Properties

Label 633.1.m.b.188.2
Level 633
Weight 1
Character 633.188
Analytic conductor 0.316
Analytic rank 0
Dimension 8
Projective image \(A_{5}\)
CM/RM No
Inner twists 4

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Newspace parameters

Level: \( N \) = \( 633 = 3 \cdot 211 \)
Weight: \( k \) = \( 1 \)
Character orbit: \([\chi]\) = 633.m (of order \(10\) and degree \(4\))

Newform invariants

Self dual: No
Analytic conductor: \(0.315908152997\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{10})\)
Coefficient field: \(\Q(\zeta_{20})\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Projective image \(A_{5}\)
Projective field Galois closure of 5.1.17839074969.1

Embedding invariants

Embedding label 188.2
Root \(-0.587785 - 0.809017i\)
Character \(\chi\) = 633.188
Dual form 633.1.m.b.266.2

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+(0.587785 + 0.190983i) q^{2}\) \(+(0.809017 - 0.587785i) q^{3}\) \(+(-0.500000 - 0.363271i) q^{4}\) \(+(0.587785 - 0.809017i) q^{5}\) \(+(0.587785 - 0.190983i) q^{6}\) \(+(0.309017 + 0.951057i) q^{7}\) \(+(-0.587785 - 0.809017i) q^{8}\) \(+(0.309017 - 0.951057i) q^{9}\) \(+O(q^{10})\) \(q\)\(+(0.587785 + 0.190983i) q^{2}\) \(+(0.809017 - 0.587785i) q^{3}\) \(+(-0.500000 - 0.363271i) q^{4}\) \(+(0.587785 - 0.809017i) q^{5}\) \(+(0.587785 - 0.190983i) q^{6}\) \(+(0.309017 + 0.951057i) q^{7}\) \(+(-0.587785 - 0.809017i) q^{8}\) \(+(0.309017 - 0.951057i) q^{9}\) \(+(0.500000 - 0.363271i) q^{10}\) \(+(-0.951057 + 1.30902i) q^{11}\) \(-0.618034 q^{12}\) \(+(-0.309017 - 0.951057i) q^{13}\) \(+0.618034i q^{14}\) \(-1.00000i q^{15}\) \(+(-1.53884 + 0.500000i) q^{17}\) \(+(0.363271 - 0.500000i) q^{18}\) \(+(0.309017 + 0.951057i) q^{19}\) \(+(-0.587785 + 0.190983i) q^{20}\) \(+(0.809017 + 0.587785i) q^{21}\) \(+(-0.809017 + 0.587785i) q^{22}\) \(+(0.951057 + 0.309017i) q^{23}\) \(+(-0.951057 - 0.309017i) q^{24}\) \(-0.618034i q^{26}\) \(+(-0.309017 - 0.951057i) q^{27}\) \(+(0.190983 - 0.587785i) q^{28}\) \(+(0.587785 - 0.190983i) q^{29}\) \(+(0.190983 - 0.587785i) q^{30}\) \(+0.618034 q^{31}\) \(+1.00000i q^{32}\) \(+1.61803i q^{33}\) \(-1.00000 q^{34}\) \(+(0.951057 + 0.309017i) q^{35}\) \(+(-0.500000 + 0.363271i) q^{36}\) \(+0.618034i q^{38}\) \(+(-0.809017 - 0.587785i) q^{39}\) \(-1.00000 q^{40}\) \(+(0.951057 - 1.30902i) q^{41}\) \(+(0.363271 + 0.500000i) q^{42}\) \(-1.00000 q^{43}\) \(+(0.951057 - 0.309017i) q^{44}\) \(+(-0.587785 - 0.809017i) q^{45}\) \(+(0.500000 + 0.363271i) q^{46}\) \(+(-0.587785 + 0.190983i) q^{47}\) \(+(-0.951057 + 1.30902i) q^{51}\) \(+(-0.190983 + 0.587785i) q^{52}\) \(-0.618034i q^{54}\) \(+(0.500000 + 1.53884i) q^{55}\) \(+(0.587785 - 0.809017i) q^{56}\) \(+(0.809017 + 0.587785i) q^{57}\) \(+0.381966 q^{58}\) \(+(-0.363271 + 0.500000i) q^{60}\) \(+(-1.30902 + 0.951057i) q^{61}\) \(+(0.363271 + 0.118034i) q^{62}\) \(+1.00000 q^{63}\) \(+(-0.190983 + 0.587785i) q^{64}\) \(+(-0.951057 - 0.309017i) q^{65}\) \(+(-0.309017 + 0.951057i) q^{66}\) \(+(0.951057 + 0.309017i) q^{68}\) \(+(0.951057 - 0.309017i) q^{69}\) \(+(0.500000 + 0.363271i) q^{70}\) \(+(-0.363271 - 0.500000i) q^{71}\) \(+(-0.951057 + 0.309017i) q^{72}\) \(-1.00000 q^{73}\) \(+(0.190983 - 0.587785i) q^{76}\) \(+(-1.53884 - 0.500000i) q^{77}\) \(+(-0.363271 - 0.500000i) q^{78}\) \(+(-0.809017 - 0.587785i) q^{81}\) \(+(0.809017 - 0.587785i) q^{82}\) \(+(-0.363271 + 0.500000i) q^{83}\) \(+(-0.190983 - 0.587785i) q^{84}\) \(+(-0.500000 + 1.53884i) q^{85}\) \(+(-0.587785 - 0.190983i) q^{86}\) \(+(0.363271 - 0.500000i) q^{87}\) \(+1.61803 q^{88}\) \(+(-0.951057 + 0.309017i) q^{89}\) \(+(-0.190983 - 0.587785i) q^{90}\) \(+(0.809017 - 0.587785i) q^{91}\) \(+(-0.363271 - 0.500000i) q^{92}\) \(+(0.500000 - 0.363271i) q^{93}\) \(-0.381966 q^{94}\) \(+(0.951057 + 0.309017i) q^{95}\) \(+(0.587785 + 0.809017i) q^{96}\) \(+(0.951057 + 1.30902i) q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(8q \) \(\mathstrut +\mathstrut 2q^{3} \) \(\mathstrut -\mathstrut 4q^{4} \) \(\mathstrut -\mathstrut 2q^{7} \) \(\mathstrut -\mathstrut 2q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(8q \) \(\mathstrut +\mathstrut 2q^{3} \) \(\mathstrut -\mathstrut 4q^{4} \) \(\mathstrut -\mathstrut 2q^{7} \) \(\mathstrut -\mathstrut 2q^{9} \) \(\mathstrut +\mathstrut 4q^{10} \) \(\mathstrut +\mathstrut 4q^{12} \) \(\mathstrut +\mathstrut 2q^{13} \) \(\mathstrut -\mathstrut 2q^{19} \) \(\mathstrut +\mathstrut 2q^{21} \) \(\mathstrut -\mathstrut 2q^{22} \) \(\mathstrut +\mathstrut 2q^{27} \) \(\mathstrut +\mathstrut 6q^{28} \) \(\mathstrut +\mathstrut 6q^{30} \) \(\mathstrut -\mathstrut 4q^{31} \) \(\mathstrut -\mathstrut 8q^{34} \) \(\mathstrut -\mathstrut 4q^{36} \) \(\mathstrut -\mathstrut 2q^{39} \) \(\mathstrut -\mathstrut 8q^{40} \) \(\mathstrut -\mathstrut 8q^{43} \) \(\mathstrut +\mathstrut 4q^{46} \) \(\mathstrut -\mathstrut 6q^{52} \) \(\mathstrut +\mathstrut 4q^{55} \) \(\mathstrut +\mathstrut 2q^{57} \) \(\mathstrut +\mathstrut 12q^{58} \) \(\mathstrut -\mathstrut 6q^{61} \) \(\mathstrut +\mathstrut 8q^{63} \) \(\mathstrut -\mathstrut 6q^{64} \) \(\mathstrut +\mathstrut 2q^{66} \) \(\mathstrut +\mathstrut 4q^{70} \) \(\mathstrut -\mathstrut 8q^{73} \) \(\mathstrut +\mathstrut 6q^{76} \) \(\mathstrut -\mathstrut 2q^{81} \) \(\mathstrut +\mathstrut 2q^{82} \) \(\mathstrut -\mathstrut 6q^{84} \) \(\mathstrut -\mathstrut 4q^{85} \) \(\mathstrut +\mathstrut 4q^{88} \) \(\mathstrut -\mathstrut 6q^{90} \) \(\mathstrut +\mathstrut 2q^{91} \) \(\mathstrut +\mathstrut 4q^{93} \) \(\mathstrut -\mathstrut 12q^{94} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Character Values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/633\mathbb{Z}\right)^\times\).

\(n\) \(212\) \(424\)
\(\chi(n)\) \(-1\) \(e\left(\frac{3}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.587785 + 0.190983i 0.587785 + 0.190983i 0.587785 0.809017i \(-0.300000\pi\)
1.00000i \(0.5\pi\)
\(3\) 0.809017 0.587785i 0.809017 0.587785i
\(4\) −0.500000 0.363271i −0.500000 0.363271i
\(5\) 0.587785 0.809017i 0.587785 0.809017i −0.406737 0.913545i \(-0.633333\pi\)
0.994522 + 0.104528i \(0.0333333\pi\)
\(6\) 0.587785 0.190983i 0.587785 0.190983i
\(7\) 0.309017 + 0.951057i 0.309017 + 0.951057i 0.978148 + 0.207912i \(0.0666667\pi\)
−0.669131 + 0.743145i \(0.733333\pi\)
\(8\) −0.587785 0.809017i −0.587785 0.809017i
\(9\) 0.309017 0.951057i 0.309017 0.951057i
\(10\) 0.500000 0.363271i 0.500000 0.363271i
\(11\) −0.951057 + 1.30902i −0.951057 + 1.30902i 1.00000i \(0.5\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(12\) −0.618034 −0.618034
\(13\) −0.309017 0.951057i −0.309017 0.951057i −0.978148 0.207912i \(-0.933333\pi\)
0.669131 0.743145i \(-0.266667\pi\)
\(14\) 0.618034i 0.618034i
\(15\) 1.00000i 1.00000i
\(16\) 0 0
\(17\) −1.53884 + 0.500000i −1.53884 + 0.500000i −0.951057 0.309017i \(-0.900000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(18\) 0.363271 0.500000i 0.363271 0.500000i
\(19\) 0.309017 + 0.951057i 0.309017 + 0.951057i 0.978148 + 0.207912i \(0.0666667\pi\)
−0.669131 + 0.743145i \(0.733333\pi\)
\(20\) −0.587785 + 0.190983i −0.587785 + 0.190983i
\(21\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(22\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(23\) 0.951057 + 0.309017i 0.951057 + 0.309017i 0.743145 0.669131i \(-0.233333\pi\)
0.207912 + 0.978148i \(0.433333\pi\)
\(24\) −0.951057 0.309017i −0.951057 0.309017i
\(25\) 0 0
\(26\) 0.618034i 0.618034i
\(27\) −0.309017 0.951057i −0.309017 0.951057i
\(28\) 0.190983 0.587785i 0.190983 0.587785i
\(29\) 0.587785 0.190983i 0.587785 0.190983i 1.00000i \(-0.5\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(30\) 0.190983 0.587785i 0.190983 0.587785i
\(31\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(32\) 1.00000i 1.00000i
\(33\) 1.61803i 1.61803i
\(34\) −1.00000 −1.00000
\(35\) 0.951057 + 0.309017i 0.951057 + 0.309017i
\(36\) −0.500000 + 0.363271i −0.500000 + 0.363271i
\(37\) 0 0 −0.587785 0.809017i \(-0.700000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(38\) 0.618034i 0.618034i
\(39\) −0.809017 0.587785i −0.809017 0.587785i
\(40\) −1.00000 −1.00000
\(41\) 0.951057 1.30902i 0.951057 1.30902i 1.00000i \(-0.5\pi\)
0.951057 0.309017i \(-0.100000\pi\)
\(42\) 0.363271 + 0.500000i 0.363271 + 0.500000i
\(43\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(44\) 0.951057 0.309017i 0.951057 0.309017i
\(45\) −0.587785 0.809017i −0.587785 0.809017i
\(46\) 0.500000 + 0.363271i 0.500000 + 0.363271i
\(47\) −0.587785 + 0.190983i −0.587785 + 0.190983i −0.587785 0.809017i \(-0.700000\pi\)
1.00000i \(0.5\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) −0.951057 + 1.30902i −0.951057 + 1.30902i
\(52\) −0.190983 + 0.587785i −0.190983 + 0.587785i
\(53\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(54\) 0.618034i 0.618034i
\(55\) 0.500000 + 1.53884i 0.500000 + 1.53884i
\(56\) 0.587785 0.809017i 0.587785 0.809017i
\(57\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(58\) 0.381966 0.381966
\(59\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(60\) −0.363271 + 0.500000i −0.363271 + 0.500000i
\(61\) −1.30902 + 0.951057i −1.30902 + 0.951057i −0.309017 + 0.951057i \(0.600000\pi\)
−1.00000 \(\pi\)
\(62\) 0.363271 + 0.118034i 0.363271 + 0.118034i
\(63\) 1.00000 1.00000
\(64\) −0.190983 + 0.587785i −0.190983 + 0.587785i
\(65\) −0.951057 0.309017i −0.951057 0.309017i
\(66\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(67\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(68\) 0.951057 + 0.309017i 0.951057 + 0.309017i
\(69\) 0.951057 0.309017i 0.951057 0.309017i
\(70\) 0.500000 + 0.363271i 0.500000 + 0.363271i
\(71\) −0.363271 0.500000i −0.363271 0.500000i 0.587785 0.809017i \(-0.300000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(72\) −0.951057 + 0.309017i −0.951057 + 0.309017i
\(73\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0.190983 0.587785i 0.190983 0.587785i
\(77\) −1.53884 0.500000i −1.53884 0.500000i
\(78\) −0.363271 0.500000i −0.363271 0.500000i
\(79\) 0 0 0.587785 0.809017i \(-0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(80\) 0 0
\(81\) −0.809017 0.587785i −0.809017 0.587785i
\(82\) 0.809017 0.587785i 0.809017 0.587785i
\(83\) −0.363271 + 0.500000i −0.363271 + 0.500000i −0.951057 0.309017i \(-0.900000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(84\) −0.190983 0.587785i −0.190983 0.587785i
\(85\) −0.500000 + 1.53884i −0.500000 + 1.53884i
\(86\) −0.587785 0.190983i −0.587785 0.190983i
\(87\) 0.363271 0.500000i 0.363271 0.500000i
\(88\) 1.61803 1.61803
\(89\) −0.951057 + 0.309017i −0.951057 + 0.309017i −0.743145 0.669131i \(-0.766667\pi\)
−0.207912 + 0.978148i \(0.566667\pi\)
\(90\) −0.190983 0.587785i −0.190983 0.587785i
\(91\) 0.809017 0.587785i 0.809017 0.587785i
\(92\) −0.363271 0.500000i −0.363271 0.500000i
\(93\) 0.500000 0.363271i 0.500000 0.363271i
\(94\) −0.381966 −0.381966
\(95\) 0.951057 + 0.309017i 0.951057 + 0.309017i
\(96\) 0.587785 + 0.809017i 0.587785 + 0.809017i
\(97\) 0 0 −0.587785 0.809017i \(-0.700000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(98\) 0 0
\(99\) 0.951057 + 1.30902i 0.951057 + 1.30902i
\(100\) 0 0
\(101\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(102\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(103\) 0 0 −0.951057 0.309017i \(-0.900000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(104\) −0.587785 + 0.809017i −0.587785 + 0.809017i
\(105\) 0.951057 0.309017i 0.951057 0.309017i
\(106\) 0 0
\(107\) 1.17557 1.61803i 1.17557 1.61803i 0.587785 0.809017i \(-0.300000\pi\)
0.587785 0.809017i \(-0.300000\pi\)
\(108\) −0.190983 + 0.587785i −0.190983 + 0.587785i
\(109\) −0.809017 + 0.587785i −0.809017 + 0.587785i −0.913545 0.406737i \(-0.866667\pi\)
0.104528 + 0.994522i \(0.466667\pi\)
\(110\) 1.00000i 1.00000i
\(111\) 0 0
\(112\) 0 0
\(113\) 0.951057 0.309017i 0.951057 0.309017i 0.207912 0.978148i \(-0.433333\pi\)
0.743145 + 0.669131i \(0.233333\pi\)
\(114\) 0.363271 + 0.500000i 0.363271 + 0.500000i
\(115\) 0.809017 0.587785i 0.809017 0.587785i
\(116\) −0.363271 0.118034i −0.363271 0.118034i
\(117\) −1.00000 −1.00000
\(118\) 0 0
\(119\) −0.951057 1.30902i −0.951057 1.30902i
\(120\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(121\) −0.500000 1.53884i −0.500000 1.53884i
\(122\) −0.951057 + 0.309017i −0.951057 + 0.309017i
\(123\) 1.61803i 1.61803i
\(124\) −0.309017 0.224514i −0.309017 0.224514i
\(125\) 0.951057 + 0.309017i 0.951057 + 0.309017i
\(126\) 0.587785 + 0.190983i 0.587785 + 0.190983i
\(127\) −0.309017 0.951057i −0.309017 0.951057i −0.978148 0.207912i \(-0.933333\pi\)
0.669131 0.743145i \(-0.266667\pi\)
\(128\) 0.363271 0.500000i 0.363271 0.500000i
\(129\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(130\) −0.500000 0.363271i −0.500000 0.363271i
\(131\) −1.53884 0.500000i −1.53884 0.500000i −0.587785 0.809017i \(-0.700000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(132\) 0.587785 0.809017i 0.587785 0.809017i
\(133\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(134\) 0 0
\(135\) −0.951057 0.309017i −0.951057 0.309017i
\(136\) 1.30902 + 0.951057i 1.30902 + 0.951057i
\(137\) 0.951057 0.309017i 0.951057 0.309017i 0.207912 0.978148i \(-0.433333\pi\)
0.743145 + 0.669131i \(0.233333\pi\)
\(138\) 0.618034 0.618034
\(139\) −0.309017 0.951057i −0.309017 0.951057i −0.978148 0.207912i \(-0.933333\pi\)
0.669131 0.743145i \(-0.266667\pi\)
\(140\) −0.363271 0.500000i −0.363271 0.500000i
\(141\) −0.363271 + 0.500000i −0.363271 + 0.500000i
\(142\) −0.118034 0.363271i −0.118034 0.363271i
\(143\) 1.53884 + 0.500000i 1.53884 + 0.500000i
\(144\) 0 0
\(145\) 0.190983 0.587785i 0.190983 0.587785i
\(146\) −0.587785 0.190983i −0.587785 0.190983i
\(147\) 0 0
\(148\) 0 0
\(149\) 0.587785 + 0.190983i 0.587785 + 0.190983i 0.587785 0.809017i \(-0.300000\pi\)
1.00000i \(0.5\pi\)
\(150\) 0 0
\(151\) 1.30902 + 0.951057i 1.30902 + 0.951057i 1.00000 \(0\)
0.309017 + 0.951057i \(0.400000\pi\)
\(152\) 0.587785 0.809017i 0.587785 0.809017i
\(153\) 1.61803i 1.61803i
\(154\) −0.809017 0.587785i −0.809017 0.587785i
\(155\) 0.363271 0.500000i 0.363271 0.500000i
\(156\) 0.190983 + 0.587785i 0.190983 + 0.587785i
\(157\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(161\) 1.00000i 1.00000i
\(162\) −0.363271 0.500000i −0.363271 0.500000i
\(163\) −0.809017 0.587785i −0.809017 0.587785i 0.104528 0.994522i \(-0.466667\pi\)
−0.913545 + 0.406737i \(0.866667\pi\)
\(164\) −0.951057 + 0.309017i −0.951057 + 0.309017i
\(165\) 1.30902 + 0.951057i 1.30902 + 0.951057i
\(166\) −0.309017 + 0.224514i −0.309017 + 0.224514i
\(167\) −0.587785 + 0.190983i −0.587785 + 0.190983i −0.587785 0.809017i \(-0.700000\pi\)
1.00000i \(0.5\pi\)
\(168\) 1.00000i 1.00000i
\(169\) 0 0
\(170\) −0.587785 + 0.809017i −0.587785 + 0.809017i
\(171\) 1.00000 1.00000
\(172\) 0.500000 + 0.363271i 0.500000 + 0.363271i
\(173\) 1.00000i 1.00000i 0.866025 + 0.500000i \(0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(174\) 0.309017 0.224514i 0.309017 0.224514i
\(175\) 0 0
\(176\) 0 0
\(177\) 0 0
\(178\) −0.618034 −0.618034
\(179\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(180\) 0.618034i 0.618034i
\(181\) 0 0 −0.951057 0.309017i \(-0.900000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(182\) 0.587785 0.190983i 0.587785 0.190983i
\(183\) −0.500000 + 1.53884i −0.500000 + 1.53884i
\(184\) −0.309017 0.951057i −0.309017 0.951057i
\(185\) 0 0
\(186\) 0.363271 0.118034i 0.363271 0.118034i
\(187\) 0.809017 2.48990i 0.809017 2.48990i
\(188\) 0.363271 + 0.118034i 0.363271 + 0.118034i
\(189\) 0.809017 0.587785i 0.809017 0.587785i
\(190\) 0.500000 + 0.363271i 0.500000 + 0.363271i
\(191\) 0.951057 0.309017i 0.951057 0.309017i 0.207912 0.978148i \(-0.433333\pi\)
0.743145 + 0.669131i \(0.233333\pi\)
\(192\) 0.190983 + 0.587785i 0.190983 + 0.587785i
\(193\) 0 0 0.587785 0.809017i \(-0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(194\) 0 0
\(195\) −0.951057 + 0.309017i −0.951057 + 0.309017i
\(196\) 0 0
\(197\) 0.618034i 0.618034i 0.951057 + 0.309017i \(0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(198\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(199\) −0.618034 −0.618034 −0.309017 0.951057i \(-0.600000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 0.363271 + 0.500000i 0.363271 + 0.500000i
\(204\) 0.951057 0.309017i 0.951057 0.309017i
\(205\) −0.500000 1.53884i −0.500000 1.53884i
\(206\) 0 0
\(207\) 0.587785 0.809017i 0.587785 0.809017i
\(208\) 0 0
\(209\) −1.53884 0.500000i −1.53884 0.500000i
\(210\) 0.618034 0.618034
\(211\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(212\) 0 0
\(213\) −0.587785 0.190983i −0.587785 0.190983i
\(214\) 1.00000 0.726543i 1.00000 0.726543i
\(215\) −0.587785 + 0.809017i −0.587785 + 0.809017i
\(216\) −0.587785 + 0.809017i −0.587785 + 0.809017i
\(217\) 0.190983 + 0.587785i 0.190983 + 0.587785i
\(218\) −0.587785 + 0.190983i −0.587785 + 0.190983i
\(219\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(220\) 0.309017 0.951057i 0.309017 0.951057i
\(221\) 0.951057 + 1.30902i 0.951057 + 1.30902i
\(222\) 0 0
\(223\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(224\) −0.951057 + 0.309017i −0.951057 + 0.309017i
\(225\) 0 0
\(226\) 0.618034 0.618034
\(227\) 0.951057 0.309017i 0.951057 0.309017i 0.207912 0.978148i \(-0.433333\pi\)
0.743145 + 0.669131i \(0.233333\pi\)
\(228\) −0.190983 0.587785i −0.190983 0.587785i
\(229\) −0.500000 0.363271i −0.500000 0.363271i 0.309017 0.951057i \(-0.400000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(230\) 0.587785 0.190983i 0.587785 0.190983i
\(231\) −1.53884 + 0.500000i −1.53884 + 0.500000i
\(232\) −0.500000 0.363271i −0.500000 0.363271i
\(233\) −0.363271 0.500000i −0.363271 0.500000i 0.587785 0.809017i \(-0.300000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(234\) −0.587785 0.190983i −0.587785 0.190983i
\(235\) −0.190983 + 0.587785i −0.190983 + 0.587785i
\(236\) 0 0
\(237\) 0 0
\(238\) −0.309017 0.951057i −0.309017 0.951057i
\(239\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(240\) 0 0
\(241\) 0.500000 1.53884i 0.500000 1.53884i −0.309017 0.951057i \(-0.600000\pi\)
0.809017 0.587785i \(-0.200000\pi\)
\(242\) 1.00000i 1.00000i
\(243\) −1.00000 −1.00000
\(244\) 1.00000 1.00000
\(245\) 0 0
\(246\) 0.309017 0.951057i 0.309017 0.951057i
\(247\) 0.809017 0.587785i 0.809017 0.587785i
\(248\) −0.363271 0.500000i −0.363271 0.500000i
\(249\) 0.618034i 0.618034i
\(250\) 0.500000 + 0.363271i 0.500000 + 0.363271i
\(251\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(252\) −0.500000 0.363271i −0.500000 0.363271i
\(253\) −1.30902 + 0.951057i −1.30902 + 0.951057i
\(254\) 0.618034i 0.618034i
\(255\) 0.500000 + 1.53884i 0.500000 + 1.53884i
\(256\) 0.809017 0.587785i 0.809017 0.587785i
\(257\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(258\) −0.587785 + 0.190983i −0.587785 + 0.190983i
\(259\) 0 0
\(260\) 0.363271 + 0.500000i 0.363271 + 0.500000i
\(261\) 0.618034i 0.618034i
\(262\) −0.809017 0.587785i −0.809017 0.587785i
\(263\) −0.951057 0.309017i −0.951057 0.309017i −0.207912 0.978148i \(-0.566667\pi\)
−0.743145 + 0.669131i \(0.766667\pi\)
\(264\) 1.30902 0.951057i 1.30902 0.951057i
\(265\) 0 0
\(266\) −0.587785 + 0.190983i −0.587785 + 0.190983i
\(267\) −0.587785 + 0.809017i −0.587785 + 0.809017i
\(268\) 0 0
\(269\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(270\) −0.500000 0.363271i −0.500000 0.363271i
\(271\) 1.30902 + 0.951057i 1.30902 + 0.951057i 1.00000 \(0\)
0.309017 + 0.951057i \(0.400000\pi\)
\(272\) 0 0
\(273\) 0.309017 0.951057i 0.309017 0.951057i
\(274\) 0.618034 0.618034
\(275\) 0 0
\(276\) −0.587785 0.190983i −0.587785 0.190983i
\(277\) 0 0 −0.951057 0.309017i \(-0.900000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(278\) 0.618034i 0.618034i
\(279\) 0.190983 0.587785i 0.190983 0.587785i
\(280\) −0.309017 0.951057i −0.309017 0.951057i
\(281\) 0.951057 1.30902i 0.951057 1.30902i 1.00000i \(-0.5\pi\)
0.951057 0.309017i \(-0.100000\pi\)
\(282\) −0.309017 + 0.224514i −0.309017 + 0.224514i
\(283\) 0.309017 + 0.951057i 0.309017 + 0.951057i 0.978148 + 0.207912i \(0.0666667\pi\)
−0.669131 + 0.743145i \(0.733333\pi\)
\(284\) 0.381966i 0.381966i
\(285\) 0.951057 0.309017i 0.951057 0.309017i
\(286\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(287\) 1.53884 + 0.500000i 1.53884 + 0.500000i
\(288\) 0.951057 + 0.309017i 0.951057 + 0.309017i
\(289\) 1.30902 0.951057i 1.30902 0.951057i
\(290\) 0.224514 0.309017i 0.224514 0.309017i
\(291\) 0 0
\(292\) 0.500000 + 0.363271i 0.500000 + 0.363271i
\(293\) −0.587785 0.809017i −0.587785 0.809017i 0.406737 0.913545i \(-0.366667\pi\)
−0.994522 + 0.104528i \(0.966667\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 1.53884 + 0.500000i 1.53884 + 0.500000i
\(298\) 0.309017 + 0.224514i 0.309017 + 0.224514i
\(299\) 1.00000i 1.00000i
\(300\) 0 0
\(301\) −0.309017 0.951057i −0.309017 0.951057i
\(302\) 0.587785 + 0.809017i 0.587785 + 0.809017i
\(303\) 0 0
\(304\) 0 0
\(305\) 1.61803i 1.61803i
\(306\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(307\) 0.809017 0.587785i 0.809017 0.587785i −0.104528 0.994522i \(-0.533333\pi\)
0.913545 + 0.406737i \(0.133333\pi\)
\(308\) 0.587785 + 0.809017i 0.587785 + 0.809017i
\(309\) 0 0
\(310\) 0.309017 0.224514i 0.309017 0.224514i
\(311\) 0.951057 + 0.309017i 0.951057 + 0.309017i 0.743145 0.669131i \(-0.233333\pi\)
0.207912 + 0.978148i \(0.433333\pi\)
\(312\) 1.00000i 1.00000i
\(313\) −0.500000 + 0.363271i −0.500000 + 0.363271i −0.809017 0.587785i \(-0.800000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(314\) −0.587785 0.190983i −0.587785 0.190983i
\(315\) 0.587785 0.809017i 0.587785 0.809017i
\(316\) 0 0
\(317\) −0.951057 + 0.309017i −0.951057 + 0.309017i −0.743145 0.669131i \(-0.766667\pi\)
−0.207912 + 0.978148i \(0.566667\pi\)
\(318\) 0 0
\(319\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(320\) 0.363271 + 0.500000i 0.363271 + 0.500000i
\(321\) 2.00000i 2.00000i
\(322\) −0.190983 + 0.587785i −0.190983 + 0.587785i
\(323\) −0.951057 1.30902i −0.951057 1.30902i
\(324\) 0.190983 + 0.587785i 0.190983 + 0.587785i
\(325\) 0 0
\(326\) −0.363271 0.500000i −0.363271 0.500000i
\(327\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(328\) −1.61803 −1.61803
\(329\) −0.363271 0.500000i −0.363271 0.500000i
\(330\) 0.587785 + 0.809017i 0.587785 + 0.809017i
\(331\) 0 0 −0.587785 0.809017i \(-0.700000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(332\) 0.363271 0.118034i 0.363271 0.118034i
\(333\) 0 0
\(334\) −0.381966 −0.381966
\(335\) 0 0
\(336\) 0 0
\(337\) −0.309017 + 0.951057i −0.309017 + 0.951057i 0.669131 + 0.743145i \(0.266667\pi\)
−0.978148 + 0.207912i \(0.933333\pi\)
\(338\) 0 0
\(339\) 0.587785 0.809017i 0.587785 0.809017i
\(340\) 0.809017 0.587785i 0.809017 0.587785i
\(341\) −0.587785 + 0.809017i −0.587785 + 0.809017i
\(342\) 0.587785 + 0.190983i 0.587785 + 0.190983i
\(343\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(344\) 0.587785 + 0.809017i 0.587785 + 0.809017i
\(345\) 0.309017 0.951057i 0.309017 0.951057i
\(346\) −0.190983 + 0.587785i −0.190983 + 0.587785i
\(347\) −0.951057 + 1.30902i −0.951057 + 1.30902i 1.00000i \(0.5\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(348\) −0.363271 + 0.118034i −0.363271 + 0.118034i
\(349\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(350\) 0 0
\(351\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(352\) −1.30902 0.951057i −1.30902 0.951057i
\(353\) 1.53884 0.500000i 1.53884 0.500000i 0.587785 0.809017i \(-0.300000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(354\) 0 0
\(355\) −0.618034 −0.618034
\(356\) 0.587785 + 0.190983i 0.587785 + 0.190983i
\(357\) −1.53884 0.500000i −1.53884 0.500000i
\(358\) 0 0
\(359\) 1.61803i 1.61803i 0.587785 + 0.809017i \(0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(360\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(361\) 0 0
\(362\) 0 0
\(363\) −1.30902 0.951057i −1.30902 0.951057i
\(364\) −0.618034 −0.618034
\(365\) −0.587785 + 0.809017i −0.587785 + 0.809017i
\(366\) −0.587785 + 0.809017i −0.587785 + 0.809017i
\(367\) −0.309017 0.951057i −0.309017 0.951057i −0.978148 0.207912i \(-0.933333\pi\)
0.669131 0.743145i \(-0.266667\pi\)
\(368\) 0 0
\(369\) −0.951057 1.30902i −0.951057 1.30902i
\(370\) 0 0
\(371\) 0 0
\(372\) −0.381966 −0.381966
\(373\) −1.30902 + 0.951057i −1.30902 + 0.951057i −0.309017 + 0.951057i \(0.600000\pi\)
−1.00000 \(\pi\)
\(374\) 0.951057 1.30902i 0.951057 1.30902i
\(375\) 0.951057 0.309017i 0.951057 0.309017i
\(376\) 0.500000 + 0.363271i 0.500000 + 0.363271i
\(377\) −0.363271 0.500000i −0.363271 0.500000i
\(378\) 0.587785 0.190983i 0.587785 0.190983i
\(379\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(380\) −0.363271 0.500000i −0.363271 0.500000i
\(381\) −0.809017 0.587785i −0.809017 0.587785i
\(382\) 0.618034 0.618034
\(383\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(384\) 0.618034i 0.618034i
\(385\) −1.30902 + 0.951057i −1.30902 + 0.951057i
\(386\) 0 0
\(387\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(388\) 0 0
\(389\) 1.00000i 1.00000i 0.866025 + 0.500000i \(0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(390\) −0.618034 −0.618034
\(391\) −1.61803 −1.61803
\(392\) 0 0
\(393\) −1.53884 + 0.500000i −1.53884 + 0.500000i
\(394\) −0.118034 + 0.363271i −0.118034 + 0.363271i
\(395\) 0 0
\(396\) 1.00000i 1.00000i
\(397\) −0.500000 1.53884i −0.500000 1.53884i −0.809017 0.587785i \(-0.800000\pi\)
0.309017 0.951057i \(-0.400000\pi\)
\(398\) −0.363271 0.118034i −0.363271 0.118034i
\(399\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(400\) 0 0
\(401\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(402\) 0 0
\(403\) −0.190983 0.587785i −0.190983 0.587785i
\(404\) 0 0
\(405\) −0.951057 + 0.309017i −0.951057 + 0.309017i
\(406\) 0.118034 + 0.363271i 0.118034 + 0.363271i
\(407\) 0 0
\(408\) 1.61803 1.61803
\(409\) 0.190983 + 0.587785i 0.190983 + 0.587785i 1.00000 \(0\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(410\) 1.00000i 1.00000i
\(411\) 0.587785 0.809017i 0.587785 0.809017i
\(412\) 0 0
\(413\) 0 0
\(414\) 0.500000 0.363271i 0.500000 0.363271i
\(415\) 0.190983 + 0.587785i 0.190983 + 0.587785i
\(416\) 0.951057 0.309017i 0.951057 0.309017i
\(417\) −0.809017 0.587785i −0.809017 0.587785i
\(418\) −0.809017 0.587785i −0.809017 0.587785i
\(419\) −0.363271 0.500000i −0.363271 0.500000i 0.587785 0.809017i \(-0.300000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(420\) −0.587785 0.190983i −0.587785 0.190983i
\(421\) 1.61803 1.61803 0.809017 0.587785i \(-0.200000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(422\) 0.618034i 0.618034i
\(423\) 0.618034i 0.618034i
\(424\) 0 0
\(425\) 0 0
\(426\) −0.309017 0.224514i −0.309017 0.224514i
\(427\) −1.30902 0.951057i −1.30902 0.951057i
\(428\) −1.17557 + 0.381966i −1.17557 + 0.381966i
\(429\) 1.53884 0.500000i 1.53884 0.500000i
\(430\) −0.500000 + 0.363271i −0.500000 + 0.363271i
\(431\) −0.951057 0.309017i −0.951057 0.309017i −0.207912 0.978148i \(-0.566667\pi\)
−0.743145 + 0.669131i \(0.766667\pi\)
\(432\) 0 0
\(433\) −0.809017 0.587785i −0.809017 0.587785i 0.104528 0.994522i \(-0.466667\pi\)
−0.913545 + 0.406737i \(0.866667\pi\)
\(434\) 0.381966i 0.381966i
\(435\) −0.190983 0.587785i −0.190983 0.587785i
\(436\) 0.618034 0.618034
\(437\) 1.00000i 1.00000i
\(438\) −0.587785 + 0.190983i −0.587785 + 0.190983i
\(439\) 0 0 0.951057 0.309017i \(-0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(440\) 0.951057 1.30902i 0.951057 1.30902i
\(441\) 0 0
\(442\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(443\) −0.587785 + 0.809017i −0.587785 + 0.809017i −0.994522 0.104528i \(-0.966667\pi\)
0.406737 + 0.913545i \(0.366667\pi\)
\(444\) 0 0
\(445\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(446\) 0.587785 + 0.190983i 0.587785 + 0.190983i
\(447\) 0.587785 0.190983i 0.587785 0.190983i
\(448\) −0.618034 −0.618034
\(449\) 0.951057 0.309017i 0.951057 0.309017i 0.207912 0.978148i \(-0.433333\pi\)
0.743145 + 0.669131i \(0.233333\pi\)
\(450\) 0 0
\(451\) 0.809017 + 2.48990i 0.809017 + 2.48990i
\(452\) −0.587785 0.190983i −0.587785 0.190983i
\(453\) 1.61803 1.61803
\(454\) 0.618034 0.618034
\(455\) 1.00000i 1.00000i
\(456\) 1.00000i 1.00000i
\(457\) −0.190983 + 0.587785i −0.190983 + 0.587785i 0.809017 + 0.587785i \(0.200000\pi\)
−1.00000 \(\pi\)
\(458\) −0.224514 0.309017i −0.224514 0.309017i
\(459\) 0.951057 + 1.30902i 0.951057 + 1.30902i
\(460\) −0.618034 −0.618034
\(461\) 0.587785 0.809017i 0.587785 0.809017i −0.406737 0.913545i \(-0.633333\pi\)
0.994522 + 0.104528i \(0.0333333\pi\)
\(462\) −1.00000 −1.00000
\(463\) 0.809017 + 0.587785i 0.809017 + 0.587785i 0.913545 0.406737i \(-0.133333\pi\)
−0.104528 + 0.994522i \(0.533333\pi\)
\(464\) 0 0
\(465\) 0.618034i 0.618034i
\(466\) −0.118034 0.363271i −0.118034 0.363271i
\(467\) −0.587785 0.809017i −0.587785 0.809017i 0.406737 0.913545i \(-0.366667\pi\)
−0.994522 + 0.104528i \(0.966667\pi\)
\(468\) 0.500000 + 0.363271i 0.500000 + 0.363271i
\(469\) 0 0
\(470\) −0.224514 + 0.309017i −0.224514 + 0.309017i
\(471\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(472\) 0 0
\(473\) 0.951057 1.30902i 0.951057 1.30902i
\(474\) 0 0
\(475\) 0 0
\(476\) 1.00000i 1.00000i
\(477\) 0 0
\(478\) 0 0
\(479\) −0.951057 + 1.30902i −0.951057 + 1.30902i 1.00000i \(0.5\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(480\) 1.00000 1.00000
\(481\) 0 0
\(482\) 0.587785 0.809017i 0.587785 0.809017i
\(483\) 0.587785 + 0.809017i 0.587785 + 0.809017i
\(484\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(485\) 0 0
\(486\) −0.587785 0.190983i −0.587785 0.190983i
\(487\) −0.190983 + 0.587785i −0.190983 + 0.587785i 0.809017 + 0.587785i \(0.200000\pi\)
−1.00000 \(\pi\)
\(488\) 1.53884 + 0.500000i 1.53884 + 0.500000i
\(489\) −1.00000 −1.00000
\(490\) 0 0
\(491\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(492\) −0.587785 + 0.809017i −0.587785 + 0.809017i
\(493\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(494\) 0.587785 0.190983i 0.587785 0.190983i
\(495\) 1.61803 1.61803
\(496\) 0 0
\(497\) 0.363271 0.500000i 0.363271 0.500000i
\(498\) −0.118034 + 0.363271i −0.118034 + 0.363271i
\(499\) −0.309017 + 0.951057i −0.309017 + 0.951057i 0.669131 + 0.743145i \(0.266667\pi\)
−0.978148 + 0.207912i \(0.933333\pi\)
\(500\) −0.363271 0.500000i −0.363271 0.500000i
\(501\) −0.363271 + 0.500000i −0.363271 + 0.500000i
\(502\) 0 0
\(503\) −0.363271 + 0.500000i −0.363271 + 0.500000i −0.951057 0.309017i \(-0.900000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(504\) −0.587785 0.809017i −0.587785 0.809017i
\(505\) 0 0
\(506\) −0.951057 + 0.309017i −0.951057 + 0.309017i
\(507\) 0 0
\(508\) −0.190983 + 0.587785i −0.190983 + 0.587785i
\(509\) −0.587785 + 0.809017i −0.587785 + 0.809017i −0.994522 0.104528i \(-0.966667\pi\)
0.406737 + 0.913545i \(0.366667\pi\)
\(510\) 1.00000i 1.00000i
\(511\) −0.309017 0.951057i −0.309017 0.951057i
\(512\) 0 0
\(513\) 0.809017 0.587785i 0.809017 0.587785i
\(514\) 0 0
\(515\) 0 0
\(516\) 0.618034 0.618034
\(517\) 0.309017 0.951057i 0.309017 0.951057i
\(518\) 0 0
\(519\) 0.587785 + 0.809017i 0.587785 + 0.809017i
\(520\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(521\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(522\) 0.118034 0.363271i 0.118034 0.363271i
\(523\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(524\) 0.587785 + 0.809017i 0.587785 + 0.809017i
\(525\) 0 0
\(526\) −0.500000 0.363271i −0.500000 0.363271i
\(527\) −0.951057 + 0.309017i −0.951057 + 0.309017i
\(528\) 0 0
\(529\) 0 0
\(530\) 0 0
\(531\) 0 0
\(532\) 0.618034 0.618034
\(533\) −1.53884 0.500000i −1.53884 0.500000i
\(534\) −0.500000 + 0.363271i −0.500000 + 0.363271i
\(535\) −0.618034 1.90211i −0.618034 1.90211i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 0 0
\(540\) 0.363271 + 0.500000i 0.363271 + 0.500000i
\(541\) 0 0 −0.587785 0.809017i \(-0.700000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(542\) 0.587785 + 0.809017i 0.587785 + 0.809017i
\(543\) 0 0
\(544\) −0.500000 1.53884i −0.500000 1.53884i
\(545\) 1.00000i 1.00000i
\(546\) 0.363271 0.500000i 0.363271 0.500000i
\(547\) 0 0 −0.951057 0.309017i \(-0.900000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(548\) −0.587785 0.190983i −0.587785 0.190983i
\(549\) 0.500000 + 1.53884i 0.500000 + 1.53884i
\(550\) 0 0
\(551\) 0.363271 + 0.500000i 0.363271 + 0.500000i
\(552\) −0.809017 0.587785i −0.809017 0.587785i
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) −0.190983 + 0.587785i −0.190983 + 0.587785i
\(557\) 1.53884 + 0.500000i 1.53884 + 0.500000i 0.951057 0.309017i \(-0.100000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(558\) 0.224514 0.309017i 0.224514 0.309017i
\(559\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(560\) 0 0
\(561\) −0.809017 2.48990i −0.809017 2.48990i
\(562\) 0.809017 0.587785i 0.809017 0.587785i
\(563\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(564\) 0.363271 0.118034i 0.363271 0.118034i
\(565\) 0.309017 0.951057i 0.309017 0.951057i
\(566\) 0.618034i 0.618034i
\(567\) 0.309017 0.951057i 0.309017 0.951057i
\(568\) −0.190983 + 0.587785i −0.190983 + 0.587785i
\(569\) −0.587785 0.190983i −0.587785 0.190983i 1.00000i \(-0.5\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(570\) 0.618034 0.618034
\(571\) 0 0 −0.951057 0.309017i \(-0.900000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(572\) −0.587785 0.809017i −0.587785 0.809017i
\(573\) 0.587785 0.809017i 0.587785 0.809017i
\(574\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(575\) 0 0
\(576\) 0.500000 + 0.363271i 0.500000 + 0.363271i
\(577\) −0.809017 0.587785i −0.809017 0.587785i 0.104528 0.994522i \(-0.466667\pi\)
−0.913545 + 0.406737i \(0.866667\pi\)
\(578\) 0.951057 0.309017i 0.951057 0.309017i
\(579\) 0 0
\(580\) −0.309017 + 0.224514i −0.309017 + 0.224514i
\(581\) −0.587785 0.190983i −0.587785 0.190983i
\(582\) 0 0
\(583\) 0 0
\(584\) 0.587785 + 0.809017i 0.587785 + 0.809017i
\(585\) −0.587785 + 0.809017i −0.587785 + 0.809017i
\(586\) −0.190983 0.587785i −0.190983 0.587785i
\(587\) −0.587785 + 0.809017i −0.587785 + 0.809017i −0.994522 0.104528i \(-0.966667\pi\)
0.406737 + 0.913545i \(0.366667\pi\)
\(588\) 0 0
\(589\) 0.190983 + 0.587785i 0.190983 + 0.587785i
\(590\) 0 0
\(591\) 0.363271 + 0.500000i 0.363271 + 0.500000i
\(592\) 0 0
\(593\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(594\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(595\) −1.61803 −1.61803
\(596\) −0.224514 0.309017i −0.224514 0.309017i
\(597\) −0.500000 + 0.363271i −0.500000 + 0.363271i
\(598\) 0.190983 0.587785i 0.190983 0.587785i
\(599\) 1.00000i 1.00000i −0.866025 0.500000i \(-0.833333\pi\)
0.866025 0.500000i \(-0.166667\pi\)
\(600\) 0 0
\(601\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(602\) 0.618034i 0.618034i
\(603\) 0 0
\(604\) −0.309017 0.951057i −0.309017 0.951057i
\(605\) −1.53884 0.500000i −1.53884 0.500000i
\(606\) 0 0
\(607\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(608\) −0.951057 + 0.309017i −0.951057 + 0.309017i
\(609\) 0.587785 + 0.190983i 0.587785 + 0.190983i
\(610\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(611\) 0.363271 + 0.500000i 0.363271 + 0.500000i
\(612\) 0.587785 0.809017i 0.587785 0.809017i
\(613\) −0.309017 0.951057i −0.309017 0.951057i −0.978148 0.207912i \(-0.933333\pi\)
0.669131 0.743145i \(-0.266667\pi\)
\(614\) 0.587785 0.190983i 0.587785 0.190983i
\(615\) −1.30902 0.951057i −1.30902 0.951057i
\(616\) 0.500000 + 1.53884i 0.500000 + 1.53884i
\(617\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(618\) 0 0
\(619\) 1.61803 1.61803 0.809017 0.587785i \(-0.200000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(620\) −0.363271 + 0.118034i −0.363271 + 0.118034i
\(621\) 1.00000i 1.00000i
\(622\) 0.500000 + 0.363271i 0.500000 + 0.363271i
\(623\) −0.587785 0.809017i −0.587785 0.809017i
\(624\) 0 0
\(625\) 0.809017 0.587785i 0.809017 0.587785i
\(626\) −0.363271 + 0.118034i −0.363271 + 0.118034i
\(627\) −1.53884 + 0.500000i −1.53884 + 0.500000i
\(628\) 0.500000 + 0.363271i 0.500000 + 0.363271i
\(629\) 0 0
\(630\) 0.500000 0.363271i 0.500000 0.363271i
\(631\) −0.190983 + 0.587785i −0.190983 + 0.587785i 0.809017 + 0.587785i \(0.200000\pi\)
−1.00000 \(\pi\)
\(632\) 0 0
\(633\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(634\) −0.618034 −0.618034
\(635\) −0.951057 0.309017i −0.951057 0.309017i
\(636\) 0 0
\(637\) 0 0
\(638\) −0.363271 + 0.500000i −0.363271 + 0.500000i
\(639\) −0.587785 + 0.190983i −0.587785 + 0.190983i
\(640\) −0.190983 0.587785i −0.190983 0.587785i
\(641\) 0.587785 + 0.809017i 0.587785 + 0.809017i 0.994522 0.104528i \(-0.0333333\pi\)
−0.406737 + 0.913545i \(0.633333\pi\)
\(642\) 0.381966 1.17557i 0.381966 1.17557i
\(643\) 0 0 −0.587785 0.809017i \(-0.700000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(644\) 0.363271 0.500000i 0.363271 0.500000i
\(645\) 1.00000i 1.00000i
\(646\) −0.309017 0.951057i −0.309017 0.951057i
\(647\) 1.00000i 1.00000i −0.866025 0.500000i \(-0.833333\pi\)
0.866025 0.500000i \(-0.166667\pi\)
\(648\) 1.00000i 1.00000i
\(649\) 0 0
\(650\) 0 0
\(651\) 0.500000 + 0.363271i 0.500000 + 0.363271i
\(652\) 0.190983 + 0.587785i 0.190983 + 0.587785i
\(653\) 1.53884 0.500000i 1.53884 0.500000i 0.587785 0.809017i \(-0.300000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(654\) −0.363271 + 0.500000i −0.363271 + 0.500000i
\(655\) −1.30902 + 0.951057i −1.30902 + 0.951057i
\(656\) 0 0
\(657\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(658\) −0.118034 0.363271i −0.118034 0.363271i
\(659\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(660\) −0.309017 0.951057i −0.309017 0.951057i
\(661\) 0 0 −0.951057 0.309017i \(-0.900000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(662\) 0 0
\(663\) 1.53884 + 0.500000i 1.53884 + 0.500000i
\(664\) 0.618034 0.618034
\(665\) 1.00000i 1.00000i
\(666\) 0 0
\(667\) 0.618034 0.618034
\(668\) 0.363271 + 0.118034i 0.363271 + 0.118034i
\(669\) 0.809017 0.587785i 0.809017 0.587785i
\(670\) 0 0
\(671\) 2.61803i 2.61803i
\(672\) −0.587785 + 0.809017i −0.587785 + 0.809017i
\(673\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(674\) −0.363271 + 0.500000i −0.363271 + 0.500000i
\(675\) 0 0
\(676\) 0 0
\(677\) 0.951057 0.309017i 0.951057 0.309017i 0.207912 0.978148i \(-0.433333\pi\)
0.743145 + 0.669131i \(0.233333\pi\)
\(678\) 0.500000 0.363271i 0.500000 0.363271i
\(679\) 0 0
\(680\) 1.53884 0.500000i 1.53884 0.500000i
\(681\) 0.587785 0.809017i 0.587785 0.809017i
\(682\) −0.500000 + 0.363271i −0.500000 + 0.363271i
\(683\) 0.618034i 0.618034i 0.951057 + 0.309017i \(0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(684\) −0.500000 0.363271i −0.500000 0.363271i
\(685\) 0.309017 0.951057i 0.309017 0.951057i
\(686\) 0.363271 + 0.500000i 0.363271 + 0.500000i
\(687\) −0.618034 −0.618034
\(688\) 0 0
\(689\) 0 0
\(690\) 0.363271 0.500000i 0.363271 0.500000i
\(691\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(692\) 0.363271 0.500000i 0.363271 0.500000i
\(693\) −0.951057 + 1.30902i −0.951057 + 1.30902i
\(694\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(695\) −0.951057 0.309017i −0.951057 0.309017i
\(696\) −0.618034 −0.618034
\(697\) −0.809017 + 2.48990i −0.809017 + 2.48990i
\(698\) 0.587785 + 0.190983i 0.587785 + 0.190983i
\(699\) −0.587785 0.190983i −0.587785 0.190983i
\(700\) 0 0
\(701\) −0.951057 0.309017i −0.951057 0.309017i −0.207912 0.978148i \(-0.566667\pi\)
−0.743145 + 0.669131i \(0.766667\pi\)
\(702\) −0.587785 + 0.190983i −0.587785 + 0.190983i
\(703\) 0 0
\(704\) −0.587785 0.809017i −0.587785 0.809017i
\(705\) 0.190983 + 0.587785i 0.190983 + 0.587785i
\(706\) 1.00000 1.00000
\(707\) 0 0
\(708\) 0 0
\(709\) −0.500000 + 1.53884i −0.500000 + 1.53884i 0.309017 + 0.951057i \(0.400000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(710\) −0.363271 0.118034i −0.363271 0.118034i
\(711\) 0 0
\(712\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(713\) 0.587785 + 0.190983i 0.587785 + 0.190983i
\(714\) −0.809017 0.587785i −0.809017 0.587785i
\(715\) 1.30902 0.951057i 1.30902 0.951057i
\(716\) 0 0
\(717\) 0 0
\(718\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(719\) −0.587785 0.190983i −0.587785 0.190983i 1.00000i \(-0.5\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) −0.500000 1.53884i −0.500000 1.53884i
\(724\) 0 0
\(725\) 0 0
\(726\) −0.587785 0.809017i −0.587785 0.809017i
\(727\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(728\) −0.951057 0.309017i −0.951057 0.309017i
\(729\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(730\) −0.500000 + 0.363271i −0.500000 + 0.363271i
\(731\) 1.53884 0.500000i 1.53884 0.500000i
\(732\) 0.809017 0.587785i 0.809017 0.587785i
\(733\) 0.500000 1.53884i 0.500000 1.53884i −0.309017 0.951057i \(-0.600000\pi\)
0.809017 0.587785i \(-0.200000\pi\)
\(734\) 0.618034i 0.618034i
\(735\) 0 0
\(736\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(737\) 0 0
\(738\) −0.309017 0.951057i −0.309017 0.951057i
\(739\) 0 0 0.951057 0.309017i \(-0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(740\) 0 0
\(741\) 0.309017 0.951057i 0.309017 0.951057i
\(742\) 0 0
\(743\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(744\) −0.587785 0.190983i −0.587785 0.190983i
\(745\) 0.500000 0.363271i 0.500000 0.363271i
\(746\) −0.951057 + 0.309017i −0.951057 + 0.309017i
\(747\) 0.363271 + 0.500000i 0.363271 + 0.500000i
\(748\) −1.30902 + 0.951057i −1.30902 + 0.951057i
\(749\) 1.90211 + 0.618034i 1.90211 + 0.618034i
\(750\) 0.618034 0.618034
\(751\) 1.30902 0.951057i 1.30902 0.951057i 0.309017 0.951057i \(-0.400000\pi\)
1.00000 \(0\)
\(752\) 0 0
\(753\) 0 0
\(754\) −0.118034 0.363271i −0.118034 0.363271i
\(755\) 1.53884 0.500000i 1.53884 0.500000i
\(756\) −0.618034 −0.618034
\(757\) −0.809017 0.587785i −0.809017 0.587785i 0.104528 0.994522i \(-0.466667\pi\)
−0.913545 + 0.406737i \(0.866667\pi\)
\(758\) 0 0
\(759\) −0.500000 + 1.53884i −0.500000 + 1.53884i
\(760\) −0.309017 0.951057i −0.309017 0.951057i
\(761\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(762\) −0.363271 0.500000i −0.363271 0.500000i
\(763\) −0.809017 0.587785i −0.809017 0.587785i
\(764\) −0.587785 0.190983i −0.587785 0.190983i
\(765\) 1.30902 + 0.951057i 1.30902 + 0.951057i
\(766\) 0 0
\(767\) 0 0
\(768\) 0.309017 0.951057i 0.309017 0.951057i
\(769\) 0.500000 + 0.363271i 0.500000 + 0.363271i 0.809017 0.587785i \(-0.200000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(770\) −0.951057 + 0.309017i −0.951057 + 0.309017i
\(771\) 0 0
\(772\) 0 0
\(773\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(774\) −0.363271 + 0.500000i −0.363271 + 0.500000i
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) −0.190983 + 0.587785i −0.190983 + 0.587785i
\(779\) 1.53884 + 0.500000i 1.53884 + 0.500000i
\(780\) 0.587785 + 0.190983i 0.587785 + 0.190983i
\(781\) 1.00000 1.00000
\(782\) −0.951057 0.309017i −0.951057 0.309017i
\(783\) −0.363271 0.500000i −0.363271 0.500000i
\(784\) 0 0
\(785\) −0.587785 + 0.809017i −0.587785 + 0.809017i