Properties

Label 560.2.q.b.81.1
Level $560$
Weight $2$
Character 560.81
Analytic conductor $4.472$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 560.q (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.47162251319\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 70)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 81.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 560.81
Dual form 560.2.q.b.401.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.00000 + 1.73205i) q^{3} +(-0.500000 - 0.866025i) q^{5} +(2.00000 - 1.73205i) q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(-1.00000 + 1.73205i) q^{3} +(-0.500000 - 0.866025i) q^{5} +(2.00000 - 1.73205i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(1.50000 - 2.59808i) q^{11} -1.00000 q^{13} +2.00000 q^{15} +(3.00000 - 5.19615i) q^{17} +(-0.500000 - 0.866025i) q^{19} +(1.00000 + 5.19615i) q^{21} +(4.50000 + 7.79423i) q^{23} +(-0.500000 + 0.866025i) q^{25} -4.00000 q^{27} +6.00000 q^{29} +(4.00000 - 6.92820i) q^{31} +(3.00000 + 5.19615i) q^{33} +(-2.50000 - 0.866025i) q^{35} +(3.50000 + 6.06218i) q^{37} +(1.00000 - 1.73205i) q^{39} +3.00000 q^{41} -2.00000 q^{43} +(-0.500000 + 0.866025i) q^{45} +(4.50000 + 7.79423i) q^{47} +(1.00000 - 6.92820i) q^{49} +(6.00000 + 10.3923i) q^{51} +(-4.50000 + 7.79423i) q^{53} -3.00000 q^{55} +2.00000 q^{57} +(-4.00000 - 6.92820i) q^{61} +(-2.50000 - 0.866025i) q^{63} +(0.500000 + 0.866025i) q^{65} +(4.00000 - 6.92820i) q^{67} -18.0000 q^{69} +(2.00000 - 3.46410i) q^{73} +(-1.00000 - 1.73205i) q^{75} +(-1.50000 - 7.79423i) q^{77} +(-5.00000 - 8.66025i) q^{79} +(5.50000 - 9.52628i) q^{81} -6.00000 q^{85} +(-6.00000 + 10.3923i) q^{87} +(-3.00000 - 5.19615i) q^{89} +(-2.00000 + 1.73205i) q^{91} +(8.00000 + 13.8564i) q^{93} +(-0.500000 + 0.866025i) q^{95} -10.0000 q^{97} -3.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - 2q^{3} - q^{5} + 4q^{7} - q^{9} + O(q^{10}) \) \( 2q - 2q^{3} - q^{5} + 4q^{7} - q^{9} + 3q^{11} - 2q^{13} + 4q^{15} + 6q^{17} - q^{19} + 2q^{21} + 9q^{23} - q^{25} - 8q^{27} + 12q^{29} + 8q^{31} + 6q^{33} - 5q^{35} + 7q^{37} + 2q^{39} + 6q^{41} - 4q^{43} - q^{45} + 9q^{47} + 2q^{49} + 12q^{51} - 9q^{53} - 6q^{55} + 4q^{57} - 8q^{61} - 5q^{63} + q^{65} + 8q^{67} - 36q^{69} + 4q^{73} - 2q^{75} - 3q^{77} - 10q^{79} + 11q^{81} - 12q^{85} - 12q^{87} - 6q^{89} - 4q^{91} + 16q^{93} - q^{95} - 20q^{97} - 6q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/560\mathbb{Z}\right)^\times\).

\(n\) \(241\) \(337\) \(351\) \(421\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(1\) \(1\)

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
\(3\) −1.00000 + 1.73205i −0.577350 + 1.00000i 0.418432 + 0.908248i \(0.362580\pi\)
−0.995782 + 0.0917517i \(0.970753\pi\)
\(4\) 0 0
\(5\) −0.500000 0.866025i −0.223607 0.387298i
\(6\) 0 0
\(7\) 2.00000 1.73205i 0.755929 0.654654i
\(8\) 0 0
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) 0 0
\(11\) 1.50000 2.59808i 0.452267 0.783349i −0.546259 0.837616i \(-0.683949\pi\)
0.998526 + 0.0542666i \(0.0172821\pi\)
\(12\) 0 0
\(13\) −1.00000 −0.277350 −0.138675 0.990338i \(-0.544284\pi\)
−0.138675 + 0.990338i \(0.544284\pi\)
\(14\) 0 0
\(15\) 2.00000 0.516398
\(16\) 0 0
\(17\) 3.00000 5.19615i 0.727607 1.26025i −0.230285 0.973123i \(-0.573966\pi\)
0.957892 0.287129i \(-0.0927008\pi\)
\(18\) 0 0
\(19\) −0.500000 0.866025i −0.114708 0.198680i 0.802955 0.596040i \(-0.203260\pi\)
−0.917663 + 0.397360i \(0.869927\pi\)
\(20\) 0 0
\(21\) 1.00000 + 5.19615i 0.218218 + 1.13389i
\(22\) 0 0
\(23\) 4.50000 + 7.79423i 0.938315 + 1.62521i 0.768613 + 0.639713i \(0.220947\pi\)
0.169701 + 0.985496i \(0.445720\pi\)
\(24\) 0 0
\(25\) −0.500000 + 0.866025i −0.100000 + 0.173205i
\(26\) 0 0
\(27\) −4.00000 −0.769800
\(28\) 0 0
\(29\) 6.00000 1.11417 0.557086 0.830455i \(-0.311919\pi\)
0.557086 + 0.830455i \(0.311919\pi\)
\(30\) 0 0
\(31\) 4.00000 6.92820i 0.718421 1.24434i −0.243204 0.969975i \(-0.578198\pi\)
0.961625 0.274367i \(-0.0884683\pi\)
\(32\) 0 0
\(33\) 3.00000 + 5.19615i 0.522233 + 0.904534i
\(34\) 0 0
\(35\) −2.50000 0.866025i −0.422577 0.146385i
\(36\) 0 0
\(37\) 3.50000 + 6.06218i 0.575396 + 0.996616i 0.995998 + 0.0893706i \(0.0284856\pi\)
−0.420602 + 0.907245i \(0.638181\pi\)
\(38\) 0 0
\(39\) 1.00000 1.73205i 0.160128 0.277350i
\(40\) 0 0
\(41\) 3.00000 0.468521 0.234261 0.972174i \(-0.424733\pi\)
0.234261 + 0.972174i \(0.424733\pi\)
\(42\) 0 0
\(43\) −2.00000 −0.304997 −0.152499 0.988304i \(-0.548732\pi\)
−0.152499 + 0.988304i \(0.548732\pi\)
\(44\) 0 0
\(45\) −0.500000 + 0.866025i −0.0745356 + 0.129099i
\(46\) 0 0
\(47\) 4.50000 + 7.79423i 0.656392 + 1.13691i 0.981543 + 0.191243i \(0.0612518\pi\)
−0.325150 + 0.945662i \(0.605415\pi\)
\(48\) 0 0
\(49\) 1.00000 6.92820i 0.142857 0.989743i
\(50\) 0 0
\(51\) 6.00000 + 10.3923i 0.840168 + 1.45521i
\(52\) 0 0
\(53\) −4.50000 + 7.79423i −0.618123 + 1.07062i 0.371706 + 0.928351i \(0.378773\pi\)
−0.989828 + 0.142269i \(0.954560\pi\)
\(54\) 0 0
\(55\) −3.00000 −0.404520
\(56\) 0 0
\(57\) 2.00000 0.264906
\(58\) 0 0
\(59\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(60\) 0 0
\(61\) −4.00000 6.92820i −0.512148 0.887066i −0.999901 0.0140840i \(-0.995517\pi\)
0.487753 0.872982i \(-0.337817\pi\)
\(62\) 0 0
\(63\) −2.50000 0.866025i −0.314970 0.109109i
\(64\) 0 0
\(65\) 0.500000 + 0.866025i 0.0620174 + 0.107417i
\(66\) 0 0
\(67\) 4.00000 6.92820i 0.488678 0.846415i −0.511237 0.859440i \(-0.670813\pi\)
0.999915 + 0.0130248i \(0.00414604\pi\)
\(68\) 0 0
\(69\) −18.0000 −2.16695
\(70\) 0 0
\(71\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(72\) 0 0
\(73\) 2.00000 3.46410i 0.234082 0.405442i −0.724923 0.688830i \(-0.758125\pi\)
0.959006 + 0.283387i \(0.0914581\pi\)
\(74\) 0 0
\(75\) −1.00000 1.73205i −0.115470 0.200000i
\(76\) 0 0
\(77\) −1.50000 7.79423i −0.170941 0.888235i
\(78\) 0 0
\(79\) −5.00000 8.66025i −0.562544 0.974355i −0.997274 0.0737937i \(-0.976489\pi\)
0.434730 0.900561i \(-0.356844\pi\)
\(80\) 0 0
\(81\) 5.50000 9.52628i 0.611111 1.05848i
\(82\) 0 0
\(83\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(84\) 0 0
\(85\) −6.00000 −0.650791
\(86\) 0 0
\(87\) −6.00000 + 10.3923i −0.643268 + 1.11417i
\(88\) 0 0
\(89\) −3.00000 5.19615i −0.317999 0.550791i 0.662071 0.749441i \(-0.269678\pi\)
−0.980071 + 0.198650i \(0.936344\pi\)
\(90\) 0 0
\(91\) −2.00000 + 1.73205i −0.209657 + 0.181568i
\(92\) 0 0
\(93\) 8.00000 + 13.8564i 0.829561 + 1.43684i
\(94\) 0 0
\(95\) −0.500000 + 0.866025i −0.0512989 + 0.0888523i
\(96\) 0 0
\(97\) −10.0000 −1.01535 −0.507673 0.861550i \(-0.669494\pi\)
−0.507673 + 0.861550i \(0.669494\pi\)
\(98\) 0 0
\(99\) −3.00000 −0.301511
\(100\) 0 0
\(101\) −6.00000 + 10.3923i −0.597022 + 1.03407i 0.396236 + 0.918149i \(0.370316\pi\)
−0.993258 + 0.115924i \(0.963017\pi\)
\(102\) 0 0
\(103\) −2.00000 3.46410i −0.197066 0.341328i 0.750510 0.660859i \(-0.229808\pi\)
−0.947576 + 0.319531i \(0.896475\pi\)
\(104\) 0 0
\(105\) 4.00000 3.46410i 0.390360 0.338062i
\(106\) 0 0
\(107\) −6.00000 10.3923i −0.580042 1.00466i −0.995474 0.0950377i \(-0.969703\pi\)
0.415432 0.909624i \(-0.363630\pi\)
\(108\) 0 0
\(109\) 8.00000 13.8564i 0.766261 1.32720i −0.173316 0.984866i \(-0.555448\pi\)
0.939577 0.342337i \(-0.111218\pi\)
\(110\) 0 0
\(111\) −14.0000 −1.32882
\(112\) 0 0
\(113\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(114\) 0 0
\(115\) 4.50000 7.79423i 0.419627 0.726816i
\(116\) 0 0
\(117\) 0.500000 + 0.866025i 0.0462250 + 0.0800641i
\(118\) 0 0
\(119\) −3.00000 15.5885i −0.275010 1.42899i
\(120\) 0 0
\(121\) 1.00000 + 1.73205i 0.0909091 + 0.157459i
\(122\) 0 0
\(123\) −3.00000 + 5.19615i −0.270501 + 0.468521i
\(124\) 0 0
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) 1.00000 0.0887357 0.0443678 0.999015i \(-0.485873\pi\)
0.0443678 + 0.999015i \(0.485873\pi\)
\(128\) 0 0
\(129\) 2.00000 3.46410i 0.176090 0.304997i
\(130\) 0 0
\(131\) 1.50000 + 2.59808i 0.131056 + 0.226995i 0.924084 0.382190i \(-0.124830\pi\)
−0.793028 + 0.609185i \(0.791497\pi\)
\(132\) 0 0
\(133\) −2.50000 0.866025i −0.216777 0.0750939i
\(134\) 0 0
\(135\) 2.00000 + 3.46410i 0.172133 + 0.298142i
\(136\) 0 0
\(137\) −6.00000 + 10.3923i −0.512615 + 0.887875i 0.487278 + 0.873247i \(0.337990\pi\)
−0.999893 + 0.0146279i \(0.995344\pi\)
\(138\) 0 0
\(139\) 4.00000 0.339276 0.169638 0.985506i \(-0.445740\pi\)
0.169638 + 0.985506i \(0.445740\pi\)
\(140\) 0 0
\(141\) −18.0000 −1.51587
\(142\) 0 0
\(143\) −1.50000 + 2.59808i −0.125436 + 0.217262i
\(144\) 0 0
\(145\) −3.00000 5.19615i −0.249136 0.431517i
\(146\) 0 0
\(147\) 11.0000 + 8.66025i 0.907265 + 0.714286i
\(148\) 0 0
\(149\) 3.00000 + 5.19615i 0.245770 + 0.425685i 0.962348 0.271821i \(-0.0876260\pi\)
−0.716578 + 0.697507i \(0.754293\pi\)
\(150\) 0 0
\(151\) −5.00000 + 8.66025i −0.406894 + 0.704761i −0.994540 0.104357i \(-0.966722\pi\)
0.587646 + 0.809118i \(0.300055\pi\)
\(152\) 0 0
\(153\) −6.00000 −0.485071
\(154\) 0 0
\(155\) −8.00000 −0.642575
\(156\) 0 0
\(157\) −11.5000 + 19.9186i −0.917800 + 1.58968i −0.115050 + 0.993360i \(0.536703\pi\)
−0.802749 + 0.596316i \(0.796630\pi\)
\(158\) 0 0
\(159\) −9.00000 15.5885i −0.713746 1.23625i
\(160\) 0 0
\(161\) 22.5000 + 7.79423i 1.77325 + 0.614271i
\(162\) 0 0
\(163\) 10.0000 + 17.3205i 0.783260 + 1.35665i 0.930033 + 0.367477i \(0.119778\pi\)
−0.146772 + 0.989170i \(0.546888\pi\)
\(164\) 0 0
\(165\) 3.00000 5.19615i 0.233550 0.404520i
\(166\) 0 0
\(167\) −3.00000 −0.232147 −0.116073 0.993241i \(-0.537031\pi\)
−0.116073 + 0.993241i \(0.537031\pi\)
\(168\) 0 0
\(169\) −12.0000 −0.923077
\(170\) 0 0
\(171\) −0.500000 + 0.866025i −0.0382360 + 0.0662266i
\(172\) 0 0
\(173\) −4.50000 7.79423i −0.342129 0.592584i 0.642699 0.766119i \(-0.277815\pi\)
−0.984828 + 0.173534i \(0.944481\pi\)
\(174\) 0 0
\(175\) 0.500000 + 2.59808i 0.0377964 + 0.196396i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −1.50000 + 2.59808i −0.112115 + 0.194189i −0.916623 0.399753i \(-0.869096\pi\)
0.804508 + 0.593942i \(0.202429\pi\)
\(180\) 0 0
\(181\) 2.00000 0.148659 0.0743294 0.997234i \(-0.476318\pi\)
0.0743294 + 0.997234i \(0.476318\pi\)
\(182\) 0 0
\(183\) 16.0000 1.18275
\(184\) 0 0
\(185\) 3.50000 6.06218i 0.257325 0.445700i
\(186\) 0 0
\(187\) −9.00000 15.5885i −0.658145 1.13994i
\(188\) 0 0
\(189\) −8.00000 + 6.92820i −0.581914 + 0.503953i
\(190\) 0 0
\(191\) 6.00000 + 10.3923i 0.434145 + 0.751961i 0.997225 0.0744412i \(-0.0237173\pi\)
−0.563081 + 0.826402i \(0.690384\pi\)
\(192\) 0 0
\(193\) 8.00000 13.8564i 0.575853 0.997406i −0.420096 0.907480i \(-0.638004\pi\)
0.995948 0.0899262i \(-0.0286631\pi\)
\(194\) 0 0
\(195\) −2.00000 −0.143223
\(196\) 0 0
\(197\) 15.0000 1.06871 0.534353 0.845262i \(-0.320555\pi\)
0.534353 + 0.845262i \(0.320555\pi\)
\(198\) 0 0
\(199\) −8.00000 + 13.8564i −0.567105 + 0.982255i 0.429745 + 0.902950i \(0.358603\pi\)
−0.996850 + 0.0793045i \(0.974730\pi\)
\(200\) 0 0
\(201\) 8.00000 + 13.8564i 0.564276 + 0.977356i
\(202\) 0 0
\(203\) 12.0000 10.3923i 0.842235 0.729397i
\(204\) 0 0
\(205\) −1.50000 2.59808i −0.104765 0.181458i
\(206\) 0 0
\(207\) 4.50000 7.79423i 0.312772 0.541736i
\(208\) 0 0
\(209\) −3.00000 −0.207514
\(210\) 0 0
\(211\) −23.0000 −1.58339 −0.791693 0.610920i \(-0.790800\pi\)
−0.791693 + 0.610920i \(0.790800\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 1.00000 + 1.73205i 0.0681994 + 0.118125i
\(216\) 0 0
\(217\) −4.00000 20.7846i −0.271538 1.41095i
\(218\) 0 0
\(219\) 4.00000 + 6.92820i 0.270295 + 0.468165i
\(220\) 0 0
\(221\) −3.00000 + 5.19615i −0.201802 + 0.349531i
\(222\) 0 0
\(223\) −8.00000 −0.535720 −0.267860 0.963458i \(-0.586316\pi\)
−0.267860 + 0.963458i \(0.586316\pi\)
\(224\) 0 0
\(225\) 1.00000 0.0666667
\(226\) 0 0
\(227\) −6.00000 + 10.3923i −0.398234 + 0.689761i −0.993508 0.113761i \(-0.963710\pi\)
0.595274 + 0.803523i \(0.297043\pi\)
\(228\) 0 0
\(229\) 2.00000 + 3.46410i 0.132164 + 0.228914i 0.924510 0.381157i \(-0.124474\pi\)
−0.792347 + 0.610071i \(0.791141\pi\)
\(230\) 0 0
\(231\) 15.0000 + 5.19615i 0.986928 + 0.341882i
\(232\) 0 0
\(233\) 3.00000 + 5.19615i 0.196537 + 0.340411i 0.947403 0.320043i \(-0.103697\pi\)
−0.750867 + 0.660454i \(0.770364\pi\)
\(234\) 0 0
\(235\) 4.50000 7.79423i 0.293548 0.508439i
\(236\) 0 0
\(237\) 20.0000 1.29914
\(238\) 0 0
\(239\) 6.00000 0.388108 0.194054 0.980991i \(-0.437836\pi\)
0.194054 + 0.980991i \(0.437836\pi\)
\(240\) 0 0
\(241\) 0.500000 0.866025i 0.0322078 0.0557856i −0.849472 0.527633i \(-0.823079\pi\)
0.881680 + 0.471848i \(0.156413\pi\)
\(242\) 0 0
\(243\) 5.00000 + 8.66025i 0.320750 + 0.555556i
\(244\) 0 0
\(245\) −6.50000 + 2.59808i −0.415270 + 0.165985i
\(246\) 0 0
\(247\) 0.500000 + 0.866025i 0.0318142 + 0.0551039i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 15.0000 0.946792 0.473396 0.880850i \(-0.343028\pi\)
0.473396 + 0.880850i \(0.343028\pi\)
\(252\) 0 0
\(253\) 27.0000 1.69748
\(254\) 0 0
\(255\) 6.00000 10.3923i 0.375735 0.650791i
\(256\) 0 0
\(257\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(258\) 0 0
\(259\) 17.5000 + 6.06218i 1.08740 + 0.376685i
\(260\) 0 0
\(261\) −3.00000 5.19615i −0.185695 0.321634i
\(262\) 0 0
\(263\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(264\) 0 0
\(265\) 9.00000 0.552866
\(266\) 0 0
\(267\) 12.0000 0.734388
\(268\) 0 0
\(269\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(270\) 0 0
\(271\) −8.00000 13.8564i −0.485965 0.841717i 0.513905 0.857847i \(-0.328199\pi\)
−0.999870 + 0.0161307i \(0.994865\pi\)
\(272\) 0 0
\(273\) −1.00000 5.19615i −0.0605228 0.314485i
\(274\) 0 0
\(275\) 1.50000 + 2.59808i 0.0904534 + 0.156670i
\(276\) 0 0
\(277\) 5.00000 8.66025i 0.300421 0.520344i −0.675810 0.737075i \(-0.736206\pi\)
0.976231 + 0.216731i \(0.0695395\pi\)
\(278\) 0 0
\(279\) −8.00000 −0.478947
\(280\) 0 0
\(281\) −27.0000 −1.61068 −0.805342 0.592810i \(-0.798019\pi\)
−0.805342 + 0.592810i \(0.798019\pi\)
\(282\) 0 0
\(283\) 7.00000 12.1244i 0.416107 0.720718i −0.579437 0.815017i \(-0.696728\pi\)
0.995544 + 0.0942988i \(0.0300609\pi\)
\(284\) 0 0
\(285\) −1.00000 1.73205i −0.0592349 0.102598i
\(286\) 0 0
\(287\) 6.00000 5.19615i 0.354169 0.306719i
\(288\) 0 0
\(289\) −9.50000 16.4545i −0.558824 0.967911i
\(290\) 0 0
\(291\) 10.0000 17.3205i 0.586210 1.01535i
\(292\) 0 0
\(293\) −9.00000 −0.525786 −0.262893 0.964825i \(-0.584677\pi\)
−0.262893 + 0.964825i \(0.584677\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) −6.00000 + 10.3923i −0.348155 + 0.603023i
\(298\) 0 0
\(299\) −4.50000 7.79423i −0.260242 0.450752i
\(300\) 0 0
\(301\) −4.00000 + 3.46410i −0.230556 + 0.199667i
\(302\) 0 0
\(303\) −12.0000 20.7846i −0.689382 1.19404i
\(304\) 0 0
\(305\) −4.00000 + 6.92820i −0.229039 + 0.396708i
\(306\) 0 0
\(307\) −14.0000 −0.799022 −0.399511 0.916728i \(-0.630820\pi\)
−0.399511 + 0.916728i \(0.630820\pi\)
\(308\) 0 0
\(309\) 8.00000 0.455104
\(310\) 0 0
\(311\) −12.0000 + 20.7846i −0.680458 + 1.17859i 0.294384 + 0.955687i \(0.404886\pi\)
−0.974841 + 0.222900i \(0.928448\pi\)
\(312\) 0 0
\(313\) 14.0000 + 24.2487i 0.791327 + 1.37062i 0.925146 + 0.379612i \(0.123943\pi\)
−0.133819 + 0.991006i \(0.542724\pi\)
\(314\) 0 0
\(315\) 0.500000 + 2.59808i 0.0281718 + 0.146385i
\(316\) 0 0
\(317\) −3.00000 5.19615i −0.168497 0.291845i 0.769395 0.638774i \(-0.220558\pi\)
−0.937892 + 0.346929i \(0.887225\pi\)
\(318\) 0 0
\(319\) 9.00000 15.5885i 0.503903 0.872786i
\(320\) 0 0
\(321\) 24.0000 1.33955
\(322\) 0 0
\(323\) −6.00000 −0.333849
\(324\) 0 0
\(325\) 0.500000 0.866025i 0.0277350 0.0480384i
\(326\) 0 0
\(327\) 16.0000 + 27.7128i 0.884802 + 1.53252i
\(328\) 0 0
\(329\) 22.5000 + 7.79423i 1.24047 + 0.429710i
\(330\) 0 0
\(331\) −3.50000 6.06218i −0.192377 0.333207i 0.753660 0.657264i \(-0.228286\pi\)
−0.946038 + 0.324057i \(0.894953\pi\)
\(332\) 0 0
\(333\) 3.50000 6.06218i 0.191799 0.332205i
\(334\) 0 0
\(335\) −8.00000 −0.437087
\(336\) 0 0
\(337\) −22.0000 −1.19842 −0.599208 0.800593i \(-0.704518\pi\)
−0.599208 + 0.800593i \(0.704518\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −12.0000 20.7846i −0.649836 1.12555i
\(342\) 0 0
\(343\) −10.0000 15.5885i −0.539949 0.841698i
\(344\) 0 0
\(345\) 9.00000 + 15.5885i 0.484544 + 0.839254i
\(346\) 0 0
\(347\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(348\) 0 0
\(349\) 26.0000 1.39175 0.695874 0.718164i \(-0.255017\pi\)
0.695874 + 0.718164i \(0.255017\pi\)
\(350\) 0 0
\(351\) 4.00000 0.213504
\(352\) 0 0
\(353\) −6.00000 + 10.3923i −0.319348 + 0.553127i −0.980352 0.197256i \(-0.936797\pi\)
0.661004 + 0.750382i \(0.270130\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 30.0000 + 10.3923i 1.58777 + 0.550019i
\(358\) 0 0
\(359\) 9.00000 + 15.5885i 0.475002 + 0.822727i 0.999590 0.0286287i \(-0.00911406\pi\)
−0.524588 + 0.851356i \(0.675781\pi\)
\(360\) 0 0
\(361\) 9.00000 15.5885i 0.473684 0.820445i
\(362\) 0 0
\(363\) −4.00000 −0.209946
\(364\) 0 0
\(365\) −4.00000 −0.209370
\(366\) 0 0
\(367\) −9.50000 + 16.4545i −0.495896 + 0.858917i −0.999989 0.00473247i \(-0.998494\pi\)
0.504093 + 0.863649i \(0.331827\pi\)
\(368\) 0 0
\(369\) −1.50000 2.59808i −0.0780869 0.135250i
\(370\) 0 0
\(371\) 4.50000 + 23.3827i 0.233628 + 1.21397i
\(372\) 0 0
\(373\) −1.00000 1.73205i −0.0517780 0.0896822i 0.838975 0.544170i \(-0.183156\pi\)
−0.890753 + 0.454488i \(0.849822\pi\)
\(374\) 0 0
\(375\) −1.00000 + 1.73205i −0.0516398 + 0.0894427i
\(376\) 0 0
\(377\) −6.00000 −0.309016
\(378\) 0 0
\(379\) −23.0000 −1.18143 −0.590715 0.806880i \(-0.701154\pi\)
−0.590715 + 0.806880i \(0.701154\pi\)
\(380\) 0 0
\(381\) −1.00000 + 1.73205i −0.0512316 + 0.0887357i
\(382\) 0 0
\(383\) 10.5000 + 18.1865i 0.536525 + 0.929288i 0.999088 + 0.0427020i \(0.0135966\pi\)
−0.462563 + 0.886586i \(0.653070\pi\)
\(384\) 0 0
\(385\) −6.00000 + 5.19615i −0.305788 + 0.264820i
\(386\) 0 0
\(387\) 1.00000 + 1.73205i 0.0508329 + 0.0880451i
\(388\) 0 0
\(389\) 6.00000 10.3923i 0.304212 0.526911i −0.672874 0.739758i \(-0.734940\pi\)
0.977086 + 0.212847i \(0.0682735\pi\)
\(390\) 0 0
\(391\) 54.0000 2.73090
\(392\) 0 0
\(393\) −6.00000 −0.302660
\(394\) 0 0
\(395\) −5.00000 + 8.66025i −0.251577 + 0.435745i
\(396\) 0 0
\(397\) −7.00000 12.1244i −0.351320 0.608504i 0.635161 0.772380i \(-0.280934\pi\)
−0.986481 + 0.163876i \(0.947600\pi\)
\(398\) 0 0
\(399\) 4.00000 3.46410i 0.200250 0.173422i
\(400\) 0 0
\(401\) 13.5000 + 23.3827i 0.674158 + 1.16768i 0.976714 + 0.214544i \(0.0688266\pi\)
−0.302556 + 0.953131i \(0.597840\pi\)
\(402\) 0 0
\(403\) −4.00000 + 6.92820i −0.199254 + 0.345118i
\(404\) 0 0
\(405\) −11.0000 −0.546594
\(406\) 0 0
\(407\) 21.0000 1.04093
\(408\) 0 0
\(409\) −13.0000 + 22.5167i −0.642809 + 1.11338i 0.341994 + 0.939702i \(0.388898\pi\)
−0.984803 + 0.173675i \(0.944436\pi\)
\(410\) 0 0
\(411\) −12.0000 20.7846i −0.591916 1.02523i
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −4.00000 + 6.92820i −0.195881 + 0.339276i
\(418\) 0 0
\(419\) 9.00000 0.439679 0.219839 0.975536i \(-0.429447\pi\)
0.219839 + 0.975536i \(0.429447\pi\)
\(420\) 0 0
\(421\) 2.00000 0.0974740 0.0487370 0.998812i \(-0.484480\pi\)
0.0487370 + 0.998812i \(0.484480\pi\)
\(422\) 0 0
\(423\) 4.50000 7.79423i 0.218797 0.378968i
\(424\) 0 0
\(425\) 3.00000 + 5.19615i 0.145521 + 0.252050i
\(426\) 0 0
\(427\) −20.0000 6.92820i −0.967868 0.335279i
\(428\) 0 0
\(429\) −3.00000 5.19615i −0.144841 0.250873i
\(430\) 0 0
\(431\) 6.00000 10.3923i 0.289010 0.500580i −0.684564 0.728953i \(-0.740007\pi\)
0.973574 + 0.228373i \(0.0733406\pi\)
\(432\) 0 0
\(433\) −40.0000 −1.92228 −0.961139 0.276066i \(-0.910969\pi\)
−0.961139 + 0.276066i \(0.910969\pi\)
\(434\) 0 0
\(435\) 12.0000 0.575356
\(436\) 0 0
\(437\) 4.50000 7.79423i 0.215264 0.372849i
\(438\) 0 0
\(439\) 13.0000 + 22.5167i 0.620456 + 1.07466i 0.989401 + 0.145210i \(0.0463858\pi\)
−0.368945 + 0.929451i \(0.620281\pi\)
\(440\) 0 0
\(441\) −6.50000 + 2.59808i −0.309524 + 0.123718i
\(442\) 0 0
\(443\) 6.00000 + 10.3923i 0.285069 + 0.493753i 0.972626 0.232377i \(-0.0746503\pi\)
−0.687557 + 0.726130i \(0.741317\pi\)
\(444\) 0 0
\(445\) −3.00000 + 5.19615i −0.142214 + 0.246321i
\(446\) 0 0
\(447\) −12.0000 −0.567581
\(448\) 0 0
\(449\) 21.0000 0.991051 0.495526 0.868593i \(-0.334975\pi\)
0.495526 + 0.868593i \(0.334975\pi\)
\(450\) 0 0
\(451\) 4.50000 7.79423i 0.211897 0.367016i
\(452\) 0 0
\(453\) −10.0000 17.3205i −0.469841 0.813788i
\(454\) 0 0
\(455\) 2.50000 + 0.866025i 0.117202 + 0.0405999i
\(456\) 0 0
\(457\) −7.00000 12.1244i −0.327446 0.567153i 0.654558 0.756012i \(-0.272855\pi\)
−0.982004 + 0.188858i \(0.939521\pi\)
\(458\) 0 0
\(459\) −12.0000 + 20.7846i −0.560112 + 0.970143i
\(460\) 0 0
\(461\) −30.0000 −1.39724 −0.698620 0.715493i \(-0.746202\pi\)
−0.698620 + 0.715493i \(0.746202\pi\)
\(462\) 0 0
\(463\) 1.00000 0.0464739 0.0232370 0.999730i \(-0.492603\pi\)
0.0232370 + 0.999730i \(0.492603\pi\)
\(464\) 0 0
\(465\) 8.00000 13.8564i 0.370991 0.642575i
\(466\) 0 0
\(467\) −3.00000 5.19615i −0.138823 0.240449i 0.788228 0.615383i \(-0.210999\pi\)
−0.927052 + 0.374934i \(0.877665\pi\)
\(468\) 0 0
\(469\) −4.00000 20.7846i −0.184703 0.959744i
\(470\) 0 0
\(471\) −23.0000 39.8372i −1.05978 1.83560i
\(472\) 0 0
\(473\) −3.00000 + 5.19615i −0.137940 + 0.238919i
\(474\) 0 0
\(475\) 1.00000 0.0458831
\(476\) 0 0
\(477\) 9.00000 0.412082
\(478\) 0 0
\(479\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(480\) 0 0
\(481\) −3.50000 6.06218i −0.159586 0.276412i
\(482\) 0 0
\(483\) −36.0000 + 31.1769i −1.63806 + 1.41860i
\(484\) 0 0
\(485\) 5.00000 + 8.66025i 0.227038 + 0.393242i
\(486\) 0 0
\(487\) −8.00000 + 13.8564i −0.362515 + 0.627894i −0.988374 0.152042i \(-0.951415\pi\)
0.625859 + 0.779936i \(0.284748\pi\)
\(488\) 0 0
\(489\) −40.0000 −1.80886
\(490\) 0 0
\(491\) −36.0000 −1.62466 −0.812329 0.583200i \(-0.801800\pi\)
−0.812329 + 0.583200i \(0.801800\pi\)
\(492\) 0 0
\(493\) 18.0000 31.1769i 0.810679 1.40414i
\(494\) 0 0
\(495\) 1.50000 + 2.59808i 0.0674200 + 0.116775i
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) −2.00000 3.46410i −0.0895323 0.155074i 0.817781 0.575529i \(-0.195204\pi\)
−0.907314 + 0.420455i \(0.861871\pi\)
\(500\) 0 0
\(501\) 3.00000 5.19615i 0.134030 0.232147i
\(502\) 0 0
\(503\) −24.0000 −1.07011 −0.535054 0.844818i \(-0.679709\pi\)
−0.535054 + 0.844818i \(0.679709\pi\)
\(504\) 0 0
\(505\) 12.0000 0.533993
\(506\) 0 0
\(507\) 12.0000 20.7846i 0.532939 0.923077i
\(508\) 0 0
\(509\) 21.0000 + 36.3731i 0.930809 + 1.61221i 0.781943 + 0.623350i \(0.214229\pi\)
0.148866 + 0.988857i \(0.452438\pi\)
\(510\) 0 0
\(511\) −2.00000 10.3923i −0.0884748 0.459728i
\(512\) 0 0
\(513\) 2.00000 + 3.46410i 0.0883022 + 0.152944i
\(514\) 0 0
\(515\) −2.00000 + 3.46410i −0.0881305 + 0.152647i
\(516\) 0 0
\(517\) 27.0000 1.18746
\(518\) 0 0
\(519\) 18.0000 0.790112
\(520\) 0 0
\(521\) 7.50000 12.9904i 0.328581 0.569119i −0.653650 0.756797i \(-0.726763\pi\)
0.982231 + 0.187678i \(0.0600963\pi\)
\(522\) 0 0
\(523\) −14.0000 24.2487i −0.612177 1.06032i −0.990873 0.134801i \(-0.956961\pi\)
0.378695 0.925521i \(-0.376373\pi\)
\(524\) 0 0
\(525\) −5.00000 1.73205i −0.218218 0.0755929i
\(526\) 0 0
\(527\) −24.0000 41.5692i −1.04546 1.81078i
\(528\) 0 0
\(529\) −29.0000 + 50.2295i −1.26087 + 2.18389i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −3.00000 −0.129944
\(534\) 0 0
\(535\) −6.00000 + 10.3923i −0.259403 + 0.449299i
\(536\) 0 0
\(537\) −3.00000 5.19615i −0.129460 0.224231i
\(538\) 0 0
\(539\) −16.5000 12.9904i −0.710705 0.559535i
\(540\) 0 0
\(541\) −4.00000 6.92820i −0.171973 0.297867i 0.767136 0.641484i \(-0.221681\pi\)
−0.939110 + 0.343617i \(0.888348\pi\)
\(542\) 0 0
\(543\) −2.00000 + 3.46410i −0.0858282 + 0.148659i
\(544\) 0 0
\(545\) −16.0000 −0.685365
\(546\) 0 0
\(547\) −8.00000 −0.342055 −0.171028 0.985266i \(-0.554709\pi\)
−0.171028 + 0.985266i \(0.554709\pi\)
\(548\) 0 0
\(549\) −4.00000 + 6.92820i −0.170716 + 0.295689i
\(550\) 0 0
\(551\) −3.00000 5.19615i −0.127804 0.221364i
\(552\) 0 0
\(553\) −25.0000 8.66025i −1.06311 0.368271i
\(554\) 0 0
\(555\) 7.00000 + 12.1244i 0.297133 + 0.514650i
\(556\) 0 0
\(557\) 4.50000 7.79423i 0.190671 0.330252i −0.754802 0.655953i \(-0.772267\pi\)
0.945473 + 0.325701i \(0.105600\pi\)
\(558\) 0 0
\(559\) 2.00000 0.0845910
\(560\) 0 0
\(561\) 36.0000 1.51992
\(562\) 0 0
\(563\) 21.0000 36.3731i 0.885044 1.53294i 0.0393818 0.999224i \(-0.487461\pi\)
0.845663 0.533718i \(-0.179206\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) −5.50000 28.5788i −0.230978 1.20020i
\(568\) 0 0
\(569\) −10.5000 18.1865i −0.440183 0.762419i 0.557520 0.830164i \(-0.311753\pi\)
−0.997703 + 0.0677445i \(0.978420\pi\)
\(570\) 0 0
\(571\) 10.0000 17.3205i 0.418487 0.724841i −0.577301 0.816532i \(-0.695894\pi\)
0.995788 + 0.0916910i \(0.0292272\pi\)
\(572\) 0 0
\(573\) −24.0000 −1.00261
\(574\) 0 0
\(575\) −9.00000 −0.375326
\(576\) 0 0
\(577\) −22.0000 + 38.1051i −0.915872 + 1.58634i −0.110252 + 0.993904i \(0.535166\pi\)
−0.805620 + 0.592433i \(0.798167\pi\)
\(578\) 0 0
\(579\) 16.0000 + 27.7128i 0.664937 + 1.15171i
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 13.5000 + 23.3827i 0.559113 + 0.968412i
\(584\) 0 0
\(585\) 0.500000 0.866025i 0.0206725 0.0358057i
\(586\) 0 0
\(587\) 24.0000 0.990586 0.495293 0.868726i \(-0.335061\pi\)
0.495293 + 0.868726i \(0.335061\pi\)
\(588\) 0 0
\(589\) −8.00000 −0.329634
\(590\) 0 0
\(591\) −15.0000 + 25.9808i −0.617018 + 1.06871i
\(592\) 0 0
\(593\) −12.0000 20.7846i −0.492781 0.853522i 0.507184 0.861838i \(-0.330686\pi\)
−0.999965 + 0.00831589i \(0.997353\pi\)
\(594\) 0 0
\(595\) −12.0000 + 10.3923i −0.491952 + 0.426043i
\(596\) 0 0
\(597\) −16.0000 27.7128i −0.654836 1.13421i
\(598\) 0 0
\(599\) −21.0000 + 36.3731i −0.858037 + 1.48616i 0.0157622 + 0.999876i \(0.494983\pi\)
−0.873799 + 0.486287i \(0.838351\pi\)
\(600\) 0 0
\(601\) 26.0000 1.06056 0.530281 0.847822i \(-0.322086\pi\)
0.530281 + 0.847822i \(0.322086\pi\)
\(602\) 0 0
\(603\) −8.00000 −0.325785
\(604\) 0 0
\(605\) 1.00000 1.73205i 0.0406558 0.0704179i
\(606\) 0 0
\(607\) −0.500000 0.866025i −0.0202944 0.0351509i 0.855700 0.517472i \(-0.173127\pi\)
−0.875994 + 0.482322i \(0.839794\pi\)
\(608\) 0 0
\(609\) 6.00000 + 31.1769i 0.243132 + 1.26335i
\(610\) 0 0
\(611\) −4.50000 7.79423i −0.182051 0.315321i
\(612\) 0 0
\(613\) −14.5000 + 25.1147i −0.585649 + 1.01437i 0.409145 + 0.912470i \(0.365827\pi\)
−0.994794 + 0.101905i \(0.967506\pi\)
\(614\) 0 0
\(615\) 6.00000 0.241943
\(616\) 0 0
\(617\) −18.0000 −0.724653 −0.362326 0.932051i \(-0.618017\pi\)
−0.362326 + 0.932051i \(0.618017\pi\)
\(618\) 0 0
\(619\) 11.5000 19.9186i 0.462224 0.800595i −0.536847 0.843679i \(-0.680385\pi\)
0.999071 + 0.0430838i \(0.0137183\pi\)
\(620\) 0 0
\(621\) −18.0000 31.1769i −0.722315 1.25109i
\(622\) 0 0
\(623\) −15.0000 5.19615i −0.600962 0.208179i
\(624\) 0 0
\(625\) −0.500000 0.866025i −0.0200000 0.0346410i
\(626\) 0 0
\(627\) 3.00000 5.19615i 0.119808 0.207514i
\(628\) 0 0
\(629\) 42.0000 1.67465
\(630\) 0 0
\(631\) −20.0000 −0.796187 −0.398094 0.917345i \(-0.630328\pi\)
−0.398094 + 0.917345i \(0.630328\pi\)
\(632\) 0 0
\(633\) 23.0000 39.8372i 0.914168 1.58339i
\(634\) 0 0
\(635\) −0.500000 0.866025i −0.0198419 0.0343672i
\(636\) 0 0
\(637\) −1.00000 + 6.92820i −0.0396214 + 0.274505i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −13.5000 + 23.3827i −0.533218 + 0.923561i 0.466029 + 0.884769i \(0.345684\pi\)
−0.999247 + 0.0387913i \(0.987649\pi\)
\(642\) 0 0
\(643\) −2.00000 −0.0788723 −0.0394362 0.999222i \(-0.512556\pi\)
−0.0394362 + 0.999222i \(0.512556\pi\)
\(644\) 0 0
\(645\) −4.00000 −0.157500
\(646\) 0 0
\(647\) 16.5000 28.5788i 0.648682 1.12355i −0.334756 0.942305i \(-0.608654\pi\)
0.983438 0.181245i \(-0.0580128\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) 40.0000 + 13.8564i 1.56772 + 0.543075i
\(652\) 0 0
\(653\) 4.50000 + 7.79423i 0.176099 + 0.305012i 0.940541 0.339680i \(-0.110319\pi\)
−0.764442 + 0.644692i \(0.776986\pi\)
\(654\) 0 0
\(655\) 1.50000 2.59808i 0.0586098 0.101515i
\(656\) 0 0
\(657\) −4.00000 −0.156055
\(658\) 0 0
\(659\) 24.0000 0.934907 0.467454 0.884018i \(-0.345171\pi\)
0.467454 + 0.884018i \(0.345171\pi\)
\(660\) 0 0
\(661\) 14.0000 24.2487i 0.544537 0.943166i −0.454099 0.890951i \(-0.650039\pi\)
0.998636 0.0522143i \(-0.0166279\pi\)
\(662\) 0 0
\(663\) −6.00000 10.3923i −0.233021 0.403604i
\(664\) 0 0
\(665\) 0.500000 + 2.59808i 0.0193892 + 0.100749i
\(666\) 0 0
\(667\) 27.0000 + 46.7654i 1.04544 + 1.81076i
\(668\) 0 0
\(669\) 8.00000 13.8564i 0.309298 0.535720i
\(670\) 0 0
\(671\) −24.0000 −0.926510
\(672\) 0 0
\(673\) −34.0000 −1.31060 −0.655302 0.755367i \(-0.727459\pi\)
−0.655302 + 0.755367i \(0.727459\pi\)
\(674\) 0 0
\(675\) 2.00000 3.46410i 0.0769800 0.133333i
\(676\) 0 0
\(677\) 4.50000 + 7.79423i 0.172949 + 0.299557i 0.939450 0.342687i \(-0.111337\pi\)
−0.766501 + 0.642244i \(0.778004\pi\)
\(678\) 0 0
\(679\) −20.0000 + 17.3205i −0.767530 + 0.664700i
\(680\) 0 0
\(681\) −12.0000 20.7846i −0.459841 0.796468i
\(682\) 0 0
\(683\) 6.00000 10.3923i 0.229584 0.397650i −0.728101 0.685470i \(-0.759597\pi\)
0.957685 + 0.287819i \(0.0929302\pi\)
\(684\) 0 0
\(685\) 12.0000 0.458496
\(686\) 0 0
\(687\) −8.00000 −0.305219
\(688\) 0 0
\(689\) 4.50000 7.79423i 0.171436 0.296936i
\(690\) 0 0
\(691\) 16.0000 + 27.7128i 0.608669 + 1.05425i 0.991460 + 0.130410i \(0.0416295\pi\)
−0.382791 + 0.923835i \(0.625037\pi\)
\(692\) 0 0
\(693\) −6.00000 + 5.19615i −0.227921 + 0.197386i
\(694\) 0 0
\(695\) −2.00000 3.46410i −0.0758643 0.131401i
\(696\) 0 0
\(697\) 9.00000 15.5885i 0.340899 0.590455i
\(698\) 0 0
\(699\) −12.0000 −0.453882
\(700\) 0 0
\(701\) −30.0000 −1.13308 −0.566542 0.824033i \(-0.691719\pi\)
−0.566542 + 0.824033i \(0.691719\pi\)
\(702\) 0 0
\(703\) 3.50000 6.06218i 0.132005 0.228639i
\(704\) 0 0
\(705\) 9.00000 + 15.5885i 0.338960 + 0.587095i
\(706\) 0 0
\(707\) 6.00000 + 31.1769i 0.225653 + 1.17253i
\(708\) 0 0
\(709\) 23.0000 + 39.8372i 0.863783 + 1.49612i 0.868250 + 0.496126i \(0.165245\pi\)
−0.00446726 + 0.999990i \(0.501422\pi\)
\(710\) 0 0
\(711\) −5.00000 + 8.66025i −0.187515 + 0.324785i
\(712\) 0 0
\(713\) 72.0000 2.69642
\(714\) 0 0
\(715\) 3.00000 0.112194
\(716\) 0 0
\(717\) −6.00000 + 10.3923i −0.224074 + 0.388108i
\(718\) 0 0
\(719\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(720\) 0 0
\(721\) −10.0000 3.46410i −0.372419 0.129010i
\(722\) 0 0
\(723\) 1.00000 + 1.73205i 0.0371904 + 0.0644157i
\(724\) 0 0
\(725\) −3.00000 + 5.19615i −0.111417 + 0.192980i
\(726\) 0 0
\(727\) 1.00000 0.0370879 0.0185440 0.999828i \(-0.494097\pi\)
0.0185440 + 0.999828i \(0.494097\pi\)
\(728\) 0 0
\(729\) 13.0000 0.481481
\(730\) 0 0
\(731\) −6.00000 + 10.3923i −0.221918 + 0.384373i
\(732\) 0 0
\(733\) 21.5000 + 37.2391i 0.794121 + 1.37546i 0.923396 + 0.383849i \(0.125402\pi\)
−0.129275 + 0.991609i \(0.541265\pi\)
\(734\) 0 0
\(735\) 2.00000 13.8564i 0.0737711 0.511101i
\(736\) 0 0
\(737\) −12.0000 20.7846i −0.442026 0.765611i
\(738\) 0 0
\(739\) 17.5000 30.3109i 0.643748 1.11500i −0.340841 0.940121i \(-0.610712\pi\)
0.984589 0.174883i \(-0.0559548\pi\)
\(740\) 0 0
\(741\) −2.00000 −0.0734718
\(742\) 0 0
\(743\) 45.0000 1.65089 0.825445 0.564483i \(-0.190924\pi\)
0.825445 + 0.564483i \(0.190924\pi\)
\(744\) 0 0
\(745\) 3.00000 5.19615i 0.109911 0.190372i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −30.0000 10.3923i −1.09618 0.379727i
\(750\) 0 0
\(751\) −5.00000 8.66025i −0.182453 0.316017i 0.760263 0.649616i \(-0.225070\pi\)
−0.942715 + 0.333599i \(0.891737\pi\)
\(752\) 0 0
\(753\) −15.0000 + 25.9808i −0.546630 + 0.946792i
\(754\) 0 0
\(755\) 10.0000 0.363937
\(756\) 0 0
\(757\) 38.0000 1.38113 0.690567 0.723269i \(-0.257361\pi\)
0.690567 + 0.723269i \(0.257361\pi\)
\(758\) 0 0
\(759\) −27.0000 + 46.7654i −0.980038 + 1.69748i
\(760\) 0 0
\(761\) 13.5000 + 23.3827i 0.489375 + 0.847622i 0.999925 0.0122260i \(-0.00389175\pi\)
−0.510551 + 0.859848i \(0.670558\pi\)
\(762\) 0 0
\(763\) −8.00000 41.5692i −0.289619 1.50491i
\(764\) 0 0
\(765\) 3.00000 + 5.19615i 0.108465 + 0.187867i
\(766\) 0 0
\(767\) 0 0
\(768\) 0 0
\(769\) 23.0000 0.829401 0.414701 0.909958i \(-0.363886\pi\)
0.414701 + 0.909958i \(0.363886\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 25.5000 44.1673i 0.917171 1.58859i 0.113480 0.993540i \(-0.463800\pi\)
0.803691 0.595047i \(-0.202867\pi\)
\(774\) 0 0
\(775\) 4.00000 + 6.92820i 0.143684 + 0.248868i
\(776\) 0 0
\(777\) −28.0000 + 24.2487i −1.00449 + 0.869918i
\(778\) 0 0
\(779\) −1.50000 2.59808i −0.0537431 0.0930857i
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) −24.0000 −0.857690
\(784\) 0 0
\(785\) 23.0000 0.820905
\(786\) 0 0
\(787\) −11.0000 + 19.0526i −0.392108 + 0.679150i −0.992727 0.120384i \(-0.961587\pi\)
0.600620 + 0.799535i \(0.294921\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 4.00000 + 6.92820i 0.142044 + 0.246028i
\(794\) 0 0
\(795\) −9.00000 + 15.5885i −0.319197 + 0.552866i
\(796\) 0 0
\(797\) 6.00000 0.212531