Properties

Label 3332.1.be.a.3263.1
Level $3332$
Weight $1$
Character 3332.3263
Analytic conductor $1.663$
Analytic rank $0$
Dimension $6$
Projective image $D_{7}$
CM discriminant -68
Inner twists $4$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 3332 = 2^{2} \cdot 7^{2} \cdot 17 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 3332.be (of order \(14\), degree \(6\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.66288462209\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: \(\Q(\zeta_{14})\)
Defining polynomial: \( x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Projective image: \(D_{7}\)
Projective field: Galois closure of \(\mathbb{Q}[x]/(x^{7} - \cdots)\)

Embedding invariants

Embedding label 3263.1
Root \(-0.623490 - 0.781831i\) of defining polynomial
Character \(\chi\) \(=\) 3332.3263
Dual form 3332.1.be.a.1835.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.900969 - 0.433884i) q^{2} +(-0.0990311 - 0.433884i) q^{3} +(0.623490 + 0.781831i) q^{4} +(-0.0990311 + 0.433884i) q^{6} +(0.222521 + 0.974928i) q^{7} +(-0.222521 - 0.974928i) q^{8} +(0.722521 - 0.347948i) q^{9} +O(q^{10})\) \(q+(-0.900969 - 0.433884i) q^{2} +(-0.0990311 - 0.433884i) q^{3} +(0.623490 + 0.781831i) q^{4} +(-0.0990311 + 0.433884i) q^{6} +(0.222521 + 0.974928i) q^{7} +(-0.222521 - 0.974928i) q^{8} +(0.722521 - 0.347948i) q^{9} +(-1.62349 - 0.781831i) q^{11} +(0.277479 - 0.347948i) q^{12} +(1.62349 + 0.781831i) q^{13} +(0.222521 - 0.974928i) q^{14} +(-0.222521 + 0.974928i) q^{16} +(0.623490 - 0.781831i) q^{17} -0.801938 q^{18} +(0.400969 - 0.193096i) q^{21} +(1.12349 + 1.40881i) q^{22} +(1.12349 + 1.40881i) q^{23} +(-0.400969 + 0.193096i) q^{24} +(-0.900969 + 0.433884i) q^{25} +(-1.12349 - 1.40881i) q^{26} +(-0.500000 - 0.626980i) q^{27} +(-0.623490 + 0.781831i) q^{28} +0.445042 q^{31} +(0.623490 - 0.781831i) q^{32} +(-0.178448 + 0.781831i) q^{33} +(-0.900969 + 0.433884i) q^{34} +(0.722521 + 0.347948i) q^{36} +(0.178448 - 0.781831i) q^{39} -0.445042 q^{42} +(-0.400969 - 1.75676i) q^{44} +(-0.400969 - 1.75676i) q^{46} +0.445042 q^{48} +(-0.900969 + 0.433884i) q^{49} +1.00000 q^{50} +(-0.400969 - 0.193096i) q^{51} +(0.400969 + 1.75676i) q^{52} +(-0.277479 - 0.347948i) q^{53} +(0.178448 + 0.781831i) q^{54} +(0.900969 - 0.433884i) q^{56} +(-0.400969 - 0.193096i) q^{62} +(0.500000 + 0.626980i) q^{63} +(-0.900969 + 0.433884i) q^{64} +(0.500000 - 0.626980i) q^{66} +1.00000 q^{68} +(0.500000 - 0.626980i) q^{69} +(0.277479 + 0.347948i) q^{71} +(-0.500000 - 0.626980i) q^{72} +(0.277479 + 0.347948i) q^{75} +(0.400969 - 1.75676i) q^{77} +(-0.500000 + 0.626980i) q^{78} +1.80194 q^{79} +(0.277479 - 0.347948i) q^{81} +(0.400969 + 0.193096i) q^{84} +(-0.400969 + 1.75676i) q^{88} +(0.400969 - 0.193096i) q^{89} +(-0.400969 + 1.75676i) q^{91} +(-0.400969 + 1.75676i) q^{92} +(-0.0440730 - 0.193096i) q^{93} +(-0.400969 - 0.193096i) q^{96} +1.00000 q^{98} -1.44504 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - q^{2} - 5 q^{3} - q^{4} - 5 q^{6} + q^{7} - q^{8} + 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q - q^{2} - 5 q^{3} - q^{4} - 5 q^{6} + q^{7} - q^{8} + 4 q^{9} - 5 q^{11} + 2 q^{12} + 5 q^{13} + q^{14} - q^{16} - q^{17} + 4 q^{18} - 2 q^{21} + 2 q^{22} + 2 q^{23} + 2 q^{24} - q^{25} - 2 q^{26} - 3 q^{27} + q^{28} + 2 q^{31} - q^{32} + 3 q^{33} - q^{34} + 4 q^{36} - 3 q^{39} - 2 q^{42} + 2 q^{44} + 2 q^{46} + 2 q^{48} - q^{49} + 6 q^{50} + 2 q^{51} - 2 q^{52} - 2 q^{53} - 3 q^{54} + q^{56} + 2 q^{62} + 3 q^{63} - q^{64} + 3 q^{66} + 6 q^{68} + 3 q^{69} + 2 q^{71} - 3 q^{72} + 2 q^{75} - 2 q^{77} - 3 q^{78} + 2 q^{79} + 2 q^{81} - 2 q^{84} + 2 q^{88} - 2 q^{89} + 2 q^{91} + 2 q^{92} - 4 q^{93} + 2 q^{96} + 6 q^{98} - 8 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3332\mathbb{Z}\right)^\times\).

\(n\) \(785\) \(885\) \(1667\)
\(\chi(n)\) \(-1\) \(e\left(\frac{3}{7}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.900969 0.433884i −0.900969 0.433884i
\(3\) −0.0990311 0.433884i −0.0990311 0.433884i 0.900969 0.433884i \(-0.142857\pi\)
−1.00000 \(\pi\)
\(4\) 0.623490 + 0.781831i 0.623490 + 0.781831i
\(5\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(6\) −0.0990311 + 0.433884i −0.0990311 + 0.433884i
\(7\) 0.222521 + 0.974928i 0.222521 + 0.974928i
\(8\) −0.222521 0.974928i −0.222521 0.974928i
\(9\) 0.722521 0.347948i 0.722521 0.347948i
\(10\) 0 0
\(11\) −1.62349 0.781831i −1.62349 0.781831i −0.623490 0.781831i \(-0.714286\pi\)
−1.00000 \(\pi\)
\(12\) 0.277479 0.347948i 0.277479 0.347948i
\(13\) 1.62349 + 0.781831i 1.62349 + 0.781831i 1.00000 \(0\)
0.623490 + 0.781831i \(0.285714\pi\)
\(14\) 0.222521 0.974928i 0.222521 0.974928i
\(15\) 0 0
\(16\) −0.222521 + 0.974928i −0.222521 + 0.974928i
\(17\) 0.623490 0.781831i 0.623490 0.781831i
\(18\) −0.801938 −0.801938
\(19\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(20\) 0 0
\(21\) 0.400969 0.193096i 0.400969 0.193096i
\(22\) 1.12349 + 1.40881i 1.12349 + 1.40881i
\(23\) 1.12349 + 1.40881i 1.12349 + 1.40881i 0.900969 + 0.433884i \(0.142857\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(24\) −0.400969 + 0.193096i −0.400969 + 0.193096i
\(25\) −0.900969 + 0.433884i −0.900969 + 0.433884i
\(26\) −1.12349 1.40881i −1.12349 1.40881i
\(27\) −0.500000 0.626980i −0.500000 0.626980i
\(28\) −0.623490 + 0.781831i −0.623490 + 0.781831i
\(29\) 0 0 0.623490 0.781831i \(-0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(30\) 0 0
\(31\) 0.445042 0.445042 0.222521 0.974928i \(-0.428571\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(32\) 0.623490 0.781831i 0.623490 0.781831i
\(33\) −0.178448 + 0.781831i −0.178448 + 0.781831i
\(34\) −0.900969 + 0.433884i −0.900969 + 0.433884i
\(35\) 0 0
\(36\) 0.722521 + 0.347948i 0.722521 + 0.347948i
\(37\) 0 0 0.623490 0.781831i \(-0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(38\) 0 0
\(39\) 0.178448 0.781831i 0.178448 0.781831i
\(40\) 0 0
\(41\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(42\) −0.445042 −0.445042
\(43\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(44\) −0.400969 1.75676i −0.400969 1.75676i
\(45\) 0 0
\(46\) −0.400969 1.75676i −0.400969 1.75676i
\(47\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(48\) 0.445042 0.445042
\(49\) −0.900969 + 0.433884i −0.900969 + 0.433884i
\(50\) 1.00000 1.00000
\(51\) −0.400969 0.193096i −0.400969 0.193096i
\(52\) 0.400969 + 1.75676i 0.400969 + 1.75676i
\(53\) −0.277479 0.347948i −0.277479 0.347948i 0.623490 0.781831i \(-0.285714\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(54\) 0.178448 + 0.781831i 0.178448 + 0.781831i
\(55\) 0 0
\(56\) 0.900969 0.433884i 0.900969 0.433884i
\(57\) 0 0
\(58\) 0 0
\(59\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(60\) 0 0
\(61\) 0 0 0.623490 0.781831i \(-0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(62\) −0.400969 0.193096i −0.400969 0.193096i
\(63\) 0.500000 + 0.626980i 0.500000 + 0.626980i
\(64\) −0.900969 + 0.433884i −0.900969 + 0.433884i
\(65\) 0 0
\(66\) 0.500000 0.626980i 0.500000 0.626980i
\(67\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(68\) 1.00000 1.00000
\(69\) 0.500000 0.626980i 0.500000 0.626980i
\(70\) 0 0
\(71\) 0.277479 + 0.347948i 0.277479 + 0.347948i 0.900969 0.433884i \(-0.142857\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(72\) −0.500000 0.626980i −0.500000 0.626980i
\(73\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(74\) 0 0
\(75\) 0.277479 + 0.347948i 0.277479 + 0.347948i
\(76\) 0 0
\(77\) 0.400969 1.75676i 0.400969 1.75676i
\(78\) −0.500000 + 0.626980i −0.500000 + 0.626980i
\(79\) 1.80194 1.80194 0.900969 0.433884i \(-0.142857\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(80\) 0 0
\(81\) 0.277479 0.347948i 0.277479 0.347948i
\(82\) 0 0
\(83\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(84\) 0.400969 + 0.193096i 0.400969 + 0.193096i
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) −0.400969 + 1.75676i −0.400969 + 1.75676i
\(89\) 0.400969 0.193096i 0.400969 0.193096i −0.222521 0.974928i \(-0.571429\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(90\) 0 0
\(91\) −0.400969 + 1.75676i −0.400969 + 1.75676i
\(92\) −0.400969 + 1.75676i −0.400969 + 1.75676i
\(93\) −0.0440730 0.193096i −0.0440730 0.193096i
\(94\) 0 0
\(95\) 0 0
\(96\) −0.400969 0.193096i −0.400969 0.193096i
\(97\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(98\) 1.00000 1.00000
\(99\) −1.44504 −1.44504
\(100\) −0.900969 0.433884i −0.900969 0.433884i
\(101\) 0.400969 + 1.75676i 0.400969 + 1.75676i 0.623490 + 0.781831i \(0.285714\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(102\) 0.277479 + 0.347948i 0.277479 + 0.347948i
\(103\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(104\) 0.400969 1.75676i 0.400969 1.75676i
\(105\) 0 0
\(106\) 0.0990311 + 0.433884i 0.0990311 + 0.433884i
\(107\) 1.12349 0.541044i 1.12349 0.541044i 0.222521 0.974928i \(-0.428571\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(108\) 0.178448 0.781831i 0.178448 0.781831i
\(109\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) −1.00000 −1.00000
\(113\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 1.44504 1.44504
\(118\) 0 0
\(119\) 0.900969 + 0.433884i 0.900969 + 0.433884i
\(120\) 0 0
\(121\) 1.40097 + 1.75676i 1.40097 + 1.75676i
\(122\) 0 0
\(123\) 0 0
\(124\) 0.277479 + 0.347948i 0.277479 + 0.347948i
\(125\) 0 0
\(126\) −0.178448 0.781831i −0.178448 0.781831i
\(127\) 0 0 0.623490 0.781831i \(-0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(128\) 1.00000 1.00000
\(129\) 0 0
\(130\) 0 0
\(131\) −0.400969 + 1.75676i −0.400969 + 1.75676i 0.222521 + 0.974928i \(0.428571\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(132\) −0.722521 + 0.347948i −0.722521 + 0.347948i
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) −0.900969 0.433884i −0.900969 0.433884i
\(137\) 0.0990311 0.433884i 0.0990311 0.433884i −0.900969 0.433884i \(-0.857143\pi\)
1.00000 \(0\)
\(138\) −0.722521 + 0.347948i −0.722521 + 0.347948i
\(139\) −0.400969 1.75676i −0.400969 1.75676i −0.623490 0.781831i \(-0.714286\pi\)
0.222521 0.974928i \(-0.428571\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −0.0990311 0.433884i −0.0990311 0.433884i
\(143\) −2.02446 2.53859i −2.02446 2.53859i
\(144\) 0.178448 + 0.781831i 0.178448 + 0.781831i
\(145\) 0 0
\(146\) 0 0
\(147\) 0.277479 + 0.347948i 0.277479 + 0.347948i
\(148\) 0 0
\(149\) 0.400969 + 0.193096i 0.400969 + 0.193096i 0.623490 0.781831i \(-0.285714\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(150\) −0.0990311 0.433884i −0.0990311 0.433884i
\(151\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(152\) 0 0
\(153\) 0.178448 0.781831i 0.178448 0.781831i
\(154\) −1.12349 + 1.40881i −1.12349 + 1.40881i
\(155\) 0 0
\(156\) 0.722521 0.347948i 0.722521 0.347948i
\(157\) 0.400969 1.75676i 0.400969 1.75676i −0.222521 0.974928i \(-0.571429\pi\)
0.623490 0.781831i \(-0.285714\pi\)
\(158\) −1.62349 0.781831i −1.62349 0.781831i
\(159\) −0.123490 + 0.154851i −0.123490 + 0.154851i
\(160\) 0 0
\(161\) −1.12349 + 1.40881i −1.12349 + 1.40881i
\(162\) −0.400969 + 0.193096i −0.400969 + 0.193096i
\(163\) 0.445042 1.94986i 0.445042 1.94986i 0.222521 0.974928i \(-0.428571\pi\)
0.222521 0.974928i \(-0.428571\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −0.777479 + 0.974928i −0.777479 + 0.974928i 0.222521 + 0.974928i \(0.428571\pi\)
−1.00000 \(\pi\)
\(168\) −0.277479 0.347948i −0.277479 0.347948i
\(169\) 1.40097 + 1.75676i 1.40097 + 1.75676i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(174\) 0 0
\(175\) −0.623490 0.781831i −0.623490 0.781831i
\(176\) 1.12349 1.40881i 1.12349 1.40881i
\(177\) 0 0
\(178\) −0.445042 −0.445042
\(179\) 0 0 0.623490 0.781831i \(-0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(180\) 0 0
\(181\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(182\) 1.12349 1.40881i 1.12349 1.40881i
\(183\) 0 0
\(184\) 1.12349 1.40881i 1.12349 1.40881i
\(185\) 0 0
\(186\) −0.0440730 + 0.193096i −0.0440730 + 0.193096i
\(187\) −1.62349 + 0.781831i −1.62349 + 0.781831i
\(188\) 0 0
\(189\) 0.500000 0.626980i 0.500000 0.626980i
\(190\) 0 0
\(191\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(192\) 0.277479 + 0.347948i 0.277479 + 0.347948i
\(193\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) −0.900969 0.433884i −0.900969 0.433884i
\(197\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(198\) 1.30194 + 0.626980i 1.30194 + 0.626980i
\(199\) −0.0990311 0.433884i −0.0990311 0.433884i 0.900969 0.433884i \(-0.142857\pi\)
−1.00000 \(\pi\)
\(200\) 0.623490 + 0.781831i 0.623490 + 0.781831i
\(201\) 0 0
\(202\) 0.400969 1.75676i 0.400969 1.75676i
\(203\) 0 0
\(204\) −0.0990311 0.433884i −0.0990311 0.433884i
\(205\) 0 0
\(206\) 0 0
\(207\) 1.30194 + 0.626980i 1.30194 + 0.626980i
\(208\) −1.12349 + 1.40881i −1.12349 + 1.40881i
\(209\) 0 0
\(210\) 0 0
\(211\) 1.12349 0.541044i 1.12349 0.541044i 0.222521 0.974928i \(-0.428571\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(212\) 0.0990311 0.433884i 0.0990311 0.433884i
\(213\) 0.123490 0.154851i 0.123490 0.154851i
\(214\) −1.24698 −1.24698
\(215\) 0 0
\(216\) −0.500000 + 0.626980i −0.500000 + 0.626980i
\(217\) 0.0990311 + 0.433884i 0.0990311 + 0.433884i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 1.62349 0.781831i 1.62349 0.781831i
\(222\) 0 0
\(223\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(224\) 0.900969 + 0.433884i 0.900969 + 0.433884i
\(225\) −0.500000 + 0.626980i −0.500000 + 0.626980i
\(226\) 0 0
\(227\) 0.445042 0.445042 0.222521 0.974928i \(-0.428571\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(228\) 0 0
\(229\) −0.277479 + 1.21572i −0.277479 + 1.21572i 0.623490 + 0.781831i \(0.285714\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(230\) 0 0
\(231\) −0.801938 −0.801938
\(232\) 0 0
\(233\) 0 0 0.623490 0.781831i \(-0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(234\) −1.30194 0.626980i −1.30194 0.626980i
\(235\) 0 0
\(236\) 0 0
\(237\) −0.178448 0.781831i −0.178448 0.781831i
\(238\) −0.623490 0.781831i −0.623490 0.781831i
\(239\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(240\) 0 0
\(241\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(242\) −0.500000 2.19064i −0.500000 2.19064i
\(243\) −0.900969 0.433884i −0.900969 0.433884i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 0 0
\(248\) −0.0990311 0.433884i −0.0990311 0.433884i
\(249\) 0 0
\(250\) 0 0
\(251\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(252\) −0.178448 + 0.781831i −0.178448 + 0.781831i
\(253\) −0.722521 3.16557i −0.722521 3.16557i
\(254\) 0 0
\(255\) 0 0
\(256\) −0.900969 0.433884i −0.900969 0.433884i
\(257\) 1.24698 1.56366i 1.24698 1.56366i 0.623490 0.781831i \(-0.285714\pi\)
0.623490 0.781831i \(-0.285714\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) 1.12349 1.40881i 1.12349 1.40881i
\(263\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(264\) 0.801938 0.801938
\(265\) 0 0
\(266\) 0 0
\(267\) −0.123490 0.154851i −0.123490 0.154851i
\(268\) 0 0
\(269\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(270\) 0 0
\(271\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(272\) 0.623490 + 0.781831i 0.623490 + 0.781831i
\(273\) 0.801938 0.801938
\(274\) −0.277479 + 0.347948i −0.277479 + 0.347948i
\(275\) 1.80194 1.80194
\(276\) 0.801938 0.801938
\(277\) 0 0 0.623490 0.781831i \(-0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(278\) −0.400969 + 1.75676i −0.400969 + 1.75676i
\(279\) 0.321552 0.154851i 0.321552 0.154851i
\(280\) 0 0
\(281\) −1.80194 0.867767i −1.80194 0.867767i −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 0.433884i \(-0.857143\pi\)
\(282\) 0 0
\(283\) −1.62349 0.781831i −1.62349 0.781831i −0.623490 0.781831i \(-0.714286\pi\)
−1.00000 \(\pi\)
\(284\) −0.0990311 + 0.433884i −0.0990311 + 0.433884i
\(285\) 0 0
\(286\) 0.722521 + 3.16557i 0.722521 + 3.16557i
\(287\) 0 0
\(288\) 0.178448 0.781831i 0.178448 0.781831i
\(289\) −0.222521 0.974928i −0.222521 0.974928i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(294\) −0.0990311 0.433884i −0.0990311 0.433884i
\(295\) 0 0
\(296\) 0 0
\(297\) 0.321552 + 1.40881i 0.321552 + 1.40881i
\(298\) −0.277479 0.347948i −0.277479 0.347948i
\(299\) 0.722521 + 3.16557i 0.722521 + 3.16557i
\(300\) −0.0990311 + 0.433884i −0.0990311 + 0.433884i
\(301\) 0 0
\(302\) 0 0
\(303\) 0.722521 0.347948i 0.722521 0.347948i
\(304\) 0 0
\(305\) 0 0
\(306\) −0.500000 + 0.626980i −0.500000 + 0.626980i
\(307\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(308\) 1.62349 0.781831i 1.62349 0.781831i
\(309\) 0 0
\(310\) 0 0
\(311\) −1.24698 + 1.56366i −1.24698 + 1.56366i −0.623490 + 0.781831i \(0.714286\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(312\) −0.801938 −0.801938
\(313\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(314\) −1.12349 + 1.40881i −1.12349 + 1.40881i
\(315\) 0 0
\(316\) 1.12349 + 1.40881i 1.12349 + 1.40881i
\(317\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(318\) 0.178448 0.0859360i 0.178448 0.0859360i
\(319\) 0 0
\(320\) 0 0
\(321\) −0.346011 0.433884i −0.346011 0.433884i
\(322\) 1.62349 0.781831i 1.62349 0.781831i
\(323\) 0 0
\(324\) 0.445042 0.445042
\(325\) −1.80194 −1.80194
\(326\) −1.24698 + 1.56366i −1.24698 + 1.56366i
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 0 0 0.623490 0.781831i \(-0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 1.12349 0.541044i 1.12349 0.541044i
\(335\) 0 0
\(336\) 0.0990311 + 0.433884i 0.0990311 + 0.433884i
\(337\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(338\) −0.500000 2.19064i −0.500000 2.19064i
\(339\) 0 0
\(340\) 0 0
\(341\) −0.722521 0.347948i −0.722521 0.347948i
\(342\) 0 0
\(343\) −0.623490 0.781831i −0.623490 0.781831i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −0.777479 0.974928i −0.777479 0.974928i 0.222521 0.974928i \(-0.428571\pi\)
−1.00000 \(\pi\)
\(348\) 0 0
\(349\) −0.277479 + 1.21572i −0.277479 + 1.21572i 0.623490 + 0.781831i \(0.285714\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(350\) 0.222521 + 0.974928i 0.222521 + 0.974928i
\(351\) −0.321552 1.40881i −0.321552 1.40881i
\(352\) −1.62349 + 0.781831i −1.62349 + 0.781831i
\(353\) −0.445042 + 1.94986i −0.445042 + 1.94986i −0.222521 + 0.974928i \(0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0.400969 + 0.193096i 0.400969 + 0.193096i
\(357\) 0.0990311 0.433884i 0.0990311 0.433884i
\(358\) 0 0
\(359\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(360\) 0 0
\(361\) 1.00000 1.00000
\(362\) 0 0
\(363\) 0.623490 0.781831i 0.623490 0.781831i
\(364\) −1.62349 + 0.781831i −1.62349 + 0.781831i
\(365\) 0 0
\(366\) 0 0
\(367\) 1.12349 0.541044i 1.12349 0.541044i 0.222521 0.974928i \(-0.428571\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(368\) −1.62349 + 0.781831i −1.62349 + 0.781831i
\(369\) 0 0
\(370\) 0 0
\(371\) 0.277479 0.347948i 0.277479 0.347948i
\(372\) 0.123490 0.154851i 0.123490 0.154851i
\(373\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(374\) 1.80194 1.80194
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) −0.722521 + 0.347948i −0.722521 + 0.347948i
\(379\) 1.80194 + 0.867767i 1.80194 + 0.867767i 0.900969 + 0.433884i \(0.142857\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(384\) −0.0990311 0.433884i −0.0990311 0.433884i
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −0.277479 1.21572i −0.277479 1.21572i −0.900969 0.433884i \(-0.857143\pi\)
0.623490 0.781831i \(-0.285714\pi\)
\(390\) 0 0
\(391\) 1.80194 1.80194
\(392\) 0.623490 + 0.781831i 0.623490 + 0.781831i
\(393\) 0.801938 0.801938
\(394\) 0 0
\(395\) 0 0
\(396\) −0.900969 1.12978i −0.900969 1.12978i
\(397\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(398\) −0.0990311 + 0.433884i −0.0990311 + 0.433884i
\(399\) 0 0
\(400\) −0.222521 0.974928i −0.222521 0.974928i
\(401\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(402\) 0 0
\(403\) 0.722521 + 0.347948i 0.722521 + 0.347948i
\(404\) −1.12349 + 1.40881i −1.12349 + 1.40881i
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) −0.0990311 + 0.433884i −0.0990311 + 0.433884i
\(409\) −0.277479 + 0.347948i −0.277479 + 0.347948i −0.900969 0.433884i \(-0.857143\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(410\) 0 0
\(411\) −0.198062 −0.198062
\(412\) 0 0
\(413\) 0 0
\(414\) −0.900969 1.12978i −0.900969 1.12978i
\(415\) 0 0
\(416\) 1.62349 0.781831i 1.62349 0.781831i
\(417\) −0.722521 + 0.347948i −0.722521 + 0.347948i
\(418\) 0 0
\(419\) 1.12349 + 1.40881i 1.12349 + 1.40881i 0.900969 + 0.433884i \(0.142857\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(420\) 0 0
\(421\) −0.277479 + 0.347948i −0.277479 + 0.347948i −0.900969 0.433884i \(-0.857143\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(422\) −1.24698 −1.24698
\(423\) 0 0
\(424\) −0.277479 + 0.347948i −0.277479 + 0.347948i
\(425\) −0.222521 + 0.974928i −0.222521 + 0.974928i
\(426\) −0.178448 + 0.0859360i −0.178448 + 0.0859360i
\(427\) 0 0
\(428\) 1.12349 + 0.541044i 1.12349 + 0.541044i
\(429\) −0.900969 + 1.12978i −0.900969 + 1.12978i
\(430\) 0 0
\(431\) 0.445042 1.94986i 0.445042 1.94986i 0.222521 0.974928i \(-0.428571\pi\)
0.222521 0.974928i \(-0.428571\pi\)
\(432\) 0.722521 0.347948i 0.722521 0.347948i
\(433\) 0.400969 + 1.75676i 0.400969 + 1.75676i 0.623490 + 0.781831i \(0.285714\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(434\) 0.0990311 0.433884i 0.0990311 0.433884i
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) −1.62349 0.781831i −1.62349 0.781831i −0.623490 0.781831i \(-0.714286\pi\)
−1.00000 \(\pi\)
\(440\) 0 0
\(441\) −0.500000 + 0.626980i −0.500000 + 0.626980i
\(442\) −1.80194 −1.80194
\(443\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0.0440730 0.193096i 0.0440730 0.193096i
\(448\) −0.623490 0.781831i −0.623490 0.781831i
\(449\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(450\) 0.722521 0.347948i 0.722521 0.347948i
\(451\) 0 0
\(452\) 0 0
\(453\) 0 0
\(454\) −0.400969 0.193096i −0.400969 0.193096i
\(455\) 0 0
\(456\) 0 0
\(457\) 0.400969 1.75676i 0.400969 1.75676i −0.222521 0.974928i \(-0.571429\pi\)
0.623490 0.781831i \(-0.285714\pi\)
\(458\) 0.777479 0.974928i 0.777479 0.974928i
\(459\) −0.801938 −0.801938
\(460\) 0 0
\(461\) −0.277479 + 0.347948i −0.277479 + 0.347948i −0.900969 0.433884i \(-0.857143\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(462\) 0.722521 + 0.347948i 0.722521 + 0.347948i
\(463\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(468\) 0.900969 + 1.12978i 0.900969 + 1.12978i
\(469\) 0 0
\(470\) 0 0
\(471\) −0.801938 −0.801938
\(472\) 0 0
\(473\) 0 0
\(474\) −0.178448 + 0.781831i −0.178448 + 0.781831i
\(475\) 0 0
\(476\) 0.222521 + 0.974928i 0.222521 + 0.974928i
\(477\) −0.321552 0.154851i −0.321552 0.154851i
\(478\) 0 0
\(479\) −1.62349 0.781831i −1.62349 0.781831i −0.623490 0.781831i \(-0.714286\pi\)
−1.00000 \(\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 0.722521 + 0.347948i 0.722521 + 0.347948i
\(484\) −0.500000 + 2.19064i −0.500000 + 2.19064i
\(485\) 0 0
\(486\) 0.623490 + 0.781831i 0.623490 + 0.781831i
\(487\) 0.445042 + 1.94986i 0.445042 + 1.94986i 0.222521 + 0.974928i \(0.428571\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(488\) 0 0
\(489\) −0.890084 −0.890084
\(490\) 0 0
\(491\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) −0.0990311 + 0.433884i −0.0990311 + 0.433884i
\(497\) −0.277479 + 0.347948i −0.277479 + 0.347948i
\(498\) 0 0
\(499\) −1.62349 + 0.781831i −1.62349 + 0.781831i −0.623490 + 0.781831i \(0.714286\pi\)
−1.00000 \(1.00000\pi\)
\(500\) 0 0
\(501\) 0.500000 + 0.240787i 0.500000 + 0.240787i
\(502\) 0 0
\(503\) 1.12349 + 0.541044i 1.12349 + 0.541044i 0.900969 0.433884i \(-0.142857\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(504\) 0.500000 0.626980i 0.500000 0.626980i
\(505\) 0 0
\(506\) −0.722521 + 3.16557i −0.722521 + 3.16557i
\(507\) 0.623490 0.781831i 0.623490 0.781831i
\(508\) 0 0
\(509\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0.623490 + 0.781831i 0.623490 + 0.781831i
\(513\) 0 0
\(514\) −1.80194 + 0.867767i −1.80194 + 0.867767i
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(522\) 0 0
\(523\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(524\) −1.62349 + 0.781831i −1.62349 + 0.781831i
\(525\) −0.277479 + 0.347948i −0.277479 + 0.347948i
\(526\) 0 0
\(527\) 0.277479 0.347948i 0.277479 0.347948i
\(528\) −0.722521 0.347948i −0.722521 0.347948i
\(529\) −0.500000 + 2.19064i −0.500000 + 2.19064i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) 0.0440730 + 0.193096i 0.0440730 + 0.193096i
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 1.80194 1.80194
\(540\) 0 0
\(541\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) −0.222521 0.974928i −0.222521 0.974928i
\(545\) 0 0
\(546\) −0.722521 0.347948i −0.722521 0.347948i
\(547\) 0.277479 + 1.21572i 0.277479 + 1.21572i 0.900969 + 0.433884i \(0.142857\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(548\) 0.400969 0.193096i 0.400969 0.193096i
\(549\) 0 0
\(550\) −1.62349 0.781831i −1.62349 0.781831i
\(551\) 0 0
\(552\) −0.722521 0.347948i −0.722521 0.347948i
\(553\) 0.400969 + 1.75676i 0.400969 + 1.75676i
\(554\) 0 0
\(555\) 0 0
\(556\) 1.12349 1.40881i 1.12349 1.40881i
\(557\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(558\) −0.356896 −0.356896
\(559\) 0 0
\(560\) 0 0
\(561\) 0.500000 + 0.626980i 0.500000 + 0.626980i
\(562\) 1.24698 + 1.56366i 1.24698 + 1.56366i
\(563\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 1.12349 + 1.40881i 1.12349 + 1.40881i
\(567\) 0.400969 + 0.193096i 0.400969 + 0.193096i
\(568\) 0.277479 0.347948i 0.277479 0.347948i
\(569\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(570\) 0 0
\(571\) 0.277479 0.347948i 0.277479 0.347948i −0.623490 0.781831i \(-0.714286\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(572\) 0.722521 3.16557i 0.722521 3.16557i
\(573\) 0 0
\(574\) 0 0
\(575\) −1.62349 0.781831i −1.62349 0.781831i
\(576\) −0.500000 + 0.626980i −0.500000 + 0.626980i
\(577\) −1.12349 0.541044i −1.12349 0.541044i −0.222521 0.974928i \(-0.571429\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(578\) −0.222521 + 0.974928i −0.222521 + 0.974928i
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0.178448 + 0.781831i 0.178448 + 0.781831i
\(584\) 0 0
\(585\) 0 0
\(586\) 1.62349 + 0.781831i 1.62349 + 0.781831i
\(587\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(588\) −0.0990311 + 0.433884i −0.0990311 + 0.433884i
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −0.277479 1.21572i −0.277479 1.21572i −0.900969 0.433884i \(-0.857143\pi\)
0.623490 0.781831i \(-0.285714\pi\)
\(594\) 0.321552 1.40881i 0.321552 1.40881i
\(595\) 0 0
\(596\) 0.0990311 + 0.433884i 0.0990311 + 0.433884i
\(597\) −0.178448 + 0.0859360i −0.178448 + 0.0859360i
\(598\) 0.722521 3.16557i 0.722521 3.16557i
\(599\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(600\) 0.277479 0.347948i 0.277479 0.347948i
\(601\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 0 0
\(606\) −0.801938 −0.801938
\(607\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0.722521 0.347948i 0.722521 0.347948i
\(613\) −1.12349 + 0.541044i −1.12349 + 0.541044i −0.900969 0.433884i \(-0.857143\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) −1.80194 −1.80194
\(617\) 0 0 0.623490 0.781831i \(-0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(618\) 0 0
\(619\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(620\) 0 0
\(621\) 0.321552 1.40881i 0.321552 1.40881i
\(622\) 1.80194 0.867767i 1.80194 0.867767i
\(623\) 0.277479 + 0.347948i 0.277479 + 0.347948i
\(624\) 0.722521 + 0.347948i 0.722521 + 0.347948i
\(625\) 0.623490 0.781831i 0.623490 0.781831i
\(626\) 0 0
\(627\) 0 0
\(628\) 1.62349 0.781831i 1.62349 0.781831i
\(629\) 0 0
\(630\) 0 0
\(631\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(632\) −0.400969 1.75676i −0.400969 1.75676i
\(633\) −0.346011 0.433884i −0.346011 0.433884i
\(634\) 0 0
\(635\) 0 0
\(636\) −0.198062 −0.198062
\(637\) −1.80194 −1.80194
\(638\) 0 0
\(639\) 0.321552 + 0.154851i 0.321552 + 0.154851i
\(640\) 0 0
\(641\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(642\) 0.123490 + 0.541044i 0.123490 + 0.541044i
\(643\) 0.277479 1.21572i 0.277479 1.21572i −0.623490 0.781831i \(-0.714286\pi\)
0.900969 0.433884i \(-0.142857\pi\)
\(644\) −1.80194 −1.80194
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(648\) −0.400969 0.193096i −0.400969 0.193096i
\(649\) 0 0
\(650\) 1.62349 + 0.781831i 1.62349 + 0.781831i
\(651\) 0.178448 0.0859360i 0.178448 0.0859360i
\(652\) 1.80194 0.867767i 1.80194 0.867767i
\(653\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(660\) 0 0
\(661\) 0.400969 0.193096i 0.400969 0.193096i −0.222521 0.974928i \(-0.571429\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(662\) 0 0
\(663\) −0.500000 0.626980i −0.500000 0.626980i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) −1.24698 −1.24698
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0.0990311 0.433884i 0.0990311 0.433884i
\(673\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(674\) 0 0
\(675\) 0.722521 + 0.347948i 0.722521 + 0.347948i
\(676\) −0.500000 + 2.19064i −0.500000 + 2.19064i
\(677\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) −0.0440730 0.193096i −0.0440730 0.193096i
\(682\) 0.500000 + 0.626980i 0.500000 + 0.626980i
\(683\) −0.0990311 0.433884i −0.0990311 0.433884i 0.900969 0.433884i \(-0.142857\pi\)
−1.00000 \(\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0.222521 + 0.974928i 0.222521 + 0.974928i
\(687\) 0.554958 0.554958
\(688\) 0 0
\(689\) −0.178448 0.781831i −0.178448 0.781831i
\(690\) 0 0
\(691\) −0.0990311 0.433884i −0.0990311 0.433884i 0.900969 0.433884i \(-0.142857\pi\)
−1.00000 \(\pi\)
\(692\) 0 0
\(693\) −0.321552 1.40881i −0.321552 1.40881i
\(694\) 0.277479 + 1.21572i 0.277479 + 1.21572i
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0.777479 0.974928i 0.777479 0.974928i
\(699\) 0 0
\(700\) 0.222521 0.974928i 0.222521 0.974928i
\(701\) 0.400969 0.193096i 0.400969 0.193096i −0.222521 0.974928i \(-0.571429\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(702\) −0.321552 + 1.40881i −0.321552 + 1.40881i
\(703\) 0 0
\(704\) 1.80194 1.80194
\(705\) 0 0
\(706\) 1.24698 1.56366i 1.24698 1.56366i
\(707\) −1.62349 + 0.781831i −1.62349 + 0.781831i
\(708\) 0 0
\(709\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(710\) 0 0
\(711\) 1.30194 0.626980i 1.30194 0.626980i
\(712\) −0.277479 0.347948i −0.277479 0.347948i
\(713\) 0.500000 + 0.626980i 0.500000 + 0.626980i
\(714\) −0.277479 + 0.347948i −0.277479 + 0.347948i
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −0.400969 + 1.75676i −0.400969 + 1.75676i 0.222521 + 0.974928i \(0.428571\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −0.900969 0.433884i −0.900969 0.433884i
\(723\) 0 0
\(724\) 0 0
\(725\) 0 0
\(726\) −0.900969 + 0.433884i −0.900969 + 0.433884i
\(727\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(728\) 1.80194 1.80194
\(729\) 0 0
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) −1.80194 0.867767i −1.80194 0.867767i −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 0.433884i \(-0.857143\pi\)
\(734\) −1.24698 −1.24698
\(735\) 0 0
\(736\) 1.80194 1.80194
\(737\) 0 0
\(738\) 0 0
\(739\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) −0.400969 + 0.193096i −0.400969 + 0.193096i
\(743\) −0.0990311 0.433884i −0.0990311 0.433884i 0.900969 0.433884i \(-0.142857\pi\)
−1.00000 \(\pi\)
\(744\) −0.178448 + 0.0859360i −0.178448 + 0.0859360i
\(745\) 0 0
\(746\) 1.62349 + 0.781831i 1.62349 + 0.781831i
\(747\) 0 0
\(748\) −1.62349 0.781831i −1.62349 0.781831i
\(749\) 0.777479 + 0.974928i 0.777479 + 0.974928i
\(750\) 0 0
\(751\) −0.400969 + 1.75676i −0.400969 + 1.75676i 0.222521 + 0.974928i \(0.428571\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 0.801938 0.801938
\(757\) 1.24698 + 1.56366i 1.24698 + 1.56366i 0.623490 + 0.781831i \(0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(758\) −1.24698 1.56366i −1.24698 1.56366i
\(759\) −1.30194 + 0.626980i −1.30194 + 0.626980i
\(760\) 0 0
\(761\) 0.777479 + 0.974928i 0.777479 + 0.974928i 1.00000 \(0\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) −0.0990311 + 0.433884i −0.0990311 + 0.433884i
\(769\) −1.80194 + 0.867767i −1.80194 + 0.867767i −0.900969 + 0.433884i \(0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(770\) 0 0
\(771\) −0.801938 0.386193i −0.801938 0.386193i
\(772\) 0 0
\(773\) −1.12349 0.541044i −1.12349 0.541044i −0.222521 0.974928i \(-0.571429\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(774\) 0 0
\(775\) −0.400969 + 0.193096i −0.400969 + 0.193096i
\(776\) 0 0
\(777\) 0 0
\(778\) −0.277479 + 1.21572i −0.277479 + 1.21572i
\(779\) 0 0
\(780\) 0 0
\(781\) −0.178448 0.781831i −0.178448 0.781831i
\(782\) −1.62349 0.781831i −1.62349 0.781831i
\(783\) 0 0
\(784\) −0.222521 0.974928i −0.222521 0.974928i
\(785\) 0 0
\(786\) −0.722521 0.347948i −0.722521 0.347948i
\(787\) 0.277479 + 1.21572i 0.277479 + 1.21572i 0.900969 + 0.433884i \(0.142857\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0.321552 + 1.40881i 0.321552 + 1.40881i