Properties

Label 712.1.y.a.107.1
Level $712$
Weight $1$
Character 712.107
Analytic conductor $0.355$
Analytic rank $0$
Dimension $20$
Projective image $D_{44}$
CM discriminant -8
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 712 = 2^{3} \cdot 89 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 712.y (of order \(44\), degree \(20\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.355334288995\)
Analytic rank: \(0\)
Dimension: \(20\)
Coefficient field: \(\Q(\zeta_{44})\)
Defining polynomial: \(x^{20} - x^{18} + x^{16} - x^{14} + x^{12} - x^{10} + x^{8} - x^{6} + x^{4} - x^{2} + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Projective image: \(D_{44}\)
Projective field: Galois closure of \(\mathbb{Q}[x]/(x^{44} - \cdots)\)

Embedding invariants

Embedding label 107.1
Root \(0.909632 - 0.415415i\) of defining polynomial
Character \(\chi\) \(=\) 712.107
Dual form 712.1.y.a.539.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.654861 + 0.755750i) q^{2} +(0.559521 + 0.418852i) q^{3} +(-0.142315 + 0.989821i) q^{4} +(0.0498610 + 0.697148i) q^{6} +(-0.841254 + 0.540641i) q^{8} +(-0.144106 - 0.490780i) q^{9} +O(q^{10})\) \(q+(0.654861 + 0.755750i) q^{2} +(0.559521 + 0.418852i) q^{3} +(-0.142315 + 0.989821i) q^{4} +(0.0498610 + 0.697148i) q^{6} +(-0.841254 + 0.540641i) q^{8} +(-0.144106 - 0.490780i) q^{9} +(0.909632 + 0.584585i) q^{11} +(-0.494217 + 0.494217i) q^{12} +(-0.959493 - 0.281733i) q^{16} +(-0.989821 - 0.857685i) q^{17} +(0.276537 - 0.430300i) q^{18} +(-0.373128 - 0.203743i) q^{19} +(0.153882 + 1.07028i) q^{22} +(-0.697148 - 0.0498610i) q^{24} +(-0.415415 + 0.909632i) q^{25} +(0.369184 - 0.989821i) q^{27} +(-0.415415 - 0.909632i) q^{32} +(0.264103 + 0.708089i) q^{33} -1.30972i q^{34} +(0.506293 - 0.0727939i) q^{36} +(-0.0903680 - 0.415415i) q^{38} +(-0.847507 - 1.13214i) q^{41} +(1.94931 - 0.424047i) q^{43} +(-0.708089 + 0.817178i) q^{44} +(-0.418852 - 0.559521i) q^{48} +(-0.909632 - 0.415415i) q^{49} +(-0.959493 + 0.281733i) q^{50} +(-0.194583 - 0.894482i) q^{51} +(0.989821 - 0.369184i) q^{54} +(-0.123435 - 0.270284i) q^{57} +(-0.114220 + 0.0855040i) q^{59} +(0.415415 - 0.909632i) q^{64} +(-0.362187 + 0.663296i) q^{66} +(0.0801894 + 0.557730i) q^{67} +(0.989821 - 0.857685i) q^{68} +(0.386565 + 0.334961i) q^{72} +(1.74557 + 0.512546i) q^{73} +(-0.613435 + 0.334961i) q^{75} +(0.254771 - 0.340335i) q^{76} +(0.190855 - 0.122655i) q^{81} +(0.300613 - 1.38189i) q^{82} +(0.114220 + 1.59700i) q^{83} +(1.59700 + 1.19550i) q^{86} -1.08128 q^{88} +(-0.415415 - 0.909632i) q^{89} +(0.148568 - 0.682956i) q^{96} +(-1.61435 + 1.03748i) q^{97} +(-0.281733 - 0.959493i) q^{98} +(0.155819 - 0.530671i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20q + 2q^{2} - 2q^{3} - 2q^{4} + 2q^{6} + 2q^{8} + O(q^{10}) \) \( 20q + 2q^{2} - 2q^{3} - 2q^{4} + 2q^{6} + 2q^{8} - 2q^{12} - 2q^{16} - 2q^{19} + 2q^{24} + 2q^{25} - 22q^{27} + 2q^{32} - 20q^{38} + 2q^{41} + 2q^{43} - 2q^{48} - 2q^{50} + 4q^{51} - 4q^{57} - 2q^{59} - 2q^{64} + 22q^{72} + 2q^{75} - 2q^{76} - 2q^{81} - 2q^{82} + 2q^{83} - 2q^{86} + 2q^{89} + 2q^{96} - 4q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/712\mathbb{Z}\right)^\times\).

\(n\) \(357\) \(535\) \(537\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{9}{44}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.654861 + 0.755750i 0.654861 + 0.755750i
\(3\) 0.559521 + 0.418852i 0.559521 + 0.418852i 0.841254 0.540641i \(-0.181818\pi\)
−0.281733 + 0.959493i \(0.590909\pi\)
\(4\) −0.142315 + 0.989821i −0.142315 + 0.989821i
\(5\) 0 0 −0.540641 0.841254i \(-0.681818\pi\)
0.540641 + 0.841254i \(0.318182\pi\)
\(6\) 0.0498610 + 0.697148i 0.0498610 + 0.697148i
\(7\) 0 0 0.212565 0.977147i \(-0.431818\pi\)
−0.212565 + 0.977147i \(0.568182\pi\)
\(8\) −0.841254 + 0.540641i −0.841254 + 0.540641i
\(9\) −0.144106 0.490780i −0.144106 0.490780i
\(10\) 0 0
\(11\) 0.909632 + 0.584585i 0.909632 + 0.584585i 0.909632 0.415415i \(-0.136364\pi\)
1.00000i \(0.5\pi\)
\(12\) −0.494217 + 0.494217i −0.494217 + 0.494217i
\(13\) 0 0 0.599278 0.800541i \(-0.295455\pi\)
−0.599278 + 0.800541i \(0.704545\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −0.959493 0.281733i −0.959493 0.281733i
\(17\) −0.989821 0.857685i −0.989821 0.857685i 1.00000i \(-0.5\pi\)
−0.989821 + 0.142315i \(0.954545\pi\)
\(18\) 0.276537 0.430300i 0.276537 0.430300i
\(19\) −0.373128 0.203743i −0.373128 0.203743i 0.281733 0.959493i \(-0.409091\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0.153882 + 1.07028i 0.153882 + 1.07028i
\(23\) 0 0 0.479249 0.877679i \(-0.340909\pi\)
−0.479249 + 0.877679i \(0.659091\pi\)
\(24\) −0.697148 0.0498610i −0.697148 0.0498610i
\(25\) −0.415415 + 0.909632i −0.415415 + 0.909632i
\(26\) 0 0
\(27\) 0.369184 0.989821i 0.369184 0.989821i
\(28\) 0 0
\(29\) 0 0 −0.977147 0.212565i \(-0.931818\pi\)
0.977147 + 0.212565i \(0.0681818\pi\)
\(30\) 0 0
\(31\) 0 0 −0.479249 0.877679i \(-0.659091\pi\)
0.479249 + 0.877679i \(0.340909\pi\)
\(32\) −0.415415 0.909632i −0.415415 0.909632i
\(33\) 0.264103 + 0.708089i 0.264103 + 0.708089i
\(34\) 1.30972i 1.30972i
\(35\) 0 0
\(36\) 0.506293 0.0727939i 0.506293 0.0727939i
\(37\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(38\) −0.0903680 0.415415i −0.0903680 0.415415i
\(39\) 0 0
\(40\) 0 0
\(41\) −0.847507 1.13214i −0.847507 1.13214i −0.989821 0.142315i \(-0.954545\pi\)
0.142315 0.989821i \(-0.454545\pi\)
\(42\) 0 0
\(43\) 1.94931 0.424047i 1.94931 0.424047i 0.959493 0.281733i \(-0.0909091\pi\)
0.989821 0.142315i \(-0.0454545\pi\)
\(44\) −0.708089 + 0.817178i −0.708089 + 0.817178i
\(45\) 0 0
\(46\) 0 0
\(47\) 0 0 −0.989821 0.142315i \(-0.954545\pi\)
0.989821 + 0.142315i \(0.0454545\pi\)
\(48\) −0.418852 0.559521i −0.418852 0.559521i
\(49\) −0.909632 0.415415i −0.909632 0.415415i
\(50\) −0.959493 + 0.281733i −0.959493 + 0.281733i
\(51\) −0.194583 0.894482i −0.194583 0.894482i
\(52\) 0 0
\(53\) 0 0 0.989821 0.142315i \(-0.0454545\pi\)
−0.989821 + 0.142315i \(0.954545\pi\)
\(54\) 0.989821 0.369184i 0.989821 0.369184i
\(55\) 0 0
\(56\) 0 0
\(57\) −0.123435 0.270284i −0.123435 0.270284i
\(58\) 0 0
\(59\) −0.114220 + 0.0855040i −0.114220 + 0.0855040i −0.654861 0.755750i \(-0.727273\pi\)
0.540641 + 0.841254i \(0.318182\pi\)
\(60\) 0 0
\(61\) 0 0 −0.936950 0.349464i \(-0.886364\pi\)
0.936950 + 0.349464i \(0.113636\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0.415415 0.909632i 0.415415 0.909632i
\(65\) 0 0
\(66\) −0.362187 + 0.663296i −0.362187 + 0.663296i
\(67\) 0.0801894 + 0.557730i 0.0801894 + 0.557730i 0.989821 + 0.142315i \(0.0454545\pi\)
−0.909632 + 0.415415i \(0.863636\pi\)
\(68\) 0.989821 0.857685i 0.989821 0.857685i
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 0.540641 0.841254i \(-0.318182\pi\)
−0.540641 + 0.841254i \(0.681818\pi\)
\(72\) 0.386565 + 0.334961i 0.386565 + 0.334961i
\(73\) 1.74557 + 0.512546i 1.74557 + 0.512546i 0.989821 0.142315i \(-0.0454545\pi\)
0.755750 + 0.654861i \(0.227273\pi\)
\(74\) 0 0
\(75\) −0.613435 + 0.334961i −0.613435 + 0.334961i
\(76\) 0.254771 0.340335i 0.254771 0.340335i
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 0.281733 0.959493i \(-0.409091\pi\)
−0.281733 + 0.959493i \(0.590909\pi\)
\(80\) 0 0
\(81\) 0.190855 0.122655i 0.190855 0.122655i
\(82\) 0.300613 1.38189i 0.300613 1.38189i
\(83\) 0.114220 + 1.59700i 0.114220 + 1.59700i 0.654861 + 0.755750i \(0.272727\pi\)
−0.540641 + 0.841254i \(0.681818\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 1.59700 + 1.19550i 1.59700 + 1.19550i
\(87\) 0 0
\(88\) −1.08128 −1.08128
\(89\) −0.415415 0.909632i −0.415415 0.909632i
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 0.148568 0.682956i 0.148568 0.682956i
\(97\) −1.61435 + 1.03748i −1.61435 + 1.03748i −0.654861 + 0.755750i \(0.727273\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(98\) −0.281733 0.959493i −0.281733 0.959493i
\(99\) 0.155819 0.530671i 0.155819 0.530671i
\(100\) −0.841254 0.540641i −0.841254 0.540641i
\(101\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(102\) 0.548580 0.732817i 0.548580 0.732817i
\(103\) 0 0 0.877679 0.479249i \(-0.159091\pi\)
−0.877679 + 0.479249i \(0.840909\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(108\) 0.927206 + 0.506293i 0.927206 + 0.506293i
\(109\) 0 0 0.909632 0.415415i \(-0.136364\pi\)
−0.909632 + 0.415415i \(0.863636\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −1.59700 0.114220i −1.59700 0.114220i −0.755750 0.654861i \(-0.772727\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(114\) 0.123435 0.270284i 0.123435 0.270284i
\(115\) 0 0
\(116\) 0 0
\(117\) 0 0
\(118\) −0.139418 0.0303285i −0.139418 0.0303285i
\(119\) 0 0
\(120\) 0 0
\(121\) 0.0702757 + 0.153882i 0.0702757 + 0.153882i
\(122\) 0 0
\(123\) 0.988434i 0.988434i
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 0 0 −0.212565 0.977147i \(-0.568182\pi\)
0.212565 + 0.977147i \(0.431818\pi\)
\(128\) 0.959493 0.281733i 0.959493 0.281733i
\(129\) 1.26830 + 0.579211i 1.26830 + 0.579211i
\(130\) 0 0
\(131\) −0.822373 0.118239i −0.822373 0.118239i −0.281733 0.959493i \(-0.590909\pi\)
−0.540641 + 0.841254i \(0.681818\pi\)
\(132\) −0.738467 + 0.160644i −0.738467 + 0.160644i
\(133\) 0 0
\(134\) −0.368991 + 0.425839i −0.368991 + 0.425839i
\(135\) 0 0
\(136\) 1.29639 + 0.186393i 1.29639 + 0.186393i
\(137\) 0.0855040 + 0.114220i 0.0855040 + 0.114220i 0.841254 0.540641i \(-0.181818\pi\)
−0.755750 + 0.654861i \(0.772727\pi\)
\(138\) 0 0
\(139\) 1.61435 0.474017i 1.61435 0.474017i 0.654861 0.755750i \(-0.272727\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) 0.511499i 0.511499i
\(145\) 0 0
\(146\) 0.755750 + 1.65486i 0.755750 + 1.65486i
\(147\) −0.334961 0.613435i −0.334961 0.613435i
\(148\) 0 0
\(149\) 0 0 −0.977147 0.212565i \(-0.931818\pi\)
0.977147 + 0.212565i \(0.0681818\pi\)
\(150\) −0.654861 0.244250i −0.654861 0.244250i
\(151\) 0 0 0.349464 0.936950i \(-0.386364\pi\)
−0.349464 + 0.936950i \(0.613636\pi\)
\(152\) 0.424047 0.0303285i 0.424047 0.0303285i
\(153\) −0.278295 + 0.609382i −0.278295 + 0.609382i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 0 0 0.755750 0.654861i \(-0.227273\pi\)
−0.755750 + 0.654861i \(0.772727\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) 0.217680 + 0.0639165i 0.217680 + 0.0639165i
\(163\) −0.133682 + 1.86912i −0.133682 + 1.86912i 0.281733 + 0.959493i \(0.409091\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(164\) 1.24123 0.677760i 1.24123 0.677760i
\(165\) 0 0
\(166\) −1.13214 + 1.13214i −1.13214 + 1.13214i
\(167\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(168\) 0 0
\(169\) −0.281733 0.959493i −0.281733 0.959493i
\(170\) 0 0
\(171\) −0.0462232 + 0.212484i −0.0462232 + 0.212484i
\(172\) 0.142315 + 1.98982i 0.142315 + 1.98982i
\(173\) 0 0 −0.540641 0.841254i \(-0.681818\pi\)
0.540641 + 0.841254i \(0.318182\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −0.708089 0.817178i −0.708089 0.817178i
\(177\) −0.0997220 −0.0997220
\(178\) 0.415415 0.909632i 0.415415 0.909632i
\(179\) −1.91899 −1.91899 −0.959493 0.281733i \(-0.909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(180\) 0 0
\(181\) 0 0 −0.800541 0.599278i \(-0.795455\pi\)
0.800541 + 0.599278i \(0.204545\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −0.398983 1.35881i −0.398983 1.35881i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 0 0 0.599278 0.800541i \(-0.295455\pi\)
−0.599278 + 0.800541i \(0.704545\pi\)
\(192\) 0.613435 0.334961i 0.613435 0.334961i
\(193\) −0.0683785 + 0.956056i −0.0683785 + 0.956056i 0.841254 + 0.540641i \(0.181818\pi\)
−0.909632 + 0.415415i \(0.863636\pi\)
\(194\) −1.84125 0.540641i −1.84125 0.540641i
\(195\) 0 0
\(196\) 0.540641 0.841254i 0.540641 0.841254i
\(197\) 0 0 −0.877679 0.479249i \(-0.840909\pi\)
0.877679 + 0.479249i \(0.159091\pi\)
\(198\) 0.503094 0.229756i 0.503094 0.229756i
\(199\) 0 0 0.755750 0.654861i \(-0.227273\pi\)
−0.755750 + 0.654861i \(0.772727\pi\)
\(200\) −0.142315 0.989821i −0.142315 0.989821i
\(201\) −0.188739 + 0.345649i −0.188739 + 0.345649i
\(202\) 0 0
\(203\) 0 0
\(204\) 0.913069 0.0653040i 0.913069 0.0653040i
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −0.220304 0.403457i −0.220304 0.403457i
\(210\) 0 0
\(211\) 0.697148 + 1.86912i 0.697148 + 1.86912i 0.415415 + 0.909632i \(0.363636\pi\)
0.281733 + 0.959493i \(0.409091\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) 0.224560 + 1.03229i 0.224560 + 1.03229i
\(217\) 0 0
\(218\) 0 0
\(219\) 0.762003 + 1.01792i 0.762003 + 1.01792i
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(224\) 0 0
\(225\) 0.506293 + 0.0727939i 0.506293 + 0.0727939i
\(226\) −0.959493 1.28173i −0.959493 1.28173i
\(227\) −1.65486 0.755750i −1.65486 0.755750i −0.654861 0.755750i \(-0.727273\pi\)
−1.00000 \(\pi\)
\(228\) 0.285100 0.0837128i 0.285100 0.0837128i
\(229\) 0 0 −0.212565 0.977147i \(-0.568182\pi\)
0.212565 + 0.977147i \(0.431818\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 0.284630i 0.284630i 0.989821 + 0.142315i \(0.0454545\pi\)
−0.989821 + 0.142315i \(0.954545\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) −0.0683785 0.125226i −0.0683785 0.125226i
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 −0.936950 0.349464i \(-0.886364\pi\)
0.936950 + 0.349464i \(0.113636\pi\)
\(240\) 0 0
\(241\) 1.19550 0.0855040i 1.19550 0.0855040i 0.540641 0.841254i \(-0.318182\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(242\) −0.0702757 + 0.153882i −0.0702757 + 0.153882i
\(243\) −0.895576 0.0640529i −0.895576 0.0640529i
\(244\) 0 0
\(245\) 0 0
\(246\) 0.747009 0.647287i 0.747009 0.647287i
\(247\) 0 0
\(248\) 0 0
\(249\) −0.605000 + 0.941398i −0.605000 + 0.941398i
\(250\) 0 0
\(251\) 0.273100 + 0.0801894i 0.273100 + 0.0801894i 0.415415 0.909632i \(-0.363636\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) 0.841254 + 0.540641i 0.841254 + 0.540641i
\(257\) −0.474017 + 1.61435i −0.474017 + 1.61435i 0.281733 + 0.959493i \(0.409091\pi\)
−0.755750 + 0.654861i \(0.772727\pi\)
\(258\) 0.392818 + 1.33782i 0.392818 + 1.33782i
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) −0.449181 0.698939i −0.449181 0.698939i
\(263\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(264\) −0.605000 0.452897i −0.605000 0.452897i
\(265\) 0 0
\(266\) 0 0
\(267\) 0.148568 0.682956i 0.148568 0.682956i
\(268\) −0.563465 −0.563465
\(269\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(270\) 0 0
\(271\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(272\) 0.708089 + 1.10181i 0.708089 + 1.10181i
\(273\) 0 0
\(274\) −0.0303285 + 0.139418i −0.0303285 + 0.139418i
\(275\) −0.909632 + 0.584585i −0.909632 + 0.584585i
\(276\) 0 0
\(277\) 0 0 0.281733 0.959493i \(-0.409091\pi\)
−0.281733 + 0.959493i \(0.590909\pi\)
\(278\) 1.41542 + 0.909632i 1.41542 + 0.909632i
\(279\) 0 0
\(280\) 0 0
\(281\) 1.71524 0.936593i 1.71524 0.936593i 0.755750 0.654861i \(-0.227273\pi\)
0.959493 0.281733i \(-0.0909091\pi\)
\(282\) 0 0
\(283\) −1.89945 0.557730i −1.89945 0.557730i −0.989821 0.142315i \(-0.954545\pi\)
−0.909632 0.415415i \(-0.863636\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) −0.386565 + 0.334961i −0.386565 + 0.334961i
\(289\) 0.101808 + 0.708089i 0.101808 + 0.708089i
\(290\) 0 0
\(291\) −1.33782 0.0956825i −1.33782 0.0956825i
\(292\) −0.755750 + 1.65486i −0.755750 + 1.65486i
\(293\) 0 0 0.997452 0.0713392i \(-0.0227273\pi\)
−0.997452 + 0.0713392i \(0.977273\pi\)
\(294\) 0.244250 0.654861i 0.244250 0.654861i
\(295\) 0 0
\(296\) 0 0
\(297\) 0.914457 0.684554i 0.914457 0.684554i
\(298\) 0 0
\(299\) 0 0
\(300\) −0.244250 0.654861i −0.244250 0.654861i
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) 0.300613 + 0.300613i 0.300613 + 0.300613i
\(305\) 0 0
\(306\) −0.642785 + 0.188739i −0.642785 + 0.188739i
\(307\) 0.258908 + 0.118239i 0.258908 + 0.118239i 0.540641 0.841254i \(-0.318182\pi\)
−0.281733 + 0.959493i \(0.590909\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(312\) 0 0
\(313\) 0.936593 0.203743i 0.936593 0.203743i 0.281733 0.959493i \(-0.409091\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 0.194583 + 0.521696i 0.194583 + 0.521696i
\(324\) 0.0942450 + 0.206368i 0.0942450 + 0.206368i
\(325\) 0 0
\(326\) −1.50013 + 1.12299i −1.50013 + 1.12299i
\(327\) 0 0
\(328\) 1.32505 + 0.494217i 1.32505 + 0.494217i
\(329\) 0 0
\(330\) 0 0
\(331\) −0.698939 + 1.53046i −0.698939 + 1.53046i 0.142315 + 0.989821i \(0.454545\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(332\) −1.59700 0.114220i −1.59700 0.114220i
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 1.71524 + 0.936593i 1.71524 + 0.936593i 0.959493 + 0.281733i \(0.0909091\pi\)
0.755750 + 0.654861i \(0.227273\pi\)
\(338\) 0.540641 0.841254i 0.540641 0.841254i
\(339\) −0.845715 0.732817i −0.845715 0.732817i
\(340\) 0 0
\(341\) 0 0
\(342\) −0.190855 + 0.104215i −0.190855 + 0.104215i
\(343\) 0 0
\(344\) −1.41061 + 1.41061i −1.41061 + 1.41061i
\(345\) 0 0
\(346\) 0 0
\(347\) 0.557730 + 1.89945i 0.557730 + 1.89945i 0.415415 + 0.909632i \(0.363636\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(348\) 0 0
\(349\) 0 0 0.212565 0.977147i \(-0.431818\pi\)
−0.212565 + 0.977147i \(0.568182\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0.153882 1.07028i 0.153882 1.07028i
\(353\) −0.767317 0.574406i −0.767317 0.574406i 0.142315 0.989821i \(-0.454545\pi\)
−0.909632 + 0.415415i \(0.863636\pi\)
\(354\) −0.0653040 0.0753648i −0.0653040 0.0753648i
\(355\) 0 0
\(356\) 0.959493 0.281733i 0.959493 0.281733i
\(357\) 0 0
\(358\) −1.25667 1.45027i −1.25667 1.45027i
\(359\) 0 0 −0.800541 0.599278i \(-0.795455\pi\)
0.800541 + 0.599278i \(0.204545\pi\)
\(360\) 0 0
\(361\) −0.442928 0.689209i −0.442928 0.689209i
\(362\) 0 0
\(363\) −0.0251332 + 0.115536i −0.0251332 + 0.115536i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(368\) 0 0
\(369\) −0.433499 + 0.579087i −0.433499 + 0.579087i
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 0 0 −0.755750 0.654861i \(-0.772727\pi\)
0.755750 + 0.654861i \(0.227273\pi\)
\(374\) 0.765644 1.19136i 0.765644 1.19136i
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 0.841254 1.54064i 0.841254 1.54064i 1.00000i \(-0.5\pi\)
0.841254 0.540641i \(-0.181818\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 0 0 0.349464 0.936950i \(-0.386364\pi\)
−0.349464 + 0.936950i \(0.613636\pi\)
\(384\) 0.654861 + 0.244250i 0.654861 + 0.244250i
\(385\) 0 0
\(386\) −0.767317 + 0.574406i −0.767317 + 0.574406i
\(387\) −0.489022 0.895576i −0.489022 0.895576i
\(388\) −0.797176 1.74557i −0.797176 1.74557i
\(389\) 0 0 −0.349464 0.936950i \(-0.613636\pi\)
0.349464 + 0.936950i \(0.386364\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0.989821 0.142315i 0.989821 0.142315i
\(393\) −0.410610 0.410610i −0.410610 0.410610i
\(394\) 0 0
\(395\) 0 0
\(396\) 0.503094 + 0.229756i 0.503094 + 0.229756i
\(397\) 0 0 −0.599278 0.800541i \(-0.704545\pi\)
0.599278 + 0.800541i \(0.295455\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0.654861 0.755750i 0.654861 0.755750i
\(401\) 0.368991 0.425839i 0.368991 0.425839i −0.540641 0.841254i \(-0.681818\pi\)
0.909632 + 0.415415i \(0.136364\pi\)
\(402\) −0.384822 + 0.0837128i −0.384822 + 0.0837128i
\(403\) 0 0
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 0.647287 + 0.647287i 0.647287 + 0.647287i
\(409\) 1.89945 0.273100i 1.89945 0.273100i 0.909632 0.415415i \(-0.136364\pi\)
0.989821 + 0.142315i \(0.0454545\pi\)
\(410\) 0 0
\(411\) 0.0997220i 0.0997220i
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 1.10181 + 0.410953i 1.10181 + 0.410953i
\(418\) 0.160644 0.430703i 0.160644 0.430703i
\(419\) −0.956056 + 0.0683785i −0.956056 + 0.0683785i −0.540641 0.841254i \(-0.681818\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(420\) 0 0
\(421\) 0 0 −0.997452 0.0713392i \(-0.977273\pi\)
0.997452 + 0.0713392i \(0.0227273\pi\)
\(422\) −0.956056 + 1.75089i −0.956056 + 1.75089i
\(423\) 0 0
\(424\) 0 0
\(425\) 1.19136 0.544078i 1.19136 0.544078i
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 0.877679 0.479249i \(-0.159091\pi\)
−0.877679 + 0.479249i \(0.840909\pi\)
\(432\) −0.633095 + 0.845715i −0.633095 + 0.845715i
\(433\) 1.32505 1.32505i 1.32505 1.32505i 0.415415 0.909632i \(-0.363636\pi\)
0.909632 0.415415i \(-0.136364\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) −0.270284 + 1.24248i −0.270284 + 1.24248i
\(439\) 0 0 −0.0713392 0.997452i \(-0.522727\pi\)
0.0713392 + 0.997452i \(0.477273\pi\)
\(440\) 0 0
\(441\) −0.0727939 + 0.506293i −0.0727939 + 0.506293i
\(442\) 0 0
\(443\) 1.29639 + 1.49611i 1.29639 + 1.49611i 0.755750 + 0.654861i \(0.227273\pi\)
0.540641 + 0.841254i \(0.318182\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 0.281733 1.95949i 0.281733 1.95949i 1.00000i \(-0.5\pi\)
0.281733 0.959493i \(-0.409091\pi\)
\(450\) 0.276537 + 0.430300i 0.276537 + 0.430300i
\(451\) −0.109089 1.52527i −0.109089 1.52527i
\(452\) 0.340335 1.56449i 0.340335 1.56449i
\(453\) 0 0
\(454\) −0.512546 1.74557i −0.512546 1.74557i
\(455\) 0 0
\(456\) 0.249967 + 0.160644i 0.249967 + 0.160644i
\(457\) −1.24123 + 1.24123i −1.24123 + 1.24123i −0.281733 + 0.959493i \(0.590909\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(458\) 0 0
\(459\) −1.21438 + 0.663103i −1.21438 + 0.663103i
\(460\) 0 0
\(461\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(462\) 0 0
\(463\) 0 0 0.540641 0.841254i \(-0.318182\pi\)
−0.540641 + 0.841254i \(0.681818\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) −0.215109 + 0.186393i −0.215109 + 0.186393i
\(467\) −0.186393 1.29639i −0.186393 1.29639i −0.841254 0.540641i \(-0.818182\pi\)
0.654861 0.755750i \(-0.272727\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 0.0498610 0.133682i 0.0498610 0.133682i
\(473\) 2.02105 + 0.753813i 2.02105 + 0.753813i
\(474\) 0 0
\(475\) 0.340335 0.254771i 0.340335 0.254771i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0.847507 + 0.847507i 0.847507 + 0.847507i
\(483\) 0 0
\(484\) −0.162317 + 0.0476607i −0.162317 + 0.0476607i
\(485\) 0 0
\(486\) −0.538070 0.718777i −0.538070 0.718777i
\(487\) 0 0 −0.989821 0.142315i \(-0.954545\pi\)
0.989821 + 0.142315i \(0.0454545\pi\)
\(488\) 0 0
\(489\) −0.857685 + 0.989821i −0.857685 + 0.989821i
\(490\) 0 0
\(491\) 1.90963 0.415415i 1.90963 0.415415i 0.909632 0.415415i \(-0.136364\pi\)
1.00000 \(0\)
\(492\) 0.978373 + 0.140669i 0.978373 + 0.140669i
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) −1.10765 + 0.159256i −1.10765 + 0.159256i
\(499\) 1.12299 0.418852i 1.12299 0.418852i 0.281733 0.959493i \(-0.409091\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0.118239 + 0.258908i 0.118239 + 0.258908i
\(503\) 0 0 −0.479249 0.877679i \(-0.659091\pi\)
0.479249 + 0.877679i \(0.340909\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 0.244250 0.654861i 0.244250 0.654861i
\(508\) 0 0
\(509\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0.142315 + 0.989821i 0.142315 + 0.989821i
\(513\) −0.339423 + 0.294111i −0.339423 + 0.294111i
\(514\) −1.53046 + 0.698939i −1.53046 + 0.698939i
\(515\) 0 0
\(516\) −0.753813 + 1.17296i −0.753813 + 1.17296i
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 1.19550 1.59700i 1.19550 1.59700i 0.540641 0.841254i \(-0.318182\pi\)
0.654861 0.755750i \(-0.272727\pi\)
\(522\) 0 0
\(523\) −1.53046 0.983568i −1.53046 0.983568i −0.989821 0.142315i \(-0.954545\pi\)
−0.540641 0.841254i \(-0.681818\pi\)
\(524\) 0.234072 0.797176i 0.234072 0.797176i
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) −0.0539138 0.753813i −0.0539138 0.753813i
\(529\) −0.540641 0.841254i −0.540641 0.841254i
\(530\) 0 0
\(531\) 0.0584234 + 0.0437352i 0.0584234 + 0.0437352i
\(532\) 0 0
\(533\) 0 0
\(534\) 0.613435 0.334961i 0.613435 0.334961i
\(535\) 0 0
\(536\) −0.368991 0.425839i −0.368991 0.425839i
\(537\) −1.07371 0.803771i −1.07371 0.803771i
\(538\) 0 0
\(539\) −0.584585 0.909632i −0.584585 0.909632i
\(540\) 0 0
\(541\) 0 0 0.212565 0.977147i \(-0.431818\pi\)
−0.212565 + 0.977147i \(0.568182\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) −0.368991 + 1.25667i −0.368991 + 1.25667i
\(545\) 0 0
\(546\) 0 0
\(547\) 1.17116 1.56449i 1.17116 1.56449i 0.415415 0.909632i \(-0.363636\pi\)
0.755750 0.654861i \(-0.227273\pi\)
\(548\) −0.125226 + 0.0683785i −0.125226 + 0.0683785i
\(549\) 0 0
\(550\) −1.03748 0.304632i −1.03748 0.304632i
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 0.239446 + 1.66538i 0.239446 + 1.66538i
\(557\) 0 0 0.479249 0.877679i \(-0.340909\pi\)
−0.479249 + 0.877679i \(0.659091\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0.345902 0.927399i 0.345902 0.927399i
\(562\) 1.83107 + 0.682956i 1.83107 + 0.682956i
\(563\) 1.90963 + 0.415415i 1.90963 + 0.415415i 1.00000 \(0\)
0.909632 + 0.415415i \(0.136364\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) −0.822373 1.80075i −0.822373 1.80075i
\(567\) 0 0
\(568\) 0 0
\(569\) −1.64468 + 0.613435i −1.64468 + 0.613435i −0.989821 0.142315i \(-0.954545\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(570\) 0 0
\(571\) −1.00000 1.00000i −1.00000 1.00000i 1.00000i \(-0.5\pi\)
−1.00000 \(\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) −0.506293 0.0727939i −0.506293 0.0727939i
\(577\) −0.415415 + 0.0903680i −0.415415 + 0.0903680i −0.415415 0.909632i \(-0.636364\pi\)
1.00000i \(0.5\pi\)
\(578\) −0.468468 + 0.540641i −0.468468 + 0.540641i
\(579\) −0.438705 + 0.506293i −0.438705 + 0.506293i
\(580\) 0 0
\(581\) 0 0
\(582\) −0.803771 1.07371i −0.803771 1.07371i
\(583\) 0 0
\(584\) −1.74557 + 0.512546i −1.74557 + 0.512546i
\(585\) 0 0
\(586\) 0 0
\(587\) 1.66538 0.239446i 1.66538 0.239446i 0.755750 0.654861i \(-0.227273\pi\)
0.909632 + 0.415415i \(0.136364\pi\)
\(588\) 0.654861 0.244250i 0.654861 0.244250i
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 1.40524 1.05195i 1.40524 1.05195i 0.415415 0.909632i \(-0.363636\pi\)
0.989821 0.142315i \(-0.0454545\pi\)
\(594\) 1.11619 + 0.242813i 1.11619 + 0.242813i
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 −0.997452 0.0713392i \(-0.977273\pi\)
0.997452 + 0.0713392i \(0.0227273\pi\)
\(600\) 0.334961 0.613435i 0.334961 0.613435i
\(601\) −0.118239 0.822373i −0.118239 0.822373i −0.959493 0.281733i \(-0.909091\pi\)
0.841254 0.540641i \(-0.181818\pi\)
\(602\) 0 0
\(603\) 0.262167 0.119728i 0.262167 0.119728i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(608\) −0.0303285 + 0.424047i −0.0303285 + 0.424047i
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) −0.563574 0.362187i −0.563574 0.362187i
\(613\) 0 0 0.281733 0.959493i \(-0.409091\pi\)
−0.281733 + 0.959493i \(0.590909\pi\)
\(614\) 0.0801894 + 0.273100i 0.0801894 + 0.273100i
\(615\) 0 0
\(616\) 0 0
\(617\) 0.133682 + 1.86912i 0.133682 + 1.86912i 0.415415 + 0.909632i \(0.363636\pi\)
−0.281733 + 0.959493i \(0.590909\pi\)
\(618\) 0 0
\(619\) 0.118239 0.822373i 0.118239 0.822373i −0.841254 0.540641i \(-0.818182\pi\)
0.959493 0.281733i \(-0.0909091\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −0.654861 0.755750i −0.654861 0.755750i
\(626\) 0.767317 + 0.574406i 0.767317 + 0.574406i
\(627\) 0.0457240 0.318017i 0.0457240 0.318017i
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(632\) 0 0
\(633\) −0.392818 + 1.33782i −0.392818 + 1.33782i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 0.449181 0.698939i 0.449181 0.698939i −0.540641 0.841254i \(-0.681818\pi\)
0.989821 + 0.142315i \(0.0454545\pi\)
\(642\) 0 0
\(643\) −1.74557 + 0.797176i −1.74557 + 0.797176i −0.755750 + 0.654861i \(0.772727\pi\)
−0.989821 + 0.142315i \(0.954545\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −0.266847 + 0.488694i −0.266847 + 0.488694i
\(647\) 0 0 −0.997452 0.0713392i \(-0.977273\pi\)
0.997452 + 0.0713392i \(0.0227273\pi\)
\(648\) −0.0942450 + 0.206368i −0.0942450 + 0.206368i
\(649\) −0.153882 + 0.0110059i −0.153882 + 0.0110059i
\(650\) 0 0
\(651\) 0 0
\(652\) −1.83107 0.398326i −1.83107 0.398326i
\(653\) 0 0 0.800541 0.599278i \(-0.204545\pi\)
−0.800541 + 0.599278i \(0.795455\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0.494217 + 1.32505i 0.494217 + 1.32505i
\(657\) 0.930552i 0.930552i
\(658\) 0 0
\(659\) −0.822373 + 0.118239i −0.822373 + 0.118239i −0.540641 0.841254i \(-0.681818\pi\)
−0.281733 + 0.959493i \(0.590909\pi\)
\(660\) 0 0
\(661\) 0 0 −0.212565 0.977147i \(-0.568182\pi\)
0.212565 + 0.977147i \(0.431818\pi\)
\(662\) −1.61435 + 0.474017i −1.61435 + 0.474017i
\(663\) 0 0
\(664\) −0.959493 1.28173i −0.959493 1.28173i
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 0 0 −0.281733 0.959493i \(-0.590909\pi\)
0.281733 + 0.959493i \(0.409091\pi\)
\(674\) 0.415415 + 1.90963i 0.415415 + 1.90963i
\(675\) 0.747009 + 0.747009i 0.747009 + 0.747009i
\(676\) 0.989821 0.142315i 0.989821 0.142315i
\(677\) 0 0 0.936950 0.349464i \(-0.113636\pi\)
−0.936950 + 0.349464i \(0.886364\pi\)
\(678\) 1.11904i 1.11904i
\(679\) 0 0
\(680\) 0 0
\(681\) −0.609382 1.11600i −0.609382 1.11600i
\(682\) 0 0
\(683\) 1.83107 + 0.398326i 1.83107 + 0.398326i 0.989821 0.142315i \(-0.0454545\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(684\) −0.203743 0.0759924i −0.203743 0.0759924i
\(685\) 0 0
\(686\) 0 0
\(687\) 0 0
\(688\) −1.98982 0.142315i −1.98982 0.142315i
\(689\) 0 0
\(690\) 0 0
\(691\) −0.215109 + 0.186393i −0.215109 + 0.186393i −0.755750 0.654861i \(-0.772727\pi\)
0.540641 + 0.841254i \(0.318182\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) −1.07028 + 1.66538i −1.07028 + 1.66538i
\(695\) 0 0
\(696\) 0 0
\(697\) −0.132136 + 1.84751i −0.132136 + 1.84751i
\(698\) 0 0
\(699\) −0.119218 + 0.159256i −0.119218 + 0.159256i
\(700\) 0 0
\(701\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0.909632 0.584585i 0.909632 0.584585i
\(705\) 0 0
\(706\) −0.0683785 0.956056i −0.0683785 0.956056i
\(707\) 0 0
\(708\) 0.0141919 0.0987069i 0.0141919 0.0987069i
\(709\) 0 0 −0.800541 0.599278i \(-0.795455\pi\)
0.800541 + 0.599278i \(0.204545\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0.841254 + 0.540641i 0.841254 + 0.540641i
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0.273100 1.89945i 0.273100 1.89945i
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 0.212565 0.977147i \(-0.431818\pi\)
−0.212565 + 0.977147i \(0.568182\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0.230813 0.786078i 0.230813 0.786078i
\(723\) 0.704722 + 0.452897i 0.704722 + 0.452897i
\(724\) 0 0
\(725\) 0 0
\(726\) −0.103775 + 0.0566653i −0.103775 + 0.0566653i
\(727\) 0 0 0.0713392 0.997452i \(-0.477273\pi\)
−0.0713392 + 0.997452i \(0.522727\pi\)
\(728\) 0 0
\(729\) −0.645722 0.559521i −0.645722 0.559521i
\(730\) 0 0
\(731\) −2.29317 1.25217i −2.29317 1.25217i
\(732\) 0 0
\(733\) 0 0 0.755750 0.654861i \(-0.227273\pi\)
−0.755750 + 0.654861i \(0.772727\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −0.253098 + 0.554206i −0.253098 + 0.554206i
\(738\) −0.721526 + 0.0516046i −0.721526 + 0.0516046i
\(739\) −0.334961 + 0.898064i −0.334961 + 0.898064i 0.654861 + 0.755750i \(0.272727\pi\)
−0.989821 + 0.142315i \(0.954545\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 −0.479249 0.877679i \(-0.659091\pi\)
0.479249 + 0.877679i \(0.340909\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 0.767317 0.286195i 0.767317 0.286195i
\(748\) 1.40176 0.201543i 1.40176 0.201543i
\(749\) 0 0
\(750\) 0 0
\(751\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(752\) 0 0
\(753\) 0.119218 + 0.159256i 0.119218 + 0.159256i
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(758\) 1.71524 0.373128i 1.71524 0.373128i
\(759\) 0 0
\(760\) 0 0
\(761\) −0.983568 0.449181i −0.983568 0.449181i −0.142315 0.989821i \(-0.545455\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 0.244250 + 0.654861i 0.244250 + 0.654861i
\(769\) 0.822373 + 1.80075i 0.822373 + 1.80075i 0.540641 + 0.841254i \(0.318182\pi\)
0.281733 + 0.959493i \(0.409091\pi\)
\(770\) 0 0
\(771\) −0.941398 + 0.704722i −0.941398 + 0.704722i
\(772\) −0.936593 0.203743i −0.936593 0.203743i
\(773\) 0 0 −0.936950 0.349464i \(-0.886364\pi\)
0.936950 + 0.349464i \(0.113636\pi\)
\(774\) 0.356590 0.956056i 0.356590 0.956056i
\(775\) 0 0
\(776\) 0.797176 1.74557i 0.797176 1.74557i
\(777\) 0 0
\(778\) 0 0
\(779\) 0.0855633 + 0.595106i 0.0855633 + 0.595106i
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 0.755750 + 0.654861i 0.755750 + 0.654861i
\(785\) 0 0
\(786\) 0.0414260 0.579211i 0.0414260 0.579211i
\(787\) 1.05195 0.574406i 1.05195 0.574406i 0.142315 0.989821i \(-0.454545\pi\)
0.909632 + 0.415415i \(0.136364\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0.155819 + 0.530671i 0.155819 + 0.530671i
\(793\) 0 0
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0