Properties

Label 3024.2.q.g.2881.1
Level 3024
Weight 2
Character 3024.2881
Analytic conductor 24.147
Analytic rank 0
Dimension 6
CM no
Inner twists 2

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Newspace parameters

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

Newform invariants

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

Embedding invariants

Embedding label 2881.1
Root \(0.500000 + 1.41036i\) of defining polynomial
Character \(\chi\) \(=\) 3024.2881
Dual form 3024.2.q.g.2305.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.59097 + 2.75564i) q^{5} +(2.56238 - 0.658939i) q^{7} +O(q^{10})\) \(q+(-1.59097 + 2.75564i) q^{5} +(2.56238 - 0.658939i) q^{7} +(-1.59097 - 2.75564i) q^{11} +(2.85185 + 4.93955i) q^{13} +(0.760877 - 1.31788i) q^{17} +(0.641315 + 1.11079i) q^{19} +(-1.11956 + 1.93914i) q^{23} +(-2.56238 - 4.43818i) q^{25} +(3.54063 - 6.13255i) q^{29} +9.42107 q^{31} +(-2.26088 + 8.10936i) q^{35} +(0.500000 + 0.866025i) q^{37} +(2.80150 + 4.85235i) q^{41} +(-3.41423 + 5.91362i) q^{43} -5.82846 q^{47} +(6.13160 - 3.37690i) q^{49} +(-1.02859 + 1.78157i) q^{53} +10.1248 q^{55} -1.12476 q^{59} +3.12476 q^{61} -18.1488 q^{65} -10.9669 q^{67} +8.69002 q^{71} +(-2.48345 + 4.30146i) q^{73} +(-5.89248 - 6.01266i) q^{77} +4.13844 q^{79} +(-4.03379 + 6.98673i) q^{83} +(2.42107 + 4.19341i) q^{85} +(-0.112725 - 0.195246i) q^{89} +(10.5624 + 10.7778i) q^{91} -4.08126 q^{95} +(7.42107 - 12.8537i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q - q^{5} - 2q^{7} + O(q^{10}) \) \( 6q - q^{5} - 2q^{7} - q^{11} + 8q^{13} + 4q^{17} + 3q^{19} - 7q^{23} + 2q^{25} + 5q^{29} + 40q^{31} - 13q^{35} + 3q^{37} + 6q^{43} + 18q^{47} + 12q^{49} - 15q^{53} + 26q^{55} + 28q^{59} - 16q^{61} - 24q^{65} + 2q^{67} + 14q^{71} + 19q^{73} - 10q^{77} + 10q^{79} + 2q^{83} - 2q^{85} + 9q^{89} + 46q^{91} + 8q^{95} + 28q^{97} + O(q^{100}) \)

Character values

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

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

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0 0
\(4\) 0 0
\(5\) −1.59097 + 2.75564i −0.711504 + 1.23236i 0.252788 + 0.967522i \(0.418652\pi\)
−0.964292 + 0.264840i \(0.914681\pi\)
\(6\) 0 0
\(7\) 2.56238 0.658939i 0.968489 0.249055i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −1.59097 2.75564i −0.479696 0.830858i 0.520033 0.854146i \(-0.325920\pi\)
−0.999729 + 0.0232884i \(0.992586\pi\)
\(12\) 0 0
\(13\) 2.85185 + 4.93955i 0.790960 + 1.36998i 0.925373 + 0.379058i \(0.123752\pi\)
−0.134412 + 0.990925i \(0.542915\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 0.760877 1.31788i 0.184540 0.319632i −0.758882 0.651229i \(-0.774254\pi\)
0.943421 + 0.331596i \(0.107587\pi\)
\(18\) 0 0
\(19\) 0.641315 + 1.11079i 0.147128 + 0.254833i 0.930165 0.367142i \(-0.119664\pi\)
−0.783037 + 0.621975i \(0.786330\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −1.11956 + 1.93914i −0.233445 + 0.404338i −0.958820 0.284016i \(-0.908333\pi\)
0.725375 + 0.688354i \(0.241666\pi\)
\(24\) 0 0
\(25\) −2.56238 4.43818i −0.512476 0.887635i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 3.54063 6.13255i 0.657478 1.13879i −0.323788 0.946130i \(-0.604957\pi\)
0.981266 0.192656i \(-0.0617101\pi\)
\(30\) 0 0
\(31\) 9.42107 1.69207 0.846037 0.533125i \(-0.178982\pi\)
0.846037 + 0.533125i \(0.178982\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −2.26088 + 8.10936i −0.382158 + 1.37073i
\(36\) 0 0
\(37\) 0.500000 + 0.866025i 0.0821995 + 0.142374i 0.904194 0.427121i \(-0.140472\pi\)
−0.821995 + 0.569495i \(0.807139\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 2.80150 + 4.85235i 0.437522 + 0.757810i 0.997498 0.0706992i \(-0.0225230\pi\)
−0.559976 + 0.828509i \(0.689190\pi\)
\(42\) 0 0
\(43\) −3.41423 + 5.91362i −0.520665 + 0.901819i 0.479046 + 0.877790i \(0.340983\pi\)
−0.999711 + 0.0240288i \(0.992351\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −5.82846 −0.850168 −0.425084 0.905154i \(-0.639755\pi\)
−0.425084 + 0.905154i \(0.639755\pi\)
\(48\) 0 0
\(49\) 6.13160 3.37690i 0.875943 0.482415i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −1.02859 + 1.78157i −0.141288 + 0.244717i −0.927982 0.372626i \(-0.878458\pi\)
0.786694 + 0.617343i \(0.211791\pi\)
\(54\) 0 0
\(55\) 10.1248 1.36522
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −1.12476 −0.146432 −0.0732159 0.997316i \(-0.523326\pi\)
−0.0732159 + 0.997316i \(0.523326\pi\)
\(60\) 0 0
\(61\) 3.12476 0.400085 0.200042 0.979787i \(-0.435892\pi\)
0.200042 + 0.979787i \(0.435892\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −18.1488 −2.25109
\(66\) 0 0
\(67\) −10.9669 −1.33982 −0.669910 0.742442i \(-0.733667\pi\)
−0.669910 + 0.742442i \(0.733667\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 8.69002 1.03132 0.515658 0.856794i \(-0.327548\pi\)
0.515658 + 0.856794i \(0.327548\pi\)
\(72\) 0 0
\(73\) −2.48345 + 4.30146i −0.290666 + 0.503448i −0.973967 0.226689i \(-0.927210\pi\)
0.683302 + 0.730136i \(0.260543\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −5.89248 6.01266i −0.671510 0.685206i
\(78\) 0 0
\(79\) 4.13844 0.465610 0.232805 0.972523i \(-0.425210\pi\)
0.232805 + 0.972523i \(0.425210\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −4.03379 + 6.98673i −0.442766 + 0.766893i −0.997894 0.0648718i \(-0.979336\pi\)
0.555127 + 0.831765i \(0.312669\pi\)
\(84\) 0 0
\(85\) 2.42107 + 4.19341i 0.262602 + 0.454839i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −0.112725 0.195246i −0.0119488 0.0206960i 0.859989 0.510312i \(-0.170470\pi\)
−0.871938 + 0.489616i \(0.837137\pi\)
\(90\) 0 0
\(91\) 10.5624 + 10.7778i 1.10724 + 1.12982i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −4.08126 −0.418728
\(96\) 0 0
\(97\) 7.42107 12.8537i 0.753495 1.30509i −0.192624 0.981273i \(-0.561700\pi\)
0.946119 0.323819i \(-0.104967\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 9.29467 + 16.0988i 0.924854 + 1.60189i 0.791796 + 0.610786i \(0.209146\pi\)
0.133058 + 0.991108i \(0.457520\pi\)
\(102\) 0 0
\(103\) −0.141315 + 0.244765i −0.0139242 + 0.0241174i −0.872904 0.487893i \(-0.837766\pi\)
0.858979 + 0.512010i \(0.171099\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 5.68878 + 9.85326i 0.549955 + 0.952550i 0.998277 + 0.0586780i \(0.0186885\pi\)
−0.448322 + 0.893872i \(0.647978\pi\)
\(108\) 0 0
\(109\) −2.21053 + 3.82876i −0.211731 + 0.366728i −0.952256 0.305300i \(-0.901243\pi\)
0.740526 + 0.672028i \(0.234577\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 1.60752 + 2.78431i 0.151223 + 0.261926i 0.931677 0.363287i \(-0.118345\pi\)
−0.780454 + 0.625213i \(0.785012\pi\)
\(114\) 0 0
\(115\) −3.56238 6.17023i −0.332194 0.575377i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 1.08126 3.87828i 0.0991186 0.355521i
\(120\) 0 0
\(121\) 0.437618 0.757977i 0.0397835 0.0689070i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 0.396990 0.0355079
\(126\) 0 0
\(127\) −20.1053 −1.78406 −0.892030 0.451976i \(-0.850719\pi\)
−0.892030 + 0.451976i \(0.850719\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −3.18194 + 5.51129i −0.278008 + 0.481523i −0.970890 0.239528i \(-0.923007\pi\)
0.692882 + 0.721051i \(0.256341\pi\)
\(132\) 0 0
\(133\) 2.37524 + 2.42368i 0.205959 + 0.210160i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 1.37072 + 2.37416i 0.117109 + 0.202838i 0.918621 0.395140i \(-0.129304\pi\)
−0.801512 + 0.597979i \(0.795971\pi\)
\(138\) 0 0
\(139\) 3.98345 + 6.89953i 0.337872 + 0.585211i 0.984032 0.177991i \(-0.0569597\pi\)
−0.646161 + 0.763202i \(0.723626\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 9.07442 15.7174i 0.758841 1.31435i
\(144\) 0 0
\(145\) 11.2661 + 19.5134i 0.935597 + 1.62050i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −11.6300 + 20.1437i −0.952764 + 1.65024i −0.213360 + 0.976974i \(0.568441\pi\)
−0.739404 + 0.673262i \(0.764893\pi\)
\(150\) 0 0
\(151\) −4.06238 7.03625i −0.330592 0.572602i 0.652036 0.758188i \(-0.273915\pi\)
−0.982628 + 0.185586i \(0.940582\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −14.9887 + 25.9611i −1.20392 + 2.08525i
\(156\) 0 0
\(157\) −11.2632 −0.898901 −0.449451 0.893305i \(-0.648380\pi\)
−0.449451 + 0.893305i \(0.648380\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −1.59097 + 5.70653i −0.125386 + 0.449738i
\(162\) 0 0
\(163\) 1.99028 + 3.44727i 0.155891 + 0.270011i 0.933383 0.358881i \(-0.116842\pi\)
−0.777492 + 0.628893i \(0.783508\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 2.61956 + 4.53721i 0.202708 + 0.351100i 0.949400 0.314070i \(-0.101693\pi\)
−0.746692 + 0.665170i \(0.768359\pi\)
\(168\) 0 0
\(169\) −9.76608 + 16.9153i −0.751237 + 1.30118i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −2.55159 −0.193994 −0.0969968 0.995285i \(-0.530924\pi\)
−0.0969968 + 0.995285i \(0.530924\pi\)
\(174\) 0 0
\(175\) −9.49028 9.68385i −0.717398 0.732030i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 3.51887 6.09487i 0.263013 0.455552i −0.704028 0.710172i \(-0.748617\pi\)
0.967041 + 0.254620i \(0.0819504\pi\)
\(180\) 0 0
\(181\) −12.9669 −0.963822 −0.481911 0.876220i \(-0.660057\pi\)
−0.481911 + 0.876220i \(0.660057\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −3.18194 −0.233941
\(186\) 0 0
\(187\) −4.84213 −0.354092
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 1.98057 0.143309 0.0716545 0.997430i \(-0.477172\pi\)
0.0716545 + 0.997430i \(0.477172\pi\)
\(192\) 0 0
\(193\) −4.54583 −0.327216 −0.163608 0.986525i \(-0.552313\pi\)
−0.163608 + 0.986525i \(0.552313\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 21.8148 1.55424 0.777120 0.629353i \(-0.216680\pi\)
0.777120 + 0.629353i \(0.216680\pi\)
\(198\) 0 0
\(199\) −6.14132 + 10.6371i −0.435346 + 0.754042i −0.997324 0.0731106i \(-0.976707\pi\)
0.561978 + 0.827152i \(0.310041\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 5.03147 18.0470i 0.353140 1.26665i
\(204\) 0 0
\(205\) −17.8285 −1.24519
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 2.04063 3.53447i 0.141153 0.244485i
\(210\) 0 0
\(211\) 8.32846 + 14.4253i 0.573355 + 0.993080i 0.996218 + 0.0868863i \(0.0276917\pi\)
−0.422863 + 0.906193i \(0.638975\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −10.8639 18.8168i −0.740911 1.28330i
\(216\) 0 0
\(217\) 24.1404 6.20790i 1.63876 0.421420i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 8.67962 0.583854
\(222\) 0 0
\(223\) 5.32846 9.22916i 0.356820 0.618031i −0.630608 0.776102i \(-0.717194\pi\)
0.987428 + 0.158071i \(0.0505276\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 7.25404 + 12.5644i 0.481468 + 0.833926i 0.999774 0.0212688i \(-0.00677059\pi\)
−0.518306 + 0.855195i \(0.673437\pi\)
\(228\) 0 0
\(229\) −5.12476 + 8.87635i −0.338654 + 0.586566i −0.984180 0.177173i \(-0.943305\pi\)
0.645526 + 0.763738i \(0.276638\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −0.540628 0.936396i −0.0354177 0.0613453i 0.847773 0.530359i \(-0.177943\pi\)
−0.883191 + 0.469014i \(0.844610\pi\)
\(234\) 0 0
\(235\) 9.27292 16.0612i 0.604898 1.04771i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −6.16019 10.6698i −0.398470 0.690170i 0.595068 0.803676i \(-0.297125\pi\)
−0.993537 + 0.113506i \(0.963792\pi\)
\(240\) 0 0
\(241\) 6.50000 + 11.2583i 0.418702 + 0.725213i 0.995809 0.0914555i \(-0.0291519\pi\)
−0.577107 + 0.816668i \(0.695819\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −0.449657 + 22.2691i −0.0287275 + 1.42272i
\(246\) 0 0
\(247\) −3.65787 + 6.33561i −0.232744 + 0.403125i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 5.11109 0.322609 0.161305 0.986905i \(-0.448430\pi\)
0.161305 + 0.986905i \(0.448430\pi\)
\(252\) 0 0
\(253\) 7.12476 0.447930
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 3.83009 6.63392i 0.238915 0.413813i −0.721488 0.692427i \(-0.756542\pi\)
0.960403 + 0.278614i \(0.0898750\pi\)
\(258\) 0 0
\(259\) 1.85185 + 1.88962i 0.115068 + 0.117415i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 1.54746 + 2.68029i 0.0954208 + 0.165274i 0.909784 0.415082i \(-0.136247\pi\)
−0.814363 + 0.580355i \(0.802914\pi\)
\(264\) 0 0
\(265\) −3.27292 5.66886i −0.201054 0.348235i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 13.4451 23.2877i 0.819765 1.41987i −0.0860906 0.996287i \(-0.527437\pi\)
0.905855 0.423587i \(-0.139229\pi\)
\(270\) 0 0
\(271\) 11.1082 + 19.2400i 0.674776 + 1.16875i 0.976534 + 0.215362i \(0.0690930\pi\)
−0.301759 + 0.953384i \(0.597574\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −8.15335 + 14.1220i −0.491666 + 0.851590i
\(276\) 0 0
\(277\) 7.31875 + 12.6764i 0.439741 + 0.761653i 0.997669 0.0682357i \(-0.0217370\pi\)
−0.557928 + 0.829889i \(0.688404\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −11.6992 + 20.2636i −0.697915 + 1.20882i 0.271273 + 0.962502i \(0.412555\pi\)
−0.969188 + 0.246322i \(0.920778\pi\)
\(282\) 0 0
\(283\) 26.1248 1.55296 0.776478 0.630144i \(-0.217004\pi\)
0.776478 + 0.630144i \(0.217004\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 10.3759 + 10.5876i 0.612471 + 0.624963i
\(288\) 0 0
\(289\) 7.34213 + 12.7169i 0.431890 + 0.748056i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −12.9315 22.3980i −0.755465 1.30850i −0.945143 0.326657i \(-0.894078\pi\)
0.189678 0.981846i \(-0.439255\pi\)
\(294\) 0 0
\(295\) 1.78947 3.09945i 0.104187 0.180457i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −12.7713 −0.738582
\(300\) 0 0
\(301\) −4.85185 + 17.4027i −0.279656 + 1.00308i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −4.97141 + 8.61073i −0.284662 + 0.493049i
\(306\) 0 0
\(307\) −3.53216 −0.201591 −0.100795 0.994907i \(-0.532139\pi\)
−0.100795 + 0.994907i \(0.532139\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 1.70370 0.0966078 0.0483039 0.998833i \(-0.484618\pi\)
0.0483039 + 0.998833i \(0.484618\pi\)
\(312\) 0 0
\(313\) −2.84213 −0.160647 −0.0803234 0.996769i \(-0.525595\pi\)
−0.0803234 + 0.996769i \(0.525595\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 24.9201 1.39965 0.699827 0.714313i \(-0.253261\pi\)
0.699827 + 0.714313i \(0.253261\pi\)
\(318\) 0 0
\(319\) −22.5322 −1.26156
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 1.95185 0.108604
\(324\) 0 0
\(325\) 14.6150 25.3140i 0.810697 1.40417i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −14.9347 + 3.84060i −0.823379 + 0.211739i
\(330\) 0 0
\(331\) 7.17154 0.394183 0.197092 0.980385i \(-0.436850\pi\)
0.197092 + 0.980385i \(0.436850\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 17.4480 30.2209i 0.953287 1.65114i
\(336\) 0 0
\(337\) −10.9211 18.9158i −0.594908 1.03041i −0.993560 0.113309i \(-0.963855\pi\)
0.398651 0.917103i \(-0.369478\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −14.9887 25.9611i −0.811681 1.40587i
\(342\) 0 0
\(343\) 13.4863 12.6933i 0.728193 0.685372i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −2.11109 −0.113329 −0.0566646 0.998393i \(-0.518047\pi\)
−0.0566646 + 0.998393i \(0.518047\pi\)
\(348\) 0 0
\(349\) 18.1082 31.3643i 0.969310 1.67889i 0.271751 0.962368i \(-0.412397\pi\)
0.697559 0.716527i \(-0.254269\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −5.24433 9.08344i −0.279127 0.483463i 0.692041 0.721858i \(-0.256712\pi\)
−0.971168 + 0.238396i \(0.923378\pi\)
\(354\) 0 0
\(355\) −13.8256 + 23.9466i −0.733786 + 1.27095i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 16.2209 + 28.0955i 0.856108 + 1.48282i 0.875613 + 0.483013i \(0.160458\pi\)
−0.0195047 + 0.999810i \(0.506209\pi\)
\(360\) 0 0
\(361\) 8.67743 15.0297i 0.456707 0.791039i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −7.90219 13.6870i −0.413620 0.716410i
\(366\) 0 0
\(367\) −9.05555 15.6847i −0.472696 0.818733i 0.526816 0.849979i \(-0.323386\pi\)
−0.999512 + 0.0312465i \(0.990052\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −1.46169 + 5.24284i −0.0758874 + 0.272195i
\(372\) 0 0
\(373\) 5.83530 10.1070i 0.302140 0.523322i −0.674480 0.738293i \(-0.735632\pi\)
0.976621 + 0.214971i \(0.0689656\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 40.3893 2.08016
\(378\) 0 0
\(379\) −14.2690 −0.732947 −0.366474 0.930428i \(-0.619435\pi\)
−0.366474 + 0.930428i \(0.619435\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 0.824893 1.42876i 0.0421501 0.0730061i −0.844181 0.536059i \(-0.819913\pi\)
0.886331 + 0.463053i \(0.153246\pi\)
\(384\) 0 0
\(385\) 25.9435 6.67160i 1.32220 0.340016i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −16.0338 27.7713i −0.812946 1.40806i −0.910794 0.412862i \(-0.864529\pi\)
0.0978483 0.995201i \(-0.468804\pi\)
\(390\) 0 0
\(391\) 1.70370 + 2.95089i 0.0861596 + 0.149233i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −6.58414 + 11.4041i −0.331284 + 0.573800i
\(396\) 0 0
\(397\) −18.9669 32.8516i −0.951921 1.64878i −0.741261 0.671217i \(-0.765772\pi\)
−0.210660 0.977559i \(-0.567561\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 5.30959 9.19647i 0.265148 0.459250i −0.702454 0.711729i \(-0.747913\pi\)
0.967602 + 0.252479i \(0.0812458\pi\)
\(402\) 0 0
\(403\) 26.8675 + 46.5358i 1.33836 + 2.31811i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 1.59097 2.75564i 0.0788615 0.136592i
\(408\) 0 0
\(409\) 5.54583 0.274224 0.137112 0.990556i \(-0.456218\pi\)
0.137112 + 0.990556i \(0.456218\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −2.88207 + 0.741150i −0.141818 + 0.0364696i
\(414\) 0 0
\(415\) −12.8353 22.2314i −0.630060 1.09130i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 2.77455 + 4.80566i 0.135546 + 0.234772i 0.925806 0.378000i \(-0.123388\pi\)
−0.790260 + 0.612772i \(0.790055\pi\)
\(420\) 0 0
\(421\) −3.42107 + 5.92546i −0.166733 + 0.288789i −0.937269 0.348606i \(-0.886655\pi\)
0.770537 + 0.637396i \(0.219988\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −7.79863 −0.378289
\(426\) 0 0
\(427\) 8.00684 2.05903i 0.387478 0.0996433i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 16.5539 28.6722i 0.797374 1.38109i −0.123947 0.992289i \(-0.539555\pi\)
0.921321 0.388803i \(-0.127111\pi\)
\(432\) 0 0
\(433\) −12.1111 −0.582022 −0.291011 0.956720i \(-0.593992\pi\)
−0.291011 + 0.956720i \(0.593992\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −2.87197 −0.137385
\(438\) 0 0
\(439\) 8.83422 0.421634 0.210817 0.977526i \(-0.432388\pi\)
0.210817 + 0.977526i \(0.432388\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 17.5185 0.832328 0.416164 0.909290i \(-0.363374\pi\)
0.416164 + 0.909290i \(0.363374\pi\)
\(444\) 0 0
\(445\) 0.717370 0.0340066
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −31.2301 −1.47384 −0.736920 0.675980i \(-0.763720\pi\)
−0.736920 + 0.675980i \(0.763720\pi\)
\(450\) 0 0
\(451\) 8.91423 15.4399i 0.419755 0.727036i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −46.5043 + 11.9590i −2.18015 + 0.560645i
\(456\) 0 0
\(457\) −32.1248 −1.50273 −0.751367 0.659885i \(-0.770605\pi\)
−0.751367 + 0.659885i \(0.770605\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −1.23229 + 2.13438i −0.0573933 + 0.0994081i −0.893295 0.449472i \(-0.851612\pi\)
0.835901 + 0.548880i \(0.184946\pi\)
\(462\) 0 0
\(463\) −15.1735 26.2812i −0.705171 1.22139i −0.966630 0.256177i \(-0.917537\pi\)
0.261459 0.965215i \(-0.415796\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −7.98181 13.8249i −0.369354 0.639740i 0.620110 0.784515i \(-0.287088\pi\)
−0.989465 + 0.144774i \(0.953754\pi\)
\(468\) 0 0
\(469\) −28.1014 + 7.22651i −1.29760 + 0.333689i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 21.7278 0.999044
\(474\) 0 0
\(475\) 3.28659 5.69254i 0.150799 0.261192i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 11.5865 + 20.0683i 0.529399 + 0.916946i 0.999412 + 0.0342863i \(0.0109158\pi\)
−0.470013 + 0.882659i \(0.655751\pi\)
\(480\) 0 0
\(481\) −2.85185 + 4.93955i −0.130033 + 0.225224i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 23.6134 + 40.8996i 1.07223 + 1.85716i
\(486\) 0 0
\(487\) −1.70658 + 2.95588i −0.0773323 + 0.133943i −0.902098 0.431531i \(-0.857974\pi\)
0.824766 + 0.565474i \(0.191307\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −9.58414 16.6002i −0.432526 0.749157i 0.564564 0.825389i \(-0.309044\pi\)
−0.997090 + 0.0762323i \(0.975711\pi\)
\(492\) 0 0
\(493\) −5.38796 9.33223i −0.242662 0.420302i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 22.2672 5.72619i 0.998819 0.256855i
\(498\) 0 0
\(499\) 20.5848 35.6540i 0.921503 1.59609i 0.124413 0.992231i \(-0.460295\pi\)
0.797090 0.603860i \(-0.206371\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −26.4542 −1.17953 −0.589767 0.807574i \(-0.700780\pi\)
−0.589767 + 0.807574i \(0.700780\pi\)
\(504\) 0 0
\(505\) −59.1502 −2.63215
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 6.38564 11.0603i 0.283039 0.490237i −0.689093 0.724673i \(-0.741991\pi\)
0.972132 + 0.234436i \(0.0753242\pi\)
\(510\) 0 0
\(511\) −3.52915 + 12.6584i −0.156120 + 0.559975i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −0.449657 0.778828i −0.0198142 0.0343193i
\(516\) 0 0
\(517\) 9.27292 + 16.0612i 0.407822 + 0.706369i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 3.40615 5.89962i 0.149226 0.258467i −0.781716 0.623635i \(-0.785655\pi\)
0.930942 + 0.365168i \(0.118988\pi\)
\(522\) 0 0
\(523\) −14.7535 25.5538i −0.645125 1.11739i −0.984273 0.176656i \(-0.943472\pi\)
0.339148 0.940733i \(-0.389861\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 7.16827 12.4158i 0.312255 0.540841i
\(528\) 0 0
\(529\) 8.99316 + 15.5766i 0.391007 + 0.677244i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −15.9789 + 27.6763i −0.692125 + 1.19879i
\(534\) 0 0
\(535\) −36.2028 −1.56518
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −19.0607 11.5239i −0.821004 0.496371i
\(540\) 0 0
\(541\) 14.7008 + 25.4626i 0.632038 + 1.09472i 0.987135 + 0.159892i \(0.0511145\pi\)
−0.355097 + 0.934829i \(0.615552\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −7.03379 12.1829i −0.301295 0.521857i
\(546\) 0 0
\(547\) −17.6150 + 30.5102i −0.753165 + 1.30452i 0.193116 + 0.981176i \(0.438141\pi\)
−0.946281 + 0.323344i \(0.895193\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 9.08263 0.386933
\(552\) 0 0
\(553\) 10.6043 2.72698i 0.450939 0.115963i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 3.36909 5.83543i 0.142753 0.247255i −0.785779 0.618507i \(-0.787738\pi\)
0.928532 + 0.371252i \(0.121071\pi\)
\(558\) 0 0
\(559\) −38.9475 −1.64730
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −1.45993 −0.0615286 −0.0307643 0.999527i \(-0.509794\pi\)
−0.0307643 + 0.999527i \(0.509794\pi\)
\(564\) 0 0
\(565\) −10.2301 −0.430383
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −19.5653 −0.820218 −0.410109 0.912036i \(-0.634509\pi\)
−0.410109 + 0.912036i \(0.634509\pi\)
\(570\) 0 0
\(571\) 21.9259 0.917569 0.458785 0.888547i \(-0.348285\pi\)
0.458785 + 0.888547i \(0.348285\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 11.4750 0.478540
\(576\) 0 0
\(577\) 12.3655 21.4177i 0.514783 0.891631i −0.485069 0.874476i \(-0.661206\pi\)
0.999853 0.0171554i \(-0.00546099\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −5.73229 + 20.5607i −0.237815 + 0.853001i
\(582\) 0 0
\(583\) 6.54583 0.271101
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −18.0796 + 31.3148i −0.746226 + 1.29250i 0.203394 + 0.979097i \(0.434803\pi\)
−0.949620 + 0.313404i \(0.898531\pi\)
\(588\) 0 0
\(589\) 6.04187 + 10.4648i 0.248951 + 0.431196i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 7.55391 + 13.0838i 0.310202 + 0.537285i 0.978406 0.206693i \(-0.0662700\pi\)
−0.668204 + 0.743978i \(0.732937\pi\)
\(594\) 0 0
\(595\) 8.96690 + 9.14978i 0.367607 + 0.375105i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −5.45417 −0.222851 −0.111426 0.993773i \(-0.535542\pi\)
−0.111426 + 0.993773i \(0.535542\pi\)
\(600\) 0 0
\(601\) −3.36840 + 5.83424i −0.137400 + 0.237984i −0.926512 0.376266i \(-0.877208\pi\)
0.789112 + 0.614250i \(0.210541\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 1.39248 + 2.41184i 0.0566122 + 0.0980553i
\(606\) 0 0
\(607\) 3.33530 5.77690i 0.135376 0.234477i −0.790365 0.612636i \(-0.790109\pi\)
0.925741 + 0.378159i \(0.123443\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −16.6219 28.7899i −0.672449 1.16472i
\(612\) 0 0
\(613\) 0.654988 1.13447i 0.0264547 0.0458209i −0.852495 0.522735i \(-0.824912\pi\)
0.878950 + 0.476915i \(0.158245\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −17.2483 29.8749i −0.694390 1.20272i −0.970386 0.241560i \(-0.922341\pi\)
0.275996 0.961159i \(-0.410992\pi\)
\(618\) 0 0
\(619\) −8.22421 14.2447i −0.330559 0.572545i 0.652063 0.758165i \(-0.273904\pi\)
−0.982622 + 0.185620i \(0.940571\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −0.417500 0.426015i −0.0167268 0.0170679i
\(624\) 0 0
\(625\) 12.1803 21.0969i 0.487212 0.843877i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 1.52175 0.0606763
\(630\) 0 0
\(631\) 30.0118 1.19475 0.597375 0.801962i \(-0.296210\pi\)
0.597375 + 0.801962i \(0.296210\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 31.9870 55.4031i 1.26937 2.19861i
\(636\) 0 0
\(637\) 34.1668 + 20.6569i 1.35374 + 0.818456i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 13.9497 + 24.1615i 0.550978 + 0.954322i 0.998204 + 0.0599014i \(0.0190786\pi\)
−0.447226 + 0.894421i \(0.647588\pi\)
\(642\) 0 0
\(643\) −14.2524 24.6859i −0.562060 0.973516i −0.997317 0.0732100i \(-0.976676\pi\)
0.435257 0.900306i \(-0.356658\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 8.35705 14.4748i 0.328550 0.569065i −0.653675 0.756776i \(-0.726774\pi\)
0.982224 + 0.187711i \(0.0601069\pi\)
\(648\) 0 0
\(649\) 1.78947 + 3.09945i 0.0702427 + 0.121664i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 19.0825 33.0519i 0.746756 1.29342i −0.202614 0.979259i \(-0.564944\pi\)
0.949370 0.314161i \(-0.101723\pi\)
\(654\) 0 0
\(655\) −10.1248 17.5366i −0.395607 0.685212i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 4.37072 7.57031i 0.170259 0.294898i −0.768251 0.640148i \(-0.778873\pi\)
0.938510 + 0.345251i \(0.112206\pi\)
\(660\) 0 0
\(661\) −20.0837 −0.781167 −0.390584 0.920567i \(-0.627727\pi\)
−0.390584 + 0.920567i \(0.627727\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −10.4577 + 2.68930i −0.405534 + 0.104286i
\(666\) 0 0
\(667\) 7.92790 + 13.7315i 0.306970 + 0.531687i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −4.97141 8.61073i −0.191919 0.332414i
\(672\) 0 0
\(673\) −17.0264 + 29.4906i −0.656319 + 1.13678i 0.325242 + 0.945631i \(0.394554\pi\)
−0.981561 + 0.191148i \(0.938779\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 0.717370 0.0275708 0.0137854 0.999905i \(-0.495612\pi\)
0.0137854 + 0.999905i \(0.495612\pi\)
\(678\) 0 0
\(679\) 10.5458 37.8260i 0.404712 1.45163i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −10.5270 + 18.2332i −0.402803 + 0.697675i −0.994063 0.108806i \(-0.965297\pi\)
0.591260 + 0.806481i \(0.298631\pi\)
\(684\) 0 0
\(685\) −8.72313 −0.333294
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −11.7335 −0.447012
\(690\) 0 0
\(691\) −5.84789 −0.222464 −0.111232 0.993794i \(-0.535480\pi\)
−0.111232 + 0.993794i \(0.535480\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −25.3502 −0.961588
\(696\) 0 0
\(697\) 8.52640 0.322960
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −10.2711 −0.387935 −0.193967 0.981008i \(-0.562136\pi\)
−0.193967 + 0.981008i \(0.562136\pi\)
\(702\) 0 0
\(703\) −0.641315 + 1.11079i −0.0241877 + 0.0418942i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 34.4246 + 35.1268i 1.29467 + 1.32108i
\(708\) 0 0
\(709\) 43.4854 1.63313 0.816564 0.577255i \(-0.195876\pi\)
0.816564 + 0.577255i \(0.195876\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −10.5475 + 18.2687i −0.395006 + 0.684170i
\(714\) 0 0
\(715\) 28.8743 + 50.0117i 1.07984 + 1.87033i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 25.4412 + 44.0654i 0.948796 + 1.64336i 0.747966 + 0.663737i \(0.231031\pi\)
0.200830 + 0.979626i \(0.435636\pi\)
\(720\) 0 0
\(721\) −0.200818 + 0.720299i −0.00747886 + 0.0268253i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −36.2898 −1.34777
\(726\) 0 0
\(727\) −6.07210 + 10.5172i −0.225202 + 0.390061i −0.956380 0.292126i \(-0.905637\pi\)
0.731178 + 0.682186i \(0.238971\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 5.19562 + 8.99907i 0.192167 + 0.332843i
\(732\) 0 0
\(733\) 23.0848 39.9841i 0.852657 1.47685i −0.0261440 0.999658i \(-0.508323\pi\)
0.878801 0.477188i \(-0.158344\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 17.4480 + 30.2209i 0.642706 + 1.11320i
\(738\) 0 0
\(739\) 2.49604 4.32327i 0.0918184 0.159034i −0.816458 0.577405i \(-0.804065\pi\)
0.908276 + 0.418371i \(0.137399\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −15.7060 27.2036i −0.576198 0.998004i −0.995910 0.0903470i \(-0.971202\pi\)
0.419712 0.907657i \(-0.362131\pi\)
\(744\) 0 0
\(745\) −37.0059 64.0961i −1.35579 2.34830i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 21.0695 + 21.4992i 0.769863 + 0.785565i
\(750\) 0 0
\(751\) 1.64815 2.85468i 0.0601419 0.104169i −0.834387 0.551179i \(-0.814178\pi\)
0.894529 + 0.447010i \(0.147511\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 25.8525 0.940870
\(756\) 0 0
\(757\) −10.1384 −0.368488 −0.184244 0.982881i \(-0.558984\pi\)
−0.184244 + 0.982881i \(0.558984\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 7.03379 12.1829i 0.254975 0.441629i −0.709914 0.704288i \(-0.751266\pi\)
0.964889 + 0.262659i \(0.0845995\pi\)
\(762\) 0 0
\(763\) −3.14132 + 11.2673i −0.113723 + 0.407905i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −3.20765 5.55582i −0.115822 0.200609i
\(768\) 0 0
\(769\) 11.3461 + 19.6520i 0.409151 + 0.708669i 0.994795 0.101899i \(-0.0324918\pi\)
−0.585644 + 0.810568i \(0.699158\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −0.327772 + 0.567717i −0.0117891 + 0.0204194i −0.871860 0.489756i \(-0.837086\pi\)
0.860071 + 0.510175i \(0.170419\pi\)
\(774\) 0 0
\(775\) −24.1404 41.8123i −0.867148 1.50194i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −3.59329 + 6.22377i −0.128743 + 0.222990i
\(780\) 0 0
\(781\) −13.8256 23.9466i −0.494718 0.856877i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 17.9194 31.0374i 0.639572 1.10777i
\(786\) 0 0
\(787\) −0.540073 −0.0192515 −0.00962576 0.999954i \(-0.503064\pi\)
−0.00962576 + 0.999954i \(0.503064\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 5.95378 + 6.07521i 0.211692 + 0.216010i
\(792\) 0 0
\(793\) 8.91135 + 15.4349i 0.316451 + 0.548110i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 12.5550 + 21.7459i 0.444721 + 0.770279i 0.998033 0.0626954i \(-0.0199697\pi\)
−0.553312 + 0.832974i \(0.686636\pi\)
\(798\) 0 0
\(799\) −4.43474 + 7.68119i −0.156890 + 0.271741i
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 15.8044 0.557725
\(804\) 0 0
\(805\) −13.1940 13.4631i −0.465027 0.474511i
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0