Properties

Label 3024.2.q.a.2305.1
Level $3024$
Weight $2$
Character 3024.2305
Analytic conductor $24.147$
Analytic rank $0$
Dimension $2$
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: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 126)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 2305.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 3024.2305
Dual form 3024.2.q.a.2881.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.50000 - 2.59808i) q^{5} +(2.00000 + 1.73205i) q^{7} +O(q^{10})\) \(q+(-1.50000 - 2.59808i) q^{5} +(2.00000 + 1.73205i) q^{7} +(1.50000 - 2.59808i) q^{11} +(-2.50000 + 4.33013i) q^{13} +(1.50000 + 2.59808i) q^{17} +(2.50000 - 4.33013i) q^{19} +(1.50000 + 2.59808i) q^{23} +(-2.00000 + 3.46410i) q^{25} +(-1.50000 - 2.59808i) q^{29} +4.00000 q^{31} +(1.50000 - 7.79423i) q^{35} +(3.50000 - 6.06218i) q^{37} +(-4.50000 + 7.79423i) q^{41} +(5.50000 + 9.52628i) q^{43} +(1.00000 + 6.92820i) q^{49} +(-1.50000 - 2.59808i) q^{53} -9.00000 q^{55} +12.0000 q^{59} +2.00000 q^{61} +15.0000 q^{65} +4.00000 q^{67} +(-5.50000 - 9.52628i) q^{73} +(7.50000 - 2.59808i) q^{77} -8.00000 q^{79} +(-1.50000 - 2.59808i) q^{83} +(4.50000 - 7.79423i) q^{85} +(7.50000 - 12.9904i) q^{89} +(-12.5000 + 4.33013i) q^{91} -15.0000 q^{95} +(0.500000 + 0.866025i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - 3q^{5} + 4q^{7} + O(q^{10}) \) \( 2q - 3q^{5} + 4q^{7} + 3q^{11} - 5q^{13} + 3q^{17} + 5q^{19} + 3q^{23} - 4q^{25} - 3q^{29} + 8q^{31} + 3q^{35} + 7q^{37} - 9q^{41} + 11q^{43} + 2q^{49} - 3q^{53} - 18q^{55} + 24q^{59} + 4q^{61} + 30q^{65} + 8q^{67} - 11q^{73} + 15q^{77} - 16q^{79} - 3q^{83} + 9q^{85} + 15q^{89} - 25q^{91} - 30q^{95} + q^{97} + O(q^{100}) \)

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
\(5\) −1.50000 2.59808i −0.670820 1.16190i −0.977672 0.210138i \(-0.932609\pi\)
0.306851 0.951757i \(-0.400725\pi\)
\(6\) 0 0
\(7\) 2.00000 + 1.73205i 0.755929 + 0.654654i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 1.50000 2.59808i 0.452267 0.783349i −0.546259 0.837616i \(-0.683949\pi\)
0.998526 + 0.0542666i \(0.0172821\pi\)
\(12\) 0 0
\(13\) −2.50000 + 4.33013i −0.693375 + 1.20096i 0.277350 + 0.960769i \(0.410544\pi\)
−0.970725 + 0.240192i \(0.922790\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 1.50000 + 2.59808i 0.363803 + 0.630126i 0.988583 0.150675i \(-0.0481447\pi\)
−0.624780 + 0.780801i \(0.714811\pi\)
\(18\) 0 0
\(19\) 2.50000 4.33013i 0.573539 0.993399i −0.422659 0.906289i \(-0.638903\pi\)
0.996199 0.0871106i \(-0.0277634\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 1.50000 + 2.59808i 0.312772 + 0.541736i 0.978961 0.204046i \(-0.0654092\pi\)
−0.666190 + 0.745782i \(0.732076\pi\)
\(24\) 0 0
\(25\) −2.00000 + 3.46410i −0.400000 + 0.692820i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −1.50000 2.59808i −0.278543 0.482451i 0.692480 0.721437i \(-0.256518\pi\)
−0.971023 + 0.238987i \(0.923185\pi\)
\(30\) 0 0
\(31\) 4.00000 0.718421 0.359211 0.933257i \(-0.383046\pi\)
0.359211 + 0.933257i \(0.383046\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 1.50000 7.79423i 0.253546 1.31747i
\(36\) 0 0
\(37\) 3.50000 6.06218i 0.575396 0.996616i −0.420602 0.907245i \(-0.638181\pi\)
0.995998 0.0893706i \(-0.0284856\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −4.50000 + 7.79423i −0.702782 + 1.21725i 0.264704 + 0.964330i \(0.414726\pi\)
−0.967486 + 0.252924i \(0.918608\pi\)
\(42\) 0 0
\(43\) 5.50000 + 9.52628i 0.838742 + 1.45274i 0.890947 + 0.454108i \(0.150042\pi\)
−0.0522047 + 0.998636i \(0.516625\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(48\) 0 0
\(49\) 1.00000 + 6.92820i 0.142857 + 0.989743i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −1.50000 2.59808i −0.206041 0.356873i 0.744423 0.667708i \(-0.232725\pi\)
−0.950464 + 0.310835i \(0.899391\pi\)
\(54\) 0 0
\(55\) −9.00000 −1.21356
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 12.0000 1.56227 0.781133 0.624364i \(-0.214642\pi\)
0.781133 + 0.624364i \(0.214642\pi\)
\(60\) 0 0
\(61\) 2.00000 0.256074 0.128037 0.991769i \(-0.459132\pi\)
0.128037 + 0.991769i \(0.459132\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 15.0000 1.86052
\(66\) 0 0
\(67\) 4.00000 0.488678 0.244339 0.969690i \(-0.421429\pi\)
0.244339 + 0.969690i \(0.421429\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(72\) 0 0
\(73\) −5.50000 9.52628i −0.643726 1.11497i −0.984594 0.174855i \(-0.944054\pi\)
0.340868 0.940111i \(-0.389279\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 7.50000 2.59808i 0.854704 0.296078i
\(78\) 0 0
\(79\) −8.00000 −0.900070 −0.450035 0.893011i \(-0.648589\pi\)
−0.450035 + 0.893011i \(0.648589\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −1.50000 2.59808i −0.164646 0.285176i 0.771883 0.635764i \(-0.219315\pi\)
−0.936530 + 0.350588i \(0.885982\pi\)
\(84\) 0 0
\(85\) 4.50000 7.79423i 0.488094 0.845403i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 7.50000 12.9904i 0.794998 1.37698i −0.127842 0.991795i \(-0.540805\pi\)
0.922840 0.385183i \(-0.125862\pi\)
\(90\) 0 0
\(91\) −12.5000 + 4.33013i −1.31036 + 0.453921i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −15.0000 −1.53897
\(96\) 0 0
\(97\) 0.500000 + 0.866025i 0.0507673 + 0.0879316i 0.890292 0.455389i \(-0.150500\pi\)
−0.839525 + 0.543321i \(0.817167\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −1.50000 + 2.59808i −0.149256 + 0.258518i −0.930953 0.365140i \(-0.881021\pi\)
0.781697 + 0.623658i \(0.214354\pi\)
\(102\) 0 0
\(103\) 2.50000 + 4.33013i 0.246332 + 0.426660i 0.962505 0.271263i \(-0.0874412\pi\)
−0.716173 + 0.697923i \(0.754108\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 7.50000 12.9904i 0.725052 1.25583i −0.233900 0.972261i \(-0.575149\pi\)
0.958952 0.283567i \(-0.0915178\pi\)
\(108\) 0 0
\(109\) 3.50000 + 6.06218i 0.335239 + 0.580651i 0.983531 0.180741i \(-0.0578495\pi\)
−0.648292 + 0.761392i \(0.724516\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 7.50000 12.9904i 0.705541 1.22203i −0.260955 0.965351i \(-0.584038\pi\)
0.966496 0.256681i \(-0.0826291\pi\)
\(114\) 0 0
\(115\) 4.50000 7.79423i 0.419627 0.726816i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −1.50000 + 7.79423i −0.137505 + 0.714496i
\(120\) 0 0
\(121\) 1.00000 + 1.73205i 0.0909091 + 0.157459i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −3.00000 −0.268328
\(126\) 0 0
\(127\) 16.0000 1.41977 0.709885 0.704317i \(-0.248747\pi\)
0.709885 + 0.704317i \(0.248747\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −1.50000 2.59808i −0.131056 0.226995i 0.793028 0.609185i \(-0.208503\pi\)
−0.924084 + 0.382190i \(0.875170\pi\)
\(132\) 0 0
\(133\) 12.5000 4.33013i 1.08389 0.375470i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 1.50000 2.59808i 0.128154 0.221969i −0.794808 0.606861i \(-0.792428\pi\)
0.922961 + 0.384893i \(0.125762\pi\)
\(138\) 0 0
\(139\) 2.50000 4.33013i 0.212047 0.367277i −0.740308 0.672268i \(-0.765320\pi\)
0.952355 + 0.304991i \(0.0986536\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 7.50000 + 12.9904i 0.627182 + 1.08631i
\(144\) 0 0
\(145\) −4.50000 + 7.79423i −0.373705 + 0.647275i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −1.50000 2.59808i −0.122885 0.212843i 0.798019 0.602632i \(-0.205881\pi\)
−0.920904 + 0.389789i \(0.872548\pi\)
\(150\) 0 0
\(151\) 5.50000 9.52628i 0.447584 0.775238i −0.550645 0.834740i \(-0.685618\pi\)
0.998228 + 0.0595022i \(0.0189513\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −6.00000 10.3923i −0.481932 0.834730i
\(156\) 0 0
\(157\) 14.0000 1.11732 0.558661 0.829396i \(-0.311315\pi\)
0.558661 + 0.829396i \(0.311315\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −1.50000 + 7.79423i −0.118217 + 0.614271i
\(162\) 0 0
\(163\) 8.50000 14.7224i 0.665771 1.15315i −0.313304 0.949653i \(-0.601436\pi\)
0.979076 0.203497i \(-0.0652307\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −1.50000 + 2.59808i −0.116073 + 0.201045i −0.918208 0.396098i \(-0.870364\pi\)
0.802135 + 0.597143i \(0.203697\pi\)
\(168\) 0 0
\(169\) −6.00000 10.3923i −0.461538 0.799408i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −6.00000 −0.456172 −0.228086 0.973641i \(-0.573247\pi\)
−0.228086 + 0.973641i \(0.573247\pi\)
\(174\) 0 0
\(175\) −10.0000 + 3.46410i −0.755929 + 0.261861i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −1.50000 2.59808i −0.112115 0.194189i 0.804508 0.593942i \(-0.202429\pi\)
−0.916623 + 0.399753i \(0.869096\pi\)
\(180\) 0 0
\(181\) −10.0000 −0.743294 −0.371647 0.928374i \(-0.621207\pi\)
−0.371647 + 0.928374i \(0.621207\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −21.0000 −1.54395
\(186\) 0 0
\(187\) 9.00000 0.658145
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 12.0000 0.868290 0.434145 0.900843i \(-0.357051\pi\)
0.434145 + 0.900843i \(0.357051\pi\)
\(192\) 0 0
\(193\) 14.0000 1.00774 0.503871 0.863779i \(-0.331909\pi\)
0.503871 + 0.863779i \(0.331909\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 6.00000 0.427482 0.213741 0.976890i \(-0.431435\pi\)
0.213741 + 0.976890i \(0.431435\pi\)
\(198\) 0 0
\(199\) −3.50000 6.06218i −0.248108 0.429736i 0.714893 0.699234i \(-0.246476\pi\)
−0.963001 + 0.269498i \(0.913142\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 1.50000 7.79423i 0.105279 0.547048i
\(204\) 0 0
\(205\) 27.0000 1.88576
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −7.50000 12.9904i −0.518786 0.898563i
\(210\) 0 0
\(211\) 2.50000 4.33013i 0.172107 0.298098i −0.767049 0.641588i \(-0.778276\pi\)
0.939156 + 0.343490i \(0.111609\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 16.5000 28.5788i 1.12529 1.94906i
\(216\) 0 0
\(217\) 8.00000 + 6.92820i 0.543075 + 0.470317i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −15.0000 −1.00901
\(222\) 0 0
\(223\) 8.50000 + 14.7224i 0.569202 + 0.985887i 0.996645 + 0.0818447i \(0.0260811\pi\)
−0.427443 + 0.904042i \(0.640586\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −4.50000 + 7.79423i −0.298675 + 0.517321i −0.975833 0.218517i \(-0.929878\pi\)
0.677158 + 0.735838i \(0.263211\pi\)
\(228\) 0 0
\(229\) −8.50000 14.7224i −0.561696 0.972886i −0.997349 0.0727709i \(-0.976816\pi\)
0.435653 0.900115i \(-0.356518\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 13.5000 23.3827i 0.884414 1.53185i 0.0380310 0.999277i \(-0.487891\pi\)
0.846383 0.532574i \(-0.178775\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −13.5000 + 23.3827i −0.873242 + 1.51250i −0.0146191 + 0.999893i \(0.504654\pi\)
−0.858623 + 0.512607i \(0.828680\pi\)
\(240\) 0 0
\(241\) −11.5000 + 19.9186i −0.740780 + 1.28307i 0.211360 + 0.977408i \(0.432211\pi\)
−0.952141 + 0.305661i \(0.901123\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 16.5000 12.9904i 1.05415 0.829925i
\(246\) 0 0
\(247\) 12.5000 + 21.6506i 0.795356 + 1.37760i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 12.0000 0.757433 0.378717 0.925513i \(-0.376365\pi\)
0.378717 + 0.925513i \(0.376365\pi\)
\(252\) 0 0
\(253\) 9.00000 0.565825
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 7.50000 + 12.9904i 0.467837 + 0.810318i 0.999325 0.0367485i \(-0.0117000\pi\)
−0.531487 + 0.847066i \(0.678367\pi\)
\(258\) 0 0
\(259\) 17.5000 6.06218i 1.08740 0.376685i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 4.50000 7.79423i 0.277482 0.480613i −0.693276 0.720672i \(-0.743833\pi\)
0.970758 + 0.240059i \(0.0771668\pi\)
\(264\) 0 0
\(265\) −4.50000 + 7.79423i −0.276433 + 0.478796i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 10.5000 + 18.1865i 0.640196 + 1.10885i 0.985389 + 0.170321i \(0.0544803\pi\)
−0.345192 + 0.938532i \(0.612186\pi\)
\(270\) 0 0
\(271\) −6.50000 + 11.2583i −0.394847 + 0.683895i −0.993082 0.117426i \(-0.962536\pi\)
0.598235 + 0.801321i \(0.295869\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 6.00000 + 10.3923i 0.361814 + 0.626680i
\(276\) 0 0
\(277\) 3.50000 6.06218i 0.210295 0.364241i −0.741512 0.670940i \(-0.765891\pi\)
0.951807 + 0.306699i \(0.0992243\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 1.50000 + 2.59808i 0.0894825 + 0.154988i 0.907293 0.420500i \(-0.138145\pi\)
−0.817810 + 0.575488i \(0.804812\pi\)
\(282\) 0 0
\(283\) −8.00000 −0.475551 −0.237775 0.971320i \(-0.576418\pi\)
−0.237775 + 0.971320i \(0.576418\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −22.5000 + 7.79423i −1.32813 + 0.460079i
\(288\) 0 0
\(289\) 4.00000 6.92820i 0.235294 0.407541i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −13.5000 + 23.3827i −0.788678 + 1.36603i 0.138098 + 0.990419i \(0.455901\pi\)
−0.926777 + 0.375613i \(0.877432\pi\)
\(294\) 0 0
\(295\) −18.0000 31.1769i −1.04800 1.81519i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −15.0000 −0.867472
\(300\) 0 0
\(301\) −5.50000 + 28.5788i −0.317015 + 1.64726i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −3.00000 5.19615i −0.171780 0.297531i
\(306\) 0 0
\(307\) 28.0000 1.59804 0.799022 0.601302i \(-0.205351\pi\)
0.799022 + 0.601302i \(0.205351\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −24.0000 −1.36092 −0.680458 0.732787i \(-0.738219\pi\)
−0.680458 + 0.732787i \(0.738219\pi\)
\(312\) 0 0
\(313\) 14.0000 0.791327 0.395663 0.918396i \(-0.370515\pi\)
0.395663 + 0.918396i \(0.370515\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −30.0000 −1.68497 −0.842484 0.538721i \(-0.818908\pi\)
−0.842484 + 0.538721i \(0.818908\pi\)
\(318\) 0 0
\(319\) −9.00000 −0.503903
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 15.0000 0.834622
\(324\) 0 0
\(325\) −10.0000 17.3205i −0.554700 0.960769i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −20.0000 −1.09930 −0.549650 0.835395i \(-0.685239\pi\)
−0.549650 + 0.835395i \(0.685239\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −6.00000 10.3923i −0.327815 0.567792i
\(336\) 0 0
\(337\) 12.5000 21.6506i 0.680918 1.17939i −0.293783 0.955872i \(-0.594914\pi\)
0.974701 0.223513i \(-0.0717525\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 6.00000 10.3923i 0.324918 0.562775i
\(342\) 0 0
\(343\) −10.0000 + 15.5885i −0.539949 + 0.841698i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −12.0000 −0.644194 −0.322097 0.946707i \(-0.604388\pi\)
−0.322097 + 0.946707i \(0.604388\pi\)
\(348\) 0 0
\(349\) −2.50000 4.33013i −0.133822 0.231786i 0.791325 0.611396i \(-0.209392\pi\)
−0.925147 + 0.379610i \(0.876058\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −4.50000 + 7.79423i −0.239511 + 0.414845i −0.960574 0.278024i \(-0.910320\pi\)
0.721063 + 0.692869i \(0.243654\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −7.50000 + 12.9904i −0.395835 + 0.685606i −0.993207 0.116358i \(-0.962878\pi\)
0.597372 + 0.801964i \(0.296211\pi\)
\(360\) 0 0
\(361\) −3.00000 5.19615i −0.157895 0.273482i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −16.5000 + 28.5788i −0.863649 + 1.49588i
\(366\) 0 0
\(367\) −0.500000 + 0.866025i −0.0260998 + 0.0452062i −0.878780 0.477227i \(-0.841642\pi\)
0.852680 + 0.522433i \(0.174975\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 1.50000 7.79423i 0.0778761 0.404656i
\(372\) 0 0
\(373\) −8.50000 14.7224i −0.440113 0.762299i 0.557584 0.830120i \(-0.311728\pi\)
−0.997697 + 0.0678218i \(0.978395\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 15.0000 0.772539
\(378\) 0 0
\(379\) 16.0000 0.821865 0.410932 0.911666i \(-0.365203\pi\)
0.410932 + 0.911666i \(0.365203\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 7.50000 + 12.9904i 0.383232 + 0.663777i 0.991522 0.129937i \(-0.0414776\pi\)
−0.608290 + 0.793715i \(0.708144\pi\)
\(384\) 0 0
\(385\) −18.0000 15.5885i −0.917365 0.794461i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 4.50000 7.79423i 0.228159 0.395183i −0.729103 0.684403i \(-0.760063\pi\)
0.957263 + 0.289220i \(0.0933960\pi\)
\(390\) 0 0
\(391\) −4.50000 + 7.79423i −0.227575 + 0.394171i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 12.0000 + 20.7846i 0.603786 + 1.04579i
\(396\) 0 0
\(397\) −14.5000 + 25.1147i −0.727734 + 1.26047i 0.230105 + 0.973166i \(0.426093\pi\)
−0.957839 + 0.287307i \(0.907240\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 13.5000 + 23.3827i 0.674158 + 1.16768i 0.976714 + 0.214544i \(0.0688266\pi\)
−0.302556 + 0.953131i \(0.597840\pi\)
\(402\) 0 0
\(403\) −10.0000 + 17.3205i −0.498135 + 0.862796i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −10.5000 18.1865i −0.520466 0.901473i
\(408\) 0 0
\(409\) −22.0000 −1.08783 −0.543915 0.839140i \(-0.683059\pi\)
−0.543915 + 0.839140i \(0.683059\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 24.0000 + 20.7846i 1.18096 + 1.02274i
\(414\) 0 0
\(415\) −4.50000 + 7.79423i −0.220896 + 0.382604i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 1.50000 2.59808i 0.0732798 0.126924i −0.827057 0.562118i \(-0.809987\pi\)
0.900337 + 0.435194i \(0.143320\pi\)
\(420\) 0 0
\(421\) 15.5000 + 26.8468i 0.755424 + 1.30843i 0.945163 + 0.326598i \(0.105902\pi\)
−0.189740 + 0.981834i \(0.560764\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −12.0000 −0.582086
\(426\) 0 0
\(427\) 4.00000 + 3.46410i 0.193574 + 0.167640i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 1.50000 + 2.59808i 0.0722525 + 0.125145i 0.899888 0.436121i \(-0.143648\pi\)
−0.827636 + 0.561266i \(0.810315\pi\)
\(432\) 0 0
\(433\) 14.0000 0.672797 0.336399 0.941720i \(-0.390791\pi\)
0.336399 + 0.941720i \(0.390791\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 15.0000 0.717547
\(438\) 0 0
\(439\) −8.00000 −0.381819 −0.190910 0.981608i \(-0.561144\pi\)
−0.190910 + 0.981608i \(0.561144\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(444\) 0 0
\(445\) −45.0000 −2.13320
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −30.0000 −1.41579 −0.707894 0.706319i \(-0.750354\pi\)
−0.707894 + 0.706319i \(0.750354\pi\)
\(450\) 0 0
\(451\) 13.5000 + 23.3827i 0.635690 + 1.10105i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 30.0000 + 25.9808i 1.40642 + 1.21800i
\(456\) 0 0
\(457\) −34.0000 −1.59045 −0.795226 0.606313i \(-0.792648\pi\)
−0.795226 + 0.606313i \(0.792648\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 4.50000 + 7.79423i 0.209586 + 0.363013i 0.951584 0.307388i \(-0.0994551\pi\)
−0.741998 + 0.670402i \(0.766122\pi\)
\(462\) 0 0
\(463\) 17.5000 30.3109i 0.813294 1.40867i −0.0972525 0.995260i \(-0.531005\pi\)
0.910546 0.413407i \(-0.135661\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 1.50000 2.59808i 0.0694117 0.120225i −0.829231 0.558906i \(-0.811221\pi\)
0.898642 + 0.438682i \(0.144554\pi\)
\(468\) 0 0
\(469\) 8.00000 + 6.92820i 0.369406 + 0.319915i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 33.0000 1.51734
\(474\) 0 0
\(475\) 10.0000 + 17.3205i 0.458831 + 0.794719i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 4.50000 7.79423i 0.205610 0.356127i −0.744717 0.667381i \(-0.767415\pi\)
0.950327 + 0.311253i \(0.100749\pi\)
\(480\) 0 0
\(481\) 17.5000 + 30.3109i 0.797931 + 1.38206i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 1.50000 2.59808i 0.0681115 0.117973i
\(486\) 0 0
\(487\) −15.5000 26.8468i −0.702372 1.21654i −0.967632 0.252367i \(-0.918791\pi\)
0.265260 0.964177i \(-0.414542\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 19.5000 33.7750i 0.880023 1.52424i 0.0287085 0.999588i \(-0.490861\pi\)
0.851314 0.524656i \(-0.175806\pi\)
\(492\) 0 0
\(493\) 4.50000 7.79423i 0.202670 0.351034i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 5.50000 + 9.52628i 0.246214 + 0.426455i 0.962472 0.271380i \(-0.0874801\pi\)
−0.716258 + 0.697835i \(0.754147\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −12.0000 −0.535054 −0.267527 0.963550i \(-0.586206\pi\)
−0.267527 + 0.963550i \(0.586206\pi\)
\(504\) 0 0
\(505\) 9.00000 0.400495
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −13.5000 23.3827i −0.598377 1.03642i −0.993061 0.117602i \(-0.962479\pi\)
0.394684 0.918817i \(-0.370854\pi\)
\(510\) 0 0
\(511\) 5.50000 28.5788i 0.243306 1.26425i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 7.50000 12.9904i 0.330489 0.572425i
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 1.50000 + 2.59808i 0.0657162 + 0.113824i 0.897011 0.442007i \(-0.145733\pi\)
−0.831295 + 0.555831i \(0.812400\pi\)
\(522\) 0 0
\(523\) −3.50000 + 6.06218i −0.153044 + 0.265081i −0.932345 0.361569i \(-0.882241\pi\)
0.779301 + 0.626650i \(0.215574\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 6.00000 + 10.3923i 0.261364 + 0.452696i
\(528\) 0 0
\(529\) 7.00000 12.1244i 0.304348 0.527146i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −22.5000 38.9711i −0.974583 1.68803i
\(534\) 0 0
\(535\) −45.0000 −1.94552
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 19.5000 + 7.79423i 0.839924 + 0.335721i
\(540\) 0 0
\(541\) −8.50000 + 14.7224i −0.365444 + 0.632967i −0.988847 0.148933i \(-0.952416\pi\)
0.623404 + 0.781900i \(0.285749\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 10.5000 18.1865i 0.449771 0.779026i
\(546\) 0 0
\(547\) 5.50000 + 9.52628i 0.235163 + 0.407314i 0.959320 0.282321i \(-0.0911043\pi\)
−0.724157 + 0.689635i \(0.757771\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −15.0000 −0.639021
\(552\) 0 0
\(553\) −16.0000 13.8564i −0.680389 0.589234i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −1.50000 2.59808i −0.0635570 0.110084i 0.832496 0.554031i \(-0.186911\pi\)
−0.896053 + 0.443947i \(0.853578\pi\)
\(558\) 0 0
\(559\) −55.0000 −2.32625
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −12.0000 −0.505740 −0.252870 0.967500i \(-0.581374\pi\)
−0.252870 + 0.967500i \(0.581374\pi\)
\(564\) 0 0
\(565\) −45.0000 −1.89316
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −30.0000 −1.25767 −0.628833 0.777541i \(-0.716467\pi\)
−0.628833 + 0.777541i \(0.716467\pi\)
\(570\) 0 0
\(571\) −20.0000 −0.836974 −0.418487 0.908223i \(-0.637439\pi\)
−0.418487 + 0.908223i \(0.637439\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −12.0000 −0.500435
\(576\) 0 0
\(577\) −5.50000 9.52628i −0.228968 0.396584i 0.728535 0.685009i \(-0.240202\pi\)
−0.957503 + 0.288425i \(0.906868\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 1.50000 7.79423i 0.0622305 0.323359i
\(582\) 0 0
\(583\) −9.00000 −0.372742
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 16.5000 + 28.5788i 0.681028 + 1.17957i 0.974668 + 0.223659i \(0.0718001\pi\)
−0.293640 + 0.955916i \(0.594867\pi\)
\(588\) 0 0
\(589\) 10.0000 17.3205i 0.412043 0.713679i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −10.5000 + 18.1865i −0.431183 + 0.746831i −0.996976 0.0777165i \(-0.975237\pi\)
0.565792 + 0.824548i \(0.308570\pi\)
\(594\) 0 0
\(595\) 22.5000 7.79423i 0.922410 0.319532i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(600\) 0 0
\(601\) 0.500000 + 0.866025i 0.0203954 + 0.0353259i 0.876043 0.482233i \(-0.160174\pi\)
−0.855648 + 0.517559i \(0.826841\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 3.00000 5.19615i 0.121967 0.211254i
\(606\) 0 0
\(607\) −21.5000 37.2391i −0.872658 1.51149i −0.859237 0.511578i \(-0.829061\pi\)
−0.0134214 0.999910i \(-0.504272\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) 15.5000 + 26.8468i 0.626039 + 1.08433i 0.988339 + 0.152270i \(0.0486583\pi\)
−0.362300 + 0.932062i \(0.618008\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 1.50000 2.59808i 0.0603877 0.104595i −0.834251 0.551385i \(-0.814100\pi\)
0.894639 + 0.446790i \(0.147433\pi\)
\(618\) 0 0
\(619\) −9.50000 + 16.4545i −0.381837 + 0.661361i −0.991325 0.131434i \(-0.958042\pi\)
0.609488 + 0.792796i \(0.291375\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 37.5000 12.9904i 1.50241 0.520449i
\(624\) 0 0
\(625\) 14.5000 + 25.1147i 0.580000 + 1.00459i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 21.0000 0.837325
\(630\) 0 0
\(631\) −8.00000 −0.318475 −0.159237 0.987240i \(-0.550904\pi\)
−0.159237 + 0.987240i \(0.550904\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −24.0000 41.5692i −0.952411 1.64962i
\(636\) 0 0
\(637\) −32.5000 12.9904i −1.28770 0.514698i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −22.5000 + 38.9711i −0.888697 + 1.53927i −0.0472793 + 0.998882i \(0.515055\pi\)
−0.841417 + 0.540386i \(0.818278\pi\)
\(642\) 0 0
\(643\) 14.5000 25.1147i 0.571824 0.990429i −0.424555 0.905402i \(-0.639569\pi\)
0.996379 0.0850262i \(-0.0270974\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 1.50000 + 2.59808i 0.0589711 + 0.102141i 0.894004 0.448059i \(-0.147885\pi\)
−0.835033 + 0.550200i \(0.814551\pi\)
\(648\) 0 0
\(649\) 18.0000 31.1769i 0.706562 1.22380i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 4.50000 + 7.79423i 0.176099 + 0.305012i 0.940541 0.339680i \(-0.110319\pi\)
−0.764442 + 0.644692i \(0.776986\pi\)
\(654\) 0 0
\(655\) −4.50000 + 7.79423i −0.175830 + 0.304546i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −19.5000 33.7750i −0.759612 1.31569i −0.943049 0.332655i \(-0.892055\pi\)
0.183436 0.983032i \(-0.441278\pi\)
\(660\) 0 0
\(661\) 14.0000 0.544537 0.272268 0.962221i \(-0.412226\pi\)
0.272268 + 0.962221i \(0.412226\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −30.0000 25.9808i −1.16335 1.00749i
\(666\) 0 0
\(667\) 4.50000 7.79423i 0.174241 0.301794i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 3.00000 5.19615i 0.115814 0.200595i
\(672\) 0 0
\(673\) −5.50000 9.52628i −0.212009 0.367211i 0.740334 0.672239i \(-0.234667\pi\)
−0.952343 + 0.305028i \(0.901334\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −6.00000 −0.230599 −0.115299 0.993331i \(-0.536783\pi\)
−0.115299 + 0.993331i \(0.536783\pi\)
\(678\) 0 0
\(679\) −0.500000 + 2.59808i −0.0191882 + 0.0997050i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 16.5000 + 28.5788i 0.631355 + 1.09354i 0.987275 + 0.159022i \(0.0508342\pi\)
−0.355920 + 0.934516i \(0.615832\pi\)
\(684\) 0 0
\(685\) −9.00000 −0.343872
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 15.0000 0.571454
\(690\) 0 0
\(691\) −20.0000 −0.760836 −0.380418 0.924815i \(-0.624220\pi\)
−0.380418 + 0.924815i \(0.624220\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −15.0000 −0.568982
\(696\) 0 0
\(697\) −27.0000 −1.02270
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −6.00000 −0.226617 −0.113308 0.993560i \(-0.536145\pi\)
−0.113308 + 0.993560i \(0.536145\pi\)
\(702\) 0 0
\(703\) −17.5000 30.3109i −0.660025 1.14320i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −7.50000 + 2.59808i −0.282067 + 0.0977107i
\(708\) 0 0
\(709\) −10.0000 −0.375558 −0.187779 0.982211i \(-0.560129\pi\)
−0.187779 + 0.982211i \(0.560129\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 6.00000 + 10.3923i 0.224702 + 0.389195i
\(714\) 0 0
\(715\) 22.5000 38.9711i 0.841452 1.45744i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −19.5000 + 33.7750i −0.727227 + 1.25959i 0.230823 + 0.972996i \(0.425858\pi\)
−0.958051 + 0.286599i \(0.907475\pi\)
\(720\) 0 0
\(721\) −2.50000 + 12.9904i −0.0931049 + 0.483787i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 12.0000 0.445669
\(726\) 0 0
\(727\) 2.50000 + 4.33013i 0.0927199 + 0.160596i 0.908655 0.417548i \(-0.137111\pi\)
−0.815935 + 0.578144i \(0.803777\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −16.5000 + 28.5788i −0.610275 + 1.05703i
\(732\) 0 0
\(733\) −20.5000 35.5070i −0.757185 1.31148i −0.944281 0.329141i \(-0.893241\pi\)
0.187096 0.982342i \(-0.440092\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 6.00000 10.3923i 0.221013 0.382805i
\(738\) 0 0
\(739\) 23.5000 + 40.7032i 0.864461 + 1.49729i 0.867581 + 0.497296i \(0.165674\pi\)
−0.00311943 + 0.999995i \(0.500993\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −1.50000 + 2.59808i −0.0550297 + 0.0953142i −0.892228 0.451585i \(-0.850859\pi\)
0.837198 + 0.546899i \(0.184192\pi\)
\(744\) 0 0
\(745\) −4.50000 + 7.79423i −0.164867 + 0.285558i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 37.5000 12.9904i 1.37022 0.474658i
\(750\) 0 0
\(751\) 14.5000 + 25.1147i 0.529113 + 0.916450i 0.999424 + 0.0339490i \(0.0108084\pi\)
−0.470311 + 0.882501i \(0.655858\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −33.0000 −1.20099
\(756\) 0 0
\(757\) 14.0000 0.508839 0.254419 0.967094i \(-0.418116\pi\)
0.254419 + 0.967094i \(0.418116\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 1.50000 + 2.59808i 0.0543750 + 0.0941802i 0.891932 0.452170i \(-0.149350\pi\)
−0.837557 + 0.546350i \(0.816017\pi\)
\(762\) 0 0
\(763\) −3.50000 + 18.1865i −0.126709 + 0.658397i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −30.0000 + 51.9615i −1.08324 + 1.87622i
\(768\) 0 0
\(769\) 0.500000 0.866025i 0.0180305 0.0312297i −0.856869 0.515534i \(-0.827594\pi\)
0.874900 + 0.484304i \(0.160927\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 10.5000 + 18.1865i 0.377659 + 0.654124i 0.990721 0.135910i \(-0.0433959\pi\)
−0.613062 + 0.790034i \(0.710063\pi\)
\(774\) 0 0
\(775\) −8.00000 + 13.8564i −0.287368 + 0.497737i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 22.5000 + 38.9711i 0.806146 + 1.39629i
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −21.0000 36.3731i −0.749522 1.29821i
\(786\) 0 0
\(787\) −44.0000 −1.56843 −0.784215 0.620489i \(-0.786934\pi\)
−0.784215 + 0.620489i \(0.786934\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 37.5000 12.9904i 1.33335 0.461885i
\(792\) 0 0
\(793\) −5.00000 + 8.66025i −0.177555 + 0.307535i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −13.5000 + 23.3827i −0.478195 + 0.828257i −0.999687 0.0249984i \(-0.992042\pi\)
0.521493 + 0.853256i \(0.325375\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −33.0000 −1.16454
\(804\) 0 0
\(805\) 22.5000 7.79423i 0.793021 0.274710i
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 19.5000 + 33.7750i 0.685583 + 1.18747i 0.973253 + 0.229736i \(0.0737862\pi\)
−0.287670 + 0.957730i \(0.592880\pi\)
\(810\) 0 0
\(811\) −20.0000 −0.702295 −0.351147 0.936320i \(-0.614208\pi\)
−0.351147 + 0.936320i \(0.614208\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −51.0000 −1.78645
\(816\) 0 0
\(817\)