Properties

Label 912.2.bn.m.65.4
Level $912$
Weight $2$
Character 912.65
Analytic conductor $7.282$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 912.bn (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.28235666434\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{24})\)
Defining polynomial: \( x^{8} - x^{4} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 57)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 65.4
Root \(-0.965926 + 0.258819i\) of defining polynomial
Character \(\chi\) \(=\) 912.65
Dual form 912.2.bn.m.449.4

$q$-expansion

\(f(q)\) \(=\) \(q+(1.57313 - 0.724745i) q^{3} +(1.22474 + 0.707107i) q^{5} +0.267949 q^{7} +(1.94949 - 2.28024i) q^{9} +O(q^{10})\) \(q+(1.57313 - 0.724745i) q^{3} +(1.22474 + 0.707107i) q^{5} +0.267949 q^{7} +(1.94949 - 2.28024i) q^{9} +5.27792i q^{11} +(-0.232051 + 0.133975i) q^{13} +(2.43916 + 0.224745i) q^{15} +(4.24264 + 2.44949i) q^{17} +(-1.73205 + 4.00000i) q^{19} +(0.421519 - 0.194195i) q^{21} +(4.57081 - 2.63896i) q^{23} +(-1.50000 - 2.59808i) q^{25} +(1.41421 - 5.00000i) q^{27} +(1.03528 + 1.79315i) q^{29} -2.46410i q^{31} +(3.82514 + 8.30286i) q^{33} +(0.328169 + 0.189469i) q^{35} -7.73205i q^{37} +(-0.267949 + 0.378937i) q^{39} +(-2.82843 + 4.89898i) q^{41} +(2.86603 - 4.96410i) q^{43} +(4.00000 - 1.41421i) q^{45} +(0.656339 - 0.378937i) q^{47} -6.92820 q^{49} +(8.44949 + 0.778539i) q^{51} +(-5.46739 - 9.46979i) q^{53} +(-3.73205 + 6.46410i) q^{55} +(0.174235 + 7.54782i) q^{57} +(-5.60609 + 9.71003i) q^{59} +(5.23205 + 9.06218i) q^{61} +(0.522364 - 0.610988i) q^{63} -0.378937 q^{65} +(0.866025 - 0.500000i) q^{67} +(5.27792 - 7.46410i) q^{69} +(6.69213 - 11.5911i) q^{71} +(1.50000 - 2.59808i) q^{73} +(-4.24264 - 3.00000i) q^{75} +1.41421i q^{77} +(-9.06218 - 5.23205i) q^{79} +(-1.39898 - 8.89060i) q^{81} -2.07055i q^{83} +(3.46410 + 6.00000i) q^{85} +(2.92820 + 2.07055i) q^{87} +(3.67423 + 6.36396i) q^{89} +(-0.0621778 + 0.0358984i) q^{91} +(-1.78585 - 3.87636i) q^{93} +(-4.94975 + 3.67423i) q^{95} +(-0.464102 - 0.267949i) q^{97} +(12.0349 + 10.2892i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 16 q^{7} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 16 q^{7} - 4 q^{9} + 12 q^{13} - 12 q^{21} - 12 q^{25} + 24 q^{33} - 16 q^{39} + 16 q^{43} + 32 q^{45} + 48 q^{51} - 16 q^{55} - 28 q^{57} + 28 q^{61} - 8 q^{63} + 12 q^{73} - 24 q^{79} + 28 q^{81} - 32 q^{87} + 48 q^{91} - 4 q^{93} + 24 q^{97} + 32 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/912\mathbb{Z}\right)^\times\).

\(n\) \(97\) \(229\) \(305\) \(799\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(1\) \(-1\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 1.57313 0.724745i 0.908248 0.418432i
\(4\) 0 0
\(5\) 1.22474 + 0.707107i 0.547723 + 0.316228i 0.748203 0.663470i \(-0.230917\pi\)
−0.200480 + 0.979698i \(0.564250\pi\)
\(6\) 0 0
\(7\) 0.267949 0.101275 0.0506376 0.998717i \(-0.483875\pi\)
0.0506376 + 0.998717i \(0.483875\pi\)
\(8\) 0 0
\(9\) 1.94949 2.28024i 0.649830 0.760080i
\(10\) 0 0
\(11\) 5.27792i 1.59135i 0.605723 + 0.795676i \(0.292884\pi\)
−0.605723 + 0.795676i \(0.707116\pi\)
\(12\) 0 0
\(13\) −0.232051 + 0.133975i −0.0643593 + 0.0371579i −0.531834 0.846848i \(-0.678497\pi\)
0.467475 + 0.884006i \(0.345164\pi\)
\(14\) 0 0
\(15\) 2.43916 + 0.224745i 0.629788 + 0.0580289i
\(16\) 0 0
\(17\) 4.24264 + 2.44949i 1.02899 + 0.594089i 0.916696 0.399586i \(-0.130846\pi\)
0.112296 + 0.993675i \(0.464180\pi\)
\(18\) 0 0
\(19\) −1.73205 + 4.00000i −0.397360 + 0.917663i
\(20\) 0 0
\(21\) 0.421519 0.194195i 0.0919831 0.0423768i
\(22\) 0 0
\(23\) 4.57081 2.63896i 0.953080 0.550261i 0.0590435 0.998255i \(-0.481195\pi\)
0.894036 + 0.447995i \(0.147862\pi\)
\(24\) 0 0
\(25\) −1.50000 2.59808i −0.300000 0.519615i
\(26\) 0 0
\(27\) 1.41421 5.00000i 0.272166 0.962250i
\(28\) 0 0
\(29\) 1.03528 + 1.79315i 0.192246 + 0.332980i 0.945994 0.324184i \(-0.105090\pi\)
−0.753748 + 0.657163i \(0.771756\pi\)
\(30\) 0 0
\(31\) 2.46410i 0.442566i −0.975210 0.221283i \(-0.928976\pi\)
0.975210 0.221283i \(-0.0710244\pi\)
\(32\) 0 0
\(33\) 3.82514 + 8.30286i 0.665872 + 1.44534i
\(34\) 0 0
\(35\) 0.328169 + 0.189469i 0.0554708 + 0.0320261i
\(36\) 0 0
\(37\) 7.73205i 1.27114i −0.772043 0.635571i \(-0.780765\pi\)
0.772043 0.635571i \(-0.219235\pi\)
\(38\) 0 0
\(39\) −0.267949 + 0.378937i −0.0429062 + 0.0606785i
\(40\) 0 0
\(41\) −2.82843 + 4.89898i −0.441726 + 0.765092i −0.997818 0.0660290i \(-0.978967\pi\)
0.556092 + 0.831121i \(0.312300\pi\)
\(42\) 0 0
\(43\) 2.86603 4.96410i 0.437065 0.757018i −0.560397 0.828224i \(-0.689351\pi\)
0.997462 + 0.0712058i \(0.0226847\pi\)
\(44\) 0 0
\(45\) 4.00000 1.41421i 0.596285 0.210819i
\(46\) 0 0
\(47\) 0.656339 0.378937i 0.0957369 0.0552737i −0.451367 0.892338i \(-0.649064\pi\)
0.547104 + 0.837065i \(0.315730\pi\)
\(48\) 0 0
\(49\) −6.92820 −0.989743
\(50\) 0 0
\(51\) 8.44949 + 0.778539i 1.18317 + 0.109017i
\(52\) 0 0
\(53\) −5.46739 9.46979i −0.751003 1.30078i −0.947337 0.320239i \(-0.896237\pi\)
0.196334 0.980537i \(-0.437096\pi\)
\(54\) 0 0
\(55\) −3.73205 + 6.46410i −0.503230 + 0.871619i
\(56\) 0 0
\(57\) 0.174235 + 7.54782i 0.0230779 + 0.999734i
\(58\) 0 0
\(59\) −5.60609 + 9.71003i −0.729850 + 1.26414i 0.227096 + 0.973872i \(0.427077\pi\)
−0.956946 + 0.290265i \(0.906256\pi\)
\(60\) 0 0
\(61\) 5.23205 + 9.06218i 0.669895 + 1.16029i 0.977933 + 0.208919i \(0.0669944\pi\)
−0.308038 + 0.951374i \(0.599672\pi\)
\(62\) 0 0
\(63\) 0.522364 0.610988i 0.0658117 0.0769773i
\(64\) 0 0
\(65\) −0.378937 −0.0470014
\(66\) 0 0
\(67\) 0.866025 0.500000i 0.105802 0.0610847i −0.446165 0.894951i \(-0.647211\pi\)
0.551967 + 0.833866i \(0.313877\pi\)
\(68\) 0 0
\(69\) 5.27792 7.46410i 0.635387 0.898572i
\(70\) 0 0
\(71\) 6.69213 11.5911i 0.794210 1.37561i −0.129130 0.991628i \(-0.541218\pi\)
0.923340 0.383984i \(-0.125448\pi\)
\(72\) 0 0
\(73\) 1.50000 2.59808i 0.175562 0.304082i −0.764794 0.644275i \(-0.777159\pi\)
0.940356 + 0.340193i \(0.110493\pi\)
\(74\) 0 0
\(75\) −4.24264 3.00000i −0.489898 0.346410i
\(76\) 0 0
\(77\) 1.41421i 0.161165i
\(78\) 0 0
\(79\) −9.06218 5.23205i −1.01957 0.588652i −0.105594 0.994409i \(-0.533674\pi\)
−0.913981 + 0.405758i \(0.867008\pi\)
\(80\) 0 0
\(81\) −1.39898 8.89060i −0.155442 0.987845i
\(82\) 0 0
\(83\) 2.07055i 0.227273i −0.993522 0.113636i \(-0.963750\pi\)
0.993522 0.113636i \(-0.0362499\pi\)
\(84\) 0 0
\(85\) 3.46410 + 6.00000i 0.375735 + 0.650791i
\(86\) 0 0
\(87\) 2.92820 + 2.07055i 0.313936 + 0.221987i
\(88\) 0 0
\(89\) 3.67423 + 6.36396i 0.389468 + 0.674579i 0.992378 0.123231i \(-0.0393255\pi\)
−0.602910 + 0.797809i \(0.705992\pi\)
\(90\) 0 0
\(91\) −0.0621778 + 0.0358984i −0.00651801 + 0.00376317i
\(92\) 0 0
\(93\) −1.78585 3.87636i −0.185184 0.401960i
\(94\) 0 0
\(95\) −4.94975 + 3.67423i −0.507833 + 0.376969i
\(96\) 0 0
\(97\) −0.464102 0.267949i −0.0471224 0.0272061i 0.476254 0.879308i \(-0.341994\pi\)
−0.523376 + 0.852102i \(0.675328\pi\)
\(98\) 0 0
\(99\) 12.0349 + 10.2892i 1.20955 + 1.03411i
\(100\) 0 0
\(101\) −1.79315 + 1.03528i −0.178425 + 0.103014i −0.586553 0.809911i \(-0.699515\pi\)
0.408127 + 0.912925i \(0.366182\pi\)
\(102\) 0 0
\(103\) 3.53590i 0.348402i −0.984710 0.174201i \(-0.944266\pi\)
0.984710 0.174201i \(-0.0557343\pi\)
\(104\) 0 0
\(105\) 0.653570 + 0.0602202i 0.0637819 + 0.00587689i
\(106\) 0 0
\(107\) −4.89898 −0.473602 −0.236801 0.971558i \(-0.576099\pi\)
−0.236801 + 0.971558i \(0.576099\pi\)
\(108\) 0 0
\(109\) −5.53590 3.19615i −0.530243 0.306136i 0.210872 0.977514i \(-0.432370\pi\)
−0.741115 + 0.671378i \(0.765703\pi\)
\(110\) 0 0
\(111\) −5.60376 12.1635i −0.531886 1.15451i
\(112\) 0 0
\(113\) 3.96524 0.373018 0.186509 0.982453i \(-0.440283\pi\)
0.186509 + 0.982453i \(0.440283\pi\)
\(114\) 0 0
\(115\) 7.46410 0.696031
\(116\) 0 0
\(117\) −0.146887 + 0.790313i −0.0135797 + 0.0730645i
\(118\) 0 0
\(119\) 1.13681 + 0.656339i 0.104211 + 0.0601665i
\(120\) 0 0
\(121\) −16.8564 −1.53240
\(122\) 0 0
\(123\) −0.898979 + 9.75663i −0.0810583 + 0.879726i
\(124\) 0 0
\(125\) 11.3137i 1.01193i
\(126\) 0 0
\(127\) −17.1962 + 9.92820i −1.52591 + 0.880986i −0.526384 + 0.850247i \(0.676453\pi\)
−0.999527 + 0.0307388i \(0.990214\pi\)
\(128\) 0 0
\(129\) 0.910930 9.88633i 0.0802029 0.870442i
\(130\) 0 0
\(131\) 10.9348 + 6.31319i 0.955375 + 0.551586i 0.894747 0.446574i \(-0.147356\pi\)
0.0606288 + 0.998160i \(0.480689\pi\)
\(132\) 0 0
\(133\) −0.464102 + 1.07180i −0.0402427 + 0.0929366i
\(134\) 0 0
\(135\) 5.26758 5.12372i 0.453362 0.440980i
\(136\) 0 0
\(137\) 9.14162 5.27792i 0.781021 0.450923i −0.0557708 0.998444i \(-0.517762\pi\)
0.836792 + 0.547521i \(0.184428\pi\)
\(138\) 0 0
\(139\) 1.40192 + 2.42820i 0.118910 + 0.205958i 0.919336 0.393474i \(-0.128727\pi\)
−0.800426 + 0.599431i \(0.795393\pi\)
\(140\) 0 0
\(141\) 0.757875 1.07180i 0.0638246 0.0902616i
\(142\) 0 0
\(143\) −0.707107 1.22474i −0.0591312 0.102418i
\(144\) 0 0
\(145\) 2.92820i 0.243174i
\(146\) 0 0
\(147\) −10.8990 + 5.02118i −0.898933 + 0.414140i
\(148\) 0 0
\(149\) 2.36156 + 1.36345i 0.193466 + 0.111698i 0.593604 0.804757i \(-0.297704\pi\)
−0.400138 + 0.916455i \(0.631038\pi\)
\(150\) 0 0
\(151\) 2.00000i 0.162758i 0.996683 + 0.0813788i \(0.0259324\pi\)
−0.996683 + 0.0813788i \(0.974068\pi\)
\(152\) 0 0
\(153\) 13.8564 4.89898i 1.12022 0.396059i
\(154\) 0 0
\(155\) 1.74238 3.01790i 0.139952 0.242403i
\(156\) 0 0
\(157\) −5.23205 + 9.06218i −0.417563 + 0.723241i −0.995694 0.0927037i \(-0.970449\pi\)
0.578131 + 0.815944i \(0.303782\pi\)
\(158\) 0 0
\(159\) −15.4641 10.9348i −1.22638 0.867184i
\(160\) 0 0
\(161\) 1.22474 0.707107i 0.0965234 0.0557278i
\(162\) 0 0
\(163\) 5.19615 0.406994 0.203497 0.979076i \(-0.434769\pi\)
0.203497 + 0.979076i \(0.434769\pi\)
\(164\) 0 0
\(165\) −1.18618 + 12.8737i −0.0923444 + 1.00221i
\(166\) 0 0
\(167\) −10.8840 18.8516i −0.842229 1.45878i −0.888006 0.459832i \(-0.847909\pi\)
0.0457762 0.998952i \(-0.485424\pi\)
\(168\) 0 0
\(169\) −6.46410 + 11.1962i −0.497239 + 0.861242i
\(170\) 0 0
\(171\) 5.74434 + 11.7474i 0.439281 + 0.898350i
\(172\) 0 0
\(173\) −8.76268 + 15.1774i −0.666214 + 1.15392i 0.312740 + 0.949839i \(0.398753\pi\)
−0.978955 + 0.204079i \(0.934580\pi\)
\(174\) 0 0
\(175\) −0.401924 0.696152i −0.0303826 0.0526242i
\(176\) 0 0
\(177\) −1.78182 + 19.3381i −0.133930 + 1.45354i
\(178\) 0 0
\(179\) −1.41421 −0.105703 −0.0528516 0.998602i \(-0.516831\pi\)
−0.0528516 + 0.998602i \(0.516831\pi\)
\(180\) 0 0
\(181\) −3.00000 + 1.73205i −0.222988 + 0.128742i −0.607333 0.794447i \(-0.707761\pi\)
0.384345 + 0.923190i \(0.374427\pi\)
\(182\) 0 0
\(183\) 14.7985 + 10.4641i 1.09393 + 0.773529i
\(184\) 0 0
\(185\) 5.46739 9.46979i 0.401970 0.696233i
\(186\) 0 0
\(187\) −12.9282 + 22.3923i −0.945404 + 1.63749i
\(188\) 0 0
\(189\) 0.378937 1.33975i 0.0275636 0.0974522i
\(190\) 0 0
\(191\) 13.0053i 0.941032i 0.882391 + 0.470516i \(0.155932\pi\)
−0.882391 + 0.470516i \(0.844068\pi\)
\(192\) 0 0
\(193\) −2.42820 1.40192i −0.174786 0.100913i 0.410055 0.912061i \(-0.365510\pi\)
−0.584841 + 0.811148i \(0.698843\pi\)
\(194\) 0 0
\(195\) −0.596119 + 0.274633i −0.0426889 + 0.0196669i
\(196\) 0 0
\(197\) 0.656339i 0.0467622i 0.999727 + 0.0233811i \(0.00744311\pi\)
−0.999727 + 0.0233811i \(0.992557\pi\)
\(198\) 0 0
\(199\) −11.5981 20.0885i −0.822166 1.42403i −0.904066 0.427392i \(-0.859432\pi\)
0.0819004 0.996641i \(-0.473901\pi\)
\(200\) 0 0
\(201\) 1.00000 1.41421i 0.0705346 0.0997509i
\(202\) 0 0
\(203\) 0.277401 + 0.480473i 0.0194698 + 0.0337226i
\(204\) 0 0
\(205\) −6.92820 + 4.00000i −0.483887 + 0.279372i
\(206\) 0 0
\(207\) 2.89329 15.5672i 0.201098 1.08199i
\(208\) 0 0
\(209\) −21.1117 9.14162i −1.46032 0.632339i
\(210\) 0 0
\(211\) −9.52628 5.50000i −0.655816 0.378636i 0.134865 0.990864i \(-0.456940\pi\)
−0.790681 + 0.612228i \(0.790273\pi\)
\(212\) 0 0
\(213\) 2.12701 23.0844i 0.145740 1.58172i
\(214\) 0 0
\(215\) 7.02030 4.05317i 0.478780 0.276424i
\(216\) 0 0
\(217\) 0.660254i 0.0448210i
\(218\) 0 0
\(219\) 0.476756 5.17423i 0.0322162 0.349642i
\(220\) 0 0
\(221\) −1.31268 −0.0883003
\(222\) 0 0
\(223\) 9.86603 + 5.69615i 0.660678 + 0.381443i 0.792535 0.609826i \(-0.208761\pi\)
−0.131857 + 0.991269i \(0.542094\pi\)
\(224\) 0 0
\(225\) −8.84847 1.64456i −0.589898 0.109638i
\(226\) 0 0
\(227\) −4.79744 −0.318418 −0.159209 0.987245i \(-0.550894\pi\)
−0.159209 + 0.987245i \(0.550894\pi\)
\(228\) 0 0
\(229\) −11.3923 −0.752825 −0.376412 0.926452i \(-0.622842\pi\)
−0.376412 + 0.926452i \(0.622842\pi\)
\(230\) 0 0
\(231\) 1.02494 + 2.22474i 0.0674364 + 0.146377i
\(232\) 0 0
\(233\) −11.5911 6.69213i −0.759359 0.438416i 0.0697066 0.997568i \(-0.477794\pi\)
−0.829066 + 0.559151i \(0.811127\pi\)
\(234\) 0 0
\(235\) 1.07180 0.0699163
\(236\) 0 0
\(237\) −18.0479 1.66294i −1.17234 0.108020i
\(238\) 0 0
\(239\) 15.2789i 0.988313i −0.869373 0.494156i \(-0.835477\pi\)
0.869373 0.494156i \(-0.164523\pi\)
\(240\) 0 0
\(241\) 9.82051 5.66987i 0.632595 0.365229i −0.149162 0.988813i \(-0.547657\pi\)
0.781756 + 0.623584i \(0.214324\pi\)
\(242\) 0 0
\(243\) −8.64420 12.9722i −0.554526 0.832167i
\(244\) 0 0
\(245\) −8.48528 4.89898i −0.542105 0.312984i
\(246\) 0 0
\(247\) −0.133975 1.16025i −0.00852460 0.0738252i
\(248\) 0 0
\(249\) −1.50062 3.25725i −0.0950981 0.206420i
\(250\) 0 0
\(251\) −12.7279 + 7.34847i −0.803379 + 0.463831i −0.844651 0.535317i \(-0.820192\pi\)
0.0412721 + 0.999148i \(0.486859\pi\)
\(252\) 0 0
\(253\) 13.9282 + 24.1244i 0.875659 + 1.51669i
\(254\) 0 0
\(255\) 9.79796 + 6.92820i 0.613572 + 0.433861i
\(256\) 0 0
\(257\) −4.05317 7.02030i −0.252830 0.437914i 0.711474 0.702713i \(-0.248028\pi\)
−0.964304 + 0.264798i \(0.914695\pi\)
\(258\) 0 0
\(259\) 2.07180i 0.128735i
\(260\) 0 0
\(261\) 6.10707 + 1.13505i 0.378018 + 0.0702580i
\(262\) 0 0
\(263\) −24.9754 14.4195i −1.54005 0.889147i −0.998835 0.0482609i \(-0.984632\pi\)
−0.541213 0.840886i \(-0.682035\pi\)
\(264\) 0 0
\(265\) 15.4641i 0.949952i
\(266\) 0 0
\(267\) 10.3923 + 7.34847i 0.635999 + 0.449719i
\(268\) 0 0
\(269\) −5.46739 + 9.46979i −0.333352 + 0.577383i −0.983167 0.182710i \(-0.941513\pi\)
0.649815 + 0.760093i \(0.274847\pi\)
\(270\) 0 0
\(271\) 3.46410 6.00000i 0.210429 0.364474i −0.741420 0.671042i \(-0.765847\pi\)
0.951849 + 0.306568i \(0.0991805\pi\)
\(272\) 0 0
\(273\) −0.0717968 + 0.101536i −0.00434534 + 0.00614524i
\(274\) 0 0
\(275\) 13.7124 7.91688i 0.826891 0.477406i
\(276\) 0 0
\(277\) 17.8564 1.07289 0.536444 0.843936i \(-0.319767\pi\)
0.536444 + 0.843936i \(0.319767\pi\)
\(278\) 0 0
\(279\) −5.61874 4.80374i −0.336385 0.287592i
\(280\) 0 0
\(281\) −4.70951 8.15711i −0.280946 0.486613i 0.690672 0.723168i \(-0.257315\pi\)
−0.971618 + 0.236556i \(0.923981\pi\)
\(282\) 0 0
\(283\) 2.92820 5.07180i 0.174064 0.301487i −0.765773 0.643111i \(-0.777643\pi\)
0.939837 + 0.341624i \(0.110977\pi\)
\(284\) 0 0
\(285\) −5.12372 + 9.36736i −0.303503 + 0.554875i
\(286\) 0 0
\(287\) −0.757875 + 1.31268i −0.0447359 + 0.0774849i
\(288\) 0 0
\(289\) 3.50000 + 6.06218i 0.205882 + 0.356599i
\(290\) 0 0
\(291\) −0.924288 0.0851642i −0.0541827 0.00499242i
\(292\) 0 0
\(293\) 13.9391 0.814329 0.407164 0.913355i \(-0.366518\pi\)
0.407164 + 0.913355i \(0.366518\pi\)
\(294\) 0 0
\(295\) −13.7321 + 7.92820i −0.799511 + 0.461598i
\(296\) 0 0
\(297\) 26.3896 + 7.46410i 1.53128 + 0.433111i
\(298\) 0 0
\(299\) −0.707107 + 1.22474i −0.0408930 + 0.0708288i
\(300\) 0 0
\(301\) 0.767949 1.33013i 0.0442639 0.0766672i
\(302\) 0 0
\(303\) −2.07055 + 2.92820i −0.118950 + 0.168221i
\(304\) 0 0
\(305\) 14.7985i 0.847358i
\(306\) 0 0
\(307\) 12.0000 + 6.92820i 0.684876 + 0.395413i 0.801690 0.597740i \(-0.203935\pi\)
−0.116814 + 0.993154i \(0.537268\pi\)
\(308\) 0 0
\(309\) −2.56262 5.56244i −0.145783 0.316436i
\(310\) 0 0
\(311\) 12.4505i 0.706004i 0.935623 + 0.353002i \(0.114839\pi\)
−0.935623 + 0.353002i \(0.885161\pi\)
\(312\) 0 0
\(313\) −8.39230 14.5359i −0.474361 0.821618i 0.525208 0.850974i \(-0.323988\pi\)
−0.999569 + 0.0293564i \(0.990654\pi\)
\(314\) 0 0
\(315\) 1.07180 0.378937i 0.0603889 0.0213507i
\(316\) 0 0
\(317\) 4.43211 + 7.67664i 0.248932 + 0.431163i 0.963230 0.268679i \(-0.0865871\pi\)
−0.714298 + 0.699842i \(0.753254\pi\)
\(318\) 0 0
\(319\) −9.46410 + 5.46410i −0.529888 + 0.305931i
\(320\) 0 0
\(321\) −7.70674 + 3.55051i −0.430148 + 0.198170i
\(322\) 0 0
\(323\) −17.1464 + 12.7279i −0.954053 + 0.708201i
\(324\) 0 0
\(325\) 0.696152 + 0.401924i 0.0386156 + 0.0222947i
\(326\) 0 0
\(327\) −11.0251 1.01586i −0.609689 0.0561770i
\(328\) 0 0
\(329\) 0.175865 0.101536i 0.00969578 0.00559786i
\(330\) 0 0
\(331\) 18.0718i 0.993316i 0.867946 + 0.496658i \(0.165440\pi\)
−0.867946 + 0.496658i \(0.834560\pi\)
\(332\) 0 0
\(333\) −17.6309 15.0736i −0.966169 0.826026i
\(334\) 0 0
\(335\) 1.41421 0.0772667
\(336\) 0 0
\(337\) −21.3564 12.3301i −1.16336 0.671665i −0.211251 0.977432i \(-0.567754\pi\)
−0.952106 + 0.305767i \(0.901087\pi\)
\(338\) 0 0
\(339\) 6.23785 2.87379i 0.338793 0.156083i
\(340\) 0 0
\(341\) 13.0053 0.704278
\(342\) 0 0
\(343\) −3.73205 −0.201512
\(344\) 0 0
\(345\) 11.7420 5.40957i 0.632169 0.291241i
\(346\) 0 0
\(347\) 16.6424 + 9.60849i 0.893410 + 0.515811i 0.875057 0.484021i \(-0.160824\pi\)
0.0183540 + 0.999832i \(0.494157\pi\)
\(348\) 0 0
\(349\) 9.39230 0.502759 0.251379 0.967889i \(-0.419116\pi\)
0.251379 + 0.967889i \(0.419116\pi\)
\(350\) 0 0
\(351\) 0.341704 + 1.34972i 0.0182388 + 0.0720429i
\(352\) 0 0
\(353\) 2.17209i 0.115609i 0.998328 + 0.0578043i \(0.0184099\pi\)
−0.998328 + 0.0578043i \(0.981590\pi\)
\(354\) 0 0
\(355\) 16.3923 9.46410i 0.870013 0.502302i
\(356\) 0 0
\(357\) 2.26403 + 0.208609i 0.119825 + 0.0110408i
\(358\) 0 0
\(359\) 6.21166 + 3.58630i 0.327839 + 0.189278i 0.654881 0.755732i \(-0.272719\pi\)
−0.327042 + 0.945010i \(0.606052\pi\)
\(360\) 0 0
\(361\) −13.0000 13.8564i −0.684211 0.729285i
\(362\) 0 0
\(363\) −26.5174 + 12.2166i −1.39180 + 0.641205i
\(364\) 0 0
\(365\) 3.67423 2.12132i 0.192318 0.111035i
\(366\) 0 0
\(367\) 10.5263 + 18.2321i 0.549467 + 0.951705i 0.998311 + 0.0580950i \(0.0185026\pi\)
−0.448844 + 0.893610i \(0.648164\pi\)
\(368\) 0 0
\(369\) 5.65685 + 16.0000i 0.294484 + 0.832927i
\(370\) 0 0
\(371\) −1.46498 2.53742i −0.0760581 0.131736i
\(372\) 0 0
\(373\) 19.4641i 1.00781i −0.863758 0.503906i \(-0.831896\pi\)
0.863758 0.503906i \(-0.168104\pi\)
\(374\) 0 0
\(375\) −8.19955 17.7980i −0.423423 0.919083i
\(376\) 0 0
\(377\) −0.480473 0.277401i −0.0247456 0.0142869i
\(378\) 0 0
\(379\) 23.7846i 1.22173i −0.791733 0.610867i \(-0.790821\pi\)
0.791733 0.610867i \(-0.209179\pi\)
\(380\) 0 0
\(381\) −19.8564 + 28.0812i −1.01727 + 1.43864i
\(382\) 0 0
\(383\) −6.26243 + 10.8468i −0.319995 + 0.554248i −0.980487 0.196586i \(-0.937015\pi\)
0.660492 + 0.750833i \(0.270348\pi\)
\(384\) 0 0
\(385\) −1.00000 + 1.73205i −0.0509647 + 0.0882735i
\(386\) 0 0
\(387\) −5.73205 16.2127i −0.291377 0.824137i
\(388\) 0 0
\(389\) 12.8159 7.39924i 0.649790 0.375156i −0.138586 0.990350i \(-0.544256\pi\)
0.788376 + 0.615194i \(0.210922\pi\)
\(390\) 0 0
\(391\) 25.8564 1.30761
\(392\) 0 0
\(393\) 21.7773 + 2.00657i 1.09852 + 0.101218i
\(394\) 0 0
\(395\) −7.39924 12.8159i −0.372296 0.644836i
\(396\) 0 0
\(397\) 13.1603 22.7942i 0.660494 1.14401i −0.319992 0.947420i \(-0.603680\pi\)
0.980486 0.196589i \(-0.0629865\pi\)
\(398\) 0 0
\(399\) 0.0466860 + 2.02243i 0.00233722 + 0.101248i
\(400\) 0 0
\(401\) −11.4016 + 19.7482i −0.569371 + 0.986179i 0.427257 + 0.904130i \(0.359480\pi\)
−0.996628 + 0.0820492i \(0.973854\pi\)
\(402\) 0 0
\(403\) 0.330127 + 0.571797i 0.0164448 + 0.0284832i
\(404\) 0 0
\(405\) 4.57321 11.8780i 0.227245 0.590220i
\(406\) 0 0
\(407\) 40.8091 2.02283
\(408\) 0 0
\(409\) 17.5359 10.1244i 0.867094 0.500617i 0.000712791 1.00000i \(-0.499773\pi\)
0.866382 + 0.499383i \(0.166440\pi\)
\(410\) 0 0
\(411\) 10.5558 14.9282i 0.520681 0.736354i
\(412\) 0 0
\(413\) −1.50215 + 2.60179i −0.0739158 + 0.128026i
\(414\) 0 0
\(415\) 1.46410 2.53590i 0.0718699 0.124482i
\(416\) 0 0
\(417\) 3.96524 + 2.80385i 0.194179 + 0.137305i
\(418\) 0 0
\(419\) 7.55154i 0.368917i −0.982840 0.184458i \(-0.940947\pi\)
0.982840 0.184458i \(-0.0590531\pi\)
\(420\) 0 0
\(421\) 24.7128 + 14.2679i 1.20443 + 0.695377i 0.961537 0.274676i \(-0.0885706\pi\)
0.242892 + 0.970053i \(0.421904\pi\)
\(422\) 0 0
\(423\) 0.415458 2.23534i 0.0202003 0.108686i
\(424\) 0 0
\(425\) 14.6969i 0.712906i
\(426\) 0 0
\(427\) 1.40192 + 2.42820i 0.0678438 + 0.117509i
\(428\) 0 0
\(429\) −2.00000 1.41421i −0.0965609 0.0682789i
\(430\) 0 0
\(431\) 12.7279 + 22.0454i 0.613082 + 1.06189i 0.990718 + 0.135935i \(0.0434040\pi\)
−0.377635 + 0.925954i \(0.623263\pi\)
\(432\) 0 0
\(433\) −17.8923 + 10.3301i −0.859849 + 0.496434i −0.863962 0.503557i \(-0.832024\pi\)
0.00411252 + 0.999992i \(0.498691\pi\)
\(434\) 0 0
\(435\) 2.12220 + 4.60645i 0.101752 + 0.220862i
\(436\) 0 0
\(437\) 2.63896 + 22.8541i 0.126239 + 1.09326i
\(438\) 0 0
\(439\) 13.4545 + 7.76795i 0.642147 + 0.370744i 0.785441 0.618936i \(-0.212436\pi\)
−0.143294 + 0.989680i \(0.545769\pi\)
\(440\) 0 0
\(441\) −13.5065 + 15.7980i −0.643165 + 0.752284i
\(442\) 0 0
\(443\) −8.96575 + 5.17638i −0.425976 + 0.245937i −0.697631 0.716457i \(-0.745762\pi\)
0.271655 + 0.962395i \(0.412429\pi\)
\(444\) 0 0
\(445\) 10.3923i 0.492642i
\(446\) 0 0
\(447\) 4.70319 + 0.433354i 0.222453 + 0.0204969i
\(448\) 0 0
\(449\) 5.10205 0.240781 0.120390 0.992727i \(-0.461585\pi\)
0.120390 + 0.992727i \(0.461585\pi\)
\(450\) 0 0
\(451\) −25.8564 14.9282i −1.21753 0.702942i
\(452\) 0 0
\(453\) 1.44949 + 3.14626i 0.0681030 + 0.147824i
\(454\) 0 0
\(455\) −0.101536 −0.00476008
\(456\) 0 0
\(457\) 34.7128 1.62380 0.811898 0.583799i \(-0.198434\pi\)
0.811898 + 0.583799i \(0.198434\pi\)
\(458\) 0 0
\(459\) 18.2474 17.7491i 0.851718 0.828457i
\(460\) 0 0
\(461\) 30.9232 + 17.8535i 1.44024 + 0.831522i 0.997865 0.0653090i \(-0.0208033\pi\)
0.442373 + 0.896831i \(0.354137\pi\)
\(462\) 0 0
\(463\) −1.58846 −0.0738219 −0.0369109 0.999319i \(-0.511752\pi\)
−0.0369109 + 0.999319i \(0.511752\pi\)
\(464\) 0 0
\(465\) 0.553794 6.01033i 0.0256816 0.278722i
\(466\) 0 0
\(467\) 22.6274i 1.04707i 0.852004 + 0.523536i \(0.175387\pi\)
−0.852004 + 0.523536i \(0.824613\pi\)
\(468\) 0 0
\(469\) 0.232051 0.133975i 0.0107151 0.00618637i
\(470\) 0 0
\(471\) −1.66294 + 18.0479i −0.0766243 + 0.831604i
\(472\) 0 0
\(473\) 26.2001 + 15.1266i 1.20468 + 0.695524i
\(474\) 0 0
\(475\) 12.9904 1.50000i 0.596040 0.0688247i
\(476\) 0 0
\(477\) −32.2520 5.99431i −1.47672 0.274461i
\(478\) 0 0
\(479\) 15.1774 8.76268i 0.693474 0.400377i −0.111438 0.993771i \(-0.535546\pi\)
0.804912 + 0.593394i \(0.202212\pi\)
\(480\) 0 0
\(481\) 1.03590 + 1.79423i 0.0472329 + 0.0818098i
\(482\) 0 0
\(483\) 1.41421 2.00000i 0.0643489 0.0910032i
\(484\) 0 0
\(485\) −0.378937 0.656339i −0.0172067 0.0298028i
\(486\) 0 0
\(487\) 11.0718i 0.501711i −0.968025 0.250856i \(-0.919288\pi\)
0.968025 0.250856i \(-0.0807119\pi\)
\(488\) 0 0
\(489\) 8.17423 3.76588i 0.369652 0.170299i
\(490\) 0 0
\(491\) 25.6317 + 14.7985i 1.15674 + 0.667846i 0.950521 0.310660i \(-0.100550\pi\)
0.206222 + 0.978505i \(0.433883\pi\)
\(492\) 0 0
\(493\) 10.1436i 0.456844i
\(494\) 0 0
\(495\) 7.46410 + 21.1117i 0.335486 + 0.948899i
\(496\) 0 0
\(497\) 1.79315 3.10583i 0.0804338 0.139315i
\(498\) 0 0
\(499\) 4.06218 7.03590i 0.181848 0.314970i −0.760662 0.649148i \(-0.775125\pi\)
0.942510 + 0.334178i \(0.108459\pi\)
\(500\) 0 0
\(501\) −30.7846 21.7680i −1.37535 0.972523i
\(502\) 0 0
\(503\) 1.13681 0.656339i 0.0506879 0.0292647i −0.474442 0.880287i \(-0.657350\pi\)
0.525130 + 0.851022i \(0.324017\pi\)
\(504\) 0 0
\(505\) −2.92820 −0.130303
\(506\) 0 0
\(507\) −2.05453 + 22.2979i −0.0912450 + 0.990282i
\(508\) 0 0
\(509\) −21.4906 37.2228i −0.952554 1.64987i −0.739868 0.672752i \(-0.765112\pi\)
−0.212686 0.977121i \(-0.568221\pi\)
\(510\) 0 0
\(511\) 0.401924 0.696152i 0.0177801 0.0307960i
\(512\) 0 0
\(513\) 17.5505 + 14.3171i 0.774874 + 0.632116i
\(514\) 0 0
\(515\) 2.50026 4.33057i 0.110175 0.190828i
\(516\) 0 0
\(517\) 2.00000 + 3.46410i 0.0879599 + 0.152351i
\(518\) 0 0
\(519\) −2.78511 + 30.2268i −0.122253 + 1.32681i
\(520\) 0 0
\(521\) 10.1769 0.445858 0.222929 0.974835i \(-0.428438\pi\)
0.222929 + 0.974835i \(0.428438\pi\)
\(522\) 0 0
\(523\) 9.40192 5.42820i 0.411117 0.237359i −0.280152 0.959956i \(-0.590385\pi\)
0.691270 + 0.722597i \(0.257052\pi\)
\(524\) 0 0
\(525\) −1.13681 0.803848i −0.0496145 0.0350828i
\(526\) 0 0
\(527\) 6.03579 10.4543i 0.262923 0.455396i
\(528\) 0 0
\(529\) 2.42820 4.20577i 0.105574 0.182860i
\(530\) 0 0
\(531\) 11.2122 + 31.7128i 0.486567 + 1.37622i
\(532\) 0 0
\(533\) 1.51575i 0.0656544i
\(534\) 0 0
\(535\) −6.00000 3.46410i −0.259403 0.149766i
\(536\) 0 0
\(537\) −2.22474 + 1.02494i −0.0960048 + 0.0442296i
\(538\) 0 0
\(539\) 36.5665i 1.57503i
\(540\) 0 0
\(541\) 12.2321 + 21.1865i 0.525897 + 0.910880i 0.999545 + 0.0301660i \(0.00960358\pi\)
−0.473648 + 0.880714i \(0.657063\pi\)
\(542\) 0 0
\(543\) −3.46410 + 4.89898i −0.148659 + 0.210235i
\(544\) 0 0
\(545\) −4.52004 7.82894i −0.193617 0.335355i
\(546\) 0 0
\(547\) 12.8660 7.42820i 0.550112 0.317607i −0.199055 0.979988i \(-0.563787\pi\)
0.749167 + 0.662381i \(0.230454\pi\)
\(548\) 0 0
\(549\) 30.8638 + 5.73630i 1.31723 + 0.244819i
\(550\) 0 0
\(551\) −8.96575 + 1.03528i −0.381954 + 0.0441042i
\(552\) 0 0
\(553\) −2.42820 1.40192i −0.103258 0.0596159i
\(554\) 0 0
\(555\) 1.73774 18.8597i 0.0737629 0.800549i
\(556\) 0 0
\(557\) −22.5259 + 13.0053i −0.954452 + 0.551053i −0.894461 0.447146i \(-0.852441\pi\)
−0.0599911 + 0.998199i \(0.519107\pi\)
\(558\) 0 0
\(559\) 1.53590i 0.0649616i
\(560\) 0 0
\(561\) −4.10906 + 44.5957i −0.173485 + 1.88283i
\(562\) 0 0
\(563\) 26.0106 1.09622 0.548109 0.836407i \(-0.315348\pi\)
0.548109 + 0.836407i \(0.315348\pi\)
\(564\) 0 0
\(565\) 4.85641 + 2.80385i 0.204311 + 0.117959i
\(566\) 0 0
\(567\) −0.374855 2.38223i −0.0157424 0.100044i
\(568\) 0 0
\(569\) 25.2528 1.05865 0.529326 0.848419i \(-0.322445\pi\)
0.529326 + 0.848419i \(0.322445\pi\)
\(570\) 0 0
\(571\) −14.8038 −0.619522 −0.309761 0.950814i \(-0.600249\pi\)
−0.309761 + 0.950814i \(0.600249\pi\)
\(572\) 0 0
\(573\) 9.42554 + 20.4591i 0.393758 + 0.854691i
\(574\) 0 0
\(575\) −13.7124 7.91688i −0.571848 0.330157i
\(576\) 0 0
\(577\) 29.0718 1.21027 0.605137 0.796121i \(-0.293118\pi\)
0.605137 + 0.796121i \(0.293118\pi\)
\(578\) 0 0
\(579\) −4.83592 0.445584i −0.200974 0.0185178i
\(580\) 0 0
\(581\) 0.554803i 0.0230171i
\(582\) 0 0
\(583\) 49.9808 28.8564i 2.06999 1.19511i
\(584\) 0 0
\(585\) −0.738735 + 0.864068i −0.0305429 + 0.0357248i
\(586\) 0 0
\(587\) −28.8898 16.6796i −1.19241 0.688439i −0.233559 0.972343i \(-0.575037\pi\)
−0.958853 + 0.283904i \(0.908370\pi\)
\(588\) 0 0
\(589\) 9.85641 + 4.26795i 0.406126 + 0.175858i
\(590\) 0 0
\(591\) 0.475678 + 1.03251i 0.0195668 + 0.0424717i
\(592\) 0 0
\(593\) −29.1301 + 16.8183i −1.19623 + 0.690643i −0.959712 0.280984i \(-0.909339\pi\)
−0.236517 + 0.971627i \(0.576006\pi\)
\(594\) 0 0
\(595\) 0.928203 + 1.60770i 0.0380526 + 0.0659091i
\(596\) 0 0
\(597\) −32.8043 23.1962i −1.34259 0.949355i
\(598\) 0 0
\(599\) −1.36345 2.36156i −0.0557089 0.0964906i 0.836826 0.547469i \(-0.184409\pi\)
−0.892535 + 0.450978i \(0.851075\pi\)
\(600\) 0 0
\(601\) 28.3731i 1.15736i −0.815554 0.578681i \(-0.803568\pi\)
0.815554 0.578681i \(-0.196432\pi\)
\(602\) 0 0
\(603\) 0.548188 2.94949i 0.0223239 0.120113i
\(604\) 0 0
\(605\) −20.6448 11.9193i −0.839330 0.484588i
\(606\) 0 0
\(607\) 35.2487i 1.43070i −0.698766 0.715351i \(-0.746267\pi\)
0.698766 0.715351i \(-0.253733\pi\)
\(608\) 0 0
\(609\) 0.784610 + 0.554803i 0.0317940 + 0.0224817i
\(610\) 0 0
\(611\) −0.101536 + 0.175865i −0.00410771 + 0.00711475i
\(612\) 0 0
\(613\) 23.3205 40.3923i 0.941906 1.63143i 0.180077 0.983653i \(-0.442365\pi\)
0.761830 0.647777i \(-0.224301\pi\)
\(614\) 0 0
\(615\) −8.00000 + 11.3137i −0.322591 + 0.456213i
\(616\) 0 0
\(617\) 19.9885 11.5403i 0.804705 0.464597i −0.0404087 0.999183i \(-0.512866\pi\)
0.845114 + 0.534587i \(0.179533\pi\)
\(618\) 0 0
\(619\) −13.1962 −0.530398 −0.265199 0.964194i \(-0.585438\pi\)
−0.265199 + 0.964194i \(0.585438\pi\)
\(620\) 0 0
\(621\) −6.73069 26.5861i −0.270093 1.06686i
\(622\) 0 0
\(623\) 0.984508 + 1.70522i 0.0394435 + 0.0683181i
\(624\) 0 0
\(625\) 0.500000 0.866025i 0.0200000 0.0346410i
\(626\) 0 0
\(627\) −39.8368 + 0.919596i −1.59093 + 0.0367251i
\(628\) 0 0
\(629\) 18.9396 32.8043i 0.755170 1.30799i
\(630\) 0 0
\(631\) 5.47372 + 9.48076i 0.217905 + 0.377423i 0.954167 0.299273i \(-0.0967442\pi\)
−0.736262 + 0.676697i \(0.763411\pi\)
\(632\) 0 0
\(633\) −18.9722 1.74810i −0.754077 0.0694809i
\(634\) 0 0
\(635\) −28.0812 −1.11437
\(636\) 0 0
\(637\) 1.60770 0.928203i 0.0636992 0.0367768i
\(638\) 0 0
\(639\) −13.3843 37.8564i −0.529473 1.49758i
\(640\) 0 0
\(641\) −16.2127 + 28.0812i −0.640363 + 1.10914i 0.344989 + 0.938607i \(0.387883\pi\)
−0.985352 + 0.170534i \(0.945451\pi\)
\(642\) 0 0
\(643\) −6.20577 + 10.7487i −0.244732 + 0.423888i −0.962056 0.272852i \(-0.912033\pi\)
0.717324 + 0.696739i \(0.245367\pi\)
\(644\) 0 0
\(645\) 8.10634 11.4641i 0.319187 0.451399i
\(646\) 0 0
\(647\) 30.3548i 1.19337i 0.802475 + 0.596686i \(0.203516\pi\)
−0.802475 + 0.596686i \(0.796484\pi\)
\(648\) 0 0
\(649\) −51.2487 29.5885i −2.01169 1.16145i
\(650\) 0 0
\(651\) −0.478516 1.03867i −0.0187545 0.0407086i
\(652\) 0 0
\(653\) 1.86748i 0.0730802i −0.999332 0.0365401i \(-0.988366\pi\)
0.999332 0.0365401i \(-0.0116337\pi\)
\(654\) 0 0
\(655\) 8.92820 + 15.4641i 0.348854 + 0.604232i
\(656\) 0 0
\(657\) −3.00000 8.48528i −0.117041 0.331042i
\(658\) 0 0
\(659\) 1.84392 + 3.19376i 0.0718289 + 0.124411i 0.899703 0.436503i \(-0.143783\pi\)
−0.827874 + 0.560914i \(0.810450\pi\)
\(660\) 0 0
\(661\) −29.3205 + 16.9282i −1.14044 + 0.658431i −0.946538 0.322591i \(-0.895446\pi\)
−0.193897 + 0.981022i \(0.562113\pi\)
\(662\) 0 0
\(663\) −2.06502 + 0.951356i −0.0801986 + 0.0369476i
\(664\) 0 0
\(665\) −1.32628 + 0.984508i −0.0514310 + 0.0381776i
\(666\) 0 0
\(667\) 9.46410 + 5.46410i 0.366451 + 0.211571i
\(668\) 0 0
\(669\) 19.6488 + 1.81045i 0.759667 + 0.0699960i
\(670\) 0 0
\(671\) −47.8294 + 27.6143i −1.84643 + 1.06604i
\(672\) 0 0
\(673\) 29.9808i 1.15567i 0.816152 + 0.577837i \(0.196103\pi\)
−0.816152 + 0.577837i \(0.803897\pi\)
\(674\) 0 0
\(675\) −15.1117 + 3.82577i −0.581650 + 0.147254i
\(676\) 0 0
\(677\) 30.1518 1.15883 0.579413 0.815034i \(-0.303282\pi\)
0.579413 + 0.815034i \(0.303282\pi\)
\(678\) 0 0
\(679\) −0.124356 0.0717968i −0.00477233 0.00275531i
\(680\) 0 0
\(681\) −7.54701 + 3.47692i −0.289202 + 0.133236i
\(682\) 0 0
\(683\) 26.1122 0.999155 0.499577 0.866269i \(-0.333489\pi\)
0.499577 + 0.866269i \(0.333489\pi\)
\(684\) 0 0
\(685\) 14.9282 0.570377
\(686\) 0 0
\(687\) −17.9216 + 8.25651i −0.683752 + 0.315006i
\(688\) 0 0
\(689\) 2.53742 + 1.46498i 0.0966681 + 0.0558114i
\(690\) 0 0
\(691\) 17.8564 0.679290 0.339645 0.940554i \(-0.389693\pi\)
0.339645 + 0.940554i \(0.389693\pi\)
\(692\) 0 0
\(693\) 3.22474 + 2.75699i 0.122498 + 0.104730i
\(694\) 0 0
\(695\) 3.96524i 0.150410i
\(696\) 0 0
\(697\) −24.0000 + 13.8564i −0.909065 + 0.524849i
\(698\) 0 0
\(699\) −23.0844 2.12701i −0.873134 0.0804508i
\(700\) 0 0
\(701\) −34.2049 19.7482i −1.29190 0.745880i −0.312911 0.949782i \(-0.601304\pi\)
−0.978991 + 0.203902i \(0.934637\pi\)
\(702\) 0 0
\(703\) 30.9282 + 13.3923i 1.16648 + 0.505100i
\(704\) 0 0
\(705\) 1.68608 0.776779i 0.0635014 0.0292552i
\(706\) 0 0
\(707\) −0.480473 + 0.277401i −0.0180701 + 0.0104328i
\(708\) 0 0
\(709\) −3.83975 6.65064i −0.144205 0.249770i 0.784871 0.619659i \(-0.212729\pi\)
−0.929076 + 0.369889i \(0.879396\pi\)
\(710\) 0 0
\(711\) −29.5969 + 10.4641i −1.10997 + 0.392434i
\(712\) 0 0
\(713\) −6.50266 11.2629i −0.243527 0.421800i
\(714\) 0 0
\(715\) 2.00000i 0.0747958i
\(716\) 0 0
\(717\) −11.0733 24.0358i −0.413541 0.897634i
\(718\) 0 0
\(719\) −9.46979 5.46739i −0.353164 0.203899i 0.312914 0.949781i \(-0.398695\pi\)
−0.666078 + 0.745882i \(0.732028\pi\)
\(720\) 0 0
\(721\) 0.947441i 0.0352846i
\(722\) 0 0
\(723\) 11.3397 16.0368i 0.421730 0.596416i
\(724\) 0 0
\(725\) 3.10583 5.37945i 0.115348 0.199788i
\(726\) 0 0
\(727\) 8.79423 15.2321i 0.326160 0.564925i −0.655587 0.755120i \(-0.727579\pi\)
0.981746 + 0.190195i \(0.0609119\pi\)
\(728\) 0 0
\(729\) −23.0000 14.1421i −0.851852 0.523783i
\(730\) 0 0
\(731\) 24.3190 14.0406i 0.899472 0.519310i
\(732\) 0 0
\(733\) 19.7128 0.728109 0.364055 0.931378i \(-0.381392\pi\)
0.364055 + 0.931378i \(0.381392\pi\)
\(734\) 0 0
\(735\) −16.8990 1.55708i −0.623328 0.0574337i
\(736\) 0 0
\(737\) 2.63896 + 4.57081i 0.0972073 + 0.168368i
\(738\) 0 0
\(739\) −22.5981 + 39.1410i −0.831284 + 1.43983i 0.0657370 + 0.997837i \(0.479060\pi\)
−0.897021 + 0.441989i \(0.854273\pi\)
\(740\) 0 0
\(741\) −1.05165 1.72814i −0.0386333 0.0634846i
\(742\) 0 0
\(743\) −3.53553 + 6.12372i −0.129706 + 0.224658i −0.923563 0.383447i \(-0.874737\pi\)
0.793857 + 0.608105i \(0.208070\pi\)
\(744\) 0 0
\(745\) 1.92820 + 3.33975i 0.0706439 + 0.122359i
\(746\) 0 0
\(747\) −4.72135 4.03652i −0.172745 0.147689i
\(748\) 0 0
\(749\) −1.31268 −0.0479642
\(750\) 0 0
\(751\) −25.4545 + 14.6962i −0.928847 + 0.536270i −0.886447 0.462830i \(-0.846834\pi\)
−0.0424005 + 0.999101i \(0.513501\pi\)
\(752\) 0 0
\(753\) −14.6969 + 20.7846i −0.535586 + 0.757433i
\(754\) 0 0
\(755\) −1.41421 + 2.44949i −0.0514685 + 0.0891461i
\(756\) 0 0
\(757\) −12.6962 + 21.9904i −0.461450 + 0.799254i −0.999033 0.0439562i \(-0.986004\pi\)
0.537584 + 0.843210i \(0.319337\pi\)
\(758\) 0 0
\(759\) 39.3949 + 27.8564i 1.42994 + 1.01112i
\(760\) 0 0
\(761\) 32.1208i 1.16438i 0.813054 + 0.582188i \(0.197803\pi\)
−0.813054 + 0.582188i \(0.802197\pi\)
\(762\) 0 0
\(763\) −1.48334 0.856406i −0.0537005 0.0310040i
\(764\) 0 0
\(765\) 20.4347 + 3.79796i 0.738817 + 0.137315i
\(766\) 0 0
\(767\) 3.00429i 0.108479i
\(768\) 0 0
\(769\) −13.4282 23.2583i −0.484233 0.838717i 0.515603 0.856828i \(-0.327568\pi\)
−0.999836 + 0.0181110i \(0.994235\pi\)
\(770\) 0 0
\(771\) −11.4641 8.10634i −0.412870 0.291943i
\(772\) 0 0
\(773\) 20.3538 + 35.2538i 0.732075 + 1.26799i 0.955995 + 0.293384i \(0.0947813\pi\)
−0.223920 + 0.974608i \(0.571885\pi\)
\(774\) 0 0
\(775\) −6.40192 + 3.69615i −0.229964 + 0.132770i
\(776\) 0 0
\(777\) −1.50152 3.25921i −0.0538669 0.116924i
\(778\) 0 0
\(779\) −14.6969 19.7990i −0.526572 0.709372i
\(780\) 0 0
\(781\) 61.1769 + 35.3205i 2.18908 + 1.26387i
\(782\) 0 0
\(783\) 10.4299 2.64048i 0.372733 0.0943631i
\(784\) 0 0
\(785\) −12.8159 + 7.39924i −0.457417 + 0.264090i
\(786\) 0 0
\(787\) 37.9282i 1.35199i −0.736904 0.675997i \(-0.763713\pi\)
0.736904 0.675997i \(-0.236287\pi\)
\(788\) 0 0
\(789\) −49.7400 4.58307i −1.77079 0.163161i
\(790\) 0 0
\(791\) 1.06248 0.0377775
\(792\) 0 0
\(793\) −2.42820 1.40192i −0.0862280