Properties

Label 1089.1.s.b.457.2
Level $1089$
Weight $1$
Character 1089.457
Analytic conductor $0.543$
Analytic rank $0$
Dimension $16$
Projective image $S_{4}$
CM/RM no
Inner twists $16$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 1089 = 3^{2} \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1089.s (of order \(30\), degree \(8\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.543481798757\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(2\) over \(\Q(\zeta_{30})\)
Coefficient field: 16.0.26873856000000000000.1
Defining polynomial: \(x^{16} + 2 x^{14} - 8 x^{10} - 16 x^{8} - 32 x^{6} + 128 x^{2} + 256\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Projective image: \(S_{4}\)
Projective field: Galois closure of 4.2.107811.1

Embedding invariants

Embedding label 457.2
Root \(0.294032 - 1.38331i\) of defining polynomial
Character \(\chi\) \(=\) 1089.457
Dual form 1089.1.s.b.112.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.294032 - 1.38331i) q^{2} +(0.104528 - 0.994522i) q^{3} +(-0.913545 - 0.406737i) q^{4} +(0.978148 - 0.207912i) q^{5} +(-1.34500 - 0.437016i) q^{6} +(-1.40647 + 0.147826i) q^{7} +(-0.978148 - 0.207912i) q^{9} +O(q^{10})\) \(q+(0.294032 - 1.38331i) q^{2} +(0.104528 - 0.994522i) q^{3} +(-0.913545 - 0.406737i) q^{4} +(0.978148 - 0.207912i) q^{5} +(-1.34500 - 0.437016i) q^{6} +(-1.40647 + 0.147826i) q^{7} +(-0.978148 - 0.207912i) q^{9} -1.41421i q^{10} +(-0.500000 + 0.866025i) q^{12} +(-0.209057 + 1.98904i) q^{14} +(-0.104528 - 0.994522i) q^{15} +(-0.669131 - 0.743145i) q^{16} +(-0.575212 + 1.29195i) q^{18} +(-0.978148 - 0.207912i) q^{20} +1.41421i q^{21} +(-0.309017 + 0.951057i) q^{27} +(1.34500 + 0.437016i) q^{28} +(1.40647 - 0.147826i) q^{29} +(-1.40647 - 0.147826i) q^{30} +(0.669131 - 0.743145i) q^{31} +(-1.22474 + 0.707107i) q^{32} +(-1.34500 + 0.437016i) q^{35} +(0.809017 + 0.587785i) q^{36} +(0.809017 - 0.587785i) q^{37} +(1.95630 + 0.415823i) q^{42} -1.00000 q^{45} +(-0.913545 + 0.406737i) q^{47} +(-0.809017 + 0.587785i) q^{48} +(0.978148 - 0.207912i) q^{49} +(0.309017 + 0.951057i) q^{53} +(1.22474 + 0.707107i) q^{54} +(0.209057 - 1.98904i) q^{58} +(0.913545 + 0.406737i) q^{59} +(-0.309017 + 0.951057i) q^{60} +(1.05097 - 0.946294i) q^{61} +(-0.831254 - 1.14412i) q^{62} +(1.40647 + 0.147826i) q^{63} +(0.309017 + 0.951057i) q^{64} +(0.500000 + 0.866025i) q^{67} +(0.209057 + 1.98904i) q^{70} +(-0.309017 + 0.951057i) q^{71} +(0.831254 + 1.14412i) q^{73} +(-0.575212 - 1.29195i) q^{74} +(-0.809017 - 0.587785i) q^{80} +(0.913545 + 0.406737i) q^{81} +(1.05097 - 0.946294i) q^{83} +(0.575212 - 1.29195i) q^{84} -1.41421i q^{87} +(-0.294032 + 1.38331i) q^{90} +(-0.669131 - 0.743145i) q^{93} +(0.294032 + 1.38331i) q^{94} +(0.575212 + 1.29195i) q^{96} +(-0.978148 - 0.207912i) q^{97} -1.41421i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q - 2q^{3} - 2q^{4} - 2q^{5} + 2q^{9} + O(q^{10}) \) \( 16q - 2q^{3} - 2q^{4} - 2q^{5} + 2q^{9} - 8q^{12} + 4q^{14} + 2q^{15} - 2q^{16} + 2q^{20} + 4q^{27} + 2q^{31} + 4q^{36} + 4q^{37} - 4q^{42} - 16q^{45} - 2q^{47} - 4q^{48} - 2q^{49} - 4q^{53} - 4q^{58} + 2q^{59} + 4q^{60} - 4q^{64} + 8q^{67} - 4q^{70} + 4q^{71} - 4q^{80} + 2q^{81} - 2q^{93} + 2q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1089\mathbb{Z}\right)^\times\).

\(n\) \(244\) \(848\)
\(\chi(n)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.294032 1.38331i 0.294032 1.38331i −0.544639 0.838671i \(-0.683333\pi\)
0.838671 0.544639i \(-0.183333\pi\)
\(3\) 0.104528 0.994522i 0.104528 0.994522i
\(4\) −0.913545 0.406737i −0.913545 0.406737i
\(5\) 0.978148 0.207912i 0.978148 0.207912i 0.309017 0.951057i \(-0.400000\pi\)
0.669131 + 0.743145i \(0.266667\pi\)
\(6\) −1.34500 0.437016i −1.34500 0.437016i
\(7\) −1.40647 + 0.147826i −1.40647 + 0.147826i −0.777146 0.629320i \(-0.783333\pi\)
−0.629320 + 0.777146i \(0.716667\pi\)
\(8\) 0 0
\(9\) −0.978148 0.207912i −0.978148 0.207912i
\(10\) 1.41421i 1.41421i
\(11\) 0 0
\(12\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(13\) 0 0 0.669131 0.743145i \(-0.266667\pi\)
−0.669131 + 0.743145i \(0.733333\pi\)
\(14\) −0.209057 + 1.98904i −0.209057 + 1.98904i
\(15\) −0.104528 0.994522i −0.104528 0.994522i
\(16\) −0.669131 0.743145i −0.669131 0.743145i
\(17\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(18\) −0.575212 + 1.29195i −0.575212 + 1.29195i
\(19\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(20\) −0.978148 0.207912i −0.978148 0.207912i
\(21\) 1.41421i 1.41421i
\(22\) 0 0
\(23\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(28\) 1.34500 + 0.437016i 1.34500 + 0.437016i
\(29\) 1.40647 0.147826i 1.40647 0.147826i 0.629320 0.777146i \(-0.283333\pi\)
0.777146 + 0.629320i \(0.216667\pi\)
\(30\) −1.40647 0.147826i −1.40647 0.147826i
\(31\) 0.669131 0.743145i 0.669131 0.743145i −0.309017 0.951057i \(-0.600000\pi\)
0.978148 + 0.207912i \(0.0666667\pi\)
\(32\) −1.22474 + 0.707107i −1.22474 + 0.707107i
\(33\) 0 0
\(34\) 0 0
\(35\) −1.34500 + 0.437016i −1.34500 + 0.437016i
\(36\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(37\) 0.809017 0.587785i 0.809017 0.587785i −0.104528 0.994522i \(-0.533333\pi\)
0.913545 + 0.406737i \(0.133333\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 0 0 0.104528 0.994522i \(-0.466667\pi\)
−0.104528 + 0.994522i \(0.533333\pi\)
\(42\) 1.95630 + 0.415823i 1.95630 + 0.415823i
\(43\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(44\) 0 0
\(45\) −1.00000 −1.00000
\(46\) 0 0
\(47\) −0.913545 + 0.406737i −0.913545 + 0.406737i −0.809017 0.587785i \(-0.800000\pi\)
−0.104528 + 0.994522i \(0.533333\pi\)
\(48\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(49\) 0.978148 0.207912i 0.978148 0.207912i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 0.309017 + 0.951057i 0.309017 + 0.951057i 0.978148 + 0.207912i \(0.0666667\pi\)
−0.669131 + 0.743145i \(0.733333\pi\)
\(54\) 1.22474 + 0.707107i 1.22474 + 0.707107i
\(55\) 0 0
\(56\) 0 0
\(57\) 0 0
\(58\) 0.209057 1.98904i 0.209057 1.98904i
\(59\) 0.913545 + 0.406737i 0.913545 + 0.406737i 0.809017 0.587785i \(-0.200000\pi\)
0.104528 + 0.994522i \(0.466667\pi\)
\(60\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(61\) 1.05097 0.946294i 1.05097 0.946294i 0.0523360 0.998630i \(-0.483333\pi\)
0.998630 + 0.0523360i \(0.0166667\pi\)
\(62\) −0.831254 1.14412i −0.831254 1.14412i
\(63\) 1.40647 + 0.147826i 1.40647 + 0.147826i
\(64\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(65\) 0 0
\(66\) 0 0
\(67\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0.209057 + 1.98904i 0.209057 + 1.98904i
\(71\) −0.309017 + 0.951057i −0.309017 + 0.951057i 0.669131 + 0.743145i \(0.266667\pi\)
−0.978148 + 0.207912i \(0.933333\pi\)
\(72\) 0 0
\(73\) 0.831254 + 1.14412i 0.831254 + 1.14412i 0.987688 + 0.156434i \(0.0500000\pi\)
−0.156434 + 0.987688i \(0.550000\pi\)
\(74\) −0.575212 1.29195i −0.575212 1.29195i
\(75\) 0 0
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 −0.978148 0.207912i \(-0.933333\pi\)
0.978148 + 0.207912i \(0.0666667\pi\)
\(80\) −0.809017 0.587785i −0.809017 0.587785i
\(81\) 0.913545 + 0.406737i 0.913545 + 0.406737i
\(82\) 0 0
\(83\) 1.05097 0.946294i 1.05097 0.946294i 0.0523360 0.998630i \(-0.483333\pi\)
0.998630 + 0.0523360i \(0.0166667\pi\)
\(84\) 0.575212 1.29195i 0.575212 1.29195i
\(85\) 0 0
\(86\) 0 0
\(87\) 1.41421i 1.41421i
\(88\) 0 0
\(89\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(90\) −0.294032 + 1.38331i −0.294032 + 1.38331i
\(91\) 0 0
\(92\) 0 0
\(93\) −0.669131 0.743145i −0.669131 0.743145i
\(94\) 0.294032 + 1.38331i 0.294032 + 1.38331i
\(95\) 0 0
\(96\) 0.575212 + 1.29195i 0.575212 + 1.29195i
\(97\) −0.978148 0.207912i −0.978148 0.207912i −0.309017 0.951057i \(-0.600000\pi\)
−0.669131 + 0.743145i \(0.733333\pi\)
\(98\) 1.41421i 1.41421i
\(99\) 0 0
\(100\) 0 0
\(101\) −0.294032 + 1.38331i −0.294032 + 1.38331i 0.544639 + 0.838671i \(0.316667\pi\)
−0.838671 + 0.544639i \(0.816667\pi\)
\(102\) 0 0
\(103\) −0.913545 0.406737i −0.913545 0.406737i −0.104528 0.994522i \(-0.533333\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(104\) 0 0
\(105\) 0.294032 + 1.38331i 0.294032 + 1.38331i
\(106\) 1.40647 0.147826i 1.40647 0.147826i
\(107\) −0.831254 + 1.14412i −0.831254 + 1.14412i 0.156434 + 0.987688i \(0.450000\pi\)
−0.987688 + 0.156434i \(0.950000\pi\)
\(108\) 0.669131 0.743145i 0.669131 0.743145i
\(109\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(110\) 0 0
\(111\) −0.500000 0.866025i −0.500000 0.866025i
\(112\) 1.05097 + 0.946294i 1.05097 + 0.946294i
\(113\) 0.104528 0.994522i 0.104528 0.994522i −0.809017 0.587785i \(-0.800000\pi\)
0.913545 0.406737i \(-0.133333\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) −1.34500 0.437016i −1.34500 0.437016i
\(117\) 0 0
\(118\) 0.831254 1.14412i 0.831254 1.14412i
\(119\) 0 0
\(120\) 0 0
\(121\) 0 0
\(122\) −1.00000 1.73205i −1.00000 1.73205i
\(123\) 0 0
\(124\) −0.913545 + 0.406737i −0.913545 + 0.406737i
\(125\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(126\) 0.618034 1.90211i 0.618034 1.90211i
\(127\) −1.34500 0.437016i −1.34500 0.437016i −0.453990 0.891007i \(-0.650000\pi\)
−0.891007 + 0.453990i \(0.850000\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 1.34500 0.437016i 1.34500 0.437016i
\(135\) −0.104528 + 0.994522i −0.104528 + 0.994522i
\(136\) 0 0
\(137\) −0.669131 0.743145i −0.669131 0.743145i 0.309017 0.951057i \(-0.400000\pi\)
−0.978148 + 0.207912i \(0.933333\pi\)
\(138\) 0 0
\(139\) 0.575212 1.29195i 0.575212 1.29195i −0.358368 0.933580i \(-0.616667\pi\)
0.933580 0.358368i \(-0.116667\pi\)
\(140\) 1.40647 + 0.147826i 1.40647 + 0.147826i
\(141\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(142\) 1.22474 + 0.707107i 1.22474 + 0.707107i
\(143\) 0 0
\(144\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(145\) 1.34500 0.437016i 1.34500 0.437016i
\(146\) 1.82709 0.813473i 1.82709 0.813473i
\(147\) −0.104528 0.994522i −0.104528 0.994522i
\(148\) −0.978148 + 0.207912i −0.978148 + 0.207912i
\(149\) 0 0 0.978148 0.207912i \(-0.0666667\pi\)
−0.978148 + 0.207912i \(0.933333\pi\)
\(150\) 0 0
\(151\) 0 0 0.913545 0.406737i \(-0.133333\pi\)
−0.913545 + 0.406737i \(0.866667\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0.500000 0.866025i 0.500000 0.866025i
\(156\) 0 0
\(157\) −0.104528 + 0.994522i −0.104528 + 0.994522i 0.809017 + 0.587785i \(0.200000\pi\)
−0.913545 + 0.406737i \(0.866667\pi\)
\(158\) 0 0
\(159\) 0.978148 0.207912i 0.978148 0.207912i
\(160\) −1.05097 + 0.946294i −1.05097 + 0.946294i
\(161\) 0 0
\(162\) 0.831254 1.14412i 0.831254 1.14412i
\(163\) −0.309017 0.951057i −0.309017 0.951057i −0.978148 0.207912i \(-0.933333\pi\)
0.669131 0.743145i \(-0.266667\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) −1.00000 1.73205i −1.00000 1.73205i
\(167\) 0 0 0.669131 0.743145i \(-0.266667\pi\)
−0.669131 + 0.743145i \(0.733333\pi\)
\(168\) 0 0
\(169\) −0.104528 0.994522i −0.104528 0.994522i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 0 0 0.913545 0.406737i \(-0.133333\pi\)
−0.913545 + 0.406737i \(0.866667\pi\)
\(174\) −1.95630 0.415823i −1.95630 0.415823i
\(175\) 0 0
\(176\) 0 0
\(177\) 0.500000 0.866025i 0.500000 0.866025i
\(178\) 0 0
\(179\) 0.809017 + 0.587785i 0.809017 + 0.587785i 0.913545 0.406737i \(-0.133333\pi\)
−0.104528 + 0.994522i \(0.533333\pi\)
\(180\) 0.913545 + 0.406737i 0.913545 + 0.406737i
\(181\) −0.309017 + 0.951057i −0.309017 + 0.951057i 0.669131 + 0.743145i \(0.266667\pi\)
−0.978148 + 0.207912i \(0.933333\pi\)
\(182\) 0 0
\(183\) −0.831254 1.14412i −0.831254 1.14412i
\(184\) 0 0
\(185\) 0.669131 0.743145i 0.669131 0.743145i
\(186\) −1.22474 + 0.707107i −1.22474 + 0.707107i
\(187\) 0 0
\(188\) 1.00000 1.00000
\(189\) 0.294032 1.38331i 0.294032 1.38331i
\(190\) 0 0
\(191\) 0.104528 + 0.994522i 0.104528 + 0.994522i 0.913545 + 0.406737i \(0.133333\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(192\) 0.978148 0.207912i 0.978148 0.207912i
\(193\) 0 0 0.978148 0.207912i \(-0.0666667\pi\)
−0.978148 + 0.207912i \(0.933333\pi\)
\(194\) −0.575212 + 1.29195i −0.575212 + 1.29195i
\(195\) 0 0
\(196\) −0.978148 0.207912i −0.978148 0.207912i
\(197\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(198\) 0 0
\(199\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(200\) 0 0
\(201\) 0.913545 0.406737i 0.913545 0.406737i
\(202\) 1.82709 + 0.813473i 1.82709 + 0.813473i
\(203\) −1.95630 + 0.415823i −1.95630 + 0.415823i
\(204\) 0 0
\(205\) 0 0
\(206\) −0.831254 + 1.14412i −0.831254 + 1.14412i
\(207\) 0 0
\(208\) 0 0
\(209\) 0 0
\(210\) 2.00000 2.00000
\(211\) −1.05097 0.946294i −1.05097 0.946294i −0.0523360 0.998630i \(-0.516667\pi\)
−0.998630 + 0.0523360i \(0.983333\pi\)
\(212\) 0.104528 0.994522i 0.104528 0.994522i
\(213\) 0.913545 + 0.406737i 0.913545 + 0.406737i
\(214\) 1.33826 + 1.48629i 1.33826 + 1.48629i
\(215\) 0 0
\(216\) 0 0
\(217\) −0.831254 + 1.14412i −0.831254 + 1.14412i
\(218\) 0 0
\(219\) 1.22474 0.707107i 1.22474 0.707107i
\(220\) 0 0
\(221\) 0 0
\(222\) −1.34500 + 0.437016i −1.34500 + 0.437016i
\(223\) 0 0 −0.406737 0.913545i \(-0.633333\pi\)
0.406737 + 0.913545i \(0.366667\pi\)
\(224\) 1.61803 1.17557i 1.61803 1.17557i
\(225\) 0 0
\(226\) −1.34500 0.437016i −1.34500 0.437016i
\(227\) 0 0 −0.104528 0.994522i \(-0.533333\pi\)
0.104528 + 0.994522i \(0.466667\pi\)
\(228\) 0 0
\(229\) 0 0 −0.743145 0.669131i \(-0.766667\pi\)
0.743145 + 0.669131i \(0.233333\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 1.34500 0.437016i 1.34500 0.437016i 0.453990 0.891007i \(-0.350000\pi\)
0.891007 + 0.453990i \(0.150000\pi\)
\(234\) 0 0
\(235\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(236\) −0.669131 0.743145i −0.669131 0.743145i
\(237\) 0 0
\(238\) 0 0
\(239\) 1.40647 + 0.147826i 1.40647 + 0.147826i 0.777146 0.629320i \(-0.216667\pi\)
0.629320 + 0.777146i \(0.283333\pi\)
\(240\) −0.669131 + 0.743145i −0.669131 + 0.743145i
\(241\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(242\) 0 0
\(243\) 0.500000 0.866025i 0.500000 0.866025i
\(244\) −1.34500 + 0.437016i −1.34500 + 0.437016i
\(245\) 0.913545 0.406737i 0.913545 0.406737i
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) −0.831254 1.14412i −0.831254 1.14412i
\(250\) 0.575212 + 1.29195i 0.575212 + 1.29195i
\(251\) 0 0 0.951057 0.309017i \(-0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(252\) −1.22474 0.707107i −1.22474 0.707107i
\(253\) 0 0
\(254\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(255\) 0 0
\(256\) −0.104528 + 0.994522i −0.104528 + 0.994522i
\(257\) −1.82709 0.813473i −1.82709 0.813473i −0.913545 0.406737i \(-0.866667\pi\)
−0.913545 0.406737i \(-0.866667\pi\)
\(258\) 0 0
\(259\) −1.05097 + 0.946294i −1.05097 + 0.946294i
\(260\) 0 0
\(261\) −1.40647 0.147826i −1.40647 0.147826i
\(262\) 0 0
\(263\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(264\) 0 0
\(265\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(266\) 0 0
\(267\) 0 0
\(268\) −0.104528 0.994522i −0.104528 0.994522i
\(269\) 0.309017 0.951057i 0.309017 0.951057i −0.669131 0.743145i \(-0.733333\pi\)
0.978148 0.207912i \(-0.0666667\pi\)
\(270\) 1.34500 + 0.437016i 1.34500 + 0.437016i
\(271\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) −1.22474 + 0.707107i −1.22474 + 0.707107i
\(275\) 0 0
\(276\) 0 0
\(277\) 0 0 −0.978148 0.207912i \(-0.933333\pi\)
0.978148 + 0.207912i \(0.0666667\pi\)
\(278\) −1.61803 1.17557i −1.61803 1.17557i
\(279\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(280\) 0 0
\(281\) 0 0 −0.669131 0.743145i \(-0.733333\pi\)
0.669131 + 0.743145i \(0.266667\pi\)
\(282\) 1.40647 0.147826i 1.40647 0.147826i
\(283\) −1.40647 0.147826i −1.40647 0.147826i −0.629320 0.777146i \(-0.716667\pi\)
−0.777146 + 0.629320i \(0.783333\pi\)
\(284\) 0.669131 0.743145i 0.669131 0.743145i
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 1.34500 0.437016i 1.34500 0.437016i
\(289\) −0.809017 0.587785i −0.809017 0.587785i
\(290\) −0.209057 1.98904i −0.209057 1.98904i
\(291\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(292\) −0.294032 1.38331i −0.294032 1.38331i
\(293\) −0.575212 + 1.29195i −0.575212 + 1.29195i 0.358368 + 0.933580i \(0.383333\pi\)
−0.933580 + 0.358368i \(0.883333\pi\)
\(294\) −1.40647 0.147826i −1.40647 0.147826i
\(295\) 0.978148 + 0.207912i 0.978148 + 0.207912i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 0 0
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 1.34500 + 0.437016i 1.34500 + 0.437016i
\(304\) 0 0
\(305\) 0.831254 1.14412i 0.831254 1.14412i
\(306\) 0 0
\(307\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(308\) 0 0
\(309\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(310\) −1.05097 0.946294i −1.05097 0.946294i
\(311\) −0.104528 + 0.994522i −0.104528 + 0.994522i 0.809017 + 0.587785i \(0.200000\pi\)
−0.913545 + 0.406737i \(0.866667\pi\)
\(312\) 0 0
\(313\) 0 0 0.743145 0.669131i \(-0.233333\pi\)
−0.743145 + 0.669131i \(0.766667\pi\)
\(314\) 1.34500 + 0.437016i 1.34500 + 0.437016i
\(315\) 1.40647 0.147826i 1.40647 0.147826i
\(316\) 0 0
\(317\) 0 0 0.207912 0.978148i \(-0.433333\pi\)
−0.207912 + 0.978148i \(0.566667\pi\)
\(318\) 1.41421i 1.41421i
\(319\) 0 0
\(320\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(321\) 1.05097 + 0.946294i 1.05097 + 0.946294i
\(322\) 0 0
\(323\) 0 0
\(324\) −0.669131 0.743145i −0.669131 0.743145i
\(325\) 0 0
\(326\) −1.40647 + 0.147826i −1.40647 + 0.147826i
\(327\) 0 0
\(328\) 0 0
\(329\) 1.22474 0.707107i 1.22474 0.707107i
\(330\) 0 0
\(331\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(332\) −1.34500 + 0.437016i −1.34500 + 0.437016i
\(333\) −0.913545 + 0.406737i −0.913545 + 0.406737i
\(334\) 0 0
\(335\) 0.669131 + 0.743145i 0.669131 + 0.743145i
\(336\) 1.05097 0.946294i 1.05097 0.946294i
\(337\) −0.575212 + 1.29195i −0.575212 + 1.29195i 0.358368 + 0.933580i \(0.383333\pi\)
−0.933580 + 0.358368i \(0.883333\pi\)
\(338\) −1.40647 0.147826i −1.40647 0.147826i
\(339\) −0.978148 0.207912i −0.978148 0.207912i
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 0.294032 + 1.38331i 0.294032 + 1.38331i 0.838671 + 0.544639i \(0.183333\pi\)
−0.544639 + 0.838671i \(0.683333\pi\)
\(348\) −0.575212 + 1.29195i −0.575212 + 1.29195i
\(349\) 0 0 0.913545 0.406737i \(-0.133333\pi\)
−0.913545 + 0.406737i \(0.866667\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(354\) −1.05097 0.946294i −1.05097 0.946294i
\(355\) −0.104528 + 0.994522i −0.104528 + 0.994522i
\(356\) 0 0
\(357\) 0 0
\(358\) 1.05097 0.946294i 1.05097 0.946294i
\(359\) 0.831254 + 1.14412i 0.831254 + 1.14412i 0.987688 + 0.156434i \(0.0500000\pi\)
−0.156434 + 0.987688i \(0.550000\pi\)
\(360\) 0 0
\(361\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(362\) 1.22474 + 0.707107i 1.22474 + 0.707107i
\(363\) 0 0
\(364\) 0 0
\(365\) 1.05097 + 0.946294i 1.05097 + 0.946294i
\(366\) −1.82709 + 0.813473i −1.82709 + 0.813473i
\(367\) 0.104528 + 0.994522i 0.104528 + 0.994522i 0.913545 + 0.406737i \(0.133333\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) −0.831254 1.14412i −0.831254 1.14412i
\(371\) −0.575212 1.29195i −0.575212 1.29195i
\(372\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(373\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(374\) 0 0
\(375\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(376\) 0 0
\(377\) 0 0
\(378\) −1.82709 0.813473i −1.82709 0.813473i
\(379\) 0 0 −0.951057 0.309017i \(-0.900000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(380\) 0 0
\(381\) −0.575212 + 1.29195i −0.575212 + 1.29195i
\(382\) 1.40647 + 0.147826i 1.40647 + 0.147826i
\(383\) 0.669131 0.743145i 0.669131 0.743145i −0.309017 0.951057i \(-0.600000\pi\)
0.978148 + 0.207912i \(0.0666667\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(389\) 0.104528 + 0.994522i 0.104528 + 0.994522i 0.913545 + 0.406737i \(0.133333\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 0 0
\(394\) 1.95630 + 0.415823i 1.95630 + 0.415823i
\(395\) 0 0
\(396\) 0 0
\(397\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(398\) −0.294032 + 1.38331i −0.294032 + 1.38331i
\(399\) 0 0
\(400\) 0 0
\(401\) 0.978148 0.207912i 0.978148 0.207912i 0.309017 0.951057i \(-0.400000\pi\)
0.669131 + 0.743145i \(0.266667\pi\)
\(402\) −0.294032 1.38331i −0.294032 1.38331i
\(403\) 0 0
\(404\) 0.831254 1.14412i 0.831254 1.14412i
\(405\) 0.978148 + 0.207912i 0.978148 + 0.207912i
\(406\) 2.82843i 2.82843i
\(407\) 0 0
\(408\) 0 0
\(409\) 0 0 0.669131 0.743145i \(-0.266667\pi\)
−0.669131 + 0.743145i \(0.733333\pi\)
\(410\) 0 0
\(411\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(412\) 0.669131 + 0.743145i 0.669131 + 0.743145i
\(413\) −1.34500 0.437016i −1.34500 0.437016i
\(414\) 0 0
\(415\) 0.831254 1.14412i 0.831254 1.14412i
\(416\) 0 0
\(417\) −1.22474 0.707107i −1.22474 0.707107i
\(418\) 0 0
\(419\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(420\) 0.294032 1.38331i 0.294032 1.38331i
\(421\) 0.913545 0.406737i 0.913545 0.406737i 0.104528 0.994522i \(-0.466667\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(422\) −1.61803 + 1.17557i −1.61803 + 1.17557i
\(423\) 0.978148 0.207912i 0.978148 0.207912i
\(424\) 0 0
\(425\) 0 0
\(426\) 0.831254 1.14412i 0.831254 1.14412i
\(427\) −1.33826 + 1.48629i −1.33826 + 1.48629i
\(428\) 1.22474 0.707107i 1.22474 0.707107i
\(429\) 0 0
\(430\) 0 0
\(431\) −1.34500 + 0.437016i −1.34500 + 0.437016i −0.891007 0.453990i \(-0.850000\pi\)
−0.453990 + 0.891007i \(0.650000\pi\)
\(432\) 0.913545 0.406737i 0.913545 0.406737i
\(433\) 0 0 −0.587785 0.809017i \(-0.700000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(434\) 1.33826 + 1.48629i 1.33826 + 1.48629i
\(435\) −0.294032 1.38331i −0.294032 1.38331i
\(436\) 0 0
\(437\) 0 0
\(438\) −0.618034 1.90211i −0.618034 1.90211i
\(439\) −1.22474 0.707107i −1.22474 0.707107i −0.258819 0.965926i \(-0.583333\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(440\) 0 0
\(441\) −1.00000 −1.00000
\(442\) 0 0
\(443\) 0.913545 0.406737i 0.913545 0.406737i 0.104528 0.994522i \(-0.466667\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(444\) 0.104528 + 0.994522i 0.104528 + 0.994522i
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) −0.575212 1.29195i −0.575212 1.29195i
\(449\) 0.309017 + 0.951057i 0.309017 + 0.951057i 0.978148 + 0.207912i \(0.0666667\pi\)
−0.669131 + 0.743145i \(0.733333\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 1.05097 0.946294i 1.05097 0.946294i 0.0523360 0.998630i \(-0.483333\pi\)
0.998630 + 0.0523360i \(0.0166667\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −1.22474 0.707107i −1.22474 0.707107i −0.258819 0.965926i \(-0.583333\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(462\) 0 0
\(463\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(464\) −1.05097 0.946294i −1.05097 0.946294i
\(465\) −0.809017 0.587785i −0.809017 0.587785i
\(466\) −0.209057 1.98904i −0.209057 1.98904i
\(467\) 0.309017 0.951057i 0.309017 0.951057i −0.669131 0.743145i \(-0.733333\pi\)
0.978148 0.207912i \(-0.0666667\pi\)
\(468\) 0 0
\(469\) −0.831254 1.14412i −0.831254 1.14412i
\(470\) 0.575212 + 1.29195i 0.575212 + 1.29195i
\(471\) 0.978148 + 0.207912i 0.978148 + 0.207912i
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −0.104528 0.994522i −0.104528 0.994522i
\(478\) 0.618034 1.90211i 0.618034 1.90211i
\(479\) −1.05097 + 0.946294i −1.05097 + 0.946294i −0.998630 0.0523360i \(-0.983333\pi\)
−0.0523360 + 0.998630i \(0.516667\pi\)
\(480\) 0.831254 + 1.14412i 0.831254 + 1.14412i
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −1.00000 −1.00000
\(486\) −1.05097 0.946294i −1.05097 0.946294i
\(487\) 0.809017 + 0.587785i 0.809017 + 0.587785i 0.913545 0.406737i \(-0.133333\pi\)
−0.104528 + 0.994522i \(0.533333\pi\)
\(488\) 0 0
\(489\) −0.978148 + 0.207912i −0.978148 + 0.207912i
\(490\) −0.294032 1.38331i −0.294032 1.38331i
\(491\) 0.575212 1.29195i 0.575212 1.29195i −0.358368 0.933580i \(-0.616667\pi\)
0.933580 0.358368i \(-0.116667\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) −1.00000 −1.00000
\(497\) 0.294032 1.38331i 0.294032 1.38331i
\(498\) −1.82709 + 0.813473i −1.82709 + 0.813473i
\(499\) 0.913545 + 0.406737i 0.913545 + 0.406737i 0.809017 0.587785i \(-0.200000\pi\)
0.104528 + 0.994522i \(0.466667\pi\)
\(500\) 0.978148 0.207912i 0.978148 0.207912i
\(501\) 0 0
\(502\) 0 0
\(503\) −0.831254 + 1.14412i −0.831254 + 1.14412i 0.156434 + 0.987688i \(0.450000\pi\)
−0.987688 + 0.156434i \(0.950000\pi\)
\(504\) 0 0
\(505\) 1.41421i 1.41421i
\(506\) 0 0
\(507\) −1.00000 −1.00000
\(508\) 1.05097 + 0.946294i 1.05097 + 0.946294i
\(509\) 0 0 −0.994522 0.104528i \(-0.966667\pi\)
0.994522 + 0.104528i \(0.0333333\pi\)
\(510\) 0 0
\(511\) −1.33826 1.48629i −1.33826 1.48629i
\(512\) 1.34500 + 0.437016i 1.34500 + 0.437016i
\(513\) 0 0
\(514\) −1.66251 + 2.28825i −1.66251 + 2.28825i
\(515\) −0.978148 0.207912i −0.978148 0.207912i
\(516\) 0 0
\(517\) 0 0
\(518\) 1.00000 + 1.73205i 1.00000 + 1.73205i
\(519\) 0 0
\(520\) 0 0
\(521\) 0.809017 0.587785i 0.809017 0.587785i −0.104528 0.994522i \(-0.533333\pi\)
0.913545 + 0.406737i \(0.133333\pi\)
\(522\) −0.618034 + 1.90211i −0.618034 + 1.90211i
\(523\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) 0.500000 0.866025i 0.500000 0.866025i
\(530\) 1.34500 0.437016i 1.34500 0.437016i
\(531\) −0.809017 0.587785i −0.809017 0.587785i
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) −0.575212 + 1.29195i −0.575212 + 1.29195i
\(536\) 0 0
\(537\) 0.669131 0.743145i 0.669131 0.743145i
\(538\) −1.22474 0.707107i −1.22474 0.707107i
\(539\) 0 0
\(540\) 0.500000 0.866025i 0.500000 0.866025i
\(541\) −1.34500 + 0.437016i −1.34500 + 0.437016i −0.891007 0.453990i \(-0.850000\pi\)
−0.453990 + 0.891007i \(0.650000\pi\)
\(542\) 0 0
\(543\) 0.913545 + 0.406737i 0.913545 + 0.406737i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −0.575212 1.29195i −0.575212 1.29195i −0.933580 0.358368i \(-0.883333\pi\)
0.358368 0.933580i \(-0.383333\pi\)
\(548\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(549\) −1.22474 + 0.707107i −1.22474 + 0.707107i
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) −0.669131 0.743145i −0.669131 0.743145i
\(556\) −1.05097 + 0.946294i −1.05097 + 0.946294i
\(557\) −0.831254 1.14412i −0.831254 1.14412i −0.987688 0.156434i \(-0.950000\pi\)
0.156434 0.987688i \(-0.450000\pi\)
\(558\) 0.575212 + 1.29195i 0.575212 + 1.29195i
\(559\) 0 0
\(560\) 1.22474 + 0.707107i 1.22474 + 0.707107i
\(561\) 0 0
\(562\) 0 0
\(563\) 0 0 0.669131 0.743145i \(-0.266667\pi\)
−0.669131 + 0.743145i \(0.733333\pi\)
\(564\) 0.104528 0.994522i 0.104528 0.994522i
\(565\) −0.104528 0.994522i −0.104528 0.994522i
\(566\) −0.618034 + 1.90211i −0.618034 + 1.90211i
\(567\) −1.34500 0.437016i −1.34500 0.437016i
\(568\) 0 0
\(569\) 0.575212 + 1.29195i 0.575212 + 1.29195i 0.933580 + 0.358368i \(0.116667\pi\)
−0.358368 + 0.933580i \(0.616667\pi\)
\(570\) 0 0
\(571\) 1.22474 0.707107i 1.22474 0.707107i 0.258819 0.965926i \(-0.416667\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(572\) 0 0
\(573\) 1.00000 1.00000
\(574\) 0 0
\(575\) 0 0
\(576\) −0.104528 0.994522i −0.104528 0.994522i
\(577\) 0.309017 0.951057i 0.309017 0.951057i −0.669131 0.743145i \(-0.733333\pi\)
0.978148 0.207912i \(-0.0666667\pi\)
\(578\) −1.05097 + 0.946294i −1.05097 + 0.946294i
\(579\) 0 0
\(580\) −1.40647 0.147826i −1.40647 0.147826i
\(581\) −1.33826 + 1.48629i −1.33826 + 1.48629i
\(582\) 1.22474 + 0.707107i 1.22474 + 0.707107i
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 1.61803 + 1.17557i 1.61803 + 1.17557i
\(587\) −0.104528 0.994522i −0.104528 0.994522i −0.913545 0.406737i \(-0.866667\pi\)
0.809017 0.587785i \(-0.200000\pi\)
\(588\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(589\) 0 0
\(590\) 0.575212 1.29195i 0.575212 1.29195i
\(591\) 1.40647 + 0.147826i 1.40647 + 0.147826i
\(592\) −0.978148 0.207912i −0.978148 0.207912i
\(593\) 1.41421i 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −0.104528 + 0.994522i −0.104528 + 0.994522i
\(598\) 0 0
\(599\) 0 0 −0.207912 0.978148i \(-0.566667\pi\)
0.207912 + 0.978148i \(0.433333\pi\)
\(600\) 0 0
\(601\) 0 0 −0.104528 0.994522i \(-0.533333\pi\)
0.104528 + 0.994522i \(0.466667\pi\)
\(602\) 0 0
\(603\) −0.309017 0.951057i −0.309017 0.951057i
\(604\) 0 0
\(605\) 0 0
\(606\) 1.00000 1.73205i 1.00000 1.73205i
\(607\) 0 0 0.669131 0.743145i \(-0.266667\pi\)
−0.669131 + 0.743145i \(0.733333\pi\)
\(608\) 0 0
\(609\) 0.209057 + 1.98904i 0.209057 + 1.98904i
\(610\) −1.33826 1.48629i −1.33826 1.48629i
\(611\) 0 0
\(612\) 0 0
\(613\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(618\) 1.05097 + 0.946294i 1.05097 + 0.946294i
\(619\) 0.913545 0.406737i 0.913545 0.406737i 0.104528 0.994522i \(-0.466667\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(620\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(621\) 0 0
\(622\) 1.34500 + 0.437016i 1.34500 + 0.437016i
\(623\) 0 0
\(624\) 0 0
\(625\) −0.669131 + 0.743145i −0.669131 + 0.743145i
\(626\) 0 0
\(627\) 0 0
\(628\) 0.500000 0.866025i 0.500000 0.866025i
\(629\) 0 0
\(630\) 0.209057 1.98904i 0.209057 1.98904i
\(631\) −0.809017 + 0.587785i −0.809017 + 0.587785i −0.913545 0.406737i \(-0.866667\pi\)
0.104528 + 0.994522i \(0.466667\pi\)
\(632\) 0 0
\(633\) −1.05097 + 0.946294i −1.05097 + 0.946294i
\(634\) 0 0
\(635\) −1.40647 0.147826i −1.40647 0.147826i
\(636\) −0.978148 0.207912i −0.978148 0.207912i
\(637\) 0 0
\(638\) 0 0
\(639\) 0.500000 0.866025i 0.500000 0.866025i
\(640\) 0 0
\(641\) −1.82709 + 0.813473i −1.82709 + 0.813473i −0.913545 + 0.406737i \(0.866667\pi\)
−0.913545 + 0.406737i \(0.866667\pi\)
\(642\) 1.61803 1.17557i 1.61803 1.17557i
\(643\) 0 0 −0.207912 0.978148i \(-0.566667\pi\)
0.207912 + 0.978148i \(0.433333\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −0.618034 1.90211i −0.618034 1.90211i −0.309017 0.951057i \(-0.600000\pi\)
−0.309017 0.951057i \(-0.600000\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) 1.05097 + 0.946294i 1.05097 + 0.946294i
\(652\) −0.104528 + 0.994522i −0.104528 + 0.994522i
\(653\) 0.913545 + 0.406737i 0.913545 + 0.406737i 0.809017 0.587785i \(-0.200000\pi\)
0.104528 + 0.994522i \(0.466667\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) −0.575212 1.29195i −0.575212 1.29195i
\(658\) −0.618034 1.90211i −0.618034 1.90211i
\(659\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(660\) 0 0
\(661\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(662\) 1.05097 + 0.946294i 1.05097 + 0.946294i
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0.294032 + 1.38331i 0.294032 + 1.38331i
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) 1.22474 0.707107i 1.22474 0.707107i
\(671\) 0 0
\(672\) −1.00000 1.73205i −1.00000 1.73205i
\(673\) 0 0 −0.978148 0.207912i \(-0.933333\pi\)
0.978148 + 0.207912i \(0.0666667\pi\)
\(674\) 1.61803 + 1.17557i 1.61803 + 1.17557i
\(675\) 0 0
\(676\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(677\) −1.05097 + 0.946294i −1.05097 + 0.946294i −0.998630 0.0523360i \(-0.983333\pi\)
−0.0523360 + 0.998630i \(0.516667\pi\)
\(678\) −0.575212 + 1.29195i −0.575212 + 1.29195i
\(679\) 1.40647 + 0.147826i 1.40647 + 0.147826i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(684\) 0 0
\(685\) −0.809017 0.587785i −0.809017 0.587785i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) 0.978148 + 0.207912i 0.978148 + 0.207912i 0.669131 0.743145i \(-0.266667\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 2.00000 2.00000
\(695\) 0.294032 1.38331i 0.294032 1.38331i
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) −0.294032 1.38331i −0.294032 1.38331i
\(700\) 0 0
\(701\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0 0
\(705\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(706\) 0 0
\(707\) 0.209057 1.98904i 0.209057 1.98904i
\(708\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(709\) 0.669131 + 0.743145i 0.669131 + 0.743145i 0.978148 0.207912i \(-0.0666667\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(710\) 1.34500 + 0.437016i 1.34500 + 0.437016i
\(711\) 0 0
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) −0.500000 0.866025i −0.500000 0.866025i
\(717\) 0.294032 1.38331i 0.294032 1.38331i
\(718\) 1.82709 0.813473i 1.82709 0.813473i
\(719\) 0.809017 0.587785i 0.809017 0.587785i −0.104528 0.994522i \(-0.533333\pi\)
0.913545 + 0.406737i \(0.133333\pi\)
\(720\) 0.669131 + 0.743145i 0.669131 + 0.743145i
\(721\) 1.34500 + 0.437016i 1.34500 + 0.437016i
\(722\) 1.40647 0.147826i 1.40647 0.147826i
\(723\) 0 0
\(724\) 0.669131 0.743145i 0.669131 0.743145i
\(725\) 0 0
\(726\) 0 0
\(727\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(728\) 0 0
\(729\) −0.809017 0.587785i −0.809017 0.587785i
\(730\) 1.61803 1.17557i 1.61803 1.17557i
\(731\) 0 0
\(732\) 0.294032 + 1.38331i 0.294032 + 1.38331i
\(733\) 0.575212 1.29195i 0.575212 1.29195i −0.358368 0.933580i \(-0.616667\pi\)
0.933580 0.358368i \(-0.116667\pi\)
\(734\) 1.40647 + 0.147826i 1.40647 + 0.147826i
\(735\) −0.309017 0.951057i −0.309017 0.951057i
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(740\) −0.913545 + 0.406737i −0.913545 + 0.406737i
\(741\) 0 0
\(742\) −1.95630 + 0.415823i −1.95630 + 0.415823i
\(743\) 0.294032 + 1.38331i 0.294032 + 1.38331i 0.838671 + 0.544639i \(0.183333\pi\)
−0.544639 + 0.838671i \(0.683333\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −1.22474 + 0.707107i −1.22474 + 0.707107i
\(748\) 0 0
\(749\) 1.00000 1.73205i 1.00000 1.73205i
\(750\) 1.34500 0.437016i 1.34500 0.437016i
\(751\) 0.104528 0.994522i 0.104528 0.994522i −0.809017 0.587785i \(-0.800000\pi\)
0.913545 0.406737i \(-0.133333\pi\)
\(752\) 0.913545 + 0.406737i 0.913545 + 0.406737i
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) −0.831254 + 1.14412i −0.831254 + 1.14412i
\(757\) −0.309017 0.951057i −0.309017 0.951057i −0.978148 0.207912i \(-0.933333\pi\)
0.669131 0.743145i \(-0.266667\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −1.05097 0.946294i −1.05097 0.946294i −0.0523360 0.998630i \(-0.516667\pi\)
−0.998630 + 0.0523360i \(0.983333\pi\)
\(762\) 1.61803 + 1.17557i 1.61803 + 1.17557i
\(763\) 0 0
\(764\) 0.309017 0.951057i 0.309017 0.951057i
\(765\) 0 0
\(766\) −0.831254 1.14412i −0.831254 1.14412i
\(767\) 0 0
\(768\) 0.978148 + 0.207912i 0.978148 + 0.207912i
\(769\) −1.22474 + 0.707107i −1.22474 + 0.707107i −0.965926 0.258819i \(-0.916667\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(770\) 0 0
\(771\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(772\) 0 0
\(773\) 0 0 0.587785 0.809017i \(-0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 0.831254 + 1.14412i 0.831254 + 1.14412i
\(778\) 1.40647 + 0.147826i 1.40647 + 0.147826i
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) −0.294032 + 1.38331i −0.294032 + 1.38331i
\(784\) −0.809017 0.587785i −0.809017 0.587785i
\(785\) 0.104528 + 0.994522i 0.104528 + 0.994522i
\(786\) 0 0
\(787\) 0 0 0.978148 0.207912i \(-0.0666667\pi\)
−0.978148 + 0.207912i \(0.933333\pi\)
\(788\) 0.575212 1.29195i 0.575212 1.29195i
\(789\) 0 0
\(790\) 0 0
\(791\) 1.41421i 1.41421i
\(792\) 0 0
\(793\) 0 0
\(794\) −0.294032 + 1.38331i −0.294032 + 1.38331i
\(795\) 0.913545 0.406737i 0.913545 0.