Properties

Label 560.2.q.b.401.1
Level $560$
Weight $2$
Character 560.401
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 401.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 560.401
Dual form 560.2.q.b.81.1

$q$-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 \(\left(\mathbb{Z}/560\mathbb{Z}\right)^\times\).

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

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 −0.995782 0.0917517i \(-0.970753\pi\)
0.418432 0.908248i \(-0.362580\pi\)
\(4\) 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 0.998526 0.0542666i \(-0.0172821\pi\)
−0.546259 + 0.837616i \(0.683949\pi\)
\(12\) 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 0.957892 + 0.287129i \(0.0927008\pi\)
−0.230285 + 0.973123i \(0.573966\pi\)
\(18\) 0 0
\(19\) −0.500000 + 0.866025i −0.114708 + 0.198680i −0.917663 0.397360i \(-0.869927\pi\)
0.802955 + 0.596040i \(0.203260\pi\)
\(20\) 0 0
\(21\) 1.00000 5.19615i 0.218218 1.13389i
\(22\) 0 0
\(23\) 4.50000 7.79423i 0.938315 1.62521i 0.169701 0.985496i \(-0.445720\pi\)
0.768613 0.639713i \(-0.220947\pi\)
\(24\) 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 0.961625 + 0.274367i \(0.0884683\pi\)
−0.243204 + 0.969975i \(0.578198\pi\)
\(32\) 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 −0.420602 0.907245i \(-0.638181\pi\)
0.995998 0.0893706i \(-0.0284856\pi\)
\(38\) 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 −0.325150 0.945662i \(-0.605415\pi\)
0.981543 0.191243i \(-0.0612518\pi\)
\(48\) 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 −0.989828 0.142269i \(-0.954560\pi\)
0.371706 0.928351i \(-0.378773\pi\)
\(54\) 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 \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(60\) 0 0
\(61\) −4.00000 + 6.92820i −0.512148 + 0.887066i 0.487753 + 0.872982i \(0.337817\pi\)
−0.999901 + 0.0140840i \(0.995517\pi\)
\(62\) 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 0.999915 0.0130248i \(-0.00414604\pi\)
−0.511237 + 0.859440i \(0.670813\pi\)
\(68\) 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 0.959006 0.283387i \(-0.0914581\pi\)
−0.724923 + 0.688830i \(0.758125\pi\)
\(74\) 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 0.434730 + 0.900561i \(0.356844\pi\)
−0.997274 + 0.0737937i \(0.976489\pi\)
\(80\) 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 −0.980071 0.198650i \(-0.936344\pi\)
0.662071 + 0.749441i \(0.269678\pi\)
\(90\) 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 −0.993258 0.115924i \(-0.963017\pi\)
0.396236 0.918149i \(-0.370316\pi\)
\(102\) 0 0
\(103\) −2.00000 + 3.46410i −0.197066 + 0.341328i −0.947576 0.319531i \(-0.896475\pi\)
0.750510 + 0.660859i \(0.229808\pi\)
\(104\) 0 0
\(105\) 4.00000 + 3.46410i 0.390360 + 0.338062i
\(106\) 0 0
\(107\) −6.00000 + 10.3923i −0.580042 + 1.00466i 0.415432 + 0.909624i \(0.363630\pi\)
−0.995474 + 0.0950377i \(0.969703\pi\)
\(108\) 0 0
\(109\) 8.00000 + 13.8564i 0.766261 + 1.32720i 0.939577 + 0.342337i \(0.111218\pi\)
−0.173316 + 0.984866i \(0.555448\pi\)
\(110\) 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 −0.793028 0.609185i \(-0.791497\pi\)
0.924084 + 0.382190i \(0.124830\pi\)
\(132\) 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 −0.999893 0.0146279i \(-0.995344\pi\)
0.487278 0.873247i \(-0.337990\pi\)
\(138\) 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 −0.716578 0.697507i \(-0.754293\pi\)
0.962348 + 0.271821i \(0.0876260\pi\)
\(150\) 0 0
\(151\) −5.00000 8.66025i −0.406894 0.704761i 0.587646 0.809118i \(-0.300055\pi\)
−0.994540 + 0.104357i \(0.966722\pi\)
\(152\) 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 −0.802749 0.596316i \(-0.796630\pi\)
−0.115050 0.993360i \(-0.536703\pi\)
\(158\) 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 −0.146772 0.989170i \(-0.546888\pi\)
0.930033 0.367477i \(-0.119778\pi\)
\(164\) 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 −0.984828 0.173534i \(-0.944481\pi\)
0.642699 + 0.766119i \(0.277815\pi\)
\(174\) 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 0.804508 0.593942i \(-0.202429\pi\)
−0.916623 + 0.399753i \(0.869096\pi\)
\(180\) 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 −0.563081 0.826402i \(-0.690384\pi\)
0.997225 + 0.0744412i \(0.0237173\pi\)
\(192\) 0 0
\(193\) 8.00000 + 13.8564i 0.575853 + 0.997406i 0.995948 + 0.0899262i \(0.0286631\pi\)
−0.420096 + 0.907480i \(0.638004\pi\)
\(194\) 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 −0.996850 0.0793045i \(-0.974730\pi\)
0.429745 0.902950i \(-0.358603\pi\)
\(200\) 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 0.595274 0.803523i \(-0.297043\pi\)
−0.993508 + 0.113761i \(0.963710\pi\)
\(228\) 0 0
\(229\) 2.00000 3.46410i 0.132164 0.228914i −0.792347 0.610071i \(-0.791141\pi\)
0.924510 + 0.381157i \(0.124474\pi\)
\(230\) 0 0
\(231\) 15.0000 5.19615i 0.986928 0.341882i
\(232\) 0 0
\(233\) 3.00000 5.19615i 0.196537 0.340411i −0.750867 0.660454i \(-0.770364\pi\)
0.947403 + 0.320043i \(0.103697\pi\)
\(234\) 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 0.881680 0.471848i \(-0.156413\pi\)
−0.849472 + 0.527633i \(0.823079\pi\)
\(242\) 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 \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(258\) 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 \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(264\) 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 \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(270\) 0 0
\(271\) −8.00000 + 13.8564i −0.485965 + 0.841717i −0.999870 0.0161307i \(-0.994865\pi\)
0.513905 + 0.857847i \(0.328199\pi\)
\(272\) 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 0.976231 0.216731i \(-0.0695395\pi\)
−0.675810 + 0.737075i \(0.736206\pi\)
\(278\) 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 0.995544 0.0942988i \(-0.0300609\pi\)
−0.579437 + 0.815017i \(0.696728\pi\)
\(284\) 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 −0.974841 0.222900i \(-0.928448\pi\)
0.294384 0.955687i \(-0.404886\pi\)
\(312\) 0 0
\(313\) 14.0000 24.2487i 0.791327 1.37062i −0.133819 0.991006i \(-0.542724\pi\)
0.925146 0.379612i \(-0.123943\pi\)
\(314\) 0 0
\(315\) 0.500000 2.59808i 0.0281718 0.146385i
\(316\) 0 0
\(317\) −3.00000 + 5.19615i −0.168497 + 0.291845i −0.937892 0.346929i \(-0.887225\pi\)
0.769395 + 0.638774i \(0.220558\pi\)
\(318\) 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 −0.946038 0.324057i \(-0.894953\pi\)
0.753660 + 0.657264i \(0.228286\pi\)
\(332\) 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 \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(348\) 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 0.661004 0.750382i \(-0.270130\pi\)
−0.980352 + 0.197256i \(0.936797\pi\)
\(354\) 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 −0.524588 0.851356i \(-0.675781\pi\)
0.999590 + 0.0286287i \(0.00911406\pi\)
\(360\) 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 0.504093 0.863649i \(-0.331827\pi\)
−0.999989 + 0.00473247i \(0.998494\pi\)
\(368\) 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 −0.890753 0.454488i \(-0.849822\pi\)
0.838975 + 0.544170i \(0.183156\pi\)
\(374\) 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 −0.462563 0.886586i \(-0.653070\pi\)
0.999088 0.0427020i \(-0.0135966\pi\)
\(384\) 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 0.977086 0.212847i \(-0.0682735\pi\)
−0.672874 + 0.739758i \(0.734940\pi\)
\(390\) 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 −0.986481 0.163876i \(-0.947600\pi\)
0.635161 + 0.772380i \(0.280934\pi\)
\(398\) 0 0
\(399\) 4.00000 + 3.46410i 0.200250 + 0.173422i
\(400\) 0 0
\(401\) 13.5000 23.3827i 0.674158 1.16768i −0.302556 0.953131i \(-0.597840\pi\)
0.976714 0.214544i \(-0.0688266\pi\)
\(402\) 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 −0.984803 0.173675i \(-0.944436\pi\)
0.341994 0.939702i \(-0.388898\pi\)
\(410\) 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 0.973574 0.228373i \(-0.0733406\pi\)
−0.684564 + 0.728953i \(0.740007\pi\)
\(432\) 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 −0.368945 0.929451i \(-0.620281\pi\)
0.989401 0.145210i \(-0.0463858\pi\)
\(440\) 0 0
\(441\) −6.50000 2.59808i −0.309524 0.123718i
\(442\) 0 0
\(443\) 6.00000 10.3923i 0.285069 0.493753i −0.687557 0.726130i \(-0.741317\pi\)
0.972626 + 0.232377i \(0.0746503\pi\)
\(444\) 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 −0.982004 0.188858i \(-0.939521\pi\)
0.654558 + 0.756012i \(0.272855\pi\)
\(458\) 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 −0.927052 0.374934i \(-0.877665\pi\)
0.788228 + 0.615383i \(0.210999\pi\)
\(468\) 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 \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(480\) 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 0.625859 0.779936i \(-0.284748\pi\)
−0.988374 + 0.152042i \(0.951415\pi\)
\(488\) 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 −0.907314 0.420455i \(-0.861871\pi\)
0.817781 + 0.575529i \(0.195204\pi\)
\(500\) 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 0.148866 0.988857i \(-0.452438\pi\)
0.781943 0.623350i \(-0.214229\pi\)
\(510\) 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 0.982231 0.187678i \(-0.0600963\pi\)
−0.653650 + 0.756797i \(0.726763\pi\)
\(522\) 0 0
\(523\) −14.0000 + 24.2487i −0.612177 + 1.06032i 0.378695 + 0.925521i \(0.376373\pi\)
−0.990873 + 0.134801i \(0.956961\pi\)
\(524\) 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 −0.939110 0.343617i \(-0.888348\pi\)
0.767136 + 0.641484i \(0.221681\pi\)
\(542\) 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 0.945473 0.325701i \(-0.105600\pi\)
−0.754802 + 0.655953i \(0.772267\pi\)
\(558\) 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 0.845663 + 0.533718i \(0.179206\pi\)
0.0393818 + 0.999224i \(0.487461\pi\)
\(564\) 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 −0.997703 0.0677445i \(-0.978420\pi\)
0.557520 + 0.830164i \(0.311753\pi\)
\(570\) 0 0
\(571\) 10.0000 + 17.3205i 0.418487 + 0.724841i 0.995788 0.0916910i \(-0.0292272\pi\)
−0.577301 + 0.816532i \(0.695894\pi\)
\(572\) 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 −0.805620 0.592433i \(-0.798167\pi\)
−0.110252 0.993904i \(-0.535166\pi\)
\(578\) 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 −0.999965 0.00831589i \(-0.997353\pi\)
0.507184 + 0.861838i \(0.330686\pi\)
\(594\) 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 −0.873799 0.486287i \(-0.838351\pi\)
0.0157622 0.999876i \(-0.494983\pi\)
\(600\) 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 −0.875994 0.482322i \(-0.839794\pi\)
0.855700 + 0.517472i \(0.173127\pi\)
\(608\) 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 −0.994794 0.101905i \(-0.967506\pi\)
0.409145 0.912470i \(-0.365827\pi\)
\(614\) 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 0.999071 0.0430838i \(-0.0137183\pi\)
−0.536847 + 0.843679i \(0.680385\pi\)
\(620\) 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 −0.999247 0.0387913i \(-0.987649\pi\)
0.466029 0.884769i \(-0.345684\pi\)
\(642\) 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 0.983438 + 0.181245i \(0.0580128\pi\)
−0.334756 + 0.942305i \(0.608654\pi\)
\(648\) 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 −0.764442 0.644692i \(-0.776986\pi\)
0.940541 + 0.339680i \(0.110319\pi\)
\(654\) 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 0.998636 + 0.0522143i \(0.0166279\pi\)
−0.454099 + 0.890951i \(0.650039\pi\)
\(662\) 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 −0.766501 0.642244i \(-0.778004\pi\)
0.939450 + 0.342687i \(0.111337\pi\)
\(678\) 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 0.957685 0.287819i \(-0.0929302\pi\)
−0.728101 + 0.685470i \(0.759597\pi\)
\(684\) 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 −0.382791 0.923835i \(-0.625037\pi\)
0.991460 0.130410i \(-0.0416295\pi\)
\(692\) 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 −0.00446726 0.999990i \(-0.501422\pi\)
0.868250 0.496126i \(-0.165245\pi\)
\(710\) 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 \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(720\) 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 −0.129275 0.991609i \(-0.541265\pi\)
0.923396 0.383849i \(-0.125402\pi\)
\(734\) 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 0.984589 + 0.174883i \(0.0559548\pi\)
−0.340841 + 0.940121i \(0.610712\pi\)
\(740\) 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 −0.942715 0.333599i \(-0.891737\pi\)
0.760263 + 0.649616i \(0.225070\pi\)
\(752\) 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 −0.510551 0.859848i \(-0.670558\pi\)
0.999925 + 0.0122260i \(0.00389175\pi\)
\(762\) 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 0.803691 + 0.595047i \(0.202867\pi\)
0.113480 + 0.993540i \(0.463800\pi\)
\(774\) 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 0.600620 0.799535i \(-0.294921\pi\)
−0.992727 + 0.120384i \(0.961587\pi\)
\(788\) 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