Properties

Label 1008.2.s.r.289.2
Level $1008$
Weight $2$
Character 1008.289
Analytic conductor $8.049$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1008.s (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.04892052375\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{-19})\)
Defining polynomial: \(x^{4} - x^{3} - 4 x^{2} - 5 x + 25\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 168)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 289.2
Root \(2.13746 - 0.656712i\) of defining polynomial
Character \(\chi\) \(=\) 1008.289
Dual form 1008.2.s.r.865.2

$q$-expansion

\(f(q)\) \(=\) \(q+(1.63746 - 2.83616i) q^{5} +(1.50000 - 2.17945i) q^{7} +O(q^{10})\) \(q+(1.63746 - 2.83616i) q^{5} +(1.50000 - 2.17945i) q^{7} +(-1.63746 - 2.83616i) q^{11} +6.27492 q^{13} +(-2.00000 - 3.46410i) q^{17} +(-3.13746 + 5.43424i) q^{19} +(-2.00000 + 3.46410i) q^{23} +(-2.86254 - 4.95807i) q^{25} -5.27492 q^{29} +(-0.500000 - 0.866025i) q^{31} +(-3.72508 - 7.82300i) q^{35} +(1.13746 - 1.97014i) q^{37} +4.54983 q^{41} -0.274917 q^{43} +(3.00000 - 5.19615i) q^{47} +(-2.50000 - 6.53835i) q^{49} +(4.63746 + 8.03231i) q^{53} -10.7251 q^{55} +(0.637459 + 1.10411i) q^{59} +(-5.00000 + 8.66025i) q^{61} +(10.2749 - 17.7967i) q^{65} +(-0.137459 - 0.238085i) q^{67} +2.00000 q^{71} +(2.13746 + 3.70219i) q^{73} +(-8.63746 - 0.685484i) q^{77} +(5.77492 - 10.0025i) q^{79} +7.27492 q^{83} -13.0997 q^{85} +(-5.27492 + 9.13642i) q^{89} +(9.41238 - 13.6759i) q^{91} +(10.2749 + 17.7967i) q^{95} +8.72508 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - q^{5} + 6q^{7} + O(q^{10}) \) \( 4q - q^{5} + 6q^{7} + q^{11} + 10q^{13} - 8q^{17} - 5q^{19} - 8q^{23} - 19q^{25} - 6q^{29} - 2q^{31} - 30q^{35} - 3q^{37} - 12q^{41} + 14q^{43} + 12q^{47} - 10q^{49} + 11q^{53} - 58q^{55} - 5q^{59} - 20q^{61} + 26q^{65} + 7q^{67} + 8q^{71} + q^{73} - 27q^{77} + 8q^{79} + 14q^{83} + 8q^{85} - 6q^{89} + 15q^{91} + 26q^{95} + 50q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(577\) \(757\) \(785\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(1\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0 0
\(4\) 0 0
\(5\) 1.63746 2.83616i 0.732294 1.26837i −0.223607 0.974679i \(-0.571783\pi\)
0.955901 0.293691i \(-0.0948835\pi\)
\(6\) 0 0
\(7\) 1.50000 2.17945i 0.566947 0.823754i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −1.63746 2.83616i −0.493712 0.855135i 0.506261 0.862380i \(-0.331027\pi\)
−0.999974 + 0.00724520i \(0.997694\pi\)
\(12\) 0 0
\(13\) 6.27492 1.74035 0.870174 0.492744i \(-0.164006\pi\)
0.870174 + 0.492744i \(0.164006\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −2.00000 3.46410i −0.485071 0.840168i 0.514782 0.857321i \(-0.327873\pi\)
−0.999853 + 0.0171533i \(0.994540\pi\)
\(18\) 0 0
\(19\) −3.13746 + 5.43424i −0.719782 + 1.24670i 0.241303 + 0.970450i \(0.422425\pi\)
−0.961086 + 0.276250i \(0.910908\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −2.00000 + 3.46410i −0.417029 + 0.722315i −0.995639 0.0932891i \(-0.970262\pi\)
0.578610 + 0.815604i \(0.303595\pi\)
\(24\) 0 0
\(25\) −2.86254 4.95807i −0.572508 0.991613i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −5.27492 −0.979528 −0.489764 0.871855i \(-0.662917\pi\)
−0.489764 + 0.871855i \(0.662917\pi\)
\(30\) 0 0
\(31\) −0.500000 0.866025i −0.0898027 0.155543i 0.817625 0.575751i \(-0.195290\pi\)
−0.907428 + 0.420208i \(0.861957\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −3.72508 7.82300i −0.629654 1.32233i
\(36\) 0 0
\(37\) 1.13746 1.97014i 0.186997 0.323888i −0.757251 0.653124i \(-0.773458\pi\)
0.944248 + 0.329236i \(0.106791\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 4.54983 0.710565 0.355282 0.934759i \(-0.384385\pi\)
0.355282 + 0.934759i \(0.384385\pi\)
\(42\) 0 0
\(43\) −0.274917 −0.0419245 −0.0209622 0.999780i \(-0.506673\pi\)
−0.0209622 + 0.999780i \(0.506673\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 3.00000 5.19615i 0.437595 0.757937i −0.559908 0.828554i \(-0.689164\pi\)
0.997503 + 0.0706177i \(0.0224970\pi\)
\(48\) 0 0
\(49\) −2.50000 6.53835i −0.357143 0.934050i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 4.63746 + 8.03231i 0.637004 + 1.10332i 0.986087 + 0.166231i \(0.0531598\pi\)
−0.349083 + 0.937092i \(0.613507\pi\)
\(54\) 0 0
\(55\) −10.7251 −1.44617
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 0.637459 + 1.10411i 0.0829900 + 0.143743i 0.904533 0.426404i \(-0.140220\pi\)
−0.821543 + 0.570147i \(0.806886\pi\)
\(60\) 0 0
\(61\) −5.00000 + 8.66025i −0.640184 + 1.10883i 0.345207 + 0.938527i \(0.387809\pi\)
−0.985391 + 0.170305i \(0.945525\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 10.2749 17.7967i 1.27445 2.20741i
\(66\) 0 0
\(67\) −0.137459 0.238085i −0.0167932 0.0290867i 0.857507 0.514473i \(-0.172012\pi\)
−0.874300 + 0.485386i \(0.838679\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 2.00000 0.237356 0.118678 0.992933i \(-0.462134\pi\)
0.118678 + 0.992933i \(0.462134\pi\)
\(72\) 0 0
\(73\) 2.13746 + 3.70219i 0.250171 + 0.433308i 0.963573 0.267447i \(-0.0861800\pi\)
−0.713402 + 0.700755i \(0.752847\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −8.63746 0.685484i −0.984330 0.0781181i
\(78\) 0 0
\(79\) 5.77492 10.0025i 0.649729 1.12536i −0.333459 0.942765i \(-0.608216\pi\)
0.983188 0.182599i \(-0.0584509\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 7.27492 0.798526 0.399263 0.916836i \(-0.369266\pi\)
0.399263 + 0.916836i \(0.369266\pi\)
\(84\) 0 0
\(85\) −13.0997 −1.42086
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −5.27492 + 9.13642i −0.559140 + 0.968459i 0.438428 + 0.898766i \(0.355535\pi\)
−0.997568 + 0.0696929i \(0.977798\pi\)
\(90\) 0 0
\(91\) 9.41238 13.6759i 0.986685 1.43362i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 10.2749 + 17.7967i 1.05418 + 1.82590i
\(96\) 0 0
\(97\) 8.72508 0.885898 0.442949 0.896547i \(-0.353932\pi\)
0.442949 + 0.896547i \(0.353932\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −3.00000 5.19615i −0.298511 0.517036i 0.677284 0.735721i \(-0.263157\pi\)
−0.975796 + 0.218685i \(0.929823\pi\)
\(102\) 0 0
\(103\) 5.41238 9.37451i 0.533297 0.923698i −0.465946 0.884813i \(-0.654286\pi\)
0.999244 0.0388850i \(-0.0123806\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 7.91238 13.7046i 0.764918 1.32488i −0.175372 0.984502i \(-0.556113\pi\)
0.940290 0.340375i \(-0.110554\pi\)
\(108\) 0 0
\(109\) −8.41238 14.5707i −0.805759 1.39562i −0.915777 0.401687i \(-0.868424\pi\)
0.110018 0.993930i \(-0.464909\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 4.54983 0.428012 0.214006 0.976832i \(-0.431349\pi\)
0.214006 + 0.976832i \(0.431349\pi\)
\(114\) 0 0
\(115\) 6.54983 + 11.3446i 0.610775 + 1.05789i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −10.5498 0.837253i −0.967102 0.0767509i
\(120\) 0 0
\(121\) 0.137459 0.238085i 0.0124962 0.0216441i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −2.37459 −0.212389
\(126\) 0 0
\(127\) 6.45017 0.572360 0.286180 0.958176i \(-0.407615\pi\)
0.286180 + 0.958176i \(0.407615\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −3.63746 + 6.30026i −0.317806 + 0.550457i −0.980030 0.198850i \(-0.936279\pi\)
0.662224 + 0.749306i \(0.269613\pi\)
\(132\) 0 0
\(133\) 7.13746 + 14.9893i 0.618896 + 1.29974i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 0.725083 + 1.25588i 0.0619480 + 0.107297i 0.895336 0.445391i \(-0.146935\pi\)
−0.833388 + 0.552688i \(0.813602\pi\)
\(138\) 0 0
\(139\) −8.27492 −0.701869 −0.350935 0.936400i \(-0.614136\pi\)
−0.350935 + 0.936400i \(0.614136\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −10.2749 17.7967i −0.859232 1.48823i
\(144\) 0 0
\(145\) −8.63746 + 14.9605i −0.717302 + 1.24240i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −7.27492 + 12.6005i −0.595984 + 1.03228i 0.397423 + 0.917636i \(0.369905\pi\)
−0.993407 + 0.114640i \(0.963429\pi\)
\(150\) 0 0
\(151\) 11.1873 + 19.3770i 0.910409 + 1.57687i 0.813487 + 0.581583i \(0.197566\pi\)
0.0969217 + 0.995292i \(0.469100\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −3.27492 −0.263048
\(156\) 0 0
\(157\) 0.274917 + 0.476171i 0.0219408 + 0.0380026i 0.876787 0.480878i \(-0.159682\pi\)
−0.854847 + 0.518881i \(0.826349\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 4.54983 + 9.55505i 0.358577 + 0.753044i
\(162\) 0 0
\(163\) −6.00000 + 10.3923i −0.469956 + 0.813988i −0.999410 0.0343508i \(-0.989064\pi\)
0.529454 + 0.848339i \(0.322397\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −6.00000 −0.464294 −0.232147 0.972681i \(-0.574575\pi\)
−0.232147 + 0.972681i \(0.574575\pi\)
\(168\) 0 0
\(169\) 26.3746 2.02881
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −11.2749 + 19.5287i −0.857216 + 1.48474i 0.0173577 + 0.999849i \(0.494475\pi\)
−0.874574 + 0.484892i \(0.838859\pi\)
\(174\) 0 0
\(175\) −15.0997 1.19834i −1.14143 0.0905857i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 8.27492 + 14.3326i 0.618496 + 1.07127i 0.989760 + 0.142740i \(0.0455912\pi\)
−0.371264 + 0.928527i \(0.621075\pi\)
\(180\) 0 0
\(181\) −18.8248 −1.39923 −0.699616 0.714519i \(-0.746646\pi\)
−0.699616 + 0.714519i \(0.746646\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −3.72508 6.45203i −0.273874 0.474363i
\(186\) 0 0
\(187\) −6.54983 + 11.3446i −0.478971 + 0.829603i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −2.27492 + 3.94027i −0.164607 + 0.285108i −0.936516 0.350626i \(-0.885969\pi\)
0.771909 + 0.635734i \(0.219302\pi\)
\(192\) 0 0
\(193\) −0.225083 0.389855i −0.0162018 0.0280624i 0.857811 0.513966i \(-0.171824\pi\)
−0.874013 + 0.485903i \(0.838491\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 1.45017 0.103320 0.0516600 0.998665i \(-0.483549\pi\)
0.0516600 + 0.998665i \(0.483549\pi\)
\(198\) 0 0
\(199\) −2.54983 4.41644i −0.180753 0.313073i 0.761384 0.648301i \(-0.224520\pi\)
−0.942137 + 0.335228i \(0.891187\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −7.91238 + 11.4964i −0.555340 + 0.806890i
\(204\) 0 0
\(205\) 7.45017 12.9041i 0.520342 0.901259i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 20.5498 1.42146
\(210\) 0 0
\(211\) 27.6495 1.90347 0.951735 0.306921i \(-0.0992986\pi\)
0.951735 + 0.306921i \(0.0992986\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −0.450166 + 0.779710i −0.0307010 + 0.0531758i
\(216\) 0 0
\(217\) −2.63746 0.209313i −0.179042 0.0142091i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −12.5498 21.7370i −0.844193 1.46219i
\(222\) 0 0
\(223\) 1.27492 0.0853748 0.0426874 0.999088i \(-0.486408\pi\)
0.0426874 + 0.999088i \(0.486408\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 5.63746 + 9.76436i 0.374171 + 0.648084i 0.990203 0.139638i \(-0.0445939\pi\)
−0.616031 + 0.787722i \(0.711261\pi\)
\(228\) 0 0
\(229\) −9.13746 + 15.8265i −0.603820 + 1.04585i 0.388416 + 0.921484i \(0.373022\pi\)
−0.992237 + 0.124363i \(0.960311\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −0.274917 + 0.476171i −0.0180104 + 0.0311950i −0.874890 0.484321i \(-0.839067\pi\)
0.856880 + 0.515516i \(0.172400\pi\)
\(234\) 0 0
\(235\) −9.82475 17.0170i −0.640896 1.11006i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 15.4502 0.999388 0.499694 0.866202i \(-0.333446\pi\)
0.499694 + 0.866202i \(0.333446\pi\)
\(240\) 0 0
\(241\) −4.91238 8.50848i −0.316434 0.548080i 0.663307 0.748347i \(-0.269152\pi\)
−0.979741 + 0.200267i \(0.935819\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −22.6375 3.61587i −1.44625 0.231010i
\(246\) 0 0
\(247\) −19.6873 + 34.0994i −1.25267 + 2.16969i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −18.3746 −1.15979 −0.579897 0.814690i \(-0.696907\pi\)
−0.579897 + 0.814690i \(0.696907\pi\)
\(252\) 0 0
\(253\) 13.0997 0.823569
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 5.54983 9.61260i 0.346189 0.599617i −0.639380 0.768891i \(-0.720809\pi\)
0.985569 + 0.169274i \(0.0541422\pi\)
\(258\) 0 0
\(259\) −2.58762 5.43424i −0.160787 0.337667i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 4.72508 + 8.18408i 0.291361 + 0.504652i 0.974132 0.225980i \(-0.0725586\pi\)
−0.682771 + 0.730633i \(0.739225\pi\)
\(264\) 0 0
\(265\) 30.3746 1.86590
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 10.3625 + 17.9484i 0.631815 + 1.09434i 0.987180 + 0.159609i \(0.0510232\pi\)
−0.355365 + 0.934728i \(0.615643\pi\)
\(270\) 0 0
\(271\) 0.637459 1.10411i 0.0387229 0.0670699i −0.846014 0.533160i \(-0.821004\pi\)
0.884737 + 0.466090i \(0.154338\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −9.37459 + 16.2373i −0.565309 + 0.979144i
\(276\) 0 0
\(277\) 13.4124 + 23.2309i 0.805872 + 1.39581i 0.915701 + 0.401860i \(0.131636\pi\)
−0.109830 + 0.993950i \(0.535030\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 26.5498 1.58383 0.791915 0.610631i \(-0.209084\pi\)
0.791915 + 0.610631i \(0.209084\pi\)
\(282\) 0 0
\(283\) −12.9622 22.4512i −0.770523 1.33459i −0.937276 0.348587i \(-0.886662\pi\)
0.166753 0.985999i \(-0.446672\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 6.82475 9.91613i 0.402852 0.585331i
\(288\) 0 0
\(289\) 0.500000 0.866025i 0.0294118 0.0509427i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 27.8248 1.62554 0.812770 0.582585i \(-0.197959\pi\)
0.812770 + 0.582585i \(0.197959\pi\)
\(294\) 0 0
\(295\) 4.17525 0.243092
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −12.5498 + 21.7370i −0.725776 + 1.25708i
\(300\) 0 0
\(301\) −0.412376 + 0.599168i −0.0237689 + 0.0345355i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 16.3746 + 28.3616i 0.937606 + 1.62398i
\(306\) 0 0
\(307\) −11.3746 −0.649182 −0.324591 0.945854i \(-0.605227\pi\)
−0.324591 + 0.945854i \(0.605227\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 2.27492 + 3.94027i 0.128999 + 0.223432i 0.923289 0.384106i \(-0.125490\pi\)
−0.794290 + 0.607539i \(0.792157\pi\)
\(312\) 0 0
\(313\) 9.77492 16.9307i 0.552511 0.956977i −0.445582 0.895241i \(-0.647003\pi\)
0.998093 0.0617357i \(-0.0196636\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −13.9124 + 24.0969i −0.781397 + 1.35342i 0.149731 + 0.988727i \(0.452159\pi\)
−0.931128 + 0.364692i \(0.881174\pi\)
\(318\) 0 0
\(319\) 8.63746 + 14.9605i 0.483605 + 0.837628i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 25.0997 1.39658
\(324\) 0 0
\(325\) −17.9622 31.1115i −0.996364 1.72575i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −6.82475 14.3326i −0.376261 0.790181i
\(330\) 0 0
\(331\) 0.587624 1.01779i 0.0322987 0.0559431i −0.849424 0.527711i \(-0.823051\pi\)
0.881723 + 0.471768i \(0.156384\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −0.900331 −0.0491903
\(336\) 0 0
\(337\) −24.0997 −1.31279 −0.656396 0.754416i \(-0.727920\pi\)
−0.656396 + 0.754416i \(0.727920\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −1.63746 + 2.83616i −0.0886734 + 0.153587i
\(342\) 0 0
\(343\) −18.0000 4.35890i −0.971909 0.235358i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −15.0997 26.1534i −0.810593 1.40399i −0.912450 0.409189i \(-0.865812\pi\)
0.101857 0.994799i \(-0.467522\pi\)
\(348\) 0 0
\(349\) −6.00000 −0.321173 −0.160586 0.987022i \(-0.551338\pi\)
−0.160586 + 0.987022i \(0.551338\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −10.2749 17.7967i −0.546879 0.947222i −0.998486 0.0550049i \(-0.982483\pi\)
0.451607 0.892217i \(-0.350851\pi\)
\(354\) 0 0
\(355\) 3.27492 5.67232i 0.173815 0.301056i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 9.82475 17.0170i 0.518531 0.898121i −0.481238 0.876590i \(-0.659813\pi\)
0.999768 0.0215311i \(-0.00685409\pi\)
\(360\) 0 0
\(361\) −10.1873 17.6449i −0.536173 0.928679i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 14.0000 0.732793
\(366\) 0 0
\(367\) 11.0498 + 19.1389i 0.576797 + 0.999041i 0.995844 + 0.0910767i \(0.0290308\pi\)
−0.419047 + 0.907964i \(0.637636\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 24.4622 + 1.94136i 1.27001 + 0.100791i
\(372\) 0 0
\(373\) 3.13746 5.43424i 0.162451 0.281374i −0.773296 0.634045i \(-0.781393\pi\)
0.935747 + 0.352671i \(0.114727\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −33.0997 −1.70472
\(378\) 0 0
\(379\) −13.1752 −0.676767 −0.338384 0.941008i \(-0.609880\pi\)
−0.338384 + 0.941008i \(0.609880\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −5.27492 + 9.13642i −0.269536 + 0.466849i −0.968742 0.248070i \(-0.920204\pi\)
0.699206 + 0.714920i \(0.253537\pi\)
\(384\) 0 0
\(385\) −16.0876 + 23.3748i −0.819901 + 1.19129i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −1.00000 1.73205i −0.0507020 0.0878185i 0.839561 0.543266i \(-0.182813\pi\)
−0.890263 + 0.455448i \(0.849479\pi\)
\(390\) 0 0
\(391\) 16.0000 0.809155
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −18.9124 32.7572i −0.951585 1.64819i
\(396\) 0 0
\(397\) 1.68729 2.92248i 0.0846828 0.146675i −0.820573 0.571541i \(-0.806346\pi\)
0.905256 + 0.424867i \(0.139679\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 12.0000 20.7846i 0.599251 1.03793i −0.393680 0.919247i \(-0.628798\pi\)
0.992932 0.118686i \(-0.0378683\pi\)
\(402\) 0 0
\(403\) −3.13746 5.43424i −0.156288 0.270699i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −7.45017 −0.369291
\(408\) 0 0
\(409\) −5.22508 9.05011i −0.258364 0.447499i 0.707440 0.706773i \(-0.249850\pi\)
−0.965804 + 0.259274i \(0.916517\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 3.36254 + 0.266857i 0.165460 + 0.0131312i
\(414\) 0 0
\(415\) 11.9124 20.6328i 0.584756 1.01283i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 28.5498 1.39475 0.697375 0.716706i \(-0.254351\pi\)
0.697375 + 0.716706i \(0.254351\pi\)
\(420\) 0 0
\(421\) 8.82475 0.430092 0.215046 0.976604i \(-0.431010\pi\)
0.215046 + 0.976604i \(0.431010\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −11.4502 + 19.8323i −0.555415 + 0.962006i
\(426\) 0 0
\(427\) 11.3746 + 23.8876i 0.550455 + 1.15600i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 8.82475 + 15.2849i 0.425073 + 0.736249i 0.996427 0.0844552i \(-0.0269150\pi\)
−0.571354 + 0.820704i \(0.693582\pi\)
\(432\) 0 0
\(433\) 3.17525 0.152593 0.0762963 0.997085i \(-0.475690\pi\)
0.0762963 + 0.997085i \(0.475690\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −12.5498 21.7370i −0.600340 1.03982i
\(438\) 0 0
\(439\) 8.63746 14.9605i 0.412243 0.714027i −0.582891 0.812550i \(-0.698079\pi\)
0.995135 + 0.0985236i \(0.0314120\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 3.18729 5.52055i 0.151433 0.262289i −0.780322 0.625378i \(-0.784945\pi\)
0.931754 + 0.363089i \(0.118278\pi\)
\(444\) 0 0
\(445\) 17.2749 + 29.9210i 0.818910 + 1.41839i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −20.5498 −0.969807 −0.484903 0.874568i \(-0.661145\pi\)
−0.484903 + 0.874568i \(0.661145\pi\)
\(450\) 0 0
\(451\) −7.45017 12.9041i −0.350815 0.607629i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −23.3746 49.0887i −1.09582 2.30131i
\(456\) 0 0
\(457\) −18.3248 + 31.7394i −0.857196 + 1.48471i 0.0173972 + 0.999849i \(0.494462\pi\)
−0.874593 + 0.484858i \(0.838871\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 3.64950 0.169974 0.0849872 0.996382i \(-0.472915\pi\)
0.0849872 + 0.996382i \(0.472915\pi\)
\(462\) 0 0
\(463\) −13.1752 −0.612306 −0.306153 0.951982i \(-0.599042\pi\)
−0.306153 + 0.951982i \(0.599042\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −20.2749 + 35.1172i −0.938211 + 1.62503i −0.169406 + 0.985546i \(0.554185\pi\)
−0.768805 + 0.639483i \(0.779148\pi\)
\(468\) 0 0
\(469\) −0.725083 0.0575438i −0.0334812 0.00265713i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 0.450166 + 0.779710i 0.0206986 + 0.0358511i
\(474\) 0 0
\(475\) 35.9244 1.64833
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 2.72508 + 4.71998i 0.124512 + 0.215661i 0.921542 0.388278i \(-0.126930\pi\)
−0.797030 + 0.603940i \(0.793597\pi\)
\(480\) 0 0
\(481\) 7.13746 12.3624i 0.325440 0.563679i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 14.2870 24.7457i 0.648738 1.12365i
\(486\) 0 0
\(487\) 0.500000 + 0.866025i 0.0226572 + 0.0392434i 0.877132 0.480250i \(-0.159454\pi\)
−0.854475 + 0.519493i \(0.826121\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 36.9244 1.66638 0.833188 0.552990i \(-0.186513\pi\)
0.833188 + 0.552990i \(0.186513\pi\)
\(492\) 0 0
\(493\) 10.5498 + 18.2728i 0.475141 + 0.822968i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 3.00000 4.35890i 0.134568 0.195523i
\(498\) 0 0
\(499\) 16.1375 27.9509i 0.722412 1.25125i −0.237619 0.971359i \(-0.576367\pi\)
0.960030 0.279896i \(-0.0902998\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −37.6495 −1.67871 −0.839354 0.543585i \(-0.817067\pi\)
−0.839354 + 0.543585i \(0.817067\pi\)
\(504\) 0 0
\(505\) −19.6495 −0.874391
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −5.63746 + 9.76436i −0.249876 + 0.432798i −0.963491 0.267740i \(-0.913723\pi\)
0.713615 + 0.700538i \(0.247057\pi\)
\(510\) 0 0
\(511\) 11.2749 + 0.894797i 0.498773 + 0.0395835i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −17.7251 30.7007i −0.781060 1.35284i
\(516\) 0 0
\(517\) −19.6495 −0.864184
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −7.27492 12.6005i −0.318720 0.552039i 0.661501 0.749944i \(-0.269920\pi\)
−0.980221 + 0.197905i \(0.936586\pi\)
\(522\) 0 0
\(523\) −8.86254 + 15.3504i −0.387532 + 0.671225i −0.992117 0.125316i \(-0.960006\pi\)
0.604585 + 0.796541i \(0.293339\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −2.00000 + 3.46410i −0.0871214 + 0.150899i
\(528\) 0 0
\(529\) 3.50000 + 6.06218i 0.152174 + 0.263573i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 28.5498 1.23663
\(534\) 0 0
\(535\) −25.9124 44.8816i −1.12029 1.94040i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −14.4502 + 17.7967i −0.622413 + 0.766557i
\(540\) 0 0
\(541\) 4.13746 7.16629i 0.177883 0.308103i −0.763272 0.646077i \(-0.776408\pi\)
0.941155 + 0.337974i \(0.109742\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −55.0997 −2.36021
\(546\) 0 0
\(547\) 28.0000 1.19719 0.598597 0.801050i \(-0.295725\pi\)
0.598597 + 0.801050i \(0.295725\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 16.5498 28.6652i 0.705047 1.22118i
\(552\) 0 0
\(553\) −13.1375 27.5898i −0.558662 1.17324i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −14.9124 25.8290i −0.631858 1.09441i −0.987172 0.159663i \(-0.948959\pi\)
0.355314 0.934747i \(-0.384374\pi\)
\(558\) 0 0
\(559\) −1.72508 −0.0729632
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −7.63746 13.2285i −0.321881 0.557513i 0.658996 0.752147i \(-0.270982\pi\)
−0.980876 + 0.194633i \(0.937648\pi\)
\(564\) 0 0
\(565\) 7.45017 12.9041i 0.313431 0.542878i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 5.72508 9.91613i 0.240008 0.415706i −0.720708 0.693238i \(-0.756183\pi\)
0.960716 + 0.277532i \(0.0895166\pi\)
\(570\) 0 0
\(571\) 4.13746 + 7.16629i 0.173147 + 0.299900i 0.939519 0.342498i \(-0.111273\pi\)
−0.766371 + 0.642398i \(0.777940\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 22.9003 0.955010
\(576\) 0 0
\(577\) 12.5000 + 21.6506i 0.520382 + 0.901328i 0.999719 + 0.0236970i \(0.00754370\pi\)
−0.479337 + 0.877631i \(0.659123\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 10.9124 15.8553i 0.452722 0.657789i
\(582\) 0 0
\(583\) 15.1873 26.3052i 0.628993 1.08945i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 9.27492 0.382817 0.191408 0.981510i \(-0.438695\pi\)
0.191408 + 0.981510i \(0.438695\pi\)
\(588\) 0 0
\(589\) 6.27492 0.258553
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −0.274917 + 0.476171i −0.0112895 + 0.0195540i −0.871615 0.490191i \(-0.836927\pi\)
0.860325 + 0.509745i \(0.170260\pi\)
\(594\) 0 0
\(595\) −19.6495 + 28.5501i −0.805551 + 1.17044i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −11.2749 19.5287i −0.460681 0.797922i 0.538314 0.842744i \(-0.319061\pi\)
−0.998995 + 0.0448219i \(0.985728\pi\)
\(600\) 0 0
\(601\) 4.09967 0.167229 0.0836145 0.996498i \(-0.473354\pi\)
0.0836145 + 0.996498i \(0.473354\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −0.450166 0.779710i −0.0183018 0.0316997i
\(606\) 0 0
\(607\) −3.50000 + 6.06218i −0.142061 + 0.246056i −0.928272 0.371901i \(-0.878706\pi\)
0.786212 + 0.617957i \(0.212039\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 18.8248 32.6054i 0.761568 1.31907i
\(612\) 0 0
\(613\) 4.27492 + 7.40437i 0.172662 + 0.299060i 0.939350 0.342961i \(-0.111430\pi\)
−0.766688 + 0.642020i \(0.778096\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 6.00000 0.241551 0.120775 0.992680i \(-0.461462\pi\)
0.120775 + 0.992680i \(0.461462\pi\)
\(618\) 0 0
\(619\) 14.4124 + 24.9630i 0.579282 + 1.00335i 0.995562 + 0.0941097i \(0.0300004\pi\)
−0.416280 + 0.909237i \(0.636666\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 12.0000 + 25.2011i 0.480770 + 1.00966i
\(624\) 0 0
\(625\) 10.4244 18.0556i 0.416977 0.722225i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −9.09967 −0.362828
\(630\) 0 0
\(631\) −19.8248 −0.789211 −0.394605 0.918851i \(-0.629119\pi\)
−0.394605 + 0.918851i \(0.629119\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 10.5619 18.2937i 0.419135 0.725964i
\(636\) 0 0
\(637\) −15.6873 41.0276i −0.621553 1.62557i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −1.82475 3.16056i −0.0720734 0.124835i 0.827736 0.561117i \(-0.189628\pi\)
−0.899810 + 0.436282i \(0.856295\pi\)
\(642\) 0 0
\(643\) −5.37459 −0.211953 −0.105976 0.994369i \(-0.533797\pi\)
−0.105976 + 0.994369i \(0.533797\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 17.0000 + 29.4449i 0.668339 + 1.15760i 0.978368 + 0.206870i \(0.0663277\pi\)
−0.310029 + 0.950727i \(0.600339\pi\)
\(648\) 0 0
\(649\) 2.08762 3.61587i 0.0819464 0.141935i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −3.46221 + 5.99672i −0.135487 + 0.234670i −0.925783 0.378055i \(-0.876593\pi\)
0.790297 + 0.612725i \(0.209926\pi\)
\(654\) 0 0
\(655\) 11.9124 + 20.6328i 0.465455 + 0.806192i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −42.1993 −1.64385 −0.821926 0.569594i \(-0.807101\pi\)
−0.821926 + 0.569594i \(0.807101\pi\)
\(660\) 0 0
\(661\) −3.58762 6.21395i −0.139542 0.241695i 0.787781 0.615955i \(-0.211230\pi\)
−0.927323 + 0.374261i \(0.877896\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 54.1993 + 4.30136i 2.10176 + 0.166799i
\(666\) 0 0
\(667\) 10.5498 18.2728i 0.408491 0.707528i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 32.7492 1.26427
\(672\) 0 0
\(673\) 41.5498 1.60163 0.800814 0.598913i \(-0.204400\pi\)
0.800814 + 0.598913i \(0.204400\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −6.63746 + 11.4964i −0.255098 + 0.441843i −0.964922 0.262536i \(-0.915441\pi\)
0.709824 + 0.704379i \(0.248774\pi\)
\(678\) 0 0
\(679\) 13.0876 19.0159i 0.502257 0.729762i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −6.08762 10.5441i −0.232936 0.403458i 0.725735 0.687975i \(-0.241500\pi\)
−0.958671 + 0.284517i \(0.908167\pi\)
\(684\) 0 0
\(685\) 4.74917 0.181457
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 29.0997 + 50.4021i 1.10861 + 1.92017i
\(690\) 0 0
\(691\) −5.41238 + 9.37451i −0.205896 + 0.356623i −0.950418 0.310975i \(-0.899344\pi\)
0.744522 + 0.667598i \(0.232678\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −13.5498 + 23.4690i −0.513975 + 0.890230i
\(696\) 0 0
\(697\) −9.09967 15.7611i −0.344675 0.596994i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 12.9244 0.488149 0.244074 0.969757i \(-0.421516\pi\)
0.244074 + 0.969757i \(0.421516\pi\)
\(702\) 0 0
\(703\) 7.13746 + 12.3624i 0.269194 + 0.466258i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −15.8248 1.25588i −0.595151 0.0472322i
\(708\) 0 0
\(709\) 14.0997 24.4213i 0.529524 0.917163i −0.469883 0.882729i \(-0.655704\pi\)
0.999407 0.0344340i \(-0.0109628\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 4.00000 0.149801
\(714\) 0 0
\(715\) −67.2990 −2.51684
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −14.0997 + 24.4213i −0.525829 + 0.910762i 0.473718 + 0.880676i \(0.342911\pi\)
−0.999547 + 0.0300860i \(0.990422\pi\)
\(720\) 0 0
\(721\) −12.3127 25.8578i −0.458549 0.962993i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 15.0997 + 26.1534i 0.560788 + 0.971313i
\(726\) 0 0
\(727\) −31.5498 −1.17012 −0.585059 0.810991i \(-0.698929\pi\)
−0.585059 + 0.810991i \(0.698929\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 0.549834 + 0.952341i 0.0203364 + 0.0352236i
\(732\) 0 0
\(733\) −2.96221 + 5.13070i −0.109412 + 0.189507i −0.915532 0.402245i \(-0.868230\pi\)
0.806120 + 0.591752i \(0.201563\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −0.450166 + 0.779710i −0.0165821 + 0.0287210i
\(738\) 0 0
\(739\) 0.687293 + 1.19043i 0.0252825 + 0.0437905i 0.878390 0.477945i \(-0.158618\pi\)
−0.853107 + 0.521735i \(0.825285\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −44.1993 −1.62152 −0.810758 0.585381i \(-0.800945\pi\)
−0.810758 + 0.585381i \(0.800945\pi\)
\(744\) 0 0
\(745\) 23.8248 + 41.2657i 0.872871 + 1.51186i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −18.0000 37.8016i −0.657706 1.38124i
\(750\) 0 0
\(751\) −5.22508 + 9.05011i −0.190666 + 0.330243i −0.945471 0.325706i \(-0.894398\pi\)
0.754805 + 0.655949i \(0.227731\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 73.2749 2.66675
\(756\) 0 0
\(757\) −22.0000 −0.799604 −0.399802 0.916602i \(-0.630921\pi\)
−0.399802 + 0.916602i \(0.630921\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −12.5498 + 21.7370i −0.454931 + 0.787964i −0.998684 0.0512814i \(-0.983669\pi\)
0.543753 + 0.839245i \(0.317003\pi\)
\(762\) 0 0
\(763\) −44.3746 3.52165i −1.60647 0.127492i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 4.00000 + 6.92820i 0.144432 + 0.250163i
\(768\) 0 0
\(769\) −32.6495 −1.17737 −0.588686 0.808362i \(-0.700354\pi\)
−0.588686 + 0.808362i \(0.700354\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 1.54983 + 2.68439i 0.0557437 + 0.0965509i 0.892551 0.450947i \(-0.148914\pi\)
−0.836807 + 0.547498i \(0.815580\pi\)
\(774\) 0 0
\(775\) −2.86254 + 4.95807i −0.102826 + 0.178099i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −14.2749 + 24.7249i −0.511452 + 0.885861i
\(780\) 0 0
\(781\) −3.27492 5.67232i −0.117186 0.202972i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 1.80066 0.0642684
\(786\) 0 0
\(787\) 1.27492 + 2.20822i 0.0454459 + 0.0787146i 0.887854 0.460126i \(-0.152196\pi\)
−0.842408 + 0.538841i \(0.818862\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 6.82475 9.91613i 0.242660 0.352577i
\(792\) 0 0
\(793\) −31.3746 + 54.3424i −1.11414 + 1.92975i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 31.4743 1.11488 0.557438 0.830219i \(-0.311785\pi\)
0.557438 + 0.830219i \(0.311785\pi\)
\(798\) 0 0
\(799\) −24.0000 −0.849059
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 7.00000 12.1244i 0.247025