Properties

Label 2001.1.bf.c.68.2
Level $2001$
Weight $1$
Character 2001.68
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 68.2
Root \(-0.563320 + 0.826239i\) of defining polynomial
Character \(\chi\) \(=\) 2001.68
Dual form 2001.1.bf.c.206.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.0397866 + 0.0633201i) q^{2} +(-0.988831 + 0.149042i) q^{3} +(0.431457 - 0.895930i) q^{4} +(-0.0487796 - 0.0566829i) q^{6} +(0.148209 - 0.0166991i) q^{8} +(0.955573 - 0.294755i) q^{9} +O(q^{10})\) \(q+(0.0397866 + 0.0633201i) q^{2} +(-0.988831 + 0.149042i) q^{3} +(0.431457 - 0.895930i) q^{4} +(-0.0487796 - 0.0566829i) q^{6} +(0.148209 - 0.0166991i) q^{8} +(0.955573 - 0.294755i) q^{9} +(-0.293107 + 0.950229i) q^{12} +(1.14625 - 0.914101i) q^{13} +(-0.613049 - 0.768739i) q^{16} +(0.0566829 + 0.0487796i) q^{18} +(-0.974928 + 0.222521i) q^{23} +(-0.144065 + 0.0386020i) q^{24} +(-0.900969 - 0.433884i) q^{25} +(0.103486 + 0.0362114i) q^{26} +(-0.900969 + 0.433884i) q^{27} +(0.563320 + 0.826239i) q^{29} +(0.438297 - 0.275400i) q^{31} +(0.0735454 - 0.210181i) q^{32} +(0.148209 - 0.983301i) q^{36} +(-0.997204 + 1.07473i) q^{39} +(1.29621 + 1.29621i) q^{41} +(-0.0528791 - 0.0528791i) q^{46} +(0.220025 - 1.95278i) q^{47} +(0.720776 + 0.668783i) q^{48} +(0.623490 - 0.781831i) q^{49} +(-0.00837297 - 0.0743122i) q^{50} +(-0.324414 - 1.42135i) q^{52} +(-0.0633201 - 0.0397866i) q^{54} +(-0.0299049 + 0.0685427i) q^{58} -1.80194i q^{59} +(0.0348767 + 0.0167957i) q^{62} +(-0.942367 + 0.215089i) q^{64} +(0.930874 - 0.365341i) q^{69} +(-0.367554 - 0.460898i) q^{71} +(0.136702 - 0.0596425i) q^{72} +(-1.10462 - 0.694076i) q^{73} +(0.955573 + 0.294755i) q^{75} +(-0.107727 - 0.0203831i) q^{78} +(0.826239 - 0.563320i) q^{81} +(-0.0305044 + 0.133648i) q^{82} +(-0.680173 - 0.733052i) q^{87} +(-0.221277 + 0.969476i) q^{92} +(-0.392355 + 0.337649i) q^{93} +(0.132404 - 0.0637624i) q^{94} +(-0.0413982 + 0.218795i) q^{96} +(0.0743122 + 0.00837297i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q - 2q^{2} + 2q^{3} + 14q^{4} - 2q^{6} + 6q^{8} + 2q^{9} + O(q^{10}) \) \( 24q - 2q^{2} + 2q^{3} + 14q^{4} - 2q^{6} + 6q^{8} + 2q^{9} - 6q^{12} - 6q^{16} + 4q^{18} - 6q^{24} - 4q^{25} + 2q^{26} - 4q^{27} - 2q^{31} + 4q^{32} + 6q^{36} + 2q^{41} + 2q^{46} - 2q^{47} - 4q^{48} - 4q^{49} - 2q^{50} - 10q^{52} + 12q^{54} + 4q^{58} + 4q^{62} - 28q^{64} + 14q^{72} - 2q^{73} + 2q^{75} + 10q^{78} + 2q^{81} - 4q^{82} + 4q^{92} - 2q^{93} - 8q^{94} - 24q^{96} - 2q^{98} + O(q^{100}) \)

Character values

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

\(n\) \(553\) \(668\) \(1132\)
\(\chi(n)\) \(e\left(\frac{23}{28}\right)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.0397866 + 0.0633201i 0.0397866 + 0.0633201i 0.866025 0.500000i \(-0.166667\pi\)
−0.826239 + 0.563320i \(0.809524\pi\)
\(3\) −0.988831 + 0.149042i −0.988831 + 0.149042i
\(4\) 0.431457 0.895930i 0.431457 0.895930i
\(5\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(6\) −0.0487796 0.0566829i −0.0487796 0.0566829i
\(7\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(8\) 0.148209 0.0166991i 0.148209 0.0166991i
\(9\) 0.955573 0.294755i 0.955573 0.294755i
\(10\) 0 0
\(11\) 0 0 −0.993712 0.111964i \(-0.964286\pi\)
0.993712 + 0.111964i \(0.0357143\pi\)
\(12\) −0.293107 + 0.950229i −0.293107 + 0.950229i
\(13\) 1.14625 0.914101i 1.14625 0.914101i 0.149042 0.988831i \(-0.452381\pi\)
0.997204 + 0.0747301i \(0.0238095\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −0.613049 0.768739i −0.613049 0.768739i
\(17\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(18\) 0.0566829 + 0.0487796i 0.0566829 + 0.0487796i
\(19\) 0 0 −0.330279 0.943883i \(-0.607143\pi\)
0.330279 + 0.943883i \(0.392857\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −0.974928 + 0.222521i −0.974928 + 0.222521i
\(24\) −0.144065 + 0.0386020i −0.144065 + 0.0386020i
\(25\) −0.900969 0.433884i −0.900969 0.433884i
\(26\) 0.103486 + 0.0362114i 0.103486 + 0.0362114i
\(27\) −0.900969 + 0.433884i −0.900969 + 0.433884i
\(28\) 0 0
\(29\) 0.563320 + 0.826239i 0.563320 + 0.826239i
\(30\) 0 0
\(31\) 0.438297 0.275400i 0.438297 0.275400i −0.294755 0.955573i \(-0.595238\pi\)
0.733052 + 0.680173i \(0.238095\pi\)
\(32\) 0.0735454 0.210181i 0.0735454 0.210181i
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) 0.148209 0.983301i 0.148209 0.983301i
\(37\) 0 0 −0.111964 0.993712i \(-0.535714\pi\)
0.111964 + 0.993712i \(0.464286\pi\)
\(38\) 0 0
\(39\) −0.997204 + 1.07473i −0.997204 + 1.07473i
\(40\) 0 0
\(41\) 1.29621 + 1.29621i 1.29621 + 1.29621i 0.930874 + 0.365341i \(0.119048\pi\)
0.365341 + 0.930874i \(0.380952\pi\)
\(42\) 0 0
\(43\) 0 0 0.532032 0.846724i \(-0.321429\pi\)
−0.532032 + 0.846724i \(0.678571\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) −0.0528791 0.0528791i −0.0528791 0.0528791i
\(47\) 0.220025 1.95278i 0.220025 1.95278i −0.0747301 0.997204i \(-0.523810\pi\)
0.294755 0.955573i \(-0.404762\pi\)
\(48\) 0.720776 + 0.668783i 0.720776 + 0.668783i
\(49\) 0.623490 0.781831i 0.623490 0.781831i
\(50\) −0.00837297 0.0743122i −0.00837297 0.0743122i
\(51\) 0 0
\(52\) −0.324414 1.42135i −0.324414 1.42135i
\(53\) 0 0 −0.974928 0.222521i \(-0.928571\pi\)
0.974928 + 0.222521i \(0.0714286\pi\)
\(54\) −0.0633201 0.0397866i −0.0633201 0.0397866i
\(55\) 0 0
\(56\) 0 0
\(57\) 0 0
\(58\) −0.0299049 + 0.0685427i −0.0299049 + 0.0685427i
\(59\) 1.80194i 1.80194i −0.433884 0.900969i \(-0.642857\pi\)
0.433884 0.900969i \(-0.357143\pi\)
\(60\) 0 0
\(61\) 0 0 −0.943883 0.330279i \(-0.892857\pi\)
0.943883 + 0.330279i \(0.107143\pi\)
\(62\) 0.0348767 + 0.0167957i 0.0348767 + 0.0167957i
\(63\) 0 0
\(64\) −0.942367 + 0.215089i −0.942367 + 0.215089i
\(65\) 0 0
\(66\) 0 0
\(67\) 0 0 −0.781831 0.623490i \(-0.785714\pi\)
0.781831 + 0.623490i \(0.214286\pi\)
\(68\) 0 0
\(69\) 0.930874 0.365341i 0.930874 0.365341i
\(70\) 0 0
\(71\) −0.367554 0.460898i −0.367554 0.460898i 0.563320 0.826239i \(-0.309524\pi\)
−0.930874 + 0.365341i \(0.880952\pi\)
\(72\) 0.136702 0.0596425i 0.136702 0.0596425i
\(73\) −1.10462 0.694076i −1.10462 0.694076i −0.149042 0.988831i \(-0.547619\pi\)
−0.955573 + 0.294755i \(0.904762\pi\)
\(74\) 0 0
\(75\) 0.955573 + 0.294755i 0.955573 + 0.294755i
\(76\) 0 0
\(77\) 0 0
\(78\) −0.107727 0.0203831i −0.107727 0.0203831i
\(79\) 0 0 0.993712 0.111964i \(-0.0357143\pi\)
−0.993712 + 0.111964i \(0.964286\pi\)
\(80\) 0 0
\(81\) 0.826239 0.563320i 0.826239 0.563320i
\(82\) −0.0305044 + 0.133648i −0.0305044 + 0.133648i
\(83\) 0 0 0.433884 0.900969i \(-0.357143\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −0.680173 0.733052i −0.680173 0.733052i
\(88\) 0 0
\(89\) 0 0 −0.532032 0.846724i \(-0.678571\pi\)
0.532032 + 0.846724i \(0.321429\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −0.221277 + 0.969476i −0.221277 + 0.969476i
\(93\) −0.392355 + 0.337649i −0.392355 + 0.337649i
\(94\) 0.132404 0.0637624i 0.132404 0.0637624i
\(95\) 0 0
\(96\) −0.0413982 + 0.218795i −0.0413982 + 0.218795i
\(97\) 0 0 0.943883 0.330279i \(-0.107143\pi\)
−0.943883 + 0.330279i \(0.892857\pi\)
\(98\) 0.0743122 + 0.00837297i 0.0743122 + 0.00837297i
\(99\) 0 0
\(100\) −0.777459 + 0.620003i −0.777459 + 0.620003i
\(101\) 0.559311 + 0.351438i 0.559311 + 0.351438i 0.781831 0.623490i \(-0.214286\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(102\) 0 0
\(103\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(104\) 0.154619 0.154619i 0.154619 0.154619i
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 −0.781831 0.623490i \(-0.785714\pi\)
0.781831 + 0.623490i \(0.214286\pi\)
\(108\) 0.994408i 0.994408i
\(109\) 0 0 −0.433884 0.900969i \(-0.642857\pi\)
0.433884 + 0.900969i \(0.357143\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 0 0 −0.943883 0.330279i \(-0.892857\pi\)
0.943883 + 0.330279i \(0.107143\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0.983301 0.148209i 0.983301 0.148209i
\(117\) 0.825886 1.21135i 0.825886 1.21135i
\(118\) 0.114099 0.0716930i 0.114099 0.0716930i
\(119\) 0 0
\(120\) 0 0
\(121\) 0.974928 + 0.222521i 0.974928 + 0.222521i
\(122\) 0 0
\(123\) −1.47493 1.08855i −1.47493 1.08855i
\(124\) −0.0576330 0.511507i −0.0576330 0.511507i
\(125\) 0 0
\(126\) 0 0
\(127\) −0.180173 + 1.59908i −0.180173 + 1.59908i 0.500000 + 0.866025i \(0.333333\pi\)
−0.680173 + 0.733052i \(0.738095\pi\)
\(128\) −0.208569 0.208569i −0.208569 0.208569i
\(129\) 0 0
\(130\) 0 0
\(131\) −1.06332 + 1.69226i −1.06332 + 1.69226i −0.500000 + 0.866025i \(0.666667\pi\)
−0.563320 + 0.826239i \(0.690476\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 0 0 −0.111964 0.993712i \(-0.535714\pi\)
0.111964 + 0.993712i \(0.464286\pi\)
\(138\) 0.0601697 + 0.0444073i 0.0601697 + 0.0444073i
\(139\) −0.131178 0.574730i −0.131178 0.574730i −0.997204 0.0747301i \(-0.976190\pi\)
0.866025 0.500000i \(-0.166667\pi\)
\(140\) 0 0
\(141\) 0.0734787 + 1.96376i 0.0734787 + 1.96376i
\(142\) 0.0145603 0.0416111i 0.0145603 0.0416111i
\(143\) 0 0
\(144\) −0.812403 0.553887i −0.812403 0.553887i
\(145\) 0 0
\(146\) 0.0975592i 0.0975592i
\(147\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(148\) 0 0
\(149\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(150\) 0.0193551 + 0.0722342i 0.0193551 + 0.0722342i
\(151\) 0.974928 0.222521i 0.974928 0.222521i 0.294755 0.955573i \(-0.404762\pi\)
0.680173 + 0.733052i \(0.261905\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 0.532632 + 1.35713i 0.532632 + 1.35713i
\(157\) 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
\(162\) 0.0685427 + 0.0299049i 0.0685427 + 0.0299049i
\(163\) 1.95278 + 0.220025i 1.95278 + 0.220025i 0.997204 0.0747301i \(-0.0238095\pi\)
0.955573 + 0.294755i \(0.0952381\pi\)
\(164\) 1.72058 0.602057i 1.72058 0.602057i
\(165\) 0 0
\(166\) 0 0
\(167\) 0.400969 0.193096i 0.400969 0.193096i −0.222521 0.974928i \(-0.571429\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(168\) 0 0
\(169\) 0.255779 1.12064i 0.255779 1.12064i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −1.24698 −1.24698 −0.623490 0.781831i \(-0.714286\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(174\) 0.0193551 0.0722342i 0.0193551 0.0722342i
\(175\) 0 0
\(176\) 0 0
\(177\) 0.268565 + 1.78181i 0.268565 + 1.78181i
\(178\) 0 0
\(179\) −0.440071 + 1.92808i −0.440071 + 1.92808i −0.0747301 + 0.997204i \(0.523810\pi\)
−0.365341 + 0.930874i \(0.619048\pi\)
\(180\) 0 0
\(181\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −0.140777 + 0.0492600i −0.140777 + 0.0492600i
\(185\) 0 0
\(186\) −0.0369904 0.0114100i −0.0369904 0.0114100i
\(187\) 0 0
\(188\) −1.65462 1.03967i −1.65462 1.03967i
\(189\) 0 0
\(190\) 0 0
\(191\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(192\) 0.899784 0.353139i 0.899784 0.353139i
\(193\) 0.500684 + 1.43087i 0.500684 + 1.43087i 0.866025 + 0.500000i \(0.166667\pi\)
−0.365341 + 0.930874i \(0.619048\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) −0.431457 0.895930i −0.431457 0.895930i
\(197\) −1.68862 + 0.385418i −1.68862 + 0.385418i −0.955573 0.294755i \(-0.904762\pi\)
−0.733052 + 0.680173i \(0.761905\pi\)
\(198\) 0 0
\(199\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(200\) −0.140777 0.0492600i −0.140777 0.0492600i
\(201\) 0 0
\(202\) 0.0493981i 0.0493981i
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(208\) −1.40541 0.320776i −1.40541 0.320776i
\(209\) 0 0
\(210\) 0 0
\(211\) 0.158342 + 1.40532i 0.158342 + 1.40532i 0.781831 + 0.623490i \(0.214286\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(212\) 0 0
\(213\) 0.432142 + 0.400969i 0.432142 + 0.400969i
\(214\) 0 0
\(215\) 0 0
\(216\) −0.126286 + 0.0793508i −0.126286 + 0.0793508i
\(217\) 0 0
\(218\) 0 0
\(219\) 1.19572 + 0.521689i 1.19572 + 0.521689i
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) −0.777479 + 0.974928i −0.777479 + 0.974928i 0.222521 + 0.974928i \(0.428571\pi\)
−1.00000 \(\pi\)
\(224\) 0 0
\(225\) −0.988831 0.149042i −0.988831 0.149042i
\(226\) 0 0
\(227\) 0 0 −0.974928 0.222521i \(-0.928571\pi\)
0.974928 + 0.222521i \(0.0714286\pi\)
\(228\) 0 0
\(229\) 0 0 0.330279 0.943883i \(-0.392857\pi\)
−0.330279 + 0.943883i \(0.607143\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0.0972864 + 0.113049i 0.0972864 + 0.113049i
\(233\) 0.730682i 0.730682i −0.930874 0.365341i \(-0.880952\pi\)
0.930874 0.365341i \(-0.119048\pi\)
\(234\) 0.109562 + 0.00409952i 0.109562 + 0.00409952i
\(235\) 0 0
\(236\) −1.61441 0.777459i −1.61441 0.777459i
\(237\) 0 0
\(238\) 0 0
\(239\) 0.807782 + 1.67738i 0.807782 + 1.67738i 0.733052 + 0.680173i \(0.238095\pi\)
0.0747301 + 0.997204i \(0.476190\pi\)
\(240\) 0 0
\(241\) 0 0 −0.781831 0.623490i \(-0.785714\pi\)
0.781831 + 0.623490i \(0.214286\pi\)
\(242\) 0.0246991 + 0.0705858i 0.0246991 + 0.0705858i
\(243\) −0.733052 + 0.680173i −0.733052 + 0.680173i
\(244\) 0 0
\(245\) 0 0
\(246\) 0.0102444 0.136702i 0.0102444 0.136702i
\(247\) 0 0
\(248\) 0.0603605 0.0481359i 0.0603605 0.0481359i
\(249\) 0 0
\(250\) 0 0
\(251\) 0 0 0.943883 0.330279i \(-0.107143\pi\)
−0.943883 + 0.330279i \(0.892857\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) −0.108422 + 0.0522133i −0.108422 + 0.0522133i
\(255\) 0 0
\(256\) −0.210181 + 0.920862i −0.210181 + 0.920862i
\(257\) 0.488831 1.01507i 0.488831 1.01507i −0.500000 0.866025i \(-0.666667\pi\)
0.988831 0.149042i \(-0.0476190\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 0.781831 + 0.623490i 0.781831 + 0.623490i
\(262\) −0.149460 −0.149460
\(263\) 0 0 −0.532032 0.846724i \(-0.678571\pi\)
0.532032 + 0.846724i \(0.321429\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 1.59908 0.180173i 1.59908 0.180173i 0.733052 0.680173i \(-0.238095\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(270\) 0 0
\(271\) −1.00435 + 0.351438i −1.00435 + 0.351438i −0.781831 0.623490i \(-0.785714\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) 0.0743122 0.991627i 0.0743122 0.991627i
\(277\) 1.19158 + 1.49419i 1.19158 + 1.49419i 0.826239 + 0.563320i \(0.190476\pi\)
0.365341 + 0.930874i \(0.380952\pi\)
\(278\) 0.0311728 0.0311728i 0.0311728 0.0311728i
\(279\) 0.337649 0.392355i 0.337649 0.392355i
\(280\) 0 0
\(281\) 0 0 −0.781831 0.623490i \(-0.785714\pi\)
0.781831 + 0.623490i \(0.214286\pi\)
\(282\) −0.121422 + 0.0827840i −0.121422 + 0.0827840i
\(283\) 0 0 −0.433884 0.900969i \(-0.642857\pi\)
0.433884 + 0.900969i \(0.357143\pi\)
\(284\) −0.571516 + 0.130445i −0.571516 + 0.130445i
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0.00832615 0.222521i 0.00832615 0.222521i
\(289\) 1.00000i 1.00000i
\(290\) 0 0
\(291\) 0 0
\(292\) −1.09844 + 0.690194i −1.09844 + 0.690194i
\(293\) 0 0 0.330279 0.943883i \(-0.392857\pi\)
−0.330279 + 0.943883i \(0.607143\pi\)
\(294\) −0.0747301 + 0.00279620i −0.0747301 + 0.00279620i
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −0.914101 + 1.14625i −0.914101 + 1.14625i
\(300\) 0.676369 0.728952i 0.676369 0.728952i
\(301\) 0 0
\(302\) 0.0528791 + 0.0528791i 0.0528791 + 0.0528791i
\(303\) −0.605443 0.264152i −0.605443 0.264152i
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 1.33485 + 1.33485i 1.33485 + 1.33485i 0.900969 + 0.433884i \(0.142857\pi\)
0.433884 + 0.900969i \(0.357143\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −0.197979 1.75711i −0.197979 1.75711i −0.563320 0.826239i \(-0.690476\pi\)
0.365341 0.930874i \(-0.380952\pi\)
\(312\) −0.129847 + 0.175937i −0.129847 + 0.175937i
\(313\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −1.43388 + 0.900969i −1.43388 + 0.900969i −0.433884 + 0.900969i \(0.642857\pi\)
−1.00000 \(1.00000\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) −0.148209 0.983301i −0.148209 0.983301i
\(325\) −1.42935 + 0.326239i −1.42935 + 0.326239i
\(326\) 0.0637624 + 0.132404i 0.0637624 + 0.132404i
\(327\) 0 0
\(328\) 0.213756 + 0.170465i 0.213756 + 0.170465i
\(329\) 0 0
\(330\) 0 0
\(331\) −0.839789 + 0.839789i −0.839789 + 0.839789i −0.988831 0.149042i \(-0.952381\pi\)
0.149042 + 0.988831i \(0.452381\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0.0281801 + 0.0177067i 0.0281801 + 0.0177067i
\(335\) 0 0
\(336\) 0 0
\(337\) 0 0 −0.993712 0.111964i \(-0.964286\pi\)
0.993712 + 0.111964i \(0.0357143\pi\)
\(338\) 0.0811356 0.0283906i 0.0811356 0.0283906i
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 0 0
\(346\) −0.0496131 0.0789588i −0.0496131 0.0789588i
\(347\) −1.56366 −1.56366 −0.781831 0.623490i \(-0.785714\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(348\) −0.950229 + 0.293107i −0.950229 + 0.293107i
\(349\) 1.65248 1.65248 0.826239 0.563320i \(-0.190476\pi\)
0.826239 + 0.563320i \(0.190476\pi\)
\(350\) 0 0
\(351\) −0.636119 + 1.32091i −0.636119 + 1.32091i
\(352\) 0 0
\(353\) 0.0663300 0.290611i 0.0663300 0.290611i −0.930874 0.365341i \(-0.880952\pi\)
0.997204 + 0.0747301i \(0.0238095\pi\)
\(354\) −0.102139 + 0.0878978i −0.102139 + 0.0878978i
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) −0.139595 + 0.0488464i −0.139595 + 0.0488464i
\(359\) 0 0 −0.993712 0.111964i \(-0.964286\pi\)
0.993712 + 0.111964i \(0.0357143\pi\)
\(360\) 0 0
\(361\) −0.781831 + 0.623490i −0.781831 + 0.623490i
\(362\) 0 0
\(363\) −0.997204 0.0747301i −0.997204 0.0747301i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 0 0 −0.330279 0.943883i \(-0.607143\pi\)
0.330279 + 0.943883i \(0.392857\pi\)
\(368\) 0.768739 + 0.613049i 0.768739 + 0.613049i
\(369\) 1.62069 + 0.856562i 1.62069 + 0.856562i
\(370\) 0 0
\(371\) 0 0
\(372\) 0.133225 + 0.497204i 0.133225 + 0.497204i
\(373\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0.293093i 0.293093i
\(377\) 1.40097 + 0.432142i 1.40097 + 0.432142i
\(378\) 0 0
\(379\) 0 0 0.846724 0.532032i \(-0.178571\pi\)
−0.846724 + 0.532032i \(0.821429\pi\)
\(380\) 0 0
\(381\) −0.0601697 1.60807i −0.0601697 1.60807i
\(382\) 0 0
\(383\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(384\) 0.237325 + 0.175154i 0.237325 + 0.175154i
\(385\) 0 0
\(386\) −0.0706825 + 0.0886330i −0.0706825 + 0.0886330i
\(387\) 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
\(392\) 0.0793508 0.126286i 0.0793508 0.126286i
\(393\) 0.799225 1.83184i 0.799225 1.83184i
\(394\) −0.0915893 0.0915893i −0.0915893 0.0915893i
\(395\) 0 0
\(396\) 0 0
\(397\) −1.16078 + 1.45557i −1.16078 + 1.45557i −0.294755 + 0.955573i \(0.595238\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0.218795 + 0.958602i 0.218795 + 0.958602i
\(401\) 0 0 −0.974928 0.222521i \(-0.928571\pi\)
0.974928 + 0.222521i \(0.0714286\pi\)
\(402\) 0 0
\(403\) 0.250652 0.716324i 0.250652 0.716324i
\(404\) 0.556183 0.349473i 0.556183 0.349473i
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) −1.73026 0.605443i −1.73026 0.605443i −0.733052 0.680173i \(-0.761905\pi\)
−0.997204 + 0.0747301i \(0.976190\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) −0.0661163 0.0349435i −0.0661163 0.0349435i
\(415\) 0 0
\(416\) −0.107825 0.308147i −0.107825 0.308147i
\(417\) 0.215372 + 0.548760i 0.215372 + 0.548760i
\(418\) 0 0
\(419\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(420\) 0 0
\(421\) 0 0 −0.846724 0.532032i \(-0.821429\pi\)
0.846724 + 0.532032i \(0.178571\pi\)
\(422\) −0.0826851 + 0.0659392i −0.0826851 + 0.0659392i
\(423\) −0.365341 1.93087i −0.365341 1.93087i
\(424\) 0 0
\(425\) 0 0
\(426\) −0.00819591 + 0.0433164i −0.00819591 + 0.0433164i
\(427\) 0 0
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 0.433884 0.900969i \(-0.357143\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(432\) 0.885881 + 0.426618i 0.885881 + 0.426618i
\(433\) 0 0 −0.532032 0.846724i \(-0.678571\pi\)
0.532032 + 0.846724i \(0.321429\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) 0.0145404 + 0.0964696i 0.0145404 + 0.0964696i
\(439\) 0.807782 1.67738i 0.807782 1.67738i 0.0747301 0.997204i \(-0.476190\pi\)
0.733052 0.680173i \(-0.238095\pi\)
\(440\) 0 0
\(441\) 0.365341 0.930874i 0.365341 0.930874i
\(442\) 0 0
\(443\) 1.50641 0.169732i 1.50641 0.169732i 0.680173 0.733052i \(-0.261905\pi\)
0.826239 + 0.563320i \(0.190476\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) −0.0926658 0.0104409i −0.0926658 0.0104409i
\(447\) 0 0
\(448\) 0 0
\(449\) −0.900969 0.566116i −0.900969 0.566116i 1.00000i \(-0.5\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(450\) −0.0299049 0.0685427i −0.0299049 0.0685427i
\(451\) 0 0
\(452\) 0 0
\(453\) −0.930874 + 0.365341i −0.930874 + 0.365341i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 0 0 −0.433884 0.900969i \(-0.642857\pi\)
0.433884 + 0.900969i \(0.357143\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −1.12099 0.392253i −1.12099 0.392253i −0.294755 0.955573i \(-0.595238\pi\)
−0.826239 + 0.563320i \(0.809524\pi\)
\(462\) 0 0
\(463\) 0.445042i 0.445042i −0.974928 0.222521i \(-0.928571\pi\)
0.974928 0.222521i \(-0.0714286\pi\)
\(464\) 0.289819 0.939571i 0.289819 0.939571i
\(465\) 0 0
\(466\) 0.0462668 0.0290714i 0.0462668 0.0290714i
\(467\) 0 0 0.330279 0.943883i \(-0.392857\pi\)
−0.330279 + 0.943883i \(0.607143\pi\)
\(468\) −0.728952 1.26258i −0.728952 1.26258i
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) −0.0300908 0.267063i −0.0300908 0.267063i
\(473\) 0 0
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 0 0
\(478\) −0.0740727 + 0.117886i −0.0740727 + 0.117886i
\(479\) 0 0 0.532032 0.846724i \(-0.321429\pi\)
−0.532032 + 0.846724i \(0.678571\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) 0.620003 0.777459i 0.620003 0.777459i
\(485\) 0 0
\(486\) −0.0722342 0.0193551i −0.0722342 0.0193551i
\(487\) 0.0663300 + 0.290611i 0.0663300 + 0.290611i 0.997204 0.0747301i \(-0.0238095\pi\)
−0.930874 + 0.365341i \(0.880952\pi\)
\(488\) 0 0
\(489\) −1.96376 + 0.0734787i −1.96376 + 0.0734787i
\(490\) 0 0
\(491\) −0.677197 + 0.425511i −0.677197 + 0.425511i −0.826239 0.563320i \(-0.809524\pi\)
0.149042 + 0.988831i \(0.452381\pi\)
\(492\) −1.61163 + 0.851771i −1.61163 + 0.851771i
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) −0.480408 0.168102i −0.480408 0.168102i
\(497\) 0 0
\(498\) 0 0
\(499\) 1.61105 0.367711i 1.61105 0.367711i 0.680173 0.733052i \(-0.261905\pi\)
0.930874 + 0.365341i \(0.119048\pi\)
\(500\) 0 0
\(501\) −0.367711 + 0.250701i −0.367711 + 0.250701i
\(502\) 0 0
\(503\) 0 0 −0.330279 0.943883i \(-0.607143\pi\)
0.330279 + 0.943883i \(0.392857\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −0.0858993 + 1.14625i −0.0858993 + 1.14625i
\(508\) 1.35492 + 0.851356i 1.35492 + 0.851356i
\(509\) 1.55929 1.24349i 1.55929 1.24349i 0.733052 0.680173i \(-0.238095\pi\)
0.826239 0.563320i \(-0.190476\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −0.345081 + 0.120749i −0.345081 + 0.120749i
\(513\) 0 0
\(514\) 0.0837231 0.00943332i 0.0837231 0.00943332i
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 1.23305 0.185853i 1.23305 0.185853i
\(520\) 0 0
\(521\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(522\) −0.00837297 + 0.0743122i −0.00837297 + 0.0743122i
\(523\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(524\) 1.05737 + 1.68280i 1.05737 + 1.68280i
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) 0.900969 0.433884i 0.900969 0.433884i
\(530\) 0 0
\(531\) −0.531130 1.72188i −0.531130 1.72188i
\(532\) 0 0
\(533\) 2.67065 + 0.300910i 2.67065 + 0.300910i
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0.147791 1.97213i 0.147791 1.97213i
\(538\) 0.0750304 + 0.0940852i 0.0750304 + 0.0940852i
\(539\) 0 0
\(540\) 0 0
\(541\) 0.122805 + 0.350958i 0.122805 + 0.350958i 0.988831 0.149042i \(-0.0476190\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(542\) −0.0622129 0.0496131i −0.0622129 0.0496131i
\(543\) 0 0
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 0.658322 + 0.317031i 0.658322 + 0.317031i 0.733052 0.680173i \(-0.238095\pi\)
−0.0747301 + 0.997204i \(0.523810\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 0 0
\(552\) 0.131863 0.0696915i 0.131863 0.0696915i
\(553\) 0 0
\(554\) −0.0472035 + 0.134900i −0.0472035 + 0.134900i
\(555\) 0 0
\(556\) −0.571516 0.130445i −0.571516 0.130445i
\(557\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(558\) 0.0382779 + 0.00576946i 0.0382779 + 0.00576946i
\(559\) 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 \(0.250000\pi\)
\(564\) 1.79109 + 0.781446i 1.79109 + 0.781446i
\(565\) 0 0
\(566\) 0 0
\(567\) 0 0
\(568\) −0.0621713 0.0621713i −0.0621713 0.0621713i
\(569\) 0 0 0.111964 0.993712i \(-0.464286\pi\)
−0.111964 + 0.993712i \(0.535714\pi\)
\(570\) 0 0
\(571\) 0 0 0.623490 0.781831i \(-0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0.974928 + 0.222521i 0.974928 + 0.222521i
\(576\) −0.837102 + 0.483301i −0.837102 + 0.483301i
\(577\) −0.392253 + 1.12099i −0.392253 + 1.12099i 0.563320 + 0.826239i \(0.309524\pi\)
−0.955573 + 0.294755i \(0.904762\pi\)
\(578\) 0.0633201 0.0397866i 0.0633201 0.0397866i
\(579\) −0.708353 1.34027i −0.708353 1.34027i
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) −0.175304 0.0844220i −0.175304 0.0844220i
\(585\) 0 0
\(586\) 0 0
\(587\) 0.129334 + 0.268565i 0.129334 + 0.268565i 0.955573 0.294755i \(-0.0952381\pi\)
−0.826239 + 0.563320i \(0.809524\pi\)
\(588\) 0.560170 + 0.821618i 0.560170 + 0.821618i
\(589\) 0 0
\(590\) 0 0
\(591\) 1.61232 0.632789i 1.61232 0.632789i
\(592\) 0 0
\(593\) 0.974928 + 1.22252i 0.974928 + 1.22252i 0.974928 + 0.222521i \(0.0714286\pi\)
1.00000i \(0.5\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) −0.108949 0.0122756i −0.108949 0.0122756i
\(599\) 1.00435 0.351438i 1.00435 0.351438i 0.222521 0.974928i \(-0.428571\pi\)
0.781831 + 0.623490i \(0.214286\pi\)
\(600\) 0.146546 + 0.0277281i 0.146546 + 0.0277281i
\(601\) 1.91970 0.216299i 1.91970 0.216299i 0.930874 0.365341i \(-0.119048\pi\)
0.988831 + 0.149042i \(0.0476190\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0.221277 0.969476i 0.221277 0.969476i
\(605\) 0 0
\(606\) −0.00736241 0.0488464i −0.00736241 0.0488464i
\(607\) −1.05737 1.68280i −1.05737 1.68280i −0.623490 0.781831i \(-0.714286\pi\)
−0.433884 0.900969i \(-0.642857\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −1.53283 2.43949i −1.53283 2.43949i
\(612\) 0 0
\(613\) 0 0 0.433884 0.900969i \(-0.357143\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(614\) −0.0314137 + 0.137632i −0.0314137 + 0.137632i
\(615\) 0 0
\(616\) 0 0
\(617\) 0 0 0.993712 0.111964i \(-0.0357143\pi\)
−0.993712 + 0.111964i \(0.964286\pi\)
\(618\) 0 0
\(619\) 0 0 0.943883 0.330279i \(-0.107143\pi\)
−0.943883 + 0.330279i \(0.892857\pi\)
\(620\) 0 0
\(621\) 0.781831 0.623490i 0.781831 0.623490i
\(622\) 0.103384 0.0824456i 0.103384 0.0824456i
\(623\) 0 0
\(624\) 1.43752 + 0.107727i 1.43752 + 0.107727i
\(625\) 0.623490 + 0.781831i 0.623490 + 0.781831i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 0 0 −0.433884 0.900969i \(-0.642857\pi\)
0.433884 + 0.900969i \(0.357143\pi\)
\(632\) 0 0
\(633\) −0.366025 1.36603i −0.366025 1.36603i
\(634\) −0.114099 0.0549471i −0.114099 0.0549471i
\(635\) 0 0
\(636\) 0 0
\(637\) 1.46610i 1.46610i
\(638\) 0 0
\(639\) −0.487076 0.332083i −0.487076 0.332083i
\(640\) 0 0
\(641\) 0 0 0.330279 0.943883i \(-0.392857\pi\)
−0.330279 + 0.943883i \(0.607143\pi\)
\(642\) 0 0
\(643\) 0 0 −0.974928 0.222521i \(-0.928571\pi\)
0.974928 + 0.222521i \(0.0714286\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −1.24349 + 1.55929i −1.24349 + 1.55929i −0.563320 + 0.826239i \(0.690476\pi\)
−0.680173 + 0.733052i \(0.738095\pi\)
\(648\) 0.113049 0.0972864i 0.113049 0.0972864i
\(649\) 0 0
\(650\) −0.0775263 0.0775263i −0.0775263 0.0775263i
\(651\) 0 0
\(652\) 1.03967 1.65462i 1.03967 1.65462i
\(653\) −1.02781 + 1.63575i −1.02781 + 1.63575i −0.294755 + 0.955573i \(0.595238\pi\)
−0.733052 + 0.680173i \(0.761905\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0.201808 1.79109i 0.201808 1.79109i
\(657\) −1.26012 0.337649i −1.26012 0.337649i
\(658\) 0 0
\(659\) 0 0 −0.111964 0.993712i \(-0.535714\pi\)
0.111964 + 0.993712i \(0.464286\pi\)
\(660\) 0 0
\(661\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(662\) −0.0865878 0.0197631i −0.0865878 0.0197631i
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −0.733052 0.680173i −0.733052 0.680173i
\(668\) 0.442553i 0.442553i
\(669\) 0.623490 1.07992i 0.623490 1.07992i
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) −0.290611 + 0.0663300i −0.290611 + 0.0663300i −0.365341 0.930874i \(-0.619048\pi\)
0.0747301 + 0.997204i \(0.476190\pi\)
\(674\) 0 0
\(675\) 1.00000 1.00000
\(676\) −0.893658 0.712669i −0.893658 0.712669i
\(677\) 0 0 −0.330279 0.943883i \(-0.607143\pi\)
0.330279 + 0.943883i \(0.392857\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 0.880843 0.702449i 0.880843 0.702449i −0.0747301 0.997204i \(-0.523810\pi\)
0.955573 + 0.294755i \(0.0952381\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) −0.433884 + 1.90097i −0.433884 + 1.90097i 1.00000i \(0.5\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(692\) −0.538018 + 1.11721i −0.538018 + 1.11721i
\(693\) 0 0
\(694\) −0.0622129 0.0990112i −0.0622129 0.0990112i
\(695\) 0 0
\(696\) −0.113049 0.0972864i −0.113049 0.0972864i
\(697\) 0 0
\(698\) 0.0657465 + 0.104635i 0.0657465 + 0.104635i
\(699\) 0.108903 + 0.722521i 0.108903 + 0.722521i
\(700\) 0 0
\(701\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(702\) −0.108949 + 0.0122756i −0.108949 + 0.0122756i
\(703\) 0 0
\(704\) 0 0
\(705\) 0 0
\(706\) 0.0210406 0.00736241i 0.0210406 0.00736241i
\(707\) 0 0
\(708\) 1.71225 + 0.528160i 1.71225 + 0.528160i
\(709\) 0 0 0.781831 0.623490i \(-0.214286\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −0.366025 + 0.366025i −0.366025 + 0.366025i
\(714\) 0 0
\(715\) 0 0
\(716\) 1.53755 + 1.22616i 1.53755 + 1.22616i
\(717\) −1.04876 1.53825i −1.04876 1.53825i
\(718\) 0 0
\(719\) 1.90097 0.433884i 1.90097 0.433884i 0.900969 0.433884i \(-0.142857\pi\)
1.00000 \(0\)
\(720\) 0 0
\(721\) 0 0
\(722\) −0.0705858 0.0246991i −0.0705858 0.0246991i
\(723\) 0 0
\(724\) 0 0
\(725\) −0.149042 0.988831i −0.149042 0.988831i
\(726\) −0.0349435 0.0661163i −0.0349435 0.0661163i
\(727\) 0 0 0.846724 0.532032i \(-0.178571\pi\)
−0.846724 + 0.532032i \(0.821429\pi\)
\(728\) 0 0
\(729\) 0.623490 0.781831i 0.623490 0.781831i
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 0 0 −0.111964 0.993712i \(-0.535714\pi\)
0.111964 + 0.993712i \(0.464286\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) −0.0249319 + 0.221277i −0.0249319 + 0.221277i
\(737\) 0 0
\(738\) 0.0102444 + 0.136702i 0.0102444 + 0.136702i
\(739\) −0.975281 + 1.55215i −0.975281 + 1.55215i −0.149042 + 0.988831i \(0.547619\pi\)
−0.826239 + 0.563320i \(0.809524\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 0.111964 0.993712i \(-0.464286\pi\)
−0.111964 + 0.993712i \(0.535714\pi\)
\(744\) −0.0525120 + 0.0565945i −0.0525120 + 0.0565945i
\(745\) 0 0
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 0 0 0.330279 0.943883i \(-0.392857\pi\)
−0.330279 + 0.943883i \(0.607143\pi\)
\(752\) −1.63606 + 1.02801i −1.63606 + 1.02801i
\(753\) 0 0
\(754\) 0.0283766 + 0.105903i 0.0283766 + 0.105903i
\(755\) 0 0
\(756\) 0 0
\(757\) 0 0 −0.943883 0.330279i \(-0.892857\pi\)
0.943883 + 0.330279i \(0.107143\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 0.829215 + 1.72188i 0.829215 + 1.72188i 0.680173 + 0.733052i \(0.261905\pi\)
0.149042 + 0.988831i \(0.452381\pi\)
\(762\) 0.0994292 0.0677896i 0.0994292 0.0677896i
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −1.64715 2.06546i −1.64715 2.06546i
\(768\) 0.0705858 0.941903i 0.0705858 0.941903i
\(769\) 0 0 −0.846724 0.532032i \(-0.821429\pi\)
0.846724 + 0.532032i \(0.178571\pi\)
\(770\) 0 0
\(771\) −0.332083 + 1.07659i −0.332083 + 1.07659i
\(772\) 1.49799 + 0.168783i 1.49799 + 0.168783i
\(773\) 0 0 0.943883 0.330279i \(-0.107143\pi\)
−0.943883 + 0.330279i \(0.892857\pi\)
\(774\) 0 0
\(775\) −0.514383 + 0.0579571i −0.514383 + 0.0579571i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) −0.866025 0.500000i −0.866025 0.500000i
\(784\) −0.983254 −0.983254
\(785\) 0 0
\(786\) 0.147791 0.0222759i 0.147791 0.0222759i
\(787\) 0 0 0.433884 0.900969i \(-0.357143\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)