Properties

Label 2001.1.bf.c.620.1
Level $2001$
Weight $1$
Character 2001.620
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 620.1
Root \(-0.149042 + 0.988831i\) of defining polynomial
Character \(\chi\) \(=\) 2001.620
Dual form 2001.1.bf.c.965.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.122805 + 0.350958i) q^{2} +(-0.733052 - 0.680173i) q^{3} +(0.673741 - 0.537291i) q^{4} +(0.148689 - 0.340799i) q^{6} +(0.586137 + 0.368294i) q^{8} +(0.0747301 + 0.997204i) q^{9} +O(q^{10})\) \(q+(0.122805 + 0.350958i) q^{2} +(-0.733052 - 0.680173i) q^{3} +(0.673741 - 0.537291i) q^{4} +(0.148689 - 0.340799i) q^{6} +(0.586137 + 0.368294i) q^{8} +(0.0747301 + 0.997204i) q^{9} +(-0.859338 - 0.0643985i) q^{12} +(1.61105 + 0.367711i) q^{13} +(0.134482 - 0.589204i) q^{16} +(-0.340799 + 0.148689i) q^{18} +(-0.433884 - 0.900969i) q^{23} +(-0.179165 - 0.668653i) q^{24} +(0.623490 + 0.781831i) q^{25} +(0.0687943 + 0.610566i) q^{26} +(0.623490 - 0.781831i) q^{27} +(0.149042 + 0.988831i) q^{29} +(-1.82344 + 0.638050i) q^{31} +(0.911189 - 0.102666i) q^{32} +(0.586137 + 0.631706i) q^{36} +(-0.930874 - 1.36534i) q^{39} +(0.660818 - 0.660818i) q^{41} +(0.262919 - 0.262919i) q^{46} +(0.631863 + 1.00560i) q^{47} +(-0.499343 + 0.340446i) q^{48} +(-0.222521 - 0.974928i) q^{49} +(-0.197822 + 0.314832i) q^{50} +(1.28300 - 0.617858i) q^{52} +(0.350958 + 0.122805i) q^{54} +(-0.328735 + 0.173741i) q^{58} -1.24698i q^{59} +(-0.447857 - 0.561595i) q^{62} +(-0.114290 - 0.237325i) q^{64} +(-0.294755 + 0.955573i) q^{69} +(0.443797 - 1.94440i) q^{71} +(-0.323462 + 0.612021i) q^{72} +(-0.754903 - 0.264152i) q^{73} +(0.0747301 - 0.997204i) q^{75} +(0.364861 - 0.494369i) q^{78} +(-0.988831 + 0.149042i) q^{81} +(0.313071 + 0.150767i) q^{82} +(0.563320 - 0.826239i) q^{87} +(-0.776408 - 0.373898i) q^{92} +(1.77066 + 0.772532i) q^{93} +(-0.275328 + 0.345251i) q^{94} +(-0.737780 - 0.544506i) q^{96} +(0.314832 - 0.197822i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q - 2q^{2} + 2q^{3} + 14q^{4} - 2q^{6} + 6q^{8} + 2q^{9} + O(q^{10}) \) \( 24q - 2q^{2} + 2q^{3} + 14q^{4} - 2q^{6} + 6q^{8} + 2q^{9} - 6q^{12} - 6q^{16} + 4q^{18} - 6q^{24} - 4q^{25} + 2q^{26} - 4q^{27} - 2q^{31} + 4q^{32} + 6q^{36} + 2q^{41} + 2q^{46} - 2q^{47} - 4q^{48} - 4q^{49} - 2q^{50} - 10q^{52} + 12q^{54} + 4q^{58} + 4q^{62} - 28q^{64} + 14q^{72} - 2q^{73} + 2q^{75} + 10q^{78} + 2q^{81} - 4q^{82} + 4q^{92} - 2q^{93} - 8q^{94} - 24q^{96} - 2q^{98} + O(q^{100}) \)

Character values

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

\(n\) \(553\) \(668\) \(1132\)
\(\chi(n)\) \(e\left(\frac{25}{28}\right)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.122805 + 0.350958i 0.122805 + 0.350958i 0.988831 0.149042i \(-0.0476190\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(3\) −0.733052 0.680173i −0.733052 0.680173i
\(4\) 0.673741 0.537291i 0.673741 0.537291i
\(5\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(6\) 0.148689 0.340799i 0.148689 0.340799i
\(7\) 0 0 0.623490 0.781831i \(-0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(8\) 0.586137 + 0.368294i 0.586137 + 0.368294i
\(9\) 0.0747301 + 0.997204i 0.0747301 + 0.997204i
\(10\) 0 0
\(11\) 0 0 0.846724 0.532032i \(-0.178571\pi\)
−0.846724 + 0.532032i \(0.821429\pi\)
\(12\) −0.859338 0.0643985i −0.859338 0.0643985i
\(13\) 1.61105 + 0.367711i 1.61105 + 0.367711i 0.930874 0.365341i \(-0.119048\pi\)
0.680173 + 0.733052i \(0.261905\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0.134482 0.589204i 0.134482 0.589204i
\(17\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(18\) −0.340799 + 0.148689i −0.340799 + 0.148689i
\(19\) 0 0 −0.993712 0.111964i \(-0.964286\pi\)
0.993712 + 0.111964i \(0.0357143\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −0.433884 0.900969i −0.433884 0.900969i
\(24\) −0.179165 0.668653i −0.179165 0.668653i
\(25\) 0.623490 + 0.781831i 0.623490 + 0.781831i
\(26\) 0.0687943 + 0.610566i 0.0687943 + 0.610566i
\(27\) 0.623490 0.781831i 0.623490 0.781831i
\(28\) 0 0
\(29\) 0.149042 + 0.988831i 0.149042 + 0.988831i
\(30\) 0 0
\(31\) −1.82344 + 0.638050i −1.82344 + 0.638050i −0.826239 + 0.563320i \(0.809524\pi\)
−0.997204 + 0.0747301i \(0.976190\pi\)
\(32\) 0.911189 0.102666i 0.911189 0.102666i
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) 0.586137 + 0.631706i 0.586137 + 0.631706i
\(37\) 0 0 0.532032 0.846724i \(-0.321429\pi\)
−0.532032 + 0.846724i \(0.678571\pi\)
\(38\) 0 0
\(39\) −0.930874 1.36534i −0.930874 1.36534i
\(40\) 0 0
\(41\) 0.660818 0.660818i 0.660818 0.660818i −0.294755 0.955573i \(-0.595238\pi\)
0.955573 + 0.294755i \(0.0952381\pi\)
\(42\) 0 0
\(43\) 0 0 0.330279 0.943883i \(-0.392857\pi\)
−0.330279 + 0.943883i \(0.607143\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0.262919 0.262919i 0.262919 0.262919i
\(47\) 0.631863 + 1.00560i 0.631863 + 1.00560i 0.997204 + 0.0747301i \(0.0238095\pi\)
−0.365341 + 0.930874i \(0.619048\pi\)
\(48\) −0.499343 + 0.340446i −0.499343 + 0.340446i
\(49\) −0.222521 0.974928i −0.222521 0.974928i
\(50\) −0.197822 + 0.314832i −0.197822 + 0.314832i
\(51\) 0 0
\(52\) 1.28300 0.617858i 1.28300 0.617858i
\(53\) 0 0 0.433884 0.900969i \(-0.357143\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(54\) 0.350958 + 0.122805i 0.350958 + 0.122805i
\(55\) 0 0
\(56\) 0 0
\(57\) 0 0
\(58\) −0.328735 + 0.173741i −0.328735 + 0.173741i
\(59\) 1.24698i 1.24698i −0.781831 0.623490i \(-0.785714\pi\)
0.781831 0.623490i \(-0.214286\pi\)
\(60\) 0 0
\(61\) 0 0 −0.111964 0.993712i \(-0.535714\pi\)
0.111964 + 0.993712i \(0.464286\pi\)
\(62\) −0.447857 0.561595i −0.447857 0.561595i
\(63\) 0 0
\(64\) −0.114290 0.237325i −0.114290 0.237325i
\(65\) 0 0
\(66\) 0 0
\(67\) 0 0 0.974928 0.222521i \(-0.0714286\pi\)
−0.974928 + 0.222521i \(0.928571\pi\)
\(68\) 0 0
\(69\) −0.294755 + 0.955573i −0.294755 + 0.955573i
\(70\) 0 0
\(71\) 0.443797 1.94440i 0.443797 1.94440i 0.149042 0.988831i \(-0.452381\pi\)
0.294755 0.955573i \(-0.404762\pi\)
\(72\) −0.323462 + 0.612021i −0.323462 + 0.612021i
\(73\) −0.754903 0.264152i −0.754903 0.264152i −0.0747301 0.997204i \(-0.523810\pi\)
−0.680173 + 0.733052i \(0.738095\pi\)
\(74\) 0 0
\(75\) 0.0747301 0.997204i 0.0747301 0.997204i
\(76\) 0 0
\(77\) 0 0
\(78\) 0.364861 0.494369i 0.364861 0.494369i
\(79\) 0 0 −0.846724 0.532032i \(-0.821429\pi\)
0.846724 + 0.532032i \(0.178571\pi\)
\(80\) 0 0
\(81\) −0.988831 + 0.149042i −0.988831 + 0.149042i
\(82\) 0.313071 + 0.150767i 0.313071 + 0.150767i
\(83\) 0 0 0.781831 0.623490i \(-0.214286\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 0.563320 0.826239i 0.563320 0.826239i
\(88\) 0 0
\(89\) 0 0 −0.330279 0.943883i \(-0.607143\pi\)
0.330279 + 0.943883i \(0.392857\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −0.776408 0.373898i −0.776408 0.373898i
\(93\) 1.77066 + 0.772532i 1.77066 + 0.772532i
\(94\) −0.275328 + 0.345251i −0.275328 + 0.345251i
\(95\) 0 0
\(96\) −0.737780 0.544506i −0.737780 0.544506i
\(97\) 0 0 0.111964 0.993712i \(-0.464286\pi\)
−0.111964 + 0.993712i \(0.535714\pi\)
\(98\) 0.314832 0.197822i 0.314832 0.197822i
\(99\) 0 0
\(100\) 0.840142 + 0.191757i 0.840142 + 0.191757i
\(101\) −1.87590 0.656405i −1.87590 0.656405i −0.974928 0.222521i \(-0.928571\pi\)
−0.900969 0.433884i \(-0.857143\pi\)
\(102\) 0 0
\(103\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(104\) 0.808868 + 0.808868i 0.808868 + 0.808868i
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 0.974928 0.222521i \(-0.0714286\pi\)
−0.974928 + 0.222521i \(0.928571\pi\)
\(108\) 0.861747i 0.861747i
\(109\) 0 0 −0.781831 0.623490i \(-0.785714\pi\)
0.781831 + 0.623490i \(0.214286\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 0 0 −0.111964 0.993712i \(-0.535714\pi\)
0.111964 + 0.993712i \(0.464286\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0.631706 + 0.586137i 0.631706 + 0.586137i
\(117\) −0.246289 + 1.63402i −0.246289 + 1.63402i
\(118\) 0.437637 0.153136i 0.437637 0.153136i
\(119\) 0 0
\(120\) 0 0
\(121\) 0.433884 0.900969i 0.433884 0.900969i
\(122\) 0 0
\(123\) −0.933884 + 0.0349435i −0.933884 + 0.0349435i
\(124\) −0.885710 + 1.40960i −0.885710 + 1.40960i
\(125\) 0 0
\(126\) 0 0
\(127\) 1.06332 + 1.69226i 1.06332 + 1.69226i 0.563320 + 0.826239i \(0.309524\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(128\) 0.717641 0.717641i 0.717641 0.717641i
\(129\) 0 0
\(130\) 0 0
\(131\) −0.649042 + 1.85486i −0.649042 + 1.85486i −0.149042 + 0.988831i \(0.547619\pi\)
−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 \(-0.321429\pi\)
−0.532032 + 0.846724i \(0.678571\pi\)
\(138\) −0.371563 + 0.0139029i −0.371563 + 0.0139029i
\(139\) −1.79690 + 0.865341i −1.79690 + 0.865341i −0.866025 + 0.500000i \(0.833333\pi\)
−0.930874 + 0.365341i \(0.880952\pi\)
\(140\) 0 0
\(141\) 0.220796 1.16694i 0.220796 1.16694i
\(142\) 0.736904 0.0830292i 0.736904 0.0830292i
\(143\) 0 0
\(144\) 0.597606 + 0.0900746i 0.597606 + 0.0900746i
\(145\) 0 0
\(146\) 0.297378i 0.297378i
\(147\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(148\) 0 0
\(149\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(150\) 0.359154 0.0962349i 0.359154 0.0962349i
\(151\) 0.433884 + 0.900969i 0.433884 + 0.900969i 0.997204 + 0.0747301i \(0.0238095\pi\)
−0.563320 + 0.826239i \(0.690476\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) −1.36075 0.419737i −1.36075 0.419737i
\(157\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) −0.173741 0.328735i −0.173741 0.328735i
\(163\) 1.00560 0.631863i 1.00560 0.631863i 0.0747301 0.997204i \(-0.476190\pi\)
0.930874 + 0.365341i \(0.119048\pi\)
\(164\) 0.0901689 0.800271i 0.0901689 0.800271i
\(165\) 0 0
\(166\) 0 0
\(167\) −1.12349 + 1.40881i −1.12349 + 1.40881i −0.222521 + 0.974928i \(0.571429\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(168\) 0 0
\(169\) 1.55929 + 0.750915i 1.55929 + 0.750915i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 0.445042 0.445042 0.222521 0.974928i \(-0.428571\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(174\) 0.359154 + 0.0962349i 0.359154 + 0.0962349i
\(175\) 0 0
\(176\) 0 0
\(177\) −0.848162 + 0.914101i −0.848162 + 0.914101i
\(178\) 0 0
\(179\) −1.32091 0.636119i −1.32091 0.636119i −0.365341 0.930874i \(-0.619048\pi\)
−0.955573 + 0.294755i \(0.904762\pi\)
\(180\) 0 0
\(181\) 0 0 0.623490 0.781831i \(-0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0.0775064 0.687888i 0.0775064 0.687888i
\(185\) 0 0
\(186\) −0.0536792 + 0.716299i −0.0536792 + 0.716299i
\(187\) 0 0
\(188\) 0.966014 + 0.338023i 0.966014 + 0.338023i
\(189\) 0 0
\(190\) 0 0
\(191\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(192\) −0.0776418 + 0.251709i −0.0776418 + 0.251709i
\(193\) −1.82160 0.205245i −1.82160 0.205245i −0.866025 0.500000i \(-0.833333\pi\)
−0.955573 + 0.294755i \(0.904762\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) −0.673741 0.537291i −0.673741 0.537291i
\(197\) 0.751509 + 1.56052i 0.751509 + 1.56052i 0.826239 + 0.563320i \(0.190476\pi\)
−0.0747301 + 0.997204i \(0.523810\pi\)
\(198\) 0 0
\(199\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(200\) 0.0775064 + 0.687888i 0.0775064 + 0.687888i
\(201\) 0 0
\(202\) 0.738971i 0.738971i
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 0.866025 0.500000i 0.866025 0.500000i
\(208\) 0.433313 0.899784i 0.433313 0.899784i
\(209\) 0 0
\(210\) 0 0
\(211\) −0.752407 + 1.19745i −0.752407 + 1.19745i 0.222521 + 0.974928i \(0.428571\pi\)
−0.974928 + 0.222521i \(0.928571\pi\)
\(212\) 0 0
\(213\) −1.64786 + 1.12349i −1.64786 + 1.12349i
\(214\) 0 0
\(215\) 0 0
\(216\) 0.653395 0.228633i 0.653395 0.228633i
\(217\) 0 0
\(218\) 0 0
\(219\) 0.373714 + 0.707101i 0.373714 + 0.707101i
\(220\) 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
\(225\) −0.733052 + 0.680173i −0.733052 + 0.680173i
\(226\) 0 0
\(227\) 0 0 0.433884 0.900969i \(-0.357143\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(228\) 0 0
\(229\) 0 0 0.993712 0.111964i \(-0.0357143\pi\)
−0.993712 + 0.111964i \(0.964286\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −0.276822 + 0.634482i −0.276822 + 0.634482i
\(233\) 1.91115i 1.91115i 0.294755 + 0.955573i \(0.404762\pi\)
−0.294755 + 0.955573i \(0.595238\pi\)
\(234\) −0.603718 + 0.114230i −0.603718 + 0.114230i
\(235\) 0 0
\(236\) −0.669991 0.840142i −0.669991 0.840142i
\(237\) 0 0
\(238\) 0 0
\(239\) −0.460898 0.367554i −0.460898 0.367554i 0.365341 0.930874i \(-0.380952\pi\)
−0.826239 + 0.563320i \(0.809524\pi\)
\(240\) 0 0
\(241\) 0 0 0.974928 0.222521i \(-0.0714286\pi\)
−0.974928 + 0.222521i \(0.928571\pi\)
\(242\) 0.369485 + 0.0416310i 0.369485 + 0.0416310i
\(243\) 0.826239 + 0.563320i 0.826239 + 0.563320i
\(244\) 0 0
\(245\) 0 0
\(246\) −0.126950 0.323462i −0.126950 0.323462i
\(247\) 0 0
\(248\) −1.30378 0.297579i −1.30378 0.297579i
\(249\) 0 0
\(250\) 0 0
\(251\) 0 0 0.111964 0.993712i \(-0.464286\pi\)
−0.111964 + 0.993712i \(0.535714\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) −0.463332 + 0.581000i −0.463332 + 0.581000i
\(255\) 0 0
\(256\) 0.102666 + 0.0494415i 0.102666 + 0.0494415i
\(257\) 0.233052 0.185853i 0.233052 0.185853i −0.500000 0.866025i \(-0.666667\pi\)
0.733052 + 0.680173i \(0.238095\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) −0.974928 + 0.222521i −0.974928 + 0.222521i
\(262\) −0.730682 −0.730682
\(263\) 0 0 −0.330279 0.943883i \(-0.607143\pi\)
0.330279 + 0.943883i \(0.392857\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −1.69226 1.06332i −1.69226 1.06332i −0.866025 0.500000i \(-0.833333\pi\)
−0.826239 0.563320i \(-0.809524\pi\)
\(270\) 0 0
\(271\) 0.0739590 0.656405i 0.0739590 0.656405i −0.900969 0.433884i \(-0.857143\pi\)
0.974928 0.222521i \(-0.0714286\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) 0.314832 + 0.802178i 0.314832 + 0.802178i
\(277\) −0.0332580 + 0.145713i −0.0332580 + 0.145713i −0.988831 0.149042i \(-0.952381\pi\)
0.955573 + 0.294755i \(0.0952381\pi\)
\(278\) −0.524367 0.524367i −0.524367 0.524367i
\(279\) −0.772532 1.77066i −0.772532 1.77066i
\(280\) 0 0
\(281\) 0 0 0.974928 0.222521i \(-0.0714286\pi\)
−0.974928 + 0.222521i \(0.928571\pi\)
\(282\) 0.436660 0.0658159i 0.436660 0.0658159i
\(283\) 0 0 −0.781831 0.623490i \(-0.785714\pi\)
0.781831 + 0.623490i \(0.214286\pi\)
\(284\) −0.745705 1.54847i −0.745705 1.54847i
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0.170473 + 0.900969i 0.170473 + 0.900969i
\(289\) 1.00000i 1.00000i
\(290\) 0 0
\(291\) 0 0
\(292\) −0.650536 + 0.227632i −0.650536 + 0.227632i
\(293\) 0 0 0.993712 0.111964i \(-0.0357143\pi\)
−0.993712 + 0.111964i \(0.964286\pi\)
\(294\) −0.365341 0.0691263i −0.365341 0.0691263i
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −0.367711 1.61105i −0.367711 1.61105i
\(300\) −0.485440 0.712009i −0.485440 0.712009i
\(301\) 0 0
\(302\) −0.262919 + 0.262919i −0.262919 + 0.262919i
\(303\) 0.928661 + 1.75711i 0.928661 + 1.75711i
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 0.158342 0.158342i 0.158342 0.158342i −0.623490 0.781831i \(-0.714286\pi\)
0.781831 + 0.623490i \(0.214286\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 0.806531 1.28359i 0.806531 1.28359i −0.149042 0.988831i \(-0.547619\pi\)
0.955573 0.294755i \(-0.0952381\pi\)
\(312\) −0.0427723 1.14311i −0.0427723 1.14311i
\(313\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(314\) 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
\(324\) −0.586137 + 0.631706i −0.586137 + 0.631706i
\(325\) 0.716983 + 1.48883i 0.716983 + 1.48883i
\(326\) 0.345251 + 0.275328i 0.345251 + 0.275328i
\(327\) 0 0
\(328\) 0.630705 0.143954i 0.630705 0.143954i
\(329\) 0 0
\(330\) 0 0
\(331\) −0.0528791 0.0528791i −0.0528791 0.0528791i 0.680173 0.733052i \(-0.261905\pi\)
−0.733052 + 0.680173i \(0.761905\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) −0.632404 0.221288i −0.632404 0.221288i
\(335\) 0 0
\(336\) 0 0
\(337\) 0 0 0.846724 0.532032i \(-0.178571\pi\)
−0.846724 + 0.532032i \(0.821429\pi\)
\(338\) −0.0720500 + 0.639462i −0.0720500 + 0.639462i
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 0 0
\(346\) 0.0546536 + 0.156191i 0.0546536 + 0.156191i
\(347\) 1.94986 1.94986 0.974928 0.222521i \(-0.0714286\pi\)
0.974928 + 0.222521i \(0.0714286\pi\)
\(348\) −0.0643985 0.859338i −0.0643985 0.859338i
\(349\) −1.97766 −1.97766 −0.988831 0.149042i \(-0.952381\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(350\) 0 0
\(351\) 1.29196 1.03030i 1.29196 1.03030i
\(352\) 0 0
\(353\) 1.22563 + 0.590232i 1.22563 + 0.590232i 0.930874 0.365341i \(-0.119048\pi\)
0.294755 + 0.955573i \(0.404762\pi\)
\(354\) −0.424970 0.185412i −0.424970 0.185412i
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0.0610354 0.541704i 0.0610354 0.541704i
\(359\) 0 0 0.846724 0.532032i \(-0.178571\pi\)
−0.846724 + 0.532032i \(0.821429\pi\)
\(360\) 0 0
\(361\) 0.974928 + 0.222521i 0.974928 + 0.222521i
\(362\) 0 0
\(363\) −0.930874 + 0.365341i −0.930874 + 0.365341i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 0 0 −0.993712 0.111964i \(-0.964286\pi\)
0.993712 + 0.111964i \(0.0357143\pi\)
\(368\) −0.589204 + 0.134482i −0.589204 + 0.134482i
\(369\) 0.708353 + 0.609587i 0.708353 + 0.609587i
\(370\) 0 0
\(371\) 0 0
\(372\) 1.60804 0.430874i 1.60804 0.430874i
\(373\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0.822133i 0.822133i
\(377\) −0.123490 + 1.64786i −0.123490 + 1.64786i
\(378\) 0 0
\(379\) 0 0 0.943883 0.330279i \(-0.107143\pi\)
−0.943883 + 0.330279i \(0.892857\pi\)
\(380\) 0 0
\(381\) 0.371563 1.96376i 0.371563 1.96376i
\(382\) 0 0
\(383\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(384\) −1.01419 + 0.0379482i −1.01419 + 0.0379482i
\(385\) 0 0
\(386\) −0.151670 0.664509i −0.151670 0.664509i
\(387\) 0 0
\(388\) 0 0
\(389\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0.228633 0.653395i 0.228633 0.653395i
\(393\) 1.73740 0.918245i 1.73740 0.918245i
\(394\) −0.455389 + 0.455389i −0.455389 + 0.455389i
\(395\) 0 0
\(396\) 0 0
\(397\) −0.131178 0.574730i −0.131178 0.574730i −0.997204 0.0747301i \(-0.976190\pi\)
0.866025 0.500000i \(-0.166667\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0.544506 0.262220i 0.544506 0.262220i
\(401\) 0 0 0.433884 0.900969i \(-0.357143\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(402\) 0 0
\(403\) −3.17227 + 0.357429i −3.17227 + 0.357429i
\(404\) −1.61655 + 0.565655i −1.61655 + 0.565655i
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) −0.104635 0.928661i −0.104635 0.928661i −0.930874 0.365341i \(-0.880952\pi\)
0.826239 0.563320i \(-0.190476\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) 0.281831 + 0.242536i 0.281831 + 0.242536i
\(415\) 0 0
\(416\) 1.50572 + 0.169654i 1.50572 + 0.169654i
\(417\) 1.90580 + 0.587862i 1.90580 + 0.587862i
\(418\) 0 0
\(419\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(420\) 0 0
\(421\) 0 0 −0.943883 0.330279i \(-0.892857\pi\)
0.943883 + 0.330279i \(0.107143\pi\)
\(422\) −0.512654 0.117010i −0.512654 0.117010i
\(423\) −0.955573 + 0.705245i −0.955573 + 0.705245i
\(424\) 0 0
\(425\) 0 0
\(426\) −0.596663 0.440357i −0.596663 0.440357i
\(427\) 0 0
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 0.781831 0.623490i \(-0.214286\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(432\) −0.376810 0.472505i −0.376810 0.472505i
\(433\) 0 0 −0.330279 0.943883i \(-0.607143\pi\)
0.330279 + 0.943883i \(0.392857\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) −0.202269 + 0.217994i −0.202269 + 0.217994i
\(439\) −0.460898 + 0.367554i −0.460898 + 0.367554i −0.826239 0.563320i \(-0.809524\pi\)
0.365341 + 0.930874i \(0.380952\pi\)
\(440\) 0 0
\(441\) 0.955573 0.294755i 0.955573 0.294755i
\(442\) 0 0
\(443\) −1.55215 0.975281i −1.55215 0.975281i −0.988831 0.149042i \(-0.952381\pi\)
−0.563320 0.826239i \(-0.690476\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0.140113 0.0880390i 0.140113 0.0880390i
\(447\) 0 0
\(448\) 0 0
\(449\) 0.623490 + 0.218169i 0.623490 + 0.218169i 0.623490 0.781831i \(-0.285714\pi\)
1.00000i \(0.5\pi\)
\(450\) −0.328735 0.173741i −0.328735 0.173741i
\(451\) 0 0
\(452\) 0 0
\(453\) 0.294755 0.955573i 0.294755 0.955573i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 0 0 −0.781831 0.623490i \(-0.785714\pi\)
0.781831 + 0.623490i \(0.214286\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −0.00837297 0.0743122i −0.00837297 0.0743122i 0.988831 0.149042i \(-0.0476190\pi\)
−0.997204 + 0.0747301i \(0.976190\pi\)
\(462\) 0 0
\(463\) 1.80194i 1.80194i 0.433884 + 0.900969i \(0.357143\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(464\) 0.602666 + 0.0451636i 0.602666 + 0.0451636i
\(465\) 0 0
\(466\) −0.670731 + 0.234699i −0.670731 + 0.234699i
\(467\) 0 0 0.993712 0.111964i \(-0.0357143\pi\)
−0.993712 + 0.111964i \(0.964286\pi\)
\(468\) 0.712009 + 1.23324i 0.712009 + 1.23324i
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 0.459256 0.730901i 0.459256 0.730901i
\(473\) 0 0
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 0 0
\(478\) 0.0723951 0.206893i 0.0723951 0.206893i
\(479\) 0 0 0.330279 0.943883i \(-0.392857\pi\)
−0.330279 + 0.943883i \(0.607143\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) −0.191757 0.840142i −0.191757 0.840142i
\(485\) 0 0
\(486\) −0.0962349 + 0.359154i −0.0962349 + 0.359154i
\(487\) 1.22563 0.590232i 1.22563 0.590232i 0.294755 0.955573i \(-0.404762\pi\)
0.930874 + 0.365341i \(0.119048\pi\)
\(488\) 0 0
\(489\) −1.16694 0.220796i −1.16694 0.220796i
\(490\) 0 0
\(491\) 1.66900 0.584010i 1.66900 0.584010i 0.680173 0.733052i \(-0.261905\pi\)
0.988831 + 0.149042i \(0.0476190\pi\)
\(492\) −0.610421 + 0.525310i −0.610421 + 0.525310i
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0.130722 + 1.16019i 0.130722 + 1.16019i
\(497\) 0 0
\(498\) 0 0
\(499\) −0.858075 1.78181i −0.858075 1.78181i −0.563320 0.826239i \(-0.690476\pi\)
−0.294755 0.955573i \(-0.595238\pi\)
\(500\) 0 0
\(501\) 1.78181 0.268565i 1.78181 0.268565i
\(502\) 0 0
\(503\) 0 0 −0.993712 0.111964i \(-0.964286\pi\)
0.993712 + 0.111964i \(0.0357143\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −0.632289 1.61105i −0.632289 1.61105i
\(508\) 1.62564 + 0.568836i 1.62564 + 0.568836i
\(509\) −1.81507 0.414278i −1.81507 0.414278i −0.826239 0.563320i \(-0.809524\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0.108889 0.966412i 0.108889 0.966412i
\(513\) 0 0
\(514\) 0.0938465 + 0.0589676i 0.0938465 + 0.0589676i
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) −0.326239 0.302705i −0.326239 0.302705i
\(520\) 0 0
\(521\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(522\) −0.197822 0.314832i −0.197822 0.314832i
\(523\) 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
\(531\) 1.24349 0.0931869i 1.24349 0.0931869i
\(532\) 0 0
\(533\) 1.30760 0.821618i 1.30760 0.821618i
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0.535628 + 1.36476i 0.535628 + 1.36476i
\(538\) 0.165361 0.724495i 0.165361 0.724495i
\(539\) 0 0
\(540\) 0 0
\(541\) 1.59908 + 0.180173i 1.59908 + 0.180173i 0.866025 0.500000i \(-0.166667\pi\)
0.733052 + 0.680173i \(0.238095\pi\)
\(542\) 0.239453 0.0546536i 0.239453 0.0546536i
\(543\) 0 0
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −1.19158 1.49419i −1.19158 1.49419i −0.826239 0.563320i \(-0.809524\pi\)
−0.365341 0.930874i \(-0.619048\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 0 0
\(552\) −0.524699 + 0.451540i −0.524699 + 0.451540i
\(553\) 0 0
\(554\) −0.0552233 + 0.00622218i −0.0552233 + 0.00622218i
\(555\) 0 0
\(556\) −0.745705 + 1.54847i −0.745705 + 1.54847i
\(557\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(558\) 0.526557 0.488573i 0.526557 0.488573i
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(564\) −0.478224 0.904844i −0.478224 0.904844i
\(565\) 0 0
\(566\) 0 0
\(567\) 0 0
\(568\) 0.976239 0.976239i 0.976239 0.976239i
\(569\) 0 0 −0.532032 0.846724i \(-0.678571\pi\)
0.532032 + 0.846724i \(0.321429\pi\)
\(570\) 0 0
\(571\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0.433884 0.900969i 0.433884 0.900969i
\(576\) 0.228121 0.131706i 0.228121 0.131706i
\(577\) 0.0743122 0.00837297i 0.0743122 0.00837297i −0.0747301 0.997204i \(-0.523810\pi\)
0.149042 + 0.988831i \(0.452381\pi\)
\(578\) −0.350958 + 0.122805i −0.350958 + 0.122805i
\(579\) 1.19572 + 1.38946i 1.19572 + 1.38946i
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) −0.345191 0.432856i −0.345191 0.432856i
\(585\) 0 0
\(586\) 0 0
\(587\) 1.06356 + 0.848162i 1.06356 + 0.848162i 0.988831 0.149042i \(-0.0476190\pi\)
0.0747301 + 0.997204i \(0.476190\pi\)
\(588\) 0.128437 + 0.852122i 0.128437 + 0.852122i
\(589\) 0 0
\(590\) 0 0
\(591\) 0.510531 1.65510i 0.510531 1.65510i
\(592\) 0 0
\(593\) 0.433884 1.90097i 0.433884 1.90097i 1.00000i \(-0.5\pi\)
0.433884 0.900969i \(-0.357143\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0.520252 0.326896i 0.520252 0.326896i
\(599\) −0.0739590 + 0.656405i −0.0739590 + 0.656405i 0.900969 + 0.433884i \(0.142857\pi\)
−0.974928 + 0.222521i \(0.928571\pi\)
\(600\) 0.411067 0.556976i 0.411067 0.556976i
\(601\) 0.438297 + 0.275400i 0.438297 + 0.275400i 0.733052 0.680173i \(-0.238095\pi\)
−0.294755 + 0.955573i \(0.595238\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0.776408 + 0.373898i 0.776408 + 0.373898i
\(605\) 0 0
\(606\) −0.502628 + 0.541704i −0.502628 + 0.541704i
\(607\) −0.559311 1.59842i −0.559311 1.59842i −0.781831 0.623490i \(-0.785714\pi\)
0.222521 0.974928i \(-0.428571\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0.648189 + 1.85242i 0.648189 + 1.85242i
\(612\) 0 0
\(613\) 0 0 0.781831 0.623490i \(-0.214286\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(614\) 0.0750165 + 0.0361260i 0.0750165 + 0.0361260i
\(615\) 0 0
\(616\) 0 0
\(617\) 0 0 −0.846724 0.532032i \(-0.821429\pi\)
0.846724 + 0.532032i \(0.178571\pi\)
\(618\) 0 0
\(619\) 0 0 0.111964 0.993712i \(-0.464286\pi\)
−0.111964 + 0.993712i \(0.535714\pi\)
\(620\) 0 0
\(621\) −0.974928 0.222521i −0.974928 0.222521i
\(622\) 0.549531 + 0.125427i 0.549531 + 0.125427i
\(623\) 0 0
\(624\) −0.929650 + 0.364861i −0.929650 + 0.364861i
\(625\) −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 \(-0.785714\pi\)
0.781831 + 0.623490i \(0.214286\pi\)
\(632\) 0 0
\(633\) 1.36603 0.366025i 1.36603 0.366025i
\(634\) −0.437637 0.548780i −0.437637 0.548780i
\(635\) 0 0
\(636\) 0 0
\(637\) 1.65248i 1.65248i
\(638\) 0 0
\(639\) 1.97213 + 0.297251i 1.97213 + 0.297251i
\(640\) 0 0
\(641\) 0 0 0.993712 0.111964i \(-0.0357143\pi\)
−0.993712 + 0.111964i \(0.964286\pi\)
\(642\) 0 0
\(643\) 0 0 0.433884 0.900969i \(-0.357143\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 0.414278 + 1.81507i 0.414278 + 1.81507i 0.563320 + 0.826239i \(0.309524\pi\)
−0.149042 + 0.988831i \(0.547619\pi\)
\(648\) −0.634482 0.276822i −0.634482 0.276822i
\(649\) 0 0
\(650\) −0.434467 + 0.434467i −0.434467 + 0.434467i
\(651\) 0 0
\(652\) 0.338023 0.966014i 0.338023 0.966014i
\(653\) −0.170965 + 0.488590i −0.170965 + 0.488590i −0.997204 0.0747301i \(-0.976190\pi\)
0.826239 + 0.563320i \(0.190476\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) −0.300488 0.478224i −0.300488 0.478224i
\(657\) 0.206999 0.772532i 0.206999 0.772532i
\(658\) 0 0
\(659\) 0 0 0.532032 0.846724i \(-0.321429\pi\)
−0.532032 + 0.846724i \(0.678571\pi\)
\(660\) 0 0
\(661\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(662\) 0.0120645 0.0250522i 0.0120645 0.0250522i
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0.826239 0.563320i 0.826239 0.563320i
\(668\) 1.55282i 1.55282i
\(669\) −0.222521 + 0.385418i −0.222521 + 0.385418i
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) −0.590232 1.22563i −0.590232 1.22563i −0.955573 0.294755i \(-0.904762\pi\)
0.365341 0.930874i \(-0.380952\pi\)
\(674\) 0 0
\(675\) 1.00000 1.00000
\(676\) 1.45402 0.331870i 1.45402 0.331870i
\(677\) 0 0 −0.993712 0.111964i \(-0.964286\pi\)
0.993712 + 0.111964i \(0.0357143\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −0.290611 0.0663300i −0.290611 0.0663300i 0.0747301 0.997204i \(-0.476190\pi\)
−0.365341 + 0.930874i \(0.619048\pi\)
\(684\) 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 1.00000i \(-0.5\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(692\) 0.299843 0.239117i 0.299843 0.239117i
\(693\) 0 0
\(694\) 0.239453 + 0.684317i 0.239453 + 0.684317i
\(695\) 0 0
\(696\) 0.634482 0.276822i 0.634482 0.276822i
\(697\) 0 0
\(698\) −0.242868 0.694076i −0.242868 0.694076i
\(699\) 1.29991 1.40097i 1.29991 1.40097i
\(700\) 0 0
\(701\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(702\) 0.520252 + 0.326896i 0.520252 + 0.326896i
\(703\) 0 0
\(704\) 0 0
\(705\) 0 0
\(706\) −0.0566325 + 0.502628i −0.0566325 + 0.502628i
\(707\) 0 0
\(708\) −0.0803036 + 1.07158i −0.0803036 + 1.07158i
\(709\) 0 0 −0.974928 0.222521i \(-0.928571\pi\)
0.974928 + 0.222521i \(0.0714286\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 1.36603 + 1.36603i 1.36603 + 1.36603i
\(714\) 0 0
\(715\) 0 0
\(716\) −1.23173 + 0.281135i −1.23173 + 0.281135i
\(717\) 0.0878620 + 0.582926i 0.0878620 + 0.582926i
\(718\) 0 0
\(719\) 0.376510 + 0.781831i 0.376510 + 0.781831i 1.00000 \(0\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0.0416310 + 0.369485i 0.0416310 + 0.369485i
\(723\) 0 0
\(724\) 0 0
\(725\) −0.680173 + 0.733052i −0.680173 + 0.733052i
\(726\) −0.242536 0.281831i −0.242536 0.281831i
\(727\) 0 0 0.943883 0.330279i \(-0.107143\pi\)
−0.943883 + 0.330279i \(0.892857\pi\)
\(728\) 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 \(-0.321429\pi\)
−0.532032 + 0.846724i \(0.678571\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) −0.487849 0.776408i −0.487849 0.776408i
\(737\) 0 0
\(738\) −0.126950 + 0.323462i −0.126950 + 0.323462i
\(739\) 0.308658 0.882094i 0.308658 0.882094i −0.680173 0.733052i \(-0.738095\pi\)
0.988831 0.149042i \(-0.0476190\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 −0.532032 0.846724i \(-0.678571\pi\)
0.532032 + 0.846724i \(0.321429\pi\)
\(744\) 0.753332 + 1.10493i 0.753332 + 1.10493i
\(745\) 0 0
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 0 0 0.993712 0.111964i \(-0.0357143\pi\)
−0.993712 + 0.111964i \(0.964286\pi\)
\(752\) 0.677480 0.237060i 0.677480 0.237060i
\(753\) 0 0
\(754\) −0.593493 + 0.159026i −0.593493 + 0.159026i
\(755\) 0 0
\(756\) 0 0
\(757\) 0 0 −0.111964 0.993712i \(-0.535714\pi\)
0.111964 + 0.993712i \(0.464286\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 0.116853 + 0.0931869i 0.116853 + 0.0931869i 0.680173 0.733052i \(-0.261905\pi\)
−0.563320 + 0.826239i \(0.690476\pi\)
\(762\) 0.734826 0.110757i 0.734826 0.110757i
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0.458528 2.00894i 0.458528 2.00894i
\(768\) −0.0416310 0.106074i −0.0416310 0.106074i
\(769\) 0 0 −0.943883 0.330279i \(-0.892857\pi\)
0.943883 + 0.330279i \(0.107143\pi\)
\(770\) 0 0
\(771\) −0.297251 0.0222759i −0.297251 0.0222759i
\(772\) −1.33756 + 0.840446i −1.33756 + 0.840446i
\(773\) 0 0 0.111964 0.993712i \(-0.464286\pi\)
−0.111964 + 0.993712i \(0.535714\pi\)
\(774\) 0 0
\(775\) −1.63575 1.02781i −1.63575 1.02781i
\(776\) 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
\(784\) −0.604356 −0.604356
\(785\) 0 0
\(786\) 0.535628 + 0.496990i 0.535628 + 0.496990i
\(787\) 0 0 0.781831 0.623490i \(-0.214286\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(788\)