Properties

Label 3024.2.q.l.2305.7
Level $3024$
Weight $2$
Character 3024.2305
Analytic conductor $24.147$
Analytic rank $0$
Dimension $22$
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: \(22\)
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 2305.7
Character \(\chi\) \(=\) 3024.2305
Dual form 3024.2.q.l.2881.7

$q$-expansion

\(f(q)\) \(=\) \(q+(0.263002 + 0.455533i) q^{5} +(0.333150 - 2.62469i) q^{7} +O(q^{10})\) \(q+(0.263002 + 0.455533i) q^{5} +(0.333150 - 2.62469i) q^{7} +(-2.30526 + 3.99283i) q^{11} +(0.244554 - 0.423580i) q^{13} +(-2.75579 - 4.77318i) q^{17} +(-1.83782 + 3.18319i) q^{19} +(0.0269769 + 0.0467253i) q^{23} +(2.36166 - 4.09051i) q^{25} +(3.28471 + 5.68929i) q^{29} -6.07640 q^{31} +(1.28325 - 0.538539i) q^{35} +(0.223731 - 0.387513i) q^{37} +(-2.52284 + 4.36968i) q^{41} +(-2.84893 - 4.93449i) q^{43} -9.19621 q^{47} +(-6.77802 - 1.74883i) q^{49} +(4.37138 + 7.57145i) q^{53} -2.42515 q^{55} -6.63076 q^{59} -0.465625 q^{61} +0.257273 q^{65} -5.19358 q^{67} +1.76328 q^{71} +(-5.23776 - 9.07207i) q^{73} +(9.71195 + 7.38081i) q^{77} -16.3702 q^{79} +(4.49251 + 7.78126i) q^{83} +(1.44956 - 2.51071i) q^{85} +(7.05145 - 12.2135i) q^{89} +(-1.03029 - 0.782994i) q^{91} -1.93340 q^{95} +(5.22413 + 9.04847i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 22q - q^{5} - 5q^{7} + O(q^{10}) \) \( 22q - q^{5} - 5q^{7} + 3q^{11} + 7q^{13} + q^{17} - 13q^{19} - 22q^{25} + 7q^{29} + 12q^{31} + 2q^{35} + 6q^{37} - 4q^{41} - 2q^{43} - 34q^{47} - 25q^{49} - q^{53} - 2q^{55} + 42q^{59} - 62q^{61} - 6q^{65} - 52q^{67} - 32q^{71} + 17q^{73} + q^{77} - 32q^{79} - 36q^{83} + 28q^{85} + 2q^{89} - 15q^{91} + 48q^{95} + 19q^{97} + O(q^{100}) \)

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
\(5\) 0.263002 + 0.455533i 0.117618 + 0.203721i 0.918823 0.394669i \(-0.129141\pi\)
−0.801205 + 0.598390i \(0.795807\pi\)
\(6\) 0 0
\(7\) 0.333150 2.62469i 0.125919 0.992041i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −2.30526 + 3.99283i −0.695062 + 1.20388i 0.275098 + 0.961416i \(0.411290\pi\)
−0.970160 + 0.242466i \(0.922044\pi\)
\(12\) 0 0
\(13\) 0.244554 0.423580i 0.0678270 0.117480i −0.830118 0.557588i \(-0.811727\pi\)
0.897945 + 0.440109i \(0.145060\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −2.75579 4.77318i −0.668378 1.15767i −0.978357 0.206922i \(-0.933655\pi\)
0.309979 0.950743i \(-0.399678\pi\)
\(18\) 0 0
\(19\) −1.83782 + 3.18319i −0.421624 + 0.730274i −0.996099 0.0882484i \(-0.971873\pi\)
0.574475 + 0.818522i \(0.305206\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 0.0269769 + 0.0467253i 0.00562506 + 0.00974289i 0.868824 0.495121i \(-0.164876\pi\)
−0.863199 + 0.504864i \(0.831543\pi\)
\(24\) 0 0
\(25\) 2.36166 4.09051i 0.472332 0.818103i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 3.28471 + 5.68929i 0.609956 + 1.05647i 0.991247 + 0.132019i \(0.0421461\pi\)
−0.381292 + 0.924455i \(0.624521\pi\)
\(30\) 0 0
\(31\) −6.07640 −1.09135 −0.545676 0.837996i \(-0.683727\pi\)
−0.545676 + 0.837996i \(0.683727\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 1.28325 0.538539i 0.216909 0.0910297i
\(36\) 0 0
\(37\) 0.223731 0.387513i 0.0367811 0.0637068i −0.847049 0.531515i \(-0.821623\pi\)
0.883830 + 0.467808i \(0.154956\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −2.52284 + 4.36968i −0.394001 + 0.682430i −0.992973 0.118340i \(-0.962243\pi\)
0.598972 + 0.800770i \(0.295576\pi\)
\(42\) 0 0
\(43\) −2.84893 4.93449i −0.434458 0.752503i 0.562794 0.826598i \(-0.309727\pi\)
−0.997251 + 0.0740947i \(0.976393\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −9.19621 −1.34140 −0.670702 0.741726i \(-0.734007\pi\)
−0.670702 + 0.741726i \(0.734007\pi\)
\(48\) 0 0
\(49\) −6.77802 1.74883i −0.968289 0.249833i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 4.37138 + 7.57145i 0.600455 + 1.04002i 0.992752 + 0.120180i \(0.0383471\pi\)
−0.392297 + 0.919839i \(0.628320\pi\)
\(54\) 0 0
\(55\) −2.42515 −0.327008
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −6.63076 −0.863252 −0.431626 0.902053i \(-0.642060\pi\)
−0.431626 + 0.902053i \(0.642060\pi\)
\(60\) 0 0
\(61\) −0.465625 −0.0596171 −0.0298086 0.999556i \(-0.509490\pi\)
−0.0298086 + 0.999556i \(0.509490\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 0.257273 0.0319108
\(66\) 0 0
\(67\) −5.19358 −0.634496 −0.317248 0.948343i \(-0.602759\pi\)
−0.317248 + 0.948343i \(0.602759\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 1.76328 0.209263 0.104632 0.994511i \(-0.466634\pi\)
0.104632 + 0.994511i \(0.466634\pi\)
\(72\) 0 0
\(73\) −5.23776 9.07207i −0.613034 1.06181i −0.990726 0.135875i \(-0.956616\pi\)
0.377692 0.925931i \(-0.376718\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 9.71195 + 7.38081i 1.10678 + 0.841121i
\(78\) 0 0
\(79\) −16.3702 −1.84179 −0.920895 0.389812i \(-0.872540\pi\)
−0.920895 + 0.389812i \(0.872540\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 4.49251 + 7.78126i 0.493117 + 0.854104i 0.999969 0.00792925i \(-0.00252399\pi\)
−0.506851 + 0.862034i \(0.669191\pi\)
\(84\) 0 0
\(85\) 1.44956 2.51071i 0.157227 0.272325i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 7.05145 12.2135i 0.747452 1.29463i −0.201588 0.979470i \(-0.564610\pi\)
0.949040 0.315155i \(-0.102056\pi\)
\(90\) 0 0
\(91\) −1.03029 0.782994i −0.108004 0.0820801i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −1.93340 −0.198363
\(96\) 0 0
\(97\) 5.22413 + 9.04847i 0.530430 + 0.918732i 0.999370 + 0.0355020i \(0.0113030\pi\)
−0.468939 + 0.883230i \(0.655364\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −4.98254 + 8.63001i −0.495781 + 0.858718i −0.999988 0.00486475i \(-0.998451\pi\)
0.504207 + 0.863583i \(0.331785\pi\)
\(102\) 0 0
\(103\) 5.82553 + 10.0901i 0.574006 + 0.994208i 0.996149 + 0.0876783i \(0.0279448\pi\)
−0.422143 + 0.906529i \(0.638722\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 2.45556 4.25316i 0.237388 0.411168i −0.722576 0.691292i \(-0.757042\pi\)
0.959964 + 0.280123i \(0.0903754\pi\)
\(108\) 0 0
\(109\) −9.76353 16.9109i −0.935177 1.61977i −0.774319 0.632796i \(-0.781907\pi\)
−0.160858 0.986978i \(-0.551426\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −5.48658 + 9.50304i −0.516134 + 0.893971i 0.483690 + 0.875239i \(0.339296\pi\)
−0.999825 + 0.0187317i \(0.994037\pi\)
\(114\) 0 0
\(115\) −0.0141899 + 0.0245777i −0.00132322 + 0.00229188i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −13.4462 + 5.64293i −1.23261 + 0.517287i
\(120\) 0 0
\(121\) −5.12844 8.88272i −0.466222 0.807520i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 5.11451 0.457456
\(126\) 0 0
\(127\) 16.6107 1.47396 0.736979 0.675915i \(-0.236252\pi\)
0.736979 + 0.675915i \(0.236252\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −2.90848 5.03763i −0.254115 0.440140i 0.710540 0.703657i \(-0.248451\pi\)
−0.964655 + 0.263517i \(0.915117\pi\)
\(132\) 0 0
\(133\) 7.74263 + 5.88418i 0.671371 + 0.510223i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −4.61313 + 7.99017i −0.394126 + 0.682647i −0.992989 0.118205i \(-0.962286\pi\)
0.598863 + 0.800852i \(0.295619\pi\)
\(138\) 0 0
\(139\) −6.88477 + 11.9248i −0.583959 + 1.01145i 0.411046 + 0.911615i \(0.365164\pi\)
−0.995004 + 0.0998314i \(0.968170\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 1.12752 + 1.95292i 0.0942880 + 0.163312i
\(144\) 0 0
\(145\) −1.72777 + 2.99259i −0.143484 + 0.248521i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −4.15043 7.18875i −0.340016 0.588926i 0.644419 0.764673i \(-0.277099\pi\)
−0.984435 + 0.175747i \(0.943766\pi\)
\(150\) 0 0
\(151\) −7.24894 + 12.5555i −0.589911 + 1.02176i 0.404333 + 0.914612i \(0.367504\pi\)
−0.994244 + 0.107143i \(0.965830\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −1.59811 2.76800i −0.128363 0.222331i
\(156\) 0 0
\(157\) −12.4887 −0.996705 −0.498352 0.866975i \(-0.666061\pi\)
−0.498352 + 0.866975i \(0.666061\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0.131627 0.0552394i 0.0103736 0.00435348i
\(162\) 0 0
\(163\) 2.48448 4.30325i 0.194600 0.337057i −0.752169 0.658970i \(-0.770993\pi\)
0.946769 + 0.321913i \(0.104326\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −10.0088 + 17.3357i −0.774504 + 1.34148i 0.160569 + 0.987025i \(0.448667\pi\)
−0.935073 + 0.354456i \(0.884666\pi\)
\(168\) 0 0
\(169\) 6.38039 + 11.0512i 0.490799 + 0.850089i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −9.05485 −0.688427 −0.344214 0.938891i \(-0.611854\pi\)
−0.344214 + 0.938891i \(0.611854\pi\)
\(174\) 0 0
\(175\) −9.94956 7.56138i −0.752116 0.571587i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −7.69175 13.3225i −0.574908 0.995770i −0.996052 0.0887763i \(-0.971704\pi\)
0.421143 0.906994i \(-0.361629\pi\)
\(180\) 0 0
\(181\) −9.54973 −0.709826 −0.354913 0.934899i \(-0.615489\pi\)
−0.354913 + 0.934899i \(0.615489\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0.235367 0.0173045
\(186\) 0 0
\(187\) 25.4113 1.85826
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −11.0433 −0.799063 −0.399531 0.916720i \(-0.630827\pi\)
−0.399531 + 0.916720i \(0.630827\pi\)
\(192\) 0 0
\(193\) 26.6991 1.92185 0.960923 0.276817i \(-0.0892796\pi\)
0.960923 + 0.276817i \(0.0892796\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −12.8386 −0.914715 −0.457357 0.889283i \(-0.651204\pi\)
−0.457357 + 0.889283i \(0.651204\pi\)
\(198\) 0 0
\(199\) −10.1408 17.5644i −0.718864 1.24511i −0.961450 0.274979i \(-0.911329\pi\)
0.242586 0.970130i \(-0.422004\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 16.0269 6.72597i 1.12487 0.472071i
\(204\) 0 0
\(205\) −2.65405 −0.185367
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −8.47329 14.6762i −0.586109 1.01517i
\(210\) 0 0
\(211\) −4.77903 + 8.27752i −0.329002 + 0.569848i −0.982314 0.187241i \(-0.940046\pi\)
0.653312 + 0.757088i \(0.273379\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 1.49855 2.59556i 0.102200 0.177016i
\(216\) 0 0
\(217\) −2.02435 + 15.9487i −0.137422 + 1.08267i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −2.69576 −0.181337
\(222\) 0 0
\(223\) −11.9155 20.6383i −0.797921 1.38204i −0.920968 0.389639i \(-0.872600\pi\)
0.123046 0.992401i \(-0.460734\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 1.33567 2.31345i 0.0886514 0.153549i −0.818290 0.574806i \(-0.805078\pi\)
0.906941 + 0.421257i \(0.138411\pi\)
\(228\) 0 0
\(229\) −3.16258 5.47775i −0.208989 0.361980i 0.742407 0.669949i \(-0.233684\pi\)
−0.951396 + 0.307969i \(0.900351\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −4.63381 + 8.02600i −0.303571 + 0.525801i −0.976942 0.213504i \(-0.931512\pi\)
0.673371 + 0.739305i \(0.264846\pi\)
\(234\) 0 0
\(235\) −2.41862 4.18918i −0.157774 0.273272i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 1.69219 2.93096i 0.109459 0.189588i −0.806092 0.591790i \(-0.798422\pi\)
0.915551 + 0.402202i \(0.131755\pi\)
\(240\) 0 0
\(241\) −6.57982 + 11.3966i −0.423844 + 0.734119i −0.996312 0.0858082i \(-0.972653\pi\)
0.572468 + 0.819927i \(0.305986\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −0.985984 3.54756i −0.0629922 0.226645i
\(246\) 0 0
\(247\) 0.898890 + 1.55692i 0.0571950 + 0.0990647i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −2.30235 −0.145323 −0.0726614 0.997357i \(-0.523149\pi\)
−0.0726614 + 0.997357i \(0.523149\pi\)
\(252\) 0 0
\(253\) −0.248755 −0.0156391
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −14.5661 25.2293i −0.908610 1.57376i −0.815997 0.578056i \(-0.803811\pi\)
−0.0926132 0.995702i \(-0.529522\pi\)
\(258\) 0 0
\(259\) −0.942567 0.716324i −0.0585683 0.0445102i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 1.35919 2.35418i 0.0838110 0.145165i −0.821073 0.570823i \(-0.806624\pi\)
0.904884 + 0.425658i \(0.139957\pi\)
\(264\) 0 0
\(265\) −2.29936 + 3.98261i −0.141249 + 0.244650i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −2.80840 4.86428i −0.171231 0.296581i 0.767620 0.640906i \(-0.221441\pi\)
−0.938850 + 0.344325i \(0.888108\pi\)
\(270\) 0 0
\(271\) 7.25164 12.5602i 0.440506 0.762978i −0.557221 0.830364i \(-0.688133\pi\)
0.997727 + 0.0673860i \(0.0214659\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 10.8885 + 18.8594i 0.656600 + 1.13726i
\(276\) 0 0
\(277\) 0.873953 1.51373i 0.0525108 0.0909513i −0.838575 0.544786i \(-0.816611\pi\)
0.891086 + 0.453835i \(0.149944\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −5.35657 9.27786i −0.319546 0.553471i 0.660847 0.750521i \(-0.270197\pi\)
−0.980393 + 0.197050i \(0.936864\pi\)
\(282\) 0 0
\(283\) 12.5967 0.748793 0.374397 0.927269i \(-0.377850\pi\)
0.374397 + 0.927269i \(0.377850\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 10.6286 + 8.07743i 0.627386 + 0.476796i
\(288\) 0 0
\(289\) −6.68881 + 11.5854i −0.393459 + 0.681491i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 1.57575 2.72928i 0.0920562 0.159446i −0.816320 0.577600i \(-0.803989\pi\)
0.908376 + 0.418154i \(0.137323\pi\)
\(294\) 0 0
\(295\) −1.74391 3.02053i −0.101534 0.175862i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 0.0263892 0.00152613
\(300\) 0 0
\(301\) −13.9006 + 5.83364i −0.801220 + 0.336245i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −0.122460 0.212107i −0.00701206 0.0121452i
\(306\) 0 0
\(307\) 20.3884 1.16363 0.581813 0.813322i \(-0.302343\pi\)
0.581813 + 0.813322i \(0.302343\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 22.7014 1.28728 0.643640 0.765328i \(-0.277423\pi\)
0.643640 + 0.765328i \(0.277423\pi\)
\(312\) 0 0
\(313\) −16.7078 −0.944380 −0.472190 0.881497i \(-0.656536\pi\)
−0.472190 + 0.881497i \(0.656536\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −10.3280 −0.580080 −0.290040 0.957015i \(-0.593669\pi\)
−0.290040 + 0.957015i \(0.593669\pi\)
\(318\) 0 0
\(319\) −30.2884 −1.69583
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 20.2586 1.12722
\(324\) 0 0
\(325\) −1.15511 2.00070i −0.0640738 0.110979i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −3.06371 + 24.1372i −0.168908 + 1.33073i
\(330\) 0 0
\(331\) 22.6315 1.24394 0.621970 0.783041i \(-0.286332\pi\)
0.621970 + 0.783041i \(0.286332\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −1.36592 2.36585i −0.0746283 0.129260i
\(336\) 0 0
\(337\) 6.78253 11.7477i 0.369468 0.639938i −0.620014 0.784590i \(-0.712873\pi\)
0.989482 + 0.144653i \(0.0462066\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 14.0077 24.2620i 0.758558 1.31386i
\(342\) 0 0
\(343\) −6.84824 + 17.2076i −0.369770 + 0.929123i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −33.0262 −1.77294 −0.886470 0.462786i \(-0.846850\pi\)
−0.886470 + 0.462786i \(0.846850\pi\)
\(348\) 0 0
\(349\) −10.1773 17.6276i −0.544778 0.943584i −0.998621 0.0525019i \(-0.983280\pi\)
0.453842 0.891082i \(-0.350053\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −2.75381 + 4.76975i −0.146571 + 0.253868i −0.929958 0.367666i \(-0.880157\pi\)
0.783387 + 0.621534i \(0.213490\pi\)
\(354\) 0 0
\(355\) 0.463748 + 0.803234i 0.0246132 + 0.0426312i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −10.4656 + 18.1270i −0.552354 + 0.956704i 0.445751 + 0.895157i \(0.352937\pi\)
−0.998104 + 0.0615472i \(0.980397\pi\)
\(360\) 0 0
\(361\) 2.74486 + 4.75424i 0.144467 + 0.250223i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 2.75509 4.77195i 0.144208 0.249775i
\(366\) 0 0
\(367\) 2.14319 3.71211i 0.111873 0.193770i −0.804652 0.593746i \(-0.797648\pi\)
0.916526 + 0.399976i \(0.130982\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 21.3290 8.95110i 1.10735 0.464718i
\(372\) 0 0
\(373\) 5.64461 + 9.77675i 0.292267 + 0.506221i 0.974345 0.225058i \(-0.0722571\pi\)
−0.682079 + 0.731279i \(0.738924\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 3.21316 0.165486
\(378\) 0 0
\(379\) 20.5828 1.05727 0.528634 0.848850i \(-0.322705\pi\)
0.528634 + 0.848850i \(0.322705\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 10.8108 + 18.7248i 0.552405 + 0.956793i 0.998100 + 0.0616083i \(0.0196230\pi\)
−0.445696 + 0.895184i \(0.647044\pi\)
\(384\) 0 0
\(385\) −0.807939 + 6.36528i −0.0411764 + 0.324405i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −7.34241 + 12.7174i −0.372275 + 0.644799i −0.989915 0.141662i \(-0.954755\pi\)
0.617640 + 0.786461i \(0.288089\pi\)
\(390\) 0 0
\(391\) 0.148685 0.257531i 0.00751934 0.0130239i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −4.30539 7.45716i −0.216628 0.375210i
\(396\) 0 0
\(397\) −3.13424 + 5.42866i −0.157303 + 0.272457i −0.933895 0.357547i \(-0.883613\pi\)
0.776592 + 0.630003i \(0.216947\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 14.6951 + 25.4526i 0.733836 + 1.27104i 0.955232 + 0.295857i \(0.0956052\pi\)
−0.221396 + 0.975184i \(0.571061\pi\)
\(402\) 0 0
\(403\) −1.48601 + 2.57384i −0.0740232 + 0.128212i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 1.03152 + 1.78664i 0.0511303 + 0.0885603i
\(408\) 0 0
\(409\) −1.63285 −0.0807392 −0.0403696 0.999185i \(-0.512854\pi\)
−0.0403696 + 0.999185i \(0.512854\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −2.20904 + 17.4037i −0.108700 + 0.856381i
\(414\) 0 0
\(415\) −2.36308 + 4.09298i −0.115999 + 0.200916i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −9.01823 + 15.6200i −0.440569 + 0.763088i −0.997732 0.0673151i \(-0.978557\pi\)
0.557162 + 0.830404i \(0.311890\pi\)
\(420\) 0 0
\(421\) 16.8278 + 29.1465i 0.820135 + 1.42052i 0.905581 + 0.424172i \(0.139435\pi\)
−0.0854466 + 0.996343i \(0.527232\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −26.0330 −1.26279
\(426\) 0 0
\(427\) −0.155123 + 1.22212i −0.00750691 + 0.0591426i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −11.1545 19.3202i −0.537295 0.930622i −0.999048 0.0436135i \(-0.986113\pi\)
0.461754 0.887008i \(-0.347220\pi\)
\(432\) 0 0
\(433\) 7.32414 0.351976 0.175988 0.984392i \(-0.443688\pi\)
0.175988 + 0.984392i \(0.443688\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −0.198314 −0.00948664
\(438\) 0 0
\(439\) 24.6728 1.17757 0.588785 0.808289i \(-0.299606\pi\)
0.588785 + 0.808289i \(0.299606\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 30.5363 1.45082 0.725412 0.688315i \(-0.241649\pi\)
0.725412 + 0.688315i \(0.241649\pi\)
\(444\) 0 0
\(445\) 7.41819 0.351656
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 41.4782 1.95748 0.978738 0.205116i \(-0.0657572\pi\)
0.978738 + 0.205116i \(0.0657572\pi\)
\(450\) 0 0
\(451\) −11.6316 20.1465i −0.547710 0.948662i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 0.0857103 0.675262i 0.00401816 0.0316568i
\(456\) 0 0
\(457\) −11.6289 −0.543978 −0.271989 0.962300i \(-0.587681\pi\)
−0.271989 + 0.962300i \(0.587681\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 5.60886 + 9.71483i 0.261231 + 0.452465i 0.966569 0.256406i \(-0.0825383\pi\)
−0.705339 + 0.708871i \(0.749205\pi\)
\(462\) 0 0
\(463\) 19.9362 34.5305i 0.926514 1.60477i 0.137405 0.990515i \(-0.456124\pi\)
0.789108 0.614254i \(-0.210543\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 11.7818 20.4067i 0.545198 0.944311i −0.453397 0.891309i \(-0.649788\pi\)
0.998594 0.0530016i \(-0.0168788\pi\)
\(468\) 0 0
\(469\) −1.73024 + 13.6315i −0.0798950 + 0.629446i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 26.2701 1.20790
\(474\) 0 0
\(475\) 8.68059 + 15.0352i 0.398293 + 0.689864i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −7.11485 + 12.3233i −0.325086 + 0.563065i −0.981530 0.191310i \(-0.938727\pi\)
0.656444 + 0.754375i \(0.272060\pi\)
\(480\) 0 0
\(481\) −0.109428 0.189536i −0.00498951 0.00864208i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −2.74792 + 4.75953i −0.124776 + 0.216119i
\(486\) 0 0
\(487\) 13.9818 + 24.2171i 0.633574 + 1.09738i 0.986815 + 0.161850i \(0.0517460\pi\)
−0.353242 + 0.935532i \(0.614921\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 17.2543 29.8853i 0.778676 1.34871i −0.154030 0.988066i \(-0.549225\pi\)
0.932705 0.360639i \(-0.117442\pi\)
\(492\) 0 0
\(493\) 18.1040 31.3570i 0.815362 1.41225i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0.587437 4.62808i 0.0263502 0.207598i
\(498\) 0 0
\(499\) 13.1436 + 22.7654i 0.588390 + 1.01912i 0.994443 + 0.105272i \(0.0335712\pi\)
−0.406054 + 0.913849i \(0.633095\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 6.09068 0.271570 0.135785 0.990738i \(-0.456644\pi\)
0.135785 + 0.990738i \(0.456644\pi\)
\(504\) 0 0
\(505\) −5.24167 −0.233251
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −4.08615 7.07742i −0.181116 0.313701i 0.761145 0.648582i \(-0.224637\pi\)
−0.942261 + 0.334880i \(0.891304\pi\)
\(510\) 0 0
\(511\) −25.5564 + 10.7252i −1.13055 + 0.474453i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −3.06425 + 5.30744i −0.135027 + 0.233874i
\(516\) 0 0
\(517\) 21.1996 36.7189i 0.932360 1.61489i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −13.0485 22.6007i −0.571666 0.990155i −0.996395 0.0848346i \(-0.972964\pi\)
0.424729 0.905321i \(-0.360370\pi\)
\(522\) 0 0
\(523\) −13.6655 + 23.6694i −0.597553 + 1.03499i 0.395628 + 0.918411i \(0.370527\pi\)
−0.993181 + 0.116581i \(0.962807\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 16.7453 + 29.0037i 0.729437 + 1.26342i
\(528\) 0 0
\(529\) 11.4985 19.9161i 0.499937 0.865916i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 1.23394 + 2.13725i 0.0534478 + 0.0925744i
\(534\) 0 0
\(535\) 2.58327 0.111685
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 22.6079 23.0320i 0.973790 0.992057i
\(540\) 0 0
\(541\) −5.79086 + 10.0301i −0.248969 + 0.431226i −0.963240 0.268643i \(-0.913425\pi\)
0.714271 + 0.699869i \(0.246758\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 5.13566 8.89522i 0.219987 0.381029i
\(546\) 0 0
\(547\) −20.3651 35.2734i −0.870750 1.50818i −0.861222 0.508228i \(-0.830301\pi\)
−0.00952755 0.999955i \(-0.503033\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −24.1468 −1.02869
\(552\) 0 0
\(553\) −5.45372 + 42.9667i −0.231916 + 1.82713i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −10.0085 17.3353i −0.424075 0.734520i 0.572258 0.820074i \(-0.306068\pi\)
−0.996334 + 0.0855533i \(0.972734\pi\)
\(558\) 0 0
\(559\) −2.78687 −0.117872
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 24.9328 1.05079 0.525396 0.850858i \(-0.323917\pi\)
0.525396 + 0.850858i \(0.323917\pi\)
\(564\) 0 0
\(565\) −5.77193 −0.242827
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 9.80025 0.410848 0.205424 0.978673i \(-0.434143\pi\)
0.205424 + 0.978673i \(0.434143\pi\)
\(570\) 0 0
\(571\) 40.7895 1.70699 0.853494 0.521103i \(-0.174479\pi\)
0.853494 + 0.521103i \(0.174479\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0.254841 0.0106276
\(576\) 0 0
\(577\) −10.2505 17.7544i −0.426734 0.739125i 0.569846 0.821751i \(-0.307003\pi\)
−0.996581 + 0.0826259i \(0.973669\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 21.9201 9.19914i 0.909399 0.381645i
\(582\) 0 0
\(583\) −40.3086 −1.66941
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −19.2916 33.4141i −0.796251 1.37915i −0.922042 0.387090i \(-0.873480\pi\)
0.125791 0.992057i \(-0.459853\pi\)
\(588\) 0 0
\(589\) 11.1673 19.3423i 0.460141 0.796987i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 1.26539 2.19172i 0.0519634 0.0900032i −0.838874 0.544326i \(-0.816785\pi\)
0.890837 + 0.454323i \(0.150119\pi\)
\(594\) 0 0
\(595\) −6.10693 4.64109i −0.250360 0.190266i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −16.0218 −0.654634 −0.327317 0.944915i \(-0.606145\pi\)
−0.327317 + 0.944915i \(0.606145\pi\)
\(600\) 0 0
\(601\) −22.1601 38.3824i −0.903929 1.56565i −0.822349 0.568983i \(-0.807337\pi\)
−0.0815796 0.996667i \(-0.525996\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 2.69758 4.67235i 0.109672 0.189958i
\(606\) 0 0
\(607\) −4.79607 8.30704i −0.194666 0.337172i 0.752125 0.659021i \(-0.229029\pi\)
−0.946791 + 0.321849i \(0.895696\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −2.24897 + 3.89533i −0.0909835 + 0.157588i
\(612\) 0 0
\(613\) 11.2371 + 19.4632i 0.453861 + 0.786110i 0.998622 0.0524815i \(-0.0167131\pi\)
−0.544761 + 0.838591i \(0.683380\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −11.7056 + 20.2746i −0.471248 + 0.816226i −0.999459 0.0328875i \(-0.989530\pi\)
0.528211 + 0.849113i \(0.322863\pi\)
\(618\) 0 0
\(619\) 7.98843 13.8364i 0.321082 0.556131i −0.659629 0.751591i \(-0.729287\pi\)
0.980712 + 0.195460i \(0.0626201\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −29.7074 22.5768i −1.19020 0.904521i
\(624\) 0 0
\(625\) −10.4632 18.1227i −0.418527 0.724910i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −2.46622 −0.0983348
\(630\) 0 0
\(631\) 0.882517 0.0351324 0.0175662 0.999846i \(-0.494408\pi\)
0.0175662 + 0.999846i \(0.494408\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 4.36864 + 7.56671i 0.173364 + 0.300276i
\(636\) 0 0
\(637\) −2.39836 + 2.44335i −0.0950265 + 0.0968090i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 20.2141 35.0118i 0.798408 1.38288i −0.122244 0.992500i \(-0.539009\pi\)
0.920652 0.390384i \(-0.127658\pi\)
\(642\) 0 0
\(643\) −2.99047 + 5.17964i −0.117932 + 0.204265i −0.918948 0.394378i \(-0.870960\pi\)
0.801016 + 0.598643i \(0.204293\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −16.4743 28.5343i −0.647672 1.12180i −0.983677 0.179941i \(-0.942409\pi\)
0.336005 0.941860i \(-0.390924\pi\)
\(648\) 0 0
\(649\) 15.2856 26.4755i 0.600014 1.03925i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 13.0166 + 22.5455i 0.509380 + 0.882272i 0.999941 + 0.0108653i \(0.00345861\pi\)
−0.490561 + 0.871407i \(0.663208\pi\)
\(654\) 0 0
\(655\) 1.52987 2.64982i 0.0597771 0.103537i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 4.91651 + 8.51565i 0.191520 + 0.331722i 0.945754 0.324883i \(-0.105325\pi\)
−0.754234 + 0.656606i \(0.771992\pi\)
\(660\) 0 0
\(661\) −5.51520 −0.214516 −0.107258 0.994231i \(-0.534207\pi\)
−0.107258 + 0.994231i \(0.534207\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −0.644111 + 5.07458i −0.0249776 + 0.196784i
\(666\) 0 0
\(667\) −0.177222 + 0.306958i −0.00686208 + 0.0118855i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 1.07339 1.85916i 0.0414376 0.0717720i
\(672\) 0 0
\(673\) 19.6176 + 33.9788i 0.756205 + 1.30978i 0.944773 + 0.327725i \(0.106282\pi\)
−0.188569 + 0.982060i \(0.560385\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 37.1632 1.42830 0.714149 0.699994i \(-0.246814\pi\)
0.714149 + 0.699994i \(0.246814\pi\)
\(678\) 0 0
\(679\) 25.4899 10.6973i 0.978211 0.410523i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −5.10586 8.84360i −0.195370 0.338391i 0.751652 0.659560i \(-0.229257\pi\)
−0.947022 + 0.321169i \(0.895924\pi\)
\(684\) 0 0
\(685\) −4.85305 −0.185426
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 4.27615 0.162908
\(690\) 0 0
\(691\) 35.0761 1.33436 0.667179 0.744897i \(-0.267501\pi\)
0.667179 + 0.744897i \(0.267501\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −7.24284 −0.274737
\(696\) 0 0
\(697\) 27.8097 1.05337
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −17.2500 −0.651522 −0.325761 0.945452i \(-0.605621\pi\)
−0.325761 + 0.945452i \(0.605621\pi\)
\(702\) 0 0
\(703\) 0.822352 + 1.42436i 0.0310156 + 0.0537206i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 20.9912 + 15.9527i 0.789455 + 0.599964i
\(708\) 0 0
\(709\) −14.5147 −0.545110 −0.272555 0.962140i \(-0.587869\pi\)
−0.272555 + 0.962140i \(0.587869\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −0.163922 0.283921i −0.00613893 0.0106329i
\(714\) 0 0
\(715\) −0.593081 + 1.02725i −0.0221800 + 0.0384168i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −22.4295 + 38.8491i −0.836480 + 1.44883i 0.0563403 + 0.998412i \(0.482057\pi\)
−0.892820 + 0.450414i \(0.851277\pi\)
\(720\) 0 0
\(721\) 28.4242 11.9287i 1.05857 0.444248i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 31.0295 1.15241
\(726\) 0 0
\(727\) 2.22039 + 3.84582i 0.0823496 + 0.142634i 0.904259 0.426985i \(-0.140424\pi\)
−0.821909 + 0.569619i \(0.807091\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −15.7021 + 27.1969i −0.580764 + 1.00591i
\(732\) 0 0
\(733\) 19.1360 + 33.1445i 0.706803 + 1.22422i 0.966037 + 0.258405i \(0.0831968\pi\)
−0.259233 + 0.965815i \(0.583470\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 11.9725 20.7370i 0.441014 0.763859i
\(738\) 0 0
\(739\) 2.59381 + 4.49261i 0.0954148 + 0.165263i 0.909782 0.415087i \(-0.136249\pi\)
−0.814367 + 0.580350i \(0.802916\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 16.3351 28.2932i 0.599276 1.03798i −0.393653 0.919259i \(-0.628789\pi\)
0.992928 0.118716i \(-0.0378779\pi\)
\(744\) 0 0
\(745\) 2.18314 3.78132i 0.0799842 0.138537i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −10.3452 7.86203i −0.378004 0.287272i
\(750\) 0 0
\(751\) −8.06106 13.9622i −0.294152 0.509487i 0.680635 0.732623i \(-0.261704\pi\)
−0.974787 + 0.223136i \(0.928371\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −7.62595 −0.277537
\(756\) 0 0
\(757\) 45.6421 1.65889 0.829444 0.558589i \(-0.188657\pi\)
0.829444 + 0.558589i \(0.188657\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 6.11500 + 10.5915i 0.221669 + 0.383942i 0.955315 0.295590i \(-0.0955163\pi\)
−0.733646 + 0.679532i \(0.762183\pi\)
\(762\) 0 0
\(763\) −47.6387 + 19.9924i −1.72464 + 0.723773i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −1.62158 + 2.80866i −0.0585518 + 0.101415i
\(768\) 0 0
\(769\) 3.17344 5.49656i 0.114437 0.198211i −0.803117 0.595821i \(-0.796827\pi\)
0.917555 + 0.397610i \(0.130160\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −24.4515 42.3512i −0.879459 1.52327i −0.851936 0.523646i \(-0.824572\pi\)
−0.0275225 0.999621i \(-0.508762\pi\)
\(774\) 0 0
\(775\) −14.3504 + 24.8556i −0.515481 + 0.892839i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −9.27302 16.0613i −0.332240 0.575457i
\(780\) 0 0
\(781\) −4.06483 + 7.04049i −0.145451 + 0.251928i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −3.28455 5.68900i −0.117231 0.203049i
\(786\) 0 0
\(787\) 23.1498 0.825201 0.412600 0.910912i \(-0.364621\pi\)
0.412600 + 0.910912i \(0.364621\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 23.1147 + 17.5665i 0.821864 + 0.624594i
\(792\) 0 0
\(793\) −0.113870 + 0.197229i −0.00404365 + 0.00700381i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −24.2284 + 41.9648i −0.858214 + 1.48647i 0.0154170 + 0.999881i \(0.495092\pi\)
−0.873631 + 0.486589i