Properties

Label 2880.1.ec.a.2179.1
Level $2880$
Weight $1$
Character 2880.2179
Analytic conductor $1.437$
Analytic rank $0$
Dimension $16$
Projective image $D_{16}$
CM discriminant -15
Inner twists $8$

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Newspace parameters

Level: \( N \) \(=\) \( 2880 = 2^{6} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 2880.ec (of order \(16\), degree \(8\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.43730723638\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(2\) over \(\Q(\zeta_{16})\)
Coefficient field: \(\Q(\zeta_{32})\)
Defining polynomial: \(x^{16} + 1\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Projective image: \(D_{16}\)
Projective field: Galois closure of \(\mathbb{Q}[x]/(x^{16} + \cdots)\)

Embedding invariants

Embedding label 2179.1
Root \(0.555570 - 0.831470i\) of defining polynomial
Character \(\chi\) \(=\) 2880.2179
Dual form 2880.1.ec.a.2539.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.831470 + 0.555570i) q^{2} +(0.382683 - 0.923880i) q^{4} +(-0.555570 + 0.831470i) q^{5} +(0.195090 + 0.980785i) q^{8} +O(q^{10})\) \(q+(-0.831470 + 0.555570i) q^{2} +(0.382683 - 0.923880i) q^{4} +(-0.555570 + 0.831470i) q^{5} +(0.195090 + 0.980785i) q^{8} -1.00000i q^{10} +(-0.707107 - 0.707107i) q^{16} +(1.17588 - 1.17588i) q^{17} +(0.324423 - 0.216773i) q^{19} +(0.555570 + 0.831470i) q^{20} +(-0.636379 + 1.53636i) q^{23} +(-0.382683 - 0.923880i) q^{25} +1.84776 q^{31} +(0.980785 + 0.195090i) q^{32} +(-0.324423 + 1.63099i) q^{34} +(-0.149316 + 0.360480i) q^{38} +(-0.923880 - 0.382683i) q^{40} +(-0.324423 - 1.63099i) q^{46} +(1.38704 + 1.38704i) q^{47} +(-0.707107 + 0.707107i) q^{49} +(0.831470 + 0.555570i) q^{50} +(-0.360480 - 1.81225i) q^{53} +(-0.382683 + 1.92388i) q^{61} +(-1.53636 + 1.02656i) q^{62} +(-0.923880 + 0.382683i) q^{64} +(-0.636379 - 1.53636i) q^{68} +(-0.0761205 - 0.382683i) q^{76} +(1.00000 + 1.00000i) q^{79} +(0.980785 - 0.195090i) q^{80} +(-0.425215 - 0.636379i) q^{83} +(0.324423 + 1.63099i) q^{85} +(1.17588 + 1.17588i) q^{92} +(-1.92388 - 0.382683i) q^{94} +0.390181i q^{95} +(0.195090 - 0.980785i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + O(q^{10}) \) \( 16 q - 16 q^{76} + 16 q^{79} - 16 q^{94} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2880\mathbb{Z}\right)^\times\).

\(n\) \(577\) \(641\) \(901\) \(2431\)
\(\chi(n)\) \(-1\) \(1\) \(e\left(\frac{3}{16}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.831470 + 0.555570i −0.831470 + 0.555570i
\(3\) 0 0
\(4\) 0.382683 0.923880i 0.382683 0.923880i
\(5\) −0.555570 + 0.831470i −0.555570 + 0.831470i
\(6\) 0 0
\(7\) 0 0 −0.382683 0.923880i \(-0.625000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(8\) 0.195090 + 0.980785i 0.195090 + 0.980785i
\(9\) 0 0
\(10\) 1.00000i 1.00000i
\(11\) 0 0 0.980785 0.195090i \(-0.0625000\pi\)
−0.980785 + 0.195090i \(0.937500\pi\)
\(12\) 0 0
\(13\) 0 0 0.831470 0.555570i \(-0.187500\pi\)
−0.831470 + 0.555570i \(0.812500\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −0.707107 0.707107i −0.707107 0.707107i
\(17\) 1.17588 1.17588i 1.17588 1.17588i 0.195090 0.980785i \(-0.437500\pi\)
0.980785 0.195090i \(-0.0625000\pi\)
\(18\) 0 0
\(19\) 0.324423 0.216773i 0.324423 0.216773i −0.382683 0.923880i \(-0.625000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(20\) 0.555570 + 0.831470i 0.555570 + 0.831470i
\(21\) 0 0
\(22\) 0 0
\(23\) −0.636379 + 1.53636i −0.636379 + 1.53636i 0.195090 + 0.980785i \(0.437500\pi\)
−0.831470 + 0.555570i \(0.812500\pi\)
\(24\) 0 0
\(25\) −0.382683 0.923880i −0.382683 0.923880i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 0 0 0.195090 0.980785i \(-0.437500\pi\)
−0.195090 + 0.980785i \(0.562500\pi\)
\(30\) 0 0
\(31\) 1.84776 1.84776 0.923880 0.382683i \(-0.125000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(32\) 0.980785 + 0.195090i 0.980785 + 0.195090i
\(33\) 0 0
\(34\) −0.324423 + 1.63099i −0.324423 + 1.63099i
\(35\) 0 0
\(36\) 0 0
\(37\) 0 0 0.555570 0.831470i \(-0.312500\pi\)
−0.555570 + 0.831470i \(0.687500\pi\)
\(38\) −0.149316 + 0.360480i −0.149316 + 0.360480i
\(39\) 0 0
\(40\) −0.923880 0.382683i −0.923880 0.382683i
\(41\) 0 0 −0.923880 0.382683i \(-0.875000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(42\) 0 0
\(43\) 0 0 0.980785 0.195090i \(-0.0625000\pi\)
−0.980785 + 0.195090i \(0.937500\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) −0.324423 1.63099i −0.324423 1.63099i
\(47\) 1.38704 + 1.38704i 1.38704 + 1.38704i 0.831470 + 0.555570i \(0.187500\pi\)
0.555570 + 0.831470i \(0.312500\pi\)
\(48\) 0 0
\(49\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(50\) 0.831470 + 0.555570i 0.831470 + 0.555570i
\(51\) 0 0
\(52\) 0 0
\(53\) −0.360480 1.81225i −0.360480 1.81225i −0.555570 0.831470i \(-0.687500\pi\)
0.195090 0.980785i \(-0.437500\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 0 0 −0.831470 0.555570i \(-0.812500\pi\)
0.831470 + 0.555570i \(0.187500\pi\)
\(60\) 0 0
\(61\) −0.382683 + 1.92388i −0.382683 + 1.92388i 1.00000i \(0.5\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(62\) −1.53636 + 1.02656i −1.53636 + 1.02656i
\(63\) 0 0
\(64\) −0.923880 + 0.382683i −0.923880 + 0.382683i
\(65\) 0 0
\(66\) 0 0
\(67\) 0 0 −0.980785 0.195090i \(-0.937500\pi\)
0.980785 + 0.195090i \(0.0625000\pi\)
\(68\) −0.636379 1.53636i −0.636379 1.53636i
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 0.923880 0.382683i \(-0.125000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(72\) 0 0
\(73\) 0 0 −0.923880 0.382683i \(-0.875000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) −0.0761205 0.382683i −0.0761205 0.382683i
\(77\) 0 0
\(78\) 0 0
\(79\) 1.00000 + 1.00000i 1.00000 + 1.00000i 1.00000 \(0\)
1.00000i \(0.5\pi\)
\(80\) 0.980785 0.195090i 0.980785 0.195090i
\(81\) 0 0
\(82\) 0 0
\(83\) −0.425215 0.636379i −0.425215 0.636379i 0.555570 0.831470i \(-0.312500\pi\)
−0.980785 + 0.195090i \(0.937500\pi\)
\(84\) 0 0
\(85\) 0.324423 + 1.63099i 0.324423 + 1.63099i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 0 0 0.923880 0.382683i \(-0.125000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 1.17588 + 1.17588i 1.17588 + 1.17588i
\(93\) 0 0
\(94\) −1.92388 0.382683i −1.92388 0.382683i
\(95\) 0.390181i 0.390181i
\(96\) 0 0
\(97\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(98\) 0.195090 0.980785i 0.195090 0.980785i
\(99\) 0 0
\(100\) −1.00000 −1.00000
\(101\) 0 0 −0.831470 0.555570i \(-0.812500\pi\)
0.831470 + 0.555570i \(0.187500\pi\)
\(102\) 0 0
\(103\) 0 0 0.923880 0.382683i \(-0.125000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 1.30656 + 1.30656i 1.30656 + 1.30656i
\(107\) 0.360480 + 1.81225i 0.360480 + 1.81225i 0.555570 + 0.831470i \(0.312500\pi\)
−0.195090 + 0.980785i \(0.562500\pi\)
\(108\) 0 0
\(109\) −0.216773 0.324423i −0.216773 0.324423i 0.707107 0.707107i \(-0.250000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 0.275899 + 0.275899i 0.275899 + 0.275899i 0.831470 0.555570i \(-0.187500\pi\)
−0.555570 + 0.831470i \(0.687500\pi\)
\(114\) 0 0
\(115\) −0.923880 1.38268i −0.923880 1.38268i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 0.923880 0.382683i 0.923880 0.382683i
\(122\) −0.750661 1.81225i −0.750661 1.81225i
\(123\) 0 0
\(124\) 0.707107 1.70711i 0.707107 1.70711i
\(125\) 0.980785 + 0.195090i 0.980785 + 0.195090i
\(126\) 0 0
\(127\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(128\) 0.555570 0.831470i 0.555570 0.831470i
\(129\) 0 0
\(130\) 0 0
\(131\) 0 0 0.195090 0.980785i \(-0.437500\pi\)
−0.195090 + 0.980785i \(0.562500\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) 1.38268 + 0.923880i 1.38268 + 0.923880i
\(137\) −0.149316 + 0.360480i −0.149316 + 0.360480i −0.980785 0.195090i \(-0.937500\pi\)
0.831470 + 0.555570i \(0.187500\pi\)
\(138\) 0 0
\(139\) 0.324423 + 1.63099i 0.324423 + 1.63099i 0.707107 + 0.707107i \(0.250000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(140\) 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 0
\(149\) 0 0 0.980785 0.195090i \(-0.0625000\pi\)
−0.980785 + 0.195090i \(0.937500\pi\)
\(150\) 0 0
\(151\) 0.707107 + 0.292893i 0.707107 + 0.292893i 0.707107 0.707107i \(-0.250000\pi\)
1.00000i \(0.5\pi\)
\(152\) 0.275899 + 0.275899i 0.275899 + 0.275899i
\(153\) 0 0
\(154\) 0 0
\(155\) −1.02656 + 1.53636i −1.02656 + 1.53636i
\(156\) 0 0
\(157\) 0 0 −0.980785 0.195090i \(-0.937500\pi\)
0.980785 + 0.195090i \(0.0625000\pi\)
\(158\) −1.38704 0.275899i −1.38704 0.275899i
\(159\) 0 0
\(160\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(161\) 0 0
\(162\) 0 0
\(163\) 0 0 0.195090 0.980785i \(-0.437500\pi\)
−0.195090 + 0.980785i \(0.562500\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0.707107 + 0.292893i 0.707107 + 0.292893i
\(167\) −0.425215 1.02656i −0.425215 1.02656i −0.980785 0.195090i \(-0.937500\pi\)
0.555570 0.831470i \(-0.312500\pi\)
\(168\) 0 0
\(169\) 0.382683 0.923880i 0.382683 0.923880i
\(170\) −1.17588 1.17588i −1.17588 1.17588i
\(171\) 0 0
\(172\) 0 0
\(173\) −0.636379 + 0.425215i −0.636379 + 0.425215i −0.831470 0.555570i \(-0.812500\pi\)
0.195090 + 0.980785i \(0.437500\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 0 0 0.831470 0.555570i \(-0.187500\pi\)
−0.831470 + 0.555570i \(0.812500\pi\)
\(180\) 0 0
\(181\) 1.63099 0.324423i 1.63099 0.324423i 0.707107 0.707107i \(-0.250000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −1.63099 0.324423i −1.63099 0.324423i
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 1.81225 0.750661i 1.81225 0.750661i
\(189\) 0 0
\(190\) −0.216773 0.324423i −0.216773 0.324423i
\(191\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(192\) 0 0
\(193\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0.382683 + 0.923880i 0.382683 + 0.923880i
\(197\) 0.785695 1.17588i 0.785695 1.17588i −0.195090 0.980785i \(-0.562500\pi\)
0.980785 0.195090i \(-0.0625000\pi\)
\(198\) 0 0
\(199\) 0.541196 + 1.30656i 0.541196 + 1.30656i 0.923880 + 0.382683i \(0.125000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(200\) 0.831470 0.555570i 0.831470 0.555570i
\(201\) 0 0
\(202\) 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
\(211\) −1.63099 + 1.08979i −1.63099 + 1.08979i −0.707107 + 0.707107i \(0.750000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(212\) −1.81225 0.360480i −1.81225 0.360480i
\(213\) 0 0
\(214\) −1.30656 1.30656i −1.30656 1.30656i
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) 0.360480 + 0.149316i 0.360480 + 0.149316i
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −0.382683 0.0761205i −0.382683 0.0761205i
\(227\) 0.750661 + 0.149316i 0.750661 + 0.149316i 0.555570 0.831470i \(-0.312500\pi\)
0.195090 + 0.980785i \(0.437500\pi\)
\(228\) 0 0
\(229\) −0.617317 + 0.923880i −0.617317 + 0.923880i 0.382683 + 0.923880i \(0.375000\pi\)
−1.00000 \(\pi\)
\(230\) 1.53636 + 0.636379i 1.53636 + 0.636379i
\(231\) 0 0
\(232\) 0 0
\(233\) −1.02656 0.425215i −1.02656 0.425215i −0.195090 0.980785i \(-0.562500\pi\)
−0.831470 + 0.555570i \(0.812500\pi\)
\(234\) 0 0
\(235\) −1.92388 + 0.382683i −1.92388 + 0.382683i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(240\) 0 0
\(241\) 0.541196 0.541196i 0.541196 0.541196i −0.382683 0.923880i \(-0.625000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(242\) −0.555570 + 0.831470i −0.555570 + 0.831470i
\(243\) 0 0
\(244\) 1.63099 + 1.08979i 1.63099 + 1.08979i
\(245\) −0.195090 0.980785i −0.195090 0.980785i
\(246\) 0 0
\(247\) 0 0
\(248\) 0.360480 + 1.81225i 0.360480 + 1.81225i
\(249\) 0 0
\(250\) −0.923880 + 0.382683i −0.923880 + 0.382683i
\(251\) 0 0 −0.831470 0.555570i \(-0.812500\pi\)
0.831470 + 0.555570i \(0.187500\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) 1.00000i 1.00000i
\(257\) 1.11114i 1.11114i −0.831470 0.555570i \(-0.812500\pi\)
0.831470 0.555570i \(-0.187500\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −1.02656 + 0.425215i −1.02656 + 0.425215i −0.831470 0.555570i \(-0.812500\pi\)
−0.195090 + 0.980785i \(0.562500\pi\)
\(264\) 0 0
\(265\) 1.70711 + 0.707107i 1.70711 + 0.707107i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 0 0 −0.555570 0.831470i \(-0.687500\pi\)
0.555570 + 0.831470i \(0.312500\pi\)
\(270\) 0 0
\(271\) −1.41421 1.41421i −1.41421 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
−0.707107 0.707107i \(-0.750000\pi\)
\(272\) −1.66294 −1.66294
\(273\) 0 0
\(274\) −0.0761205 0.382683i −0.0761205 0.382683i
\(275\) 0 0
\(276\) 0 0
\(277\) 0 0 −0.195090 0.980785i \(-0.562500\pi\)
0.195090 + 0.980785i \(0.437500\pi\)
\(278\) −1.17588 1.17588i −1.17588 1.17588i
\(279\) 0 0
\(280\) 0 0
\(281\) 0 0 0.923880 0.382683i \(-0.125000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(282\) 0 0
\(283\) 0 0 −0.831470 0.555570i \(-0.812500\pi\)
0.831470 + 0.555570i \(0.187500\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 1.76537i 1.76537i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −1.53636 1.02656i −1.53636 1.02656i −0.980785 0.195090i \(-0.937500\pi\)
−0.555570 0.831470i \(-0.687500\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 0 0
\(300\) 0 0
\(301\) 0 0
\(302\) −0.750661 + 0.149316i −0.750661 + 0.149316i
\(303\) 0 0
\(304\) −0.382683 0.0761205i −0.382683 0.0761205i
\(305\) −1.38704 1.38704i −1.38704 1.38704i
\(306\) 0 0
\(307\) 0 0 −0.555570 0.831470i \(-0.687500\pi\)
0.555570 + 0.831470i \(0.312500\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 1.84776i 1.84776i
\(311\) 0 0 −0.923880 0.382683i \(-0.875000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(312\) 0 0
\(313\) 0 0 0.923880 0.382683i \(-0.125000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 1.30656 0.541196i 1.30656 0.541196i
\(317\) 1.38704 + 0.275899i 1.38704 + 0.275899i 0.831470 0.555570i \(-0.187500\pi\)
0.555570 + 0.831470i \(0.312500\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0.195090 0.980785i 0.195090 0.980785i
\(321\) 0 0
\(322\) 0 0
\(323\) 0.126584 0.636379i 0.126584 0.636379i
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −0.216773 1.08979i −0.216773 1.08979i −0.923880 0.382683i \(-0.875000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(332\) −0.750661 + 0.149316i −0.750661 + 0.149316i
\(333\) 0 0
\(334\) 0.923880 + 0.617317i 0.923880 + 0.617317i
\(335\) 0 0
\(336\) 0 0
\(337\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(338\) 0.195090 + 0.980785i 0.195090 + 0.980785i
\(339\) 0 0
\(340\) 1.63099 + 0.324423i 1.63099 + 0.324423i
\(341\) 0 0
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 0 0
\(346\) 0.292893 0.707107i 0.292893 0.707107i
\(347\) 0.785695 1.17588i 0.785695 1.17588i −0.195090 0.980785i \(-0.562500\pi\)
0.980785 0.195090i \(-0.0625000\pi\)
\(348\) 0 0
\(349\) −1.92388 0.382683i −1.92388 0.382683i −0.923880 0.382683i \(-0.875000\pi\)
−1.00000 \(\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 1.96157 1.96157 0.980785 0.195090i \(-0.0625000\pi\)
0.980785 + 0.195090i \(0.0625000\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 0 0 −0.382683 0.923880i \(-0.625000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(360\) 0 0
\(361\) −0.324423 + 0.783227i −0.324423 + 0.783227i
\(362\) −1.17588 + 1.17588i −1.17588 + 1.17588i
\(363\) 0 0
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(368\) 1.53636 0.636379i 1.53636 0.636379i
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 0 0 0.980785 0.195090i \(-0.0625000\pi\)
−0.980785 + 0.195090i \(0.937500\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) −1.08979 + 1.63099i −1.08979 + 1.63099i
\(377\) 0 0
\(378\) 0 0
\(379\) 0.617317 0.923880i 0.617317 0.923880i −0.382683 0.923880i \(-0.625000\pi\)
1.00000 \(0\)
\(380\) 0.360480 + 0.149316i 0.360480 + 0.149316i
\(381\) 0 0
\(382\) 0 0
\(383\) −0.390181 −0.390181 −0.195090 0.980785i \(-0.562500\pi\)
−0.195090 + 0.980785i \(0.562500\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 0 0 0.555570 0.831470i \(-0.312500\pi\)
−0.555570 + 0.831470i \(0.687500\pi\)
\(390\) 0 0
\(391\) 1.05826 + 2.55487i 1.05826 + 2.55487i
\(392\) −0.831470 0.555570i −0.831470 0.555570i
\(393\) 0 0
\(394\) 1.41421i 1.41421i
\(395\) −1.38704 + 0.275899i −1.38704 + 0.275899i
\(396\) 0 0
\(397\) 0 0 0.831470 0.555570i \(-0.187500\pi\)
−0.831470 + 0.555570i \(0.812500\pi\)
\(398\) −1.17588 0.785695i −1.17588 0.785695i
\(399\) 0 0
\(400\) −0.382683 + 0.923880i −0.382683 + 0.923880i
\(401\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) −0.707107 1.70711i −0.707107 1.70711i −0.707107 0.707107i \(-0.750000\pi\)
1.00000i \(-0.5\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 0.765367 0.765367
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 0 0 −0.980785 0.195090i \(-0.937500\pi\)
0.980785 + 0.195090i \(0.0625000\pi\)
\(420\) 0 0
\(421\) −0.617317 + 0.923880i −0.617317 + 0.923880i 0.382683 + 0.923880i \(0.375000\pi\)
−1.00000 \(\pi\)
\(422\) 0.750661 1.81225i 0.750661 1.81225i
\(423\) 0 0
\(424\) 1.70711 0.707107i 1.70711 0.707107i
\(425\) −1.53636 0.636379i −1.53636 0.636379i
\(426\) 0 0
\(427\) 0 0
\(428\) 1.81225 + 0.360480i 1.81225 + 0.360480i
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(432\) 0 0
\(433\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −0.382683 + 0.0761205i −0.382683 + 0.0761205i
\(437\) 0.126584 + 0.636379i 0.126584 + 0.636379i
\(438\) 0 0
\(439\) 0.541196 1.30656i 0.541196 1.30656i −0.382683 0.923880i \(-0.625000\pi\)
0.923880 0.382683i \(-0.125000\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 1.53636 + 1.02656i 1.53636 + 1.02656i 0.980785 + 0.195090i \(0.0625000\pi\)
0.555570 + 0.831470i \(0.312500\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0.360480 0.149316i 0.360480 0.149316i
\(453\) 0 0
\(454\) −0.707107 + 0.292893i −0.707107 + 0.292893i
\(455\) 0 0
\(456\) 0 0
\(457\) 0 0 −0.923880 0.382683i \(-0.875000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(458\) 1.11114i 1.11114i
\(459\) 0 0
\(460\) −1.63099 + 0.324423i −1.63099 + 0.324423i
\(461\) 0 0 −0.555570 0.831470i \(-0.687500\pi\)
0.555570 + 0.831470i \(0.312500\pi\)
\(462\) 0 0
\(463\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 1.08979 0.216773i 1.08979 0.216773i
\(467\) −0.785695 1.17588i −0.785695 1.17588i −0.980785 0.195090i \(-0.937500\pi\)
0.195090 0.980785i \(-0.437500\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 1.38704 1.38704i 1.38704 1.38704i
\(471\) 0 0
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) −0.324423 0.216773i −0.324423 0.216773i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) −0.149316 + 0.750661i −0.149316 + 0.750661i
\(483\) 0 0
\(484\) 1.00000i 1.00000i
\(485\) 0 0
\(486\) 0 0
\(487\) 0 0 0.923880 0.382683i \(-0.125000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(488\) −1.96157 −1.96157
\(489\) 0 0
\(490\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(491\) 0 0 −0.195090 0.980785i \(-0.562500\pi\)
0.195090 + 0.980785i \(0.437500\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) −1.30656 1.30656i −1.30656 1.30656i
\(497\) 0 0
\(498\) 0 0
\(499\) −0.923880 1.38268i −0.923880 1.38268i −0.923880 0.382683i \(-0.875000\pi\)
1.00000i \(-0.5\pi\)
\(500\) 0.555570 0.831470i 0.555570 0.831470i
\(501\) 0 0
\(502\) 0 0
\(503\) −1.81225 0.750661i −1.81225 0.750661i −0.980785 0.195090i \(-0.937500\pi\)
−0.831470 0.555570i \(-0.812500\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 0 0 −0.980785 0.195090i \(-0.937500\pi\)
0.980785 + 0.195090i \(0.0625000\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −0.555570 0.831470i −0.555570 0.831470i
\(513\) 0 0
\(514\) 0.617317 + 0.923880i 0.617317 + 0.923880i
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 0 0 0.382683 0.923880i \(-0.375000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(522\) 0 0
\(523\) 0 0 −0.195090 0.980785i \(-0.562500\pi\)
0.195090 + 0.980785i \(0.437500\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0.617317 0.923880i 0.617317 0.923880i
\(527\) 2.17273 2.17273i 2.17273 2.17273i
\(528\) 0 0
\(529\) −1.24830 1.24830i −1.24830 1.24830i
\(530\) −1.81225 + 0.360480i −1.81225 + 0.360480i
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) −1.70711 0.707107i −1.70711 0.707107i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) 1.63099 + 0.324423i 1.63099 + 0.324423i 0.923880 0.382683i \(-0.125000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(542\) 1.96157 + 0.390181i 1.96157 + 0.390181i
\(543\) 0 0
\(544\) 1.38268 0.923880i 1.38268 0.923880i
\(545\) 0.390181 0.390181
\(546\) 0 0
\(547\) 0 0 0.195090 0.980785i \(-0.437500\pi\)
−0.195090 + 0.980785i \(0.562500\pi\)
\(548\) 0.275899 + 0.275899i 0.275899 + 0.275899i
\(549\) 0 0
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 1.63099 + 0.324423i 1.63099 + 0.324423i
\(557\) 1.53636 1.02656i 1.53636 1.02656i 0.555570 0.831470i \(-0.312500\pi\)
0.980785 0.195090i \(-0.0625000\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 1.17588 0.785695i 1.17588 0.785695i 0.195090 0.980785i \(-0.437500\pi\)
0.980785 + 0.195090i \(0.0625000\pi\)
\(564\) 0 0
\(565\) −0.382683 + 0.0761205i −0.382683 + 0.0761205i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 0 0 −0.382683 0.923880i \(-0.625000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(570\) 0 0
\(571\) 0.923880 1.38268i 0.923880 1.38268i 1.00000i \(-0.5\pi\)
0.923880 0.382683i \(-0.125000\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 1.66294 1.66294
\(576\) 0 0
\(577\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(578\) 0.980785 + 1.46785i 0.980785 + 1.46785i
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 1.84776 1.84776
\(587\) −1.81225 + 0.360480i −1.81225 + 0.360480i −0.980785 0.195090i \(-0.937500\pi\)
−0.831470 + 0.555570i \(0.812500\pi\)
\(588\) 0 0
\(589\) 0.599456 0.400544i 0.599456 0.400544i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 0.785695 0.785695i 0.785695 0.785695i −0.195090 0.980785i \(-0.562500\pi\)
0.980785 + 0.195090i \(0.0625000\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 0.382683 0.923880i \(-0.375000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(600\) 0 0
\(601\) −0.707107 1.70711i −0.707107 1.70711i −0.707107 0.707107i \(-0.750000\pi\)
1.00000i \(-0.5\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0.541196 0.541196i 0.541196 0.541196i
\(605\) −0.195090 + 0.980785i −0.195090 + 0.980785i
\(606\) 0 0
\(607\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(608\) 0.360480 0.149316i 0.360480 0.149316i
\(609\) 0 0
\(610\) 1.92388 + 0.382683i 1.92388 + 0.382683i
\(611\) 0 0
\(612\) 0 0
\(613\) 0 0 0.555570 0.831470i \(-0.312500\pi\)
−0.555570 + 0.831470i \(0.687500\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 0.360480 + 0.149316i 0.360480 + 0.149316i 0.555570 0.831470i \(-0.312500\pi\)
−0.195090 + 0.980785i \(0.562500\pi\)
\(618\) 0 0
\(619\) −1.92388 + 0.382683i −1.92388 + 0.382683i −0.923880 + 0.382683i \(0.875000\pi\)
−1.00000 \(\pi\)
\(620\) 1.02656 + 1.53636i 1.02656 + 1.53636i
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 0.765367 1.84776i 0.765367 1.84776i 0.382683 0.923880i \(-0.375000\pi\)
0.382683 0.923880i \(-0.375000\pi\)
\(632\) −0.785695 + 1.17588i −0.785695 + 1.17588i
\(633\) 0 0
\(634\) −1.30656 + 0.541196i −1.30656 + 0.541196i
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 0.382683 + 0.923880i 0.382683 + 0.923880i
\(641\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(642\) 0 0
\(643\) 0 0 −0.980785 0.195090i \(-0.937500\pi\)
0.980785 + 0.195090i \(0.0625000\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0.248303 + 0.599456i 0.248303 + 0.599456i
\(647\) −0.360480 + 0.149316i −0.360480 + 0.149316i −0.555570 0.831470i \(-0.687500\pi\)
0.195090 + 0.980785i \(0.437500\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −0.425215 0.636379i −0.425215 0.636379i 0.555570 0.831470i \(-0.312500\pi\)
−0.980785 + 0.195090i \(0.937500\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 0 0 −0.555570 0.831470i \(-0.687500\pi\)
0.555570 + 0.831470i \(0.312500\pi\)
\(660\) 0 0
\(661\) 0.0761205 + 0.382683i 0.0761205 + 0.382683i 1.00000 \(0\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(662\) 0.785695 + 0.785695i 0.785695 + 0.785695i
\(663\) 0 0
\(664\) 0.541196 0.541196i 0.541196 0.541196i
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) −1.11114 −1.11114
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) −0.707107 0.707107i −0.707107 0.707107i
\(677\) −0.636379 0.425215i −0.636379 0.425215i 0.195090 0.980785i \(-0.437500\pi\)
−0.831470 + 0.555570i \(0.812500\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) −1.53636 + 0.636379i −1.53636 + 0.636379i
\(681\) 0 0
\(682\) 0 0
\(683\) 0.275899 + 1.38704i 0.275899 + 1.38704i 0.831470 + 0.555570i \(0.187500\pi\)
−0.555570 + 0.831470i \(0.687500\pi\)
\(684\) 0 0
\(685\) −0.216773 0.324423i −0.216773 0.324423i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) −0.617317 0.923880i −0.617317 0.923880i 0.382683 0.923880i \(-0.375000\pi\)
−1.00000 \(\pi\)
\(692\) 0.149316 + 0.750661i 0.149316 + 0.750661i
\(693\) 0 0
\(694\) 1.41421i 1.41421i
\(695\) −1.53636 0.636379i −1.53636 0.636379i
\(696\) 0 0
\(697\) 0 0
\(698\) 1.81225 0.750661i 1.81225 0.750661i
\(699\) 0 0
\(700\) 0 0
\(701\) 0 0 −0.980785 0.195090i \(-0.937500\pi\)
0.980785 + 0.195090i \(0.0625000\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0 0
\(705\) 0 0
\(706\) −1.63099 + 1.08979i −1.63099 + 1.08979i
\(707\) 0 0
\(708\) 0 0
\(709\) −1.63099 1.08979i −1.63099 1.08979i −0.923880 0.382683i \(-0.875000\pi\)
−0.707107 0.707107i \(-0.750000\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −1.17588 + 2.83881i −1.17588 + 2.83881i
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −0.165390 0.831470i −0.165390 0.831470i
\(723\) 0 0
\(724\) 0.324423 1.63099i 0.324423 1.63099i
\(725\) 0 0
\(726\) 0 0
\(727\) 0 0 −0.923880 0.382683i \(-0.875000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 0 0 −0.980785 0.195090i \(-0.937500\pi\)
0.980785 + 0.195090i \(0.0625000\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) −0.923880 + 1.38268i −0.923880 + 1.38268i
\(737\) 0 0
\(738\) 0 0
\(739\) −0.382683 + 1.92388i −0.382683 + 1.92388i 1.00000i \(0.5\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 0.149316 + 0.360480i 0.149316 + 0.360480i 0.980785 0.195090i \(-0.0625000\pi\)
−0.831470 + 0.555570i \(0.812500\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −1.30656 + 1.30656i −1.30656 + 1.30656i −0.382683 + 0.923880i \(0.625000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(752\) 1.96157i 1.96157i
\(753\) 0 0
\(754\) 0 0
\(755\) −0.636379 + 0.425215i −0.636379 + 0.425215i
\(756\) 0 0
\(757\) 0 0 0.980785 0.195090i \(-0.0625000\pi\)
−0.980785 + 0.195090i \(0.937500\pi\)
\(758\) 1.11114i 1.11114i
\(759\) 0 0
\(760\) −0.382683 + 0.0761205i −0.382683 + 0.0761205i
\(761\) 0 0 −0.382683 0.923880i \(-0.625000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0.324423 0.216773i 0.324423 0.216773i
\(767\) 0 0
\(768\) 0 0
\(769\) 0.765367 0.765367 0.382683 0.923880i \(-0.375000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 0 0 −0.831470 0.555570i \(-0.812500\pi\)
0.831470 + 0.555570i \(0.187500\pi\)
\(774\) 0 0
\(775\) −0.707107 1.70711i −0.707107 1.70711i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) −2.29932 1.53636i −2.29932 1.53636i
\(783\) 0 0
\(784\) 1.00000 1.00000
\(785\) 0 0
\(786\) 0 0
\(787\) 0 0 0.831470 0.555570i \(-0.187500\pi\)
−0.831470 + 0.555570i \(0.812500\pi\)
\(788\) −0.785695 1.17588i −0.785695 1.17588i
\(789\) 0 0
\(790\) 1.00000 1.00000i 1.00000 1.00000i
\(791\) 0 0
\(792\) 0 0
\(793\) 0 0
\(794\) 0 0
\(795\) 0 0
\(796\) 1.41421 1.41421
\(797\) −0.275899 + 1.38704i −0.275899 + 1.38704i 0.555570 + 0.831470i \(0.312500\pi\)
−0.831470 + 0.555570i \(0.812500\pi\)
\(798\) 0 0
\(799\) 3.26197 3.26197
\(800\) −0.195090 0.980785i −0.195090 0.980785i
\(801\) 0 0
\(802\) 0 0
\(803\) 0 0
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0