Properties

Label 927.1.v.a.127.1
Level $927$
Weight $1$
Character 927.127
Analytic conductor $0.463$
Analytic rank $0$
Dimension $16$
Projective image $D_{34}$
CM discriminant -3
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 927 = 3^{2} \cdot 103 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 927.v (of order \(34\), degree \(16\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.462633266711\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\Q(\zeta_{34})\)
Defining polynomial: \(x^{16} - x^{15} + x^{14} - x^{13} + x^{12} - x^{11} + x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Projective image: \(D_{34}\)
Projective field: Galois closure of \(\mathbb{Q}[x]/(x^{34} - \cdots)\)

Embedding invariants

Embedding label 127.1
Root \(0.273663 + 0.961826i\) of defining polynomial
Character \(\chi\) \(=\) 927.127
Dual form 927.1.v.a.73.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.0922684 + 0.995734i) q^{4} +(-1.12388 + 1.48826i) q^{7} +O(q^{10})\) \(q+(-0.0922684 + 0.995734i) q^{4} +(-1.12388 + 1.48826i) q^{7} +(0.111208 - 0.147263i) q^{13} +(-0.982973 - 0.183750i) q^{16} +(-1.58561 - 0.614268i) q^{19} +(0.445738 + 0.895163i) q^{25} +(-1.37821 - 1.25640i) q^{28} +(-0.353470 + 1.89090i) q^{31} +(1.53511 - 0.436776i) q^{37} +(1.72198 + 0.489946i) q^{43} +(-0.678142 - 2.38342i) q^{49} +(0.136374 + 0.124322i) q^{52} +(0.876298 + 1.75984i) q^{61} +(0.273663 - 0.961826i) q^{64} +(1.07524 - 0.811985i) q^{67} +(0.193463 + 0.312454i) q^{73} +(0.757949 - 1.52217i) q^{76} +(-1.02474 - 0.634493i) q^{79} +(0.0941813 + 0.331013i) q^{91} +(-0.397365 + 0.798017i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + q^{4} - 2q^{7} + O(q^{10}) \) \( 16q + q^{4} - 2q^{7} + 2q^{13} - q^{16} - 2q^{19} - q^{25} + 2q^{28} - 3q^{49} - 2q^{52} + 2q^{61} + q^{64} + 2q^{76} + 2q^{79} - 13q^{91} - 15q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/927\mathbb{Z}\right)^\times\).

\(n\) \(722\) \(829\)
\(\chi(n)\) \(1\) \(e\left(\frac{23}{34}\right)\)

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 −0.673696 0.739009i \(-0.735294\pi\)
0.673696 + 0.739009i \(0.264706\pi\)
\(3\) 0 0
\(4\) −0.0922684 + 0.995734i −0.0922684 + 0.995734i
\(5\) 0 0 −0.850217 0.526432i \(-0.823529\pi\)
0.850217 + 0.526432i \(0.176471\pi\)
\(6\) 0 0
\(7\) −1.12388 + 1.48826i −1.12388 + 1.48826i −0.273663 + 0.961826i \(0.588235\pi\)
−0.850217 + 0.526432i \(0.823529\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 0 0 0.739009 0.673696i \(-0.235294\pi\)
−0.739009 + 0.673696i \(0.764706\pi\)
\(12\) 0 0
\(13\) 0.111208 0.147263i 0.111208 0.147263i −0.739009 0.673696i \(-0.764706\pi\)
0.850217 + 0.526432i \(0.176471\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −0.982973 0.183750i −0.982973 0.183750i
\(17\) 0 0 0.895163 0.445738i \(-0.147059\pi\)
−0.895163 + 0.445738i \(0.852941\pi\)
\(18\) 0 0
\(19\) −1.58561 0.614268i −1.58561 0.614268i −0.602635 0.798017i \(-0.705882\pi\)
−0.982973 + 0.183750i \(0.941176\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 0 0 0.673696 0.739009i \(-0.264706\pi\)
−0.673696 + 0.739009i \(0.735294\pi\)
\(24\) 0 0
\(25\) 0.445738 + 0.895163i 0.445738 + 0.895163i
\(26\) 0 0
\(27\) 0 0
\(28\) −1.37821 1.25640i −1.37821 1.25640i
\(29\) 0 0 0.526432 0.850217i \(-0.323529\pi\)
−0.526432 + 0.850217i \(0.676471\pi\)
\(30\) 0 0
\(31\) −0.353470 + 1.89090i −0.353470 + 1.89090i 0.0922684 + 0.995734i \(0.470588\pi\)
−0.445738 + 0.895163i \(0.647059\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 1.53511 0.436776i 1.53511 0.436776i 0.602635 0.798017i \(-0.294118\pi\)
0.932472 + 0.361242i \(0.117647\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 0 0 −0.526432 0.850217i \(-0.676471\pi\)
0.526432 + 0.850217i \(0.323529\pi\)
\(42\) 0 0
\(43\) 1.72198 + 0.489946i 1.72198 + 0.489946i 0.982973 0.183750i \(-0.0588235\pi\)
0.739009 + 0.673696i \(0.235294\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(48\) 0 0
\(49\) −0.678142 2.38342i −0.678142 2.38342i
\(50\) 0 0
\(51\) 0 0
\(52\) 0.136374 + 0.124322i 0.136374 + 0.124322i
\(53\) 0 0 −0.932472 0.361242i \(-0.882353\pi\)
0.932472 + 0.361242i \(0.117647\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 0 0 0.798017 0.602635i \(-0.205882\pi\)
−0.798017 + 0.602635i \(0.794118\pi\)
\(60\) 0 0
\(61\) 0.876298 + 1.75984i 0.876298 + 1.75984i 0.602635 + 0.798017i \(0.294118\pi\)
0.273663 + 0.961826i \(0.411765\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0.273663 0.961826i 0.273663 0.961826i
\(65\) 0 0
\(66\) 0 0
\(67\) 1.07524 0.811985i 1.07524 0.811985i 0.0922684 0.995734i \(-0.470588\pi\)
0.982973 + 0.183750i \(0.0588235\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 0.850217 0.526432i \(-0.176471\pi\)
−0.850217 + 0.526432i \(0.823529\pi\)
\(72\) 0 0
\(73\) 0.193463 + 0.312454i 0.193463 + 0.312454i 0.932472 0.361242i \(-0.117647\pi\)
−0.739009 + 0.673696i \(0.764706\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0.757949 1.52217i 0.757949 1.52217i
\(77\) 0 0
\(78\) 0 0
\(79\) −1.02474 0.634493i −1.02474 0.634493i −0.0922684 0.995734i \(-0.529412\pi\)
−0.932472 + 0.361242i \(0.882353\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 0 0 −0.798017 0.602635i \(-0.794118\pi\)
0.798017 + 0.602635i \(0.205882\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 0 0 −0.0922684 0.995734i \(-0.529412\pi\)
0.0922684 + 0.995734i \(0.470588\pi\)
\(90\) 0 0
\(91\) 0.0941813 + 0.331013i 0.0941813 + 0.331013i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −0.397365 + 0.798017i −0.397365 + 0.798017i 0.602635 + 0.798017i \(0.294118\pi\)
−1.00000 \(\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −0.932472 + 0.361242i −0.932472 + 0.361242i
\(101\) 0 0 0.739009 0.673696i \(-0.235294\pi\)
−0.739009 + 0.673696i \(0.764706\pi\)
\(102\) 0 0
\(103\) 0.273663 + 0.961826i 0.273663 + 0.961826i
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 −0.995734 0.0922684i \(-0.970588\pi\)
0.995734 + 0.0922684i \(0.0294118\pi\)
\(108\) 0 0
\(109\) −0.328972 0.163808i −0.328972 0.163808i 0.273663 0.961826i \(-0.411765\pi\)
−0.602635 + 0.798017i \(0.705882\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 1.37821 1.25640i 1.37821 1.25640i
\(113\) 0 0 0.982973 0.183750i \(-0.0588235\pi\)
−0.982973 + 0.183750i \(0.941176\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 0.0922684 0.995734i 0.0922684 0.995734i
\(122\) 0 0
\(123\) 0 0
\(124\) −1.85022 0.526432i −1.85022 0.526432i
\(125\) 0 0
\(126\) 0 0
\(127\) 0.709310 1.14558i 0.709310 1.14558i −0.273663 0.961826i \(-0.588235\pi\)
0.982973 0.183750i \(-0.0588235\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 0 0 0.673696 0.739009i \(-0.264706\pi\)
−0.673696 + 0.739009i \(0.735294\pi\)
\(132\) 0 0
\(133\) 2.69622 1.66943i 2.69622 1.66943i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 0 0 0.361242 0.932472i \(-0.382353\pi\)
−0.361242 + 0.932472i \(0.617647\pi\)
\(138\) 0 0
\(139\) −0.329838 0.436776i −0.329838 0.436776i 0.602635 0.798017i \(-0.294118\pi\)
−0.932472 + 0.361242i \(0.882353\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 0 0
\(148\) 0.293271 + 1.56886i 0.293271 + 1.56886i
\(149\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(150\) 0 0
\(151\) −0.193463 1.03494i −0.193463 1.03494i −0.932472 0.361242i \(-0.882353\pi\)
0.739009 0.673696i \(-0.235294\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 1.01267 0.288130i 1.01267 0.288130i 0.273663 0.961826i \(-0.411765\pi\)
0.739009 + 0.673696i \(0.235294\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 0.404479 1.42160i 0.404479 1.42160i −0.445738 0.895163i \(-0.647059\pi\)
0.850217 0.526432i \(-0.176471\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 0 0 −0.961826 0.273663i \(-0.911765\pi\)
0.961826 + 0.273663i \(0.0882353\pi\)
\(168\) 0 0
\(169\) 0.264344 + 0.929072i 0.264344 + 0.929072i
\(170\) 0 0
\(171\) 0 0
\(172\) −0.646741 + 1.66943i −0.646741 + 1.66943i
\(173\) 0 0 0.445738 0.895163i \(-0.352941\pi\)
−0.445738 + 0.895163i \(0.647059\pi\)
\(174\) 0 0
\(175\) −1.83319 0.342683i −1.83319 0.342683i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 0 0 −0.895163 0.445738i \(-0.852941\pi\)
0.895163 + 0.445738i \(0.147059\pi\)
\(180\) 0 0
\(181\) −0.328972 + 0.163808i −0.328972 + 0.163808i −0.602635 0.798017i \(-0.705882\pi\)
0.273663 + 0.961826i \(0.411765\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 0 0 −0.982973 0.183750i \(-0.941176\pi\)
0.982973 + 0.183750i \(0.0588235\pi\)
\(192\) 0 0
\(193\) −1.42871 1.07891i −1.42871 1.07891i −0.982973 0.183750i \(-0.941176\pi\)
−0.445738 0.895163i \(-0.647059\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 2.43582 0.455335i 2.43582 0.455335i
\(197\) 0 0 0.739009 0.673696i \(-0.235294\pi\)
−0.739009 + 0.673696i \(0.764706\pi\)
\(198\) 0 0
\(199\) 1.42871 + 1.07891i 1.42871 + 1.07891i 0.982973 + 0.183750i \(0.0588235\pi\)
0.445738 + 0.895163i \(0.352941\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) −0.136374 + 0.124322i −0.136374 + 0.124322i
\(209\) 0 0
\(210\) 0 0
\(211\) −1.04837 + 1.69318i −1.04837 + 1.69318i −0.445738 + 0.895163i \(0.647059\pi\)
−0.602635 + 0.798017i \(0.705882\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) −2.41689 2.65120i −2.41689 2.65120i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 0.658809 + 1.32307i 0.658809 + 1.32307i 0.932472 + 0.361242i \(0.117647\pi\)
−0.273663 + 0.961826i \(0.588235\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 0 0 0.273663 0.961826i \(-0.411765\pi\)
−0.273663 + 0.961826i \(0.588235\pi\)
\(228\) 0 0
\(229\) −0.404479 0.368731i −0.404479 0.368731i 0.445738 0.895163i \(-0.352941\pi\)
−0.850217 + 0.526432i \(0.823529\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 0 0 0.445738 0.895163i \(-0.352941\pi\)
−0.445738 + 0.895163i \(0.647059\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 −0.895163 0.445738i \(-0.852941\pi\)
0.895163 + 0.445738i \(0.147059\pi\)
\(240\) 0 0
\(241\) −0.486734 1.25640i −0.486734 1.25640i −0.932472 0.361242i \(-0.882353\pi\)
0.445738 0.895163i \(-0.352941\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) −1.83319 + 0.710182i −1.83319 + 0.710182i
\(245\) 0 0
\(246\) 0 0
\(247\) −0.266792 + 0.165190i −0.266792 + 0.165190i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 0 0 0.982973 0.183750i \(-0.0588235\pi\)
−0.982973 + 0.183750i \(0.941176\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) 0.932472 + 0.361242i 0.932472 + 0.361242i
\(257\) 0 0 −0.739009 0.673696i \(-0.764706\pi\)
0.739009 + 0.673696i \(0.235294\pi\)
\(258\) 0 0
\(259\) −1.07524 + 2.77552i −1.07524 + 2.77552i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) 0.709310 + 1.14558i 0.709310 + 1.14558i
\(269\) 0 0 0.995734 0.0922684i \(-0.0294118\pi\)
−0.995734 + 0.0922684i \(0.970588\pi\)
\(270\) 0 0
\(271\) 0.576554 + 1.48826i 0.576554 + 1.48826i 0.850217 + 0.526432i \(0.176471\pi\)
−0.273663 + 0.961826i \(0.588235\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 0.554262 + 0.895163i 0.554262 + 0.895163i 1.00000 \(0\)
−0.445738 + 0.895163i \(0.647059\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 0 0 −0.739009 0.673696i \(-0.764706\pi\)
0.739009 + 0.673696i \(0.235294\pi\)
\(282\) 0 0
\(283\) 1.98297 0.183750i 1.98297 0.183750i 0.982973 0.183750i \(-0.0588235\pi\)
1.00000 \(0\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 0.602635 0.798017i 0.602635 0.798017i
\(290\) 0 0
\(291\) 0 0
\(292\) −0.328972 + 0.163808i −0.328972 + 0.163808i
\(293\) 0 0 −0.982973 0.183750i \(-0.941176\pi\)
0.982973 + 0.183750i \(0.0588235\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 0 0
\(300\) 0 0
\(301\) −2.66447 + 2.01211i −2.66447 + 2.01211i
\(302\) 0 0
\(303\) 0 0
\(304\) 1.44574 + 0.895163i 1.44574 + 0.895163i
\(305\) 0 0
\(306\) 0 0
\(307\) −1.29596 1.42160i −1.29596 1.42160i −0.850217 0.526432i \(-0.823529\pi\)
−0.445738 0.895163i \(-0.647059\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 −0.673696 0.739009i \(-0.735294\pi\)
0.673696 + 0.739009i \(0.264706\pi\)
\(312\) 0 0
\(313\) 0.111208 1.20013i 0.111208 1.20013i −0.739009 0.673696i \(-0.764706\pi\)
0.850217 0.526432i \(-0.176471\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0.726337 0.961826i 0.726337 0.961826i
\(317\) 0 0 0.798017 0.602635i \(-0.205882\pi\)
−0.798017 + 0.602635i \(0.794118\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) 0 0
\(325\) 0.181395 + 0.0339085i 0.181395 + 0.0339085i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −1.58923 0.147263i −1.58923 0.147263i −0.739009 0.673696i \(-0.764706\pi\)
−0.850217 + 0.526432i \(0.823529\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 1.09227 + 0.995734i 1.09227 + 0.995734i 1.00000 \(0\)
0.0922684 + 0.995734i \(0.470588\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 2.57029 + 0.995734i 2.57029 + 0.995734i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 0 0 −0.361242 0.932472i \(-0.617647\pi\)
0.361242 + 0.932472i \(0.382353\pi\)
\(348\) 0 0
\(349\) −1.91545 + 0.177492i −1.91545 + 0.177492i −0.982973 0.183750i \(-0.941176\pi\)
−0.932472 + 0.361242i \(0.882353\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 0 0 −0.602635 0.798017i \(-0.705882\pi\)
0.602635 + 0.798017i \(0.294118\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 0 0 0.361242 0.932472i \(-0.382353\pi\)
−0.361242 + 0.932472i \(0.617647\pi\)
\(360\) 0 0
\(361\) 1.39782 + 1.27428i 1.39782 + 1.27428i
\(362\) 0 0
\(363\) 0 0
\(364\) −0.338291 + 0.0632375i −0.338291 + 0.0632375i
\(365\) 0 0
\(366\) 0 0
\(367\) −0.538007 + 0.100571i −0.538007 + 0.100571i −0.445738 0.895163i \(-0.647059\pi\)
−0.0922684 + 0.995734i \(0.529412\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) −0.149783 + 0.526432i −0.149783 + 0.526432i 0.850217 + 0.526432i \(0.176471\pi\)
−1.00000 \(\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 0.646741 + 0.322039i 0.646741 + 0.322039i 0.739009 0.673696i \(-0.235294\pi\)
−0.0922684 + 0.995734i \(0.529412\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 0 0 −0.850217 0.526432i \(-0.823529\pi\)
0.850217 + 0.526432i \(0.176471\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) −0.757949 0.469302i −0.757949 0.469302i
\(389\) 0 0 −0.739009 0.673696i \(-0.764706\pi\)
0.739009 + 0.673696i \(0.235294\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −0.132756 + 0.710182i −0.132756 + 0.710182i 0.850217 + 0.526432i \(0.176471\pi\)
−0.982973 + 0.183750i \(0.941176\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) −0.273663 0.961826i −0.273663 0.961826i
\(401\) 0 0 −0.673696 0.739009i \(-0.735294\pi\)
0.673696 + 0.739009i \(0.264706\pi\)
\(402\) 0 0
\(403\) 0.239151 + 0.262337i 0.239151 + 0.262337i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) −1.12388 + 0.435393i −1.12388 + 0.435393i −0.850217 0.526432i \(-0.823529\pi\)
−0.273663 + 0.961826i \(0.588235\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) −0.982973 + 0.183750i −0.982973 + 0.183750i
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 0 0 −0.798017 0.602635i \(-0.794118\pi\)
0.798017 + 0.602635i \(0.205882\pi\)
\(420\) 0 0
\(421\) 1.25664 1.14558i 1.25664 1.14558i 0.273663 0.961826i \(-0.411765\pi\)
0.982973 0.183750i \(-0.0588235\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −3.60395 0.673696i −3.60395 0.673696i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 0.361242 0.932472i \(-0.382353\pi\)
−0.361242 + 0.932472i \(0.617647\pi\)
\(432\) 0 0
\(433\) −1.91545 0.544991i −1.91545 0.544991i −0.982973 0.183750i \(-0.941176\pi\)
−0.932472 0.361242i \(-0.882353\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0.193463 0.312454i 0.193463 0.312454i
\(437\) 0 0
\(438\) 0 0
\(439\) −1.60263 0.798017i −1.60263 0.798017i −0.602635 0.798017i \(-0.705882\pi\)
−1.00000 \(\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 0 0 −0.982973 0.183750i \(-0.941176\pi\)
0.982973 + 0.183750i \(0.0588235\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 1.12388 + 1.48826i 1.12388 + 1.48826i
\(449\) 0 0 −0.273663 0.961826i \(-0.588235\pi\)
0.273663 + 0.961826i \(0.411765\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −0.132756 0.710182i −0.132756 0.710182i −0.982973 0.183750i \(-0.941176\pi\)
0.850217 0.526432i \(-0.176471\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 0 0 0.961826 0.273663i \(-0.0882353\pi\)
−0.961826 + 0.273663i \(0.911765\pi\)
\(462\) 0 0
\(463\) −1.34164 + 1.47171i −1.34164 + 1.47171i −0.602635 + 0.798017i \(0.705882\pi\)
−0.739009 + 0.673696i \(0.764706\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 0 0 −0.183750 0.982973i \(-0.558824\pi\)
0.183750 + 0.982973i \(0.441176\pi\)
\(468\) 0 0
\(469\) 2.51281i 2.51281i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) −0.156896 1.69318i −0.156896 1.69318i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 0 0 −0.602635 0.798017i \(-0.705882\pi\)
0.602635 + 0.798017i \(0.294118\pi\)
\(480\) 0 0
\(481\) 0.106395 0.274638i 0.106395 0.274638i
\(482\) 0 0
\(483\) 0 0
\(484\) 0.982973 + 0.183750i 0.982973 + 0.183750i
\(485\) 0 0
\(486\) 0 0
\(487\) 1.29596 1.42160i 1.29596 1.42160i 0.445738 0.895163i \(-0.352941\pi\)
0.850217 0.526432i \(-0.176471\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 0 0 0.526432 0.850217i \(-0.323529\pi\)
−0.526432 + 0.850217i \(0.676471\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0.694903 1.79375i 0.694903 1.79375i
\(497\) 0 0
\(498\) 0 0
\(499\) −0.293271 + 1.56886i −0.293271 + 1.56886i 0.445738 + 0.895163i \(0.352941\pi\)
−0.739009 + 0.673696i \(0.764706\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 0 0 0.961826 0.273663i \(-0.0882353\pi\)
−0.961826 + 0.273663i \(0.911765\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 0 0
\(508\) 1.07524 + 0.811985i 1.07524 + 0.811985i
\(509\) 0 0 −0.895163 0.445738i \(-0.852941\pi\)
0.895163 + 0.445738i \(0.147059\pi\)
\(510\) 0 0
\(511\) −0.682442 0.0632375i −0.682442 0.0632375i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 0 0 0.445738 0.895163i \(-0.352941\pi\)
−0.445738 + 0.895163i \(0.647059\pi\)
\(522\) 0 0
\(523\) −1.02474 1.35698i −1.02474 1.35698i −0.932472 0.361242i \(-0.882353\pi\)
−0.0922684 0.995734i \(-0.529412\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) −0.0922684 0.995734i −0.0922684 0.995734i
\(530\) 0 0
\(531\) 0 0
\(532\) 1.41353 + 2.83876i 1.41353 + 2.83876i
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) −0.111208 1.20013i −0.111208 1.20013i −0.850217 0.526432i \(-0.823529\pi\)
0.739009 0.673696i \(-0.235294\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 0.465346 0.288130i 0.465346 0.288130i −0.273663 0.961826i \(-0.588235\pi\)
0.739009 + 0.673696i \(0.235294\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 2.09597 0.811985i 2.09597 0.811985i
\(554\) 0 0
\(555\) 0 0
\(556\) 0.465346 0.288130i 0.465346 0.288130i
\(557\) 0 0 −0.445738 0.895163i \(-0.647059\pi\)
0.445738 + 0.895163i \(0.352941\pi\)
\(558\) 0 0
\(559\) 0.263650 0.199099i 0.263650 0.199099i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 0 0 0.982973 0.183750i \(-0.0588235\pi\)
−0.982973 + 0.183750i \(0.941176\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 0 0 −0.273663 0.961826i \(-0.588235\pi\)
0.273663 + 0.961826i \(0.411765\pi\)
\(570\) 0 0
\(571\) 1.47802 1.47802 0.739009 0.673696i \(-0.235294\pi\)
0.739009 + 0.673696i \(0.235294\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 0.380338 + 0.614268i 0.380338 + 0.614268i 0.982973 0.183750i \(-0.0588235\pi\)
−0.602635 + 0.798017i \(0.705882\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 0 0 0.183750 0.982973i \(-0.441176\pi\)
−0.183750 + 0.982973i \(0.558824\pi\)
\(588\) 0 0
\(589\) 1.72198 2.78110i 1.72198 2.78110i
\(590\) 0 0
\(591\) 0 0
\(592\) −1.58923 + 0.147263i −1.58923 + 0.147263i
\(593\) 0 0 −0.445738 0.895163i \(-0.647059\pi\)
0.445738 + 0.895163i \(0.352941\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 −0.932472 0.361242i \(-0.882353\pi\)
0.932472 + 0.361242i \(0.117647\pi\)
\(600\) 0 0
\(601\) 1.42871 0.711414i 1.42871 0.711414i 0.445738 0.895163i \(-0.352941\pi\)
0.982973 + 0.183750i \(0.0588235\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 1.04837 0.0971461i 1.04837 0.0971461i
\(605\) 0 0
\(606\) 0 0
\(607\) 1.45285 1.32445i 1.45285 1.32445i 0.602635 0.798017i \(-0.294118\pi\)
0.850217 0.526432i \(-0.176471\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) −0.156896 0.0971461i −0.156896 0.0971461i 0.445738 0.895163i \(-0.352941\pi\)
−0.602635 + 0.798017i \(0.705882\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(618\) 0 0
\(619\) 0.184537 0.184537 0.0922684 0.995734i \(-0.470588\pi\)
0.0922684 + 0.995734i \(0.470588\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −0.602635 + 0.798017i −0.602635 + 0.798017i
\(626\) 0 0
\(627\) 0 0
\(628\) 0.193463 + 1.03494i 0.193463 + 1.03494i
\(629\) 0 0
\(630\) 0 0
\(631\) 1.02474 1.35698i 1.02474 1.35698i 0.0922684 0.995734i \(-0.470588\pi\)
0.932472 0.361242i \(-0.117647\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) −0.426406 0.165190i −0.426406 0.165190i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 0 0 0.673696 0.739009i \(-0.264706\pi\)
−0.673696 + 0.739009i \(0.735294\pi\)
\(642\) 0 0
\(643\) 0.876298 + 1.75984i 0.876298 + 1.75984i 0.602635 + 0.798017i \(0.294118\pi\)
0.273663 + 0.961826i \(0.411765\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 0.526432 0.850217i \(-0.323529\pi\)
−0.526432 + 0.850217i \(0.676471\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) 1.37821 + 0.533922i 1.37821 + 0.533922i
\(653\) 0 0 0.932472 0.361242i \(-0.117647\pi\)
−0.932472 + 0.361242i \(0.882353\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 0 0 −0.526432 0.850217i \(-0.676471\pi\)
0.526432 + 0.850217i \(0.323529\pi\)
\(660\) 0 0
\(661\) 1.91545 + 0.544991i 1.91545 + 0.544991i 0.982973 + 0.183750i \(0.0588235\pi\)
0.932472 + 0.361242i \(0.117647\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) −1.67148 + 0.312454i −1.67148 + 0.312454i −0.932472 0.361242i \(-0.882353\pi\)
−0.739009 + 0.673696i \(0.764706\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) −0.949499 + 0.177492i −0.949499 + 0.177492i
\(677\) 0 0 0.798017 0.602635i \(-0.205882\pi\)
−0.798017 + 0.602635i \(0.794118\pi\)
\(678\) 0 0
\(679\) −0.741064 1.48826i −0.741064 1.48826i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 0 0 0.932472 0.361242i \(-0.117647\pi\)
−0.932472 + 0.361242i \(0.882353\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 0 0
\(688\) −1.60263 0.798017i −1.60263 0.798017i
\(689\) 0 0
\(690\) 0 0
\(691\) −0.942485 1.52217i −0.942485 1.52217i −0.850217 0.526432i \(-0.823529\pi\)
−0.0922684 0.995734i \(-0.529412\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) 0.510366 1.79375i 0.510366 1.79375i
\(701\) 0 0 −0.798017 0.602635i \(-0.794118\pi\)
0.798017 + 0.602635i \(0.205882\pi\)
\(702\) 0 0
\(703\) −2.70237 0.250412i −2.70237 0.250412i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) −0.0505009 0.177492i −0.0505009 0.177492i 0.932472 0.361242i \(-0.117647\pi\)
−0.982973 + 0.183750i \(0.941176\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 0.739009 0.673696i \(-0.235294\pi\)
−0.739009 + 0.673696i \(0.764706\pi\)
\(720\) 0 0
\(721\) −1.73901 0.673696i −1.73901 0.673696i
\(722\) 0 0
\(723\) 0 0
\(724\) −0.132756 0.342683i −0.132756 0.342683i
\(725\) 0 0
\(726\) 0 0
\(727\) −0.646741 0.322039i −0.646741 0.322039i 0.0922684 0.995734i \(-0.470588\pi\)
−0.739009 + 0.673696i \(0.764706\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 1.72198 0.489946i 1.72198 0.489946i 0.739009 0.673696i \(-0.235294\pi\)
0.982973 + 0.183750i \(0.0588235\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) −0.0822551 + 0.887674i −0.0822551 + 0.887674i 0.850217 + 0.526432i \(0.176471\pi\)
−0.932472 + 0.361242i \(0.882353\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 0.0922684 0.995734i \(-0.470588\pi\)
−0.0922684 + 0.995734i \(0.529412\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 0.156896 0.0971461i 0.156896 0.0971461i −0.445738 0.895163i \(-0.647059\pi\)
0.602635 + 0.798017i \(0.294118\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 1.18475 + 1.56886i 1.18475 + 1.56886i 0.739009 + 0.673696i \(0.235294\pi\)
0.445738 + 0.895163i \(0.352941\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 0 0 −0.0922684 0.995734i \(-0.529412\pi\)
0.0922684 + 0.995734i \(0.470588\pi\)
\(762\) 0 0
\(763\) 0.613514 0.305494i 0.613514 0.305494i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 0 0
\(769\) −0.0675278 0.361242i −0.0675278 0.361242i 0.932472 0.361242i \(-0.117647\pi\)
−1.00000 \(\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 1.20614 1.32307i 1.20614 1.32307i
\(773\) 0 0 0.673696 0.739009i \(-0.264706\pi\)
−0.673696 + 0.739009i \(0.735294\pi\)
\(774\) 0 0
\(775\) −1.85022 + 0.526432i −1.85022 + 0.526432i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 0.228643 + 2.46745i 0.228643 + 2.46745i
\(785\) 0 0
\(786\) 0 0
\(787\) −0.243964 0.857445i −0.243964 0.857445i −0.982973 0.183750i \(-0.941176\pi\)
0.739009 0.673696i \(-0.235294\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 0.356612 + 0.0666624i 0.356612 + 0.0666624i
\(794\) 0 0
\(795\) 0 0
\(796\) −1.20614 + 1.32307i −1.20614 + 1.32307i
\(797\) 0 0 −0.895163 0.445738i \(-0.852941\pi\)
0.895163 + 0.445738i \(0.147059\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 0 0
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\)