Properties

Label 2001.1.bf.c.827.1
Level $2001$
Weight $1$
Character 2001.827
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 827.1
Root \(0.680173 - 0.733052i\) of defining polynomial
Character \(\chi\) \(=\) 2001.827
Dual form 2001.1.bf.c.1655.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.132974 - 1.18017i) q^{2} +(0.826239 + 0.563320i) q^{3} +(-0.400198 + 0.0913425i) q^{4} +(0.554947 - 1.05001i) q^{6} +(-0.231237 - 0.660838i) q^{8} +(0.365341 + 0.930874i) q^{9} +O(q^{10})\) \(q+(-0.132974 - 1.18017i) q^{2} +(0.826239 + 0.563320i) q^{3} +(-0.400198 + 0.0913425i) q^{4} +(0.554947 - 1.05001i) q^{6} +(-0.231237 - 0.660838i) q^{8} +(0.365341 + 0.930874i) q^{9} +(-0.382114 - 0.149969i) q^{12} +(0.858075 + 1.78181i) q^{13} +(-1.11899 + 0.538878i) q^{16} +(1.05001 - 0.554947i) q^{18} +(0.781831 - 0.623490i) q^{23} +(0.181206 - 0.676270i) q^{24} +(-0.222521 - 0.974928i) q^{25} +(1.98874 - 1.24961i) q^{26} +(-0.222521 + 0.974928i) q^{27} +(-0.680173 - 0.733052i) q^{29} +(1.91970 - 0.216299i) q^{31} +(0.412276 + 0.656134i) q^{32} +(-0.231237 - 0.339162i) q^{36} +(-0.294755 + 1.95557i) q^{39} +(1.07193 + 1.07193i) q^{41} +(-0.839789 - 0.839789i) q^{46} +(-1.88645 - 0.660096i) q^{47} +(-1.22812 - 0.185109i) q^{48} +(-0.900969 - 0.433884i) q^{49} +(-1.12099 + 0.392253i) q^{50} +(-0.506155 - 0.634698i) q^{52} +(1.18017 + 0.132974i) q^{54} +(-0.774683 + 0.900198i) q^{58} -0.445042i q^{59} +(-0.510540 - 2.23682i) q^{62} +(-0.251496 + 0.200561i) q^{64} +(0.997204 - 0.0747301i) q^{69} +(-1.67738 + 0.807782i) q^{71} +(0.530676 - 0.456684i) q^{72} +(-0.928661 - 0.104635i) q^{73} +(0.365341 - 0.930874i) q^{75} +(2.34711 + 0.0878226i) q^{78} +(-0.733052 + 0.680173i) q^{81} +(1.12253 - 1.40761i) q^{82} +(-0.149042 - 0.988831i) q^{87} +(-0.255936 + 0.320934i) q^{92} +(1.70798 + 0.902694i) q^{93} +(-0.528180 + 2.31411i) q^{94} +(-0.0289748 + 0.774367i) q^{96} +(-0.392253 + 1.12099i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q - 2q^{2} + 2q^{3} + 14q^{4} - 2q^{6} + 6q^{8} + 2q^{9} + O(q^{10}) \) \( 24q - 2q^{2} + 2q^{3} + 14q^{4} - 2q^{6} + 6q^{8} + 2q^{9} - 6q^{12} - 6q^{16} + 4q^{18} - 6q^{24} - 4q^{25} + 2q^{26} - 4q^{27} - 2q^{31} + 4q^{32} + 6q^{36} + 2q^{41} + 2q^{46} - 2q^{47} - 4q^{48} - 4q^{49} - 2q^{50} - 10q^{52} + 12q^{54} + 4q^{58} + 4q^{62} - 28q^{64} + 14q^{72} - 2q^{73} + 2q^{75} + 10q^{78} + 2q^{81} - 4q^{82} + 4q^{92} - 2q^{93} - 8q^{94} - 24q^{96} - 2q^{98} + O(q^{100}) \)

Character values

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

\(n\) \(553\) \(668\) \(1132\)
\(\chi(n)\) \(e\left(\frac{27}{28}\right)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.132974 1.18017i −0.132974 1.18017i −0.866025 0.500000i \(-0.833333\pi\)
0.733052 0.680173i \(-0.238095\pi\)
\(3\) 0.826239 + 0.563320i 0.826239 + 0.563320i
\(4\) −0.400198 + 0.0913425i −0.400198 + 0.0913425i
\(5\) 0 0 0.623490 0.781831i \(-0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(6\) 0.554947 1.05001i 0.554947 1.05001i
\(7\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(8\) −0.231237 0.660838i −0.231237 0.660838i
\(9\) 0.365341 + 0.930874i 0.365341 + 0.930874i
\(10\) 0 0
\(11\) 0 0 0.330279 0.943883i \(-0.392857\pi\)
−0.330279 + 0.943883i \(0.607143\pi\)
\(12\) −0.382114 0.149969i −0.382114 0.149969i
\(13\) 0.858075 + 1.78181i 0.858075 + 1.78181i 0.563320 + 0.826239i \(0.309524\pi\)
0.294755 + 0.955573i \(0.404762\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −1.11899 + 0.538878i −1.11899 + 0.538878i
\(17\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(18\) 1.05001 0.554947i 1.05001 0.554947i
\(19\) 0 0 0.532032 0.846724i \(-0.321429\pi\)
−0.532032 + 0.846724i \(0.678571\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 0.781831 0.623490i 0.781831 0.623490i
\(24\) 0.181206 0.676270i 0.181206 0.676270i
\(25\) −0.222521 0.974928i −0.222521 0.974928i
\(26\) 1.98874 1.24961i 1.98874 1.24961i
\(27\) −0.222521 + 0.974928i −0.222521 + 0.974928i
\(28\) 0 0
\(29\) −0.680173 0.733052i −0.680173 0.733052i
\(30\) 0 0
\(31\) 1.91970 0.216299i 1.91970 0.216299i 0.930874 0.365341i \(-0.119048\pi\)
0.988831 + 0.149042i \(0.0476190\pi\)
\(32\) 0.412276 + 0.656134i 0.412276 + 0.656134i
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) −0.231237 0.339162i −0.231237 0.339162i
\(37\) 0 0 0.943883 0.330279i \(-0.107143\pi\)
−0.943883 + 0.330279i \(0.892857\pi\)
\(38\) 0 0
\(39\) −0.294755 + 1.95557i −0.294755 + 1.95557i
\(40\) 0 0
\(41\) 1.07193 + 1.07193i 1.07193 + 1.07193i 0.997204 + 0.0747301i \(0.0238095\pi\)
0.0747301 + 0.997204i \(0.476190\pi\)
\(42\) 0 0
\(43\) 0 0 0.111964 0.993712i \(-0.464286\pi\)
−0.111964 + 0.993712i \(0.535714\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) −0.839789 0.839789i −0.839789 0.839789i
\(47\) −1.88645 0.660096i −1.88645 0.660096i −0.955573 0.294755i \(-0.904762\pi\)
−0.930874 0.365341i \(-0.880952\pi\)
\(48\) −1.22812 0.185109i −1.22812 0.185109i
\(49\) −0.900969 0.433884i −0.900969 0.433884i
\(50\) −1.12099 + 0.392253i −1.12099 + 0.392253i
\(51\) 0 0
\(52\) −0.506155 0.634698i −0.506155 0.634698i
\(53\) 0 0 −0.781831 0.623490i \(-0.785714\pi\)
0.781831 + 0.623490i \(0.214286\pi\)
\(54\) 1.18017 + 0.132974i 1.18017 + 0.132974i
\(55\) 0 0
\(56\) 0 0
\(57\) 0 0
\(58\) −0.774683 + 0.900198i −0.774683 + 0.900198i
\(59\) 0.445042i 0.445042i −0.974928 0.222521i \(-0.928571\pi\)
0.974928 0.222521i \(-0.0714286\pi\)
\(60\) 0 0
\(61\) 0 0 0.846724 0.532032i \(-0.178571\pi\)
−0.846724 + 0.532032i \(0.821429\pi\)
\(62\) −0.510540 2.23682i −0.510540 2.23682i
\(63\) 0 0
\(64\) −0.251496 + 0.200561i −0.251496 + 0.200561i
\(65\) 0 0
\(66\) 0 0
\(67\) 0 0 0.433884 0.900969i \(-0.357143\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(68\) 0 0
\(69\) 0.997204 0.0747301i 0.997204 0.0747301i
\(70\) 0 0
\(71\) −1.67738 + 0.807782i −1.67738 + 0.807782i −0.680173 + 0.733052i \(0.738095\pi\)
−0.997204 + 0.0747301i \(0.976190\pi\)
\(72\) 0.530676 0.456684i 0.530676 0.456684i
\(73\) −0.928661 0.104635i −0.928661 0.104635i −0.365341 0.930874i \(-0.619048\pi\)
−0.563320 + 0.826239i \(0.690476\pi\)
\(74\) 0 0
\(75\) 0.365341 0.930874i 0.365341 0.930874i
\(76\) 0 0
\(77\) 0 0
\(78\) 2.34711 + 0.0878226i 2.34711 + 0.0878226i
\(79\) 0 0 −0.330279 0.943883i \(-0.607143\pi\)
0.330279 + 0.943883i \(0.392857\pi\)
\(80\) 0 0
\(81\) −0.733052 + 0.680173i −0.733052 + 0.680173i
\(82\) 1.12253 1.40761i 1.12253 1.40761i
\(83\) 0 0 0.974928 0.222521i \(-0.0714286\pi\)
−0.974928 + 0.222521i \(0.928571\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −0.149042 0.988831i −0.149042 0.988831i
\(88\) 0 0
\(89\) 0 0 −0.111964 0.993712i \(-0.535714\pi\)
0.111964 + 0.993712i \(0.464286\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −0.255936 + 0.320934i −0.255936 + 0.320934i
\(93\) 1.70798 + 0.902694i 1.70798 + 0.902694i
\(94\) −0.528180 + 2.31411i −0.528180 + 2.31411i
\(95\) 0 0
\(96\) −0.0289748 + 0.774367i −0.0289748 + 0.774367i
\(97\) 0 0 −0.846724 0.532032i \(-0.821429\pi\)
0.846724 + 0.532032i \(0.178571\pi\)
\(98\) −0.392253 + 1.12099i −0.392253 + 1.12099i
\(99\) 0 0
\(100\) 0.178105 + 0.369838i 0.178105 + 0.369838i
\(101\) 1.05737 + 0.119137i 1.05737 + 0.119137i 0.623490 0.781831i \(-0.285714\pi\)
0.433884 + 0.900969i \(0.357143\pi\)
\(102\) 0 0
\(103\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(104\) 0.979069 0.979069i 0.979069 0.979069i
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 0.433884 0.900969i \(-0.357143\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(108\) 0.410490i 0.410490i
\(109\) 0 0 −0.974928 0.222521i \(-0.928571\pi\)
0.974928 + 0.222521i \(0.0714286\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 0 0 0.846724 0.532032i \(-0.178571\pi\)
−0.846724 + 0.532032i \(0.821429\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0.339162 + 0.231237i 0.339162 + 0.231237i
\(117\) −1.34515 + 1.44973i −1.34515 + 1.44973i
\(118\) −0.525226 + 0.0591788i −0.525226 + 0.0591788i
\(119\) 0 0
\(120\) 0 0
\(121\) −0.781831 0.623490i −0.781831 0.623490i
\(122\) 0 0
\(123\) 0.281831 + 1.48952i 0.281831 + 1.48952i
\(124\) −0.748504 + 0.261913i −0.748504 + 0.261913i
\(125\) 0 0
\(126\) 0 0
\(127\) 0.350958 + 0.122805i 0.350958 + 0.122805i 0.500000 0.866025i \(-0.333333\pi\)
−0.149042 + 0.988831i \(0.547619\pi\)
\(128\) 0.818082 + 0.818082i 0.818082 + 0.818082i
\(129\) 0 0
\(130\) 0 0
\(131\) 0.180173 1.59908i 0.180173 1.59908i −0.500000 0.866025i \(-0.666667\pi\)
0.680173 0.733052i \(-0.261905\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 0 0 0.943883 0.330279i \(-0.107143\pi\)
−0.943883 + 0.330279i \(0.892857\pi\)
\(138\) −0.220796 1.16694i −0.220796 1.16694i
\(139\) −1.16078 1.45557i −1.16078 1.45557i −0.866025 0.500000i \(-0.833333\pi\)
−0.294755 0.955573i \(-0.595238\pi\)
\(140\) 0 0
\(141\) −1.18681 1.60807i −1.18681 1.60807i
\(142\) 1.17637 + 1.87218i 1.17637 + 1.87218i
\(143\) 0 0
\(144\) −0.910442 0.844766i −0.910442 0.844766i
\(145\) 0 0
\(146\) 1.10989i 1.10989i
\(147\) −0.500000 0.866025i −0.500000 0.866025i
\(148\) 0 0
\(149\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(150\) −1.14717 0.307384i −1.14717 0.307384i
\(151\) −0.781831 + 0.623490i −0.781831 + 0.623490i −0.930874 0.365341i \(-0.880952\pi\)
0.149042 + 0.988831i \(0.452381\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) −0.0606666 0.809540i −0.0606666 0.809540i
\(157\) 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
\(162\) 0.900198 + 0.774683i 0.900198 + 0.774683i
\(163\) 0.660096 1.88645i 0.660096 1.88645i 0.294755 0.955573i \(-0.404762\pi\)
0.365341 0.930874i \(-0.380952\pi\)
\(164\) −0.526899 0.331072i −0.526899 0.331072i
\(165\) 0 0
\(166\) 0 0
\(167\) −0.277479 + 1.21572i −0.277479 + 1.21572i 0.623490 + 0.781831i \(0.285714\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(168\) 0 0
\(169\) −1.81507 + 2.27603i −1.81507 + 2.27603i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 1.80194 1.80194 0.900969 0.433884i \(-0.142857\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(174\) −1.14717 + 0.307384i −1.14717 + 0.307384i
\(175\) 0 0
\(176\) 0 0
\(177\) 0.250701 0.367711i 0.250701 0.367711i
\(178\) 0 0
\(179\) −1.03030 + 1.29196i −1.03030 + 1.29196i −0.0747301 + 0.997204i \(0.523810\pi\)
−0.955573 + 0.294755i \(0.904762\pi\)
\(180\) 0 0
\(181\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −0.592814 0.372490i −0.592814 0.372490i
\(185\) 0 0
\(186\) 0.838218 2.13575i 0.838218 2.13575i
\(187\) 0 0
\(188\) 0.815247 + 0.0918562i 0.815247 + 0.0918562i
\(189\) 0 0
\(190\) 0 0
\(191\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(192\) −0.320776 + 0.0240388i −0.320776 + 0.0240388i
\(193\) −0.940755 + 1.49720i −0.940755 + 1.49720i −0.0747301 + 0.997204i \(0.523810\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0.400198 + 0.0913425i 0.400198 + 0.0913425i
\(197\) −1.35417 + 1.07992i −1.35417 + 1.07992i −0.365341 + 0.930874i \(0.619048\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(198\) 0 0
\(199\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(200\) −0.592814 + 0.372490i −0.592814 + 0.372490i
\(201\) 0 0
\(202\) 1.26373i 1.26373i
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(208\) −1.92036 1.53144i −1.92036 1.53144i
\(209\) 0 0
\(210\) 0 0
\(211\) 1.33485 0.467085i 1.33485 0.467085i 0.433884 0.900969i \(-0.357143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(212\) 0 0
\(213\) −1.84095 0.277479i −1.84095 0.277479i
\(214\) 0 0
\(215\) 0 0
\(216\) 0.695724 0.0783893i 0.695724 0.0783893i
\(217\) 0 0
\(218\) 0 0
\(219\) −0.708353 0.609587i −0.708353 0.609587i
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) −1.62349 0.781831i −1.62349 0.781831i −0.623490 0.781831i \(-0.714286\pi\)
−1.00000 \(\pi\)
\(224\) 0 0
\(225\) 0.826239 0.563320i 0.826239 0.563320i
\(226\) 0 0
\(227\) 0 0 −0.781831 0.623490i \(-0.785714\pi\)
0.781831 + 0.623490i \(0.214286\pi\)
\(228\) 0 0
\(229\) 0 0 −0.532032 0.846724i \(-0.678571\pi\)
0.532032 + 0.846724i \(0.321429\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −0.327147 + 0.618992i −0.327147 + 0.618992i
\(233\) 0.149460i 0.149460i −0.997204 0.0747301i \(-0.976190\pi\)
0.997204 0.0747301i \(-0.0238095\pi\)
\(234\) 1.88980 + 1.39474i 1.88980 + 1.39474i
\(235\) 0 0
\(236\) 0.0406513 + 0.178105i 0.0406513 + 0.178105i
\(237\) 0 0
\(238\) 0 0
\(239\) 1.94440 + 0.443797i 1.94440 + 0.443797i 0.988831 + 0.149042i \(0.0476190\pi\)
0.955573 + 0.294755i \(0.0952381\pi\)
\(240\) 0 0
\(241\) 0 0 0.433884 0.900969i \(-0.357143\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(242\) −0.631863 + 1.00560i −0.631863 + 1.00560i
\(243\) −0.988831 + 0.149042i −0.988831 + 0.149042i
\(244\) 0 0
\(245\) 0 0
\(246\) 1.72041 0.530676i 1.72041 0.530676i
\(247\) 0 0
\(248\) −0.586845 1.21860i −0.586845 1.21860i
\(249\) 0 0
\(250\) 0 0
\(251\) 0 0 −0.846724 0.532032i \(-0.821429\pi\)
0.846724 + 0.532032i \(0.178571\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0.0982635 0.430521i 0.0982635 0.430521i
\(255\) 0 0
\(256\) 0.656134 0.822766i 0.656134 0.822766i
\(257\) −1.32624 + 0.302705i −1.32624 + 0.302705i −0.826239 0.563320i \(-0.809524\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 0.433884 0.900969i 0.433884 0.900969i
\(262\) −1.91115 −1.91115
\(263\) 0 0 −0.111964 0.993712i \(-0.535714\pi\)
0.111964 + 0.993712i \(0.464286\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 0.122805 + 0.350958i 0.122805 + 0.350958i 0.988831 0.149042i \(-0.0476190\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(270\) 0 0
\(271\) 0.189606 + 0.119137i 0.189606 + 0.119137i 0.623490 0.781831i \(-0.285714\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) −0.392253 + 0.120994i −0.392253 + 0.120994i
\(277\) −0.658322 + 0.317031i −0.658322 + 0.317031i −0.733052 0.680173i \(-0.761905\pi\)
0.0747301 + 0.997204i \(0.476190\pi\)
\(278\) −1.56347 + 1.56347i −1.56347 + 1.56347i
\(279\) 0.902694 + 1.70798i 0.902694 + 1.70798i
\(280\) 0 0
\(281\) 0 0 0.433884 0.900969i \(-0.357143\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(282\) −1.73999 + 1.61447i −1.73999 + 1.61447i
\(283\) 0 0 −0.974928 0.222521i \(-0.928571\pi\)
0.974928 + 0.222521i \(0.0714286\pi\)
\(284\) 0.597498 0.476488i 0.597498 0.476488i
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) −0.460156 + 0.623490i −0.460156 + 0.623490i
\(289\) 1.00000i 1.00000i
\(290\) 0 0
\(291\) 0 0
\(292\) 0.381206 0.0429516i 0.381206 0.0429516i
\(293\) 0 0 −0.532032 0.846724i \(-0.678571\pi\)
0.532032 + 0.846724i \(0.321429\pi\)
\(294\) −0.955573 + 0.705245i −0.955573 + 0.705245i
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 1.78181 + 0.858075i 1.78181 + 0.858075i
\(300\) −0.0611803 + 0.405905i −0.0611803 + 0.405905i
\(301\) 0 0
\(302\) 0.839789 + 0.839789i 0.839789 + 0.839789i
\(303\) 0.806531 + 0.694076i 0.806531 + 0.694076i
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 1.19745 + 1.19745i 1.19745 + 1.19745i 0.974928 + 0.222521i \(0.0714286\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 0.754903 0.264152i 0.754903 0.264152i 0.0747301 0.997204i \(-0.476190\pi\)
0.680173 + 0.733052i \(0.261905\pi\)
\(312\) 1.36047 0.257416i 1.36047 0.257416i
\(313\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −1.97493 + 0.222521i −1.97493 + 0.222521i −0.974928 + 0.222521i \(0.928571\pi\)
−1.00000 \(\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) 0.231237 0.339162i 0.231237 0.339162i
\(325\) 1.54620 1.23305i 1.54620 1.23305i
\(326\) −2.31411 0.528180i −2.31411 0.528180i
\(327\) 0 0
\(328\) 0.460503 0.956245i 0.460503 0.956245i
\(329\) 0 0
\(330\) 0 0
\(331\) 1.38956 1.38956i 1.38956 1.38956i 0.563320 0.826239i \(-0.309524\pi\)
0.826239 0.563320i \(-0.190476\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 1.47165 + 0.165815i 1.47165 + 0.165815i
\(335\) 0 0
\(336\) 0 0
\(337\) 0 0 0.330279 0.943883i \(-0.392857\pi\)
−0.330279 + 0.943883i \(0.607143\pi\)
\(338\) 2.92746 + 1.83944i 2.92746 + 1.83944i
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 0 0
\(346\) −0.239610 2.12660i −0.239610 2.12660i
\(347\) −0.867767 −0.867767 −0.433884 0.900969i \(-0.642857\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(348\) 0.149969 + 0.382114i 0.149969 + 0.382114i
\(349\) −1.46610 −1.46610 −0.733052 0.680173i \(-0.761905\pi\)
−0.733052 + 0.680173i \(0.761905\pi\)
\(350\) 0 0
\(351\) −1.92808 + 0.440071i −1.92808 + 0.440071i
\(352\) 0 0
\(353\) −0.702449 + 0.880843i −0.702449 + 0.880843i −0.997204 0.0747301i \(-0.976190\pi\)
0.294755 + 0.955573i \(0.404762\pi\)
\(354\) −0.467299 0.246975i −0.467299 0.246975i
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 1.66174 + 1.04414i 1.66174 + 1.04414i
\(359\) 0 0 0.330279 0.943883i \(-0.392857\pi\)
−0.330279 + 0.943883i \(0.607143\pi\)
\(360\) 0 0
\(361\) −0.433884 0.900969i −0.433884 0.900969i
\(362\) 0 0
\(363\) −0.294755 0.955573i −0.294755 0.955573i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 0 0 0.532032 0.846724i \(-0.321429\pi\)
−0.532032 + 0.846724i \(0.678571\pi\)
\(368\) −0.538878 + 1.11899i −0.538878 + 1.11899i
\(369\) −0.606214 + 1.38946i −0.606214 + 1.38946i
\(370\) 0 0
\(371\) 0 0
\(372\) −0.765984 0.205245i −0.765984 0.205245i
\(373\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 1.39927i 1.39927i
\(377\) 0.722521 1.84095i 0.722521 1.84095i
\(378\) 0 0
\(379\) 0 0 0.993712 0.111964i \(-0.0357143\pi\)
−0.993712 + 0.111964i \(0.964286\pi\)
\(380\) 0 0
\(381\) 0.220796 + 0.299168i 0.220796 + 0.299168i
\(382\) 0 0
\(383\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(384\) 0.215089 + 1.13677i 0.215089 + 1.13677i
\(385\) 0 0
\(386\) 1.89205 + 0.911166i 1.89205 + 0.911166i
\(387\) 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
\(392\) −0.0783893 + 0.695724i −0.0783893 + 0.695724i
\(393\) 1.04966 1.21972i 1.04966 1.21972i
\(394\) 1.45456 + 1.45456i 1.45456 + 1.45456i
\(395\) 0 0
\(396\) 0 0
\(397\) 1.79690 + 0.865341i 1.79690 + 0.865341i 0.930874 + 0.365341i \(0.119048\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0.774367 + 0.971025i 0.774367 + 0.971025i
\(401\) 0 0 −0.781831 0.623490i \(-0.785714\pi\)
0.781831 + 0.623490i \(0.214286\pi\)
\(402\) 0 0
\(403\) 2.03265 + 3.23495i 2.03265 + 3.23495i
\(404\) −0.434041 + 0.0489047i −0.434041 + 0.0489047i
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) −1.28359 + 0.806531i −1.28359 + 0.806531i −0.988831 0.149042i \(-0.952381\pi\)
−0.294755 + 0.955573i \(0.595238\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) 0.474928 1.08855i 0.474928 1.08855i
\(415\) 0 0
\(416\) −0.815343 + 1.29761i −0.815343 + 1.29761i
\(417\) −0.139129 1.85654i −0.139129 1.85654i
\(418\) 0 0
\(419\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(420\) 0 0
\(421\) 0 0 −0.993712 0.111964i \(-0.964286\pi\)
0.993712 + 0.111964i \(0.0357143\pi\)
\(422\) −0.728741 1.51325i −0.728741 1.51325i
\(423\) −0.0747301 1.99720i −0.0747301 1.99720i
\(424\) 0 0
\(425\) 0 0
\(426\) −0.0826752 + 2.20954i −0.0826752 + 2.20954i
\(427\) 0 0
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 0.974928 0.222521i \(-0.0714286\pi\)
−0.974928 + 0.222521i \(0.928571\pi\)
\(432\) −0.276368 1.21085i −0.276368 1.21085i
\(433\) 0 0 −0.111964 0.993712i \(-0.535714\pi\)
0.111964 + 0.993712i \(0.464286\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) −0.625226 + 0.917038i −0.625226 + 0.917038i
\(439\) 1.94440 0.443797i 1.94440 0.443797i 0.955573 0.294755i \(-0.0952381\pi\)
0.988831 0.149042i \(-0.0476190\pi\)
\(440\) 0 0
\(441\) 0.0747301 0.997204i 0.0747301 0.997204i
\(442\) 0 0
\(443\) −0.584010 1.66900i −0.584010 1.66900i −0.733052 0.680173i \(-0.761905\pi\)
0.149042 0.988831i \(-0.452381\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) −0.706815 + 2.01996i −0.706815 + 2.01996i
\(447\) 0 0
\(448\) 0 0
\(449\) −0.222521 0.0250721i −0.222521 0.0250721i 1.00000i \(-0.5\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(450\) −0.774683 0.900198i −0.774683 0.900198i
\(451\) 0 0
\(452\) 0 0
\(453\) −0.997204 + 0.0747301i −0.997204 + 0.0747301i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 0 0 −0.974928 0.222521i \(-0.928571\pi\)
0.974928 + 0.222521i \(0.0714286\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 1.66393 1.04551i 1.66393 1.04551i 0.733052 0.680173i \(-0.238095\pi\)
0.930874 0.365341i \(-0.119048\pi\)
\(462\) 0 0
\(463\) 1.24698i 1.24698i 0.781831 + 0.623490i \(0.214286\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(464\) 1.15613 + 0.453749i 1.15613 + 0.453749i
\(465\) 0 0
\(466\) −0.176389 + 0.0198742i −0.176389 + 0.0198742i
\(467\) 0 0 −0.532032 0.846724i \(-0.678571\pi\)
0.532032 + 0.846724i \(0.321429\pi\)
\(468\) 0.405905 0.703048i 0.405905 0.703048i
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) −0.294100 + 0.102910i −0.294100 + 0.102910i
\(473\) 0 0
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 0 0
\(478\) 0.265203 2.35375i 0.265203 2.35375i
\(479\) 0 0 0.111964 0.993712i \(-0.464286\pi\)
−0.111964 + 0.993712i \(0.535714\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) 0.369838 + 0.178105i 0.369838 + 0.178105i
\(485\) 0 0
\(486\) 0.307384 + 1.14717i 0.307384 + 1.14717i
\(487\) −0.702449 0.880843i −0.702449 0.880843i 0.294755 0.955573i \(-0.404762\pi\)
−0.997204 + 0.0747301i \(0.976190\pi\)
\(488\) 0 0
\(489\) 1.60807 1.18681i 1.60807 1.18681i
\(490\) 0 0
\(491\) 1.29637 0.146066i 1.29637 0.146066i 0.563320 0.826239i \(-0.309524\pi\)
0.733052 + 0.680173i \(0.238095\pi\)
\(492\) −0.248844 0.570358i −0.248844 0.570358i
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) −2.03158 + 1.27652i −2.03158 + 1.27652i
\(497\) 0 0
\(498\) 0 0
\(499\) 1.14625 0.914101i 1.14625 0.914101i 0.149042 0.988831i \(-0.452381\pi\)
0.997204 + 0.0747301i \(0.0238095\pi\)
\(500\) 0 0
\(501\) −0.914101 + 0.848162i −0.914101 + 0.848162i
\(502\) 0 0
\(503\) 0 0 0.532032 0.846724i \(-0.321429\pi\)
−0.532032 + 0.846724i \(0.678571\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −2.78181 + 0.858075i −2.78181 + 0.858075i
\(508\) −0.151670 0.0170891i −0.151670 0.0170891i
\(509\) 0.255779 + 0.531130i 0.255779 + 0.531130i 0.988831 0.149042i \(-0.0476190\pi\)
−0.733052 + 0.680173i \(0.761905\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −0.0786427 0.0494145i −0.0786427 0.0494145i
\(513\) 0 0
\(514\) 0.533599 + 1.52494i 0.533599 + 1.52494i
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 1.48883 + 1.01507i 1.48883 + 1.01507i
\(520\) 0 0
\(521\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(522\) −1.12099 0.392253i −1.12099 0.392253i
\(523\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(524\) 0.0739590 + 0.656405i 0.0739590 + 0.656405i
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) 0.222521 0.974928i 0.222521 0.974928i
\(530\) 0 0
\(531\) 0.414278 0.162592i 0.414278 0.162592i
\(532\) 0 0
\(533\) −0.990184 + 2.82978i −0.990184 + 2.82978i
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) −1.57906 + 0.487076i −1.57906 + 0.487076i
\(538\) 0.397861 0.191600i 0.397861 0.191600i
\(539\) 0 0
\(540\) 0 0
\(541\) 0.0397866 0.0633201i 0.0397866 0.0633201i −0.826239 0.563320i \(-0.809524\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(542\) 0.115390 0.239610i 0.115390 0.239610i
\(543\) 0 0
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 0.0332580 + 0.145713i 0.0332580 + 0.145713i 0.988831 0.149042i \(-0.0476190\pi\)
−0.955573 + 0.294755i \(0.904762\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 0 0
\(552\) −0.279975 0.641709i −0.279975 0.641709i
\(553\) 0 0
\(554\) 0.461691 + 0.734777i 0.461691 + 0.734777i
\(555\) 0 0
\(556\) 0.597498 + 0.476488i 0.597498 + 0.476488i
\(557\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(558\) 1.89568 1.29245i 1.89568 1.29245i
\(559\) 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 \(0.250000\pi\)
\(564\) 0.621844 + 0.535140i 0.621844 + 0.535140i
\(565\) 0 0
\(566\) 0 0
\(567\) 0 0
\(568\) 0.921684 + 0.921684i 0.921684 + 0.921684i
\(569\) 0 0 −0.943883 0.330279i \(-0.892857\pi\)
0.943883 + 0.330279i \(0.107143\pi\)
\(570\) 0 0
\(571\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −0.781831 0.623490i −0.781831 0.623490i
\(576\) −0.278579 0.160838i −0.278579 0.160838i
\(577\) −1.04551 1.66393i −1.04551 1.66393i −0.680173 0.733052i \(-0.738095\pi\)
−0.365341 0.930874i \(-0.619048\pi\)
\(578\) −1.18017 + 0.132974i −1.18017 + 0.132974i
\(579\) −1.62069 + 0.707101i −1.62069 + 0.707101i
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) 0.145594 + 0.637890i 0.145594 + 0.637890i
\(585\) 0 0
\(586\) 0 0
\(587\) 1.09839 + 0.250701i 1.09839 + 0.250701i 0.733052 0.680173i \(-0.238095\pi\)
0.365341 + 0.930874i \(0.380952\pi\)
\(588\) 0.279204 + 0.300910i 0.279204 + 0.300910i
\(589\) 0 0
\(590\) 0 0
\(591\) −1.72721 + 0.129436i −1.72721 + 0.129436i
\(592\) 0 0
\(593\) −0.781831 + 0.376510i −0.781831 + 0.376510i −0.781831 0.623490i \(-0.785714\pi\)
1.00000i \(0.5\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0.775743 2.21695i 0.775743 2.21695i
\(599\) −0.189606 0.119137i −0.189606 0.119137i 0.433884 0.900969i \(-0.357143\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(600\) −0.699637 0.0261786i −0.699637 0.0261786i
\(601\) 0.170965 + 0.488590i 0.170965 + 0.488590i 0.997204 0.0747301i \(-0.0238095\pi\)
−0.826239 + 0.563320i \(0.809524\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0.255936 0.320934i 0.255936 0.320934i
\(605\) 0 0
\(606\) 0.711882 1.04414i 0.711882 1.04414i
\(607\) −0.0739590 0.656405i −0.0739590 0.656405i −0.974928 0.222521i \(-0.928571\pi\)
0.900969 0.433884i \(-0.142857\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −0.442546 3.92770i −0.442546 3.92770i
\(612\) 0 0
\(613\) 0 0 0.974928 0.222521i \(-0.0714286\pi\)
−0.974928 + 0.222521i \(0.928571\pi\)
\(614\) 1.25397 1.57243i 1.25397 1.57243i
\(615\) 0 0
\(616\) 0 0
\(617\) 0 0 −0.330279 0.943883i \(-0.607143\pi\)
0.330279 + 0.943883i \(0.392857\pi\)
\(618\) 0 0
\(619\) 0 0 −0.846724 0.532032i \(-0.821429\pi\)
0.846724 + 0.532032i \(0.178571\pi\)
\(620\) 0 0
\(621\) 0.433884 + 0.900969i 0.433884 + 0.900969i
\(622\) −0.412127 0.855791i −0.412127 0.855791i
\(623\) 0 0
\(624\) −0.723987 2.34711i −0.723987 2.34711i
\(625\) −0.900969 + 0.433884i −0.900969 + 0.433884i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 0 0 −0.974928 0.222521i \(-0.928571\pi\)
0.974928 + 0.222521i \(0.0714286\pi\)
\(632\) 0 0
\(633\) 1.36603 + 0.366025i 1.36603 + 0.366025i
\(634\) 0.525226 + 2.30117i 0.525226 + 2.30117i
\(635\) 0 0
\(636\) 0 0
\(637\) 1.97766i 1.97766i
\(638\) 0 0
\(639\) −1.36476 1.26631i −1.36476 1.26631i
\(640\) 0 0
\(641\) 0 0 −0.532032 0.846724i \(-0.678571\pi\)
0.532032 + 0.846724i \(0.321429\pi\)
\(642\) 0 0
\(643\) 0 0 −0.781831 0.623490i \(-0.785714\pi\)
0.781831 + 0.623490i \(0.214286\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 0.531130 + 0.255779i 0.531130 + 0.255779i 0.680173 0.733052i \(-0.261905\pi\)
−0.149042 + 0.988831i \(0.547619\pi\)
\(648\) 0.618992 + 0.327147i 0.618992 + 0.327147i
\(649\) 0 0
\(650\) −1.66082 1.66082i −1.66082 1.66082i
\(651\) 0 0
\(652\) −0.0918562 + 0.815247i −0.0918562 + 0.815247i
\(653\) −0.0579571 + 0.514383i −0.0579571 + 0.514383i 0.930874 + 0.365341i \(0.119048\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) −1.77713 0.621844i −1.77713 0.621844i
\(657\) −0.241876 0.902694i −0.241876 0.902694i
\(658\) 0 0
\(659\) 0 0 0.943883 0.330279i \(-0.107143\pi\)
−0.943883 + 0.330279i \(0.892857\pi\)
\(660\) 0 0
\(661\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(662\) −1.82469 1.45514i −1.82469 1.45514i
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −0.988831 0.149042i −0.988831 0.149042i
\(668\) 0.511872i 0.511872i
\(669\) −0.900969 1.56052i −0.900969 1.56052i
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 0.880843 0.702449i 0.880843 0.702449i −0.0747301 0.997204i \(-0.523810\pi\)
0.955573 + 0.294755i \(0.0952381\pi\)
\(674\) 0 0
\(675\) 1.00000 1.00000
\(676\) 0.518489 1.07665i 0.518489 1.07665i
\(677\) 0 0 0.532032 0.846724i \(-0.321429\pi\)
−0.532032 + 0.846724i \(0.678571\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −0.590232 1.22563i −0.590232 1.22563i −0.955573 0.294755i \(-0.904762\pi\)
0.365341 0.930874i \(-0.380952\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) −0.974928 + 1.22252i −0.974928 + 1.22252i 1.00000i \(0.5\pi\)
−0.974928 + 0.222521i \(0.928571\pi\)
\(692\) −0.721132 + 0.164594i −0.721132 + 0.164594i
\(693\) 0 0
\(694\) 0.115390 + 1.02412i 0.115390 + 1.02412i
\(695\) 0 0
\(696\) −0.618992 + 0.327147i −0.618992 + 0.327147i
\(697\) 0 0
\(698\) 0.194953 + 1.73026i 0.194953 + 1.73026i
\(699\) 0.0841939 0.123490i 0.0841939 0.123490i
\(700\) 0 0
\(701\) 0 0 0.623490 0.781831i \(-0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(702\) 0.775743 + 2.21695i 0.775743 + 2.21695i
\(703\) 0 0
\(704\) 0 0
\(705\) 0 0
\(706\) 1.13295 + 0.711882i 1.13295 + 0.711882i
\(707\) 0 0
\(708\) −0.0667424 + 0.170057i −0.0667424 + 0.170057i
\(709\) 0 0 −0.433884 0.900969i \(-0.642857\pi\)
0.433884 + 0.900969i \(0.357143\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 1.36603 1.36603i 1.36603 1.36603i
\(714\) 0 0
\(715\) 0 0
\(716\) 0.294314 0.611150i 0.294314 0.611150i
\(717\) 1.35654 + 1.46200i 1.35654 + 1.46200i
\(718\) 0 0
\(719\) 1.22252 0.974928i 1.22252 0.974928i 0.222521 0.974928i \(-0.428571\pi\)
1.00000 \(0\)
\(720\) 0 0
\(721\) 0 0
\(722\) −1.00560 + 0.631863i −1.00560 + 0.631863i
\(723\) 0 0
\(724\) 0 0
\(725\) −0.563320 + 0.826239i −0.563320 + 0.826239i
\(726\) −1.08855 + 0.474928i −1.08855 + 0.474928i
\(727\) 0 0 0.993712 0.111964i \(-0.0357143\pi\)
−0.993712 + 0.111964i \(0.964286\pi\)
\(728\) 0 0
\(729\) −0.900969 0.433884i −0.900969 0.433884i
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 0 0 0.943883 0.330279i \(-0.107143\pi\)
−0.943883 + 0.330279i \(0.892857\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0.731423 + 0.255936i 0.731423 + 0.255936i
\(737\) 0 0
\(738\) 1.72041 + 0.530676i 1.72041 + 0.530676i
\(739\) 0.169732 1.50641i 0.169732 1.50641i −0.563320 0.826239i \(-0.690476\pi\)
0.733052 0.680173i \(-0.238095\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 −0.943883 0.330279i \(-0.892857\pi\)
0.943883 + 0.330279i \(0.107143\pi\)
\(744\) 0.201586 1.33743i 0.201586 1.33743i
\(745\) 0 0
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 0 0 −0.532032 0.846724i \(-0.678571\pi\)
0.532032 + 0.846724i \(0.321429\pi\)
\(752\) 2.46663 0.277923i 2.46663 0.277923i
\(753\) 0 0
\(754\) −2.26872 0.607901i −2.26872 0.607901i
\(755\) 0 0
\(756\) 0 0
\(757\) 0 0 0.846724 0.532032i \(-0.178571\pi\)
−0.846724 + 0.532032i \(0.821429\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 0.712362 + 0.162592i 0.712362 + 0.162592i 0.563320 0.826239i \(-0.309524\pi\)
0.149042 + 0.988831i \(0.452381\pi\)
\(762\) 0.323710 0.300359i 0.323710 0.300359i
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0.792981 0.381879i 0.792981 0.381879i
\(768\) 1.00560 0.310188i 1.00560 0.310188i
\(769\) 0 0 −0.993712 0.111964i \(-0.964286\pi\)
0.993712 + 0.111964i \(0.0357143\pi\)
\(770\) 0 0
\(771\) −1.26631 0.496990i −1.26631 0.496990i
\(772\) 0.239730 0.685109i 0.239730 0.685109i
\(773\) 0 0 −0.846724 0.532032i \(-0.821429\pi\)
0.846724 + 0.532032i \(0.178571\pi\)
\(774\) 0 0
\(775\) −0.638050 1.82344i −0.638050 1.82344i
\(776\) 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
\(784\) 1.24199 1.24199
\(785\) 0 0
\(786\) −1.57906 1.07659i −1.57906 1.07659i
\(787\) 0 0 0.974928 0.222521i \(-0.0714286\pi\)
−0.974928 + 0.222521i \(0.928571\pi\)
\(788\) 0.443294