Properties

Label 2520.2.bi.k.361.1
Level $2520$
Weight $2$
Character 2520.361
Analytic conductor $20.122$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 2520 = 2^{3} \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2520.bi (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(20.1223013094\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{2}, \sqrt{-3})\)
Defining polynomial: \(x^{4} + 2 x^{2} + 4\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 280)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 361.1
Root \(-0.707107 + 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 2520.361
Dual form 2520.2.bi.k.1801.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{5} +(-2.62132 - 0.358719i) q^{7} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{5} +(-2.62132 - 0.358719i) q^{7} +(-2.41421 + 4.18154i) q^{11} +2.00000 q^{13} +(1.82843 - 3.16693i) q^{17} +(-2.82843 - 4.89898i) q^{19} +(-4.20711 - 7.28692i) q^{23} +(-0.500000 + 0.866025i) q^{25} +2.17157 q^{29} +(2.41421 - 4.18154i) q^{31} +(-1.00000 - 2.44949i) q^{35} +(2.82843 + 4.89898i) q^{37} -0.171573 q^{41} +12.8995 q^{43} +(0.171573 + 0.297173i) q^{47} +(6.74264 + 1.88064i) q^{49} +(2.82843 - 4.89898i) q^{53} -4.82843 q^{55} +(-2.00000 + 3.46410i) q^{59} +(2.32843 + 4.03295i) q^{61} +(1.00000 + 1.73205i) q^{65} +(-3.44975 + 5.97514i) q^{67} +12.0000 q^{71} +(3.82843 - 6.63103i) q^{73} +(7.82843 - 10.0951i) q^{77} +(2.00000 + 3.46410i) q^{79} +13.2426 q^{83} +3.65685 q^{85} +(-8.32843 - 14.4253i) q^{89} +(-5.24264 - 0.717439i) q^{91} +(2.82843 - 4.89898i) q^{95} +6.00000 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 2q^{5} - 2q^{7} + O(q^{10}) \) \( 4q + 2q^{5} - 2q^{7} - 4q^{11} + 8q^{13} - 4q^{17} - 14q^{23} - 2q^{25} + 20q^{29} + 4q^{31} - 4q^{35} - 12q^{41} + 12q^{43} + 12q^{47} + 10q^{49} - 8q^{55} - 8q^{59} - 2q^{61} + 4q^{65} + 6q^{67} + 48q^{71} + 4q^{73} + 20q^{77} + 8q^{79} + 36q^{83} - 8q^{85} - 22q^{89} - 4q^{91} + 24q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2520\mathbb{Z}\right)^\times\).

\(n\) \(281\) \(631\) \(1081\) \(1261\) \(2017\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\) \(1\)

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
\(5\) 0.500000 + 0.866025i 0.223607 + 0.387298i
\(6\) 0 0
\(7\) −2.62132 0.358719i −0.990766 0.135583i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −2.41421 + 4.18154i −0.727913 + 1.26078i 0.229851 + 0.973226i \(0.426176\pi\)
−0.957764 + 0.287556i \(0.907157\pi\)
\(12\) 0 0
\(13\) 2.00000 0.554700 0.277350 0.960769i \(-0.410544\pi\)
0.277350 + 0.960769i \(0.410544\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 1.82843 3.16693i 0.443459 0.768093i −0.554485 0.832194i \(-0.687085\pi\)
0.997943 + 0.0641009i \(0.0204179\pi\)
\(18\) 0 0
\(19\) −2.82843 4.89898i −0.648886 1.12390i −0.983389 0.181509i \(-0.941902\pi\)
0.334504 0.942394i \(-0.391431\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −4.20711 7.28692i −0.877242 1.51943i −0.854355 0.519690i \(-0.826047\pi\)
−0.0228877 0.999738i \(-0.507286\pi\)
\(24\) 0 0
\(25\) −0.500000 + 0.866025i −0.100000 + 0.173205i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 2.17157 0.403251 0.201625 0.979463i \(-0.435378\pi\)
0.201625 + 0.979463i \(0.435378\pi\)
\(30\) 0 0
\(31\) 2.41421 4.18154i 0.433606 0.751027i −0.563575 0.826065i \(-0.690574\pi\)
0.997181 + 0.0750380i \(0.0239078\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −1.00000 2.44949i −0.169031 0.414039i
\(36\) 0 0
\(37\) 2.82843 + 4.89898i 0.464991 + 0.805387i 0.999201 0.0399642i \(-0.0127244\pi\)
−0.534211 + 0.845351i \(0.679391\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −0.171573 −0.0267952 −0.0133976 0.999910i \(-0.504265\pi\)
−0.0133976 + 0.999910i \(0.504265\pi\)
\(42\) 0 0
\(43\) 12.8995 1.96715 0.983577 0.180488i \(-0.0577676\pi\)
0.983577 + 0.180488i \(0.0577676\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 0.171573 + 0.297173i 0.0250265 + 0.0433471i 0.878267 0.478170i \(-0.158700\pi\)
−0.853241 + 0.521517i \(0.825366\pi\)
\(48\) 0 0
\(49\) 6.74264 + 1.88064i 0.963234 + 0.268662i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 2.82843 4.89898i 0.388514 0.672927i −0.603736 0.797185i \(-0.706322\pi\)
0.992250 + 0.124258i \(0.0396551\pi\)
\(54\) 0 0
\(55\) −4.82843 −0.651065
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −2.00000 + 3.46410i −0.260378 + 0.450988i −0.966342 0.257260i \(-0.917180\pi\)
0.705965 + 0.708247i \(0.250514\pi\)
\(60\) 0 0
\(61\) 2.32843 + 4.03295i 0.298125 + 0.516367i 0.975707 0.219080i \(-0.0703056\pi\)
−0.677582 + 0.735447i \(0.736972\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 1.00000 + 1.73205i 0.124035 + 0.214834i
\(66\) 0 0
\(67\) −3.44975 + 5.97514i −0.421454 + 0.729979i −0.996082 0.0884353i \(-0.971813\pi\)
0.574628 + 0.818415i \(0.305147\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 12.0000 1.42414 0.712069 0.702109i \(-0.247758\pi\)
0.712069 + 0.702109i \(0.247758\pi\)
\(72\) 0 0
\(73\) 3.82843 6.63103i 0.448084 0.776103i −0.550178 0.835048i \(-0.685440\pi\)
0.998261 + 0.0589442i \(0.0187734\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 7.82843 10.0951i 0.892132 1.15045i
\(78\) 0 0
\(79\) 2.00000 + 3.46410i 0.225018 + 0.389742i 0.956325 0.292306i \(-0.0944227\pi\)
−0.731307 + 0.682048i \(0.761089\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 13.2426 1.45357 0.726784 0.686866i \(-0.241014\pi\)
0.726784 + 0.686866i \(0.241014\pi\)
\(84\) 0 0
\(85\) 3.65685 0.396642
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −8.32843 14.4253i −0.882812 1.52907i −0.848202 0.529673i \(-0.822314\pi\)
−0.0346099 0.999401i \(-0.511019\pi\)
\(90\) 0 0
\(91\) −5.24264 0.717439i −0.549578 0.0752080i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 2.82843 4.89898i 0.290191 0.502625i
\(96\) 0 0
\(97\) 6.00000 0.609208 0.304604 0.952479i \(-0.401476\pi\)
0.304604 + 0.952479i \(0.401476\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 2.74264 4.75039i 0.272903 0.472682i −0.696701 0.717362i \(-0.745350\pi\)
0.969604 + 0.244680i \(0.0786829\pi\)
\(102\) 0 0
\(103\) −5.20711 9.01897i −0.513071 0.888666i −0.999885 0.0151600i \(-0.995174\pi\)
0.486814 0.873506i \(-0.338159\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −4.20711 7.28692i −0.406716 0.704453i 0.587803 0.809004i \(-0.299993\pi\)
−0.994520 + 0.104551i \(0.966660\pi\)
\(108\) 0 0
\(109\) 2.15685 3.73578i 0.206589 0.357823i −0.744049 0.668125i \(-0.767097\pi\)
0.950638 + 0.310302i \(0.100430\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 11.3137 1.06430 0.532152 0.846649i \(-0.321383\pi\)
0.532152 + 0.846649i \(0.321383\pi\)
\(114\) 0 0
\(115\) 4.20711 7.28692i 0.392315 0.679509i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −5.92893 + 7.64564i −0.543504 + 0.700875i
\(120\) 0 0
\(121\) −6.15685 10.6640i −0.559714 0.969453i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) −15.6569 −1.38932 −0.694661 0.719338i \(-0.744445\pi\)
−0.694661 + 0.719338i \(0.744445\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 1.17157 + 2.02922i 0.102361 + 0.177294i 0.912657 0.408727i \(-0.134027\pi\)
−0.810296 + 0.586021i \(0.800694\pi\)
\(132\) 0 0
\(133\) 5.65685 + 13.8564i 0.490511 + 1.20150i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −2.00000 + 3.46410i −0.170872 + 0.295958i −0.938725 0.344668i \(-0.887992\pi\)
0.767853 + 0.640626i \(0.221325\pi\)
\(138\) 0 0
\(139\) −14.4853 −1.22863 −0.614313 0.789063i \(-0.710567\pi\)
−0.614313 + 0.789063i \(0.710567\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −4.82843 + 8.36308i −0.403773 + 0.699356i
\(144\) 0 0
\(145\) 1.08579 + 1.88064i 0.0901697 + 0.156178i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −3.32843 5.76500i −0.272675 0.472288i 0.696871 0.717197i \(-0.254575\pi\)
−0.969546 + 0.244909i \(0.921242\pi\)
\(150\) 0 0
\(151\) 8.41421 14.5738i 0.684739 1.18600i −0.288780 0.957396i \(-0.593250\pi\)
0.973519 0.228607i \(-0.0734171\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 4.82843 0.387829
\(156\) 0 0
\(157\) 10.6569 18.4582i 0.850510 1.47313i −0.0302396 0.999543i \(-0.509627\pi\)
0.880749 0.473583i \(-0.157040\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 8.41421 + 20.6105i 0.663133 + 1.62434i
\(162\) 0 0
\(163\) 2.17157 + 3.76127i 0.170091 + 0.294606i 0.938451 0.345411i \(-0.112261\pi\)
−0.768361 + 0.640017i \(0.778927\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 12.0711 0.934087 0.467044 0.884234i \(-0.345319\pi\)
0.467044 + 0.884234i \(0.345319\pi\)
\(168\) 0 0
\(169\) −9.00000 −0.692308
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 10.8284 + 18.7554i 0.823270 + 1.42595i 0.903234 + 0.429148i \(0.141186\pi\)
−0.0799642 + 0.996798i \(0.525481\pi\)
\(174\) 0 0
\(175\) 1.62132 2.09077i 0.122560 0.158047i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 5.24264 9.08052i 0.391853 0.678710i −0.600841 0.799369i \(-0.705167\pi\)
0.992694 + 0.120659i \(0.0385007\pi\)
\(180\) 0 0
\(181\) −9.82843 −0.730541 −0.365271 0.930901i \(-0.619024\pi\)
−0.365271 + 0.930901i \(0.619024\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −2.82843 + 4.89898i −0.207950 + 0.360180i
\(186\) 0 0
\(187\) 8.82843 + 15.2913i 0.645599 + 1.11821i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −11.2426 19.4728i −0.813489 1.40900i −0.910408 0.413712i \(-0.864232\pi\)
0.0969189 0.995292i \(-0.469101\pi\)
\(192\) 0 0
\(193\) −8.65685 + 14.9941i −0.623134 + 1.07930i 0.365765 + 0.930707i \(0.380808\pi\)
−0.988899 + 0.148592i \(0.952526\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −11.6569 −0.830516 −0.415258 0.909704i \(-0.636309\pi\)
−0.415258 + 0.909704i \(0.636309\pi\)
\(198\) 0 0
\(199\) 0.343146 0.594346i 0.0243250 0.0421321i −0.853607 0.520918i \(-0.825590\pi\)
0.877932 + 0.478786i \(0.158923\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −5.69239 0.778985i −0.399527 0.0546741i
\(204\) 0 0
\(205\) −0.0857864 0.148586i −0.00599158 0.0103777i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 27.3137 1.88933
\(210\) 0 0
\(211\) −18.6274 −1.28236 −0.641182 0.767389i \(-0.721556\pi\)
−0.641182 + 0.767389i \(0.721556\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 6.44975 + 11.1713i 0.439869 + 0.761876i
\(216\) 0 0
\(217\) −7.82843 + 10.0951i −0.531428 + 0.685302i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 3.65685 6.33386i 0.245987 0.426061i
\(222\) 0 0
\(223\) 18.9706 1.27036 0.635181 0.772363i \(-0.280925\pi\)
0.635181 + 0.772363i \(0.280925\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 7.00000 12.1244i 0.464606 0.804722i −0.534577 0.845120i \(-0.679529\pi\)
0.999184 + 0.0403978i \(0.0128625\pi\)
\(228\) 0 0
\(229\) 7.00000 + 12.1244i 0.462573 + 0.801200i 0.999088 0.0426906i \(-0.0135930\pi\)
−0.536515 + 0.843891i \(0.680260\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 0.171573 + 0.297173i 0.0112401 + 0.0194684i 0.871591 0.490234i \(-0.163089\pi\)
−0.860351 + 0.509703i \(0.829755\pi\)
\(234\) 0 0
\(235\) −0.171573 + 0.297173i −0.0111922 + 0.0193854i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 13.5147 0.874194 0.437097 0.899414i \(-0.356007\pi\)
0.437097 + 0.899414i \(0.356007\pi\)
\(240\) 0 0
\(241\) 5.00000 8.66025i 0.322078 0.557856i −0.658838 0.752285i \(-0.728952\pi\)
0.980917 + 0.194429i \(0.0622852\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 1.74264 + 6.77962i 0.111333 + 0.433134i
\(246\) 0 0
\(247\) −5.65685 9.79796i −0.359937 0.623429i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −23.4558 −1.48052 −0.740260 0.672321i \(-0.765298\pi\)
−0.740260 + 0.672321i \(0.765298\pi\)
\(252\) 0 0
\(253\) 40.6274 2.55422
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −3.65685 6.33386i −0.228108 0.395095i 0.729139 0.684365i \(-0.239921\pi\)
−0.957247 + 0.289270i \(0.906587\pi\)
\(258\) 0 0
\(259\) −5.65685 13.8564i −0.351500 0.860995i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 4.86396 8.42463i 0.299925 0.519485i −0.676194 0.736724i \(-0.736372\pi\)
0.976118 + 0.217239i \(0.0697051\pi\)
\(264\) 0 0
\(265\) 5.65685 0.347498
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 2.32843 4.03295i 0.141967 0.245894i −0.786270 0.617882i \(-0.787991\pi\)
0.928237 + 0.371989i \(0.121324\pi\)
\(270\) 0 0
\(271\) −9.65685 16.7262i −0.586612 1.01604i −0.994672 0.103087i \(-0.967128\pi\)
0.408060 0.912955i \(-0.366205\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −2.41421 4.18154i −0.145583 0.252156i
\(276\) 0 0
\(277\) 8.31371 14.3998i 0.499522 0.865198i −0.500478 0.865750i \(-0.666842\pi\)
1.00000 0.000551476i \(0.000175540\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −25.3137 −1.51009 −0.755045 0.655673i \(-0.772385\pi\)
−0.755045 + 0.655673i \(0.772385\pi\)
\(282\) 0 0
\(283\) −9.00000 + 15.5885i −0.534994 + 0.926638i 0.464169 + 0.885747i \(0.346353\pi\)
−0.999164 + 0.0408910i \(0.986980\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0.449747 + 0.0615465i 0.0265478 + 0.00363298i
\(288\) 0 0
\(289\) 1.81371 + 3.14144i 0.106689 + 0.184790i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 16.9706 0.991431 0.495715 0.868485i \(-0.334906\pi\)
0.495715 + 0.868485i \(0.334906\pi\)
\(294\) 0 0
\(295\) −4.00000 −0.232889
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −8.41421 14.5738i −0.486607 0.842827i
\(300\) 0 0
\(301\) −33.8137 4.62730i −1.94899 0.266713i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −2.32843 + 4.03295i −0.133325 + 0.230926i
\(306\) 0 0
\(307\) 13.2426 0.755797 0.377899 0.925847i \(-0.376647\pi\)
0.377899 + 0.925847i \(0.376647\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 5.17157 8.95743i 0.293253 0.507929i −0.681324 0.731982i \(-0.738596\pi\)
0.974577 + 0.224053i \(0.0719288\pi\)
\(312\) 0 0
\(313\) 6.48528 + 11.2328i 0.366570 + 0.634917i 0.989027 0.147737i \(-0.0471988\pi\)
−0.622457 + 0.782654i \(0.713865\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −11.0000 19.0526i −0.617822 1.07010i −0.989882 0.141890i \(-0.954682\pi\)
0.372061 0.928208i \(-0.378651\pi\)
\(318\) 0 0
\(319\) −5.24264 + 9.08052i −0.293532 + 0.508412i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −20.6863 −1.15102
\(324\) 0 0
\(325\) −1.00000 + 1.73205i −0.0554700 + 0.0960769i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −0.343146 0.840532i −0.0189182 0.0463400i
\(330\) 0 0
\(331\) −4.75736 8.23999i −0.261488 0.452911i 0.705149 0.709059i \(-0.250880\pi\)
−0.966638 + 0.256148i \(0.917547\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −6.89949 −0.376960
\(336\) 0 0
\(337\) −8.97056 −0.488658 −0.244329 0.969692i \(-0.578568\pi\)
−0.244329 + 0.969692i \(0.578568\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 11.6569 + 20.1903i 0.631254 + 1.09336i
\(342\) 0 0
\(343\) −17.0000 7.34847i −0.917914 0.396780i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −12.6924 + 21.9839i −0.681363 + 1.18016i 0.293202 + 0.956051i \(0.405279\pi\)
−0.974565 + 0.224105i \(0.928054\pi\)
\(348\) 0 0
\(349\) 4.17157 0.223299 0.111650 0.993748i \(-0.464387\pi\)
0.111650 + 0.993748i \(0.464387\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 11.1716 19.3497i 0.594603 1.02988i −0.399000 0.916951i \(-0.630643\pi\)
0.993603 0.112931i \(-0.0360240\pi\)
\(354\) 0 0
\(355\) 6.00000 + 10.3923i 0.318447 + 0.551566i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 5.24264 + 9.08052i 0.276696 + 0.479252i 0.970562 0.240853i \(-0.0774272\pi\)
−0.693866 + 0.720105i \(0.744094\pi\)
\(360\) 0 0
\(361\) −6.50000 + 11.2583i −0.342105 + 0.592544i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 7.65685 0.400778
\(366\) 0 0
\(367\) −12.2071 + 21.1433i −0.637206 + 1.10367i 0.348837 + 0.937183i \(0.386577\pi\)
−0.986043 + 0.166490i \(0.946757\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −9.17157 + 11.8272i −0.476164 + 0.614037i
\(372\) 0 0
\(373\) −6.00000 10.3923i −0.310668 0.538093i 0.667839 0.744306i \(-0.267219\pi\)
−0.978507 + 0.206213i \(0.933886\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 4.34315 0.223683
\(378\) 0 0
\(379\) 27.3137 1.40301 0.701505 0.712664i \(-0.252512\pi\)
0.701505 + 0.712664i \(0.252512\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 9.44975 + 16.3674i 0.482860 + 0.836337i 0.999806 0.0196803i \(-0.00626483\pi\)
−0.516947 + 0.856018i \(0.672931\pi\)
\(384\) 0 0
\(385\) 12.6569 + 1.73205i 0.645053 + 0.0882735i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −8.65685 + 14.9941i −0.438920 + 0.760232i −0.997606 0.0691473i \(-0.977972\pi\)
0.558687 + 0.829379i \(0.311305\pi\)
\(390\) 0 0
\(391\) −30.7696 −1.55608
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −2.00000 + 3.46410i −0.100631 + 0.174298i
\(396\) 0 0
\(397\) −10.3137 17.8639i −0.517630 0.896562i −0.999790 0.0204787i \(-0.993481\pi\)
0.482160 0.876083i \(-0.339852\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −4.84315 8.38857i −0.241855 0.418905i 0.719388 0.694609i \(-0.244423\pi\)
−0.961243 + 0.275703i \(0.911089\pi\)
\(402\) 0 0
\(403\) 4.82843 8.36308i 0.240521 0.416595i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −27.3137 −1.35389
\(408\) 0 0
\(409\) −1.57107 + 2.72117i −0.0776843 + 0.134553i −0.902250 0.431212i \(-0.858086\pi\)
0.824566 + 0.565766i \(0.191419\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 6.48528 8.36308i 0.319120 0.411520i
\(414\) 0 0
\(415\) 6.62132 + 11.4685i 0.325028 + 0.562965i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −7.31371 −0.357298 −0.178649 0.983913i \(-0.557173\pi\)
−0.178649 + 0.983913i \(0.557173\pi\)
\(420\) 0 0
\(421\) 38.6569 1.88402 0.942010 0.335585i \(-0.108934\pi\)
0.942010 + 0.335585i \(0.108934\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 1.82843 + 3.16693i 0.0886917 + 0.153619i
\(426\) 0 0
\(427\) −4.65685 11.4069i −0.225361 0.552019i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 2.41421 4.18154i 0.116289 0.201418i −0.802006 0.597317i \(-0.796234\pi\)
0.918294 + 0.395899i \(0.129567\pi\)
\(432\) 0 0
\(433\) 3.31371 0.159247 0.0796233 0.996825i \(-0.474628\pi\)
0.0796233 + 0.996825i \(0.474628\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −23.7990 + 41.2211i −1.13846 + 1.97187i
\(438\) 0 0
\(439\) 14.8284 + 25.6836i 0.707722 + 1.22581i 0.965700 + 0.259660i \(0.0836105\pi\)
−0.257978 + 0.966151i \(0.583056\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −9.20711 15.9472i −0.437443 0.757673i 0.560049 0.828460i \(-0.310782\pi\)
−0.997491 + 0.0707865i \(0.977449\pi\)
\(444\) 0 0
\(445\) 8.32843 14.4253i 0.394805 0.683823i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −9.48528 −0.447638 −0.223819 0.974631i \(-0.571852\pi\)
−0.223819 + 0.974631i \(0.571852\pi\)
\(450\) 0 0
\(451\) 0.414214 0.717439i 0.0195046 0.0337829i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −2.00000 4.89898i −0.0937614 0.229668i
\(456\) 0 0
\(457\) 2.48528 + 4.30463i 0.116257 + 0.201362i 0.918281 0.395928i \(-0.129577\pi\)
−0.802025 + 0.597291i \(0.796244\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 21.3137 0.992678 0.496339 0.868129i \(-0.334677\pi\)
0.496339 + 0.868129i \(0.334677\pi\)
\(462\) 0 0
\(463\) −4.89949 −0.227699 −0.113849 0.993498i \(-0.536318\pi\)
−0.113849 + 0.993498i \(0.536318\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 7.93503 + 13.7439i 0.367189 + 0.635991i 0.989125 0.147078i \(-0.0469868\pi\)
−0.621936 + 0.783068i \(0.713653\pi\)
\(468\) 0 0
\(469\) 11.1863 14.4253i 0.516535 0.666097i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −31.1421 + 53.9398i −1.43192 + 2.48015i
\(474\) 0 0
\(475\) 5.65685 0.259554
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −9.24264 + 16.0087i −0.422307 + 0.731457i −0.996165 0.0874978i \(-0.972113\pi\)
0.573858 + 0.818955i \(0.305446\pi\)
\(480\) 0 0
\(481\) 5.65685 + 9.79796i 0.257930 + 0.446748i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 3.00000 + 5.19615i 0.136223 + 0.235945i
\(486\) 0 0
\(487\) −9.14214 + 15.8346i −0.414270 + 0.717536i −0.995351 0.0963090i \(-0.969296\pi\)
0.581082 + 0.813845i \(0.302630\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −18.4853 −0.834229 −0.417115 0.908854i \(-0.636959\pi\)
−0.417115 + 0.908854i \(0.636959\pi\)
\(492\) 0 0
\(493\) 3.97056 6.87722i 0.178825 0.309734i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −31.4558 4.30463i −1.41099 0.193089i
\(498\) 0 0
\(499\) −7.92893 13.7333i −0.354948 0.614788i 0.632161 0.774837i \(-0.282168\pi\)
−0.987109 + 0.160049i \(0.948835\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 18.0711 0.805749 0.402875 0.915255i \(-0.368011\pi\)
0.402875 + 0.915255i \(0.368011\pi\)
\(504\) 0 0
\(505\) 5.48528 0.244092
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −8.25736 14.3022i −0.366001 0.633932i 0.622935 0.782273i \(-0.285940\pi\)
−0.988936 + 0.148341i \(0.952607\pi\)
\(510\) 0 0
\(511\) −12.4142 + 16.0087i −0.549172 + 0.708184i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 5.20711 9.01897i 0.229453 0.397423i
\(516\) 0 0
\(517\) −1.65685 −0.0728684
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −4.31371 + 7.47156i −0.188987 + 0.327335i −0.944913 0.327322i \(-0.893854\pi\)
0.755926 + 0.654657i \(0.227187\pi\)
\(522\) 0 0
\(523\) 19.9706 + 34.5900i 0.873252 + 1.51252i 0.858613 + 0.512624i \(0.171326\pi\)
0.0146382 + 0.999893i \(0.495340\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −8.82843 15.2913i −0.384572 0.666099i
\(528\) 0 0
\(529\) −23.8995 + 41.3951i −1.03911 + 1.79979i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −0.343146 −0.0148633
\(534\) 0 0
\(535\) 4.20711 7.28692i 0.181889 0.315041i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −24.1421 + 23.6544i −1.03988 + 1.01887i
\(540\) 0 0
\(541\) 3.25736 + 5.64191i 0.140045 + 0.242565i 0.927513 0.373790i \(-0.121942\pi\)
−0.787468 + 0.616355i \(0.788609\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 4.31371 0.184779
\(546\) 0 0
\(547\) −27.7279 −1.18556 −0.592780 0.805364i \(-0.701970\pi\)
−0.592780 + 0.805364i \(0.701970\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −6.14214 10.6385i −0.261664 0.453215i
\(552\) 0 0
\(553\) −4.00000 9.79796i −0.170097 0.416652i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 2.65685 4.60181i 0.112575 0.194985i −0.804233 0.594314i \(-0.797424\pi\)
0.916808 + 0.399329i \(0.130757\pi\)
\(558\) 0 0
\(559\) 25.7990 1.09118
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 5.03553 8.72180i 0.212222 0.367580i −0.740187 0.672401i \(-0.765263\pi\)
0.952410 + 0.304821i \(0.0985965\pi\)
\(564\) 0 0
\(565\) 5.65685 + 9.79796i 0.237986 + 0.412203i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 4.31371 + 7.47156i 0.180840 + 0.313224i 0.942167 0.335144i \(-0.108785\pi\)
−0.761327 + 0.648368i \(0.775452\pi\)
\(570\) 0 0
\(571\) −6.48528 + 11.2328i −0.271401 + 0.470080i −0.969221 0.246193i \(-0.920820\pi\)
0.697820 + 0.716273i \(0.254153\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 8.41421 0.350897
\(576\) 0 0
\(577\) −17.1421 + 29.6910i −0.713636 + 1.23605i 0.249847 + 0.968285i \(0.419620\pi\)
−0.963483 + 0.267769i \(0.913714\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −34.7132 4.75039i −1.44015 0.197080i
\(582\) 0 0
\(583\) 13.6569 + 23.6544i 0.565609 + 0.979664i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 45.3137 1.87030 0.935148 0.354256i \(-0.115266\pi\)
0.935148 + 0.354256i \(0.115266\pi\)
\(588\) 0 0
\(589\) −27.3137 −1.12544
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −18.9706 32.8580i −0.779028 1.34932i −0.932503 0.361163i \(-0.882380\pi\)
0.153475 0.988153i \(-0.450954\pi\)
\(594\) 0 0
\(595\) −9.58579 1.31178i −0.392979 0.0537779i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −1.31371 + 2.27541i −0.0536767 + 0.0929707i −0.891615 0.452794i \(-0.850427\pi\)
0.837939 + 0.545765i \(0.183761\pi\)
\(600\) 0 0
\(601\) −34.0000 −1.38689 −0.693444 0.720510i \(-0.743908\pi\)
−0.693444 + 0.720510i \(0.743908\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 6.15685 10.6640i 0.250312 0.433553i
\(606\) 0 0
\(607\) −9.37868 16.2443i −0.380669 0.659338i 0.610489 0.792025i \(-0.290973\pi\)
−0.991158 + 0.132687i \(0.957640\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0.343146 + 0.594346i 0.0138822 + 0.0240447i
\(612\) 0 0
\(613\) −2.51472 + 4.35562i −0.101569 + 0.175922i −0.912331 0.409453i \(-0.865719\pi\)
0.810763 + 0.585375i \(0.199053\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 35.3137 1.42168 0.710838 0.703356i \(-0.248316\pi\)
0.710838 + 0.703356i \(0.248316\pi\)
\(618\) 0 0
\(619\) 5.72792 9.92105i 0.230225 0.398761i −0.727649 0.685949i \(-0.759387\pi\)
0.957874 + 0.287188i \(0.0927206\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 16.6569 + 40.8008i 0.667343 + 1.63465i
\(624\) 0 0
\(625\) −0.500000 0.866025i −0.0200000 0.0346410i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 20.6863 0.824816
\(630\) 0 0
\(631\) −18.4853 −0.735887 −0.367944 0.929848i \(-0.619938\pi\)
−0.367944 + 0.929848i \(0.619938\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −7.82843 13.5592i −0.310662 0.538082i
\(636\) 0 0
\(637\) 13.4853 + 3.76127i 0.534306 + 0.149027i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −24.0563 + 41.6668i −0.950169 + 1.64574i −0.205113 + 0.978738i \(0.565756\pi\)
−0.745056 + 0.667002i \(0.767577\pi\)
\(642\) 0 0
\(643\) 26.0000 1.02534 0.512670 0.858586i \(-0.328656\pi\)
0.512670 + 0.858586i \(0.328656\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −14.6213 + 25.3249i −0.574823 + 0.995623i 0.421237 + 0.906950i \(0.361596\pi\)
−0.996061 + 0.0886729i \(0.971737\pi\)
\(648\) 0 0
\(649\) −9.65685 16.7262i −0.379065 0.656559i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −2.17157 3.76127i −0.0849802 0.147190i 0.820403 0.571786i \(-0.193749\pi\)
−0.905383 + 0.424596i \(0.860416\pi\)
\(654\) 0 0
\(655\) −1.17157 + 2.02922i −0.0457771 + 0.0792883i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −35.3137 −1.37563 −0.687813 0.725888i \(-0.741429\pi\)
−0.687813 + 0.725888i \(0.741429\pi\)
\(660\) 0 0
\(661\) 13.8431 23.9770i 0.538436 0.932598i −0.460553 0.887632i \(-0.652349\pi\)
0.998989 0.0449660i \(-0.0143180\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −9.17157 + 11.8272i −0.355658 + 0.458638i
\(666\) 0 0
\(667\) −9.13604 15.8241i −0.353749 0.612711i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −22.4853 −0.868035
\(672\) 0 0
\(673\) 5.65685 0.218056 0.109028 0.994039i \(-0.465226\pi\)
0.109028 + 0.994039i \(0.465226\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −5.48528 9.50079i −0.210816 0.365145i 0.741154 0.671335i \(-0.234279\pi\)
−0.951970 + 0.306190i \(0.900946\pi\)
\(678\) 0 0
\(679\) −15.7279 2.15232i −0.603582 0.0825983i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −8.03553 + 13.9180i −0.307471 + 0.532556i −0.977808 0.209501i \(-0.932816\pi\)
0.670337 + 0.742057i \(0.266149\pi\)
\(684\) 0 0
\(685\) −4.00000 −0.152832
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 5.65685 9.79796i 0.215509 0.373273i
\(690\) 0 0
\(691\) −15.3848 26.6472i −0.585264 1.01371i −0.994842 0.101433i \(-0.967657\pi\)
0.409578 0.912275i \(-0.365676\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −7.24264 12.5446i −0.274729 0.475845i
\(696\) 0 0
\(697\) −0.313708 + 0.543359i −0.0118826 + 0.0205812i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 11.0000 0.415464 0.207732 0.978186i \(-0.433392\pi\)
0.207732 + 0.978186i \(0.433392\pi\)
\(702\) 0 0
\(703\) 16.0000 27.7128i 0.603451 1.04521i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −8.89340 + 11.4685i −0.334471 + 0.431316i
\(708\) 0 0
\(709\) −24.7132 42.8045i −0.928124 1.60756i −0.786459 0.617643i \(-0.788088\pi\)
−0.141665 0.989915i \(-0.545246\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −40.6274 −1.52151
\(714\) 0 0
\(715\) −9.65685 −0.361146
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 6.89949 + 11.9503i 0.257308 + 0.445670i 0.965520 0.260330i \(-0.0838313\pi\)
−0.708212 + 0.706000i \(0.750498\pi\)
\(720\) 0 0
\(721\) 10.4142 + 25.5095i 0.387846 + 0.950024i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −1.08579 + 1.88064i −0.0403251 + 0.0698451i
\(726\) 0 0
\(727\) 23.9289 0.887475 0.443737 0.896157i \(-0.353652\pi\)
0.443737 + 0.896157i \(0.353652\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 23.5858 40.8518i 0.872352 1.51096i
\(732\) 0 0
\(733\) 1.82843 + 3.16693i 0.0675345 + 0.116973i 0.897815 0.440372i \(-0.145153\pi\)
−0.830281 + 0.557345i \(0.811820\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −16.6569 28.8505i −0.613563 1.06272i
\(738\) 0 0
\(739\) −5.58579 + 9.67487i −0.205476 + 0.355896i −0.950284 0.311383i \(-0.899208\pi\)
0.744808 + 0.667279i \(0.232541\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 19.2426 0.705944 0.352972 0.935634i \(-0.385171\pi\)
0.352972 + 0.935634i \(0.385171\pi\)
\(744\) 0 0
\(745\) 3.32843 5.76500i 0.121944 0.211213i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 8.41421 + 20.6105i 0.307449 + 0.753092i
\(750\) 0 0
\(751\) 6.00000 + 10.3923i 0.218943 + 0.379221i 0.954485 0.298259i \(-0.0964058\pi\)
−0.735542 + 0.677479i \(0.763072\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 16.8284 0.612449
\(756\) 0 0
\(757\) 6.00000 0.218074 0.109037 0.994038i \(-0.465223\pi\)
0.109037 + 0.994038i \(0.465223\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 11.9706 + 20.7336i 0.433933 + 0.751593i 0.997208 0.0746761i \(-0.0237923\pi\)
−0.563275 + 0.826269i \(0.690459\pi\)
\(762\) 0 0
\(763\) −6.99390 + 9.01897i −0.253196 + 0.326509i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −4.00000 + 6.92820i −0.144432 + 0.250163i
\(768\) 0 0
\(769\) −47.2548 −1.70405 −0.852026 0.523499i \(-0.824626\pi\)
−0.852026 + 0.523499i \(0.824626\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 17.8284 30.8797i 0.641244 1.11067i −0.343911 0.939002i \(-0.611752\pi\)
0.985155 0.171665i \(-0.0549147\pi\)
\(774\) 0 0
\(775\) 2.41421 + 4.18154i 0.0867211 + 0.150205i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0.485281 + 0.840532i 0.0173870 + 0.0301152i
\(780\) 0 0
\(781\) −28.9706 + 50.1785i −1.03665 + 1.79553i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 21.3137 0.760719
\(786\) 0 0
\(787\) 2.20711 3.82282i 0.0786749 0.136269i −0.824004 0.566585i \(-0.808264\pi\)
0.902678 + 0.430316i \(0.141598\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −29.6569 4.05845i −1.05448 0.144302i
\(792\) 0 0
\(793\) 4.65685 + 8.06591i 0.165370 + 0.286429i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 12.6863 0.449372 0.224686 0.974431i \(-0.427864\pi\)
0.224686 + 0.974431i \(0.427864\pi\)
\(798\) 0 0
\(799\) 1.25483 0.0443928
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 18.4853 + 32.0174i 0.652331 + 1.12987i