Properties

Label 560.2.q.j.401.1
Level $560$
Weight $2$
Character 560.401
Analytic conductor $4.472$
Analytic rank $0$
Dimension $4$
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: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{2}, \sqrt{-3})\)
Defining polynomial: \(x^{4} + 2 x^{2} + 4\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 280)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 401.1
Root \(-0.707107 - 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 560.401
Dual form 560.2.q.j.81.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.20711 - 2.09077i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(2.62132 - 0.358719i) q^{7} +(-1.41421 + 2.44949i) q^{9} +O(q^{10})\) \(q+(-1.20711 - 2.09077i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(2.62132 - 0.358719i) q^{7} +(-1.41421 + 2.44949i) q^{9} +(-2.41421 - 4.18154i) q^{11} +2.00000 q^{13} +2.41421 q^{15} +(-1.82843 - 3.16693i) q^{17} +(2.82843 - 4.89898i) q^{19} +(-3.91421 - 5.04757i) q^{21} +(-4.20711 + 7.28692i) q^{23} +(-0.500000 - 0.866025i) q^{25} -0.414214 q^{27} -2.17157 q^{29} +(-2.41421 - 4.18154i) q^{31} +(-5.82843 + 10.0951i) q^{33} +(-1.00000 + 2.44949i) q^{35} +(2.82843 - 4.89898i) q^{37} +(-2.41421 - 4.18154i) q^{39} +0.171573 q^{41} -12.8995 q^{43} +(-1.41421 - 2.44949i) q^{45} +(0.171573 - 0.297173i) q^{47} +(6.74264 - 1.88064i) q^{49} +(-4.41421 + 7.64564i) q^{51} +(-2.82843 - 4.89898i) q^{53} +4.82843 q^{55} -13.6569 q^{57} +(-2.00000 - 3.46410i) q^{59} +(2.32843 - 4.03295i) q^{61} +(-2.82843 + 6.92820i) q^{63} +(-1.00000 + 1.73205i) q^{65} +(3.44975 + 5.97514i) q^{67} +20.3137 q^{69} +12.0000 q^{71} +(3.82843 + 6.63103i) q^{73} +(-1.20711 + 2.09077i) q^{75} +(-7.82843 - 10.0951i) q^{77} +(-2.00000 + 3.46410i) q^{79} +(4.74264 + 8.21449i) q^{81} +13.2426 q^{83} +3.65685 q^{85} +(2.62132 + 4.54026i) q^{87} +(8.32843 - 14.4253i) q^{89} +(5.24264 - 0.717439i) q^{91} +(-5.82843 + 10.0951i) q^{93} +(2.82843 + 4.89898i) q^{95} +6.00000 q^{97} +13.6569 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 2q^{3} - 2q^{5} + 2q^{7} + O(q^{10}) \) \( 4q - 2q^{3} - 2q^{5} + 2q^{7} - 4q^{11} + 8q^{13} + 4q^{15} + 4q^{17} - 10q^{21} - 14q^{23} - 2q^{25} + 4q^{27} - 20q^{29} - 4q^{31} - 12q^{33} - 4q^{35} - 4q^{39} + 12q^{41} - 12q^{43} + 12q^{47} + 10q^{49} - 12q^{51} + 8q^{55} - 32q^{57} - 8q^{59} - 2q^{61} - 4q^{65} - 6q^{67} + 36q^{69} + 48q^{71} + 4q^{73} - 2q^{75} - 20q^{77} - 8q^{79} + 2q^{81} + 36q^{83} - 8q^{85} + 2q^{87} + 22q^{89} + 4q^{91} - 12q^{93} + 24q^{97} + 32q^{99} + O(q^{100}) \)

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
\(3\) −1.20711 2.09077i −0.696923 1.20711i −0.969528 0.244981i \(-0.921218\pi\)
0.272605 0.962126i \(-0.412115\pi\)
\(4\) 0 0
\(5\) −0.500000 + 0.866025i −0.223607 + 0.387298i
\(6\) 0 0
\(7\) 2.62132 0.358719i 0.990766 0.135583i
\(8\) 0 0
\(9\) −1.41421 + 2.44949i −0.471405 + 0.816497i
\(10\) 0 0
\(11\) −2.41421 4.18154i −0.727913 1.26078i −0.957764 0.287556i \(-0.907157\pi\)
0.229851 0.973226i \(-0.426176\pi\)
\(12\) 0 0
\(13\) 2.00000 0.554700 0.277350 0.960769i \(-0.410544\pi\)
0.277350 + 0.960769i \(0.410544\pi\)
\(14\) 0 0
\(15\) 2.41421 0.623347
\(16\) 0 0
\(17\) −1.82843 3.16693i −0.443459 0.768093i 0.554485 0.832194i \(-0.312915\pi\)
−0.997943 + 0.0641009i \(0.979582\pi\)
\(18\) 0 0
\(19\) 2.82843 4.89898i 0.648886 1.12390i −0.334504 0.942394i \(-0.608569\pi\)
0.983389 0.181509i \(-0.0580980\pi\)
\(20\) 0 0
\(21\) −3.91421 5.04757i −0.854151 1.10147i
\(22\) 0 0
\(23\) −4.20711 + 7.28692i −0.877242 + 1.51943i −0.0228877 + 0.999738i \(0.507286\pi\)
−0.854355 + 0.519690i \(0.826047\pi\)
\(24\) 0 0
\(25\) −0.500000 0.866025i −0.100000 0.173205i
\(26\) 0 0
\(27\) −0.414214 −0.0797154
\(28\) 0 0
\(29\) −2.17157 −0.403251 −0.201625 0.979463i \(-0.564622\pi\)
−0.201625 + 0.979463i \(0.564622\pi\)
\(30\) 0 0
\(31\) −2.41421 4.18154i −0.433606 0.751027i 0.563575 0.826065i \(-0.309426\pi\)
−0.997181 + 0.0750380i \(0.976092\pi\)
\(32\) 0 0
\(33\) −5.82843 + 10.0951i −1.01460 + 1.75734i
\(34\) 0 0
\(35\) −1.00000 + 2.44949i −0.169031 + 0.414039i
\(36\) 0 0
\(37\) 2.82843 4.89898i 0.464991 0.805387i −0.534211 0.845351i \(-0.679391\pi\)
0.999201 + 0.0399642i \(0.0127244\pi\)
\(38\) 0 0
\(39\) −2.41421 4.18154i −0.386584 0.669582i
\(40\) 0 0
\(41\) 0.171573 0.0267952 0.0133976 0.999910i \(-0.495735\pi\)
0.0133976 + 0.999910i \(0.495735\pi\)
\(42\) 0 0
\(43\) −12.8995 −1.96715 −0.983577 0.180488i \(-0.942232\pi\)
−0.983577 + 0.180488i \(0.942232\pi\)
\(44\) 0 0
\(45\) −1.41421 2.44949i −0.210819 0.365148i
\(46\) 0 0
\(47\) 0.171573 0.297173i 0.0250265 0.0433471i −0.853241 0.521517i \(-0.825366\pi\)
0.878267 + 0.478170i \(0.158700\pi\)
\(48\) 0 0
\(49\) 6.74264 1.88064i 0.963234 0.268662i
\(50\) 0 0
\(51\) −4.41421 + 7.64564i −0.618114 + 1.07060i
\(52\) 0 0
\(53\) −2.82843 4.89898i −0.388514 0.672927i 0.603736 0.797185i \(-0.293678\pi\)
−0.992250 + 0.124258i \(0.960345\pi\)
\(54\) 0 0
\(55\) 4.82843 0.651065
\(56\) 0 0
\(57\) −13.6569 −1.80889
\(58\) 0 0
\(59\) −2.00000 3.46410i −0.260378 0.450988i 0.705965 0.708247i \(-0.250514\pi\)
−0.966342 + 0.257260i \(0.917180\pi\)
\(60\) 0 0
\(61\) 2.32843 4.03295i 0.298125 0.516367i −0.677582 0.735447i \(-0.736972\pi\)
0.975707 + 0.219080i \(0.0703056\pi\)
\(62\) 0 0
\(63\) −2.82843 + 6.92820i −0.356348 + 0.872872i
\(64\) 0 0
\(65\) −1.00000 + 1.73205i −0.124035 + 0.214834i
\(66\) 0 0
\(67\) 3.44975 + 5.97514i 0.421454 + 0.729979i 0.996082 0.0884353i \(-0.0281867\pi\)
−0.574628 + 0.818415i \(0.694853\pi\)
\(68\) 0 0
\(69\) 20.3137 2.44548
\(70\) 0 0
\(71\) 12.0000 1.42414 0.712069 0.702109i \(-0.247758\pi\)
0.712069 + 0.702109i \(0.247758\pi\)
\(72\) 0 0
\(73\) 3.82843 + 6.63103i 0.448084 + 0.776103i 0.998261 0.0589442i \(-0.0187734\pi\)
−0.550178 + 0.835048i \(0.685440\pi\)
\(74\) 0 0
\(75\) −1.20711 + 2.09077i −0.139385 + 0.241421i
\(76\) 0 0
\(77\) −7.82843 10.0951i −0.892132 1.15045i
\(78\) 0 0
\(79\) −2.00000 + 3.46410i −0.225018 + 0.389742i −0.956325 0.292306i \(-0.905577\pi\)
0.731307 + 0.682048i \(0.238911\pi\)
\(80\) 0 0
\(81\) 4.74264 + 8.21449i 0.526960 + 0.912722i
\(82\) 0 0
\(83\) 13.2426 1.45357 0.726784 0.686866i \(-0.241014\pi\)
0.726784 + 0.686866i \(0.241014\pi\)
\(84\) 0 0
\(85\) 3.65685 0.396642
\(86\) 0 0
\(87\) 2.62132 + 4.54026i 0.281035 + 0.486767i
\(88\) 0 0
\(89\) 8.32843 14.4253i 0.882812 1.52907i 0.0346099 0.999401i \(-0.488981\pi\)
0.848202 0.529673i \(-0.177686\pi\)
\(90\) 0 0
\(91\) 5.24264 0.717439i 0.549578 0.0752080i
\(92\) 0 0
\(93\) −5.82843 + 10.0951i −0.604380 + 1.04682i
\(94\) 0 0
\(95\) 2.82843 + 4.89898i 0.290191 + 0.502625i
\(96\) 0 0
\(97\) 6.00000 0.609208 0.304604 0.952479i \(-0.401476\pi\)
0.304604 + 0.952479i \(0.401476\pi\)
\(98\) 0 0
\(99\) 13.6569 1.37257
\(100\) 0 0
\(101\) −2.74264 4.75039i −0.272903 0.472682i 0.696701 0.717362i \(-0.254650\pi\)
−0.969604 + 0.244680i \(0.921317\pi\)
\(102\) 0 0
\(103\) 5.20711 9.01897i 0.513071 0.888666i −0.486814 0.873506i \(-0.661841\pi\)
0.999885 0.0151600i \(-0.00482576\pi\)
\(104\) 0 0
\(105\) 6.32843 0.866025i 0.617591 0.0845154i
\(106\) 0 0
\(107\) −4.20711 + 7.28692i −0.406716 + 0.704453i −0.994520 0.104551i \(-0.966660\pi\)
0.587803 + 0.809004i \(0.299993\pi\)
\(108\) 0 0
\(109\) 2.15685 + 3.73578i 0.206589 + 0.357823i 0.950638 0.310302i \(-0.100430\pi\)
−0.744049 + 0.668125i \(0.767097\pi\)
\(110\) 0 0
\(111\) −13.6569 −1.29625
\(112\) 0 0
\(113\) −11.3137 −1.06430 −0.532152 0.846649i \(-0.678617\pi\)
−0.532152 + 0.846649i \(0.678617\pi\)
\(114\) 0 0
\(115\) −4.20711 7.28692i −0.392315 0.679509i
\(116\) 0 0
\(117\) −2.82843 + 4.89898i −0.261488 + 0.452911i
\(118\) 0 0
\(119\) −5.92893 7.64564i −0.543504 0.700875i
\(120\) 0 0
\(121\) −6.15685 + 10.6640i −0.559714 + 0.969453i
\(122\) 0 0
\(123\) −0.207107 0.358719i −0.0186742 0.0323446i
\(124\) 0 0
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) 15.6569 1.38932 0.694661 0.719338i \(-0.255555\pi\)
0.694661 + 0.719338i \(0.255555\pi\)
\(128\) 0 0
\(129\) 15.5711 + 26.9699i 1.37096 + 2.37457i
\(130\) 0 0
\(131\) 1.17157 2.02922i 0.102361 0.177294i −0.810296 0.586021i \(-0.800694\pi\)
0.912657 + 0.408727i \(0.134027\pi\)
\(132\) 0 0
\(133\) 5.65685 13.8564i 0.490511 1.20150i
\(134\) 0 0
\(135\) 0.207107 0.358719i 0.0178249 0.0308737i
\(136\) 0 0
\(137\) 2.00000 + 3.46410i 0.170872 + 0.295958i 0.938725 0.344668i \(-0.112008\pi\)
−0.767853 + 0.640626i \(0.778675\pi\)
\(138\) 0 0
\(139\) 14.4853 1.22863 0.614313 0.789063i \(-0.289433\pi\)
0.614313 + 0.789063i \(0.289433\pi\)
\(140\) 0 0
\(141\) −0.828427 −0.0697661
\(142\) 0 0
\(143\) −4.82843 8.36308i −0.403773 0.699356i
\(144\) 0 0
\(145\) 1.08579 1.88064i 0.0901697 0.156178i
\(146\) 0 0
\(147\) −12.0711 11.8272i −0.995605 0.975490i
\(148\) 0 0
\(149\) 3.32843 5.76500i 0.272675 0.472288i −0.696871 0.717197i \(-0.745425\pi\)
0.969546 + 0.244909i \(0.0787582\pi\)
\(150\) 0 0
\(151\) −8.41421 14.5738i −0.684739 1.18600i −0.973519 0.228607i \(-0.926583\pi\)
0.288780 0.957396i \(-0.406750\pi\)
\(152\) 0 0
\(153\) 10.3431 0.836194
\(154\) 0 0
\(155\) 4.82843 0.387829
\(156\) 0 0
\(157\) 10.6569 + 18.4582i 0.850510 + 1.47313i 0.880749 + 0.473583i \(0.157040\pi\)
−0.0302396 + 0.999543i \(0.509627\pi\)
\(158\) 0 0
\(159\) −6.82843 + 11.8272i −0.541529 + 0.937957i
\(160\) 0 0
\(161\) −8.41421 + 20.6105i −0.663133 + 1.62434i
\(162\) 0 0
\(163\) −2.17157 + 3.76127i −0.170091 + 0.294606i −0.938451 0.345411i \(-0.887739\pi\)
0.768361 + 0.640017i \(0.221073\pi\)
\(164\) 0 0
\(165\) −5.82843 10.0951i −0.453742 0.785905i
\(166\) 0 0
\(167\) 12.0711 0.934087 0.467044 0.884234i \(-0.345319\pi\)
0.467044 + 0.884234i \(0.345319\pi\)
\(168\) 0 0
\(169\) −9.00000 −0.692308
\(170\) 0 0
\(171\) 8.00000 + 13.8564i 0.611775 + 1.05963i
\(172\) 0 0
\(173\) −10.8284 + 18.7554i −0.823270 + 1.42595i 0.0799642 + 0.996798i \(0.474519\pi\)
−0.903234 + 0.429148i \(0.858814\pi\)
\(174\) 0 0
\(175\) −1.62132 2.09077i −0.122560 0.158047i
\(176\) 0 0
\(177\) −4.82843 + 8.36308i −0.362927 + 0.628608i
\(178\) 0 0
\(179\) 5.24264 + 9.08052i 0.391853 + 0.678710i 0.992694 0.120659i \(-0.0385007\pi\)
−0.600841 + 0.799369i \(0.705167\pi\)
\(180\) 0 0
\(181\) −9.82843 −0.730541 −0.365271 0.930901i \(-0.619024\pi\)
−0.365271 + 0.930901i \(0.619024\pi\)
\(182\) 0 0
\(183\) −11.2426 −0.831080
\(184\) 0 0
\(185\) 2.82843 + 4.89898i 0.207950 + 0.360180i
\(186\) 0 0
\(187\) −8.82843 + 15.2913i −0.645599 + 1.11821i
\(188\) 0 0
\(189\) −1.08579 + 0.148586i −0.0789793 + 0.0108081i
\(190\) 0 0
\(191\) −11.2426 + 19.4728i −0.813489 + 1.40900i 0.0969189 + 0.995292i \(0.469101\pi\)
−0.910408 + 0.413712i \(0.864232\pi\)
\(192\) 0 0
\(193\) −8.65685 14.9941i −0.623134 1.07930i −0.988899 0.148592i \(-0.952526\pi\)
0.365765 0.930707i \(-0.380808\pi\)
\(194\) 0 0
\(195\) 4.82843 0.345771
\(196\) 0 0
\(197\) 11.6569 0.830516 0.415258 0.909704i \(-0.363691\pi\)
0.415258 + 0.909704i \(0.363691\pi\)
\(198\) 0 0
\(199\) −0.343146 0.594346i −0.0243250 0.0421321i 0.853607 0.520918i \(-0.174410\pi\)
−0.877932 + 0.478786i \(0.841077\pi\)
\(200\) 0 0
\(201\) 8.32843 14.4253i 0.587442 1.01748i
\(202\) 0 0
\(203\) −5.69239 + 0.778985i −0.399527 + 0.0546741i
\(204\) 0 0
\(205\) −0.0857864 + 0.148586i −0.00599158 + 0.0103777i
\(206\) 0 0
\(207\) −11.8995 20.6105i −0.827072 1.43253i
\(208\) 0 0
\(209\) −27.3137 −1.88933
\(210\) 0 0
\(211\) 18.6274 1.28236 0.641182 0.767389i \(-0.278444\pi\)
0.641182 + 0.767389i \(0.278444\pi\)
\(212\) 0 0
\(213\) −14.4853 25.0892i −0.992515 1.71909i
\(214\) 0 0
\(215\) 6.44975 11.1713i 0.439869 0.761876i
\(216\) 0 0
\(217\) −7.82843 10.0951i −0.531428 0.685302i
\(218\) 0 0
\(219\) 9.24264 16.0087i 0.624560 1.08177i
\(220\) 0 0
\(221\) −3.65685 6.33386i −0.245987 0.426061i
\(222\) 0 0
\(223\) −18.9706 −1.27036 −0.635181 0.772363i \(-0.719075\pi\)
−0.635181 + 0.772363i \(0.719075\pi\)
\(224\) 0 0
\(225\) 2.82843 0.188562
\(226\) 0 0
\(227\) 7.00000 + 12.1244i 0.464606 + 0.804722i 0.999184 0.0403978i \(-0.0128625\pi\)
−0.534577 + 0.845120i \(0.679529\pi\)
\(228\) 0 0
\(229\) 7.00000 12.1244i 0.462573 0.801200i −0.536515 0.843891i \(-0.680260\pi\)
0.999088 + 0.0426906i \(0.0135930\pi\)
\(230\) 0 0
\(231\) −11.6569 + 28.5533i −0.766965 + 1.87867i
\(232\) 0 0
\(233\) −0.171573 + 0.297173i −0.0112401 + 0.0194684i −0.871591 0.490234i \(-0.836911\pi\)
0.860351 + 0.509703i \(0.170245\pi\)
\(234\) 0 0
\(235\) 0.171573 + 0.297173i 0.0111922 + 0.0193854i
\(236\) 0 0
\(237\) 9.65685 0.627280
\(238\) 0 0
\(239\) 13.5147 0.874194 0.437097 0.899414i \(-0.356007\pi\)
0.437097 + 0.899414i \(0.356007\pi\)
\(240\) 0 0
\(241\) 5.00000 + 8.66025i 0.322078 + 0.557856i 0.980917 0.194429i \(-0.0622852\pi\)
−0.658838 + 0.752285i \(0.728952\pi\)
\(242\) 0 0
\(243\) 10.8284 18.7554i 0.694644 1.20316i
\(244\) 0 0
\(245\) −1.74264 + 6.77962i −0.111333 + 0.433134i
\(246\) 0 0
\(247\) 5.65685 9.79796i 0.359937 0.623429i
\(248\) 0 0
\(249\) −15.9853 27.6873i −1.01303 1.75461i
\(250\) 0 0
\(251\) −23.4558 −1.48052 −0.740260 0.672321i \(-0.765298\pi\)
−0.740260 + 0.672321i \(0.765298\pi\)
\(252\) 0 0
\(253\) 40.6274 2.55422
\(254\) 0 0
\(255\) −4.41421 7.64564i −0.276429 0.478789i
\(256\) 0 0
\(257\) 3.65685 6.33386i 0.228108 0.395095i −0.729139 0.684365i \(-0.760079\pi\)
0.957247 + 0.289270i \(0.0934126\pi\)
\(258\) 0 0
\(259\) 5.65685 13.8564i 0.351500 0.860995i
\(260\) 0 0
\(261\) 3.07107 5.31925i 0.190094 0.329253i
\(262\) 0 0
\(263\) 4.86396 + 8.42463i 0.299925 + 0.519485i 0.976118 0.217239i \(-0.0697051\pi\)
−0.676194 + 0.736724i \(0.736372\pi\)
\(264\) 0 0
\(265\) 5.65685 0.347498
\(266\) 0 0
\(267\) −40.2132 −2.46101
\(268\) 0 0
\(269\) −2.32843 4.03295i −0.141967 0.245894i 0.786270 0.617882i \(-0.212009\pi\)
−0.928237 + 0.371989i \(0.878676\pi\)
\(270\) 0 0
\(271\) 9.65685 16.7262i 0.586612 1.01604i −0.408060 0.912955i \(-0.633795\pi\)
0.994672 0.103087i \(-0.0328720\pi\)
\(272\) 0 0
\(273\) −7.82843 10.0951i −0.473798 0.610985i
\(274\) 0 0
\(275\) −2.41421 + 4.18154i −0.145583 + 0.252156i
\(276\) 0 0
\(277\) 8.31371 + 14.3998i 0.499522 + 0.865198i 1.00000 0.000551476i \(-0.000175540\pi\)
−0.500478 + 0.865750i \(0.666842\pi\)
\(278\) 0 0
\(279\) 13.6569 0.817614
\(280\) 0 0
\(281\) 25.3137 1.51009 0.755045 0.655673i \(-0.227615\pi\)
0.755045 + 0.655673i \(0.227615\pi\)
\(282\) 0 0
\(283\) 9.00000 + 15.5885i 0.534994 + 0.926638i 0.999164 + 0.0408910i \(0.0130196\pi\)
−0.464169 + 0.885747i \(0.653647\pi\)
\(284\) 0 0
\(285\) 6.82843 11.8272i 0.404481 0.700582i
\(286\) 0 0
\(287\) 0.449747 0.0615465i 0.0265478 0.00363298i
\(288\) 0 0
\(289\) 1.81371 3.14144i 0.106689 0.184790i
\(290\) 0 0
\(291\) −7.24264 12.5446i −0.424571 0.735379i
\(292\) 0 0
\(293\) −16.9706 −0.991431 −0.495715 0.868485i \(-0.665094\pi\)
−0.495715 + 0.868485i \(0.665094\pi\)
\(294\) 0 0
\(295\) 4.00000 0.232889
\(296\) 0 0
\(297\) 1.00000 + 1.73205i 0.0580259 + 0.100504i
\(298\) 0 0
\(299\) −8.41421 + 14.5738i −0.486607 + 0.842827i
\(300\) 0 0
\(301\) −33.8137 + 4.62730i −1.94899 + 0.266713i
\(302\) 0 0
\(303\) −6.62132 + 11.4685i −0.380385 + 0.658846i
\(304\) 0 0
\(305\) 2.32843 + 4.03295i 0.133325 + 0.230926i
\(306\) 0 0
\(307\) −13.2426 −0.755797 −0.377899 0.925847i \(-0.623353\pi\)
−0.377899 + 0.925847i \(0.623353\pi\)
\(308\) 0 0
\(309\) −25.1421 −1.43029
\(310\) 0 0
\(311\) 5.17157 + 8.95743i 0.293253 + 0.507929i 0.974577 0.224053i \(-0.0719288\pi\)
−0.681324 + 0.731982i \(0.738596\pi\)
\(312\) 0 0
\(313\) 6.48528 11.2328i 0.366570 0.634917i −0.622457 0.782654i \(-0.713865\pi\)
0.989027 + 0.147737i \(0.0471988\pi\)
\(314\) 0 0
\(315\) −4.58579 5.91359i −0.258380 0.333193i
\(316\) 0 0
\(317\) 11.0000 19.0526i 0.617822 1.07010i −0.372061 0.928208i \(-0.621349\pi\)
0.989882 0.141890i \(-0.0453179\pi\)
\(318\) 0 0
\(319\) 5.24264 + 9.08052i 0.293532 + 0.508412i
\(320\) 0 0
\(321\) 20.3137 1.13380
\(322\) 0 0
\(323\) −20.6863 −1.15102
\(324\) 0 0
\(325\) −1.00000 1.73205i −0.0554700 0.0960769i
\(326\) 0 0
\(327\) 5.20711 9.01897i 0.287954 0.498750i
\(328\) 0 0
\(329\) 0.343146 0.840532i 0.0189182 0.0463400i
\(330\) 0 0
\(331\) 4.75736 8.23999i 0.261488 0.452911i −0.705149 0.709059i \(-0.749120\pi\)
0.966638 + 0.256148i \(0.0824534\pi\)
\(332\) 0 0
\(333\) 8.00000 + 13.8564i 0.438397 + 0.759326i
\(334\) 0 0
\(335\) −6.89949 −0.376960
\(336\) 0 0
\(337\) −8.97056 −0.488658 −0.244329 0.969692i \(-0.578568\pi\)
−0.244329 + 0.969692i \(0.578568\pi\)
\(338\) 0 0
\(339\) 13.6569 + 23.6544i 0.741739 + 1.28473i
\(340\) 0 0
\(341\) −11.6569 + 20.1903i −0.631254 + 1.09336i
\(342\) 0 0
\(343\) 17.0000 7.34847i 0.917914 0.396780i
\(344\) 0 0
\(345\) −10.1569 + 17.5922i −0.546827 + 0.947132i
\(346\) 0 0
\(347\) −12.6924 21.9839i −0.681363 1.18016i −0.974565 0.224105i \(-0.928054\pi\)
0.293202 0.956051i \(-0.405279\pi\)
\(348\) 0 0
\(349\) 4.17157 0.223299 0.111650 0.993748i \(-0.464387\pi\)
0.111650 + 0.993748i \(0.464387\pi\)
\(350\) 0 0
\(351\) −0.828427 −0.0442182
\(352\) 0 0
\(353\) −11.1716 19.3497i −0.594603 1.02988i −0.993603 0.112931i \(-0.963976\pi\)
0.399000 0.916951i \(-0.369357\pi\)
\(354\) 0 0
\(355\) −6.00000 + 10.3923i −0.318447 + 0.551566i
\(356\) 0 0
\(357\) −8.82843 + 21.6251i −0.467250 + 1.14452i
\(358\) 0 0
\(359\) 5.24264 9.08052i 0.276696 0.479252i −0.693866 0.720105i \(-0.744094\pi\)
0.970562 + 0.240853i \(0.0774272\pi\)
\(360\) 0 0
\(361\) −6.50000 11.2583i −0.342105 0.592544i
\(362\) 0 0
\(363\) 29.7279 1.56031
\(364\) 0 0
\(365\) −7.65685 −0.400778
\(366\) 0 0
\(367\) 12.2071 + 21.1433i 0.637206 + 1.10367i 0.986043 + 0.166490i \(0.0532432\pi\)
−0.348837 + 0.937183i \(0.613423\pi\)
\(368\) 0 0
\(369\) −0.242641 + 0.420266i −0.0126314 + 0.0218782i
\(370\) 0 0
\(371\) −9.17157 11.8272i −0.476164 0.614037i
\(372\) 0 0
\(373\) −6.00000 + 10.3923i −0.310668 + 0.538093i −0.978507 0.206213i \(-0.933886\pi\)
0.667839 + 0.744306i \(0.267219\pi\)
\(374\) 0 0
\(375\) −1.20711 2.09077i −0.0623347 0.107967i
\(376\) 0 0
\(377\) −4.34315 −0.223683
\(378\) 0 0
\(379\) −27.3137 −1.40301 −0.701505 0.712664i \(-0.747488\pi\)
−0.701505 + 0.712664i \(0.747488\pi\)
\(380\) 0 0
\(381\) −18.8995 32.7349i −0.968250 1.67706i
\(382\) 0 0
\(383\) 9.44975 16.3674i 0.482860 0.836337i −0.516947 0.856018i \(-0.672931\pi\)
0.999806 + 0.0196803i \(0.00626483\pi\)
\(384\) 0 0
\(385\) 12.6569 1.73205i 0.645053 0.0882735i
\(386\) 0 0
\(387\) 18.2426 31.5972i 0.927326 1.60617i
\(388\) 0 0
\(389\) 8.65685 + 14.9941i 0.438920 + 0.760232i 0.997606 0.0691473i \(-0.0220278\pi\)
−0.558687 + 0.829379i \(0.688695\pi\)
\(390\) 0 0
\(391\) 30.7696 1.55608
\(392\) 0 0
\(393\) −5.65685 −0.285351
\(394\) 0 0
\(395\) −2.00000 3.46410i −0.100631 0.174298i
\(396\) 0 0
\(397\) −10.3137 + 17.8639i −0.517630 + 0.896562i 0.482160 + 0.876083i \(0.339852\pi\)
−0.999790 + 0.0204787i \(0.993481\pi\)
\(398\) 0 0
\(399\) −35.7990 + 4.89898i −1.79219 + 0.245256i
\(400\) 0 0
\(401\) 4.84315 8.38857i 0.241855 0.418905i −0.719388 0.694609i \(-0.755577\pi\)
0.961243 + 0.275703i \(0.0889108\pi\)
\(402\) 0 0
\(403\) −4.82843 8.36308i −0.240521 0.416595i
\(404\) 0 0
\(405\) −9.48528 −0.471327
\(406\) 0 0
\(407\) −27.3137 −1.35389
\(408\) 0 0
\(409\) −1.57107 2.72117i −0.0776843 0.134553i 0.824566 0.565766i \(-0.191419\pi\)
−0.902250 + 0.431212i \(0.858086\pi\)
\(410\) 0 0
\(411\) 4.82843 8.36308i 0.238169 0.412520i
\(412\) 0 0
\(413\) −6.48528 8.36308i −0.319120 0.411520i
\(414\) 0 0
\(415\) −6.62132 + 11.4685i −0.325028 + 0.562965i
\(416\) 0 0
\(417\) −17.4853 30.2854i −0.856258 1.48308i
\(418\) 0 0
\(419\) −7.31371 −0.357298 −0.178649 0.983913i \(-0.557173\pi\)
−0.178649 + 0.983913i \(0.557173\pi\)
\(420\) 0 0
\(421\) 38.6569 1.88402 0.942010 0.335585i \(-0.108934\pi\)
0.942010 + 0.335585i \(0.108934\pi\)
\(422\) 0 0
\(423\) 0.485281 + 0.840532i 0.0235952 + 0.0408681i
\(424\) 0 0
\(425\) −1.82843 + 3.16693i −0.0886917 + 0.153619i
\(426\) 0 0
\(427\) 4.65685 11.4069i 0.225361 0.552019i
\(428\) 0 0
\(429\) −11.6569 + 20.1903i −0.562798 + 0.974795i
\(430\) 0 0
\(431\) 2.41421 + 4.18154i 0.116289 + 0.201418i 0.918294 0.395899i \(-0.129567\pi\)
−0.802006 + 0.597317i \(0.796234\pi\)
\(432\) 0 0
\(433\) 3.31371 0.159247 0.0796233 0.996825i \(-0.474628\pi\)
0.0796233 + 0.996825i \(0.474628\pi\)
\(434\) 0 0
\(435\) −5.24264 −0.251365
\(436\) 0 0
\(437\) 23.7990 + 41.2211i 1.13846 + 1.97187i
\(438\) 0 0
\(439\) −14.8284 + 25.6836i −0.707722 + 1.22581i 0.257978 + 0.966151i \(0.416944\pi\)
−0.965700 + 0.259660i \(0.916390\pi\)
\(440\) 0 0
\(441\) −4.92893 + 19.1757i −0.234711 + 0.913126i
\(442\) 0 0
\(443\) −9.20711 + 15.9472i −0.437443 + 0.757673i −0.997491 0.0707865i \(-0.977449\pi\)
0.560049 + 0.828460i \(0.310782\pi\)
\(444\) 0 0
\(445\) 8.32843 + 14.4253i 0.394805 + 0.683823i
\(446\) 0 0
\(447\) −16.0711 −0.760135
\(448\) 0 0
\(449\) 9.48528 0.447638 0.223819 0.974631i \(-0.428148\pi\)
0.223819 + 0.974631i \(0.428148\pi\)
\(450\) 0 0
\(451\) −0.414214 0.717439i −0.0195046 0.0337829i
\(452\) 0 0
\(453\) −20.3137 + 35.1844i −0.954421 + 1.65311i
\(454\) 0 0
\(455\) −2.00000 + 4.89898i −0.0937614 + 0.229668i
\(456\) 0 0
\(457\) 2.48528 4.30463i 0.116257 0.201362i −0.802025 0.597291i \(-0.796244\pi\)
0.918281 + 0.395928i \(0.129577\pi\)
\(458\) 0 0
\(459\) 0.757359 + 1.31178i 0.0353505 + 0.0612289i
\(460\) 0 0
\(461\) −21.3137 −0.992678 −0.496339 0.868129i \(-0.665323\pi\)
−0.496339 + 0.868129i \(0.665323\pi\)
\(462\) 0 0
\(463\) 4.89949 0.227699 0.113849 0.993498i \(-0.463682\pi\)
0.113849 + 0.993498i \(0.463682\pi\)
\(464\) 0 0
\(465\) −5.82843 10.0951i −0.270287 0.468151i
\(466\) 0 0
\(467\) 7.93503 13.7439i 0.367189 0.635991i −0.621936 0.783068i \(-0.713653\pi\)
0.989125 + 0.147078i \(0.0469868\pi\)
\(468\) 0 0
\(469\) 11.1863 + 14.4253i 0.516535 + 0.666097i
\(470\) 0 0
\(471\) 25.7279 44.5621i 1.18548 2.05331i
\(472\) 0 0
\(473\) 31.1421 + 53.9398i 1.43192 + 2.48015i
\(474\) 0 0
\(475\) −5.65685 −0.259554
\(476\) 0 0
\(477\) 16.0000 0.732590
\(478\) 0 0
\(479\) −9.24264 16.0087i −0.422307 0.731457i 0.573858 0.818955i \(-0.305446\pi\)
−0.996165 + 0.0874978i \(0.972113\pi\)
\(480\) 0 0
\(481\) 5.65685 9.79796i 0.257930 0.446748i
\(482\) 0 0
\(483\) 53.2487 7.28692i 2.42290 0.331566i
\(484\) 0 0
\(485\) −3.00000 + 5.19615i −0.136223 + 0.235945i
\(486\) 0 0
\(487\) 9.14214 + 15.8346i 0.414270 + 0.717536i 0.995351 0.0963090i \(-0.0307037\pi\)
−0.581082 + 0.813845i \(0.697370\pi\)
\(488\) 0 0
\(489\) 10.4853 0.474161
\(490\) 0 0
\(491\) −18.4853 −0.834229 −0.417115 0.908854i \(-0.636959\pi\)
−0.417115 + 0.908854i \(0.636959\pi\)
\(492\) 0 0
\(493\) 3.97056 + 6.87722i 0.178825 + 0.309734i
\(494\) 0 0
\(495\) −6.82843 + 11.8272i −0.306915 + 0.531592i
\(496\) 0 0
\(497\) 31.4558 4.30463i 1.41099 0.193089i
\(498\) 0 0
\(499\) 7.92893 13.7333i 0.354948 0.614788i −0.632161 0.774837i \(-0.717832\pi\)
0.987109 + 0.160049i \(0.0511653\pi\)
\(500\) 0 0
\(501\) −14.5711 25.2378i −0.650987 1.12754i
\(502\) 0 0
\(503\) 18.0711 0.805749 0.402875 0.915255i \(-0.368011\pi\)
0.402875 + 0.915255i \(0.368011\pi\)
\(504\) 0 0
\(505\) 5.48528 0.244092
\(506\) 0 0
\(507\) 10.8640 + 18.8169i 0.482485 + 0.835689i
\(508\) 0 0
\(509\) 8.25736 14.3022i 0.366001 0.633932i −0.622935 0.782273i \(-0.714060\pi\)
0.988936 + 0.148341i \(0.0473933\pi\)
\(510\) 0 0
\(511\) 12.4142 + 16.0087i 0.549172 + 0.708184i
\(512\) 0 0
\(513\) −1.17157 + 2.02922i −0.0517262 + 0.0895924i
\(514\) 0 0
\(515\) 5.20711 + 9.01897i 0.229453 + 0.397423i
\(516\) 0 0
\(517\) −1.65685 −0.0728684
\(518\) 0 0
\(519\) 52.2843 2.29502
\(520\) 0 0
\(521\) 4.31371 + 7.47156i 0.188987 + 0.327335i 0.944913 0.327322i \(-0.106146\pi\)
−0.755926 + 0.654657i \(0.772813\pi\)
\(522\) 0 0
\(523\) −19.9706 + 34.5900i −0.873252 + 1.51252i −0.0146382 + 0.999893i \(0.504660\pi\)
−0.858613 + 0.512624i \(0.828674\pi\)
\(524\) 0 0
\(525\) −2.41421 + 5.91359i −0.105365 + 0.258090i
\(526\) 0 0
\(527\) −8.82843 + 15.2913i −0.384572 + 0.666099i
\(528\) 0 0
\(529\) −23.8995 41.3951i −1.03911 1.79979i
\(530\) 0 0
\(531\) 11.3137 0.490973
\(532\) 0 0
\(533\) 0.343146 0.0148633
\(534\) 0 0
\(535\) −4.20711 7.28692i −0.181889 0.315041i
\(536\) 0 0
\(537\) 12.6569 21.9223i 0.546184 0.946018i
\(538\) 0 0
\(539\) −24.1421 23.6544i −1.03988 1.01887i
\(540\) 0 0
\(541\) 3.25736 5.64191i 0.140045 0.242565i −0.787468 0.616355i \(-0.788609\pi\)
0.927513 + 0.373790i \(0.121942\pi\)
\(542\) 0 0
\(543\) 11.8640 + 20.5490i 0.509131 + 0.881841i
\(544\) 0 0
\(545\) −4.31371 −0.184779
\(546\) 0 0
\(547\) 27.7279 1.18556 0.592780 0.805364i \(-0.298030\pi\)
0.592780 + 0.805364i \(0.298030\pi\)
\(548\) 0 0
\(549\) 6.58579 + 11.4069i 0.281075 + 0.486835i
\(550\) 0 0
\(551\) −6.14214 + 10.6385i −0.261664 + 0.453215i
\(552\) 0 0
\(553\) −4.00000 + 9.79796i −0.170097 + 0.416652i
\(554\) 0 0
\(555\) 6.82843 11.8272i 0.289851 0.502036i
\(556\) 0 0
\(557\) −2.65685 4.60181i −0.112575 0.194985i 0.804233 0.594314i \(-0.202576\pi\)
−0.916808 + 0.399329i \(0.869243\pi\)
\(558\) 0 0
\(559\) −25.7990 −1.09118
\(560\) 0 0
\(561\) 42.6274 1.79973
\(562\) 0 0
\(563\) 5.03553 + 8.72180i 0.212222 + 0.367580i 0.952410 0.304821i \(-0.0985965\pi\)
−0.740187 + 0.672401i \(0.765263\pi\)
\(564\) 0 0
\(565\) 5.65685 9.79796i 0.237986 0.412203i
\(566\) 0 0
\(567\) 15.3787 + 19.8315i 0.645844 + 0.832847i
\(568\) 0 0
\(569\) −4.31371 + 7.47156i −0.180840 + 0.313224i −0.942167 0.335144i \(-0.891215\pi\)
0.761327 + 0.648368i \(0.224548\pi\)
\(570\) 0 0
\(571\) 6.48528 + 11.2328i 0.271401 + 0.470080i 0.969221 0.246193i \(-0.0791799\pi\)
−0.697820 + 0.716273i \(0.745847\pi\)
\(572\) 0 0
\(573\) 54.2843 2.26776
\(574\) 0 0
\(575\) 8.41421 0.350897
\(576\) 0 0
\(577\) −17.1421 29.6910i −0.713636 1.23605i −0.963483 0.267769i \(-0.913714\pi\)
0.249847 0.968285i \(-0.419620\pi\)
\(578\) 0 0
\(579\) −20.8995 + 36.1990i −0.868553 + 1.50438i
\(580\) 0 0
\(581\) 34.7132 4.75039i 1.44015 0.197080i
\(582\) 0 0
\(583\) −13.6569 + 23.6544i −0.565609 + 0.979664i
\(584\) 0 0
\(585\) −2.82843 4.89898i −0.116941 0.202548i
\(586\) 0 0
\(587\) 45.3137 1.87030 0.935148 0.354256i \(-0.115266\pi\)
0.935148 + 0.354256i \(0.115266\pi\)
\(588\) 0 0
\(589\) −27.3137 −1.12544
\(590\) 0 0
\(591\) −14.0711 24.3718i −0.578806 1.00252i
\(592\) 0 0
\(593\) 18.9706 32.8580i 0.779028 1.34932i −0.153475 0.988153i \(-0.549046\pi\)
0.932503 0.361163i \(-0.117620\pi\)
\(594\) 0 0
\(595\) 9.58579 1.31178i 0.392979 0.0537779i
\(596\) 0 0
\(597\) −0.828427 + 1.43488i −0.0339053 + 0.0587256i
\(598\) 0 0
\(599\) −1.31371 2.27541i −0.0536767 0.0929707i 0.837939 0.545765i \(-0.183761\pi\)
−0.891615 + 0.452794i \(0.850427\pi\)
\(600\) 0 0
\(601\) −34.0000 −1.38689 −0.693444 0.720510i \(-0.743908\pi\)
−0.693444 + 0.720510i \(0.743908\pi\)
\(602\) 0 0
\(603\) −19.5147 −0.794701
\(604\) 0 0
\(605\) −6.15685 10.6640i −0.250312 0.433553i
\(606\) 0 0
\(607\) 9.37868 16.2443i 0.380669 0.659338i −0.610489 0.792025i \(-0.709027\pi\)
0.991158 + 0.132687i \(0.0423604\pi\)
\(608\) 0 0
\(609\) 8.50000 + 10.9612i 0.344437 + 0.444169i
\(610\) 0 0
\(611\) 0.343146 0.594346i 0.0138822 0.0240447i
\(612\) 0 0
\(613\) −2.51472 4.35562i −0.101569 0.175922i 0.810763 0.585375i \(-0.199053\pi\)
−0.912331 + 0.409453i \(0.865719\pi\)
\(614\) 0 0
\(615\) 0.414214 0.0167027
\(616\) 0 0
\(617\) −35.3137 −1.42168 −0.710838 0.703356i \(-0.751684\pi\)
−0.710838 + 0.703356i \(0.751684\pi\)
\(618\) 0 0
\(619\) −5.72792 9.92105i −0.230225 0.398761i 0.727649 0.685949i \(-0.240613\pi\)
−0.957874 + 0.287188i \(0.907279\pi\)
\(620\) 0 0
\(621\) 1.74264 3.01834i 0.0699298 0.121122i
\(622\) 0 0
\(623\) 16.6569 40.8008i 0.667343 1.63465i
\(624\) 0 0
\(625\) −0.500000 + 0.866025i −0.0200000 + 0.0346410i
\(626\) 0 0
\(627\) 32.9706 + 57.1067i 1.31672 + 2.28062i
\(628\) 0 0
\(629\) −20.6863 −0.824816
\(630\) 0 0
\(631\) 18.4853 0.735887 0.367944 0.929848i \(-0.380062\pi\)
0.367944 + 0.929848i \(0.380062\pi\)
\(632\) 0 0
\(633\) −22.4853 38.9456i −0.893710 1.54795i
\(634\) 0 0
\(635\) −7.82843 + 13.5592i −0.310662 + 0.538082i
\(636\) 0 0
\(637\) 13.4853 3.76127i 0.534306 0.149027i
\(638\) 0 0
\(639\) −16.9706 + 29.3939i −0.671345 + 1.16280i
\(640\) 0 0
\(641\) 24.0563 + 41.6668i 0.950169 + 1.64574i 0.745056 + 0.667002i \(0.232423\pi\)
0.205113 + 0.978738i \(0.434244\pi\)
\(642\) 0 0
\(643\) −26.0000 −1.02534 −0.512670 0.858586i \(-0.671344\pi\)
−0.512670 + 0.858586i \(0.671344\pi\)
\(644\) 0 0
\(645\) −31.1421 −1.22622
\(646\) 0 0
\(647\) −14.6213 25.3249i −0.574823 0.995623i −0.996061 0.0886729i \(-0.971737\pi\)
0.421237 0.906950i \(-0.361596\pi\)
\(648\) 0 0
\(649\) −9.65685 + 16.7262i −0.379065 + 0.656559i
\(650\) 0 0
\(651\) −11.6569 + 28.5533i −0.456868 + 1.11909i
\(652\) 0 0
\(653\) 2.17157 3.76127i 0.0849802 0.147190i −0.820403 0.571786i \(-0.806251\pi\)
0.905383 + 0.424596i \(0.139584\pi\)
\(654\) 0 0
\(655\) 1.17157 + 2.02922i 0.0457771 + 0.0792883i
\(656\) 0 0
\(657\) −21.6569 −0.844914
\(658\) 0 0
\(659\) −35.3137 −1.37563 −0.687813 0.725888i \(-0.741429\pi\)
−0.687813 + 0.725888i \(0.741429\pi\)
\(660\) 0 0
\(661\) 13.8431 + 23.9770i 0.538436 + 0.932598i 0.998989 + 0.0449660i \(0.0143180\pi\)
−0.460553 + 0.887632i \(0.652349\pi\)
\(662\) 0 0
\(663\) −8.82843 + 15.2913i −0.342868 + 0.593864i
\(664\) 0 0
\(665\) 9.17157 + 11.8272i 0.355658 + 0.458638i
\(666\) 0 0
\(667\) 9.13604 15.8241i 0.353749 0.612711i
\(668\) 0 0
\(669\) 22.8995 + 39.6631i 0.885346 + 1.53346i
\(670\) 0 0
\(671\) −22.4853 −0.868035
\(672\) 0 0
\(673\) 5.65685 0.218056 0.109028 0.994039i \(-0.465226\pi\)
0.109028 + 0.994039i \(0.465226\pi\)
\(674\) 0 0
\(675\) 0.207107 + 0.358719i 0.00797154 + 0.0138071i
\(676\) 0 0
\(677\) 5.48528 9.50079i 0.210816 0.365145i −0.741154 0.671335i \(-0.765721\pi\)
0.951970 + 0.306190i \(0.0990544\pi\)
\(678\) 0 0
\(679\) 15.7279 2.15232i 0.603582 0.0825983i
\(680\) 0 0
\(681\) 16.8995 29.2708i 0.647590 1.12166i
\(682\) 0 0
\(683\) −8.03553 13.9180i −0.307471 0.532556i 0.670337 0.742057i \(-0.266149\pi\)
−0.977808 + 0.209501i \(0.932816\pi\)
\(684\) 0 0
\(685\) −4.00000 −0.152832
\(686\) 0 0
\(687\) −33.7990 −1.28951
\(688\) 0 0
\(689\) −5.65685 9.79796i −0.215509 0.373273i
\(690\) 0 0
\(691\) 15.3848 26.6472i 0.585264 1.01371i −0.409578 0.912275i \(-0.634324\pi\)
0.994842 0.101433i \(-0.0323426\pi\)
\(692\) 0 0
\(693\) 35.7990 4.89898i 1.35989 0.186097i
\(694\) 0 0
\(695\) −7.24264 + 12.5446i −0.274729 + 0.475845i
\(696\) 0 0
\(697\) −0.313708 0.543359i −0.0118826 0.0205812i
\(698\) 0 0
\(699\) 0.828427 0.0313340
\(700\) 0 0
\(701\) −11.0000 −0.415464 −0.207732 0.978186i \(-0.566608\pi\)
−0.207732 + 0.978186i \(0.566608\pi\)
\(702\) 0 0
\(703\) −16.0000 27.7128i −0.603451 1.04521i
\(704\) 0 0
\(705\) 0.414214 0.717439i 0.0156002 0.0270203i
\(706\) 0 0
\(707\) −8.89340 11.4685i −0.334471 0.431316i
\(708\) 0 0
\(709\) −24.7132 + 42.8045i −0.928124 + 1.60756i −0.141665 + 0.989915i \(0.545246\pi\)
−0.786459 + 0.617643i \(0.788088\pi\)
\(710\) 0 0
\(711\) −5.65685 9.79796i −0.212149 0.367452i
\(712\) 0 0
\(713\) 40.6274 1.52151
\(714\) 0 0
\(715\) 9.65685 0.361146
\(716\) 0 0
\(717\) −16.3137 28.2562i −0.609247 1.05525i
\(718\) 0 0
\(719\) 6.89949 11.9503i 0.257308 0.445670i −0.708212 0.706000i \(-0.750498\pi\)
0.965520 + 0.260330i \(0.0838313\pi\)
\(720\) 0 0
\(721\) 10.4142 25.5095i 0.387846 0.950024i
\(722\) 0 0
\(723\) 12.0711 20.9077i 0.448928 0.777566i
\(724\) 0 0
\(725\) 1.08579 + 1.88064i 0.0403251 + 0.0698451i
\(726\) 0 0
\(727\) −23.9289 −0.887475 −0.443737 0.896157i \(-0.646348\pi\)
−0.443737 + 0.896157i \(0.646348\pi\)
\(728\) 0 0
\(729\) −23.8284 −0.882534
\(730\) 0 0
\(731\) 23.5858 + 40.8518i 0.872352 + 1.51096i
\(732\) 0 0
\(733\) 1.82843 3.16693i 0.0675345 0.116973i −0.830281 0.557345i \(-0.811820\pi\)
0.897815 + 0.440372i \(0.145153\pi\)
\(734\) 0 0
\(735\) 16.2782 4.54026i 0.600430 0.167470i
\(736\) 0 0
\(737\) 16.6569 28.8505i 0.613563 1.06272i
\(738\) 0 0
\(739\) 5.58579 + 9.67487i 0.205476 + 0.355896i 0.950284 0.311383i \(-0.100792\pi\)
−0.744808 + 0.667279i \(0.767459\pi\)
\(740\) 0 0
\(741\) −27.3137 −1.00339
\(742\) 0 0
\(743\) 19.2426 0.705944 0.352972 0.935634i \(-0.385171\pi\)
0.352972 + 0.935634i \(0.385171\pi\)
\(744\) 0 0
\(745\) 3.32843 + 5.76500i 0.121944 + 0.211213i
\(746\) 0 0
\(747\) −18.7279 + 32.4377i −0.685219 + 1.18683i
\(748\) 0 0
\(749\) −8.41421 + 20.6105i −0.307449 + 0.753092i
\(750\) 0 0
\(751\) −6.00000 + 10.3923i −0.218943 + 0.379221i −0.954485 0.298259i \(-0.903594\pi\)
0.735542 + 0.677479i \(0.236928\pi\)
\(752\) 0 0
\(753\) 28.3137 + 49.0408i 1.03181 + 1.78715i
\(754\) 0 0
\(755\) 16.8284 0.612449
\(756\) 0 0
\(757\) 6.00000 0.218074 0.109037 0.994038i \(-0.465223\pi\)
0.109037 + 0.994038i \(0.465223\pi\)
\(758\) 0 0
\(759\) −49.0416 84.9426i −1.78010 3.08322i
\(760\) 0 0
\(761\) −11.9706 + 20.7336i −0.433933 + 0.751593i −0.997208 0.0746761i \(-0.976208\pi\)
0.563275 + 0.826269i \(0.309541\pi\)
\(762\) 0 0
\(763\) 6.99390 + 9.01897i 0.253196 + 0.326509i
\(764\) 0 0
\(765\) −5.17157 + 8.95743i −0.186979 + 0.323856i
\(766\) 0 0
\(767\) −4.00000 6.92820i −0.144432 0.250163i
\(768\) 0 0
\(769\) −47.2548 −1.70405 −0.852026 0.523499i \(-0.824626\pi\)
−0.852026 + 0.523499i \(0.824626\pi\)
\(770\) 0 0
\(771\) −17.6569 −0.635896
\(772\) 0 0
\(773\) −17.8284 30.8797i −0.641244 1.11067i −0.985155 0.171665i \(-0.945085\pi\)
0.343911 0.939002i \(-0.388248\pi\)
\(774\) 0 0
\(775\) −2.41421 + 4.18154i −0.0867211 + 0.150205i
\(776\) 0 0
\(777\) −35.7990 + 4.89898i −1.28428 + 0.175750i
\(778\) 0 0
\(779\) 0.485281 0.840532i 0.0173870 0.0301152i
\(780\) 0 0
\(781\) −28.9706 50.1785i −1.03665 1.79553i
\(782\) 0 0
\(783\) 0.899495 0.0321453
\(784\) 0 0
\(785\) −21.3137 −0.760719
\(786\) 0 0
\(787\) −2.20711 3.82282i −0.0786749 0.136269i 0.824004 0.566585i \(-0.191736\pi\)
−0.902678 + 0.430316i \(0.858402\pi\)
\(788\) 0 0
\(789\) 11.7426 20.3389i 0.418049 0.724082i
\(790\) 0 0
\(791\) −29.6569 + 4.05845i −1.05448 + 0.144302i
\(792\) 0 0
\(793\) 4.65685 8.06591i 0.165370 0.286429i
\(794\) 0 0
\(795\) −6.82843 11.8272i −0.242179 0.419467i
\(796\) 0