Properties

Label 3024.2.q.g.2305.1
Level 3024
Weight 2
Character 3024.2305
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 2305.1
Root \(0.500000 - 1.41036i\) of defining polynomial
Character \(\chi\) \(=\) 3024.2305
Dual form 3024.2.q.g.2881.1

$q$-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 \(\left(\mathbb{Z}/3024\mathbb{Z}\right)^\times\).

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

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
\(5\) −1.59097 2.75564i −0.711504 1.23236i −0.964292 0.264840i \(-0.914681\pi\)
0.252788 0.967522i \(-0.418652\pi\)
\(6\) 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 −0.999729 0.0232884i \(-0.992586\pi\)
0.520033 + 0.854146i \(0.325920\pi\)
\(12\) 0 0
\(13\) 2.85185 4.93955i 0.790960 1.36998i −0.134412 0.990925i \(-0.542915\pi\)
0.925373 0.379058i \(-0.123752\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 0.760877 + 1.31788i 0.184540 + 0.319632i 0.943421 0.331596i \(-0.107587\pi\)
−0.758882 + 0.651229i \(0.774254\pi\)
\(18\) 0 0
\(19\) 0.641315 1.11079i 0.147128 0.254833i −0.783037 0.621975i \(-0.786330\pi\)
0.930165 + 0.367142i \(0.119664\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −1.11956 1.93914i −0.233445 0.404338i 0.725375 0.688354i \(-0.241666\pi\)
−0.958820 + 0.284016i \(0.908333\pi\)
\(24\) 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 0.981266 + 0.192656i \(0.0617101\pi\)
−0.323788 + 0.946130i \(0.604957\pi\)
\(30\) 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 −0.821995 0.569495i \(-0.807139\pi\)
0.904194 + 0.427121i \(0.140472\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 2.80150 4.85235i 0.437522 0.757810i −0.559976 0.828509i \(-0.689190\pi\)
0.997498 + 0.0706992i \(0.0225230\pi\)
\(42\) 0 0
\(43\) −3.41423 5.91362i −0.520665 0.901819i −0.999711 0.0240288i \(-0.992351\pi\)
0.479046 0.877790i \(-0.340983\pi\)
\(44\) 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 0.786694 0.617343i \(-0.211791\pi\)
−0.927982 + 0.372626i \(0.878458\pi\)
\(54\) 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 0.683302 0.730136i \(-0.260543\pi\)
−0.973967 + 0.226689i \(0.927210\pi\)
\(74\) 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 0.555127 0.831765i \(-0.312669\pi\)
−0.997894 + 0.0648718i \(0.979336\pi\)
\(84\) 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 −0.871938 0.489616i \(-0.837137\pi\)
0.859989 + 0.510312i \(0.170470\pi\)
\(90\) 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 0.946119 + 0.323819i \(0.104967\pi\)
−0.192624 + 0.981273i \(0.561700\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 9.29467 16.0988i 0.924854 1.60189i 0.133058 0.991108i \(-0.457520\pi\)
0.791796 0.610786i \(-0.209146\pi\)
\(102\) 0 0
\(103\) −0.141315 0.244765i −0.0139242 0.0241174i 0.858979 0.512010i \(-0.171099\pi\)
−0.872904 + 0.487893i \(0.837766\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 5.68878 9.85326i 0.549955 0.952550i −0.448322 0.893872i \(-0.647978\pi\)
0.998277 0.0586780i \(-0.0186885\pi\)
\(108\) 0 0
\(109\) −2.21053 3.82876i −0.211731 0.366728i 0.740526 0.672028i \(-0.234577\pi\)
−0.952256 + 0.305300i \(0.901243\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 1.60752 2.78431i 0.151223 0.261926i −0.780454 0.625213i \(-0.785012\pi\)
0.931677 + 0.363287i \(0.118345\pi\)
\(114\) 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 0.692882 0.721051i \(-0.256341\pi\)
−0.970890 + 0.239528i \(0.923007\pi\)
\(132\) 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 −0.801512 0.597979i \(-0.795971\pi\)
0.918621 + 0.395140i \(0.129304\pi\)
\(138\) 0 0
\(139\) 3.98345 6.89953i 0.337872 0.585211i −0.646161 0.763202i \(-0.723626\pi\)
0.984032 + 0.177991i \(0.0569597\pi\)
\(140\) 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 −0.739404 0.673262i \(-0.764893\pi\)
−0.213360 0.976974i \(-0.568441\pi\)
\(150\) 0 0
\(151\) −4.06238 + 7.03625i −0.330592 + 0.572602i −0.982628 0.185586i \(-0.940582\pi\)
0.652036 + 0.758188i \(0.273915\pi\)
\(152\) 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 −0.777492 0.628893i \(-0.783508\pi\)
0.933383 + 0.358881i \(0.116842\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 2.61956 4.53721i 0.202708 0.351100i −0.746692 0.665170i \(-0.768359\pi\)
0.949400 + 0.314070i \(0.101693\pi\)
\(168\) 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 0.967041 0.254620i \(-0.0819504\pi\)
−0.704028 + 0.710172i \(0.748617\pi\)
\(180\) 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 0.561978 0.827152i \(-0.310041\pi\)
−0.997324 + 0.0731106i \(0.976707\pi\)
\(200\) 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 −0.422863 0.906193i \(-0.638975\pi\)
0.996218 0.0868863i \(-0.0276917\pi\)
\(212\) 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 0.987428 0.158071i \(-0.0505276\pi\)
−0.630608 + 0.776102i \(0.717194\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 7.25404 12.5644i 0.481468 0.833926i −0.518306 0.855195i \(-0.673437\pi\)
0.999774 + 0.0212688i \(0.00677059\pi\)
\(228\) 0 0
\(229\) −5.12476 8.87635i −0.338654 0.586566i 0.645526 0.763738i \(-0.276638\pi\)
−0.984180 + 0.177173i \(0.943305\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −0.540628 + 0.936396i −0.0354177 + 0.0613453i −0.883191 0.469014i \(-0.844610\pi\)
0.847773 + 0.530359i \(0.177943\pi\)
\(234\) 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 −0.993537 0.113506i \(-0.963792\pi\)
0.595068 + 0.803676i \(0.297125\pi\)
\(240\) 0 0
\(241\) 6.50000 11.2583i 0.418702 0.725213i −0.577107 0.816668i \(-0.695819\pi\)
0.995809 + 0.0914555i \(0.0291519\pi\)
\(242\) 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 0.960403 0.278614i \(-0.0898750\pi\)
−0.721488 + 0.692427i \(0.756542\pi\)
\(258\) 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 −0.814363 0.580355i \(-0.802914\pi\)
0.909784 + 0.415082i \(0.136247\pi\)
\(264\) 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 0.905855 + 0.423587i \(0.139229\pi\)
−0.0860906 + 0.996287i \(0.527437\pi\)
\(270\) 0 0
\(271\) 11.1082 19.2400i 0.674776 1.16875i −0.301759 0.953384i \(-0.597574\pi\)
0.976534 0.215362i \(-0.0690930\pi\)
\(272\) 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 −0.557928 0.829889i \(-0.688404\pi\)
0.997669 + 0.0682357i \(0.0217370\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −11.6992 20.2636i −0.697915 1.20882i −0.969188 0.246322i \(-0.920778\pi\)
0.271273 0.962502i \(-0.412555\pi\)
\(282\) 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 0.189678 + 0.981846i \(0.439255\pi\)
−0.945143 + 0.326657i \(0.894078\pi\)
\(294\) 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 0.398651 + 0.917103i \(0.369478\pi\)
−0.993560 + 0.113309i \(0.963855\pi\)
\(338\) 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 0.697559 + 0.716527i \(0.254269\pi\)
0.271751 + 0.962368i \(0.412397\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −5.24433 + 9.08344i −0.279127 + 0.483463i −0.971168 0.238396i \(-0.923378\pi\)
0.692041 + 0.721858i \(0.256712\pi\)
\(354\) 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 −0.0195047 0.999810i \(-0.506209\pi\)
0.875613 0.483013i \(-0.160458\pi\)
\(360\) 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 −0.999512 0.0312465i \(-0.990052\pi\)
0.526816 + 0.849979i \(0.323386\pi\)
\(368\) 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 0.976621 0.214971i \(-0.0689656\pi\)
−0.674480 + 0.738293i \(0.735632\pi\)
\(374\) 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 0.886331 0.463053i \(-0.153246\pi\)
−0.844181 + 0.536059i \(0.819913\pi\)
\(384\) 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 0.0978483 + 0.995201i \(0.468804\pi\)
−0.910794 + 0.412862i \(0.864529\pi\)
\(390\) 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 −0.210660 + 0.977559i \(0.567561\pi\)
−0.741261 + 0.671217i \(0.765772\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 5.30959 + 9.19647i 0.265148 + 0.459250i 0.967602 0.252479i \(-0.0812458\pi\)
−0.702454 + 0.711729i \(0.747913\pi\)
\(402\) 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 −0.790260 0.612772i \(-0.790055\pi\)
0.925806 + 0.378000i \(0.123388\pi\)
\(420\) 0 0
\(421\) −3.42107 5.92546i −0.166733 0.288789i 0.770537 0.637396i \(-0.219988\pi\)
−0.937269 + 0.348606i \(0.886655\pi\)
\(422\) 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 0.921321 + 0.388803i \(0.127111\pi\)
−0.123947 + 0.992289i \(0.539555\pi\)
\(432\) 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 0.835901 0.548880i \(-0.184946\pi\)
−0.893295 + 0.449472i \(0.851612\pi\)
\(462\) 0 0
\(463\) −15.1735 + 26.2812i −0.705171 + 1.22139i 0.261459 + 0.965215i \(0.415796\pi\)
−0.966630 + 0.256177i \(0.917537\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −7.98181 + 13.8249i −0.369354 + 0.639740i −0.989465 0.144774i \(-0.953754\pi\)
0.620110 + 0.784515i \(0.287088\pi\)
\(468\) 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 −0.470013 0.882659i \(-0.655751\pi\)
0.999412 0.0342863i \(-0.0109158\pi\)
\(480\) 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 0.824766 0.565474i \(-0.191307\pi\)
−0.902098 + 0.431531i \(0.857974\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −9.58414 + 16.6002i −0.432526 + 0.749157i −0.997090 0.0762323i \(-0.975711\pi\)
0.564564 + 0.825389i \(0.309044\pi\)
\(492\) 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 0.797090 + 0.603860i \(0.206371\pi\)
0.124413 + 0.992231i \(0.460295\pi\)
\(500\) 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 0.972132 0.234436i \(-0.0753242\pi\)
−0.689093 + 0.724673i \(0.741991\pi\)
\(510\) 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 0.930942 0.365168i \(-0.118988\pi\)
−0.781716 + 0.623635i \(0.785655\pi\)
\(522\) 0 0
\(523\) −14.7535 + 25.5538i −0.645125 + 1.11739i 0.339148 + 0.940733i \(0.389861\pi\)
−0.984273 + 0.176656i \(0.943472\pi\)
\(524\) 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 −0.355097 0.934829i \(-0.615552\pi\)
0.987135 0.159892i \(-0.0511145\pi\)
\(542\) 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 −0.946281 0.323344i \(-0.895193\pi\)
0.193116 0.981176i \(-0.438141\pi\)
\(548\) 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 0.928532 0.371252i \(-0.121071\pi\)
−0.785779 + 0.618507i \(0.787738\pi\)
\(558\) 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 0.999853 + 0.0171554i \(0.00546099\pi\)
−0.485069 + 0.874476i \(0.661206\pi\)
\(578\) 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 −0.949620 0.313404i \(-0.898531\pi\)
0.203394 0.979097i \(-0.434803\pi\)
\(588\) 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 −0.668204 0.743978i \(-0.732937\pi\)
0.978406 + 0.206693i \(0.0662700\pi\)
\(594\) 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 0.789112 0.614250i \(-0.210541\pi\)
−0.926512 + 0.376266i \(0.877208\pi\)
\(602\) 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 0.925741 0.378159i \(-0.123443\pi\)
−0.790365 + 0.612636i \(0.790109\pi\)
\(608\) 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 0.878950 0.476915i \(-0.158245\pi\)
−0.852495 + 0.522735i \(0.824912\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −17.2483 + 29.8749i −0.694390 + 1.20272i 0.275996 + 0.961159i \(0.410992\pi\)
−0.970386 + 0.241560i \(0.922341\pi\)
\(618\) 0 0
\(619\) −8.22421 + 14.2447i −0.330559 + 0.572545i −0.982622 0.185620i \(-0.940571\pi\)
0.652063 + 0.758165i \(0.273904\pi\)
\(620\) 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 −0.447226 0.894421i \(-0.647588\pi\)
0.998204 0.0599014i \(-0.0190786\pi\)
\(642\) 0 0
\(643\) −14.2524 + 24.6859i −0.562060 + 0.973516i 0.435257 + 0.900306i \(0.356658\pi\)
−0.997317 + 0.0732100i \(0.976676\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 8.35705 + 14.4748i 0.328550 + 0.569065i 0.982224 0.187711i \(-0.0601069\pi\)
−0.653675 + 0.756776i \(0.726774\pi\)
\(648\) 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 0.949370 + 0.314161i \(0.101723\pi\)
−0.202614 + 0.979259i \(0.564944\pi\)
\(654\) 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 0.938510 0.345251i \(-0.112206\pi\)
−0.768251 + 0.640148i \(0.778873\pi\)
\(660\) 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 −0.981561 0.191148i \(-0.938779\pi\)
0.325242 0.945631i \(-0.394554\pi\)
\(674\) 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 0.591260 0.806481i \(-0.298631\pi\)
−0.994063 + 0.108806i \(0.965297\pi\)
\(684\) 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 0.200830 0.979626i \(-0.435636\pi\)
0.747966 0.663737i \(-0.231031\pi\)
\(720\) 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 0.731178 0.682186i \(-0.238971\pi\)
−0.956380 + 0.292126i \(0.905637\pi\)
\(728\) 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 0.878801 + 0.477188i \(0.158344\pi\)
−0.0261440 + 0.999658i \(0.508323\pi\)
\(734\) 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 0.908276 0.418371i \(-0.137399\pi\)
−0.816458 + 0.577405i \(0.804065\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −15.7060 + 27.2036i −0.576198 + 0.998004i 0.419712 + 0.907657i \(0.362131\pi\)
−0.995910 + 0.0903470i \(0.971202\pi\)
\(744\) 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 0.894529 0.447010i \(-0.147511\pi\)
−0.834387 + 0.551179i \(0.814178\pi\)
\(752\) 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 0.964889 0.262659i \(-0.0845995\pi\)
−0.709914 + 0.704288i \(0.751266\pi\)
\(762\) 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 −0.585644 0.810568i \(-0.699158\pi\)
0.994795 + 0.101899i \(0.0324918\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −0.327772 0.567717i −0.0117891 0.0204194i 0.860071 0.510175i \(-0.170419\pi\)
−0.871860 + 0.489756i \(0.837086\pi\)
\(774\) 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 −0.553312 0.832974i \(-0.686636\pi\)
0.998033 + 0.0626954i \(0.0199697\pi\)
\(798\) 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