Properties

Label 804.2.ba.a.593.1
Level 804
Weight 2
Character 804.593
Analytic conductor 6.420
Analytic rank 0
Dimension 20
CM discriminant -3
Inner twists 4

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Newspace parameters

Level: \( N \) = \( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 804.ba (of order \(66\), degree \(20\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.41997232251\)
Analytic rank: \(0\)
Dimension: \(20\)
Coefficient field: \(\Q(\zeta_{33})\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{U}(1)[D_{66}]$

Embedding invariants

Embedding label 593.1
Root \(0.928368 + 0.371662i\)
Character \(\chi\) = 804.593
Dual form 804.2.ba.a.221.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.71442 + 0.246497i) q^{3} +(4.93365 + 1.19689i) q^{7} +(2.87848 - 0.845198i) q^{9} +O(q^{10})\) \(q+(-1.71442 + 0.246497i) q^{3} +(4.93365 + 1.19689i) q^{7} +(2.87848 - 0.845198i) q^{9} +(-3.38028 - 1.16993i) q^{13} +(-0.539964 - 2.22576i) q^{19} +(-8.75337 - 0.835846i) q^{21} +(3.27430 + 3.77875i) q^{25} +(-4.72659 + 2.15856i) q^{27} +(8.77569 - 3.03729i) q^{31} +(5.89230 + 10.2058i) q^{37} +(6.08360 + 1.17252i) q^{39} +(4.69843 - 7.31091i) q^{43} +(16.6865 + 8.60247i) q^{49} +(1.47437 + 3.68280i) q^{57} +(1.00083 + 0.712685i) q^{61} +(15.2130 - 0.724685i) q^{63} +(8.18322 + 0.186740i) q^{67} +(-6.53832 + 9.18178i) q^{73} +(-6.54498 - 5.67126i) q^{75} +(0.356735 + 1.85092i) q^{79} +(7.57128 - 4.86577i) q^{81} +(-15.2768 - 9.81781i) q^{91} +(-14.2965 + 7.37038i) q^{93} +(-1.93786 + 1.11882i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20q + 6q^{7} + 6q^{9} + O(q^{10}) \) \( 20q + 6q^{7} + 6q^{9} + 9q^{13} - 8q^{19} + 6q^{21} + 10q^{25} - 3q^{31} + 10q^{37} - 9q^{39} - 5q^{49} + 141q^{57} + 27q^{61} + 147q^{63} + 11q^{67} - 180q^{73} - 166q^{79} - 18q^{81} - 36q^{91} - 3q^{93} + 33q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/804\mathbb{Z}\right)^\times\).

\(n\) \(269\) \(337\) \(403\)
\(\chi(n)\) \(-1\) \(e\left(\frac{49}{66}\right)\) \(1\)

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
\(3\) −1.71442 + 0.246497i −0.989821 + 0.142315i
\(4\) 0 0
\(5\) 0 0 −0.909632 0.415415i \(-0.863636\pi\)
0.909632 + 0.415415i \(0.136364\pi\)
\(6\) 0 0
\(7\) 4.93365 + 1.19689i 1.86474 + 0.452382i 0.998854 0.0478556i \(-0.0152387\pi\)
0.865888 + 0.500237i \(0.166754\pi\)
\(8\) 0 0
\(9\) 2.87848 0.845198i 0.959493 0.281733i
\(10\) 0 0
\(11\) 0 0 0.814576 0.580057i \(-0.196970\pi\)
−0.814576 + 0.580057i \(0.803030\pi\)
\(12\) 0 0
\(13\) −3.38028 1.16993i −0.937520 0.324479i −0.184767 0.982782i \(-0.559153\pi\)
−0.752753 + 0.658303i \(0.771274\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 0 0 0.0475819 0.998867i \(-0.484848\pi\)
−0.0475819 + 0.998867i \(0.515152\pi\)
\(18\) 0 0
\(19\) −0.539964 2.22576i −0.123876 0.510625i −0.999613 0.0278351i \(-0.991139\pi\)
0.875736 0.482790i \(-0.160376\pi\)
\(20\) 0 0
\(21\) −8.75337 0.835846i −1.91014 0.182397i
\(22\) 0 0
\(23\) 0 0 0.786053 0.618159i \(-0.212121\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(24\) 0 0
\(25\) 3.27430 + 3.77875i 0.654861 + 0.755750i
\(26\) 0 0
\(27\) −4.72659 + 2.15856i −0.909632 + 0.415415i
\(28\) 0 0
\(29\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(30\) 0 0
\(31\) 8.77569 3.03729i 1.57616 0.545514i 0.607589 0.794252i \(-0.292137\pi\)
0.968571 + 0.248738i \(0.0800157\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 5.89230 + 10.2058i 0.968688 + 1.67782i 0.699363 + 0.714767i \(0.253467\pi\)
0.269325 + 0.963049i \(0.413199\pi\)
\(38\) 0 0
\(39\) 6.08360 + 1.17252i 0.974156 + 0.187753i
\(40\) 0 0
\(41\) 0 0 −0.458227 0.888835i \(-0.651515\pi\)
0.458227 + 0.888835i \(0.348485\pi\)
\(42\) 0 0
\(43\) 4.69843 7.31091i 0.716505 1.11490i −0.271792 0.962356i \(-0.587616\pi\)
0.988296 0.152547i \(-0.0487475\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 0 0 −0.928368 0.371662i \(-0.878788\pi\)
0.928368 + 0.371662i \(0.121212\pi\)
\(48\) 0 0
\(49\) 16.6865 + 8.60247i 2.38378 + 1.22892i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 0 0 −0.540641 0.841254i \(-0.681818\pi\)
0.540641 + 0.841254i \(0.318182\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 1.47437 + 3.68280i 0.195285 + 0.487798i
\(58\) 0 0
\(59\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(60\) 0 0
\(61\) 1.00083 + 0.712685i 0.128143 + 0.0912500i 0.642331 0.766427i \(-0.277967\pi\)
−0.514188 + 0.857677i \(0.671907\pi\)
\(62\) 0 0
\(63\) 15.2130 0.724685i 1.91666 0.0913017i
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 8.18322 + 0.186740i 0.999740 + 0.0228140i
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 −0.0475819 0.998867i \(-0.515152\pi\)
0.0475819 + 0.998867i \(0.484848\pi\)
\(72\) 0 0
\(73\) −6.53832 + 9.18178i −0.765252 + 1.07465i 0.229598 + 0.973286i \(0.426259\pi\)
−0.994850 + 0.101361i \(0.967680\pi\)
\(74\) 0 0
\(75\) −6.54498 5.67126i −0.755750 0.654861i
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 0.356735 + 1.85092i 0.0401358 + 0.208244i 0.996461 0.0840621i \(-0.0267894\pi\)
−0.956325 + 0.292306i \(0.905577\pi\)
\(80\) 0 0
\(81\) 7.57128 4.86577i 0.841254 0.540641i
\(82\) 0 0
\(83\) 0 0 0.995472 0.0950560i \(-0.0303030\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(90\) 0 0
\(91\) −15.2768 9.81781i −1.60145 1.02919i
\(92\) 0 0
\(93\) −14.2965 + 7.37038i −1.48248 + 0.764273i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −1.93786 + 1.11882i −0.196760 + 0.113599i −0.595143 0.803620i \(-0.702905\pi\)
0.398384 + 0.917219i \(0.369571\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 0 0 −0.690079 0.723734i \(-0.742424\pi\)
0.690079 + 0.723734i \(0.257576\pi\)
\(102\) 0 0
\(103\) −6.59559 19.0567i −0.649883 1.87771i −0.432528 0.901620i \(-0.642378\pi\)
−0.217355 0.976093i \(-0.569743\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(108\) 0 0
\(109\) −15.7805 + 13.6739i −1.51150 + 1.30972i −0.755271 + 0.655412i \(0.772495\pi\)
−0.756227 + 0.654309i \(0.772960\pi\)
\(110\) 0 0
\(111\) −12.6176 16.0445i −1.19761 1.52288i
\(112\) 0 0
\(113\) 0 0 0.0950560 0.995472i \(-0.469697\pi\)
−0.0950560 + 0.995472i \(0.530303\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −10.7189 0.510603i −0.990960 0.0472052i
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 3.59775 10.3950i 0.327068 0.945001i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) −5.09365 + 20.9963i −0.451988 + 1.86312i 0.0507955 + 0.998709i \(0.483824\pi\)
−0.502784 + 0.864412i \(0.667691\pi\)
\(128\) 0 0
\(129\) −6.25298 + 13.6921i −0.550544 + 1.20552i
\(130\) 0 0
\(131\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(132\) 0 0
\(133\) 11.6274i 1.00822i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 0 0 0.989821 0.142315i \(-0.0454545\pi\)
−0.989821 + 0.142315i \(0.954545\pi\)
\(138\) 0 0
\(139\) 21.3812 + 9.76449i 1.81353 + 0.828213i 0.939712 + 0.341967i \(0.111093\pi\)
0.873822 + 0.486246i \(0.161634\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) −30.7281 10.6351i −2.53441 0.877168i
\(148\) 0 0
\(149\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(150\) 0 0
\(151\) 0.829457 17.4124i 0.0675003 1.41700i −0.670352 0.742043i \(-0.733857\pi\)
0.737853 0.674962i \(-0.235840\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 5.95608 4.68391i 0.475347 0.373817i −0.351551 0.936169i \(-0.614346\pi\)
0.826898 + 0.562352i \(0.190103\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 11.9203 20.6466i 0.933670 1.61716i 0.156680 0.987649i \(-0.449921\pi\)
0.776989 0.629514i \(-0.216746\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 0 0 0.723734 0.690079i \(-0.242424\pi\)
−0.723734 + 0.690079i \(0.757576\pi\)
\(168\) 0 0
\(169\) −0.161146 0.126727i −0.0123959 0.00974822i
\(170\) 0 0
\(171\) −3.43549 5.95043i −0.262718 0.455041i
\(172\) 0 0
\(173\) 0 0 −0.981929 0.189251i \(-0.939394\pi\)
0.981929 + 0.189251i \(0.0606061\pi\)
\(174\) 0 0
\(175\) 11.6315 + 22.5620i 0.879259 + 1.70553i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 0 0 −0.989821 0.142315i \(-0.954545\pi\)
0.989821 + 0.142315i \(0.0454545\pi\)
\(180\) 0 0
\(181\) −14.9975 6.00408i −1.11475 0.446280i −0.260153 0.965567i \(-0.583773\pi\)
−0.854599 + 0.519288i \(0.826197\pi\)
\(182\) 0 0
\(183\) −1.89151 0.975143i −0.139825 0.0720846i
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) −25.9029 + 4.99237i −1.88416 + 0.363141i
\(190\) 0 0
\(191\) 0 0 −0.371662 0.928368i \(-0.621212\pi\)
0.371662 + 0.928368i \(0.378788\pi\)
\(192\) 0 0
\(193\) −13.4715 + 15.5469i −0.969697 + 1.11909i 0.0231538 + 0.999732i \(0.492629\pi\)
−0.992851 + 0.119359i \(0.961916\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 0 0 0.998867 0.0475819i \(-0.0151515\pi\)
−0.998867 + 0.0475819i \(0.984848\pi\)
\(198\) 0 0
\(199\) −19.1607 18.2697i −1.35826 1.29510i −0.917642 0.397409i \(-0.869909\pi\)
−0.440622 0.897693i \(-0.645242\pi\)
\(200\) 0 0
\(201\) −14.0755 + 1.69698i −0.992811 + 0.119696i
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) −12.6468 + 5.06300i −0.870638 + 0.348551i −0.763589 0.645703i \(-0.776565\pi\)
−0.107049 + 0.994254i \(0.534140\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 46.9314 4.48141i 3.18591 0.304218i
\(218\) 0 0
\(219\) 8.94615 17.3531i 0.604525 1.17261i
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) −4.04652 + 28.1442i −0.270975 + 1.88467i 0.167412 + 0.985887i \(0.446459\pi\)
−0.438387 + 0.898786i \(0.644450\pi\)
\(224\) 0 0
\(225\) 12.6188 + 8.10961i 0.841254 + 0.540641i
\(226\) 0 0
\(227\) 0 0 0.888835 0.458227i \(-0.151515\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(228\) 0 0
\(229\) 5.22106 27.0894i 0.345018 1.79012i −0.231287 0.972886i \(-0.574293\pi\)
0.576304 0.817235i \(-0.304494\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 0 0 0.618159 0.786053i \(-0.287879\pi\)
−0.618159 + 0.786053i \(0.712121\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) −1.06784 3.08532i −0.0693635 0.200413i
\(238\) 0 0
\(239\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(240\) 0 0
\(241\) −12.7813 27.9872i −0.823317 1.80281i −0.533712 0.845666i \(-0.679203\pi\)
−0.289605 0.957146i \(-0.593524\pi\)
\(242\) 0 0
\(243\) −11.7810 + 10.2083i −0.755750 + 0.654861i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −0.778747 + 8.15541i −0.0495505 + 0.518916i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 0 0 −0.998867 0.0475819i \(-0.984848\pi\)
0.998867 + 0.0475819i \(0.0151515\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 0 0 −0.580057 0.814576i \(-0.696970\pi\)
0.580057 + 0.814576i \(0.303030\pi\)
\(258\) 0 0
\(259\) 16.8553 + 57.4040i 1.04734 + 3.56691i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(270\) 0 0
\(271\) −6.71769 + 0.965858i −0.408071 + 0.0586717i −0.343294 0.939228i \(-0.611543\pi\)
−0.0647769 + 0.997900i \(0.520634\pi\)
\(272\) 0 0
\(273\) 28.6109 + 13.0662i 1.73161 + 0.790801i
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −18.7331 + 5.50053i −1.12556 + 0.330495i −0.790962 0.611866i \(-0.790419\pi\)
−0.334600 + 0.942360i \(0.608601\pi\)
\(278\) 0 0
\(279\) 22.6935 16.1600i 1.35863 0.967473i
\(280\) 0 0
\(281\) 0 0 −0.945001 0.327068i \(-0.893939\pi\)
0.945001 + 0.327068i \(0.106061\pi\)
\(282\) 0 0
\(283\) −21.8251 6.40842i −1.29737 0.380941i −0.441091 0.897462i \(-0.645408\pi\)
−0.856274 + 0.516522i \(0.827227\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −16.9230 1.61595i −0.995472 0.0950560i
\(290\) 0 0
\(291\) 3.04652 2.39581i 0.178590 0.140445i
\(292\) 0 0
\(293\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 0 0
\(300\) 0 0
\(301\) 31.9308 30.4459i 1.84046 1.75487i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) −0.0635523 0.0122487i −0.00362712 0.000699071i 0.187437 0.982277i \(-0.439982\pi\)
−0.191064 + 0.981577i \(0.561194\pi\)
\(308\) 0 0
\(309\) 16.0050 + 31.0454i 0.910494 + 1.76611i
\(310\) 0 0
\(311\) 0 0 0.540641 0.841254i \(-0.318182\pi\)
−0.540641 + 0.841254i \(0.681818\pi\)
\(312\) 0 0
\(313\) −20.1846 2.90210i −1.14090 0.164037i −0.454146 0.890927i \(-0.650056\pi\)
−0.686753 + 0.726891i \(0.740965\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 0 0 −0.888835 0.458227i \(-0.848485\pi\)
0.888835 + 0.458227i \(0.151515\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) 0 0
\(325\) −6.64720 16.6039i −0.368720 0.921019i
\(326\) 0 0
\(327\) 23.6839 27.3326i 1.30972 1.51150i
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −27.9413 + 1.33101i −1.53579 + 0.0731589i −0.798327 0.602224i \(-0.794281\pi\)
−0.737467 + 0.675383i \(0.763978\pi\)
\(332\) 0 0
\(333\) 25.5867 + 24.3969i 1.40214 + 1.33694i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −13.8296 + 14.5040i −0.753344 + 0.790085i −0.983082 0.183168i \(-0.941365\pi\)
0.229737 + 0.973253i \(0.426213\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 45.1716 + 39.1414i 2.43904 + 2.11344i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 0 0 −0.189251 0.981929i \(-0.560606\pi\)
0.189251 + 0.981929i \(0.439394\pi\)
\(348\) 0 0
\(349\) 25.5438 16.4160i 1.36733 0.878727i 0.368620 0.929580i \(-0.379831\pi\)
0.998706 + 0.0508535i \(0.0161942\pi\)
\(350\) 0 0
\(351\) 18.5025 1.76678i 0.987592 0.0943036i
\(352\) 0 0
\(353\) 0 0 0.458227 0.888835i \(-0.348485\pi\)
−0.458227 + 0.888835i \(0.651515\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(360\) 0 0
\(361\) 12.2254 6.30264i 0.643443 0.331718i
\(362\) 0 0
\(363\) −3.60572 + 18.7083i −0.189251 + 0.981929i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 12.0343 15.3029i 0.628185 0.798803i −0.362929 0.931817i \(-0.618223\pi\)
0.991114 + 0.133014i \(0.0424656\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 18.3674 + 10.6044i 0.951027 + 0.549076i 0.893400 0.449262i \(-0.148313\pi\)
0.0576272 + 0.998338i \(0.481647\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) −13.6349 17.3382i −0.700380 0.890606i 0.297564 0.954702i \(-0.403826\pi\)
−0.997944 + 0.0640964i \(0.979583\pi\)
\(380\) 0 0
\(381\) 3.55714 37.2521i 0.182238 1.90848i
\(382\) 0 0
\(383\) 0 0 0.971812 0.235759i \(-0.0757576\pi\)
−0.971812 + 0.235759i \(0.924242\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 7.34518 25.0154i 0.373377 1.27160i
\(388\) 0 0
\(389\) 0 0 0.327068 0.945001i \(-0.393939\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −16.5104 + 36.1528i −0.828636 + 1.81446i −0.348249 + 0.937402i \(0.613224\pi\)
−0.480387 + 0.877057i \(0.659504\pi\)
\(398\) 0 0
\(399\) 2.86611 + 19.9343i 0.143485 + 0.997961i
\(400\) 0 0
\(401\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(402\) 0 0
\(403\) −33.2177 −1.65469
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) −39.1856 9.50631i −1.93760 0.470057i −0.987345 0.158587i \(-0.949306\pi\)
−0.950256 0.311470i \(-0.899179\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −39.0634 11.4700i −1.91294 0.561690i
\(418\) 0 0
\(419\) 0 0 0.0475819 0.998867i \(-0.484848\pi\)
−0.0475819 + 0.998867i \(0.515152\pi\)
\(420\) 0 0
\(421\) 6.63857 + 27.3645i 0.323544 + 1.33367i 0.868703 + 0.495334i \(0.164954\pi\)
−0.545159 + 0.838333i \(0.683531\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 4.08472 + 4.71402i 0.197673 + 0.228127i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(432\) 0 0
\(433\) 27.1532 9.39782i 1.30490 0.451631i 0.415848 0.909434i \(-0.363485\pi\)
0.889053 + 0.457804i \(0.151364\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) −16.2369 28.1232i −0.774947 1.34225i −0.934824 0.355111i \(-0.884443\pi\)
0.159877 0.987137i \(-0.448890\pi\)
\(440\) 0 0
\(441\) 55.3024 + 10.6587i 2.63345 + 0.507556i
\(442\) 0 0
\(443\) 0 0 −0.458227 0.888835i \(-0.651515\pi\)
0.458227 + 0.888835i \(0.348485\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 0 0 −0.928368 0.371662i \(-0.878788\pi\)
0.928368 + 0.371662i \(0.121212\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) 2.87007 + 30.0567i 0.134848 + 1.41219i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −41.9824 + 8.09144i −1.96385 + 0.378502i −0.981563 + 0.191139i \(0.938782\pi\)
−0.982291 + 0.187363i \(0.940006\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(462\) 0 0
\(463\) 34.3720 + 24.4762i 1.59740 + 1.13751i 0.912657 + 0.408726i \(0.134027\pi\)
0.684747 + 0.728781i \(0.259913\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 0 0 −0.723734 0.690079i \(-0.757576\pi\)
0.723734 + 0.690079i \(0.242424\pi\)
\(468\) 0 0
\(469\) 40.1496 + 10.7157i 1.85394 + 0.494806i
\(470\) 0 0
\(471\) −9.05666 + 9.49836i −0.417309 + 0.437661i
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 6.64259 9.32821i 0.304783 0.428008i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 0 0 0.928368 0.371662i \(-0.121212\pi\)
−0.928368 + 0.371662i \(0.878788\pi\)
\(480\) 0 0
\(481\) −7.97762 41.3918i −0.363748 1.88730i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 20.0636 38.9180i 0.909169 1.76354i 0.342739 0.939430i \(-0.388645\pi\)
0.566429 0.824110i \(-0.308325\pi\)
\(488\) 0 0
\(489\) −15.3471 + 38.3352i −0.694020 + 1.73358i
\(490\) 0 0
\(491\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 3.26271 1.88372i 0.146059 0.0843271i −0.425190 0.905104i \(-0.639793\pi\)
0.571248 + 0.820777i \(0.306459\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 0 0 −0.690079 0.723734i \(-0.742424\pi\)
0.690079 + 0.723734i \(0.257576\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 0.307510 + 0.177541i 0.0136570 + 0.00788488i
\(508\) 0 0
\(509\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(510\) 0 0
\(511\) −43.2473 + 37.4740i −1.91315 + 1.65775i
\(512\) 0 0
\(513\) 7.35663 + 9.35472i 0.324803 + 0.413021i
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 0 0 0.281733 0.959493i \(-0.409091\pi\)
−0.281733 + 0.959493i \(0.590909\pi\)
\(522\) 0 0
\(523\) 1.63907 4.73579i 0.0716716 0.207081i −0.903476 0.428640i \(-0.858993\pi\)
0.975147 + 0.221558i \(0.0711142\pi\)
\(524\) 0 0
\(525\) −25.5028 35.8136i −1.11303 1.56303i
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) 5.42246 22.3517i 0.235759 0.971812i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) 42.0955 + 19.2244i 1.80983 + 0.826521i 0.947168 + 0.320739i \(0.103931\pi\)
0.862661 + 0.505782i \(0.168796\pi\)
\(542\) 0 0
\(543\) 27.1919 + 6.59669i 1.16692 + 0.283091i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 31.6063 22.5067i 1.35139 0.962318i 0.351730 0.936101i \(-0.385593\pi\)
0.999656 0.0262168i \(-0.00834602\pi\)
\(548\) 0 0
\(549\) 3.48322 + 1.20555i 0.148660 + 0.0514518i
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) −0.455339 + 9.55874i −0.0193630 + 0.406479i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 0 0 −0.995472 0.0950560i \(-0.969697\pi\)
0.995472 + 0.0950560i \(0.0303030\pi\)
\(558\) 0 0
\(559\) −24.4352 + 19.2161i −1.03350 + 0.812753i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 0 0 0.909632 0.415415i \(-0.136364\pi\)
−0.909632 + 0.415415i \(0.863636\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 43.1778 14.9440i 1.81330 0.627588i
\(568\) 0 0
\(569\) 0 0 0.723734 0.690079i \(-0.242424\pi\)
−0.723734 + 0.690079i \(0.757576\pi\)
\(570\) 0 0
\(571\) 24.8323 + 19.5283i 1.03920 + 0.817234i 0.983444 0.181210i \(-0.0580014\pi\)
0.0557537 + 0.998445i \(0.482244\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 8.32425 + 16.1468i 0.346543 + 0.672200i 0.996111 0.0881033i \(-0.0280806\pi\)
−0.649568 + 0.760303i \(0.725050\pi\)
\(578\) 0 0
\(579\) 19.2635 29.9746i 0.800564 1.24570i
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 0 0 −0.0950560 0.995472i \(-0.530303\pi\)
0.0950560 + 0.995472i \(0.469697\pi\)
\(588\) 0 0
\(589\) −11.4989 17.8926i −0.473802 0.737250i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 0 0 −0.371662 0.928368i \(-0.621212\pi\)
0.371662 + 0.928368i \(0.378788\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 37.3529 + 26.5989i 1.52875 + 1.08862i
\(598\) 0 0
\(599\) 0 0 0.998867 0.0475819i \(-0.0151515\pi\)
−0.998867 + 0.0475819i \(0.984848\pi\)
\(600\) 0 0
\(601\) 13.5916 + 12.9596i 0.554412 + 0.528631i 0.914659 0.404226i \(-0.132459\pi\)
−0.360247 + 0.932857i \(0.617308\pi\)
\(602\) 0 0
\(603\) 23.7131 6.37891i 0.965671 0.259769i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 2.16741 + 45.4996i 0.0879727 + 1.84677i 0.424897 + 0.905242i \(0.360310\pi\)
−0.336925 + 0.941532i \(0.609387\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) −12.3793 + 4.95591i −0.499994 + 0.200168i −0.607930 0.793990i \(-0.708000\pi\)
0.107936 + 0.994158i \(0.465576\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(618\) 0 0
\(619\) −49.3767 + 4.71491i −1.98462 + 0.189508i −0.984738 + 0.174042i \(0.944317\pi\)
−0.999880 + 0.0154656i \(0.995077\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −3.55787 + 24.7455i −0.142315 + 0.989821i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 7.58920 39.3765i 0.302121 1.56755i −0.440444 0.897780i \(-0.645179\pi\)
0.742565 0.669774i \(-0.233609\pi\)
\(632\) 0 0
\(633\) 20.4338 11.7975i 0.812172 0.468908i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) −46.3406 48.6006i −1.83608 1.92563i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(642\) 0 0
\(643\) 6.97674 + 15.2769i 0.275136 + 0.602463i 0.995874 0.0907437i \(-0.0289244\pi\)
−0.720738 + 0.693207i \(0.756197\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 −0.618159 0.786053i \(-0.712121\pi\)
0.618159 + 0.786053i \(0.287879\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) −79.3556 + 19.2515i −3.11019 + 0.754524i
\(652\) 0 0
\(653\) 0 0 −0.998867 0.0475819i \(-0.984848\pi\)
0.998867 + 0.0475819i \(0.0151515\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) −11.0600 + 31.9557i −0.431491 + 1.24671i
\(658\) 0 0
\(659\) 0 0 −0.580057 0.814576i \(-0.696970\pi\)
0.580057 + 0.814576i \(0.303030\pi\)
\(660\) 0 0
\(661\) −10.2293 34.8379i −0.397875 1.35504i −0.878345 0.478027i \(-0.841352\pi\)
0.480470 0.877011i \(-0.340466\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 49.2484i 1.90405i
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) −48.2699 + 6.94017i −1.86067 + 0.267524i −0.978927 0.204209i \(-0.934538\pi\)
−0.881742 + 0.471732i \(0.843629\pi\)
\(674\) 0 0
\(675\) −23.6329 10.7928i −0.909632 0.415415i
\(676\) 0 0
\(677\) 0 0 −0.971812 0.235759i \(-0.924242\pi\)
0.971812 + 0.235759i \(0.0757576\pi\)
\(678\) 0 0
\(679\) −10.8998 + 3.20047i −0.418296 + 0.122823i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 0 0 −0.945001 0.327068i \(-0.893939\pi\)
0.945001 + 0.327068i \(0.106061\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) −2.27365 + 47.7297i −0.0867450 + 1.82100i
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) −44.3072 4.23083i −1.68553 0.160948i −0.792171 0.610299i \(-0.791049\pi\)
−0.893356 + 0.449350i \(0.851656\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 0 0 0.945001 0.327068i \(-0.106061\pi\)
−0.945001 + 0.327068i \(0.893939\pi\)
\(702\) 0 0
\(703\) 19.5340 18.6256i 0.736737 0.702478i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) −50.2106 9.67731i −1.88570 0.363439i −0.889991 0.455978i \(-0.849290\pi\)
−0.995709 + 0.0925387i \(0.970502\pi\)
\(710\) 0 0
\(711\) 2.59124 + 5.02631i 0.0971792 + 0.188501i
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 −0.888835 0.458227i \(-0.848485\pi\)
0.888835 + 0.458227i \(0.151515\pi\)
\(720\) 0 0
\(721\) −9.73153 101.913i −0.362421 3.79545i
\(722\) 0 0
\(723\) 28.8113 + 44.8313i 1.07150 + 1.66729i
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 2.80575 + 7.00842i 0.104059 + 0.259928i 0.971256 0.238039i \(-0.0765045\pi\)
−0.867196 + 0.497966i \(0.834080\pi\)
\(728\) 0 0
\(729\) 17.6812 20.4052i 0.654861 0.755750i
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 5.84943 0.278643i 0.216053 0.0102919i 0.0607239 0.998155i \(-0.480659\pi\)
0.155330 + 0.987863i \(0.450356\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) −36.9309 + 38.7320i −1.35852 + 1.42478i −0.551621 + 0.834095i \(0.685990\pi\)
−0.806903 + 0.590684i \(0.798858\pi\)
\(740\) 0 0
\(741\) −0.675180 14.1738i −0.0248033 0.520686i
\(742\) 0 0
\(743\) 0 0 0.580057 0.814576i \(-0.303030\pi\)
−0.580057 + 0.814576i \(0.696970\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −28.9231 + 18.5878i −1.05542 + 0.678278i −0.948753 0.316017i \(-0.897654\pi\)
−0.106667 + 0.994295i \(0.534018\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 2.58391 6.45428i 0.0939136 0.234585i −0.873972 0.485977i \(-0.838464\pi\)
0.967885 + 0.251392i \(0.0808882\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(762\) 0 0
\(763\) −94.2216 + 48.5746i −3.41105 + 1.75852i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 0 0
\(769\) 33.8767 43.0777i 1.22162 1.55342i 0.489981 0.871733i \(-0.337004\pi\)
0.731643 0.681688i \(-0.238754\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 0 0 −0.327068 0.945001i \(-0.606061\pi\)
0.327068 + 0.945001i \(0.393939\pi\)
\(774\) 0 0
\(775\) 40.2114 + 23.2161i 1.44444 + 0.833946i
\(776\) 0 0
\(777\) −43.0470 94.2599i −1.54430 3.38155i
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) −44.5400 2.12170i −1.58768 0.0756305i −0.764959 0.644078i \(-0.777241\pi\)
−0.822719 + 0.568448i \(0.807544\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) −2.54928 3.57997i −0.0905277 0.127128i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 0 0 0.235759 0.971812i \(-0.424242\pi\)
−0.235759 + 0.971812i \(0.575758\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0 0