Properties

Label 3479.1.g.e.851.1
Level $3479$
Weight $1$
Character 3479.851
Analytic conductor $1.736$
Analytic rank $0$
Dimension $6$
Projective image $D_{7}$
CM discriminant -71
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 3479 = 7^{2} \cdot 71 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 3479.g (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.73624717895\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{6})\)
Coefficient field: 6.0.64827.1
Defining polynomial: \(x^{6} - x^{5} + 3 x^{4} + 5 x^{2} - 2 x + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 71)
Projective image: \(D_{7}\)
Projective field: Galois closure of 7.1.357911.1
Artin image: $C_3\times D_7$
Artin field: Galois closure of 21.3.31095511042786085990206459319.1

Embedding invariants

Embedding label 851.1
Root \(0.222521 + 0.385418i\) of defining polynomial
Character \(\chi\) \(=\) 3479.851
Dual form 3479.1.g.e.1206.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.623490 - 1.07992i) q^{2} +(0.900969 - 1.56052i) q^{3} +(-0.277479 + 0.480608i) q^{4} +(0.222521 + 0.385418i) q^{5} -2.24698 q^{6} -0.554958 q^{8} +(-1.12349 - 1.94594i) q^{9} +O(q^{10})\) \(q+(-0.623490 - 1.07992i) q^{2} +(0.900969 - 1.56052i) q^{3} +(-0.277479 + 0.480608i) q^{4} +(0.222521 + 0.385418i) q^{5} -2.24698 q^{6} -0.554958 q^{8} +(-1.12349 - 1.94594i) q^{9} +(0.277479 - 0.480608i) q^{10} +(0.500000 + 0.866025i) q^{12} +0.801938 q^{15} +(0.623490 + 1.07992i) q^{16} +(-1.40097 + 2.42655i) q^{18} +(-0.623490 - 1.07992i) q^{19} -0.246980 q^{20} +(-0.500000 + 0.866025i) q^{24} +(0.400969 - 0.694498i) q^{25} -2.24698 q^{27} -1.80194 q^{29} +(-0.500000 - 0.866025i) q^{30} +(0.500000 - 0.866025i) q^{32} +1.24698 q^{36} +(-0.623490 - 1.07992i) q^{37} +(-0.777479 + 1.34663i) q^{38} +(-0.123490 - 0.213891i) q^{40} -0.445042 q^{43} +(0.500000 - 0.866025i) q^{45} +2.24698 q^{48} -1.00000 q^{50} +(1.40097 + 2.42655i) q^{54} -2.24698 q^{57} +(1.12349 + 1.94594i) q^{58} +(-0.222521 + 0.385418i) q^{60} +1.00000 q^{71} +(0.623490 + 1.07992i) q^{72} +(0.222521 - 0.385418i) q^{73} +(-0.777479 + 1.34663i) q^{74} +(-0.722521 - 1.25144i) q^{75} +0.692021 q^{76} +(0.222521 + 0.385418i) q^{79} +(-0.277479 + 0.480608i) q^{80} +(-0.900969 + 1.56052i) q^{81} +1.24698 q^{83} +(0.277479 + 0.480608i) q^{86} +(-1.62349 + 2.81197i) q^{87} +(0.900969 + 1.56052i) q^{89} -1.24698 q^{90} +(0.277479 - 0.480608i) q^{95} +(-0.900969 - 1.56052i) q^{96} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + q^{2} + q^{3} - 2 q^{4} + q^{5} - 4 q^{6} - 4 q^{8} - 2 q^{9} + O(q^{10}) \) \( 6 q + q^{2} + q^{3} - 2 q^{4} + q^{5} - 4 q^{6} - 4 q^{8} - 2 q^{9} + 2 q^{10} + 3 q^{12} - 4 q^{15} - q^{16} - 4 q^{18} + q^{19} + 8 q^{20} - 3 q^{24} - 2 q^{25} - 4 q^{27} - 2 q^{29} - 3 q^{30} + 3 q^{32} - 2 q^{36} + q^{37} - 5 q^{38} + 4 q^{40} - 2 q^{43} + 3 q^{45} + 4 q^{48} - 6 q^{50} + 4 q^{54} - 4 q^{57} + 2 q^{58} - q^{60} + 6 q^{71} - q^{72} + q^{73} - 5 q^{74} - 4 q^{75} - 6 q^{76} + q^{79} - 2 q^{80} - q^{81} - 2 q^{83} + 2 q^{86} - 5 q^{87} + q^{89} + 2 q^{90} + 2 q^{95} - q^{96} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3479\mathbb{Z}\right)^\times\).

\(n\) \(640\) \(1569\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.623490 1.07992i −0.623490 1.07992i −0.988831 0.149042i \(-0.952381\pi\)
0.365341 0.930874i \(-0.380952\pi\)
\(3\) 0.900969 1.56052i 0.900969 1.56052i 0.0747301 0.997204i \(-0.476190\pi\)
0.826239 0.563320i \(-0.190476\pi\)
\(4\) −0.277479 + 0.480608i −0.277479 + 0.480608i
\(5\) 0.222521 + 0.385418i 0.222521 + 0.385418i 0.955573 0.294755i \(-0.0952381\pi\)
−0.733052 + 0.680173i \(0.761905\pi\)
\(6\) −2.24698 −2.24698
\(7\) 0 0
\(8\) −0.554958 −0.554958
\(9\) −1.12349 1.94594i −1.12349 1.94594i
\(10\) 0.277479 0.480608i 0.277479 0.480608i
\(11\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(12\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(13\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(14\) 0 0
\(15\) 0.801938 0.801938
\(16\) 0.623490 + 1.07992i 0.623490 + 1.07992i
\(17\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(18\) −1.40097 + 2.42655i −1.40097 + 2.42655i
\(19\) −0.623490 1.07992i −0.623490 1.07992i −0.988831 0.149042i \(-0.952381\pi\)
0.365341 0.930874i \(-0.380952\pi\)
\(20\) −0.246980 −0.246980
\(21\) 0 0
\(22\) 0 0
\(23\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(24\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(25\) 0.400969 0.694498i 0.400969 0.694498i
\(26\) 0 0
\(27\) −2.24698 −2.24698
\(28\) 0 0
\(29\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(30\) −0.500000 0.866025i −0.500000 0.866025i
\(31\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(32\) 0.500000 0.866025i 0.500000 0.866025i
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) 1.24698 1.24698
\(37\) −0.623490 1.07992i −0.623490 1.07992i −0.988831 0.149042i \(-0.952381\pi\)
0.365341 0.930874i \(-0.380952\pi\)
\(38\) −0.777479 + 1.34663i −0.777479 + 1.34663i
\(39\) 0 0
\(40\) −0.123490 0.213891i −0.123490 0.213891i
\(41\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(42\) 0 0
\(43\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(44\) 0 0
\(45\) 0.500000 0.866025i 0.500000 0.866025i
\(46\) 0 0
\(47\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(48\) 2.24698 2.24698
\(49\) 0 0
\(50\) −1.00000 −1.00000
\(51\) 0 0
\(52\) 0 0
\(53\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(54\) 1.40097 + 2.42655i 1.40097 + 2.42655i
\(55\) 0 0
\(56\) 0 0
\(57\) −2.24698 −2.24698
\(58\) 1.12349 + 1.94594i 1.12349 + 1.94594i
\(59\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(60\) −0.222521 + 0.385418i −0.222521 + 0.385418i
\(61\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 1.00000 1.00000
\(72\) 0.623490 + 1.07992i 0.623490 + 1.07992i
\(73\) 0.222521 0.385418i 0.222521 0.385418i −0.733052 0.680173i \(-0.761905\pi\)
0.955573 + 0.294755i \(0.0952381\pi\)
\(74\) −0.777479 + 1.34663i −0.777479 + 1.34663i
\(75\) −0.722521 1.25144i −0.722521 1.25144i
\(76\) 0.692021 0.692021
\(77\) 0 0
\(78\) 0 0
\(79\) 0.222521 + 0.385418i 0.222521 + 0.385418i 0.955573 0.294755i \(-0.0952381\pi\)
−0.733052 + 0.680173i \(0.761905\pi\)
\(80\) −0.277479 + 0.480608i −0.277479 + 0.480608i
\(81\) −0.900969 + 1.56052i −0.900969 + 1.56052i
\(82\) 0 0
\(83\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0.277479 + 0.480608i 0.277479 + 0.480608i
\(87\) −1.62349 + 2.81197i −1.62349 + 2.81197i
\(88\) 0 0
\(89\) 0.900969 + 1.56052i 0.900969 + 1.56052i 0.826239 + 0.563320i \(0.190476\pi\)
0.0747301 + 0.997204i \(0.476190\pi\)
\(90\) −1.24698 −1.24698
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0.277479 0.480608i 0.277479 0.480608i
\(96\) −0.900969 1.56052i −0.900969 1.56052i
\(97\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0.222521 + 0.385418i 0.222521 + 0.385418i
\(101\) −0.623490 + 1.07992i −0.623490 + 1.07992i 0.365341 + 0.930874i \(0.380952\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(102\) 0 0
\(103\) 0.900969 + 1.56052i 0.900969 + 1.56052i 0.826239 + 0.563320i \(0.190476\pi\)
0.0747301 + 0.997204i \(0.476190\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −1.00000 1.73205i −1.00000 1.73205i −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 0.866025i \(-0.666667\pi\)
\(108\) 0.623490 1.07992i 0.623490 1.07992i
\(109\) 0.900969 1.56052i 0.900969 1.56052i 0.0747301 0.997204i \(-0.476190\pi\)
0.826239 0.563320i \(-0.190476\pi\)
\(110\) 0 0
\(111\) −2.24698 −2.24698
\(112\) 0 0
\(113\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(114\) 1.40097 + 2.42655i 1.40097 + 2.42655i
\(115\) 0 0
\(116\) 0.500000 0.866025i 0.500000 0.866025i
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) −0.445042 −0.445042
\(121\) −0.500000 0.866025i −0.500000 0.866025i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 0.801938 0.801938
\(126\) 0 0
\(127\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(128\) −0.500000 0.866025i −0.500000 0.866025i
\(129\) −0.400969 + 0.694498i −0.400969 + 0.694498i
\(130\) 0 0
\(131\) 0.222521 + 0.385418i 0.222521 + 0.385418i 0.955573 0.294755i \(-0.0952381\pi\)
−0.733052 + 0.680173i \(0.761905\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) −0.500000 0.866025i −0.500000 0.866025i
\(136\) 0 0
\(137\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(138\) 0 0
\(139\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −0.623490 1.07992i −0.623490 1.07992i
\(143\) 0 0
\(144\) 1.40097 2.42655i 1.40097 2.42655i
\(145\) −0.400969 0.694498i −0.400969 0.694498i
\(146\) −0.554958 −0.554958
\(147\) 0 0
\(148\) 0.692021 0.692021
\(149\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(150\) −0.900969 + 1.56052i −0.900969 + 1.56052i
\(151\) 0.900969 1.56052i 0.900969 1.56052i 0.0747301 0.997204i \(-0.476190\pi\)
0.826239 0.563320i \(-0.190476\pi\)
\(152\) 0.346011 + 0.599308i 0.346011 + 0.599308i
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 0.900969 1.56052i 0.900969 1.56052i 0.0747301 0.997204i \(-0.476190\pi\)
0.826239 0.563320i \(-0.190476\pi\)
\(158\) 0.277479 0.480608i 0.277479 0.480608i
\(159\) 0 0
\(160\) 0.445042 0.445042
\(161\) 0 0
\(162\) 2.24698 2.24698
\(163\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) −0.777479 1.34663i −0.777479 1.34663i
\(167\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(168\) 0 0
\(169\) 1.00000 1.00000
\(170\) 0 0
\(171\) −1.40097 + 2.42655i −1.40097 + 2.42655i
\(172\) 0.123490 0.213891i 0.123490 0.213891i
\(173\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(174\) 4.04892 4.04892
\(175\) 0 0
\(176\) 0 0
\(177\) 0 0
\(178\) 1.12349 1.94594i 1.12349 1.94594i
\(179\) 0.222521 0.385418i 0.222521 0.385418i −0.733052 0.680173i \(-0.761905\pi\)
0.955573 + 0.294755i \(0.0952381\pi\)
\(180\) 0.277479 + 0.480608i 0.277479 + 0.480608i
\(181\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0.277479 0.480608i 0.277479 0.480608i
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 0 0
\(190\) −0.692021 −0.692021
\(191\) 0.900969 + 1.56052i 0.900969 + 1.56052i 0.826239 + 0.563320i \(0.190476\pi\)
0.0747301 + 0.997204i \(0.476190\pi\)
\(192\) 0 0
\(193\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(198\) 0 0
\(199\) −0.623490 + 1.07992i −0.623490 + 1.07992i 0.365341 + 0.930874i \(0.380952\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(200\) −0.222521 + 0.385418i −0.222521 + 0.385418i
\(201\) 0 0
\(202\) 1.55496 1.55496
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 1.12349 1.94594i 1.12349 1.94594i
\(207\) 0 0
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(212\) 0 0
\(213\) 0.900969 1.56052i 0.900969 1.56052i
\(214\) −1.24698 + 2.15983i −1.24698 + 2.15983i
\(215\) −0.0990311 0.171527i −0.0990311 0.171527i
\(216\) 1.24698 1.24698
\(217\) 0 0
\(218\) −2.24698 −2.24698
\(219\) −0.400969 0.694498i −0.400969 0.694498i
\(220\) 0 0
\(221\) 0 0
\(222\) 1.40097 + 2.42655i 1.40097 + 2.42655i
\(223\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(224\) 0 0
\(225\) −1.80194 −1.80194
\(226\) 0 0
\(227\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(228\) 0.623490 1.07992i 0.623490 1.07992i
\(229\) 0.222521 + 0.385418i 0.222521 + 0.385418i 0.955573 0.294755i \(-0.0952381\pi\)
−0.733052 + 0.680173i \(0.761905\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 1.00000 1.00000
\(233\) −0.623490 1.07992i −0.623490 1.07992i −0.988831 0.149042i \(-0.952381\pi\)
0.365341 0.930874i \(-0.380952\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 0.801938 0.801938
\(238\) 0 0
\(239\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(240\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(241\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(242\) −0.623490 + 1.07992i −0.623490 + 1.07992i
\(243\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 1.12349 1.94594i 1.12349 1.94594i
\(250\) −0.500000 0.866025i −0.500000 0.866025i
\(251\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) −0.623490 + 1.07992i −0.623490 + 1.07992i
\(257\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(258\) 1.00000 1.00000
\(259\) 0 0
\(260\) 0 0
\(261\) 2.02446 + 3.50647i 2.02446 + 3.50647i
\(262\) 0.277479 0.480608i 0.277479 0.480608i
\(263\) 0.222521 0.385418i 0.222521 0.385418i −0.733052 0.680173i \(-0.761905\pi\)
0.955573 + 0.294755i \(0.0952381\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 3.24698 3.24698
\(268\) 0 0
\(269\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(270\) −0.623490 + 1.07992i −0.623490 + 1.07992i
\(271\) 0.900969 + 1.56052i 0.900969 + 1.56052i 0.826239 + 0.563320i \(0.190476\pi\)
0.0747301 + 0.997204i \(0.476190\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −0.623490 + 1.07992i −0.623490 + 1.07992i 0.365341 + 0.930874i \(0.380952\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(282\) 0 0
\(283\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(284\) −0.277479 + 0.480608i −0.277479 + 0.480608i
\(285\) −0.500000 0.866025i −0.500000 0.866025i
\(286\) 0 0
\(287\) 0 0
\(288\) −2.24698 −2.24698
\(289\) −0.500000 0.866025i −0.500000 0.866025i
\(290\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(291\) 0 0
\(292\) 0.123490 + 0.213891i 0.123490 + 0.213891i
\(293\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0.346011 + 0.599308i 0.346011 + 0.599308i
\(297\) 0 0
\(298\) 0 0
\(299\) 0 0
\(300\) 0.801938 0.801938
\(301\) 0 0
\(302\) −2.24698 −2.24698
\(303\) 1.12349 + 1.94594i 1.12349 + 1.94594i
\(304\) 0.777479 1.34663i 0.777479 1.34663i
\(305\) 0 0
\(306\) 0 0
\(307\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(308\) 0 0
\(309\) 3.24698 3.24698
\(310\) 0 0
\(311\) −0.623490 + 1.07992i −0.623490 + 1.07992i 0.365341 + 0.930874i \(0.380952\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(312\) 0 0
\(313\) −0.623490 1.07992i −0.623490 1.07992i −0.988831 0.149042i \(-0.952381\pi\)
0.365341 0.930874i \(-0.380952\pi\)
\(314\) −2.24698 −2.24698
\(315\) 0 0
\(316\) −0.246980 −0.246980
\(317\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) −3.60388 −3.60388
\(322\) 0 0
\(323\) 0 0
\(324\) −0.500000 0.866025i −0.500000 0.866025i
\(325\) 0 0
\(326\) 0 0
\(327\) −1.62349 2.81197i −1.62349 2.81197i
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(332\) −0.346011 + 0.599308i −0.346011 + 0.599308i
\(333\) −1.40097 + 2.42655i −1.40097 + 2.42655i
\(334\) 0.277479 + 0.480608i 0.277479 + 0.480608i
\(335\) 0 0
\(336\) 0 0
\(337\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(338\) −0.623490 1.07992i −0.623490 1.07992i
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 3.49396 3.49396
\(343\) 0 0
\(344\) 0.246980 0.246980
\(345\) 0 0
\(346\) 0 0
\(347\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(348\) −0.900969 1.56052i −0.900969 1.56052i
\(349\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(354\) 0 0
\(355\) 0.222521 + 0.385418i 0.222521 + 0.385418i
\(356\) −1.00000 −1.00000
\(357\) 0 0
\(358\) −0.554958 −0.554958
\(359\) 0.222521 + 0.385418i 0.222521 + 0.385418i 0.955573 0.294755i \(-0.0952381\pi\)
−0.733052 + 0.680173i \(0.761905\pi\)
\(360\) −0.277479 + 0.480608i −0.277479 + 0.480608i
\(361\) −0.277479 + 0.480608i −0.277479 + 0.480608i
\(362\) 0 0
\(363\) −1.80194 −1.80194
\(364\) 0 0
\(365\) 0.198062 0.198062
\(366\) 0 0
\(367\) 0.222521 0.385418i 0.222521 0.385418i −0.733052 0.680173i \(-0.761905\pi\)
0.955573 + 0.294755i \(0.0952381\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) −0.692021 −0.692021
\(371\) 0 0
\(372\) 0 0
\(373\) 0.222521 + 0.385418i 0.222521 + 0.385418i 0.955573 0.294755i \(-0.0952381\pi\)
−0.733052 + 0.680173i \(0.761905\pi\)
\(374\) 0 0
\(375\) 0.722521 1.25144i 0.722521 1.25144i
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(380\) 0.153989 + 0.266717i 0.153989 + 0.266717i
\(381\) 0 0
\(382\) 1.12349 1.94594i 1.12349 1.94594i
\(383\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(384\) −1.80194 −1.80194
\(385\) 0 0
\(386\) 0 0
\(387\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(388\) 0 0
\(389\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 0.801938 0.801938
\(394\) 0 0
\(395\) −0.0990311 + 0.171527i −0.0990311 + 0.171527i
\(396\) 0 0
\(397\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(398\) 1.55496 1.55496
\(399\) 0 0
\(400\) 1.00000 1.00000
\(401\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) −0.346011 0.599308i −0.346011 0.599308i
\(405\) −0.801938 −0.801938
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 0.900969 1.56052i 0.900969 1.56052i 0.0747301 0.997204i \(-0.476190\pi\)
0.826239 0.563320i \(-0.190476\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) −1.00000 −1.00000
\(413\) 0 0
\(414\) 0 0
\(415\) 0.277479 + 0.480608i 0.277479 + 0.480608i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(420\) 0 0
\(421\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 0 0
\(426\) −2.24698 −2.24698
\(427\) 0 0
\(428\) 1.10992 1.10992
\(429\) 0 0
\(430\) −0.123490 + 0.213891i −0.123490 + 0.213891i
\(431\) −0.623490 + 1.07992i −0.623490 + 1.07992i 0.365341 + 0.930874i \(0.380952\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(432\) −1.40097 2.42655i −1.40097 2.42655i
\(433\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(434\) 0 0
\(435\) −1.44504 −1.44504
\(436\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(437\) 0 0
\(438\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(439\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(444\) 0.623490 1.07992i 0.623490 1.07992i
\(445\) −0.400969 + 0.694498i −0.400969 + 0.694498i
\(446\) −0.777479 1.34663i −0.777479 1.34663i
\(447\) 0 0
\(448\) 0 0
\(449\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(450\) 1.12349 + 1.94594i 1.12349 + 1.94594i
\(451\) 0 0
\(452\) 0 0
\(453\) −1.62349 2.81197i −1.62349 2.81197i
\(454\) 0 0
\(455\) 0 0
\(456\) 1.24698 1.24698
\(457\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(458\) 0.277479 0.480608i 0.277479 0.480608i
\(459\) 0 0
\(460\) 0 0
\(461\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(462\) 0 0
\(463\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(464\) −1.12349 1.94594i −1.12349 1.94594i
\(465\) 0 0
\(466\) −0.777479 + 1.34663i −0.777479 + 1.34663i
\(467\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) −1.62349 2.81197i −1.62349 2.81197i
\(472\) 0 0
\(473\) 0 0
\(474\) −0.500000 0.866025i −0.500000 0.866025i
\(475\) −1.00000 −1.00000
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(480\) 0.400969 0.694498i 0.400969 0.694498i
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) 0.554958 0.554958
\(485\) 0 0
\(486\) 0.623490 1.07992i 0.623490 1.07992i
\(487\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) −2.80194 −2.80194
\(499\) 0.900969 + 1.56052i 0.900969 + 1.56052i 0.826239 + 0.563320i \(0.190476\pi\)
0.0747301 + 0.997204i \(0.476190\pi\)
\(500\) −0.222521 + 0.385418i −0.222521 + 0.385418i
\(501\) −0.400969 + 0.694498i −0.400969 + 0.694498i
\(502\) −0.777479 1.34663i −0.777479 1.34663i
\(503\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(504\) 0 0
\(505\) −0.554958 −0.554958
\(506\) 0 0
\(507\) 0.900969 1.56052i 0.900969 1.56052i
\(508\) 0 0
\(509\) −1.00000 1.73205i −1.00000 1.73205i −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 0.866025i \(-0.666667\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0.554958 0.554958
\(513\) 1.40097 + 2.42655i 1.40097 + 2.42655i
\(514\) 0 0
\(515\) −0.400969 + 0.694498i −0.400969 + 0.694498i
\(516\) −0.222521 0.385418i −0.222521 0.385418i
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 0.222521 0.385418i 0.222521 0.385418i −0.733052 0.680173i \(-0.761905\pi\)
0.955573 + 0.294755i \(0.0952381\pi\)
\(522\) 2.52446 4.37249i 2.52446 4.37249i
\(523\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(524\) −0.246980 −0.246980
\(525\) 0 0
\(526\) −0.554958 −0.554958
\(527\) 0 0
\(528\) 0 0
\(529\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) −2.02446 3.50647i −2.02446 3.50647i
\(535\) 0.445042 0.770835i 0.445042 0.770835i
\(536\) 0 0
\(537\) −0.400969 0.694498i −0.400969 0.694498i
\(538\) 0 0
\(539\) 0 0
\(540\) 0.554958 0.554958
\(541\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(542\) 1.12349 1.94594i 1.12349 1.94594i
\(543\) 0 0
\(544\) 0 0
\(545\) 0.801938 0.801938
\(546\) 0 0
\(547\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 1.12349 + 1.94594i 1.12349 + 1.94594i
\(552\) 0 0
\(553\) 0 0
\(554\) 1.55496 1.55496
\(555\) −0.500000 0.866025i −0.500000 0.866025i
\(556\) 0 0
\(557\) 0.900969 1.56052i 0.900969 1.56052i 0.0747301 0.997204i \(-0.476190\pi\)
0.826239 0.563320i \(-0.190476\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 0 0
\(568\) −0.554958 −0.554958
\(569\) 0.222521 + 0.385418i 0.222521 + 0.385418i 0.955573 0.294755i \(-0.0952381\pi\)
−0.733052 + 0.680173i \(0.761905\pi\)
\(570\) −0.623490 + 1.07992i −0.623490 + 1.07992i
\(571\) −0.623490 + 1.07992i −0.623490 + 1.07992i 0.365341 + 0.930874i \(0.380952\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(572\) 0 0
\(573\) 3.24698 3.24698
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 0.222521 0.385418i 0.222521 0.385418i −0.733052 0.680173i \(-0.761905\pi\)
0.955573 + 0.294755i \(0.0952381\pi\)
\(578\) −0.623490 + 1.07992i −0.623490 + 1.07992i
\(579\) 0 0
\(580\) 0.445042 0.445042
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) −0.123490 + 0.213891i −0.123490 + 0.213891i
\(585\) 0 0
\(586\) −1.24698 2.15983i −1.24698 2.15983i
\(587\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0.777479 1.34663i 0.777479 1.34663i
\(593\) 0.900969 + 1.56052i 0.900969 + 1.56052i 0.826239 + 0.563320i \(0.190476\pi\)
0.0747301 + 0.997204i \(0.476190\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 1.12349 + 1.94594i 1.12349 + 1.94594i
\(598\) 0 0
\(599\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(600\) 0.400969 + 0.694498i 0.400969 + 0.694498i
\(601\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(605\) 0.222521 0.385418i 0.222521 0.385418i
\(606\) 1.40097 2.42655i 1.40097 2.42655i
\(607\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(608\) −1.24698 −1.24698
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) 0.900969 1.56052i 0.900969 1.56052i 0.0747301 0.997204i \(-0.476190\pi\)
0.826239 0.563320i \(-0.190476\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(618\) −2.02446 3.50647i −2.02446 3.50647i
\(619\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 1.55496 1.55496
\(623\) 0 0
\(624\) 0 0
\(625\) −0.222521 0.385418i −0.222521 0.385418i
\(626\) −0.777479 + 1.34663i −0.777479 + 1.34663i
\(627\) 0 0
\(628\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(629\) 0 0
\(630\) 0 0
\(631\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(632\) −0.123490 0.213891i −0.123490 0.213891i
\(633\) 0 0
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) −1.12349 1.94594i −1.12349 1.94594i
\(640\) 0.222521 0.385418i 0.222521 0.385418i
\(641\) −0.623490 + 1.07992i −0.623490 + 1.07992i 0.365341 + 0.930874i \(0.380952\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(642\) 2.24698 + 3.89188i 2.24698 + 3.89188i
\(643\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(644\) 0 0
\(645\) −0.356896 −0.356896
\(646\) 0 0
\(647\) −1.00000 + 1.73205i −1.00000 + 1.73205i −0.500000 + 0.866025i \(0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(648\) 0.500000 0.866025i 0.500000 0.866025i
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(654\) −2.02446 + 3.50647i −2.02446 + 3.50647i
\(655\) −0.0990311 + 0.171527i −0.0990311 + 0.171527i
\(656\) 0 0
\(657\) −1.00000 −1.00000
\(658\) 0 0
\(659\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(660\) 0 0
\(661\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) −0.692021 −0.692021
\(665\) 0 0
\(666\) 3.49396 3.49396
\(667\) 0 0
\(668\) 0.123490 0.213891i 0.123490 0.213891i
\(669\) 1.12349 1.94594i 1.12349 1.94594i
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(674\) 0 0
\(675\) −0.900969 + 1.56052i −0.900969 + 1.56052i
\(676\) −0.277479 + 0.480608i −0.277479 + 0.480608i
\(677\) 0.900969 + 1.56052i 0.900969 + 1.56052i 0.826239 + 0.563320i \(0.190476\pi\)
0.0747301 + 0.997204i \(0.476190\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(684\) −0.777479 1.34663i −0.777479 1.34663i
\(685\) 0 0
\(686\) 0 0
\(687\) 0.801938 0.801938
\(688\) −0.277479 0.480608i −0.277479 0.480608i
\(689\) 0 0
\(690\) 0 0
\(691\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0.900969 1.56052i 0.900969 1.56052i
\(697\) 0 0
\(698\) 0 0
\(699\) −2.24698 −2.24698
\(700\) 0 0
\(701\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(702\) 0 0
\(703\) −0.777479 + 1.34663i −0.777479 + 1.34663i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(710\) 0.277479 0.480608i 0.277479 0.480608i
\(711\) 0.500000 0.866025i 0.500000 0.866025i
\(712\) −0.500000 0.866025i −0.500000 0.866025i
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0.123490 + 0.213891i 0.123490 + 0.213891i
\(717\) 0 0
\(718\) 0.277479 0.480608i 0.277479 0.480608i
\(719\) −0.623490 1.07992i −0.623490 1.07992i −0.988831 0.149042i \(-0.952381\pi\)
0.365341 0.930874i \(-0.380952\pi\)
\(720\) 1.24698 1.24698
\(721\) 0 0
\(722\) 0.692021 0.692021
\(723\) 0 0
\(724\) 0 0
\(725\) −0.722521 + 1.25144i −0.722521 + 1.25144i
\(726\) 1.12349 + 1.94594i 1.12349 + 1.94594i
\(727\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) −0.123490 0.213891i −0.123490 0.213891i
\(731\) 0 0
\(732\) 0 0
\(733\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(734\) −0.554958 −0.554958
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) −1.00000 + 1.73205i −1.00000 + 1.73205i −0.500000 + 0.866025i \(0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(740\) 0.153989 + 0.266717i 0.153989 + 0.266717i
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0.277479 0.480608i 0.277479 0.480608i
\(747\) −1.40097 2.42655i −1.40097 2.42655i
\(748\) 0 0
\(749\) 0 0
\(750\) −1.80194 −1.80194
\(751\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(752\) 0 0
\(753\) 1.12349 1.94594i 1.12349 1.94594i
\(754\) 0 0
\(755\) 0.801938 0.801938
\(756\) 0 0
\(757\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(758\) 1.12349 + 1.94594i 1.12349 + 1.94594i
\(759\) 0 0
\(760\) −0.153989 + 0.266717i −0.153989 + 0.266717i
\(761\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −1.00000 −1.00000
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 1.12349 + 1.94594i 1.12349 + 1.94594i
\(769\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(774\) 0.623490 1.07992i 0.623490 1.07992i
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 4.04892 4.04892
\(784\) 0 0
\(785\) 0.801938 0.801938
\(786\) −0.500000 0.866025i −0.500000 0.866025i
\(787\) 0.900969 1.56052i 0.900969 1.56052i 0.0747301 0.997204i \(-0.476190\pi\)
0.826239 0.563320i \(-0.190476\pi\)
\(788\) 0 0
\(789\) −0.400969 0.694498i −0.400969 0.694498i
\(790\) 0.246980 0.246980
\(791\) 0 0
\(792\) 0 0
\(793\) 0 0
\(794\) 0 0
\(795\) 0 0
\(796\) −0.346011 0.599308i −0.346011 0.599308i
\(797\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) −0.400969 0.694498i −0.400969 0.694498i
\(801\) 2.02446 3.50647i 2.02446 3.50647i
\(802\) 0