Properties

Label 192.2.j.a.49.3
Level $192$
Weight $2$
Character 192.49
Analytic conductor $1.533$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 192 = 2^{6} \cdot 3 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 192.j (of order \(4\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.53312771881\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(i)\)
Coefficient field: 8.0.18939904.2
Defining polynomial: \(x^{8} - 4 x^{7} + 14 x^{6} - 28 x^{5} + 43 x^{4} - 44 x^{3} + 30 x^{2} - 12 x + 2\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{4} \)
Twist minimal: no (minimal twist has level 48)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 49.3
Root \(0.500000 - 0.0297061i\) of defining polynomial
Character \(\chi\) \(=\) 192.49
Dual form 192.2.j.a.145.3

$q$-expansion

\(f(q)\) \(=\) \(q+(0.707107 - 0.707107i) q^{3} +(-0.334904 - 0.334904i) q^{5} -4.55765i q^{7} -1.00000i q^{9} +O(q^{10})\) \(q+(0.707107 - 0.707107i) q^{3} +(-0.334904 - 0.334904i) q^{5} -4.55765i q^{7} -1.00000i q^{9} +(2.47363 + 2.47363i) q^{11} +(-0.0594122 + 0.0594122i) q^{13} -0.473626 q^{15} +3.61706 q^{17} +(-2.55765 + 2.55765i) q^{19} +(-3.22274 - 3.22274i) q^{21} +2.82843i q^{23} -4.77568i q^{25} +(-0.707107 - 0.707107i) q^{27} +(-5.16333 + 5.16333i) q^{29} +0.557647 q^{31} +3.49824 q^{33} +(-1.52637 + 1.52637i) q^{35} +(4.38607 + 4.38607i) q^{37} +0.0840215i q^{39} +9.27391i q^{41} +(1.61040 + 1.61040i) q^{43} +(-0.334904 + 0.334904i) q^{45} -2.82843 q^{47} -13.7721 q^{49} +(2.55765 - 2.55765i) q^{51} +(-0.493523 - 0.493523i) q^{53} -1.65685i q^{55} +3.61706i q^{57} +(-4.00000 - 4.00000i) q^{59} +(2.72922 - 2.72922i) q^{61} -4.55765 q^{63} +0.0397948 q^{65} +(-3.77568 + 3.77568i) q^{67} +(2.00000 + 2.00000i) q^{69} +9.11529i q^{71} +0.541560i q^{73} +(-3.37691 - 3.37691i) q^{75} +(11.2739 - 11.2739i) q^{77} +10.9937 q^{79} -1.00000 q^{81} +(10.6417 - 10.6417i) q^{83} +(-1.21137 - 1.21137i) q^{85} +7.30205i q^{87} -14.6533i q^{89} +(0.270780 + 0.270780i) q^{91} +(0.394316 - 0.394316i) q^{93} +1.71313 q^{95} +4.31724 q^{97} +(2.47363 - 2.47363i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + O(q^{10}) \) \( 8q + 8q^{11} + 8q^{15} + 8q^{19} - 16q^{29} - 24q^{31} - 24q^{35} - 16q^{37} + 8q^{43} - 8q^{49} - 8q^{51} + 16q^{53} - 32q^{59} + 16q^{61} - 8q^{63} - 16q^{65} + 16q^{67} + 16q^{69} - 16q^{75} + 16q^{77} + 24q^{79} - 8q^{81} + 40q^{83} - 16q^{85} + 8q^{91} + 48q^{95} + 8q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/192\mathbb{Z}\right)^\times\).

\(n\) \(65\) \(127\) \(133\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{4}\right)\)

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
\(3\) 0.707107 0.707107i 0.408248 0.408248i
\(4\) 0 0
\(5\) −0.334904 0.334904i −0.149774 0.149774i 0.628243 0.778017i \(-0.283774\pi\)
−0.778017 + 0.628243i \(0.783774\pi\)
\(6\) 0 0
\(7\) 4.55765i 1.72263i −0.508072 0.861314i \(-0.669642\pi\)
0.508072 0.861314i \(-0.330358\pi\)
\(8\) 0 0
\(9\) 1.00000i 0.333333i
\(10\) 0 0
\(11\) 2.47363 + 2.47363i 0.745826 + 0.745826i 0.973692 0.227866i \(-0.0731749\pi\)
−0.227866 + 0.973692i \(0.573175\pi\)
\(12\) 0 0
\(13\) −0.0594122 + 0.0594122i −0.0164780 + 0.0164780i −0.715298 0.698820i \(-0.753709\pi\)
0.698820 + 0.715298i \(0.253709\pi\)
\(14\) 0 0
\(15\) −0.473626 −0.122290
\(16\) 0 0
\(17\) 3.61706 0.877266 0.438633 0.898666i \(-0.355463\pi\)
0.438633 + 0.898666i \(0.355463\pi\)
\(18\) 0 0
\(19\) −2.55765 + 2.55765i −0.586765 + 0.586765i −0.936754 0.349989i \(-0.886185\pi\)
0.349989 + 0.936754i \(0.386185\pi\)
\(20\) 0 0
\(21\) −3.22274 3.22274i −0.703260 0.703260i
\(22\) 0 0
\(23\) 2.82843i 0.589768i 0.955533 + 0.294884i \(0.0952810\pi\)
−0.955533 + 0.294884i \(0.904719\pi\)
\(24\) 0 0
\(25\) 4.77568i 0.955136i
\(26\) 0 0
\(27\) −0.707107 0.707107i −0.136083 0.136083i
\(28\) 0 0
\(29\) −5.16333 + 5.16333i −0.958807 + 0.958807i −0.999184 0.0403780i \(-0.987144\pi\)
0.0403780 + 0.999184i \(0.487144\pi\)
\(30\) 0 0
\(31\) 0.557647 0.100156 0.0500782 0.998745i \(-0.484053\pi\)
0.0500782 + 0.998745i \(0.484053\pi\)
\(32\) 0 0
\(33\) 3.49824 0.608965
\(34\) 0 0
\(35\) −1.52637 + 1.52637i −0.258004 + 0.258004i
\(36\) 0 0
\(37\) 4.38607 + 4.38607i 0.721066 + 0.721066i 0.968822 0.247756i \(-0.0796932\pi\)
−0.247756 + 0.968822i \(0.579693\pi\)
\(38\) 0 0
\(39\) 0.0840215i 0.0134542i
\(40\) 0 0
\(41\) 9.27391i 1.44834i 0.689620 + 0.724171i \(0.257777\pi\)
−0.689620 + 0.724171i \(0.742223\pi\)
\(42\) 0 0
\(43\) 1.61040 + 1.61040i 0.245583 + 0.245583i 0.819155 0.573572i \(-0.194443\pi\)
−0.573572 + 0.819155i \(0.694443\pi\)
\(44\) 0 0
\(45\) −0.334904 + 0.334904i −0.0499245 + 0.0499245i
\(46\) 0 0
\(47\) −2.82843 −0.412568 −0.206284 0.978492i \(-0.566137\pi\)
−0.206284 + 0.978492i \(0.566137\pi\)
\(48\) 0 0
\(49\) −13.7721 −1.96745
\(50\) 0 0
\(51\) 2.55765 2.55765i 0.358142 0.358142i
\(52\) 0 0
\(53\) −0.493523 0.493523i −0.0677906 0.0677906i 0.672399 0.740189i \(-0.265264\pi\)
−0.740189 + 0.672399i \(0.765264\pi\)
\(54\) 0 0
\(55\) 1.65685i 0.223410i
\(56\) 0 0
\(57\) 3.61706i 0.479091i
\(58\) 0 0
\(59\) −4.00000 4.00000i −0.520756 0.520756i 0.397044 0.917800i \(-0.370036\pi\)
−0.917800 + 0.397044i \(0.870036\pi\)
\(60\) 0 0
\(61\) 2.72922 2.72922i 0.349441 0.349441i −0.510460 0.859901i \(-0.670525\pi\)
0.859901 + 0.510460i \(0.170525\pi\)
\(62\) 0 0
\(63\) −4.55765 −0.574210
\(64\) 0 0
\(65\) 0.0397948 0.00493593
\(66\) 0 0
\(67\) −3.77568 + 3.77568i −0.461273 + 0.461273i −0.899072 0.437800i \(-0.855758\pi\)
0.437800 + 0.899072i \(0.355758\pi\)
\(68\) 0 0
\(69\) 2.00000 + 2.00000i 0.240772 + 0.240772i
\(70\) 0 0
\(71\) 9.11529i 1.08179i 0.841091 + 0.540893i \(0.181914\pi\)
−0.841091 + 0.540893i \(0.818086\pi\)
\(72\) 0 0
\(73\) 0.541560i 0.0633848i 0.999498 + 0.0316924i \(0.0100897\pi\)
−0.999498 + 0.0316924i \(0.989910\pi\)
\(74\) 0 0
\(75\) −3.37691 3.37691i −0.389933 0.389933i
\(76\) 0 0
\(77\) 11.2739 11.2739i 1.28478 1.28478i
\(78\) 0 0
\(79\) 10.9937 1.23689 0.618445 0.785828i \(-0.287763\pi\)
0.618445 + 0.785828i \(0.287763\pi\)
\(80\) 0 0
\(81\) −1.00000 −0.111111
\(82\) 0 0
\(83\) 10.6417 10.6417i 1.16807 1.16807i 0.185415 0.982660i \(-0.440637\pi\)
0.982660 0.185415i \(-0.0593628\pi\)
\(84\) 0 0
\(85\) −1.21137 1.21137i −0.131391 0.131391i
\(86\) 0 0
\(87\) 7.30205i 0.782862i
\(88\) 0 0
\(89\) 14.6533i 1.55325i −0.629964 0.776625i \(-0.716930\pi\)
0.629964 0.776625i \(-0.283070\pi\)
\(90\) 0 0
\(91\) 0.270780 + 0.270780i 0.0283854 + 0.0283854i
\(92\) 0 0
\(93\) 0.394316 0.394316i 0.0408887 0.0408887i
\(94\) 0 0
\(95\) 1.71313 0.175764
\(96\) 0 0
\(97\) 4.31724 0.438349 0.219175 0.975686i \(-0.429664\pi\)
0.219175 + 0.975686i \(0.429664\pi\)
\(98\) 0 0
\(99\) 2.47363 2.47363i 0.248609 0.248609i
\(100\) 0 0
\(101\) −0.453728 0.453728i −0.0451477 0.0451477i 0.684173 0.729320i \(-0.260164\pi\)
−0.729320 + 0.684173i \(0.760164\pi\)
\(102\) 0 0
\(103\) 1.33686i 0.131724i 0.997829 + 0.0658622i \(0.0209798\pi\)
−0.997829 + 0.0658622i \(0.979020\pi\)
\(104\) 0 0
\(105\) 2.15862i 0.210660i
\(106\) 0 0
\(107\) −6.06255 6.06255i −0.586088 0.586088i 0.350481 0.936570i \(-0.386018\pi\)
−0.936570 + 0.350481i \(0.886018\pi\)
\(108\) 0 0
\(109\) 5.71627 5.71627i 0.547519 0.547519i −0.378203 0.925722i \(-0.623458\pi\)
0.925722 + 0.378203i \(0.123458\pi\)
\(110\) 0 0
\(111\) 6.20285 0.588748
\(112\) 0 0
\(113\) −9.55136 −0.898516 −0.449258 0.893402i \(-0.648312\pi\)
−0.449258 + 0.893402i \(0.648312\pi\)
\(114\) 0 0
\(115\) 0.947252 0.947252i 0.0883317 0.0883317i
\(116\) 0 0
\(117\) 0.0594122 + 0.0594122i 0.00549266 + 0.00549266i
\(118\) 0 0
\(119\) 16.4853i 1.51120i
\(120\) 0 0
\(121\) 1.23765i 0.112514i
\(122\) 0 0
\(123\) 6.55765 + 6.55765i 0.591283 + 0.591283i
\(124\) 0 0
\(125\) −3.27391 + 3.27391i −0.292828 + 0.292828i
\(126\) 0 0
\(127\) −5.09921 −0.452481 −0.226241 0.974071i \(-0.572644\pi\)
−0.226241 + 0.974071i \(0.572644\pi\)
\(128\) 0 0
\(129\) 2.27744 0.200518
\(130\) 0 0
\(131\) −2.11882 + 2.11882i −0.185123 + 0.185123i −0.793584 0.608461i \(-0.791787\pi\)
0.608461 + 0.793584i \(0.291787\pi\)
\(132\) 0 0
\(133\) 11.6569 + 11.6569i 1.01078 + 1.01078i
\(134\) 0 0
\(135\) 0.473626i 0.0407632i
\(136\) 0 0
\(137\) 3.37941i 0.288723i 0.989525 + 0.144361i \(0.0461127\pi\)
−0.989525 + 0.144361i \(0.953887\pi\)
\(138\) 0 0
\(139\) −5.88118 5.88118i −0.498835 0.498835i 0.412240 0.911075i \(-0.364746\pi\)
−0.911075 + 0.412240i \(0.864746\pi\)
\(140\) 0 0
\(141\) −2.00000 + 2.00000i −0.168430 + 0.168430i
\(142\) 0 0
\(143\) −0.293927 −0.0245794
\(144\) 0 0
\(145\) 3.45844 0.287208
\(146\) 0 0
\(147\) −9.73838 + 9.73838i −0.803208 + 0.803208i
\(148\) 0 0
\(149\) −9.99176 9.99176i −0.818557 0.818557i 0.167342 0.985899i \(-0.446482\pi\)
−0.985899 + 0.167342i \(0.946482\pi\)
\(150\) 0 0
\(151\) 9.97685i 0.811905i 0.913894 + 0.405952i \(0.133060\pi\)
−0.913894 + 0.405952i \(0.866940\pi\)
\(152\) 0 0
\(153\) 3.61706i 0.292422i
\(154\) 0 0
\(155\) −0.186758 0.186758i −0.0150008 0.0150008i
\(156\) 0 0
\(157\) −16.1618 + 16.1618i −1.28985 + 1.28985i −0.354971 + 0.934877i \(0.615509\pi\)
−0.934877 + 0.354971i \(0.884491\pi\)
\(158\) 0 0
\(159\) −0.697947 −0.0553508
\(160\) 0 0
\(161\) 12.8910 1.01595
\(162\) 0 0
\(163\) 7.50490 7.50490i 0.587829 0.587829i −0.349214 0.937043i \(-0.613551\pi\)
0.937043 + 0.349214i \(0.113551\pi\)
\(164\) 0 0
\(165\) −1.17157 1.17157i −0.0912068 0.0912068i
\(166\) 0 0
\(167\) 5.83822i 0.451775i −0.974153 0.225888i \(-0.927472\pi\)
0.974153 0.225888i \(-0.0725282\pi\)
\(168\) 0 0
\(169\) 12.9929i 0.999457i
\(170\) 0 0
\(171\) 2.55765 + 2.55765i 0.195588 + 0.195588i
\(172\) 0 0
\(173\) −3.62530 + 3.62530i −0.275627 + 0.275627i −0.831360 0.555734i \(-0.812437\pi\)
0.555734 + 0.831360i \(0.312437\pi\)
\(174\) 0 0
\(175\) −21.7659 −1.64534
\(176\) 0 0
\(177\) −5.65685 −0.425195
\(178\) 0 0
\(179\) −9.28334 + 9.28334i −0.693869 + 0.693869i −0.963081 0.269212i \(-0.913237\pi\)
0.269212 + 0.963081i \(0.413237\pi\)
\(180\) 0 0
\(181\) −10.8316 10.8316i −0.805104 0.805104i 0.178785 0.983888i \(-0.442783\pi\)
−0.983888 + 0.178785i \(0.942783\pi\)
\(182\) 0 0
\(183\) 3.85970i 0.285317i
\(184\) 0 0
\(185\) 2.93783i 0.215993i
\(186\) 0 0
\(187\) 8.94725 + 8.94725i 0.654288 + 0.654288i
\(188\) 0 0
\(189\) −3.22274 + 3.22274i −0.234420 + 0.234420i
\(190\) 0 0
\(191\) 8.63001 0.624446 0.312223 0.950009i \(-0.398926\pi\)
0.312223 + 0.950009i \(0.398926\pi\)
\(192\) 0 0
\(193\) 11.4514 0.824288 0.412144 0.911119i \(-0.364780\pi\)
0.412144 + 0.911119i \(0.364780\pi\)
\(194\) 0 0
\(195\) 0.0281391 0.0281391i 0.00201509 0.00201509i
\(196\) 0 0
\(197\) 7.48999 + 7.48999i 0.533640 + 0.533640i 0.921654 0.388014i \(-0.126839\pi\)
−0.388014 + 0.921654i \(0.626839\pi\)
\(198\) 0 0
\(199\) 3.68000i 0.260868i −0.991457 0.130434i \(-0.958363\pi\)
0.991457 0.130434i \(-0.0416371\pi\)
\(200\) 0 0
\(201\) 5.33962i 0.376627i
\(202\) 0 0
\(203\) 23.5326 + 23.5326i 1.65167 + 1.65167i
\(204\) 0 0
\(205\) 3.10587 3.10587i 0.216923 0.216923i
\(206\) 0 0
\(207\) 2.82843 0.196589
\(208\) 0 0
\(209\) −12.6533 −0.875249
\(210\) 0 0
\(211\) −10.1188 + 10.1188i −0.696609 + 0.696609i −0.963677 0.267069i \(-0.913945\pi\)
0.267069 + 0.963677i \(0.413945\pi\)
\(212\) 0 0
\(213\) 6.44549 + 6.44549i 0.441637 + 0.441637i
\(214\) 0 0
\(215\) 1.07866i 0.0735637i
\(216\) 0 0
\(217\) 2.54156i 0.172532i
\(218\) 0 0
\(219\) 0.382941 + 0.382941i 0.0258767 + 0.0258767i
\(220\) 0 0
\(221\) −0.214897 + 0.214897i −0.0144556 + 0.0144556i
\(222\) 0 0
\(223\) 4.86156 0.325554 0.162777 0.986663i \(-0.447955\pi\)
0.162777 + 0.986663i \(0.447955\pi\)
\(224\) 0 0
\(225\) −4.77568 −0.318379
\(226\) 0 0
\(227\) −10.6417 + 10.6417i −0.706312 + 0.706312i −0.965758 0.259445i \(-0.916460\pi\)
0.259445 + 0.965758i \(0.416460\pi\)
\(228\) 0 0
\(229\) −20.1712 20.1712i −1.33295 1.33295i −0.902720 0.430229i \(-0.858433\pi\)
−0.430229 0.902720i \(-0.641567\pi\)
\(230\) 0 0
\(231\) 15.9437i 1.04902i
\(232\) 0 0
\(233\) 13.5702i 0.889014i −0.895775 0.444507i \(-0.853379\pi\)
0.895775 0.444507i \(-0.146621\pi\)
\(234\) 0 0
\(235\) 0.947252 + 0.947252i 0.0617919 + 0.0617919i
\(236\) 0 0
\(237\) 7.77373 7.77373i 0.504958 0.504958i
\(238\) 0 0
\(239\) −29.3629 −1.89933 −0.949665 0.313267i \(-0.898576\pi\)
−0.949665 + 0.313267i \(0.898576\pi\)
\(240\) 0 0
\(241\) 24.0063 1.54638 0.773190 0.634175i \(-0.218660\pi\)
0.773190 + 0.634175i \(0.218660\pi\)
\(242\) 0 0
\(243\) −0.707107 + 0.707107i −0.0453609 + 0.0453609i
\(244\) 0 0
\(245\) 4.61235 + 4.61235i 0.294672 + 0.294672i
\(246\) 0 0
\(247\) 0.303911i 0.0193374i
\(248\) 0 0
\(249\) 15.0496i 0.953729i
\(250\) 0 0
\(251\) −15.7570 15.7570i −0.994571 0.994571i 0.00541463 0.999985i \(-0.498276\pi\)
−0.999985 + 0.00541463i \(0.998276\pi\)
\(252\) 0 0
\(253\) −6.99647 + 6.99647i −0.439864 + 0.439864i
\(254\) 0 0
\(255\) −1.71313 −0.107281
\(256\) 0 0
\(257\) 8.66038 0.540220 0.270110 0.962829i \(-0.412940\pi\)
0.270110 + 0.962829i \(0.412940\pi\)
\(258\) 0 0
\(259\) 19.9902 19.9902i 1.24213 1.24213i
\(260\) 0 0
\(261\) 5.16333 + 5.16333i 0.319602 + 0.319602i
\(262\) 0 0
\(263\) 13.3208i 0.821394i 0.911772 + 0.410697i \(0.134715\pi\)
−0.911772 + 0.410697i \(0.865285\pi\)
\(264\) 0 0
\(265\) 0.330566i 0.0203065i
\(266\) 0 0
\(267\) −10.3615 10.3615i −0.634111 0.634111i
\(268\) 0 0
\(269\) −11.6714 + 11.6714i −0.711616 + 0.711616i −0.966873 0.255257i \(-0.917840\pi\)
0.255257 + 0.966873i \(0.417840\pi\)
\(270\) 0 0
\(271\) 21.9769 1.33500 0.667499 0.744610i \(-0.267365\pi\)
0.667499 + 0.744610i \(0.267365\pi\)
\(272\) 0 0
\(273\) 0.382941 0.0231766
\(274\) 0 0
\(275\) 11.8132 11.8132i 0.712365 0.712365i
\(276\) 0 0
\(277\) −10.9504 10.9504i −0.657945 0.657945i 0.296949 0.954893i \(-0.404031\pi\)
−0.954893 + 0.296949i \(0.904031\pi\)
\(278\) 0 0
\(279\) 0.557647i 0.0333855i
\(280\) 0 0
\(281\) 22.8910i 1.36556i 0.730624 + 0.682780i \(0.239229\pi\)
−0.730624 + 0.682780i \(0.760771\pi\)
\(282\) 0 0
\(283\) −4.48528 4.48528i −0.266622 0.266622i 0.561115 0.827738i \(-0.310372\pi\)
−0.827738 + 0.561115i \(0.810372\pi\)
\(284\) 0 0
\(285\) 1.21137 1.21137i 0.0717552 0.0717552i
\(286\) 0 0
\(287\) 42.2672 2.49496
\(288\) 0 0
\(289\) −3.91688 −0.230405
\(290\) 0 0
\(291\) 3.05275 3.05275i 0.178955 0.178955i
\(292\) 0 0
\(293\) 21.6221 + 21.6221i 1.26318 + 1.26318i 0.949543 + 0.313636i \(0.101547\pi\)
0.313636 + 0.949543i \(0.398453\pi\)
\(294\) 0 0
\(295\) 2.67923i 0.155991i
\(296\) 0 0
\(297\) 3.49824i 0.202988i
\(298\) 0 0
\(299\) −0.168043 0.168043i −0.00971818 0.00971818i
\(300\) 0 0
\(301\) 7.33962 7.33962i 0.423048 0.423048i
\(302\) 0 0
\(303\) −0.641669 −0.0368629
\(304\) 0 0
\(305\) −1.82805 −0.104674
\(306\) 0 0
\(307\) 12.1118 12.1118i 0.691255 0.691255i −0.271253 0.962508i \(-0.587438\pi\)
0.962508 + 0.271253i \(0.0874380\pi\)
\(308\) 0 0
\(309\) 0.945300 + 0.945300i 0.0537762 + 0.0537762i
\(310\) 0 0
\(311\) 26.8651i 1.52338i −0.647943 0.761689i \(-0.724370\pi\)
0.647943 0.761689i \(-0.275630\pi\)
\(312\) 0 0
\(313\) 19.6890i 1.11289i −0.830885 0.556445i \(-0.812165\pi\)
0.830885 0.556445i \(-0.187835\pi\)
\(314\) 0 0
\(315\) 1.52637 + 1.52637i 0.0860014 + 0.0860014i
\(316\) 0 0
\(317\) 21.3447 21.3447i 1.19884 1.19884i 0.224323 0.974515i \(-0.427983\pi\)
0.974515 0.224323i \(-0.0720171\pi\)
\(318\) 0 0
\(319\) −25.5443 −1.43021
\(320\) 0 0
\(321\) −8.57373 −0.478539
\(322\) 0 0
\(323\) −9.25116 + 9.25116i −0.514748 + 0.514748i
\(324\) 0 0
\(325\) 0.283734 + 0.283734i 0.0157387 + 0.0157387i
\(326\) 0 0
\(327\) 8.08402i 0.447047i
\(328\) 0 0
\(329\) 12.8910i 0.710702i
\(330\) 0 0
\(331\) −14.6926 14.6926i −0.807576 0.807576i 0.176690 0.984266i \(-0.443461\pi\)
−0.984266 + 0.176690i \(0.943461\pi\)
\(332\) 0 0
\(333\) 4.38607 4.38607i 0.240355 0.240355i
\(334\) 0 0
\(335\) 2.52898 0.138173
\(336\) 0 0
\(337\) −23.0098 −1.25342 −0.626712 0.779251i \(-0.715600\pi\)
−0.626712 + 0.779251i \(0.715600\pi\)
\(338\) 0 0
\(339\) −6.75383 + 6.75383i −0.366818 + 0.366818i
\(340\) 0 0
\(341\) 1.37941 + 1.37941i 0.0746993 + 0.0746993i
\(342\) 0 0
\(343\) 30.8651i 1.66656i
\(344\) 0 0
\(345\) 1.33962i 0.0721225i
\(346\) 0 0
\(347\) 10.9026 + 10.9026i 0.585284 + 0.585284i 0.936350 0.351067i \(-0.114181\pi\)
−0.351067 + 0.936350i \(0.614181\pi\)
\(348\) 0 0
\(349\) 20.0563 20.0563i 1.07359 1.07359i 0.0765186 0.997068i \(-0.475620\pi\)
0.997068 0.0765186i \(-0.0243805\pi\)
\(350\) 0 0
\(351\) 0.0840215 0.00448474
\(352\) 0 0
\(353\) −12.2117 −0.649965 −0.324983 0.945720i \(-0.605358\pi\)
−0.324983 + 0.945720i \(0.605358\pi\)
\(354\) 0 0
\(355\) 3.05275 3.05275i 0.162023 0.162023i
\(356\) 0 0
\(357\) −11.6569 11.6569i −0.616946 0.616946i
\(358\) 0 0
\(359\) 33.4780i 1.76690i 0.468522 + 0.883452i \(0.344786\pi\)
−0.468522 + 0.883452i \(0.655214\pi\)
\(360\) 0 0
\(361\) 5.91688i 0.311415i
\(362\) 0 0
\(363\) 0.875150 + 0.875150i 0.0459335 + 0.0459335i
\(364\) 0 0
\(365\) 0.181370 0.181370i 0.00949337 0.00949337i
\(366\) 0 0
\(367\) 0.702379 0.0366639 0.0183319 0.999832i \(-0.494164\pi\)
0.0183319 + 0.999832i \(0.494164\pi\)
\(368\) 0 0
\(369\) 9.27391 0.482781
\(370\) 0 0
\(371\) −2.24930 + 2.24930i −0.116778 + 0.116778i
\(372\) 0 0
\(373\) 18.9598 + 18.9598i 0.981702 + 0.981702i 0.999836 0.0181339i \(-0.00577250\pi\)
−0.0181339 + 0.999836i \(0.505773\pi\)
\(374\) 0 0
\(375\) 4.63001i 0.239093i
\(376\) 0 0
\(377\) 0.613530i 0.0315984i
\(378\) 0 0
\(379\) 1.77844 + 1.77844i 0.0913523 + 0.0913523i 0.751306 0.659954i \(-0.229424\pi\)
−0.659954 + 0.751306i \(0.729424\pi\)
\(380\) 0 0
\(381\) −3.60568 + 3.60568i −0.184725 + 0.184725i
\(382\) 0 0
\(383\) −25.4880 −1.30238 −0.651188 0.758916i \(-0.725729\pi\)
−0.651188 + 0.758916i \(0.725729\pi\)
\(384\) 0 0
\(385\) −7.55136 −0.384853
\(386\) 0 0
\(387\) 1.61040 1.61040i 0.0818610 0.0818610i
\(388\) 0 0
\(389\) −11.7049 11.7049i −0.593462 0.593462i 0.345103 0.938565i \(-0.387844\pi\)
−0.938565 + 0.345103i \(0.887844\pi\)
\(390\) 0 0
\(391\) 10.2306i 0.517383i
\(392\) 0 0
\(393\) 2.99647i 0.151152i
\(394\) 0 0
\(395\) −3.68184 3.68184i −0.185253 0.185253i
\(396\) 0 0
\(397\) −9.04646 + 9.04646i −0.454029 + 0.454029i −0.896689 0.442661i \(-0.854035\pi\)
0.442661 + 0.896689i \(0.354035\pi\)
\(398\) 0 0
\(399\) 16.4853 0.825296
\(400\) 0 0
\(401\) −18.0853 −0.903137 −0.451568 0.892237i \(-0.649135\pi\)
−0.451568 + 0.892237i \(0.649135\pi\)
\(402\) 0 0
\(403\) −0.0331311 + 0.0331311i −0.00165038 + 0.00165038i
\(404\) 0 0
\(405\) 0.334904 + 0.334904i 0.0166415 + 0.0166415i
\(406\) 0 0
\(407\) 21.6990i 1.07558i
\(408\) 0 0
\(409\) 25.2271i 1.24740i 0.781665 + 0.623699i \(0.214371\pi\)
−0.781665 + 0.623699i \(0.785629\pi\)
\(410\) 0 0
\(411\) 2.38960 + 2.38960i 0.117870 + 0.117870i
\(412\) 0 0
\(413\) −18.2306 + 18.2306i −0.897069 + 0.897069i
\(414\) 0 0
\(415\) −7.12787 −0.349894
\(416\) 0 0
\(417\) −8.31724 −0.407297
\(418\) 0 0
\(419\) −7.25283 + 7.25283i −0.354324 + 0.354324i −0.861716 0.507392i \(-0.830610\pi\)
0.507392 + 0.861716i \(0.330610\pi\)
\(420\) 0 0
\(421\) 2.39550 + 2.39550i 0.116749 + 0.116749i 0.763068 0.646318i \(-0.223692\pi\)
−0.646318 + 0.763068i \(0.723692\pi\)
\(422\) 0 0
\(423\) 2.82843i 0.137523i
\(424\) 0 0
\(425\) 17.2739i 0.837908i
\(426\) 0 0
\(427\) −12.4388 12.4388i −0.601957 0.601957i
\(428\) 0 0
\(429\) −0.207838 + 0.207838i −0.0100345 + 0.0100345i
\(430\) 0 0
\(431\) 4.42454 0.213123 0.106561 0.994306i \(-0.466016\pi\)
0.106561 + 0.994306i \(0.466016\pi\)
\(432\) 0 0
\(433\) 7.31371 0.351474 0.175737 0.984437i \(-0.443769\pi\)
0.175737 + 0.984437i \(0.443769\pi\)
\(434\) 0 0
\(435\) 2.44549 2.44549i 0.117252 0.117252i
\(436\) 0 0
\(437\) −7.23412 7.23412i −0.346055 0.346055i
\(438\) 0 0
\(439\) 29.6533i 1.41527i −0.706576 0.707637i \(-0.749761\pi\)
0.706576 0.707637i \(-0.250239\pi\)
\(440\) 0 0
\(441\) 13.7721i 0.655817i
\(442\) 0 0
\(443\) −10.3056 10.3056i −0.489633 0.489633i 0.418557 0.908190i \(-0.362536\pi\)
−0.908190 + 0.418557i \(0.862536\pi\)
\(444\) 0 0
\(445\) −4.90746 + 4.90746i −0.232636 + 0.232636i
\(446\) 0 0
\(447\) −14.1305 −0.668349
\(448\) 0 0
\(449\) −6.48844 −0.306208 −0.153104 0.988210i \(-0.548927\pi\)
−0.153104 + 0.988210i \(0.548927\pi\)
\(450\) 0 0
\(451\) −22.9402 + 22.9402i −1.08021 + 1.08021i
\(452\) 0 0
\(453\) 7.05470 + 7.05470i 0.331459 + 0.331459i
\(454\) 0 0
\(455\) 0.181370i 0.00850278i
\(456\) 0 0
\(457\) 9.00353i 0.421167i 0.977576 + 0.210584i \(0.0675364\pi\)
−0.977576 + 0.210584i \(0.932464\pi\)
\(458\) 0 0
\(459\) −2.55765 2.55765i −0.119381 0.119381i
\(460\) 0 0
\(461\) 14.6218 14.6218i 0.681004 0.681004i −0.279223 0.960226i \(-0.590077\pi\)
0.960226 + 0.279223i \(0.0900767\pi\)
\(462\) 0 0
\(463\) 18.6435 0.866437 0.433219 0.901289i \(-0.357378\pi\)
0.433219 + 0.901289i \(0.357378\pi\)
\(464\) 0 0
\(465\) −0.264116 −0.0122481
\(466\) 0 0
\(467\) 23.5138 23.5138i 1.08809 1.08809i 0.0923633 0.995725i \(-0.470558\pi\)
0.995725 0.0923633i \(-0.0294421\pi\)
\(468\) 0 0
\(469\) 17.2082 + 17.2082i 0.794601 + 0.794601i
\(470\) 0 0
\(471\) 22.8562i 1.05316i
\(472\) 0 0
\(473\) 7.96703i 0.366325i
\(474\) 0 0
\(475\) 12.2145 + 12.2145i 0.560440 + 0.560440i
\(476\) 0 0
\(477\) −0.493523 + 0.493523i −0.0225969 + 0.0225969i
\(478\) 0 0
\(479\) 1.08864 0.0497412 0.0248706 0.999691i \(-0.492083\pi\)
0.0248706 + 0.999691i \(0.492083\pi\)
\(480\) 0 0
\(481\) −0.521173 −0.0237634
\(482\) 0 0
\(483\) 9.11529 9.11529i 0.414760 0.414760i
\(484\) 0 0
\(485\) −1.44586 1.44586i −0.0656531 0.0656531i
\(486\) 0 0
\(487\) 35.3298i 1.60095i −0.599369 0.800473i \(-0.704582\pi\)
0.599369 0.800473i \(-0.295418\pi\)
\(488\) 0 0
\(489\) 10.6135i 0.479960i
\(490\) 0 0
\(491\) 12.8910 + 12.8910i 0.581761 + 0.581761i 0.935387 0.353626i \(-0.115051\pi\)
−0.353626 + 0.935387i \(0.615051\pi\)
\(492\) 0 0
\(493\) −18.6761 + 18.6761i −0.841128 + 0.841128i
\(494\) 0 0
\(495\) −1.65685 −0.0744701
\(496\) 0 0
\(497\) 41.5443 1.86352
\(498\) 0 0
\(499\) −14.3798 + 14.3798i −0.643728 + 0.643728i −0.951470 0.307742i \(-0.900427\pi\)
0.307742 + 0.951470i \(0.400427\pi\)
\(500\) 0 0
\(501\) −4.12825 4.12825i −0.184437 0.184437i
\(502\) 0 0
\(503\) 30.2969i 1.35087i −0.737420 0.675435i \(-0.763956\pi\)
0.737420 0.675435i \(-0.236044\pi\)
\(504\) 0 0
\(505\) 0.303911i 0.0135239i
\(506\) 0 0
\(507\) 9.18740 + 9.18740i 0.408027 + 0.408027i
\(508\) 0 0
\(509\) 10.5825 10.5825i 0.469063 0.469063i −0.432548 0.901611i \(-0.642385\pi\)
0.901611 + 0.432548i \(0.142385\pi\)
\(510\) 0 0
\(511\) 2.46824 0.109188
\(512\) 0 0
\(513\) 3.61706 0.159697
\(514\) 0 0
\(515\) 0.447718 0.447718i 0.0197288 0.0197288i
\(516\) 0 0
\(517\) −6.99647 6.99647i −0.307704 0.307704i
\(518\) 0 0
\(519\) 5.12695i 0.225048i
\(520\) 0 0
\(521\) 24.9049i 1.09110i −0.838078 0.545551i \(-0.816320\pi\)
0.838078 0.545551i \(-0.183680\pi\)
\(522\) 0 0
\(523\) 12.9008 + 12.9008i 0.564112 + 0.564112i 0.930473 0.366361i \(-0.119396\pi\)
−0.366361 + 0.930473i \(0.619396\pi\)
\(524\) 0 0
\(525\) −15.3908 + 15.3908i −0.671709 + 0.671709i
\(526\) 0 0
\(527\) 2.01704 0.0878638
\(528\) 0 0
\(529\) 15.0000 0.652174
\(530\) 0 0
\(531\) −4.00000 + 4.00000i −0.173585 + 0.173585i
\(532\) 0 0
\(533\) −0.550984 0.550984i −0.0238657 0.0238657i
\(534\) 0 0
\(535\) 4.06074i 0.175561i
\(536\) 0 0
\(537\) 13.1286i 0.566542i
\(538\) 0 0
\(539\) −34.0671 34.0671i −1.46738 1.46738i
\(540\) 0 0
\(541\) 18.2767 18.2767i 0.785776 0.785776i −0.195023 0.980799i \(-0.562478\pi\)
0.980799 + 0.195023i \(0.0624782\pi\)
\(542\) 0 0
\(543\) −15.3181 −0.657364
\(544\) 0 0
\(545\) −3.82880 −0.164008
\(546\) 0 0
\(547\) −13.7355 + 13.7355i −0.587287 + 0.587287i −0.936896 0.349609i \(-0.886315\pi\)
0.349609 + 0.936896i \(0.386315\pi\)
\(548\) 0 0
\(549\) −2.72922 2.72922i −0.116480 0.116480i
\(550\) 0 0
\(551\) 26.4120i 1.12519i
\(552\) 0 0
\(553\) 50.1055i 2.13070i
\(554\) 0 0
\(555\) −2.07736 2.07736i −0.0881789 0.0881789i
\(556\) 0 0
\(557\) −27.5525 + 27.5525i −1.16744 + 1.16744i −0.184631 + 0.982808i \(0.559109\pi\)
−0.982808 + 0.184631i \(0.940891\pi\)
\(558\) 0 0
\(559\) −0.191354 −0.00809342
\(560\) 0 0
\(561\) 12.6533 0.534224
\(562\) 0 0
\(563\) 19.8928 19.8928i 0.838383 0.838383i −0.150263 0.988646i \(-0.548012\pi\)
0.988646 + 0.150263i \(0.0480121\pi\)
\(564\) 0 0
\(565\) 3.19879 + 3.19879i 0.134574 + 0.134574i
\(566\) 0 0
\(567\) 4.55765i 0.191403i
\(568\) 0 0
\(569\) 13.4849i 0.565317i −0.959221 0.282658i \(-0.908784\pi\)
0.959221 0.282658i \(-0.0912163\pi\)
\(570\) 0 0
\(571\) 14.8284 + 14.8284i 0.620550 + 0.620550i 0.945672 0.325122i \(-0.105405\pi\)
−0.325122 + 0.945672i \(0.605405\pi\)
\(572\) 0 0
\(573\) 6.10234 6.10234i 0.254929 0.254929i
\(574\) 0 0
\(575\) 13.5077 0.563308
\(576\) 0 0
\(577\) −11.6176 −0.483648 −0.241824 0.970320i \(-0.577746\pi\)
−0.241824 + 0.970320i \(0.577746\pi\)
\(578\) 0 0
\(579\) 8.09735 8.09735i 0.336514 0.336514i
\(580\) 0 0
\(581\) −48.5010 48.5010i −2.01216 2.01216i
\(582\) 0 0
\(583\) 2.44158i 0.101120i
\(584\) 0 0
\(585\) 0.0397948i 0.00164531i
\(586\) 0 0
\(587\) 17.0268 + 17.0268i 0.702773 + 0.702773i 0.965005 0.262232i \(-0.0844585\pi\)
−0.262232 + 0.965005i \(0.584459\pi\)
\(588\) 0 0
\(589\) −1.42627 + 1.42627i −0.0587682 + 0.0587682i
\(590\) 0 0
\(591\) 10.5925 0.435715
\(592\) 0 0
\(593\) 41.5372 1.70573 0.852865 0.522132i \(-0.174863\pi\)
0.852865 + 0.522132i \(0.174863\pi\)
\(594\) 0 0
\(595\) −5.52099 + 5.52099i −0.226338 + 0.226338i
\(596\) 0 0
\(597\) −2.60215 2.60215i −0.106499 0.106499i
\(598\) 0 0
\(599\) 6.43160i 0.262788i −0.991330 0.131394i \(-0.958055\pi\)
0.991330 0.131394i \(-0.0419453\pi\)
\(600\) 0 0
\(601\) 3.45844i 0.141073i −0.997509 0.0705364i \(-0.977529\pi\)
0.997509 0.0705364i \(-0.0224711\pi\)
\(602\) 0 0
\(603\) 3.77568 + 3.77568i 0.153758 + 0.153758i
\(604\) 0 0
\(605\) 0.414494 0.414494i 0.0168516 0.0168516i
\(606\) 0 0
\(607\) 30.1019 1.22180 0.610900 0.791708i \(-0.290808\pi\)
0.610900 + 0.791708i \(0.290808\pi\)
\(608\) 0 0
\(609\) 33.2802 1.34858
\(610\) 0 0
\(611\) 0.168043 0.168043i 0.00679829 0.00679829i
\(612\) 0 0
\(613\) 2.50490 + 2.50490i 0.101172 + 0.101172i 0.755881 0.654709i \(-0.227209\pi\)
−0.654709 + 0.755881i \(0.727209\pi\)
\(614\) 0 0
\(615\) 4.39236i 0.177117i
\(616\) 0 0
\(617\) 22.9098i 0.922315i 0.887318 + 0.461157i \(0.152566\pi\)
−0.887318 + 0.461157i \(0.847434\pi\)
\(618\) 0 0
\(619\) 28.6104 + 28.6104i 1.14995 + 1.14995i 0.986562 + 0.163386i \(0.0522415\pi\)
0.163386 + 0.986562i \(0.447758\pi\)
\(620\) 0 0
\(621\) 2.00000 2.00000i 0.0802572 0.0802572i
\(622\) 0 0
\(623\) −66.7847 −2.67567
\(624\) 0 0
\(625\) −21.6855 −0.867420
\(626\) 0 0
\(627\) −8.94725 + 8.94725i −0.357319 + 0.357319i
\(628\) 0 0
\(629\) 15.8647 + 15.8647i 0.632567 + 0.632567i
\(630\) 0 0
\(631\) 11.1851i 0.445270i −0.974902 0.222635i \(-0.928534\pi\)
0.974902 0.222635i \(-0.0714659\pi\)
\(632\) 0 0
\(633\) 14.3102i 0.568779i
\(634\) 0 0
\(635\) 1.70774 + 1.70774i 0.0677698 + 0.0677698i
\(636\) 0 0
\(637\) 0.818234 0.818234i 0.0324196 0.0324196i
\(638\) 0 0
\(639\) 9.11529 0.360595
\(640\) 0 0
\(641\) −6.69312 −0.264362 −0.132181 0.991226i \(-0.542198\pi\)
−0.132181 + 0.991226i \(0.542198\pi\)
\(642\) 0 0
\(643\) 17.9410 17.9410i 0.707522 0.707522i −0.258491 0.966014i \(-0.583225\pi\)
0.966014 + 0.258491i \(0.0832253\pi\)
\(644\) 0 0
\(645\) −0.762725 0.762725i −0.0300323 0.0300323i
\(646\) 0 0
\(647\) 6.72999i 0.264583i −0.991211 0.132292i \(-0.957766\pi\)
0.991211 0.132292i \(-0.0422335\pi\)
\(648\) 0 0
\(649\) 19.7890i 0.776786i
\(650\) 0 0
\(651\) −1.79715 1.79715i −0.0704360 0.0704360i
\(652\) 0 0
\(653\) 26.1731 26.1731i 1.02423 1.02423i 0.0245347 0.999699i \(-0.492190\pi\)
0.999699 0.0245347i \(-0.00781042\pi\)
\(654\) 0 0
\(655\) 1.41921 0.0554529
\(656\) 0 0
\(657\) 0.541560 0.0211283
\(658\) 0 0
\(659\) −13.9741 + 13.9741i −0.544353 + 0.544353i −0.924802 0.380449i \(-0.875770\pi\)
0.380449 + 0.924802i \(0.375770\pi\)
\(660\) 0 0
\(661\) 11.9241 + 11.9241i 0.463794 + 0.463794i 0.899897 0.436103i \(-0.143642\pi\)
−0.436103 + 0.899897i \(0.643642\pi\)
\(662\) 0 0
\(663\) 0.303911i 0.0118029i
\(664\) 0 0
\(665\) 7.80785i 0.302776i
\(666\) 0 0
\(667\) −14.6041 14.6041i −0.565473 0.565473i
\(668\) 0 0
\(669\) 3.43764 3.43764i 0.132907 0.132907i
\(670\) 0 0
\(671\) 13.5021 0.521244
\(672\) 0 0
\(673\) −37.3066 −1.43807 −0.719033 0.694976i \(-0.755415\pi\)
−0.719033 + 0.694976i \(0.755415\pi\)
\(674\) 0 0
\(675\) −3.37691 + 3.37691i −0.129978 + 0.129978i
\(676\) 0 0
\(677\) 0.447461 + 0.447461i 0.0171973 + 0.0171973i 0.715653 0.698456i \(-0.246129\pi\)
−0.698456 + 0.715653i \(0.746129\pi\)
\(678\) 0 0
\(679\) 19.6764i 0.755113i
\(680\) 0 0
\(681\) 15.0496i 0.576702i
\(682\) 0 0
\(683\) 4.27521 + 4.27521i 0.163586 + 0.163586i 0.784153 0.620567i \(-0.213098\pi\)
−0.620567 + 0.784153i \(0.713098\pi\)
\(684\) 0 0
\(685\) 1.13178 1.13178i 0.0432430 0.0432430i
\(686\) 0 0
\(687\) −28.5264 −1.08835
\(688\) 0 0
\(689\) 0.0586426 0.00223410
\(690\) 0 0
\(691\) −20.0786 + 20.0786i −0.763827 + 0.763827i −0.977012 0.213185i \(-0.931616\pi\)
0.213185 + 0.977012i \(0.431616\pi\)
\(692\) 0 0
\(693\) −11.2739 11.2739i −0.428261 0.428261i
\(694\) 0 0
\(695\) 3.93926i 0.149425i
\(696\) 0 0
\(697\) 33.5443i 1.27058i
\(698\) 0 0
\(699\) −9.59558 9.59558i −0.362938 0.362938i
\(700\) 0 0
\(701\) −10.4467 + 10.4467i −0.394565 + 0.394565i −0.876311 0.481746i \(-0.840003\pi\)
0.481746 + 0.876311i \(0.340003\pi\)
\(702\) 0 0
\(703\) −22.4361 −0.846192
\(704\) 0 0
\(705\) 1.33962 0.0504529
\(706\) 0 0
\(707\) −2.06793 + 2.06793i −0.0777727 + 0.0777727i
\(708\) 0 0
\(709\) 16.0916 + 16.0916i 0.604332 + 0.604332i 0.941459 0.337127i \(-0.109455\pi\)
−0.337127 + 0.941459i \(0.609455\pi\)
\(710\) 0 0
\(711\) 10.9937i 0.412296i
\(712\) 0 0
\(713\) 1.57726i 0.0590690i
\(714\) 0 0
\(715\) 0.0984373 + 0.0984373i 0.00368135 + 0.00368135i
\(716\) 0 0
\(717\) −20.7627 + 20.7627i −0.775398 + 0.775398i
\(718\) 0 0
\(719\) 30.9957 1.15594 0.577972 0.816057i \(-0.303844\pi\)
0.577972 + 0.816057i \(0.303844\pi\)
\(720\) 0 0
\(721\) 6.09292 0.226912
\(722\) 0 0
\(723\) 16.9750 16.9750i 0.631307 0.631307i
\(724\) 0 0
\(725\) 24.6584 + 24.6584i 0.915790 + 0.915790i
\(726\) 0 0
\(727\) 41.1117i 1.52475i 0.647135 + 0.762375i \(0.275967\pi\)
−0.647135 + 0.762375i \(0.724033\pi\)
\(728\) 0 0
\(729\) 1.00000i 0.0370370i
\(730\) 0 0
\(731\) 5.82490 + 5.82490i 0.215442 + 0.215442i
\(732\) 0 0
\(733\) 0.146061 0.146061i 0.00539490 0.00539490i −0.704404 0.709799i \(-0.748786\pi\)
0.709799 + 0.704404i \(0.248786\pi\)
\(734\) 0 0
\(735\) 6.52284 0.240599
\(736\) 0 0
\(737\) −18.6792 −0.688058
\(738\) 0 0
\(739\) 1.50766 1.50766i 0.0554601 0.0554601i −0.678833 0.734293i \(-0.737514\pi\)
0.734293 + 0.678833i \(0.237514\pi\)
\(740\) 0 0
\(741\) −0.214897 0.214897i −0.00789445 0.00789445i
\(742\) 0 0
\(743\) 40.5175i 1.48644i 0.669046 + 0.743221i \(0.266703\pi\)
−0.669046 + 0.743221i \(0.733297\pi\)
\(744\) 0 0
\(745\) 6.69256i 0.245196i
\(746\) 0 0
\(747\) −10.6417 10.6417i −0.389358 0.389358i
\(748\) 0 0
\(749\) −27.6309 + 27.6309i −1.00961 + 1.00961i
\(750\) 0 0
\(751\) 12.5843 0.459208 0.229604 0.973284i \(-0.426257\pi\)
0.229604 + 0.973284i \(0.426257\pi\)
\(752\) 0 0
\(753\) −22.2837 −0.812064
\(754\) 0 0
\(755\) 3.34129 3.34129i 0.121602 0.121602i
\(756\) 0 0
\(757\) −7.49900 7.49900i −0.272556 0.272556i 0.557572 0.830128i \(-0.311733\pi\)
−0.830128 + 0.557572i \(0.811733\pi\)
\(758\) 0 0
\(759\) 9.89450i 0.359148i
\(760\) 0 0
\(761\) 42.8182i 1.55216i 0.630635 + 0.776079i \(0.282794\pi\)
−0.630635 + 0.776079i \(0.717206\pi\)
\(762\) 0 0
\(763\) −26.0527 26.0527i −0.943172 0.943172i
\(764\) 0 0
\(765\) −1.21137 + 1.21137i −0.0437971 + 0.0437971i
\(766\) 0 0
\(767\) 0.475298 0.0171620
\(768\) 0 0
\(769\) 12.7455 0.459614 0.229807 0.973236i \(-0.426190\pi\)
0.229807 + 0.973236i \(0.426190\pi\)
\(770\) 0 0
\(771\) 6.12382 6.12382i 0.220544 0.220544i
\(772\) 0 0
\(773\) −22.8765 22.8765i −0.822809 0.822809i 0.163701 0.986510i \(-0.447657\pi\)
−0.986510 + 0.163701i \(0.947657\pi\)
\(774\) 0 0
\(775\) 2.66314i 0.0956630i
\(776\) 0 0
\(777\) 28.2704i 1.01419i
\(778\) 0 0
\(779\) −23.7194 23.7194i −0.849836 0.849836i
\(780\) 0 0
\(781\) −22.5478 + 22.5478i −0.806825 + 0.806825i
\(782\) 0 0
\(783\) 7.30205 0.260954
\(784\) 0 0
\(785\) 10.8253 0.386370
\(786\) 0 0
\(787\) −5.20470 + 5.20470i −0.185528 + 0.185528i −0.793759 0.608232i \(-0.791879\pi\)
0.608232 + 0.793759i \(0.291879\pi\)
\(788\) 0 0
\(789\) 9.41921 + 9.41921i 0.335333 + 0.335333i
\(790\) 0 0
\(791\) 43.5317i 1.54781i
\(792\) 0 0
\(793\) 0.324298i 0.0115162i
\(794\) 0 0
\(795\) 0.233745 + 0.233745i 0.00829009 + 0.00829009i
\(796\) 0 0
\(797\) 17.0149 17.0149i 0.602698 0.602698i −0.338330 0.941028i \(-0.609862\pi\)
0.941028 + 0.338330i \(0.109862\pi\)
\(798\) 0 0
\(799\) −10.2306 −0.361932