Properties

Label 2001.1.bf.c.965.2
Level $2001$
Weight $1$
Character 2001.965
Analytic conductor $0.999$
Analytic rank $0$
Dimension $24$
Projective image $D_{84}$
CM discriminant -23
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 2001 = 3 \cdot 23 \cdot 29 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 2001.bf (of order \(28\), degree \(12\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.998629090279\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(2\) over \(\Q(\zeta_{28})\)
Coefficient field: \(\Q(\zeta_{84})\)
Defining polynomial: \(x^{24} + x^{22} - x^{18} - x^{16} + x^{12} - x^{8} - x^{6} + x^{2} + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Projective image: \(D_{84}\)
Projective field: Galois closure of \(\mathbb{Q}[x]/(x^{84} - \cdots)\)

Embedding invariants

Embedding label 965.2
Root \(0.930874 + 0.365341i\) of defining polynomial
Character \(\chi\) \(=\) 2001.965
Dual form 2001.1.bf.c.620.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500684 - 1.43087i) q^{2} +(0.955573 + 0.294755i) q^{3} +(-1.01488 - 0.809342i) q^{4} +(0.900198 - 1.21972i) q^{6} +(-0.382617 + 0.240414i) q^{8} +(0.826239 + 0.563320i) q^{9} +O(q^{10})\) \(q+(0.500684 - 1.43087i) q^{2} +(0.955573 + 0.294755i) q^{3} +(-1.01488 - 0.809342i) q^{4} +(0.900198 - 1.21972i) q^{6} +(-0.382617 + 0.240414i) q^{8} +(0.826239 + 0.563320i) q^{9} +(-0.731237 - 1.07253i) q^{12} +(0.145713 - 0.0332580i) q^{13} +(-0.136419 - 0.597690i) q^{16} +(1.21972 - 0.900198i) q^{18} +(-0.433884 + 0.900969i) q^{23} +(-0.436482 + 0.116955i) q^{24} +(0.623490 - 0.781831i) q^{25} +(0.0253681 - 0.225149i) q^{26} +(0.623490 + 0.781831i) q^{27} +(-0.930874 + 0.365341i) q^{29} +(0.488590 + 0.170965i) q^{31} +(-1.37256 - 0.154650i) q^{32} +(-0.382617 - 1.24041i) q^{36} +(0.149042 + 0.0111692i) q^{39} +(-1.41322 - 1.41322i) q^{41} +(1.07193 + 1.07193i) q^{46} +(0.425511 - 0.677197i) q^{47} +(0.0458141 - 0.611347i) q^{48} +(-0.222521 + 0.974928i) q^{49} +(-0.806531 - 1.28359i) q^{50} +(-0.174799 - 0.0841786i) q^{52} +(1.43087 - 0.500684i) q^{54} +(0.0566829 + 1.51488i) q^{58} +1.24698i q^{59} +(0.489259 - 0.613511i) q^{62} +(-0.642507 + 1.33418i) q^{64} +(-0.680173 + 0.733052i) q^{69} +(-0.250701 - 1.09839i) q^{71} +(-0.451563 - 0.0168963i) q^{72} +(-1.12099 + 0.392253i) q^{73} +(0.826239 - 0.563320i) q^{75} +(0.0906048 - 0.207668i) q^{78} +(0.365341 + 0.930874i) q^{81} +(-2.72973 + 1.31457i) q^{82} +(-0.997204 + 0.0747301i) q^{87} +(1.16953 - 0.563218i) q^{92} +(0.416490 + 0.307384i) q^{93} +(-0.755936 - 0.947914i) q^{94} +(-1.26600 - 0.552349i) q^{96} +(1.28359 + 0.806531i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q - 2q^{2} + 2q^{3} + 14q^{4} - 2q^{6} + 6q^{8} + 2q^{9} + O(q^{10}) \) \( 24q - 2q^{2} + 2q^{3} + 14q^{4} - 2q^{6} + 6q^{8} + 2q^{9} - 6q^{12} - 6q^{16} + 4q^{18} - 6q^{24} - 4q^{25} + 2q^{26} - 4q^{27} - 2q^{31} + 4q^{32} + 6q^{36} + 2q^{41} + 2q^{46} - 2q^{47} - 4q^{48} - 4q^{49} - 2q^{50} - 10q^{52} + 12q^{54} + 4q^{58} + 4q^{62} - 28q^{64} + 14q^{72} - 2q^{73} + 2q^{75} + 10q^{78} + 2q^{81} - 4q^{82} + 4q^{92} - 2q^{93} - 8q^{94} - 24q^{96} - 2q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2001\mathbb{Z}\right)^\times\).

\(n\) \(553\) \(668\) \(1132\)
\(\chi(n)\) \(e\left(\frac{3}{28}\right)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500684 1.43087i 0.500684 1.43087i −0.365341 0.930874i \(-0.619048\pi\)
0.866025 0.500000i \(-0.166667\pi\)
\(3\) 0.955573 + 0.294755i 0.955573 + 0.294755i
\(4\) −1.01488 0.809342i −1.01488 0.809342i
\(5\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(6\) 0.900198 1.21972i 0.900198 1.21972i
\(7\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(8\) −0.382617 + 0.240414i −0.382617 + 0.240414i
\(9\) 0.826239 + 0.563320i 0.826239 + 0.563320i
\(10\) 0 0
\(11\) 0 0 −0.846724 0.532032i \(-0.821429\pi\)
0.846724 + 0.532032i \(0.178571\pi\)
\(12\) −0.731237 1.07253i −0.731237 1.07253i
\(13\) 0.145713 0.0332580i 0.145713 0.0332580i −0.149042 0.988831i \(-0.547619\pi\)
0.294755 + 0.955573i \(0.404762\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −0.136419 0.597690i −0.136419 0.597690i
\(17\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(18\) 1.21972 0.900198i 1.21972 0.900198i
\(19\) 0 0 0.993712 0.111964i \(-0.0357143\pi\)
−0.993712 + 0.111964i \(0.964286\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −0.433884 + 0.900969i −0.433884 + 0.900969i
\(24\) −0.436482 + 0.116955i −0.436482 + 0.116955i
\(25\) 0.623490 0.781831i 0.623490 0.781831i
\(26\) 0.0253681 0.225149i 0.0253681 0.225149i
\(27\) 0.623490 + 0.781831i 0.623490 + 0.781831i
\(28\) 0 0
\(29\) −0.930874 + 0.365341i −0.930874 + 0.365341i
\(30\) 0 0
\(31\) 0.488590 + 0.170965i 0.488590 + 0.170965i 0.563320 0.826239i \(-0.309524\pi\)
−0.0747301 + 0.997204i \(0.523810\pi\)
\(32\) −1.37256 0.154650i −1.37256 0.154650i
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) −0.382617 1.24041i −0.382617 1.24041i
\(37\) 0 0 −0.532032 0.846724i \(-0.678571\pi\)
0.532032 + 0.846724i \(0.321429\pi\)
\(38\) 0 0
\(39\) 0.149042 + 0.0111692i 0.149042 + 0.0111692i
\(40\) 0 0
\(41\) −1.41322 1.41322i −1.41322 1.41322i −0.733052 0.680173i \(-0.761905\pi\)
−0.680173 0.733052i \(-0.738095\pi\)
\(42\) 0 0
\(43\) 0 0 −0.330279 0.943883i \(-0.607143\pi\)
0.330279 + 0.943883i \(0.392857\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 1.07193 + 1.07193i 1.07193 + 1.07193i
\(47\) 0.425511 0.677197i 0.425511 0.677197i −0.563320 0.826239i \(-0.690476\pi\)
0.988831 + 0.149042i \(0.0476190\pi\)
\(48\) 0.0458141 0.611347i 0.0458141 0.611347i
\(49\) −0.222521 + 0.974928i −0.222521 + 0.974928i
\(50\) −0.806531 1.28359i −0.806531 1.28359i
\(51\) 0 0
\(52\) −0.174799 0.0841786i −0.174799 0.0841786i
\(53\) 0 0 −0.433884 0.900969i \(-0.642857\pi\)
0.433884 + 0.900969i \(0.357143\pi\)
\(54\) 1.43087 0.500684i 1.43087 0.500684i
\(55\) 0 0
\(56\) 0 0
\(57\) 0 0
\(58\) 0.0566829 + 1.51488i 0.0566829 + 1.51488i
\(59\) 1.24698i 1.24698i 0.781831 + 0.623490i \(0.214286\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(60\) 0 0
\(61\) 0 0 0.111964 0.993712i \(-0.464286\pi\)
−0.111964 + 0.993712i \(0.535714\pi\)
\(62\) 0.489259 0.613511i 0.489259 0.613511i
\(63\) 0 0
\(64\) −0.642507 + 1.33418i −0.642507 + 1.33418i
\(65\) 0 0
\(66\) 0 0
\(67\) 0 0 −0.974928 0.222521i \(-0.928571\pi\)
0.974928 + 0.222521i \(0.0714286\pi\)
\(68\) 0 0
\(69\) −0.680173 + 0.733052i −0.680173 + 0.733052i
\(70\) 0 0
\(71\) −0.250701 1.09839i −0.250701 1.09839i −0.930874 0.365341i \(-0.880952\pi\)
0.680173 0.733052i \(-0.261905\pi\)
\(72\) −0.451563 0.0168963i −0.451563 0.0168963i
\(73\) −1.12099 + 0.392253i −1.12099 + 0.392253i −0.826239 0.563320i \(-0.809524\pi\)
−0.294755 + 0.955573i \(0.595238\pi\)
\(74\) 0 0
\(75\) 0.826239 0.563320i 0.826239 0.563320i
\(76\) 0 0
\(77\) 0 0
\(78\) 0.0906048 0.207668i 0.0906048 0.207668i
\(79\) 0 0 0.846724 0.532032i \(-0.178571\pi\)
−0.846724 + 0.532032i \(0.821429\pi\)
\(80\) 0 0
\(81\) 0.365341 + 0.930874i 0.365341 + 0.930874i
\(82\) −2.72973 + 1.31457i −2.72973 + 1.31457i
\(83\) 0 0 −0.781831 0.623490i \(-0.785714\pi\)
0.781831 + 0.623490i \(0.214286\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −0.997204 + 0.0747301i −0.997204 + 0.0747301i
\(88\) 0 0
\(89\) 0 0 0.330279 0.943883i \(-0.392857\pi\)
−0.330279 + 0.943883i \(0.607143\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 1.16953 0.563218i 1.16953 0.563218i
\(93\) 0.416490 + 0.307384i 0.416490 + 0.307384i
\(94\) −0.755936 0.947914i −0.755936 0.947914i
\(95\) 0 0
\(96\) −1.26600 0.552349i −1.26600 0.552349i
\(97\) 0 0 −0.111964 0.993712i \(-0.535714\pi\)
0.111964 + 0.993712i \(0.464286\pi\)
\(98\) 1.28359 + 0.806531i 1.28359 + 0.806531i
\(99\) 0 0
\(100\) −1.26554 + 0.288851i −1.26554 + 0.288851i
\(101\) −1.87590 + 0.656405i −1.87590 + 0.656405i −0.900969 + 0.433884i \(0.857143\pi\)
−0.974928 + 0.222521i \(0.928571\pi\)
\(102\) 0 0
\(103\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(104\) −0.0477566 + 0.0477566i −0.0477566 + 0.0477566i
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 −0.974928 0.222521i \(-0.928571\pi\)
0.974928 + 0.222521i \(0.0714286\pi\)
\(108\) 1.29808i 1.29808i
\(109\) 0 0 0.781831 0.623490i \(-0.214286\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 0 0 0.111964 0.993712i \(-0.464286\pi\)
−0.111964 + 0.993712i \(0.535714\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 1.24041 + 0.382617i 1.24041 + 0.382617i
\(117\) 0.139129 + 0.0546039i 0.139129 + 0.0546039i
\(118\) 1.78427 + 0.624343i 1.78427 + 0.624343i
\(119\) 0 0
\(120\) 0 0
\(121\) 0.433884 + 0.900969i 0.433884 + 0.900969i
\(122\) 0 0
\(123\) −0.933884 1.76699i −0.933884 1.76699i
\(124\) −0.357493 0.568946i −0.357493 0.568946i
\(125\) 0 0
\(126\) 0 0
\(127\) −0.497204 + 0.791295i −0.497204 + 0.791295i −0.997204 0.0747301i \(-0.976190\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(128\) 0.610662 + 0.610662i 0.610662 + 0.610662i
\(129\) 0 0
\(130\) 0 0
\(131\) 0.430874 + 1.23137i 0.430874 + 1.23137i 0.930874 + 0.365341i \(0.119048\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 0 0 −0.532032 0.846724i \(-0.678571\pi\)
0.532032 + 0.846724i \(0.321429\pi\)
\(138\) 0.708353 + 1.34027i 0.708353 + 1.34027i
\(139\) 1.01507 + 0.488831i 1.01507 + 0.488831i 0.866025 0.500000i \(-0.166667\pi\)
0.149042 + 0.988831i \(0.452381\pi\)
\(140\) 0 0
\(141\) 0.606214 0.521689i 0.606214 0.521689i
\(142\) −1.69718 0.191227i −1.69718 0.191227i
\(143\) 0 0
\(144\) 0.223976 0.570682i 0.223976 0.570682i
\(145\) 0 0
\(146\) 1.80040i 1.80040i
\(147\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(148\) 0 0
\(149\) 0 0 0.623490 0.781831i \(-0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(150\) −0.392355 1.46429i −0.392355 1.46429i
\(151\) 0.433884 0.900969i 0.433884 0.900969i −0.563320 0.826239i \(-0.690476\pi\)
0.997204 0.0747301i \(-0.0238095\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) −0.142221 0.131962i −0.142221 0.131962i
\(157\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) 1.51488 0.0566829i 1.51488 0.0566829i
\(163\) 0.677197 + 0.425511i 0.677197 + 0.425511i 0.826239 0.563320i \(-0.190476\pi\)
−0.149042 + 0.988831i \(0.547619\pi\)
\(164\) 0.290475 + 2.57804i 0.290475 + 2.57804i
\(165\) 0 0
\(166\) 0 0
\(167\) −1.12349 1.40881i −1.12349 1.40881i −0.900969 0.433884i \(-0.857143\pi\)
−0.222521 0.974928i \(-0.571429\pi\)
\(168\) 0 0
\(169\) −0.880843 + 0.424191i −0.880843 + 0.424191i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 0.445042 0.445042 0.222521 0.974928i \(-0.428571\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(174\) −0.392355 + 1.46429i −0.392355 + 1.46429i
\(175\) 0 0
\(176\) 0 0
\(177\) −0.367554 + 1.19158i −0.367554 + 1.19158i
\(178\) 0 0
\(179\) 1.72188 0.829215i 1.72188 0.829215i 0.733052 0.680173i \(-0.238095\pi\)
0.988831 0.149042i \(-0.0476190\pi\)
\(180\) 0 0
\(181\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −0.0505944 0.449038i −0.0505944 0.449038i
\(185\) 0 0
\(186\) 0.648358 0.442043i 0.648358 0.442043i
\(187\) 0 0
\(188\) −0.979928 + 0.342892i −0.979928 + 0.342892i
\(189\) 0 0
\(190\) 0 0
\(191\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(192\) −1.00722 + 1.08552i −1.00722 + 1.08552i
\(193\) 1.59908 0.180173i 1.59908 0.180173i 0.733052 0.680173i \(-0.238095\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 1.01488 0.809342i 1.01488 0.809342i
\(197\) −0.751509 + 1.56052i −0.751509 + 1.56052i 0.0747301 + 0.997204i \(0.476190\pi\)
−0.826239 + 0.563320i \(0.809524\pi\)
\(198\) 0 0
\(199\) 0 0 0.623490 0.781831i \(-0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(200\) −0.0505944 + 0.449038i −0.0505944 + 0.449038i
\(201\) 0 0
\(202\) 3.01282i 3.01282i
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(208\) −0.0397560 0.0825542i −0.0397560 0.0825542i
\(209\) 0 0
\(210\) 0 0
\(211\) −0.752407 1.19745i −0.752407 1.19745i −0.974928 0.222521i \(-0.928571\pi\)
0.222521 0.974928i \(-0.428571\pi\)
\(212\) 0 0
\(213\) 0.0841939 1.12349i 0.0841939 1.12349i
\(214\) 0 0
\(215\) 0 0
\(216\) −0.426521 0.149246i −0.426521 0.149246i
\(217\) 0 0
\(218\) 0 0
\(219\) −1.18681 + 0.0444073i −1.18681 + 0.0444073i
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) −0.0990311 + 0.433884i −0.0990311 + 0.433884i 0.900969 + 0.433884i \(0.142857\pi\)
−1.00000 \(\pi\)
\(224\) 0 0
\(225\) 0.955573 0.294755i 0.955573 0.294755i
\(226\) 0 0
\(227\) 0 0 −0.433884 0.900969i \(-0.642857\pi\)
0.433884 + 0.900969i \(0.357143\pi\)
\(228\) 0 0
\(229\) 0 0 −0.993712 0.111964i \(-0.964286\pi\)
0.993712 + 0.111964i \(0.0357143\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0.268335 0.363581i 0.268335 0.363581i
\(233\) 1.46610i 1.46610i 0.680173 + 0.733052i \(0.261905\pi\)
−0.680173 + 0.733052i \(0.738095\pi\)
\(234\) 0.147791 0.171736i 0.147791 0.171736i
\(235\) 0 0
\(236\) 1.00923 1.26554i 1.00923 1.26554i
\(237\) 0 0
\(238\) 0 0
\(239\) −1.06356 + 0.848162i −1.06356 + 0.848162i −0.988831 0.149042i \(-0.952381\pi\)
−0.0747301 + 0.997204i \(0.523810\pi\)
\(240\) 0 0
\(241\) 0 0 −0.974928 0.222521i \(-0.928571\pi\)
0.974928 + 0.222521i \(0.0714286\pi\)
\(242\) 1.50641 0.169732i 1.50641 0.169732i
\(243\) 0.0747301 + 0.997204i 0.0747301 + 0.997204i
\(244\) 0 0
\(245\) 0 0
\(246\) −2.99593 + 0.451563i −2.99593 + 0.451563i
\(247\) 0 0
\(248\) −0.228045 + 0.0520499i −0.228045 + 0.0520499i
\(249\) 0 0
\(250\) 0 0
\(251\) 0 0 −0.111964 0.993712i \(-0.535714\pi\)
0.111964 + 0.993712i \(0.464286\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0.883302 + 1.10763i 0.883302 + 1.10763i
\(255\) 0 0
\(256\) −0.154650 + 0.0744757i −0.154650 + 0.0744757i
\(257\) −1.45557 1.16078i −1.45557 1.16078i −0.955573 0.294755i \(-0.904762\pi\)
−0.500000 0.866025i \(-0.666667\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) −0.974928 0.222521i −0.974928 0.222521i
\(262\) 1.97766 1.97766
\(263\) 0 0 0.330279 0.943883i \(-0.392857\pi\)
−0.330279 + 0.943883i \(0.607143\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 0.791295 0.497204i 0.791295 0.497204i −0.0747301 0.997204i \(-0.523810\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(270\) 0 0
\(271\) 0.0739590 + 0.656405i 0.0739590 + 0.656405i 0.974928 + 0.222521i \(0.0714286\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) 1.28359 0.193469i 1.28359 0.193469i
\(277\) −0.367711 1.61105i −0.367711 1.61105i −0.733052 0.680173i \(-0.761905\pi\)
0.365341 0.930874i \(-0.380952\pi\)
\(278\) 1.20768 1.20768i 1.20768 1.20768i
\(279\) 0.307384 + 0.416490i 0.307384 + 0.416490i
\(280\) 0 0
\(281\) 0 0 −0.974928 0.222521i \(-0.928571\pi\)
0.974928 + 0.222521i \(0.0714286\pi\)
\(282\) −0.442949 1.12862i −0.442949 1.12862i
\(283\) 0 0 0.781831 0.623490i \(-0.214286\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(284\) −0.634544 + 1.31764i −0.634544 + 1.31764i
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) −1.04694 0.900969i −1.04694 0.900969i
\(289\) 1.00000i 1.00000i
\(290\) 0 0
\(291\) 0 0
\(292\) 1.45514 + 0.509177i 1.45514 + 0.509177i
\(293\) 0 0 −0.993712 0.111964i \(-0.964286\pi\)
0.993712 + 0.111964i \(0.0357143\pi\)
\(294\) 0.988831 + 1.14904i 0.988831 + 1.14904i
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −0.0332580 + 0.145713i −0.0332580 + 0.145713i
\(300\) −1.29445 0.0970060i −1.29445 0.0970060i
\(301\) 0 0
\(302\) −1.07193 1.07193i −1.07193 1.07193i
\(303\) −1.98603 + 0.0743122i −1.98603 + 0.0743122i
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 0.158342 + 0.158342i 0.158342 + 0.158342i 0.781831 0.623490i \(-0.214286\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 0.197822 + 0.314832i 0.197822 + 0.314832i 0.930874 0.365341i \(-0.119048\pi\)
−0.733052 + 0.680173i \(0.761905\pi\)
\(312\) −0.0597114 + 0.0315584i −0.0597114 + 0.0315584i
\(313\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −1.78183 0.623490i −1.78183 0.623490i −0.781831 0.623490i \(-0.785714\pi\)
−1.00000 \(\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) 0.382617 1.24041i 0.382617 1.24041i
\(325\) 0.0648483 0.134659i 0.0648483 0.134659i
\(326\) 0.947914 0.755936i 0.947914 0.755936i
\(327\) 0 0
\(328\) 0.880483 + 0.200965i 0.880483 + 0.200965i
\(329\) 0 0
\(330\) 0 0
\(331\) 1.25033 1.25033i 1.25033 1.25033i 0.294755 0.955573i \(-0.404762\pi\)
0.955573 0.294755i \(-0.0952381\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) −2.57835 + 0.902202i −2.57835 + 0.902202i
\(335\) 0 0
\(336\) 0 0
\(337\) 0 0 −0.846724 0.532032i \(-0.821429\pi\)
0.846724 + 0.532032i \(0.178571\pi\)
\(338\) 0.165940 + 1.47276i 0.165940 + 1.47276i
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 0 0
\(346\) 0.222826 0.636799i 0.222826 0.636799i
\(347\) 1.94986 1.94986 0.974928 0.222521i \(-0.0714286\pi\)
0.974928 + 0.222521i \(0.0714286\pi\)
\(348\) 1.07253 + 0.731237i 1.07253 + 0.731237i
\(349\) 0.730682 0.730682 0.365341 0.930874i \(-0.380952\pi\)
0.365341 + 0.930874i \(0.380952\pi\)
\(350\) 0 0
\(351\) 0.116853 + 0.0931869i 0.116853 + 0.0931869i
\(352\) 0 0
\(353\) 0.531130 0.255779i 0.531130 0.255779i −0.149042 0.988831i \(-0.547619\pi\)
0.680173 + 0.733052i \(0.261905\pi\)
\(354\) 1.52097 + 1.12253i 1.52097 + 1.12253i
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) −0.324382 2.87897i −0.324382 2.87897i
\(359\) 0 0 −0.846724 0.532032i \(-0.821429\pi\)
0.846724 + 0.532032i \(0.178571\pi\)
\(360\) 0 0
\(361\) 0.974928 0.222521i 0.974928 0.222521i
\(362\) 0 0
\(363\) 0.149042 + 0.988831i 0.149042 + 0.988831i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 0 0 0.993712 0.111964i \(-0.0357143\pi\)
−0.993712 + 0.111964i \(0.964286\pi\)
\(368\) 0.597690 + 0.136419i 0.597690 + 0.136419i
\(369\) −0.371563 1.96376i −0.371563 1.96376i
\(370\) 0 0
\(371\) 0 0
\(372\) −0.173910 0.649042i −0.173910 0.649042i
\(373\) 0 0 0.623490 0.781831i \(-0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0.361406i 0.361406i
\(377\) −0.123490 + 0.0841939i −0.123490 + 0.0841939i
\(378\) 0 0
\(379\) 0 0 −0.943883 0.330279i \(-0.892857\pi\)
0.943883 + 0.330279i \(0.107143\pi\)
\(380\) 0 0
\(381\) −0.708353 + 0.609587i −0.708353 + 0.609587i
\(382\) 0 0
\(383\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(384\) 0.403537 + 0.763528i 0.403537 + 0.763528i
\(385\) 0 0
\(386\) 0.542829 2.37829i 0.542829 2.37829i
\(387\) 0 0
\(388\) 0 0
\(389\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) −0.149246 0.426521i −0.149246 0.426521i
\(393\) 0.0487796 + 1.30366i 0.0487796 + 1.30366i
\(394\) 1.85664 + 1.85664i 1.85664 + 1.85664i
\(395\) 0 0
\(396\) 0 0
\(397\) −0.302705 + 1.32624i −0.302705 + 1.32624i 0.563320 + 0.826239i \(0.309524\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) −0.552349 0.265997i −0.552349 0.265997i
\(401\) 0 0 −0.433884 0.900969i \(-0.642857\pi\)
0.433884 + 0.900969i \(0.357143\pi\)
\(402\) 0 0
\(403\) 0.0768798 + 0.00866228i 0.0768798 + 0.00866228i
\(404\) 2.43507 + 0.852069i 2.43507 + 0.852069i
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 0.223772 1.98603i 0.223772 1.98603i 0.0747301 0.997204i \(-0.476190\pi\)
0.149042 0.988831i \(-0.452381\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) 0.281831 + 1.48952i 0.281831 + 1.48952i
\(415\) 0 0
\(416\) −0.205143 + 0.0231141i −0.205143 + 0.0231141i
\(417\) 0.825886 + 0.766310i 0.825886 + 0.766310i
\(418\) 0 0
\(419\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(420\) 0 0
\(421\) 0 0 0.943883 0.330279i \(-0.107143\pi\)
−0.943883 + 0.330279i \(0.892857\pi\)
\(422\) −2.09012 + 0.477055i −2.09012 + 0.477055i
\(423\) 0.733052 0.319827i 0.733052 0.319827i
\(424\) 0 0
\(425\) 0 0
\(426\) −1.56542 0.682985i −1.56542 0.682985i
\(427\) 0 0
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 −0.781831 0.623490i \(-0.785714\pi\)
0.781831 + 0.623490i \(0.214286\pi\)
\(432\) 0.382237 0.479310i 0.382237 0.479310i
\(433\) 0 0 0.330279 0.943883i \(-0.392857\pi\)
−0.330279 + 0.943883i \(0.607143\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) −0.530676 + 1.72041i −0.530676 + 1.72041i
\(439\) −1.06356 0.848162i −1.06356 0.848162i −0.0747301 0.997204i \(-0.523810\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(440\) 0 0
\(441\) −0.733052 + 0.680173i −0.733052 + 0.680173i
\(442\) 0 0
\(443\) 1.36254 0.856144i 1.36254 0.856144i 0.365341 0.930874i \(-0.380952\pi\)
0.997204 + 0.0747301i \(0.0238095\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0.571250 + 0.358940i 0.571250 + 0.358940i
\(447\) 0 0
\(448\) 0 0
\(449\) 0.623490 0.218169i 0.623490 0.218169i 1.00000i \(-0.5\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(450\) 0.0566829 1.51488i 0.0566829 1.51488i
\(451\) 0 0
\(452\) 0 0
\(453\) 0.680173 0.733052i 0.680173 0.733052i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 0 0 0.781831 0.623490i \(-0.214286\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 0.197979 1.75711i 0.197979 1.75711i −0.365341 0.930874i \(-0.619048\pi\)
0.563320 0.826239i \(-0.309524\pi\)
\(462\) 0 0
\(463\) 1.80194i 1.80194i −0.433884 0.900969i \(-0.642857\pi\)
0.433884 0.900969i \(-0.357143\pi\)
\(464\) 0.345350 + 0.506535i 0.345350 + 0.506535i
\(465\) 0 0
\(466\) 2.09781 + 0.734055i 2.09781 + 0.734055i
\(467\) 0 0 −0.993712 0.111964i \(-0.964286\pi\)
0.993712 + 0.111964i \(0.0357143\pi\)
\(468\) −0.0970060 0.168019i −0.0970060 0.168019i
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) −0.299792 0.477116i −0.299792 0.477116i
\(473\) 0 0
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 0 0
\(478\) 0.681104 + 1.94648i 0.681104 + 1.94648i
\(479\) 0 0 −0.330279 0.943883i \(-0.607143\pi\)
0.330279 + 0.943883i \(0.392857\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) 0.288851 1.26554i 0.288851 1.26554i
\(485\) 0 0
\(486\) 1.46429 + 0.392355i 1.46429 + 0.392355i
\(487\) 0.531130 + 0.255779i 0.531130 + 0.255779i 0.680173 0.733052i \(-0.261905\pi\)
−0.149042 + 0.988831i \(0.547619\pi\)
\(488\) 0 0
\(489\) 0.521689 + 0.606214i 0.521689 + 0.606214i
\(490\) 0 0
\(491\) −0.0705858 0.0246991i −0.0705858 0.0246991i 0.294755 0.955573i \(-0.404762\pi\)
−0.365341 + 0.930874i \(0.619048\pi\)
\(492\) −0.482320 + 2.54912i −0.482320 + 2.54912i
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0.0355312 0.315348i 0.0355312 0.315348i
\(497\) 0 0
\(498\) 0 0
\(499\) 0.317031 0.658322i 0.317031 0.658322i −0.680173 0.733052i \(-0.738095\pi\)
0.997204 + 0.0747301i \(0.0238095\pi\)
\(500\) 0 0
\(501\) −0.658322 1.67738i −0.658322 1.67738i
\(502\) 0 0
\(503\) 0 0 0.993712 0.111964i \(-0.0357143\pi\)
−0.993712 + 0.111964i \(0.964286\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −0.966742 + 0.145713i −0.966742 + 0.145713i
\(508\) 1.14503 0.400664i 1.14503 0.400664i
\(509\) 0.290611 0.0663300i 0.290611 0.0663300i −0.0747301 0.997204i \(-0.523810\pi\)
0.365341 + 0.930874i \(0.380952\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0.125828 + 1.11675i 0.125828 + 1.11675i
\(513\) 0 0
\(514\) −2.38971 + 1.50156i −2.38971 + 1.50156i
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 0.425270 + 0.131178i 0.425270 + 0.131178i
\(520\) 0 0
\(521\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(522\) −0.806531 + 1.28359i −0.806531 + 1.28359i
\(523\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(524\) 0.559311 1.59842i 0.559311 1.59842i
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) −0.623490 0.781831i −0.623490 0.781831i
\(530\) 0 0
\(531\) −0.702449 + 1.03030i −0.702449 + 1.03030i
\(532\) 0 0
\(533\) −0.252926 0.158924i −0.252926 0.158924i
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 1.88980 0.284841i 1.88980 0.284841i
\(538\) −0.315247 1.38119i −0.315247 1.38119i
\(539\) 0 0
\(540\) 0 0
\(541\) −1.82160 + 0.205245i −1.82160 + 0.205245i −0.955573 0.294755i \(-0.904762\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(542\) 0.976262 + 0.222826i 0.976262 + 0.222826i
\(543\) 0 0
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 0.914101 1.14625i 0.914101 1.14625i −0.0747301 0.997204i \(-0.523810\pi\)
0.988831 0.149042i \(-0.0476190\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 0 0
\(552\) 0.0840096 0.444001i 0.0840096 0.444001i
\(553\) 0 0
\(554\) −2.48931 0.280478i −2.48931 0.280478i
\(555\) 0 0
\(556\) −0.634544 1.31764i −0.634544 1.31764i
\(557\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(558\) 0.749848 0.231297i 0.749848 0.231297i
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(564\) −1.03746 + 0.0388191i −1.03746 + 0.0388191i
\(565\) 0 0
\(566\) 0 0
\(567\) 0 0
\(568\) 0.359992 + 0.359992i 0.359992 + 0.359992i
\(569\) 0 0 0.532032 0.846724i \(-0.321429\pi\)
−0.532032 + 0.846724i \(0.678571\pi\)
\(570\) 0 0
\(571\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0.433884 + 0.900969i 0.433884 + 0.900969i
\(576\) −1.28244 + 0.740414i −1.28244 + 0.740414i
\(577\) −1.75711 0.197979i −1.75711 0.197979i −0.826239 0.563320i \(-0.809524\pi\)
−0.930874 + 0.365341i \(0.880952\pi\)
\(578\) −1.43087 0.500684i −1.43087 0.500684i
\(579\) 1.58114 + 0.299168i 1.58114 + 0.299168i
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) 0.334608 0.419586i 0.334608 0.419586i
\(585\) 0 0
\(586\) 0 0
\(587\) 0.460898 0.367554i 0.460898 0.367554i −0.365341 0.930874i \(-0.619048\pi\)
0.826239 + 0.563320i \(0.190476\pi\)
\(588\) 1.20835 0.474244i 1.20835 0.474244i
\(589\) 0 0
\(590\) 0 0
\(591\) −1.17809 + 1.26968i −1.17809 + 1.26968i
\(592\) 0 0
\(593\) 0.433884 + 1.90097i 0.433884 + 1.90097i 0.433884 + 0.900969i \(0.357143\pi\)
1.00000i \(0.500000\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0.191845 + 0.120544i 0.191845 + 0.120544i
\(599\) −0.0739590 0.656405i −0.0739590 0.656405i −0.974928 0.222521i \(-0.928571\pi\)
0.900969 0.433884i \(-0.142857\pi\)
\(600\) −0.180703 + 0.414176i −0.180703 + 0.414176i
\(601\) −1.63575 + 1.02781i −1.63575 + 1.02781i −0.680173 + 0.733052i \(0.738095\pi\)
−0.955573 + 0.294755i \(0.904762\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −1.16953 + 0.563218i −1.16953 + 0.563218i
\(605\) 0 0
\(606\) −0.888045 + 2.87897i −0.888045 + 2.87897i
\(607\) −0.559311 + 1.59842i −0.559311 + 1.59842i 0.222521 + 0.974928i \(0.428571\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0.0394802 0.112828i 0.0394802 0.112828i
\(612\) 0 0
\(613\) 0 0 −0.781831 0.623490i \(-0.785714\pi\)
0.781831 + 0.623490i \(0.214286\pi\)
\(614\) 0.305846 0.147288i 0.305846 0.147288i
\(615\) 0 0
\(616\) 0 0
\(617\) 0 0 0.846724 0.532032i \(-0.178571\pi\)
−0.846724 + 0.532032i \(0.821429\pi\)
\(618\) 0 0
\(619\) 0 0 −0.111964 0.993712i \(-0.535714\pi\)
0.111964 + 0.993712i \(0.464286\pi\)
\(620\) 0 0
\(621\) −0.974928 + 0.222521i −0.974928 + 0.222521i
\(622\) 0.549531 0.125427i 0.549531 0.125427i
\(623\) 0 0
\(624\) −0.0136565 0.0906048i −0.0136565 0.0906048i
\(625\) −0.222521 0.974928i −0.222521 0.974928i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 0 0 0.781831 0.623490i \(-0.214286\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(632\) 0 0
\(633\) −0.366025 1.36603i −0.366025 1.36603i
\(634\) −1.78427 + 2.23740i −1.78427 + 2.23740i
\(635\) 0 0
\(636\) 0 0
\(637\) 0.149460i 0.149460i
\(638\) 0 0
\(639\) 0.411608 1.04876i 0.411608 1.04876i
\(640\) 0 0
\(641\) 0 0 −0.993712 0.111964i \(-0.964286\pi\)
0.993712 + 0.111964i \(0.0357143\pi\)
\(642\) 0 0
\(643\) 0 0 −0.433884 0.900969i \(-0.642857\pi\)
0.433884 + 0.900969i \(0.357143\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −0.0663300 + 0.290611i −0.0663300 + 0.290611i −0.997204 0.0747301i \(-0.976190\pi\)
0.930874 + 0.365341i \(0.119048\pi\)
\(648\) −0.363581 0.268335i −0.363581 0.268335i
\(649\) 0 0
\(650\) −0.160211 0.160211i −0.160211 0.160211i
\(651\) 0 0
\(652\) −0.342892 0.979928i −0.342892 0.979928i
\(653\) 0.638050 + 1.82344i 0.638050 + 1.82344i 0.563320 + 0.826239i \(0.309524\pi\)
0.0747301 + 0.997204i \(0.476190\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) −0.651880 + 1.03746i −0.651880 + 1.03746i
\(657\) −1.14717 0.307384i −1.14717 0.307384i
\(658\) 0 0
\(659\) 0 0 −0.532032 0.846724i \(-0.678571\pi\)
0.532032 + 0.846724i \(0.321429\pi\)
\(660\) 0 0
\(661\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(662\) −1.16304 2.41508i −1.16304 2.41508i
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0.0747301 0.997204i 0.0747301 0.997204i
\(668\) 2.33907i 2.33907i
\(669\) −0.222521 + 0.385418i −0.222521 + 0.385418i
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) −0.255779 + 0.531130i −0.255779 + 0.531130i −0.988831 0.149042i \(-0.952381\pi\)
0.733052 + 0.680173i \(0.238095\pi\)
\(674\) 0 0
\(675\) 1.00000 1.00000
\(676\) 1.23727 + 0.282399i 1.23727 + 0.282399i
\(677\) 0 0 0.993712 0.111964i \(-0.0357143\pi\)
−0.993712 + 0.111964i \(0.964286\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 1.81507 0.414278i 1.81507 0.414278i 0.826239 0.563320i \(-0.190476\pi\)
0.988831 + 0.149042i \(0.0476190\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) −0.781831 + 0.376510i −0.781831 + 0.376510i −0.781831 0.623490i \(-0.785714\pi\)
1.00000i \(0.5\pi\)
\(692\) −0.451666 0.360191i −0.451666 0.360191i
\(693\) 0 0
\(694\) 0.976262 2.79000i 0.976262 2.79000i
\(695\) 0 0
\(696\) 0.363581 0.268335i 0.363581 0.268335i
\(697\) 0 0
\(698\) 0.365841 1.04551i 0.365841 1.04551i
\(699\) −0.432142 + 1.40097i −0.432142 + 1.40097i
\(700\) 0 0
\(701\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(702\) 0.191845 0.120544i 0.191845 0.120544i
\(703\) 0 0
\(704\) 0 0
\(705\) 0 0
\(706\) −0.100059 0.888045i −0.100059 0.888045i
\(707\) 0 0
\(708\) 1.33742 0.911838i 1.33742 0.911838i
\(709\) 0 0 0.974928 0.222521i \(-0.0714286\pi\)
−0.974928 + 0.222521i \(0.928571\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −0.366025 + 0.366025i −0.366025 + 0.366025i
\(714\) 0 0
\(715\) 0 0
\(716\) −2.41863 0.552036i −2.41863 0.552036i
\(717\) −1.26631 + 0.496990i −1.26631 + 0.496990i
\(718\) 0 0
\(719\) 0.376510 0.781831i 0.376510 0.781831i −0.623490 0.781831i \(-0.714286\pi\)
1.00000 \(0\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0.169732 1.50641i 0.169732 1.50641i
\(723\) 0 0
\(724\) 0 0
\(725\) −0.294755 + 0.955573i −0.294755 + 0.955573i
\(726\) 1.48952 + 0.281831i 1.48952 + 0.281831i
\(727\) 0 0 −0.943883 0.330279i \(-0.892857\pi\)
0.943883 + 0.330279i \(0.107143\pi\)
\(728\) 0 0
\(729\) −0.222521 + 0.974928i −0.222521 + 0.974928i
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 0 0 −0.532032 0.846724i \(-0.678571\pi\)
0.532032 + 0.846724i \(0.321429\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0.734867 1.16953i 0.734867 1.16953i
\(737\) 0 0
\(738\) −2.99593 0.451563i −2.99593 0.451563i
\(739\) −0.660096 1.88645i −0.660096 1.88645i −0.365341 0.930874i \(-0.619048\pi\)
−0.294755 0.955573i \(-0.595238\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 0.532032 0.846724i \(-0.321429\pi\)
−0.532032 + 0.846724i \(0.678571\pi\)
\(744\) −0.233256 0.0174801i −0.233256 0.0174801i
\(745\) 0 0
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 0 0 −0.993712 0.111964i \(-0.964286\pi\)
0.993712 + 0.111964i \(0.0357143\pi\)
\(752\) −0.462802 0.161941i −0.462802 0.161941i
\(753\) 0 0
\(754\) 0.0586415 + 0.218853i 0.0586415 + 0.218853i
\(755\) 0 0
\(756\) 0 0
\(757\) 0 0 0.111964 0.993712i \(-0.464286\pi\)
−0.111964 + 0.993712i \(0.535714\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 1.29196 1.03030i 1.29196 1.03030i 0.294755 0.955573i \(-0.404762\pi\)
0.997204 0.0747301i \(-0.0238095\pi\)
\(762\) 0.517581 + 1.31877i 0.517581 + 1.31877i
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0.0414721 + 0.181701i 0.0414721 + 0.181701i
\(768\) −0.169732 + 0.0255830i −0.169732 + 0.0255830i
\(769\) 0 0 0.943883 0.330279i \(-0.107143\pi\)
−0.943883 + 0.330279i \(0.892857\pi\)
\(770\) 0 0
\(771\) −1.04876 1.53825i −1.04876 1.53825i
\(772\) −1.76870 1.11135i −1.76870 1.11135i
\(773\) 0 0 −0.111964 0.993712i \(-0.535714\pi\)
0.111964 + 0.993712i \(0.464286\pi\)
\(774\) 0 0
\(775\) 0.438297 0.275400i 0.438297 0.275400i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) −0.866025 0.500000i −0.866025 0.500000i
\(784\) 0.613061 0.613061
\(785\) 0 0
\(786\) 1.88980 + 0.582926i 1.88980 + 0.582926i
\(787\) 0 0 −0.781831 0.623490i \(-0.785714\pi\)
0.781831 + 0.623490i \(0.214286\pi\)
\(788\) 2