Properties

Label 2001.1.bf.d.206.2
Level $2001$
Weight $1$
Character 2001.206
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 206.2
Root \(0.997204 - 0.0747301i\) of defining polynomial
Character \(\chi\) \(=\) 2001.206
Dual form 2001.1.bf.d.68.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.940755 - 1.49720i) q^{2} +(-0.294755 - 0.955573i) q^{3} +(-0.922715 - 1.91604i) q^{4} +(-1.70798 - 0.457652i) q^{6} +(-1.97963 - 0.223051i) q^{8} +(-0.826239 + 0.563320i) q^{9} +O(q^{10})\) \(q+(0.940755 - 1.49720i) q^{2} +(-0.294755 - 0.955573i) q^{3} +(-0.922715 - 1.91604i) q^{4} +(-1.70798 - 0.457652i) q^{6} +(-1.97963 - 0.223051i) q^{8} +(-0.826239 + 0.563320i) q^{9} +(-1.55894 + 1.44648i) q^{12} +(-1.49419 - 1.19158i) q^{13} +(-0.870366 + 1.09140i) q^{16} +(0.0661163 + 1.76699i) q^{18} +(0.974928 + 0.222521i) q^{23} +(0.370366 + 1.95743i) q^{24} +(-0.900969 + 0.433884i) q^{25} +(-3.18971 + 1.11613i) q^{26} +(0.781831 + 0.623490i) q^{27} +(0.997204 + 0.0747301i) q^{29} +(-1.63575 - 1.02781i) q^{31} +(0.157284 + 0.449493i) q^{32} +(1.84172 + 1.06332i) q^{36} +(-0.698220 + 1.77904i) q^{39} +(1.13787 - 1.13787i) q^{41} +(1.25033 - 1.25033i) q^{46} +(0.146066 + 1.29637i) q^{47} +(1.29946 + 0.510001i) q^{48} +(0.623490 + 0.781831i) q^{49} +(-0.197979 + 1.75711i) q^{50} +(-0.904396 + 3.96242i) q^{52} +(1.66900 - 0.584010i) q^{54} +(1.05001 - 1.42271i) q^{58} -1.80194i q^{59} +(-3.07767 + 1.48213i) q^{62} +(-0.540010 - 0.123254i) q^{64} +(-0.0747301 - 0.997204i) q^{69} +(0.848162 - 1.06356i) q^{71} +(1.76130 - 0.930874i) q^{72} +(1.66393 - 1.04551i) q^{73} +(0.680173 + 0.733052i) q^{75} +(2.00672 + 2.71901i) q^{78} +(0.365341 - 0.930874i) q^{81} +(-0.633168 - 2.77409i) q^{82} +(-0.222521 - 0.974928i) q^{87} +(-0.473222 - 2.07332i) q^{92} +(-0.500000 + 1.86603i) q^{93} +(2.07835 + 1.00088i) q^{94} +(0.383163 - 0.282787i) q^{96} +(1.75711 - 0.197979i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q + 2q^{2} + 14q^{4} + 2q^{6} - 6q^{8} - 2q^{9} + O(q^{10}) \) \( 24q + 2q^{2} + 14q^{4} + 2q^{6} - 6q^{8} - 2q^{9} + 2q^{12} - 6q^{16} + 12q^{18} - 6q^{24} - 4q^{25} - 2q^{26} - 2q^{31} - 4q^{32} + 6q^{36} + 2q^{39} - 2q^{41} + 2q^{46} + 2q^{47} + 6q^{48} - 4q^{49} + 2q^{50} - 10q^{52} - 2q^{54} + 4q^{58} - 4q^{62} - 28q^{64} - 2q^{69} + 22q^{72} - 2q^{73} - 4q^{78} + 2q^{81} - 4q^{82} - 4q^{87} - 4q^{92} - 12q^{93} - 8q^{94} - 18q^{96} + 2q^{98} + O(q^{100}) \)

Character values

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

\(n\) \(553\) \(668\) \(1132\)
\(\chi(n)\) \(e\left(\frac{5}{28}\right)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.940755 1.49720i 0.940755 1.49720i 0.0747301 0.997204i \(-0.476190\pi\)
0.866025 0.500000i \(-0.166667\pi\)
\(3\) −0.294755 0.955573i −0.294755 0.955573i
\(4\) −0.922715 1.91604i −0.922715 1.91604i
\(5\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(6\) −1.70798 0.457652i −1.70798 0.457652i
\(7\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(8\) −1.97963 0.223051i −1.97963 0.223051i
\(9\) −0.826239 + 0.563320i −0.826239 + 0.563320i
\(10\) 0 0
\(11\) 0 0 0.993712 0.111964i \(-0.0357143\pi\)
−0.993712 + 0.111964i \(0.964286\pi\)
\(12\) −1.55894 + 1.44648i −1.55894 + 1.44648i
\(13\) −1.49419 1.19158i −1.49419 1.19158i −0.930874 0.365341i \(-0.880952\pi\)
−0.563320 0.826239i \(-0.690476\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −0.870366 + 1.09140i −0.870366 + 1.09140i
\(17\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(18\) 0.0661163 + 1.76699i 0.0661163 + 1.76699i
\(19\) 0 0 0.330279 0.943883i \(-0.392857\pi\)
−0.330279 + 0.943883i \(0.607143\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 0.974928 + 0.222521i 0.974928 + 0.222521i
\(24\) 0.370366 + 1.95743i 0.370366 + 1.95743i
\(25\) −0.900969 + 0.433884i −0.900969 + 0.433884i
\(26\) −3.18971 + 1.11613i −3.18971 + 1.11613i
\(27\) 0.781831 + 0.623490i 0.781831 + 0.623490i
\(28\) 0 0
\(29\) 0.997204 + 0.0747301i 0.997204 + 0.0747301i
\(30\) 0 0
\(31\) −1.63575 1.02781i −1.63575 1.02781i −0.955573 0.294755i \(-0.904762\pi\)
−0.680173 0.733052i \(-0.738095\pi\)
\(32\) 0.157284 + 0.449493i 0.157284 + 0.449493i
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) 1.84172 + 1.06332i 1.84172 + 1.06332i
\(37\) 0 0 0.111964 0.993712i \(-0.464286\pi\)
−0.111964 + 0.993712i \(0.535714\pi\)
\(38\) 0 0
\(39\) −0.698220 + 1.77904i −0.698220 + 1.77904i
\(40\) 0 0
\(41\) 1.13787 1.13787i 1.13787 1.13787i 0.149042 0.988831i \(-0.452381\pi\)
0.988831 0.149042i \(-0.0476190\pi\)
\(42\) 0 0
\(43\) 0 0 −0.532032 0.846724i \(-0.678571\pi\)
0.532032 + 0.846724i \(0.321429\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 1.25033 1.25033i 1.25033 1.25033i
\(47\) 0.146066 + 1.29637i 0.146066 + 1.29637i 0.826239 + 0.563320i \(0.190476\pi\)
−0.680173 + 0.733052i \(0.738095\pi\)
\(48\) 1.29946 + 0.510001i 1.29946 + 0.510001i
\(49\) 0.623490 + 0.781831i 0.623490 + 0.781831i
\(50\) −0.197979 + 1.75711i −0.197979 + 1.75711i
\(51\) 0 0
\(52\) −0.904396 + 3.96242i −0.904396 + 3.96242i
\(53\) 0 0 0.974928 0.222521i \(-0.0714286\pi\)
−0.974928 + 0.222521i \(0.928571\pi\)
\(54\) 1.66900 0.584010i 1.66900 0.584010i
\(55\) 0 0
\(56\) 0 0
\(57\) 0 0
\(58\) 1.05001 1.42271i 1.05001 1.42271i
\(59\) 1.80194i 1.80194i −0.433884 0.900969i \(-0.642857\pi\)
0.433884 0.900969i \(-0.357143\pi\)
\(60\) 0 0
\(61\) 0 0 0.943883 0.330279i \(-0.107143\pi\)
−0.943883 + 0.330279i \(0.892857\pi\)
\(62\) −3.07767 + 1.48213i −3.07767 + 1.48213i
\(63\) 0 0
\(64\) −0.540010 0.123254i −0.540010 0.123254i
\(65\) 0 0
\(66\) 0 0
\(67\) 0 0 0.781831 0.623490i \(-0.214286\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(68\) 0 0
\(69\) −0.0747301 0.997204i −0.0747301 0.997204i
\(70\) 0 0
\(71\) 0.848162 1.06356i 0.848162 1.06356i −0.149042 0.988831i \(-0.547619\pi\)
0.997204 0.0747301i \(-0.0238095\pi\)
\(72\) 1.76130 0.930874i 1.76130 0.930874i
\(73\) 1.66393 1.04551i 1.66393 1.04551i 0.733052 0.680173i \(-0.238095\pi\)
0.930874 0.365341i \(-0.119048\pi\)
\(74\) 0 0
\(75\) 0.680173 + 0.733052i 0.680173 + 0.733052i
\(76\) 0 0
\(77\) 0 0
\(78\) 2.00672 + 2.71901i 2.00672 + 2.71901i
\(79\) 0 0 −0.993712 0.111964i \(-0.964286\pi\)
0.993712 + 0.111964i \(0.0357143\pi\)
\(80\) 0 0
\(81\) 0.365341 0.930874i 0.365341 0.930874i
\(82\) −0.633168 2.77409i −0.633168 2.77409i
\(83\) 0 0 −0.433884 0.900969i \(-0.642857\pi\)
0.433884 + 0.900969i \(0.357143\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −0.222521 0.974928i −0.222521 0.974928i
\(88\) 0 0
\(89\) 0 0 0.532032 0.846724i \(-0.321429\pi\)
−0.532032 + 0.846724i \(0.678571\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −0.473222 2.07332i −0.473222 2.07332i
\(93\) −0.500000 + 1.86603i −0.500000 + 1.86603i
\(94\) 2.07835 + 1.00088i 2.07835 + 1.00088i
\(95\) 0 0
\(96\) 0.383163 0.282787i 0.383163 0.282787i
\(97\) 0 0 −0.943883 0.330279i \(-0.892857\pi\)
0.943883 + 0.330279i \(0.107143\pi\)
\(98\) 1.75711 0.197979i 1.75711 0.197979i
\(99\) 0 0
\(100\) 1.66267 + 1.32594i 1.66267 + 1.32594i
\(101\) −0.559311 + 0.351438i −0.559311 + 0.351438i −0.781831 0.623490i \(-0.785714\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(102\) 0 0
\(103\) 0 0 0.623490 0.781831i \(-0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(104\) 2.69217 + 2.69217i 2.69217 + 2.69217i
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 0.781831 0.623490i \(-0.214286\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(108\) 0.473222 2.07332i 0.473222 2.07332i
\(109\) 0 0 0.433884 0.900969i \(-0.357143\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 0 0 0.943883 0.330279i \(-0.107143\pi\)
−0.943883 + 0.330279i \(0.892857\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) −0.776949 1.97963i −0.776949 1.97963i
\(117\) 1.90580 + 0.142820i 1.90580 + 0.142820i
\(118\) −2.69787 1.69518i −2.69787 1.69518i
\(119\) 0 0
\(120\) 0 0
\(121\) 0.974928 0.222521i 0.974928 0.222521i
\(122\) 0 0
\(123\) −1.42271 0.751927i −1.42271 0.751927i
\(124\) −0.459990 + 4.08252i −0.459990 + 4.08252i
\(125\) 0 0
\(126\) 0 0
\(127\) 0.205245 + 1.82160i 0.205245 + 1.82160i 0.500000 + 0.866025i \(0.333333\pi\)
−0.294755 + 0.955573i \(0.595238\pi\)
\(128\) −1.02929 + 1.02929i −1.02929 + 1.02929i
\(129\) 0 0
\(130\) 0 0
\(131\) −0.497204 0.791295i −0.497204 0.791295i 0.500000 0.866025i \(-0.333333\pi\)
−0.997204 + 0.0747301i \(0.976190\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 0 0 0.111964 0.993712i \(-0.464286\pi\)
−0.111964 + 0.993712i \(0.535714\pi\)
\(138\) −1.56332 0.826239i −1.56332 0.826239i
\(139\) −0.302705 + 1.32624i −0.302705 + 1.32624i 0.563320 + 0.826239i \(0.309524\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(140\) 0 0
\(141\) 1.19572 0.521689i 1.19572 0.521689i
\(142\) −0.794455 2.27042i −0.794455 2.27042i
\(143\) 0 0
\(144\) 0.104320 1.39205i 0.104320 1.39205i
\(145\) 0 0
\(146\) 3.47481i 3.47481i
\(147\) 0.563320 0.826239i 0.563320 0.826239i
\(148\) 0 0
\(149\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(150\) 1.73740 0.328735i 1.73740 0.328735i
\(151\) 0.974928 + 0.222521i 0.974928 + 0.222521i 0.680173 0.733052i \(-0.261905\pi\)
0.294755 + 0.955573i \(0.404762\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 4.05295 0.303727i 4.05295 0.303727i
\(157\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) −1.05001 1.42271i −1.05001 1.42271i
\(163\) −1.29637 + 0.146066i −1.29637 + 0.146066i −0.733052 0.680173i \(-0.761905\pi\)
−0.563320 + 0.826239i \(0.690476\pi\)
\(164\) −3.23014 1.13027i −3.23014 1.13027i
\(165\) 0 0
\(166\) 0 0
\(167\) −0.400969 0.193096i −0.400969 0.193096i 0.222521 0.974928i \(-0.428571\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(168\) 0 0
\(169\) 0.590232 + 2.58597i 0.590232 + 2.58597i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(174\) −1.66900 0.584010i −1.66900 0.584010i
\(175\) 0 0
\(176\) 0 0
\(177\) −1.72188 + 0.531130i −1.72188 + 0.531130i
\(178\) 0 0
\(179\) −0.162592 0.712362i −0.162592 0.712362i −0.988831 0.149042i \(-0.952381\pi\)
0.826239 0.563320i \(-0.190476\pi\)
\(180\) 0 0
\(181\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −1.88037 0.657969i −1.88037 0.657969i
\(185\) 0 0
\(186\) 2.32344 + 2.50408i 2.32344 + 2.50408i
\(187\) 0 0
\(188\) 2.34912 1.47605i 2.34912 1.47605i
\(189\) 0 0
\(190\) 0 0
\(191\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(192\) 0.0413928 + 0.552349i 0.0413928 + 0.552349i
\(193\) 0.122805 0.350958i 0.122805 0.350958i −0.866025 0.500000i \(-0.833333\pi\)
0.988831 + 0.149042i \(0.0476190\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0.922715 1.91604i 0.922715 1.91604i
\(197\) −1.68862 0.385418i −1.68862 0.385418i −0.733052 0.680173i \(-0.761905\pi\)
−0.955573 + 0.294755i \(0.904762\pi\)
\(198\) 0 0
\(199\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(200\) 1.88037 0.657969i 1.88037 0.657969i
\(201\) 0 0
\(202\) 1.16802i 1.16802i
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −0.930874 + 0.365341i −0.930874 + 0.365341i
\(208\) 2.60099 0.593659i 2.60099 0.593659i
\(209\) 0 0
\(210\) 0 0
\(211\) 0.158342 1.40532i 0.158342 1.40532i −0.623490 0.781831i \(-0.714286\pi\)
0.781831 0.623490i \(-0.214286\pi\)
\(212\) 0 0
\(213\) −1.26631 0.496990i −1.26631 0.496990i
\(214\) 0 0
\(215\) 0 0
\(216\) −1.40867 1.40867i −1.40867 1.40867i
\(217\) 0 0
\(218\) 0 0
\(219\) −1.48952 1.28183i −1.48952 1.28183i
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) −0.777479 0.974928i −0.777479 0.974928i 0.222521 0.974928i \(-0.428571\pi\)
−1.00000 \(\pi\)
\(224\) 0 0
\(225\) 0.500000 0.866025i 0.500000 0.866025i
\(226\) 0 0
\(227\) 0 0 0.974928 0.222521i \(-0.0714286\pi\)
−0.974928 + 0.222521i \(0.928571\pi\)
\(228\) 0 0
\(229\) 0 0 −0.330279 0.943883i \(-0.607143\pi\)
0.330279 + 0.943883i \(0.392857\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −1.95743 0.370366i −1.95743 0.370366i
\(233\) 1.97766i 1.97766i 0.149042 + 0.988831i \(0.452381\pi\)
−0.149042 + 0.988831i \(0.547619\pi\)
\(234\) 2.00672 2.71901i 2.00672 2.71901i
\(235\) 0 0
\(236\) −3.45258 + 1.66267i −3.45258 + 1.66267i
\(237\) 0 0
\(238\) 0 0
\(239\) 0.129334 0.268565i 0.129334 0.268565i −0.826239 0.563320i \(-0.809524\pi\)
0.955573 + 0.294755i \(0.0952381\pi\)
\(240\) 0 0
\(241\) 0 0 0.781831 0.623490i \(-0.214286\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(242\) 0.584010 1.66900i 0.584010 1.66900i
\(243\) −0.997204 0.0747301i −0.997204 0.0747301i
\(244\) 0 0
\(245\) 0 0
\(246\) −2.46421 + 1.42271i −2.46421 + 1.42271i
\(247\) 0 0
\(248\) 3.00892 + 2.39954i 3.00892 + 2.39954i
\(249\) 0 0
\(250\) 0 0
\(251\) 0 0 −0.943883 0.330279i \(-0.892857\pi\)
0.943883 + 0.330279i \(0.107143\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 2.92039 + 1.40639i 2.92039 + 1.40639i
\(255\) 0 0
\(256\) 0.449493 + 1.96936i 0.449493 + 1.96936i
\(257\) 0.865341 + 1.79690i 0.865341 + 1.79690i 0.500000 + 0.866025i \(0.333333\pi\)
0.365341 + 0.930874i \(0.380952\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(262\) −1.65248 −1.65248
\(263\) 0 0 0.532032 0.846724i \(-0.321429\pi\)
−0.532032 + 0.846724i \(0.678571\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 1.82160 + 0.205245i 1.82160 + 0.205245i 0.955573 0.294755i \(-0.0952381\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(270\) 0 0
\(271\) −1.00435 0.351438i −1.00435 0.351438i −0.222521 0.974928i \(-0.571429\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) −1.84172 + 1.06332i −1.84172 + 1.06332i
\(277\) −0.914101 + 1.14625i −0.914101 + 1.14625i 0.0747301 + 0.997204i \(0.476190\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(278\) 1.70088 + 1.70088i 1.70088 + 1.70088i
\(279\) 1.93050 0.0722342i 1.93050 0.0722342i
\(280\) 0 0
\(281\) 0 0 0.781831 0.623490i \(-0.214286\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(282\) 0.343809 2.28102i 0.343809 2.28102i
\(283\) 0 0 0.433884 0.900969i \(-0.357143\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(284\) −2.82043 0.643745i −2.82043 0.643745i
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) −0.383163 0.282787i −0.383163 0.282787i
\(289\) 1.00000i 1.00000i
\(290\) 0 0
\(291\) 0 0
\(292\) −3.53857 2.22343i −3.53857 2.22343i
\(293\) 0 0 −0.330279 0.943883i \(-0.607143\pi\)
0.330279 + 0.943883i \(0.392857\pi\)
\(294\) −0.707101 1.62069i −0.707101 1.62069i
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −1.19158 1.49419i −1.19158 1.49419i
\(300\) 0.776949 1.97963i 0.776949 1.97963i
\(301\) 0 0
\(302\) 1.25033 1.25033i 1.25033 1.25033i
\(303\) 0.500684 + 0.430874i 0.500684 + 0.430874i
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 1.33485 1.33485i 1.33485 1.33485i 0.433884 0.900969i \(-0.357143\pi\)
0.900969 0.433884i \(-0.142857\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −0.00837297 + 0.0743122i −0.00837297 + 0.0743122i −0.997204 0.0747301i \(-0.976190\pi\)
0.988831 + 0.149042i \(0.0476190\pi\)
\(312\) 1.77904 3.36610i 1.77904 3.36610i
\(313\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 1.43388 + 0.900969i 1.43388 + 0.900969i 1.00000 \(0\)
0.433884 + 0.900969i \(0.357143\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) −2.12069 + 0.158924i −2.12069 + 0.158924i
\(325\) 1.86323 + 0.425270i 1.86323 + 0.425270i
\(326\) −1.00088 + 2.07835i −1.00088 + 2.07835i
\(327\) 0 0
\(328\) −2.50638 + 1.99877i −2.50638 + 1.99877i
\(329\) 0 0
\(330\) 0 0
\(331\) −0.565533 0.565533i −0.565533 0.565533i 0.365341 0.930874i \(-0.380952\pi\)
−0.930874 + 0.365341i \(0.880952\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) −0.666318 + 0.418676i −0.666318 + 0.418676i
\(335\) 0 0
\(336\) 0 0
\(337\) 0 0 0.993712 0.111964i \(-0.0357143\pi\)
−0.993712 + 0.111964i \(0.964286\pi\)
\(338\) 4.42699 + 1.54907i 4.42699 + 1.54907i
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 0 0
\(346\) 1.17310 1.86698i 1.17310 1.86698i
\(347\) 1.56366 1.56366 0.781831 0.623490i \(-0.214286\pi\)
0.781831 + 0.623490i \(0.214286\pi\)
\(348\) −1.66267 + 1.32594i −1.66267 + 1.32594i
\(349\) 0.149460 0.149460 0.0747301 0.997204i \(-0.476190\pi\)
0.0747301 + 0.997204i \(0.476190\pi\)
\(350\) 0 0
\(351\) −0.425270 1.86323i −0.425270 1.86323i
\(352\) 0 0
\(353\) 0.414278 + 1.81507i 0.414278 + 1.81507i 0.563320 + 0.826239i \(0.309524\pi\)
−0.149042 + 0.988831i \(0.547619\pi\)
\(354\) −0.824660 + 3.07767i −0.824660 + 3.07767i
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) −1.21951 0.426725i −1.21951 0.426725i
\(359\) 0 0 0.993712 0.111964i \(-0.0357143\pi\)
−0.993712 + 0.111964i \(0.964286\pi\)
\(360\) 0 0
\(361\) −0.781831 0.623490i −0.781831 0.623490i
\(362\) 0 0
\(363\) −0.500000 0.866025i −0.500000 0.866025i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 0 0 0.330279 0.943883i \(-0.392857\pi\)
−0.330279 + 0.943883i \(0.607143\pi\)
\(368\) −1.09140 + 0.870366i −1.09140 + 0.870366i
\(369\) −0.299168 + 1.58114i −0.299168 + 1.58114i
\(370\) 0 0
\(371\) 0 0
\(372\) 4.03673 0.763791i 4.03673 0.763791i
\(373\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 2.59892i 2.59892i
\(377\) −1.40097 1.29991i −1.40097 1.29991i
\(378\) 0 0
\(379\) 0 0 −0.846724 0.532032i \(-0.821429\pi\)
0.846724 + 0.532032i \(0.178571\pi\)
\(380\) 0 0
\(381\) 1.68017 0.733052i 1.68017 0.733052i
\(382\) 0 0
\(383\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(384\) 1.28695 + 0.680173i 1.28695 + 0.680173i
\(385\) 0 0
\(386\) −0.409925 0.514030i −0.409925 0.514030i
\(387\) 0 0
\(388\) 0 0
\(389\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) −1.05989 1.68681i −1.05989 1.68681i
\(393\) −0.609587 + 0.708353i −0.609587 + 0.708353i
\(394\) −2.16563 + 2.16563i −2.16563 + 2.16563i
\(395\) 0 0
\(396\) 0 0
\(397\) 0.185853 + 0.233052i 0.185853 + 0.233052i 0.866025 0.500000i \(-0.166667\pi\)
−0.680173 + 0.733052i \(0.738095\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0.310630 1.36096i 0.310630 1.36096i
\(401\) 0 0 0.974928 0.222521i \(-0.0714286\pi\)
−0.974928 + 0.222521i \(0.928571\pi\)
\(402\) 0 0
\(403\) 1.21941 + 3.48486i 1.21941 + 3.48486i
\(404\) 1.18945 + 0.747382i 1.18945 + 0.747382i
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 1.51889 0.531484i 1.51889 0.531484i 0.563320 0.826239i \(-0.309524\pi\)
0.955573 + 0.294755i \(0.0952381\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) −0.328735 + 1.73740i −0.328735 + 1.73740i
\(415\) 0 0
\(416\) 0.300593 0.859046i 0.300593 0.859046i
\(417\) 1.35654 0.101659i 1.35654 0.101659i
\(418\) 0 0
\(419\) 0 0 0.623490 0.781831i \(-0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(420\) 0 0
\(421\) 0 0 0.846724 0.532032i \(-0.178571\pi\)
−0.846724 + 0.532032i \(0.821429\pi\)
\(422\) −1.95509 1.55913i −1.95509 1.55913i
\(423\) −0.850958 0.988831i −0.850958 0.988831i
\(424\) 0 0
\(425\) 0 0
\(426\) −1.93538 + 1.42838i −1.93538 + 1.42838i
\(427\) 0 0
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 −0.433884 0.900969i \(-0.642857\pi\)
0.433884 + 0.900969i \(0.357143\pi\)
\(432\) −1.36096 + 0.310630i −1.36096 + 0.310630i
\(433\) 0 0 0.532032 0.846724i \(-0.321429\pi\)
−0.532032 + 0.846724i \(0.678571\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) −3.32043 + 1.02422i −3.32043 + 1.02422i
\(439\) −0.129334 0.268565i −0.129334 0.268565i 0.826239 0.563320i \(-0.190476\pi\)
−0.955573 + 0.294755i \(0.904762\pi\)
\(440\) 0 0
\(441\) −0.955573 0.294755i −0.955573 0.294755i
\(442\) 0 0
\(443\) −0.369485 0.0416310i −0.369485 0.0416310i −0.0747301 0.997204i \(-0.523810\pi\)
−0.294755 + 0.955573i \(0.595238\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) −2.19108 + 0.246876i −2.19108 + 0.246876i
\(447\) 0 0
\(448\) 0 0
\(449\) 0.900969 0.566116i 0.900969 0.566116i 1.00000i \(-0.5\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(450\) −0.826239 1.56332i −0.826239 1.56332i
\(451\) 0 0
\(452\) 0 0
\(453\) −0.0747301 0.997204i −0.0747301 0.997204i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 0 0 0.433884 0.900969i \(-0.357143\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 0.754903 0.264152i 0.754903 0.264152i 0.0747301 0.997204i \(-0.476190\pi\)
0.680173 + 0.733052i \(0.261905\pi\)
\(462\) 0 0
\(463\) 0.445042i 0.445042i 0.974928 + 0.222521i \(0.0714286\pi\)
−0.974928 + 0.222521i \(0.928571\pi\)
\(464\) −0.949493 + 1.02331i −0.949493 + 1.02331i
\(465\) 0 0
\(466\) 2.96096 + 1.86050i 2.96096 + 1.86050i
\(467\) 0 0 −0.330279 0.943883i \(-0.607143\pi\)
0.330279 + 0.943883i \(0.392857\pi\)
\(468\) −1.48486 3.78337i −1.48486 3.78337i
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) −0.401924 + 3.56718i −0.401924 + 3.56718i
\(473\) 0 0
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 0 0
\(478\) −0.280425 0.446293i −0.280425 0.446293i
\(479\) 0 0 −0.532032 0.846724i \(-0.678571\pi\)
0.532032 + 0.846724i \(0.321429\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) −1.32594 1.66267i −1.32594 1.66267i
\(485\) 0 0
\(486\) −1.05001 + 1.42271i −1.05001 + 1.42271i
\(487\) −0.414278 + 1.81507i −0.414278 + 1.81507i 0.149042 + 0.988831i \(0.452381\pi\)
−0.563320 + 0.826239i \(0.690476\pi\)
\(488\) 0 0
\(489\) 0.521689 + 1.19572i 0.521689 + 1.19572i
\(490\) 0 0
\(491\) 1.00560 + 0.631863i 1.00560 + 0.631863i 0.930874 0.365341i \(-0.119048\pi\)
0.0747301 + 0.997204i \(0.476190\pi\)
\(492\) −0.127959 + 3.41979i −0.127959 + 3.41979i
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 2.54545 0.890691i 2.54545 0.890691i
\(497\) 0 0
\(498\) 0 0
\(499\) 0.145713 + 0.0332580i 0.145713 + 0.0332580i 0.294755 0.955573i \(-0.404762\pi\)
−0.149042 + 0.988831i \(0.547619\pi\)
\(500\) 0 0
\(501\) −0.0663300 + 0.440071i −0.0663300 + 0.440071i
\(502\) 0 0
\(503\) 0 0 0.330279 0.943883i \(-0.392857\pi\)
−0.330279 + 0.943883i \(0.607143\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 2.29711 1.32624i 2.29711 1.32624i
\(508\) 3.30087 2.07407i 3.30087 2.07407i
\(509\) 0.880843 + 0.702449i 0.880843 + 0.702449i 0.955573 0.294755i \(-0.0952381\pi\)
−0.0747301 + 0.997204i \(0.523810\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 1.99744 + 0.698934i 1.99744 + 0.698934i
\(513\) 0 0
\(514\) 3.50440 + 0.394851i 3.50440 + 0.394851i
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) −0.367554 1.19158i −0.367554 1.19158i
\(520\) 0 0
\(521\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(522\) −0.0661163 + 1.76699i −0.0661163 + 1.76699i
\(523\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(524\) −1.05737 + 1.68280i −1.05737 + 1.68280i
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) 0.900969 + 0.433884i 0.900969 + 0.433884i
\(530\) 0 0
\(531\) 1.01507 + 1.48883i 1.01507 + 1.48883i
\(532\) 0 0
\(533\) −3.05607 + 0.344336i −3.05607 + 0.344336i
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) −0.632789 + 0.365341i −0.632789 + 0.365341i
\(538\) 2.02097 2.53422i 2.02097 2.53422i
\(539\) 0 0
\(540\) 0 0
\(541\) 0.500684 1.43087i 0.500684 1.43087i −0.365341 0.930874i \(-0.619048\pi\)
0.866025 0.500000i \(-0.166667\pi\)
\(542\) −1.47102 + 1.17310i −1.47102 + 1.17310i
\(543\) 0 0
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −1.78181 + 0.858075i −1.78181 + 0.858075i −0.826239 + 0.563320i \(0.809524\pi\)
−0.955573 + 0.294755i \(0.904762\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 0 0
\(552\) −0.0744892 + 1.99077i −0.0744892 + 1.99077i
\(553\) 0 0
\(554\) 0.856219 + 2.44693i 0.856219 + 2.44693i
\(555\) 0 0
\(556\) 2.82043 0.643745i 2.82043 0.643745i
\(557\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(558\) 1.70798 2.95831i 1.70798 2.95831i
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(564\) −2.10289 1.80968i −2.10289 1.80968i
\(565\) 0 0
\(566\) 0 0
\(567\) 0 0
\(568\) −1.91628 + 1.91628i −1.91628 + 1.91628i
\(569\) 0 0 −0.111964 0.993712i \(-0.535714\pi\)
0.111964 + 0.993712i \(0.464286\pi\)
\(570\) 0 0
\(571\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −0.974928 + 0.222521i −0.974928 + 0.222521i
\(576\) 0.515609 0.202362i 0.515609 0.202362i
\(577\) −0.264152 0.754903i −0.264152 0.754903i −0.997204 0.0747301i \(-0.976190\pi\)
0.733052 0.680173i \(-0.238095\pi\)
\(578\) 1.49720 + 0.940755i 1.49720 + 0.940755i
\(579\) −0.371563 0.0139029i −0.371563 0.0139029i
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) −3.52717 + 1.69859i −3.52717 + 1.69859i
\(585\) 0 0
\(586\) 0 0
\(587\) 0.807782 1.67738i 0.807782 1.67738i 0.0747301 0.997204i \(-0.476190\pi\)
0.733052 0.680173i \(-0.238095\pi\)
\(588\) −2.10289 0.316959i −2.10289 0.316959i
\(589\) 0 0
\(590\) 0 0
\(591\) 0.129436 + 1.72721i 0.129436 + 1.72721i
\(592\) 0 0
\(593\) −0.974928 + 1.22252i −0.974928 + 1.22252i 1.00000i \(0.5\pi\)
−0.974928 + 0.222521i \(0.928571\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) −3.35810 + 0.378367i −3.35810 + 0.378367i
\(599\) −1.00435 0.351438i −1.00435 0.351438i −0.222521 0.974928i \(-0.571429\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(600\) −1.18298 1.60289i −1.18298 1.60289i
\(601\) −0.514383 0.0579571i −0.514383 0.0579571i −0.149042 0.988831i \(-0.547619\pi\)
−0.365341 + 0.930874i \(0.619048\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −0.473222 2.07332i −0.473222 2.07332i
\(605\) 0 0
\(606\) 1.11613 0.344280i 1.11613 0.344280i
\(607\) −1.05737 + 1.68280i −1.05737 + 1.68280i −0.433884 + 0.900969i \(0.642857\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 1.32648 2.11108i 1.32648 2.11108i
\(612\) 0 0
\(613\) 0 0 −0.433884 0.900969i \(-0.642857\pi\)
0.433884 + 0.900969i \(0.357143\pi\)
\(614\) −0.742776 3.25432i −0.742776 3.25432i
\(615\) 0 0
\(616\) 0 0
\(617\) 0 0 −0.993712 0.111964i \(-0.964286\pi\)
0.993712 + 0.111964i \(0.0357143\pi\)
\(618\) 0 0
\(619\) 0 0 −0.943883 0.330279i \(-0.892857\pi\)
0.943883 + 0.330279i \(0.107143\pi\)
\(620\) 0 0
\(621\) 0.623490 + 0.781831i 0.623490 + 0.781831i
\(622\) 0.103384 + 0.0824456i 0.103384 + 0.0824456i
\(623\) 0 0
\(624\) −1.33394 2.31045i −1.33394 2.31045i
\(625\) 0.623490 0.781831i 0.623490 0.781831i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 0 0 0.433884 0.900969i \(-0.357143\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(632\) 0 0
\(633\) −1.38956 + 0.262919i −1.38956 + 0.262919i
\(634\) 2.69787 1.29922i 2.69787 1.29922i
\(635\) 0 0
\(636\) 0 0
\(637\) 1.91115i 1.91115i
\(638\) 0 0
\(639\) −0.101659 + 1.35654i −0.101659 + 1.35654i
\(640\) 0 0
\(641\) 0 0 −0.330279 0.943883i \(-0.607143\pi\)
0.330279 + 0.943883i \(0.392857\pi\)
\(642\) 0 0
\(643\) 0 0 0.974928 0.222521i \(-0.0714286\pi\)
−0.974928 + 0.222521i \(0.928571\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −0.702449 0.880843i −0.702449 0.880843i 0.294755 0.955573i \(-0.404762\pi\)
−0.997204 + 0.0747301i \(0.976190\pi\)
\(648\) −0.930874 + 1.76130i −0.930874 + 1.76130i
\(649\) 0 0
\(650\) 2.38956 2.38956i 2.38956 2.38956i
\(651\) 0 0
\(652\) 1.47605 + 2.34912i 1.47605 + 2.34912i
\(653\) −0.275400 0.438297i −0.275400 0.438297i 0.680173 0.733052i \(-0.261905\pi\)
−0.955573 + 0.294755i \(0.904762\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0.251514 + 2.23224i 0.251514 + 2.23224i
\(657\) −0.785841 + 1.80117i −0.785841 + 1.80117i
\(658\) 0 0
\(659\) 0 0 0.111964 0.993712i \(-0.464286\pi\)
−0.111964 + 0.993712i \(0.535714\pi\)
\(660\) 0 0
\(661\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(662\) −1.37875 + 0.314690i −1.37875 + 0.314690i
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0.955573 + 0.294755i 0.955573 + 0.294755i
\(668\) 0.946444i 0.946444i
\(669\) −0.702449 + 1.03030i −0.702449 + 1.03030i
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 1.81507 + 0.414278i 1.81507 + 0.414278i 0.988831 0.149042i \(-0.0476190\pi\)
0.826239 + 0.563320i \(0.190476\pi\)
\(674\) 0 0
\(675\) −0.974928 0.222521i −0.974928 0.222521i
\(676\) 4.41021 3.51702i 4.41021 3.51702i
\(677\) 0 0 0.330279 0.943883i \(-0.392857\pi\)
−0.330279 + 0.943883i \(0.607143\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 1.55929 + 1.24349i 1.55929 + 1.24349i 0.826239 + 0.563320i \(0.190476\pi\)
0.733052 + 0.680173i \(0.238095\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) −0.433884 1.90097i −0.433884 1.90097i −0.433884 0.900969i \(-0.642857\pi\)
1.00000i \(-0.5\pi\)
\(692\) −1.15061 2.38926i −1.15061 2.38926i
\(693\) 0 0
\(694\) 1.47102 2.34112i 1.47102 2.34112i
\(695\) 0 0
\(696\) 0.223051 + 1.97963i 0.223051 + 1.97963i
\(697\) 0 0
\(698\) 0.140605 0.223772i 0.140605 0.223772i
\(699\) 1.88980 0.582926i 1.88980 0.582926i
\(700\) 0 0
\(701\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(702\) −3.18971 1.11613i −3.18971 1.11613i
\(703\) 0 0
\(704\) 0 0
\(705\) 0 0
\(706\) 3.10726 + 1.08728i 3.10726 + 1.08728i
\(707\) 0 0
\(708\) 2.60647 + 2.80911i 2.60647 + 2.80911i
\(709\) 0 0 −0.781831 0.623490i \(-0.785714\pi\)
0.781831 + 0.623490i \(0.214286\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −1.36603 1.36603i −1.36603 1.36603i
\(714\) 0 0
\(715\) 0 0
\(716\) −1.21489 + 0.968839i −1.21489 + 0.968839i
\(717\) −0.294755 0.0444272i −0.294755 0.0444272i
\(718\) 0 0
\(719\) −1.90097 0.433884i −1.90097 0.433884i −0.900969 0.433884i \(-0.857143\pi\)
−1.00000 \(\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −1.66900 + 0.584010i −1.66900 + 0.584010i
\(723\) 0 0
\(724\) 0 0
\(725\) −0.930874 + 0.365341i −0.930874 + 0.365341i
\(726\) −1.76699 0.0661163i −1.76699 0.0661163i
\(727\) 0 0 −0.846724 0.532032i \(-0.821429\pi\)
0.846724 + 0.532032i \(0.178571\pi\)
\(728\) 0 0
\(729\) 0.222521 + 0.974928i 0.222521 + 0.974928i
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 0 0 0.111964 0.993712i \(-0.464286\pi\)
−0.111964 + 0.993712i \(0.535714\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0.0533193 + 0.473222i 0.0533193 + 0.473222i
\(737\) 0 0
\(738\) 2.08585 + 1.93538i 2.08585 + 1.93538i
\(739\) 0.856144 + 1.36254i 0.856144 + 1.36254i 0.930874 + 0.365341i \(0.119048\pi\)
−0.0747301 + 0.997204i \(0.523810\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 −0.111964 0.993712i \(-0.535714\pi\)
0.111964 + 0.993712i \(0.464286\pi\)
\(744\) 1.40604 3.58252i 1.40604 3.58252i
\(745\) 0 0
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 0 0 −0.330279 0.943883i \(-0.607143\pi\)
0.330279 + 0.943883i \(0.392857\pi\)
\(752\) −1.54200 0.968901i −1.54200 0.968901i
\(753\) 0 0
\(754\) −3.26420 + 0.874639i −3.26420 + 0.874639i
\(755\) 0 0
\(756\) 0 0
\(757\) 0 0 0.943883 0.330279i \(-0.107143\pi\)
−0.943883 + 0.330279i \(0.892857\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 0.636119 1.32091i 0.636119 1.32091i −0.294755 0.955573i \(-0.595238\pi\)
0.930874 0.365341i \(-0.119048\pi\)
\(762\) 0.483104 3.20518i 0.483104 3.20518i
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −2.14715 + 2.69244i −2.14715 + 2.69244i
\(768\) 1.74937 1.01000i 1.74937 1.01000i
\(769\) 0 0 0.846724 0.532032i \(-0.178571\pi\)
−0.846724 + 0.532032i \(0.821429\pi\)
\(770\) 0 0
\(771\) 1.46200 1.35654i 1.46200 1.35654i
\(772\) −0.785762 + 0.0885341i −0.785762 + 0.0885341i
\(773\) 0 0 −0.943883 0.330279i \(-0.892857\pi\)
0.943883 + 0.330279i \(0.107143\pi\)
\(774\) 0 0
\(775\) 1.91970 + 0.216299i 1.91970 + 0.216299i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0.733052 + 0.680173i 0.733052 + 0.680173i
\(784\) −1.39596 −1.39596
\(785\) 0 0
\(786\) 0.487076 + 1.57906i 0.487076 + 1.57906i
\(787\) 0 0 −0.433884 0.900969i \(-0.642857\pi\)
0.433884 + 0.900969i \(0.357143\pi\)
\(788\)