Properties

Label 2001.1.bf.c.896.2
Level $2001$
Weight $1$
Character 2001.896
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 896.2
Root \(-0.997204 + 0.0747301i\) of defining polynomial
Character \(\chi\) \(=\) 2001.896
Dual form 2001.1.bf.c.1034.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.791295 + 0.497204i) q^{2} +(0.365341 + 0.930874i) q^{3} +(-0.0549471 - 0.114099i) q^{4} +(-0.173741 + 0.918245i) q^{6} +(0.117886 - 1.04627i) q^{8} +(-0.733052 + 0.680173i) q^{9} +O(q^{10})\) \(q+(0.791295 + 0.497204i) q^{2} +(0.365341 + 0.930874i) q^{3} +(-0.0549471 - 0.114099i) q^{4} +(-0.173741 + 0.918245i) q^{6} +(0.117886 - 1.04627i) q^{8} +(-0.733052 + 0.680173i) q^{9} +(0.0861372 - 0.0928338i) q^{12} +(1.49419 + 1.19158i) q^{13} +(0.534532 - 0.670281i) q^{16} +(-0.918245 + 0.173741i) q^{18} +(0.974928 + 0.222521i) q^{23} +(1.01701 - 0.272507i) q^{24} +(-0.900969 + 0.433884i) q^{25} +(0.589891 + 1.68581i) q^{26} +(-0.900969 - 0.433884i) q^{27} +(0.997204 + 0.0747301i) q^{29} +(-0.275400 + 0.438297i) q^{31} +(-0.237564 + 0.0831272i) q^{32} +(0.117886 + 0.0462668i) q^{36} +(-0.563320 + 1.82624i) q^{39} +(-0.839789 - 0.839789i) q^{41} +(0.660818 + 0.660818i) q^{46} +(-1.50641 + 0.169732i) q^{47} +(0.819234 + 0.252700i) q^{48} +(0.623490 + 0.781831i) q^{49} +(-0.928661 - 0.104635i) q^{50} +(0.0538562 - 0.235960i) q^{52} +(-0.497204 - 0.791295i) q^{54} +(0.751927 + 0.554947i) q^{58} -1.80194i q^{59} +(-0.435846 + 0.209892i) q^{62} +(-1.06514 - 0.243112i) q^{64} +(0.149042 + 0.988831i) q^{69} +(0.848162 - 1.06356i) q^{71} +(0.625226 + 0.847151i) q^{72} +(-0.197822 - 0.314832i) q^{73} +(-0.733052 - 0.680173i) q^{75} +(-1.35377 + 1.16501i) q^{78} +(0.0747301 - 0.997204i) q^{81} +(-0.246975 - 1.08207i) q^{82} +(0.294755 + 0.955573i) q^{87} +(-0.0281801 - 0.123465i) q^{92} +(-0.508614 - 0.0962349i) q^{93} +(-1.27641 - 0.614686i) q^{94} +(-0.164173 - 0.190772i) q^{96} +(0.104635 + 0.928661i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q - 2q^{2} + 2q^{3} + 14q^{4} - 2q^{6} + 6q^{8} + 2q^{9} + O(q^{10}) \) \( 24q - 2q^{2} + 2q^{3} + 14q^{4} - 2q^{6} + 6q^{8} + 2q^{9} - 6q^{12} - 6q^{16} + 4q^{18} - 6q^{24} - 4q^{25} + 2q^{26} - 4q^{27} - 2q^{31} + 4q^{32} + 6q^{36} + 2q^{41} + 2q^{46} - 2q^{47} - 4q^{48} - 4q^{49} - 2q^{50} - 10q^{52} + 12q^{54} + 4q^{58} + 4q^{62} - 28q^{64} + 14q^{72} - 2q^{73} + 2q^{75} + 10q^{78} + 2q^{81} - 4q^{82} + 4q^{92} - 2q^{93} - 8q^{94} - 24q^{96} - 2q^{98} + O(q^{100}) \)

Character values

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

\(n\) \(553\) \(668\) \(1132\)
\(\chi(n)\) \(e\left(\frac{19}{28}\right)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.791295 + 0.497204i 0.791295 + 0.497204i 0.866025 0.500000i \(-0.166667\pi\)
−0.0747301 + 0.997204i \(0.523810\pi\)
\(3\) 0.365341 + 0.930874i 0.365341 + 0.930874i
\(4\) −0.0549471 0.114099i −0.0549471 0.114099i
\(5\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(6\) −0.173741 + 0.918245i −0.173741 + 0.918245i
\(7\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(8\) 0.117886 1.04627i 0.117886 1.04627i
\(9\) −0.733052 + 0.680173i −0.733052 + 0.680173i
\(10\) 0 0
\(11\) 0 0 −0.111964 0.993712i \(-0.535714\pi\)
0.111964 + 0.993712i \(0.464286\pi\)
\(12\) 0.0861372 0.0928338i 0.0861372 0.0928338i
\(13\) 1.49419 + 1.19158i 1.49419 + 1.19158i 0.930874 + 0.365341i \(0.119048\pi\)
0.563320 + 0.826239i \(0.309524\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0.534532 0.670281i 0.534532 0.670281i
\(17\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(18\) −0.918245 + 0.173741i −0.918245 + 0.173741i
\(19\) 0 0 −0.943883 0.330279i \(-0.892857\pi\)
0.943883 + 0.330279i \(0.107143\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 0.974928 + 0.222521i 0.974928 + 0.222521i
\(24\) 1.01701 0.272507i 1.01701 0.272507i
\(25\) −0.900969 + 0.433884i −0.900969 + 0.433884i
\(26\) 0.589891 + 1.68581i 0.589891 + 1.68581i
\(27\) −0.900969 0.433884i −0.900969 0.433884i
\(28\) 0 0
\(29\) 0.997204 + 0.0747301i 0.997204 + 0.0747301i
\(30\) 0 0
\(31\) −0.275400 + 0.438297i −0.275400 + 0.438297i −0.955573 0.294755i \(-0.904762\pi\)
0.680173 + 0.733052i \(0.261905\pi\)
\(32\) −0.237564 + 0.0831272i −0.237564 + 0.0831272i
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) 0.117886 + 0.0462668i 0.117886 + 0.0462668i
\(37\) 0 0 −0.993712 0.111964i \(-0.964286\pi\)
0.993712 + 0.111964i \(0.0357143\pi\)
\(38\) 0 0
\(39\) −0.563320 + 1.82624i −0.563320 + 1.82624i
\(40\) 0 0
\(41\) −0.839789 0.839789i −0.839789 0.839789i 0.149042 0.988831i \(-0.452381\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(42\) 0 0
\(43\) 0 0 0.846724 0.532032i \(-0.178571\pi\)
−0.846724 + 0.532032i \(0.821429\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0.660818 + 0.660818i 0.660818 + 0.660818i
\(47\) −1.50641 + 0.169732i −1.50641 + 0.169732i −0.826239 0.563320i \(-0.809524\pi\)
−0.680173 + 0.733052i \(0.738095\pi\)
\(48\) 0.819234 + 0.252700i 0.819234 + 0.252700i
\(49\) 0.623490 + 0.781831i 0.623490 + 0.781831i
\(50\) −0.928661 0.104635i −0.928661 0.104635i
\(51\) 0 0
\(52\) 0.0538562 0.235960i 0.0538562 0.235960i
\(53\) 0 0 0.974928 0.222521i \(-0.0714286\pi\)
−0.974928 + 0.222521i \(0.928571\pi\)
\(54\) −0.497204 0.791295i −0.497204 0.791295i
\(55\) 0 0
\(56\) 0 0
\(57\) 0 0
\(58\) 0.751927 + 0.554947i 0.751927 + 0.554947i
\(59\) 1.80194i 1.80194i −0.433884 0.900969i \(-0.642857\pi\)
0.433884 0.900969i \(-0.357143\pi\)
\(60\) 0 0
\(61\) 0 0 −0.330279 0.943883i \(-0.607143\pi\)
0.330279 + 0.943883i \(0.392857\pi\)
\(62\) −0.435846 + 0.209892i −0.435846 + 0.209892i
\(63\) 0 0
\(64\) −1.06514 0.243112i −1.06514 0.243112i
\(65\) 0 0
\(66\) 0 0
\(67\) 0 0 0.781831 0.623490i \(-0.214286\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(68\) 0 0
\(69\) 0.149042 + 0.988831i 0.149042 + 0.988831i
\(70\) 0 0
\(71\) 0.848162 1.06356i 0.848162 1.06356i −0.149042 0.988831i \(-0.547619\pi\)
0.997204 0.0747301i \(-0.0238095\pi\)
\(72\) 0.625226 + 0.847151i 0.625226 + 0.847151i
\(73\) −0.197822 0.314832i −0.197822 0.314832i 0.733052 0.680173i \(-0.238095\pi\)
−0.930874 + 0.365341i \(0.880952\pi\)
\(74\) 0 0
\(75\) −0.733052 0.680173i −0.733052 0.680173i
\(76\) 0 0
\(77\) 0 0
\(78\) −1.35377 + 1.16501i −1.35377 + 1.16501i
\(79\) 0 0 0.111964 0.993712i \(-0.464286\pi\)
−0.111964 + 0.993712i \(0.535714\pi\)
\(80\) 0 0
\(81\) 0.0747301 0.997204i 0.0747301 0.997204i
\(82\) −0.246975 1.08207i −0.246975 1.08207i
\(83\) 0 0 −0.433884 0.900969i \(-0.642857\pi\)
0.433884 + 0.900969i \(0.357143\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 0.294755 + 0.955573i 0.294755 + 0.955573i
\(88\) 0 0
\(89\) 0 0 −0.846724 0.532032i \(-0.821429\pi\)
0.846724 + 0.532032i \(0.178571\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −0.0281801 0.123465i −0.0281801 0.123465i
\(93\) −0.508614 0.0962349i −0.508614 0.0962349i
\(94\) −1.27641 0.614686i −1.27641 0.614686i
\(95\) 0 0
\(96\) −0.164173 0.190772i −0.164173 0.190772i
\(97\) 0 0 0.330279 0.943883i \(-0.392857\pi\)
−0.330279 + 0.943883i \(0.607143\pi\)
\(98\) 0.104635 + 0.928661i 0.104635 + 0.928661i
\(99\) 0 0
\(100\) 0.0990112 + 0.0789588i 0.0990112 + 0.0789588i
\(101\) −1.00435 1.59842i −1.00435 1.59842i −0.781831 0.623490i \(-0.785714\pi\)
−0.222521 0.974928i \(-0.571429\pi\)
\(102\) 0 0
\(103\) 0 0 0.623490 0.781831i \(-0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(104\) 1.42285 1.42285i 1.42285 1.42285i
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 0.781831 0.623490i \(-0.214286\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(108\) 0.126640i 0.126640i
\(109\) 0 0 0.433884 0.900969i \(-0.357143\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 0 0 −0.330279 0.943883i \(-0.607143\pi\)
0.330279 + 0.943883i \(0.392857\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) −0.0462668 0.117886i −0.0462668 0.117886i
\(117\) −1.90580 + 0.142820i −1.90580 + 0.142820i
\(118\) 0.895930 1.42586i 0.895930 1.42586i
\(119\) 0 0
\(120\) 0 0
\(121\) −0.974928 + 0.222521i −0.974928 + 0.222521i
\(122\) 0 0
\(123\) 0.474928 1.08855i 0.474928 1.08855i
\(124\) 0.0651416 + 0.00733969i 0.0651416 + 0.00733969i
\(125\) 0 0
\(126\) 0 0
\(127\) 0.794755 0.0895474i 0.794755 0.0895474i 0.294755 0.955573i \(-0.404762\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(128\) −0.543995 0.543995i −0.543995 0.543995i
\(129\) 0 0
\(130\) 0 0
\(131\) −1.49720 + 0.940755i −1.49720 + 0.940755i −0.500000 + 0.866025i \(0.666667\pi\)
−0.997204 + 0.0747301i \(0.976190\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 0 0 −0.993712 0.111964i \(-0.964286\pi\)
0.993712 + 0.111964i \(0.0357143\pi\)
\(138\) −0.373714 + 0.856562i −0.373714 + 0.856562i
\(139\) 0.302705 1.32624i 0.302705 1.32624i −0.563320 0.826239i \(-0.690476\pi\)
0.866025 0.500000i \(-0.166667\pi\)
\(140\) 0 0
\(141\) −0.708353 1.34027i −0.708353 1.34027i
\(142\) 1.19995 0.419882i 1.19995 0.419882i
\(143\) 0 0
\(144\) 0.0640678 + 0.854925i 0.0640678 + 0.854925i
\(145\) 0 0
\(146\) 0.347483i 0.347483i
\(147\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(148\) 0 0
\(149\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(150\) −0.241876 0.902694i −0.241876 0.902694i
\(151\) −0.974928 0.222521i −0.974928 0.222521i −0.294755 0.955573i \(-0.595238\pi\)
−0.680173 + 0.733052i \(0.738095\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 0.239324 0.0360724i 0.239324 0.0360724i
\(157\) 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
\(162\) 0.554947 0.751927i 0.554947 0.751927i
\(163\) −0.169732 1.50641i −0.169732 1.50641i −0.733052 0.680173i \(-0.761905\pi\)
0.563320 0.826239i \(-0.309524\pi\)
\(164\) −0.0496749 + 0.141963i −0.0496749 + 0.141963i
\(165\) 0 0
\(166\) 0 0
\(167\) 0.400969 + 0.193096i 0.400969 + 0.193096i 0.623490 0.781831i \(-0.285714\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(168\) 0 0
\(169\) 0.590232 + 2.58597i 0.590232 + 2.58597i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −1.24698 −1.24698 −0.623490 0.781831i \(-0.714286\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(174\) −0.241876 + 0.902694i −0.241876 + 0.902694i
\(175\) 0 0
\(176\) 0 0
\(177\) 1.67738 0.658322i 1.67738 0.658322i
\(178\) 0 0
\(179\) 0.162592 + 0.712362i 0.162592 + 0.712362i 0.988831 + 0.149042i \(0.0476190\pi\)
−0.826239 + 0.563320i \(0.809524\pi\)
\(180\) 0 0
\(181\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0.347747 0.993803i 0.347747 0.993803i
\(185\) 0 0
\(186\) −0.354615 0.329035i −0.354615 0.329035i
\(187\) 0 0
\(188\) 0.102139 + 0.162553i 0.102139 + 0.162553i
\(189\) 0 0
\(190\) 0 0
\(191\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(192\) −0.162834 1.08033i −0.162834 1.08033i
\(193\) 1.85486 + 0.649042i 1.85486 + 0.649042i 0.988831 + 0.149042i \(0.0476190\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0.0549471 0.114099i 0.0549471 0.114099i
\(197\) 1.68862 + 0.385418i 1.68862 + 0.385418i 0.955573 0.294755i \(-0.0952381\pi\)
0.733052 + 0.680173i \(0.238095\pi\)
\(198\) 0 0
\(199\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(200\) 0.347747 + 0.993803i 0.347747 + 0.993803i
\(201\) 0 0
\(202\) 1.76419i 1.76419i
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(208\) 1.59739 0.364593i 1.59739 0.364593i
\(209\) 0 0
\(210\) 0 0
\(211\) −1.40532 0.158342i −1.40532 0.158342i −0.623490 0.781831i \(-0.714286\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(212\) 0 0
\(213\) 1.29991 + 0.400969i 1.29991 + 0.400969i
\(214\) 0 0
\(215\) 0 0
\(216\) −0.560170 + 0.891505i −0.560170 + 0.891505i
\(217\) 0 0
\(218\) 0 0
\(219\) 0.220796 0.299168i 0.220796 0.299168i
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) −0.777479 0.974928i −0.777479 0.974928i 0.222521 0.974928i \(-0.428571\pi\)
−1.00000 \(\pi\)
\(224\) 0 0
\(225\) 0.365341 0.930874i 0.365341 0.930874i
\(226\) 0 0
\(227\) 0 0 0.974928 0.222521i \(-0.0714286\pi\)
−0.974928 + 0.222521i \(0.928571\pi\)
\(228\) 0 0
\(229\) 0 0 0.943883 0.330279i \(-0.107143\pi\)
−0.943883 + 0.330279i \(0.892857\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0.195744 1.03453i 0.195744 1.03453i
\(233\) 1.97766i 1.97766i 0.149042 + 0.988831i \(0.452381\pi\)
−0.149042 + 0.988831i \(0.547619\pi\)
\(234\) −1.57906 0.834559i −1.57906 0.834559i
\(235\) 0 0
\(236\) −0.205599 + 0.0990112i −0.205599 + 0.0990112i
\(237\) 0 0
\(238\) 0 0
\(239\) −0.129334 + 0.268565i −0.129334 + 0.268565i −0.955573 0.294755i \(-0.904762\pi\)
0.826239 + 0.563320i \(0.190476\pi\)
\(240\) 0 0
\(241\) 0 0 0.781831 0.623490i \(-0.214286\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(242\) −0.882094 0.308658i −0.882094 0.308658i
\(243\) 0.955573 0.294755i 0.955573 0.294755i
\(244\) 0 0
\(245\) 0 0
\(246\) 0.917038 0.625226i 0.917038 0.625226i
\(247\) 0 0
\(248\) 0.426109 + 0.339811i 0.426109 + 0.339811i
\(249\) 0 0
\(250\) 0 0
\(251\) 0 0 0.330279 0.943883i \(-0.392857\pi\)
−0.330279 + 0.943883i \(0.607143\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0.673409 + 0.324297i 0.673409 + 0.324297i
\(255\) 0 0
\(256\) 0.0831272 + 0.364204i 0.0831272 + 0.364204i
\(257\) −0.865341 1.79690i −0.865341 1.79690i −0.500000 0.866025i \(-0.666667\pi\)
−0.365341 0.930874i \(-0.619048\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) −0.781831 + 0.623490i −0.781831 + 0.623490i
\(262\) −1.65248 −1.65248
\(263\) 0 0 −0.846724 0.532032i \(-0.821429\pi\)
0.846724 + 0.532032i \(0.178571\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −0.0895474 + 0.794755i −0.0895474 + 0.794755i 0.866025 + 0.500000i \(0.166667\pi\)
−0.955573 + 0.294755i \(0.904762\pi\)
\(270\) 0 0
\(271\) 0.559311 1.59842i 0.559311 1.59842i −0.222521 0.974928i \(-0.571429\pi\)
0.781831 0.623490i \(-0.214286\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) 0.104635 0.0713389i 0.104635 0.0713389i
\(277\) −0.914101 + 1.14625i −0.914101 + 1.14625i 0.0747301 + 0.997204i \(0.476190\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(278\) 0.898940 0.898940i 0.898940 0.898940i
\(279\) −0.0962349 0.508614i −0.0962349 0.508614i
\(280\) 0 0
\(281\) 0 0 0.781831 0.623490i \(-0.214286\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(282\) 0.105871 1.41274i 0.105871 1.41274i
\(283\) 0 0 0.433884 0.900969i \(-0.357143\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(284\) −0.167955 0.0383346i −0.167955 0.0383346i
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0.117606 0.222521i 0.117606 0.222521i
\(289\) 1.00000i 1.00000i
\(290\) 0 0
\(291\) 0 0
\(292\) −0.0250522 + 0.0398703i −0.0250522 + 0.0398703i
\(293\) 0 0 0.943883 0.330279i \(-0.107143\pi\)
−0.943883 + 0.330279i \(0.892857\pi\)
\(294\) −0.826239 + 0.436680i −0.826239 + 0.436680i
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 1.19158 + 1.49419i 1.19158 + 1.49419i
\(300\) −0.0373278 + 0.121014i −0.0373278 + 0.121014i
\(301\) 0 0
\(302\) −0.660818 0.660818i −0.660818 0.660818i
\(303\) 1.12099 1.51889i 1.12099 1.51889i
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 0.467085 + 0.467085i 0.467085 + 0.467085i 0.900969 0.433884i \(-0.142857\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −1.98603 0.223772i −1.98603 0.223772i −0.997204 0.0747301i \(-0.976190\pi\)
−0.988831 0.149042i \(-0.952381\pi\)
\(312\) 1.84433 + 0.804671i 1.84433 + 0.804671i
\(313\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −0.566116 + 0.900969i −0.566116 + 0.900969i 0.433884 + 0.900969i \(0.357143\pi\)
−1.00000 \(\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) −0.117886 + 0.0462668i −0.117886 + 0.0462668i
\(325\) −1.86323 0.425270i −1.86323 0.425270i
\(326\) 0.614686 1.27641i 0.614686 1.27641i
\(327\) 0 0
\(328\) −0.977642 + 0.779644i −0.977642 + 0.779644i
\(329\) 0 0
\(330\) 0 0
\(331\) 1.29621 1.29621i 1.29621 1.29621i 0.365341 0.930874i \(-0.380952\pi\)
0.930874 0.365341i \(-0.119048\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0.221277 + 0.352160i 0.221277 + 0.352160i
\(335\) 0 0
\(336\) 0 0
\(337\) 0 0 −0.111964 0.993712i \(-0.535714\pi\)
0.111964 + 0.993712i \(0.464286\pi\)
\(338\) −0.818709 + 2.33973i −0.818709 + 2.33973i
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 0 0
\(346\) −0.986729 0.620003i −0.986729 0.620003i
\(347\) 1.56366 1.56366 0.781831 0.623490i \(-0.214286\pi\)
0.781831 + 0.623490i \(0.214286\pi\)
\(348\) 0.0928338 0.0861372i 0.0928338 0.0861372i
\(349\) 0.149460 0.149460 0.0747301 0.997204i \(-0.476190\pi\)
0.0747301 + 0.997204i \(0.476190\pi\)
\(350\) 0 0
\(351\) −0.829215 1.72188i −0.829215 1.72188i
\(352\) 0 0
\(353\) 0.414278 + 1.81507i 0.414278 + 1.81507i 0.563320 + 0.826239i \(0.309524\pi\)
−0.149042 + 0.988831i \(0.547619\pi\)
\(354\) 1.65462 + 0.313071i 1.65462 + 0.313071i
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) −0.225531 + 0.644530i −0.225531 + 0.644530i
\(359\) 0 0 −0.111964 0.993712i \(-0.535714\pi\)
0.111964 + 0.993712i \(0.464286\pi\)
\(360\) 0 0
\(361\) 0.781831 + 0.623490i 0.781831 + 0.623490i
\(362\) 0 0
\(363\) −0.563320 0.826239i −0.563320 0.826239i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 0 0 −0.943883 0.330279i \(-0.892857\pi\)
0.943883 + 0.330279i \(0.107143\pi\)
\(368\) 0.670281 0.534532i 0.670281 0.534532i
\(369\) 1.18681 + 0.0444073i 1.18681 + 0.0444073i
\(370\) 0 0
\(371\) 0 0
\(372\) 0.0169666 + 0.0633201i 0.0169666 + 0.0633201i
\(373\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 1.59612i 1.59612i
\(377\) 1.40097 + 1.29991i 1.40097 + 1.29991i
\(378\) 0 0
\(379\) 0 0 0.532032 0.846724i \(-0.321429\pi\)
−0.532032 + 0.846724i \(0.678571\pi\)
\(380\) 0 0
\(381\) 0.373714 + 0.707101i 0.373714 + 0.707101i
\(382\) 0 0
\(383\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(384\) 0.307647 0.705135i 0.307647 0.705135i
\(385\) 0 0
\(386\) 1.14503 + 1.43583i 1.14503 + 1.43583i
\(387\) 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
\(392\) 0.891505 0.560170i 0.891505 0.560170i
\(393\) −1.42271 1.05001i −1.42271 1.05001i
\(394\) 1.14457 + 1.14457i 1.14457 + 1.14457i
\(395\) 0 0
\(396\) 0 0
\(397\) −0.185853 0.233052i −0.185853 0.233052i 0.680173 0.733052i \(-0.261905\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) −0.190772 + 0.835827i −0.190772 + 0.835827i
\(401\) 0 0 0.974928 0.222521i \(-0.0714286\pi\)
−0.974928 + 0.222521i \(0.928571\pi\)
\(402\) 0 0
\(403\) −0.933767 + 0.326739i −0.933767 + 0.326739i
\(404\) −0.127191 + 0.202424i −0.127191 + 0.202424i
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 0.392253 + 1.12099i 0.392253 + 1.12099i 0.955573 + 0.294755i \(0.0952381\pi\)
−0.563320 + 0.826239i \(0.690476\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) −0.933884 0.0349435i −0.933884 0.0349435i
\(415\) 0 0
\(416\) −0.454019 0.158868i −0.454019 0.158868i
\(417\) 1.34515 0.202749i 1.34515 0.202749i
\(418\) 0 0
\(419\) 0 0 0.623490 0.781831i \(-0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(420\) 0 0
\(421\) 0 0 −0.532032 0.846724i \(-0.678571\pi\)
0.532032 + 0.846724i \(0.321429\pi\)
\(422\) −1.03330 0.824026i −1.03330 0.824026i
\(423\) 0.988831 1.14904i 0.988831 1.14904i
\(424\) 0 0
\(425\) 0 0
\(426\) 0.829249 + 0.963605i 0.829249 + 0.963605i
\(427\) 0 0
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 −0.433884 0.900969i \(-0.642857\pi\)
0.433884 + 0.900969i \(0.357143\pi\)
\(432\) −0.772421 + 0.371978i −0.772421 + 0.371978i
\(433\) 0 0 −0.846724 0.532032i \(-0.821429\pi\)
0.846724 + 0.532032i \(0.178571\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) 0.323462 0.126950i 0.323462 0.126950i
\(439\) −0.129334 0.268565i −0.129334 0.268565i 0.826239 0.563320i \(-0.190476\pi\)
−0.955573 + 0.294755i \(0.904762\pi\)
\(440\) 0 0
\(441\) −0.988831 0.149042i −0.988831 0.149042i
\(442\) 0 0
\(443\) −0.220025 + 1.95278i −0.220025 + 1.95278i 0.0747301 + 0.997204i \(0.476190\pi\)
−0.294755 + 0.955573i \(0.595238\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) −0.130478 1.15802i −0.130478 1.15802i
\(447\) 0 0
\(448\) 0 0
\(449\) −0.900969 1.43388i −0.900969 1.43388i −0.900969 0.433884i \(-0.857143\pi\)
1.00000i \(-0.5\pi\)
\(450\) 0.751927 0.554947i 0.751927 0.554947i
\(451\) 0 0
\(452\) 0 0
\(453\) −0.149042 0.988831i −0.149042 0.988831i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 0 0 0.433884 0.900969i \(-0.357143\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 0.605443 + 1.73026i 0.605443 + 1.73026i 0.680173 + 0.733052i \(0.261905\pi\)
−0.0747301 + 0.997204i \(0.523810\pi\)
\(462\) 0 0
\(463\) 0.445042i 0.445042i −0.974928 0.222521i \(-0.928571\pi\)
0.974928 0.222521i \(-0.0714286\pi\)
\(464\) 0.583127 0.628462i 0.583127 0.628462i
\(465\) 0 0
\(466\) −0.983301 + 1.56491i −0.983301 + 1.56491i
\(467\) 0 0 0.943883 0.330279i \(-0.107143\pi\)
−0.943883 + 0.330279i \(0.892857\pi\)
\(468\) 0.121014 + 0.209602i 0.121014 + 0.209602i
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) −1.88531 0.212423i −1.88531 0.212423i
\(473\) 0 0
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 0 0
\(478\) −0.235873 + 0.148209i −0.235873 + 0.148209i
\(479\) 0 0 0.846724 0.532032i \(-0.178571\pi\)
−0.846724 + 0.532032i \(0.821429\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) 0.0789588 + 0.0990112i 0.0789588 + 0.0990112i
\(485\) 0 0
\(486\) 0.902694 + 0.241876i 0.902694 + 0.241876i
\(487\) 0.414278 1.81507i 0.414278 1.81507i −0.149042 0.988831i \(-0.547619\pi\)
0.563320 0.826239i \(-0.309524\pi\)
\(488\) 0 0
\(489\) 1.34027 0.708353i 1.34027 0.708353i
\(490\) 0 0
\(491\) 0.856144 1.36254i 0.856144 1.36254i −0.0747301 0.997204i \(-0.523810\pi\)
0.930874 0.365341i \(-0.119048\pi\)
\(492\) −0.150298 + 0.00562374i −0.150298 + 0.00562374i
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0.146572 + 0.418879i 0.146572 + 0.418879i
\(497\) 0 0
\(498\) 0 0
\(499\) −0.145713 0.0332580i −0.145713 0.0332580i 0.149042 0.988831i \(-0.452381\pi\)
−0.294755 + 0.955573i \(0.595238\pi\)
\(500\) 0 0
\(501\) −0.0332580 + 0.443797i −0.0332580 + 0.443797i
\(502\) 0 0
\(503\) 0 0 −0.943883 0.330279i \(-0.892857\pi\)
0.943883 + 0.330279i \(0.107143\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −2.19158 + 1.49419i −2.19158 + 1.49419i
\(508\) −0.0538867 0.0857602i −0.0538867 0.0857602i
\(509\) −0.880843 0.702449i −0.880843 0.702449i 0.0747301 0.997204i \(-0.476190\pi\)
−0.955573 + 0.294755i \(0.904762\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −0.369398 + 1.05568i −0.369398 + 1.05568i
\(513\) 0 0
\(514\) 0.208685 1.85213i 0.208685 1.85213i
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) −0.455573 1.16078i −0.455573 1.16078i
\(520\) 0 0
\(521\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(522\) −0.928661 + 0.104635i −0.928661 + 0.104635i
\(523\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(524\) 0.189606 + 0.119137i 0.189606 + 0.119137i
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) 0.900969 + 0.433884i 0.900969 + 0.433884i
\(530\) 0 0
\(531\) 1.22563 + 1.32091i 1.22563 + 1.32091i
\(532\) 0 0
\(533\) −0.254132 2.25548i −0.254132 2.25548i
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) −0.603718 + 0.411608i −0.603718 + 0.411608i
\(538\) −0.466014 + 0.584363i −0.466014 + 0.584363i
\(539\) 0 0
\(540\) 0 0
\(541\) −1.23137 0.430874i −1.23137 0.430874i −0.365341 0.930874i \(-0.619048\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(542\) 1.23732 0.986729i 1.23732 0.986729i
\(543\) 0 0
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −1.78181 + 0.858075i −1.78181 + 0.858075i −0.826239 + 0.563320i \(0.809524\pi\)
−0.955573 + 0.294755i \(0.904762\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 0 0
\(552\) 1.05215 0.0393687i 1.05215 0.0393687i
\(553\) 0 0
\(554\) −1.29324 + 0.452525i −1.29324 + 0.452525i
\(555\) 0 0
\(556\) −0.167955 + 0.0383346i −0.167955 + 0.0383346i
\(557\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(558\) 0.176734 0.450312i 0.176734 0.450312i
\(559\) 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 \(0.250000\pi\)
\(564\) −0.114001 + 0.154466i −0.114001 + 0.154466i
\(565\) 0 0
\(566\) 0 0
\(567\) 0 0
\(568\) −1.01278 1.01278i −1.01278 1.01278i
\(569\) 0 0 0.993712 0.111964i \(-0.0357143\pi\)
−0.993712 + 0.111964i \(0.964286\pi\)
\(570\) 0 0
\(571\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −0.974928 + 0.222521i −0.974928 + 0.222521i
\(576\) 0.946162 0.546267i 0.946162 0.546267i
\(577\) 1.73026 0.605443i 1.73026 0.605443i 0.733052 0.680173i \(-0.238095\pi\)
0.997204 + 0.0747301i \(0.0238095\pi\)
\(578\) 0.497204 0.791295i 0.497204 0.791295i
\(579\) 0.0734787 + 1.96376i 0.0734787 + 1.96376i
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) −0.352718 + 0.169860i −0.352718 + 0.169860i
\(585\) 0 0
\(586\) 0 0
\(587\) −0.807782 + 1.67738i −0.807782 + 1.67738i −0.0747301 + 0.997204i \(0.523810\pi\)
−0.733052 + 0.680173i \(0.761905\pi\)
\(588\) 0.126286 + 0.00946383i 0.126286 + 0.00946383i
\(589\) 0 0
\(590\) 0 0
\(591\) 0.258149 + 1.71271i 0.258149 + 1.71271i
\(592\) 0 0
\(593\) −0.974928 + 1.22252i −0.974928 + 1.22252i 1.00000i \(0.5\pi\)
−0.974928 + 0.222521i \(0.928571\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0.199973 + 1.77481i 0.199973 + 1.77481i
\(599\) −0.559311 + 1.59842i −0.559311 + 1.59842i 0.222521 + 0.974928i \(0.428571\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(600\) −0.798059 + 0.686785i −0.798059 + 0.686785i
\(601\) −0.216299 + 1.91970i −0.216299 + 1.91970i 0.149042 + 0.988831i \(0.452381\pi\)
−0.365341 + 0.930874i \(0.619048\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0.0281801 + 0.123465i 0.0281801 + 0.123465i
\(605\) 0 0
\(606\) 1.64224 0.644530i 1.64224 0.644530i
\(607\) −0.189606 0.119137i −0.189606 0.119137i 0.433884 0.900969i \(-0.357143\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −2.45312 1.54140i −2.45312 1.54140i
\(612\) 0 0
\(613\) 0 0 −0.433884 0.900969i \(-0.642857\pi\)
0.433884 + 0.900969i \(0.357143\pi\)
\(614\) 0.137366 + 0.601839i 0.137366 + 0.601839i
\(615\) 0 0
\(616\) 0 0
\(617\) 0 0 0.111964 0.993712i \(-0.464286\pi\)
−0.111964 + 0.993712i \(0.535714\pi\)
\(618\) 0 0
\(619\) 0 0 0.330279 0.943883i \(-0.392857\pi\)
−0.330279 + 0.943883i \(0.607143\pi\)
\(620\) 0 0
\(621\) −0.781831 0.623490i −0.781831 0.623490i
\(622\) −1.46028 1.16453i −1.46028 1.16453i
\(623\) 0 0
\(624\) 0.922982 + 1.35377i 0.922982 + 1.35377i
\(625\) 0.623490 0.781831i 0.623490 0.781831i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 0 0 0.433884 0.900969i \(-0.357143\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(632\) 0 0
\(633\) −0.366025 1.36603i −0.366025 1.36603i
\(634\) −0.895930 + 0.431457i −0.895930 + 0.431457i
\(635\) 0 0
\(636\) 0 0
\(637\) 1.91115i 1.91115i
\(638\) 0 0
\(639\) 0.101659 + 1.35654i 0.101659 + 1.35654i
\(640\) 0 0
\(641\) 0 0 0.943883 0.330279i \(-0.107143\pi\)
−0.943883 + 0.330279i \(0.892857\pi\)
\(642\) 0 0
\(643\) 0 0 0.974928 0.222521i \(-0.0714286\pi\)
−0.974928 + 0.222521i \(0.928571\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −0.702449 0.880843i −0.702449 0.880843i 0.294755 0.955573i \(-0.404762\pi\)
−0.997204 + 0.0747301i \(0.976190\pi\)
\(648\) −1.03453 0.195744i −1.03453 0.195744i
\(649\) 0 0
\(650\) −1.26292 1.26292i −1.26292 1.26292i
\(651\) 0 0
\(652\) −0.162553 + 0.102139i −0.162553 + 0.102139i
\(653\) 1.63575 1.02781i 1.63575 1.02781i 0.680173 0.733052i \(-0.261905\pi\)
0.955573 0.294755i \(-0.0952381\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) −1.01179 + 0.114001i −1.01179 + 0.114001i
\(657\) 0.359154 + 0.0962349i 0.359154 + 0.0962349i
\(658\) 0 0
\(659\) 0 0 −0.993712 0.111964i \(-0.964286\pi\)
0.993712 + 0.111964i \(0.0357143\pi\)
\(660\) 0 0
\(661\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(662\) 1.67017 0.381206i 1.67017 0.381206i
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0.955573 + 0.294755i 0.955573 + 0.294755i
\(668\) 0.0563602i 0.0563602i
\(669\) 0.623490 1.07992i 0.623490 1.07992i
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 1.81507 + 0.414278i 1.81507 + 0.414278i 0.988831 0.149042i \(-0.0476190\pi\)
0.826239 + 0.563320i \(0.190476\pi\)
\(674\) 0 0
\(675\) 1.00000 1.00000
\(676\) 0.262625 0.209436i 0.262625 0.209436i
\(677\) 0 0 −0.943883 0.330279i \(-0.892857\pi\)
0.943883 + 0.330279i \(0.107143\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −1.55929 1.24349i −1.55929 1.24349i −0.826239 0.563320i \(-0.809524\pi\)
−0.733052 0.680173i \(-0.761905\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) 0.433884 + 1.90097i 0.433884 + 1.90097i 0.433884 + 0.900969i \(0.357143\pi\)
1.00000i \(0.500000\pi\)
\(692\) 0.0685179 + 0.142279i 0.0685179 + 0.142279i
\(693\) 0 0
\(694\) 1.23732 + 0.777459i 1.23732 + 0.777459i
\(695\) 0 0
\(696\) 1.03453 0.195744i 1.03453 0.195744i
\(697\) 0 0
\(698\) 0.118267 + 0.0743122i 0.118267 + 0.0743122i
\(699\) −1.84095 + 0.722521i −1.84095 + 0.722521i
\(700\) 0 0
\(701\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(702\) 0.199973 1.77481i 0.199973 1.77481i
\(703\) 0 0
\(704\) 0 0
\(705\) 0 0
\(706\) −0.574643 + 1.64224i −0.574643 + 1.64224i
\(707\) 0 0
\(708\) −0.167281 0.155214i −0.167281 0.155214i
\(709\) 0 0 −0.781831 0.623490i \(-0.785714\pi\)
0.781831 + 0.623490i \(0.214286\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −0.366025 + 0.366025i −0.366025 + 0.366025i
\(714\) 0 0
\(715\) 0 0
\(716\) 0.0723457 0.0576938i 0.0723457 0.0576938i
\(717\) −0.297251 0.0222759i −0.297251 0.0222759i
\(718\) 0 0
\(719\) 1.90097 + 0.433884i 1.90097 + 0.433884i 1.00000 \(0\)
0.900969 + 0.433884i \(0.142857\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0.308658 + 0.882094i 0.308658 + 0.882094i
\(723\) 0 0
\(724\) 0 0
\(725\) −0.930874 + 0.365341i −0.930874 + 0.365341i
\(726\) −0.0349435 0.933884i −0.0349435 0.933884i
\(727\) 0 0 0.532032 0.846724i \(-0.321429\pi\)
−0.532032 + 0.846724i \(0.678571\pi\)
\(728\) 0 0
\(729\) 0.623490 + 0.781831i 0.623490 + 0.781831i
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 0 0 −0.993712 0.111964i \(-0.964286\pi\)
0.993712 + 0.111964i \(0.0357143\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) −0.250105 + 0.0281801i −0.250105 + 0.0281801i
\(737\) 0 0
\(738\) 0.917038 + 0.625226i 0.917038 + 0.625226i
\(739\) −1.00560 + 0.631863i −1.00560 + 0.631863i −0.930874 0.365341i \(-0.880952\pi\)
−0.0747301 + 0.997204i \(0.523810\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 0.993712 0.111964i \(-0.0357143\pi\)
−0.993712 + 0.111964i \(0.964286\pi\)
\(744\) −0.160646 + 0.520801i −0.160646 + 0.520801i
\(745\) 0 0
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 0 0 0.943883 0.330279i \(-0.107143\pi\)
−0.943883 + 0.330279i \(0.892857\pi\)
\(752\) −0.691457 + 1.10045i −0.691457 + 1.10045i
\(753\) 0 0
\(754\) 0.462260 + 1.72518i 0.462260 + 1.72518i
\(755\) 0 0
\(756\) 0 0
\(757\) 0 0 −0.330279 0.943883i \(-0.607143\pi\)
0.330279 + 0.943883i \(0.392857\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 0.636119 1.32091i 0.636119 1.32091i −0.294755 0.955573i \(-0.595238\pi\)
0.930874 0.365341i \(-0.119048\pi\)
\(762\) −0.0558554 + 0.745338i −0.0558554 + 0.745338i
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 2.14715 2.69244i 2.14715 2.69244i
\(768\) −0.308658 + 0.210440i −0.308658 + 0.210440i
\(769\) 0 0 −0.532032 0.846724i \(-0.678571\pi\)
0.532032 + 0.846724i \(0.321429\pi\)
\(770\) 0 0
\(771\) 1.35654 1.46200i 1.35654 1.46200i
\(772\) −0.0278640 0.247300i −0.0278640 0.247300i
\(773\) 0 0 0.330279 0.943883i \(-0.392857\pi\)
−0.330279 + 0.943883i \(0.607143\pi\)
\(774\) 0 0
\(775\) 0.0579571 0.514383i 0.0579571 0.514383i
\(776\) 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
\(784\) 0.857322 0.857322
\(785\) 0 0
\(786\) −0.603718 1.53825i −0.603718 1.53825i
\(787\) 0 0 −0.433884 0.900969i \(-0.642857\pi\)
0.433884 + 0.900969i \(0.357143\pi\)
\(788\) −0.0488093