Properties

Label 2001.1.bf.d.482.2
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 482.2
Root \(-0.930874 + 0.365341i\) of defining polynomial
Character \(\chi\) \(=\) 2001.482
Dual form 2001.1.bf.d.137.2

$q$-expansion

\(f(q)\) \(=\) \(q+(1.23137 - 0.430874i) q^{2} +(0.997204 + 0.0747301i) q^{3} +(0.548780 - 0.437637i) q^{4} +(1.26012 - 0.337649i) q^{6} +(-0.206893 + 0.329269i) q^{8} +(0.988831 + 0.149042i) q^{9} +O(q^{10})\) \(q+(1.23137 - 0.430874i) q^{2} +(0.997204 + 0.0747301i) q^{3} +(0.548780 - 0.437637i) q^{4} +(1.26012 - 0.337649i) q^{6} +(-0.206893 + 0.329269i) q^{8} +(0.988831 + 0.149042i) q^{9} +(0.579950 - 0.395403i) q^{12} +(-0.145713 - 0.0332580i) q^{13} +(-0.269079 + 1.17891i) q^{16} +(1.28183 - 0.242536i) q^{18} +(-0.433884 - 0.900969i) q^{23} +(-0.230921 + 0.312887i) q^{24} +(0.623490 + 0.781831i) q^{25} +(-0.193756 + 0.0218311i) q^{26} +(0.974928 + 0.222521i) q^{27} +(-0.930874 - 0.365341i) q^{29} +(-0.638050 - 1.82344i) q^{31} +(0.133087 + 1.18118i) q^{32} +(0.607877 - 0.350958i) q^{36} +(-0.142820 - 0.0440542i) q^{39} +(0.0528791 + 0.0528791i) q^{41} +(-0.922474 - 0.922474i) q^{46} +(-1.55215 + 0.975281i) q^{47} +(-0.356427 + 1.15551i) q^{48} +(-0.222521 - 0.974928i) q^{49} +(1.10462 + 0.694076i) q^{50} +(-0.0945192 + 0.0455181i) q^{52} +(1.29637 - 0.146066i) q^{54} +(-1.30366 - 0.0487796i) q^{58} -1.24698i q^{59} +(-1.57135 - 1.97041i) q^{62} +(0.148155 + 0.307647i) q^{64} +(-0.365341 - 0.930874i) q^{69} +(-0.250701 + 1.09839i) q^{71} +(-0.253657 + 0.294755i) q^{72} +(-0.531484 + 1.51889i) q^{73} +(0.563320 + 0.826239i) q^{75} +(-0.194846 + 0.00729061i) q^{78} +(0.955573 + 0.294755i) q^{81} +(0.0878978 + 0.0423294i) q^{82} +(-0.900969 - 0.433884i) q^{87} +(-0.632404 - 0.304550i) q^{92} +(-0.500000 - 1.86603i) q^{93} +(-1.49104 + 1.86971i) q^{94} +(0.0444453 + 1.18783i) q^{96} +(-0.694076 - 1.10462i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q + 2q^{2} + 14q^{4} + 2q^{6} - 6q^{8} - 2q^{9} + O(q^{10}) \) \( 24q + 2q^{2} + 14q^{4} + 2q^{6} - 6q^{8} - 2q^{9} + 2q^{12} - 6q^{16} + 12q^{18} - 6q^{24} - 4q^{25} - 2q^{26} - 2q^{31} - 4q^{32} + 6q^{36} + 2q^{39} - 2q^{41} + 2q^{46} + 2q^{47} + 6q^{48} - 4q^{49} + 2q^{50} - 10q^{52} - 2q^{54} + 4q^{58} - 4q^{62} - 28q^{64} - 2q^{69} + 22q^{72} - 2q^{73} - 4q^{78} + 2q^{81} - 4q^{82} - 4q^{87} - 4q^{92} - 12q^{93} - 8q^{94} - 18q^{96} + 2q^{98} + O(q^{100}) \)

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 0.365341 0.930874i \(-0.380952\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(3\) 0.997204 + 0.0747301i 0.997204 + 0.0747301i
\(4\) 0.548780 0.437637i 0.548780 0.437637i
\(5\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(6\) 1.26012 0.337649i 1.26012 0.337649i
\(7\) 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
\(9\) 0.988831 + 0.149042i 0.988831 + 0.149042i
\(10\) 0 0
\(11\) 0 0 −0.532032 0.846724i \(-0.678571\pi\)
0.532032 + 0.846724i \(0.321429\pi\)
\(12\) 0.579950 0.395403i 0.579950 0.395403i
\(13\) −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 \(0.750000\pi\)
\(18\) 1.28183 0.242536i 1.28183 0.242536i
\(19\) 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
\(24\) −0.230921 + 0.312887i −0.230921 + 0.312887i
\(25\) 0.623490 + 0.781831i 0.623490 + 0.781831i
\(26\) −0.193756 + 0.0218311i −0.193756 + 0.0218311i
\(27\) 0.974928 + 0.222521i 0.974928 + 0.222521i
\(28\) 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
\(36\) 0.607877 0.350958i 0.607877 0.350958i
\(37\) 0 0 −0.846724 0.532032i \(-0.821429\pi\)
0.846724 + 0.532032i \(0.178571\pi\)
\(38\) 0 0
\(39\) −0.142820 0.0440542i −0.142820 0.0440542i
\(40\) 0 0
\(41\) 0.0528791 + 0.0528791i 0.0528791 + 0.0528791i 0.733052 0.680173i \(-0.238095\pi\)
−0.680173 + 0.733052i \(0.738095\pi\)
\(42\) 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 \(0.690476\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(48\) −0.356427 + 1.15551i −0.356427 + 1.15551i
\(49\) −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 \(0.642857\pi\)
\(54\) 1.29637 0.146066i 1.29637 0.146066i
\(55\) 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 \(-0.785714\pi\)
0.781831 0.623490i \(-0.214286\pi\)
\(60\) 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
\(69\) −0.365341 0.930874i −0.365341 0.930874i
\(70\) 0 0
\(71\) −0.250701 + 1.09839i −0.250701 + 1.09839i 0.680173 + 0.733052i \(0.261905\pi\)
−0.930874 + 0.365341i \(0.880952\pi\)
\(72\) −0.253657 + 0.294755i −0.253657 + 0.294755i
\(73\) −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
\(75\) 0.563320 + 0.826239i 0.563320 + 0.826239i
\(76\) 0 0
\(77\) 0 0
\(78\) −0.194846 + 0.00729061i −0.194846 + 0.00729061i
\(79\) 0 0 0.532032 0.846724i \(-0.321429\pi\)
−0.532032 + 0.846724i \(0.678571\pi\)
\(80\) 0 0
\(81\) 0.955573 + 0.294755i 0.955573 + 0.294755i
\(82\) 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
\(87\) −0.900969 0.433884i −0.900969 0.433884i
\(88\) 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
\(93\) −0.500000 1.86603i −0.500000 1.86603i
\(94\) −1.49104 + 1.86971i −1.49104 + 1.86971i
\(95\) 0 0
\(96\) 0.0444453 + 1.18783i 0.0444453 + 1.18783i
\(97\) 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 −0.974928 0.222521i \(-0.928571\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(102\) 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 \(0.928571\pi\)
\(108\) 0.632404 0.304550i 0.632404 0.304550i
\(109\) 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
\(123\) 0.0487796 + 0.0566829i 0.0487796 + 0.0566829i
\(124\) −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 0.930874 0.365341i \(-0.119048\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(132\) 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 \(0.178571\pi\)
\(138\) −0.850958 0.988831i −0.850958 0.988831i
\(139\) −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
\(141\) −1.62069 + 0.856562i −1.62069 + 0.856562i
\(142\) 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
\(147\) −0.149042 0.988831i −0.149042 0.988831i
\(148\) 0 0
\(149\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(150\) 1.04966 + 0.774683i 1.04966 + 0.774683i
\(151\) −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
\(156\) −0.0976565 + 0.0383273i −0.0976565 + 0.0383273i
\(157\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) 1.30366 0.0487796i 1.30366 0.0487796i
\(163\) 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 \(-0.428571\pi\)
0.900969 0.433884i \(-0.142857\pi\)
\(168\) 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 \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(174\) −1.29637 0.146066i −1.29637 0.146066i
\(175\) 0 0
\(176\) 0 0
\(177\) 0.0931869 1.24349i 0.0931869 1.24349i
\(178\) 0 0
\(179\) −1.72188 0.829215i −1.72188 0.829215i −0.988831 0.149042i \(-0.952381\pi\)
−0.733052 0.680173i \(-0.761905\pi\)
\(180\) 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
\(186\) −1.41970 2.08232i −1.41970 2.08232i
\(187\) 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 \(0.750000\pi\)
\(192\) 0.124750 + 0.317859i 0.124750 + 0.317859i
\(193\) −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 \(0.190476\pi\)
−0.0747301 + 0.997204i \(0.523810\pi\)
\(198\) 0 0
\(199\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(200\) −0.386428 + 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
\(207\) −0.294755 0.955573i −0.294755 0.955573i
\(208\) 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
\(213\) −0.332083 + 1.07659i −0.332083 + 1.07659i
\(214\) 0 0
\(215\) 0 0
\(216\) −0.274975 + 0.274975i −0.274975 + 0.274975i
\(217\) 0 0
\(218\) 0 0
\(219\) −0.643504 + 1.47493i −0.643504 + 1.47493i
\(220\) 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
\(225\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(226\) 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 \(-0.738095\pi\)
0.680173 0.733052i \(-0.261905\pi\)
\(234\) −0.194846 0.00729061i −0.194846 0.00729061i
\(235\) 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 0.988831 0.149042i \(-0.0476190\pi\)
0.0747301 + 0.997204i \(0.476190\pi\)
\(240\) 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
\(243\) 0.930874 + 0.365341i 0.930874 + 0.365341i
\(244\) 0 0
\(245\) 0 0
\(246\) 0.0844888 + 0.0487796i 0.0844888 + 0.0487796i
\(247\) 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 \(-0.333333\pi\)
0.955573 0.294755i \(-0.0952381\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) −0.866025 0.500000i −0.866025 0.500000i
\(262\) 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 \(-0.476190\pi\)
0.866025 0.500000i \(-0.166667\pi\)
\(270\) 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
\(276\) −0.607877 0.350958i −0.607877 0.350958i
\(277\) −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
\(279\) −0.359154 1.89817i −0.359154 1.89817i
\(280\) 0 0
\(281\) 0 0 0.974928 0.222521i \(-0.0714286\pi\)
−0.974928 + 0.222521i \(0.928571\pi\)
\(282\) −1.62660 + 1.75306i −1.62660 + 1.75306i
\(283\) 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
\(288\) −0.0444453 + 1.18783i −0.0444453 + 1.18783i
\(289\) 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 \(0.464286\pi\)
\(294\) −0.609587 1.15339i −0.609587 1.15339i
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 0.0332580 + 0.145713i 0.0332580 + 0.145713i
\(300\) 0.670731 + 0.206893i 0.670731 + 0.206893i
\(301\) 0 0
\(302\) −0.922474 0.922474i −0.922474 0.922474i
\(303\) −0.0895474 + 0.205245i −0.0895474 + 0.205245i
\(304\) 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 \(0.119048\pi\)
0.733052 + 0.680173i \(0.238095\pi\)
\(312\) 0.0440542 0.0379117i 0.0440542 0.0379117i
\(313\) 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 1.00000 \(0\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) 0.653395 0.256439i 0.653395 0.256439i
\(325\) −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 \(-0.0714286\pi\)
0.974928 + 0.222521i \(0.0714286\pi\)
\(348\) −0.684317 + 0.156191i −0.684317 + 0.156191i
\(349\) 0.730682 0.730682 0.365341 0.930874i \(-0.380952\pi\)
0.365341 + 0.930874i \(0.380952\pi\)
\(350\) 0 0
\(351\) −0.134659 0.0648483i −0.134659 0.0648483i
\(352\) 0 0
\(353\) 0.531130 + 0.255779i 0.531130 + 0.255779i 0.680173 0.733052i \(-0.261905\pi\)
−0.149042 + 0.988831i \(0.547619\pi\)
\(354\) −0.421041 1.57135i −0.421041 1.57135i
\(355\) 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
\(363\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(364\) 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
\(369\) 0.0444073 + 0.0601697i 0.0444073 + 0.0601697i
\(370\) 0 0
\(371\) 0 0
\(372\) −1.09103 0.805218i −1.09103 0.805218i
\(373\) 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
\(381\) 1.56332 0.826239i 1.56332 0.826239i
\(382\) 0 0
\(383\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(384\) −0.484776 0.563320i −0.484776 0.563320i
\(385\) 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
\(393\) 1.38946 + 0.606214i 1.38946 + 0.606214i
\(394\) 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
\(414\) −0.774683 1.04966i −0.774683 1.04966i
\(415\) 0 0
\(416\) 0.0198913 0.176540i 0.0198913 0.176540i
\(417\) −1.04876 + 0.411608i −1.04876 + 0.411608i
\(418\) 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
\(423\) −1.68017 + 0.733052i −1.68017 + 0.733052i
\(424\) 0 0
\(425\) 0 0
\(426\) 0.0549571 + 1.46876i 0.0549571 + 1.46876i
\(427\) 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 \(0.785714\pi\)
\(432\) −0.524665 + 1.08948i −0.524665 + 1.08948i
\(433\) 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
\(438\) −0.156882 + 2.09345i −0.156882 + 2.09345i
\(439\) −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
\(441\) −0.0747301 0.997204i −0.0747301 0.997204i
\(442\) 0 0
\(443\) 0.631863 1.00560i 0.631863 1.00560i −0.365341 0.930874i \(-0.619048\pi\)
0.997204 0.0747301i \(-0.0238095\pi\)
\(444\) 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 \(0.714286\pi\)
\(450\) 0.988831 + 0.850958i 0.988831 + 0.850958i
\(451\) 0 0
\(452\) 0 0
\(453\) −0.365341 0.930874i −0.365341 0.930874i
\(454\) 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 0.365341 0.930874i \(-0.380952\pi\)
0.563320 + 0.826239i \(0.309524\pi\)
\(462\) 0 0
\(463\) 1.80194i 1.80194i −0.433884 0.900969i \(-0.642857\pi\)
0.433884 0.900969i \(-0.357143\pi\)
\(464\) 0.681184 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 \(0.464286\pi\)
\(468\) −0.100248 + 0.0309223i −0.100248 + 0.0309223i
\(469\) 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
\(486\) 1.30366 + 0.0487796i 1.30366 + 0.0487796i
\(487\) −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
\(489\) 0.856562 + 1.62069i 0.856562 + 1.62069i
\(490\) 0 0
\(491\) 0.660096 + 1.88645i 0.660096 + 1.88645i 0.365341 + 0.930874i \(0.380952\pi\)
0.294755 + 0.955573i \(0.404762\pi\)
\(492\) 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
\(501\) 1.22563 1.32091i 1.22563 1.32091i
\(502\) 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
\(507\) −0.846680 0.488831i −0.846680 0.488831i
\(508\) 0.409925 1.17150i 0.409925 1.17150i
\(509\) −0.290611 0.0663300i −0.290611 0.0663300i 0.0747301 0.997204i \(-0.476190\pi\)
−0.365341 + 0.930874i \(0.619048\pi\)
\(510\) 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
\(519\) −0.443797 0.0332580i −0.443797 0.0332580i
\(520\) 0 0
\(521\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(522\) −1.28183 0.242536i −1.28183 0.242536i
\(523\) 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
\(531\) 0.185853 1.23305i 0.185853 1.23305i
\(532\) 0 0
\(533\) −0.00594652 0.00946383i −0.00594652 0.00946383i
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) −1.65510 0.955573i −1.65510 0.955573i
\(538\) 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 \(0.857143\pi\)
\(558\) −1.26012 2.18260i −1.26012 2.18260i
\(559\) 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 \(0.250000\pi\)
\(564\) −0.514540 + 1.17934i −0.514540 + 1.17934i
\(565\) 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
\(576\) 0.100648 + 0.326292i 0.100648 + 0.326292i
\(577\) 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 0.365341 0.930874i \(-0.380952\pi\)
−0.826239 + 0.563320i \(0.809524\pi\)
\(588\) −0.514540 0.477424i −0.514540 0.477424i
\(589\) 0 0
\(590\) 0 0
\(591\) 0.632789 + 1.61232i 0.632789 + 1.61232i
\(592\) 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
\(598\) 0.103737 + 0.165096i 0.103737 + 0.165096i
\(599\) −1.87590 0.211363i −1.87590 0.211363i −0.900969 0.433884i \(-0.857143\pi\)
−0.974928 + 0.222521i \(0.928571\pi\)
\(600\) −0.388602 + 0.0145404i −0.388602 + 0.0145404i
\(601\) −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
\(606\) −0.0218311 + 0.291315i −0.0218311 + 0.291315i
\(607\) 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
\(621\) −0.222521 0.974928i −0.222521 0.974928i
\(622\) 2.49939 + 0.570469i 2.49939 + 0.570469i
\(623\) 0 0
\(624\) 0.0903659 0.156518i 0.0903659 0.156518i
\(625\) −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
\(633\) 1.13787 + 0.839789i 1.13787 + 0.839789i
\(634\) 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 0.930874 0.365341i \(-0.119048\pi\)
−0.997204 + 0.0747301i \(0.976190\pi\)
\(648\) −0.294755 + 0.253657i −0.294755 + 0.253657i
\(649\) 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 0.563320 0.826239i \(-0.309524\pi\)
−0.0747301 + 0.997204i \(0.523810\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) −0.0765685 + 0.0481112i −0.0765685 + 0.0481112i
\(657\) −0.751927 + 1.42271i −0.751927 + 1.42271i
\(658\) 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
\(669\) −0.0663300 0.440071i −0.0663300 0.440071i
\(670\) 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
\(675\) 0.433884 + 0.900969i 0.433884 + 0.900969i
\(676\) −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 −0.826239 0.563320i \(-0.809524\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(684\) 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
\(696\) 0.329269 0.206893i 0.329269 0.206893i
\(697\) 0 0
\(698\) 0.899737 0.314832i 0.899737 0.314832i
\(699\) 0.109562 1.46200i 0.109562 1.46200i
\(700\) 0 0
\(701\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(702\) −0.193756 0.0218311i −0.193756 0.0218311i
\(703\) 0 0
\(704\) 0 0
\(705\) 0 0
\(706\) 0.764225 + 0.0861074i 0.764225 + 0.0861074i
\(707\) 0 0
\(708\) −0.493060 0.723186i −0.493060 0.723186i
\(709\) 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
\(717\) 0.997204 + 0.925270i 0.997204 + 0.925270i
\(718\) 0 0
\(719\) −0.376510 0.781831i −0.376510 0.781831i 0.623490 0.781831i \(-0.285714\pi\)
−1.00000 \(\pi\)
\(720\) 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
\(729\) 0.900969 + 0.433884i 0.900969 + 0.433884i
\(730\) 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
\(738\) 0.0806072 + 0.0549571i 0.0806072 + 0.0549571i
\(739\) −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 \(0.821429\pi\)
\(744\) 0.717870 + 0.221434i 0.717870 + 0.221434i
\(745\) 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 \(0.0238095\pi\)
0.294755 + 0.955573i \(0.404762\pi\)
\(762\) 1.56902 1.69100i 1.56902 1.69100i
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −0.0414721 + 0.181701i −0.0414721 + 0.181701i
\(768\) −1.13537 0.655507i −1.13537 0.655507i
\(769\) 0 0 0.330279 0.943883i \(-0.392857\pi\)
−0.330279 + 0.943883i \(0.607143\pi\)
\(770\) 0 0
\(771\) 1.53825 1.04876i 1.53825 1.04876i
\(772\) 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
\(783\) −0.826239 0.563320i −0.826239 0.563320i
\(784\) 1.20923 1.20923
\(785\) 0 0
\(786\) 1.97213 + 0.147791i 1.97213 + 0.147791i
\(787\) 0 0 0.781831 0.623490i \(-0.214286\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)