Properties

Label 2268.2.l.n.109.8
Level $2268$
Weight $2$
Character 2268.109
Analytic conductor $18.110$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 2268 = 2^{2} \cdot 3^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2268.l (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(18.1100711784\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \( x^{16} - 9x^{14} + 31x^{12} - 282x^{10} + 1695x^{8} - 3318x^{6} + 4606x^{4} - 4116x^{2} + 2401 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 3^{7} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 109.8
Root \(1.04556 + 0.339889i\) of defining polynomial
Character \(\chi\) \(=\) 2268.109
Dual form 2268.2.l.n.541.8

$q$-expansion

\(f(q)\) \(=\) \(q+3.67687 q^{5} +(-1.07542 - 2.41733i) q^{7} +O(q^{10})\) \(q+3.67687 q^{5} +(-1.07542 - 2.41733i) q^{7} +0.603143 q^{11} +(2.62851 - 4.55271i) q^{13} +(-2.12557 + 3.68159i) q^{17} +(3.68426 + 6.38133i) q^{19} +1.15778 q^{23} +8.51937 q^{25} +(3.98826 + 6.90786i) q^{29} +(-1.57542 - 2.72871i) q^{31} +(-3.95419 - 8.88819i) q^{35} +(0.00266923 + 0.00462323i) q^{37} +(2.00937 - 3.48033i) q^{41} +(-3.66193 - 6.34264i) q^{43} +(6.10863 - 10.5805i) q^{47} +(-4.68693 + 5.19930i) q^{49} +(4.64928 - 8.05279i) q^{53} +2.21768 q^{55} +(3.30760 + 5.72894i) q^{59} +(0.969252 - 1.67879i) q^{61} +(9.66468 - 16.7397i) q^{65} +(-4.31544 - 7.47456i) q^{67} -1.13815 q^{71} +(-5.33511 + 9.24068i) q^{73} +(-0.648634 - 1.45799i) q^{77} +(-2.07275 + 3.59011i) q^{79} +(-6.24088 - 10.8095i) q^{83} +(-7.81544 + 13.5367i) q^{85} +(4.09464 + 7.09212i) q^{89} +(-13.8321 - 1.45787i) q^{91} +(13.5466 + 23.4633i) q^{95} +(6.77935 + 11.7422i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 10 q^{13} + 8 q^{19} - 8 q^{31} - 4 q^{37} - 10 q^{43} - 20 q^{49} - 32 q^{55} + 28 q^{61} + 18 q^{67} - 20 q^{79} - 38 q^{85} - 2 q^{91} + 42 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2268\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(1135\) \(1541\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(e\left(\frac{1}{3}\right)\)

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
\(5\) 3.67687 1.64435 0.822173 0.569238i \(-0.192762\pi\)
0.822173 + 0.569238i \(0.192762\pi\)
\(6\) 0 0
\(7\) −1.07542 2.41733i −0.406472 0.913663i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 0.603143 0.181855 0.0909273 0.995858i \(-0.471017\pi\)
0.0909273 + 0.995858i \(0.471017\pi\)
\(12\) 0 0
\(13\) 2.62851 4.55271i 0.729017 1.26269i −0.228282 0.973595i \(-0.573311\pi\)
0.957299 0.289099i \(-0.0933558\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −2.12557 + 3.68159i −0.515526 + 0.892918i 0.484311 + 0.874896i \(0.339070\pi\)
−0.999838 + 0.0180219i \(0.994263\pi\)
\(18\) 0 0
\(19\) 3.68426 + 6.38133i 0.845228 + 1.46398i 0.885423 + 0.464786i \(0.153869\pi\)
−0.0401954 + 0.999192i \(0.512798\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 1.15778 0.241414 0.120707 0.992688i \(-0.461484\pi\)
0.120707 + 0.992688i \(0.461484\pi\)
\(24\) 0 0
\(25\) 8.51937 1.70387
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 3.98826 + 6.90786i 0.740601 + 1.28276i 0.952222 + 0.305406i \(0.0987922\pi\)
−0.211622 + 0.977352i \(0.567874\pi\)
\(30\) 0 0
\(31\) −1.57542 2.72871i −0.282954 0.490091i 0.689157 0.724612i \(-0.257981\pi\)
−0.972111 + 0.234521i \(0.924648\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −3.95419 8.88819i −0.668380 1.50238i
\(36\) 0 0
\(37\) 0.00266923 + 0.00462323i 0.000438818 + 0.000760055i 0.866245 0.499620i \(-0.166527\pi\)
−0.865806 + 0.500380i \(0.833194\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 2.00937 3.48033i 0.313811 0.543537i −0.665373 0.746511i \(-0.731728\pi\)
0.979184 + 0.202974i \(0.0650609\pi\)
\(42\) 0 0
\(43\) −3.66193 6.34264i −0.558438 0.967244i −0.997627 0.0688488i \(-0.978067\pi\)
0.439189 0.898395i \(-0.355266\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 6.10863 10.5805i 0.891036 1.54332i 0.0524003 0.998626i \(-0.483313\pi\)
0.838635 0.544693i \(-0.183354\pi\)
\(48\) 0 0
\(49\) −4.68693 + 5.19930i −0.669562 + 0.742756i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 4.64928 8.05279i 0.638628 1.10614i −0.347107 0.937826i \(-0.612836\pi\)
0.985734 0.168310i \(-0.0538309\pi\)
\(54\) 0 0
\(55\) 2.21768 0.299032
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 3.30760 + 5.72894i 0.430613 + 0.745844i 0.996926 0.0783462i \(-0.0249640\pi\)
−0.566313 + 0.824190i \(0.691631\pi\)
\(60\) 0 0
\(61\) 0.969252 1.67879i 0.124100 0.214948i −0.797281 0.603609i \(-0.793729\pi\)
0.921381 + 0.388661i \(0.127062\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 9.66468 16.7397i 1.19876 2.07631i
\(66\) 0 0
\(67\) −4.31544 7.47456i −0.527215 0.913163i −0.999497 0.0317155i \(-0.989903\pi\)
0.472282 0.881447i \(-0.343430\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −1.13815 −0.135074 −0.0675370 0.997717i \(-0.521514\pi\)
−0.0675370 + 0.997717i \(0.521514\pi\)
\(72\) 0 0
\(73\) −5.33511 + 9.24068i −0.624427 + 1.08154i 0.364224 + 0.931311i \(0.381334\pi\)
−0.988651 + 0.150228i \(0.951999\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −0.648634 1.45799i −0.0739187 0.166154i
\(78\) 0 0
\(79\) −2.07275 + 3.59011i −0.233203 + 0.403919i −0.958749 0.284254i \(-0.908254\pi\)
0.725546 + 0.688174i \(0.241587\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −6.24088 10.8095i −0.685026 1.18650i −0.973429 0.228990i \(-0.926458\pi\)
0.288403 0.957509i \(-0.406876\pi\)
\(84\) 0 0
\(85\) −7.81544 + 13.5367i −0.847703 + 1.46827i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 4.09464 + 7.09212i 0.434031 + 0.751764i 0.997216 0.0745672i \(-0.0237575\pi\)
−0.563185 + 0.826331i \(0.690424\pi\)
\(90\) 0 0
\(91\) −13.8321 1.45787i −1.45000 0.152827i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 13.5466 + 23.4633i 1.38985 + 2.40729i
\(96\) 0 0
\(97\) 6.77935 + 11.7422i 0.688339 + 1.19224i 0.972375 + 0.233425i \(0.0749932\pi\)
−0.284036 + 0.958814i \(0.591673\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 15.3395 1.52634 0.763169 0.646200i \(-0.223643\pi\)
0.763169 + 0.646200i \(0.223643\pi\)
\(102\) 0 0
\(103\) −4.96066 −0.488789 −0.244394 0.969676i \(-0.578589\pi\)
−0.244394 + 0.969676i \(0.578589\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −3.41399 5.91320i −0.330043 0.571651i 0.652477 0.757808i \(-0.273730\pi\)
−0.982520 + 0.186158i \(0.940396\pi\)
\(108\) 0 0
\(109\) 8.90194 15.4186i 0.852651 1.47684i −0.0261554 0.999658i \(-0.508326\pi\)
0.878807 0.477178i \(-0.158340\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 4.63946 8.03579i 0.436444 0.755943i −0.560968 0.827837i \(-0.689571\pi\)
0.997412 + 0.0718940i \(0.0229043\pi\)
\(114\) 0 0
\(115\) 4.25702 0.396969
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 11.1855 + 1.17892i 1.02537 + 0.108072i
\(120\) 0 0
\(121\) −10.6362 −0.966929
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 12.9403 1.15741
\(126\) 0 0
\(127\) −14.9941 −1.33051 −0.665254 0.746617i \(-0.731677\pi\)
−0.665254 + 0.746617i \(0.731677\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −22.8327 −1.99490 −0.997452 0.0713394i \(-0.977273\pi\)
−0.997452 + 0.0713394i \(0.977273\pi\)
\(132\) 0 0
\(133\) 11.4636 15.7687i 0.994022 1.36732i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −1.52557 −0.130338 −0.0651690 0.997874i \(-0.520759\pi\)
−0.0651690 + 0.997874i \(0.520759\pi\)
\(138\) 0 0
\(139\) −3.31277 + 5.73789i −0.280986 + 0.486681i −0.971628 0.236515i \(-0.923995\pi\)
0.690642 + 0.723197i \(0.257328\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 1.58537 2.74594i 0.132575 0.229627i
\(144\) 0 0
\(145\) 14.6643 + 25.3993i 1.21780 + 2.10930i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 17.7749 1.45618 0.728089 0.685483i \(-0.240409\pi\)
0.728089 + 0.685483i \(0.240409\pi\)
\(150\) 0 0
\(151\) 4.63622 0.377290 0.188645 0.982045i \(-0.439590\pi\)
0.188645 + 0.982045i \(0.439590\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −5.79262 10.0331i −0.465275 0.805880i
\(156\) 0 0
\(157\) −1.70660 2.95592i −0.136202 0.235908i 0.789854 0.613295i \(-0.210156\pi\)
−0.926056 + 0.377387i \(0.876823\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −1.24511 2.79874i −0.0981281 0.220571i
\(162\) 0 0
\(163\) 7.55012 + 13.0772i 0.591371 + 1.02428i 0.994048 + 0.108942i \(0.0347464\pi\)
−0.402677 + 0.915342i \(0.631920\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 2.85782 4.94988i 0.221144 0.383033i −0.734011 0.679137i \(-0.762354\pi\)
0.955156 + 0.296104i \(0.0956875\pi\)
\(168\) 0 0
\(169\) −7.31811 12.6753i −0.562931 0.975026i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 0.948157 1.64226i 0.0720871 0.124858i −0.827729 0.561128i \(-0.810367\pi\)
0.899816 + 0.436270i \(0.143701\pi\)
\(174\) 0 0
\(175\) −9.16193 20.5941i −0.692576 1.55677i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −7.29747 + 12.6396i −0.545438 + 0.944727i 0.453141 + 0.891439i \(0.350304\pi\)
−0.998579 + 0.0532881i \(0.983030\pi\)
\(180\) 0 0
\(181\) 7.89857 0.587096 0.293548 0.955944i \(-0.405164\pi\)
0.293548 + 0.955944i \(0.405164\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0.00981439 + 0.0169990i 0.000721569 + 0.00124979i
\(186\) 0 0
\(187\) −1.28202 + 2.22053i −0.0937508 + 0.162381i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −4.23670 + 7.33818i −0.306557 + 0.530972i −0.977607 0.210440i \(-0.932510\pi\)
0.671050 + 0.741412i \(0.265844\pi\)
\(192\) 0 0
\(193\) 3.48300 + 6.03273i 0.250712 + 0.434246i 0.963722 0.266908i \(-0.0860020\pi\)
−0.713010 + 0.701154i \(0.752669\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −16.2371 −1.15685 −0.578424 0.815736i \(-0.696332\pi\)
−0.578424 + 0.815736i \(0.696332\pi\)
\(198\) 0 0
\(199\) −7.35153 + 12.7332i −0.521136 + 0.902634i 0.478562 + 0.878054i \(0.341158\pi\)
−0.999698 + 0.0245800i \(0.992175\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 12.4095 17.0698i 0.870976 1.19806i
\(204\) 0 0
\(205\) 7.38819 12.7967i 0.516014 0.893762i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 2.22214 + 3.84886i 0.153709 + 0.266231i
\(210\) 0 0
\(211\) 8.41053 14.5675i 0.579005 1.00287i −0.416589 0.909095i \(-0.636775\pi\)
0.995594 0.0937708i \(-0.0298921\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −13.4644 23.3211i −0.918266 1.59048i
\(216\) 0 0
\(217\) −4.90194 + 6.74283i −0.332766 + 0.457733i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 11.1741 + 19.3542i 0.751655 + 1.30190i
\(222\) 0 0
\(223\) 3.45799 + 5.98942i 0.231564 + 0.401081i 0.958269 0.285869i \(-0.0922823\pi\)
−0.726704 + 0.686950i \(0.758949\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 6.99634 0.464363 0.232182 0.972672i \(-0.425414\pi\)
0.232182 + 0.972672i \(0.425414\pi\)
\(228\) 0 0
\(229\) −2.82700 −0.186813 −0.0934066 0.995628i \(-0.529776\pi\)
−0.0934066 + 0.995628i \(0.529776\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 11.1679 + 19.3434i 0.731635 + 1.26723i 0.956184 + 0.292766i \(0.0945756\pi\)
−0.224550 + 0.974463i \(0.572091\pi\)
\(234\) 0 0
\(235\) 22.4606 38.9030i 1.46517 2.53775i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −0.954829 + 1.65381i −0.0617628 + 0.106976i −0.895253 0.445557i \(-0.853006\pi\)
0.833491 + 0.552534i \(0.186339\pi\)
\(240\) 0 0
\(241\) −19.6870 −1.26815 −0.634077 0.773270i \(-0.718620\pi\)
−0.634077 + 0.773270i \(0.718620\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −17.2332 + 19.1171i −1.10099 + 1.22135i
\(246\) 0 0
\(247\) 38.7365 2.46474
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 12.2990 0.776306 0.388153 0.921595i \(-0.373113\pi\)
0.388153 + 0.921595i \(0.373113\pi\)
\(252\) 0 0
\(253\) 0.698309 0.0439023
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −11.4242 −0.712622 −0.356311 0.934367i \(-0.615966\pi\)
−0.356311 + 0.934367i \(0.615966\pi\)
\(258\) 0 0
\(259\) 0.00830532 0.0114243i 0.000516067 0.000709873i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 19.3109 1.19076 0.595380 0.803445i \(-0.297002\pi\)
0.595380 + 0.803445i \(0.297002\pi\)
\(264\) 0 0
\(265\) 17.0948 29.6091i 1.05012 1.81887i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 4.00745 6.94110i 0.244338 0.423206i −0.717607 0.696448i \(-0.754763\pi\)
0.961945 + 0.273242i \(0.0880959\pi\)
\(270\) 0 0
\(271\) 2.96658 + 5.13827i 0.180207 + 0.312128i 0.941951 0.335750i \(-0.108990\pi\)
−0.761744 + 0.647878i \(0.775657\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 5.13840 0.309857
\(276\) 0 0
\(277\) −12.0554 −0.724336 −0.362168 0.932113i \(-0.617963\pi\)
−0.362168 + 0.932113i \(0.617963\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 9.73700 + 16.8650i 0.580861 + 1.00608i 0.995378 + 0.0960386i \(0.0306172\pi\)
−0.414517 + 0.910042i \(0.636049\pi\)
\(282\) 0 0
\(283\) 14.3518 + 24.8581i 0.853127 + 1.47766i 0.878372 + 0.477977i \(0.158630\pi\)
−0.0252457 + 0.999681i \(0.508037\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −10.5740 1.11448i −0.624165 0.0657854i
\(288\) 0 0
\(289\) −0.536086 0.928529i −0.0315345 0.0546193i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 11.3503 19.6593i 0.663090 1.14851i −0.316709 0.948523i \(-0.602578\pi\)
0.979799 0.199983i \(-0.0640888\pi\)
\(294\) 0 0
\(295\) 12.1616 + 21.0646i 0.708077 + 1.22643i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 3.04324 5.27105i 0.175995 0.304833i
\(300\) 0 0
\(301\) −11.3941 + 15.6731i −0.656746 + 0.903382i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 3.56381 6.17271i 0.204063 0.353448i
\(306\) 0 0
\(307\) −27.9486 −1.59511 −0.797555 0.603246i \(-0.793874\pi\)
−0.797555 + 0.603246i \(0.793874\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −7.64908 13.2486i −0.433739 0.751259i 0.563452 0.826149i \(-0.309473\pi\)
−0.997192 + 0.0748898i \(0.976139\pi\)
\(312\) 0 0
\(313\) −1.67051 + 2.89341i −0.0944230 + 0.163545i −0.909368 0.415993i \(-0.863434\pi\)
0.814945 + 0.579539i \(0.196767\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −4.50722 + 7.80673i −0.253151 + 0.438470i −0.964392 0.264479i \(-0.914800\pi\)
0.711241 + 0.702948i \(0.248133\pi\)
\(318\) 0 0
\(319\) 2.40549 + 4.16643i 0.134682 + 0.233275i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −31.3246 −1.74295
\(324\) 0 0
\(325\) 22.3932 38.7862i 1.24215 2.15147i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −32.1458 3.38809i −1.77226 0.186791i
\(330\) 0 0
\(331\) −9.14760 + 15.8441i −0.502797 + 0.870870i 0.497197 + 0.867637i \(0.334362\pi\)
−0.999995 + 0.00323307i \(0.998971\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −15.8673 27.4830i −0.866924 1.50156i
\(336\) 0 0
\(337\) −0.868823 + 1.50485i −0.0473278 + 0.0819741i −0.888719 0.458453i \(-0.848404\pi\)
0.841391 + 0.540427i \(0.181737\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −0.950206 1.64580i −0.0514565 0.0891253i
\(342\) 0 0
\(343\) 17.6088 + 5.73840i 0.950787 + 0.309845i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −0.546358 0.946319i −0.0293300 0.0508011i 0.850988 0.525185i \(-0.176004\pi\)
−0.880318 + 0.474384i \(0.842671\pi\)
\(348\) 0 0
\(349\) −4.70096 8.14231i −0.251637 0.435848i 0.712340 0.701835i \(-0.247636\pi\)
−0.963977 + 0.265987i \(0.914302\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −19.2910 −1.02676 −0.513378 0.858163i \(-0.671606\pi\)
−0.513378 + 0.858163i \(0.671606\pi\)
\(354\) 0 0
\(355\) −4.18484 −0.222108
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 2.94976 + 5.10914i 0.155682 + 0.269650i 0.933307 0.359079i \(-0.116909\pi\)
−0.777625 + 0.628729i \(0.783576\pi\)
\(360\) 0 0
\(361\) −17.6476 + 30.5665i −0.928820 + 1.60876i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −19.6165 + 33.9768i −1.02677 + 1.77843i
\(366\) 0 0
\(367\) 10.9660 0.572421 0.286210 0.958167i \(-0.407604\pi\)
0.286210 + 0.958167i \(0.407604\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −24.4662 2.57867i −1.27022 0.133878i
\(372\) 0 0
\(373\) −31.9381 −1.65369 −0.826847 0.562428i \(-0.809868\pi\)
−0.826847 + 0.562428i \(0.809868\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 41.9326 2.15964
\(378\) 0 0
\(379\) −14.4354 −0.741495 −0.370747 0.928734i \(-0.620898\pi\)
−0.370747 + 0.928734i \(0.620898\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −17.7201 −0.905456 −0.452728 0.891649i \(-0.649549\pi\)
−0.452728 + 0.891649i \(0.649549\pi\)
\(384\) 0 0
\(385\) −2.38494 5.36085i −0.121548 0.273214i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −18.9750 −0.962072 −0.481036 0.876701i \(-0.659739\pi\)
−0.481036 + 0.876701i \(0.659739\pi\)
\(390\) 0 0
\(391\) −2.46095 + 4.26249i −0.124455 + 0.215563i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −7.62124 + 13.2004i −0.383466 + 0.664183i
\(396\) 0 0
\(397\) −10.5889 18.3405i −0.531440 0.920482i −0.999327 0.0366930i \(-0.988318\pi\)
0.467886 0.883789i \(-0.345016\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −14.7808 −0.738116 −0.369058 0.929406i \(-0.620320\pi\)
−0.369058 + 0.929406i \(0.620320\pi\)
\(402\) 0 0
\(403\) −16.5640 −0.825114
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0.00160993 + 0.00278847i 7.98011e−5 + 0.000138219i
\(408\) 0 0
\(409\) 1.86575 + 3.23158i 0.0922554 + 0.159791i 0.908460 0.417972i \(-0.137259\pi\)
−0.816204 + 0.577763i \(0.803926\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 10.2916 14.1566i 0.506418 0.696600i
\(414\) 0 0
\(415\) −22.9469 39.7452i −1.12642 1.95102i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 14.1678 24.5393i 0.692142 1.19883i −0.278993 0.960293i \(-0.590001\pi\)
0.971135 0.238532i \(-0.0766661\pi\)
\(420\) 0 0
\(421\) −8.09776 14.0257i −0.394661 0.683572i 0.598397 0.801200i \(-0.295805\pi\)
−0.993058 + 0.117627i \(0.962471\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −18.1085 + 31.3649i −0.878392 + 1.52142i
\(426\) 0 0
\(427\) −5.10055 0.537585i −0.246833 0.0260156i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −13.5528 + 23.4741i −0.652815 + 1.13071i 0.329622 + 0.944113i \(0.393079\pi\)
−0.982437 + 0.186595i \(0.940255\pi\)
\(432\) 0 0
\(433\) −11.5028 −0.552789 −0.276394 0.961044i \(-0.589140\pi\)
−0.276394 + 0.961044i \(0.589140\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 4.26558 + 7.38819i 0.204050 + 0.353425i
\(438\) 0 0
\(439\) 1.43357 2.48301i 0.0684205 0.118508i −0.829786 0.558082i \(-0.811537\pi\)
0.898206 + 0.439574i \(0.144871\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −4.42151 + 7.65827i −0.210072 + 0.363855i −0.951737 0.306915i \(-0.900703\pi\)
0.741665 + 0.670771i \(0.234037\pi\)
\(444\) 0 0
\(445\) 15.0555 + 26.0768i 0.713697 + 1.23616i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 40.5033 1.91147 0.955735 0.294229i \(-0.0950629\pi\)
0.955735 + 0.294229i \(0.0950629\pi\)
\(450\) 0 0
\(451\) 1.21194 2.09914i 0.0570680 0.0988446i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −50.8590 5.36041i −2.38431 0.251300i
\(456\) 0 0
\(457\) −19.4049 + 33.6103i −0.907723 + 1.57222i −0.0905025 + 0.995896i \(0.528847\pi\)
−0.817220 + 0.576326i \(0.804486\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 16.1328 + 27.9428i 0.751378 + 1.30142i 0.947155 + 0.320776i \(0.103944\pi\)
−0.195777 + 0.980648i \(0.562723\pi\)
\(462\) 0 0
\(463\) −16.7430 + 28.9997i −0.778112 + 1.34773i 0.154917 + 0.987927i \(0.450489\pi\)
−0.933029 + 0.359802i \(0.882844\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 5.04280 + 8.73438i 0.233353 + 0.404179i 0.958793 0.284107i \(-0.0916970\pi\)
−0.725440 + 0.688286i \(0.758364\pi\)
\(468\) 0 0
\(469\) −13.4275 + 18.4701i −0.620026 + 0.852872i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −2.20867 3.82552i −0.101555 0.175898i
\(474\) 0 0
\(475\) 31.3876 + 54.3649i 1.44016 + 2.49443i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −8.59519 −0.392724 −0.196362 0.980531i \(-0.562913\pi\)
−0.196362 + 0.980531i \(0.562913\pi\)
\(480\) 0 0
\(481\) 0.0280643 0.00127962
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 24.9268 + 43.1745i 1.13187 + 1.96045i
\(486\) 0 0
\(487\) −0.298843 + 0.517612i −0.0135419 + 0.0234552i −0.872717 0.488227i \(-0.837644\pi\)
0.859175 + 0.511682i \(0.170977\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −17.1521 + 29.7084i −0.774066 + 1.34072i 0.161253 + 0.986913i \(0.448447\pi\)
−0.935318 + 0.353808i \(0.884887\pi\)
\(492\) 0 0
\(493\) −33.9092 −1.52720
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 1.22400 + 2.75129i 0.0549038 + 0.123412i
\(498\) 0 0
\(499\) 30.0494 1.34520 0.672598 0.740008i \(-0.265178\pi\)
0.672598 + 0.740008i \(0.265178\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −18.5650 −0.827773 −0.413887 0.910328i \(-0.635829\pi\)
−0.413887 + 0.910328i \(0.635829\pi\)
\(504\) 0 0
\(505\) 56.4013 2.50983
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 7.01815 0.311074 0.155537 0.987830i \(-0.450289\pi\)
0.155537 + 0.987830i \(0.450289\pi\)
\(510\) 0 0
\(511\) 28.0752 + 2.95906i 1.24198 + 0.130901i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −18.2397 −0.803738
\(516\) 0 0
\(517\) 3.68438 6.38154i 0.162039 0.280660i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −15.0742 + 26.1092i −0.660411 + 1.14387i 0.320096 + 0.947385i \(0.396285\pi\)
−0.980508 + 0.196481i \(0.937049\pi\)
\(522\) 0 0
\(523\) −14.1726 24.5476i −0.619724 1.07339i −0.989536 0.144287i \(-0.953911\pi\)
0.369812 0.929107i \(-0.379422\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 13.3947 0.583481
\(528\) 0 0
\(529\) −21.6595 −0.941719
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −10.5633 18.2962i −0.457547 0.792495i
\(534\) 0 0
\(535\) −12.5528 21.7421i −0.542704 0.939991i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −2.82689 + 3.13592i −0.121763 + 0.135074i
\(540\) 0 0
\(541\) −14.5245 25.1572i −0.624458 1.08159i −0.988645 0.150268i \(-0.951986\pi\)
0.364187 0.931326i \(-0.381347\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 32.7313 56.6922i 1.40205 2.42843i
\(546\) 0 0
\(547\) −8.68455 15.0421i −0.371324 0.643153i 0.618445 0.785828i \(-0.287763\pi\)
−0.989770 + 0.142675i \(0.954430\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −29.3876 + 50.9008i −1.25195 + 2.16844i
\(552\) 0 0
\(553\) 10.9076 + 1.14963i 0.463837 + 0.0488873i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −19.5927 + 33.9355i −0.830169 + 1.43789i 0.0677355 + 0.997703i \(0.478423\pi\)
−0.897904 + 0.440191i \(0.854911\pi\)
\(558\) 0 0
\(559\) −38.5016 −1.62844
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 19.2039 + 33.2622i 0.809349 + 1.40183i 0.913316 + 0.407252i \(0.133513\pi\)
−0.103967 + 0.994581i \(0.533154\pi\)
\(564\) 0 0
\(565\) 17.0587 29.5465i 0.717665 1.24303i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 4.54032 7.86407i 0.190340 0.329679i −0.755023 0.655698i \(-0.772374\pi\)
0.945363 + 0.326020i \(0.105708\pi\)
\(570\) 0 0
\(571\) 18.5274 + 32.0904i 0.775347 + 1.34294i 0.934599 + 0.355702i \(0.115758\pi\)
−0.159253 + 0.987238i \(0.550908\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 9.86358 0.411340
\(576\) 0 0
\(577\) 1.04241 1.80550i 0.0433960 0.0751641i −0.843512 0.537111i \(-0.819516\pi\)
0.886908 + 0.461947i \(0.152849\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −19.4186 + 26.7110i −0.805617 + 1.10816i
\(582\) 0 0
\(583\) 2.80418 4.85699i 0.116137 0.201156i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −4.75919 8.24316i −0.196433 0.340232i 0.750936 0.660374i \(-0.229602\pi\)
−0.947369 + 0.320143i \(0.896269\pi\)
\(588\) 0 0
\(589\) 11.6085 20.1066i 0.478322 0.828477i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −7.63267 13.2202i −0.313436 0.542887i 0.665668 0.746248i \(-0.268147\pi\)
−0.979104 + 0.203361i \(0.934814\pi\)
\(594\) 0 0
\(595\) 41.1276 + 4.33475i 1.68607 + 0.177707i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −10.0597 17.4240i −0.411030 0.711924i 0.583973 0.811773i \(-0.301497\pi\)
−0.995003 + 0.0998490i \(0.968164\pi\)
\(600\) 0 0
\(601\) −10.1529 17.5854i −0.414146 0.717322i 0.581192 0.813766i \(-0.302586\pi\)
−0.995338 + 0.0964440i \(0.969253\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −39.1080 −1.58997
\(606\) 0 0
\(607\) −2.07298 −0.0841396 −0.0420698 0.999115i \(-0.513395\pi\)
−0.0420698 + 0.999115i \(0.513395\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −32.1132 55.6217i −1.29916 2.25021i
\(612\) 0 0
\(613\) −1.10053 + 1.90618i −0.0444502 + 0.0769900i −0.887395 0.461011i \(-0.847487\pi\)
0.842944 + 0.538001i \(0.180820\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 21.1904 36.7029i 0.853095 1.47760i −0.0253061 0.999680i \(-0.508056\pi\)
0.878401 0.477924i \(-0.158611\pi\)
\(618\) 0 0
\(619\) 13.8707 0.557511 0.278756 0.960362i \(-0.410078\pi\)
0.278756 + 0.960362i \(0.410078\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 12.7405 17.5251i 0.510438 0.702129i
\(624\) 0 0
\(625\) 4.98282 0.199313
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −0.0226945 −0.000904889
\(630\) 0 0
\(631\) 45.1845 1.79876 0.899382 0.437163i \(-0.144017\pi\)
0.899382 + 0.437163i \(0.144017\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −55.1312 −2.18782
\(636\) 0 0
\(637\) 11.3512 + 35.0046i 0.449753 + 1.38693i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 26.5128 1.04719 0.523597 0.851966i \(-0.324590\pi\)
0.523597 + 0.851966i \(0.324590\pi\)
\(642\) 0 0
\(643\) 24.3184 42.1207i 0.959024 1.66108i 0.234145 0.972202i \(-0.424771\pi\)
0.724879 0.688876i \(-0.241896\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 10.7224 18.5717i 0.421540 0.730128i −0.574551 0.818469i \(-0.694823\pi\)
0.996090 + 0.0883409i \(0.0281565\pi\)
\(648\) 0 0
\(649\) 1.99496 + 3.45537i 0.0783090 + 0.135635i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 3.48991 0.136571 0.0682854 0.997666i \(-0.478247\pi\)
0.0682854 + 0.997666i \(0.478247\pi\)
\(654\) 0 0
\(655\) −83.9529 −3.28031
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 18.2754 + 31.6539i 0.711908 + 1.23306i 0.964140 + 0.265394i \(0.0855021\pi\)
−0.252232 + 0.967667i \(0.581165\pi\)
\(660\) 0 0
\(661\) 2.78748 + 4.82806i 0.108420 + 0.187790i 0.915131 0.403158i \(-0.132087\pi\)
−0.806710 + 0.590947i \(0.798754\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 42.1502 57.9794i 1.63452 2.24835i
\(666\) 0 0
\(667\) 4.61753 + 7.99780i 0.178792 + 0.309676i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0.584598 1.01255i 0.0225682 0.0390892i
\(672\) 0 0
\(673\) 1.25661 + 2.17652i 0.0484389 + 0.0838986i 0.889228 0.457464i \(-0.151242\pi\)
−0.840789 + 0.541362i \(0.817909\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −15.8606 + 27.4714i −0.609574 + 1.05581i 0.381737 + 0.924271i \(0.375326\pi\)
−0.991311 + 0.131542i \(0.958007\pi\)
\(678\) 0 0
\(679\) 21.0940 29.0157i 0.809514 1.11352i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −21.4275 + 37.1136i −0.819902 + 1.42011i 0.0858521 + 0.996308i \(0.472639\pi\)
−0.905754 + 0.423804i \(0.860695\pi\)
\(684\) 0 0
\(685\) −5.60932 −0.214321
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −24.4413 42.3336i −0.931141 1.61278i
\(690\) 0 0
\(691\) 7.38187 12.7858i 0.280820 0.486394i −0.690767 0.723077i \(-0.742727\pi\)
0.971587 + 0.236683i \(0.0760604\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −12.1806 + 21.0975i −0.462037 + 0.800272i
\(696\) 0 0
\(697\) 8.54211 + 14.7954i 0.323556 + 0.560415i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −19.8352 −0.749167 −0.374583 0.927193i \(-0.622214\pi\)
−0.374583 + 0.927193i \(0.622214\pi\)
\(702\) 0 0
\(703\) −0.0196683 + 0.0340664i −0.000741802 + 0.00128484i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −16.4964 37.0806i −0.620413 1.39456i
\(708\) 0 0
\(709\) −5.10292 + 8.83852i −0.191644 + 0.331937i −0.945795 0.324763i \(-0.894715\pi\)
0.754151 + 0.656701i \(0.228049\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −1.82400 3.15926i −0.0683092 0.118315i
\(714\) 0 0
\(715\) 5.82919 10.0965i 0.217999 0.377586i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −16.2769 28.1924i −0.607025 1.05140i −0.991728 0.128358i \(-0.959029\pi\)
0.384703 0.923040i \(-0.374304\pi\)
\(720\) 0 0
\(721\) 5.33481 + 11.9915i 0.198679 + 0.446588i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 33.9774 + 58.8506i 1.26189 + 2.18566i
\(726\) 0 0
\(727\) −7.65095 13.2518i −0.283758 0.491483i 0.688549 0.725190i \(-0.258248\pi\)
−0.972307 + 0.233706i \(0.924915\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 31.1347 1.15156
\(732\) 0 0
\(733\) −8.69354 −0.321103 −0.160552 0.987027i \(-0.551327\pi\)
−0.160552 + 0.987027i \(0.551327\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −2.60283 4.50823i −0.0958764 0.166063i
\(738\) 0 0
\(739\) −6.61922 + 11.4648i −0.243492 + 0.421740i −0.961707 0.274081i \(-0.911626\pi\)
0.718215 + 0.695822i \(0.244960\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −10.7693 + 18.6530i −0.395089 + 0.684314i −0.993112 0.117165i \(-0.962619\pi\)
0.598024 + 0.801478i \(0.295953\pi\)
\(744\) 0 0
\(745\) 65.3561 2.39446
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −10.6227 + 14.6119i −0.388143 + 0.533908i
\(750\) 0 0
\(751\) 39.6483 1.44679 0.723393 0.690437i \(-0.242582\pi\)
0.723393 + 0.690437i \(0.242582\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 17.0468 0.620395
\(756\) 0 0
\(757\) 13.0719 0.475108 0.237554 0.971374i \(-0.423654\pi\)
0.237554 + 0.971374i \(0.423654\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −18.3429 −0.664930 −0.332465 0.943116i \(-0.607880\pi\)
−0.332465 + 0.943116i \(0.607880\pi\)
\(762\) 0 0
\(763\) −46.8452 4.93737i −1.69591 0.178745i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 34.7763 1.25570
\(768\) 0 0
\(769\) 7.46351 12.9272i 0.269141 0.466166i −0.699499 0.714633i \(-0.746594\pi\)
0.968640 + 0.248467i \(0.0799269\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −14.7818 + 25.6029i −0.531666 + 0.920873i 0.467651 + 0.883913i \(0.345100\pi\)
−0.999317 + 0.0369592i \(0.988233\pi\)
\(774\) 0 0
\(775\) −13.4216 23.2469i −0.482118 0.835054i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 29.6122 1.06097
\(780\) 0 0
\(781\) −0.686470 −0.0245638
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −6.27495 10.8685i −0.223962 0.387914i
\(786\) 0 0
\(787\) 4.66430 + 8.07880i 0.166264 + 0.287978i 0.937104 0.349052i \(-0.113496\pi\)
−0.770839 + 0.637030i \(0.780163\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −24.4145 2.57323i −0.868080 0.0914935i
\(792\) 0 0
\(793\) −5.09537 8.82545i −0.180942 0.313401i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 11.9334 20.6692i 0.422701 0.732140i −0.573502 0.819204i \(-0.694415\pi\)
0.996203 + 0.0870647i \(0.0277487\pi\)
\(798\) 0 0
\(799\) 25.9686 + 44.9790i 0.918705 + 1.59124i
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\)