Properties

Label 1400.1.cc.a.69.2
Level $1400$
Weight $1$
Character 1400.69
Analytic conductor $0.699$
Analytic rank $0$
Dimension $16$
Projective image $D_{20}$
CM discriminant -56
Inner twists $8$

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Newspace parameters

Level: \( N \) \(=\) \( 1400 = 2^{3} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1400.cc (of order \(10\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.698691017686\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(4\) over \(\Q(\zeta_{10})\)
Coefficient field: \(\Q(\zeta_{40})\)
Defining polynomial: \(x^{16} - x^{12} + x^{8} - x^{4} + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Projective image: \(D_{20}\)
Projective field: Galois closure of \(\mathbb{Q}[x]/(x^{20} - \cdots)\)

Embedding invariants

Embedding label 69.2
Root \(-0.891007 - 0.453990i\) of defining polynomial
Character \(\chi\) \(=\) 1400.69
Dual form 1400.1.cc.a.629.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.951057 + 0.309017i) q^{2} +(1.16110 + 1.59811i) q^{3} +(0.809017 - 0.587785i) q^{4} +(-0.453990 + 0.891007i) q^{5} +(-1.59811 - 1.16110i) q^{6} -1.00000i q^{7} +(-0.587785 + 0.809017i) q^{8} +(-0.896802 + 2.76007i) q^{9} +O(q^{10})\) \(q+(-0.951057 + 0.309017i) q^{2} +(1.16110 + 1.59811i) q^{3} +(0.809017 - 0.587785i) q^{4} +(-0.453990 + 0.891007i) q^{5} +(-1.59811 - 1.16110i) q^{6} -1.00000i q^{7} +(-0.587785 + 0.809017i) q^{8} +(-0.896802 + 2.76007i) q^{9} +(0.156434 - 0.987688i) q^{10} +(1.87869 + 0.610425i) q^{12} +(0.297556 + 0.0966818i) q^{13} +(0.309017 + 0.951057i) q^{14} +(-1.95106 + 0.309017i) q^{15} +(0.309017 - 0.951057i) q^{16} -2.90211i q^{18} +(1.14412 + 0.831254i) q^{19} +(0.156434 + 0.987688i) q^{20} +(1.59811 - 1.16110i) q^{21} +(-1.11803 + 0.363271i) q^{23} -1.97538 q^{24} +(-0.587785 - 0.809017i) q^{25} -0.312869 q^{26} +(-3.57349 + 1.16110i) q^{27} +(-0.587785 - 0.809017i) q^{28} +(1.76007 - 0.896802i) q^{30} +1.00000i q^{32} +(0.891007 + 0.453990i) q^{35} +(0.896802 + 2.76007i) q^{36} +(-1.34500 - 0.437016i) q^{38} +(0.190983 + 0.587785i) q^{39} +(-0.453990 - 0.891007i) q^{40} +(-1.16110 + 1.59811i) q^{42} +(-2.05210 - 2.05210i) q^{45} +(0.951057 - 0.690983i) q^{46} +(1.87869 - 0.610425i) q^{48} -1.00000 q^{49} +(0.809017 + 0.587785i) q^{50} +(0.297556 - 0.0966818i) q^{52} +(3.03979 - 2.20854i) q^{54} +(0.809017 + 0.587785i) q^{56} +2.79360i q^{57} +(0.550672 - 1.69480i) q^{59} +(-1.39680 + 1.39680i) q^{60} +(0.280582 + 0.863541i) q^{61} +(2.76007 + 0.896802i) q^{63} +(-0.309017 - 0.951057i) q^{64} +(-0.221232 + 0.221232i) q^{65} +(-1.87869 - 1.36495i) q^{69} +(-0.987688 - 0.156434i) q^{70} +(1.53884 - 1.11803i) q^{71} +(-1.70582 - 2.34786i) q^{72} +(0.610425 - 1.87869i) q^{75} +1.41421 q^{76} +(-0.363271 - 0.500000i) q^{78} +(0.951057 - 0.690983i) q^{79} +(0.707107 + 0.707107i) q^{80} +(-3.65688 - 2.65688i) q^{81} +(0.533698 - 0.734572i) q^{83} +(0.610425 - 1.87869i) q^{84} +(2.58580 + 1.31753i) q^{90} +(0.0966818 - 0.297556i) q^{91} +(-0.690983 + 0.951057i) q^{92} +(-1.26007 + 0.642040i) q^{95} +(-1.59811 + 1.16110i) q^{96} +(0.951057 - 0.309017i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + 4q^{4} + 4q^{9} + O(q^{10}) \) \( 16q + 4q^{4} + 4q^{9} - 4q^{14} - 16q^{15} - 4q^{16} + 4q^{30} - 4q^{36} + 12q^{39} - 16q^{49} + 4q^{50} + 4q^{56} - 4q^{60} + 20q^{63} + 4q^{64} - 4q^{65} - 16q^{81} - 20q^{92} + 4q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1400\mathbb{Z}\right)^\times\).

\(n\) \(351\) \(701\) \(801\) \(1177\)
\(\chi(n)\) \(1\) \(-1\) \(-1\) \(e\left(\frac{9}{10}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.951057 + 0.309017i −0.951057 + 0.309017i
\(3\) 1.16110 + 1.59811i 1.16110 + 1.59811i 0.707107 + 0.707107i \(0.250000\pi\)
0.453990 + 0.891007i \(0.350000\pi\)
\(4\) 0.809017 0.587785i 0.809017 0.587785i
\(5\) −0.453990 + 0.891007i −0.453990 + 0.891007i
\(6\) −1.59811 1.16110i −1.59811 1.16110i
\(7\) 1.00000i 1.00000i
\(8\) −0.587785 + 0.809017i −0.587785 + 0.809017i
\(9\) −0.896802 + 2.76007i −0.896802 + 2.76007i
\(10\) 0.156434 0.987688i 0.156434 0.987688i
\(11\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(12\) 1.87869 + 0.610425i 1.87869 + 0.610425i
\(13\) 0.297556 + 0.0966818i 0.297556 + 0.0966818i 0.453990 0.891007i \(-0.350000\pi\)
−0.156434 + 0.987688i \(0.550000\pi\)
\(14\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(15\) −1.95106 + 0.309017i −1.95106 + 0.309017i
\(16\) 0.309017 0.951057i 0.309017 0.951057i
\(17\) 0 0 0.587785 0.809017i \(-0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(18\) 2.90211i 2.90211i
\(19\) 1.14412 + 0.831254i 1.14412 + 0.831254i 0.987688 0.156434i \(-0.0500000\pi\)
0.156434 + 0.987688i \(0.450000\pi\)
\(20\) 0.156434 + 0.987688i 0.156434 + 0.987688i
\(21\) 1.59811 1.16110i 1.59811 1.16110i
\(22\) 0 0
\(23\) −1.11803 + 0.363271i −1.11803 + 0.363271i −0.809017 0.587785i \(-0.800000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(24\) −1.97538 −1.97538
\(25\) −0.587785 0.809017i −0.587785 0.809017i
\(26\) −0.312869 −0.312869
\(27\) −3.57349 + 1.16110i −3.57349 + 1.16110i
\(28\) −0.587785 0.809017i −0.587785 0.809017i
\(29\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(30\) 1.76007 0.896802i 1.76007 0.896802i
\(31\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(32\) 1.00000i 1.00000i
\(33\) 0 0
\(34\) 0 0
\(35\) 0.891007 + 0.453990i 0.891007 + 0.453990i
\(36\) 0.896802 + 2.76007i 0.896802 + 2.76007i
\(37\) 0 0 −0.951057 0.309017i \(-0.900000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(38\) −1.34500 0.437016i −1.34500 0.437016i
\(39\) 0.190983 + 0.587785i 0.190983 + 0.587785i
\(40\) −0.453990 0.891007i −0.453990 0.891007i
\(41\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(42\) −1.16110 + 1.59811i −1.16110 + 1.59811i
\(43\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(44\) 0 0
\(45\) −2.05210 2.05210i −2.05210 2.05210i
\(46\) 0.951057 0.690983i 0.951057 0.690983i
\(47\) 0 0 −0.587785 0.809017i \(-0.700000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(48\) 1.87869 0.610425i 1.87869 0.610425i
\(49\) −1.00000 −1.00000
\(50\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(51\) 0 0
\(52\) 0.297556 0.0966818i 0.297556 0.0966818i
\(53\) 0 0 −0.587785 0.809017i \(-0.700000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(54\) 3.03979 2.20854i 3.03979 2.20854i
\(55\) 0 0
\(56\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(57\) 2.79360i 2.79360i
\(58\) 0 0
\(59\) 0.550672 1.69480i 0.550672 1.69480i −0.156434 0.987688i \(-0.550000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(60\) −1.39680 + 1.39680i −1.39680 + 1.39680i
\(61\) 0.280582 + 0.863541i 0.280582 + 0.863541i 0.987688 + 0.156434i \(0.0500000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(62\) 0 0
\(63\) 2.76007 + 0.896802i 2.76007 + 0.896802i
\(64\) −0.309017 0.951057i −0.309017 0.951057i
\(65\) −0.221232 + 0.221232i −0.221232 + 0.221232i
\(66\) 0 0
\(67\) 0 0 0.587785 0.809017i \(-0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(68\) 0 0
\(69\) −1.87869 1.36495i −1.87869 1.36495i
\(70\) −0.987688 0.156434i −0.987688 0.156434i
\(71\) 1.53884 1.11803i 1.53884 1.11803i 0.587785 0.809017i \(-0.300000\pi\)
0.951057 0.309017i \(-0.100000\pi\)
\(72\) −1.70582 2.34786i −1.70582 2.34786i
\(73\) 0 0 0.951057 0.309017i \(-0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(74\) 0 0
\(75\) 0.610425 1.87869i 0.610425 1.87869i
\(76\) 1.41421 1.41421
\(77\) 0 0
\(78\) −0.363271 0.500000i −0.363271 0.500000i
\(79\) 0.951057 0.690983i 0.951057 0.690983i 1.00000i \(-0.5\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(80\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(81\) −3.65688 2.65688i −3.65688 2.65688i
\(82\) 0 0
\(83\) 0.533698 0.734572i 0.533698 0.734572i −0.453990 0.891007i \(-0.650000\pi\)
0.987688 + 0.156434i \(0.0500000\pi\)
\(84\) 0.610425 1.87869i 0.610425 1.87869i
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(90\) 2.58580 + 1.31753i 2.58580 + 1.31753i
\(91\) 0.0966818 0.297556i 0.0966818 0.297556i
\(92\) −0.690983 + 0.951057i −0.690983 + 0.951057i
\(93\) 0 0
\(94\) 0 0
\(95\) −1.26007 + 0.642040i −1.26007 + 0.642040i
\(96\) −1.59811 + 1.16110i −1.59811 + 1.16110i
\(97\) 0 0 −0.587785 0.809017i \(-0.700000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(98\) 0.951057 0.309017i 0.951057 0.309017i
\(99\) 0 0
\(100\) −0.951057 0.309017i −0.951057 0.309017i
\(101\) 0.312869 0.312869 0.156434 0.987688i \(-0.450000\pi\)
0.156434 + 0.987688i \(0.450000\pi\)
\(102\) 0 0
\(103\) 0 0 −0.587785 0.809017i \(-0.700000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(104\) −0.253116 + 0.183900i −0.253116 + 0.183900i
\(105\) 0.309017 + 1.95106i 0.309017 + 1.95106i
\(106\) 0 0
\(107\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(108\) −2.20854 + 3.03979i −2.20854 + 3.03979i
\(109\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) −0.951057 0.309017i −0.951057 0.309017i
\(113\) 0.587785 + 0.190983i 0.587785 + 0.190983i 0.587785 0.809017i \(-0.300000\pi\)
1.00000i \(0.5\pi\)
\(114\) −0.863271 2.65688i −0.863271 2.65688i
\(115\) 0.183900 1.16110i 0.183900 1.16110i
\(116\) 0 0
\(117\) −0.533698 + 0.734572i −0.533698 + 0.734572i
\(118\) 1.78201i 1.78201i
\(119\) 0 0
\(120\) 0.896802 1.76007i 0.896802 1.76007i
\(121\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(122\) −0.533698 0.734572i −0.533698 0.734572i
\(123\) 0 0
\(124\) 0 0
\(125\) 0.987688 0.156434i 0.987688 0.156434i
\(126\) −2.90211 −2.90211
\(127\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(128\) 0.587785 + 0.809017i 0.587785 + 0.809017i
\(129\) 0 0
\(130\) 0.142040 0.278768i 0.142040 0.278768i
\(131\) 0.734572 + 0.533698i 0.734572 + 0.533698i 0.891007 0.453990i \(-0.150000\pi\)
−0.156434 + 0.987688i \(0.550000\pi\)
\(132\) 0 0
\(133\) 0.831254 1.14412i 0.831254 1.14412i
\(134\) 0 0
\(135\) 0.587785 3.71113i 0.587785 3.71113i
\(136\) 0 0
\(137\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(138\) 2.20854 + 0.717598i 2.20854 + 0.717598i
\(139\) 0.437016 + 1.34500i 0.437016 + 1.34500i 0.891007 + 0.453990i \(0.150000\pi\)
−0.453990 + 0.891007i \(0.650000\pi\)
\(140\) 0.987688 0.156434i 0.987688 0.156434i
\(141\) 0 0
\(142\) −1.11803 + 1.53884i −1.11803 + 1.53884i
\(143\) 0 0
\(144\) 2.34786 + 1.70582i 2.34786 + 1.70582i
\(145\) 0 0
\(146\) 0 0
\(147\) −1.16110 1.59811i −1.16110 1.59811i
\(148\) 0 0
\(149\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(150\) 1.97538i 1.97538i
\(151\) 1.61803 1.61803 0.809017 0.587785i \(-0.200000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(152\) −1.34500 + 0.437016i −1.34500 + 0.437016i
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 0.500000 + 0.363271i 0.500000 + 0.363271i
\(157\) 0.907981i 0.907981i 0.891007 + 0.453990i \(0.150000\pi\)
−0.891007 + 0.453990i \(0.850000\pi\)
\(158\) −0.690983 + 0.951057i −0.690983 + 0.951057i
\(159\) 0 0
\(160\) −0.891007 0.453990i −0.891007 0.453990i
\(161\) 0.363271 + 1.11803i 0.363271 + 1.11803i
\(162\) 4.29892 + 1.39680i 4.29892 + 1.39680i
\(163\) 0 0 −0.951057 0.309017i \(-0.900000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) −0.280582 + 0.863541i −0.280582 + 0.863541i
\(167\) 0 0 0.587785 0.809017i \(-0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(168\) 1.97538i 1.97538i
\(169\) −0.729825 0.530249i −0.729825 0.530249i
\(170\) 0 0
\(171\) −3.32037 + 2.41239i −3.32037 + 2.41239i
\(172\) 0 0
\(173\) −1.69480 + 0.550672i −1.69480 + 0.550672i −0.987688 0.156434i \(-0.950000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(174\) 0 0
\(175\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(176\) 0 0
\(177\) 3.34786 1.08779i 3.34786 1.08779i
\(178\) 0 0
\(179\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(180\) −2.86638 0.453990i −2.86638 0.453990i
\(181\) −1.44168 1.04744i −1.44168 1.04744i −0.987688 0.156434i \(-0.950000\pi\)
−0.453990 0.891007i \(-0.650000\pi\)
\(182\) 0.312869i 0.312869i
\(183\) −1.05425 + 1.45106i −1.05425 + 1.45106i
\(184\) 0.363271 1.11803i 0.363271 1.11803i
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 1.16110 + 3.57349i 1.16110 + 3.57349i
\(190\) 1.00000 1.00000i 1.00000 1.00000i
\(191\) −0.363271 + 1.11803i −0.363271 + 1.11803i 0.587785 + 0.809017i \(0.300000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(192\) 1.16110 1.59811i 1.16110 1.59811i
\(193\) 0.618034i 0.618034i −0.951057 0.309017i \(-0.900000\pi\)
0.951057 0.309017i \(-0.100000\pi\)
\(194\) 0 0
\(195\) −0.610425 0.0966818i −0.610425 0.0966818i
\(196\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(197\) 0 0 −0.587785 0.809017i \(-0.700000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(198\) 0 0
\(199\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(200\) 1.00000 1.00000
\(201\) 0 0
\(202\) −0.297556 + 0.0966818i −0.297556 + 0.0966818i
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 3.41164i 3.41164i
\(208\) 0.183900 0.253116i 0.183900 0.253116i
\(209\) 0 0
\(210\) −0.896802 1.76007i −0.896802 1.76007i
\(211\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(212\) 0 0
\(213\) 3.57349 + 1.16110i 3.57349 + 1.16110i
\(214\) 0 0
\(215\) 0 0
\(216\) 1.16110 3.57349i 1.16110 3.57349i
\(217\) 0 0
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 0 0 0.951057 0.309017i \(-0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(224\) 1.00000 1.00000
\(225\) 2.76007 0.896802i 2.76007 0.896802i
\(226\) −0.618034 −0.618034
\(227\) 1.87869 0.610425i 1.87869 0.610425i 0.891007 0.453990i \(-0.150000\pi\)
0.987688 0.156434i \(-0.0500000\pi\)
\(228\) 1.64204 + 2.26007i 1.64204 + 2.26007i
\(229\) −1.44168 + 1.04744i −1.44168 + 1.04744i −0.453990 + 0.891007i \(0.650000\pi\)
−0.987688 + 0.156434i \(0.950000\pi\)
\(230\) 0.183900 + 1.16110i 0.183900 + 1.16110i
\(231\) 0 0
\(232\) 0 0
\(233\) 1.11803 1.53884i 1.11803 1.53884i 0.309017 0.951057i \(-0.400000\pi\)
0.809017 0.587785i \(-0.200000\pi\)
\(234\) 0.280582 0.863541i 0.280582 0.863541i
\(235\) 0 0
\(236\) −0.550672 1.69480i −0.550672 1.69480i
\(237\) 2.20854 + 0.717598i 2.20854 + 0.717598i
\(238\) 0 0
\(239\) −0.500000 1.53884i −0.500000 1.53884i −0.809017 0.587785i \(-0.800000\pi\)
0.309017 0.951057i \(-0.400000\pi\)
\(240\) −0.309017 + 1.95106i −0.309017 + 1.95106i
\(241\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(242\) 0.587785 0.809017i 0.587785 0.809017i
\(243\) 5.17160i 5.17160i
\(244\) 0.734572 + 0.533698i 0.734572 + 0.533698i
\(245\) 0.453990 0.891007i 0.453990 0.891007i
\(246\) 0 0
\(247\) 0.260074 + 0.357960i 0.260074 + 0.357960i
\(248\) 0 0
\(249\) 1.79360 1.79360
\(250\) −0.891007 + 0.453990i −0.891007 + 0.453990i
\(251\) 0.907981 0.907981 0.453990 0.891007i \(-0.350000\pi\)
0.453990 + 0.891007i \(0.350000\pi\)
\(252\) 2.76007 0.896802i 2.76007 0.896802i
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) −0.809017 0.587785i −0.809017 0.587785i
\(257\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) −0.0489435 + 0.309017i −0.0489435 + 0.309017i
\(261\) 0 0
\(262\) −0.863541 0.280582i −0.863541 0.280582i
\(263\) −1.53884 0.500000i −1.53884 0.500000i −0.587785 0.809017i \(-0.700000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) −0.437016 + 1.34500i −0.437016 + 1.34500i
\(267\) 0 0
\(268\) 0 0
\(269\) 1.44168 + 1.04744i 1.44168 + 1.04744i 0.987688 + 0.156434i \(0.0500000\pi\)
0.453990 + 0.891007i \(0.350000\pi\)
\(270\) 0.587785 + 3.71113i 0.587785 + 3.71113i
\(271\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(272\) 0 0
\(273\) 0.587785 0.190983i 0.587785 0.190983i
\(274\) 0 0
\(275\) 0 0
\(276\) −2.32219 −2.32219
\(277\) 0 0 0.951057 0.309017i \(-0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(278\) −0.831254 1.14412i −0.831254 1.14412i
\(279\) 0 0
\(280\) −0.891007 + 0.453990i −0.891007 + 0.453990i
\(281\) 0.500000 + 0.363271i 0.500000 + 0.363271i 0.809017 0.587785i \(-0.200000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(282\) 0 0
\(283\) 1.16110 1.59811i 1.16110 1.59811i 0.453990 0.891007i \(-0.350000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(284\) 0.587785 1.80902i 0.587785 1.80902i
\(285\) −2.48912 1.26827i −2.48912 1.26827i
\(286\) 0 0
\(287\) 0 0
\(288\) −2.76007 0.896802i −2.76007 0.896802i
\(289\) −0.309017 0.951057i −0.309017 0.951057i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(294\) 1.59811 + 1.16110i 1.59811 + 1.16110i
\(295\) 1.26007 + 1.26007i 1.26007 + 1.26007i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −0.367799 −0.367799
\(300\) −0.610425 1.87869i −0.610425 1.87869i
\(301\) 0 0
\(302\) −1.53884 + 0.500000i −1.53884 + 0.500000i
\(303\) 0.363271 + 0.500000i 0.363271 + 0.500000i
\(304\) 1.14412 0.831254i 1.14412 0.831254i
\(305\) −0.896802 0.142040i −0.896802 0.142040i
\(306\) 0 0
\(307\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(312\) −0.587785 0.190983i −0.587785 0.190983i
\(313\) 0 0 −0.951057 0.309017i \(-0.900000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(314\) −0.280582 0.863541i −0.280582 0.863541i
\(315\) −2.05210 + 2.05210i −2.05210 + 2.05210i
\(316\) 0.363271 1.11803i 0.363271 1.11803i
\(317\) 0 0 0.587785 0.809017i \(-0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0.987688 + 0.156434i 0.987688 + 0.156434i
\(321\) 0 0
\(322\) −0.690983 0.951057i −0.690983 0.951057i
\(323\) 0 0
\(324\) −4.52015 −4.52015
\(325\) −0.0966818 0.297556i −0.0966818 0.297556i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(332\) 0.907981i 0.907981i
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) −0.610425 1.87869i −0.610425 1.87869i
\(337\) −1.53884 0.500000i −1.53884 0.500000i −0.587785 0.809017i \(-0.700000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(338\) 0.857960 + 0.278768i 0.857960 + 0.278768i
\(339\) 0.377263 + 1.16110i 0.377263 + 1.16110i
\(340\) 0 0
\(341\) 0 0
\(342\) 2.41239 3.32037i 2.41239 3.32037i
\(343\) 1.00000i 1.00000i
\(344\) 0 0
\(345\) 2.06909 1.05425i 2.06909 1.05425i
\(346\) 1.44168 1.04744i 1.44168 1.04744i
\(347\) 0 0 −0.587785 0.809017i \(-0.700000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(348\) 0 0
\(349\) 0.312869 0.312869 0.156434 0.987688i \(-0.450000\pi\)
0.156434 + 0.987688i \(0.450000\pi\)
\(350\) 0.587785 0.809017i 0.587785 0.809017i
\(351\) −1.17557 −1.17557
\(352\) 0 0
\(353\) 0 0 −0.587785 0.809017i \(-0.700000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(354\) −2.84786 + 2.06909i −2.84786 + 2.06909i
\(355\) 0.297556 + 1.87869i 0.297556 + 1.87869i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 0.500000 1.53884i 0.500000 1.53884i −0.309017 0.951057i \(-0.600000\pi\)
0.809017 0.587785i \(-0.200000\pi\)
\(360\) 2.86638 0.453990i 2.86638 0.453990i
\(361\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(362\) 1.69480 + 0.550672i 1.69480 + 0.550672i
\(363\) −1.87869 0.610425i −1.87869 0.610425i
\(364\) −0.0966818 0.297556i −0.0966818 0.297556i
\(365\) 0 0
\(366\) 0.554254 1.70582i 0.554254 1.70582i
\(367\) 0 0 0.587785 0.809017i \(-0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(368\) 1.17557i 1.17557i
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 0 0 0.951057 0.309017i \(-0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(374\) 0 0
\(375\) 1.39680 + 1.39680i 1.39680 + 1.39680i
\(376\) 0 0
\(377\) 0 0
\(378\) −2.20854 3.03979i −2.20854 3.03979i
\(379\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(380\) −0.642040 + 1.26007i −0.642040 + 1.26007i
\(381\) 0 0
\(382\) 1.17557i 1.17557i
\(383\) 0 0 0.587785 0.809017i \(-0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(384\) −0.610425 + 1.87869i −0.610425 + 1.87869i
\(385\) 0 0
\(386\) 0.190983 + 0.587785i 0.190983 + 0.587785i
\(387\) 0 0
\(388\) 0 0
\(389\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(390\) 0.610425 0.0966818i 0.610425 0.0966818i
\(391\) 0 0
\(392\) 0.587785 0.809017i 0.587785 0.809017i
\(393\) 1.79360i 1.79360i
\(394\) 0 0
\(395\) 0.183900 + 1.16110i 0.183900 + 1.16110i
\(396\) 0 0
\(397\) −0.183900 0.253116i −0.183900 0.253116i 0.707107 0.707107i \(-0.250000\pi\)
−0.891007 + 0.453990i \(0.850000\pi\)
\(398\) 0 0
\(399\) 2.79360 2.79360
\(400\) −0.951057 + 0.309017i −0.951057 + 0.309017i
\(401\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0.253116 0.183900i 0.253116 0.183900i
\(405\) 4.02748 2.05210i 4.02748 2.05210i
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −1.69480 0.550672i −1.69480 0.550672i
\(414\) 1.05425 + 3.24466i 1.05425 + 3.24466i
\(415\) 0.412215 + 0.809017i 0.412215 + 0.809017i
\(416\) −0.0966818 + 0.297556i −0.0966818 + 0.297556i
\(417\) −1.64204 + 2.26007i −1.64204 + 2.26007i
\(418\) 0 0
\(419\) −1.59811 1.16110i −1.59811 1.16110i −0.891007 0.453990i \(-0.850000\pi\)
−0.707107 0.707107i \(-0.750000\pi\)
\(420\) 1.39680 + 1.39680i 1.39680 + 1.39680i
\(421\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 0 0
\(426\) −3.75739 −3.75739
\(427\) 0.863541 0.280582i 0.863541 0.280582i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −0.500000 0.363271i −0.500000 0.363271i 0.309017 0.951057i \(-0.400000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(432\) 3.75739i 3.75739i
\(433\) 0 0 0.587785 0.809017i \(-0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −1.58114 0.513743i −1.58114 0.513743i
\(438\) 0 0
\(439\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(440\) 0 0
\(441\) 0.896802 2.76007i 0.896802 2.76007i
\(442\) 0 0
\(443\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) −0.951057 + 0.309017i −0.951057 + 0.309017i
\(449\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(450\) −2.34786 + 1.70582i −2.34786 + 1.70582i
\(451\) 0 0
\(452\) 0.587785 0.190983i 0.587785 0.190983i
\(453\) 1.87869 + 2.58580i 1.87869 + 2.58580i
\(454\) −1.59811 + 1.16110i −1.59811 + 1.16110i
\(455\) 0.221232 + 0.221232i 0.221232 + 0.221232i
\(456\) −2.26007 1.64204i −2.26007 1.64204i
\(457\) 0.618034i 0.618034i −0.951057 0.309017i \(-0.900000\pi\)
0.951057 0.309017i \(-0.100000\pi\)
\(458\) 1.04744 1.44168i 1.04744 1.44168i
\(459\) 0 0
\(460\) −0.533698 1.04744i −0.533698 1.04744i
\(461\) 0.437016 + 1.34500i 0.437016 + 1.34500i 0.891007 + 0.453990i \(0.150000\pi\)
−0.453990 + 0.891007i \(0.650000\pi\)
\(462\) 0 0
\(463\) −0.587785 0.190983i −0.587785 0.190983i 1.00000i \(-0.5\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) −0.587785 + 1.80902i −0.587785 + 1.80902i
\(467\) −0.831254 + 1.14412i −0.831254 + 1.14412i 0.156434 + 0.987688i \(0.450000\pi\)
−0.987688 + 0.156434i \(0.950000\pi\)
\(468\) 0.907981i 0.907981i
\(469\) 0 0
\(470\) 0 0
\(471\) −1.45106 + 1.05425i −1.45106 + 1.05425i
\(472\) 1.04744 + 1.44168i 1.04744 + 1.44168i
\(473\) 0 0
\(474\) −2.32219 −2.32219
\(475\) 1.41421i 1.41421i
\(476\) 0 0
\(477\) 0 0
\(478\) 0.951057 + 1.30902i 0.951057 + 1.30902i
\(479\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(480\) −0.309017 1.95106i −0.309017 1.95106i
\(481\) 0 0
\(482\) 0 0
\(483\) −1.36495 + 1.87869i −1.36495 + 1.87869i
\(484\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(485\) 0 0
\(486\) 1.59811 + 4.91849i 1.59811 + 4.91849i
\(487\) 1.80902 + 0.587785i 1.80902 + 0.587785i 1.00000 \(0\)
0.809017 + 0.587785i \(0.200000\pi\)
\(488\) −0.863541 0.280582i −0.863541 0.280582i
\(489\) 0 0
\(490\) −0.156434 + 0.987688i −0.156434 + 0.987688i
\(491\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) −0.357960 0.260074i −0.357960 0.260074i
\(495\) 0 0
\(496\) 0 0
\(497\) −1.11803 1.53884i −1.11803 1.53884i
\(498\) −1.70582 + 0.554254i −1.70582 + 0.554254i
\(499\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(500\) 0.707107 0.707107i 0.707107 0.707107i
\(501\) 0 0
\(502\) −0.863541 + 0.280582i −0.863541 + 0.280582i
\(503\) 0 0 −0.587785 0.809017i \(-0.700000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(504\) −2.34786 + 1.70582i −2.34786 + 1.70582i
\(505\) −0.142040 + 0.278768i −0.142040 + 0.278768i
\(506\) 0 0
\(507\) 1.78201i 1.78201i
\(508\) 0 0
\(509\) 0.437016 1.34500i 0.437016 1.34500i −0.453990 0.891007i \(-0.650000\pi\)
0.891007 0.453990i \(-0.150000\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0.951057 + 0.309017i 0.951057 + 0.309017i
\(513\) −5.05368 1.64204i −5.05368 1.64204i
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) −2.84786 2.06909i −2.84786 2.06909i
\(520\) −0.0489435 0.309017i −0.0489435 0.309017i
\(521\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(522\) 0 0
\(523\) 0.297556 0.0966818i 0.297556 0.0966818i −0.156434 0.987688i \(-0.550000\pi\)
0.453990 + 0.891007i \(0.350000\pi\)
\(524\) 0.907981 0.907981
\(525\) −1.87869 0.610425i −1.87869 0.610425i
\(526\) 1.61803 1.61803
\(527\) 0 0
\(528\) 0 0
\(529\) 0.309017 0.224514i 0.309017 0.224514i
\(530\) 0 0
\(531\) 4.18391 + 3.03979i 4.18391 + 3.03979i
\(532\) 1.41421i 1.41421i
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) −1.69480 0.550672i −1.69480 0.550672i
\(539\) 0 0
\(540\) −1.70582 3.34786i −1.70582 3.34786i
\(541\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(542\) 0 0
\(543\) 3.52015i 3.52015i
\(544\) 0 0
\(545\) 0 0
\(546\) −0.500000 + 0.363271i −0.500000 + 0.363271i
\(547\) 0 0 −0.587785 0.809017i \(-0.700000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(548\) 0 0
\(549\) −2.63506 −2.63506
\(550\) 0 0
\(551\) 0 0
\(552\) 2.20854 0.717598i 2.20854 0.717598i
\(553\) −0.690983 0.951057i −0.690983 0.951057i
\(554\) 0 0
\(555\) 0 0
\(556\) 1.14412 + 0.831254i 1.14412 + 0.831254i
\(557\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0.707107 0.707107i 0.707107 0.707107i
\(561\) 0 0
\(562\) −0.587785 0.190983i −0.587785 0.190983i
\(563\) −0.297556 0.0966818i −0.297556 0.0966818i 0.156434 0.987688i \(-0.450000\pi\)
−0.453990 + 0.891007i \(0.650000\pi\)
\(564\) 0 0
\(565\) −0.437016 + 0.437016i −0.437016 + 0.437016i
\(566\) −0.610425 + 1.87869i −0.610425 + 1.87869i
\(567\) −2.65688 + 3.65688i −2.65688 + 3.65688i
\(568\) 1.90211i 1.90211i
\(569\) −0.951057 0.690983i −0.951057 0.690983i 1.00000i \(-0.5\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(570\) 2.75921 + 0.437016i 2.75921 + 0.437016i
\(571\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(572\) 0 0
\(573\) −2.20854 + 0.717598i −2.20854 + 0.717598i
\(574\) 0 0
\(575\) 0.951057 + 0.690983i 0.951057 + 0.690983i
\(576\) 2.90211 2.90211
\(577\) 0 0 0.951057 0.309017i \(-0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(578\) 0.587785 + 0.809017i 0.587785 + 0.809017i
\(579\) 0.987688 0.717598i 0.987688 0.717598i
\(580\) 0 0
\(581\) −0.734572 0.533698i −0.734572 0.533698i
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) −0.412215 0.809017i −0.412215 0.809017i
\(586\) −0.437016 1.34500i −0.437016 1.34500i
\(587\) −1.69480 0.550672i −1.69480 0.550672i −0.707107 0.707107i \(-0.750000\pi\)
−0.987688 + 0.156434i \(0.950000\pi\)
\(588\) −1.87869 0.610425i −1.87869 0.610425i
\(589\) 0 0
\(590\) −1.58779 0.809017i −1.58779 0.809017i
\(591\) 0 0
\(592\) 0 0
\(593\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0.349798 0.113656i 0.349798 0.113656i
\(599\) −1.17557 −1.17557 −0.587785 0.809017i \(-0.700000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(600\) 1.16110 + 1.59811i 1.16110 + 1.59811i
\(601\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 1.30902 0.951057i 1.30902 0.951057i
\(605\) −0.156434 0.987688i −0.156434 0.987688i
\(606\) −0.500000 0.363271i −0.500000 0.363271i
\(607\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(608\) −0.831254 + 1.14412i −0.831254 + 1.14412i
\(609\) 0 0
\(610\) 0.896802 0.142040i 0.896802 0.142040i
\(611\) 0 0
\(612\) 0 0
\(613\) 0 0 −0.951057 0.309017i \(-0.900000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(614\) −0.437016 1.34500i −0.437016 1.34500i
\(615\) 0 0
\(616\) 0 0
\(617\) 0.951057 1.30902i 0.951057 1.30902i 1.00000i \(-0.5\pi\)
0.951057 0.309017i \(-0.100000\pi\)
\(618\) 0 0
\(619\) −1.44168 1.04744i −1.44168 1.04744i −0.987688 0.156434i \(-0.950000\pi\)
−0.453990 0.891007i \(-0.650000\pi\)
\(620\) 0 0
\(621\) 3.57349 2.59629i 3.57349 2.59629i
\(622\) 0 0
\(623\) 0 0
\(624\) 0.618034 0.618034
\(625\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(626\) 0 0
\(627\) 0 0
\(628\) 0.533698 + 0.734572i 0.533698 + 0.734572i
\(629\) 0 0
\(630\) 1.31753 2.58580i 1.31753 2.58580i
\(631\) 1.53884 + 1.11803i 1.53884 + 1.11803i 0.951057 + 0.309017i \(0.100000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(632\) 1.17557i 1.17557i
\(633\) 0 0
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) −0.297556 0.0966818i −0.297556 0.0966818i
\(638\) 0 0
\(639\) 1.70582 + 5.24997i 1.70582 + 5.24997i
\(640\) −0.987688 + 0.156434i −0.987688 + 0.156434i
\(641\) −0.363271 + 1.11803i −0.363271 + 1.11803i 0.587785 + 0.809017i \(0.300000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(642\) 0 0
\(643\) 0.907981i 0.907981i −0.891007 0.453990i \(-0.850000\pi\)
0.891007 0.453990i \(-0.150000\pi\)
\(644\) 0.951057 + 0.690983i 0.951057 + 0.690983i
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 −0.587785 0.809017i \(-0.700000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(648\) 4.29892 1.39680i 4.29892 1.39680i
\(649\) 0 0
\(650\) 0.183900 + 0.253116i 0.183900 + 0.253116i
\(651\) 0 0
\(652\) 0 0
\(653\) 0 0 −0.587785 0.809017i \(-0.700000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(654\) 0 0
\(655\) −0.809017 + 0.412215i −0.809017 + 0.412215i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(660\) 0 0
\(661\) −0.280582 0.863541i −0.280582 0.863541i −0.987688 0.156434i \(-0.950000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0.280582 + 0.863541i 0.280582 + 0.863541i
\(665\) 0.642040 + 1.26007i 0.642040 + 1.26007i
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 1.16110 + 1.59811i 1.16110 + 1.59811i
\(673\) 1.80902 0.587785i 1.80902 0.587785i 0.809017 0.587785i \(-0.200000\pi\)
1.00000 \(0\)
\(674\) 1.61803 1.61803
\(675\) 3.03979 + 2.20854i 3.03979 + 2.20854i
\(676\) −0.902113 −0.902113
\(677\) −0.863541 + 0.280582i −0.863541 + 0.280582i −0.707107 0.707107i \(-0.750000\pi\)
−0.156434 + 0.987688i \(0.550000\pi\)
\(678\) −0.717598 0.987688i −0.717598 0.987688i
\(679\) 0 0
\(680\) 0 0
\(681\) 3.15688 + 2.29360i 3.15688 + 2.29360i
\(682\) 0 0
\(683\) 0 0 0.587785 0.809017i \(-0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(684\) −1.26827 + 3.90333i −1.26827 + 3.90333i
\(685\) 0 0
\(686\) −0.309017 0.951057i −0.309017 0.951057i
\(687\) −3.34786 1.08779i −3.34786 1.08779i
\(688\) 0 0
\(689\) 0 0
\(690\) −1.64204 + 1.64204i −1.64204 + 1.64204i
\(691\) −0.0966818 + 0.297556i −0.0966818 + 0.297556i −0.987688 0.156434i \(-0.950000\pi\)
0.891007 + 0.453990i \(0.150000\pi\)
\(692\) −1.04744 + 1.44168i −1.04744 + 1.44168i
\(693\) 0 0
\(694\) 0 0
\(695\) −1.39680 0.221232i −1.39680 0.221232i
\(696\) 0 0
\(697\) 0 0
\(698\) −0.297556 + 0.0966818i −0.297556 + 0.0966818i
\(699\) 3.75739 3.75739
\(700\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(701\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(702\) 1.11803 0.363271i 1.11803 0.363271i
\(703\) 0 0
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 0.312869i 0.312869i
\(708\) 2.06909 2.84786i 2.06909 2.84786i
\(709\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(710\) −0.863541 1.69480i −0.863541 1.69480i
\(711\) 1.05425 + 3.24466i 1.05425 + 3.24466i
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 1.87869 2.58580i 1.87869 2.58580i
\(718\) 1.61803i 1.61803i
\(719\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(720\) −2.58580 + 1.31753i −2.58580 + 1.31753i
\(721\) 0 0
\(722\) −0.587785 0.809017i −0.587785 0.809017i
\(723\) 0 0
\(724\) −1.78201 −1.78201
\(725\) 0 0
\(726\) 1.97538 1.97538
\(727\) 0 0 0.951057 0.309017i \(-0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(728\) 0.183900 + 0.253116i 0.183900 + 0.253116i
\(729\) 4.60793 3.34786i 4.60793 3.34786i
\(730\) 0 0
\(731\) 0 0
\(732\) 1.79360i 1.79360i
\(733\) 1.04744 1.44168i 1.04744 1.44168i 0.156434 0.987688i \(-0.450000\pi\)
0.891007 0.453990i \(-0.150000\pi\)
\(734\) 0 0
\(735\) 1.95106 0.309017i 1.95106 0.309017i
\(736\) −0.363271 1.11803i −0.363271 1.11803i
\(737\) 0 0
\(738\) 0 0
\(739\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(740\) 0 0
\(741\) −0.270091 + 0.831254i −0.270091 + 0.831254i
\(742\) 0 0
\(743\) 1.90211i 1.90211i −0.309017 0.951057i \(-0.600000\pi\)
0.309017 0.951057i \(-0.400000\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 1.54885 + 2.13181i 1.54885 + 2.13181i
\(748\) 0 0
\(749\) 0 0
\(750\) −1.76007 0.896802i −1.76007 0.896802i
\(751\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(752\) 0 0
\(753\) 1.05425 + 1.45106i 1.05425 + 1.45106i
\(754\) 0 0
\(755\) −0.734572 + 1.44168i −0.734572 + 1.44168i
\(756\) 3.03979 + 2.20854i 3.03979 + 2.20854i
\(757\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0.221232 1.39680i 0.221232 1.39680i
\(761\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0.363271 + 1.11803i 0.363271 + 1.11803i
\(765\) 0 0
\(766\) 0 0
\(767\) 0.327712 0.451057i 0.327712 0.451057i
\(768\) 1.97538i 1.97538i
\(769\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −0.363271 0.500000i −0.363271 0.500000i
\(773\) −1.87869 + 0.610425i −1.87869 + 0.610425i −0.891007 + 0.453990i \(0.850000\pi\)
−0.987688 + 0.156434i \(0.950000\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0 0
\(780\) −0.550672 + 0.280582i −0.550672 + 0.280582i
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(785\) −0.809017 0.412215i −0.809017 0.412215i
\(786\) −0.554254 1.70582i −0.554254 1.70582i
\(787\) −1.34500 0.437016i −1.34500 0.437016i −0.453990 0.891007i \(-0.650000\pi\)
−0.891007 + 0.453990i \(0.850000\pi\)
\(788\) 0 0
\(789\) −0.987688 3.03979i −0.987688 3.03979i
\(790\) −0.533698 1.04744i −0.533698 1.04744i
\(791\) 0.190983 0.587785i 0.190983 0.587785i
\(792\) 0 0
\(793\) 0.284079i 0.284079i
\(794\) 0.253116 + 0.183900i 0.253116 + 0.183900i
\(795\) 0 0
\(796\)