Properties

Label 280.2.q.d.81.2
Level $280$
Weight $2$
Character 280.81
Analytic conductor $2.236$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 280.q (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.23581125660\)
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: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 81.2
Root \(0.707107 - 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 280.81
Dual form 280.2.q.d.121.2

$q$-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 \(\left(\mathbb{Z}/280\mathbb{Z}\right)^\times\).

\(n\) \(57\) \(71\) \(141\) \(241\)
\(\chi(n)\) \(1\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 1.20711 2.09077i 0.696923 1.20711i −0.272605 0.962126i \(-0.587885\pi\)
0.969528 0.244981i \(-0.0787816\pi\)
\(4\) 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 −0.229851 0.973226i \(-0.573824\pi\)
0.957764 0.287556i \(-0.0928428\pi\)
\(12\) 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 −0.997943 0.0641009i \(-0.979582\pi\)
0.554485 + 0.832194i \(0.312915\pi\)
\(18\) 0 0
\(19\) −2.82843 4.89898i −0.648886 1.12390i −0.983389 0.181509i \(-0.941902\pi\)
0.334504 0.942394i \(-0.391431\pi\)
\(20\) 0 0
\(21\) −3.91421 + 5.04757i −0.854151 + 1.10147i
\(22\) 0 0
\(23\) 4.20711 + 7.28692i 0.877242 + 1.51943i 0.854355 + 0.519690i \(0.173953\pi\)
0.0228877 + 0.999738i \(0.492714\pi\)
\(24\) 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 \(-0.690574\pi\)
0.997181 + 0.0750380i \(0.0239078\pi\)
\(32\) 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 0.999201 0.0399642i \(-0.0127244\pi\)
−0.534211 + 0.845351i \(0.679391\pi\)
\(38\) 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 \(-0.0577676\pi\)
0.983577 + 0.180488i \(0.0577676\pi\)
\(44\) 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 \(-0.174634\pi\)
−0.878267 + 0.478170i \(0.841300\pi\)
\(48\) 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 −0.992250 0.124258i \(-0.960345\pi\)
0.603736 + 0.797185i \(0.293678\pi\)
\(54\) 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 \(-0.749486\pi\)
0.966342 + 0.257260i \(0.0828195\pi\)
\(60\) 0 0
\(61\) 2.32843 + 4.03295i 0.298125 + 0.516367i 0.975707 0.219080i \(-0.0703056\pi\)
−0.677582 + 0.735447i \(0.736972\pi\)
\(62\) 0 0
\(63\) 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 \(-0.971813\pi\)
0.574628 + 0.818415i \(0.305147\pi\)
\(68\) 0 0
\(69\) 20.3137 2.44548
\(70\) 0 0
\(71\) −12.0000 −1.42414 −0.712069 0.702109i \(-0.752242\pi\)
−0.712069 + 0.702109i \(0.752242\pi\)
\(72\) 0 0
\(73\) 3.82843 6.63103i 0.448084 0.776103i −0.550178 0.835048i \(-0.685440\pi\)
0.998261 + 0.0589442i \(0.0187734\pi\)
\(74\) 0 0
\(75\) 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 \(-0.0944227\pi\)
−0.731307 + 0.682048i \(0.761089\pi\)
\(80\) 0 0
\(81\) 4.74264 8.21449i 0.526960 0.912722i
\(82\) 0 0
\(83\) −13.2426 −1.45357 −0.726784 0.686866i \(-0.758986\pi\)
−0.726784 + 0.686866i \(0.758986\pi\)
\(84\) 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 0.848202 + 0.529673i \(0.177686\pi\)
0.0346099 + 0.999401i \(0.488981\pi\)
\(90\) 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 −0.969604 0.244680i \(-0.921317\pi\)
0.696701 + 0.717362i \(0.254650\pi\)
\(102\) 0 0
\(103\) −5.20711 9.01897i −0.513071 0.888666i −0.999885 0.0151600i \(-0.995174\pi\)
0.486814 0.873506i \(-0.338159\pi\)
\(104\) 0 0
\(105\) 6.32843 + 0.866025i 0.617591 + 0.0845154i
\(106\) 0 0
\(107\) 4.20711 + 7.28692i 0.406716 + 0.704453i 0.994520 0.104551i \(-0.0333404\pi\)
−0.587803 + 0.809004i \(0.700007\pi\)
\(108\) 0 0
\(109\) 2.15685 3.73578i 0.206589 0.357823i −0.744049 0.668125i \(-0.767097\pi\)
0.950638 + 0.310302i \(0.100430\pi\)
\(110\) 0 0
\(111\) 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 \(-0.744445\pi\)
−0.694661 + 0.719338i \(0.744445\pi\)
\(128\) 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 \(-0.199306\pi\)
−0.912657 + 0.408727i \(0.865973\pi\)
\(132\) 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 −0.767853 0.640626i \(-0.778675\pi\)
0.938725 + 0.344668i \(0.112008\pi\)
\(138\) 0 0
\(139\) −14.4853 −1.22863 −0.614313 0.789063i \(-0.710567\pi\)
−0.614313 + 0.789063i \(0.710567\pi\)
\(140\) 0 0
\(141\) −0.828427 −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 0.969546 0.244909i \(-0.0787582\pi\)
−0.696871 + 0.717197i \(0.745425\pi\)
\(150\) 0 0
\(151\) 8.41421 14.5738i 0.684739 1.18600i −0.288780 0.957396i \(-0.593250\pi\)
0.973519 0.228607i \(-0.0734171\pi\)
\(152\) 0 0
\(153\) 10.3431 0.836194
\(154\) 0 0
\(155\) −4.82843 −0.387829
\(156\) 0 0
\(157\) 10.6569 18.4582i 0.850510 1.47313i −0.0302396 0.999543i \(-0.509627\pi\)
0.880749 0.473583i \(-0.157040\pi\)
\(158\) 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 \(-0.112261\pi\)
−0.768361 + 0.640017i \(0.778927\pi\)
\(164\) 0 0
\(165\) −5.82843 + 10.0951i −0.453742 + 0.785905i
\(166\) 0 0
\(167\) −12.0711 −0.934087 −0.467044 0.884234i \(-0.654681\pi\)
−0.467044 + 0.884234i \(0.654681\pi\)
\(168\) 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 −0.903234 0.429148i \(-0.858814\pi\)
0.0799642 0.996798i \(-0.474519\pi\)
\(174\) 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 \(-0.961499\pi\)
0.600841 + 0.799369i \(0.294833\pi\)
\(180\) 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 0.910408 + 0.413712i \(0.135768\pi\)
−0.0969189 + 0.995292i \(0.530899\pi\)
\(192\) 0 0
\(193\) −8.65685 + 14.9941i −0.623134 + 1.07930i 0.365765 + 0.930707i \(0.380808\pi\)
−0.988899 + 0.148592i \(0.952526\pi\)
\(194\) 0 0
\(195\) −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 \(-0.825590\pi\)
0.877932 + 0.478786i \(0.158923\pi\)
\(200\) 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 \(-0.721556\pi\)
−0.641182 + 0.767389i \(0.721556\pi\)
\(212\) 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 \(-0.280925\pi\)
0.635181 + 0.772363i \(0.280925\pi\)
\(224\) 0 0
\(225\) 2.82843 0.188562
\(226\) 0 0
\(227\) −7.00000 + 12.1244i −0.464606 + 0.804722i −0.999184 0.0403978i \(-0.987137\pi\)
0.534577 + 0.845120i \(0.320471\pi\)
\(228\) 0 0
\(229\) 7.00000 + 12.1244i 0.462573 + 0.801200i 0.999088 0.0426906i \(-0.0135930\pi\)
−0.536515 + 0.843891i \(0.680260\pi\)
\(230\) 0 0
\(231\) 11.6569 + 28.5533i 0.766965 + 1.87867i
\(232\) 0 0
\(233\) −0.171573 0.297173i −0.0112401 0.0194684i 0.860351 0.509703i \(-0.170245\pi\)
−0.871591 + 0.490234i \(0.836911\pi\)
\(234\) 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 \(-0.643993\pi\)
−0.437097 + 0.899414i \(0.643993\pi\)
\(240\) 0 0
\(241\) 5.00000 8.66025i 0.322078 0.557856i −0.658838 0.752285i \(-0.728952\pi\)
0.980917 + 0.194429i \(0.0622852\pi\)
\(242\) 0 0
\(243\) −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 \(-0.234702\pi\)
0.740260 + 0.672321i \(0.234702\pi\)
\(252\) 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 0.957247 0.289270i \(-0.0934126\pi\)
−0.729139 + 0.684365i \(0.760079\pi\)
\(258\) 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 \(-0.930295\pi\)
0.676194 + 0.736724i \(0.263628\pi\)
\(264\) 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 −0.928237 0.371989i \(-0.878676\pi\)
0.786270 + 0.617882i \(0.212009\pi\)
\(270\) 0 0
\(271\) −9.65685 16.7262i −0.586612 1.01604i −0.994672 0.103087i \(-0.967128\pi\)
0.408060 0.912955i \(-0.366205\pi\)
\(272\) 0 0
\(273\) −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 −0.500478 0.865750i \(-0.666842\pi\)
1.00000 0.000551476i \(0.000175540\pi\)
\(278\) 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 0.464169 + 0.885747i \(0.346353\pi\)
−0.999164 + 0.0408910i \(0.986980\pi\)
\(284\) 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 \(-0.376647\pi\)
0.377899 + 0.925847i \(0.376647\pi\)
\(308\) 0 0
\(309\) −25.1421 −1.43029
\(310\) 0 0
\(311\) −5.17157 + 8.95743i −0.293253 + 0.507929i −0.974577 0.224053i \(-0.928071\pi\)
0.681324 + 0.731982i \(0.261404\pi\)
\(312\) 0 0
\(313\) 6.48528 + 11.2328i 0.366570 + 0.634917i 0.989027 0.147737i \(-0.0471988\pi\)
−0.622457 + 0.782654i \(0.713865\pi\)
\(314\) 0 0
\(315\) 4.58579 5.91359i 0.258380 0.333193i
\(316\) 0 0
\(317\) 11.0000 + 19.0526i 0.617822 + 1.07010i 0.989882 + 0.141890i \(0.0453179\pi\)
−0.372061 + 0.928208i \(0.621349\pi\)
\(318\) 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 \(-0.250880\pi\)
−0.966638 + 0.256148i \(0.917547\pi\)
\(332\) 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 −0.293202 0.956051i \(-0.594721\pi\)
0.974565 0.224105i \(-0.0719458\pi\)
\(348\) 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 0.399000 + 0.916951i \(0.369357\pi\)
−0.993603 + 0.112931i \(0.963976\pi\)
\(354\) 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 \(-0.255906\pi\)
−0.970562 + 0.240853i \(0.922573\pi\)
\(360\) 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 0.348837 + 0.937183i \(0.386577\pi\)
−0.986043 + 0.166490i \(0.946757\pi\)
\(368\) 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 0.667839 0.744306i \(-0.267219\pi\)
−0.978507 + 0.206213i \(0.933886\pi\)
\(374\) 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 \(-0.252512\pi\)
0.701505 + 0.712664i \(0.252512\pi\)
\(380\) 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 \(-0.327069\pi\)
−0.999806 + 0.0196803i \(0.993735\pi\)
\(384\) 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 −0.558687 0.829379i \(-0.688695\pi\)
0.997606 + 0.0691473i \(0.0220278\pi\)
\(390\) 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 −0.999790 0.0204787i \(-0.993481\pi\)
0.482160 0.876083i \(-0.339852\pi\)
\(398\) 0 0
\(399\) 35.7990 + 4.89898i 1.79219 + 0.245256i
\(400\) 0 0
\(401\) 4.84315 + 8.38857i 0.241855 + 0.418905i 0.961243 0.275703i \(-0.0889108\pi\)
−0.719388 + 0.694609i \(0.755577\pi\)
\(402\) 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 −0.902250 0.431212i \(-0.858086\pi\)
0.824566 + 0.565766i \(0.191419\pi\)
\(410\) 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 \(-0.442827\pi\)
0.178649 + 0.983913i \(0.442827\pi\)
\(420\) 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 \(-0.870433\pi\)
0.802006 + 0.597317i \(0.203766\pi\)
\(432\) 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 0.965700 + 0.259660i \(0.0836105\pi\)
−0.257978 + 0.966151i \(0.583056\pi\)
\(440\) 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 \(-0.0225509\pi\)
−0.560049 + 0.828460i \(0.689218\pi\)
\(444\) 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 0.918281 0.395928i \(-0.129577\pi\)
−0.802025 + 0.597291i \(0.796244\pi\)
\(458\) 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 \(-0.536318\pi\)
−0.113849 + 0.993498i \(0.536318\pi\)
\(464\) 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 \(-0.286347\pi\)
−0.989125 + 0.147078i \(0.953013\pi\)
\(468\) 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 \(-0.694554\pi\)
0.996165 + 0.0874978i \(0.0278871\pi\)
\(480\) 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 \(-0.969296\pi\)
0.581082 + 0.813845i \(0.302630\pi\)
\(488\) 0 0
\(489\) 10.4853 0.474161
\(490\) 0 0
\(491\) 18.4853 0.834229 0.417115 0.908854i \(-0.363041\pi\)
0.417115 + 0.908854i \(0.363041\pi\)
\(492\) 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 \(-0.282168\pi\)
−0.987109 + 0.160049i \(0.948835\pi\)
\(500\) 0 0
\(501\) −14.5711 + 25.2378i −0.650987 + 1.12754i
\(502\) 0 0
\(503\) −18.0711 −0.805749 −0.402875 0.915255i \(-0.631989\pi\)
−0.402875 + 0.915255i \(0.631989\pi\)
\(504\) 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 0.988936 0.148341i \(-0.0473933\pi\)
−0.622935 + 0.782273i \(0.714060\pi\)
\(510\) 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 −0.755926 0.654657i \(-0.772813\pi\)
0.944913 + 0.327322i \(0.106146\pi\)
\(522\) 0 0
\(523\) 19.9706 + 34.5900i 0.873252 + 1.51252i 0.858613 + 0.512624i \(0.171326\pi\)
0.0146382 + 0.999893i \(0.495340\pi\)
\(524\) 0 0
\(525\) −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 0.927513 0.373790i \(-0.121942\pi\)
−0.787468 + 0.616355i \(0.788609\pi\)
\(542\) 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 \(-0.701970\pi\)
−0.592780 + 0.805364i \(0.701970\pi\)
\(548\) 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 −0.916808 0.399329i \(-0.869243\pi\)
0.804233 + 0.594314i \(0.202576\pi\)
\(558\) 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 \(-0.901403\pi\)
0.740187 + 0.672401i \(0.234737\pi\)
\(564\) 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 0.761327 0.648368i \(-0.224548\pi\)
−0.942167 + 0.335144i \(0.891215\pi\)
\(570\) 0 0
\(571\) −6.48528 + 11.2328i −0.271401 + 0.470080i −0.969221 0.246193i \(-0.920820\pi\)
0.697820 + 0.716273i \(0.254153\pi\)
\(572\) 0 0
\(573\) 54.2843 2.26776
\(574\) 0 0
\(575\) −8.41421 −0.350897
\(576\) 0 0
\(577\) −17.1421 + 29.6910i −0.713636 + 1.23605i 0.249847 + 0.968285i \(0.419620\pi\)
−0.963483 + 0.267769i \(0.913714\pi\)
\(578\) 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 \(-0.884734\pi\)
−0.935148 + 0.354256i \(0.884734\pi\)
\(588\) 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 0.932503 + 0.361163i \(0.117620\pi\)
−0.153475 + 0.988153i \(0.549046\pi\)
\(594\) 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 \(-0.816239\pi\)
0.891615 + 0.452794i \(0.149573\pi\)
\(600\) 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 \(-0.290973\pi\)
−0.991158 + 0.132687i \(0.957640\pi\)
\(608\) 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 −0.912331 0.409453i \(-0.865719\pi\)
0.810763 + 0.585375i \(0.199053\pi\)
\(614\) 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 \(-0.759387\pi\)
0.957874 + 0.287188i \(0.0927206\pi\)
\(620\) 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 \(-0.619938\pi\)
−0.367944 + 0.929848i \(0.619938\pi\)
\(632\) 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 0.205113 0.978738i \(-0.434244\pi\)
0.745056 0.667002i \(-0.232423\pi\)
\(642\) 0 0
\(643\) 26.0000 1.02534 0.512670 0.858586i \(-0.328656\pi\)
0.512670 + 0.858586i \(0.328656\pi\)
\(644\) 0 0
\(645\) −31.1421 −1.22622
\(646\) 0 0
\(647\) 14.6213 25.3249i 0.574823 0.995623i −0.421237 0.906950i \(-0.638404\pi\)
0.996061 0.0886729i \(-0.0282626\pi\)
\(648\) 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 0.905383 0.424596i \(-0.139584\pi\)
−0.820403 + 0.571786i \(0.806251\pi\)
\(654\) 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 \(-0.258571\pi\)
0.687813 + 0.725888i \(0.258571\pi\)
\(660\) 0 0
\(661\) 13.8431 23.9770i 0.538436 0.932598i −0.460553 0.887632i \(-0.652349\pi\)
0.998989 0.0449660i \(-0.0143180\pi\)
\(662\) 0 0
\(663\) 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 0.951970 0.306190i \(-0.0990544\pi\)
−0.741154 + 0.671335i \(0.765721\pi\)
\(678\) 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 \(-0.733851\pi\)
0.977808 + 0.209501i \(0.0671839\pi\)
\(684\) 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 −0.994842 0.101433i \(-0.967657\pi\)
0.409578 0.912275i \(-0.365676\pi\)
\(692\) 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 −0.786459 0.617643i \(-0.788088\pi\)
−0.141665 0.989915i \(-0.545246\pi\)
\(710\) 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 \(-0.249502\pi\)
−0.965520 + 0.260330i \(0.916169\pi\)
\(720\) 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 \(-0.353652\pi\)
0.443737 + 0.896157i \(0.353652\pi\)
\(728\) 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 0.897815 0.440372i \(-0.145153\pi\)
−0.830281 + 0.557345i \(0.811820\pi\)
\(734\) 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 \(-0.899208\pi\)
0.744808 + 0.667279i \(0.232541\pi\)
\(740\) 0 0
\(741\) −27.3137 −1.00339
\(742\) 0 0
\(743\) −19.2426 −0.705944 −0.352972 0.935634i \(-0.614829\pi\)
−0.352972 + 0.935634i \(0.614829\pi\)
\(744\) 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 \(-0.0964058\pi\)
−0.735542 + 0.677479i \(0.763072\pi\)
\(752\) 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 0.563275 0.826269i \(-0.309541\pi\)
−0.997208 + 0.0746761i \(0.976208\pi\)
\(762\) 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 0.343911 + 0.939002i \(0.388248\pi\)
−0.985155 + 0.171665i \(0.945085\pi\)
\(774\) 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 \(-0.808264\pi\)
0.902678 + 0.430316i \(0.141598\pi\)
\(788\) 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 0
\(797\) −12.6863 −0.449372