Properties

Label 3024.2.t.l.1873.1
Level $3024$
Weight $2$
Character 3024.1873
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.t (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 1873.1
Character \(\chi\) \(=\) 3024.1873
Dual form 3024.2.t.l.289.1

$q$-expansion

\(f(q)\) \(=\) \(q-3.84095 q^{5} +(-0.676469 + 2.55781i) q^{7} +O(q^{10})\) \(q-3.84095 q^{5} +(-0.676469 + 2.55781i) q^{7} +1.80663 q^{11} +(-0.692713 + 1.19981i) q^{13} +(0.833405 - 1.44350i) q^{17} +(0.0802084 + 0.138925i) q^{19} +3.20038 q^{23} +9.75291 q^{25} +(3.78000 + 6.54716i) q^{29} +(1.61011 + 2.78879i) q^{31} +(2.59829 - 9.82442i) q^{35} +(1.58395 + 2.74348i) q^{37} +(-6.00329 + 10.3980i) q^{41} +(-3.45480 - 5.98389i) q^{43} +(-5.71921 + 9.90595i) q^{47} +(-6.08478 - 3.46056i) q^{49} +(-1.37450 + 2.38071i) q^{53} -6.93918 q^{55} +(-7.53527 - 13.0515i) q^{59} +(4.60143 - 7.96990i) q^{61} +(2.66068 - 4.60843i) q^{65} +(-6.16830 - 10.6838i) q^{67} -6.93289 q^{71} +(-6.22457 + 10.7813i) q^{73} +(-1.22213 + 4.62102i) q^{77} +(8.03716 - 13.9208i) q^{79} +(-1.45280 - 2.51633i) q^{83} +(-3.20107 + 5.54441i) q^{85} +(-5.04034 - 8.73012i) q^{89} +(-2.60030 - 2.58347i) q^{91} +(-0.308077 - 0.533604i) q^{95} +(4.18830 + 7.25435i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 22q + 6q^{5} - 7q^{7} + O(q^{10}) \) \( 22q + 6q^{5} - 7q^{7} + 6q^{11} - 3q^{13} - 7q^{17} + q^{19} - 4q^{23} + 20q^{25} - 9q^{29} + 4q^{31} + 14q^{35} + 2q^{37} - 16q^{41} + 5q^{47} - 15q^{49} - 11q^{53} - 22q^{55} - 19q^{59} - 13q^{61} - 13q^{65} - 26q^{67} - 48q^{71} - 35q^{73} + 4q^{77} - 10q^{79} - 28q^{83} - 20q^{85} - 6q^{89} + 37q^{91} + 12q^{95} - 29q^{97} + O(q^{100}) \)

Character values

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

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

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
\(5\) −3.84095 −1.71773 −0.858863 0.512205i \(-0.828829\pi\)
−0.858863 + 0.512205i \(0.828829\pi\)
\(6\) 0 0
\(7\) −0.676469 + 2.55781i −0.255681 + 0.966761i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 1.80663 0.544720 0.272360 0.962195i \(-0.412196\pi\)
0.272360 + 0.962195i \(0.412196\pi\)
\(12\) 0 0
\(13\) −0.692713 + 1.19981i −0.192124 + 0.332769i −0.945954 0.324301i \(-0.894871\pi\)
0.753830 + 0.657070i \(0.228204\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 0.833405 1.44350i 0.202130 0.350100i −0.747084 0.664729i \(-0.768547\pi\)
0.949215 + 0.314629i \(0.101880\pi\)
\(18\) 0 0
\(19\) 0.0802084 + 0.138925i 0.0184011 + 0.0318716i 0.875079 0.483980i \(-0.160809\pi\)
−0.856678 + 0.515851i \(0.827476\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 3.20038 0.667326 0.333663 0.942692i \(-0.391715\pi\)
0.333663 + 0.942692i \(0.391715\pi\)
\(24\) 0 0
\(25\) 9.75291 1.95058
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 3.78000 + 6.54716i 0.701929 + 1.21578i 0.967788 + 0.251765i \(0.0810110\pi\)
−0.265859 + 0.964012i \(0.585656\pi\)
\(30\) 0 0
\(31\) 1.61011 + 2.78879i 0.289184 + 0.500881i 0.973615 0.228196i \(-0.0732828\pi\)
−0.684431 + 0.729077i \(0.739949\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 2.59829 9.82442i 0.439190 1.66063i
\(36\) 0 0
\(37\) 1.58395 + 2.74348i 0.260399 + 0.451025i 0.966348 0.257238i \(-0.0828124\pi\)
−0.705949 + 0.708263i \(0.749479\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −6.00329 + 10.3980i −0.937556 + 1.62389i −0.167545 + 0.985864i \(0.553584\pi\)
−0.770011 + 0.638030i \(0.779750\pi\)
\(42\) 0 0
\(43\) −3.45480 5.98389i −0.526852 0.912535i −0.999510 0.0312891i \(-0.990039\pi\)
0.472658 0.881246i \(-0.343295\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −5.71921 + 9.90595i −0.834232 + 1.44493i 0.0604225 + 0.998173i \(0.480755\pi\)
−0.894654 + 0.446759i \(0.852578\pi\)
\(48\) 0 0
\(49\) −6.08478 3.46056i −0.869254 0.494366i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −1.37450 + 2.38071i −0.188802 + 0.327015i −0.944851 0.327500i \(-0.893794\pi\)
0.756049 + 0.654515i \(0.227127\pi\)
\(54\) 0 0
\(55\) −6.93918 −0.935679
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −7.53527 13.0515i −0.981009 1.69916i −0.658482 0.752597i \(-0.728801\pi\)
−0.322527 0.946560i \(-0.604532\pi\)
\(60\) 0 0
\(61\) 4.60143 7.96990i 0.589152 1.02044i −0.405192 0.914232i \(-0.632795\pi\)
0.994344 0.106210i \(-0.0338715\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 2.66068 4.60843i 0.330016 0.571605i
\(66\) 0 0
\(67\) −6.16830 10.6838i −0.753578 1.30523i −0.946078 0.323938i \(-0.894993\pi\)
0.192501 0.981297i \(-0.438340\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −6.93289 −0.822783 −0.411391 0.911459i \(-0.634957\pi\)
−0.411391 + 0.911459i \(0.634957\pi\)
\(72\) 0 0
\(73\) −6.22457 + 10.7813i −0.728531 + 1.26185i 0.228973 + 0.973433i \(0.426463\pi\)
−0.957504 + 0.288420i \(0.906870\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −1.22213 + 4.62102i −0.139275 + 0.526614i
\(78\) 0 0
\(79\) 8.03716 13.9208i 0.904251 1.56621i 0.0823313 0.996605i \(-0.473763\pi\)
0.821920 0.569604i \(-0.192903\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −1.45280 2.51633i −0.159466 0.276203i 0.775210 0.631703i \(-0.217644\pi\)
−0.934676 + 0.355500i \(0.884311\pi\)
\(84\) 0 0
\(85\) −3.20107 + 5.54441i −0.347205 + 0.601376i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −5.04034 8.73012i −0.534275 0.925391i −0.999198 0.0400399i \(-0.987251\pi\)
0.464923 0.885351i \(-0.346082\pi\)
\(90\) 0 0
\(91\) −2.60030 2.58347i −0.272585 0.270821i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −0.308077 0.533604i −0.0316080 0.0547466i
\(96\) 0 0
\(97\) 4.18830 + 7.25435i 0.425257 + 0.736567i 0.996444 0.0842527i \(-0.0268503\pi\)
−0.571187 + 0.820820i \(0.693517\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −8.11500 −0.807473 −0.403736 0.914875i \(-0.632289\pi\)
−0.403736 + 0.914875i \(0.632289\pi\)
\(102\) 0 0
\(103\) 7.53782 0.742723 0.371362 0.928488i \(-0.378891\pi\)
0.371362 + 0.928488i \(0.378891\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −2.95731 5.12221i −0.285894 0.495183i 0.686932 0.726722i \(-0.258957\pi\)
−0.972826 + 0.231539i \(0.925624\pi\)
\(108\) 0 0
\(109\) −4.48409 + 7.76668i −0.429498 + 0.743913i −0.996829 0.0795776i \(-0.974643\pi\)
0.567331 + 0.823490i \(0.307976\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 7.98131 13.8240i 0.750819 1.30046i −0.196608 0.980482i \(-0.562993\pi\)
0.947426 0.319974i \(-0.103674\pi\)
\(114\) 0 0
\(115\) −12.2925 −1.14628
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 3.12842 + 3.10817i 0.286782 + 0.284926i
\(120\) 0 0
\(121\) −7.73608 −0.703280
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −18.2557 −1.63284
\(126\) 0 0
\(127\) −8.60913 −0.763937 −0.381968 0.924175i \(-0.624754\pi\)
−0.381968 + 0.924175i \(0.624754\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −1.92966 −0.168595 −0.0842976 0.996441i \(-0.526865\pi\)
−0.0842976 + 0.996441i \(0.526865\pi\)
\(132\) 0 0
\(133\) −0.409602 + 0.111179i −0.0355170 + 0.00964047i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 3.70885 0.316868 0.158434 0.987370i \(-0.449355\pi\)
0.158434 + 0.987370i \(0.449355\pi\)
\(138\) 0 0
\(139\) −0.134568 + 0.233079i −0.0114139 + 0.0197695i −0.871676 0.490083i \(-0.836967\pi\)
0.860262 + 0.509852i \(0.170300\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −1.25148 + 2.16762i −0.104654 + 0.181266i
\(144\) 0 0
\(145\) −14.5188 25.1473i −1.20572 2.08837i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −8.31760 −0.681404 −0.340702 0.940171i \(-0.610665\pi\)
−0.340702 + 0.940171i \(0.610665\pi\)
\(150\) 0 0
\(151\) −9.74138 −0.792742 −0.396371 0.918090i \(-0.629731\pi\)
−0.396371 + 0.918090i \(0.629731\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −6.18434 10.7116i −0.496738 0.860376i
\(156\) 0 0
\(157\) −12.1290 21.0081i −0.968001 1.67663i −0.701327 0.712840i \(-0.747409\pi\)
−0.266674 0.963787i \(-0.585925\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −2.16496 + 8.18597i −0.170623 + 0.645145i
\(162\) 0 0
\(163\) −3.91401 6.77927i −0.306569 0.530993i 0.671040 0.741421i \(-0.265848\pi\)
−0.977609 + 0.210428i \(0.932514\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −2.15395 + 3.73076i −0.166678 + 0.288695i −0.937250 0.348658i \(-0.886637\pi\)
0.770572 + 0.637353i \(0.219971\pi\)
\(168\) 0 0
\(169\) 5.54030 + 9.59608i 0.426177 + 0.738160i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −8.66797 + 15.0134i −0.659014 + 1.14144i 0.321858 + 0.946788i \(0.395693\pi\)
−0.980871 + 0.194657i \(0.937641\pi\)
\(174\) 0 0
\(175\) −6.59754 + 24.9461i −0.498728 + 1.88575i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −9.68644 + 16.7774i −0.723998 + 1.25400i 0.235387 + 0.971902i \(0.424364\pi\)
−0.959385 + 0.282100i \(0.908969\pi\)
\(180\) 0 0
\(181\) 2.89036 0.214839 0.107420 0.994214i \(-0.465741\pi\)
0.107420 + 0.994214i \(0.465741\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −6.08387 10.5376i −0.447295 0.774737i
\(186\) 0 0
\(187\) 1.50566 2.60787i 0.110104 0.190706i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −1.85022 + 3.20468i −0.133877 + 0.231882i −0.925168 0.379558i \(-0.876076\pi\)
0.791291 + 0.611440i \(0.209409\pi\)
\(192\) 0 0
\(193\) 6.38351 + 11.0566i 0.459495 + 0.795869i 0.998934 0.0461554i \(-0.0146970\pi\)
−0.539439 + 0.842025i \(0.681364\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −2.44715 −0.174352 −0.0871762 0.996193i \(-0.527784\pi\)
−0.0871762 + 0.996193i \(0.527784\pi\)
\(198\) 0 0
\(199\) −2.24829 + 3.89415i −0.159377 + 0.276049i −0.934644 0.355584i \(-0.884282\pi\)
0.775267 + 0.631633i \(0.217615\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −19.3034 + 5.23958i −1.35484 + 0.367746i
\(204\) 0 0
\(205\) 23.0583 39.9382i 1.61046 2.78941i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 0.144907 + 0.250986i 0.0100234 + 0.0173611i
\(210\) 0 0
\(211\) −1.09087 + 1.88945i −0.0750987 + 0.130075i −0.901129 0.433551i \(-0.857261\pi\)
0.826030 + 0.563625i \(0.190594\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 13.2697 + 22.9838i 0.904988 + 1.56749i
\(216\) 0 0
\(217\) −8.22237 + 2.23182i −0.558171 + 0.151506i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 1.15462 + 1.99986i 0.0776682 + 0.134525i
\(222\) 0 0
\(223\) 2.87967 + 4.98773i 0.192837 + 0.334003i 0.946189 0.323614i \(-0.104898\pi\)
−0.753352 + 0.657617i \(0.771564\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 16.5827 1.10063 0.550316 0.834956i \(-0.314507\pi\)
0.550316 + 0.834956i \(0.314507\pi\)
\(228\) 0 0
\(229\) −14.5938 −0.964382 −0.482191 0.876066i \(-0.660159\pi\)
−0.482191 + 0.876066i \(0.660159\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −0.949438 1.64448i −0.0621998 0.107733i 0.833249 0.552898i \(-0.186478\pi\)
−0.895448 + 0.445165i \(0.853145\pi\)
\(234\) 0 0
\(235\) 21.9672 38.0483i 1.43298 2.48200i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −4.46351 + 7.73103i −0.288721 + 0.500079i −0.973505 0.228667i \(-0.926563\pi\)
0.684784 + 0.728746i \(0.259897\pi\)
\(240\) 0 0
\(241\) −24.2929 −1.56485 −0.782423 0.622748i \(-0.786016\pi\)
−0.782423 + 0.622748i \(0.786016\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 23.3713 + 13.2918i 1.49314 + 0.849185i
\(246\) 0 0
\(247\) −0.222246 −0.0141411
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −5.64873 −0.356545 −0.178272 0.983981i \(-0.557051\pi\)
−0.178272 + 0.983981i \(0.557051\pi\)
\(252\) 0 0
\(253\) 5.78191 0.363506
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 23.5711 1.47033 0.735163 0.677891i \(-0.237106\pi\)
0.735163 + 0.677891i \(0.237106\pi\)
\(258\) 0 0
\(259\) −8.08879 + 2.19556i −0.502613 + 0.136425i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 25.6405 1.58106 0.790531 0.612422i \(-0.209805\pi\)
0.790531 + 0.612422i \(0.209805\pi\)
\(264\) 0 0
\(265\) 5.27940 9.14419i 0.324311 0.561723i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 8.27239 14.3282i 0.504376 0.873606i −0.495611 0.868545i \(-0.665056\pi\)
0.999987 0.00506090i \(-0.00161094\pi\)
\(270\) 0 0
\(271\) −8.90748 15.4282i −0.541091 0.937197i −0.998842 0.0481166i \(-0.984678\pi\)
0.457751 0.889081i \(-0.348655\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 17.6199 1.06252
\(276\) 0 0
\(277\) −5.84382 −0.351121 −0.175560 0.984469i \(-0.556174\pi\)
−0.175560 + 0.984469i \(0.556174\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 10.5591 + 18.2889i 0.629905 + 1.09103i 0.987570 + 0.157177i \(0.0502394\pi\)
−0.357666 + 0.933850i \(0.616427\pi\)
\(282\) 0 0
\(283\) −6.38811 11.0645i −0.379734 0.657718i 0.611289 0.791407i \(-0.290651\pi\)
−0.991023 + 0.133689i \(0.957318\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −22.5351 22.3892i −1.33020 1.32159i
\(288\) 0 0
\(289\) 7.11087 + 12.3164i 0.418287 + 0.724494i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −5.93828 + 10.2854i −0.346918 + 0.600880i −0.985700 0.168508i \(-0.946105\pi\)
0.638782 + 0.769388i \(0.279439\pi\)
\(294\) 0 0
\(295\) 28.9426 + 50.1301i 1.68510 + 2.91869i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −2.21695 + 3.83986i −0.128209 + 0.222065i
\(300\) 0 0
\(301\) 17.6427 4.78881i 1.01691 0.276022i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −17.6739 + 30.6120i −1.01200 + 1.75284i
\(306\) 0 0
\(307\) 3.93298 0.224467 0.112234 0.993682i \(-0.464200\pi\)
0.112234 + 0.993682i \(0.464200\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −0.991107 1.71665i −0.0562005 0.0973422i 0.836556 0.547881i \(-0.184565\pi\)
−0.892757 + 0.450539i \(0.851232\pi\)
\(312\) 0 0
\(313\) −10.2497 + 17.7530i −0.579349 + 1.00346i 0.416205 + 0.909271i \(0.363360\pi\)
−0.995554 + 0.0941908i \(0.969974\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 4.75708 8.23951i 0.267184 0.462777i −0.700949 0.713211i \(-0.747240\pi\)
0.968134 + 0.250434i \(0.0805734\pi\)
\(318\) 0 0
\(319\) 6.82907 + 11.8283i 0.382355 + 0.662258i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 0.267384 0.0148777
\(324\) 0 0
\(325\) −6.75597 + 11.7017i −0.374754 + 0.649093i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −21.4687 21.3297i −1.18361 1.17595i
\(330\) 0 0
\(331\) 0.764929 1.32490i 0.0420443 0.0728228i −0.844237 0.535969i \(-0.819946\pi\)
0.886282 + 0.463146i \(0.153280\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 23.6921 + 41.0360i 1.29444 + 2.24204i
\(336\) 0 0
\(337\) 10.6972 18.5281i 0.582714 1.00929i −0.412442 0.910984i \(-0.635324\pi\)
0.995156 0.0983063i \(-0.0313425\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 2.90887 + 5.03831i 0.157524 + 0.272840i
\(342\) 0 0
\(343\) 12.9676 13.2227i 0.700185 0.713961i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −2.57191 4.45467i −0.138067 0.239139i 0.788698 0.614781i \(-0.210756\pi\)
−0.926765 + 0.375642i \(0.877422\pi\)
\(348\) 0 0
\(349\) 0.207526 + 0.359446i 0.0111086 + 0.0192407i 0.871526 0.490349i \(-0.163131\pi\)
−0.860418 + 0.509590i \(0.829797\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 12.0824 0.643083 0.321542 0.946895i \(-0.395799\pi\)
0.321542 + 0.946895i \(0.395799\pi\)
\(354\) 0 0
\(355\) 26.6289 1.41332
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −8.14926 14.1149i −0.430102 0.744958i 0.566780 0.823869i \(-0.308189\pi\)
−0.996882 + 0.0789113i \(0.974856\pi\)
\(360\) 0 0
\(361\) 9.48713 16.4322i 0.499323 0.864852i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 23.9083 41.4104i 1.25142 2.16752i
\(366\) 0 0
\(367\) −34.7000 −1.81133 −0.905664 0.423996i \(-0.860627\pi\)
−0.905664 + 0.423996i \(0.860627\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −5.15959 5.12619i −0.267873 0.266139i
\(372\) 0 0
\(373\) −15.5066 −0.802900 −0.401450 0.915881i \(-0.631494\pi\)
−0.401450 + 0.915881i \(0.631494\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −10.4738 −0.539430
\(378\) 0 0
\(379\) 16.1820 0.831214 0.415607 0.909544i \(-0.363569\pi\)
0.415607 + 0.909544i \(0.363569\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 4.34054 0.221791 0.110896 0.993832i \(-0.464628\pi\)
0.110896 + 0.993832i \(0.464628\pi\)
\(384\) 0 0
\(385\) 4.69414 17.7491i 0.239236 0.904578i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −25.5463 −1.29525 −0.647624 0.761960i \(-0.724237\pi\)
−0.647624 + 0.761960i \(0.724237\pi\)
\(390\) 0 0
\(391\) 2.66722 4.61975i 0.134887 0.233631i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −30.8703 + 53.4690i −1.55326 + 2.69032i
\(396\) 0 0
\(397\) 2.28225 + 3.95297i 0.114543 + 0.198394i 0.917597 0.397512i \(-0.130126\pi\)
−0.803054 + 0.595906i \(0.796793\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −1.33626 −0.0667294 −0.0333647 0.999443i \(-0.510622\pi\)
−0.0333647 + 0.999443i \(0.510622\pi\)
\(402\) 0 0
\(403\) −4.46137 −0.222237
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 2.86161 + 4.95645i 0.141845 + 0.245682i
\(408\) 0 0
\(409\) −10.3332 17.8976i −0.510944 0.884981i −0.999920 0.0126832i \(-0.995963\pi\)
0.488976 0.872297i \(-0.337371\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 38.4806 10.4449i 1.89350 0.513958i
\(414\) 0 0
\(415\) 5.58015 + 9.66510i 0.273919 + 0.474441i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 10.5227 18.2259i 0.514069 0.890394i −0.485797 0.874071i \(-0.661471\pi\)
0.999867 0.0163228i \(-0.00519594\pi\)
\(420\) 0 0
\(421\) −8.51630 14.7507i −0.415059 0.718903i 0.580376 0.814349i \(-0.302906\pi\)
−0.995435 + 0.0954456i \(0.969572\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 8.12813 14.0783i 0.394272 0.682899i
\(426\) 0 0
\(427\) 17.2728 + 17.1610i 0.835888 + 0.830477i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 18.2925 31.6836i 0.881121 1.52615i 0.0310244 0.999519i \(-0.490123\pi\)
0.850096 0.526627i \(-0.176544\pi\)
\(432\) 0 0
\(433\) −23.6571 −1.13689 −0.568444 0.822722i \(-0.692454\pi\)
−0.568444 + 0.822722i \(0.692454\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0.256698 + 0.444613i 0.0122795 + 0.0212687i
\(438\) 0 0
\(439\) 10.3932 18.0016i 0.496041 0.859168i −0.503949 0.863734i \(-0.668120\pi\)
0.999990 + 0.00456551i \(0.00145325\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −3.71404 + 6.43290i −0.176459 + 0.305636i −0.940665 0.339336i \(-0.889798\pi\)
0.764206 + 0.644972i \(0.223131\pi\)
\(444\) 0 0
\(445\) 19.3597 + 33.5320i 0.917737 + 1.58957i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 8.15800 0.385000 0.192500 0.981297i \(-0.438340\pi\)
0.192500 + 0.981297i \(0.438340\pi\)
\(450\) 0 0
\(451\) −10.8457 + 18.7854i −0.510705 + 0.884568i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 9.98762 + 9.92297i 0.468227 + 0.465196i
\(456\) 0 0
\(457\) −7.15292 + 12.3892i −0.334600 + 0.579544i −0.983408 0.181408i \(-0.941934\pi\)
0.648808 + 0.760952i \(0.275268\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −7.71961 13.3708i −0.359538 0.622738i 0.628346 0.777934i \(-0.283732\pi\)
−0.987884 + 0.155196i \(0.950399\pi\)
\(462\) 0 0
\(463\) −10.5531 + 18.2785i −0.490444 + 0.849474i −0.999940 0.0109995i \(-0.996499\pi\)
0.509496 + 0.860473i \(0.329832\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 3.49896 + 6.06037i 0.161912 + 0.280440i 0.935555 0.353182i \(-0.114900\pi\)
−0.773642 + 0.633623i \(0.781567\pi\)
\(468\) 0 0
\(469\) 31.4998 8.55007i 1.45453 0.394805i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −6.24155 10.8107i −0.286987 0.497076i
\(474\) 0 0
\(475\) 0.782265 + 1.35492i 0.0358928 + 0.0621681i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 3.08813 0.141100 0.0705500 0.997508i \(-0.477525\pi\)
0.0705500 + 0.997508i \(0.477525\pi\)
\(480\) 0 0
\(481\) −4.38888 −0.200116
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −16.0871 27.8636i −0.730475 1.26522i
\(486\) 0 0
\(487\) −4.90011 + 8.48725i −0.222045 + 0.384594i −0.955429 0.295221i \(-0.904607\pi\)
0.733384 + 0.679815i \(0.237940\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 9.98641 17.2970i 0.450680 0.780601i −0.547748 0.836643i \(-0.684515\pi\)
0.998428 + 0.0560419i \(0.0178481\pi\)
\(492\) 0 0
\(493\) 12.6011 0.567525
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 4.68989 17.7330i 0.210370 0.795435i
\(498\) 0 0
\(499\) 20.3299 0.910092 0.455046 0.890468i \(-0.349623\pi\)
0.455046 + 0.890468i \(0.349623\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −23.9595 −1.06830 −0.534151 0.845389i \(-0.679369\pi\)
−0.534151 + 0.845389i \(0.679369\pi\)
\(504\) 0 0
\(505\) 31.1693 1.38702
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −10.0609 −0.445943 −0.222971 0.974825i \(-0.571576\pi\)
−0.222971 + 0.974825i \(0.571576\pi\)
\(510\) 0 0
\(511\) −23.3657 23.2145i −1.03364 1.02695i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −28.9524 −1.27580
\(516\) 0 0
\(517\) −10.3325 + 17.8964i −0.454423 + 0.787083i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −7.99821 + 13.8533i −0.350408 + 0.606924i −0.986321 0.164836i \(-0.947290\pi\)
0.635913 + 0.771761i \(0.280624\pi\)
\(522\) 0 0
\(523\) 18.7103 + 32.4072i 0.818146 + 1.41707i 0.907047 + 0.421029i \(0.138331\pi\)
−0.0889016 + 0.996040i \(0.528336\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 5.36748 0.233811
\(528\) 0 0
\(529\) −12.7575 −0.554676
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −8.31711 14.4057i −0.360254 0.623978i
\(534\) 0 0
\(535\) 11.3589 + 19.6742i 0.491087 + 0.850588i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −10.9930 6.25195i −0.473500 0.269291i
\(540\) 0 0
\(541\) 0.229159 + 0.396916i 0.00985233 + 0.0170647i 0.870910 0.491443i \(-0.163531\pi\)
−0.861057 + 0.508508i \(0.830197\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 17.2232 29.8314i 0.737760 1.27784i
\(546\) 0 0
\(547\) 11.2013 + 19.4011i 0.478931 + 0.829533i 0.999708 0.0241596i \(-0.00769098\pi\)
−0.520777 + 0.853693i \(0.674358\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −0.606376 + 1.05027i −0.0258325 + 0.0447432i
\(552\) 0 0
\(553\) 30.1698 + 29.9745i 1.28295 + 1.27464i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −10.4155 + 18.0401i −0.441317 + 0.764383i −0.997787 0.0664841i \(-0.978822\pi\)
0.556471 + 0.830867i \(0.312155\pi\)
\(558\) 0 0
\(559\) 9.57275 0.404884
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −4.40302 7.62626i −0.185565 0.321409i 0.758202 0.652020i \(-0.226078\pi\)
−0.943767 + 0.330612i \(0.892745\pi\)
\(564\) 0 0
\(565\) −30.6558 + 53.0975i −1.28970 + 2.23383i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 9.49287 16.4421i 0.397962 0.689290i −0.595513 0.803346i \(-0.703051\pi\)
0.993474 + 0.114056i \(0.0363844\pi\)
\(570\) 0 0
\(571\) −7.87986 13.6483i −0.329762 0.571164i 0.652703 0.757614i \(-0.273635\pi\)
−0.982464 + 0.186450i \(0.940302\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 31.2131 1.30167
\(576\) 0 0
\(577\) −15.9306 + 27.5927i −0.663201 + 1.14870i 0.316569 + 0.948570i \(0.397469\pi\)
−0.979770 + 0.200128i \(0.935864\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 7.41907 2.01377i 0.307795 0.0835454i
\(582\) 0 0
\(583\) −2.48322 + 4.30106i −0.102844 + 0.178132i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −20.3597 35.2640i −0.840333 1.45550i −0.889613 0.456715i \(-0.849026\pi\)
0.0492799 0.998785i \(-0.484307\pi\)
\(588\) 0 0
\(589\) −0.258288 + 0.447368i −0.0106426 + 0.0184335i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 14.0693 + 24.3688i 0.577759 + 1.00071i 0.995736 + 0.0922500i \(0.0294059\pi\)
−0.417977 + 0.908458i \(0.637261\pi\)
\(594\) 0 0
\(595\) −12.0161 11.9383i −0.492613 0.489425i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −16.4963 28.5724i −0.674020 1.16744i −0.976754 0.214361i \(-0.931233\pi\)
0.302735 0.953075i \(-0.402100\pi\)
\(600\) 0 0
\(601\) −1.98103 3.43124i −0.0808079 0.139963i 0.822789 0.568347i \(-0.192417\pi\)
−0.903597 + 0.428383i \(0.859083\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 29.7139 1.20804
\(606\) 0 0
\(607\) −34.0263 −1.38109 −0.690543 0.723292i \(-0.742628\pi\)
−0.690543 + 0.723292i \(0.742628\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −7.92354 13.7240i −0.320552 0.555212i
\(612\) 0 0
\(613\) −15.2967 + 26.4946i −0.617827 + 1.07011i 0.372054 + 0.928211i \(0.378654\pi\)
−0.989881 + 0.141897i \(0.954680\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −18.7646 + 32.5013i −0.755435 + 1.30845i 0.189723 + 0.981838i \(0.439241\pi\)
−0.945158 + 0.326614i \(0.894092\pi\)
\(618\) 0 0
\(619\) 5.84604 0.234972 0.117486 0.993075i \(-0.462516\pi\)
0.117486 + 0.993075i \(0.462516\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 25.7396 6.98656i 1.03124 0.279911i
\(624\) 0 0
\(625\) 21.3547 0.854189
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 5.28028 0.210539
\(630\) 0 0
\(631\) −25.6347 −1.02050 −0.510251 0.860025i \(-0.670448\pi\)
−0.510251 + 0.860025i \(0.670448\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 33.0673 1.31223
\(636\) 0 0
\(637\) 8.36703 4.90343i 0.331514 0.194281i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −25.9647 −1.02554 −0.512772 0.858525i \(-0.671381\pi\)
−0.512772 + 0.858525i \(0.671381\pi\)
\(642\) 0 0
\(643\) 22.5634 39.0809i 0.889812 1.54120i 0.0497151 0.998763i \(-0.484169\pi\)
0.840097 0.542436i \(-0.182498\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 2.70324 4.68215i 0.106275 0.184074i −0.807983 0.589206i \(-0.799441\pi\)
0.914259 + 0.405131i \(0.132774\pi\)
\(648\) 0 0
\(649\) −13.6135 23.5792i −0.534375 0.925564i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 31.9030 1.24846 0.624231 0.781240i \(-0.285412\pi\)
0.624231 + 0.781240i \(0.285412\pi\)
\(654\) 0 0
\(655\) 7.41174 0.289600
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 2.50215 + 4.33385i 0.0974699 + 0.168823i 0.910637 0.413208i \(-0.135592\pi\)
−0.813167 + 0.582031i \(0.802258\pi\)
\(660\) 0 0
\(661\) −4.81703 8.34334i −0.187361 0.324518i 0.757009 0.653405i \(-0.226660\pi\)
−0.944369 + 0.328887i \(0.893327\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 1.57326 0.427034i 0.0610085 0.0165597i
\(666\) 0 0
\(667\) 12.0975 + 20.9534i 0.468415 + 0.811319i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 8.31308 14.3987i 0.320923 0.555855i
\(672\) 0 0
\(673\) 13.5885 + 23.5359i 0.523797 + 0.907243i 0.999616 + 0.0276998i \(0.00881825\pi\)
−0.475819 + 0.879543i \(0.657848\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −19.0251 + 32.9525i −0.731194 + 1.26647i 0.225179 + 0.974318i \(0.427703\pi\)
−0.956373 + 0.292148i \(0.905630\pi\)
\(678\) 0 0
\(679\) −21.3885 + 5.80553i −0.820815 + 0.222796i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 15.0571 26.0797i 0.576146 0.997913i −0.419771 0.907630i \(-0.637889\pi\)
0.995916 0.0902831i \(-0.0287772\pi\)
\(684\) 0 0
\(685\) −14.2455 −0.544293
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −1.90427 3.29830i −0.0725470 0.125655i
\(690\) 0 0
\(691\) 7.19510 12.4623i 0.273714 0.474087i −0.696096 0.717949i \(-0.745081\pi\)
0.969810 + 0.243862i \(0.0784143\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 0.516871 0.895246i 0.0196060 0.0339586i
\(696\) 0 0
\(697\) 10.0063 + 17.3315i 0.379017 + 0.656477i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −14.4170 −0.544521 −0.272261 0.962224i \(-0.587771\pi\)
−0.272261 + 0.962224i \(0.587771\pi\)
\(702\) 0 0
\(703\) −0.254092 + 0.440100i −0.00958325 + 0.0165987i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 5.48955 20.7566i 0.206456 0.780633i
\(708\) 0 0
\(709\) −5.74410 + 9.94907i −0.215724 + 0.373645i −0.953496 0.301405i \(-0.902545\pi\)
0.737772 + 0.675050i \(0.235878\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 5.15296 + 8.92519i 0.192980 + 0.334251i
\(714\) 0 0
\(715\) 4.80686 8.32573i 0.179766 0.311365i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 17.9451 + 31.0818i 0.669240 + 1.15916i 0.978117 + 0.208055i \(0.0667134\pi\)
−0.308877 + 0.951102i \(0.599953\pi\)
\(720\) 0 0
\(721\) −5.09910 + 19.2803i −0.189901 + 0.718036i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 36.8660 + 63.8539i 1.36917 + 2.37147i
\(726\) 0 0
\(727\) 5.03060 + 8.71326i 0.186575 + 0.323157i 0.944106 0.329642i \(-0.106928\pi\)
−0.757531 + 0.652799i \(0.773595\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −11.5170 −0.425972
\(732\) 0 0
\(733\) 33.1381 1.22398 0.611992 0.790864i \(-0.290369\pi\)
0.611992 + 0.790864i \(0.290369\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −11.1438 19.3017i −0.410489 0.710987i
\(738\) 0 0
\(739\) −21.9237 + 37.9729i −0.806475 + 1.39686i 0.108816 + 0.994062i \(0.465294\pi\)
−0.915291 + 0.402793i \(0.868039\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 4.50115 7.79622i 0.165131 0.286016i −0.771571 0.636144i \(-0.780529\pi\)
0.936702 + 0.350128i \(0.113862\pi\)
\(744\) 0 0
\(745\) 31.9475 1.17047
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 15.1022 4.09922i 0.551821 0.149782i
\(750\) 0 0
\(751\) −11.1828 −0.408067 −0.204033 0.978964i \(-0.565405\pi\)
−0.204033 + 0.978964i \(0.565405\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 37.4162 1.36171
\(756\) 0 0
\(757\) 42.1431 1.53172 0.765859 0.643009i \(-0.222314\pi\)
0.765859 + 0.643009i \(0.222314\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −2.28309 −0.0827620 −0.0413810 0.999143i \(-0.513176\pi\)
−0.0413810 + 0.999143i \(0.513176\pi\)
\(762\) 0 0
\(763\) −16.8323 16.7234i −0.609371 0.605427i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 20.8791 0.753901
\(768\) 0 0
\(769\) 8.96676 15.5309i 0.323350 0.560058i −0.657827 0.753169i \(-0.728524\pi\)
0.981177 + 0.193111i \(0.0618577\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −17.4807 + 30.2775i −0.628737 + 1.08901i 0.359068 + 0.933311i \(0.383095\pi\)
−0.987805 + 0.155694i \(0.950239\pi\)
\(774\) 0 0
\(775\) 15.7032 + 27.1988i 0.564077 + 0.977009i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −1.92606 −0.0690081
\(780\) 0 0
\(781\) −12.5252 −0.448186
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 46.5870 + 80.6910i 1.66276 + 2.87998i
\(786\) 0 0
\(787\) −14.1782 24.5573i −0.505397 0.875374i −0.999981 0.00624370i \(-0.998013\pi\)
0.494583 0.869130i \(-0.335321\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 29.9601 + 29.7662i 1.06526 + 1.05836i
\(792\) 0 0
\(793\) 6.37494 + 11.0417i 0.226381 + 0.392103i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 9.51922 16.4878i 0.337188 0.584027i −0.646715 0.762732i \(-0.723857\pi\)
0.983903 + 0.178705i \(0.0571908\pi\)
\(798\) 0 0
\(799\) 9.53283 + 16.5113i 0.337247 + 0.584129i
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −11.2455 + 19.4778i −0.396845 + 0.687356i
\(804\) 0 0
\(805\) 8.31551 31.4419i 0.293083 1.10818i
\(806\) 0 0