Properties

Label 3024.2.q.i.2881.5
Level $3024$
Weight $2$
Character 3024.2881
Analytic conductor $24.147$
Analytic rank $0$
Dimension $10$
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: \(10\)
Relative dimension: \(5\) over \(\Q(\zeta_{3})\)
Coefficient field: 10.0.991381711347.1
Defining polynomial: \(x^{10} - 2 x^{9} + 9 x^{8} - 8 x^{7} + 40 x^{6} - 36 x^{5} + 90 x^{4} - 3 x^{3} + 36 x^{2} - 9 x + 9\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 3^{2} \)
Twist minimal: no (minimal twist has level 63)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 2881.5
Root \(-0.335166 + 0.580525i\) of defining polynomial
Character \(\chi\) \(=\) 3024.2881
Dual form 3024.2.q.i.2305.5

$q$-expansion

\(f(q)\) \(=\) \(q+(0.712469 - 1.23403i) q^{5} +(2.36039 + 1.19522i) q^{7} +O(q^{10})\) \(q+(0.712469 - 1.23403i) q^{5} +(2.36039 + 1.19522i) q^{7} +(2.46539 + 4.27018i) q^{11} +(-1.37730 - 2.38556i) q^{13} +(-0.559839 + 0.969670i) q^{17} +(2.00752 + 3.47713i) q^{19} +(-2.71830 + 4.70824i) q^{23} +(1.48478 + 2.57171i) q^{25} +(-3.40555 + 5.89858i) q^{29} -2.50584 q^{31} +(3.15664 - 2.06124i) q^{35} +(0.709787 + 1.22939i) q^{37} +(-0.124384 - 0.215440i) q^{41} +(0.498313 - 0.863104i) q^{43} -9.47579 q^{47} +(4.14291 + 5.64237i) q^{49} +(0.410229 - 0.710537i) q^{53} +7.02604 q^{55} -6.58407 q^{59} +0.0752645 q^{61} -3.92514 q^{65} +12.5877 q^{67} +0.0804951 q^{71} +(5.34551 - 9.25869i) q^{73} +(0.715488 + 13.0260i) q^{77} +1.84491 q^{79} +(-7.23583 + 12.5328i) q^{83} +(0.797736 + 1.38172i) q^{85} +(-6.76292 - 11.7137i) q^{89} +(-0.399711 - 7.27703i) q^{91} +5.72119 q^{95} +(2.70160 - 4.67930i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10q - 4q^{5} + 4q^{7} + O(q^{10}) \) \( 10q - 4q^{5} + 4q^{7} + 4q^{11} - 8q^{13} - 12q^{17} - q^{19} + 3q^{23} - q^{25} - 7q^{29} - 6q^{31} + 5q^{35} - 5q^{41} + 7q^{43} - 54q^{47} - 8q^{49} + 21q^{53} - 4q^{55} - 60q^{59} + 28q^{61} - 22q^{65} - 4q^{67} - 6q^{71} + 15q^{73} - 11q^{77} - 8q^{79} + 9q^{83} - 6q^{85} - 28q^{89} + 4q^{91} + 28q^{95} - 12q^{97} + O(q^{100}) \)

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
\(5\) 0.712469 1.23403i 0.318626 0.551876i −0.661576 0.749878i \(-0.730112\pi\)
0.980202 + 0.198002i \(0.0634454\pi\)
\(6\) 0 0
\(7\) 2.36039 + 1.19522i 0.892144 + 0.451750i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 2.46539 + 4.27018i 0.743342 + 1.28751i 0.950965 + 0.309297i \(0.100094\pi\)
−0.207623 + 0.978209i \(0.566573\pi\)
\(12\) 0 0
\(13\) −1.37730 2.38556i −0.381995 0.661635i 0.609352 0.792900i \(-0.291429\pi\)
−0.991347 + 0.131265i \(0.958096\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −0.559839 + 0.969670i −0.135781 + 0.235180i −0.925896 0.377780i \(-0.876688\pi\)
0.790115 + 0.612959i \(0.210021\pi\)
\(18\) 0 0
\(19\) 2.00752 + 3.47713i 0.460557 + 0.797709i 0.998989 0.0449606i \(-0.0143162\pi\)
−0.538431 + 0.842669i \(0.680983\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −2.71830 + 4.70824i −0.566806 + 0.981736i 0.430073 + 0.902794i \(0.358488\pi\)
−0.996879 + 0.0789424i \(0.974846\pi\)
\(24\) 0 0
\(25\) 1.48478 + 2.57171i 0.296955 + 0.514342i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −3.40555 + 5.89858i −0.632394 + 1.09534i 0.354667 + 0.934993i \(0.384594\pi\)
−0.987061 + 0.160346i \(0.948739\pi\)
\(30\) 0 0
\(31\) −2.50584 −0.450061 −0.225031 0.974352i \(-0.572248\pi\)
−0.225031 + 0.974352i \(0.572248\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 3.15664 2.06124i 0.533570 0.348414i
\(36\) 0 0
\(37\) 0.709787 + 1.22939i 0.116688 + 0.202110i 0.918453 0.395529i \(-0.129439\pi\)
−0.801765 + 0.597639i \(0.796106\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −0.124384 0.215440i −0.0194256 0.0336460i 0.856149 0.516729i \(-0.172850\pi\)
−0.875575 + 0.483083i \(0.839517\pi\)
\(42\) 0 0
\(43\) 0.498313 0.863104i 0.0759921 0.131622i −0.825525 0.564365i \(-0.809121\pi\)
0.901517 + 0.432743i \(0.142454\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −9.47579 −1.38219 −0.691093 0.722766i \(-0.742871\pi\)
−0.691093 + 0.722766i \(0.742871\pi\)
\(48\) 0 0
\(49\) 4.14291 + 5.64237i 0.591844 + 0.806053i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 0.410229 0.710537i 0.0563493 0.0975998i −0.836475 0.548005i \(-0.815387\pi\)
0.892824 + 0.450406i \(0.148721\pi\)
\(54\) 0 0
\(55\) 7.02604 0.947392
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −6.58407 −0.857173 −0.428586 0.903501i \(-0.640988\pi\)
−0.428586 + 0.903501i \(0.640988\pi\)
\(60\) 0 0
\(61\) 0.0752645 0.00963663 0.00481831 0.999988i \(-0.498466\pi\)
0.00481831 + 0.999988i \(0.498466\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −3.92514 −0.486854
\(66\) 0 0
\(67\) 12.5877 1.53783 0.768916 0.639350i \(-0.220796\pi\)
0.768916 + 0.639350i \(0.220796\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 0.0804951 0.00955301 0.00477651 0.999989i \(-0.498480\pi\)
0.00477651 + 0.999989i \(0.498480\pi\)
\(72\) 0 0
\(73\) 5.34551 9.25869i 0.625644 1.08365i −0.362772 0.931878i \(-0.618170\pi\)
0.988416 0.151769i \(-0.0484971\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 0.715488 + 13.0260i 0.0815374 + 1.48445i
\(78\) 0 0
\(79\) 1.84491 0.207569 0.103785 0.994600i \(-0.466905\pi\)
0.103785 + 0.994600i \(0.466905\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −7.23583 + 12.5328i −0.794236 + 1.37566i 0.129088 + 0.991633i \(0.458795\pi\)
−0.923323 + 0.384023i \(0.874538\pi\)
\(84\) 0 0
\(85\) 0.797736 + 1.38172i 0.0865266 + 0.149868i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −6.76292 11.7137i −0.716868 1.24165i −0.962235 0.272222i \(-0.912242\pi\)
0.245366 0.969430i \(-0.421092\pi\)
\(90\) 0 0
\(91\) −0.399711 7.27703i −0.0419011 0.762840i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 5.72119 0.586982
\(96\) 0 0
\(97\) 2.70160 4.67930i 0.274306 0.475111i −0.695654 0.718377i \(-0.744885\pi\)
0.969960 + 0.243266i \(0.0782187\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −2.56770 4.44739i −0.255496 0.442531i 0.709534 0.704671i \(-0.248905\pi\)
−0.965030 + 0.262139i \(0.915572\pi\)
\(102\) 0 0
\(103\) −7.10561 + 12.3073i −0.700137 + 1.21267i 0.268282 + 0.963341i \(0.413544\pi\)
−0.968418 + 0.249332i \(0.919789\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 3.83015 + 6.63401i 0.370274 + 0.641334i 0.989608 0.143794i \(-0.0459303\pi\)
−0.619333 + 0.785128i \(0.712597\pi\)
\(108\) 0 0
\(109\) −0.849394 + 1.47119i −0.0813572 + 0.140915i −0.903833 0.427885i \(-0.859259\pi\)
0.822476 + 0.568800i \(0.192592\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 0.300351 + 0.520224i 0.0282547 + 0.0489385i 0.879807 0.475331i \(-0.157672\pi\)
−0.851552 + 0.524270i \(0.824338\pi\)
\(114\) 0 0
\(115\) 3.87341 + 6.70895i 0.361198 + 0.625613i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −2.48041 + 1.61967i −0.227379 + 0.148475i
\(120\) 0 0
\(121\) −6.65626 + 11.5290i −0.605115 + 1.04809i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 11.3561 1.01572
\(126\) 0 0
\(127\) −7.25977 −0.644200 −0.322100 0.946706i \(-0.604389\pi\)
−0.322100 + 0.946706i \(0.604389\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 10.2265 17.7128i 0.893492 1.54757i 0.0578326 0.998326i \(-0.481581\pi\)
0.835660 0.549248i \(-0.185086\pi\)
\(132\) 0 0
\(133\) 0.582610 + 10.6068i 0.0505187 + 0.919728i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 6.10581 + 10.5756i 0.521655 + 0.903532i 0.999683 + 0.0251879i \(0.00801840\pi\)
−0.478028 + 0.878345i \(0.658648\pi\)
\(138\) 0 0
\(139\) 1.24092 + 2.14933i 0.105253 + 0.182304i 0.913842 0.406071i \(-0.133101\pi\)
−0.808588 + 0.588375i \(0.799768\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 6.79117 11.7626i 0.567906 0.983642i
\(144\) 0 0
\(145\) 4.85269 + 8.40511i 0.402994 + 0.698006i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −4.27797 + 7.40966i −0.350465 + 0.607023i −0.986331 0.164777i \(-0.947310\pi\)
0.635866 + 0.771799i \(0.280643\pi\)
\(150\) 0 0
\(151\) −8.82962 15.2933i −0.718544 1.24455i −0.961577 0.274537i \(-0.911476\pi\)
0.243033 0.970018i \(-0.421858\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −1.78533 + 3.09228i −0.143401 + 0.248378i
\(156\) 0 0
\(157\) 6.32149 0.504510 0.252255 0.967661i \(-0.418828\pi\)
0.252255 + 0.967661i \(0.418828\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −12.0436 + 7.86433i −0.949172 + 0.619796i
\(162\) 0 0
\(163\) 4.01134 + 6.94784i 0.314192 + 0.544197i 0.979265 0.202581i \(-0.0649331\pi\)
−0.665073 + 0.746778i \(0.731600\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 1.06038 + 1.83663i 0.0820545 + 0.142123i 0.904132 0.427253i \(-0.140518\pi\)
−0.822078 + 0.569375i \(0.807185\pi\)
\(168\) 0 0
\(169\) 2.70608 4.68706i 0.208160 0.360543i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 18.2881 1.39042 0.695208 0.718808i \(-0.255312\pi\)
0.695208 + 0.718808i \(0.255312\pi\)
\(174\) 0 0
\(175\) 0.430902 + 7.84487i 0.0325731 + 0.593017i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 3.81276 6.60389i 0.284979 0.493598i −0.687625 0.726066i \(-0.741347\pi\)
0.972604 + 0.232468i \(0.0746801\pi\)
\(180\) 0 0
\(181\) 15.5305 1.15438 0.577188 0.816611i \(-0.304150\pi\)
0.577188 + 0.816611i \(0.304150\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 2.02280 0.148719
\(186\) 0 0
\(187\) −5.52088 −0.403727
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 14.8325 1.07324 0.536620 0.843824i \(-0.319701\pi\)
0.536620 + 0.843824i \(0.319701\pi\)
\(192\) 0 0
\(193\) 16.5677 1.19257 0.596286 0.802772i \(-0.296642\pi\)
0.596286 + 0.802772i \(0.296642\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 4.03740 0.287653 0.143826 0.989603i \(-0.454059\pi\)
0.143826 + 0.989603i \(0.454059\pi\)
\(198\) 0 0
\(199\) 12.6407 21.8943i 0.896076 1.55205i 0.0636081 0.997975i \(-0.479739\pi\)
0.832468 0.554074i \(-0.186927\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −15.0885 + 9.85259i −1.05901 + 0.691516i
\(204\) 0 0
\(205\) −0.354480 −0.0247579
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −9.89864 + 17.1449i −0.684703 + 1.18594i
\(210\) 0 0
\(211\) 3.76246 + 6.51678i 0.259019 + 0.448634i 0.965979 0.258619i \(-0.0832675\pi\)
−0.706961 + 0.707253i \(0.749934\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −0.710065 1.22987i −0.0484261 0.0838764i
\(216\) 0 0
\(217\) −5.91476 2.99502i −0.401520 0.203315i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 3.08427 0.207471
\(222\) 0 0
\(223\) −6.49230 + 11.2450i −0.434757 + 0.753020i −0.997276 0.0737638i \(-0.976499\pi\)
0.562519 + 0.826784i \(0.309832\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 14.4832 + 25.0857i 0.961286 + 1.66500i 0.719277 + 0.694723i \(0.244473\pi\)
0.242009 + 0.970274i \(0.422194\pi\)
\(228\) 0 0
\(229\) −7.71790 + 13.3678i −0.510013 + 0.883369i 0.489919 + 0.871768i \(0.337026\pi\)
−0.999933 + 0.0116012i \(0.996307\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 2.47324 + 4.28378i 0.162027 + 0.280640i 0.935596 0.353073i \(-0.114863\pi\)
−0.773568 + 0.633713i \(0.781530\pi\)
\(234\) 0 0
\(235\) −6.75121 + 11.6934i −0.440400 + 0.762795i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 6.51732 + 11.2883i 0.421571 + 0.730182i 0.996093 0.0883069i \(-0.0281456\pi\)
−0.574523 + 0.818489i \(0.694812\pi\)
\(240\) 0 0
\(241\) −7.29123 12.6288i −0.469670 0.813492i 0.529729 0.848167i \(-0.322294\pi\)
−0.999399 + 0.0346754i \(0.988960\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 9.91456 1.09247i 0.633418 0.0697951i
\(246\) 0 0
\(247\) 5.52993 9.57812i 0.351861 0.609441i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −14.0715 −0.888187 −0.444094 0.895980i \(-0.646474\pi\)
−0.444094 + 0.895980i \(0.646474\pi\)
\(252\) 0 0
\(253\) −26.8067 −1.68532
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −4.18108 + 7.24184i −0.260808 + 0.451733i −0.966457 0.256829i \(-0.917322\pi\)
0.705649 + 0.708562i \(0.250656\pi\)
\(258\) 0 0
\(259\) 0.205989 + 3.75019i 0.0127996 + 0.233025i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −1.63533 2.83247i −0.100839 0.174658i 0.811192 0.584780i \(-0.198819\pi\)
−0.912030 + 0.410122i \(0.865486\pi\)
\(264\) 0 0
\(265\) −0.584551 1.01247i −0.0359087 0.0621956i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 7.69349 13.3255i 0.469081 0.812471i −0.530295 0.847813i \(-0.677919\pi\)
0.999375 + 0.0353420i \(0.0112521\pi\)
\(270\) 0 0
\(271\) −4.06308 7.03747i −0.246815 0.427496i 0.715825 0.698279i \(-0.246051\pi\)
−0.962640 + 0.270783i \(0.912717\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −7.32110 + 12.6805i −0.441479 + 0.764664i
\(276\) 0 0
\(277\) −6.42287 11.1247i −0.385913 0.668421i 0.605982 0.795478i \(-0.292780\pi\)
−0.991895 + 0.127057i \(0.959447\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 0.724081 1.25415i 0.0431951 0.0748161i −0.843620 0.536941i \(-0.819580\pi\)
0.886815 + 0.462125i \(0.152913\pi\)
\(282\) 0 0
\(283\) 17.4385 1.03661 0.518306 0.855195i \(-0.326563\pi\)
0.518306 + 0.855195i \(0.326563\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −0.0360979 0.657189i −0.00213079 0.0387926i
\(288\) 0 0
\(289\) 7.87316 + 13.6367i 0.463127 + 0.802160i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 0.900048 + 1.55893i 0.0525814 + 0.0910736i 0.891118 0.453772i \(-0.149922\pi\)
−0.838537 + 0.544845i \(0.816588\pi\)
\(294\) 0 0
\(295\) −4.69094 + 8.12495i −0.273117 + 0.473053i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 14.9757 0.866068
\(300\) 0 0
\(301\) 2.20781 1.44167i 0.127256 0.0830965i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 0.0536236 0.0928787i 0.00307048 0.00531822i
\(306\) 0 0
\(307\) −1.06478 −0.0607699 −0.0303850 0.999538i \(-0.509673\pi\)
−0.0303850 + 0.999538i \(0.509673\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −16.9293 −0.959970 −0.479985 0.877277i \(-0.659358\pi\)
−0.479985 + 0.877277i \(0.659358\pi\)
\(312\) 0 0
\(313\) −8.27856 −0.467932 −0.233966 0.972245i \(-0.575170\pi\)
−0.233966 + 0.972245i \(0.575170\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −6.54741 −0.367739 −0.183870 0.982951i \(-0.558862\pi\)
−0.183870 + 0.982951i \(0.558862\pi\)
\(318\) 0 0
\(319\) −33.5840 −1.88034
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −4.49556 −0.250140
\(324\) 0 0
\(325\) 4.08997 7.08404i 0.226871 0.392952i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −22.3666 11.3256i −1.23311 0.624403i
\(330\) 0 0
\(331\) 26.7258 1.46899 0.734493 0.678617i \(-0.237420\pi\)
0.734493 + 0.678617i \(0.237420\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 8.96834 15.5336i 0.489993 0.848692i
\(336\) 0 0
\(337\) −4.76164 8.24740i −0.259383 0.449264i 0.706694 0.707520i \(-0.250186\pi\)
−0.966077 + 0.258255i \(0.916853\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −6.17786 10.7004i −0.334550 0.579457i
\(342\) 0 0
\(343\) 3.03502 + 18.2699i 0.163876 + 0.986481i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −18.7031 −1.00404 −0.502018 0.864857i \(-0.667409\pi\)
−0.502018 + 0.864857i \(0.667409\pi\)
\(348\) 0 0
\(349\) −15.0542 + 26.0747i −0.805834 + 1.39574i 0.109893 + 0.993943i \(0.464949\pi\)
−0.915727 + 0.401801i \(0.868384\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 3.12966 + 5.42074i 0.166575 + 0.288517i 0.937214 0.348756i \(-0.113396\pi\)
−0.770638 + 0.637273i \(0.780062\pi\)
\(354\) 0 0
\(355\) 0.0573502 0.0993335i 0.00304383 0.00527208i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −5.09755 8.82921i −0.269038 0.465988i 0.699575 0.714559i \(-0.253372\pi\)
−0.968614 + 0.248571i \(0.920039\pi\)
\(360\) 0 0
\(361\) 1.43970 2.49364i 0.0757739 0.131244i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −7.61701 13.1931i −0.398693 0.690556i
\(366\) 0 0
\(367\) −14.3278 24.8165i −0.747906 1.29541i −0.948824 0.315804i \(-0.897726\pi\)
0.200918 0.979608i \(-0.435608\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 1.81755 1.18683i 0.0943624 0.0616173i
\(372\) 0 0
\(373\) 8.03670 13.9200i 0.416124 0.720749i −0.579421 0.815028i \(-0.696721\pi\)
0.995546 + 0.0942796i \(0.0300548\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 18.7619 0.966286
\(378\) 0 0
\(379\) 1.01893 0.0523388 0.0261694 0.999658i \(-0.491669\pi\)
0.0261694 + 0.999658i \(0.491669\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 5.79327 10.0342i 0.296022 0.512725i −0.679200 0.733953i \(-0.737673\pi\)
0.975222 + 0.221228i \(0.0710065\pi\)
\(384\) 0 0
\(385\) 16.5842 + 8.39766i 0.845210 + 0.427984i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 8.90675 + 15.4270i 0.451590 + 0.782178i 0.998485 0.0550239i \(-0.0175235\pi\)
−0.546895 + 0.837201i \(0.684190\pi\)
\(390\) 0 0
\(391\) −3.04363 5.27172i −0.153923 0.266602i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 1.31444 2.27668i 0.0661369 0.114552i
\(396\) 0 0
\(397\) −6.54229 11.3316i −0.328348 0.568715i 0.653836 0.756636i \(-0.273159\pi\)
−0.982184 + 0.187921i \(0.939825\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 7.05165 12.2138i 0.352143 0.609929i −0.634482 0.772938i \(-0.718787\pi\)
0.986625 + 0.163009i \(0.0521199\pi\)
\(402\) 0 0
\(403\) 3.45129 + 5.97782i 0.171921 + 0.297776i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −3.49980 + 6.06183i −0.173479 + 0.300474i
\(408\) 0 0
\(409\) −2.64599 −0.130836 −0.0654179 0.997858i \(-0.520838\pi\)
−0.0654179 + 0.997858i \(0.520838\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −15.5410 7.86940i −0.764722 0.387228i
\(414\) 0 0
\(415\) 10.3106 + 17.8585i 0.506128 + 0.876639i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 16.7567 + 29.0235i 0.818619 + 1.41789i 0.906700 + 0.421776i \(0.138593\pi\)
−0.0880816 + 0.996113i \(0.528074\pi\)
\(420\) 0 0
\(421\) −2.41950 + 4.19071i −0.117919 + 0.204242i −0.918943 0.394390i \(-0.870956\pi\)
0.801024 + 0.598633i \(0.204289\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −3.32495 −0.161284
\(426\) 0 0
\(427\) 0.177654 + 0.0899575i 0.00859726 + 0.00435335i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 17.6643 30.5954i 0.850858 1.47373i −0.0295774 0.999562i \(-0.509416\pi\)
0.880435 0.474166i \(-0.157251\pi\)
\(432\) 0 0
\(433\) 5.47404 0.263066 0.131533 0.991312i \(-0.458010\pi\)
0.131533 + 0.991312i \(0.458010\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −21.8282 −1.04419
\(438\) 0 0
\(439\) −6.39812 −0.305365 −0.152683 0.988275i \(-0.548791\pi\)
−0.152683 + 0.988275i \(0.548791\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −6.38682 −0.303447 −0.151723 0.988423i \(-0.548482\pi\)
−0.151723 + 0.988423i \(0.548482\pi\)
\(444\) 0 0
\(445\) −19.2735 −0.913650
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 11.7460 0.554327 0.277163 0.960823i \(-0.410606\pi\)
0.277163 + 0.960823i \(0.410606\pi\)
\(450\) 0 0
\(451\) 0.613311 1.06229i 0.0288797 0.0500210i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −9.26487 4.69140i −0.434344 0.219936i
\(456\) 0 0
\(457\) 10.5224 0.492217 0.246108 0.969242i \(-0.420848\pi\)
0.246108 + 0.969242i \(0.420848\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 3.54278 6.13627i 0.165004 0.285794i −0.771653 0.636044i \(-0.780570\pi\)
0.936657 + 0.350249i \(0.113903\pi\)
\(462\) 0 0
\(463\) −16.3760 28.3641i −0.761059 1.31819i −0.942305 0.334755i \(-0.891346\pi\)
0.181246 0.983438i \(-0.441987\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 1.96216 + 3.39856i 0.0907978 + 0.157266i 0.907847 0.419301i \(-0.137725\pi\)
−0.817049 + 0.576568i \(0.804392\pi\)
\(468\) 0 0
\(469\) 29.7119 + 15.0450i 1.37197 + 0.694716i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 4.91414 0.225952
\(474\) 0 0
\(475\) −5.96145 + 10.3255i −0.273530 + 0.473768i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −8.04324 13.9313i −0.367505 0.636537i 0.621670 0.783279i \(-0.286455\pi\)
−0.989175 + 0.146742i \(0.953121\pi\)
\(480\) 0 0
\(481\) 1.95518 3.38647i 0.0891486 0.154410i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −3.84961 6.66771i −0.174802 0.302765i
\(486\) 0 0
\(487\) 1.75172 3.03407i 0.0793781 0.137487i −0.823604 0.567166i \(-0.808040\pi\)
0.902982 + 0.429679i \(0.141373\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −20.5546 35.6017i −0.927618 1.60668i −0.787296 0.616575i \(-0.788520\pi\)
−0.140321 0.990106i \(-0.544814\pi\)
\(492\) 0 0
\(493\) −3.81312 6.60452i −0.171734 0.297452i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0.190000 + 0.0962092i 0.00852267 + 0.00431557i
\(498\) 0 0
\(499\) 5.91486 10.2448i 0.264785 0.458622i −0.702722 0.711465i \(-0.748032\pi\)
0.967507 + 0.252843i \(0.0813655\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 21.8595 0.974665 0.487332 0.873217i \(-0.337970\pi\)
0.487332 + 0.873217i \(0.337970\pi\)
\(504\) 0 0
\(505\) −7.31762 −0.325630
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 8.44831 14.6329i 0.374465 0.648592i −0.615782 0.787917i \(-0.711160\pi\)
0.990247 + 0.139324i \(0.0444931\pi\)
\(510\) 0 0
\(511\) 23.6836 15.4651i 1.04770 0.684135i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 10.1250 + 17.5371i 0.446163 + 0.772777i
\(516\) 0 0
\(517\) −23.3615 40.4633i −1.02744 1.77957i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 17.2466 29.8720i 0.755587 1.30872i −0.189495 0.981882i \(-0.560685\pi\)
0.945082 0.326834i \(-0.105982\pi\)
\(522\) 0 0
\(523\) −0.995615 1.72445i −0.0435352 0.0754051i 0.843437 0.537229i \(-0.180529\pi\)
−0.886972 + 0.461823i \(0.847195\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 1.40287 2.42983i 0.0611098 0.105845i
\(528\) 0 0
\(529\) −3.27836 5.67829i −0.142538 0.246882i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −0.342629 + 0.593452i −0.0148409 + 0.0257052i
\(534\) 0 0
\(535\) 10.9154 0.471916
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −13.8800 + 31.6016i −0.597856 + 1.36118i
\(540\) 0 0
\(541\) −15.0681 26.0988i −0.647830 1.12207i −0.983640 0.180145i \(-0.942343\pi\)
0.335810 0.941930i \(-0.390990\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 1.21033 + 2.09636i 0.0518450 + 0.0897982i
\(546\) 0 0
\(547\) −7.68070 + 13.3034i −0.328403 + 0.568810i −0.982195 0.187864i \(-0.939844\pi\)
0.653792 + 0.756674i \(0.273177\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −27.3469 −1.16502
\(552\) 0 0
\(553\) 4.35472 + 2.20508i 0.185182 + 0.0937694i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 11.6412 20.1631i 0.493252 0.854338i −0.506718 0.862112i \(-0.669141\pi\)
0.999970 + 0.00777438i \(0.00247469\pi\)
\(558\) 0 0
\(559\) −2.74531 −0.116114
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 4.55885 0.192133 0.0960663 0.995375i \(-0.469374\pi\)
0.0960663 + 0.995375i \(0.469374\pi\)
\(564\) 0 0
\(565\) 0.855964 0.0360107
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −18.1995 −0.762963 −0.381482 0.924376i \(-0.624586\pi\)
−0.381482 + 0.924376i \(0.624586\pi\)
\(570\) 0 0
\(571\) 17.0455 0.713332 0.356666 0.934232i \(-0.383913\pi\)
0.356666 + 0.934232i \(0.383913\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −16.1443 −0.673264
\(576\) 0 0
\(577\) −5.70473 + 9.88088i −0.237491 + 0.411346i −0.959994 0.280022i \(-0.909658\pi\)
0.722503 + 0.691368i \(0.242992\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −32.0589 + 20.9340i −1.33003 + 0.868488i
\(582\) 0 0
\(583\) 4.04549 0.167547
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 2.52544 4.37420i 0.104236 0.180543i −0.809190 0.587548i \(-0.800094\pi\)
0.913426 + 0.407005i \(0.133427\pi\)
\(588\) 0 0
\(589\) −5.03052 8.71312i −0.207279 0.359018i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 9.98892 + 17.3013i 0.410196 + 0.710480i 0.994911 0.100759i \(-0.0321271\pi\)
−0.584715 + 0.811239i \(0.698794\pi\)
\(594\) 0 0
\(595\) 0.231513 + 4.21487i 0.00949113 + 0.172793i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 4.39321 0.179502 0.0897508 0.995964i \(-0.471393\pi\)
0.0897508 + 0.995964i \(0.471393\pi\)
\(600\) 0 0
\(601\) 12.1778 21.0926i 0.496743 0.860385i −0.503250 0.864141i \(-0.667862\pi\)
0.999993 + 0.00375637i \(0.00119569\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 9.48476 + 16.4281i 0.385610 + 0.667897i
\(606\) 0 0
\(607\) 6.56281 11.3671i 0.266376 0.461377i −0.701547 0.712623i \(-0.747507\pi\)
0.967923 + 0.251246i \(0.0808403\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 13.0510 + 22.6051i 0.527988 + 0.914502i
\(612\) 0 0
\(613\) −23.2403 + 40.2534i −0.938667 + 1.62582i −0.170707 + 0.985322i \(0.554605\pi\)
−0.767960 + 0.640497i \(0.778728\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −14.1948 24.5862i −0.571463 0.989803i −0.996416 0.0845873i \(-0.973043\pi\)
0.424953 0.905215i \(-0.360291\pi\)
\(618\) 0 0
\(619\) 15.9606 + 27.6446i 0.641511 + 1.11113i 0.985096 + 0.172008i \(0.0550254\pi\)
−0.343585 + 0.939122i \(0.611641\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −1.96269 35.7322i −0.0786335 1.43158i
\(624\) 0 0
\(625\) 0.666993 1.15527i 0.0266797 0.0462106i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −1.58947 −0.0633762
\(630\) 0 0
\(631\) −38.7184 −1.54135 −0.770677 0.637226i \(-0.780082\pi\)
−0.770677 + 0.637226i \(0.780082\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −5.17236 + 8.95878i −0.205259 + 0.355519i
\(636\) 0 0
\(637\) 7.75417 17.6544i 0.307231 0.699492i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −20.2001 34.9875i −0.797854 1.38192i −0.921011 0.389537i \(-0.872635\pi\)
0.123157 0.992387i \(-0.460698\pi\)
\(642\) 0 0
\(643\) −6.27355 10.8661i −0.247405 0.428517i 0.715400 0.698715i \(-0.246244\pi\)
−0.962805 + 0.270198i \(0.912911\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 17.2774 29.9253i 0.679245 1.17649i −0.295964 0.955199i \(-0.595641\pi\)
0.975209 0.221287i \(-0.0710258\pi\)
\(648\) 0 0
\(649\) −16.2323 28.1151i −0.637173 1.10362i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −11.1472 + 19.3075i −0.436223 + 0.755560i −0.997395 0.0721392i \(-0.977017\pi\)
0.561172 + 0.827699i \(0.310351\pi\)
\(654\) 0 0
\(655\) −14.5721 25.2396i −0.569379 0.986194i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 3.57493 6.19196i 0.139259 0.241204i −0.787957 0.615730i \(-0.788861\pi\)
0.927217 + 0.374526i \(0.122194\pi\)
\(660\) 0 0
\(661\) 42.9060 1.66885 0.834425 0.551122i \(-0.185800\pi\)
0.834425 + 0.551122i \(0.185800\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 13.5043 + 6.83807i 0.523672 + 0.265169i
\(666\) 0 0
\(667\) −18.5146 32.0683i −0.716889 1.24169i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0.185556 + 0.321392i 0.00716331 + 0.0124072i
\(672\) 0 0
\(673\) −18.8270 + 32.6094i −0.725729 + 1.25700i 0.232944 + 0.972490i \(0.425164\pi\)
−0.958673 + 0.284510i \(0.908169\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 26.3616 1.01316 0.506580 0.862193i \(-0.330910\pi\)
0.506580 + 0.862193i \(0.330910\pi\)
\(678\) 0 0
\(679\) 11.9696 7.81599i 0.459352 0.299950i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 1.96588 3.40500i 0.0752222 0.130289i −0.825961 0.563728i \(-0.809367\pi\)
0.901183 + 0.433439i \(0.142700\pi\)
\(684\) 0 0
\(685\) 17.4008 0.664850
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −2.26004 −0.0861006
\(690\) 0 0
\(691\) −19.9010 −0.757072 −0.378536 0.925587i \(-0.623572\pi\)
−0.378536 + 0.925587i \(0.623572\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 3.53645 0.134145
\(696\) 0 0
\(697\) 0.278541 0.0105505
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −43.7908 −1.65396 −0.826979 0.562234i \(-0.809942\pi\)
−0.826979 + 0.562234i \(0.809942\pi\)
\(702\) 0 0
\(703\) −2.84983 + 4.93604i −0.107483 + 0.186166i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −0.745180 13.5665i −0.0280254 0.510222i
\(708\) 0 0
\(709\) 44.6344 1.67628 0.838139 0.545457i \(-0.183644\pi\)
0.838139 + 0.545457i \(0.183644\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 6.81163 11.7981i 0.255097 0.441842i
\(714\) 0 0
\(715\) −9.67699 16.7610i −0.361899 0.626827i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −19.5096 33.7917i −0.727586 1.26022i −0.957901 0.287100i \(-0.907309\pi\)
0.230315 0.973116i \(-0.426024\pi\)
\(720\) 0 0
\(721\) −31.4819 + 20.5572i −1.17245 + 0.765592i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −20.2259 −0.751171
\(726\) 0 0
\(727\) 11.2554 19.4949i 0.417439 0.723025i −0.578242 0.815865i \(-0.696261\pi\)
0.995681 + 0.0928402i \(0.0295946\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 0.557951 + 0.966399i 0.0206366 + 0.0357436i
\(732\) 0 0
\(733\) 0.448519 0.776858i 0.0165664 0.0286939i −0.857623 0.514278i \(-0.828060\pi\)
0.874190 + 0.485584i \(0.161393\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 31.0335 + 53.7517i 1.14314 + 1.97997i
\(738\) 0 0
\(739\) −1.79032 + 3.10092i −0.0658578 + 0.114069i −0.897074 0.441880i \(-0.854312\pi\)
0.831216 + 0.555949i \(0.187645\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −24.7964 42.9486i −0.909691 1.57563i −0.814493 0.580173i \(-0.802985\pi\)
−0.0951977 0.995458i \(-0.530348\pi\)
\(744\) 0 0
\(745\) 6.09583 + 10.5583i 0.223334 + 0.386826i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 1.11156 + 20.2367i 0.0406155 + 0.739434i
\(750\) 0 0
\(751\) −21.4515 + 37.1551i −0.782776 + 1.35581i 0.147543 + 0.989056i \(0.452864\pi\)
−0.930319 + 0.366752i \(0.880470\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −25.1633 −0.915786
\(756\) 0 0
\(757\) 13.8029 0.501677 0.250838 0.968029i \(-0.419294\pi\)
0.250838 + 0.968029i \(0.419294\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 20.3599 35.2643i 0.738044 1.27833i −0.215330 0.976541i \(-0.569083\pi\)
0.953375 0.301789i \(-0.0975839\pi\)
\(762\) 0 0
\(763\) −3.76330 + 2.45738i −0.136241 + 0.0889633i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 9.06826 + 15.7067i 0.327436 + 0.567135i
\(768\) 0 0
\(769\) 5.57381 + 9.65413i 0.200997 + 0.348137i 0.948850 0.315728i \(-0.102249\pi\)
−0.747853 + 0.663864i \(0.768915\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 0.462831 0.801647i 0.0166469 0.0288332i −0.857582 0.514347i \(-0.828034\pi\)
0.874229 + 0.485514i \(0.161368\pi\)
\(774\) 0 0
\(775\) −3.72061 6.44428i −0.133648 0.231485i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0.499408 0.865001i 0.0178932 0.0309919i
\(780\) 0 0
\(781\) 0.198452 + 0.343728i 0.00710116 + 0.0122996i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 4.50386 7.80092i 0.160750 0.278427i
\(786\) 0 0
\(787\) −23.0240 −0.820716 −0.410358 0.911925i \(-0.634596\pi\)
−0.410358 + 0.911925i \(0.634596\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0.0871659 + 1.58692i 0.00309926 + 0.0564243i
\(792\) 0 0
\(793\) −0.103662 0.179548i −0.00368114 0.00637593i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −11.3925 19.7325i −0.403544 0.698960i 0.590606 0.806960i \(-0.298889\pi\)
−0.994151 + 0.108000i \(0.965555\pi\)
\(798\) 0 0
\(799\) 5.30492 9.18839i 0.187675 0.325062i
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 52.7150 1.86027
\(804\)