Properties

Label 2001.1.bf.d.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 \(0.294755 + 0.955573i\) of defining polynomial
Character \(\chi\) \(=\) 2001.827
Dual form 2001.1.bf.d.1655.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.0895474 + 0.794755i) q^{2} +(0.930874 + 0.365341i) q^{3} +(0.351311 - 0.0801844i) q^{4} +(-0.206999 + 0.772532i) q^{6} +(0.359338 + 1.02693i) q^{8} +(0.733052 + 0.680173i) q^{9} +O(q^{10})\) \(q+(0.0895474 + 0.794755i) q^{2} +(0.930874 + 0.365341i) q^{3} +(0.351311 - 0.0801844i) q^{4} +(-0.206999 + 0.772532i) q^{6} +(0.359338 + 1.02693i) q^{8} +(0.733052 + 0.680173i) q^{9} +(0.356321 + 0.0537067i) q^{12} +(-0.317031 - 0.658322i) q^{13} +(-0.459319 + 0.221196i) q^{16} +(-0.474928 + 0.643504i) q^{18} +(-0.781831 + 0.623490i) q^{23} +(-0.0406810 + 1.08722i) q^{24} +(-0.222521 - 0.974928i) q^{25} +(0.494815 - 0.310913i) q^{26} +(0.433884 + 0.900969i) q^{27} +(0.294755 - 0.955573i) q^{29} +(-0.514383 + 0.0579571i) q^{31} +(0.361914 + 0.575983i) q^{32} +(0.312068 + 0.180173i) q^{36} +(-0.0546039 - 0.728639i) q^{39} +(-0.262919 - 0.262919i) q^{41} +(-0.565533 - 0.565533i) q^{46} +(-0.882094 - 0.308658i) q^{47} +(-0.508380 + 0.0380978i) q^{48} +(-0.900969 - 0.433884i) q^{49} +(0.754903 - 0.264152i) q^{50} +(-0.164164 - 0.205855i) q^{52} +(-0.677197 + 0.425511i) q^{54} +(0.785841 + 0.148689i) q^{58} +0.445042i q^{59} +(-0.0921234 - 0.403619i) q^{62} +(-0.823939 + 0.657069i) q^{64} +(-0.955573 + 0.294755i) q^{69} +(-0.268565 + 0.129334i) q^{71} +(-0.435076 + 0.997204i) q^{72} +(1.98603 + 0.223772i) q^{73} +(0.149042 - 0.988831i) q^{75} +(0.574200 - 0.108644i) q^{78} +(0.0747301 + 0.997204i) q^{81} +(0.185412 - 0.232500i) q^{82} +(0.623490 - 0.781831i) q^{87} +(-0.224672 + 0.281729i) q^{92} +(-0.500000 - 0.133975i) q^{93} +(0.166318 - 0.728688i) q^{94} +(0.126466 + 0.668389i) q^{96} +(0.264152 - 0.754903i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q + 2q^{2} + 14q^{4} + 2q^{6} - 6q^{8} - 2q^{9} + O(q^{10}) \) \( 24q + 2q^{2} + 14q^{4} + 2q^{6} - 6q^{8} - 2q^{9} + 2q^{12} - 6q^{16} + 12q^{18} - 6q^{24} - 4q^{25} - 2q^{26} - 2q^{31} - 4q^{32} + 6q^{36} + 2q^{39} - 2q^{41} + 2q^{46} + 2q^{47} + 6q^{48} - 4q^{49} + 2q^{50} - 10q^{52} - 2q^{54} + 4q^{58} - 4q^{62} - 28q^{64} - 2q^{69} + 22q^{72} - 2q^{73} - 4q^{78} + 2q^{81} - 4q^{82} - 4q^{87} - 4q^{92} - 12q^{93} - 8q^{94} - 18q^{96} + 2q^{98} + O(q^{100}) \)

Character values

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

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.0895474 + 0.794755i 0.0895474 + 0.794755i 0.955573 + 0.294755i \(0.0952381\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(3\) 0.930874 + 0.365341i 0.930874 + 0.365341i
\(4\) 0.351311 0.0801844i 0.351311 0.0801844i
\(5\) 0 0 0.623490 0.781831i \(-0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(6\) −0.206999 + 0.772532i −0.206999 + 0.772532i
\(7\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(8\) 0.359338 + 1.02693i 0.359338 + 1.02693i
\(9\) 0.733052 + 0.680173i 0.733052 + 0.680173i
\(10\) 0 0
\(11\) 0 0 0.330279 0.943883i \(-0.392857\pi\)
−0.330279 + 0.943883i \(0.607143\pi\)
\(12\) 0.356321 + 0.0537067i 0.356321 + 0.0537067i
\(13\) −0.317031 0.658322i −0.317031 0.658322i 0.680173 0.733052i \(-0.261905\pi\)
−0.997204 + 0.0747301i \(0.976190\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −0.459319 + 0.221196i −0.459319 + 0.221196i
\(17\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(18\) −0.474928 + 0.643504i −0.474928 + 0.643504i
\(19\) 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
\(24\) −0.0406810 + 1.08722i −0.0406810 + 1.08722i
\(25\) −0.222521 0.974928i −0.222521 0.974928i
\(26\) 0.494815 0.310913i 0.494815 0.310913i
\(27\) 0.433884 + 0.900969i 0.433884 + 0.900969i
\(28\) 0 0
\(29\) 0.294755 0.955573i 0.294755 0.955573i
\(30\) 0 0
\(31\) −0.514383 + 0.0579571i −0.514383 + 0.0579571i −0.365341 0.930874i \(-0.619048\pi\)
−0.149042 + 0.988831i \(0.547619\pi\)
\(32\) 0.361914 + 0.575983i 0.361914 + 0.575983i
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) 0.312068 + 0.180173i 0.312068 + 0.180173i
\(37\) 0 0 0.943883 0.330279i \(-0.107143\pi\)
−0.943883 + 0.330279i \(0.892857\pi\)
\(38\) 0 0
\(39\) −0.0546039 0.728639i −0.0546039 0.728639i
\(40\) 0 0
\(41\) −0.262919 0.262919i −0.262919 0.262919i 0.563320 0.826239i \(-0.309524\pi\)
−0.826239 + 0.563320i \(0.809524\pi\)
\(42\) 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
\(46\) −0.565533 0.565533i −0.565533 0.565533i
\(47\) −0.882094 0.308658i −0.882094 0.308658i −0.149042 0.988831i \(-0.547619\pi\)
−0.733052 + 0.680173i \(0.761905\pi\)
\(48\) −0.508380 + 0.0380978i −0.508380 + 0.0380978i
\(49\) −0.900969 0.433884i −0.900969 0.433884i
\(50\) 0.754903 0.264152i 0.754903 0.264152i
\(51\) 0 0
\(52\) −0.164164 0.205855i −0.164164 0.205855i
\(53\) 0 0 −0.781831 0.623490i \(-0.785714\pi\)
0.781831 + 0.623490i \(0.214286\pi\)
\(54\) −0.677197 + 0.425511i −0.677197 + 0.425511i
\(55\) 0 0
\(56\) 0 0
\(57\) 0 0
\(58\) 0.785841 + 0.148689i 0.785841 + 0.148689i
\(59\) 0.445042i 0.445042i 0.974928 + 0.222521i \(0.0714286\pi\)
−0.974928 + 0.222521i \(0.928571\pi\)
\(60\) 0 0
\(61\) 0 0 0.846724 0.532032i \(-0.178571\pi\)
−0.846724 + 0.532032i \(0.821429\pi\)
\(62\) −0.0921234 0.403619i −0.0921234 0.403619i
\(63\) 0 0
\(64\) −0.823939 + 0.657069i −0.823939 + 0.657069i
\(65\) 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
\(69\) −0.955573 + 0.294755i −0.955573 + 0.294755i
\(70\) 0 0
\(71\) −0.268565 + 0.129334i −0.268565 + 0.129334i −0.563320 0.826239i \(-0.690476\pi\)
0.294755 + 0.955573i \(0.404762\pi\)
\(72\) −0.435076 + 0.997204i −0.435076 + 0.997204i
\(73\) 1.98603 + 0.223772i 1.98603 + 0.223772i 0.997204 + 0.0747301i \(0.0238095\pi\)
0.988831 + 0.149042i \(0.0476190\pi\)
\(74\) 0 0
\(75\) 0.149042 0.988831i 0.149042 0.988831i
\(76\) 0 0
\(77\) 0 0
\(78\) 0.574200 0.108644i 0.574200 0.108644i
\(79\) 0 0 −0.330279 0.943883i \(-0.607143\pi\)
0.330279 + 0.943883i \(0.392857\pi\)
\(80\) 0 0
\(81\) 0.0747301 + 0.997204i 0.0747301 + 0.997204i
\(82\) 0.185412 0.232500i 0.185412 0.232500i
\(83\) 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
\(87\) 0.623490 0.781831i 0.623490 0.781831i
\(88\) 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
\(92\) −0.224672 + 0.281729i −0.224672 + 0.281729i
\(93\) −0.500000 0.133975i −0.500000 0.133975i
\(94\) 0.166318 0.728688i 0.166318 0.728688i
\(95\) 0 0
\(96\) 0.126466 + 0.668389i 0.126466 + 0.668389i
\(97\) 0 0 −0.846724 0.532032i \(-0.821429\pi\)
0.846724 + 0.532032i \(0.178571\pi\)
\(98\) 0.264152 0.754903i 0.264152 0.754903i
\(99\) 0 0
\(100\) −0.156348 0.324660i −0.156348 0.324660i
\(101\) −1.05737 0.119137i −1.05737 0.119137i −0.433884 0.900969i \(-0.642857\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(102\) 0 0
\(103\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(104\) 0.562128 0.562128i 0.562128 0.562128i
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 0.433884 0.900969i \(-0.357143\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(108\) 0.224672 + 0.281729i 0.224672 + 0.281729i
\(109\) 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
\(116\) 0.0269287 0.359338i 0.0269287 0.359338i
\(117\) 0.215372 0.698220i 0.215372 0.698220i
\(118\) −0.353699 + 0.0398523i −0.353699 + 0.0398523i
\(119\) 0 0
\(120\) 0 0
\(121\) −0.781831 0.623490i −0.781831 0.623490i
\(122\) 0 0
\(123\) −0.148689 0.340799i −0.148689 0.340799i
\(124\) −0.176061 + 0.0616065i −0.176061 + 0.0616065i
\(125\) 0 0
\(126\) 0 0
\(127\) 1.43087 + 0.500684i 1.43087 + 0.500684i 0.930874 0.365341i \(-0.119048\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(128\) −0.114983 0.114983i −0.114983 0.114983i
\(129\) 0 0
\(130\) 0 0
\(131\) 0.205245 1.82160i 0.205245 1.82160i −0.294755 0.955573i \(-0.595238\pi\)
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 0.943883 0.330279i \(-0.107143\pi\)
−0.943883 + 0.330279i \(0.892857\pi\)
\(138\) −0.319827 0.733052i −0.319827 0.733052i
\(139\) 0.185853 + 0.233052i 0.185853 + 0.233052i 0.866025 0.500000i \(-0.166667\pi\)
−0.680173 + 0.733052i \(0.738095\pi\)
\(140\) 0 0
\(141\) −0.708353 0.609587i −0.708353 0.609587i
\(142\) −0.126838 0.201862i −0.126838 0.201862i
\(143\) 0 0
\(144\) −0.487156 0.150268i −0.487156 0.150268i
\(145\) 0 0
\(146\) 1.59845i 1.59845i
\(147\) −0.680173 0.733052i −0.680173 0.733052i
\(148\) 0 0
\(149\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(150\) 0.799225 + 0.0299049i 0.799225 + 0.0299049i
\(151\) −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
\(156\) −0.0776084 0.251600i −0.0776084 0.251600i
\(157\) 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
\(162\) −0.785841 + 0.148689i −0.785841 + 0.148689i
\(163\) −0.308658 + 0.882094i −0.308658 + 0.882094i 0.680173 + 0.733052i \(0.261905\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(164\) −0.113448 0.0712842i −0.113448 0.0712842i
\(165\) 0 0
\(166\) 0 0
\(167\) 0.277479 1.21572i 0.277479 1.21572i −0.623490 0.781831i \(-0.714286\pi\)
0.900969 0.433884i \(-0.142857\pi\)
\(168\) 0 0
\(169\) 0.290611 0.364415i 0.290611 0.364415i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(174\) 0.677197 + 0.425511i 0.677197 + 0.425511i
\(175\) 0 0
\(176\) 0 0
\(177\) −0.162592 + 0.414278i −0.162592 + 0.414278i
\(178\) 0 0
\(179\) 0.0931869 0.116853i 0.0931869 0.116853i −0.733052 0.680173i \(-0.761905\pi\)
0.826239 + 0.563320i \(0.190476\pi\)
\(180\) 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
\(184\) −0.921221 0.578842i −0.921221 0.578842i
\(185\) 0 0
\(186\) 0.0617033 0.409375i 0.0617033 0.409375i
\(187\) 0 0
\(188\) −0.334639 0.0377047i −0.334639 0.0377047i
\(189\) 0 0
\(190\) 0 0
\(191\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(192\) −1.00704 + 0.310630i −1.00704 + 0.310630i
\(193\) 0.0397866 0.0633201i 0.0397866 0.0633201i −0.826239 0.563320i \(-0.809524\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) −0.351311 0.0801844i −0.351311 0.0801844i
\(197\) −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 \(0.428571\pi\)
\(200\) 0.921221 0.578842i 0.921221 0.578842i
\(201\) 0 0
\(202\) 0.851022i 0.851022i
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −0.997204 0.0747301i −0.997204 0.0747301i
\(208\) 0.291237 + 0.232254i 0.291237 + 0.232254i
\(209\) 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
\(213\) −0.297251 + 0.0222759i −0.297251 + 0.0222759i
\(214\) 0 0
\(215\) 0 0
\(216\) −0.769320 + 0.769320i −0.769320 + 0.769320i
\(217\) 0 0
\(218\) 0 0
\(219\) 1.76699 + 0.933884i 1.76699 + 0.933884i
\(220\) 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
\(225\) 0.500000 0.866025i 0.500000 0.866025i
\(226\) 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
\(232\) 1.08722 0.0406810i 1.08722 0.0406810i
\(233\) 1.65248i 1.65248i 0.563320 + 0.826239i \(0.309524\pi\)
−0.563320 + 0.826239i \(0.690476\pi\)
\(234\) 0.574200 + 0.108644i 0.574200 + 0.108644i
\(235\) 0 0
\(236\) 0.0356854 + 0.156348i 0.0356854 + 0.156348i
\(237\) 0 0
\(238\) 0 0
\(239\) 1.09839 + 0.250701i 1.09839 + 0.250701i 0.733052 0.680173i \(-0.238095\pi\)
0.365341 + 0.930874i \(0.380952\pi\)
\(240\) 0 0
\(241\) 0 0 0.433884 0.900969i \(-0.357143\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(242\) 0.425511 0.677197i 0.425511 0.677197i
\(243\) −0.294755 + 0.955573i −0.294755 + 0.955573i
\(244\) 0 0
\(245\) 0 0
\(246\) 0.257537 0.148689i 0.257537 0.148689i
\(247\) 0 0
\(248\) −0.244355 0.507409i −0.244355 0.507409i
\(249\) 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
\(254\) −0.269790 + 1.18203i −0.269790 + 1.18203i
\(255\) 0 0
\(256\) −0.575983 + 0.722259i −0.575983 + 0.722259i
\(257\) 0.574730 0.131178i 0.574730 0.131178i 0.0747301 0.997204i \(-0.476190\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 0.866025 0.500000i 0.866025 0.500000i
\(262\) 1.46610 1.46610
\(263\) 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
\(269\) −0.500684 1.43087i −0.500684 1.43087i −0.866025 0.500000i \(-0.833333\pi\)
0.365341 0.930874i \(-0.380952\pi\)
\(270\) 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
\(276\) −0.312068 + 0.180173i −0.312068 + 0.180173i
\(277\) 1.78181 0.858075i 1.78181 0.858075i 0.826239 0.563320i \(-0.190476\pi\)
0.955573 0.294755i \(-0.0952381\pi\)
\(278\) −0.168577 + 0.168577i −0.168577 + 0.168577i
\(279\) −0.416490 0.307384i −0.416490 0.307384i
\(280\) 0 0
\(281\) 0 0 0.433884 0.900969i \(-0.357143\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(282\) 0.421041 0.617554i 0.421041 0.617554i
\(283\) 0 0 −0.974928 0.222521i \(-0.928571\pi\)
0.974928 + 0.222521i \(0.0714286\pi\)
\(284\) −0.0839792 + 0.0669712i −0.0839792 + 0.0669712i
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) −0.126466 + 0.668389i −0.126466 + 0.668389i
\(289\) 1.00000i 1.00000i
\(290\) 0 0
\(291\) 0 0
\(292\) 0.715659 0.0806354i 0.715659 0.0806354i
\(293\) 0 0 −0.532032 0.846724i \(-0.678571\pi\)
0.532032 + 0.846724i \(0.321429\pi\)
\(294\) 0.521689 0.606214i 0.521689 0.606214i
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 0.658322 + 0.317031i 0.658322 + 0.317031i
\(300\) −0.0269287 0.359338i −0.0269287 0.359338i
\(301\) 0 0
\(302\) −0.565533 0.565533i −0.565533 0.565533i
\(303\) −0.940755 0.497204i −0.940755 0.497204i
\(304\) 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
\(311\) −1.12099 + 0.392253i −1.12099 + 0.392253i −0.826239 0.563320i \(-0.809524\pi\)
−0.294755 + 0.955573i \(0.595238\pi\)
\(312\) 0.728639 0.317902i 0.728639 0.317902i
\(313\) 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 \(-0.0714286\pi\)
1.00000 \(0\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) 0.106214 + 0.344336i 0.106214 + 0.344336i
\(325\) −0.571270 + 0.455573i −0.571270 + 0.455573i
\(326\) −0.728688 0.166318i −0.728688 0.166318i
\(327\) 0 0
\(328\) 0.175522 0.364475i 0.175522 0.364475i
\(329\) 0 0
\(330\) 0 0
\(331\) −0.922474 + 0.922474i −0.922474 + 0.922474i −0.997204 0.0747301i \(-0.976190\pi\)
0.0747301 + 0.997204i \(0.476190\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0.991043 + 0.111664i 0.991043 + 0.111664i
\(335\) 0 0
\(336\) 0 0
\(337\) 0 0 0.330279 0.943883i \(-0.392857\pi\)
−0.330279 + 0.943883i \(0.607143\pi\)
\(338\) 0.315644 + 0.198332i 0.315644 + 0.198332i
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 0 0
\(346\) −0.161359 1.43210i −0.161359 1.43210i
\(347\) 0.867767 0.867767 0.433884 0.900969i \(-0.357143\pi\)
0.433884 + 0.900969i \(0.357143\pi\)
\(348\) 0.156348 0.324660i 0.156348 0.324660i
\(349\) 1.91115 1.91115 0.955573 0.294755i \(-0.0952381\pi\)
0.955573 + 0.294755i \(0.0952381\pi\)
\(350\) 0 0
\(351\) 0.455573 0.571270i 0.455573 0.571270i
\(352\) 0 0
\(353\) −1.24349 + 1.55929i −1.24349 + 1.55929i −0.563320 + 0.826239i \(0.690476\pi\)
−0.680173 + 0.733052i \(0.738095\pi\)
\(354\) −0.343809 0.0921234i −0.343809 0.0921234i
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0.101214 + 0.0635969i 0.101214 + 0.0635969i
\(359\) 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
\(363\) −0.500000 0.866025i −0.500000 0.866025i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 0 0 0.532032 0.846724i \(-0.321429\pi\)
−0.532032 + 0.846724i \(0.678571\pi\)
\(368\) 0.221196 0.459319i 0.221196 0.459319i
\(369\) −0.0139029 0.371563i −0.0139029 0.371563i
\(370\) 0 0
\(371\) 0 0
\(372\) −0.186398 0.00697453i −0.186398 0.00697453i
\(373\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 1.01676i 1.01676i
\(377\) −0.722521 + 0.108903i −0.722521 + 0.108903i
\(378\) 0 0
\(379\) 0 0 0.993712 0.111964i \(-0.0357143\pi\)
−0.993712 + 0.111964i \(0.964286\pi\)
\(380\) 0 0
\(381\) 1.14904 + 0.988831i 1.14904 + 0.988831i
\(382\) 0 0
\(383\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(384\) −0.0650265 0.149042i −0.0650265 0.149042i
\(385\) 0 0
\(386\) 0.0538867 + 0.0259505i 0.0538867 + 0.0259505i
\(387\) 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
\(392\) 0.121815 1.08114i 0.121815 1.08114i
\(393\) 0.856562 1.62069i 0.856562 1.62069i
\(394\) −0.979531 0.979531i −0.979531 0.979531i
\(395\) 0 0
\(396\) 0 0
\(397\) −1.01507 0.488831i −1.01507 0.488831i −0.149042 0.988831i \(-0.547619\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0.317859 + 0.398582i 0.317859 + 0.398582i
\(401\) 0 0 −0.781831 0.623490i \(-0.785714\pi\)
0.781831 + 0.623490i \(0.214286\pi\)
\(402\) 0 0
\(403\) 0.201230 + 0.320256i 0.201230 + 0.320256i
\(404\) −0.381020 + 0.0429306i −0.381020 + 0.0429306i
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) −0.314832 + 0.197822i −0.314832 + 0.197822i −0.680173 0.733052i \(-0.738095\pi\)
0.365341 + 0.930874i \(0.380952\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) −0.0299049 0.799225i −0.0299049 0.799225i
\(415\) 0 0
\(416\) 0.264444 0.420860i 0.264444 0.420860i
\(417\) 0.0878620 + 0.284841i 0.0878620 + 0.284841i
\(418\) 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 \(0.0357143\pi\)
\(422\) 0.490751 + 1.01905i 0.490751 + 1.01905i
\(423\) −0.436680 0.826239i −0.436680 0.826239i
\(424\) 0 0
\(425\) 0 0
\(426\) −0.0443219 0.234247i −0.0443219 0.234247i
\(427\) 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 \(0.928571\pi\)
\(432\) −0.398582 0.317859i −0.398582 0.317859i
\(433\) 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
\(438\) −0.583979 + 1.48795i −0.583979 + 1.48795i
\(439\) −1.09839 + 0.250701i −1.09839 + 0.250701i −0.733052 0.680173i \(-0.761905\pi\)
−0.365341 + 0.930874i \(0.619048\pi\)
\(440\) 0 0
\(441\) −0.365341 0.930874i −0.365341 0.930874i
\(442\) 0 0
\(443\) −0.0246991 0.0705858i −0.0246991 0.0705858i 0.930874 0.365341i \(-0.119048\pi\)
−0.955573 + 0.294755i \(0.904762\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0.475985 1.36029i 0.475985 1.36029i
\(447\) 0 0
\(448\) 0 0
\(449\) 0.222521 + 0.0250721i 0.222521 + 0.0250721i 0.222521 0.974928i \(-0.428571\pi\)
1.00000i \(0.5\pi\)
\(450\) 0.733052 + 0.319827i 0.733052 + 0.319827i
\(451\) 0 0
\(452\) 0 0
\(453\) −0.955573 + 0.294755i −0.955573 + 0.294755i
\(454\) 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
\(461\) 1.10462 0.694076i 1.10462 0.694076i 0.149042 0.988831i \(-0.452381\pi\)
0.955573 + 0.294755i \(0.0952381\pi\)
\(462\) 0 0
\(463\) 1.24698i 1.24698i 0.781831 + 0.623490i \(0.214286\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(464\) 0.0759826 + 0.504112i 0.0759826 + 0.504112i
\(465\) 0 0
\(466\) −1.31332 + 0.147975i −1.31332 + 0.147975i
\(467\) 0 0 −0.532032 0.846724i \(-0.678571\pi\)
0.532032 + 0.846724i \(0.321429\pi\)
\(468\) 0.0196763 0.262562i 0.0196763 0.262562i
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) −0.457026 + 0.159920i −0.457026 + 0.159920i
\(473\) 0 0
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 0 0
\(478\) −0.100888 + 0.895403i −0.100888 + 0.895403i
\(479\) 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
\(484\) −0.324660 0.156348i −0.324660 0.156348i
\(485\) 0 0
\(486\) −0.785841 0.148689i −0.785841 0.148689i
\(487\) 1.24349 + 1.55929i 1.24349 + 1.55929i 0.680173 + 0.733052i \(0.261905\pi\)
0.563320 + 0.826239i \(0.309524\pi\)
\(488\) 0 0
\(489\) −0.609587 + 0.708353i −0.609587 + 0.708353i
\(490\) 0 0
\(491\) 1.95278 0.220025i 1.95278 0.220025i 0.955573 0.294755i \(-0.0952381\pi\)
0.997204 + 0.0747301i \(0.0238095\pi\)
\(492\) −0.0795629 0.107804i −0.0795629 0.107804i
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0.223446 0.140401i 0.223446 0.140401i
\(497\) 0 0
\(498\) 0 0
\(499\) −1.49419 + 1.19158i −1.49419 + 1.19158i −0.563320 + 0.826239i \(0.690476\pi\)
−0.930874 + 0.365341i \(0.880952\pi\)
\(500\) 0 0
\(501\) 0.702449 1.03030i 0.702449 1.03030i
\(502\) 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
\(507\) 0.403658 0.233052i 0.403658 0.233052i
\(508\) 0.542829 + 0.0611621i 0.542829 + 0.0611621i
\(509\) −0.590232 1.22563i −0.590232 1.22563i −0.955573 0.294755i \(-0.904762\pi\)
0.365341 0.930874i \(-0.380952\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −0.763283 0.479602i −0.763283 0.479602i
\(513\) 0 0
\(514\) 0.155720 + 0.445023i 0.155720 + 0.445023i
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) −1.67738 0.658322i −1.67738 0.658322i
\(520\) 0 0
\(521\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(522\) 0.474928 + 0.643504i 0.474928 + 0.643504i
\(523\) 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
\(531\) −0.302705 + 0.326239i −0.302705 + 0.326239i
\(532\) 0 0
\(533\) −0.0897317 + 0.256439i −0.0897317 + 0.256439i
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0.129436 0.0747301i 0.129436 0.0747301i
\(538\) 1.09236 0.526053i 1.09236 0.526053i
\(539\) 0 0
\(540\) 0 0
\(541\) −0.940755 + 1.49720i −0.940755 + 1.49720i −0.0747301 + 0.997204i \(0.523810\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(542\) −0.0777063 + 0.161359i −0.0777063 + 0.161359i
\(543\) 0 0
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 0.367711 + 1.61105i 0.367711 + 1.61105i 0.733052 + 0.680173i \(0.238095\pi\)
−0.365341 + 0.930874i \(0.619048\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 0 0
\(552\) −0.646066 0.875388i −0.646066 0.875388i
\(553\) 0 0
\(554\) 0.841516 + 1.33927i 0.841516 + 1.33927i
\(555\) 0 0
\(556\) 0.0839792 + 0.0669712i 0.0839792 + 0.0669712i
\(557\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(558\) 0.206999 0.358533i 0.206999 0.358533i
\(559\) 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 \(0.250000\pi\)
\(564\) −0.297731 0.157356i −0.297731 0.157356i
\(565\) 0 0
\(566\) 0 0
\(567\) 0 0
\(568\) −0.229322 0.229322i −0.229322 0.229322i
\(569\) 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
\(576\) −1.05091 0.0787549i −1.05091 0.0787549i
\(577\) 0.694076 + 1.10462i 0.694076 + 1.10462i 0.988831 + 0.149042i \(0.0476190\pi\)
−0.294755 + 0.955573i \(0.595238\pi\)
\(578\) 0.794755 0.0895474i 0.794755 0.0895474i
\(579\) 0.0601697 0.0444073i 0.0601697 0.0444073i
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) 0.483859 + 2.11993i 0.483859 + 2.11993i
\(585\) 0 0
\(586\) 0 0
\(587\) 1.94440 + 0.443797i 1.94440 + 0.443797i 0.988831 + 0.149042i \(0.0476190\pi\)
0.955573 + 0.294755i \(0.0952381\pi\)
\(588\) −0.297731 0.202990i −0.297731 0.202990i
\(589\) 0 0
\(590\) 0 0
\(591\) −1.65510 + 0.510531i −1.65510 + 0.510531i
\(592\) 0 0
\(593\) 0.781831 0.376510i 0.781831 0.376510i 1.00000i \(-0.5\pi\)
0.781831 + 0.623490i \(0.214286\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) −0.193011 + 0.551594i −0.193011 + 0.551594i
\(599\) 0.189606 + 0.119137i 0.189606 + 0.119137i 0.623490 0.781831i \(-0.285714\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(600\) 1.06902 0.202269i 1.06902 0.202269i
\(601\) −0.638050 1.82344i −0.638050 1.82344i −0.563320 0.826239i \(-0.690476\pi\)
−0.0747301 0.997204i \(-0.523810\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −0.224672 + 0.281729i −0.224672 + 0.281729i
\(605\) 0 0
\(606\) 0.310913 0.792194i 0.310913 0.792194i
\(607\) −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
\(611\) 0.0764549 + 0.678556i 0.0764549 + 0.678556i
\(612\) 0 0
\(613\) 0 0 0.974928 0.222521i \(-0.0714286\pi\)
−0.974928 + 0.222521i \(0.928571\pi\)
\(614\) −0.844450 + 1.05891i −0.844450 + 1.05891i
\(615\) 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
\(621\) −0.900969 0.433884i −0.900969 0.433884i
\(622\) −0.412127 0.855791i −0.412127 0.855791i
\(623\) 0 0
\(624\) 0.186253 + 0.322600i 0.186253 + 0.322600i
\(625\) −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
\(633\) 1.41322 + 0.0528791i 1.41322 + 0.0528791i
\(634\) 0.353699 + 1.54966i 0.353699 + 1.54966i
\(635\) 0 0
\(636\) 0 0
\(637\) 0.730682i 0.730682i
\(638\) 0 0
\(639\) −0.284841 0.0878620i −0.284841 0.0878620i
\(640\) 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
\(647\) −1.22563 0.590232i −1.22563 0.590232i −0.294755 0.955573i \(-0.595238\pi\)
−0.930874 + 0.365341i \(0.880952\pi\)
\(648\) −0.997204 + 0.435076i −0.997204 + 0.435076i
\(649\) 0 0
\(650\) −0.413225 0.413225i −0.413225 0.413225i
\(651\) 0 0
\(652\) −0.0377047 + 0.334639i −0.0377047 + 0.334639i
\(653\) −0.216299 + 1.91970i −0.216299 + 1.91970i 0.149042 + 0.988831i \(0.452381\pi\)
−0.365341 + 0.930874i \(0.619048\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0.178920 + 0.0626069i 0.178920 + 0.0626069i
\(657\) 1.30366 + 1.51488i 1.30366 + 1.51488i
\(658\) 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 \(0.285714\pi\)
\(662\) −0.815746 0.650536i −0.815746 0.650536i
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0.365341 + 0.930874i 0.365341 + 0.930874i
\(668\) 0.449343i 0.449343i
\(669\) −1.22563 1.32091i −1.22563 1.32091i
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) −1.55929 + 1.24349i −1.55929 + 1.24349i −0.733052 + 0.680173i \(0.761905\pi\)
−0.826239 + 0.563320i \(0.809524\pi\)
\(674\) 0 0
\(675\) 0.781831 0.623490i 0.781831 0.623490i
\(676\) 0.0728744 0.151325i 0.0728744 0.151325i
\(677\) 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
\(683\) 0.255779 + 0.531130i 0.255779 + 0.531130i 0.988831 0.149042i \(-0.0476190\pi\)
−0.733052 + 0.680173i \(0.761905\pi\)
\(684\) 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 \(0.928571\pi\)
\(692\) −0.633040 + 0.144487i −0.633040 + 0.144487i
\(693\) 0 0
\(694\) 0.0777063 + 0.689663i 0.0777063 + 0.689663i
\(695\) 0 0
\(696\) 1.02693 + 0.359338i 1.02693 + 0.359338i
\(697\) 0 0
\(698\) 0.171138 + 1.51889i 0.171138 + 1.51889i
\(699\) −0.603718 + 1.53825i −0.603718 + 1.53825i
\(700\) 0 0
\(701\) 0 0 0.623490 0.781831i \(-0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(702\) 0.494815 + 0.310913i 0.494815 + 0.310913i
\(703\) 0 0
\(704\) 0 0
\(705\) 0 0
\(706\) −1.35061 0.848642i −1.35061 0.848642i
\(707\) 0 0
\(708\) −0.0239017 + 0.158578i −0.0239017 + 0.158578i
\(709\) 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
\(713\) 0.366025 0.366025i 0.366025 0.366025i
\(714\) 0 0
\(715\) 0 0
\(716\) 0.0233678 0.0485238i 0.0233678 0.0485238i
\(717\) 0.930874 + 0.634659i 0.930874 + 0.634659i
\(718\) 0 0
\(719\) −1.22252 + 0.974928i −1.22252 + 0.974928i −0.222521 + 0.974928i \(0.571429\pi\)
−1.00000 \(\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0.677197 0.425511i 0.677197 0.425511i
\(723\) 0 0
\(724\) 0 0
\(725\) −0.997204 0.0747301i −0.997204 0.0747301i
\(726\) 0.643504 0.474928i 0.643504 0.474928i
\(727\) 0 0 0.993712 0.111964i \(-0.0357143\pi\)
−0.993712 + 0.111964i \(0.964286\pi\)
\(728\) 0 0
\(729\) −0.623490 + 0.781831i −0.623490 + 0.781831i
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 0 0 0.943883 0.330279i \(-0.107143\pi\)
−0.943883 + 0.330279i \(0.892857\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) −0.642075 0.224672i −0.642075 0.224672i
\(737\) 0 0
\(738\) 0.294057 0.0443219i 0.294057 0.0443219i
\(739\) 0.0416310 0.369485i 0.0416310 0.369485i −0.955573 0.294755i \(-0.904762\pi\)
0.997204 0.0747301i \(-0.0238095\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 −0.943883 0.330279i \(-0.892857\pi\)
0.943883 + 0.330279i \(0.107143\pi\)
\(744\) −0.0420866 0.561606i −0.0420866 0.561606i
\(745\) 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 \(0.321429\pi\)
\(752\) 0.473437 0.0533435i 0.473437 0.0533435i
\(753\) 0 0
\(754\) −0.151251 0.564475i −0.151251 0.564475i
\(755\) 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
\(761\) 1.92808 + 0.440071i 1.92808 + 0.440071i 0.997204 + 0.0747301i \(0.0238095\pi\)
0.930874 + 0.365341i \(0.119048\pi\)
\(762\) −0.682985 + 1.00175i −0.682985 + 1.00175i
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0.292981 0.141092i 0.292981 0.141092i
\(768\) −0.800038 + 0.461902i −0.800038 + 0.461902i
\(769\) 0 0 −0.993712 0.111964i \(-0.964286\pi\)
0.993712 + 0.111964i \(0.0357143\pi\)
\(770\) 0 0
\(771\) 0.582926 + 0.0878620i 0.582926 + 0.0878620i
\(772\) 0.00890019 0.0254353i 0.00890019 0.0254353i
\(773\) 0 0 −0.846724 0.532032i \(-0.821429\pi\)
0.846724 + 0.532032i \(0.178571\pi\)
\(774\) 0 0
\(775\) 0.170965 + 0.488590i 0.170965 + 0.488590i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0.988831 0.149042i 0.988831 0.149042i
\(784\) 0.509806 0.509806
\(785\) 0 0
\(786\) 1.36476 + 0.535628i 1.36476 + 0.535628i
\(787\) 0 0 0.974928 0.222521i \(-0.0714286\pi\)
−0.974928 + 0.222521i \(0.928571\