i 0.861801 0.507246i \(-0.169336\pi\)
−0.870188 + 0.492719i \(0.836003\pi\)
\(480\) 0 0
\(481\) 1.25729 2.17770i 0.0573277 0.0992945i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −3.48249 6.03184i −0.158132 0.273892i
\(486\) 0 0
\(487\) 14.9538 25.9007i 0.677621 1.17367i −0.298075 0.954543i \(-0.596344\pi\)
0.975695 0.219131i \(-0.0703222\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −0.255158 0.441947i −0.0115151 0.0199448i 0.860210 0.509939i \(-0.170332\pi\)
−0.871726 + 0.489994i \(0.836999\pi\)
\(492\) 0 0
\(493\) 9.04689 + 15.6697i 0.407451 + 0.705726i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 33.4880 18.2271i 1.50214 0.817599i
\(498\) 0 0
\(499\) −9.50953 + 16.4710i −0.425705 + 0.737343i −0.996486 0.0837597i \(-0.973307\pi\)
0.570781 + 0.821102i \(0.306641\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −37.7807 −1.68456 −0.842280 0.539040i \(-0.818787\pi\)
−0.842280 + 0.539040i \(0.818787\pi\)
\(504\) 0 0
\(505\) −0.963235 −0.0428634
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −5.60817 + 9.71363i −0.248578 + 0.430549i −0.963131 0.269031i \(-0.913296\pi\)
0.714554 + 0.699581i \(0.246630\pi\)
\(510\) 0 0
\(511\) −0.526563 + 20.9314i −0.0232938 + 0.925949i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −1.89397 3.28045i −0.0834582 0.144554i
\(516\) 0 0
\(517\) 3.60963 + 6.25206i 0.158751 + 0.274965i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 13.7360 23.7914i 0.601785 1.04232i −0.390766 0.920490i \(-0.627790\pi\)
0.992551 0.121831i \(-0.0388767\pi\)
\(522\) 0 0
\(523\) −11.0919 19.2118i −0.485016 0.840072i 0.514836 0.857289i \(-0.327853\pi\)
−0.999852 + 0.0172166i \(0.994520\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −11.4897 + 19.9007i −0.500498 + 0.866889i
\(528\) 0 0
\(529\) 1.55195 + 2.68805i 0.0674760 + 0.116872i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 0.343677 0.595265i 0.0148863 0.0257838i
\(534\) 0 0
\(535\) 11.1052 0.480122
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 4.14980 + 0.208922i 0.178745 + 0.00899893i
\(540\) 0 0
\(541\) 14.9246 + 25.8502i 0.641659 + 1.11139i 0.985062 + 0.172198i \(0.0550869\pi\)
−0.343403 + 0.939188i \(0.611580\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 0.850874 + 1.47376i 0.0364474 + 0.0631288i
\(546\) 0 0
\(547\) −8.84348 + 15.3174i −0.378120 + 0.654923i −0.990789 0.135417i \(-0.956763\pi\)
0.612669 + 0.790340i \(0.290096\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −33.3350 −1.42012
\(552\) 0 0
\(553\) −21.4918 + 11.6977i −0.913925 + 0.497439i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −15.0651 + 26.0935i −0.638328 + 1.10562i 0.347472 + 0.937690i \(0.387040\pi\)
−0.985800 + 0.167926i \(0.946293\pi\)
\(558\) 0 0
\(559\) −28.0685 −1.18717
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 4.09766 0.172696 0.0863478 0.996265i \(-0.472480\pi\)
0.0863478 + 0.996265i \(0.472480\pi\)
\(564\) 0 0
\(565\) 7.31304 0.307662
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −6.23697 −0.261467 −0.130734 0.991418i \(-0.541733\pi\)
−0.130734 + 0.991418i \(0.541733\pi\)
\(570\) 0 0
\(571\) −35.6021 −1.48990 −0.744951 0.667119i \(-0.767527\pi\)
−0.744951 + 0.667119i \(0.767527\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −20.7309 −0.864539
\(576\) 0 0
\(577\) 23.1388 40.0776i 0.963281 1.66845i 0.249118 0.968473i \(-0.419859\pi\)
0.714164 0.699979i \(-0.246807\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −0.512453 + 20.3705i −0.0212601 + 0.845109i
\(582\) 0 0
\(583\) −4.78074 −0.197998
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 1.13161 1.96001i 0.0467066 0.0808982i −0.841727 0.539903i \(-0.818461\pi\)
0.888434 + 0.459005i \(0.151794\pi\)
\(588\) 0 0
\(589\) −21.1680 36.6640i −0.872212 1.51072i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −23.0979 40.0067i −0.948515 1.64288i −0.748555 0.663072i \(-0.769252\pi\)
−0.199960 0.979804i \(-0.564081\pi\)
\(594\) 0 0
\(595\) −3.91381 2.39285i −0.160451 0.0980974i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −16.7807 −0.685642 −0.342821 0.939401i \(-0.611382\pi\)
−0.342821 + 0.939401i \(0.611382\pi\)
\(600\) 0 0
\(601\) −5.69961 + 9.87202i −0.232492 + 0.402688i −0.958541 0.284955i \(-0.908021\pi\)
0.726049 + 0.687643i \(0.241355\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −3.16012 5.47348i −0.128477 0.222529i
\(606\) 0 0
\(607\) −7.21420 + 12.4954i −0.292815 + 0.507171i −0.974474 0.224499i \(-0.927925\pi\)
0.681659 + 0.731670i \(0.261259\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −15.2915 26.4857i −0.618629 1.07150i
\(612\) 0 0
\(613\) 12.2053 21.1403i 0.492969 0.853848i −0.506998 0.861947i \(-0.669245\pi\)
0.999967 + 0.00809942i \(0.00257815\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −24.4698 42.3830i −0.985119 1.70628i −0.641408 0.767200i \(-0.721650\pi\)
−0.343710 0.939076i \(-0.611684\pi\)
\(618\) 0 0
\(619\) −22.3296 38.6759i −0.897501 1.55452i −0.830678 0.556753i \(-0.812047\pi\)
−0.0668227 0.997765i \(-0.521286\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −28.0708 17.1621i −1.12463 0.687586i
\(624\) 0 0
\(625\) −9.91955 + 17.1812i −0.396782 + 0.687246i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −2.92101 −0.116468
\(630\) 0 0
\(631\) −33.2852 −1.32506 −0.662532 0.749034i \(-0.730518\pi\)
−0.662532 + 0.749034i \(0.730518\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −3.66079 + 6.34067i −0.145274 + 0.251622i
\(636\) 0 0
\(637\) −17.5799 0.885061i −0.696539 0.0350674i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 15.3940 + 26.6631i 0.608025 + 1.05313i 0.991566 + 0.129606i \(0.0413714\pi\)
−0.383540 + 0.923524i \(0.625295\pi\)
\(642\) 0 0
\(643\) 13.7345 + 23.7889i 0.541637 + 0.938142i 0.998810 + 0.0487649i \(0.0155285\pi\)
−0.457174 + 0.889378i \(0.651138\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −6.63521 + 11.4925i −0.260857 + 0.451818i −0.966470 0.256780i \(-0.917338\pi\)
0.705613 + 0.708598i \(0.250672\pi\)
\(648\) 0 0
\(649\) 2.56654 + 4.44537i 0.100745 + 0.174496i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −8.57081 + 14.8451i −0.335402 + 0.580933i −0.983562 0.180571i \(-0.942205\pi\)
0.648160 + 0.761504i \(0.275539\pi\)
\(654\) 0 0
\(655\) −0.352336 0.610265i −0.0137669 0.0238450i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 4.26089 7.38008i 0.165981 0.287487i −0.771022 0.636808i \(-0.780254\pi\)
0.937003 + 0.349321i \(0.113588\pi\)
\(660\) 0 0
\(661\) 34.3360 1.33551 0.667757 0.744379i \(-0.267254\pi\)
0.667757 + 0.744379i \(0.267254\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 7.42315 4.04033i 0.287857 0.156677i
\(666\) 0 0
\(667\) 13.8150 + 23.9282i 0.534918 + 0.926505i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −1.97296 3.41726i −0.0761652 0.131922i
\(672\) 0 0
\(673\) −7.70155 + 13.3395i −0.296873 + 0.514199i −0.975419 0.220359i \(-0.929277\pi\)
0.678546 + 0.734558i \(0.262610\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 7.38151 0.283695 0.141847 0.989889i \(-0.454696\pi\)
0.141847 + 0.989889i \(0.454696\pi\)
\(678\) 0 0
\(679\) −0.780738 + 31.0350i −0.0299620 + 1.19102i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 4.79893 8.31198i 0.183626 0.318049i −0.759487 0.650523i \(-0.774550\pi\)
0.943113 + 0.332474i \(0.107883\pi\)
\(684\) 0 0
\(685\) 1.49688 0.0571929
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 20.2527 0.771567
\(690\) 0 0
\(691\) 14.1445 0.538084 0.269042 0.963128i \(-0.413293\pi\)
0.269042 + 0.963128i \(0.413293\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −2.91674 −0.110638
\(696\) 0 0
\(697\) −0.798447 −0.0302433
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −37.3753 −1.41164 −0.705822 0.708389i \(-0.749422\pi\)
−0.705822 + 0.708389i \(0.749422\pi\)
\(702\) 0 0
\(703\) 2.69076 4.66053i 0.101484 0.175775i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 3.66304 + 2.23954i 0.137763 + 0.0842264i
\(708\) 0 0
\(709\) −10.4868 −0.393838 −0.196919 0.980420i \(-0.563094\pi\)
−0.196919 + 0.980420i \(0.563094\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −17.5452 + 30.3892i −0.657074 + 1.13809i
\(714\) 0 0
\(715\) −0.442991 0.767282i −0.0165669 0.0286947i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 1.11995 + 1.93981i 0.0417670 + 0.0723426i 0.886153 0.463392i \(-0.153368\pi\)
−0.844386 + 0.535735i \(0.820035\pi\)
\(720\) 0 0
\(721\) −0.424608 + 16.8786i −0.0158132 + 0.628590i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 28.7893 1.06921
\(726\) 0 0
\(727\) −0.185023 + 0.320469i −0.00686211 + 0.0118855i −0.869436 0.494045i \(-0.835518\pi\)
0.862574 + 0.505931i \(0.168851\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 16.3025 + 28.2368i 0.602971 + 1.04438i
\(732\) 0 0
\(733\) −7.00953 + 12.1409i −0.258903 + 0.448433i −0.965948 0.258735i \(-0.916694\pi\)
0.707045 + 0.707168i \(0.250028\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0.568000 + 0.983804i 0.0209225 + 0.0362389i
\(738\) 0 0
\(739\) −13.3872 + 23.1874i −0.492458 + 0.852962i −0.999962 0.00868705i \(-0.997235\pi\)
0.507504 + 0.861649i \(0.330568\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −5.04669 8.74113i −0.185145 0.320681i 0.758480 0.651696i \(-0.225942\pi\)
−0.943625 + 0.331015i \(0.892609\pi\)
\(744\) 0 0
\(745\) −5.35740 9.27928i −0.196280 0.339967i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −42.2316 25.8198i −1.54311 0.943437i
\(750\) 0 0
\(751\) 5.75729 9.97193i 0.210087 0.363881i −0.741655 0.670782i \(-0.765959\pi\)
0.951741 + 0.306901i \(0.0992921\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0.978019 0.0355938
\(756\) 0 0
\(757\) −15.2484 −0.554214 −0.277107 0.960839i \(-0.589376\pi\)
−0.277107 + 0.960839i \(0.589376\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −0.850874 + 1.47376i −0.0308442 + 0.0534236i −0.881035 0.473050i \(-0.843153\pi\)
0.850191 + 0.526474i \(0.176486\pi\)
\(762\) 0 0
\(763\) 0.190757 7.58277i 0.00690588 0.274515i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −10.8727 18.8320i −0.392589 0.679984i
\(768\) 0 0
\(769\) 24.1211 + 41.7790i 0.869829 + 1.50659i 0.862171 + 0.506618i \(0.169104\pi\)
0.00765823 + 0.999971i \(0.497562\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −3.10243 + 5.37357i −0.111587 + 0.193274i −0.916410 0.400240i \(-0.868927\pi\)
0.804823 + 0.593514i \(0.202260\pi\)
\(774\) 0 0
\(775\) 18.2814 + 31.6643i 0.656688 + 1.13742i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0.735508 1.27394i 0.0263523 0.0456436i
\(780\) 0 0
\(781\) −4.27694 7.40789i −0.153041 0.265075i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −1.95904 + 3.39316i −0.0699212 + 0.121107i
\(786\) 0 0
\(787\) −6.09766 −0.217358 −0.108679 0.994077i \(-0.534662\pi\)
−0.108679 + 0.994077i \(0.534662\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −27.8104 17.0029i −0.988824 0.604554i
\(792\) 0 0
\(793\) 8.35807 + 14.4766i 0.296804 + 0.514079i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 6.22860 + 10.7882i 0.220628 + 0.382139i 0.954999 0.296609i \(-0.0958559\pi\)
−0.734371 + 0.678749i \(0.762523\pi\)
\(798\) 0 0
\(799\) −17.7630 + 30.7665i −0.628411 + 1.08844i
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 4.69748 0.165770
\(804\) 0 0
\(805\) −5.97656 3.65399i −0.210646 0.128786i
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0