Properties

Label 1400.1.cc.a.629.3
Level $1400$
Weight $1$
Character 1400.629
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 629.3
Root \(0.453990 + 0.891007i\) of defining polynomial
Character \(\chi\) \(=\) 1400.629
Dual form 1400.1.cc.a.69.3

$q$-expansion

\(f(q)\) \(=\) \(q+(0.951057 + 0.309017i) q^{2} +(-0.183900 + 0.253116i) q^{3} +(0.809017 + 0.587785i) q^{4} +(0.891007 - 0.453990i) q^{5} +(-0.253116 + 0.183900i) q^{6} -1.00000i q^{7} +(0.587785 + 0.809017i) q^{8} +(0.278768 + 0.857960i) q^{9} +O(q^{10})\) \(q+(0.951057 + 0.309017i) q^{2} +(-0.183900 + 0.253116i) q^{3} +(0.809017 + 0.587785i) q^{4} +(0.891007 - 0.453990i) q^{5} +(-0.253116 + 0.183900i) q^{6} -1.00000i q^{7} +(0.587785 + 0.809017i) q^{8} +(0.278768 + 0.857960i) q^{9} +(0.987688 - 0.156434i) q^{10} +(-0.297556 + 0.0966818i) q^{12} +(-1.87869 + 0.610425i) q^{13} +(0.309017 - 0.951057i) q^{14} +(-0.0489435 + 0.309017i) q^{15} +(0.309017 + 0.951057i) q^{16} +0.902113i q^{18} +(1.14412 - 0.831254i) q^{19} +(0.987688 + 0.156434i) q^{20} +(0.253116 + 0.183900i) q^{21} +(-1.11803 - 0.363271i) q^{23} -0.312869 q^{24} +(0.587785 - 0.809017i) q^{25} -1.97538 q^{26} +(-0.565985 - 0.183900i) q^{27} +(0.587785 - 0.809017i) q^{28} +(-0.142040 + 0.278768i) q^{30} +1.00000i q^{32} +(-0.453990 - 0.891007i) q^{35} +(-0.278768 + 0.857960i) q^{36} +(1.34500 - 0.437016i) q^{38} +(0.190983 - 0.587785i) q^{39} +(0.891007 + 0.453990i) q^{40} +(0.183900 + 0.253116i) q^{42} +(0.637890 + 0.637890i) q^{45} +(-0.951057 - 0.690983i) q^{46} +(-0.297556 - 0.0966818i) q^{48} -1.00000 q^{49} +(0.809017 - 0.587785i) q^{50} +(-1.87869 - 0.610425i) q^{52} +(-0.481456 - 0.349798i) q^{54} +(0.809017 - 0.587785i) q^{56} +0.442463i q^{57} +(-0.280582 - 0.863541i) q^{59} +(-0.221232 + 0.221232i) q^{60} +(-0.550672 + 1.69480i) q^{61} +(0.857960 - 0.278768i) q^{63} +(-0.309017 + 0.951057i) q^{64} +(-1.39680 + 1.39680i) q^{65} +(0.297556 - 0.216187i) q^{69} +(-0.156434 - 0.987688i) q^{70} +(-1.53884 - 1.11803i) q^{71} +(-0.530249 + 0.729825i) q^{72} +(0.0966818 + 0.297556i) q^{75} +1.41421 q^{76} +(0.363271 - 0.500000i) q^{78} +(-0.951057 - 0.690983i) q^{79} +(0.707107 + 0.707107i) q^{80} +(-0.579192 + 0.420808i) q^{81} +(1.04744 + 1.44168i) q^{83} +(0.0966818 + 0.297556i) q^{84} +(0.409551 + 0.803789i) q^{90} +(0.610425 + 1.87869i) q^{91} +(-0.690983 - 0.951057i) q^{92} +(0.642040 - 1.26007i) q^{95} +(-0.253116 - 0.183900i) q^{96} +(-0.951057 - 0.309017i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + 4q^{4} + 4q^{9} + O(q^{10}) \) \( 16q + 4q^{4} + 4q^{9} - 4q^{14} - 16q^{15} - 4q^{16} + 4q^{30} - 4q^{36} + 12q^{39} - 16q^{49} + 4q^{50} + 4q^{56} - 4q^{60} + 20q^{63} + 4q^{64} - 4q^{65} - 16q^{81} - 20q^{92} + 4q^{95} + O(q^{100}) \)

Character values

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

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

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
\(3\) −0.183900 + 0.253116i −0.183900 + 0.253116i −0.891007 0.453990i \(-0.850000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(4\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(5\) 0.891007 0.453990i 0.891007 0.453990i
\(6\) −0.253116 + 0.183900i −0.253116 + 0.183900i
\(7\) 1.00000i 1.00000i
\(8\) 0.587785 + 0.809017i 0.587785 + 0.809017i
\(9\) 0.278768 + 0.857960i 0.278768 + 0.857960i
\(10\) 0.987688 0.156434i 0.987688 0.156434i
\(11\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(12\) −0.297556 + 0.0966818i −0.297556 + 0.0966818i
\(13\) −1.87869 + 0.610425i −1.87869 + 0.610425i −0.891007 + 0.453990i \(0.850000\pi\)
−0.987688 + 0.156434i \(0.950000\pi\)
\(14\) 0.309017 0.951057i 0.309017 0.951057i
\(15\) −0.0489435 + 0.309017i −0.0489435 + 0.309017i
\(16\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(17\) 0 0 −0.587785 0.809017i \(-0.700000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(18\) 0.902113i 0.902113i
\(19\) 1.14412 0.831254i 1.14412 0.831254i 0.156434 0.987688i \(-0.450000\pi\)
0.987688 + 0.156434i \(0.0500000\pi\)
\(20\) 0.987688 + 0.156434i 0.987688 + 0.156434i
\(21\) 0.253116 + 0.183900i 0.253116 + 0.183900i
\(22\) 0 0
\(23\) −1.11803 0.363271i −1.11803 0.363271i −0.309017 0.951057i \(-0.600000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(24\) −0.312869 −0.312869
\(25\) 0.587785 0.809017i 0.587785 0.809017i
\(26\) −1.97538 −1.97538
\(27\) −0.565985 0.183900i −0.565985 0.183900i
\(28\) 0.587785 0.809017i 0.587785 0.809017i
\(29\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(30\) −0.142040 + 0.278768i −0.142040 + 0.278768i
\(31\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(32\) 1.00000i 1.00000i
\(33\) 0 0
\(34\) 0 0
\(35\) −0.453990 0.891007i −0.453990 0.891007i
\(36\) −0.278768 + 0.857960i −0.278768 + 0.857960i
\(37\) 0 0 0.951057 0.309017i \(-0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(38\) 1.34500 0.437016i 1.34500 0.437016i
\(39\) 0.190983 0.587785i 0.190983 0.587785i
\(40\) 0.891007 + 0.453990i 0.891007 + 0.453990i
\(41\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(42\) 0.183900 + 0.253116i 0.183900 + 0.253116i
\(43\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(44\) 0 0
\(45\) 0.637890 + 0.637890i 0.637890 + 0.637890i
\(46\) −0.951057 0.690983i −0.951057 0.690983i
\(47\) 0 0 0.587785 0.809017i \(-0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(48\) −0.297556 0.0966818i −0.297556 0.0966818i
\(49\) −1.00000 −1.00000
\(50\) 0.809017 0.587785i 0.809017 0.587785i
\(51\) 0 0
\(52\) −1.87869 0.610425i −1.87869 0.610425i
\(53\) 0 0 0.587785 0.809017i \(-0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(54\) −0.481456 0.349798i −0.481456 0.349798i
\(55\) 0 0
\(56\) 0.809017 0.587785i 0.809017 0.587785i
\(57\) 0.442463i 0.442463i
\(58\) 0 0
\(59\) −0.280582 0.863541i −0.280582 0.863541i −0.987688 0.156434i \(-0.950000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(60\) −0.221232 + 0.221232i −0.221232 + 0.221232i
\(61\) −0.550672 + 1.69480i −0.550672 + 1.69480i 0.156434 + 0.987688i \(0.450000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(62\) 0 0
\(63\) 0.857960 0.278768i 0.857960 0.278768i
\(64\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(65\) −1.39680 + 1.39680i −1.39680 + 1.39680i
\(66\) 0 0
\(67\) 0 0 −0.587785 0.809017i \(-0.700000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(68\) 0 0
\(69\) 0.297556 0.216187i 0.297556 0.216187i
\(70\) −0.156434 0.987688i −0.156434 0.987688i
\(71\) −1.53884 1.11803i −1.53884 1.11803i −0.951057 0.309017i \(-0.900000\pi\)
−0.587785 0.809017i \(-0.700000\pi\)
\(72\) −0.530249 + 0.729825i −0.530249 + 0.729825i
\(73\) 0 0 −0.951057 0.309017i \(-0.900000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(74\) 0 0
\(75\) 0.0966818 + 0.297556i 0.0966818 + 0.297556i
\(76\) 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 \(0.900000\pi\)
\(80\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(81\) −0.579192 + 0.420808i −0.579192 + 0.420808i
\(82\) 0 0
\(83\) 1.04744 + 1.44168i 1.04744 + 1.44168i 0.891007 + 0.453990i \(0.150000\pi\)
0.156434 + 0.987688i \(0.450000\pi\)
\(84\) 0.0966818 + 0.297556i 0.0966818 + 0.297556i
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(90\) 0.409551 + 0.803789i 0.409551 + 0.803789i
\(91\) 0.610425 + 1.87869i 0.610425 + 1.87869i
\(92\) −0.690983 0.951057i −0.690983 0.951057i
\(93\) 0 0
\(94\) 0 0
\(95\) 0.642040 1.26007i 0.642040 1.26007i
\(96\) −0.253116 0.183900i −0.253116 0.183900i
\(97\) 0 0 0.587785 0.809017i \(-0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(98\) −0.951057 0.309017i −0.951057 0.309017i
\(99\) 0 0
\(100\) 0.951057 0.309017i 0.951057 0.309017i
\(101\) 1.97538 1.97538 0.987688 0.156434i \(-0.0500000\pi\)
0.987688 + 0.156434i \(0.0500000\pi\)
\(102\) 0 0
\(103\) 0 0 0.587785 0.809017i \(-0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(104\) −1.59811 1.16110i −1.59811 1.16110i
\(105\) 0.309017 + 0.0489435i 0.309017 + 0.0489435i
\(106\) 0 0
\(107\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(108\) −0.349798 0.481456i −0.349798 0.481456i
\(109\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(110\) 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 \(-0.700000\pi\)
1.00000i \(0.5\pi\)
\(114\) −0.136729 + 0.420808i −0.136729 + 0.420808i
\(115\) −1.16110 + 0.183900i −1.16110 + 0.183900i
\(116\) 0 0
\(117\) −1.04744 1.44168i −1.04744 1.44168i
\(118\) 0.907981i 0.907981i
\(119\) 0 0
\(120\) −0.278768 + 0.142040i −0.278768 + 0.142040i
\(121\) −0.809017 0.587785i −0.809017 0.587785i
\(122\) −1.04744 + 1.44168i −1.04744 + 1.44168i
\(123\) 0 0
\(124\) 0 0
\(125\) 0.156434 0.987688i 0.156434 0.987688i
\(126\) 0.902113 0.902113
\(127\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(128\) −0.587785 + 0.809017i −0.587785 + 0.809017i
\(129\) 0 0
\(130\) −1.76007 + 0.896802i −1.76007 + 0.896802i
\(131\) −1.44168 + 1.04744i −1.44168 + 1.04744i −0.453990 + 0.891007i \(0.650000\pi\)
−0.987688 + 0.156434i \(0.950000\pi\)
\(132\) 0 0
\(133\) −0.831254 1.14412i −0.831254 1.14412i
\(134\) 0 0
\(135\) −0.587785 + 0.0930960i −0.587785 + 0.0930960i
\(136\) 0 0
\(137\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(138\) 0.349798 0.113656i 0.349798 0.113656i
\(139\) 0.437016 1.34500i 0.437016 1.34500i −0.453990 0.891007i \(-0.650000\pi\)
0.891007 0.453990i \(-0.150000\pi\)
\(140\) 0.156434 0.987688i 0.156434 0.987688i
\(141\) 0 0
\(142\) −1.11803 1.53884i −1.11803 1.53884i
\(143\) 0 0
\(144\) −0.729825 + 0.530249i −0.729825 + 0.530249i
\(145\) 0 0
\(146\) 0 0
\(147\) 0.183900 0.253116i 0.183900 0.253116i
\(148\) 0 0
\(149\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(150\) 0.312869i 0.312869i
\(151\) 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
\(157\) 1.78201i 1.78201i −0.453990 0.891007i \(-0.650000\pi\)
0.453990 0.891007i \(-0.350000\pi\)
\(158\) −0.690983 0.951057i −0.690983 0.951057i
\(159\) 0 0
\(160\) 0.453990 + 0.891007i 0.453990 + 0.891007i
\(161\) −0.363271 + 1.11803i −0.363271 + 1.11803i
\(162\) −0.680881 + 0.221232i −0.680881 + 0.221232i
\(163\) 0 0 0.951057 0.309017i \(-0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0.550672 + 1.69480i 0.550672 + 1.69480i
\(167\) 0 0 −0.587785 0.809017i \(-0.700000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(168\) 0.312869i 0.312869i
\(169\) 2.34786 1.70582i 2.34786 1.70582i
\(170\) 0 0
\(171\) 1.03213 + 0.749885i 1.03213 + 0.749885i
\(172\) 0 0
\(173\) −0.863541 0.280582i −0.863541 0.280582i −0.156434 0.987688i \(-0.550000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(174\) 0 0
\(175\) −0.809017 0.587785i −0.809017 0.587785i
\(176\) 0 0
\(177\) 0.270175 + 0.0877853i 0.270175 + 0.0877853i
\(178\) 0 0
\(179\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(180\) 0.141122 + 0.891007i 0.141122 + 0.891007i
\(181\) 0.734572 0.533698i 0.734572 0.533698i −0.156434 0.987688i \(-0.550000\pi\)
0.891007 + 0.453990i \(0.150000\pi\)
\(182\) 1.97538i 1.97538i
\(183\) −0.327712 0.451057i −0.327712 0.451057i
\(184\) −0.363271 1.11803i −0.363271 1.11803i
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) −0.183900 + 0.565985i −0.183900 + 0.565985i
\(190\) 1.00000 1.00000i 1.00000 1.00000i
\(191\) 0.363271 + 1.11803i 0.363271 + 1.11803i 0.951057 + 0.309017i \(0.100000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(192\) −0.183900 0.253116i −0.183900 0.253116i
\(193\) 0.618034i 0.618034i −0.951057 0.309017i \(-0.900000\pi\)
0.951057 0.309017i \(-0.100000\pi\)
\(194\) 0 0
\(195\) −0.0966818 0.610425i −0.0966818 0.610425i
\(196\) −0.809017 0.587785i −0.809017 0.587785i
\(197\) 0 0 0.587785 0.809017i \(-0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(198\) 0 0
\(199\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(200\) 1.00000 1.00000
\(201\) 0 0
\(202\) 1.87869 + 0.610425i 1.87869 + 0.610425i
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 1.06050i 1.06050i
\(208\) −1.16110 1.59811i −1.16110 1.59811i
\(209\) 0 0
\(210\) 0.278768 + 0.142040i 0.278768 + 0.142040i
\(211\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(212\) 0 0
\(213\) 0.565985 0.183900i 0.565985 0.183900i
\(214\) 0 0
\(215\) 0 0
\(216\) −0.183900 0.565985i −0.183900 0.565985i
\(217\) 0 0
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 0 0 −0.951057 0.309017i \(-0.900000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(224\) 1.00000 1.00000
\(225\) 0.857960 + 0.278768i 0.857960 + 0.278768i
\(226\) −0.618034 −0.618034
\(227\) −0.297556 0.0966818i −0.297556 0.0966818i 0.156434 0.987688i \(-0.450000\pi\)
−0.453990 + 0.891007i \(0.650000\pi\)
\(228\) −0.260074 + 0.357960i −0.260074 + 0.357960i
\(229\) 0.734572 + 0.533698i 0.734572 + 0.533698i 0.891007 0.453990i \(-0.150000\pi\)
−0.156434 + 0.987688i \(0.550000\pi\)
\(230\) −1.16110 0.183900i −1.16110 0.183900i
\(231\) 0 0
\(232\) 0 0
\(233\) 1.11803 + 1.53884i 1.11803 + 1.53884i 0.809017 + 0.587785i \(0.200000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(234\) −0.550672 1.69480i −0.550672 1.69480i
\(235\) 0 0
\(236\) 0.280582 0.863541i 0.280582 0.863541i
\(237\) 0.349798 0.113656i 0.349798 0.113656i
\(238\) 0 0
\(239\) −0.500000 + 1.53884i −0.500000 + 1.53884i 0.309017 + 0.951057i \(0.400000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(240\) −0.309017 + 0.0489435i −0.309017 + 0.0489435i
\(241\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(242\) −0.587785 0.809017i −0.587785 0.809017i
\(243\) 0.819101i 0.819101i
\(244\) −1.44168 + 1.04744i −1.44168 + 1.04744i
\(245\) −0.891007 + 0.453990i −0.891007 + 0.453990i
\(246\) 0 0
\(247\) −1.64204 + 2.26007i −1.64204 + 2.26007i
\(248\) 0 0
\(249\) −0.557537 −0.557537
\(250\) 0.453990 0.891007i 0.453990 0.891007i
\(251\) −1.78201 −1.78201 −0.891007 0.453990i \(-0.850000\pi\)
−0.891007 + 0.453990i \(0.850000\pi\)
\(252\) 0.857960 + 0.278768i 0.857960 + 0.278768i
\(253\) 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
\(260\) −1.95106 + 0.309017i −1.95106 + 0.309017i
\(261\) 0 0
\(262\) −1.69480 + 0.550672i −1.69480 + 0.550672i
\(263\) 1.53884 0.500000i 1.53884 0.500000i 0.587785 0.809017i \(-0.300000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) −0.437016 1.34500i −0.437016 1.34500i
\(267\) 0 0
\(268\) 0 0
\(269\) −0.734572 + 0.533698i −0.734572 + 0.533698i −0.891007 0.453990i \(-0.850000\pi\)
0.156434 + 0.987688i \(0.450000\pi\)
\(270\) −0.587785 0.0930960i −0.587785 0.0930960i
\(271\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(272\) 0 0
\(273\) −0.587785 0.190983i −0.587785 0.190983i
\(274\) 0 0
\(275\) 0 0
\(276\) 0.367799 0.367799
\(277\) 0 0 −0.951057 0.309017i \(-0.900000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(278\) 0.831254 1.14412i 0.831254 1.14412i
\(279\) 0 0
\(280\) 0.453990 0.891007i 0.453990 0.891007i
\(281\) 0.500000 0.363271i 0.500000 0.363271i −0.309017 0.951057i \(-0.600000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(282\) 0 0
\(283\) −0.183900 0.253116i −0.183900 0.253116i 0.707107 0.707107i \(-0.250000\pi\)
−0.891007 + 0.453990i \(0.850000\pi\)
\(284\) −0.587785 1.80902i −0.587785 1.80902i
\(285\) 0.200874 + 0.394238i 0.200874 + 0.394238i
\(286\) 0 0
\(287\) 0 0
\(288\) −0.857960 + 0.278768i −0.857960 + 0.278768i
\(289\) −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 \(0.750000\pi\)
\(294\) 0.253116 0.183900i 0.253116 0.183900i
\(295\) −0.642040 0.642040i −0.642040 0.642040i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 2.32219 2.32219
\(300\) −0.0966818 + 0.297556i −0.0966818 + 0.297556i
\(301\) 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
\(305\) 0.278768 + 1.76007i 0.278768 + 1.76007i
\(306\) 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 \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(312\) 0.587785 0.190983i 0.587785 0.190983i
\(313\) 0 0 0.951057 0.309017i \(-0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(314\) 0.550672 1.69480i 0.550672 1.69480i
\(315\) 0.637890 0.637890i 0.637890 0.637890i
\(316\) −0.363271 1.11803i −0.363271 1.11803i
\(317\) 0 0 −0.587785 0.809017i \(-0.700000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0.156434 + 0.987688i 0.156434 + 0.987688i
\(321\) 0 0
\(322\) −0.690983 + 0.951057i −0.690983 + 0.951057i
\(323\) 0 0
\(324\) −0.715921 −0.715921
\(325\) −0.610425 + 1.87869i −0.610425 + 1.87869i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(332\) 1.78201i 1.78201i
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) −0.0966818 + 0.297556i −0.0966818 + 0.297556i
\(337\) 1.53884 0.500000i 1.53884 0.500000i 0.587785 0.809017i \(-0.300000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(338\) 2.76007 0.896802i 2.76007 0.896802i
\(339\) 0.0597526 0.183900i 0.0597526 0.183900i
\(340\) 0 0
\(341\) 0 0
\(342\) 0.749885 + 1.03213i 0.749885 + 1.03213i
\(343\) 1.00000i 1.00000i
\(344\) 0 0
\(345\) 0.166977 0.327712i 0.166977 0.327712i
\(346\) −0.734572 0.533698i −0.734572 0.533698i
\(347\) 0 0 0.587785 0.809017i \(-0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(348\) 0 0
\(349\) 1.97538 1.97538 0.987688 0.156434i \(-0.0500000\pi\)
0.987688 + 0.156434i \(0.0500000\pi\)
\(350\) −0.587785 0.809017i −0.587785 0.809017i
\(351\) 1.17557 1.17557
\(352\) 0 0
\(353\) 0 0 0.587785 0.809017i \(-0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(354\) 0.229825 + 0.166977i 0.229825 + 0.166977i
\(355\) −1.87869 0.297556i −1.87869 0.297556i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 0.500000 + 1.53884i 0.500000 + 1.53884i 0.809017 + 0.587785i \(0.200000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(360\) −0.141122 + 0.891007i −0.141122 + 0.891007i
\(361\) 0.309017 0.951057i 0.309017 0.951057i
\(362\) 0.863541 0.280582i 0.863541 0.280582i
\(363\) 0.297556 0.0966818i 0.297556 0.0966818i
\(364\) −0.610425 + 1.87869i −0.610425 + 1.87869i
\(365\) 0 0
\(366\) −0.172288 0.530249i −0.172288 0.530249i
\(367\) 0 0 −0.587785 0.809017i \(-0.700000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(368\) 1.17557i 1.17557i
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 0 0 −0.951057 0.309017i \(-0.900000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(374\) 0 0
\(375\) 0.221232 + 0.221232i 0.221232 + 0.221232i
\(376\) 0 0
\(377\) 0 0
\(378\) −0.349798 + 0.481456i −0.349798 + 0.481456i
\(379\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(380\) 1.26007 0.642040i 1.26007 0.642040i
\(381\) 0 0
\(382\) 1.17557i 1.17557i
\(383\) 0 0 −0.587785 0.809017i \(-0.700000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(384\) −0.0966818 0.297556i −0.0966818 0.297556i
\(385\) 0 0
\(386\) 0.190983 0.587785i 0.190983 0.587785i
\(387\) 0 0
\(388\) 0 0
\(389\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(390\) 0.0966818 0.610425i 0.0966818 0.610425i
\(391\) 0 0
\(392\) −0.587785 0.809017i −0.587785 0.809017i
\(393\) 0.557537i 0.557537i
\(394\) 0 0
\(395\) −1.16110 0.183900i −1.16110 0.183900i
\(396\) 0 0
\(397\) 1.16110 1.59811i 1.16110 1.59811i 0.453990 0.891007i \(-0.350000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(398\) 0 0
\(399\) 0.442463 0.442463
\(400\) 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
\(404\) 1.59811 + 1.16110i 1.59811 + 1.16110i
\(405\) −0.325021 + 0.637890i −0.325021 + 0.637890i
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −0.863541 + 0.280582i −0.863541 + 0.280582i
\(414\) 0.327712 1.00859i 0.327712 1.00859i
\(415\) 1.58779 + 0.809017i 1.58779 + 0.809017i
\(416\) −0.610425 1.87869i −0.610425 1.87869i
\(417\) 0.260074 + 0.357960i 0.260074 + 0.357960i
\(418\) 0 0
\(419\) −0.253116 + 0.183900i −0.253116 + 0.183900i −0.707107 0.707107i \(-0.750000\pi\)
0.453990 + 0.891007i \(0.350000\pi\)
\(420\) 0.221232 + 0.221232i 0.221232 + 0.221232i
\(421\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 0 0
\(426\) 0.595112 0.595112
\(427\) 1.69480 + 0.550672i 1.69480 + 0.550672i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −0.500000 + 0.363271i −0.500000 + 0.363271i −0.809017 0.587785i \(-0.800000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(432\) 0.595112i 0.595112i
\(433\) 0 0 −0.587785 0.809017i \(-0.700000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(434\) 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 \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(440\) 0 0
\(441\) −0.278768 0.857960i −0.278768 0.857960i
\(442\) 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 \(0.800000\pi\)
\(450\) 0.729825 + 0.530249i 0.729825 + 0.530249i
\(451\) 0 0
\(452\) −0.587785 0.190983i −0.587785 0.190983i
\(453\) −0.297556 + 0.409551i −0.297556 + 0.409551i
\(454\) −0.253116 0.183900i −0.253116 0.183900i
\(455\) 1.39680 + 1.39680i 1.39680 + 1.39680i
\(456\) −0.357960 + 0.260074i −0.357960 + 0.260074i
\(457\) 0.618034i 0.618034i −0.951057 0.309017i \(-0.900000\pi\)
0.951057 0.309017i \(-0.100000\pi\)
\(458\) 0.533698 + 0.734572i 0.533698 + 0.734572i
\(459\) 0 0
\(460\) −1.04744 0.533698i −1.04744 0.533698i
\(461\) 0.437016 1.34500i 0.437016 1.34500i −0.453990 0.891007i \(-0.650000\pi\)
0.891007 0.453990i \(-0.150000\pi\)
\(462\) 0 0
\(463\) 0.587785 0.190983i 0.587785 0.190983i 1.00000i \(-0.5\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0.587785 + 1.80902i 0.587785 + 1.80902i
\(467\) 0.831254 + 1.14412i 0.831254 + 1.14412i 0.987688 + 0.156434i \(0.0500000\pi\)
−0.156434 + 0.987688i \(0.550000\pi\)
\(468\) 1.78201i 1.78201i
\(469\) 0 0
\(470\) 0 0
\(471\) 0.451057 + 0.327712i 0.451057 + 0.327712i
\(472\) 0.533698 0.734572i 0.533698 0.734572i
\(473\) 0 0
\(474\) 0.367799 0.367799
\(475\) 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 \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(480\) −0.309017 0.0489435i −0.309017 0.0489435i
\(481\) 0 0
\(482\) 0 0
\(483\) −0.216187 0.297556i −0.216187 0.297556i
\(484\) −0.309017 0.951057i −0.309017 0.951057i
\(485\) 0 0
\(486\) 0.253116 0.779012i 0.253116 0.779012i
\(487\) 1.80902 0.587785i 1.80902 0.587785i 0.809017 0.587785i \(-0.200000\pi\)
1.00000 \(0\)
\(488\) −1.69480 + 0.550672i −1.69480 + 0.550672i
\(489\) 0 0
\(490\) −0.987688 + 0.156434i −0.987688 + 0.156434i
\(491\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) −2.26007 + 1.64204i −2.26007 + 1.64204i
\(495\) 0 0
\(496\) 0 0
\(497\) −1.11803 + 1.53884i −1.11803 + 1.53884i
\(498\) −0.530249 0.172288i −0.530249 0.172288i
\(499\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(500\) 0.707107 0.707107i 0.707107 0.707107i
\(501\) 0 0
\(502\) −1.69480 0.550672i −1.69480 0.550672i
\(503\) 0 0 0.587785 0.809017i \(-0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(504\) 0.729825 + 0.530249i 0.729825 + 0.530249i
\(505\) 1.76007 0.896802i 1.76007 0.896802i
\(506\) 0 0
\(507\) 0.907981i 0.907981i
\(508\) 0 0
\(509\) 0.437016 + 1.34500i 0.437016 + 1.34500i 0.891007 + 0.453990i \(0.150000\pi\)
−0.453990 + 0.891007i \(0.650000\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −0.951057 + 0.309017i −0.951057 + 0.309017i
\(513\) −0.800424 + 0.260074i −0.800424 + 0.260074i
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 0.229825 0.166977i 0.229825 0.166977i
\(520\) −1.95106 0.309017i −1.95106 0.309017i
\(521\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(522\) 0 0
\(523\) −1.87869 0.610425i −1.87869 0.610425i −0.987688 0.156434i \(-0.950000\pi\)
−0.891007 0.453990i \(-0.850000\pi\)
\(524\) −1.78201 −1.78201
\(525\) 0.297556 0.0966818i 0.297556 0.0966818i
\(526\) 1.61803 1.61803
\(527\) 0 0
\(528\) 0 0
\(529\) 0.309017 + 0.224514i 0.309017 + 0.224514i
\(530\) 0 0
\(531\) 0.662667 0.481456i 0.662667 0.481456i
\(532\) 1.41421i 1.41421i
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) −0.863541 + 0.280582i −0.863541 + 0.280582i
\(539\) 0 0
\(540\) −0.530249 0.270175i −0.530249 0.270175i
\(541\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(542\) 0 0
\(543\) 0.284079i 0.284079i
\(544\) 0 0
\(545\) 0 0
\(546\) −0.500000 0.363271i −0.500000 0.363271i
\(547\) 0 0 0.587785 0.809017i \(-0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(548\) 0 0
\(549\) −1.60758 −1.60758
\(550\) 0 0
\(551\) 0 0
\(552\) 0.349798 + 0.113656i 0.349798 + 0.113656i
\(553\) −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
\(563\) 1.87869 0.610425i 1.87869 0.610425i 0.891007 0.453990i \(-0.150000\pi\)
0.987688 0.156434i \(-0.0500000\pi\)
\(564\) 0 0
\(565\) −0.437016 + 0.437016i −0.437016 + 0.437016i
\(566\) −0.0966818 0.297556i −0.0966818 0.297556i
\(567\) 0.420808 + 0.579192i 0.420808 + 0.579192i
\(568\) 1.90211i 1.90211i
\(569\) 0.951057 0.690983i 0.951057 0.690983i 1.00000i \(-0.5\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(570\) 0.0692165 + 0.437016i 0.0692165 + 0.437016i
\(571\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(572\) 0 0
\(573\) −0.349798 0.113656i −0.349798 0.113656i
\(574\) 0 0
\(575\) −0.951057 + 0.690983i −0.951057 + 0.690983i
\(576\) −0.902113 −0.902113
\(577\) 0 0 −0.951057 0.309017i \(-0.900000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(578\) −0.587785 + 0.809017i −0.587785 + 0.809017i
\(579\) 0.156434 + 0.113656i 0.156434 + 0.113656i
\(580\) 0 0
\(581\) 1.44168 1.04744i 1.44168 1.04744i
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) −1.58779 0.809017i −1.58779 0.809017i
\(586\) −0.437016 + 1.34500i −0.437016 + 1.34500i
\(587\) −0.863541 + 0.280582i −0.863541 + 0.280582i −0.707107 0.707107i \(-0.750000\pi\)
−0.156434 + 0.987688i \(0.550000\pi\)
\(588\) 0.297556 0.0966818i 0.297556 0.0966818i
\(589\) 0 0
\(590\) −0.412215 0.809017i −0.412215 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
\(598\) 2.20854 + 0.717598i 2.20854 + 0.717598i
\(599\) 1.17557 1.17557 0.587785 0.809017i \(-0.300000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(600\) −0.183900 + 0.253116i −0.183900 + 0.253116i
\(601\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 1.30902 + 0.951057i 1.30902 + 0.951057i
\(605\) −0.987688 0.156434i −0.987688 0.156434i
\(606\) −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
\(610\) −0.278768 + 1.76007i −0.278768 + 1.76007i
\(611\) 0 0
\(612\) 0 0
\(613\) 0 0 0.951057 0.309017i \(-0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(614\) −0.437016 + 1.34500i −0.437016 + 1.34500i
\(615\) 0 0
\(616\) 0 0
\(617\) −0.951057 1.30902i −0.951057 1.30902i −0.951057 0.309017i \(-0.900000\pi\)
1.00000i \(-0.5\pi\)
\(618\) 0 0
\(619\) 0.734572 0.533698i 0.734572 0.533698i −0.156434 0.987688i \(-0.550000\pi\)
0.891007 + 0.453990i \(0.150000\pi\)
\(620\) 0 0
\(621\) 0.565985 + 0.411212i 0.565985 + 0.411212i
\(622\) 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
\(628\) 1.04744 1.44168i 1.04744 1.44168i
\(629\) 0 0
\(630\) 0.803789 0.409551i 0.803789 0.409551i
\(631\) −1.53884 + 1.11803i −1.53884 + 1.11803i −0.587785 + 0.809017i \(0.700000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(632\) 1.17557i 1.17557i
\(633\) 0 0
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 1.87869 0.610425i 1.87869 0.610425i
\(638\) 0 0
\(639\) 0.530249 1.63194i 0.530249 1.63194i
\(640\) −0.156434 + 0.987688i −0.156434 + 0.987688i
\(641\) 0.363271 + 1.11803i 0.363271 + 1.11803i 0.951057 + 0.309017i \(0.100000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(642\) 0 0
\(643\) 1.78201i 1.78201i 0.453990 + 0.891007i \(0.350000\pi\)
−0.453990 + 0.891007i \(0.650000\pi\)
\(644\) −0.951057 + 0.690983i −0.951057 + 0.690983i
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 0.587785 0.809017i \(-0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(648\) −0.680881 0.221232i −0.680881 0.221232i
\(649\) 0 0
\(650\) −1.16110 + 1.59811i −1.16110 + 1.59811i
\(651\) 0 0
\(652\) 0 0
\(653\) 0 0 0.587785 0.809017i \(-0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(654\) 0 0
\(655\) −0.809017 + 1.58779i −0.809017 + 1.58779i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(660\) 0 0
\(661\) 0.550672 1.69480i 0.550672 1.69480i −0.156434 0.987688i \(-0.550000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) −0.550672 + 1.69480i −0.550672 + 1.69480i
\(665\) −1.26007 0.642040i −1.26007 0.642040i
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) −0.183900 + 0.253116i −0.183900 + 0.253116i
\(673\) 1.80902 + 0.587785i 1.80902 + 0.587785i 1.00000 \(0\)
0.809017 + 0.587785i \(0.200000\pi\)
\(674\) 1.61803 1.61803
\(675\) −0.481456 + 0.349798i −0.481456 + 0.349798i
\(676\) 2.90211 2.90211
\(677\) −1.69480 0.550672i −1.69480 0.550672i −0.707107 0.707107i \(-0.750000\pi\)
−0.987688 + 0.156434i \(0.950000\pi\)
\(678\) 0.113656 0.156434i 0.113656 0.156434i
\(679\) 0 0
\(680\) 0 0
\(681\) 0.0791922 0.0575365i 0.0791922 0.0575365i
\(682\) 0 0
\(683\) 0 0 −0.587785 0.809017i \(-0.700000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(684\) 0.394238 + 1.21334i 0.394238 + 1.21334i
\(685\) 0 0
\(686\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(687\) −0.270175 + 0.0877853i −0.270175 + 0.0877853i
\(688\) 0 0
\(689\) 0 0
\(690\) 0.260074 0.260074i 0.260074 0.260074i
\(691\) −0.610425 1.87869i −0.610425 1.87869i −0.453990 0.891007i \(-0.650000\pi\)
−0.156434 0.987688i \(-0.550000\pi\)
\(692\) −0.533698 0.734572i −0.533698 0.734572i
\(693\) 0 0
\(694\) 0 0
\(695\) −0.221232 1.39680i −0.221232 1.39680i
\(696\) 0 0
\(697\) 0 0
\(698\) 1.87869 + 0.610425i 1.87869 + 0.610425i
\(699\) −0.595112 −0.595112
\(700\) −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
\(707\) 1.97538i 1.97538i
\(708\) 0.166977 + 0.229825i 0.166977 + 0.229825i
\(709\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(710\) −1.69480 0.863541i −1.69480 0.863541i
\(711\) 0.327712 1.00859i 0.327712 1.00859i
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −0.297556 0.409551i −0.297556 0.409551i
\(718\) 1.61803i 1.61803i
\(719\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(720\) −0.409551 + 0.803789i −0.409551 + 0.803789i
\(721\) 0 0
\(722\) 0.587785 0.809017i 0.587785 0.809017i
\(723\) 0 0
\(724\) 0.907981 0.907981
\(725\) 0 0
\(726\) 0.312869 0.312869
\(727\) 0 0 −0.951057 0.309017i \(-0.900000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(728\) −1.16110 + 1.59811i −1.16110 + 1.59811i
\(729\) −0.371864 0.270175i −0.371864 0.270175i
\(730\) 0 0
\(731\) 0 0
\(732\) 0.557537i 0.557537i
\(733\) 0.533698 + 0.734572i 0.533698 + 0.734572i 0.987688 0.156434i \(-0.0500000\pi\)
−0.453990 + 0.891007i \(0.650000\pi\)
\(734\) 0 0
\(735\) 0.0489435 0.309017i 0.0489435 0.309017i
\(736\) 0.363271 1.11803i 0.363271 1.11803i
\(737\) 0 0
\(738\) 0 0
\(739\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(740\) 0 0
\(741\) −0.270091 0.831254i −0.270091 0.831254i
\(742\) 0 0
\(743\) 1.90211i 1.90211i 0.309017 + 0.951057i \(0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −0.944910 + 1.30056i −0.944910 + 1.30056i
\(748\) 0 0
\(749\) 0 0
\(750\) 0.142040 + 0.278768i 0.142040 + 0.278768i
\(751\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(752\) 0 0
\(753\) 0.327712 0.451057i 0.327712 0.451057i
\(754\) 0 0
\(755\) 1.44168 0.734572i 1.44168 0.734572i
\(756\) −0.481456 + 0.349798i −0.481456 + 0.349798i
\(757\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 1.39680 0.221232i 1.39680 0.221232i
\(761\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −0.363271 + 1.11803i −0.363271 + 1.11803i
\(765\) 0 0
\(766\) 0 0
\(767\) 1.05425 + 1.45106i 1.05425 + 1.45106i
\(768\) 0.312869i 0.312869i
\(769\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0.363271 0.500000i 0.363271 0.500000i
\(773\) 0.297556 + 0.0966818i 0.297556 + 0.0966818i 0.453990 0.891007i \(-0.350000\pi\)
−0.156434 + 0.987688i \(0.550000\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0 0
\(780\) 0.280582 0.550672i 0.280582 0.550672i
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) −0.309017 0.951057i −0.309017 0.951057i
\(785\) −0.809017 1.58779i −0.809017 1.58779i
\(786\) 0.172288 0.530249i 0.172288 0.530249i
\(787\) 1.34500 0.437016i 1.34500 0.437016i 0.453990 0.891007i \(-0.350000\pi\)
0.891007 + 0.453990i \(0.150000\pi\)
\(788\) 0 0
\(789\) −0.156434 + 0.481456i −0.156434 + 0.481456i
\(790\) −1.04744 0.533698i −1.04744 0.533698i
\(791\) 0.190983 + 0.587785i 0.190983 + 0.587785i
\(792\) 0 0
\(793\) 3.52015i 3.52015i
\(794\) 1.59811 1.16110i 1.59811 1.16110i
\(795\) 0 0
\(796\) 0