Properties

Label 912.2.bn.m.449.3
Level $912$
Weight $2$
Character 912.449
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 449.3
Root \(0.965926 + 0.258819i\) of defining polynomial
Character \(\chi\) \(=\) 912.449
Dual form 912.2.bn.m.65.3

$q$-expansion

\(f(q)\) \(=\) \(q+(0.158919 - 1.72474i) q^{3} +(-1.22474 + 0.707107i) q^{5} +0.267949 q^{7} +(-2.94949 - 0.548188i) q^{9} +O(q^{10})\) \(q+(0.158919 - 1.72474i) q^{3} +(-1.22474 + 0.707107i) q^{5} +0.267949 q^{7} +(-2.94949 - 0.548188i) q^{9} +5.27792i q^{11} +(-0.232051 - 0.133975i) q^{13} +(1.02494 + 2.22474i) q^{15} +(-4.24264 + 2.44949i) q^{17} +(-1.73205 - 4.00000i) q^{19} +(0.0425821 - 0.462144i) q^{21} +(-4.57081 - 2.63896i) q^{23} +(-1.50000 + 2.59808i) q^{25} +(-1.41421 + 5.00000i) q^{27} +(-1.03528 + 1.79315i) q^{29} +2.46410i q^{31} +(9.10306 + 0.838759i) q^{33} +(-0.328169 + 0.189469i) q^{35} +7.73205i q^{37} +(-0.267949 + 0.378937i) q^{39} +(2.82843 + 4.89898i) q^{41} +(2.86603 + 4.96410i) q^{43} +(4.00000 - 1.41421i) q^{45} +(-0.656339 - 0.378937i) q^{47} -6.92820 q^{49} +(3.55051 + 7.70674i) q^{51} +(5.46739 - 9.46979i) q^{53} +(-3.73205 - 6.46410i) q^{55} +(-7.17423 + 2.35167i) q^{57} +(5.60609 + 9.71003i) q^{59} +(5.23205 - 9.06218i) q^{61} +(-0.790313 - 0.146887i) q^{63} +0.378937 q^{65} +(0.866025 + 0.500000i) q^{67} +(-5.27792 + 7.46410i) q^{69} +(-6.69213 - 11.5911i) q^{71} +(1.50000 + 2.59808i) q^{73} +(4.24264 + 3.00000i) q^{75} +1.41421i q^{77} +(-9.06218 + 5.23205i) q^{79} +(8.39898 + 3.23375i) q^{81} -2.07055i q^{83} +(3.46410 - 6.00000i) q^{85} +(2.92820 + 2.07055i) q^{87} +(-3.67423 + 6.36396i) q^{89} +(-0.0621778 - 0.0358984i) q^{91} +(4.24995 + 0.391592i) q^{93} +(4.94975 + 3.67423i) q^{95} +(-0.464102 + 0.267949i) q^{97} +(2.89329 - 15.5672i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 16 q^{7} - 4 q^{9}+O(q^{10}) \) 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 \(\left(\mathbb{Z}/912\mathbb{Z}\right)^\times\).

\(n\) \(97\) \(229\) \(305\) \(799\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(1\) \(-1\) \(1\)

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
\(3\) 0.158919 1.72474i 0.0917517 0.995782i
\(4\) 0 0
\(5\) −1.22474 + 0.707107i −0.547723 + 0.316228i −0.748203 0.663470i \(-0.769083\pi\)
0.200480 + 0.979698i \(0.435750\pi\)
\(6\) 0 0
\(7\) 0.267949 0.101275 0.0506376 0.998717i \(-0.483875\pi\)
0.0506376 + 0.998717i \(0.483875\pi\)
\(8\) 0 0
\(9\) −2.94949 0.548188i −0.983163 0.182729i
\(10\) 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 0.467475 0.884006i \(-0.345164\pi\)
−0.531834 + 0.846848i \(0.678497\pi\)
\(14\) 0 0
\(15\) 1.02494 + 2.22474i 0.264639 + 0.574427i
\(16\) 0 0
\(17\) −4.24264 + 2.44949i −1.02899 + 0.594089i −0.916696 0.399586i \(-0.869154\pi\)
−0.112296 + 0.993675i \(0.535820\pi\)
\(18\) 0 0
\(19\) −1.73205 4.00000i −0.397360 0.917663i
\(20\) 0 0
\(21\) 0.0425821 0.462144i 0.00929218 0.100848i
\(22\) 0 0
\(23\) −4.57081 2.63896i −0.953080 0.550261i −0.0590435 0.998255i \(-0.518805\pi\)
−0.894036 + 0.447995i \(0.852138\pi\)
\(24\) 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 \(-0.894910\pi\)
0.753748 + 0.657163i \(0.228244\pi\)
\(30\) 0 0
\(31\) 2.46410i 0.442566i 0.975210 + 0.221283i \(0.0710244\pi\)
−0.975210 + 0.221283i \(0.928976\pi\)
\(32\) 0 0
\(33\) 9.10306 + 0.838759i 1.58464 + 0.146009i
\(34\) 0 0
\(35\) −0.328169 + 0.189469i −0.0554708 + 0.0320261i
\(36\) 0 0
\(37\) 7.73205i 1.27114i 0.772043 + 0.635571i \(0.219235\pi\)
−0.772043 + 0.635571i \(0.780765\pi\)
\(38\) 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 \(-0.0210330\pi\)
−0.556092 + 0.831121i \(0.687700\pi\)
\(42\) 0 0
\(43\) 2.86603 + 4.96410i 0.437065 + 0.757018i 0.997462 0.0712058i \(-0.0226847\pi\)
−0.560397 + 0.828224i \(0.689351\pi\)
\(44\) 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 \(-0.350936\pi\)
−0.547104 + 0.837065i \(0.684270\pi\)
\(48\) 0 0
\(49\) −6.92820 −0.989743
\(50\) 0 0
\(51\) 3.55051 + 7.70674i 0.497171 + 1.07916i
\(52\) 0 0
\(53\) 5.46739 9.46979i 0.751003 1.30078i −0.196334 0.980537i \(-0.562904\pi\)
0.947337 0.320239i \(-0.103763\pi\)
\(54\) 0 0
\(55\) −3.73205 6.46410i −0.503230 0.871619i
\(56\) 0 0
\(57\) −7.17423 + 2.35167i −0.950251 + 0.311486i
\(58\) 0 0
\(59\) 5.60609 + 9.71003i 0.729850 + 1.26414i 0.956946 + 0.290265i \(0.0937436\pi\)
−0.227096 + 0.973872i \(0.572923\pi\)
\(60\) 0 0
\(61\) 5.23205 9.06218i 0.669895 1.16029i −0.308038 0.951374i \(-0.599672\pi\)
0.977933 0.208919i \(-0.0669944\pi\)
\(62\) 0 0
\(63\) −0.790313 0.146887i −0.0995701 0.0185060i
\(64\) 0 0
\(65\) 0.378937 0.0470014
\(66\) 0 0
\(67\) 0.866025 + 0.500000i 0.105802 + 0.0610847i 0.551967 0.833866i \(-0.313877\pi\)
−0.446165 + 0.894951i \(0.647211\pi\)
\(68\) 0 0
\(69\) −5.27792 + 7.46410i −0.635387 + 0.898572i
\(70\) 0 0
\(71\) −6.69213 11.5911i −0.794210 1.37561i −0.923340 0.383984i \(-0.874552\pi\)
0.129130 0.991628i \(-0.458782\pi\)
\(72\) 0 0
\(73\) 1.50000 + 2.59808i 0.175562 + 0.304082i 0.940356 0.340193i \(-0.110493\pi\)
−0.764794 + 0.644275i \(0.777159\pi\)
\(74\) 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 −0.913981 0.405758i \(-0.867008\pi\)
−0.105594 + 0.994409i \(0.533674\pi\)
\(80\) 0 0
\(81\) 8.39898 + 3.23375i 0.933220 + 0.359306i
\(82\) 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 \(-0.960674\pi\)
0.602910 + 0.797809i \(0.294008\pi\)
\(90\) 0 0
\(91\) −0.0621778 0.0358984i −0.00651801 0.00376317i
\(92\) 0 0
\(93\) 4.24995 + 0.391592i 0.440699 + 0.0406062i
\(94\) 0 0
\(95\) 4.94975 + 3.67423i 0.507833 + 0.376969i
\(96\) 0 0
\(97\) −0.464102 + 0.267949i −0.0471224 + 0.0272061i −0.523376 0.852102i \(-0.675328\pi\)
0.476254 + 0.879308i \(0.341994\pi\)
\(98\) 0 0
\(99\) 2.89329 15.5672i 0.290787 1.56456i
\(100\) 0 0
\(101\) 1.79315 + 1.03528i 0.178425 + 0.103014i 0.586553 0.809911i \(-0.300485\pi\)
−0.408127 + 0.912925i \(0.633818\pi\)
\(102\) 0 0
\(103\) 3.53590i 0.348402i 0.984710 + 0.174201i \(0.0557343\pi\)
−0.984710 + 0.174201i \(0.944266\pi\)
\(104\) 0 0
\(105\) 0.274633 + 0.596119i 0.0268014 + 0.0581752i
\(106\) 0 0
\(107\) 4.89898 0.473602 0.236801 0.971558i \(-0.423901\pi\)
0.236801 + 0.971558i \(0.423901\pi\)
\(108\) 0 0
\(109\) −5.53590 + 3.19615i −0.530243 + 0.306136i −0.741115 0.671378i \(-0.765703\pi\)
0.210872 + 0.977514i \(0.432370\pi\)
\(110\) 0 0
\(111\) 13.3358 + 1.22877i 1.26578 + 0.116629i
\(112\) 0 0
\(113\) −3.96524 −0.373018 −0.186509 0.982453i \(-0.559717\pi\)
−0.186509 + 0.982453i \(0.559717\pi\)
\(114\) 0 0
\(115\) 7.46410 0.696031
\(116\) 0 0
\(117\) 0.610988 + 0.522364i 0.0564859 + 0.0482926i
\(118\) 0 0
\(119\) −1.13681 + 0.656339i −0.104211 + 0.0601665i
\(120\) 0 0
\(121\) −16.8564 −1.53240
\(122\) 0 0
\(123\) 8.89898 4.09978i 0.802394 0.369664i
\(124\) 0 0
\(125\) 11.3137i 1.01193i
\(126\) 0 0
\(127\) −17.1962 9.92820i −1.52591 0.880986i −0.999527 0.0307388i \(-0.990214\pi\)
−0.526384 0.850247i \(-0.676453\pi\)
\(128\) 0 0
\(129\) 9.01727 4.15427i 0.793927 0.365763i
\(130\) 0 0
\(131\) −10.9348 + 6.31319i −0.955375 + 0.551586i −0.894747 0.446574i \(-0.852644\pi\)
−0.0606288 + 0.998160i \(0.519311\pi\)
\(132\) 0 0
\(133\) −0.464102 1.07180i −0.0402427 0.0929366i
\(134\) 0 0
\(135\) −1.80348 7.12372i −0.155219 0.613113i
\(136\) 0 0
\(137\) −9.14162 5.27792i −0.781021 0.450923i 0.0557708 0.998444i \(-0.482238\pi\)
−0.836792 + 0.547521i \(0.815572\pi\)
\(138\) 0 0
\(139\) 1.40192 2.42820i 0.118910 0.205958i −0.800426 0.599431i \(-0.795393\pi\)
0.919336 + 0.393474i \(0.128727\pi\)
\(140\) 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
\(147\) −1.10102 + 11.9494i −0.0908106 + 0.985568i
\(148\) 0 0
\(149\) −2.36156 + 1.36345i −0.193466 + 0.111698i −0.593604 0.804757i \(-0.702296\pi\)
0.400138 + 0.916455i \(0.368962\pi\)
\(150\) 0 0
\(151\) 2.00000i 0.162758i −0.996683 0.0813788i \(-0.974068\pi\)
0.996683 0.0813788i \(-0.0259324\pi\)
\(152\) 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 0.578131 0.815944i \(-0.303782\pi\)
−0.995694 + 0.0927037i \(0.970449\pi\)
\(158\) 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
\(165\) −11.7420 + 5.40957i −0.914115 + 0.421134i
\(166\) 0 0
\(167\) 10.8840 18.8516i 0.842229 1.45878i −0.0457762 0.998952i \(-0.514576\pi\)
0.888006 0.459832i \(-0.152091\pi\)
\(168\) 0 0
\(169\) −6.46410 11.1962i −0.497239 0.861242i
\(170\) 0 0
\(171\) 2.91591 + 12.7474i 0.222985 + 0.974822i
\(172\) 0 0
\(173\) 8.76268 + 15.1774i 0.666214 + 1.15392i 0.978955 + 0.204079i \(0.0654198\pi\)
−0.312740 + 0.949839i \(0.601247\pi\)
\(174\) 0 0
\(175\) −0.401924 + 0.696152i −0.0303826 + 0.0526242i
\(176\) 0 0
\(177\) 17.6382 8.12596i 1.32577 0.610785i
\(178\) 0 0
\(179\) 1.41421 0.105703 0.0528516 0.998602i \(-0.483169\pi\)
0.0528516 + 0.998602i \(0.483169\pi\)
\(180\) 0 0
\(181\) −3.00000 1.73205i −0.222988 0.128742i 0.384345 0.923190i \(-0.374427\pi\)
−0.607333 + 0.794447i \(0.707761\pi\)
\(182\) 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 −0.584841 0.811148i \(-0.698843\pi\)
0.410055 + 0.912061i \(0.365510\pi\)
\(194\) 0 0
\(195\) 0.0602202 0.653570i 0.00431246 0.0468031i
\(196\) 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 0.0819004 + 0.996641i \(0.473901\pi\)
−0.904066 + 0.427392i \(0.859432\pi\)
\(200\) 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
\(207\) 12.0349 + 10.2892i 0.836484 + 0.715152i
\(208\) 0 0
\(209\) 21.1117 9.14162i 1.46032 0.632339i
\(210\) 0 0
\(211\) −9.52628 + 5.50000i −0.655816 + 0.378636i −0.790681 0.612228i \(-0.790273\pi\)
0.134865 + 0.990864i \(0.456940\pi\)
\(212\) 0 0
\(213\) −21.0552 + 9.70017i −1.44268 + 0.664645i
\(214\) 0 0
\(215\) −7.02030 4.05317i −0.478780 0.276424i
\(216\) 0 0
\(217\) 0.660254i 0.0448210i
\(218\) 0 0
\(219\) 4.71940 2.17423i 0.318907 0.146921i
\(220\) 0 0
\(221\) 1.31268 0.0883003
\(222\) 0 0
\(223\) 9.86603 5.69615i 0.660678 0.381443i −0.131857 0.991269i \(-0.542094\pi\)
0.792535 + 0.609826i \(0.208761\pi\)
\(224\) 0 0
\(225\) 5.84847 6.84072i 0.389898 0.456048i
\(226\) 0 0
\(227\) 4.79744 0.318418 0.159209 0.987245i \(-0.449106\pi\)
0.159209 + 0.987245i \(0.449106\pi\)
\(228\) 0 0
\(229\) −11.3923 −0.752825 −0.376412 0.926452i \(-0.622842\pi\)
−0.376412 + 0.926452i \(0.622842\pi\)
\(230\) 0 0
\(231\) 2.43916 + 0.224745i 0.160485 + 0.0147871i
\(232\) 0 0
\(233\) 11.5911 6.69213i 0.759359 0.438416i −0.0697066 0.997568i \(-0.522206\pi\)
0.829066 + 0.559151i \(0.188873\pi\)
\(234\) 0 0
\(235\) 1.07180 0.0699163
\(236\) 0 0
\(237\) 7.58380 + 16.4614i 0.492621 + 1.06928i
\(238\) 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 0.781756 0.623584i \(-0.214324\pi\)
−0.149162 + 0.988813i \(0.547657\pi\)
\(242\) 0 0
\(243\) 6.91215 13.9722i 0.443415 0.896317i
\(244\) 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
\(249\) −3.57117 0.329049i −0.226314 0.0208527i
\(250\) 0 0
\(251\) 12.7279 + 7.34847i 0.803379 + 0.463831i 0.844651 0.535317i \(-0.179808\pi\)
−0.0412721 + 0.999148i \(0.513141\pi\)
\(252\) 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 \(-0.751972\pi\)
0.964304 + 0.264798i \(0.0853054\pi\)
\(258\) 0 0
\(259\) 2.07180i 0.128735i
\(260\) 0 0
\(261\) 4.03652 4.72135i 0.249854 0.292244i
\(262\) 0 0
\(263\) 24.9754 14.4195i 1.54005 0.889147i 0.541213 0.840886i \(-0.317965\pi\)
0.998835 0.0482609i \(-0.0153679\pi\)
\(264\) 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 \(-0.0584868\pi\)
−0.649815 + 0.760093i \(0.725153\pi\)
\(270\) 0 0
\(271\) 3.46410 + 6.00000i 0.210429 + 0.364474i 0.951849 0.306568i \(-0.0991805\pi\)
−0.741420 + 0.671042i \(0.765847\pi\)
\(272\) 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
\(279\) 1.35079 7.26784i 0.0808698 0.435114i
\(280\) 0 0
\(281\) 4.70951 8.15711i 0.280946 0.486613i −0.690672 0.723168i \(-0.742685\pi\)
0.971618 + 0.236556i \(0.0760185\pi\)
\(282\) 0 0
\(283\) 2.92820 + 5.07180i 0.174064 + 0.301487i 0.939837 0.341624i \(-0.110977\pi\)
−0.765773 + 0.643111i \(0.777643\pi\)
\(284\) 0 0
\(285\) 7.12372 7.95315i 0.421973 0.471104i
\(286\) 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
\(291\) 0.388390 + 0.843039i 0.0227678 + 0.0494198i
\(292\) 0 0
\(293\) −13.9391 −0.814329 −0.407164 0.913355i \(-0.633482\pi\)
−0.407164 + 0.913355i \(0.633482\pi\)
\(294\) 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 −0.116814 0.993154i \(-0.537268\pi\)
0.801690 + 0.597740i \(0.203935\pi\)
\(308\) 0 0
\(309\) 6.09852 + 0.561920i 0.346933 + 0.0319665i
\(310\) 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 −0.999569 0.0293564i \(-0.990654\pi\)
0.525208 + 0.850974i \(0.323988\pi\)
\(314\) 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 \(-0.913413\pi\)
0.714298 + 0.699842i \(0.246746\pi\)
\(318\) 0 0
\(319\) −9.46410 5.46410i −0.529888 0.305931i
\(320\) 0 0
\(321\) 0.778539 8.44949i 0.0434538 0.471605i
\(322\) 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
\(327\) 4.63279 + 10.0559i 0.256194 + 0.556095i
\(328\) 0 0
\(329\) −0.175865 0.101536i −0.00969578 0.00559786i
\(330\) 0 0
\(331\) 18.0718i 0.993316i −0.867946 0.496658i \(-0.834560\pi\)
0.867946 0.496658i \(-0.165440\pi\)
\(332\) 0 0
\(333\) 4.23862 22.8056i 0.232275 1.24974i
\(334\) 0 0
\(335\) −1.41421 −0.0772667
\(336\) 0 0
\(337\) −21.3564 + 12.3301i −1.16336 + 0.671665i −0.952106 0.305767i \(-0.901087\pi\)
−0.211251 + 0.977432i \(0.567754\pi\)
\(338\) 0 0
\(339\) −0.630150 + 6.83903i −0.0342251 + 0.371445i
\(340\) 0 0
\(341\) −13.0053 −0.704278
\(342\) 0 0
\(343\) −3.73205 −0.201512
\(344\) 0 0
\(345\) 1.18618 12.8737i 0.0638620 0.693095i
\(346\) 0 0
\(347\) −16.6424 + 9.60849i −0.893410 + 0.515811i −0.875057 0.484021i \(-0.839176\pi\)
−0.0183540 + 0.999832i \(0.505843\pi\)
\(348\) 0 0
\(349\) 9.39230 0.502759 0.251379 0.967889i \(-0.419116\pi\)
0.251379 + 0.967889i \(0.419116\pi\)
\(350\) 0 0
\(351\) 0.998042 0.970785i 0.0532716 0.0518167i
\(352\) 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
\(357\) 0.951356 + 2.06502i 0.0503511 + 0.109292i
\(358\) 0 0
\(359\) −6.21166 + 3.58630i −0.327839 + 0.189278i −0.654881 0.755732i \(-0.727281\pi\)
0.327042 + 0.945010i \(0.393948\pi\)
\(360\) 0 0
\(361\) −13.0000 + 13.8564i −0.684211 + 0.729285i
\(362\) 0 0
\(363\) −2.67880 + 29.0730i −0.140600 + 1.52594i
\(364\) 0 0
\(365\) −3.67423 2.12132i −0.192318 0.111035i
\(366\) 0 0
\(367\) 10.5263 18.2321i 0.549467 0.951705i −0.448844 0.893610i \(-0.648164\pi\)
0.998311 0.0580950i \(-0.0185026\pi\)
\(368\) 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 \(0.168104\pi\)
−0.863758 + 0.503906i \(0.831896\pi\)
\(374\) 0 0
\(375\) −19.5133 1.79796i −1.00766 0.0928462i
\(376\) 0 0
\(377\) 0.480473 0.277401i 0.0247456 0.0142869i
\(378\) 0 0
\(379\) 23.7846i 1.22173i 0.791733 + 0.610867i \(0.209179\pi\)
−0.791733 + 0.610867i \(0.790821\pi\)
\(380\) 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 \(-0.0629854\pi\)
−0.660492 + 0.750833i \(0.729652\pi\)
\(384\) 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 \(-0.455744\pi\)
−0.788376 + 0.615194i \(0.789078\pi\)
\(390\) 0 0
\(391\) 25.8564 1.30761
\(392\) 0 0
\(393\) 9.15091 + 19.8630i 0.461602 + 1.00195i
\(394\) 0 0
\(395\) 7.39924 12.8159i 0.372296 0.644836i
\(396\) 0 0
\(397\) 13.1603 + 22.7942i 0.660494 + 1.14401i 0.980486 + 0.196589i \(0.0629865\pi\)
−0.319992 + 0.947420i \(0.603680\pi\)
\(398\) 0 0
\(399\) −1.92233 + 0.630128i −0.0962369 + 0.0315459i
\(400\) 0 0
\(401\) 11.4016 + 19.7482i 0.569371 + 0.986179i 0.996628 + 0.0820492i \(0.0261464\pi\)
−0.427257 + 0.904130i \(0.640520\pi\)
\(402\) 0 0
\(403\) 0.330127 0.571797i 0.0164448 0.0284832i
\(404\) 0 0
\(405\) −12.5732 + 1.97846i −0.624768 + 0.0983103i
\(406\) 0 0
\(407\) −40.8091 −2.02283
\(408\) 0 0
\(409\) 17.5359 + 10.1244i 0.867094 + 0.500617i 0.866382 0.499383i \(-0.166440\pi\)
0.000712791 1.00000i \(0.499773\pi\)
\(410\) 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 0.242892 0.970053i \(-0.421904\pi\)
0.961537 + 0.274676i \(0.0885706\pi\)
\(422\) 0 0
\(423\) 1.72814 + 1.47747i 0.0840248 + 0.0718370i
\(424\) 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 0.377635 + 0.925954i \(0.376737\pi\)
−0.990718 + 0.135935i \(0.956596\pi\)
\(432\) 0 0
\(433\) −17.8923 10.3301i −0.859849 0.496434i 0.00411252 0.999992i \(-0.498691\pi\)
−0.863962 + 0.503557i \(0.832024\pi\)
\(434\) 0 0
\(435\) −5.05040 0.465346i −0.242148 0.0223116i
\(436\) 0 0
\(437\) −2.63896 + 22.8541i −0.126239 + 1.09326i
\(438\) 0 0
\(439\) 13.4545 7.76795i 0.642147 0.370744i −0.143294 0.989680i \(-0.545769\pi\)
0.785441 + 0.618936i \(0.212436\pi\)
\(440\) 0 0
\(441\) 20.4347 + 3.79796i 0.973079 + 0.180855i
\(442\) 0 0
\(443\) 8.96575 + 5.17638i 0.425976 + 0.245937i 0.697631 0.716457i \(-0.254238\pi\)
−0.271655 + 0.962395i \(0.587571\pi\)
\(444\) 0 0
\(445\) 10.3923i 0.492642i
\(446\) 0 0
\(447\) 1.97630 + 4.28976i 0.0934758 + 0.202899i
\(448\) 0 0
\(449\) −5.10205 −0.240781 −0.120390 0.992727i \(-0.538415\pi\)
−0.120390 + 0.992727i \(0.538415\pi\)
\(450\) 0 0
\(451\) −25.8564 + 14.9282i −1.21753 + 0.702942i
\(452\) 0 0
\(453\) −3.44949 0.317837i −0.162071 0.0149333i
\(454\) 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
\(459\) −6.24745 24.6773i −0.291606 1.15184i
\(460\) 0 0
\(461\) −30.9232 + 17.8535i −1.44024 + 0.831522i −0.997865 0.0653090i \(-0.979197\pi\)
−0.442373 + 0.896831i \(0.645863\pi\)
\(462\) 0 0
\(463\) −1.58846 −0.0738219 −0.0369109 0.999319i \(-0.511752\pi\)
−0.0369109 + 0.999319i \(0.511752\pi\)
\(464\) 0 0
\(465\) −5.48200 + 2.52557i −0.254222 + 0.117120i
\(466\) 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
\(471\) −16.4614 + 7.58380i −0.758502 + 0.349443i
\(472\) 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
\(477\) −21.3172 + 24.9339i −0.976049 + 1.14164i
\(478\) 0 0
\(479\) −15.1774 8.76268i −0.693474 0.400377i 0.111438 0.993771i \(-0.464454\pi\)
−0.804912 + 0.593394i \(0.797788\pi\)
\(480\) 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 \(0.0807119\pi\)
−0.968025 + 0.250856i \(0.919288\pi\)
\(488\) 0 0
\(489\) 0.825765 8.96204i 0.0373424 0.405277i
\(490\) 0 0
\(491\) −25.6317 + 14.7985i −1.15674 + 0.667846i −0.950521 0.310660i \(-0.899450\pi\)
−0.206222 + 0.978505i \(0.566117\pi\)
\(492\) 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 0.942510 0.334178i \(-0.108459\pi\)
−0.760662 + 0.649148i \(0.775125\pi\)
\(500\) 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 \(-0.342650\pi\)
−0.525130 + 0.851022i \(0.675983\pi\)
\(504\) 0 0
\(505\) −2.92820 −0.130303
\(506\) 0 0
\(507\) −20.3378 + 9.36965i −0.903232 + 0.416121i
\(508\) 0 0
\(509\) 21.4906 37.2228i 0.952554 1.64987i 0.212686 0.977121i \(-0.431779\pi\)
0.739868 0.672752i \(-0.234888\pi\)
\(510\) 0 0
\(511\) 0.401924 + 0.696152i 0.0177801 + 0.0307960i
\(512\) 0 0
\(513\) 22.4495 3.00340i 0.991169 0.132603i
\(514\) 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
\(519\) 27.5697 12.7014i 1.21018 0.557530i
\(520\) 0 0
\(521\) −10.1769 −0.445858 −0.222929 0.974835i \(-0.571562\pi\)
−0.222929 + 0.974835i \(0.571562\pi\)
\(522\) 0 0
\(523\) 9.40192 + 5.42820i 0.411117 + 0.237359i 0.691270 0.722597i \(-0.257052\pi\)
−0.280152 + 0.959956i \(0.590385\pi\)
\(524\) 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
\(537\) 0.224745 2.43916i 0.00969846 0.105257i
\(538\) 0 0
\(539\) 36.5665i 1.57503i
\(540\) 0 0
\(541\) 12.2321 21.1865i 0.525897 0.910880i −0.473648 0.880714i \(-0.657063\pi\)
0.999545 0.0301660i \(-0.00960358\pi\)
\(542\) 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 0.749167 0.662381i \(-0.230454\pi\)
−0.199055 + 0.979988i \(0.563787\pi\)
\(548\) 0 0
\(549\) −20.3997 + 23.8607i −0.870636 + 1.01835i
\(550\) 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
\(555\) −17.2018 + 7.92492i −0.730177 + 0.336394i
\(556\) 0 0
\(557\) 22.5259 + 13.0053i 0.954452 + 0.551053i 0.894461 0.447146i \(-0.147559\pi\)
0.0599911 + 0.998199i \(0.480893\pi\)
\(558\) 0 0
\(559\) 1.53590i 0.0649616i
\(560\) 0 0
\(561\) −40.6755 + 18.7393i −1.71732 + 0.791174i
\(562\) 0 0
\(563\) −26.0106 −1.09622 −0.548109 0.836407i \(-0.684652\pi\)
−0.548109 + 0.836407i \(0.684652\pi\)
\(564\) 0 0
\(565\) 4.85641 2.80385i 0.204311 0.117959i
\(566\) 0 0
\(567\) 2.25050 + 0.866481i 0.0945121 + 0.0363888i
\(568\) 0 0
\(569\) −25.2528 −1.05865 −0.529326 0.848419i \(-0.677555\pi\)
−0.529326 + 0.848419i \(0.677555\pi\)
\(570\) 0 0
\(571\) −14.8038 −0.619522 −0.309761 0.950814i \(-0.600249\pi\)
−0.309761 + 0.950814i \(0.600249\pi\)
\(572\) 0 0
\(573\) 22.4309 + 2.06679i 0.937063 + 0.0863413i
\(574\) 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
\(579\) 2.03207 + 4.41082i 0.0844501 + 0.183308i
\(580\) 0 0
\(581\) 0.554803i 0.0230171i
\(582\) 0 0
\(583\) 49.9808 + 28.8564i 2.06999 + 1.19511i
\(584\) 0 0
\(585\) −1.11767 0.207729i −0.0462100 0.00858854i
\(586\) 0 0
\(587\) 28.8898 16.6796i 1.19241 0.688439i 0.233559 0.972343i \(-0.424963\pi\)
0.958853 + 0.283904i \(0.0916296\pi\)
\(588\) 0 0
\(589\) 9.85641 4.26795i 0.406126 0.175858i
\(590\) 0 0
\(591\) 1.13202 + 0.104304i 0.0465650 + 0.00429051i
\(592\) 0 0
\(593\) 29.1301 + 16.8183i 1.19623 + 0.690643i 0.959712 0.280984i \(-0.0906609\pi\)
0.236517 + 0.971627i \(0.423994\pi\)
\(594\) 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 \(-0.815591\pi\)
0.892535 + 0.450978i \(0.148925\pi\)
\(600\) 0 0
\(601\) 28.3731i 1.15736i 0.815554 + 0.578681i \(0.196432\pi\)
−0.815554 + 0.578681i \(0.803568\pi\)
\(602\) 0 0
\(603\) −2.28024 1.94949i −0.0928585 0.0793894i
\(604\) 0 0
\(605\) 20.6448 11.9193i 0.839330 0.484588i
\(606\) 0 0
\(607\) 35.2487i 1.43070i 0.698766 + 0.715351i \(0.253733\pi\)
−0.698766 + 0.715351i \(0.746267\pi\)
\(608\) 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 0.761830 + 0.647777i \(0.224301\pi\)
0.180077 + 0.983653i \(0.442365\pi\)
\(614\) 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 \(-0.487134\pi\)
−0.845114 + 0.534587i \(0.820467\pi\)
\(618\) 0 0
\(619\) −13.1962 −0.530398 −0.265199 0.964194i \(-0.585438\pi\)
−0.265199 + 0.964194i \(0.585438\pi\)
\(620\) 0 0
\(621\) 19.6589 19.1220i 0.788884 0.767339i
\(622\) 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
\(627\) −12.4119 37.8650i −0.495685 1.51218i
\(628\) 0 0
\(629\) −18.9396 32.8043i −0.755170 1.30799i
\(630\) 0 0
\(631\) 5.47372 9.48076i 0.217905 0.377423i −0.736262 0.676697i \(-0.763411\pi\)
0.954167 + 0.299273i \(0.0967442\pi\)
\(632\) 0 0
\(633\) 7.97219 + 17.3045i 0.316866 + 0.687790i
\(634\) 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 0.985352 + 0.170534i \(0.0545493\pi\)
−0.344989 + 0.938607i \(0.612117\pi\)
\(642\) 0 0
\(643\) −6.20577 10.7487i −0.244732 0.423888i 0.717324 0.696739i \(-0.245367\pi\)
−0.962056 + 0.272852i \(0.912033\pi\)
\(644\) 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
\(651\) 1.13877 + 0.104927i 0.0446319 + 0.00411240i
\(652\) 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 \(-0.856217\pi\)
0.827874 + 0.560914i \(0.189550\pi\)
\(660\) 0 0
\(661\) −29.3205 16.9282i −1.14044 0.658431i −0.193897 0.981022i \(-0.562113\pi\)
−0.946538 + 0.322591i \(0.895446\pi\)
\(662\) 0 0
\(663\) 0.208609 2.26403i 0.00810170 0.0879278i
\(664\) 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
\(669\) −8.25651 17.9216i −0.319215 0.692889i
\(670\) 0 0
\(671\) 47.8294 + 27.6143i 1.84643 + 1.06604i
\(672\) 0 0
\(673\) 29.9808i 1.15567i −0.816152 0.577837i \(-0.803897\pi\)
0.816152 0.577837i \(-0.196103\pi\)
\(674\) 0 0
\(675\) −10.8691 11.1742i −0.418350 0.430096i
\(676\) 0 0
\(677\) −30.1518 −1.15883 −0.579413 0.815034i \(-0.696718\pi\)
−0.579413 + 0.815034i \(0.696718\pi\)
\(678\) 0 0
\(679\) −0.124356 + 0.0717968i −0.00477233 + 0.00275531i
\(680\) 0 0
\(681\) 0.762403 8.27437i 0.0292154 0.317074i
\(682\) 0 0
\(683\) −26.1122 −0.999155 −0.499577 0.866269i \(-0.666511\pi\)
−0.499577 + 0.866269i \(0.666511\pi\)
\(684\) 0 0
\(685\) 14.9282 0.570377
\(686\) 0 0
\(687\) −1.81045 + 19.6488i −0.0690730 + 0.749649i
\(688\) 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
\(693\) 0.775255 4.17121i 0.0294495 0.158451i
\(694\) 0 0
\(695\) 3.96524i 0.150410i
\(696\) 0 0
\(697\) −24.0000 13.8564i −0.909065 0.524849i
\(698\) 0 0
\(699\) −9.70017 21.0552i −0.366894 0.796381i
\(700\) 0 0
\(701\) 34.2049 19.7482i 1.29190 0.745880i 0.312911 0.949782i \(-0.398696\pi\)
0.978991 + 0.203902i \(0.0653625\pi\)
\(702\) 0 0
\(703\) 30.9282 13.3923i 1.16648 0.505100i
\(704\) 0 0
\(705\) 0.170328 1.84858i 0.00641494 0.0696214i
\(706\) 0 0
\(707\) 0.480473 + 0.277401i 0.0180701 + 0.0104328i
\(708\) 0 0
\(709\) −3.83975 + 6.65064i −0.144205 + 0.249770i −0.929076 0.369889i \(-0.879396\pi\)
0.784871 + 0.619659i \(0.212729\pi\)
\(710\) 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
\(717\) −26.3523 2.42811i −0.984144 0.0906794i
\(718\) 0 0
\(719\) 9.46979 5.46739i 0.353164 0.203899i −0.312914 0.949781i \(-0.601305\pi\)
0.666078 + 0.745882i \(0.267972\pi\)
\(720\) 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 0.981746 0.190195i \(-0.0609119\pi\)
−0.655587 + 0.755120i \(0.727579\pi\)
\(728\) 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
\(735\) −7.10102 15.4135i −0.261925 0.568535i
\(736\) 0 0
\(737\) −2.63896 + 4.57081i −0.0972073 + 0.168368i
\(738\) 0 0
\(739\) −22.5981 39.1410i −0.831284 1.43983i −0.897021 0.441989i \(-0.854273\pi\)
0.0657370 0.997837i \(-0.479060\pi\)
\(740\) 0 0
\(741\) 1.97985 + 0.415458i 0.0727316 + 0.0152622i
\(742\) 0 0
\(743\) 3.53553 + 6.12372i 0.129706 + 0.224658i 0.923563 0.383447i \(-0.125263\pi\)
−0.793857 + 0.608105i \(0.791930\pi\)
\(744\) 0 0
\(745\) 1.92820 3.33975i 0.0706439 0.122359i
\(746\) 0 0
\(747\) −1.13505 + 6.10707i −0.0415294 + 0.223446i
\(748\) 0 0
\(749\) 1.31268 0.0479642
\(750\) 0 0
\(751\) −25.4545 14.6962i −0.928847 0.536270i −0.0424005 0.999101i \(-0.513501\pi\)
−0.886447 + 0.462830i \(0.846834\pi\)
\(752\) 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 0.537584 0.843210i \(-0.319337\pi\)
−0.999033 + 0.0439562i \(0.986004\pi\)
\(758\) 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
\(765\) −13.5065 + 15.7980i −0.488327 + 0.571176i
\(766\) 0 0
\(767\) 3.00429i 0.108479i
\(768\) 0 0
\(769\) −13.4282 + 23.2583i −0.484233 + 0.838717i −0.999836 0.0181110i \(-0.994235\pi\)
0.515603 + 0.856828i \(0.327568\pi\)
\(770\) 0 0
\(771\) −11.4641 8.10634i −0.412870 0.291943i
\(772\) 0 0
\(773\) −20.3538 + 35.2538i −0.732075 + 1.26799i 0.223920 + 0.974608i \(0.428115\pi\)
−0.955995 + 0.293384i \(0.905219\pi\)
\(774\) 0 0
\(775\) −6.40192 3.69615i −0.229964 0.132770i
\(776\) 0 0
\(777\) 3.57332 + 0.329247i 0.128192 + 0.0118117i
\(778\) 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
\(783\) −7.50165 7.71228i −0.268087 0.275614i
\(784\) 0 0
\(785\) 12.8159 + 7.39924i 0.457417 + 0.264090i
\(786\) 0 0
\(787\) 37.9282i 1.35199i 0.736904 + 0.675997i \(0.236287\pi\)
−0.736904 + 0.675997i \(0.763713\pi\)
\(788\) 0 0
\(789\) −20.9010 45.3677i −0.744094 1.61513i
\(790\) 0 0
\(791\) −1.06248 −0.0377775
\(792\) 0 0
\(793\) −2.42820 + 1.40192i −0.0862280 +