Properties

Label 882.2.g.m.667.2
Level $882$
Weight $2$
Character 882.667
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 667.2
Root \(0.707107 - 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 882.667
Dual form 882.2.g.m.361.2

$q$-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 \(\left(\mathbb{Z}/882\mathbb{Z}\right)^\times\).

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

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 \(-0.730917\pi\)
0.979698 + 0.200480i \(0.0642503\pi\)
\(6\) 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 0.992361 + 0.123371i \(0.0393705\pi\)
−0.389338 + 0.921095i \(0.627296\pi\)
\(12\) 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 −0.874313 0.485363i \(-0.838688\pi\)
0.0168199 0.999859i \(-0.494646\pi\)
\(18\) 0 0
\(19\) 2.82843 4.89898i 0.648886 1.12390i −0.334504 0.942394i \(-0.608569\pi\)
0.983389 0.181509i \(-0.0580980\pi\)
\(20\) −1.41421 −0.316228
\(21\) 0 0
\(22\) 4.00000 0.852803
\(23\) 4.00000 6.92820i 0.834058 1.44463i −0.0607377 0.998154i \(-0.519345\pi\)
0.894795 0.446476i \(-0.147321\pi\)
\(24\) 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 \(-0.559454\pi\)
−0.185695 + 0.982607i \(0.559454\pi\)
\(30\) 0 0
\(31\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(32\) 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 −0.982274 0.187453i \(-0.939977\pi\)
0.653476 + 0.756948i \(0.273310\pi\)
\(38\) −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 \(-0.781255\pi\)
−0.773021 + 0.634381i \(0.781255\pi\)
\(42\) 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 \(-0.697965\pi\)
0.995170 + 0.0981685i \(0.0312984\pi\)
\(48\) 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 \(-0.0780811\pi\)
−0.695344 + 0.718677i \(0.744748\pi\)
\(54\) 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 −0.954080 0.299552i \(-0.903163\pi\)
0.217620 0.976034i \(-0.430171\pi\)
\(60\) 0 0
\(61\) −0.707107 + 1.22474i −0.0905357 + 0.156813i −0.907737 0.419540i \(-0.862191\pi\)
0.817201 + 0.576353i \(0.195525\pi\)
\(62\) 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 0.955588 + 0.294706i \(0.0952216\pi\)
−0.222571 + 0.974916i \(0.571445\pi\)
\(68\) −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 0.813547 + 0.581499i \(0.197534\pi\)
0.0968194 + 0.995302i \(0.469133\pi\)
\(74\) 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 0.0726692 0.997356i \(-0.476848\pi\)
0.827401 0.561611i \(-0.189818\pi\)
\(80\) 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 \(-0.399517\pi\)
0.310460 + 0.950586i \(0.399517\pi\)
\(84\) 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 \(-0.711056\pi\)
0.990292 + 0.139003i \(0.0443898\pi\)
\(90\) 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 0.986886 + 0.161421i \(0.0516078\pi\)
−0.353648 + 0.935379i \(0.615059\pi\)
\(102\) 0 0
\(103\) −2.82843 + 4.89898i −0.278693 + 0.482711i −0.971060 0.238835i \(-0.923235\pi\)
0.692367 + 0.721545i \(0.256568\pi\)
\(104\) −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 \(-0.895268\pi\)
0.753010 + 0.658009i \(0.228601\pi\)
\(108\) 0 0
\(109\) −2.00000 3.46410i −0.191565 0.331801i 0.754204 0.656640i \(-0.228023\pi\)
−0.945769 + 0.324840i \(0.894690\pi\)
\(110\) 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 0.210513 + 0.977591i \(0.432487\pi\)
−0.951875 + 0.306486i \(0.900847\pi\)
\(132\) 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 \(-0.0841608\pi\)
−0.708942 + 0.705266i \(0.750827\pi\)
\(138\) 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 0.0870170 + 0.996207i \(0.472267\pi\)
−0.906249 + 0.422744i \(0.861067\pi\)
\(150\) 0 0
\(151\) 8.00000 + 13.8564i 0.651031 + 1.12762i 0.982873 + 0.184284i \(0.0589965\pi\)
−0.331842 + 0.943335i \(0.607670\pi\)
\(152\) −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 0.955321 + 0.295571i \(0.0955099\pi\)
−0.221688 + 0.975118i \(0.571157\pi\)
\(158\) −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 −0.933659 0.358162i \(-0.883403\pi\)
0.777007 + 0.629492i \(0.216737\pi\)
\(164\) 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 \(-0.644221\pi\)
−0.437741 + 0.899101i \(0.644221\pi\)
\(168\) 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 \(-0.994093\pi\)
0.515985 + 0.856598i \(0.327426\pi\)
\(174\) 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 \(-0.314694\pi\)
−0.998286 + 0.0585225i \(0.981361\pi\)
\(180\) 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 0.416751 + 0.909021i \(0.363169\pi\)
−0.995610 + 0.0935936i \(0.970165\pi\)
\(192\) 0 0
\(193\) −7.00000 12.1244i −0.503871 0.872730i −0.999990 0.00447566i \(-0.998575\pi\)
0.496119 0.868255i \(-0.334758\pi\)
\(194\) 3.53553 6.12372i 0.253837 0.439658i
\(195\) 0 0
\(196\) 0 0
\(197\) 4.00000 0.284988 0.142494 0.989796i \(-0.454488\pi\)
0.142494 + 0.989796i \(0.454488\pi\)
\(198\) 0 0
\(199\) −8.48528 14.6969i −0.601506 1.04184i −0.992593 0.121485i \(-0.961234\pi\)
0.391088 0.920353i \(-0.372099\pi\)
\(200\) −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 0.997216 + 0.0745706i \(0.0237586\pi\)
−0.434028 + 0.900899i \(0.642908\pi\)
\(228\) 0 0
\(229\) −6.36396 + 11.0227i −0.420542 + 0.728401i −0.995993 0.0894361i \(-0.971494\pi\)
0.575450 + 0.817837i \(0.304827\pi\)
\(230\) −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 \(-0.896303\pi\)
0.750867 + 0.660454i \(0.229636\pi\)
\(234\) 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 \(-0.217137\pi\)
0.776215 + 0.630468i \(0.217137\pi\)
\(240\) 0 0
\(241\) −2.12132 3.67423i −0.136646 0.236678i 0.789579 0.613649i \(-0.210299\pi\)
−0.926225 + 0.376971i \(0.876966\pi\)
\(242\) 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 \(-0.442866\pi\)
0.178529 + 0.983935i \(0.442866\pi\)
\(252\) 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 \(-0.963273\pi\)
0.596378 + 0.802704i \(0.296606\pi\)
\(258\) 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 0.952517 + 0.304487i \(0.0984850\pi\)
−0.212565 + 0.977147i \(0.568182\pi\)
\(264\) 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 \(-0.180394\pi\)
−0.886777 + 0.462198i \(0.847061\pi\)
\(270\) 0 0
\(271\) 2.82843 4.89898i 0.171815 0.297592i −0.767240 0.641361i \(-0.778370\pi\)
0.939054 + 0.343769i \(0.111704\pi\)
\(272\) 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 0.675810 0.737075i \(-0.263794\pi\)
−0.976231 + 0.216731i \(0.930460\pi\)
\(278\) −2.82843 + 4.89898i −0.169638 + 0.293821i
\(279\) 0 0
\(280\) 0 0
\(281\) −10.0000 −0.596550 −0.298275 0.954480i \(-0.596411\pi\)
−0.298275 + 0.954480i \(0.596411\pi\)
\(282\) 0 0
\(283\) −11.3137 19.5959i −0.672530 1.16486i −0.977184 0.212393i \(-0.931874\pi\)
0.304654 0.952463i \(-0.401459\pi\)
\(284\) 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 \(-0.747827\pi\)
−0.702264 + 0.711917i \(0.747827\pi\)
\(294\) 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 \(-0.217940\pi\)
−0.935007 + 0.354629i \(0.884607\pi\)
\(312\) 0 0
\(313\) −10.6066 + 18.3712i −0.599521 + 1.03840i 0.393371 + 0.919380i \(0.371309\pi\)
−0.992892 + 0.119020i \(0.962025\pi\)
\(314\) 18.3848 1.03751
\(315\) 0 0
\(316\) −16.0000 −0.900070
\(317\) 14.0000 24.2487i 0.786318 1.36194i −0.141890 0.989882i \(-0.545318\pi\)
0.928208 0.372061i \(-0.121349\pi\)
\(318\) 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 −0.448649 0.893708i \(-0.648095\pi\)
0.998298 0.0583130i \(-0.0185721\pi\)
\(332\) −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 \(-0.271054\pi\)
−0.980921 + 0.194409i \(0.937721\pi\)
\(348\) 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 \(-0.154684\pi\)
−0.846594 + 0.532239i \(0.821351\pi\)
\(354\) 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 \(-0.694583\pi\)
0.996157 + 0.0875892i \(0.0279163\pi\)
\(360\) 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 0.782713 0.622383i \(-0.213835\pi\)
−0.930356 + 0.366658i \(0.880502\pi\)
\(368\) 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 −0.965945 0.258748i \(-0.916690\pi\)
0.707055 + 0.707159i \(0.250023\pi\)
\(374\) −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 \(-0.879499\pi\)
0.784670 + 0.619914i \(0.212832\pi\)
\(384\) 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 0.980842 + 0.194804i \(0.0624070\pi\)
−0.321716 + 0.946836i \(0.604260\pi\)
\(390\) 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 −0.941004 0.338395i \(-0.890116\pi\)
0.763561 + 0.645736i \(0.223449\pi\)
\(398\) −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 \(-0.684957\pi\)
0.998350 + 0.0574304i \(0.0182907\pi\)
\(402\) 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 0.999594 + 0.0284813i \(0.00906711\pi\)
−0.475132 + 0.879915i \(0.657600\pi\)
\(410\) 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 \(-0.686407\pi\)
−0.552711 + 0.833373i \(0.686407\pi\)
\(420\) 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 0.995706 + 0.0925683i \(0.0295076\pi\)
−0.417687 + 0.908591i \(0.637159\pi\)
\(432\) 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 0.102930 + 0.994689i \(0.467178\pi\)
−0.912890 + 0.408205i \(0.866155\pi\)
\(440\) −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 \(-0.675740\pi\)
0.999594 + 0.0285009i \(0.00907336\pi\)
\(444\) 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 \(-0.308369\pi\)
0.566315 + 0.824189i \(0.308369\pi\)
\(450\) 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 −0.787288 0.616585i \(-0.788516\pi\)
0.927622 + 0.373519i \(0.121849\pi\)
\(458\) 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 \(-0.489515\pi\)
0.0329332 + 0.999458i \(0.489515\pi\)
\(462\) 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 \(-0.791552\pi\)
0.924018 + 0.382350i \(0.124885\pi\)
\(468\) 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 −0.984030 0.178004i \(-0.943036\pi\)
0.337859 0.941197i \(-0.390297\pi\)
\(480\) 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 0.998683 + 0.0513038i \(0.0163377\pi\)
−0.454911 + 0.890537i \(0.650329\pi\)
\(488\) 0.707107 1.22474i 0.0320092 0.0554416i
\(489\) 0 0
\(490\) 0 0
\(491\) 12.0000 0.541552 0.270776 0.962642i \(-0.412720\pi\)
0.270776 + 0.962642i \(0.412720\pi\)
\(492\) 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 −0.817781 0.575529i \(-0.804796\pi\)
0.907314 + 0.420455i \(0.138129\pi\)
\(500\) −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 \(-0.717177\pi\)
−0.630567 + 0.776135i \(0.717177\pi\)
\(504\) 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 −0.239788 0.970825i \(-0.577078\pi\)
0.960653 0.277750i \(-0.0895886\pi\)
\(510\) 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 \(-0.156804\pi\)
−0.850120 + 0.526589i \(0.823471\pi\)
\(522\) 0 0
\(523\) 16.9706 29.3939i 0.742071 1.28530i −0.209480 0.977813i \(-0.567177\pi\)
0.951551 0.307492i \(-0.0994896\pi\)
\(524\) 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 −0.843728 0.536771i \(-0.819644\pi\)
0.886721 + 0.462304i \(0.152977\pi\)
\(542\) −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 0.941462 + 0.337119i \(0.109452\pi\)
−0.178778 + 0.983890i \(0.557214\pi\)
\(558\) 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 \(-0.243292\pi\)
−0.960258 + 0.279115i \(0.909959\pi\)
\(564\) 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 0.453619 + 0.891196i \(0.350133\pi\)
−0.998608 + 0.0527519i \(0.983201\pi\)
\(570\) 0 0
\(571\) −2.00000 3.46410i −0.0836974 0.144968i 0.821138 0.570730i \(-0.193340\pi\)
−0.904835 + 0.425762i \(0.860006\pi\)
\(572\) 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 0.702611 0.711574i \(-0.252017\pi\)
−0.967547 + 0.252693i \(0.918684\pi\)
\(578\) 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 \(-0.386105\pi\)
0.350225 + 0.936666i \(0.386105\pi\)
\(588\) 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 0.232653 + 0.972560i \(0.425259\pi\)
−0.958588 + 0.284796i \(0.908074\pi\)
\(594\) 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 \(-0.272661\pi\)
−0.981889 + 0.189456i \(0.939328\pi\)
\(600\) 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 −0.985246 0.171145i \(-0.945253\pi\)
0.640839 + 0.767675i \(0.278587\pi\)
\(608\) 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 0.719042 0.694967i \(-0.244581\pi\)
−0.961380 + 0.275225i \(0.911248\pi\)
\(614\) 2.82843 4.89898i 0.114146 0.197707i
\(615\) 0 0
\(616\) 0 0
\(617\) −22.0000 −0.885687 −0.442843 0.896599i \(-0.646030\pi\)
−0.442843 + 0.896599i \(0.646030\pi\)
\(618\) 0 0
\(619\) −5.65685 9.79796i −0.227368 0.393813i 0.729659 0.683811i \(-0.239679\pi\)
−0.957027 + 0.289998i \(0.906345\pi\)
\(620\) 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 \(-0.154091\pi\)
−0.845601 + 0.533816i \(0.820758\pi\)
\(642\) 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 0.978689 + 0.205349i \(0.0658329\pi\)
−0.311507 + 0.950244i \(0.600834\pi\)
\(648\) 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 \(-0.718768\pi\)
0.986634 + 0.162951i \(0.0521013\pi\)
\(654\) 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 \(-0.252657\pi\)
0.701180 + 0.712984i \(0.252657\pi\)
\(660\) 0 0
\(661\) −2.12132 3.67423i −0.0825098 0.142911i 0.821818 0.569751i \(-0.192960\pi\)
−0.904327 + 0.426840i \(0.859627\pi\)
\(662\) −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 \(-0.807353\pi\)
0.903907 + 0.427729i \(0.140686\pi\)
\(678\) 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 \(-0.240403\pi\)
−0.957685 + 0.287819i \(0.907070\pi\)
\(684\) 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 0.268157 0.963375i \(-0.413585\pi\)
0.700229 0.713918i \(-0.253081\pi\)
\(692\) 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 \(-0.691719\pi\)
−0.566542 + 0.824033i \(0.691719\pi\)
\(702\) 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 0.473768 + 0.880650i \(0.342894\pi\)
−0.999549 + 0.0300298i \(0.990440\pi\)
\(710\) 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 −0.214848 0.976648i \(-0.568926\pi\)
0.953225 0.302260i \(-0.0977411\pi\)
\(720\) 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 −0.959290 0.282424i \(-0.908861\pi\)
0.724231 + 0.689557i \(0.242195\pi\)
\(734\) −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 0.734311 0.678813i \(-0.237505\pi\)
−0.955025 + 0.296526i \(0.904172\pi\)
\(740\) 2.82843 4.89898i 0.103975 0.180090i
\(741\) 0 0
\(742\) 0 0
\(743\) −16.0000 −0.586983 −0.293492 0.955962i \(-0.594817\pi\)
−0.293492 + 0.955962i \(0.594817\pi\)
\(744\) 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 −0.227153 0.973859i \(-0.572942\pi\)
0.956963 0.290209i \(-0.0937250\pi\)
\(752\) 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 \(-0.890758\pi\)
0.762257 + 0.647275i \(0.224091\pi\)
\(762\) 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 0.994881 + 0.101054i \(0.0322215\pi\)
−0.409925 + 0.912119i \(0.634445\pi\)
\(774\) 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 0.811201 0.584767i \(-0.198814\pi\)
−0.912024 + 0.410137i \(0.865481\pi\)
\(788\) −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
\(797\)