Properties

Label 3024.2.q.i.2305.3
Level $3024$
Weight $2$
Character 3024.2305
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 2305.3
Root \(-1.02682 - 1.77851i\) of defining polynomial
Character \(\chi\) \(=\) 3024.2305
Dual form 3024.2.q.i.2881.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.0731228 - 0.126652i) q^{5} +(2.33035 + 1.25278i) q^{7} +O(q^{10})\) \(q+(-0.0731228 - 0.126652i) q^{5} +(2.33035 + 1.25278i) q^{7} +(-0.832020 + 1.44110i) q^{11} +(0.0999454 - 0.173111i) q^{13} +(-3.13555 - 5.43093i) q^{17} +(-3.45879 + 5.99080i) q^{19} +(3.09092 + 5.35363i) q^{23} +(2.48931 - 4.31160i) q^{25} +(2.46757 + 4.27396i) q^{29} +2.51780 q^{31} +(-0.0117348 - 0.386752i) q^{35} +(-3.50023 + 6.06257i) q^{37} +(-1.15895 + 2.00736i) q^{41} +(0.940993 + 1.62985i) q^{43} -1.81177 q^{47} +(3.86110 + 5.83883i) q^{49} +(2.67307 + 4.62989i) q^{53} +0.243359 q^{55} -4.57099 q^{59} -0.678276 q^{61} -0.0292332 q^{65} +6.18684 q^{67} +1.27749 q^{71} +(-0.778603 - 1.34858i) q^{73} +(-3.74428 + 2.31594i) q^{77} -12.7957 q^{79} +(3.75687 + 6.50709i) q^{83} +(-0.458561 + 0.794251i) q^{85} +(-4.53394 + 7.85301i) q^{89} +(0.449777 - 0.278199i) q^{91} +1.01167 q^{95} +(-3.98514 - 6.90246i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10q - 4q^{5} + 4q^{7} + O(q^{10}) \) \( 10q - 4q^{5} + 4q^{7} + 4q^{11} - 8q^{13} - 12q^{17} - q^{19} + 3q^{23} - q^{25} - 7q^{29} - 6q^{31} + 5q^{35} - 5q^{41} + 7q^{43} - 54q^{47} - 8q^{49} + 21q^{53} - 4q^{55} - 60q^{59} + 28q^{61} - 22q^{65} - 4q^{67} - 6q^{71} + 15q^{73} - 11q^{77} - 8q^{79} + 9q^{83} - 6q^{85} - 28q^{89} + 4q^{91} + 28q^{95} - 12q^{97} + O(q^{100}) \)

Character values

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

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

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
\(5\) −0.0731228 0.126652i −0.0327015 0.0566407i 0.849211 0.528053i \(-0.177078\pi\)
−0.881913 + 0.471412i \(0.843744\pi\)
\(6\) 0 0
\(7\) 2.33035 + 1.25278i 0.880791 + 0.473505i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −0.832020 + 1.44110i −0.250864 + 0.434508i −0.963764 0.266757i \(-0.914048\pi\)
0.712900 + 0.701265i \(0.247381\pi\)
\(12\) 0 0
\(13\) 0.0999454 0.173111i 0.0277199 0.0480122i −0.851833 0.523814i \(-0.824509\pi\)
0.879553 + 0.475802i \(0.157842\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −3.13555 5.43093i −0.760483 1.31720i −0.942602 0.333919i \(-0.891629\pi\)
0.182119 0.983277i \(-0.441704\pi\)
\(18\) 0 0
\(19\) −3.45879 + 5.99080i −0.793500 + 1.37438i 0.130287 + 0.991476i \(0.458410\pi\)
−0.923787 + 0.382907i \(0.874923\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 3.09092 + 5.35363i 0.644501 + 1.11631i 0.984417 + 0.175852i \(0.0562682\pi\)
−0.339916 + 0.940456i \(0.610399\pi\)
\(24\) 0 0
\(25\) 2.48931 4.31160i 0.497861 0.862321i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 2.46757 + 4.27396i 0.458217 + 0.793655i 0.998867 0.0475930i \(-0.0151551\pi\)
−0.540650 + 0.841248i \(0.681822\pi\)
\(30\) 0 0
\(31\) 2.51780 0.452209 0.226105 0.974103i \(-0.427401\pi\)
0.226105 + 0.974103i \(0.427401\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −0.0117348 0.386752i −0.00198354 0.0653730i
\(36\) 0 0
\(37\) −3.50023 + 6.06257i −0.575434 + 0.996681i 0.420560 + 0.907264i \(0.361833\pi\)
−0.995994 + 0.0894162i \(0.971500\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −1.15895 + 2.00736i −0.180998 + 0.313498i −0.942221 0.334993i \(-0.891266\pi\)
0.761223 + 0.648491i \(0.224599\pi\)
\(42\) 0 0
\(43\) 0.940993 + 1.62985i 0.143500 + 0.248550i 0.928812 0.370550i \(-0.120831\pi\)
−0.785312 + 0.619100i \(0.787498\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −1.81177 −0.264275 −0.132137 0.991231i \(-0.542184\pi\)
−0.132137 + 0.991231i \(0.542184\pi\)
\(48\) 0 0
\(49\) 3.86110 + 5.83883i 0.551586 + 0.834118i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 2.67307 + 4.62989i 0.367174 + 0.635964i 0.989123 0.147094i \(-0.0469920\pi\)
−0.621948 + 0.783058i \(0.713659\pi\)
\(54\) 0 0
\(55\) 0.243359 0.0328145
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −4.57099 −0.595092 −0.297546 0.954708i \(-0.596168\pi\)
−0.297546 + 0.954708i \(0.596168\pi\)
\(60\) 0 0
\(61\) −0.678276 −0.0868443 −0.0434221 0.999057i \(-0.513826\pi\)
−0.0434221 + 0.999057i \(0.513826\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −0.0292332 −0.00362593
\(66\) 0 0
\(67\) 6.18684 0.755842 0.377921 0.925838i \(-0.376639\pi\)
0.377921 + 0.925838i \(0.376639\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 1.27749 0.151611 0.0758053 0.997123i \(-0.475847\pi\)
0.0758053 + 0.997123i \(0.475847\pi\)
\(72\) 0 0
\(73\) −0.778603 1.34858i −0.0911286 0.157839i 0.816858 0.576839i \(-0.195714\pi\)
−0.907986 + 0.419000i \(0.862381\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −3.74428 + 2.31594i −0.426700 + 0.263926i
\(78\) 0 0
\(79\) −12.7957 −1.43963 −0.719817 0.694164i \(-0.755774\pi\)
−0.719817 + 0.694164i \(0.755774\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 3.75687 + 6.50709i 0.412370 + 0.714246i 0.995148 0.0983854i \(-0.0313678\pi\)
−0.582778 + 0.812631i \(0.698034\pi\)
\(84\) 0 0
\(85\) −0.458561 + 0.794251i −0.0497379 + 0.0861486i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −4.53394 + 7.85301i −0.480597 + 0.832418i −0.999752 0.0222619i \(-0.992913\pi\)
0.519155 + 0.854680i \(0.326247\pi\)
\(90\) 0 0
\(91\) 0.449777 0.278199i 0.0471494 0.0291632i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 1.01167 0.103795
\(96\) 0 0
\(97\) −3.98514 6.90246i −0.404630 0.700839i 0.589649 0.807660i \(-0.299266\pi\)
−0.994278 + 0.106821i \(0.965933\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 7.42150 12.8544i 0.738467 1.27906i −0.214719 0.976676i \(-0.568883\pi\)
0.953186 0.302386i \(-0.0977832\pi\)
\(102\) 0 0
\(103\) −0.101974 0.176624i −0.0100478 0.0174033i 0.860958 0.508676i \(-0.169865\pi\)
−0.871006 + 0.491273i \(0.836532\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 3.48444 6.03524i 0.336854 0.583448i −0.646985 0.762503i \(-0.723970\pi\)
0.983839 + 0.179054i \(0.0573038\pi\)
\(108\) 0 0
\(109\) 3.33058 + 5.76874i 0.319012 + 0.552545i 0.980282 0.197603i \(-0.0633157\pi\)
−0.661270 + 0.750148i \(0.729982\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 0.0193234 0.0334691i 0.00181779 0.00314851i −0.865115 0.501573i \(-0.832755\pi\)
0.866933 + 0.498425i \(0.166088\pi\)
\(114\) 0 0
\(115\) 0.452033 0.782945i 0.0421523 0.0730100i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −0.503195 16.5841i −0.0461278 1.52027i
\(120\) 0 0
\(121\) 4.11548 + 7.12823i 0.374135 + 0.648021i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −1.45933 −0.130526
\(126\) 0 0
\(127\) −13.4788 −1.19605 −0.598027 0.801476i \(-0.704048\pi\)
−0.598027 + 0.801476i \(0.704048\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 9.91665 + 17.1761i 0.866422 + 1.50069i 0.865628 + 0.500687i \(0.166919\pi\)
0.000793988 1.00000i \(0.499747\pi\)
\(132\) 0 0
\(133\) −15.5653 + 9.62759i −1.34969 + 0.834818i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −3.22255 + 5.58162i −0.275321 + 0.476870i −0.970216 0.242241i \(-0.922117\pi\)
0.694895 + 0.719111i \(0.255451\pi\)
\(138\) 0 0
\(139\) −6.26527 + 10.8518i −0.531413 + 0.920435i 0.467914 + 0.883774i \(0.345006\pi\)
−0.999328 + 0.0366611i \(0.988328\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0.166313 + 0.288063i 0.0139078 + 0.0240890i
\(144\) 0 0
\(145\) 0.360872 0.625048i 0.0299688 0.0519074i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 8.88364 + 15.3869i 0.727776 + 1.26054i 0.957821 + 0.287365i \(0.0927792\pi\)
−0.230045 + 0.973180i \(0.573887\pi\)
\(150\) 0 0
\(151\) 4.23300 7.33177i 0.344476 0.596651i −0.640782 0.767723i \(-0.721390\pi\)
0.985259 + 0.171072i \(0.0547231\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −0.184108 0.318885i −0.0147879 0.0256135i
\(156\) 0 0
\(157\) 5.69935 0.454858 0.227429 0.973795i \(-0.426968\pi\)
0.227429 + 0.973795i \(0.426968\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0.496032 + 16.3481i 0.0390928 + 1.28841i
\(162\) 0 0
\(163\) 1.06267 1.84060i 0.0832349 0.144167i −0.821403 0.570349i \(-0.806808\pi\)
0.904638 + 0.426181i \(0.140141\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −5.78723 + 10.0238i −0.447829 + 0.775663i −0.998244 0.0592278i \(-0.981136\pi\)
0.550415 + 0.834891i \(0.314470\pi\)
\(168\) 0 0
\(169\) 6.48002 + 11.2237i 0.498463 + 0.863364i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 15.9109 1.20968 0.604842 0.796345i \(-0.293236\pi\)
0.604842 + 0.796345i \(0.293236\pi\)
\(174\) 0 0
\(175\) 11.2024 6.92902i 0.846825 0.523785i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 3.87665 + 6.71456i 0.289755 + 0.501870i 0.973751 0.227615i \(-0.0730929\pi\)
−0.683996 + 0.729485i \(0.739760\pi\)
\(180\) 0 0
\(181\) −12.1618 −0.903982 −0.451991 0.892022i \(-0.649286\pi\)
−0.451991 + 0.892022i \(0.649286\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 1.02379 0.0752703
\(186\) 0 0
\(187\) 10.4354 0.763110
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −4.96765 −0.359447 −0.179723 0.983717i \(-0.557520\pi\)
−0.179723 + 0.983717i \(0.557520\pi\)
\(192\) 0 0
\(193\) −14.9044 −1.07284 −0.536422 0.843950i \(-0.680224\pi\)
−0.536422 + 0.843950i \(0.680224\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 21.2608 1.51477 0.757386 0.652968i \(-0.226476\pi\)
0.757386 + 0.652968i \(0.226476\pi\)
\(198\) 0 0
\(199\) 9.97208 + 17.2722i 0.706902 + 1.22439i 0.966001 + 0.258540i \(0.0832413\pi\)
−0.259098 + 0.965851i \(0.583425\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 0.395997 + 13.0512i 0.0277935 + 0.916012i
\(204\) 0 0
\(205\) 0.338983 0.0236756
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −5.75556 9.96893i −0.398121 0.689565i
\(210\) 0 0
\(211\) −11.7569 + 20.3636i −0.809381 + 1.40189i 0.103912 + 0.994587i \(0.466864\pi\)
−0.913293 + 0.407303i \(0.866469\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 0.137616 0.238358i 0.00938535 0.0162559i
\(216\) 0 0
\(217\) 5.86735 + 3.15424i 0.398302 + 0.214123i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −1.25354 −0.0843220
\(222\) 0 0
\(223\) −2.03052 3.51696i −0.135974 0.235513i 0.789995 0.613113i \(-0.210083\pi\)
−0.925969 + 0.377600i \(0.876750\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 1.92643 3.33667i 0.127861 0.221462i −0.794986 0.606627i \(-0.792522\pi\)
0.922848 + 0.385165i \(0.125855\pi\)
\(228\) 0 0
\(229\) −6.55812 11.3590i −0.433373 0.750624i 0.563788 0.825919i \(-0.309343\pi\)
−0.997161 + 0.0752952i \(0.976010\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 8.75115 15.1574i 0.573307 0.992997i −0.422916 0.906169i \(-0.638993\pi\)
0.996223 0.0868284i \(-0.0276732\pi\)
\(234\) 0 0
\(235\) 0.132482 + 0.229466i 0.00864218 + 0.0149687i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 3.65857 6.33683i 0.236653 0.409895i −0.723099 0.690745i \(-0.757283\pi\)
0.959752 + 0.280849i \(0.0906161\pi\)
\(240\) 0 0
\(241\) −3.11553 + 5.39626i −0.200689 + 0.347604i −0.948751 0.316026i \(-0.897651\pi\)
0.748062 + 0.663629i \(0.230985\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 0.457167 0.915969i 0.0292074 0.0585191i
\(246\) 0 0
\(247\) 0.691380 + 1.19751i 0.0439915 + 0.0761954i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 5.65283 0.356803 0.178402 0.983958i \(-0.442907\pi\)
0.178402 + 0.983958i \(0.442907\pi\)
\(252\) 0 0
\(253\) −10.2868 −0.646727
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 5.90082 + 10.2205i 0.368083 + 0.637539i 0.989266 0.146127i \(-0.0466808\pi\)
−0.621183 + 0.783666i \(0.713347\pi\)
\(258\) 0 0
\(259\) −15.7518 + 9.74293i −0.978770 + 0.605396i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 11.1200 19.2605i 0.685691 1.18765i −0.287528 0.957772i \(-0.592834\pi\)
0.973219 0.229879i \(-0.0738331\pi\)
\(264\) 0 0
\(265\) 0.390925 0.677101i 0.0240143 0.0415940i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 1.19442 + 2.06880i 0.0728251 + 0.126137i 0.900138 0.435604i \(-0.143465\pi\)
−0.827313 + 0.561741i \(0.810132\pi\)
\(270\) 0 0
\(271\) 11.6129 20.1142i 0.705435 1.22185i −0.261100 0.965312i \(-0.584085\pi\)
0.966534 0.256537i \(-0.0825815\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 4.14231 + 7.17469i 0.249790 + 0.432650i
\(276\) 0 0
\(277\) 2.30900 3.99931i 0.138734 0.240295i −0.788283 0.615312i \(-0.789030\pi\)
0.927018 + 0.375017i \(0.122363\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −5.90841 10.2337i −0.352466 0.610489i 0.634215 0.773157i \(-0.281324\pi\)
−0.986681 + 0.162668i \(0.947990\pi\)
\(282\) 0 0
\(283\) −15.8497 −0.942165 −0.471082 0.882089i \(-0.656137\pi\)
−0.471082 + 0.882089i \(0.656137\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −5.21555 + 3.22596i −0.307864 + 0.190422i
\(288\) 0 0
\(289\) −11.1634 + 19.3355i −0.656669 + 1.13738i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −7.04804 + 12.2076i −0.411751 + 0.713173i −0.995081 0.0990615i \(-0.968416\pi\)
0.583330 + 0.812235i \(0.301749\pi\)
\(294\) 0 0
\(295\) 0.334243 + 0.578927i 0.0194604 + 0.0337064i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 1.23569 0.0714619
\(300\) 0 0
\(301\) 0.151011 + 4.97698i 0.00870413 + 0.286868i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 0.0495974 + 0.0859053i 0.00283994 + 0.00491892i
\(306\) 0 0
\(307\) −27.3916 −1.56332 −0.781660 0.623704i \(-0.785627\pi\)
−0.781660 + 0.623704i \(0.785627\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −14.0557 −0.797026 −0.398513 0.917163i \(-0.630474\pi\)
−0.398513 + 0.917163i \(0.630474\pi\)
\(312\) 0 0
\(313\) 21.7446 1.22908 0.614540 0.788886i \(-0.289342\pi\)
0.614540 + 0.788886i \(0.289342\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −8.56297 −0.480944 −0.240472 0.970656i \(-0.577302\pi\)
−0.240472 + 0.970656i \(0.577302\pi\)
\(318\) 0 0
\(319\) −8.21228 −0.459799
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 43.3808 2.41377
\(324\) 0 0
\(325\) −0.497589 0.861850i −0.0276013 0.0478068i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −4.22208 2.26975i −0.232771 0.125135i
\(330\) 0 0
\(331\) −10.8472 −0.596216 −0.298108 0.954532i \(-0.596356\pi\)
−0.298108 + 0.954532i \(0.596356\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −0.452399 0.783578i −0.0247172 0.0428114i
\(336\) 0 0
\(337\) 1.67411 2.89964i 0.0911945 0.157954i −0.816819 0.576893i \(-0.804265\pi\)
0.908014 + 0.418940i \(0.137598\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −2.09486 + 3.62840i −0.113443 + 0.196489i
\(342\) 0 0
\(343\) 1.68298 + 18.4436i 0.0908723 + 0.995863i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −11.5330 −0.619126 −0.309563 0.950879i \(-0.600183\pi\)
−0.309563 + 0.950879i \(0.600183\pi\)
\(348\) 0 0
\(349\) −4.44917 7.70619i −0.238159 0.412503i 0.722027 0.691865i \(-0.243211\pi\)
−0.960186 + 0.279362i \(0.909877\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −1.32349 + 2.29236i −0.0704424 + 0.122010i −0.899095 0.437753i \(-0.855774\pi\)
0.828653 + 0.559763i \(0.189108\pi\)
\(354\) 0 0
\(355\) −0.0934139 0.161798i −0.00495790 0.00858733i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −12.9835 + 22.4882i −0.685245 + 1.18688i 0.288114 + 0.957596i \(0.406972\pi\)
−0.973360 + 0.229284i \(0.926362\pi\)
\(360\) 0 0
\(361\) −14.4264 24.9873i −0.759286 1.31512i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −0.113867 + 0.197224i −0.00596009 + 0.0103232i
\(366\) 0 0
\(367\) 8.79371 15.2312i 0.459028 0.795060i −0.539882 0.841741i \(-0.681531\pi\)
0.998910 + 0.0466808i \(0.0148644\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 0.428975 + 14.1380i 0.0222713 + 0.734011i
\(372\) 0 0
\(373\) −0.407538 0.705876i −0.0211015 0.0365489i 0.855282 0.518163i \(-0.173384\pi\)
−0.876383 + 0.481614i \(0.840051\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 0.986490 0.0508068
\(378\) 0 0
\(379\) 20.4312 1.04948 0.524741 0.851262i \(-0.324162\pi\)
0.524741 + 0.851262i \(0.324162\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −8.94638 15.4956i −0.457139 0.791788i 0.541670 0.840591i \(-0.317792\pi\)
−0.998808 + 0.0488039i \(0.984459\pi\)
\(384\) 0 0
\(385\) 0.567112 + 0.304874i 0.0289027 + 0.0155378i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 7.81392 13.5341i 0.396181 0.686206i −0.597070 0.802189i \(-0.703669\pi\)
0.993251 + 0.115983i \(0.0370018\pi\)
\(390\) 0 0
\(391\) 19.3835 33.5731i 0.980264 1.69787i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 0.935661 + 1.62061i 0.0470782 + 0.0815419i
\(396\) 0 0
\(397\) 9.63064 16.6808i 0.483348 0.837183i −0.516469 0.856306i \(-0.672754\pi\)
0.999817 + 0.0191225i \(0.00608724\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 7.15064 + 12.3853i 0.357086 + 0.618491i 0.987473 0.157790i \(-0.0504370\pi\)
−0.630387 + 0.776281i \(0.717104\pi\)
\(402\) 0 0
\(403\) 0.251642 0.435857i 0.0125352 0.0217116i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −5.82452 10.0884i −0.288711 0.500062i
\(408\) 0 0
\(409\) 31.8610 1.57542 0.787712 0.616044i \(-0.211266\pi\)
0.787712 + 0.616044i \(0.211266\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −10.6520 5.72643i −0.524151 0.281779i
\(414\) 0 0
\(415\) 0.549426 0.951633i 0.0269702 0.0467138i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 11.9480 20.6945i 0.583697 1.01099i −0.411339 0.911482i \(-0.634939\pi\)
0.995036 0.0995110i \(-0.0317278\pi\)
\(420\) 0 0
\(421\) −1.22251 2.11744i −0.0595813 0.103198i 0.834696 0.550711i \(-0.185643\pi\)
−0.894278 + 0.447513i \(0.852310\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −31.2214 −1.51446
\(426\) 0 0
\(427\) −1.58062 0.849728i −0.0764917 0.0411212i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 2.46382 + 4.26746i 0.118678 + 0.205556i 0.919244 0.393688i \(-0.128801\pi\)
−0.800566 + 0.599244i \(0.795468\pi\)
\(432\) 0 0
\(433\) 30.8539 1.48274 0.741371 0.671095i \(-0.234176\pi\)
0.741371 + 0.671095i \(0.234176\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −42.7633 −2.04565
\(438\) 0 0
\(439\) −2.44822 −0.116847 −0.0584235 0.998292i \(-0.518607\pi\)
−0.0584235 + 0.998292i \(0.518607\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −26.2950 −1.24931 −0.624657 0.780899i \(-0.714761\pi\)
−0.624657 + 0.780899i \(0.714761\pi\)
\(444\) 0 0
\(445\) 1.32614 0.0628650
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 38.7077 1.82673 0.913365 0.407141i \(-0.133474\pi\)
0.913365 + 0.407141i \(0.133474\pi\)
\(450\) 0 0
\(451\) −1.92854 3.34034i −0.0908116 0.157290i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −0.0681236 0.0366226i −0.00319368 0.00171690i
\(456\) 0 0
\(457\) −9.15511 −0.428258 −0.214129 0.976805i \(-0.568691\pi\)
−0.214129 + 0.976805i \(0.568691\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −14.6152 25.3143i −0.680698 1.17900i −0.974768 0.223220i \(-0.928343\pi\)
0.294070 0.955784i \(-0.404990\pi\)
\(462\) 0 0
\(463\) 8.21031 14.2207i 0.381565 0.660891i −0.609721 0.792616i \(-0.708718\pi\)
0.991286 + 0.131726i \(0.0420518\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 7.68632 13.3131i 0.355680 0.616057i −0.631554 0.775332i \(-0.717582\pi\)
0.987234 + 0.159276i \(0.0509158\pi\)
\(468\) 0 0
\(469\) 14.4175 + 7.75073i 0.665739 + 0.357895i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −3.13170 −0.143996
\(474\) 0 0
\(475\) 17.2200 + 29.8259i 0.790106 + 1.36850i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 18.9646 32.8476i 0.866513 1.50084i 0.000975329 1.00000i \(-0.499690\pi\)
0.865537 0.500844i \(-0.166977\pi\)
\(480\) 0 0
\(481\) 0.699663 + 1.21185i 0.0319019 + 0.0552557i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −0.582809 + 1.00946i −0.0264640 + 0.0458370i
\(486\) 0 0
\(487\) −2.30247 3.98800i −0.104335 0.180714i 0.809131 0.587628i \(-0.199938\pi\)
−0.913466 + 0.406914i \(0.866605\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −15.1876 + 26.3056i −0.685405 + 1.18716i 0.287904 + 0.957659i \(0.407042\pi\)
−0.973309 + 0.229497i \(0.926292\pi\)
\(492\) 0 0
\(493\) 15.4744 26.8024i 0.696932 1.20712i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 2.97701 + 1.60041i 0.133537 + 0.0717884i
\(498\) 0 0
\(499\) 4.63436 + 8.02694i 0.207462 + 0.359335i 0.950914 0.309454i \(-0.100146\pi\)
−0.743452 + 0.668789i \(0.766813\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −22.4230 −0.999791 −0.499896 0.866086i \(-0.666628\pi\)
−0.499896 + 0.866086i \(0.666628\pi\)
\(504\) 0 0
\(505\) −2.17072 −0.0965960
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −18.8207 32.5984i −0.834213 1.44490i −0.894670 0.446728i \(-0.852589\pi\)
0.0604572 0.998171i \(-0.480744\pi\)
\(510\) 0 0
\(511\) −0.124951 4.11808i −0.00552748 0.182173i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −0.0149133 + 0.0258306i −0.000657158 + 0.00113823i
\(516\) 0 0
\(517\) 1.50743 2.61095i 0.0662969 0.114830i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −17.4641 30.2488i −0.765117 1.32522i −0.940185 0.340666i \(-0.889348\pi\)
0.175067 0.984556i \(-0.443986\pi\)
\(522\) 0 0
\(523\) 11.8735 20.5656i 0.519194 0.899270i −0.480557 0.876963i \(-0.659566\pi\)
0.999751 0.0223069i \(-0.00710109\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −7.89468 13.6740i −0.343898 0.595648i
\(528\) 0 0
\(529\) −7.60755 + 13.1767i −0.330763 + 0.572898i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 0.231664 + 0.401254i 0.0100345 + 0.0173802i
\(534\) 0 0
\(535\) −1.01917 −0.0440626
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −11.6269 + 0.706212i −0.500804 + 0.0304187i
\(540\) 0 0
\(541\) 8.58542 14.8704i 0.369116 0.639328i −0.620311 0.784356i \(-0.712994\pi\)
0.989428 + 0.145028i \(0.0463271\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 0.487083 0.843653i 0.0208643 0.0361381i
\(546\) 0 0
\(547\) 10.0046 + 17.3284i 0.427765 + 0.740910i 0.996674 0.0814901i \(-0.0259679\pi\)
−0.568910 + 0.822400i \(0.692635\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −34.1392 −1.45438
\(552\) 0 0
\(553\) −29.8186 16.0302i −1.26802 0.681674i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 0.122740 + 0.212593i 0.00520068 + 0.00900784i 0.868614 0.495489i \(-0.165011\pi\)
−0.863413 + 0.504497i \(0.831678\pi\)
\(558\) 0 0
\(559\) 0.376192 0.0159112
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −44.2509 −1.86495 −0.932477 0.361230i \(-0.882357\pi\)
−0.932477 + 0.361230i \(0.882357\pi\)
\(564\) 0 0
\(565\) −0.00565192 −0.000237778
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 5.53533 0.232053 0.116027 0.993246i \(-0.462984\pi\)
0.116027 + 0.993246i \(0.462984\pi\)
\(570\) 0 0
\(571\) 4.10381 0.171739 0.0858696 0.996306i \(-0.472633\pi\)
0.0858696 + 0.996306i \(0.472633\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 30.7770 1.28349
\(576\) 0 0
\(577\) −2.82275 4.88915i −0.117513 0.203538i 0.801269 0.598305i \(-0.204159\pi\)
−0.918781 + 0.394767i \(0.870825\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 0.602904 + 19.8703i 0.0250127 + 0.824360i
\(582\) 0 0
\(583\) −8.89619 −0.368442
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 9.36644 + 16.2232i 0.386595 + 0.669601i 0.991989 0.126324i \(-0.0403180\pi\)
−0.605394 + 0.795926i \(0.706985\pi\)
\(588\) 0 0
\(589\) −8.70852 + 15.0836i −0.358828 + 0.621509i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 9.43516 16.3422i 0.387456 0.671093i −0.604651 0.796491i \(-0.706687\pi\)
0.992107 + 0.125398i \(0.0400207\pi\)
\(594\) 0 0
\(595\) −2.06363 + 1.27641i −0.0846005 + 0.0523277i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 2.67451 0.109278 0.0546388 0.998506i \(-0.482599\pi\)
0.0546388 + 0.998506i \(0.482599\pi\)
\(600\) 0 0
\(601\) −6.60716 11.4439i −0.269511 0.466808i 0.699224 0.714902i \(-0.253529\pi\)
−0.968736 + 0.248095i \(0.920196\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 0.601872 1.04247i 0.0244696 0.0423825i
\(606\) 0 0
\(607\) 12.9026 + 22.3480i 0.523701 + 0.907076i 0.999619 + 0.0275869i \(0.00878231\pi\)
−0.475919 + 0.879489i \(0.657884\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −0.181079 + 0.313637i −0.00732565 + 0.0126884i
\(612\) 0 0
\(613\) 13.4766 + 23.3422i 0.544316 + 0.942784i 0.998650 + 0.0519519i \(0.0165443\pi\)
−0.454333 + 0.890832i \(0.650122\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 4.76588 8.25474i 0.191867 0.332323i −0.754002 0.656872i \(-0.771879\pi\)
0.945869 + 0.324549i \(0.105212\pi\)
\(618\) 0 0
\(619\) 17.3536 30.0573i 0.697499 1.20810i −0.271832 0.962345i \(-0.587630\pi\)
0.969331 0.245759i \(-0.0790371\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −20.4038 + 12.6203i −0.817459 + 0.505621i
\(624\) 0 0
\(625\) −12.3398 21.3732i −0.493593 0.854928i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 43.9006 1.75043
\(630\) 0 0
\(631\) 36.7963 1.46484 0.732419 0.680854i \(-0.238391\pi\)
0.732419 + 0.680854i \(0.238391\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 0.985611 + 1.70713i 0.0391128 + 0.0677453i
\(636\) 0 0
\(637\) 1.39666 0.0848329i 0.0553378 0.00336120i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −22.0922 + 38.2648i −0.872590 + 1.51137i −0.0132813 + 0.999912i \(0.504228\pi\)
−0.859308 + 0.511458i \(0.829106\pi\)
\(642\) 0 0
\(643\) −7.24065 + 12.5412i −0.285543 + 0.494575i −0.972741 0.231895i \(-0.925507\pi\)
0.687197 + 0.726471i \(0.258841\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −16.6536 28.8448i −0.654719 1.13401i −0.981964 0.189068i \(-0.939453\pi\)
0.327245 0.944940i \(-0.393880\pi\)
\(648\) 0 0
\(649\) 3.80315 6.58725i 0.149287 0.258572i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −4.53322 7.85176i −0.177398 0.307263i 0.763590 0.645701i \(-0.223435\pi\)
−0.940989 + 0.338438i \(0.890101\pi\)
\(654\) 0 0
\(655\) 1.45027 2.51194i 0.0566666 0.0981495i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 16.1806 + 28.0256i 0.630305 + 1.09172i 0.987489 + 0.157686i \(0.0504035\pi\)
−0.357184 + 0.934034i \(0.616263\pi\)
\(660\) 0 0
\(661\) −8.65915 −0.336802 −0.168401 0.985719i \(-0.553860\pi\)
−0.168401 + 0.985719i \(0.553860\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 2.35754 + 1.26739i 0.0914214 + 0.0491473i
\(666\) 0 0
\(667\) −15.2541 + 26.4209i −0.590642 + 1.02302i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0.564339 0.977464i 0.0217861 0.0377346i
\(672\) 0 0
\(673\) 7.24842 + 12.5546i 0.279406 + 0.483946i 0.971237 0.238114i \(-0.0765291\pi\)
−0.691831 + 0.722059i \(0.743196\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −38.3315 −1.47320 −0.736600 0.676329i \(-0.763570\pi\)
−0.736600 + 0.676329i \(0.763570\pi\)
\(678\) 0 0
\(679\) −0.639537 21.0777i −0.0245432 0.808887i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −3.31659 5.74450i −0.126906 0.219807i 0.795570 0.605861i \(-0.207171\pi\)
−0.922476 + 0.386054i \(0.873838\pi\)
\(684\) 0 0
\(685\) 0.942567 0.0360136
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 1.06864 0.0407121
\(690\) 0 0
\(691\) 23.3875 0.889704 0.444852 0.895604i \(-0.353256\pi\)
0.444852 + 0.895604i \(0.353256\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 1.83254 0.0695121
\(696\) 0 0
\(697\) 14.5358 0.550583
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −9.26736 −0.350023 −0.175012 0.984566i \(-0.555996\pi\)
−0.175012 + 0.984566i \(0.555996\pi\)
\(702\) 0 0
\(703\) −24.2131 41.9383i −0.913214 1.58173i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 33.3984 20.6579i 1.25608 0.776918i
\(708\) 0 0
\(709\) 14.2355 0.534626 0.267313 0.963610i \(-0.413864\pi\)
0.267313 + 0.963610i \(0.413864\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 7.78230 + 13.4793i 0.291449 + 0.504805i
\(714\) 0 0
\(715\) 0.0243226 0.0421280i 0.000909613 0.00157550i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 6.92848 12.0005i 0.258389 0.447542i −0.707422 0.706792i \(-0.750142\pi\)
0.965810 + 0.259249i \(0.0834752\pi\)
\(720\) 0 0
\(721\) −0.0163649 0.539348i −0.000609459 0.0200864i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 24.5702 0.912513
\(726\) 0 0
\(727\) −15.7000 27.1932i −0.582280 1.00854i −0.995208 0.0977755i \(-0.968827\pi\)
0.412928 0.910764i \(-0.364506\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 5.90107 10.2209i 0.218259 0.378035i
\(732\) 0 0
\(733\) 13.3003 + 23.0368i 0.491257 + 0.850883i 0.999949 0.0100658i \(-0.00320409\pi\)
−0.508692 + 0.860949i \(0.669871\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −5.14757 + 8.91586i −0.189613 + 0.328420i
\(738\) 0 0
\(739\) −16.5019 28.5822i −0.607034 1.05141i −0.991727 0.128368i \(-0.959026\pi\)
0.384693 0.923045i \(-0.374307\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 19.3008 33.4299i 0.708076 1.22642i −0.257493 0.966280i \(-0.582897\pi\)
0.965570 0.260144i \(-0.0837701\pi\)
\(744\) 0 0
\(745\) 1.29919 2.25027i 0.0475988 0.0824435i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 15.6808 9.69900i 0.572964 0.354394i
\(750\) 0 0
\(751\) −18.9498 32.8220i −0.691487 1.19769i −0.971351 0.237651i \(-0.923622\pi\)
0.279863 0.960040i \(-0.409711\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −1.23811 −0.0450596
\(756\) 0 0
\(757\) 22.5927 0.821147 0.410573 0.911828i \(-0.365329\pi\)
0.410573 + 0.911828i \(0.365329\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 13.8735 + 24.0296i 0.502913 + 0.871072i 0.999994 + 0.00336738i \(0.00107187\pi\)
−0.497081 + 0.867704i \(0.665595\pi\)
\(762\) 0 0
\(763\) 0.534493 + 17.6157i 0.0193500 + 0.637730i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −0.456849 + 0.791286i −0.0164959 + 0.0285717i
\(768\) 0 0
\(769\) −6.07668 + 10.5251i −0.219131 + 0.379546i −0.954542 0.298075i \(-0.903655\pi\)
0.735412 + 0.677621i \(0.236989\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 20.7795 + 35.9912i 0.747388 + 1.29451i 0.949071 + 0.315063i \(0.102026\pi\)
−0.201682 + 0.979451i \(0.564641\pi\)
\(774\) 0 0
\(775\) 6.26756 10.8557i 0.225137 0.389950i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −8.01714 13.8861i −0.287244 0.497521i
\(780\) 0 0
\(781\) −1.06290 + 1.84100i −0.0380336 + 0.0658761i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −0.416753 0.721837i −0.0148746 0.0257635i
\(786\) 0 0
\(787\) 20.8969 0.744893 0.372446 0.928054i \(-0.378519\pi\)
0.372446 + 0.928054i \(0.378519\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0.0869596 0.0537869i 0.00309193 0.00191244i
\(792\) 0 0
\(793\) −0.0677905 + 0.117417i −0.00240731 + 0.00416959i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 0.319383 0.553188i 0.0113131 0.0195949i −0.860313 0.509765i \(-0.829732\pi\)
0.871627 + 0.490171i \(0.163066\pi\)
\(798\) 0 0
\(799\) 5.68091 + 9.83963i 0.200976 + 0.348101i
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 2.59125 0.0914433