Properties

Label 882.2.g.k.361.1
Level $882$
Weight $2$
Character 882.361
Analytic conductor $7.043$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 882.g (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.04280545828\)
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 361.1
Root \(-0.707107 - 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 882.361
Dual form 882.2.g.k.667.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.707107 - 1.22474i) q^{5} +1.00000 q^{8} +O(q^{10})\) \(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.707107 - 1.22474i) q^{5} +1.00000 q^{8} +(-0.707107 + 1.22474i) q^{10} +(-2.00000 + 3.46410i) q^{11} +4.24264 q^{13} +(-0.500000 - 0.866025i) q^{16} +(3.53553 - 6.12372i) q^{17} +(2.82843 + 4.89898i) q^{19} +1.41421 q^{20} +4.00000 q^{22} +(-4.00000 - 6.92820i) q^{23} +(1.50000 - 2.59808i) q^{25} +(-2.12132 - 3.67423i) q^{26} +2.00000 q^{29} +(-0.500000 + 0.866025i) q^{32} -7.07107 q^{34} +(-2.00000 - 3.46410i) q^{37} +(2.82843 - 4.89898i) q^{38} +(-0.707107 - 1.22474i) q^{40} +9.89949 q^{41} -4.00000 q^{43} +(-2.00000 - 3.46410i) q^{44} +(-4.00000 + 6.92820i) q^{46} +(-2.82843 - 4.89898i) q^{47} -3.00000 q^{50} +(-2.12132 + 3.67423i) q^{52} +(-2.00000 + 3.46410i) q^{53} +5.65685 q^{55} +(-1.00000 - 1.73205i) q^{58} +(5.65685 - 9.79796i) q^{59} +(-0.707107 - 1.22474i) q^{61} +1.00000 q^{64} +(-3.00000 - 5.19615i) q^{65} +(6.00000 - 10.3923i) q^{67} +(3.53553 + 6.12372i) q^{68} +(7.77817 - 13.4722i) q^{73} +(-2.00000 + 3.46410i) q^{74} -5.65685 q^{76} +(8.00000 + 13.8564i) q^{79} +(-0.707107 + 1.22474i) q^{80} +(-4.94975 - 8.57321i) q^{82} -5.65685 q^{83} -10.0000 q^{85} +(2.00000 + 3.46410i) q^{86} +(-2.00000 + 3.46410i) q^{88} +(-3.53553 - 6.12372i) q^{89} +8.00000 q^{92} +(-2.82843 + 4.89898i) q^{94} +(4.00000 - 6.92820i) q^{95} +7.07107 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 2q^{2} - 2q^{4} + 4q^{8} + O(q^{10}) \) \( 4q - 2q^{2} - 2q^{4} + 4q^{8} - 8q^{11} - 2q^{16} + 16q^{22} - 16q^{23} + 6q^{25} + 8q^{29} - 2q^{32} - 8q^{37} - 16q^{43} - 8q^{44} - 16q^{46} - 12q^{50} - 8q^{53} - 4q^{58} + 4q^{64} - 12q^{65} + 24q^{67} - 8q^{74} + 32q^{79} - 40q^{85} + 8q^{86} - 8q^{88} + 32q^{92} + 16q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/882\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(785\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 0.866025i −0.353553 0.612372i
\(3\) 0 0
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) −0.707107 1.22474i −0.316228 0.547723i 0.663470 0.748203i \(-0.269083\pi\)
−0.979698 + 0.200480i \(0.935750\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 1.00000 0.353553
\(9\) 0 0
\(10\) −0.707107 + 1.22474i −0.223607 + 0.387298i
\(11\) −2.00000 + 3.46410i −0.603023 + 1.04447i 0.389338 + 0.921095i \(0.372704\pi\)
−0.992361 + 0.123371i \(0.960630\pi\)
\(12\) 0 0
\(13\) 4.24264 1.17670 0.588348 0.808608i \(-0.299778\pi\)
0.588348 + 0.808608i \(0.299778\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 3.53553 6.12372i 0.857493 1.48522i −0.0168199 0.999859i \(-0.505354\pi\)
0.874313 0.485363i \(-0.161312\pi\)
\(18\) 0 0
\(19\) 2.82843 + 4.89898i 0.648886 + 1.12390i 0.983389 + 0.181509i \(0.0580980\pi\)
−0.334504 + 0.942394i \(0.608569\pi\)
\(20\) 1.41421 0.316228
\(21\) 0 0
\(22\) 4.00000 0.852803
\(23\) −4.00000 6.92820i −0.834058 1.44463i −0.894795 0.446476i \(-0.852679\pi\)
0.0607377 0.998154i \(-0.480655\pi\)
\(24\) 0 0
\(25\) 1.50000 2.59808i 0.300000 0.519615i
\(26\) −2.12132 3.67423i −0.416025 0.720577i
\(27\) 0 0
\(28\) 0 0
\(29\) 2.00000 0.371391 0.185695 0.982607i \(-0.440546\pi\)
0.185695 + 0.982607i \(0.440546\pi\)
\(30\) 0 0
\(31\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(32\) −0.500000 + 0.866025i −0.0883883 + 0.153093i
\(33\) 0 0
\(34\) −7.07107 −1.21268
\(35\) 0 0
\(36\) 0 0
\(37\) −2.00000 3.46410i −0.328798 0.569495i 0.653476 0.756948i \(-0.273310\pi\)
−0.982274 + 0.187453i \(0.939977\pi\)
\(38\) 2.82843 4.89898i 0.458831 0.794719i
\(39\) 0 0
\(40\) −0.707107 1.22474i −0.111803 0.193649i
\(41\) 9.89949 1.54604 0.773021 0.634381i \(-0.218745\pi\)
0.773021 + 0.634381i \(0.218745\pi\)
\(42\) 0 0
\(43\) −4.00000 −0.609994 −0.304997 0.952353i \(-0.598656\pi\)
−0.304997 + 0.952353i \(0.598656\pi\)
\(44\) −2.00000 3.46410i −0.301511 0.522233i
\(45\) 0 0
\(46\) −4.00000 + 6.92820i −0.589768 + 1.02151i
\(47\) −2.82843 4.89898i −0.412568 0.714590i 0.582601 0.812758i \(-0.302035\pi\)
−0.995170 + 0.0981685i \(0.968702\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) −3.00000 −0.424264
\(51\) 0 0
\(52\) −2.12132 + 3.67423i −0.294174 + 0.509525i
\(53\) −2.00000 + 3.46410i −0.274721 + 0.475831i −0.970065 0.242846i \(-0.921919\pi\)
0.695344 + 0.718677i \(0.255252\pi\)
\(54\) 0 0
\(55\) 5.65685 0.762770
\(56\) 0 0
\(57\) 0 0
\(58\) −1.00000 1.73205i −0.131306 0.227429i
\(59\) 5.65685 9.79796i 0.736460 1.27559i −0.217620 0.976034i \(-0.569829\pi\)
0.954080 0.299552i \(-0.0968372\pi\)
\(60\) 0 0
\(61\) −0.707107 1.22474i −0.0905357 0.156813i 0.817201 0.576353i \(-0.195525\pi\)
−0.907737 + 0.419540i \(0.862191\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) −3.00000 5.19615i −0.372104 0.644503i
\(66\) 0 0
\(67\) 6.00000 10.3923i 0.733017 1.26962i −0.222571 0.974916i \(-0.571445\pi\)
0.955588 0.294706i \(-0.0952216\pi\)
\(68\) 3.53553 + 6.12372i 0.428746 + 0.742611i
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(72\) 0 0
\(73\) 7.77817 13.4722i 0.910366 1.57680i 0.0968194 0.995302i \(-0.469133\pi\)
0.813547 0.581499i \(-0.197534\pi\)
\(74\) −2.00000 + 3.46410i −0.232495 + 0.402694i
\(75\) 0 0
\(76\) −5.65685 −0.648886
\(77\) 0 0
\(78\) 0 0
\(79\) 8.00000 + 13.8564i 0.900070 + 1.55897i 0.827401 + 0.561611i \(0.189818\pi\)
0.0726692 + 0.997356i \(0.476848\pi\)
\(80\) −0.707107 + 1.22474i −0.0790569 + 0.136931i
\(81\) 0 0
\(82\) −4.94975 8.57321i −0.546608 0.946753i
\(83\) −5.65685 −0.620920 −0.310460 0.950586i \(-0.600483\pi\)
−0.310460 + 0.950586i \(0.600483\pi\)
\(84\) 0 0
\(85\) −10.0000 −1.08465
\(86\) 2.00000 + 3.46410i 0.215666 + 0.373544i
\(87\) 0 0
\(88\) −2.00000 + 3.46410i −0.213201 + 0.369274i
\(89\) −3.53553 6.12372i −0.374766 0.649113i 0.615526 0.788116i \(-0.288944\pi\)
−0.990292 + 0.139003i \(0.955610\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 8.00000 0.834058
\(93\) 0 0
\(94\) −2.82843 + 4.89898i −0.291730 + 0.505291i
\(95\) 4.00000 6.92820i 0.410391 0.710819i
\(96\) 0 0
\(97\) 7.07107 0.717958 0.358979 0.933346i \(-0.383125\pi\)
0.358979 + 0.933346i \(0.383125\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 1.50000 + 2.59808i 0.150000 + 0.259808i
\(101\) −6.36396 + 11.0227i −0.633238 + 1.09680i 0.353648 + 0.935379i \(0.384941\pi\)
−0.986886 + 0.161421i \(0.948392\pi\)
\(102\) 0 0
\(103\) −2.82843 4.89898i −0.278693 0.482711i 0.692367 0.721545i \(-0.256568\pi\)
−0.971060 + 0.238835i \(0.923235\pi\)
\(104\) 4.24264 0.416025
\(105\) 0 0
\(106\) 4.00000 0.388514
\(107\) 2.00000 + 3.46410i 0.193347 + 0.334887i 0.946357 0.323122i \(-0.104732\pi\)
−0.753010 + 0.658009i \(0.771399\pi\)
\(108\) 0 0
\(109\) −2.00000 + 3.46410i −0.191565 + 0.331801i −0.945769 0.324840i \(-0.894690\pi\)
0.754204 + 0.656640i \(0.228023\pi\)
\(110\) −2.82843 4.89898i −0.269680 0.467099i
\(111\) 0 0
\(112\) 0 0
\(113\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(114\) 0 0
\(115\) −5.65685 + 9.79796i −0.527504 + 0.913664i
\(116\) −1.00000 + 1.73205i −0.0928477 + 0.160817i
\(117\) 0 0
\(118\) −11.3137 −1.04151
\(119\) 0 0
\(120\) 0 0
\(121\) −2.50000 4.33013i −0.227273 0.393648i
\(122\) −0.707107 + 1.22474i −0.0640184 + 0.110883i
\(123\) 0 0
\(124\) 0 0
\(125\) −11.3137 −1.01193
\(126\) 0 0
\(127\) −8.00000 −0.709885 −0.354943 0.934888i \(-0.615500\pi\)
−0.354943 + 0.934888i \(0.615500\pi\)
\(128\) −0.500000 0.866025i −0.0441942 0.0765466i
\(129\) 0 0
\(130\) −3.00000 + 5.19615i −0.263117 + 0.455733i
\(131\) 8.48528 + 14.6969i 0.741362 + 1.28408i 0.951875 + 0.306486i \(0.0991534\pi\)
−0.210513 + 0.977591i \(0.567513\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −12.0000 −1.03664
\(135\) 0 0
\(136\) 3.53553 6.12372i 0.303170 0.525105i
\(137\) −3.00000 + 5.19615i −0.256307 + 0.443937i −0.965250 0.261329i \(-0.915839\pi\)
0.708942 + 0.705266i \(0.249173\pi\)
\(138\) 0 0
\(139\) −5.65685 −0.479808 −0.239904 0.970797i \(-0.577116\pi\)
−0.239904 + 0.970797i \(0.577116\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −8.48528 + 14.6969i −0.709575 + 1.22902i
\(144\) 0 0
\(145\) −1.41421 2.44949i −0.117444 0.203419i
\(146\) −15.5563 −1.28745
\(147\) 0 0
\(148\) 4.00000 0.328798
\(149\) 10.0000 + 17.3205i 0.819232 + 1.41895i 0.906249 + 0.422744i \(0.138933\pi\)
−0.0870170 + 0.996207i \(0.527733\pi\)
\(150\) 0 0
\(151\) 8.00000 13.8564i 0.651031 1.12762i −0.331842 0.943335i \(-0.607670\pi\)
0.982873 0.184284i \(-0.0589965\pi\)
\(152\) 2.82843 + 4.89898i 0.229416 + 0.397360i
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 9.19239 15.9217i 0.733632 1.27069i −0.221688 0.975118i \(-0.571157\pi\)
0.955321 0.295571i \(-0.0955099\pi\)
\(158\) 8.00000 13.8564i 0.636446 1.10236i
\(159\) 0 0
\(160\) 1.41421 0.111803
\(161\) 0 0
\(162\) 0 0
\(163\) −2.00000 3.46410i −0.156652 0.271329i 0.777007 0.629492i \(-0.216737\pi\)
−0.933659 + 0.358162i \(0.883403\pi\)
\(164\) −4.94975 + 8.57321i −0.386510 + 0.669456i
\(165\) 0 0
\(166\) 2.82843 + 4.89898i 0.219529 + 0.380235i
\(167\) 11.3137 0.875481 0.437741 0.899101i \(-0.355779\pi\)
0.437741 + 0.899101i \(0.355779\pi\)
\(168\) 0 0
\(169\) 5.00000 0.384615
\(170\) 5.00000 + 8.66025i 0.383482 + 0.664211i
\(171\) 0 0
\(172\) 2.00000 3.46410i 0.152499 0.264135i
\(173\) 6.36396 + 11.0227i 0.483843 + 0.838041i 0.999828 0.0185571i \(-0.00590724\pi\)
−0.515985 + 0.856598i \(0.672574\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 4.00000 0.301511
\(177\) 0 0
\(178\) −3.53553 + 6.12372i −0.264999 + 0.458993i
\(179\) 6.00000 10.3923i 0.448461 0.776757i −0.549825 0.835280i \(-0.685306\pi\)
0.998286 + 0.0585225i \(0.0186389\pi\)
\(180\) 0 0
\(181\) 12.7279 0.946059 0.473029 0.881047i \(-0.343160\pi\)
0.473029 + 0.881047i \(0.343160\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −4.00000 6.92820i −0.294884 0.510754i
\(185\) −2.82843 + 4.89898i −0.207950 + 0.360180i
\(186\) 0 0
\(187\) 14.1421 + 24.4949i 1.03418 + 1.79124i
\(188\) 5.65685 0.412568
\(189\) 0 0
\(190\) −8.00000 −0.580381
\(191\) 8.00000 + 13.8564i 0.578860 + 1.00261i 0.995610 + 0.0935936i \(0.0298354\pi\)
−0.416751 + 0.909021i \(0.636831\pi\)
\(192\) 0 0
\(193\) −7.00000 + 12.1244i −0.503871 + 0.872730i 0.496119 + 0.868255i \(0.334758\pi\)
−0.999990 + 0.00447566i \(0.998575\pi\)
\(194\) −3.53553 6.12372i −0.253837 0.439658i
\(195\) 0 0
\(196\) 0 0
\(197\) −4.00000 −0.284988 −0.142494 0.989796i \(-0.545512\pi\)
−0.142494 + 0.989796i \(0.545512\pi\)
\(198\) 0 0
\(199\) −8.48528 + 14.6969i −0.601506 + 1.04184i 0.391088 + 0.920353i \(0.372099\pi\)
−0.992593 + 0.121485i \(0.961234\pi\)
\(200\) 1.50000 2.59808i 0.106066 0.183712i
\(201\) 0 0
\(202\) 12.7279 0.895533
\(203\) 0 0
\(204\) 0 0
\(205\) −7.00000 12.1244i −0.488901 0.846802i
\(206\) −2.82843 + 4.89898i −0.197066 + 0.341328i
\(207\) 0 0
\(208\) −2.12132 3.67423i −0.147087 0.254762i
\(209\) −22.6274 −1.56517
\(210\) 0 0
\(211\) 12.0000 0.826114 0.413057 0.910705i \(-0.364461\pi\)
0.413057 + 0.910705i \(0.364461\pi\)
\(212\) −2.00000 3.46410i −0.137361 0.237915i
\(213\) 0 0
\(214\) 2.00000 3.46410i 0.136717 0.236801i
\(215\) 2.82843 + 4.89898i 0.192897 + 0.334108i
\(216\) 0 0
\(217\) 0 0
\(218\) 4.00000 0.270914
\(219\) 0 0
\(220\) −2.82843 + 4.89898i −0.190693 + 0.330289i
\(221\) 15.0000 25.9808i 1.00901 1.74766i
\(222\) 0 0
\(223\) −16.9706 −1.13643 −0.568216 0.822879i \(-0.692366\pi\)
−0.568216 + 0.822879i \(0.692366\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −8.48528 + 14.6969i −0.563188 + 0.975470i 0.434028 + 0.900899i \(0.357092\pi\)
−0.997216 + 0.0745706i \(0.976241\pi\)
\(228\) 0 0
\(229\) −6.36396 11.0227i −0.420542 0.728401i 0.575450 0.817837i \(-0.304827\pi\)
−0.995993 + 0.0894361i \(0.971494\pi\)
\(230\) 11.3137 0.746004
\(231\) 0 0
\(232\) 2.00000 0.131306
\(233\) 3.00000 + 5.19615i 0.196537 + 0.340411i 0.947403 0.320043i \(-0.103697\pi\)
−0.750867 + 0.660454i \(0.770364\pi\)
\(234\) 0 0
\(235\) −4.00000 + 6.92820i −0.260931 + 0.451946i
\(236\) 5.65685 + 9.79796i 0.368230 + 0.637793i
\(237\) 0 0
\(238\) 0 0
\(239\) −24.0000 −1.55243 −0.776215 0.630468i \(-0.782863\pi\)
−0.776215 + 0.630468i \(0.782863\pi\)
\(240\) 0 0
\(241\) −2.12132 + 3.67423i −0.136646 + 0.236678i −0.926225 0.376971i \(-0.876966\pi\)
0.789579 + 0.613649i \(0.210299\pi\)
\(242\) −2.50000 + 4.33013i −0.160706 + 0.278351i
\(243\) 0 0
\(244\) 1.41421 0.0905357
\(245\) 0 0
\(246\) 0 0
\(247\) 12.0000 + 20.7846i 0.763542 + 1.32249i
\(248\) 0 0
\(249\) 0 0
\(250\) 5.65685 + 9.79796i 0.357771 + 0.619677i
\(251\) −5.65685 −0.357057 −0.178529 0.983935i \(-0.557134\pi\)
−0.178529 + 0.983935i \(0.557134\pi\)
\(252\) 0 0
\(253\) 32.0000 2.01182
\(254\) 4.00000 + 6.92820i 0.250982 + 0.434714i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 6.36396 + 11.0227i 0.396973 + 0.687577i 0.993351 0.115126i \(-0.0367273\pi\)
−0.596378 + 0.802704i \(0.703394\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 6.00000 0.372104
\(261\) 0 0
\(262\) 8.48528 14.6969i 0.524222 0.907980i
\(263\) −12.0000 + 20.7846i −0.739952 + 1.28163i 0.212565 + 0.977147i \(0.431818\pi\)
−0.952517 + 0.304487i \(0.901515\pi\)
\(264\) 0 0
\(265\) 5.65685 0.347498
\(266\) 0 0
\(267\) 0 0
\(268\) 6.00000 + 10.3923i 0.366508 + 0.634811i
\(269\) 0.707107 1.22474i 0.0431131 0.0746740i −0.843664 0.536872i \(-0.819606\pi\)
0.886777 + 0.462198i \(0.152939\pi\)
\(270\) 0 0
\(271\) 2.82843 + 4.89898i 0.171815 + 0.297592i 0.939054 0.343769i \(-0.111704\pi\)
−0.767240 + 0.641361i \(0.778370\pi\)
\(272\) −7.07107 −0.428746
\(273\) 0 0
\(274\) 6.00000 0.362473
\(275\) 6.00000 + 10.3923i 0.361814 + 0.626680i
\(276\) 0 0
\(277\) −5.00000 + 8.66025i −0.300421 + 0.520344i −0.976231 0.216731i \(-0.930460\pi\)
0.675810 + 0.737075i \(0.263794\pi\)
\(278\) 2.82843 + 4.89898i 0.169638 + 0.293821i
\(279\) 0 0
\(280\) 0 0
\(281\) 10.0000 0.596550 0.298275 0.954480i \(-0.403589\pi\)
0.298275 + 0.954480i \(0.403589\pi\)
\(282\) 0 0
\(283\) −11.3137 + 19.5959i −0.672530 + 1.16486i 0.304654 + 0.952463i \(0.401459\pi\)
−0.977184 + 0.212393i \(0.931874\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 16.9706 1.00349
\(287\) 0 0
\(288\) 0 0
\(289\) −16.5000 28.5788i −0.970588 1.68111i
\(290\) −1.41421 + 2.44949i −0.0830455 + 0.143839i
\(291\) 0 0
\(292\) 7.77817 + 13.4722i 0.455183 + 0.788400i
\(293\) 24.0416 1.40453 0.702264 0.711917i \(-0.252173\pi\)
0.702264 + 0.711917i \(0.252173\pi\)
\(294\) 0 0
\(295\) −16.0000 −0.931556
\(296\) −2.00000 3.46410i −0.116248 0.201347i
\(297\) 0 0
\(298\) 10.0000 17.3205i 0.579284 1.00335i
\(299\) −16.9706 29.3939i −0.981433 1.69989i
\(300\) 0 0
\(301\) 0 0
\(302\) −16.0000 −0.920697
\(303\) 0 0
\(304\) 2.82843 4.89898i 0.162221 0.280976i
\(305\) −1.00000 + 1.73205i −0.0572598 + 0.0991769i
\(306\) 0 0
\(307\) 5.65685 0.322854 0.161427 0.986885i \(-0.448390\pi\)
0.161427 + 0.986885i \(0.448390\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 2.82843 4.89898i 0.160385 0.277796i −0.774622 0.632425i \(-0.782060\pi\)
0.935007 + 0.354629i \(0.115393\pi\)
\(312\) 0 0
\(313\) −10.6066 18.3712i −0.599521 1.03840i −0.992892 0.119020i \(-0.962025\pi\)
0.393371 0.919380i \(-0.371309\pi\)
\(314\) −18.3848 −1.03751
\(315\) 0 0
\(316\) −16.0000 −0.900070
\(317\) −14.0000 24.2487i −0.786318 1.36194i −0.928208 0.372061i \(-0.878651\pi\)
0.141890 0.989882i \(-0.454682\pi\)
\(318\) 0 0
\(319\) −4.00000 + 6.92820i −0.223957 + 0.387905i
\(320\) −0.707107 1.22474i −0.0395285 0.0684653i
\(321\) 0 0
\(322\) 0 0
\(323\) 40.0000 2.22566
\(324\) 0 0
\(325\) 6.36396 11.0227i 0.353009 0.611430i
\(326\) −2.00000 + 3.46410i −0.110770 + 0.191859i
\(327\) 0 0
\(328\) 9.89949 0.546608
\(329\) 0 0
\(330\) 0 0
\(331\) 10.0000 + 17.3205i 0.549650 + 0.952021i 0.998298 + 0.0583130i \(0.0185721\pi\)
−0.448649 + 0.893708i \(0.648095\pi\)
\(332\) 2.82843 4.89898i 0.155230 0.268866i
\(333\) 0 0
\(334\) −5.65685 9.79796i −0.309529 0.536120i
\(335\) −16.9706 −0.927201
\(336\) 0 0
\(337\) −16.0000 −0.871576 −0.435788 0.900049i \(-0.643530\pi\)
−0.435788 + 0.900049i \(0.643530\pi\)
\(338\) −2.50000 4.33013i −0.135982 0.235528i
\(339\) 0 0
\(340\) 5.00000 8.66025i 0.271163 0.469668i
\(341\) 0 0
\(342\) 0 0
\(343\) 0 0
\(344\) −4.00000 −0.215666
\(345\) 0 0
\(346\) 6.36396 11.0227i 0.342129 0.592584i
\(347\) 6.00000 10.3923i 0.322097 0.557888i −0.658824 0.752297i \(-0.728946\pi\)
0.980921 + 0.194409i \(0.0622790\pi\)
\(348\) 0 0
\(349\) −29.6985 −1.58972 −0.794862 0.606791i \(-0.792457\pi\)
−0.794862 + 0.606791i \(0.792457\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −2.00000 3.46410i −0.106600 0.184637i
\(353\) −0.707107 + 1.22474i −0.0376355 + 0.0651866i −0.884230 0.467052i \(-0.845316\pi\)
0.846594 + 0.532239i \(0.178649\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 7.07107 0.374766
\(357\) 0 0
\(358\) −12.0000 −0.634220
\(359\) −8.00000 13.8564i −0.422224 0.731313i 0.573933 0.818902i \(-0.305417\pi\)
−0.996157 + 0.0875892i \(0.972084\pi\)
\(360\) 0 0
\(361\) −6.50000 + 11.2583i −0.342105 + 0.592544i
\(362\) −6.36396 11.0227i −0.334482 0.579340i
\(363\) 0 0
\(364\) 0 0
\(365\) −22.0000 −1.15153
\(366\) 0 0
\(367\) −2.82843 + 4.89898i −0.147643 + 0.255725i −0.930356 0.366658i \(-0.880502\pi\)
0.782713 + 0.622383i \(0.213835\pi\)
\(368\) −4.00000 + 6.92820i −0.208514 + 0.361158i
\(369\) 0 0
\(370\) 5.65685 0.294086
\(371\) 0 0
\(372\) 0 0
\(373\) −5.00000 8.66025i −0.258890 0.448411i 0.707055 0.707159i \(-0.250023\pi\)
−0.965945 + 0.258748i \(0.916690\pi\)
\(374\) 14.1421 24.4949i 0.731272 1.26660i
\(375\) 0 0
\(376\) −2.82843 4.89898i −0.145865 0.252646i
\(377\) 8.48528 0.437014
\(378\) 0 0
\(379\) 28.0000 1.43826 0.719132 0.694874i \(-0.244540\pi\)
0.719132 + 0.694874i \(0.244540\pi\)
\(380\) 4.00000 + 6.92820i 0.205196 + 0.355409i
\(381\) 0 0
\(382\) 8.00000 13.8564i 0.409316 0.708955i
\(383\) 2.82843 + 4.89898i 0.144526 + 0.250326i 0.929196 0.369587i \(-0.120501\pi\)
−0.784670 + 0.619914i \(0.787168\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 14.0000 0.712581
\(387\) 0 0
\(388\) −3.53553 + 6.12372i −0.179490 + 0.310885i
\(389\) −13.0000 + 22.5167i −0.659126 + 1.14164i 0.321716 + 0.946836i \(0.395740\pi\)
−0.980842 + 0.194804i \(0.937593\pi\)
\(390\) 0 0
\(391\) −56.5685 −2.86079
\(392\) 0 0
\(393\) 0 0
\(394\) 2.00000 + 3.46410i 0.100759 + 0.174519i
\(395\) 11.3137 19.5959i 0.569254 0.985978i
\(396\) 0 0
\(397\) −3.53553 6.12372i −0.177443 0.307341i 0.763561 0.645736i \(-0.223449\pi\)
−0.941004 + 0.338395i \(0.890116\pi\)
\(398\) 16.9706 0.850657
\(399\) 0 0
\(400\) −3.00000 −0.150000
\(401\) −9.00000 15.5885i −0.449439 0.778450i 0.548911 0.835881i \(-0.315043\pi\)
−0.998350 + 0.0574304i \(0.981709\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) −6.36396 11.0227i −0.316619 0.548400i
\(405\) 0 0
\(406\) 0 0
\(407\) 16.0000 0.793091
\(408\) 0 0
\(409\) 10.6066 18.3712i 0.524463 0.908396i −0.475132 0.879915i \(-0.657600\pi\)
0.999594 0.0284813i \(-0.00906711\pi\)
\(410\) −7.00000 + 12.1244i −0.345705 + 0.598779i
\(411\) 0 0
\(412\) 5.65685 0.278693
\(413\) 0 0
\(414\) 0 0
\(415\) 4.00000 + 6.92820i 0.196352 + 0.340092i
\(416\) −2.12132 + 3.67423i −0.104006 + 0.180144i
\(417\) 0 0
\(418\) 11.3137 + 19.5959i 0.553372 + 0.958468i
\(419\) 22.6274 1.10542 0.552711 0.833373i \(-0.313593\pi\)
0.552711 + 0.833373i \(0.313593\pi\)
\(420\) 0 0
\(421\) −6.00000 −0.292422 −0.146211 0.989253i \(-0.546708\pi\)
−0.146211 + 0.989253i \(0.546708\pi\)
\(422\) −6.00000 10.3923i −0.292075 0.505889i
\(423\) 0 0
\(424\) −2.00000 + 3.46410i −0.0971286 + 0.168232i
\(425\) −10.6066 18.3712i −0.514496 0.891133i
\(426\) 0 0
\(427\) 0 0
\(428\) −4.00000 −0.193347
\(429\) 0 0
\(430\) 2.82843 4.89898i 0.136399 0.236250i
\(431\) −12.0000 + 20.7846i −0.578020 + 1.00116i 0.417687 + 0.908591i \(0.362841\pi\)
−0.995706 + 0.0925683i \(0.970492\pi\)
\(432\) 0 0
\(433\) −4.24264 −0.203888 −0.101944 0.994790i \(-0.532506\pi\)
−0.101944 + 0.994790i \(0.532506\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −2.00000 3.46410i −0.0957826 0.165900i
\(437\) 22.6274 39.1918i 1.08242 1.87480i
\(438\) 0 0
\(439\) −16.9706 29.3939i −0.809961 1.40289i −0.912890 0.408205i \(-0.866155\pi\)
0.102930 0.994689i \(-0.467178\pi\)
\(440\) 5.65685 0.269680
\(441\) 0 0
\(442\) −30.0000 −1.42695
\(443\) −10.0000 17.3205i −0.475114 0.822922i 0.524479 0.851423i \(-0.324260\pi\)
−0.999594 + 0.0285009i \(0.990927\pi\)
\(444\) 0 0
\(445\) −5.00000 + 8.66025i −0.237023 + 0.410535i
\(446\) 8.48528 + 14.6969i 0.401790 + 0.695920i
\(447\) 0 0
\(448\) 0 0
\(449\) −24.0000 −1.13263 −0.566315 0.824189i \(-0.691631\pi\)
−0.566315 + 0.824189i \(0.691631\pi\)
\(450\) 0 0
\(451\) −19.7990 + 34.2929i −0.932298 + 1.61479i
\(452\) 0 0
\(453\) 0 0
\(454\) 16.9706 0.796468
\(455\) 0 0
\(456\) 0 0
\(457\) 3.00000 + 5.19615i 0.140334 + 0.243066i 0.927622 0.373519i \(-0.121849\pi\)
−0.787288 + 0.616585i \(0.788516\pi\)
\(458\) −6.36396 + 11.0227i −0.297368 + 0.515057i
\(459\) 0 0
\(460\) −5.65685 9.79796i −0.263752 0.456832i
\(461\) −1.41421 −0.0658665 −0.0329332 0.999458i \(-0.510485\pi\)
−0.0329332 + 0.999458i \(0.510485\pi\)
\(462\) 0 0
\(463\) −32.0000 −1.48717 −0.743583 0.668644i \(-0.766875\pi\)
−0.743583 + 0.668644i \(0.766875\pi\)
\(464\) −1.00000 1.73205i −0.0464238 0.0804084i
\(465\) 0 0
\(466\) 3.00000 5.19615i 0.138972 0.240707i
\(467\) −2.82843 4.89898i −0.130884 0.226698i 0.793134 0.609048i \(-0.208448\pi\)
−0.924018 + 0.382350i \(0.875115\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 8.00000 0.369012
\(471\) 0 0
\(472\) 5.65685 9.79796i 0.260378 0.450988i
\(473\) 8.00000 13.8564i 0.367840 0.637118i
\(474\) 0 0
\(475\) 16.9706 0.778663
\(476\) 0 0
\(477\) 0 0
\(478\) 12.0000 + 20.7846i 0.548867 + 0.950666i
\(479\) 14.1421 24.4949i 0.646171 1.11920i −0.337859 0.941197i \(-0.609703\pi\)
0.984030 0.178004i \(-0.0569639\pi\)
\(480\) 0 0
\(481\) −8.48528 14.6969i −0.386896 0.670123i
\(482\) 4.24264 0.193247
\(483\) 0 0
\(484\) 5.00000 0.227273
\(485\) −5.00000 8.66025i −0.227038 0.393242i
\(486\) 0 0
\(487\) 12.0000 20.7846i 0.543772 0.941841i −0.454911 0.890537i \(-0.650329\pi\)
0.998683 0.0513038i \(-0.0163377\pi\)
\(488\) −0.707107 1.22474i −0.0320092 0.0554416i
\(489\) 0 0
\(490\) 0 0
\(491\) −12.0000 −0.541552 −0.270776 0.962642i \(-0.587280\pi\)
−0.270776 + 0.962642i \(0.587280\pi\)
\(492\) 0 0
\(493\) 7.07107 12.2474i 0.318465 0.551597i
\(494\) 12.0000 20.7846i 0.539906 0.935144i
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 2.00000 + 3.46410i 0.0895323 + 0.155074i 0.907314 0.420455i \(-0.138129\pi\)
−0.817781 + 0.575529i \(0.804796\pi\)
\(500\) 5.65685 9.79796i 0.252982 0.438178i
\(501\) 0 0
\(502\) 2.82843 + 4.89898i 0.126239 + 0.218652i
\(503\) 28.2843 1.26113 0.630567 0.776135i \(-0.282823\pi\)
0.630567 + 0.776135i \(0.282823\pi\)
\(504\) 0 0
\(505\) 18.0000 0.800989
\(506\) −16.0000 27.7128i −0.711287 1.23198i
\(507\) 0 0
\(508\) 4.00000 6.92820i 0.177471 0.307389i
\(509\) −16.2635 28.1691i −0.720865 1.24857i −0.960653 0.277750i \(-0.910411\pi\)
0.239788 0.970825i \(-0.422922\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 1.00000 0.0441942
\(513\) 0 0
\(514\) 6.36396 11.0227i 0.280702 0.486191i
\(515\) −4.00000 + 6.92820i −0.176261 + 0.305293i
\(516\) 0 0
\(517\) 22.6274 0.995153
\(518\) 0 0
\(519\) 0 0
\(520\) −3.00000 5.19615i −0.131559 0.227866i
\(521\) −0.707107 + 1.22474i −0.0309789 + 0.0536570i −0.881099 0.472931i \(-0.843196\pi\)
0.850120 + 0.526589i \(0.176529\pi\)
\(522\) 0 0
\(523\) 16.9706 + 29.3939i 0.742071 + 1.28530i 0.951551 + 0.307492i \(0.0994896\pi\)
−0.209480 + 0.977813i \(0.567177\pi\)
\(524\) −16.9706 −0.741362
\(525\) 0 0
\(526\) 24.0000 1.04645
\(527\) 0 0
\(528\) 0 0
\(529\) −20.5000 + 35.5070i −0.891304 + 1.54378i
\(530\) −2.82843 4.89898i −0.122859 0.212798i
\(531\) 0 0
\(532\) 0 0
\(533\) 42.0000 1.81922
\(534\) 0 0
\(535\) 2.82843 4.89898i 0.122284 0.211801i
\(536\) 6.00000 10.3923i 0.259161 0.448879i
\(537\) 0 0
\(538\) −1.41421 −0.0609711
\(539\) 0 0
\(540\) 0 0
\(541\) 1.00000 + 1.73205i 0.0429934 + 0.0744667i 0.886721 0.462304i \(-0.152977\pi\)
−0.843728 + 0.536771i \(0.819644\pi\)
\(542\) 2.82843 4.89898i 0.121491 0.210429i
\(543\) 0 0
\(544\) 3.53553 + 6.12372i 0.151585 + 0.262553i
\(545\) 5.65685 0.242313
\(546\) 0 0
\(547\) 28.0000 1.19719 0.598597 0.801050i \(-0.295725\pi\)
0.598597 + 0.801050i \(0.295725\pi\)
\(548\) −3.00000 5.19615i −0.128154 0.221969i
\(549\) 0 0
\(550\) 6.00000 10.3923i 0.255841 0.443129i
\(551\) 5.65685 + 9.79796i 0.240990 + 0.417407i
\(552\) 0 0
\(553\) 0 0
\(554\) 10.0000 0.424859
\(555\) 0 0
\(556\) 2.82843 4.89898i 0.119952 0.207763i
\(557\) −18.0000 + 31.1769i −0.762684 + 1.32101i 0.178778 + 0.983890i \(0.442786\pi\)
−0.941462 + 0.337119i \(0.890548\pi\)
\(558\) 0 0
\(559\) −16.9706 −0.717778
\(560\) 0 0
\(561\) 0 0
\(562\) −5.00000 8.66025i −0.210912 0.365311i
\(563\) 5.65685 9.79796i 0.238408 0.412935i −0.721850 0.692050i \(-0.756708\pi\)
0.960258 + 0.279115i \(0.0900411\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 22.6274 0.951101
\(567\) 0 0
\(568\) 0 0
\(569\) 13.0000 + 22.5167i 0.544988 + 0.943948i 0.998608 + 0.0527519i \(0.0167993\pi\)
−0.453619 + 0.891196i \(0.649867\pi\)
\(570\) 0 0
\(571\) −2.00000 + 3.46410i −0.0836974 + 0.144968i −0.904835 0.425762i \(-0.860006\pi\)
0.821138 + 0.570730i \(0.193340\pi\)
\(572\) −8.48528 14.6969i −0.354787 0.614510i
\(573\) 0 0
\(574\) 0 0
\(575\) −24.0000 −1.00087
\(576\) 0 0
\(577\) −6.36396 + 11.0227i −0.264935 + 0.458881i −0.967547 0.252693i \(-0.918684\pi\)
0.702611 + 0.711574i \(0.252017\pi\)
\(578\) −16.5000 + 28.5788i −0.686310 + 1.18872i
\(579\) 0 0
\(580\) 2.82843 0.117444
\(581\) 0 0
\(582\) 0 0
\(583\) −8.00000 13.8564i −0.331326 0.573874i
\(584\) 7.77817 13.4722i 0.321863 0.557483i
\(585\) 0 0
\(586\) −12.0208 20.8207i −0.496575 0.860094i
\(587\) −16.9706 −0.700450 −0.350225 0.936666i \(-0.613895\pi\)
−0.350225 + 0.936666i \(0.613895\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 8.00000 + 13.8564i 0.329355 + 0.570459i
\(591\) 0 0
\(592\) −2.00000 + 3.46410i −0.0821995 + 0.142374i
\(593\) 17.6777 + 30.6186i 0.725935 + 1.25736i 0.958588 + 0.284796i \(0.0919260\pi\)
−0.232653 + 0.972560i \(0.574741\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −20.0000 −0.819232
\(597\) 0 0
\(598\) −16.9706 + 29.3939i −0.693978 + 1.20201i
\(599\) 8.00000 13.8564i 0.326871 0.566157i −0.655018 0.755613i \(-0.727339\pi\)
0.981889 + 0.189456i \(0.0606724\pi\)
\(600\) 0 0
\(601\) 4.24264 0.173061 0.0865305 0.996249i \(-0.472422\pi\)
0.0865305 + 0.996249i \(0.472422\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 8.00000 + 13.8564i 0.325515 + 0.563809i
\(605\) −3.53553 + 6.12372i −0.143740 + 0.248965i
\(606\) 0 0
\(607\) −8.48528 14.6969i −0.344407 0.596530i 0.640839 0.767675i \(-0.278587\pi\)
−0.985246 + 0.171145i \(0.945253\pi\)
\(608\) −5.65685 −0.229416
\(609\) 0 0
\(610\) 2.00000 0.0809776
\(611\) −12.0000 20.7846i −0.485468 0.840855i
\(612\) 0 0
\(613\) −6.00000 + 10.3923i −0.242338 + 0.419741i −0.961380 0.275225i \(-0.911248\pi\)
0.719042 + 0.694967i \(0.244581\pi\)
\(614\) −2.82843 4.89898i −0.114146 0.197707i
\(615\) 0 0
\(616\) 0 0
\(617\) 22.0000 0.885687 0.442843 0.896599i \(-0.353970\pi\)
0.442843 + 0.896599i \(0.353970\pi\)
\(618\) 0 0
\(619\) −5.65685 + 9.79796i −0.227368 + 0.393813i −0.957027 0.289998i \(-0.906345\pi\)
0.729659 + 0.683811i \(0.239679\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) −5.65685 −0.226819
\(623\) 0 0
\(624\) 0 0
\(625\) 0.500000 + 0.866025i 0.0200000 + 0.0346410i
\(626\) −10.6066 + 18.3712i −0.423925 + 0.734260i
\(627\) 0 0
\(628\) 9.19239 + 15.9217i 0.366816 + 0.635344i
\(629\) −28.2843 −1.12777
\(630\) 0 0
\(631\) −16.0000 −0.636950 −0.318475 0.947931i \(-0.603171\pi\)
−0.318475 + 0.947931i \(0.603171\pi\)
\(632\) 8.00000 + 13.8564i 0.318223 + 0.551178i
\(633\) 0 0
\(634\) −14.0000 + 24.2487i −0.556011 + 0.963039i
\(635\) 5.65685 + 9.79796i 0.224485 + 0.388820i
\(636\) 0 0
\(637\) 0 0
\(638\) 8.00000 0.316723
\(639\) 0 0
\(640\) −0.707107 + 1.22474i −0.0279508 + 0.0484123i
\(641\) −1.00000 + 1.73205i −0.0394976 + 0.0684119i −0.885098 0.465404i \(-0.845909\pi\)
0.845601 + 0.533816i \(0.179242\pi\)
\(642\) 0 0
\(643\) 11.3137 0.446169 0.223085 0.974799i \(-0.428387\pi\)
0.223085 + 0.974799i \(0.428387\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −20.0000 34.6410i −0.786889 1.36293i
\(647\) −16.9706 + 29.3939i −0.667182 + 1.15559i 0.311507 + 0.950244i \(0.399166\pi\)
−0.978689 + 0.205349i \(0.934167\pi\)
\(648\) 0 0
\(649\) 22.6274 + 39.1918i 0.888204 + 1.53841i
\(650\) −12.7279 −0.499230
\(651\) 0 0
\(652\) 4.00000 0.156652
\(653\) −9.00000 15.5885i −0.352197 0.610023i 0.634437 0.772975i \(-0.281232\pi\)
−0.986634 + 0.162951i \(0.947899\pi\)
\(654\) 0 0
\(655\) 12.0000 20.7846i 0.468879 0.812122i
\(656\) −4.94975 8.57321i −0.193255 0.334728i
\(657\) 0 0
\(658\) 0 0
\(659\) −36.0000 −1.40236 −0.701180 0.712984i \(-0.747343\pi\)
−0.701180 + 0.712984i \(0.747343\pi\)
\(660\) 0 0
\(661\) −2.12132 + 3.67423i −0.0825098 + 0.142911i −0.904327 0.426840i \(-0.859627\pi\)
0.821818 + 0.569751i \(0.192960\pi\)
\(662\) 10.0000 17.3205i 0.388661 0.673181i
\(663\) 0 0
\(664\) −5.65685 −0.219529
\(665\) 0 0
\(666\) 0 0
\(667\) −8.00000 13.8564i −0.309761 0.536522i
\(668\) −5.65685 + 9.79796i −0.218870 + 0.379094i
\(669\) 0 0
\(670\) 8.48528 + 14.6969i 0.327815 + 0.567792i
\(671\) 5.65685 0.218380
\(672\) 0 0
\(673\) 24.0000 0.925132 0.462566 0.886585i \(-0.346929\pi\)
0.462566 + 0.886585i \(0.346929\pi\)
\(674\) 8.00000 + 13.8564i 0.308148 + 0.533729i
\(675\) 0 0
\(676\) −2.50000 + 4.33013i −0.0961538 + 0.166543i
\(677\) −2.12132 3.67423i −0.0815290 0.141212i 0.822378 0.568942i \(-0.192647\pi\)
−0.903907 + 0.427729i \(0.859314\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) −10.0000 −0.383482
\(681\) 0 0
\(682\) 0 0
\(683\) 6.00000 10.3923i 0.229584 0.397650i −0.728101 0.685470i \(-0.759597\pi\)
0.957685 + 0.287819i \(0.0929302\pi\)
\(684\) 0 0
\(685\) 8.48528 0.324206
\(686\) 0 0
\(687\) 0 0
\(688\) 2.00000 + 3.46410i 0.0762493 + 0.132068i
\(689\) −8.48528 + 14.6969i −0.323263 + 0.559909i
\(690\) 0 0
\(691\) 25.4558 + 44.0908i 0.968386 + 1.67729i 0.700229 + 0.713918i \(0.253081\pi\)
0.268157 + 0.963375i \(0.413585\pi\)
\(692\) −12.7279 −0.483843
\(693\) 0 0
\(694\) −12.0000 −0.455514
\(695\) 4.00000 + 6.92820i 0.151729 + 0.262802i
\(696\) 0 0
\(697\) 35.0000 60.6218i 1.32572 2.29621i
\(698\) 14.8492 + 25.7196i 0.562052 + 0.973503i
\(699\) 0 0
\(700\) 0 0
\(701\) 30.0000 1.13308 0.566542 0.824033i \(-0.308281\pi\)
0.566542 + 0.824033i \(0.308281\pi\)
\(702\) 0 0
\(703\) 11.3137 19.5959i 0.426705 0.739074i
\(704\) −2.00000 + 3.46410i −0.0753778 + 0.130558i
\(705\) 0 0
\(706\) 1.41421 0.0532246
\(707\) 0 0
\(708\) 0 0
\(709\) −14.0000 24.2487i −0.525781 0.910679i −0.999549 0.0300298i \(-0.990440\pi\)
0.473768 0.880650i \(-0.342894\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) −3.53553 6.12372i −0.132500 0.229496i
\(713\) 0 0
\(714\) 0 0
\(715\) 24.0000 0.897549
\(716\) 6.00000 + 10.3923i 0.224231 + 0.388379i
\(717\) 0 0
\(718\) −8.00000 + 13.8564i −0.298557 + 0.517116i
\(719\) −19.7990 34.2929i −0.738378 1.27891i −0.953225 0.302260i \(-0.902259\pi\)
0.214848 0.976648i \(-0.431074\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 13.0000 0.483810
\(723\) 0 0
\(724\) −6.36396 + 11.0227i −0.236515 + 0.409656i
\(725\) 3.00000 5.19615i 0.111417 0.192980i
\(726\) 0 0
\(727\) 28.2843 1.04901 0.524503 0.851409i \(-0.324251\pi\)
0.524503 + 0.851409i \(0.324251\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 11.0000 + 19.0526i 0.407128 + 0.705167i
\(731\) −14.1421 + 24.4949i −0.523066 + 0.905977i
\(732\) 0 0
\(733\) −6.36396 11.0227i −0.235058 0.407133i 0.724231 0.689557i \(-0.242195\pi\)
−0.959290 + 0.282424i \(0.908861\pi\)
\(734\) 5.65685 0.208798
\(735\) 0 0
\(736\) 8.00000 0.294884
\(737\) 24.0000 + 41.5692i 0.884051 + 1.53122i
\(738\) 0 0
\(739\) −6.00000 + 10.3923i −0.220714 + 0.382287i −0.955025 0.296526i \(-0.904172\pi\)
0.734311 + 0.678813i \(0.237505\pi\)
\(740\) −2.82843 4.89898i −0.103975 0.180090i
\(741\) 0 0
\(742\) 0 0
\(743\) 16.0000 0.586983 0.293492 0.955962i \(-0.405183\pi\)
0.293492 + 0.955962i \(0.405183\pi\)
\(744\) 0 0
\(745\) 14.1421 24.4949i 0.518128 0.897424i
\(746\) −5.00000 + 8.66025i −0.183063 + 0.317074i
\(747\) 0 0
\(748\) −28.2843 −1.03418
\(749\) 0 0
\(750\) 0 0
\(751\) 20.0000 + 34.6410i 0.729810 + 1.26407i 0.956963 + 0.290209i \(0.0937250\pi\)
−0.227153 + 0.973859i \(0.572942\pi\)
\(752\) −2.82843 + 4.89898i −0.103142 + 0.178647i
\(753\) 0 0
\(754\) −4.24264 7.34847i −0.154508 0.267615i
\(755\) −22.6274 −0.823496
\(756\) 0 0
\(757\) −28.0000 −1.01768 −0.508839 0.860862i \(-0.669925\pi\)
−0.508839 + 0.860862i \(0.669925\pi\)
\(758\) −14.0000 24.2487i −0.508503 0.880753i
\(759\) 0 0
\(760\) 4.00000 6.92820i 0.145095 0.251312i
\(761\) 4.94975 + 8.57321i 0.179428 + 0.310779i 0.941685 0.336496i \(-0.109242\pi\)
−0.762257 + 0.647275i \(0.775909\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −16.0000 −0.578860
\(765\) 0 0
\(766\) 2.82843 4.89898i 0.102195 0.177007i
\(767\) 24.0000 41.5692i 0.866590 1.50098i
\(768\) 0 0
\(769\) −4.24264 −0.152994 −0.0764968 0.997070i \(-0.524373\pi\)
−0.0764968 + 0.997070i \(0.524373\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −7.00000 12.1244i −0.251936 0.436365i
\(773\) −16.2635 + 28.1691i −0.584956 + 1.01317i 0.409925 + 0.912119i \(0.365555\pi\)
−0.994881 + 0.101054i \(0.967778\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 7.07107 0.253837
\(777\) 0 0
\(778\) 26.0000 0.932145
\(779\) 28.0000 + 48.4974i 1.00320 + 1.73760i
\(780\) 0 0
\(781\) 0 0
\(782\) 28.2843 + 48.9898i 1.01144 + 1.75187i
\(783\) 0 0
\(784\) 0 0
\(785\) −26.0000 −0.927980
\(786\) 0 0
\(787\) −2.82843 + 4.89898i −0.100823 + 0.174630i −0.912024 0.410137i \(-0.865481\pi\)
0.811201 + 0.584767i \(0.198814\pi\)
\(788\) 2.00000 3.46410i 0.0712470 0.123404i
\(789\) 0 0
\(790\) −22.6274 −0.805047
\(791\) 0 0
\(792\) 0 0
\(793\) −3.00000 5.19615i −0.106533 0.184521i
\(794\) −3.53553 + 6.12372i −0.125471 + 0.217323i
\(795\) 0 0
\(796\) −8.48528 14.6969i −0.300753 0.520919i