Properties

Label 3024.2.t.l.289.5
Level $3024$
Weight $2$
Character 3024.289
Analytic conductor $24.147$
Analytic rank $0$
Dimension $22$
CM no
Inner twists $2$

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3024.t (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(24.1467615712\)
Analytic rank: \(0\)
Dimension: \(22\)
Relative dimension: \(11\) over \(\Q(\zeta_{3})\)
Twist minimal: no (minimal twist has level 504)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 289.5
Character \(\chi\) \(=\) 3024.289
Dual form 3024.2.t.l.1873.5

$q$-expansion

\(f(q)\) \(=\) \(q-0.340200 q^{5} +(-1.09748 - 2.40739i) q^{7} +O(q^{10})\) \(q-0.340200 q^{5} +(-1.09748 - 2.40739i) q^{7} -0.671588 q^{11} +(1.62370 + 2.81233i) q^{13} +(1.10014 + 1.90550i) q^{17} +(-0.242085 + 0.419303i) q^{19} +4.18990 q^{23} -4.88426 q^{25} +(-0.478868 + 0.829424i) q^{29} +(1.04132 - 1.80361i) q^{31} +(0.373363 + 0.818995i) q^{35} +(4.81613 - 8.34178i) q^{37} +(3.90207 + 6.75858i) q^{41} +(3.66119 - 6.34136i) q^{43} +(1.34951 + 2.33742i) q^{47} +(-4.59108 + 5.28413i) q^{49} +(6.12335 + 10.6059i) q^{53} +0.228474 q^{55} +(2.47148 - 4.28074i) q^{59} +(1.76059 + 3.04944i) q^{61} +(-0.552383 - 0.956755i) q^{65} +(6.16012 - 10.6696i) q^{67} -5.57304 q^{71} +(-3.71686 - 6.43779i) q^{73} +(0.737054 + 1.61677i) q^{77} +(-5.00637 - 8.67128i) q^{79} +(2.47376 - 4.28468i) q^{83} +(-0.374269 - 0.648252i) q^{85} +(8.52177 - 14.7601i) q^{89} +(4.98840 - 6.99536i) q^{91} +(0.0823572 - 0.142647i) q^{95} +(4.23657 - 7.33795i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 22q + 6q^{5} - 7q^{7} + O(q^{10}) \) \( 22q + 6q^{5} - 7q^{7} + 6q^{11} - 3q^{13} - 7q^{17} + q^{19} - 4q^{23} + 20q^{25} - 9q^{29} + 4q^{31} + 14q^{35} + 2q^{37} - 16q^{41} + 5q^{47} - 15q^{49} - 11q^{53} - 22q^{55} - 19q^{59} - 13q^{61} - 13q^{65} - 26q^{67} - 48q^{71} - 35q^{73} + 4q^{77} - 10q^{79} - 28q^{83} - 20q^{85} - 6q^{89} + 37q^{91} + 12q^{95} - 29q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3024\mathbb{Z}\right)^\times\).

\(n\) \(757\) \(785\) \(1135\) \(2593\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\) \(e\left(\frac{1}{3}\right)\)

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 0
\(4\) 0 0
\(5\) −0.340200 −0.152142 −0.0760711 0.997102i \(-0.524238\pi\)
−0.0760711 + 0.997102i \(0.524238\pi\)
\(6\) 0 0
\(7\) −1.09748 2.40739i −0.414808 0.909909i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −0.671588 −0.202491 −0.101246 0.994861i \(-0.532283\pi\)
−0.101246 + 0.994861i \(0.532283\pi\)
\(12\) 0 0
\(13\) 1.62370 + 2.81233i 0.450333 + 0.780000i 0.998407 0.0564303i \(-0.0179719\pi\)
−0.548073 + 0.836430i \(0.684639\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 1.10014 + 1.90550i 0.266824 + 0.462152i 0.968040 0.250796i \(-0.0806925\pi\)
−0.701216 + 0.712949i \(0.747359\pi\)
\(18\) 0 0
\(19\) −0.242085 + 0.419303i −0.0555380 + 0.0961946i −0.892458 0.451131i \(-0.851021\pi\)
0.836920 + 0.547326i \(0.184354\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 4.18990 0.873655 0.436827 0.899545i \(-0.356102\pi\)
0.436827 + 0.899545i \(0.356102\pi\)
\(24\) 0 0
\(25\) −4.88426 −0.976853
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −0.478868 + 0.829424i −0.0889235 + 0.154020i −0.907056 0.421009i \(-0.861676\pi\)
0.818133 + 0.575029i \(0.195009\pi\)
\(30\) 0 0
\(31\) 1.04132 1.80361i 0.187026 0.323938i −0.757231 0.653147i \(-0.773449\pi\)
0.944257 + 0.329208i \(0.106782\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 0.373363 + 0.818995i 0.0631098 + 0.138435i
\(36\) 0 0
\(37\) 4.81613 8.34178i 0.791767 1.37138i −0.133105 0.991102i \(-0.542495\pi\)
0.924872 0.380278i \(-0.124172\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 3.90207 + 6.75858i 0.609400 + 1.05551i 0.991339 + 0.131325i \(0.0419231\pi\)
−0.381939 + 0.924188i \(0.624744\pi\)
\(42\) 0 0
\(43\) 3.66119 6.34136i 0.558326 0.967048i −0.439311 0.898335i \(-0.644777\pi\)
0.997636 0.0687132i \(-0.0218893\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 1.34951 + 2.33742i 0.196846 + 0.340947i 0.947504 0.319744i \(-0.103597\pi\)
−0.750658 + 0.660691i \(0.770263\pi\)
\(48\) 0 0
\(49\) −4.59108 + 5.28413i −0.655868 + 0.754876i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 6.12335 + 10.6059i 0.841107 + 1.45684i 0.888960 + 0.457985i \(0.151429\pi\)
−0.0478535 + 0.998854i \(0.515238\pi\)
\(54\) 0 0
\(55\) 0.228474 0.0308075
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 2.47148 4.28074i 0.321760 0.557304i −0.659091 0.752063i \(-0.729059\pi\)
0.980851 + 0.194758i \(0.0623923\pi\)
\(60\) 0 0
\(61\) 1.76059 + 3.04944i 0.225421 + 0.390441i 0.956446 0.291910i \(-0.0942909\pi\)
−0.731025 + 0.682351i \(0.760958\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −0.552383 0.956755i −0.0685147 0.118671i
\(66\) 0 0
\(67\) 6.16012 10.6696i 0.752579 1.30350i −0.193990 0.981003i \(-0.562143\pi\)
0.946569 0.322501i \(-0.104524\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −5.57304 −0.661398 −0.330699 0.943736i \(-0.607285\pi\)
−0.330699 + 0.943736i \(0.607285\pi\)
\(72\) 0 0
\(73\) −3.71686 6.43779i −0.435026 0.753487i 0.562272 0.826952i \(-0.309927\pi\)
−0.997298 + 0.0734657i \(0.976594\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 0.737054 + 1.61677i 0.0839951 + 0.184249i
\(78\) 0 0
\(79\) −5.00637 8.67128i −0.563260 0.975596i −0.997209 0.0746582i \(-0.976213\pi\)
0.433949 0.900938i \(-0.357120\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 2.47376 4.28468i 0.271530 0.470305i −0.697723 0.716367i \(-0.745804\pi\)
0.969254 + 0.246063i \(0.0791369\pi\)
\(84\) 0 0
\(85\) −0.374269 0.648252i −0.0405951 0.0703128i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 8.52177 14.7601i 0.903306 1.56457i 0.0801310 0.996784i \(-0.474466\pi\)
0.823175 0.567788i \(-0.192201\pi\)
\(90\) 0 0
\(91\) 4.98840 6.99536i 0.522927 0.733313i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0.0823572 0.142647i 0.00844967 0.0146353i
\(96\) 0 0
\(97\) 4.23657 7.33795i 0.430159 0.745056i −0.566728 0.823905i \(-0.691791\pi\)
0.996887 + 0.0788485i \(0.0251243\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 4.57385 0.455115 0.227558 0.973765i \(-0.426926\pi\)
0.227558 + 0.973765i \(0.426926\pi\)
\(102\) 0 0
\(103\) 1.80713 0.178061 0.0890307 0.996029i \(-0.471623\pi\)
0.0890307 + 0.996029i \(0.471623\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 3.88188 6.72361i 0.375275 0.649996i −0.615093 0.788454i \(-0.710882\pi\)
0.990368 + 0.138459i \(0.0442149\pi\)
\(108\) 0 0
\(109\) −1.07178 1.85638i −0.102658 0.177809i 0.810121 0.586263i \(-0.199401\pi\)
−0.912779 + 0.408454i \(0.866068\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 7.91006 + 13.7006i 0.744116 + 1.28885i 0.950607 + 0.310398i \(0.100462\pi\)
−0.206491 + 0.978449i \(0.566204\pi\)
\(114\) 0 0
\(115\) −1.42540 −0.132920
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 3.37991 4.73973i 0.309836 0.434490i
\(120\) 0 0
\(121\) −10.5490 −0.958997
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 3.36263 0.300763
\(126\) 0 0
\(127\) 13.8820 1.23183 0.615915 0.787812i \(-0.288786\pi\)
0.615915 + 0.787812i \(0.288786\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −4.17538 −0.364805 −0.182402 0.983224i \(-0.558387\pi\)
−0.182402 + 0.983224i \(0.558387\pi\)
\(132\) 0 0
\(133\) 1.27511 + 0.122616i 0.110566 + 0.0106322i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 12.7609 1.09023 0.545117 0.838360i \(-0.316485\pi\)
0.545117 + 0.838360i \(0.316485\pi\)
\(138\) 0 0
\(139\) −5.95986 10.3228i −0.505509 0.875567i −0.999980 0.00637264i \(-0.997972\pi\)
0.494471 0.869194i \(-0.335362\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −1.09046 1.88873i −0.0911885 0.157943i
\(144\) 0 0
\(145\) 0.162911 0.282170i 0.0135290 0.0234329i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 10.7510 0.880753 0.440376 0.897813i \(-0.354845\pi\)
0.440376 + 0.897813i \(0.354845\pi\)
\(150\) 0 0
\(151\) 2.58099 0.210038 0.105019 0.994470i \(-0.466510\pi\)
0.105019 + 0.994470i \(0.466510\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −0.354256 + 0.613589i −0.0284545 + 0.0492846i
\(156\) 0 0
\(157\) −3.99846 + 6.92554i −0.319112 + 0.552718i −0.980303 0.197499i \(-0.936718\pi\)
0.661191 + 0.750218i \(0.270051\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −4.59833 10.0867i −0.362399 0.794946i
\(162\) 0 0
\(163\) −4.13306 + 7.15868i −0.323727 + 0.560711i −0.981254 0.192720i \(-0.938269\pi\)
0.657527 + 0.753431i \(0.271602\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 8.99384 + 15.5778i 0.695964 + 1.20544i 0.969855 + 0.243684i \(0.0783560\pi\)
−0.273891 + 0.961761i \(0.588311\pi\)
\(168\) 0 0
\(169\) 1.22720 2.12557i 0.0944000 0.163506i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −8.49915 14.7210i −0.646179 1.11921i −0.984028 0.178014i \(-0.943033\pi\)
0.337849 0.941200i \(-0.390301\pi\)
\(174\) 0 0
\(175\) 5.36038 + 11.7583i 0.405207 + 0.888847i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −9.65073 16.7156i −0.721329 1.24938i −0.960467 0.278393i \(-0.910198\pi\)
0.239138 0.970986i \(-0.423135\pi\)
\(180\) 0 0
\(181\) 21.9640 1.63257 0.816287 0.577646i \(-0.196029\pi\)
0.816287 + 0.577646i \(0.196029\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −1.63845 + 2.83788i −0.120461 + 0.208645i
\(186\) 0 0
\(187\) −0.738842 1.27971i −0.0540295 0.0935818i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −3.32872 5.76552i −0.240858 0.417178i 0.720101 0.693869i \(-0.244095\pi\)
−0.960959 + 0.276691i \(0.910762\pi\)
\(192\) 0 0
\(193\) −3.17453 + 5.49845i −0.228508 + 0.395787i −0.957366 0.288878i \(-0.906718\pi\)
0.728858 + 0.684665i \(0.240051\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −23.8112 −1.69648 −0.848239 0.529614i \(-0.822337\pi\)
−0.848239 + 0.529614i \(0.822337\pi\)
\(198\) 0 0
\(199\) 10.4771 + 18.1468i 0.742701 + 1.28640i 0.951261 + 0.308386i \(0.0997887\pi\)
−0.208561 + 0.978009i \(0.566878\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 2.52230 + 0.242547i 0.177030 + 0.0170235i
\(204\) 0 0
\(205\) −1.32748 2.29927i −0.0927155 0.160588i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 0.162581 0.281599i 0.0112460 0.0194786i
\(210\) 0 0
\(211\) 6.32431 + 10.9540i 0.435384 + 0.754106i 0.997327 0.0730693i \(-0.0232794\pi\)
−0.561943 + 0.827176i \(0.689946\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −1.24554 + 2.15733i −0.0849448 + 0.147129i
\(216\) 0 0
\(217\) −5.48482 0.527427i −0.372334 0.0358041i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −3.57260 + 6.18793i −0.240319 + 0.416245i
\(222\) 0 0
\(223\) 1.34432 2.32843i 0.0900225 0.155924i −0.817498 0.575932i \(-0.804639\pi\)
0.907520 + 0.420008i \(0.137973\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 27.9885 1.85766 0.928829 0.370508i \(-0.120816\pi\)
0.928829 + 0.370508i \(0.120816\pi\)
\(228\) 0 0
\(229\) 24.5390 1.62158 0.810790 0.585337i \(-0.199038\pi\)
0.810790 + 0.585337i \(0.199038\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 4.61844 7.99938i 0.302564 0.524057i −0.674152 0.738593i \(-0.735491\pi\)
0.976716 + 0.214536i \(0.0688240\pi\)
\(234\) 0 0
\(235\) −0.459103 0.795189i −0.0299486 0.0518724i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 14.0126 + 24.2706i 0.906403 + 1.56994i 0.819023 + 0.573760i \(0.194516\pi\)
0.0873796 + 0.996175i \(0.472151\pi\)
\(240\) 0 0
\(241\) 19.8282 1.27725 0.638624 0.769519i \(-0.279504\pi\)
0.638624 + 0.769519i \(0.279504\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 1.56188 1.79766i 0.0997851 0.114848i
\(246\) 0 0
\(247\) −1.57229 −0.100042
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 16.5759 1.04626 0.523132 0.852252i \(-0.324764\pi\)
0.523132 + 0.852252i \(0.324764\pi\)
\(252\) 0 0
\(253\) −2.81389 −0.176907
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −7.29501 −0.455050 −0.227525 0.973772i \(-0.573063\pi\)
−0.227525 + 0.973772i \(0.573063\pi\)
\(258\) 0 0
\(259\) −25.3675 2.43937i −1.57626 0.151575i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −26.7798 −1.65131 −0.825657 0.564172i \(-0.809196\pi\)
−0.825657 + 0.564172i \(0.809196\pi\)
\(264\) 0 0
\(265\) −2.08316 3.60815i −0.127968 0.221647i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −10.1791 17.6307i −0.620630 1.07496i −0.989369 0.145429i \(-0.953544\pi\)
0.368739 0.929533i \(-0.379790\pi\)
\(270\) 0 0
\(271\) −5.45842 + 9.45427i −0.331576 + 0.574306i −0.982821 0.184561i \(-0.940914\pi\)
0.651245 + 0.758867i \(0.274247\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 3.28021 0.197804
\(276\) 0 0
\(277\) 17.6738 1.06191 0.530957 0.847399i \(-0.321832\pi\)
0.530957 + 0.847399i \(0.321832\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −7.17614 + 12.4294i −0.428092 + 0.741478i −0.996704 0.0811286i \(-0.974148\pi\)
0.568611 + 0.822606i \(0.307481\pi\)
\(282\) 0 0
\(283\) 4.86420 8.42505i 0.289147 0.500817i −0.684459 0.729051i \(-0.739962\pi\)
0.973606 + 0.228234i \(0.0732950\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 11.9881 16.8112i 0.707636 0.992334i
\(288\) 0 0
\(289\) 6.07937 10.5298i 0.357610 0.619399i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −6.26345 10.8486i −0.365915 0.633783i 0.623008 0.782216i \(-0.285911\pi\)
−0.988923 + 0.148433i \(0.952577\pi\)
\(294\) 0 0
\(295\) −0.840799 + 1.45631i −0.0489532 + 0.0847895i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 6.80314 + 11.7834i 0.393436 + 0.681451i
\(300\) 0 0
\(301\) −19.2842 1.85439i −1.11152 0.106886i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −0.598954 1.03742i −0.0342960 0.0594025i
\(306\) 0 0
\(307\) −25.8747 −1.47675 −0.738375 0.674391i \(-0.764406\pi\)
−0.738375 + 0.674391i \(0.764406\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −14.2001 + 24.5952i −0.805211 + 1.39467i 0.110937 + 0.993827i \(0.464615\pi\)
−0.916148 + 0.400840i \(0.868718\pi\)
\(312\) 0 0
\(313\) 6.10074 + 10.5668i 0.344834 + 0.597270i 0.985324 0.170697i \(-0.0546019\pi\)
−0.640490 + 0.767967i \(0.721269\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −1.97609 3.42270i −0.110988 0.192238i 0.805181 0.593030i \(-0.202068\pi\)
−0.916169 + 0.400792i \(0.868735\pi\)
\(318\) 0 0
\(319\) 0.321602 0.557031i 0.0180062 0.0311877i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −1.06531 −0.0592754
\(324\) 0 0
\(325\) −7.93058 13.7362i −0.439909 0.761945i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 4.14602 5.81406i 0.228577 0.320540i
\(330\) 0 0
\(331\) −4.44143 7.69278i −0.244123 0.422834i 0.717762 0.696289i \(-0.245167\pi\)
−0.961885 + 0.273455i \(0.911833\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −2.09567 + 3.62981i −0.114499 + 0.198318i
\(336\) 0 0
\(337\) −11.9741 20.7397i −0.652269 1.12976i −0.982571 0.185887i \(-0.940484\pi\)
0.330302 0.943875i \(-0.392849\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −0.699335 + 1.21128i −0.0378711 + 0.0655947i
\(342\) 0 0
\(343\) 17.7596 + 5.25329i 0.958928 + 0.283651i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −4.74529 + 8.21909i −0.254741 + 0.441224i −0.964825 0.262893i \(-0.915323\pi\)
0.710084 + 0.704117i \(0.248657\pi\)
\(348\) 0 0
\(349\) 4.26145 7.38104i 0.228110 0.395098i −0.729138 0.684367i \(-0.760079\pi\)
0.957248 + 0.289269i \(0.0934121\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 37.1744 1.97859 0.989297 0.145919i \(-0.0466138\pi\)
0.989297 + 0.145919i \(0.0466138\pi\)
\(354\) 0 0
\(355\) 1.89595 0.100627
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −5.30964 + 9.19657i −0.280232 + 0.485376i −0.971442 0.237278i \(-0.923745\pi\)
0.691210 + 0.722654i \(0.257078\pi\)
\(360\) 0 0
\(361\) 9.38279 + 16.2515i 0.493831 + 0.855340i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 1.26448 + 2.19014i 0.0661857 + 0.114637i
\(366\) 0 0
\(367\) −22.3598 −1.16717 −0.583586 0.812051i \(-0.698351\pi\)
−0.583586 + 0.812051i \(0.698351\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 18.8124 26.3811i 0.976693 1.36964i
\(372\) 0 0
\(373\) −17.5853 −0.910532 −0.455266 0.890356i \(-0.650456\pi\)
−0.455266 + 0.890356i \(0.650456\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −3.11015 −0.160181
\(378\) 0 0
\(379\) −10.0443 −0.515939 −0.257969 0.966153i \(-0.583053\pi\)
−0.257969 + 0.966153i \(0.583053\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −7.87238 −0.402260 −0.201130 0.979565i \(-0.564461\pi\)
−0.201130 + 0.979565i \(0.564461\pi\)
\(384\) 0 0
\(385\) −0.250746 0.550027i −0.0127792 0.0280320i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 3.64835 0.184979 0.0924893 0.995714i \(-0.470518\pi\)
0.0924893 + 0.995714i \(0.470518\pi\)
\(390\) 0 0
\(391\) 4.60949 + 7.98387i 0.233112 + 0.403762i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 1.70317 + 2.94997i 0.0856956 + 0.148429i
\(396\) 0 0
\(397\) 6.56071 11.3635i 0.329272 0.570317i −0.653095 0.757276i \(-0.726530\pi\)
0.982368 + 0.186959i \(0.0598632\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −11.4374 −0.571159 −0.285579 0.958355i \(-0.592186\pi\)
−0.285579 + 0.958355i \(0.592186\pi\)
\(402\) 0 0
\(403\) 6.76313 0.336896
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −3.23445 + 5.60224i −0.160326 + 0.277693i
\(408\) 0 0
\(409\) 9.24106 16.0060i 0.456941 0.791445i −0.541857 0.840471i \(-0.682278\pi\)
0.998797 + 0.0490262i \(0.0156118\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −13.0178 1.25181i −0.640565 0.0615975i
\(414\) 0 0
\(415\) −0.841574 + 1.45765i −0.0413112 + 0.0715531i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −10.6290 18.4099i −0.519260 0.899385i −0.999749 0.0223843i \(-0.992874\pi\)
0.480489 0.877001i \(-0.340459\pi\)
\(420\) 0 0
\(421\) −8.60478 + 14.9039i −0.419371 + 0.726373i −0.995876 0.0907211i \(-0.971083\pi\)
0.576505 + 0.817094i \(0.304416\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −5.37339 9.30698i −0.260648 0.451455i
\(426\) 0 0
\(427\) 5.40898 7.58514i 0.261759 0.367071i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 3.02962 + 5.24745i 0.145931 + 0.252761i 0.929720 0.368267i \(-0.120049\pi\)
−0.783789 + 0.621028i \(0.786715\pi\)
\(432\) 0 0
\(433\) −17.6963 −0.850432 −0.425216 0.905092i \(-0.639802\pi\)
−0.425216 + 0.905092i \(0.639802\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −1.01431 + 1.75684i −0.0485210 + 0.0840409i
\(438\) 0 0
\(439\) 13.6687 + 23.6748i 0.652370 + 1.12994i 0.982546 + 0.186018i \(0.0595584\pi\)
−0.330177 + 0.943919i \(0.607108\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −0.958856 1.66079i −0.0455566 0.0789064i 0.842348 0.538934i \(-0.181173\pi\)
−0.887905 + 0.460028i \(0.847839\pi\)
\(444\) 0 0
\(445\) −2.89911 + 5.02140i −0.137431 + 0.238037i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −28.3249 −1.33674 −0.668368 0.743831i \(-0.733007\pi\)
−0.668368 + 0.743831i \(0.733007\pi\)
\(450\) 0 0
\(451\) −2.62058 4.53898i −0.123398 0.213732i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −1.69706 + 2.37982i −0.0795592 + 0.111568i
\(456\) 0 0
\(457\) −6.50427 11.2657i −0.304257 0.526988i 0.672839 0.739789i \(-0.265075\pi\)
−0.977096 + 0.212801i \(0.931741\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 11.8278 20.4863i 0.550875 0.954144i −0.447336 0.894366i \(-0.647627\pi\)
0.998212 0.0597782i \(-0.0190393\pi\)
\(462\) 0 0
\(463\) 20.2403 + 35.0572i 0.940647 + 1.62925i 0.764241 + 0.644931i \(0.223114\pi\)
0.176406 + 0.984317i \(0.443553\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −18.6010 + 32.2179i −0.860753 + 1.49087i 0.0104492 + 0.999945i \(0.496674\pi\)
−0.871203 + 0.490923i \(0.836659\pi\)
\(468\) 0 0
\(469\) −32.4466 3.12011i −1.49825 0.144073i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −2.45881 + 4.25878i −0.113056 + 0.195819i
\(474\) 0 0
\(475\) 1.18240 2.04799i 0.0542525 0.0939680i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 40.5835 1.85431 0.927154 0.374681i \(-0.122248\pi\)
0.927154 + 0.374681i \(0.122248\pi\)
\(480\) 0 0
\(481\) 31.2798 1.42624
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −1.44128 + 2.49637i −0.0654452 + 0.113354i
\(486\) 0 0
\(487\) −10.5255 18.2307i −0.476956 0.826113i 0.522695 0.852520i \(-0.324927\pi\)
−0.999651 + 0.0264072i \(0.991593\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −4.97925 8.62432i −0.224711 0.389210i 0.731522 0.681818i \(-0.238810\pi\)
−0.956233 + 0.292608i \(0.905477\pi\)
\(492\) 0 0
\(493\) −2.10729 −0.0949077
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 6.11630 + 13.4165i 0.274354 + 0.601812i
\(498\) 0 0
\(499\) −22.6301 −1.01306 −0.506531 0.862222i \(-0.669072\pi\)
−0.506531 + 0.862222i \(0.669072\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −43.4520 −1.93743 −0.968714 0.248179i \(-0.920168\pi\)
−0.968714 + 0.248179i \(0.920168\pi\)
\(504\) 0 0
\(505\) −1.55602 −0.0692422
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 9.55477 0.423508 0.211754 0.977323i \(-0.432082\pi\)
0.211754 + 0.977323i \(0.432082\pi\)
\(510\) 0 0
\(511\) −11.4191 + 16.0133i −0.505152 + 0.708386i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −0.614785 −0.0270906
\(516\) 0 0
\(517\) −0.906312 1.56978i −0.0398596 0.0690388i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −0.581462 1.00712i −0.0254743 0.0441228i 0.853007 0.521899i \(-0.174776\pi\)
−0.878482 + 0.477776i \(0.841443\pi\)
\(522\) 0 0
\(523\) 3.20567 5.55239i 0.140174 0.242789i −0.787388 0.616458i \(-0.788567\pi\)
0.927562 + 0.373669i \(0.121900\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 4.58238 0.199612
\(528\) 0 0
\(529\) −5.44474 −0.236728
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −12.6716 + 21.9478i −0.548866 + 0.950665i
\(534\) 0 0
\(535\) −1.32061 + 2.28737i −0.0570952 + 0.0988917i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 3.08331 3.54876i 0.132808 0.152856i
\(540\) 0 0
\(541\) −7.37443 + 12.7729i −0.317052 + 0.549150i −0.979871 0.199629i \(-0.936026\pi\)
0.662820 + 0.748779i \(0.269360\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 0.364621 + 0.631542i 0.0156187 + 0.0270523i
\(546\) 0 0
\(547\) −6.57905 + 11.3952i −0.281300 + 0.487226i −0.971705 0.236197i \(-0.924099\pi\)
0.690405 + 0.723423i \(0.257432\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −0.231853 0.401581i −0.00987727 0.0171079i
\(552\) 0 0
\(553\) −15.3808 + 21.5689i −0.654058 + 0.917201i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 12.1869 + 21.1083i 0.516374 + 0.894385i 0.999819 + 0.0190111i \(0.00605177\pi\)
−0.483446 + 0.875374i \(0.660615\pi\)
\(558\) 0 0
\(559\) 23.7787 1.00573
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 1.55982 2.70169i 0.0657388 0.113863i −0.831283 0.555850i \(-0.812393\pi\)
0.897021 + 0.441987i \(0.145726\pi\)
\(564\) 0 0
\(565\) −2.69100 4.66096i −0.113211 0.196088i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −10.7384 18.5995i −0.450179 0.779733i 0.548218 0.836336i \(-0.315307\pi\)
−0.998397 + 0.0566027i \(0.981973\pi\)
\(570\) 0 0
\(571\) 16.5230 28.6187i 0.691466 1.19765i −0.279891 0.960032i \(-0.590298\pi\)
0.971358 0.237623i \(-0.0763682\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −20.4646 −0.853432
\(576\) 0 0
\(577\) 0.904826 + 1.56720i 0.0376684 + 0.0652436i 0.884245 0.467023i \(-0.154674\pi\)
−0.846577 + 0.532267i \(0.821340\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −13.0298 1.25296i −0.540567 0.0519816i
\(582\) 0 0
\(583\) −4.11236 7.12282i −0.170317 0.294997i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 1.65901 2.87349i 0.0684746 0.118601i −0.829755 0.558127i \(-0.811520\pi\)
0.898230 + 0.439526i \(0.144853\pi\)
\(588\) 0 0
\(589\) 0.504173 + 0.873253i 0.0207741 + 0.0359818i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −15.3784 + 26.6362i −0.631516 + 1.09382i 0.355726 + 0.934590i \(0.384234\pi\)
−0.987242 + 0.159228i \(0.949100\pi\)
\(594\) 0 0
\(595\) −1.14985 + 1.61246i −0.0471391 + 0.0661042i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −6.98523 + 12.0988i −0.285409 + 0.494342i −0.972708 0.232032i \(-0.925463\pi\)
0.687299 + 0.726374i \(0.258796\pi\)
\(600\) 0 0
\(601\) −7.50432 + 12.9979i −0.306108 + 0.530194i −0.977507 0.210901i \(-0.932360\pi\)
0.671400 + 0.741096i \(0.265693\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 3.58876 0.145904
\(606\) 0 0
\(607\) −23.3289 −0.946889 −0.473444 0.880824i \(-0.656990\pi\)
−0.473444 + 0.880824i \(0.656990\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −4.38239 + 7.59052i −0.177292 + 0.307080i
\(612\) 0 0
\(613\) 22.3374 + 38.6895i 0.902198 + 1.56265i 0.824635 + 0.565666i \(0.191381\pi\)
0.0775635 + 0.996987i \(0.475286\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 1.18488 + 2.05227i 0.0477013 + 0.0826212i 0.888890 0.458120i \(-0.151477\pi\)
−0.841189 + 0.540741i \(0.818144\pi\)
\(618\) 0 0
\(619\) 22.7727 0.915311 0.457655 0.889130i \(-0.348689\pi\)
0.457655 + 0.889130i \(0.348689\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −44.8859 4.31629i −1.79832 0.172928i
\(624\) 0 0
\(625\) 23.2774 0.931094
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 21.1937 0.845049
\(630\) 0 0
\(631\) −17.8652 −0.711201 −0.355600 0.934638i \(-0.615724\pi\)
−0.355600 + 0.934638i \(0.615724\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −4.72267 −0.187413
\(636\) 0 0
\(637\) −22.3152 4.33178i −0.884162 0.171631i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 25.5800 1.01035 0.505175 0.863017i \(-0.331428\pi\)
0.505175 + 0.863017i \(0.331428\pi\)
\(642\) 0 0
\(643\) −7.99334 13.8449i −0.315227 0.545989i 0.664259 0.747503i \(-0.268747\pi\)
−0.979486 + 0.201514i \(0.935414\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 7.47306 + 12.9437i 0.293796 + 0.508870i 0.974704 0.223499i \(-0.0717479\pi\)
−0.680908 + 0.732369i \(0.738415\pi\)
\(648\) 0 0
\(649\) −1.65982 + 2.87489i −0.0651536 + 0.112849i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 9.65770 0.377935 0.188967 0.981983i \(-0.439486\pi\)
0.188967 + 0.981983i \(0.439486\pi\)
\(654\) 0 0
\(655\) 1.42047 0.0555022
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 9.80353 16.9802i 0.381891 0.661455i −0.609441 0.792831i \(-0.708606\pi\)
0.991333 + 0.131376i \(0.0419396\pi\)
\(660\) 0 0
\(661\) 5.13275 8.89018i 0.199641 0.345788i −0.748771 0.662829i \(-0.769356\pi\)
0.948412 + 0.317041i \(0.102689\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −0.433792 0.0417140i −0.0168217 0.00161760i
\(666\) 0 0
\(667\) −2.00641 + 3.47520i −0.0776885 + 0.134560i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −1.18239 2.04797i −0.0456458 0.0790608i
\(672\) 0 0
\(673\) −17.1584 + 29.7191i −0.661406 + 1.14559i 0.318840 + 0.947808i \(0.396707\pi\)
−0.980246 + 0.197780i \(0.936627\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 3.73709 + 6.47283i 0.143628 + 0.248771i 0.928860 0.370430i \(-0.120790\pi\)
−0.785232 + 0.619201i \(0.787456\pi\)
\(678\) 0 0
\(679\) −22.3149 2.14583i −0.856367 0.0823493i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −18.1577 31.4501i −0.694786 1.20340i −0.970253 0.242094i \(-0.922166\pi\)
0.275467 0.961310i \(-0.411167\pi\)
\(684\) 0 0
\(685\) −4.34125 −0.165871
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −19.8850 + 34.4417i −0.757556 + 1.31213i
\(690\) 0 0
\(691\) 25.4812 + 44.1347i 0.969350 + 1.67896i 0.697444 + 0.716640i \(0.254321\pi\)
0.271906 + 0.962324i \(0.412346\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 2.02755 + 3.51181i 0.0769092 + 0.133211i
\(696\) 0 0
\(697\) −8.58566 + 14.8708i −0.325205 + 0.563272i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −36.6075 −1.38265 −0.691324 0.722545i \(-0.742972\pi\)
−0.691324 + 0.722545i \(0.742972\pi\)
\(702\) 0 0
\(703\) 2.33182 + 4.03883i 0.0879463 + 0.152327i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −5.01971 11.0111i −0.188786 0.414113i
\(708\) 0 0
\(709\) 2.93789 + 5.08858i 0.110335 + 0.191106i 0.915905 0.401394i \(-0.131474\pi\)
−0.805570 + 0.592500i \(0.798141\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 4.36301 7.55695i 0.163396 0.283010i
\(714\) 0 0
\(715\) 0.370973 + 0.642545i 0.0138736 + 0.0240298i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −8.09642 + 14.0234i −0.301945 + 0.522985i −0.976577 0.215170i \(-0.930969\pi\)
0.674631 + 0.738155i \(0.264303\pi\)
\(720\) 0 0
\(721\) −1.98328 4.35046i −0.0738614 0.162020i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 2.33892 4.05112i 0.0868652 0.150455i
\(726\) 0 0
\(727\) 22.8771 39.6243i 0.848464 1.46958i −0.0341138 0.999418i \(-0.510861\pi\)
0.882578 0.470166i \(-0.155806\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 16.1113 0.595898
\(732\) 0 0
\(733\) 27.1833 1.00404 0.502019 0.864857i \(-0.332591\pi\)
0.502019 + 0.864857i \(0.332591\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −4.13706 + 7.16560i −0.152391 + 0.263948i
\(738\) 0 0
\(739\) −12.1738 21.0856i −0.447821 0.775648i 0.550423 0.834886i \(-0.314466\pi\)
−0.998244 + 0.0592377i \(0.981133\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −0.0683178 0.118330i −0.00250634 0.00434110i 0.864770 0.502169i \(-0.167464\pi\)
−0.867276 + 0.497828i \(0.834131\pi\)
\(744\) 0 0
\(745\) −3.65748 −0.134000
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −20.4466 1.96617i −0.747104 0.0718424i
\(750\) 0 0
\(751\) −7.42893 −0.271085 −0.135543 0.990772i \(-0.543278\pi\)
−0.135543 + 0.990772i \(0.543278\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −0.878055 −0.0319557
\(756\) 0 0
\(757\) −14.0794 −0.511723 −0.255861 0.966713i \(-0.582359\pi\)
−0.255861 + 0.966713i \(0.582359\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −38.7232 −1.40372 −0.701858 0.712317i \(-0.747646\pi\)
−0.701858 + 0.712317i \(0.747646\pi\)
\(762\) 0 0
\(763\) −3.29278 + 4.61755i −0.119207 + 0.167167i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 16.0518 0.579597
\(768\) 0 0
\(769\) 5.14295 + 8.90786i 0.185460 + 0.321226i 0.943731 0.330713i \(-0.107289\pi\)
−0.758272 + 0.651939i \(0.773956\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 22.6768 + 39.2773i 0.815627 + 1.41271i 0.908877 + 0.417064i \(0.136941\pi\)
−0.0932501 + 0.995643i \(0.529726\pi\)
\(774\) 0 0
\(775\) −5.08606 + 8.80931i −0.182697 + 0.316440i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −3.77852 −0.135380
\(780\) 0 0
\(781\) 3.74279 0.133927
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 1.36028 2.35607i 0.0485504 0.0840917i
\(786\) 0 0
\(787\) 13.0543 22.6108i 0.465337 0.805988i −0.533879 0.845561i \(-0.679266\pi\)
0.999217 + 0.0395728i \(0.0125997\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 24.3017 34.0788i 0.864067 1.21170i
\(792\) 0 0
\(793\) −5.71735 + 9.90274i −0.203029 + 0.351657i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 16.1618 + 27.9931i 0.572481 + 0.991567i 0.996310 + 0.0858244i \(0.0273524\pi\)
−0.423829 + 0.905742i \(0.639314\pi\)
\(798\) 0 0
\(799\) −2.96930 + 5.14298i −0.105046 + 0.181946i
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 2.49620 + 4.32354i 0.0880889 + 0.152574i
\(804\) 0 0
\(805\) 1.56435 + 3.43151i 0.0551362 + 0.120945i
\(806\) 0