Properties

Label 2001.1.bf.d.965.2
Level $2001$
Weight $1$
Character 2001.965
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 965.2
Root \(-0.149042 - 0.988831i\) of defining polynomial
Character \(\chi\) \(=\) 2001.965
Dual form 2001.1.bf.d.620.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.122805 + 0.350958i) q^{2} +(0.563320 + 0.826239i) q^{3} +(0.673741 + 0.537291i) q^{4} +(-0.359154 + 0.0962349i) q^{6} +(-0.586137 + 0.368294i) q^{8} +(-0.365341 + 0.930874i) q^{9} +O(q^{10})\) \(q+(-0.122805 + 0.350958i) q^{2} +(0.563320 + 0.826239i) q^{3} +(0.673741 + 0.537291i) q^{4} +(-0.359154 + 0.0962349i) q^{6} +(-0.586137 + 0.368294i) q^{8} +(-0.365341 + 0.930874i) q^{9} +(-0.0643985 + 0.859338i) q^{12} +(1.61105 - 0.367711i) q^{13} +(0.134482 + 0.589204i) q^{16} +(-0.281831 - 0.242536i) q^{18} +(0.433884 - 0.900969i) q^{23} +(-0.634482 - 0.276822i) q^{24} +(0.623490 - 0.781831i) q^{25} +(-0.0687943 + 0.610566i) q^{26} +(-0.974928 + 0.222521i) q^{27} +(-0.149042 + 0.988831i) q^{29} +(-1.82344 - 0.638050i) q^{31} +(-0.911189 - 0.102666i) q^{32} +(-0.746295 + 0.430874i) q^{36} +(1.21135 + 1.12397i) q^{39} +(-0.660818 - 0.660818i) q^{41} +(0.262919 + 0.262919i) q^{46} +(-0.631863 + 1.00560i) q^{47} +(-0.411067 + 0.443024i) q^{48} +(-0.222521 + 0.974928i) q^{49} +(0.197822 + 0.314832i) q^{50} +(1.28300 + 0.617858i) q^{52} +(0.0416310 - 0.369485i) q^{54} +(-0.328735 - 0.173741i) q^{58} -1.24698i q^{59} +(0.447857 - 0.561595i) q^{62} +(-0.114290 + 0.237325i) q^{64} +(0.988831 - 0.149042i) q^{69} +(-0.443797 - 1.94440i) q^{71} +(-0.128696 - 0.680173i) q^{72} +(-0.754903 + 0.264152i) q^{73} +(0.997204 + 0.0747301i) q^{75} +(-0.543227 + 0.287104i) q^{78} +(-0.733052 - 0.680173i) q^{81} +(0.313071 - 0.150767i) q^{82} +(-0.900969 + 0.433884i) q^{87} +(0.776408 - 0.373898i) q^{92} +(-0.500000 - 1.86603i) q^{93} +(-0.275328 - 0.345251i) q^{94} +(-0.428464 - 0.810694i) q^{96} +(-0.314832 - 0.197822i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q + 2q^{2} + 14q^{4} + 2q^{6} - 6q^{8} - 2q^{9} + O(q^{10}) \) \( 24q + 2q^{2} + 14q^{4} + 2q^{6} - 6q^{8} - 2q^{9} + 2q^{12} - 6q^{16} + 12q^{18} - 6q^{24} - 4q^{25} - 2q^{26} - 2q^{31} - 4q^{32} + 6q^{36} + 2q^{39} - 2q^{41} + 2q^{46} + 2q^{47} + 6q^{48} - 4q^{49} + 2q^{50} - 10q^{52} - 2q^{54} + 4q^{58} - 4q^{62} - 28q^{64} - 2q^{69} + 22q^{72} - 2q^{73} - 4q^{78} + 2q^{81} - 4q^{82} - 4q^{87} - 4q^{92} - 12q^{93} - 8q^{94} - 18q^{96} + 2q^{98} + O(q^{100}) \)

Character values

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

\(n\) \(553\) \(668\) \(1132\)
\(\chi(n)\) \(e\left(\frac{3}{28}\right)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.122805 + 0.350958i −0.122805 + 0.350958i −0.988831 0.149042i \(-0.952381\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(3\) 0.563320 + 0.826239i 0.563320 + 0.826239i
\(4\) 0.673741 + 0.537291i 0.673741 + 0.537291i
\(5\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(6\) −0.359154 + 0.0962349i −0.359154 + 0.0962349i
\(7\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(8\) −0.586137 + 0.368294i −0.586137 + 0.368294i
\(9\) −0.365341 + 0.930874i −0.365341 + 0.930874i
\(10\) 0 0
\(11\) 0 0 −0.846724 0.532032i \(-0.821429\pi\)
0.846724 + 0.532032i \(0.178571\pi\)
\(12\) −0.0643985 + 0.859338i −0.0643985 + 0.859338i
\(13\) 1.61105 0.367711i 1.61105 0.367711i 0.680173 0.733052i \(-0.261905\pi\)
0.930874 + 0.365341i \(0.119048\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0.134482 + 0.589204i 0.134482 + 0.589204i
\(17\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(18\) −0.281831 0.242536i −0.281831 0.242536i
\(19\) 0 0 0.993712 0.111964i \(-0.0357143\pi\)
−0.993712 + 0.111964i \(0.964286\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 0.433884 0.900969i 0.433884 0.900969i
\(24\) −0.634482 0.276822i −0.634482 0.276822i
\(25\) 0.623490 0.781831i 0.623490 0.781831i
\(26\) −0.0687943 + 0.610566i −0.0687943 + 0.610566i
\(27\) −0.974928 + 0.222521i −0.974928 + 0.222521i
\(28\) 0 0
\(29\) −0.149042 + 0.988831i −0.149042 + 0.988831i
\(30\) 0 0
\(31\) −1.82344 0.638050i −1.82344 0.638050i −0.997204 0.0747301i \(-0.976190\pi\)
−0.826239 0.563320i \(-0.809524\pi\)
\(32\) −0.911189 0.102666i −0.911189 0.102666i
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) −0.746295 + 0.430874i −0.746295 + 0.430874i
\(37\) 0 0 −0.532032 0.846724i \(-0.678571\pi\)
0.532032 + 0.846724i \(0.321429\pi\)
\(38\) 0 0
\(39\) 1.21135 + 1.12397i 1.21135 + 1.12397i
\(40\) 0 0
\(41\) −0.660818 0.660818i −0.660818 0.660818i 0.294755 0.955573i \(-0.404762\pi\)
−0.955573 + 0.294755i \(0.904762\pi\)
\(42\) 0 0
\(43\) 0 0 −0.330279 0.943883i \(-0.607143\pi\)
0.330279 + 0.943883i \(0.392857\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0.262919 + 0.262919i 0.262919 + 0.262919i
\(47\) −0.631863 + 1.00560i −0.631863 + 1.00560i 0.365341 + 0.930874i \(0.380952\pi\)
−0.997204 + 0.0747301i \(0.976190\pi\)
\(48\) −0.411067 + 0.443024i −0.411067 + 0.443024i
\(49\) −0.222521 + 0.974928i −0.222521 + 0.974928i
\(50\) 0.197822 + 0.314832i 0.197822 + 0.314832i
\(51\) 0 0
\(52\) 1.28300 + 0.617858i 1.28300 + 0.617858i
\(53\) 0 0 −0.433884 0.900969i \(-0.642857\pi\)
0.433884 + 0.900969i \(0.357143\pi\)
\(54\) 0.0416310 0.369485i 0.0416310 0.369485i
\(55\) 0 0
\(56\) 0 0
\(57\) 0 0
\(58\) −0.328735 0.173741i −0.328735 0.173741i
\(59\) 1.24698i 1.24698i −0.781831 0.623490i \(-0.785714\pi\)
0.781831 0.623490i \(-0.214286\pi\)
\(60\) 0 0
\(61\) 0 0 0.111964 0.993712i \(-0.464286\pi\)
−0.111964 + 0.993712i \(0.535714\pi\)
\(62\) 0.447857 0.561595i 0.447857 0.561595i
\(63\) 0 0
\(64\) −0.114290 + 0.237325i −0.114290 + 0.237325i
\(65\) 0 0
\(66\) 0 0
\(67\) 0 0 −0.974928 0.222521i \(-0.928571\pi\)
0.974928 + 0.222521i \(0.0714286\pi\)
\(68\) 0 0
\(69\) 0.988831 0.149042i 0.988831 0.149042i
\(70\) 0 0
\(71\) −0.443797 1.94440i −0.443797 1.94440i −0.294755 0.955573i \(-0.595238\pi\)
−0.149042 0.988831i \(-0.547619\pi\)
\(72\) −0.128696 0.680173i −0.128696 0.680173i
\(73\) −0.754903 + 0.264152i −0.754903 + 0.264152i −0.680173 0.733052i \(-0.738095\pi\)
−0.0747301 + 0.997204i \(0.523810\pi\)
\(74\) 0 0
\(75\) 0.997204 + 0.0747301i 0.997204 + 0.0747301i
\(76\) 0 0
\(77\) 0 0
\(78\) −0.543227 + 0.287104i −0.543227 + 0.287104i
\(79\) 0 0 0.846724 0.532032i \(-0.178571\pi\)
−0.846724 + 0.532032i \(0.821429\pi\)
\(80\) 0 0
\(81\) −0.733052 0.680173i −0.733052 0.680173i
\(82\) 0.313071 0.150767i 0.313071 0.150767i
\(83\) 0 0 −0.781831 0.623490i \(-0.785714\pi\)
0.781831 + 0.623490i \(0.214286\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −0.900969 + 0.433884i −0.900969 + 0.433884i
\(88\) 0 0
\(89\) 0 0 0.330279 0.943883i \(-0.392857\pi\)
−0.330279 + 0.943883i \(0.607143\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0.776408 0.373898i 0.776408 0.373898i
\(93\) −0.500000 1.86603i −0.500000 1.86603i
\(94\) −0.275328 0.345251i −0.275328 0.345251i
\(95\) 0 0
\(96\) −0.428464 0.810694i −0.428464 0.810694i
\(97\) 0 0 −0.111964 0.993712i \(-0.535714\pi\)
0.111964 + 0.993712i \(0.464286\pi\)
\(98\) −0.314832 0.197822i −0.314832 0.197822i
\(99\) 0 0
\(100\) 0.840142 0.191757i 0.840142 0.191757i
\(101\) 1.87590 0.656405i 1.87590 0.656405i 0.900969 0.433884i \(-0.142857\pi\)
0.974928 0.222521i \(-0.0714286\pi\)
\(102\) 0 0
\(103\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(104\) −0.808868 + 0.808868i −0.808868 + 0.808868i
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 −0.974928 0.222521i \(-0.928571\pi\)
0.974928 + 0.222521i \(0.0714286\pi\)
\(108\) −0.776408 0.373898i −0.776408 0.373898i
\(109\) 0 0 0.781831 0.623490i \(-0.214286\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 0 0 0.111964 0.993712i \(-0.464286\pi\)
−0.111964 + 0.993712i \(0.535714\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) −0.631706 + 0.586137i −0.631706 + 0.586137i
\(117\) −0.246289 + 1.63402i −0.246289 + 1.63402i
\(118\) 0.437637 + 0.153136i 0.437637 + 0.153136i
\(119\) 0 0
\(120\) 0 0
\(121\) 0.433884 + 0.900969i 0.433884 + 0.900969i
\(122\) 0 0
\(123\) 0.173741 0.918245i 0.173741 0.918245i
\(124\) −0.885710 1.40960i −0.885710 1.40960i
\(125\) 0 0
\(126\) 0 0
\(127\) 1.06332 1.69226i 1.06332 1.69226i 0.500000 0.866025i \(-0.333333\pi\)
0.563320 0.826239i \(-0.309524\pi\)
\(128\) −0.717641 0.717641i −0.717641 0.717641i
\(129\) 0 0
\(130\) 0 0
\(131\) 0.649042 + 1.85486i 0.649042 + 1.85486i 0.500000 + 0.866025i \(0.333333\pi\)
0.149042 + 0.988831i \(0.452381\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 0 0 −0.532032 0.846724i \(-0.678571\pi\)
0.532032 + 0.846724i \(0.321429\pi\)
\(138\) −0.0691263 + 0.365341i −0.0691263 + 0.365341i
\(139\) −1.79690 0.865341i −1.79690 0.865341i −0.930874 0.365341i \(-0.880952\pi\)
−0.866025 0.500000i \(-0.833333\pi\)
\(140\) 0 0
\(141\) −1.18681 + 0.0444073i −1.18681 + 0.0444073i
\(142\) 0.736904 + 0.0830292i 0.736904 + 0.0830292i
\(143\) 0 0
\(144\) −0.597606 0.0900746i −0.597606 0.0900746i
\(145\) 0 0
\(146\) 0.297378i 0.297378i
\(147\) −0.930874 + 0.365341i −0.930874 + 0.365341i
\(148\) 0 0
\(149\) 0 0 0.623490 0.781831i \(-0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(150\) −0.148689 + 0.340799i −0.148689 + 0.340799i
\(151\) 0.433884 0.900969i 0.433884 0.900969i −0.563320 0.826239i \(-0.690476\pi\)
0.997204 0.0747301i \(-0.0238095\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 0.212239 + 1.40811i 0.212239 + 1.40811i
\(157\) 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
\(162\) 0.328735 0.173741i 0.328735 0.173741i
\(163\) 1.00560 + 0.631863i 1.00560 + 0.631863i 0.930874 0.365341i \(-0.119048\pi\)
0.0747301 + 0.997204i \(0.476190\pi\)
\(164\) −0.0901689 0.800271i −0.0901689 0.800271i
\(165\) 0 0
\(166\) 0 0
\(167\) 1.12349 + 1.40881i 1.12349 + 1.40881i 0.900969 + 0.433884i \(0.142857\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(168\) 0 0
\(169\) 1.55929 0.750915i 1.55929 0.750915i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(174\) −0.0416310 0.369485i −0.0416310 0.369485i
\(175\) 0 0
\(176\) 0 0
\(177\) 1.03030 0.702449i 1.03030 0.702449i
\(178\) 0 0
\(179\) 1.32091 0.636119i 1.32091 0.636119i 0.365341 0.930874i \(-0.380952\pi\)
0.955573 + 0.294755i \(0.0952381\pi\)
\(180\) 0 0
\(181\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0.0775064 + 0.687888i 0.0775064 + 0.687888i
\(185\) 0 0
\(186\) 0.716299 + 0.0536792i 0.716299 + 0.0536792i
\(187\) 0 0
\(188\) −0.966014 + 0.338023i −0.966014 + 0.338023i
\(189\) 0 0
\(190\) 0 0
\(191\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(192\) −0.260469 + 0.0392594i −0.260469 + 0.0392594i
\(193\) −1.82160 + 0.205245i −1.82160 + 0.205245i −0.955573 0.294755i \(-0.904762\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) −0.673741 + 0.537291i −0.673741 + 0.537291i
\(197\) −0.751509 + 1.56052i −0.751509 + 1.56052i 0.0747301 + 0.997204i \(0.476190\pi\)
−0.826239 + 0.563320i \(0.809524\pi\)
\(198\) 0 0
\(199\) 0 0 0.623490 0.781831i \(-0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(200\) −0.0775064 + 0.687888i −0.0775064 + 0.687888i
\(201\) 0 0
\(202\) 0.738971i 0.738971i
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 0.680173 + 0.733052i 0.680173 + 0.733052i
\(208\) 0.433313 + 0.899784i 0.433313 + 0.899784i
\(209\) 0 0
\(210\) 0 0
\(211\) −0.752407 1.19745i −0.752407 1.19745i −0.974928 0.222521i \(-0.928571\pi\)
0.222521 0.974928i \(-0.428571\pi\)
\(212\) 0 0
\(213\) 1.35654 1.46200i 1.35654 1.46200i
\(214\) 0 0
\(215\) 0 0
\(216\) 0.489488 0.489488i 0.489488 0.489488i
\(217\) 0 0
\(218\) 0 0
\(219\) −0.643504 0.474928i −0.643504 0.474928i
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) −0.0990311 + 0.433884i −0.0990311 + 0.433884i 0.900969 + 0.433884i \(0.142857\pi\)
−1.00000 \(\pi\)
\(224\) 0 0
\(225\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(226\) 0 0
\(227\) 0 0 −0.433884 0.900969i \(-0.642857\pi\)
0.433884 + 0.900969i \(0.357143\pi\)
\(228\) 0 0
\(229\) 0 0 −0.993712 0.111964i \(-0.964286\pi\)
0.993712 + 0.111964i \(0.0357143\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −0.276822 0.634482i −0.276822 0.634482i
\(233\) 1.91115i 1.91115i 0.294755 + 0.955573i \(0.404762\pi\)
−0.294755 + 0.955573i \(0.595238\pi\)
\(234\) −0.543227 0.287104i −0.543227 0.287104i
\(235\) 0 0
\(236\) 0.669991 0.840142i 0.669991 0.840142i
\(237\) 0 0
\(238\) 0 0
\(239\) 0.460898 0.367554i 0.460898 0.367554i −0.365341 0.930874i \(-0.619048\pi\)
0.826239 + 0.563320i \(0.190476\pi\)
\(240\) 0 0
\(241\) 0 0 −0.974928 0.222521i \(-0.928571\pi\)
0.974928 + 0.222521i \(0.0714286\pi\)
\(242\) −0.369485 + 0.0416310i −0.369485 + 0.0416310i
\(243\) 0.149042 0.988831i 0.149042 0.988831i
\(244\) 0 0
\(245\) 0 0
\(246\) 0.300929 + 0.173741i 0.300929 + 0.173741i
\(247\) 0 0
\(248\) 1.30378 0.297579i 1.30378 0.297579i
\(249\) 0 0
\(250\) 0 0
\(251\) 0 0 −0.111964 0.993712i \(-0.535714\pi\)
0.111964 + 0.993712i \(0.464286\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0.463332 + 0.581000i 0.463332 + 0.581000i
\(255\) 0 0
\(256\) 0.102666 0.0494415i 0.102666 0.0494415i
\(257\) −0.233052 0.185853i −0.233052 0.185853i 0.500000 0.866025i \(-0.333333\pi\)
−0.733052 + 0.680173i \(0.761905\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) −0.866025 0.500000i −0.866025 0.500000i
\(262\) −0.730682 −0.730682
\(263\) 0 0 0.330279 0.943883i \(-0.392857\pi\)
−0.330279 + 0.943883i \(0.607143\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 1.69226 1.06332i 1.69226 1.06332i 0.826239 0.563320i \(-0.190476\pi\)
0.866025 0.500000i \(-0.166667\pi\)
\(270\) 0 0
\(271\) 0.0739590 + 0.656405i 0.0739590 + 0.656405i 0.974928 + 0.222521i \(0.0714286\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) 0.746295 + 0.430874i 0.746295 + 0.430874i
\(277\) −0.0332580 0.145713i −0.0332580 0.145713i 0.955573 0.294755i \(-0.0952381\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(278\) 0.524367 0.524367i 0.524367 0.524367i
\(279\) 1.26012 1.46429i 1.26012 1.46429i
\(280\) 0 0
\(281\) 0 0 −0.974928 0.222521i \(-0.928571\pi\)
0.974928 + 0.222521i \(0.0714286\pi\)
\(282\) 0.130162 0.421974i 0.130162 0.421974i
\(283\) 0 0 0.781831 0.623490i \(-0.214286\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(284\) 0.745705 1.54847i 0.745705 1.54847i
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0.428464 0.810694i 0.428464 0.810694i
\(289\) 1.00000i 1.00000i
\(290\) 0 0
\(291\) 0 0
\(292\) −0.650536 0.227632i −0.650536 0.227632i
\(293\) 0 0 −0.993712 0.111964i \(-0.964286\pi\)
0.993712 + 0.111964i \(0.0357143\pi\)
\(294\) −0.0139029 0.371563i −0.0139029 0.371563i
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 0.367711 1.61105i 0.367711 1.61105i
\(300\) 0.631706 + 0.586137i 0.631706 + 0.586137i
\(301\) 0 0
\(302\) 0.262919 + 0.262919i 0.262919 + 0.262919i
\(303\) 1.59908 + 1.18017i 1.59908 + 1.18017i
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 0.158342 + 0.158342i 0.158342 + 0.158342i 0.781831 0.623490i \(-0.214286\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −0.806531 1.28359i −0.806531 1.28359i −0.955573 0.294755i \(-0.904762\pi\)
0.149042 0.988831i \(-0.452381\pi\)
\(312\) −1.12397 0.212667i −1.12397 0.212667i
\(313\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 1.78183 + 0.623490i 1.78183 + 0.623490i 1.00000 \(0\)
0.781831 + 0.623490i \(0.214286\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) −0.128437 0.852122i −0.128437 0.852122i
\(325\) 0.716983 1.48883i 0.716983 1.48883i
\(326\) −0.345251 + 0.275328i −0.345251 + 0.275328i
\(327\) 0 0
\(328\) 0.630705 + 0.143954i 0.630705 + 0.143954i
\(329\) 0 0
\(330\) 0 0
\(331\) −0.0528791 + 0.0528791i −0.0528791 + 0.0528791i −0.733052 0.680173i \(-0.761905\pi\)
0.680173 + 0.733052i \(0.261905\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) −0.632404 + 0.221288i −0.632404 + 0.221288i
\(335\) 0 0
\(336\) 0 0
\(337\) 0 0 −0.846724 0.532032i \(-0.821429\pi\)
0.846724 + 0.532032i \(0.178571\pi\)
\(338\) 0.0720500 + 0.639462i 0.0720500 + 0.639462i
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 0 0
\(346\) 0.0546536 0.156191i 0.0546536 0.156191i
\(347\) −1.94986 −1.94986 −0.974928 0.222521i \(-0.928571\pi\)
−0.974928 + 0.222521i \(0.928571\pi\)
\(348\) −0.840142 0.191757i −0.840142 0.191757i
\(349\) −1.97766 −1.97766 −0.988831 0.149042i \(-0.952381\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(350\) 0 0
\(351\) −1.48883 + 0.716983i −1.48883 + 0.716983i
\(352\) 0 0
\(353\) −1.22563 + 0.590232i −1.22563 + 0.590232i −0.930874 0.365341i \(-0.880952\pi\)
−0.294755 + 0.955573i \(0.595238\pi\)
\(354\) 0.120003 + 0.447857i 0.120003 + 0.447857i
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0.0610354 + 0.541704i 0.0610354 + 0.541704i
\(359\) 0 0 −0.846724 0.532032i \(-0.821429\pi\)
0.846724 + 0.532032i \(0.178571\pi\)
\(360\) 0 0
\(361\) 0.974928 0.222521i 0.974928 0.222521i
\(362\) 0 0
\(363\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 0 0 0.993712 0.111964i \(-0.0357143\pi\)
−0.993712 + 0.111964i \(0.964286\pi\)
\(368\) 0.589204 + 0.134482i 0.589204 + 0.134482i
\(369\) 0.856562 0.373714i 0.856562 0.373714i
\(370\) 0 0
\(371\) 0 0
\(372\) 0.665728 1.52586i 0.665728 1.52586i
\(373\) 0 0 0.623490 0.781831i \(-0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0.822133i 0.822133i
\(377\) 0.123490 + 1.64786i 0.123490 + 1.64786i
\(378\) 0 0
\(379\) 0 0 −0.943883 0.330279i \(-0.892857\pi\)
0.943883 + 0.330279i \(0.107143\pi\)
\(380\) 0 0
\(381\) 1.99720 0.0747301i 1.99720 0.0747301i
\(382\) 0 0
\(383\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(384\) 0.188681 0.997204i 0.188681 0.997204i
\(385\) 0 0
\(386\) 0.151670 0.664509i 0.151670 0.664509i
\(387\) 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
\(392\) −0.228633 0.653395i −0.228633 0.653395i
\(393\) −1.16694 + 1.58114i −1.16694 + 1.58114i
\(394\) −0.455389 0.455389i −0.455389 0.455389i
\(395\) 0 0
\(396\) 0 0
\(397\) −0.131178 + 0.574730i −0.131178 + 0.574730i 0.866025 + 0.500000i \(0.166667\pi\)
−0.997204 + 0.0747301i \(0.976190\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0.544506 + 0.262220i 0.544506 + 0.262220i
\(401\) 0 0 −0.433884 0.900969i \(-0.642857\pi\)
0.433884 + 0.900969i \(0.357143\pi\)
\(402\) 0 0
\(403\) −3.17227 0.357429i −3.17227 0.357429i
\(404\) 1.61655 + 0.565655i 1.61655 + 0.565655i
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) −0.104635 + 0.928661i −0.104635 + 0.928661i 0.826239 + 0.563320i \(0.190476\pi\)
−0.930874 + 0.365341i \(0.880952\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) −0.340799 + 0.148689i −0.340799 + 0.148689i
\(415\) 0 0
\(416\) −1.50572 + 0.169654i −1.50572 + 0.169654i
\(417\) −0.297251 1.97213i −0.297251 1.97213i
\(418\) 0 0
\(419\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(420\) 0 0
\(421\) 0 0 0.943883 0.330279i \(-0.107143\pi\)
−0.943883 + 0.330279i \(0.892857\pi\)
\(422\) 0.512654 0.117010i 0.512654 0.117010i
\(423\) −0.705245 0.955573i −0.705245 0.955573i
\(424\) 0 0
\(425\) 0 0
\(426\) 0.346511 + 0.655631i 0.346511 + 0.655631i
\(427\) 0 0
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 −0.781831 0.623490i \(-0.785714\pi\)
0.781831 + 0.623490i \(0.214286\pi\)
\(432\) −0.262220 0.544506i −0.262220 0.544506i
\(433\) 0 0 0.330279 0.943883i \(-0.392857\pi\)
−0.330279 + 0.943883i \(0.607143\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) 0.245705 0.167519i 0.245705 0.167519i
\(439\) −0.460898 0.367554i −0.460898 0.367554i 0.365341 0.930874i \(-0.380952\pi\)
−0.826239 + 0.563320i \(0.809524\pi\)
\(440\) 0 0
\(441\) −0.826239 0.563320i −0.826239 0.563320i
\(442\) 0 0
\(443\) 1.55215 0.975281i 1.55215 0.975281i 0.563320 0.826239i \(-0.309524\pi\)
0.988831 0.149042i \(-0.0476190\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) −0.140113 0.0880390i −0.140113 0.0880390i
\(447\) 0 0
\(448\) 0 0
\(449\) −0.623490 + 0.218169i −0.623490 + 0.218169i −0.623490 0.781831i \(-0.714286\pi\)
1.00000i \(0.5\pi\)
\(450\) −0.365341 + 0.0691263i −0.365341 + 0.0691263i
\(451\) 0 0
\(452\) 0 0
\(453\) 0.988831 0.149042i 0.988831 0.149042i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 0 0 0.781831 0.623490i \(-0.214286\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 0.00837297 0.0743122i 0.00837297 0.0743122i −0.988831 0.149042i \(-0.952381\pi\)
0.997204 + 0.0747301i \(0.0238095\pi\)
\(462\) 0 0
\(463\) 1.80194i 1.80194i −0.433884 0.900969i \(-0.642857\pi\)
0.433884 0.900969i \(-0.357143\pi\)
\(464\) −0.602666 + 0.0451636i −0.602666 + 0.0451636i
\(465\) 0 0
\(466\) −0.670731 0.234699i −0.670731 0.234699i
\(467\) 0 0 −0.993712 0.111964i \(-0.964286\pi\)
0.993712 + 0.111964i \(0.0357143\pi\)
\(468\) −1.04388 + 0.968578i −1.04388 + 0.968578i
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 0.459256 + 0.730901i 0.459256 + 0.730901i
\(473\) 0 0
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 0 0
\(478\) 0.0723951 + 0.206893i 0.0723951 + 0.206893i
\(479\) 0 0 −0.330279 0.943883i \(-0.607143\pi\)
0.330279 + 0.943883i \(0.392857\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) −0.191757 + 0.840142i −0.191757 + 0.840142i
\(485\) 0 0
\(486\) 0.328735 + 0.173741i 0.328735 + 0.173741i
\(487\) 1.22563 + 0.590232i 1.22563 + 0.590232i 0.930874 0.365341i \(-0.119048\pi\)
0.294755 + 0.955573i \(0.404762\pi\)
\(488\) 0 0
\(489\) 0.0444073 + 1.18681i 0.0444073 + 1.18681i
\(490\) 0 0
\(491\) −1.66900 0.584010i −1.66900 0.584010i −0.680173 0.733052i \(-0.738095\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(492\) 0.610421 0.525310i 0.610421 0.525310i
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0.130722 1.16019i 0.130722 1.16019i
\(497\) 0 0
\(498\) 0 0
\(499\) −0.858075 + 1.78181i −0.858075 + 1.78181i −0.294755 + 0.955573i \(0.595238\pi\)
−0.563320 + 0.826239i \(0.690476\pi\)
\(500\) 0 0
\(501\) −0.531130 + 1.72188i −0.531130 + 1.72188i
\(502\) 0 0
\(503\) 0 0 0.993712 0.111964i \(-0.0357143\pi\)
−0.993712 + 0.111964i \(0.964286\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 1.49881 + 0.865341i 1.49881 + 0.865341i
\(508\) 1.62564 0.568836i 1.62564 0.568836i
\(509\) 1.81507 0.414278i 1.81507 0.414278i 0.826239 0.563320i \(-0.190476\pi\)
0.988831 + 0.149042i \(0.0476190\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −0.108889 0.966412i −0.108889 0.966412i
\(513\) 0 0
\(514\) 0.0938465 0.0589676i 0.0938465 0.0589676i
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) −0.250701 0.367711i −0.250701 0.367711i
\(520\) 0 0
\(521\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(522\) 0.281831 0.242536i 0.281831 0.242536i
\(523\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(524\) −0.559311 + 1.59842i −0.559311 + 1.59842i
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) −0.623490 0.781831i −0.623490 0.781831i
\(530\) 0 0
\(531\) 1.16078 + 0.455573i 1.16078 + 0.455573i
\(532\) 0 0
\(533\) −1.30760 0.821618i −1.30760 0.821618i
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 1.26968 + 0.733052i 1.26968 + 0.733052i
\(538\) 0.165361 + 0.724495i 0.165361 + 0.724495i
\(539\) 0 0
\(540\) 0 0
\(541\) 1.59908 0.180173i 1.59908 0.180173i 0.733052 0.680173i \(-0.238095\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(542\) −0.239453 0.0546536i −0.239453 0.0546536i
\(543\) 0 0
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −1.19158 + 1.49419i −1.19158 + 1.49419i −0.365341 + 0.930874i \(0.619048\pi\)
−0.826239 + 0.563320i \(0.809524\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 0 0
\(552\) −0.524699 + 0.451540i −0.524699 + 0.451540i
\(553\) 0 0
\(554\) 0.0552233 + 0.00622218i 0.0552233 + 0.00622218i
\(555\) 0 0
\(556\) −0.745705 1.54847i −0.745705 1.54847i
\(557\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(558\) 0.359154 + 0.622072i 0.359154 + 0.622072i
\(559\) 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 \(0.250000\pi\)
\(564\) −0.823462 0.607743i −0.823462 0.607743i
\(565\) 0 0
\(566\) 0 0
\(567\) 0 0
\(568\) 0.976239 + 0.976239i 0.976239 + 0.976239i
\(569\) 0 0 0.532032 0.846724i \(-0.321429\pi\)
−0.532032 + 0.846724i \(0.678571\pi\)
\(570\) 0 0
\(571\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −0.433884 0.900969i −0.433884 0.900969i
\(576\) −0.179165 0.193094i −0.179165 0.193094i
\(577\) 0.0743122 + 0.00837297i 0.0743122 + 0.00837297i 0.149042 0.988831i \(-0.452381\pi\)
−0.0747301 + 0.997204i \(0.523810\pi\)
\(578\) 0.350958 + 0.122805i 0.350958 + 0.122805i
\(579\) −1.19572 1.38946i −1.19572 1.38946i
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) 0.345191 0.432856i 0.345191 0.432856i
\(585\) 0 0
\(586\) 0 0
\(587\) −1.06356 + 0.848162i −1.06356 + 0.848162i −0.988831 0.149042i \(-0.952381\pi\)
−0.0747301 + 0.997204i \(0.523810\pi\)
\(588\) −0.823462 0.254005i −0.823462 0.254005i
\(589\) 0 0
\(590\) 0 0
\(591\) −1.71271 + 0.258149i −1.71271 + 0.258149i
\(592\) 0 0
\(593\) −0.433884 1.90097i −0.433884 1.90097i −0.433884 0.900969i \(-0.642857\pi\)
1.00000i \(-0.5\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0.520252 + 0.326896i 0.520252 + 0.326896i
\(599\) 0.0739590 + 0.656405i 0.0739590 + 0.656405i 0.974928 + 0.222521i \(0.0714286\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(600\) −0.612021 + 0.323462i −0.612021 + 0.323462i
\(601\) 0.438297 0.275400i 0.438297 0.275400i −0.294755 0.955573i \(-0.595238\pi\)
0.733052 + 0.680173i \(0.238095\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0.776408 0.373898i 0.776408 0.373898i
\(605\) 0 0
\(606\) −0.610566 + 0.416277i −0.610566 + 0.416277i
\(607\) −0.559311 + 1.59842i −0.559311 + 1.59842i 0.222521 + 0.974928i \(0.428571\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −0.648189 + 1.85242i −0.648189 + 1.85242i
\(612\) 0 0
\(613\) 0 0 −0.781831 0.623490i \(-0.785714\pi\)
0.781831 + 0.623490i \(0.214286\pi\)
\(614\) −0.0750165 + 0.0361260i −0.0750165 + 0.0361260i
\(615\) 0 0
\(616\) 0 0
\(617\) 0 0 0.846724 0.532032i \(-0.178571\pi\)
−0.846724 + 0.532032i \(0.821429\pi\)
\(618\) 0 0
\(619\) 0 0 −0.111964 0.993712i \(-0.535714\pi\)
0.111964 + 0.993712i \(0.464286\pi\)
\(620\) 0 0
\(621\) −0.222521 + 0.974928i −0.222521 + 0.974928i
\(622\) 0.549531 0.125427i 0.549531 0.125427i
\(623\) 0 0
\(624\) −0.499343 + 0.864887i −0.499343 + 0.864887i
\(625\) −0.222521 0.974928i −0.222521 0.974928i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 0 0 0.781831 0.623490i \(-0.214286\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(632\) 0 0
\(633\) 0.565533 1.29621i 0.565533 1.29621i
\(634\) −0.437637 + 0.548780i −0.437637 + 0.548780i
\(635\) 0 0
\(636\) 0 0
\(637\) 1.65248i 1.65248i
\(638\) 0 0
\(639\) 1.97213 + 0.297251i 1.97213 + 0.297251i
\(640\) 0 0
\(641\) 0 0 −0.993712 0.111964i \(-0.964286\pi\)
0.993712 + 0.111964i \(0.0357143\pi\)
\(642\) 0 0
\(643\) 0 0 −0.433884 0.900969i \(-0.642857\pi\)
0.433884 + 0.900969i \(0.357143\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −0.414278 + 1.81507i −0.414278 + 1.81507i 0.149042 + 0.988831i \(0.452381\pi\)
−0.563320 + 0.826239i \(0.690476\pi\)
\(648\) 0.680173 + 0.128696i 0.680173 + 0.128696i
\(649\) 0 0
\(650\) 0.434467 + 0.434467i 0.434467 + 0.434467i
\(651\) 0 0
\(652\) 0.338023 + 0.966014i 0.338023 + 0.966014i
\(653\) 0.170965 + 0.488590i 0.170965 + 0.488590i 0.997204 0.0747301i \(-0.0238095\pi\)
−0.826239 + 0.563320i \(0.809524\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0.300488 0.478224i 0.300488 0.478224i
\(657\) 0.0299049 0.799225i 0.0299049 0.799225i
\(658\) 0 0
\(659\) 0 0 −0.532032 0.846724i \(-0.678571\pi\)
0.532032 + 0.846724i \(0.321429\pi\)
\(660\) 0 0
\(661\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(662\) −0.0120645 0.0250522i −0.0120645 0.0250522i
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0.826239 + 0.563320i 0.826239 + 0.563320i
\(668\) 1.55282i 1.55282i
\(669\) −0.414278 + 0.162592i −0.414278 + 0.162592i
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) −0.590232 + 1.22563i −0.590232 + 1.22563i 0.365341 + 0.930874i \(0.380952\pi\)
−0.955573 + 0.294755i \(0.904762\pi\)
\(674\) 0 0
\(675\) −0.433884 + 0.900969i −0.433884 + 0.900969i
\(676\) 1.45402 + 0.331870i 1.45402 + 0.331870i
\(677\) 0 0 0.993712 0.111964i \(-0.0357143\pi\)
−0.993712 + 0.111964i \(0.964286\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 0.290611 0.0663300i 0.290611 0.0663300i −0.0747301 0.997204i \(-0.523810\pi\)
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
\(691\) −0.781831 + 0.376510i −0.781831 + 0.376510i −0.781831 0.623490i \(-0.785714\pi\)
1.00000i \(0.5\pi\)
\(692\) −0.299843 0.239117i −0.299843 0.239117i
\(693\) 0 0
\(694\) 0.239453 0.684317i 0.239453 0.684317i
\(695\) 0 0
\(696\) 0.368294 0.586137i 0.368294 0.586137i
\(697\) 0 0
\(698\) 0.242868 0.694076i 0.242868 0.694076i
\(699\) −1.57906 + 1.07659i −1.57906 + 1.07659i
\(700\) 0 0
\(701\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(702\) −0.0687943 0.610566i −0.0687943 0.610566i
\(703\) 0 0
\(704\) 0 0
\(705\) 0 0
\(706\) −0.0566325 0.502628i −0.0566325 0.502628i
\(707\) 0 0
\(708\) 1.07158 + 0.0803036i 1.07158 + 0.0803036i
\(709\) 0 0 0.974928 0.222521i \(-0.0714286\pi\)
−0.974928 + 0.222521i \(0.928571\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −1.36603 + 1.36603i −1.36603 + 1.36603i
\(714\) 0 0
\(715\) 0 0
\(716\) 1.23173 + 0.281135i 1.23173 + 0.281135i
\(717\) 0.563320 + 0.173761i 0.563320 + 0.173761i
\(718\) 0 0
\(719\) −0.376510 + 0.781831i −0.376510 + 0.781831i 0.623490 + 0.781831i \(0.285714\pi\)
−1.00000 \(\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −0.0416310 + 0.369485i −0.0416310 + 0.369485i
\(723\) 0 0
\(724\) 0 0
\(725\) 0.680173 + 0.733052i 0.680173 + 0.733052i
\(726\) −0.242536 0.281831i −0.242536 0.281831i
\(727\) 0 0 −0.943883 0.330279i \(-0.892857\pi\)
0.943883 + 0.330279i \(0.107143\pi\)
\(728\) 0 0
\(729\) 0.900969 0.433884i 0.900969 0.433884i
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 0 0 −0.532032 0.846724i \(-0.678571\pi\)
0.532032 + 0.846724i \(0.321429\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) −0.487849 + 0.776408i −0.487849 + 0.776408i
\(737\) 0 0
\(738\) 0.0259674 + 0.346511i 0.0259674 + 0.346511i
\(739\) 0.308658 + 0.882094i 0.308658 + 0.882094i 0.988831 + 0.149042i \(0.0476190\pi\)
−0.680173 + 0.733052i \(0.738095\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 0.532032 0.846724i \(-0.321429\pi\)
−0.532032 + 0.846724i \(0.678571\pi\)
\(744\) 0.980315 + 0.909600i 0.980315 + 0.909600i
\(745\) 0 0
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 0 0 −0.993712 0.111964i \(-0.964286\pi\)
0.993712 + 0.111964i \(0.0357143\pi\)
\(752\) −0.677480 0.237060i −0.677480 0.237060i
\(753\) 0 0
\(754\) −0.593493 0.159026i −0.593493 0.159026i
\(755\) 0 0
\(756\) 0 0
\(757\) 0 0 0.111964 0.993712i \(-0.464286\pi\)
−0.111964 + 0.993712i \(0.535714\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −0.116853 + 0.0931869i −0.116853 + 0.0931869i −0.680173 0.733052i \(-0.738095\pi\)
0.563320 + 0.826239i \(0.309524\pi\)
\(762\) −0.219040 + 0.710111i −0.219040 + 0.710111i
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −0.458528 2.00894i −0.458528 2.00894i
\(768\) 0.0986845 + 0.0569755i 0.0986845 + 0.0569755i
\(769\) 0 0 0.943883 0.330279i \(-0.107143\pi\)
−0.943883 + 0.330279i \(0.892857\pi\)
\(770\) 0 0
\(771\) 0.0222759 0.297251i 0.0222759 0.297251i
\(772\) −1.33756 0.840446i −1.33756 0.840446i
\(773\) 0 0 −0.111964 0.993712i \(-0.535714\pi\)
0.111964 + 0.993712i \(0.464286\pi\)
\(774\) 0 0
\(775\) −1.63575 + 1.02781i −1.63575 + 1.02781i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) −0.0747301 0.997204i −0.0747301 0.997204i
\(784\) −0.604356 −0.604356
\(785\) 0 0
\(786\) −0.411608 0.603718i −0.411608 0.603718i
\(787\) 0 0 −0.781831 0.623490i \(-0.785714\pi\)
0.781831 + 0.623490i \(0.214286\pi\)