Properties

Label 2001.1.bf.d.482.1
Level $2001$
Weight $1$
Character 2001.482
Analytic conductor $0.999$
Analytic rank $0$
Dimension $24$
Projective image $D_{84}$
CM discriminant -23
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 2001 = 3 \cdot 23 \cdot 29 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 2001.bf (of order \(28\), degree \(12\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.998629090279\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(2\) over \(\Q(\zeta_{28})\)
Coefficient field: \(\Q(\zeta_{84})\)
Defining polynomial: \(x^{24} + x^{22} - x^{18} - x^{16} + x^{12} - x^{8} - x^{6} + x^{2} + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Projective image: \(D_{84}\)
Projective field: Galois closure of \(\mathbb{Q}[x]/(x^{84} - \cdots)\)

Embedding invariants

Embedding label 482.1
Root \(0.149042 - 0.988831i\) of defining polynomial
Character \(\chi\) \(=\) 2001.482
Dual form 2001.1.bf.d.137.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.85486 + 0.649042i) q^{2} +(-0.563320 + 0.826239i) q^{3} +(2.23740 - 1.78427i) q^{4} +(0.508614 - 1.89817i) q^{6} +(-1.94648 + 3.09781i) q^{8} +(-0.365341 - 0.930874i) q^{9} +O(q^{10})\) \(q+(-1.85486 + 0.649042i) q^{2} +(-0.563320 + 0.826239i) q^{3} +(2.23740 - 1.78427i) q^{4} +(0.508614 - 1.89817i) q^{6} +(-1.94648 + 3.09781i) q^{8} +(-0.365341 - 0.930874i) q^{9} +(0.213859 + 2.85375i) q^{12} +(-1.61105 - 0.367711i) q^{13} +(0.963038 - 4.21934i) q^{16} +(1.28183 + 1.48952i) q^{18} +(-0.433884 - 0.900969i) q^{23} +(-1.46304 - 3.35332i) q^{24} +(0.623490 + 0.781831i) q^{25} +(3.22692 - 0.363587i) q^{26} +(0.974928 + 0.222521i) q^{27} +(0.149042 + 0.988831i) q^{29} +(0.170965 + 0.488590i) q^{31} +(0.542605 + 4.81575i) q^{32} +(-2.47835 - 1.43087i) q^{36} +(1.21135 - 1.12397i) q^{39} +(-1.25033 - 1.25033i) q^{41} +(1.38956 + 1.38956i) q^{46} +(1.36254 - 0.856144i) q^{47} +(2.94369 + 3.17254i) q^{48} +(-0.222521 - 0.974928i) q^{49} +(-1.66393 - 1.04551i) q^{50} +(-4.26066 + 2.05182i) q^{52} +(-1.95278 + 0.220025i) q^{54} +(-0.918245 - 1.73740i) q^{58} -1.24698i q^{59} +(-0.634231 - 0.795301i) q^{62} +(-2.25429 - 4.68109i) q^{64} +(0.988831 + 0.149042i) q^{69} +(0.443797 - 1.94440i) q^{71} +(3.59480 + 0.680173i) q^{72} +(0.605443 - 1.73026i) q^{73} +(-0.997204 + 0.0747301i) q^{75} +(-1.51738 + 2.87102i) q^{78} +(-0.733052 + 0.680173i) q^{81} +(3.13069 + 1.50766i) q^{82} +(-0.900969 - 0.433884i) q^{87} +(-2.57835 - 1.24167i) q^{92} +(-0.500000 - 0.133975i) q^{93} +(-1.97165 + 2.47237i) q^{94} +(-4.28462 - 2.26449i) q^{96} +(1.04551 + 1.66393i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q + 2q^{2} + 14q^{4} + 2q^{6} - 6q^{8} - 2q^{9} + O(q^{10}) \) \( 24q + 2q^{2} + 14q^{4} + 2q^{6} - 6q^{8} - 2q^{9} + 2q^{12} - 6q^{16} + 12q^{18} - 6q^{24} - 4q^{25} - 2q^{26} - 2q^{31} - 4q^{32} + 6q^{36} + 2q^{39} - 2q^{41} + 2q^{46} + 2q^{47} + 6q^{48} - 4q^{49} + 2q^{50} - 10q^{52} - 2q^{54} + 4q^{58} - 4q^{62} - 28q^{64} - 2q^{69} + 22q^{72} - 2q^{73} - 4q^{78} + 2q^{81} - 4q^{82} - 4q^{87} - 4q^{92} - 12q^{93} - 8q^{94} - 18q^{96} + 2q^{98} + O(q^{100}) \)

Character values

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

\(n\) \(553\) \(668\) \(1132\)
\(\chi(n)\) \(e\left(\frac{11}{28}\right)\) \(-1\) \(-1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.85486 + 0.649042i −1.85486 + 0.649042i −0.866025 + 0.500000i \(0.833333\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(3\) −0.563320 + 0.826239i −0.563320 + 0.826239i
\(4\) 2.23740 1.78427i 2.23740 1.78427i
\(5\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(6\) 0.508614 1.89817i 0.508614 1.89817i
\(7\) 0 0 0.623490 0.781831i \(-0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(8\) −1.94648 + 3.09781i −1.94648 + 3.09781i
\(9\) −0.365341 0.930874i −0.365341 0.930874i
\(10\) 0 0
\(11\) 0 0 −0.532032 0.846724i \(-0.678571\pi\)
0.532032 + 0.846724i \(0.321429\pi\)
\(12\) 0.213859 + 2.85375i 0.213859 + 2.85375i
\(13\) −1.61105 0.367711i −1.61105 0.367711i −0.680173 0.733052i \(-0.738095\pi\)
−0.930874 + 0.365341i \(0.880952\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0.963038 4.21934i 0.963038 4.21934i
\(17\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(18\) 1.28183 + 1.48952i 1.28183 + 1.48952i
\(19\) 0 0 0.111964 0.993712i \(-0.464286\pi\)
−0.111964 + 0.993712i \(0.535714\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −0.433884 0.900969i −0.433884 0.900969i
\(24\) −1.46304 3.35332i −1.46304 3.35332i
\(25\) 0.623490 + 0.781831i 0.623490 + 0.781831i
\(26\) 3.22692 0.363587i 3.22692 0.363587i
\(27\) 0.974928 + 0.222521i 0.974928 + 0.222521i
\(28\) 0 0
\(29\) 0.149042 + 0.988831i 0.149042 + 0.988831i
\(30\) 0 0
\(31\) 0.170965 + 0.488590i 0.170965 + 0.488590i 0.997204 0.0747301i \(-0.0238095\pi\)
−0.826239 + 0.563320i \(0.809524\pi\)
\(32\) 0.542605 + 4.81575i 0.542605 + 4.81575i
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) −2.47835 1.43087i −2.47835 1.43087i
\(37\) 0 0 −0.846724 0.532032i \(-0.821429\pi\)
0.846724 + 0.532032i \(0.178571\pi\)
\(38\) 0 0
\(39\) 1.21135 1.12397i 1.21135 1.12397i
\(40\) 0 0
\(41\) −1.25033 1.25033i −1.25033 1.25033i −0.955573 0.294755i \(-0.904762\pi\)
−0.294755 0.955573i \(-0.595238\pi\)
\(42\) 0 0
\(43\) 0 0 −0.943883 0.330279i \(-0.892857\pi\)
0.943883 + 0.330279i \(0.107143\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 1.38956 + 1.38956i 1.38956 + 1.38956i
\(47\) 1.36254 0.856144i 1.36254 0.856144i 0.365341 0.930874i \(-0.380952\pi\)
0.997204 + 0.0747301i \(0.0238095\pi\)
\(48\) 2.94369 + 3.17254i 2.94369 + 3.17254i
\(49\) −0.222521 0.974928i −0.222521 0.974928i
\(50\) −1.66393 1.04551i −1.66393 1.04551i
\(51\) 0 0
\(52\) −4.26066 + 2.05182i −4.26066 + 2.05182i
\(53\) 0 0 0.433884 0.900969i \(-0.357143\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(54\) −1.95278 + 0.220025i −1.95278 + 0.220025i
\(55\) 0 0
\(56\) 0 0
\(57\) 0 0
\(58\) −0.918245 1.73740i −0.918245 1.73740i
\(59\) 1.24698i 1.24698i −0.781831 0.623490i \(-0.785714\pi\)
0.781831 0.623490i \(-0.214286\pi\)
\(60\) 0 0
\(61\) 0 0 0.993712 0.111964i \(-0.0357143\pi\)
−0.993712 + 0.111964i \(0.964286\pi\)
\(62\) −0.634231 0.795301i −0.634231 0.795301i
\(63\) 0 0
\(64\) −2.25429 4.68109i −2.25429 4.68109i
\(65\) 0 0
\(66\) 0 0
\(67\) 0 0 0.974928 0.222521i \(-0.0714286\pi\)
−0.974928 + 0.222521i \(0.928571\pi\)
\(68\) 0 0
\(69\) 0.988831 + 0.149042i 0.988831 + 0.149042i
\(70\) 0 0
\(71\) 0.443797 1.94440i 0.443797 1.94440i 0.149042 0.988831i \(-0.452381\pi\)
0.294755 0.955573i \(-0.404762\pi\)
\(72\) 3.59480 + 0.680173i 3.59480 + 0.680173i
\(73\) 0.605443 1.73026i 0.605443 1.73026i −0.0747301 0.997204i \(-0.523810\pi\)
0.680173 0.733052i \(-0.261905\pi\)
\(74\) 0 0
\(75\) −0.997204 + 0.0747301i −0.997204 + 0.0747301i
\(76\) 0 0
\(77\) 0 0
\(78\) −1.51738 + 2.87102i −1.51738 + 2.87102i
\(79\) 0 0 0.532032 0.846724i \(-0.321429\pi\)
−0.532032 + 0.846724i \(0.678571\pi\)
\(80\) 0 0
\(81\) −0.733052 + 0.680173i −0.733052 + 0.680173i
\(82\) 3.13069 + 1.50766i 3.13069 + 1.50766i
\(83\) 0 0 0.781831 0.623490i \(-0.214286\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −0.900969 0.433884i −0.900969 0.433884i
\(88\) 0 0
\(89\) 0 0 0.943883 0.330279i \(-0.107143\pi\)
−0.943883 + 0.330279i \(0.892857\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −2.57835 1.24167i −2.57835 1.24167i
\(93\) −0.500000 0.133975i −0.500000 0.133975i
\(94\) −1.97165 + 2.47237i −1.97165 + 2.47237i
\(95\) 0 0
\(96\) −4.28462 2.26449i −4.28462 2.26449i
\(97\) 0 0 −0.993712 0.111964i \(-0.964286\pi\)
0.993712 + 0.111964i \(0.0357143\pi\)
\(98\) 1.04551 + 1.66393i 1.04551 + 1.66393i
\(99\) 0 0
\(100\) 2.79000 + 0.636799i 2.79000 + 0.636799i
\(101\) −0.0739590 + 0.211363i −0.0739590 + 0.211363i −0.974928 0.222521i \(-0.928571\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(102\) 0 0
\(103\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(104\) 4.27497 4.27497i 4.27497 4.27497i
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 0.974928 0.222521i \(-0.0714286\pi\)
−0.974928 + 0.222521i \(0.928571\pi\)
\(108\) 2.57835 1.24167i 2.57835 1.24167i
\(109\) 0 0 −0.781831 0.623490i \(-0.785714\pi\)
0.781831 + 0.623490i \(0.214286\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 0 0 0.993712 0.111964i \(-0.0357143\pi\)
−0.993712 + 0.111964i \(0.964286\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 2.09781 + 1.94648i 2.09781 + 1.94648i
\(117\) 0.246289 + 1.63402i 0.246289 + 1.63402i
\(118\) 0.809342 + 2.31297i 0.809342 + 2.31297i
\(119\) 0 0
\(120\) 0 0
\(121\) −0.433884 + 0.900969i −0.433884 + 0.900969i
\(122\) 0 0
\(123\) 1.73740 0.328735i 1.73740 0.328735i
\(124\) 1.25429 + 0.788125i 1.25429 + 0.788125i
\(125\) 0 0
\(126\) 0 0
\(127\) −0.0633201 + 0.0397866i −0.0633201 + 0.0397866i −0.563320 0.826239i \(-0.690476\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(128\) 3.79282 + 3.79282i 3.79282 + 3.79282i
\(129\) 0 0
\(130\) 0 0
\(131\) 0.350958 + 0.122805i 0.350958 + 0.122805i 0.500000 0.866025i \(-0.333333\pi\)
−0.149042 + 0.988831i \(0.547619\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 0 0 −0.846724 0.532032i \(-0.821429\pi\)
0.846724 + 0.532032i \(0.178571\pi\)
\(138\) −1.93087 + 0.365341i −1.93087 + 0.365341i
\(139\) 1.79690 0.865341i 1.79690 0.865341i 0.866025 0.500000i \(-0.166667\pi\)
0.930874 0.365341i \(-0.119048\pi\)
\(140\) 0 0
\(141\) −0.0601697 + 1.60807i −0.0601697 + 1.60807i
\(142\) 0.438820 + 3.89463i 0.438820 + 3.89463i
\(143\) 0 0
\(144\) −4.27951 + 0.645033i −4.27951 + 0.645033i
\(145\) 0 0
\(146\) 3.60233i 3.60233i
\(147\) 0.930874 + 0.365341i 0.930874 + 0.365341i
\(148\) 0 0
\(149\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(150\) 1.80117 0.785841i 1.80117 0.785841i
\(151\) −0.433884 0.900969i −0.433884 0.900969i −0.997204 0.0747301i \(-0.976190\pi\)
0.563320 0.826239i \(-0.309524\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 0.704817 4.67615i 0.704817 4.67615i
\(157\) 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
\(162\) 0.918245 1.73740i 0.918245 1.73740i
\(163\) −0.856144 1.36254i −0.856144 1.36254i −0.930874 0.365341i \(-0.880952\pi\)
0.0747301 0.997204i \(-0.476190\pi\)
\(164\) −5.02841 0.566566i −5.02841 0.566566i
\(165\) 0 0
\(166\) 0 0
\(167\) 1.12349 1.40881i 1.12349 1.40881i 0.222521 0.974928i \(-0.428571\pi\)
0.900969 0.433884i \(-0.142857\pi\)
\(168\) 0 0
\(169\) 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 \(0.571429\pi\)
\(174\) 1.95278 + 0.220025i 1.95278 + 0.220025i
\(175\) 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 0.955573 0.294755i \(-0.0952381\pi\)
0.365341 + 0.930874i \(0.380952\pi\)
\(180\) 0 0
\(181\) 0 0 0.623490 0.781831i \(-0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 3.63558 + 0.409631i 3.63558 + 0.409631i
\(185\) 0 0
\(186\) 1.01438 0.0760175i 1.01438 0.0760175i
\(187\) 0 0
\(188\) 1.52097 4.34669i 1.52097 4.34669i
\(189\) 0 0
\(190\) 0 0
\(191\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(192\) 5.13759 + 0.774367i 5.13759 + 0.774367i
\(193\) −0.0895474 + 0.794755i −0.0895474 + 0.794755i 0.866025 + 0.500000i \(0.166667\pi\)
−0.955573 + 0.294755i \(0.904762\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) −2.23740 1.78427i −2.23740 1.78427i
\(197\) −0.751509 1.56052i −0.751509 1.56052i −0.826239 0.563320i \(-0.809524\pi\)
0.0747301 0.997204i \(-0.476190\pi\)
\(198\) 0 0
\(199\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(200\) −3.63558 + 0.409631i −3.63558 + 0.409631i
\(201\) 0 0
\(202\) 0.440050i 0.440050i
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −0.680173 + 0.733052i −0.680173 + 0.733052i
\(208\) −3.10300 + 6.44344i −3.10300 + 6.44344i
\(209\) 0 0
\(210\) 0 0
\(211\) 1.19745 + 0.752407i 1.19745 + 0.752407i 0.974928 0.222521i \(-0.0714286\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(212\) 0 0
\(213\) 1.35654 + 1.46200i 1.35654 + 1.46200i
\(214\) 0 0
\(215\) 0 0
\(216\) −2.58701 + 2.58701i −2.58701 + 2.58701i
\(217\) 0 0
\(218\) 0 0
\(219\) 1.08855 + 1.47493i 1.08855 + 1.47493i
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) −0.0990311 0.433884i −0.0990311 0.433884i 0.900969 0.433884i \(-0.142857\pi\)
−1.00000 \(\pi\)
\(224\) 0 0
\(225\) 0.500000 0.866025i 0.500000 0.866025i
\(226\) 0 0
\(227\) 0 0 0.433884 0.900969i \(-0.357143\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(228\) 0 0
\(229\) 0 0 −0.111964 0.993712i \(-0.535714\pi\)
0.111964 + 0.993712i \(0.464286\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −3.35332 1.46304i −3.35332 1.46304i
\(233\) 1.91115i 1.91115i 0.294755 + 0.955573i \(0.404762\pi\)
−0.294755 + 0.955573i \(0.595238\pi\)
\(234\) −1.51738 2.87102i −1.51738 2.87102i
\(235\) 0 0
\(236\) −2.22495 2.79000i −2.22495 2.79000i
\(237\) 0 0
\(238\) 0 0
\(239\) 0.460898 + 0.367554i 0.460898 + 0.367554i 0.826239 0.563320i \(-0.190476\pi\)
−0.365341 + 0.930874i \(0.619048\pi\)
\(240\) 0 0
\(241\) 0 0 0.974928 0.222521i \(-0.0714286\pi\)
−0.974928 + 0.222521i \(0.928571\pi\)
\(242\) 0.220025 1.95278i 0.220025 1.95278i
\(243\) −0.149042 0.988831i −0.149042 0.988831i
\(244\) 0 0
\(245\) 0 0
\(246\) −3.00927 + 1.73740i −3.00927 + 1.73740i
\(247\) 0 0
\(248\) −1.84634 0.421415i −1.84634 0.421415i
\(249\) 0 0
\(250\) 0 0
\(251\) 0 0 −0.993712 0.111964i \(-0.964286\pi\)
0.993712 + 0.111964i \(0.0357143\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0.0916264 0.114896i 0.0916264 0.114896i
\(255\) 0 0
\(256\) −4.81575 2.31914i −4.81575 2.31914i
\(257\) −0.233052 + 0.185853i −0.233052 + 0.185853i −0.733052 0.680173i \(-0.761905\pi\)
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
\(262\) −0.730682 −0.730682
\(263\) 0 0 0.943883 0.330279i \(-0.107143\pi\)
−0.943883 + 0.330279i \(0.892857\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −0.0397866 + 0.0633201i −0.0397866 + 0.0633201i −0.866025 0.500000i \(-0.833333\pi\)
0.826239 + 0.563320i \(0.190476\pi\)
\(270\) 0 0
\(271\) −1.87590 0.211363i −1.87590 0.211363i −0.900969 0.433884i \(-0.857143\pi\)
−0.974928 + 0.222521i \(0.928571\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) 2.47835 1.43087i 2.47835 1.43087i
\(277\) −0.0332580 + 0.145713i −0.0332580 + 0.145713i −0.988831 0.149042i \(-0.952381\pi\)
0.955573 + 0.294755i \(0.0952381\pi\)
\(278\) −2.77135 + 2.77135i −2.77135 + 2.77135i
\(279\) 0.392355 0.337649i 0.392355 0.337649i
\(280\) 0 0
\(281\) 0 0 0.974928 0.222521i \(-0.0714286\pi\)
−0.974928 + 0.222521i \(0.928571\pi\)
\(282\) −0.932099 3.02179i −0.932099 3.02179i
\(283\) 0 0 −0.781831 0.623490i \(-0.785714\pi\)
0.781831 + 0.623490i \(0.214286\pi\)
\(284\) −2.47639 5.14227i −2.47639 5.14227i
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 4.28462 2.26449i 4.28462 2.26449i
\(289\) 1.00000i 1.00000i
\(290\) 0 0
\(291\) 0 0
\(292\) −1.73262 4.95155i −1.73262 4.95155i
\(293\) 0 0 −0.111964 0.993712i \(-0.535714\pi\)
0.111964 + 0.993712i \(0.464286\pi\)
\(294\) −1.96376 0.0734787i −1.96376 0.0734787i
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 0.367711 + 1.61105i 0.367711 + 1.61105i
\(300\) −2.09781 + 1.94648i −2.09781 + 1.94648i
\(301\) 0 0
\(302\) 1.38956 + 1.38956i 1.38956 + 1.38956i
\(303\) −0.132974 0.180173i −0.132974 0.180173i
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) −1.40532 1.40532i −1.40532 1.40532i −0.781831 0.623490i \(-0.785714\pi\)
−0.623490 0.781831i \(-0.714286\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −1.10462 0.694076i −1.10462 0.694076i −0.149042 0.988831i \(-0.547619\pi\)
−0.955573 + 0.294755i \(0.904762\pi\)
\(312\) 1.12397 + 5.94033i 1.12397 + 5.94033i
\(313\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 0.218169 + 0.623490i 0.218169 + 0.623490i 1.00000 \(0\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) −0.426521 + 2.82978i −0.426521 + 2.82978i
\(325\) −0.716983 1.48883i −0.716983 1.48883i
\(326\) 2.47237 + 1.97165i 2.47237 + 1.97165i
\(327\) 0 0
\(328\) 6.30702 1.43954i 6.30702 1.43954i
\(329\) 0 0
\(330\) 0 0
\(331\) −1.41322 + 1.41322i −1.41322 + 1.41322i −0.680173 + 0.733052i \(0.738095\pi\)
−0.733052 + 0.680173i \(0.761905\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) −1.16953 + 3.34234i −1.16953 + 3.34234i
\(335\) 0 0
\(336\) 0 0
\(337\) 0 0 −0.532032 0.846724i \(-0.678571\pi\)
0.532032 + 0.846724i \(0.321429\pi\)
\(338\) −3.37964 0.380793i −3.37964 0.380793i
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 0 0
\(346\) 0.825489 0.288851i 0.825489 0.288851i
\(347\) 1.94986 1.94986 0.974928 0.222521i \(-0.0714286\pi\)
0.974928 + 0.222521i \(0.0714286\pi\)
\(348\) −2.79000 + 0.636799i −2.79000 + 0.636799i
\(349\) −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 \(-0.119048\pi\)
0.294755 + 0.955573i \(0.404762\pi\)
\(354\) −2.36698 0.634231i −2.36698 0.634231i
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) −2.86297 0.322580i −2.86297 0.322580i
\(359\) 0 0 −0.532032 0.846724i \(-0.678571\pi\)
0.532032 + 0.846724i \(0.321429\pi\)
\(360\) 0 0
\(361\) −0.974928 0.222521i −0.974928 0.222521i
\(362\) 0 0
\(363\) −0.500000 0.866025i −0.500000 0.866025i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 0 0 0.111964 0.993712i \(-0.464286\pi\)
−0.111964 + 0.993712i \(0.535714\pi\)
\(368\) −4.21934 + 0.963038i −4.21934 + 0.963038i
\(369\) −0.707101 + 1.62069i −0.707101 + 1.62069i
\(370\) 0 0
\(371\) 0 0
\(372\) −1.35775 + 0.592380i −1.35775 + 0.592380i
\(373\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 5.88737i 5.88737i
\(377\) 0.123490 1.64786i 0.123490 1.64786i
\(378\) 0 0
\(379\) 0 0 −0.330279 0.943883i \(-0.607143\pi\)
0.330279 + 0.943883i \(0.392857\pi\)
\(380\) 0 0
\(381\) 0.00279620 0.0747301i 0.00279620 0.0747301i
\(382\) 0 0
\(383\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(384\) −5.27035 + 0.997204i −5.27035 + 0.997204i
\(385\) 0 0
\(386\) −0.349732 1.53228i −0.349732 1.53228i
\(387\) 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
\(392\) 3.45327 + 1.20835i 3.45327 + 1.20835i
\(393\) −0.299168 + 0.220796i −0.299168 + 0.220796i
\(394\) 2.40679 + 2.40679i 2.40679 + 2.40679i
\(395\) 0 0
\(396\) 0 0
\(397\) 0.131178 + 0.574730i 0.131178 + 0.574730i 0.997204 + 0.0747301i \(0.0238095\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 3.89926 1.87778i 3.89926 1.87778i
\(401\) 0 0 0.433884 0.900969i \(-0.357143\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(402\) 0 0
\(403\) −0.0957728 0.850007i −0.0957728 0.850007i
\(404\) 0.211652 + 0.604867i 0.211652 + 0.604867i
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 1.75711 0.197979i 1.75711 0.197979i 0.826239 0.563320i \(-0.190476\pi\)
0.930874 + 0.365341i \(0.119048\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) 0.785841 1.80117i 0.785841 1.80117i
\(415\) 0 0
\(416\) 0.896642 7.95792i 0.896642 7.95792i
\(417\) −0.297251 + 1.97213i −0.297251 + 1.97213i
\(418\) 0 0
\(419\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(420\) 0 0
\(421\) 0 0 0.330279 0.943883i \(-0.392857\pi\)
−0.330279 + 0.943883i \(0.607143\pi\)
\(422\) −2.70944 0.618412i −2.70944 0.618412i
\(423\) −1.29476 0.955573i −1.29476 0.955573i
\(424\) 0 0
\(425\) 0 0
\(426\) −3.46509 1.83135i −3.46509 1.83135i
\(427\) 0 0
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 0.781831 0.623490i \(-0.214286\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(432\) 1.87778 3.89926i 1.87778 3.89926i
\(433\) 0 0 0.943883 0.330279i \(-0.107143\pi\)
−0.943883 + 0.330279i \(0.892857\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) −2.97639 2.02927i −2.97639 2.02927i
\(439\) −0.460898 + 0.367554i −0.460898 + 0.367554i −0.826239 0.563320i \(-0.809524\pi\)
0.365341 + 0.930874i \(0.380952\pi\)
\(440\) 0 0
\(441\) −0.826239 + 0.563320i −0.826239 + 0.563320i
\(442\) 0 0
\(443\) 0.425511 0.677197i 0.425511 0.677197i −0.563320 0.826239i \(-0.690476\pi\)
0.988831 + 0.149042i \(0.0476190\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0.465297 + 0.740517i 0.465297 + 0.740517i
\(447\) 0 0
\(448\) 0 0
\(449\) −0.623490 + 1.78183i −0.623490 + 1.78183i 1.00000i \(0.5\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(450\) −0.365341 + 1.93087i −0.365341 + 1.93087i
\(451\) 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 \(-0.785714\pi\)
0.781831 + 0.623490i \(0.214286\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −1.98603 + 0.223772i −1.98603 + 0.223772i −0.988831 + 0.149042i \(0.952381\pi\)
−0.997204 + 0.0747301i \(0.976190\pi\)
\(462\) 0 0
\(463\) 1.80194i 1.80194i −0.433884 0.900969i \(-0.642857\pi\)
0.433884 0.900969i \(-0.357143\pi\)
\(464\) 4.31575 + 0.323421i 4.31575 + 0.323421i
\(465\) 0 0
\(466\) −1.24041 3.54490i −1.24041 3.54490i
\(467\) 0 0 −0.111964 0.993712i \(-0.535714\pi\)
0.111964 + 0.993712i \(0.464286\pi\)
\(468\) 3.46658 + 3.21652i 3.46658 + 3.21652i
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 3.86291 + 2.42722i 3.86291 + 2.42722i
\(473\) 0 0
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 0 0
\(478\) −1.09346 0.382617i −1.09346 0.382617i
\(479\) 0 0 −0.943883 0.330279i \(-0.892857\pi\)
0.943883 + 0.330279i \(0.107143\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) 0.636799 + 2.79000i 0.636799 + 2.79000i
\(485\) 0 0
\(486\) 0.918245 + 1.73740i 0.918245 + 1.73740i
\(487\) −1.22563 + 0.590232i −1.22563 + 0.590232i −0.930874 0.365341i \(-0.880952\pi\)
−0.294755 + 0.955573i \(0.595238\pi\)
\(488\) 0 0
\(489\) 1.60807 + 0.0601697i 1.60807 + 0.0601697i
\(490\) 0 0
\(491\) −0.308658 0.882094i −0.308658 0.882094i −0.988831 0.149042i \(-0.952381\pi\)
0.680173 0.733052i \(-0.261905\pi\)
\(492\) 3.30072 3.83551i 3.30072 3.83551i
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 2.22617 0.250830i 2.22617 0.250830i
\(497\) 0 0
\(498\) 0 0
\(499\) 0.858075 + 1.78181i 0.858075 + 1.78181i 0.563320 + 0.826239i \(0.309524\pi\)
0.294755 + 0.955573i \(0.404762\pi\)
\(500\) 0 0
\(501\) 0.531130 + 1.72188i 0.531130 + 1.72188i
\(502\) 0 0
\(503\) 0 0 0.111964 0.993712i \(-0.464286\pi\)
−0.111964 + 0.993712i \(0.535714\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −1.49881 + 0.865341i −1.49881 + 0.865341i
\(508\) −0.0706825 + 0.201999i −0.0706825 + 0.201999i
\(509\) 1.81507 + 0.414278i 1.81507 + 0.414278i 0.988831 0.149042i \(-0.0476190\pi\)
0.826239 + 0.563320i \(0.190476\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 5.10761 + 0.575490i 5.10761 + 0.575490i
\(513\) 0 0
\(514\) 0.311651 0.495990i 0.311651 0.495990i
\(515\) 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 \(\pi\)
\(522\) −1.28183 + 1.48952i −1.28183 + 1.48952i
\(523\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(524\) 1.00435 0.351438i 1.00435 0.351438i
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) −0.623490 + 0.781831i −0.623490 + 0.781831i
\(530\) 0 0
\(531\) −1.16078 + 0.455573i −1.16078 + 0.455573i
\(532\) 0 0
\(533\) 1.55458 + 2.47410i 1.55458 + 2.47410i
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) −1.26968 + 0.733052i −1.26968 + 0.733052i
\(538\) 0.0327011 0.143273i 0.0327011 0.143273i
\(539\) 0 0
\(540\) 0 0
\(541\) −0.132974 + 1.18017i −0.132974 + 1.18017i 0.733052 + 0.680173i \(0.238095\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(542\) 3.61670 0.825489i 3.61670 0.825489i
\(543\) 0 0
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −1.19158 1.49419i −1.19158 1.49419i −0.826239 0.563320i \(-0.809524\pi\)
−0.365341 0.930874i \(-0.619048\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 0 0
\(552\) −2.38645 + 2.77310i −2.38645 + 2.77310i
\(553\) 0 0
\(554\) −0.0328850 0.291862i −0.0328850 0.291862i
\(555\) 0 0
\(556\) 2.47639 5.14227i 2.47639 5.14227i
\(557\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(558\) −0.508614 + 0.880945i −0.508614 + 0.880945i
\(559\) 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 \(0.250000\pi\)
\(564\) 2.73461 + 3.70526i 2.73461 + 3.70526i
\(565\) 0 0
\(566\) 0 0
\(567\) 0 0
\(568\) 5.15955 + 5.15955i 5.15955 + 5.15955i
\(569\) 0 0 0.846724 0.532032i \(-0.178571\pi\)
−0.846724 + 0.532032i \(0.821429\pi\)
\(570\) 0 0
\(571\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0.433884 0.900969i 0.433884 0.900969i
\(576\) −3.53392 + 3.80866i −3.53392 + 3.80866i
\(577\) −0.223772 1.98603i −0.223772 1.98603i −0.149042 0.988831i \(-0.547619\pi\)
−0.0747301 0.997204i \(-0.523810\pi\)
\(578\) 0.649042 + 1.85486i 0.649042 + 1.85486i
\(579\) −0.606214 0.521689i −0.606214 0.521689i
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) 4.18152 + 5.24346i 4.18152 + 5.24346i
\(585\) 0 0
\(586\) 0 0
\(587\) −1.06356 0.848162i −1.06356 0.848162i −0.0747301 0.997204i \(-0.523810\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(588\) 2.73461 0.843515i 2.73461 0.843515i
\(589\) 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 1.00000i \(-0.5\pi\)
0.433884 0.900969i \(-0.357143\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) −1.72769 2.74960i −1.72769 2.74960i
\(599\) −1.87590 0.211363i −1.87590 0.211363i −0.900969 0.433884i \(-0.857143\pi\)
−0.974928 + 0.222521i \(0.928571\pi\)
\(600\) 1.70954 3.23461i 1.70954 3.23461i
\(601\) 1.02781 1.63575i 1.02781 1.63575i 0.294755 0.955573i \(-0.404762\pi\)
0.733052 0.680173i \(-0.238095\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −2.57835 1.24167i −2.57835 1.24167i
\(605\) 0 0
\(606\) 0.363587 + 0.247889i 0.363587 + 0.247889i
\(607\) 1.00435 0.351438i 1.00435 0.351438i 0.222521 0.974928i \(-0.428571\pi\)
0.781831 + 0.623490i \(0.214286\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −2.50994 + 0.878265i −2.50994 + 0.878265i
\(612\) 0 0
\(613\) 0 0 0.781831 0.623490i \(-0.214286\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(614\) 3.51878 + 1.69456i 3.51878 + 1.69456i
\(615\) 0 0
\(616\) 0 0
\(617\) 0 0 0.532032 0.846724i \(-0.321429\pi\)
−0.532032 + 0.846724i \(0.678571\pi\)
\(618\) 0 0
\(619\) 0 0 −0.993712 0.111964i \(-0.964286\pi\)
0.993712 + 0.111964i \(0.0357143\pi\)
\(620\) 0 0
\(621\) −0.222521 0.974928i −0.222521 0.974928i
\(622\) 2.49939 + 0.570469i 2.49939 + 0.570469i
\(623\) 0 0
\(624\) −3.57584 6.19353i −3.57584 6.19353i
\(625\) −0.222521 + 0.974928i −0.222521 + 0.974928i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 0 0 −0.781831 0.623490i \(-0.785714\pi\)
0.781831 + 0.623490i \(0.214286\pi\)
\(632\) 0 0
\(633\) −1.29621 + 0.565533i −1.29621 + 0.565533i
\(634\) −0.809342 1.01488i −0.809342 1.01488i
\(635\) 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 −0.111964 0.993712i \(-0.535714\pi\)
0.111964 + 0.993712i \(0.464286\pi\)
\(642\) 0 0
\(643\) 0 0 0.433884 0.900969i \(-0.357143\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 0.414278 + 1.81507i 0.414278 + 1.81507i 0.563320 + 0.826239i \(0.309524\pi\)
−0.149042 + 0.988831i \(0.547619\pi\)
\(648\) −0.680173 3.59480i −0.680173 3.59480i
\(649\) 0 0
\(650\) 2.29621 + 2.29621i 2.29621 + 2.29621i
\(651\) 0 0
\(652\) −4.34669 1.52097i −4.34669 1.52097i
\(653\) −1.82344 0.638050i −1.82344 0.638050i −0.997204 0.0747301i \(-0.976190\pi\)
−0.826239 0.563320i \(-0.809524\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) −6.47968 + 4.07145i −6.47968 + 4.07145i
\(657\) −1.83184 + 0.0685427i −1.83184 + 0.0685427i
\(658\) 0 0
\(659\) 0 0 −0.846724 0.532032i \(-0.821429\pi\)
0.846724 + 0.532032i \(0.178571\pi\)
\(660\) 0 0
\(661\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(662\) 1.70409 3.53857i 1.70409 3.53857i
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0.826239 0.563320i 0.826239 0.563320i
\(668\) 5.15669i 5.15669i
\(669\) 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 −0.955573 0.294755i \(-0.904762\pi\)
0.365341 0.930874i \(-0.380952\pi\)
\(674\) 0 0
\(675\) 0.433884 + 0.900969i 0.433884 + 0.900969i
\(676\) 4.82860 1.10210i 4.82860 1.10210i
\(677\) 0 0 0.111964 0.993712i \(-0.464286\pi\)
−0.111964 + 0.993712i \(0.535714\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 0.290611 + 0.0663300i 0.290611 + 0.0663300i 0.365341 0.930874i \(-0.380952\pi\)
−0.0747301 + 0.997204i \(0.523810\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) 0.781831 + 0.376510i 0.781831 + 0.376510i 0.781831 0.623490i \(-0.214286\pi\)
1.00000i \(0.5\pi\)
\(692\) −0.995739 + 0.794075i −0.995739 + 0.794075i
\(693\) 0 0
\(694\) −3.61670 + 1.26554i −3.61670 + 1.26554i
\(695\) 0 0
\(696\) 3.09781 1.94648i 3.09781 1.94648i
\(697\) 0 0
\(698\) 3.66828 1.28359i 3.66828 1.28359i
\(699\) −1.57906 1.07659i −1.57906 1.07659i
\(700\) 0 0
\(701\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(702\) 3.22692 + 0.363587i 3.22692 + 0.363587i
\(703\) 0 0
\(704\) 0 0
\(705\) 0 0
\(706\) −2.65645 0.299310i −2.65645 0.299310i
\(707\) 0 0
\(708\) 3.55856 0.266677i 3.55856 0.266677i
\(709\) 0 0 −0.974928 0.222521i \(-0.928571\pi\)
0.974928 + 0.222521i \(0.0714286\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 0.366025 0.366025i 0.366025 0.366025i
\(714\) 0 0
\(715\) 0 0
\(716\) 4.09043 0.933613i 4.09043 0.933613i
\(717\) −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
\(722\) 1.95278 0.220025i 1.95278 0.220025i
\(723\) 0 0
\(724\) 0 0
\(725\) −0.680173 + 0.733052i −0.680173 + 0.733052i
\(726\) 1.48952 + 1.28183i 1.48952 + 1.28183i
\(727\) 0 0 −0.330279 0.943883i \(-0.607143\pi\)
0.330279 + 0.943883i \(0.392857\pi\)
\(728\) 0 0
\(729\) 0.900969 + 0.433884i 0.900969 + 0.433884i
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 0 0 −0.846724 0.532032i \(-0.821429\pi\)
0.846724 + 0.532032i \(0.178571\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 4.10341 2.57835i 4.10341 2.57835i
\(737\) 0 0
\(738\) 0.259673 3.46509i 0.259673 3.46509i
\(739\) 1.66900 + 0.584010i 1.66900 + 0.584010i 0.988831 0.149042i \(-0.0476190\pi\)
0.680173 + 0.733052i \(0.261905\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 0.846724 0.532032i \(-0.178571\pi\)
−0.846724 + 0.532032i \(0.821429\pi\)
\(744\) 1.38827 1.28813i 1.38827 1.28813i
\(745\) 0 0
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 0 0 −0.111964 0.993712i \(-0.535714\pi\)
0.111964 + 0.993712i \(0.464286\pi\)
\(752\) −2.30018 6.57354i −2.30018 6.57354i
\(753\) 0 0
\(754\) 0.840473 + 3.13669i 0.840473 + 3.13669i
\(755\) 0 0
\(756\) 0 0
\(757\) 0 0 0.993712 0.111964i \(-0.0357143\pi\)
−0.993712 + 0.111964i \(0.964286\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 0.116853 + 0.0931869i 0.116853 + 0.0931869i 0.680173 0.733052i \(-0.261905\pi\)
−0.563320 + 0.826239i \(0.690476\pi\)
\(762\) 0.0433164 + 0.140428i 0.0433164 + 0.140428i
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −0.458528 + 2.00894i −0.458528 + 2.00894i
\(768\) 4.62897 2.67254i 4.62897 2.67254i
\(769\) 0 0 0.330279 0.943883i \(-0.392857\pi\)
−0.330279 + 0.943883i \(0.607143\pi\)
\(770\) 0 0
\(771\) −0.0222759 0.297251i −0.0222759 0.297251i
\(772\) 1.21770 + 1.93797i 1.21770 + 1.93797i
\(773\) 0 0 −0.993712 0.111964i \(-0.964286\pi\)
0.993712 + 0.111964i \(0.0357143\pi\)
\(774\) 0 0
\(775\) −0.275400 + 0.438297i −0.275400 + 0.438297i
\(776\) 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
\(784\) −4.32785 −4.32785
\(785\) 0 0
\(786\) 0.411608 0.603718i 0.411608 0.603718i
\(787\) 0 0 0.781831 0.623490i \(-0.214286\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(788\) −4.46583