Properties

Label 96.3.e.a.65.3
Level $96$
Weight $3$
Character 96.65
Analytic conductor $2.616$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 96 = 2^{5} \cdot 3 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 96.e (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.61581053786\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\sqrt{-2}, \sqrt{3})\)
Defining polynomial: \(x^{4} + 4 x^{2} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{3}\cdot 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 65.3
Root \(-0.517638i\) of defining polynomial
Character \(\chi\) \(=\) 96.65
Dual form 96.3.e.a.65.4

$q$-expansion

\(f(q)\) \(=\) \(q+(1.73205 - 2.44949i) q^{3} +2.82843i q^{5} +10.3923 q^{7} +(-3.00000 - 8.48528i) q^{9} +O(q^{10})\) \(q+(1.73205 - 2.44949i) q^{3} +2.82843i q^{5} +10.3923 q^{7} +(-3.00000 - 8.48528i) q^{9} -14.6969i q^{11} -6.00000 q^{13} +(6.92820 + 4.89898i) q^{15} +22.6274i q^{17} -10.3923 q^{19} +(18.0000 - 25.4558i) q^{21} +29.3939i q^{23} +17.0000 q^{25} +(-25.9808 - 7.34847i) q^{27} +31.1127i q^{29} -31.1769 q^{31} +(-36.0000 - 25.4558i) q^{33} +29.3939i q^{35} -38.0000 q^{37} +(-10.3923 + 14.6969i) q^{39} -5.65685i q^{41} -10.3923 q^{43} +(24.0000 - 8.48528i) q^{45} -58.7878i q^{47} +59.0000 q^{49} +(55.4256 + 39.1918i) q^{51} +14.1421i q^{53} +41.5692 q^{55} +(-18.0000 + 25.4558i) q^{57} -14.6969i q^{59} -22.0000 q^{61} +(-31.1769 - 88.1816i) q^{63} -16.9706i q^{65} +114.315 q^{67} +(72.0000 + 50.9117i) q^{69} -29.3939i q^{71} -30.0000 q^{73} +(29.4449 - 41.6413i) q^{75} -152.735i q^{77} -31.1769 q^{79} +(-63.0000 + 50.9117i) q^{81} +73.4847i q^{83} -64.0000 q^{85} +(76.2102 + 53.8888i) q^{87} -5.65685i q^{89} -62.3538 q^{91} +(-54.0000 + 76.3675i) q^{93} -29.3939i q^{95} +90.0000 q^{97} +(-124.708 + 44.0908i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 12q^{9} + O(q^{10}) \) \( 4q - 12q^{9} - 24q^{13} + 72q^{21} + 68q^{25} - 144q^{33} - 152q^{37} + 96q^{45} + 236q^{49} - 72q^{57} - 88q^{61} + 288q^{69} - 120q^{73} - 252q^{81} - 256q^{85} - 216q^{93} + 360q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/96\mathbb{Z}\right)^\times\).

\(n\) \(31\) \(37\) \(65\)
\(\chi(n)\) \(1\) \(1\) \(-1\)

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
\(3\) 1.73205 2.44949i 0.577350 0.816497i
\(4\) 0 0
\(5\) 2.82843i 0.565685i 0.959166 + 0.282843i \(0.0912774\pi\)
−0.959166 + 0.282843i \(0.908723\pi\)
\(6\) 0 0
\(7\) 10.3923 1.48461 0.742307 0.670059i \(-0.233731\pi\)
0.742307 + 0.670059i \(0.233731\pi\)
\(8\) 0 0
\(9\) −3.00000 8.48528i −0.333333 0.942809i
\(10\) 0 0
\(11\) 14.6969i 1.33609i −0.744123 0.668043i \(-0.767132\pi\)
0.744123 0.668043i \(-0.232868\pi\)
\(12\) 0 0
\(13\) −6.00000 −0.461538 −0.230769 0.973009i \(-0.574124\pi\)
−0.230769 + 0.973009i \(0.574124\pi\)
\(14\) 0 0
\(15\) 6.92820 + 4.89898i 0.461880 + 0.326599i
\(16\) 0 0
\(17\) 22.6274i 1.33102i 0.746387 + 0.665512i \(0.231787\pi\)
−0.746387 + 0.665512i \(0.768213\pi\)
\(18\) 0 0
\(19\) −10.3923 −0.546963 −0.273482 0.961877i \(-0.588175\pi\)
−0.273482 + 0.961877i \(0.588175\pi\)
\(20\) 0 0
\(21\) 18.0000 25.4558i 0.857143 1.21218i
\(22\) 0 0
\(23\) 29.3939i 1.27799i 0.769209 + 0.638997i \(0.220651\pi\)
−0.769209 + 0.638997i \(0.779349\pi\)
\(24\) 0 0
\(25\) 17.0000 0.680000
\(26\) 0 0
\(27\) −25.9808 7.34847i −0.962250 0.272166i
\(28\) 0 0
\(29\) 31.1127i 1.07285i 0.843947 + 0.536426i \(0.180226\pi\)
−0.843947 + 0.536426i \(0.819774\pi\)
\(30\) 0 0
\(31\) −31.1769 −1.00571 −0.502853 0.864372i \(-0.667716\pi\)
−0.502853 + 0.864372i \(0.667716\pi\)
\(32\) 0 0
\(33\) −36.0000 25.4558i −1.09091 0.771389i
\(34\) 0 0
\(35\) 29.3939i 0.839825i
\(36\) 0 0
\(37\) −38.0000 −1.02703 −0.513514 0.858082i \(-0.671656\pi\)
−0.513514 + 0.858082i \(0.671656\pi\)
\(38\) 0 0
\(39\) −10.3923 + 14.6969i −0.266469 + 0.376845i
\(40\) 0 0
\(41\) 5.65685i 0.137972i −0.997618 0.0689860i \(-0.978024\pi\)
0.997618 0.0689860i \(-0.0219764\pi\)
\(42\) 0 0
\(43\) −10.3923 −0.241682 −0.120841 0.992672i \(-0.538559\pi\)
−0.120841 + 0.992672i \(0.538559\pi\)
\(44\) 0 0
\(45\) 24.0000 8.48528i 0.533333 0.188562i
\(46\) 0 0
\(47\) 58.7878i 1.25080i −0.780303 0.625402i \(-0.784935\pi\)
0.780303 0.625402i \(-0.215065\pi\)
\(48\) 0 0
\(49\) 59.0000 1.20408
\(50\) 0 0
\(51\) 55.4256 + 39.1918i 1.08678 + 0.768467i
\(52\) 0 0
\(53\) 14.1421i 0.266833i 0.991060 + 0.133416i \(0.0425948\pi\)
−0.991060 + 0.133416i \(0.957405\pi\)
\(54\) 0 0
\(55\) 41.5692 0.755804
\(56\) 0 0
\(57\) −18.0000 + 25.4558i −0.315789 + 0.446594i
\(58\) 0 0
\(59\) 14.6969i 0.249101i −0.992213 0.124550i \(-0.960251\pi\)
0.992213 0.124550i \(-0.0397488\pi\)
\(60\) 0 0
\(61\) −22.0000 −0.360656 −0.180328 0.983607i \(-0.557716\pi\)
−0.180328 + 0.983607i \(0.557716\pi\)
\(62\) 0 0
\(63\) −31.1769 88.1816i −0.494872 1.39971i
\(64\) 0 0
\(65\) 16.9706i 0.261086i
\(66\) 0 0
\(67\) 114.315 1.70620 0.853100 0.521748i \(-0.174720\pi\)
0.853100 + 0.521748i \(0.174720\pi\)
\(68\) 0 0
\(69\) 72.0000 + 50.9117i 1.04348 + 0.737851i
\(70\) 0 0
\(71\) 29.3939i 0.413998i −0.978341 0.206999i \(-0.933630\pi\)
0.978341 0.206999i \(-0.0663697\pi\)
\(72\) 0 0
\(73\) −30.0000 −0.410959 −0.205479 0.978661i \(-0.565875\pi\)
−0.205479 + 0.978661i \(0.565875\pi\)
\(74\) 0 0
\(75\) 29.4449 41.6413i 0.392598 0.555218i
\(76\) 0 0
\(77\) 152.735i 1.98357i
\(78\) 0 0
\(79\) −31.1769 −0.394644 −0.197322 0.980339i \(-0.563225\pi\)
−0.197322 + 0.980339i \(0.563225\pi\)
\(80\) 0 0
\(81\) −63.0000 + 50.9117i −0.777778 + 0.628539i
\(82\) 0 0
\(83\) 73.4847i 0.885358i 0.896680 + 0.442679i \(0.145972\pi\)
−0.896680 + 0.442679i \(0.854028\pi\)
\(84\) 0 0
\(85\) −64.0000 −0.752941
\(86\) 0 0
\(87\) 76.2102 + 53.8888i 0.875980 + 0.619411i
\(88\) 0 0
\(89\) 5.65685i 0.0635602i −0.999495 0.0317801i \(-0.989882\pi\)
0.999495 0.0317801i \(-0.0101176\pi\)
\(90\) 0 0
\(91\) −62.3538 −0.685207
\(92\) 0 0
\(93\) −54.0000 + 76.3675i −0.580645 + 0.821156i
\(94\) 0 0
\(95\) 29.3939i 0.309409i
\(96\) 0 0
\(97\) 90.0000 0.927835 0.463918 0.885878i \(-0.346443\pi\)
0.463918 + 0.885878i \(0.346443\pi\)
\(98\) 0 0
\(99\) −124.708 + 44.0908i −1.25967 + 0.445362i
\(100\) 0 0
\(101\) 2.82843i 0.0280042i 0.999902 + 0.0140021i \(0.00445716\pi\)
−0.999902 + 0.0140021i \(0.995543\pi\)
\(102\) 0 0
\(103\) −72.7461 −0.706273 −0.353137 0.935572i \(-0.614885\pi\)
−0.353137 + 0.935572i \(0.614885\pi\)
\(104\) 0 0
\(105\) 72.0000 + 50.9117i 0.685714 + 0.484873i
\(106\) 0 0
\(107\) 73.4847i 0.686773i −0.939194 0.343386i \(-0.888426\pi\)
0.939194 0.343386i \(-0.111574\pi\)
\(108\) 0 0
\(109\) 138.000 1.26606 0.633028 0.774129i \(-0.281812\pi\)
0.633028 + 0.774129i \(0.281812\pi\)
\(110\) 0 0
\(111\) −65.8179 + 93.0806i −0.592954 + 0.838564i
\(112\) 0 0
\(113\) 192.333i 1.70206i −0.525115 0.851031i \(-0.675978\pi\)
0.525115 0.851031i \(-0.324022\pi\)
\(114\) 0 0
\(115\) −83.1384 −0.722943
\(116\) 0 0
\(117\) 18.0000 + 50.9117i 0.153846 + 0.435143i
\(118\) 0 0
\(119\) 235.151i 1.97606i
\(120\) 0 0
\(121\) −95.0000 −0.785124
\(122\) 0 0
\(123\) −13.8564 9.79796i −0.112654 0.0796582i
\(124\) 0 0
\(125\) 118.794i 0.950352i
\(126\) 0 0
\(127\) 51.9615 0.409146 0.204573 0.978851i \(-0.434419\pi\)
0.204573 + 0.978851i \(0.434419\pi\)
\(128\) 0 0
\(129\) −18.0000 + 25.4558i −0.139535 + 0.197332i
\(130\) 0 0
\(131\) 44.0908i 0.336571i −0.985738 0.168286i \(-0.946177\pi\)
0.985738 0.168286i \(-0.0538231\pi\)
\(132\) 0 0
\(133\) −108.000 −0.812030
\(134\) 0 0
\(135\) 20.7846 73.4847i 0.153960 0.544331i
\(136\) 0 0
\(137\) 39.5980i 0.289036i 0.989502 + 0.144518i \(0.0461632\pi\)
−0.989502 + 0.144518i \(0.953837\pi\)
\(138\) 0 0
\(139\) −135.100 −0.971942 −0.485971 0.873975i \(-0.661534\pi\)
−0.485971 + 0.873975i \(0.661534\pi\)
\(140\) 0 0
\(141\) −144.000 101.823i −1.02128 0.722152i
\(142\) 0 0
\(143\) 88.1816i 0.616655i
\(144\) 0 0
\(145\) −88.0000 −0.606897
\(146\) 0 0
\(147\) 102.191 144.520i 0.695177 0.983129i
\(148\) 0 0
\(149\) 189.505i 1.27184i −0.771754 0.635922i \(-0.780620\pi\)
0.771754 0.635922i \(-0.219380\pi\)
\(150\) 0 0
\(151\) 176.669 1.16999 0.584997 0.811035i \(-0.301096\pi\)
0.584997 + 0.811035i \(0.301096\pi\)
\(152\) 0 0
\(153\) 192.000 67.8823i 1.25490 0.443675i
\(154\) 0 0
\(155\) 88.1816i 0.568914i
\(156\) 0 0
\(157\) 154.000 0.980892 0.490446 0.871472i \(-0.336834\pi\)
0.490446 + 0.871472i \(0.336834\pi\)
\(158\) 0 0
\(159\) 34.6410 + 24.4949i 0.217868 + 0.154056i
\(160\) 0 0
\(161\) 305.470i 1.89733i
\(162\) 0 0
\(163\) 72.7461 0.446295 0.223148 0.974785i \(-0.428367\pi\)
0.223148 + 0.974785i \(0.428367\pi\)
\(164\) 0 0
\(165\) 72.0000 101.823i 0.436364 0.617111i
\(166\) 0 0
\(167\) 264.545i 1.58410i −0.610455 0.792051i \(-0.709014\pi\)
0.610455 0.792051i \(-0.290986\pi\)
\(168\) 0 0
\(169\) −133.000 −0.786982
\(170\) 0 0
\(171\) 31.1769 + 88.1816i 0.182321 + 0.515682i
\(172\) 0 0
\(173\) 223.446i 1.29159i 0.763509 + 0.645797i \(0.223475\pi\)
−0.763509 + 0.645797i \(0.776525\pi\)
\(174\) 0 0
\(175\) 176.669 1.00954
\(176\) 0 0
\(177\) −36.0000 25.4558i −0.203390 0.143818i
\(178\) 0 0
\(179\) 102.879i 0.574741i −0.957820 0.287370i \(-0.907219\pi\)
0.957820 0.287370i \(-0.0927810\pi\)
\(180\) 0 0
\(181\) 234.000 1.29282 0.646409 0.762991i \(-0.276270\pi\)
0.646409 + 0.762991i \(0.276270\pi\)
\(182\) 0 0
\(183\) −38.1051 + 53.8888i −0.208225 + 0.294474i
\(184\) 0 0
\(185\) 107.480i 0.580974i
\(186\) 0 0
\(187\) 332.554 1.77836
\(188\) 0 0
\(189\) −270.000 76.3675i −1.42857 0.404061i
\(190\) 0 0
\(191\) 117.576i 0.615579i −0.951455 0.307789i \(-0.900411\pi\)
0.951455 0.307789i \(-0.0995892\pi\)
\(192\) 0 0
\(193\) 82.0000 0.424870 0.212435 0.977175i \(-0.431861\pi\)
0.212435 + 0.977175i \(0.431861\pi\)
\(194\) 0 0
\(195\) −41.5692 29.3939i −0.213175 0.150738i
\(196\) 0 0
\(197\) 206.475i 1.04810i 0.851688 + 0.524049i \(0.175579\pi\)
−0.851688 + 0.524049i \(0.824421\pi\)
\(198\) 0 0
\(199\) −322.161 −1.61890 −0.809451 0.587188i \(-0.800235\pi\)
−0.809451 + 0.587188i \(0.800235\pi\)
\(200\) 0 0
\(201\) 198.000 280.014i 0.985075 1.39311i
\(202\) 0 0
\(203\) 323.333i 1.59277i
\(204\) 0 0
\(205\) 16.0000 0.0780488
\(206\) 0 0
\(207\) 249.415 88.1816i 1.20490 0.425998i
\(208\) 0 0
\(209\) 152.735i 0.730790i
\(210\) 0 0
\(211\) −135.100 −0.640284 −0.320142 0.947370i \(-0.603731\pi\)
−0.320142 + 0.947370i \(0.603731\pi\)
\(212\) 0 0
\(213\) −72.0000 50.9117i −0.338028 0.239022i
\(214\) 0 0
\(215\) 29.3939i 0.136716i
\(216\) 0 0
\(217\) −324.000 −1.49309
\(218\) 0 0
\(219\) −51.9615 + 73.4847i −0.237267 + 0.335547i
\(220\) 0 0
\(221\) 135.765i 0.614319i
\(222\) 0 0
\(223\) −363.731 −1.63108 −0.815540 0.578701i \(-0.803560\pi\)
−0.815540 + 0.578701i \(0.803560\pi\)
\(224\) 0 0
\(225\) −51.0000 144.250i −0.226667 0.641110i
\(226\) 0 0
\(227\) 14.6969i 0.0647442i 0.999476 + 0.0323721i \(0.0103062\pi\)
−0.999476 + 0.0323721i \(0.989694\pi\)
\(228\) 0 0
\(229\) −246.000 −1.07424 −0.537118 0.843507i \(-0.680487\pi\)
−0.537118 + 0.843507i \(0.680487\pi\)
\(230\) 0 0
\(231\) −374.123 264.545i −1.61958 1.14522i
\(232\) 0 0
\(233\) 209.304i 0.898299i 0.893457 + 0.449149i \(0.148273\pi\)
−0.893457 + 0.449149i \(0.851727\pi\)
\(234\) 0 0
\(235\) 166.277 0.707561
\(236\) 0 0
\(237\) −54.0000 + 76.3675i −0.227848 + 0.322226i
\(238\) 0 0
\(239\) 411.514i 1.72182i 0.508760 + 0.860909i \(0.330104\pi\)
−0.508760 + 0.860909i \(0.669896\pi\)
\(240\) 0 0
\(241\) 210.000 0.871369 0.435685 0.900099i \(-0.356506\pi\)
0.435685 + 0.900099i \(0.356506\pi\)
\(242\) 0 0
\(243\) 15.5885 + 242.499i 0.0641500 + 0.997940i
\(244\) 0 0
\(245\) 166.877i 0.681131i
\(246\) 0 0
\(247\) 62.3538 0.252445
\(248\) 0 0
\(249\) 180.000 + 127.279i 0.722892 + 0.511162i
\(250\) 0 0
\(251\) 396.817i 1.58095i 0.612497 + 0.790473i \(0.290165\pi\)
−0.612497 + 0.790473i \(0.709835\pi\)
\(252\) 0 0
\(253\) 432.000 1.70751
\(254\) 0 0
\(255\) −110.851 + 156.767i −0.434711 + 0.614774i
\(256\) 0 0
\(257\) 384.666i 1.49676i −0.663273 0.748378i \(-0.730833\pi\)
0.663273 0.748378i \(-0.269167\pi\)
\(258\) 0 0
\(259\) −394.908 −1.52474
\(260\) 0 0
\(261\) 264.000 93.3381i 1.01149 0.357617i
\(262\) 0 0
\(263\) 499.696i 1.89998i −0.312274 0.949992i \(-0.601091\pi\)
0.312274 0.949992i \(-0.398909\pi\)
\(264\) 0 0
\(265\) −40.0000 −0.150943
\(266\) 0 0
\(267\) −13.8564 9.79796i −0.0518967 0.0366965i
\(268\) 0 0
\(269\) 19.7990i 0.0736022i 0.999323 + 0.0368011i \(0.0117168\pi\)
−0.999323 + 0.0368011i \(0.988283\pi\)
\(270\) 0 0
\(271\) 135.100 0.498524 0.249262 0.968436i \(-0.419812\pi\)
0.249262 + 0.968436i \(0.419812\pi\)
\(272\) 0 0
\(273\) −108.000 + 152.735i −0.395604 + 0.559469i
\(274\) 0 0
\(275\) 249.848i 0.908538i
\(276\) 0 0
\(277\) −198.000 −0.714801 −0.357401 0.933951i \(-0.616337\pi\)
−0.357401 + 0.933951i \(0.616337\pi\)
\(278\) 0 0
\(279\) 93.5307 + 264.545i 0.335236 + 0.948190i
\(280\) 0 0
\(281\) 197.990i 0.704590i 0.935889 + 0.352295i \(0.114599\pi\)
−0.935889 + 0.352295i \(0.885401\pi\)
\(282\) 0 0
\(283\) −51.9615 −0.183610 −0.0918048 0.995777i \(-0.529264\pi\)
−0.0918048 + 0.995777i \(0.529264\pi\)
\(284\) 0 0
\(285\) −72.0000 50.9117i −0.252632 0.178638i
\(286\) 0 0
\(287\) 58.7878i 0.204835i
\(288\) 0 0
\(289\) −223.000 −0.771626
\(290\) 0 0
\(291\) 155.885 220.454i 0.535686 0.757574i
\(292\) 0 0
\(293\) 359.210i 1.22597i −0.790093 0.612987i \(-0.789968\pi\)
0.790093 0.612987i \(-0.210032\pi\)
\(294\) 0 0
\(295\) 41.5692 0.140913
\(296\) 0 0
\(297\) −108.000 + 381.838i −0.363636 + 1.28565i
\(298\) 0 0
\(299\) 176.363i 0.589844i
\(300\) 0 0
\(301\) −108.000 −0.358804
\(302\) 0 0
\(303\) 6.92820 + 4.89898i 0.0228654 + 0.0161682i
\(304\) 0 0
\(305\) 62.2254i 0.204018i
\(306\) 0 0
\(307\) 197.454 0.643172 0.321586 0.946880i \(-0.395784\pi\)
0.321586 + 0.946880i \(0.395784\pi\)
\(308\) 0 0
\(309\) −126.000 + 178.191i −0.407767 + 0.576670i
\(310\) 0 0
\(311\) 264.545i 0.850627i 0.905046 + 0.425313i \(0.139836\pi\)
−0.905046 + 0.425313i \(0.860164\pi\)
\(312\) 0 0
\(313\) 266.000 0.849840 0.424920 0.905231i \(-0.360302\pi\)
0.424920 + 0.905231i \(0.360302\pi\)
\(314\) 0 0
\(315\) 249.415 88.1816i 0.791795 0.279942i
\(316\) 0 0
\(317\) 421.436i 1.32945i −0.747088 0.664725i \(-0.768549\pi\)
0.747088 0.664725i \(-0.231451\pi\)
\(318\) 0 0
\(319\) 457.261 1.43342
\(320\) 0 0
\(321\) −180.000 127.279i −0.560748 0.396508i
\(322\) 0 0
\(323\) 235.151i 0.728022i
\(324\) 0 0
\(325\) −102.000 −0.313846
\(326\) 0 0
\(327\) 239.023 338.030i 0.730957 1.03373i
\(328\) 0 0
\(329\) 610.940i 1.85696i
\(330\) 0 0
\(331\) 197.454 0.596537 0.298269 0.954482i \(-0.403591\pi\)
0.298269 + 0.954482i \(0.403591\pi\)
\(332\) 0 0
\(333\) 114.000 + 322.441i 0.342342 + 0.968290i
\(334\) 0 0
\(335\) 323.333i 0.965172i
\(336\) 0 0
\(337\) 522.000 1.54896 0.774481 0.632598i \(-0.218011\pi\)
0.774481 + 0.632598i \(0.218011\pi\)
\(338\) 0 0
\(339\) −471.118 333.131i −1.38973 0.982686i
\(340\) 0 0
\(341\) 458.205i 1.34371i
\(342\) 0 0
\(343\) 103.923 0.302983
\(344\) 0 0
\(345\) −144.000 + 203.647i −0.417391 + 0.590280i
\(346\) 0 0
\(347\) 426.211i 1.22827i −0.789199 0.614137i \(-0.789504\pi\)
0.789199 0.614137i \(-0.210496\pi\)
\(348\) 0 0
\(349\) −166.000 −0.475645 −0.237822 0.971309i \(-0.576434\pi\)
−0.237822 + 0.971309i \(0.576434\pi\)
\(350\) 0 0
\(351\) 155.885 + 44.0908i 0.444116 + 0.125615i
\(352\) 0 0
\(353\) 22.6274i 0.0641003i −0.999486 0.0320502i \(-0.989796\pi\)
0.999486 0.0320502i \(-0.0102036\pi\)
\(354\) 0 0
\(355\) 83.1384 0.234193
\(356\) 0 0
\(357\) 576.000 + 407.294i 1.61345 + 1.14088i
\(358\) 0 0
\(359\) 88.1816i 0.245631i 0.992430 + 0.122816i \(0.0391924\pi\)
−0.992430 + 0.122816i \(0.960808\pi\)
\(360\) 0 0
\(361\) −253.000 −0.700831
\(362\) 0 0
\(363\) −164.545 + 232.702i −0.453292 + 0.641051i
\(364\) 0 0
\(365\) 84.8528i 0.232473i
\(366\) 0 0
\(367\) 135.100 0.368120 0.184060 0.982915i \(-0.441076\pi\)
0.184060 + 0.982915i \(0.441076\pi\)
\(368\) 0 0
\(369\) −48.0000 + 16.9706i −0.130081 + 0.0459907i
\(370\) 0 0
\(371\) 146.969i 0.396144i
\(372\) 0 0
\(373\) −118.000 −0.316354 −0.158177 0.987411i \(-0.550562\pi\)
−0.158177 + 0.987411i \(0.550562\pi\)
\(374\) 0 0
\(375\) 290.985 + 205.757i 0.775959 + 0.548686i
\(376\) 0 0
\(377\) 186.676i 0.495162i
\(378\) 0 0
\(379\) −592.361 −1.56296 −0.781479 0.623931i \(-0.785535\pi\)
−0.781479 + 0.623931i \(0.785535\pi\)
\(380\) 0 0
\(381\) 90.0000 127.279i 0.236220 0.334066i
\(382\) 0 0
\(383\) 352.727i 0.920957i −0.887671 0.460478i \(-0.847678\pi\)
0.887671 0.460478i \(-0.152322\pi\)
\(384\) 0 0
\(385\) 432.000 1.12208
\(386\) 0 0
\(387\) 31.1769 + 88.1816i 0.0805605 + 0.227860i
\(388\) 0 0
\(389\) 359.210i 0.923420i −0.887031 0.461710i \(-0.847236\pi\)
0.887031 0.461710i \(-0.152764\pi\)
\(390\) 0 0
\(391\) −665.108 −1.70104
\(392\) 0 0
\(393\) −108.000 76.3675i −0.274809 0.194319i
\(394\) 0 0
\(395\) 88.1816i 0.223245i
\(396\) 0 0
\(397\) −214.000 −0.539043 −0.269521 0.962994i \(-0.586865\pi\)
−0.269521 + 0.962994i \(0.586865\pi\)
\(398\) 0 0
\(399\) −187.061 + 264.545i −0.468826 + 0.663020i
\(400\) 0 0
\(401\) 226.274i 0.564275i 0.959374 + 0.282137i \(0.0910434\pi\)
−0.959374 + 0.282137i \(0.908957\pi\)
\(402\) 0 0
\(403\) 187.061 0.464172
\(404\) 0 0
\(405\) −144.000 178.191i −0.355556 0.439978i
\(406\) 0 0
\(407\) 558.484i 1.37220i
\(408\) 0 0
\(409\) 114.000 0.278729 0.139364 0.990241i \(-0.455494\pi\)
0.139364 + 0.990241i \(0.455494\pi\)
\(410\) 0 0
\(411\) 96.9948 + 68.5857i 0.235997 + 0.166875i
\(412\) 0 0
\(413\) 152.735i 0.369819i
\(414\) 0 0
\(415\) −207.846 −0.500834
\(416\) 0 0
\(417\) −234.000 + 330.926i −0.561151 + 0.793587i
\(418\) 0 0
\(419\) 367.423i 0.876906i 0.898754 + 0.438453i \(0.144473\pi\)
−0.898754 + 0.438453i \(0.855527\pi\)
\(420\) 0 0
\(421\) −534.000 −1.26841 −0.634204 0.773166i \(-0.718672\pi\)
−0.634204 + 0.773166i \(0.718672\pi\)
\(422\) 0 0
\(423\) −498.831 + 176.363i −1.17927 + 0.416934i
\(424\) 0 0
\(425\) 384.666i 0.905097i
\(426\) 0 0
\(427\) −228.631 −0.535435
\(428\) 0 0
\(429\) 216.000 + 152.735i 0.503497 + 0.356026i
\(430\) 0 0
\(431\) 293.939i 0.681993i −0.940065 0.340996i \(-0.889236\pi\)
0.940065 0.340996i \(-0.110764\pi\)
\(432\) 0 0
\(433\) −614.000 −1.41801 −0.709007 0.705202i \(-0.750857\pi\)
−0.709007 + 0.705202i \(0.750857\pi\)
\(434\) 0 0
\(435\) −152.420 + 215.555i −0.350392 + 0.495529i
\(436\) 0 0
\(437\) 305.470i 0.699016i
\(438\) 0 0
\(439\) 342.946 0.781198 0.390599 0.920561i \(-0.372268\pi\)
0.390599 + 0.920561i \(0.372268\pi\)
\(440\) 0 0
\(441\) −177.000 500.632i −0.401361 1.13522i
\(442\) 0 0
\(443\) 514.393i 1.16116i 0.814204 + 0.580579i \(0.197174\pi\)
−0.814204 + 0.580579i \(0.802826\pi\)
\(444\) 0 0
\(445\) 16.0000 0.0359551
\(446\) 0 0
\(447\) −464.190 328.232i −1.03846 0.734299i
\(448\) 0 0
\(449\) 214.960i 0.478754i 0.970927 + 0.239377i \(0.0769432\pi\)
−0.970927 + 0.239377i \(0.923057\pi\)
\(450\) 0 0
\(451\) −83.1384 −0.184342
\(452\) 0 0
\(453\) 306.000 432.749i 0.675497 0.955297i
\(454\) 0 0
\(455\) 176.363i 0.387612i
\(456\) 0 0
\(457\) 786.000 1.71991 0.859956 0.510368i \(-0.170491\pi\)
0.859956 + 0.510368i \(0.170491\pi\)
\(458\) 0 0
\(459\) 166.277 587.878i 0.362259 1.28078i
\(460\) 0 0
\(461\) 811.759i 1.76086i 0.474172 + 0.880432i \(0.342748\pi\)
−0.474172 + 0.880432i \(0.657252\pi\)
\(462\) 0 0
\(463\) −446.869 −0.965160 −0.482580 0.875852i \(-0.660300\pi\)
−0.482580 + 0.875852i \(0.660300\pi\)
\(464\) 0 0
\(465\) −216.000 152.735i −0.464516 0.328463i
\(466\) 0 0
\(467\) 426.211i 0.912658i 0.889811 + 0.456329i \(0.150836\pi\)
−0.889811 + 0.456329i \(0.849164\pi\)
\(468\) 0 0
\(469\) 1188.00 2.53305
\(470\) 0 0
\(471\) 266.736 377.221i 0.566318 0.800895i
\(472\) 0 0
\(473\) 152.735i 0.322907i
\(474\) 0 0
\(475\) −176.669 −0.371935
\(476\) 0 0
\(477\) 120.000 42.4264i 0.251572 0.0889442i
\(478\) 0 0
\(479\) 117.576i 0.245460i −0.992440 0.122730i \(-0.960835\pi\)
0.992440 0.122730i \(-0.0391650\pi\)
\(480\) 0 0
\(481\) 228.000 0.474012
\(482\) 0 0
\(483\) 748.246 + 529.090i 1.54916 + 1.09542i
\(484\) 0 0
\(485\) 254.558i 0.524863i
\(486\) 0 0
\(487\) 426.084 0.874917 0.437458 0.899239i \(-0.355879\pi\)
0.437458 + 0.899239i \(0.355879\pi\)
\(488\) 0 0
\(489\) 126.000 178.191i 0.257669 0.364399i
\(490\) 0 0
\(491\) 191.060i 0.389125i −0.980890 0.194562i \(-0.937671\pi\)
0.980890 0.194562i \(-0.0623286\pi\)
\(492\) 0 0
\(493\) −704.000 −1.42799
\(494\) 0 0
\(495\) −124.708 352.727i −0.251935 0.712579i
\(496\) 0 0
\(497\) 305.470i 0.614628i
\(498\) 0 0
\(499\) 862.561 1.72858 0.864290 0.502994i \(-0.167768\pi\)
0.864290 + 0.502994i \(0.167768\pi\)
\(500\) 0 0
\(501\) −648.000 458.205i −1.29341 0.914581i
\(502\) 0 0
\(503\) 205.757i 0.409060i −0.978860 0.204530i \(-0.934433\pi\)
0.978860 0.204530i \(-0.0655666\pi\)
\(504\) 0 0
\(505\) −8.00000 −0.0158416
\(506\) 0 0
\(507\) −230.363 + 325.782i −0.454364 + 0.642568i
\(508\) 0 0
\(509\) 845.700i 1.66149i 0.556651 + 0.830746i \(0.312086\pi\)
−0.556651 + 0.830746i \(0.687914\pi\)
\(510\) 0 0
\(511\) −311.769 −0.610116
\(512\) 0 0
\(513\) 270.000 + 76.3675i 0.526316 + 0.148865i
\(514\) 0 0
\(515\) 205.757i 0.399528i
\(516\) 0 0
\(517\) −864.000 −1.67118
\(518\) 0 0
\(519\) 547.328 + 387.019i 1.05458 + 0.745702i
\(520\) 0 0
\(521\) 39.5980i 0.0760038i 0.999278 + 0.0380019i \(0.0120993\pi\)
−0.999278 + 0.0380019i \(0.987901\pi\)
\(522\) 0 0
\(523\) 654.715 1.25185 0.625923 0.779885i \(-0.284723\pi\)
0.625923 + 0.779885i \(0.284723\pi\)
\(524\) 0 0
\(525\) 306.000 432.749i 0.582857 0.824284i
\(526\) 0 0
\(527\) 705.453i 1.33862i
\(528\) 0 0
\(529\) −335.000 −0.633270
\(530\) 0 0
\(531\) −124.708 + 44.0908i −0.234854 + 0.0830336i
\(532\) 0 0
\(533\) 33.9411i 0.0636794i
\(534\) 0 0
\(535\) 207.846 0.388497
\(536\) 0 0
\(537\) −252.000 178.191i −0.469274 0.331827i
\(538\) 0 0
\(539\) 867.119i 1.60876i
\(540\) 0 0
\(541\) 330.000 0.609982 0.304991 0.952355i \(-0.401347\pi\)
0.304991 + 0.952355i \(0.401347\pi\)
\(542\) 0 0
\(543\) 405.300 573.181i 0.746409 1.05558i
\(544\) 0 0
\(545\) 390.323i 0.716189i
\(546\) 0 0
\(547\) −93.5307 −0.170989 −0.0854943 0.996339i \(-0.527247\pi\)
−0.0854943 + 0.996339i \(0.527247\pi\)
\(548\) 0 0
\(549\) 66.0000 + 186.676i 0.120219 + 0.340029i
\(550\) 0 0
\(551\) 323.333i 0.586811i
\(552\) 0 0
\(553\) −324.000 −0.585895
\(554\) 0 0
\(555\) −263.272 186.161i −0.474363 0.335426i
\(556\) 0 0
\(557\) 613.769i 1.10192i −0.834532 0.550959i \(-0.814262\pi\)
0.834532 0.550959i \(-0.185738\pi\)
\(558\) 0 0
\(559\) 62.3538 0.111545
\(560\) 0 0
\(561\) 576.000 814.587i 1.02674 1.45203i
\(562\) 0 0
\(563\) 543.787i 0.965873i 0.875655 + 0.482937i \(0.160430\pi\)
−0.875655 + 0.482937i \(0.839570\pi\)
\(564\) 0 0
\(565\) 544.000 0.962832
\(566\) 0 0
\(567\) −654.715 + 529.090i −1.15470 + 0.933139i
\(568\) 0 0
\(569\) 5.65685i 0.00994175i 0.999988 + 0.00497087i \(0.00158228\pi\)
−0.999988 + 0.00497087i \(0.998418\pi\)
\(570\) 0 0
\(571\) 613.146 1.07381 0.536905 0.843642i \(-0.319593\pi\)
0.536905 + 0.843642i \(0.319593\pi\)
\(572\) 0 0
\(573\) −288.000 203.647i −0.502618 0.355404i
\(574\) 0 0
\(575\) 499.696i 0.869036i
\(576\) 0 0
\(577\) −502.000 −0.870017 −0.435009 0.900426i \(-0.643255\pi\)
−0.435009 + 0.900426i \(0.643255\pi\)
\(578\) 0 0
\(579\) 142.028 200.858i 0.245299 0.346905i
\(580\) 0 0
\(581\) 763.675i 1.31442i
\(582\) 0 0
\(583\) 207.846 0.356511
\(584\) 0 0
\(585\) −144.000 + 50.9117i −0.246154 + 0.0870285i
\(586\) 0 0
\(587\) 44.0908i 0.0751121i 0.999295 + 0.0375561i \(0.0119573\pi\)
−0.999295 + 0.0375561i \(0.988043\pi\)
\(588\) 0 0
\(589\) 324.000 0.550085
\(590\) 0 0
\(591\) 505.759 + 357.626i 0.855768 + 0.605119i
\(592\) 0 0
\(593\) 260.215i 0.438812i 0.975634 + 0.219406i \(0.0704119\pi\)
−0.975634 + 0.219406i \(0.929588\pi\)
\(594\) 0 0
\(595\) −665.108 −1.11783
\(596\) 0 0
\(597\) −558.000 + 789.131i −0.934673 + 1.32183i
\(598\) 0 0
\(599\) 734.847i 1.22679i 0.789776 + 0.613395i \(0.210197\pi\)
−0.789776 + 0.613395i \(0.789803\pi\)
\(600\) 0 0
\(601\) 130.000 0.216306 0.108153 0.994134i \(-0.465506\pi\)
0.108153 + 0.994134i \(0.465506\pi\)
\(602\) 0 0
\(603\) −342.946 969.998i −0.568733 1.60862i
\(604\) 0 0
\(605\) 268.701i 0.444133i
\(606\) 0 0
\(607\) −613.146 −1.01013 −0.505063 0.863083i \(-0.668531\pi\)
−0.505063 + 0.863083i \(0.668531\pi\)
\(608\) 0 0
\(609\) 792.000 + 560.029i 1.30049 + 0.919587i
\(610\) 0 0
\(611\) 352.727i 0.577294i
\(612\) 0 0
\(613\) 794.000 1.29527 0.647635 0.761951i \(-0.275758\pi\)
0.647635 + 0.761951i \(0.275758\pi\)
\(614\) 0 0
\(615\) 27.7128 39.1918i 0.0450615 0.0637266i
\(616\) 0 0
\(617\) 639.225i 1.03602i 0.855374 + 0.518010i \(0.173327\pi\)
−0.855374 + 0.518010i \(0.826673\pi\)
\(618\) 0 0
\(619\) −966.484 −1.56136 −0.780682 0.624928i \(-0.785128\pi\)
−0.780682 + 0.624928i \(0.785128\pi\)
\(620\) 0 0
\(621\) 216.000 763.675i 0.347826 1.22975i
\(622\) 0 0
\(623\) 58.7878i 0.0943624i
\(624\) 0 0
\(625\) 89.0000 0.142400
\(626\) 0 0
\(627\) 374.123 + 264.545i 0.596687 + 0.421922i
\(628\) 0 0
\(629\) 859.842i 1.36700i
\(630\) 0 0
\(631\) 93.5307 0.148226 0.0741131 0.997250i \(-0.476387\pi\)
0.0741131 + 0.997250i \(0.476387\pi\)
\(632\) 0 0
\(633\) −234.000 + 330.926i −0.369668 + 0.522790i
\(634\) 0 0
\(635\) 146.969i 0.231448i
\(636\) 0 0
\(637\) −354.000 −0.555730
\(638\) 0 0
\(639\) −249.415 + 88.1816i −0.390321 + 0.137999i
\(640\) 0 0
\(641\) 622.254i 0.970755i −0.874305 0.485378i \(-0.838682\pi\)
0.874305 0.485378i \(-0.161318\pi\)
\(642\) 0 0
\(643\) −592.361 −0.921246 −0.460623 0.887596i \(-0.652374\pi\)
−0.460623 + 0.887596i \(0.652374\pi\)
\(644\) 0 0
\(645\) −72.0000 50.9117i −0.111628 0.0789328i
\(646\) 0 0
\(647\) 1263.94i 1.95353i 0.214303 + 0.976767i \(0.431252\pi\)
−0.214303 + 0.976767i \(0.568748\pi\)
\(648\) 0 0
\(649\) −216.000 −0.332820
\(650\) 0 0
\(651\) −561.184 + 793.635i −0.862035 + 1.21910i
\(652\) 0 0
\(653\) 591.141i 0.905270i −0.891696 0.452635i \(-0.850484\pi\)
0.891696 0.452635i \(-0.149516\pi\)
\(654\) 0 0
\(655\) 124.708 0.190393
\(656\) 0 0
\(657\) 90.0000 + 254.558i 0.136986 + 0.387456i
\(658\) 0 0
\(659\) 1161.06i 1.76185i −0.473257 0.880924i \(-0.656922\pi\)
0.473257 0.880924i \(-0.343078\pi\)
\(660\) 0 0
\(661\) 442.000 0.668684 0.334342 0.942452i \(-0.391486\pi\)
0.334342 + 0.942452i \(0.391486\pi\)
\(662\) 0 0
\(663\) −332.554 235.151i −0.501589 0.354677i
\(664\) 0 0
\(665\) 305.470i 0.459354i
\(666\) 0 0
\(667\) −914.523 −1.37110
\(668\) 0 0
\(669\) −630.000 + 890.955i −0.941704 + 1.33177i
\(670\) 0 0
\(671\) 323.333i 0.481867i
\(672\) 0 0
\(673\) −742.000 −1.10253 −0.551263 0.834332i \(-0.685854\pi\)
−0.551263 + 0.834332i \(0.685854\pi\)
\(674\) 0 0
\(675\) −441.673 124.924i −0.654330 0.185073i
\(676\) 0 0
\(677\) 2.82843i 0.00417788i 0.999998 + 0.00208894i \(0.000664931\pi\)
−0.999998 + 0.00208894i \(0.999335\pi\)
\(678\) 0 0
\(679\) 935.307 1.37748
\(680\) 0 0
\(681\) 36.0000 + 25.4558i 0.0528634 + 0.0373801i
\(682\) 0 0
\(683\) 249.848i 0.365810i −0.983131 0.182905i \(-0.941450\pi\)
0.983131 0.182905i \(-0.0585500\pi\)
\(684\) 0 0
\(685\) −112.000 −0.163504
\(686\) 0 0
\(687\) −426.084 + 602.574i −0.620210 + 0.877110i
\(688\) 0 0
\(689\) 84.8528i 0.123154i
\(690\) 0 0
\(691\) 322.161 0.466225 0.233112 0.972450i \(-0.425109\pi\)
0.233112 + 0.972450i \(0.425109\pi\)
\(692\) 0 0
\(693\) −1296.00 + 458.205i −1.87013 + 0.661191i
\(694\) 0 0
\(695\) 382.120i 0.549814i
\(696\) 0 0
\(697\) 128.000 0.183644
\(698\) 0 0
\(699\) 512.687 + 362.524i 0.733458 + 0.518633i
\(700\) 0 0
\(701\) 234.759i 0.334892i 0.985881 + 0.167446i \(0.0535520\pi\)
−0.985881 + 0.167446i \(0.946448\pi\)
\(702\) 0 0
\(703\) 394.908 0.561746
\(704\) 0 0
\(705\) 288.000 407.294i 0.408511 0.577721i
\(706\) 0 0
\(707\) 29.3939i 0.0415755i
\(708\) 0 0
\(709\) −102.000 −0.143865 −0.0719323 0.997410i \(-0.522917\pi\)
−0.0719323 + 0.997410i \(0.522917\pi\)
\(710\) 0 0
\(711\) 93.5307 + 264.545i 0.131548 + 0.372074i
\(712\) 0 0
\(713\) 916.410i 1.28529i
\(714\) 0 0
\(715\) −249.415 −0.348833
\(716\) 0 0
\(717\) 1008.00 + 712.764i 1.40586 + 0.994092i
\(718\) 0 0
\(719\) 529.090i 0.735869i −0.929852 0.367934i \(-0.880065\pi\)
0.929852 0.367934i \(-0.119935\pi\)
\(720\) 0 0
\(721\) −756.000 −1.04854
\(722\) 0 0
\(723\) 363.731 514.393i 0.503085 0.711470i
\(724\) 0 0
\(725\) 528.916i 0.729539i
\(726\) 0 0
\(727\) −1070.41 −1.47236 −0.736181 0.676785i \(-0.763373\pi\)
−0.736181 + 0.676785i \(0.763373\pi\)
\(728\) 0 0
\(729\) 621.000 + 381.838i 0.851852 + 0.523783i
\(730\) 0 0
\(731\) 235.151i 0.321684i
\(732\) 0 0
\(733\) 378.000 0.515689 0.257844 0.966186i \(-0.416988\pi\)
0.257844 + 0.966186i \(0.416988\pi\)
\(734\) 0 0
\(735\) 408.764 + 289.040i 0.556141 + 0.393251i
\(736\) 0 0
\(737\) 1680.09i 2.27963i
\(738\) 0 0
\(739\) 1111.98 1.50470 0.752352 0.658761i \(-0.228919\pi\)
0.752352 + 0.658761i \(0.228919\pi\)
\(740\) 0 0
\(741\) 108.000 152.735i 0.145749 0.206120i
\(742\) 0 0
\(743\) 205.757i 0.276928i 0.990368 + 0.138464i \(0.0442164\pi\)
−0.990368 + 0.138464i \(0.955784\pi\)
\(744\) 0 0
\(745\) 536.000 0.719463
\(746\) 0 0
\(747\) 623.538 220.454i 0.834723 0.295119i
\(748\) 0 0
\(749\) 763.675i 1.01959i
\(750\) 0 0
\(751\) 218.238 0.290597 0.145299 0.989388i \(-0.453586\pi\)
0.145299 + 0.989388i \(0.453586\pi\)
\(752\) 0 0
\(753\) 972.000 + 687.308i 1.29084 + 0.912759i
\(754\) 0 0
\(755\) 499.696i 0.661849i
\(756\) 0 0
\(757\) 1098.00 1.45046 0.725231 0.688505i \(-0.241733\pi\)
0.725231 + 0.688505i \(0.241733\pi\)
\(758\) 0 0
\(759\) 748.246 1058.18i 0.985831 1.39418i
\(760\) 0 0
\(761\) 1250.16i 1.64279i 0.570358 + 0.821396i \(0.306804\pi\)
−0.570358 + 0.821396i \(0.693196\pi\)
\(762\) 0 0
\(763\) 1434.14 1.87960
\(764\) 0 0
\(765\) 192.000 + 543.058i 0.250980 + 0.709880i
\(766\) 0 0
\(767\) 88.1816i 0.114970i
\(768\) 0 0
\(769\) −334.000 −0.434330 −0.217165 0.976135i \(-0.569681\pi\)
−0.217165 + 0.976135i \(0.569681\pi\)
\(770\) 0 0
\(771\) −942.236 666.261i −1.22210 0.864152i
\(772\) 0 0
\(773\) 562.857i 0.728146i −0.931370 0.364073i \(-0.881386\pi\)
0.931370 0.364073i \(-0.118614\pi\)
\(774\) 0 0
\(775\) −530.008 −0.683881
\(776\) 0 0
\(777\) −684.000 + 967.322i −0.880309 + 1.24494i
\(778\) 0 0
\(779\) 58.7878i 0.0754657i
\(780\) 0 0
\(781\) −432.000 −0.553137
\(782\) 0 0
\(783\) 228.631 808.332i 0.291993 1.03235i
\(784\) 0 0
\(785\) 435.578i 0.554876i
\(786\) 0 0
\(787\) −841.777 −1.06960 −0.534801 0.844978i \(-0.679613\pi\)
−0.534801 + 0.844978i \(0.679613\pi\)
\(788\) 0 0
\(789\) −1224.00 865.499i −1.55133 1.09696i
\(790\) 0 0
\(791\) 1998.78i 2.52691i
\(792\) 0 0
\(793\) 132.000 0.166456
\(794\) 0 0
\(795\) −69.2820 + 97.9796i −0.0871472 + 0.123245i
\(796\) 0 0
\(797\) 393.151i 0.493289i 0.969106 + 0.246645i \(0.0793280\pi\)
−0.969106 + 0.246645i \(0.920672\pi\)
\(798\) 0 0
\(799\) 1330.22 1.66485
\