Properties

Label 2001.1.bf.c.482.1
Level $2001$
Weight $1$
Character 2001.482
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 482.1
Root \(-0.930874 + 0.365341i\) of defining polynomial
Character \(\chi\) \(=\) 2001.482
Dual form 2001.1.bf.c.137.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.23137 + 0.430874i) q^{2} +(0.955573 - 0.294755i) q^{3} +(0.548780 - 0.437637i) q^{4} +(-1.04966 + 0.774683i) q^{6} +(0.206893 - 0.329269i) q^{8} +(0.826239 - 0.563320i) q^{9} +O(q^{10})\) \(q+(-1.23137 + 0.430874i) q^{2} +(0.955573 - 0.294755i) q^{3} +(0.548780 - 0.437637i) q^{4} +(-1.04966 + 0.774683i) q^{6} +(0.206893 - 0.329269i) q^{8} +(0.826239 - 0.563320i) q^{9} +(0.395403 - 0.579950i) q^{12} +(-0.145713 - 0.0332580i) q^{13} +(-0.269079 + 1.17891i) q^{16} +(-0.774683 + 1.04966i) q^{18} +(0.433884 + 0.900969i) q^{23} +(0.100648 - 0.375623i) q^{24} +(0.623490 + 0.781831i) q^{25} +(0.193756 - 0.0218311i) q^{26} +(0.623490 - 0.781831i) q^{27} +(0.930874 + 0.365341i) q^{29} +(-0.638050 - 1.82344i) q^{31} +(-0.133087 - 1.18118i) q^{32} +(0.206893 - 0.670731i) q^{36} +(-0.149042 + 0.0111692i) q^{39} +(-0.0528791 - 0.0528791i) q^{41} +(-0.922474 - 0.922474i) q^{46} +(1.55215 - 0.975281i) q^{47} +(0.0903659 + 1.20585i) q^{48} +(-0.222521 - 0.974928i) q^{49} +(-1.10462 - 0.694076i) q^{50} +(-0.0945192 + 0.0455181i) q^{52} +(-0.430874 + 1.23137i) q^{54} +(-1.30366 - 0.0487796i) q^{58} +1.24698i q^{59} +(1.57135 + 1.97041i) q^{62} +(0.148155 + 0.307647i) q^{64} +(0.680173 + 0.733052i) q^{69} +(0.250701 - 1.09839i) q^{71} +(-0.0145404 - 0.388602i) q^{72} +(-0.531484 + 1.51889i) q^{73} +(0.826239 + 0.563320i) q^{75} +(0.178713 - 0.0779717i) q^{78} +(0.365341 - 0.930874i) q^{81} +(0.0878978 + 0.0423294i) q^{82} +(0.997204 + 0.0747301i) q^{87} +(0.632404 + 0.304550i) q^{92} +(-1.14717 - 1.55436i) q^{93} +(-1.49104 + 1.86971i) q^{94} +(-0.475335 - 1.08948i) q^{96} +(0.694076 + 1.10462i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q - 2q^{2} + 2q^{3} + 14q^{4} - 2q^{6} + 6q^{8} + 2q^{9} + O(q^{10}) \) \( 24q - 2q^{2} + 2q^{3} + 14q^{4} - 2q^{6} + 6q^{8} + 2q^{9} - 6q^{12} - 6q^{16} + 4q^{18} - 6q^{24} - 4q^{25} + 2q^{26} - 4q^{27} - 2q^{31} + 4q^{32} + 6q^{36} + 2q^{41} + 2q^{46} - 2q^{47} - 4q^{48} - 4q^{49} - 2q^{50} - 10q^{52} + 12q^{54} + 4q^{58} + 4q^{62} - 28q^{64} + 14q^{72} - 2q^{73} + 2q^{75} + 10q^{78} + 2q^{81} - 4q^{82} + 4q^{92} - 2q^{93} - 8q^{94} - 24q^{96} - 2q^{98} + O(q^{100}) \)

Character values

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

\(n\) \(553\) \(668\) \(1132\)
\(\chi(n)\) \(e\left(\frac{11}{28}\right)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.23137 + 0.430874i −1.23137 + 0.430874i −0.866025 0.500000i \(-0.833333\pi\)
−0.365341 + 0.930874i \(0.619048\pi\)
\(3\) 0.955573 0.294755i 0.955573 0.294755i
\(4\) 0.548780 0.437637i 0.548780 0.437637i
\(5\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(6\) −1.04966 + 0.774683i −1.04966 + 0.774683i
\(7\) 0 0 0.623490 0.781831i \(-0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(8\) 0.206893 0.329269i 0.206893 0.329269i
\(9\) 0.826239 0.563320i 0.826239 0.563320i
\(10\) 0 0
\(11\) 0 0 −0.532032 0.846724i \(-0.678571\pi\)
0.532032 + 0.846724i \(0.321429\pi\)
\(12\) 0.395403 0.579950i 0.395403 0.579950i
\(13\) −0.145713 0.0332580i −0.145713 0.0332580i 0.149042 0.988831i \(-0.452381\pi\)
−0.294755 + 0.955573i \(0.595238\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −0.269079 + 1.17891i −0.269079 + 1.17891i
\(17\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(18\) −0.774683 + 1.04966i −0.774683 + 1.04966i
\(19\) 0 0 0.111964 0.993712i \(-0.464286\pi\)
−0.111964 + 0.993712i \(0.535714\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 0.433884 + 0.900969i 0.433884 + 0.900969i
\(24\) 0.100648 0.375623i 0.100648 0.375623i
\(25\) 0.623490 + 0.781831i 0.623490 + 0.781831i
\(26\) 0.193756 0.0218311i 0.193756 0.0218311i
\(27\) 0.623490 0.781831i 0.623490 0.781831i
\(28\) 0 0
\(29\) 0.930874 + 0.365341i 0.930874 + 0.365341i
\(30\) 0 0
\(31\) −0.638050 1.82344i −0.638050 1.82344i −0.563320 0.826239i \(-0.690476\pi\)
−0.0747301 0.997204i \(-0.523810\pi\)
\(32\) −0.133087 1.18118i −0.133087 1.18118i
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) 0.206893 0.670731i 0.206893 0.670731i
\(37\) 0 0 −0.846724 0.532032i \(-0.821429\pi\)
0.846724 + 0.532032i \(0.178571\pi\)
\(38\) 0 0
\(39\) −0.149042 + 0.0111692i −0.149042 + 0.0111692i
\(40\) 0 0
\(41\) −0.0528791 0.0528791i −0.0528791 0.0528791i 0.680173 0.733052i \(-0.261905\pi\)
−0.733052 + 0.680173i \(0.761905\pi\)
\(42\) 0 0
\(43\) 0 0 −0.943883 0.330279i \(-0.892857\pi\)
0.943883 + 0.330279i \(0.107143\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) −0.922474 0.922474i −0.922474 0.922474i
\(47\) 1.55215 0.975281i 1.55215 0.975281i 0.563320 0.826239i \(-0.309524\pi\)
0.988831 0.149042i \(-0.0476190\pi\)
\(48\) 0.0903659 + 1.20585i 0.0903659 + 1.20585i
\(49\) −0.222521 0.974928i −0.222521 0.974928i
\(50\) −1.10462 0.694076i −1.10462 0.694076i
\(51\) 0 0
\(52\) −0.0945192 + 0.0455181i −0.0945192 + 0.0455181i
\(53\) 0 0 0.433884 0.900969i \(-0.357143\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(54\) −0.430874 + 1.23137i −0.430874 + 1.23137i
\(55\) 0 0
\(56\) 0 0
\(57\) 0 0
\(58\) −1.30366 0.0487796i −1.30366 0.0487796i
\(59\) 1.24698i 1.24698i 0.781831 + 0.623490i \(0.214286\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(60\) 0 0
\(61\) 0 0 0.993712 0.111964i \(-0.0357143\pi\)
−0.993712 + 0.111964i \(0.964286\pi\)
\(62\) 1.57135 + 1.97041i 1.57135 + 1.97041i
\(63\) 0 0
\(64\) 0.148155 + 0.307647i 0.148155 + 0.307647i
\(65\) 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
\(69\) 0.680173 + 0.733052i 0.680173 + 0.733052i
\(70\) 0 0
\(71\) 0.250701 1.09839i 0.250701 1.09839i −0.680173 0.733052i \(-0.738095\pi\)
0.930874 0.365341i \(-0.119048\pi\)
\(72\) −0.0145404 0.388602i −0.0145404 0.388602i
\(73\) −0.531484 + 1.51889i −0.531484 + 1.51889i 0.294755 + 0.955573i \(0.404762\pi\)
−0.826239 + 0.563320i \(0.809524\pi\)
\(74\) 0 0
\(75\) 0.826239 + 0.563320i 0.826239 + 0.563320i
\(76\) 0 0
\(77\) 0 0
\(78\) 0.178713 0.0779717i 0.178713 0.0779717i
\(79\) 0 0 0.532032 0.846724i \(-0.321429\pi\)
−0.532032 + 0.846724i \(0.678571\pi\)
\(80\) 0 0
\(81\) 0.365341 0.930874i 0.365341 0.930874i
\(82\) 0.0878978 + 0.0423294i 0.0878978 + 0.0423294i
\(83\) 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
\(87\) 0.997204 + 0.0747301i 0.997204 + 0.0747301i
\(88\) 0 0
\(89\) 0 0 0.943883 0.330279i \(-0.107143\pi\)
−0.943883 + 0.330279i \(0.892857\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0.632404 + 0.304550i 0.632404 + 0.304550i
\(93\) −1.14717 1.55436i −1.14717 1.55436i
\(94\) −1.49104 + 1.86971i −1.49104 + 1.86971i
\(95\) 0 0
\(96\) −0.475335 1.08948i −0.475335 1.08948i
\(97\) 0 0 −0.993712 0.111964i \(-0.964286\pi\)
0.993712 + 0.111964i \(0.0357143\pi\)
\(98\) 0.694076 + 1.10462i 0.694076 + 1.10462i
\(99\) 0 0
\(100\) 0.684317 + 0.156191i 0.684317 + 0.156191i
\(101\) 0.0739590 0.211363i 0.0739590 0.211363i −0.900969 0.433884i \(-0.857143\pi\)
0.974928 + 0.222521i \(0.0714286\pi\)
\(102\) 0 0
\(103\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(104\) −0.0410978 + 0.0410978i −0.0410978 + 0.0410978i
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 0.974928 0.222521i \(-0.0714286\pi\)
−0.974928 + 0.222521i \(0.928571\pi\)
\(108\) 0.701915i 0.701915i
\(109\) 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 0.993712 0.111964i \(-0.0357143\pi\)
−0.993712 + 0.111964i \(0.964286\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0.670731 0.206893i 0.670731 0.206893i
\(117\) −0.139129 + 0.0546039i −0.139129 + 0.0546039i
\(118\) −0.537291 1.53549i −0.537291 1.53549i
\(119\) 0 0
\(120\) 0 0
\(121\) −0.433884 + 0.900969i −0.433884 + 0.900969i
\(122\) 0 0
\(123\) −0.0661163 0.0349435i −0.0661163 0.0349435i
\(124\) −1.14816 0.721434i −1.14816 0.721434i
\(125\) 0 0
\(126\) 0 0
\(127\) 1.49720 0.940755i 1.49720 0.940755i 0.500000 0.866025i \(-0.333333\pi\)
0.997204 0.0747301i \(-0.0238095\pi\)
\(128\) 0.525518 + 0.525518i 0.525518 + 0.525518i
\(129\) 0 0
\(130\) 0 0
\(131\) −1.43087 0.500684i −1.43087 0.500684i −0.500000 0.866025i \(-0.666667\pi\)
−0.930874 + 0.365341i \(0.880952\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 0 0 −0.846724 0.532032i \(-0.821429\pi\)
0.846724 + 0.532032i \(0.178571\pi\)
\(138\) −1.15339 0.609587i −1.15339 0.609587i
\(139\) −1.01507 + 0.488831i −1.01507 + 0.488831i −0.866025 0.500000i \(-0.833333\pi\)
−0.149042 + 0.988831i \(0.547619\pi\)
\(140\) 0 0
\(141\) 1.19572 1.38946i 1.19572 1.38946i
\(142\) 0.164564 + 1.46054i 0.164564 + 1.46054i
\(143\) 0 0
\(144\) 0.441781 + 1.12564i 0.441781 + 1.12564i
\(145\) 0 0
\(146\) 2.09932i 2.09932i
\(147\) −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 \(0.285714\pi\)
\(150\) −1.26012 0.337649i −1.26012 0.337649i
\(151\) −0.433884 0.900969i −0.433884 0.900969i −0.997204 0.0747301i \(-0.976190\pi\)
0.563320 0.826239i \(-0.309524\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) −0.0769033 + 0.0713558i −0.0769033 + 0.0713558i
\(157\) 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
\(162\) −0.0487796 + 1.30366i −0.0487796 + 1.30366i
\(163\) 0.975281 + 1.55215i 0.975281 + 1.55215i 0.826239 + 0.563320i \(0.190476\pi\)
0.149042 + 0.988831i \(0.452381\pi\)
\(164\) −0.0521609 0.00587712i −0.0521609 0.00587712i
\(165\) 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
\(169\) −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 \(0.428571\pi\)
\(174\) −1.26012 + 0.337649i −1.26012 + 0.337649i
\(175\) 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 0.988831 + 0.149042i \(0.0476190\pi\)
0.733052 + 0.680173i \(0.238095\pi\)
\(180\) 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
\(184\) 0.386428 + 0.0435400i 0.386428 + 0.0435400i
\(185\) 0 0
\(186\) 2.08232 + 1.41970i 2.08232 + 1.41970i
\(187\) 0 0
\(188\) 0.424970 1.21449i 0.424970 1.21449i
\(189\) 0 0
\(190\) 0 0
\(191\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(192\) 0.232254 + 0.250310i 0.232254 + 0.250310i
\(193\) −0.132974 + 1.18017i −0.132974 + 1.18017i 0.733052 + 0.680173i \(0.238095\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) −0.548780 0.437637i −0.548780 0.437637i
\(197\) −0.751509 1.56052i −0.751509 1.56052i −0.826239 0.563320i \(-0.809524\pi\)
0.0747301 0.997204i \(-0.476190\pi\)
\(198\) 0 0
\(199\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(200\) 0.386428 0.0435400i 0.386428 0.0435400i
\(201\) 0 0
\(202\) 0.292132i 0.292132i
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(208\) 0.0784166 0.162834i 0.0784166 0.162834i
\(209\) 0 0
\(210\) 0 0
\(211\) 1.19745 + 0.752407i 1.19745 + 0.752407i 0.974928 0.222521i \(-0.0714286\pi\)
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
\(216\) −0.128437 0.367051i −0.128437 0.367051i
\(217\) 0 0
\(218\) 0 0
\(219\) −0.0601697 + 1.60807i −0.0601697 + 1.60807i
\(220\) 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 \(-0.357143\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(228\) 0 0
\(229\) 0 0 −0.111964 0.993712i \(-0.535714\pi\)
0.111964 + 0.993712i \(0.464286\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0.312887 0.230921i 0.312887 0.230921i
\(233\) 1.46610i 1.46610i 0.680173 + 0.733052i \(0.261905\pi\)
−0.680173 + 0.733052i \(0.738095\pi\)
\(234\) 0.147791 0.127184i 0.147791 0.127184i
\(235\) 0 0
\(236\) 0.545725 + 0.684317i 0.545725 + 0.684317i
\(237\) 0 0
\(238\) 0 0
\(239\) −1.06356 0.848162i −1.06356 0.848162i −0.0747301 0.997204i \(-0.523810\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(240\) 0 0
\(241\) 0 0 0.974928 0.222521i \(-0.0714286\pi\)
−0.974928 + 0.222521i \(0.928571\pi\)
\(242\) 0.146066 1.29637i 0.146066 1.29637i
\(243\) 0.0747301 0.997204i 0.0747301 0.997204i
\(244\) 0 0
\(245\) 0 0
\(246\) 0.0964696 + 0.0145404i 0.0964696 + 0.0145404i
\(247\) 0 0
\(248\) −0.732411 0.167168i −0.732411 0.167168i
\(249\) 0 0
\(250\) 0 0
\(251\) 0 0 −0.993712 0.111964i \(-0.964286\pi\)
0.993712 + 0.111964i \(0.0357143\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) −1.43826 + 1.80352i −1.43826 + 1.80352i
\(255\) 0 0
\(256\) −1.18118 0.568828i −1.18118 0.568828i
\(257\) −1.45557 + 1.16078i −1.45557 + 1.16078i −0.500000 + 0.866025i \(0.666667\pi\)
−0.955573 + 0.294755i \(0.904762\pi\)
\(258\) 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 0.943883 0.330279i \(-0.107143\pi\)
−0.943883 + 0.330279i \(0.892857\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −0.940755 + 1.49720i −0.940755 + 1.49720i −0.0747301 + 0.997204i \(0.523810\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(270\) 0 0
\(271\) −1.87590 0.211363i −1.87590 0.211363i −0.900969 0.433884i \(-0.857143\pi\)
−0.974928 + 0.222521i \(0.928571\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) 0.694076 + 0.104615i 0.694076 + 0.104615i
\(277\) −0.367711 + 1.61105i −0.367711 + 1.61105i 0.365341 + 0.930874i \(0.380952\pi\)
−0.733052 + 0.680173i \(0.761905\pi\)
\(278\) 1.03930 1.03930i 1.03930 1.03930i
\(279\) −1.55436 1.14717i −1.55436 1.14717i
\(280\) 0 0
\(281\) 0 0 0.974928 0.222521i \(-0.0714286\pi\)
−0.974928 + 0.222521i \(0.928571\pi\)
\(282\) −0.873694 + 2.22614i −0.873694 + 2.22614i
\(283\) 0 0 −0.781831 0.623490i \(-0.785714\pi\)
0.781831 + 0.623490i \(0.214286\pi\)
\(284\) −0.343118 0.712492i −0.343118 0.712492i
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) −0.775346 0.900969i −0.775346 0.900969i
\(289\) 1.00000i 1.00000i
\(290\) 0 0
\(291\) 0 0
\(292\) 0.373057 + 1.06613i 0.373057 + 1.06613i
\(293\) 0 0 −0.111964 0.993712i \(-0.535714\pi\)
0.111964 + 0.993712i \(0.464286\pi\)
\(294\) 0.988831 + 0.850958i 0.988831 + 0.850958i
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −0.0332580 0.145713i −0.0332580 0.145713i
\(300\) 0.699953 0.0524542i 0.699953 0.0524542i
\(301\) 0 0
\(302\) 0.922474 + 0.922474i 0.922474 + 0.922474i
\(303\) 0.00837297 0.223772i 0.00837297 0.223772i
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) −1.40532 1.40532i −1.40532 1.40532i −0.781831 0.623490i \(-0.785714\pi\)
−0.623490 0.781831i \(-0.714286\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −1.66393 1.04551i −1.66393 1.04551i −0.930874 0.365341i \(-0.880952\pi\)
−0.733052 0.680173i \(-0.761905\pi\)
\(312\) −0.0271582 + 0.0513858i −0.0271582 + 0.0513858i
\(313\) 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
\(317\) −0.218169 0.623490i −0.218169 0.623490i 0.781831 0.623490i \(-0.214286\pi\)
−1.00000 \(\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) −0.206893 0.670731i −0.206893 0.670731i
\(325\) −0.0648483 0.134659i −0.0648483 0.134659i
\(326\) −1.86971 1.49104i −1.86971 1.49104i
\(327\) 0 0
\(328\) −0.0283518 + 0.00647111i −0.0283518 + 0.00647111i
\(329\) 0 0
\(330\) 0 0
\(331\) 0.660818 0.660818i 0.660818 0.660818i −0.294755 0.955573i \(-0.595238\pi\)
0.955573 + 0.294755i \(0.0952381\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0.776408 2.21885i 0.776408 2.21885i
\(335\) 0 0
\(336\) 0 0
\(337\) 0 0 −0.532032 0.846724i \(-0.678571\pi\)
0.532032 + 0.846724i \(0.321429\pi\)
\(338\) 1.26741 + 0.142803i 1.26741 + 0.142803i
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 0 0
\(346\) −0.548010 + 0.191757i −0.548010 + 0.191757i
\(347\) −1.94986 −1.94986 −0.974928 0.222521i \(-0.928571\pi\)
−0.974928 + 0.222521i \(0.928571\pi\)
\(348\) 0.579950 0.395403i 0.579950 0.395403i
\(349\) 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 \(-0.452381\pi\)
−0.680173 + 0.733052i \(0.738095\pi\)
\(354\) −0.966014 1.30890i −0.966014 1.30890i
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) −2.47756 0.279153i −2.47756 0.279153i
\(359\) 0 0 −0.532032 0.846724i \(-0.678571\pi\)
0.532032 + 0.846724i \(0.321429\pi\)
\(360\) 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 0.111964 0.993712i \(-0.464286\pi\)
−0.111964 + 0.993712i \(0.535714\pi\)
\(368\) −1.17891 + 0.269079i −1.17891 + 0.269079i
\(369\) −0.0734787 0.0139029i −0.0734787 0.0139029i
\(370\) 0 0
\(371\) 0 0
\(372\) −1.30979 0.350958i −1.30979 0.350958i
\(373\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0.712854i 0.712854i
\(377\) −0.123490 0.0841939i −0.123490 0.0841939i
\(378\) 0 0
\(379\) 0 0 −0.330279 0.943883i \(-0.607143\pi\)
0.330279 + 0.943883i \(0.392857\pi\)
\(380\) 0 0
\(381\) 1.15339 1.34027i 1.15339 1.34027i
\(382\) 0 0
\(383\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(384\) 0.657069 + 0.347271i 0.657069 + 0.347271i
\(385\) 0 0
\(386\) −0.344766 1.51052i −0.344766 1.51052i
\(387\) 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
\(392\) −0.367051 0.128437i −0.367051 0.128437i
\(393\) −1.51488 0.0566829i −1.51488 0.0566829i
\(394\) 1.59777 + 1.59777i 1.59777 + 1.59777i
\(395\) 0 0
\(396\) 0 0
\(397\) 0.302705 + 1.32624i 0.302705 + 1.32624i 0.866025 + 0.500000i \(0.166667\pi\)
−0.563320 + 0.826239i \(0.690476\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) −1.08948 + 0.524665i −1.08948 + 0.524665i
\(401\) 0 0 0.433884 0.900969i \(-0.357143\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(402\) 0 0
\(403\) 0.0323281 + 0.286919i 0.0323281 + 0.286919i
\(404\) −0.0519130 0.148359i −0.0519130 0.148359i
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) −0.0743122 + 0.00837297i −0.0743122 + 0.00837297i −0.149042 0.988831i \(-0.547619\pi\)
0.0747301 + 0.997204i \(0.476190\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) −1.28183 0.242536i −1.28183 0.242536i
\(415\) 0 0
\(416\) −0.0198913 + 0.176540i −0.0198913 + 0.176540i
\(417\) −0.825886 + 0.766310i −0.825886 + 0.766310i
\(418\) 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 0.330279 0.943883i \(-0.392857\pi\)
−0.330279 + 0.943883i \(0.607143\pi\)
\(422\) −1.79869 0.410539i −1.79869 0.410539i
\(423\) 0.733052 1.68017i 0.733052 1.68017i
\(424\) 0 0
\(425\) 0 0
\(426\) 0.587756 + 1.34715i 0.587756 + 1.34715i
\(427\) 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 \(0.785714\pi\)
\(432\) 0.753943 + 0.945414i 0.753943 + 0.945414i
\(433\) 0 0 0.943883 0.330279i \(-0.107143\pi\)
−0.943883 + 0.330279i \(0.892857\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) −0.618784 2.00605i −0.618784 2.00605i
\(439\) −1.06356 + 0.848162i −1.06356 + 0.848162i −0.988831 0.149042i \(-0.952381\pi\)
−0.0747301 + 0.997204i \(0.523810\pi\)
\(440\) 0 0
\(441\) −0.733052 0.680173i −0.733052 0.680173i
\(442\) 0 0
\(443\) −0.631863 + 1.00560i −0.631863 + 1.00560i 0.365341 + 0.930874i \(0.380952\pi\)
−0.997204 + 0.0747301i \(0.976190\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0.308893 + 0.491600i 0.308893 + 0.491600i
\(447\) 0 0
\(448\) 0 0
\(449\) 0.623490 1.78183i 0.623490 1.78183i 1.00000i \(-0.5\pi\)
0.623490 0.781831i \(-0.285714\pi\)
\(450\) −1.30366 + 0.0487796i −1.30366 + 0.0487796i
\(451\) 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 \(-0.785714\pi\)
0.781831 + 0.623490i \(0.214286\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −0.928661 + 0.104635i −0.928661 + 0.104635i −0.563320 0.826239i \(-0.690476\pi\)
−0.365341 + 0.930874i \(0.619048\pi\)
\(462\) 0 0
\(463\) 1.80194i 1.80194i −0.433884 0.900969i \(-0.642857\pi\)
0.433884 0.900969i \(-0.357143\pi\)
\(464\) −0.681184 + 0.999113i −0.681184 + 0.999113i
\(465\) 0 0
\(466\) −0.631706 1.80531i −0.631706 1.80531i
\(467\) 0 0 −0.111964 0.993712i \(-0.535714\pi\)
0.111964 + 0.993712i \(0.464286\pi\)
\(468\) −0.0524542 + 0.0908534i −0.0524542 + 0.0908534i
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 0.410591 + 0.257992i 0.410591 + 0.257992i
\(473\) 0 0
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 0 0
\(478\) 1.67508 + 0.586137i 1.67508 + 0.586137i
\(479\) 0 0 −0.943883 0.330279i \(-0.892857\pi\)
0.943883 + 0.330279i \(0.107143\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) 0.156191 + 0.684317i 0.156191 + 0.684317i
\(485\) 0 0
\(486\) 0.337649 + 1.26012i 0.337649 + 1.26012i
\(487\) −0.531130 + 0.255779i −0.531130 + 0.255779i −0.680173 0.733052i \(-0.738095\pi\)
0.149042 + 0.988831i \(0.452381\pi\)
\(488\) 0 0
\(489\) 1.38946 + 1.19572i 1.38946 + 1.19572i
\(490\) 0 0
\(491\) −0.660096 1.88645i −0.660096 1.88645i −0.365341 0.930874i \(-0.619048\pi\)
−0.294755 0.955573i \(-0.595238\pi\)
\(492\) −0.0515758 + 0.00975867i −0.0515758 + 0.00975867i
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 2.32136 0.261555i 2.32136 0.261555i
\(497\) 0 0
\(498\) 0 0
\(499\) −0.317031 0.658322i −0.317031 0.658322i 0.680173 0.733052i \(-0.261905\pi\)
−0.997204 + 0.0747301i \(0.976190\pi\)
\(500\) 0 0
\(501\) −0.658322 + 1.67738i −0.658322 + 1.67738i
\(502\) 0 0
\(503\) 0 0 0.111964 0.993712i \(-0.464286\pi\)
−0.111964 + 0.993712i \(0.535714\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −0.966742 0.145713i −0.966742 0.145713i
\(508\) 0.409925 1.17150i 0.409925 1.17150i
\(509\) 0.290611 + 0.0663300i 0.290611 + 0.0663300i 0.365341 0.930874i \(-0.380952\pi\)
−0.0747301 + 0.997204i \(0.523810\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0.961042 + 0.108283i 0.961042 + 0.108283i
\(513\) 0 0
\(514\) 1.29219 2.05651i 1.29219 2.05651i
\(515\) 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 \(\pi\)
\(522\) −1.10462 + 0.694076i −1.10462 + 0.694076i
\(523\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(524\) −1.00435 + 0.351438i −1.00435 + 0.351438i
\(525\) 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
\(533\) 0.00594652 + 0.00946383i 0.00594652 + 0.00946383i
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 1.88980 + 0.284841i 1.88980 + 0.284841i
\(538\) 0.513309 2.24895i 0.513309 2.24895i
\(539\) 0 0
\(540\) 0 0
\(541\) −0.0895474 + 0.794755i −0.0895474 + 0.794755i 0.866025 + 0.500000i \(0.166667\pi\)
−0.955573 + 0.294755i \(0.904762\pi\)
\(542\) 2.40099 0.548010i 2.40099 0.548010i
\(543\) 0 0
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 0.914101 + 1.14625i 0.914101 + 1.14625i 0.988831 + 0.149042i \(0.0476190\pi\)
−0.0747301 + 0.997204i \(0.523810\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 0 0
\(552\) 0.382094 0.0722961i 0.382094 0.0722961i
\(553\) 0 0
\(554\) −0.241371 2.14223i −0.241371 2.14223i
\(555\) 0 0
\(556\) −0.343118 + 0.712492i −0.343118 + 0.712492i
\(557\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(558\) 2.40828 + 0.742855i 2.40828 + 0.742855i
\(559\) 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 \(0.250000\pi\)
\(564\) 0.0481112 1.28580i 0.0481112 1.28580i
\(565\) 0 0
\(566\) 0 0
\(567\) 0 0
\(568\) −0.309798 0.309798i −0.309798 0.309798i
\(569\) 0 0 0.846724 0.532032i \(-0.178571\pi\)
−0.846724 + 0.532032i \(0.821429\pi\)
\(570\) 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
\(576\) 0.295715 + 0.170731i 0.295715 + 0.170731i
\(577\) 0.104635 + 0.928661i 0.104635 + 0.928661i 0.930874 + 0.365341i \(0.119048\pi\)
−0.826239 + 0.563320i \(0.809524\pi\)
\(578\) 0.430874 + 1.23137i 0.430874 + 1.23137i
\(579\) 0.220796 + 1.16694i 0.220796 + 1.16694i
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) 0.390163 + 0.489250i 0.390163 + 0.489250i
\(585\) 0 0
\(586\) 0 0
\(587\) 0.460898 + 0.367554i 0.460898 + 0.367554i 0.826239 0.563320i \(-0.190476\pi\)
−0.365341 + 0.930874i \(0.619048\pi\)
\(588\) −0.653395 0.256439i −0.653395 0.256439i
\(589\) 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 1.00000i \(0.5\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0.103737 + 0.165096i 0.103737 + 0.165096i
\(599\) 1.87590 + 0.211363i 1.87590 + 0.211363i 0.974928 0.222521i \(-0.0714286\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(600\) 0.356427 0.155507i 0.356427 0.155507i
\(601\) −0.275400 + 0.438297i −0.275400 + 0.438297i −0.955573 0.294755i \(-0.904762\pi\)
0.680173 + 0.733052i \(0.261905\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −0.632404 0.304550i −0.632404 0.304550i
\(605\) 0 0
\(606\) 0.0861074 + 0.279153i 0.0861074 + 0.279153i
\(607\) 1.00435 0.351438i 1.00435 0.351438i 0.222521 0.974928i \(-0.428571\pi\)
0.781831 + 0.623490i \(0.214286\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −0.258604 + 0.0904896i −0.258604 + 0.0904896i
\(612\) 0 0
\(613\) 0 0 0.781831 0.623490i \(-0.214286\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(614\) 2.33598 + 1.12495i 2.33598 + 1.12495i
\(615\) 0 0
\(616\) 0 0
\(617\) 0 0 0.532032 0.846724i \(-0.321429\pi\)
−0.532032 + 0.846724i \(0.678571\pi\)
\(618\) 0 0
\(619\) 0 0 −0.993712 0.111964i \(-0.964286\pi\)
0.993712 + 0.111964i \(0.0357143\pi\)
\(620\) 0 0
\(621\) 0.974928 + 0.222521i 0.974928 + 0.222521i
\(622\) 2.49939 + 0.570469i 2.49939 + 0.570469i
\(623\) 0 0
\(624\) 0.0269367 0.178713i 0.0269367 0.178713i
\(625\) −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
\(634\) 0.537291 + 0.673741i 0.537291 + 0.673741i
\(635\) 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 −0.111964 0.993712i \(-0.535714\pi\)
0.111964 + 0.993712i \(0.464286\pi\)
\(642\) 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
\(647\) 0.0663300 + 0.290611i 0.0663300 + 0.290611i 0.997204 0.0747301i \(-0.0238095\pi\)
−0.930874 + 0.365341i \(0.880952\pi\)
\(648\) −0.230921 0.312887i −0.230921 0.312887i
\(649\) 0 0
\(650\) 0.137873 + 0.137873i 0.137873 + 0.137873i
\(651\) 0 0
\(652\) 1.21449 + 0.424970i 1.21449 + 0.424970i
\(653\) −0.488590 0.170965i −0.488590 0.170965i 0.0747301 0.997204i \(-0.476190\pi\)
−0.563320 + 0.826239i \(0.690476\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0.0765685 0.0481112i 0.0765685 0.0481112i
\(657\) 0.416490 + 1.55436i 0.416490 + 1.55436i
\(658\) 0 0
\(659\) 0 0 −0.846724 0.532032i \(-0.821429\pi\)
0.846724 + 0.532032i \(0.178571\pi\)
\(660\) 0 0
\(661\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(662\) −0.528980 + 1.09844i −0.528980 + 1.09844i
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0.0747301 + 0.997204i 0.0747301 + 0.997204i
\(668\) 1.26481i 1.26481i
\(669\) −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 0.733052 0.680173i \(-0.238095\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(674\) 0 0
\(675\) 1.00000 1.00000
\(676\) −0.669030 + 0.152702i −0.669030 + 0.152702i
\(677\) 0 0 0.111964 0.993712i \(-0.464286\pi\)
−0.111964 + 0.993712i \(0.535714\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 1.81507 + 0.414278i 1.81507 + 0.414278i 0.988831 0.149042i \(-0.0476190\pi\)
0.826239 + 0.563320i \(0.190476\pi\)
\(684\) 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 \(-0.214286\pi\)
1.00000i \(0.5\pi\)
\(692\) 0.244230 0.194767i 0.244230 0.194767i
\(693\) 0 0
\(694\) 2.40099 0.840142i 2.40099 0.840142i
\(695\) 0 0
\(696\) 0.230921 0.312887i 0.230921 0.312887i
\(697\) 0 0
\(698\) −0.899737 + 0.314832i −0.899737 + 0.314832i
\(699\) 0.432142 + 1.40097i 0.432142 + 1.40097i
\(700\) 0 0
\(701\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(702\) 0.103737 0.165096i 0.103737 0.165096i
\(703\) 0 0
\(704\) 0 0
\(705\) 0 0
\(706\) 0.764225 + 0.0861074i 0.764225 + 0.0861074i
\(707\) 0 0
\(708\) 0.723186 + 0.493060i 0.723186 + 0.493060i
\(709\) 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
\(716\) 1.30783 0.298504i 1.30783 0.298504i
\(717\) −1.26631 0.496990i −1.26631 0.496990i
\(718\) 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
\(722\) 1.29637 0.146066i 1.29637 0.146066i
\(723\) 0 0
\(724\) 0 0
\(725\) 0.294755 + 0.955573i 0.294755 + 0.955573i
\(726\) −0.242536 1.28183i −0.242536 1.28183i
\(727\) 0 0 −0.330279 0.943883i \(-0.607143\pi\)
0.330279 + 0.943883i \(0.392857\pi\)
\(728\) 0 0
\(729\) −0.222521 0.974928i −0.222521 0.974928i
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 0 0 −0.846724 0.532032i \(-0.821429\pi\)
0.846724 + 0.532032i \(0.178571\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 1.00647 0.632404i 1.00647 0.632404i
\(737\) 0 0
\(738\) 0.0964696 0.0145404i 0.0964696 0.0145404i
\(739\) −0.0705858 0.0246991i −0.0705858 0.0246991i 0.294755 0.955573i \(-0.404762\pi\)
−0.365341 + 0.930874i \(0.619048\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 0.846724 0.532032i \(-0.178571\pi\)
−0.846724 + 0.532032i \(0.821429\pi\)
\(744\) −0.749145 + 0.0561407i −0.749145 + 0.0561407i
\(745\) 0 0
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 0 0 −0.111964 0.993712i \(-0.535714\pi\)
0.111964 + 0.993712i \(0.464286\pi\)
\(752\) 0.732119 + 2.09228i 0.732119 + 2.09228i
\(753\) 0 0
\(754\) 0.188338 + 0.0504651i 0.188338 + 0.0504651i
\(755\) 0 0
\(756\) 0 0
\(757\) 0 0 0.993712 0.111964i \(-0.0357143\pi\)
−0.993712 + 0.111964i \(0.964286\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −1.29196 1.03030i −1.29196 1.03030i −0.997204 0.0747301i \(-0.976190\pi\)
−0.294755 0.955573i \(-0.595238\pi\)
\(762\) −0.842765 + 2.14733i −0.842765 + 2.14733i
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0.0414721 0.181701i 0.0414721 0.181701i
\(768\) −1.29637 0.195397i −1.29637 0.195397i
\(769\) 0 0 0.330279 0.943883i \(-0.392857\pi\)
−0.330279 + 0.943883i \(0.607143\pi\)
\(770\) 0 0
\(771\) −1.04876 + 1.53825i −1.04876 + 1.53825i
\(772\) 0.443514 + 0.705849i 0.443514 + 0.705849i
\(773\) 0 0 −0.993712 0.111964i \(-0.964286\pi\)
0.993712 + 0.111964i \(0.0357143\pi\)
\(774\) 0 0
\(775\) 1.02781 1.63575i 1.02781 1.63575i
\(776\) 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
\(784\) 1.20923 1.20923
\(785\) 0 0
\(786\) 1.88980 0.582926i 1.88980 0.582926i
\(787\) 0 0 0.781831 0.623490i \(-0.214286\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(788\)