Properties

Label 3024.2.q.k.2305.4
Level $3024$
Weight $2$
Character 3024.2305
Analytic conductor $24.147$
Analytic rank $0$
Dimension $22$
CM no
Inner twists $2$

Related objects

Downloads

Learn more about

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: \(22\)
Relative dimension: \(11\) over \(\Q(\zeta_{3})\)
Twist minimal: no (minimal twist has level 504)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 2305.4
Character \(\chi\) \(=\) 3024.2305
Dual form 3024.2.q.k.2881.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.918286 - 1.59052i) q^{5} +(0.361656 - 2.62092i) q^{7} +O(q^{10})\) \(q+(-0.918286 - 1.59052i) q^{5} +(0.361656 - 2.62092i) q^{7} +(1.54860 - 2.68225i) q^{11} +(2.40225 - 4.16081i) q^{13} +(-1.87185 - 3.24214i) q^{17} +(2.71408 - 4.70093i) q^{19} +(3.97914 + 6.89208i) q^{23} +(0.813503 - 1.40903i) q^{25} +(0.325267 + 0.563379i) q^{29} -1.03668 q^{31} +(-4.50072 + 1.83153i) q^{35} +(0.873712 - 1.51331i) q^{37} +(-2.52260 + 4.36927i) q^{41} +(6.09645 + 10.5594i) q^{43} -4.61383 q^{47} +(-6.73841 - 1.89574i) q^{49} +(-4.55082 - 7.88226i) q^{53} -5.68821 q^{55} -5.79727 q^{59} -4.81245 q^{61} -8.82379 q^{65} +14.4774 q^{67} -5.00714 q^{71} +(-1.81364 - 3.14131i) q^{73} +(-6.46989 - 5.02879i) q^{77} +14.3581 q^{79} +(3.83139 + 6.63616i) q^{83} +(-3.43778 + 5.95441i) q^{85} +(5.76798 - 9.99043i) q^{89} +(-10.0364 - 7.80087i) q^{91} -9.96922 q^{95} +(-1.04480 - 1.80964i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 22q - 3q^{5} + 5q^{7} + O(q^{10}) \) \( 22q - 3q^{5} + 5q^{7} - 3q^{11} - 3q^{13} - 7q^{17} + q^{19} + 2q^{23} - 10q^{25} - 9q^{29} - 8q^{31} + 14q^{35} + 2q^{37} - 16q^{41} - 10q^{47} + 15q^{49} - 11q^{53} - 22q^{55} + 38q^{59} + 26q^{61} + 26q^{65} + 52q^{67} - 48q^{71} - 35q^{73} - 17q^{77} + 20q^{79} - 28q^{83} - 20q^{85} - 6q^{89} + 37q^{91} - 24q^{95} - 29q^{97} + O(q^{100}) \)

Character values

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

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

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0 0
\(4\) 0 0
\(5\) −0.918286 1.59052i −0.410670 0.711301i 0.584293 0.811543i \(-0.301372\pi\)
−0.994963 + 0.100242i \(0.968038\pi\)
\(6\) 0 0
\(7\) 0.361656 2.62092i 0.136693 0.990613i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 1.54860 2.68225i 0.466919 0.808728i −0.532367 0.846514i \(-0.678697\pi\)
0.999286 + 0.0377862i \(0.0120306\pi\)
\(12\) 0 0
\(13\) 2.40225 4.16081i 0.666263 1.15400i −0.312678 0.949859i \(-0.601226\pi\)
0.978941 0.204143i \(-0.0654406\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −1.87185 3.24214i −0.453990 0.786333i 0.544640 0.838670i \(-0.316666\pi\)
−0.998629 + 0.0523367i \(0.983333\pi\)
\(18\) 0 0
\(19\) 2.71408 4.70093i 0.622654 1.07847i −0.366336 0.930483i \(-0.619388\pi\)
0.988990 0.147985i \(-0.0472788\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 3.97914 + 6.89208i 0.829709 + 1.43710i 0.898267 + 0.439450i \(0.144827\pi\)
−0.0685581 + 0.997647i \(0.521840\pi\)
\(24\) 0 0
\(25\) 0.813503 1.40903i 0.162701 0.281806i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 0.325267 + 0.563379i 0.0604006 + 0.104617i 0.894645 0.446779i \(-0.147429\pi\)
−0.834244 + 0.551396i \(0.814096\pi\)
\(30\) 0 0
\(31\) −1.03668 −0.186194 −0.0930970 0.995657i \(-0.529677\pi\)
−0.0930970 + 0.995657i \(0.529677\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −4.50072 + 1.83153i −0.760760 + 0.309585i
\(36\) 0 0
\(37\) 0.873712 1.51331i 0.143637 0.248787i −0.785226 0.619209i \(-0.787453\pi\)
0.928864 + 0.370422i \(0.120787\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −2.52260 + 4.36927i −0.393964 + 0.682365i −0.992968 0.118381i \(-0.962230\pi\)
0.599005 + 0.800745i \(0.295563\pi\)
\(42\) 0 0
\(43\) 6.09645 + 10.5594i 0.929699 + 1.61029i 0.783824 + 0.620984i \(0.213267\pi\)
0.145876 + 0.989303i \(0.453400\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −4.61383 −0.672996 −0.336498 0.941684i \(-0.609243\pi\)
−0.336498 + 0.941684i \(0.609243\pi\)
\(48\) 0 0
\(49\) −6.73841 1.89574i −0.962630 0.270820i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −4.55082 7.88226i −0.625104 1.08271i −0.988521 0.151085i \(-0.951723\pi\)
0.363417 0.931626i \(-0.381610\pi\)
\(54\) 0 0
\(55\) −5.68821 −0.766998
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −5.79727 −0.754740 −0.377370 0.926063i \(-0.623172\pi\)
−0.377370 + 0.926063i \(0.623172\pi\)
\(60\) 0 0
\(61\) −4.81245 −0.616172 −0.308086 0.951359i \(-0.599688\pi\)
−0.308086 + 0.951359i \(0.599688\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −8.82379 −1.09446
\(66\) 0 0
\(67\) 14.4774 1.76870 0.884348 0.466828i \(-0.154603\pi\)
0.884348 + 0.466828i \(0.154603\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −5.00714 −0.594238 −0.297119 0.954840i \(-0.596026\pi\)
−0.297119 + 0.954840i \(0.596026\pi\)
\(72\) 0 0
\(73\) −1.81364 3.14131i −0.212270 0.367662i 0.740155 0.672437i \(-0.234752\pi\)
−0.952425 + 0.304774i \(0.901419\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −6.46989 5.02879i −0.737312 0.573084i
\(78\) 0 0
\(79\) 14.3581 1.61541 0.807705 0.589587i \(-0.200710\pi\)
0.807705 + 0.589587i \(0.200710\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 3.83139 + 6.63616i 0.420550 + 0.728414i 0.995993 0.0894279i \(-0.0285038\pi\)
−0.575443 + 0.817842i \(0.695171\pi\)
\(84\) 0 0
\(85\) −3.43778 + 5.95441i −0.372880 + 0.645847i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 5.76798 9.99043i 0.611405 1.05898i −0.379599 0.925151i \(-0.623938\pi\)
0.991004 0.133833i \(-0.0427286\pi\)
\(90\) 0 0
\(91\) −10.0364 7.80087i −1.05210 0.817753i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −9.96922 −1.02282
\(96\) 0 0
\(97\) −1.04480 1.80964i −0.106083 0.183741i 0.808097 0.589049i \(-0.200498\pi\)
−0.914180 + 0.405308i \(0.867164\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −8.22661 + 14.2489i −0.818578 + 1.41782i 0.0881520 + 0.996107i \(0.471904\pi\)
−0.906730 + 0.421712i \(0.861429\pi\)
\(102\) 0 0
\(103\) −3.87346 6.70903i −0.381663 0.661060i 0.609637 0.792681i \(-0.291315\pi\)
−0.991300 + 0.131621i \(0.957982\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 3.74746 6.49080i 0.362281 0.627489i −0.626055 0.779779i \(-0.715331\pi\)
0.988336 + 0.152290i \(0.0486647\pi\)
\(108\) 0 0
\(109\) −4.30644 7.45897i −0.412482 0.714440i 0.582678 0.812703i \(-0.302005\pi\)
−0.995160 + 0.0982628i \(0.968671\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 1.55747 2.69762i 0.146514 0.253771i −0.783422 0.621490i \(-0.786528\pi\)
0.929937 + 0.367719i \(0.119861\pi\)
\(114\) 0 0
\(115\) 7.30798 12.6578i 0.681473 1.18035i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −9.17433 + 3.73342i −0.841010 + 0.342242i
\(120\) 0 0
\(121\) 0.703704 + 1.21885i 0.0639731 + 0.110805i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −12.1710 −1.08860
\(126\) 0 0
\(127\) −10.8866 −0.966033 −0.483017 0.875611i \(-0.660459\pi\)
−0.483017 + 0.875611i \(0.660459\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 8.02790 + 13.9047i 0.701401 + 1.21486i 0.967975 + 0.251048i \(0.0807751\pi\)
−0.266574 + 0.963815i \(0.585892\pi\)
\(132\) 0 0
\(133\) −11.3392 8.81351i −0.983232 0.764228i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 6.72031 11.6399i 0.574155 0.994465i −0.421978 0.906606i \(-0.638664\pi\)
0.996133 0.0878590i \(-0.0280025\pi\)
\(138\) 0 0
\(139\) 4.06953 7.04863i 0.345173 0.597857i −0.640212 0.768198i \(-0.721154\pi\)
0.985385 + 0.170341i \(0.0544869\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −7.44022 12.8868i −0.622182 1.07765i
\(144\) 0 0
\(145\) 0.597376 1.03469i 0.0496094 0.0859260i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 3.76479 + 6.52081i 0.308424 + 0.534205i 0.978018 0.208522i \(-0.0668652\pi\)
−0.669594 + 0.742727i \(0.733532\pi\)
\(150\) 0 0
\(151\) −2.83616 + 4.91237i −0.230803 + 0.399763i −0.958045 0.286619i \(-0.907469\pi\)
0.727241 + 0.686382i \(0.240802\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0.951973 + 1.64886i 0.0764643 + 0.132440i
\(156\) 0 0
\(157\) 0.436763 0.0348575 0.0174287 0.999848i \(-0.494452\pi\)
0.0174287 + 0.999848i \(0.494452\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 19.5026 7.93644i 1.53702 0.625479i
\(162\) 0 0
\(163\) −9.12649 + 15.8076i −0.714842 + 1.23814i 0.248178 + 0.968714i \(0.420168\pi\)
−0.963020 + 0.269429i \(0.913165\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 0.765108 1.32521i 0.0592058 0.102548i −0.834903 0.550397i \(-0.814477\pi\)
0.894109 + 0.447849i \(0.147810\pi\)
\(168\) 0 0
\(169\) −5.04157 8.73226i −0.387813 0.671713i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −2.16949 −0.164943 −0.0824716 0.996593i \(-0.526281\pi\)
−0.0824716 + 0.996593i \(0.526281\pi\)
\(174\) 0 0
\(175\) −3.39874 2.64171i −0.256921 0.199694i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −1.08263 1.87517i −0.0809195 0.140157i 0.822726 0.568439i \(-0.192452\pi\)
−0.903645 + 0.428282i \(0.859119\pi\)
\(180\) 0 0
\(181\) 0.557838 0.0414638 0.0207319 0.999785i \(-0.493400\pi\)
0.0207319 + 0.999785i \(0.493400\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −3.20927 −0.235950
\(186\) 0 0
\(187\) −11.5949 −0.847906
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −23.9997 −1.73655 −0.868277 0.496079i \(-0.834773\pi\)
−0.868277 + 0.496079i \(0.834773\pi\)
\(192\) 0 0
\(193\) −21.2794 −1.53172 −0.765862 0.643005i \(-0.777687\pi\)
−0.765862 + 0.643005i \(0.777687\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 14.8768 1.05993 0.529964 0.848020i \(-0.322205\pi\)
0.529964 + 0.848020i \(0.322205\pi\)
\(198\) 0 0
\(199\) −6.17884 10.7021i −0.438006 0.758649i 0.559530 0.828810i \(-0.310982\pi\)
−0.997536 + 0.0701616i \(0.977649\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 1.59420 0.648749i 0.111891 0.0455332i
\(204\) 0 0
\(205\) 9.26586 0.647156
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −8.40604 14.5597i −0.581458 1.00711i
\(210\) 0 0
\(211\) −8.65802 + 14.9961i −0.596043 + 1.03238i 0.397356 + 0.917664i \(0.369928\pi\)
−0.993399 + 0.114712i \(0.963406\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 11.1966 19.3930i 0.763599 1.32259i
\(216\) 0 0
\(217\) −0.374923 + 2.71706i −0.0254514 + 0.184446i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −17.9866 −1.20991
\(222\) 0 0
\(223\) −1.14489 1.98301i −0.0766677 0.132792i 0.825143 0.564925i \(-0.191095\pi\)
−0.901810 + 0.432132i \(0.857761\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 1.78013 3.08328i 0.118152 0.204644i −0.800884 0.598820i \(-0.795636\pi\)
0.919035 + 0.394176i \(0.128970\pi\)
\(228\) 0 0
\(229\) 13.4799 + 23.3478i 0.890775 + 1.54287i 0.838949 + 0.544211i \(0.183171\pi\)
0.0518260 + 0.998656i \(0.483496\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −10.7321 + 18.5885i −0.703081 + 1.21777i 0.264298 + 0.964441i \(0.414860\pi\)
−0.967380 + 0.253332i \(0.918474\pi\)
\(234\) 0 0
\(235\) 4.23681 + 7.33837i 0.276379 + 0.478703i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 4.65970 8.07083i 0.301411 0.522059i −0.675045 0.737777i \(-0.735876\pi\)
0.976456 + 0.215718i \(0.0692091\pi\)
\(240\) 0 0
\(241\) 10.1003 17.4943i 0.650620 1.12691i −0.332353 0.943155i \(-0.607842\pi\)
0.982973 0.183752i \(-0.0588242\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 3.17258 + 12.4584i 0.202689 + 0.795937i
\(246\) 0 0
\(247\) −13.0398 22.5856i −0.829702 1.43709i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 27.1837 1.71582 0.857910 0.513800i \(-0.171762\pi\)
0.857910 + 0.513800i \(0.171762\pi\)
\(252\) 0 0
\(253\) 24.6483 1.54963
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 14.2411 + 24.6662i 0.888333 + 1.53864i 0.841845 + 0.539719i \(0.181469\pi\)
0.0464876 + 0.998919i \(0.485197\pi\)
\(258\) 0 0
\(259\) −3.65028 2.83722i −0.226818 0.176297i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −1.79907 + 3.11608i −0.110935 + 0.192146i −0.916148 0.400841i \(-0.868718\pi\)
0.805212 + 0.592987i \(0.202051\pi\)
\(264\) 0 0
\(265\) −8.35791 + 14.4763i −0.513422 + 0.889274i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −11.2261 19.4443i −0.684470 1.18554i −0.973603 0.228248i \(-0.926700\pi\)
0.289133 0.957289i \(-0.406633\pi\)
\(270\) 0 0
\(271\) 14.7935 25.6231i 0.898642 1.55649i 0.0694115 0.997588i \(-0.477888\pi\)
0.829231 0.558906i \(-0.188779\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −2.51958 4.36403i −0.151936 0.263161i
\(276\) 0 0
\(277\) 10.1933 17.6554i 0.612459 1.06081i −0.378366 0.925656i \(-0.623514\pi\)
0.990825 0.135153i \(-0.0431527\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 2.23968 + 3.87924i 0.133608 + 0.231416i 0.925065 0.379809i \(-0.124010\pi\)
−0.791457 + 0.611225i \(0.790677\pi\)
\(282\) 0 0
\(283\) −2.07680 −0.123453 −0.0617264 0.998093i \(-0.519661\pi\)
−0.0617264 + 0.998093i \(0.519661\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 10.5392 + 8.19169i 0.622108 + 0.483540i
\(288\) 0 0
\(289\) 1.49237 2.58486i 0.0877865 0.152051i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 0.887340 1.53692i 0.0518389 0.0897877i −0.838942 0.544222i \(-0.816825\pi\)
0.890780 + 0.454434i \(0.150158\pi\)
\(294\) 0 0
\(295\) 5.32355 + 9.22066i 0.309949 + 0.536847i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 38.2355 2.21122
\(300\) 0 0
\(301\) 29.8800 12.1594i 1.72225 0.700858i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 4.41921 + 7.65429i 0.253043 + 0.438283i
\(306\) 0 0
\(307\) −19.6315 −1.12043 −0.560215 0.828347i \(-0.689282\pi\)
−0.560215 + 0.828347i \(0.689282\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −13.3159 −0.755076 −0.377538 0.925994i \(-0.623229\pi\)
−0.377538 + 0.925994i \(0.623229\pi\)
\(312\) 0 0
\(313\) 4.65281 0.262992 0.131496 0.991317i \(-0.458022\pi\)
0.131496 + 0.991317i \(0.458022\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 4.12552 0.231713 0.115856 0.993266i \(-0.463039\pi\)
0.115856 + 0.993266i \(0.463039\pi\)
\(318\) 0 0
\(319\) 2.01483 0.112809
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −20.3214 −1.13071
\(324\) 0 0
\(325\) −3.90847 6.76967i −0.216803 0.375514i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −1.66862 + 12.0925i −0.0919939 + 0.666679i
\(330\) 0 0
\(331\) −0.0440594 −0.00242172 −0.00121086 0.999999i \(-0.500385\pi\)
−0.00121086 + 0.999999i \(0.500385\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −13.2944 23.0266i −0.726350 1.25808i
\(336\) 0 0
\(337\) −13.3351 + 23.0970i −0.726407 + 1.25817i 0.231986 + 0.972719i \(0.425478\pi\)
−0.958392 + 0.285454i \(0.907856\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −1.60541 + 2.78064i −0.0869376 + 0.150580i
\(342\) 0 0
\(343\) −7.40556 + 16.9752i −0.399863 + 0.916575i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 10.8252 0.581126 0.290563 0.956856i \(-0.406157\pi\)
0.290563 + 0.956856i \(0.406157\pi\)
\(348\) 0 0
\(349\) −2.69555 4.66884i −0.144290 0.249917i 0.784818 0.619726i \(-0.212756\pi\)
−0.929108 + 0.369809i \(0.879423\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −4.47307 + 7.74759i −0.238078 + 0.412362i −0.960163 0.279442i \(-0.909851\pi\)
0.722085 + 0.691804i \(0.243184\pi\)
\(354\) 0 0
\(355\) 4.59798 + 7.96394i 0.244036 + 0.422682i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 1.84157 3.18969i 0.0971942 0.168345i −0.813328 0.581805i \(-0.802347\pi\)
0.910522 + 0.413460i \(0.135680\pi\)
\(360\) 0 0
\(361\) −5.23251 9.06297i −0.275395 0.476998i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −3.33087 + 5.76924i −0.174346 + 0.301976i
\(366\) 0 0
\(367\) −3.74988 + 6.49498i −0.195742 + 0.339035i −0.947144 0.320810i \(-0.896045\pi\)
0.751401 + 0.659845i \(0.229378\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −22.3046 + 9.07666i −1.15800 + 0.471237i
\(372\) 0 0
\(373\) −4.11917 7.13461i −0.213282 0.369416i 0.739458 0.673203i \(-0.235082\pi\)
−0.952740 + 0.303787i \(0.901749\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 3.12549 0.160971
\(378\) 0 0
\(379\) 3.92853 0.201795 0.100897 0.994897i \(-0.467829\pi\)
0.100897 + 0.994897i \(0.467829\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −11.9632 20.7210i −0.611293 1.05879i −0.991023 0.133694i \(-0.957316\pi\)
0.379729 0.925098i \(-0.376017\pi\)
\(384\) 0 0
\(385\) −2.05718 + 14.9083i −0.104843 + 0.759799i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 6.32875 10.9617i 0.320881 0.555781i −0.659789 0.751451i \(-0.729355\pi\)
0.980670 + 0.195669i \(0.0626879\pi\)
\(390\) 0 0
\(391\) 14.8967 25.8018i 0.753359 1.30486i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −13.1848 22.8368i −0.663400 1.14904i
\(396\) 0 0
\(397\) −17.7703 + 30.7791i −0.891866 + 1.54476i −0.0542297 + 0.998528i \(0.517270\pi\)
−0.837636 + 0.546229i \(0.816063\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −1.66166 2.87808i −0.0829794 0.143724i 0.821549 0.570138i \(-0.193110\pi\)
−0.904528 + 0.426413i \(0.859777\pi\)
\(402\) 0 0
\(403\) −2.49037 + 4.31345i −0.124054 + 0.214868i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −2.70605 4.68702i −0.134134 0.232327i
\(408\) 0 0
\(409\) 22.5129 1.11319 0.556595 0.830784i \(-0.312107\pi\)
0.556595 + 0.830784i \(0.312107\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −2.09662 + 15.1942i −0.103168 + 0.747656i
\(414\) 0 0
\(415\) 7.03662 12.1878i 0.345414 0.598275i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −3.59772 + 6.23144i −0.175760 + 0.304426i −0.940424 0.340004i \(-0.889572\pi\)
0.764664 + 0.644429i \(0.222905\pi\)
\(420\) 0 0
\(421\) 16.8121 + 29.1193i 0.819370 + 1.41919i 0.906147 + 0.422962i \(0.139010\pi\)
−0.0867773 + 0.996228i \(0.527657\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −6.09102 −0.295458
\(426\) 0 0
\(427\) −1.74045 + 12.6130i −0.0842264 + 0.610388i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 16.4871 + 28.5565i 0.794156 + 1.37552i 0.923373 + 0.383903i \(0.125420\pi\)
−0.129217 + 0.991616i \(0.541246\pi\)
\(432\) 0 0
\(433\) 19.8977 0.956221 0.478110 0.878300i \(-0.341322\pi\)
0.478110 + 0.878300i \(0.341322\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 43.1989 2.06648
\(438\) 0 0
\(439\) −29.1268 −1.39015 −0.695074 0.718938i \(-0.744628\pi\)
−0.695074 + 0.718938i \(0.744628\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 13.7663 0.654058 0.327029 0.945014i \(-0.393952\pi\)
0.327029 + 0.945014i \(0.393952\pi\)
\(444\) 0 0
\(445\) −21.1866 −1.00434
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 12.0958 0.570838 0.285419 0.958403i \(-0.407867\pi\)
0.285419 + 0.958403i \(0.407867\pi\)
\(450\) 0 0
\(451\) 7.81297 + 13.5325i 0.367898 + 0.637218i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −3.19118 + 23.1264i −0.149605 + 1.08418i
\(456\) 0 0
\(457\) −8.35476 −0.390819 −0.195410 0.980722i \(-0.562604\pi\)
−0.195410 + 0.980722i \(0.562604\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −11.1673 19.3423i −0.520112 0.900860i −0.999727 0.0233807i \(-0.992557\pi\)
0.479615 0.877479i \(-0.340776\pi\)
\(462\) 0 0
\(463\) 0.0370790 0.0642228i 0.00172321 0.00298469i −0.865163 0.501492i \(-0.832785\pi\)
0.866886 + 0.498507i \(0.166118\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 14.5828 25.2581i 0.674810 1.16880i −0.301715 0.953398i \(-0.597559\pi\)
0.976524 0.215407i \(-0.0691077\pi\)
\(468\) 0 0
\(469\) 5.23584 37.9441i 0.241769 1.75209i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 37.7637 1.73638
\(474\) 0 0
\(475\) −4.41583 7.64845i −0.202612 0.350935i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −13.9551 + 24.1710i −0.637626 + 1.10440i 0.348326 + 0.937373i \(0.386750\pi\)
−0.985952 + 0.167027i \(0.946583\pi\)
\(480\) 0 0
\(481\) −4.19774 7.27070i −0.191401 0.331515i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −1.91884 + 3.32353i −0.0871301 + 0.150914i
\(486\) 0 0
\(487\) 2.14409 + 3.71367i 0.0971580 + 0.168283i 0.910507 0.413493i \(-0.135691\pi\)
−0.813349 + 0.581776i \(0.802358\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −5.22215 + 9.04503i −0.235672 + 0.408196i −0.959468 0.281818i \(-0.909063\pi\)
0.723796 + 0.690015i \(0.242396\pi\)
\(492\) 0 0
\(493\) 1.21770 2.10912i 0.0548425 0.0949900i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −1.81086 + 13.1233i −0.0812282 + 0.588660i
\(498\) 0 0
\(499\) −3.06312 5.30548i −0.137124 0.237506i 0.789283 0.614030i \(-0.210453\pi\)
−0.926407 + 0.376524i \(0.877119\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −12.4469 −0.554982 −0.277491 0.960728i \(-0.589503\pi\)
−0.277491 + 0.960728i \(0.589503\pi\)
\(504\) 0 0
\(505\) 30.2175 1.34466
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 5.90450 + 10.2269i 0.261712 + 0.453299i 0.966697 0.255923i \(-0.0823795\pi\)
−0.704985 + 0.709222i \(0.749046\pi\)
\(510\) 0 0
\(511\) −8.88902 + 3.61731i −0.393227 + 0.160021i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −7.11388 + 12.3216i −0.313475 + 0.542955i
\(516\) 0 0
\(517\) −7.14495 + 12.3754i −0.314235 + 0.544271i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −5.54828 9.60991i −0.243075 0.421018i 0.718514 0.695513i \(-0.244823\pi\)
−0.961589 + 0.274495i \(0.911489\pi\)
\(522\) 0 0
\(523\) −10.6209 + 18.3960i −0.464421 + 0.804401i −0.999175 0.0406065i \(-0.987071\pi\)
0.534754 + 0.845008i \(0.320404\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 1.94052 + 3.36107i 0.0845302 + 0.146411i
\(528\) 0 0
\(529\) −20.1672 + 34.9305i −0.876833 + 1.51872i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 12.1198 + 20.9921i 0.524967 + 0.909269i
\(534\) 0 0
\(535\) −13.7650 −0.595111
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −15.5199 + 15.1383i −0.668490 + 0.652054i
\(540\) 0 0
\(541\) −6.33567 + 10.9737i −0.272392 + 0.471796i −0.969474 0.245195i \(-0.921148\pi\)
0.697082 + 0.716991i \(0.254481\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −7.90908 + 13.6989i −0.338788 + 0.586798i
\(546\) 0 0
\(547\) 21.4805 + 37.2053i 0.918438 + 1.59078i 0.801788 + 0.597609i \(0.203883\pi\)
0.116651 + 0.993173i \(0.462784\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 3.53121 0.150435
\(552\) 0 0
\(553\) 5.19268 37.6313i 0.220815 1.60025i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −16.5129 28.6012i −0.699673 1.21187i −0.968580 0.248703i \(-0.919996\pi\)
0.268906 0.963166i \(-0.413338\pi\)
\(558\) 0 0
\(559\) 58.5807 2.47770
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 36.8132 1.55149 0.775746 0.631046i \(-0.217374\pi\)
0.775746 + 0.631046i \(0.217374\pi\)
\(564\) 0 0
\(565\) −5.72081 −0.240676
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −44.3571 −1.85955 −0.929774 0.368132i \(-0.879998\pi\)
−0.929774 + 0.368132i \(0.879998\pi\)
\(570\) 0 0
\(571\) 42.5872 1.78222 0.891110 0.453787i \(-0.149927\pi\)
0.891110 + 0.453787i \(0.149927\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 12.9482 0.539977
\(576\) 0 0
\(577\) 16.3209 + 28.2687i 0.679450 + 1.17684i 0.975147 + 0.221559i \(0.0711147\pi\)
−0.295697 + 0.955282i \(0.595552\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 18.7785 7.64175i 0.779063 0.317033i
\(582\) 0 0
\(583\) −28.1895 −1.16749
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −13.1270 22.7366i −0.541809 0.938441i −0.998800 0.0489701i \(-0.984406\pi\)
0.456991 0.889471i \(-0.348927\pi\)
\(588\) 0 0
\(589\) −2.81365 + 4.87338i −0.115934 + 0.200804i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 2.59998 4.50330i 0.106768 0.184928i −0.807691 0.589606i \(-0.799283\pi\)
0.914459 + 0.404678i \(0.132616\pi\)
\(594\) 0 0
\(595\) 14.3627 + 11.1636i 0.588814 + 0.457663i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 26.3675 1.07735 0.538673 0.842515i \(-0.318926\pi\)
0.538673 + 0.842515i \(0.318926\pi\)
\(600\) 0 0
\(601\) −15.4505 26.7611i −0.630239 1.09161i −0.987503 0.157603i \(-0.949623\pi\)
0.357263 0.934004i \(-0.383710\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 1.29240 2.23851i 0.0525436 0.0910082i
\(606\) 0 0
\(607\) 3.83661 + 6.64519i 0.155723 + 0.269720i 0.933322 0.359040i \(-0.116896\pi\)
−0.777599 + 0.628760i \(0.783563\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −11.0836 + 19.1973i −0.448393 + 0.776639i
\(612\) 0 0
\(613\) 7.97498 + 13.8131i 0.322106 + 0.557905i 0.980922 0.194399i \(-0.0622758\pi\)
−0.658816 + 0.752304i \(0.728942\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 3.67011 6.35682i 0.147753 0.255916i −0.782644 0.622470i \(-0.786129\pi\)
0.930397 + 0.366554i \(0.119463\pi\)
\(618\) 0 0
\(619\) 10.2842 17.8127i 0.413357 0.715955i −0.581898 0.813262i \(-0.697690\pi\)
0.995254 + 0.0973072i \(0.0310229\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −24.0981 18.7305i −0.965469 0.750421i
\(624\) 0 0
\(625\) 7.10891 + 12.3130i 0.284356 + 0.492520i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −6.54182 −0.260840
\(630\) 0 0
\(631\) 5.09394 0.202787 0.101393 0.994846i \(-0.467670\pi\)
0.101393 + 0.994846i \(0.467670\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 9.99705 + 17.3154i 0.396721 + 0.687141i
\(636\) 0 0
\(637\) −24.0751 + 23.4832i −0.953892 + 0.930439i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 6.31861 10.9442i 0.249570 0.432268i −0.713836 0.700312i \(-0.753044\pi\)
0.963407 + 0.268044i \(0.0863773\pi\)
\(642\) 0 0
\(643\) −12.4329 + 21.5344i −0.490306 + 0.849235i −0.999938 0.0111579i \(-0.996448\pi\)
0.509632 + 0.860393i \(0.329782\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 1.12339 + 1.94577i 0.0441650 + 0.0764960i 0.887263 0.461264i \(-0.152604\pi\)
−0.843098 + 0.537760i \(0.819271\pi\)
\(648\) 0 0
\(649\) −8.97762 + 15.5497i −0.352403 + 0.610379i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 1.02881 + 1.78195i 0.0402604 + 0.0697330i 0.885453 0.464728i \(-0.153848\pi\)
−0.845193 + 0.534461i \(0.820515\pi\)
\(654\) 0 0
\(655\) 14.7438 25.5370i 0.576088 0.997815i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −4.16599 7.21571i −0.162284 0.281084i 0.773403 0.633914i \(-0.218553\pi\)
−0.935687 + 0.352830i \(0.885219\pi\)
\(660\) 0 0
\(661\) 34.0926 1.32605 0.663024 0.748598i \(-0.269273\pi\)
0.663024 + 0.748598i \(0.269273\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −3.60543 + 26.1285i −0.139812 + 1.01322i
\(666\) 0 0
\(667\) −2.58857 + 4.48353i −0.100230 + 0.173603i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −7.45255 + 12.9082i −0.287702 + 0.498315i
\(672\) 0 0
\(673\) 0.571008 + 0.989016i 0.0220108 + 0.0381237i 0.876821 0.480817i \(-0.159660\pi\)
−0.854810 + 0.518941i \(0.826327\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −36.3812 −1.39824 −0.699121 0.715004i \(-0.746425\pi\)
−0.699121 + 0.715004i \(0.746425\pi\)
\(678\) 0 0
\(679\) −5.12077 + 2.08386i −0.196517 + 0.0799711i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 3.11274 + 5.39142i 0.119106 + 0.206297i 0.919414 0.393292i \(-0.128664\pi\)
−0.800308 + 0.599589i \(0.795331\pi\)
\(684\) 0 0
\(685\) −24.6846 −0.943152
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −43.7288 −1.66593
\(690\) 0 0
\(691\) 39.8259 1.51505 0.757525 0.652806i \(-0.226408\pi\)
0.757525 + 0.652806i \(0.226408\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −14.9480 −0.567008
\(696\) 0 0
\(697\) 18.8877 0.715422
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 48.3337 1.82554 0.912769 0.408477i \(-0.133940\pi\)
0.912769 + 0.408477i \(0.133940\pi\)
\(702\) 0 0
\(703\) −4.74265 8.21452i −0.178873 0.309816i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 34.3700 + 26.7145i 1.29262 + 1.00470i
\(708\) 0 0
\(709\) −16.0840 −0.604046 −0.302023 0.953301i \(-0.597662\pi\)
−0.302023 + 0.953301i \(0.597662\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −4.12512 7.14491i −0.154487 0.267579i
\(714\) 0 0
\(715\) −13.6645 + 23.6676i −0.511023 + 0.885117i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 21.0734 36.5002i 0.785906 1.36123i −0.142550 0.989788i \(-0.545530\pi\)
0.928456 0.371442i \(-0.121136\pi\)
\(720\) 0 0
\(721\) −18.9847 + 7.72566i −0.707026 + 0.287718i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 1.05842 0.0393089
\(726\) 0 0
\(727\) 12.9548 + 22.4384i 0.480467 + 0.832192i 0.999749 0.0224103i \(-0.00713401\pi\)
−0.519282 + 0.854603i \(0.673801\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 22.8232 39.5310i 0.844148 1.46211i
\(732\) 0 0
\(733\) −10.2027 17.6716i −0.376846 0.652716i 0.613756 0.789496i \(-0.289658\pi\)
−0.990601 + 0.136780i \(0.956325\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 22.4196 38.8320i 0.825838 1.43039i
\(738\) 0 0
\(739\) 11.8953 + 20.6033i 0.437576 + 0.757903i 0.997502 0.0706392i \(-0.0225039\pi\)
−0.559926 + 0.828542i \(0.689171\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 21.6320 37.4678i 0.793603 1.37456i −0.130120 0.991498i \(-0.541536\pi\)
0.923723 0.383062i \(-0.125130\pi\)
\(744\) 0 0
\(745\) 6.91430 11.9759i 0.253321 0.438764i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −15.6565 12.1692i −0.572078 0.444654i
\(750\) 0 0
\(751\) −7.18465 12.4442i −0.262172 0.454095i 0.704647 0.709558i \(-0.251105\pi\)
−0.966819 + 0.255463i \(0.917772\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 10.4176 0.379136
\(756\) 0 0
\(757\) 39.7854 1.44603 0.723013 0.690835i \(-0.242757\pi\)
0.723013 + 0.690835i \(0.242757\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −11.1966 19.3932i −0.405878 0.703002i 0.588545 0.808464i \(-0.299701\pi\)
−0.994423 + 0.105463i \(0.966368\pi\)
\(762\) 0 0
\(763\) −21.1068 + 8.58924i −0.764117 + 0.310951i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −13.9265 + 24.1213i −0.502856 + 0.870971i
\(768\) 0 0
\(769\) −1.45546 + 2.52093i −0.0524853 + 0.0909071i −0.891074 0.453857i \(-0.850048\pi\)
0.838589 + 0.544764i \(0.183381\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 6.68612 + 11.5807i 0.240483 + 0.416529i 0.960852 0.277062i \(-0.0893609\pi\)
−0.720369 + 0.693591i \(0.756028\pi\)
\(774\) 0 0
\(775\) −0.843347 + 1.46072i −0.0302939 + 0.0524706i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 13.6931 + 23.7171i 0.490606 + 0.849754i
\(780\) 0 0
\(781\) −7.75403 + 13.4304i −0.277461 + 0.480577i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −0.401073 0.694679i −0.0143149 0.0247941i
\(786\) 0 0
\(787\) 23.8528 0.850260 0.425130 0.905132i \(-0.360228\pi\)
0.425130 + 0.905132i \(0.360228\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −6.50696 5.05761i −0.231361 0.179828i
\(792\) 0 0
\(793\) −11.5607 + 20.0237i −0.410533 + 0.711063i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 6.10559 10.5752i 0.216271 0.374593i −0.737394 0.675463i \(-0.763944\pi\)
0.953665 + 0.300870i \(0.0972772\pi\)