Properties

Label 1960.2.q.q.961.1
Level $1960$
Weight $2$
Character 1960.961
Analytic conductor $15.651$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1960 = 2^{3} \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1960.q (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(15.6506787962\)
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 961.1
Root \(-0.707107 - 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 1960.961
Dual form 1960.2.q.q.361.1

$q$-expansion

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

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1960\mathbb{Z}\right)^\times\).

\(n\) \(981\) \(1081\) \(1177\) \(1471\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(1\) \(1\)

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
\(7\) 0 0
\(8\) 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 \(0.0928428\pi\)
−0.229851 + 0.973226i \(0.573824\pi\)
\(12\) 0 0
\(13\) −2.00000 −0.554700 −0.277350 0.960769i \(-0.589456\pi\)
−0.277350 + 0.960769i \(0.589456\pi\)
\(14\) 0 0
\(15\) −2.41421 −0.623347
\(16\) 0 0
\(17\) 1.82843 + 3.16693i 0.443459 + 0.768093i 0.997943 0.0641009i \(-0.0204179\pi\)
−0.554485 + 0.832194i \(0.687085\pi\)
\(18\) 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
\(21\) 0 0
\(22\) 0 0
\(23\) 4.20711 7.28692i 0.877242 1.51943i 0.0228877 0.999738i \(-0.492714\pi\)
0.854355 0.519690i \(-0.173953\pi\)
\(24\) 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
\(35\) 0 0
\(36\) 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 \(-0.504265\pi\)
−0.0133976 + 0.999910i \(0.504265\pi\)
\(42\) 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 \(-0.825366\pi\)
0.878267 + 0.478170i \(0.158700\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 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 −0.975707 0.219080i \(-0.929694\pi\)
0.677582 + 0.735447i \(0.263028\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −1.00000 + 1.73205i −0.124035 + 0.214834i
\(66\) 0 0
\(67\) −3.44975 5.97514i −0.421454 0.729979i 0.574628 0.818415i \(-0.305147\pi\)
−0.996082 + 0.0884353i \(0.971813\pi\)
\(68\) 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 \(-0.314560\pi\)
−0.998261 + 0.0589442i \(0.981227\pi\)
\(74\) 0 0
\(75\) −1.20711 + 2.09077i −0.139385 + 0.241421i
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 2.00000 3.46410i 0.225018 0.389742i −0.731307 0.682048i \(-0.761089\pi\)
0.956325 + 0.292306i \(0.0944227\pi\)
\(80\) 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 \(0.511019\pi\)
−0.848202 + 0.529673i \(0.822314\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 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 \(-0.598524\pi\)
−0.304604 + 0.952479i \(0.598524\pi\)
\(98\) 0 0
\(99\) −13.6569 −1.37257
\(100\) 0 0
\(101\) 2.74264 + 4.75039i 0.272903 + 0.472682i 0.969604 0.244680i \(-0.0786829\pi\)
−0.696701 + 0.717362i \(0.745350\pi\)
\(102\) 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
\(105\) 0 0
\(106\) 0 0
\(107\) 4.20711 7.28692i 0.406716 0.704453i −0.587803 0.809004i \(-0.700007\pi\)
0.994520 + 0.104551i \(0.0333404\pi\)
\(108\) 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
\(119\) 0 0
\(120\) 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 \(-0.800694\pi\)
0.912657 + 0.408727i \(0.134027\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 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
\(147\) 0 0
\(148\) 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 \(0.0734171\pi\)
−0.288780 + 0.957396i \(0.593250\pi\)
\(152\) 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 \(-0.842960\pi\)
0.0302396 0.999543i \(-0.490373\pi\)
\(158\) 0 0
\(159\) −6.82843 + 11.8272i −0.541529 + 0.937957i
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 2.17157 3.76127i 0.170091 0.294606i −0.768361 0.640017i \(-0.778927\pi\)
0.938451 + 0.345411i \(0.112261\pi\)
\(164\) 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 \(-0.525481\pi\)
0.903234 0.429148i \(-0.141186\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −4.82843 + 8.36308i −0.362927 + 0.628608i
\(178\) 0 0
\(179\) −5.24264 9.08052i −0.391853 0.678710i 0.600841 0.799369i \(-0.294833\pi\)
−0.992694 + 0.120659i \(0.961499\pi\)
\(180\) 0 0
\(181\) 9.82843 0.730541 0.365271 0.930901i \(-0.380976\pi\)
0.365271 + 0.930901i \(0.380976\pi\)
\(182\) 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
\(189\) 0 0
\(190\) 0 0
\(191\) 11.2426 19.4728i 0.813489 1.40900i −0.0969189 0.995292i \(-0.530899\pi\)
0.910408 0.413712i \(-0.135768\pi\)
\(192\) 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
\(203\) 0 0
\(204\) 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
\(217\) 0 0
\(218\) 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 −0.999088 0.0426906i \(-0.986407\pi\)
0.536515 + 0.843891i \(0.319740\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 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 \(-0.643993\pi\)
−0.437097 + 0.899414i \(0.643993\pi\)
\(240\) 0 0
\(241\) −5.00000 8.66025i −0.322078 0.557856i 0.658838 0.752285i \(-0.271048\pi\)
−0.980917 + 0.194429i \(0.937715\pi\)
\(242\) 0 0
\(243\) 10.8284 18.7554i 0.694644 1.20316i
\(244\) 0 0
\(245\) 0 0
\(246\) 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 −0.957247 0.289270i \(-0.906587\pi\)
0.729139 + 0.684365i \(0.239921\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 3.07107 5.31925i 0.190094 0.329253i
\(262\) 0 0
\(263\) −4.86396 8.42463i −0.299925 0.519485i 0.676194 0.736724i \(-0.263628\pi\)
−0.976118 + 0.217239i \(0.930295\pi\)
\(264\) 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 \(-0.121324\pi\)
−0.786270 + 0.617882i \(0.787991\pi\)
\(270\) 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
\(273\) 0 0
\(274\) 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 0
\(288\) 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 \(-0.334906\pi\)
0.495715 + 0.868485i \(0.334906\pi\)
\(294\) 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
\(301\) 0 0
\(302\) 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 −0.989027 0.147737i \(-0.952801\pi\)
0.622457 + 0.782654i \(0.286135\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 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 0
\(330\) 0 0
\(331\) −4.75736 + 8.23999i −0.261488 + 0.452911i −0.966638 0.256148i \(-0.917547\pi\)
0.705149 + 0.709059i \(0.250880\pi\)
\(332\) 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
\(343\) 0 0
\(344\) 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 \(0.0719458\pi\)
−0.293202 + 0.956051i \(0.594721\pi\)
\(348\) 0 0
\(349\) −4.17157 −0.223299 −0.111650 0.993748i \(-0.535613\pi\)
−0.111650 + 0.993748i \(0.535613\pi\)
\(350\) 0 0
\(351\) 0.828427 0.0442182
\(352\) 0 0
\(353\) 11.1716 + 19.3497i 0.594603 + 1.02988i 0.993603 + 0.112931i \(0.0360240\pi\)
−0.399000 + 0.916951i \(0.630643\pi\)
\(354\) 0 0
\(355\) −6.00000 + 10.3923i −0.318447 + 0.551566i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −5.24264 + 9.08052i −0.276696 + 0.479252i −0.970562 0.240853i \(-0.922573\pi\)
0.693866 + 0.720105i \(0.255906\pi\)
\(360\) 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
\(371\) 0 0
\(372\) 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 \(-0.252512\pi\)
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 \(-0.672931\pi\)
0.999806 + 0.0196803i \(0.00626483\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 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 \(-0.660148\pi\)
0.999790 0.0204787i \(-0.00651902\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 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 0.902250 0.431212i \(-0.141914\pi\)
−0.824566 + 0.565766i \(0.808581\pi\)
\(410\) 0 0
\(411\) 4.82843 8.36308i 0.238169 0.412520i
\(412\) 0 0
\(413\) 0 0
\(414\) 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
\(427\) 0 0
\(428\) 0 0
\(429\) −11.6569 + 20.1903i −0.562798 + 0.974795i
\(430\) 0 0
\(431\) −2.41421 4.18154i −0.116289 0.201418i 0.802006 0.597317i \(-0.203766\pi\)
−0.918294 + 0.395899i \(0.870433\pi\)
\(432\) 0 0
\(433\) −3.31371 −0.159247 −0.0796233 0.996825i \(-0.525372\pi\)
−0.0796233 + 0.996825i \(0.525372\pi\)
\(434\) 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
\(441\) 0 0
\(442\) 0 0
\(443\) 9.20711 15.9472i 0.437443 0.757673i −0.560049 0.828460i \(-0.689218\pi\)
0.997491 + 0.0707865i \(0.0225509\pi\)
\(444\) 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
\(455\) 0 0
\(456\) 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 \(-0.334677\pi\)
0.496339 + 0.868129i \(0.334677\pi\)
\(462\) 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 \(-0.713653\pi\)
0.989125 + 0.147078i \(0.0469868\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 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
\(483\) 0 0
\(484\) 0 0
\(485\) −3.00000 + 5.19615i −0.136223 + 0.235945i
\(486\) 0 0
\(487\) −9.14214 15.8346i −0.414270 0.717536i 0.581082 0.813845i \(-0.302630\pi\)
−0.995351 + 0.0963090i \(0.969296\pi\)
\(488\) 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
\(497\) 0 0
\(498\) 0 0
\(499\) −7.92893 + 13.7333i −0.354948 + 0.614788i −0.987109 0.160049i \(-0.948835\pi\)
0.632161 + 0.774837i \(0.282168\pi\)
\(500\) 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 −0.988936 0.148341i \(-0.952607\pi\)
0.622935 + 0.782273i \(0.285940\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 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 \(-0.227187\pi\)
−0.944913 + 0.327322i \(0.893854\pi\)
\(522\) 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
\(525\) 0 0
\(526\) 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
\(539\) 0 0
\(540\) 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 \(-0.701970\pi\)
−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
\(553\) 0 0
\(554\) 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
\(567\) 0 0
\(568\) 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 0.697820 0.716273i \(-0.254153\pi\)
−0.969221 + 0.246193i \(0.920820\pi\)
\(572\) 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 \(0.0862865\pi\)
−0.249847 + 0.968285i \(0.580380\pi\)
\(578\) 0 0
\(579\) −20.8995 + 36.1990i −0.868553 + 1.50438i
\(580\) 0 0
\(581\) 0 0
\(582\) 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 \(0.450954\pi\)
−0.932503 + 0.361163i \(0.882380\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −0.828427 + 1.43488i −0.0339053 + 0.0587256i
\(598\) 0 0
\(599\) 1.31371 + 2.27541i 0.0536767 + 0.0929707i 0.891615 0.452794i \(-0.149573\pi\)
−0.837939 + 0.545765i \(0.816239\pi\)
\(600\) 0 0
\(601\) 34.0000 1.38689 0.693444 0.720510i \(-0.256092\pi\)
0.693444 + 0.720510i \(0.256092\pi\)
\(602\) 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
\(609\) 0 0
\(610\) 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
\(623\) 0 0
\(624\) 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
\(637\) 0 0
\(638\) 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
\(651\) 0 0
\(652\) 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 \(-0.258571\pi\)
0.687813 + 0.725888i \(0.258571\pi\)
\(660\) 0 0
\(661\) −13.8431 23.9770i −0.538436 0.932598i −0.998989 0.0449660i \(-0.985682\pi\)
0.460553 0.887632i \(-0.347651\pi\)
\(662\) 0 0
\(663\) −8.82843 + 15.2913i −0.342868 + 0.593864i
\(664\) 0 0
\(665\) 0 0
\(666\) 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 \(-0.900946\pi\)
0.741154 + 0.671335i \(0.234279\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 16.8995 29.2708i 0.647590 1.12166i
\(682\) 0 0
\(683\) 8.03553 + 13.9180i 0.307471 + 0.532556i 0.977808 0.209501i \(-0.0671839\pi\)
−0.670337 + 0.742057i \(0.733851\pi\)
\(684\) 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
\(693\) 0 0
\(694\) 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
\(707\) 0 0
\(708\) 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
\(721\) 0 0
\(722\) 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 −0.897815 0.440372i \(-0.854847\pi\)
0.830281 + 0.557345i \(0.188180\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 16.6569 28.8505i 0.613563 1.06272i
\(738\) 0 0
\(739\) −5.58579 9.67487i −0.205476 0.355896i 0.744808 0.667279i \(-0.232541\pi\)
−0.950284 + 0.311383i \(0.899208\pi\)
\(740\) 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
\(749\) 0 0
\(750\) 0 0
\(751\) 6.00000 10.3923i 0.218943 0.379221i −0.735542 0.677479i \(-0.763072\pi\)
0.954485 + 0.298259i \(0.0964058\pi\)
\(752\) 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 \(-0.690459\pi\)
0.997208 + 0.0746761i \(0.0237923\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 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 \(-0.175374\pi\)
0.852026 + 0.523499i \(0.175374\pi\)
\(770\) 0 0
\(771\) 17.6569 0.635896
\(772\) 0 0
\(773\) 17.8284 + 30.8797i 0.641244 + 1.11067i 0.985155 + 0.171665i \(0.0549147\pi\)
−0.343911 + 0.939002i \(0.611752\pi\)
\(774\) 0 0
\(775\) −2.41421 + 4.18154i −0.0867211 + 0.150205i
\(776\) 0 0
\(777\) 0 0
\(778\) 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
\(791\) 0 0
\(792\) 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 0.224686 0.974431i \(-0.427864\pi\)
0.224686 + 0.974431i \(0.427864\pi\)
\(798\) 0 0
\(799\) 1.25483 0.0443928