Properties

Label 536.1.ba.a.475.1
Level $536$
Weight $1$
Character 536.475
Analytic conductor $0.267$
Analytic rank $0$
Dimension $20$
Projective image $D_{33}$
CM discriminant -8
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 536 = 2^{3} \cdot 67 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 536.ba (of order \(66\), degree \(20\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.267498846771\)
Analytic rank: \(0\)
Dimension: \(20\)
Coefficient field: \(\Q(\zeta_{33})\)
Defining polynomial: \(x^{20} - x^{19} + x^{17} - x^{16} + x^{14} - x^{13} + x^{11} - x^{10} + x^{9} - x^{7} + x^{6} - x^{4} + x^{3} - x + 1\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Projective image: \(D_{33}\)
Projective field: Galois closure of \(\mathbb{Q}[x]/(x^{33} - \cdots)\)

Embedding invariants

Embedding label 475.1
Root \(0.981929 - 0.189251i\) of defining polynomial
Character \(\chi\) \(=\) 536.475
Dual form 536.1.ba.a.123.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.327068 + 0.945001i) q^{2} +(0.0395325 - 0.0865641i) q^{3} +(-0.786053 - 0.618159i) q^{4} +(0.0688733 + 0.0656706i) q^{6} +(0.841254 - 0.540641i) q^{8} +(0.648930 + 0.748905i) q^{9} +O(q^{10})\) \(q+(-0.327068 + 0.945001i) q^{2} +(0.0395325 - 0.0865641i) q^{3} +(-0.786053 - 0.618159i) q^{4} +(0.0688733 + 0.0656706i) q^{6} +(0.841254 - 0.540641i) q^{8} +(0.648930 + 0.748905i) q^{9} +(1.21769 - 1.16106i) q^{11} +(-0.0845850 + 0.0436066i) q^{12} +(0.235759 + 0.971812i) q^{16} +(-1.45949 + 1.14776i) q^{17} +(-0.919960 + 0.368297i) q^{18} +(0.462997 + 0.0892353i) q^{19} +(0.698939 + 1.53046i) q^{22} +(-0.0135432 - 0.0941952i) q^{24} +(0.841254 + 0.540641i) q^{25} +(0.181791 - 0.0533787i) q^{27} +(-0.995472 - 0.0950560i) q^{32} +(-0.0523681 - 0.151308i) q^{33} +(-0.607279 - 1.75462i) q^{34} +(-0.0471510 - 0.989821i) q^{36} +(-0.235759 + 0.408346i) q^{38} +(-1.21590 - 0.486774i) q^{41} +(-0.205996 - 1.43273i) q^{43} +(-1.67489 + 0.159932i) q^{44} +(0.0934441 + 0.0180099i) q^{48} +(0.928368 - 0.371662i) q^{49} +(-0.786053 + 0.618159i) q^{50} +(0.0416572 + 0.171713i) q^{51} +(-0.00901515 + 0.189251i) q^{54} +(0.0260280 - 0.0365512i) q^{57} +(-1.49547 + 0.961081i) q^{59} +(0.415415 - 0.909632i) q^{64} +0.160114 q^{66} +(-0.959493 - 0.281733i) q^{67} +1.85674 q^{68} +(0.950804 + 0.279181i) q^{72} +(-1.13779 - 1.08488i) q^{73} +(0.0800569 - 0.0514495i) q^{75} +(-0.308779 - 0.356349i) q^{76} +(-0.138460 + 0.963011i) q^{81} +(0.857685 - 0.989821i) q^{82} +(-0.452418 - 1.86489i) q^{83} +(1.42131 + 0.273935i) q^{86} +(0.396666 - 1.63508i) q^{88} +(-0.271738 - 0.595023i) q^{89} +(-0.0475819 + 0.0824143i) q^{96} +(0.786053 + 1.36148i) q^{97} +(0.0475819 + 0.998867i) q^{98} +(1.65972 + 0.158484i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20q + q^{2} + 2q^{3} + q^{4} - q^{6} - 2q^{8} + O(q^{10}) \) \( 20q + q^{2} + 2q^{3} + q^{4} - q^{6} - 2q^{8} + 2q^{11} - 12q^{12} + q^{16} - 12q^{17} - q^{19} - 4q^{22} + 2q^{24} - 2q^{25} - 2q^{27} + q^{32} - 2q^{33} - q^{34} - q^{38} + 2q^{41} + 2q^{43} + 2q^{44} - q^{48} + q^{49} + q^{50} + q^{51} + 23q^{54} + q^{57} - 9q^{59} - 2q^{64} - 18q^{66} - 2q^{67} + 2q^{68} - q^{73} - 9q^{75} + 2q^{76} + 2q^{81} + 18q^{82} - 9q^{83} - q^{86} + 2q^{88} + 2q^{89} - q^{96} - q^{97} + q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/536\mathbb{Z}\right)^\times\).

\(n\) \(135\) \(269\) \(337\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{20}{33}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.327068 + 0.945001i −0.327068 + 0.945001i
\(3\) 0.0395325 0.0865641i 0.0395325 0.0865641i −0.888835 0.458227i \(-0.848485\pi\)
0.928368 + 0.371662i \(0.121212\pi\)
\(4\) −0.786053 0.618159i −0.786053 0.618159i
\(5\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(6\) 0.0688733 + 0.0656706i 0.0688733 + 0.0656706i
\(7\) 0 0 0.981929 0.189251i \(-0.0606061\pi\)
−0.981929 + 0.189251i \(0.939394\pi\)
\(8\) 0.841254 0.540641i 0.841254 0.540641i
\(9\) 0.648930 + 0.748905i 0.648930 + 0.748905i
\(10\) 0 0
\(11\) 1.21769 1.16106i 1.21769 1.16106i 0.235759 0.971812i \(-0.424242\pi\)
0.981929 0.189251i \(-0.0606061\pi\)
\(12\) −0.0845850 + 0.0436066i −0.0845850 + 0.0436066i
\(13\) 0 0 0.0475819 0.998867i \(-0.484848\pi\)
−0.0475819 + 0.998867i \(0.515152\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0.235759 + 0.971812i 0.235759 + 0.971812i
\(17\) −1.45949 + 1.14776i −1.45949 + 1.14776i −0.500000 + 0.866025i \(0.666667\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(18\) −0.919960 + 0.368297i −0.919960 + 0.368297i
\(19\) 0.462997 + 0.0892353i 0.462997 + 0.0892353i 0.415415 0.909632i \(-0.363636\pi\)
0.0475819 + 0.998867i \(0.484848\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0.698939 + 1.53046i 0.698939 + 1.53046i
\(23\) 0 0 0.995472 0.0950560i \(-0.0303030\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(24\) −0.0135432 0.0941952i −0.0135432 0.0941952i
\(25\) 0.841254 + 0.540641i 0.841254 + 0.540641i
\(26\) 0 0
\(27\) 0.181791 0.0533787i 0.181791 0.0533787i
\(28\) 0 0
\(29\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(30\) 0 0
\(31\) 0 0 −0.0475819 0.998867i \(-0.515152\pi\)
0.0475819 + 0.998867i \(0.484848\pi\)
\(32\) −0.995472 0.0950560i −0.995472 0.0950560i
\(33\) −0.0523681 0.151308i −0.0523681 0.151308i
\(34\) −0.607279 1.75462i −0.607279 1.75462i
\(35\) 0 0
\(36\) −0.0471510 0.989821i −0.0471510 0.989821i
\(37\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(38\) −0.235759 + 0.408346i −0.235759 + 0.408346i
\(39\) 0 0
\(40\) 0 0
\(41\) −1.21590 0.486774i −1.21590 0.486774i −0.327068 0.945001i \(-0.606061\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(42\) 0 0
\(43\) −0.205996 1.43273i −0.205996 1.43273i −0.786053 0.618159i \(-0.787879\pi\)
0.580057 0.814576i \(-0.303030\pi\)
\(44\) −1.67489 + 0.159932i −1.67489 + 0.159932i
\(45\) 0 0
\(46\) 0 0
\(47\) 0 0 −0.580057 0.814576i \(-0.696970\pi\)
0.580057 + 0.814576i \(0.303030\pi\)
\(48\) 0.0934441 + 0.0180099i 0.0934441 + 0.0180099i
\(49\) 0.928368 0.371662i 0.928368 0.371662i
\(50\) −0.786053 + 0.618159i −0.786053 + 0.618159i
\(51\) 0.0416572 + 0.171713i 0.0416572 + 0.171713i
\(52\) 0 0
\(53\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(54\) −0.00901515 + 0.189251i −0.00901515 + 0.189251i
\(55\) 0 0
\(56\) 0 0
\(57\) 0.0260280 0.0365512i 0.0260280 0.0365512i
\(58\) 0 0
\(59\) −1.49547 + 0.961081i −1.49547 + 0.961081i −0.500000 + 0.866025i \(0.666667\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(60\) 0 0
\(61\) 0 0 −0.723734 0.690079i \(-0.757576\pi\)
0.723734 + 0.690079i \(0.242424\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0.415415 0.909632i 0.415415 0.909632i
\(65\) 0 0
\(66\) 0.160114 0.160114
\(67\) −0.959493 0.281733i −0.959493 0.281733i
\(68\) 1.85674 1.85674
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 −0.786053 0.618159i \(-0.787879\pi\)
0.786053 + 0.618159i \(0.212121\pi\)
\(72\) 0.950804 + 0.279181i 0.950804 + 0.279181i
\(73\) −1.13779 1.08488i −1.13779 1.08488i −0.995472 0.0950560i \(-0.969697\pi\)
−0.142315 0.989821i \(-0.545455\pi\)
\(74\) 0 0
\(75\) 0.0800569 0.0514495i 0.0800569 0.0514495i
\(76\) −0.308779 0.356349i −0.308779 0.356349i
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 0.888835 0.458227i \(-0.151515\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(80\) 0 0
\(81\) −0.138460 + 0.963011i −0.138460 + 0.963011i
\(82\) 0.857685 0.989821i 0.857685 0.989821i
\(83\) −0.452418 1.86489i −0.452418 1.86489i −0.500000 0.866025i \(-0.666667\pi\)
0.0475819 0.998867i \(-0.484848\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 1.42131 + 0.273935i 1.42131 + 0.273935i
\(87\) 0 0
\(88\) 0.396666 1.63508i 0.396666 1.63508i
\(89\) −0.271738 0.595023i −0.271738 0.595023i 0.723734 0.690079i \(-0.242424\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) −0.0475819 + 0.0824143i −0.0475819 + 0.0824143i
\(97\) 0.786053 + 1.36148i 0.786053 + 1.36148i 0.928368 + 0.371662i \(0.121212\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(98\) 0.0475819 + 0.998867i 0.0475819 + 0.998867i
\(99\) 1.65972 + 0.158484i 1.65972 + 0.158484i
\(100\) −0.327068 0.945001i −0.327068 0.945001i
\(101\) 0 0 −0.327068 0.945001i \(-0.606061\pi\)
0.327068 + 0.945001i \(0.393939\pi\)
\(102\) −0.175894 0.0167958i −0.175894 0.0167958i
\(103\) 0 0 −0.0475819 0.998867i \(-0.515152\pi\)
0.0475819 + 0.998867i \(0.484848\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −0.797176 + 0.234072i −0.797176 + 0.234072i −0.654861 0.755750i \(-0.727273\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(108\) −0.175894 0.0704173i −0.175894 0.0704173i
\(109\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −0.419102 + 1.72756i −0.419102 + 1.72756i 0.235759 + 0.971812i \(0.424242\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(114\) 0.0260280 + 0.0365512i 0.0260280 + 0.0365512i
\(115\) 0 0
\(116\) 0 0
\(117\) 0 0
\(118\) −0.419102 1.72756i −0.419102 1.72756i
\(119\) 0 0
\(120\) 0 0
\(121\) 0.0871144 1.82876i 0.0871144 1.82876i
\(122\) 0 0
\(123\) −0.0902048 + 0.0860101i −0.0902048 + 0.0860101i
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 0 0 0.981929 0.189251i \(-0.0606061\pi\)
−0.981929 + 0.189251i \(0.939394\pi\)
\(128\) 0.723734 + 0.690079i 0.723734 + 0.690079i
\(129\) −0.132167 0.0388077i −0.132167 0.0388077i
\(130\) 0 0
\(131\) −0.544078 + 1.19136i −0.544078 + 1.19136i 0.415415 + 0.909632i \(0.363636\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(132\) −0.0523681 + 0.151308i −0.0523681 + 0.151308i
\(133\) 0 0
\(134\) 0.580057 0.814576i 0.580057 0.814576i
\(135\) 0 0
\(136\) −0.607279 + 1.75462i −0.607279 + 1.75462i
\(137\) 0.481929 1.05528i 0.481929 1.05528i −0.500000 0.866025i \(-0.666667\pi\)
0.981929 0.189251i \(-0.0606061\pi\)
\(138\) 0 0
\(139\) 0.959493 + 0.281733i 0.959493 + 0.281733i 0.723734 0.690079i \(-0.242424\pi\)
0.235759 + 0.971812i \(0.424242\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) −0.574804 + 0.807199i −0.574804 + 0.807199i
\(145\) 0 0
\(146\) 1.39734 0.720381i 1.39734 0.720381i
\(147\) 0.00452808 0.0950560i 0.00452808 0.0950560i
\(148\) 0 0
\(149\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(150\) 0.0224357 + 0.0924813i 0.0224357 + 0.0924813i
\(151\) 0 0 0.786053 0.618159i \(-0.212121\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(152\) 0.437742 0.175245i 0.437742 0.175245i
\(153\) −1.80667 0.348207i −1.80667 0.348207i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 0 0 0.995472 0.0950560i \(-0.0303030\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) −0.864760 0.445815i −0.864760 0.445815i
\(163\) −0.981929 + 1.70075i −0.981929 + 1.70075i −0.327068 + 0.945001i \(0.606061\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(164\) 0.654861 + 1.13425i 0.654861 + 1.13425i
\(165\) 0 0
\(166\) 1.91030 + 0.182411i 1.91030 + 0.182411i
\(167\) 0 0 −0.327068 0.945001i \(-0.606061\pi\)
0.327068 + 0.945001i \(0.393939\pi\)
\(168\) 0 0
\(169\) −0.995472 0.0950560i −0.995472 0.0950560i
\(170\) 0 0
\(171\) 0.233624 + 0.404648i 0.233624 + 0.404648i
\(172\) −0.723734 + 1.25354i −0.723734 + 1.25354i
\(173\) 0 0 −0.888835 0.458227i \(-0.848485\pi\)
0.888835 + 0.458227i \(0.151515\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 1.41542 + 0.909632i 1.41542 + 0.909632i
\(177\) 0.0240754 + 0.167448i 0.0240754 + 0.167448i
\(178\) 0.651174 0.0621796i 0.651174 0.0621796i
\(179\) −0.797176 1.74557i −0.797176 1.74557i −0.654861 0.755750i \(-0.727273\pi\)
−0.142315 0.989821i \(-0.545455\pi\)
\(180\) 0 0
\(181\) 0 0 −0.580057 0.814576i \(-0.696970\pi\)
0.580057 + 0.814576i \(0.303030\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −0.444587 + 3.09217i −0.444587 + 3.09217i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 0 0 0.580057 0.814576i \(-0.303030\pi\)
−0.580057 + 0.814576i \(0.696970\pi\)
\(192\) −0.0623191 0.0719200i −0.0623191 0.0719200i
\(193\) −0.239446 + 0.153882i −0.239446 + 0.153882i −0.654861 0.755750i \(-0.727273\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(194\) −1.54370 + 0.297523i −1.54370 + 0.297523i
\(195\) 0 0
\(196\) −0.959493 0.281733i −0.959493 0.281733i
\(197\) 0 0 −0.786053 0.618159i \(-0.787879\pi\)
0.786053 + 0.618159i \(0.212121\pi\)
\(198\) −0.692609 + 1.51660i −0.692609 + 1.51660i
\(199\) 0 0 0.327068 0.945001i \(-0.393939\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(200\) 1.00000 1.00000
\(201\) −0.0623191 + 0.0719200i −0.0623191 + 0.0719200i
\(202\) 0 0
\(203\) 0 0
\(204\) 0.0734014 0.160727i 0.0734014 0.160727i
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 0.667393 0.428908i 0.667393 0.428908i
\(210\) 0 0
\(211\) −0.379436 + 0.532843i −0.379436 + 0.532843i −0.959493 0.281733i \(-0.909091\pi\)
0.580057 + 0.814576i \(0.303030\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0.0395325 0.829889i 0.0395325 0.829889i
\(215\) 0 0
\(216\) 0.124074 0.143189i 0.124074 0.143189i
\(217\) 0 0
\(218\) 0 0
\(219\) −0.138891 + 0.0556035i −0.138891 + 0.0556035i
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(224\) 0 0
\(225\) 0.141026 + 0.980857i 0.141026 + 0.980857i
\(226\) −1.49547 0.961081i −1.49547 0.961081i
\(227\) 1.82318 + 0.729892i 1.82318 + 0.729892i 0.981929 + 0.189251i \(0.0606061\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(228\) −0.0430538 + 0.0126417i −0.0430538 + 0.0126417i
\(229\) 0 0 −0.888835 0.458227i \(-0.848485\pi\)
0.888835 + 0.458227i \(0.151515\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 0.995472 + 0.0950560i 0.995472 + 0.0950560i 0.580057 0.814576i \(-0.303030\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 1.76962 + 0.168978i 1.76962 + 0.168978i
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(240\) 0 0
\(241\) 1.84125 0.540641i 1.84125 0.540641i 0.841254 0.540641i \(-0.181818\pi\)
1.00000 \(0\)
\(242\) 1.69968 + 0.680451i 1.69968 + 0.680451i
\(243\) 0.237277 + 0.152489i 0.237277 + 0.152489i
\(244\) 0 0
\(245\) 0 0
\(246\) −0.0517765 0.113375i −0.0517765 0.113375i
\(247\) 0 0
\(248\) 0 0
\(249\) −0.179318 0.0345607i −0.179318 0.0345607i
\(250\) 0 0
\(251\) −1.54370 + 1.21398i −1.54370 + 1.21398i −0.654861 + 0.755750i \(0.727273\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) −0.888835 + 0.458227i −0.888835 + 0.458227i
\(257\) −0.205996 + 0.196417i −0.205996 + 0.196417i −0.786053 0.618159i \(-0.787879\pi\)
0.580057 + 0.814576i \(0.303030\pi\)
\(258\) 0.0799009 0.112205i 0.0799009 0.112205i
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) −0.947890 0.903811i −0.947890 0.903811i
\(263\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(264\) −0.125858 0.0989758i −0.125858 0.0989758i
\(265\) 0 0
\(266\) 0 0
\(267\) −0.0622501 −0.0622501
\(268\) 0.580057 + 0.814576i 0.580057 + 0.814576i
\(269\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(270\) 0 0
\(271\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(272\) −1.45949 1.14776i −1.45949 1.14776i
\(273\) 0 0
\(274\) 0.839614 + 0.800570i 0.839614 + 0.800570i
\(275\) 1.65210 0.318417i 1.65210 0.318417i
\(276\) 0 0
\(277\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(278\) −0.580057 + 0.814576i −0.580057 + 0.814576i
\(279\) 0 0
\(280\) 0 0
\(281\) 0.0883470 1.85463i 0.0883470 1.85463i −0.327068 0.945001i \(-0.606061\pi\)
0.415415 0.909632i \(-0.363636\pi\)
\(282\) 0 0
\(283\) 0.654861 0.755750i 0.654861 0.755750i −0.327068 0.945001i \(-0.606061\pi\)
0.981929 + 0.189251i \(0.0606061\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) −0.574804 0.807199i −0.574804 0.807199i
\(289\) 0.577012 2.37848i 0.577012 2.37848i
\(290\) 0 0
\(291\) 0.148930 0.0142211i 0.148930 0.0142211i
\(292\) 0.223734 + 1.55610i 0.223734 + 1.55610i
\(293\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(294\) 0.0883470 + 0.0353688i 0.0883470 + 0.0353688i
\(295\) 0 0
\(296\) 0 0
\(297\) 0.159389 0.276070i 0.159389 0.276070i
\(298\) 0 0
\(299\) 0 0
\(300\) −0.0947329 0.00904590i −0.0947329 0.00904590i
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) 0.0224357 + 0.470984i 0.0224357 + 0.470984i
\(305\) 0 0
\(306\) 0.919960 1.59342i 0.919960 1.59342i
\(307\) −1.28656 0.663268i −1.28656 0.663268i −0.327068 0.945001i \(-0.606061\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(312\) 0 0
\(313\) 0.195876 + 0.428908i 0.195876 + 0.428908i 0.981929 0.189251i \(-0.0606061\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 0 0 0.928368 0.371662i \(-0.121212\pi\)
−0.928368 + 0.371662i \(0.878788\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) −0.0112521 + 0.0782602i −0.0112521 + 0.0782602i
\(322\) 0 0
\(323\) −0.778161 + 0.401170i −0.778161 + 0.401170i
\(324\) 0.704131 0.671387i 0.704131 0.671387i
\(325\) 0 0
\(326\) −1.28605 1.48418i −1.28605 1.48418i
\(327\) 0 0
\(328\) −1.28605 + 0.247866i −1.28605 + 0.247866i
\(329\) 0 0
\(330\) 0 0
\(331\) −0.370638 0.291473i −0.370638 0.291473i 0.415415 0.909632i \(-0.363636\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(332\) −0.797176 + 1.74557i −0.797176 + 1.74557i
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 0.0930932 0.268975i 0.0930932 0.268975i −0.888835 0.458227i \(-0.848485\pi\)
0.981929 + 0.189251i \(0.0606061\pi\)
\(338\) 0.415415 0.909632i 0.415415 0.909632i
\(339\) 0.132977 + 0.104574i 0.132977 + 0.104574i
\(340\) 0 0
\(341\) 0 0
\(342\) −0.458804 + 0.0884272i −0.458804 + 0.0884272i
\(343\) 0 0
\(344\) −0.947890 1.09392i −0.947890 1.09392i
\(345\) 0 0
\(346\) 0 0
\(347\) 0.888835 0.458227i 0.888835 0.458227i 0.0475819 0.998867i \(-0.484848\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(348\) 0 0
\(349\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −1.32254 + 1.04006i −1.32254 + 1.04006i
\(353\) 0.771316 0.308788i 0.771316 0.308788i 0.0475819 0.998867i \(-0.484848\pi\)
0.723734 + 0.690079i \(0.242424\pi\)
\(354\) −0.166113 0.0320156i −0.166113 0.0320156i
\(355\) 0 0
\(356\) −0.154218 + 0.635697i −0.154218 + 0.635697i
\(357\) 0 0
\(358\) 1.91030 0.182411i 1.91030 0.182411i
\(359\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(360\) 0 0
\(361\) −0.721965 0.289031i −0.721965 0.289031i
\(362\) 0 0
\(363\) −0.154861 0.0798363i −0.154861 0.0798363i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 0 0 −0.995472 0.0950560i \(-0.969697\pi\)
0.995472 + 0.0950560i \(0.0303030\pi\)
\(368\) 0 0
\(369\) −0.424489 1.22648i −0.424489 1.22648i
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(374\) −2.77670 1.43149i −2.77670 1.43149i
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 1.30379 0.124497i 1.30379 0.124497i 0.580057 0.814576i \(-0.303030\pi\)
0.723734 + 0.690079i \(0.242424\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 0 0 −0.981929 0.189251i \(-0.939394\pi\)
0.981929 + 0.189251i \(0.0606061\pi\)
\(384\) 0.0883470 0.0353688i 0.0883470 0.0353688i
\(385\) 0 0
\(386\) −0.0671040 0.276606i −0.0671040 0.276606i
\(387\) 0.939306 1.08402i 0.939306 1.08402i
\(388\) 0.223734 1.55610i 0.223734 1.55610i
\(389\) 0 0 0.0475819 0.998867i \(-0.484848\pi\)
−0.0475819 + 0.998867i \(0.515152\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0.580057 0.814576i 0.580057 0.814576i
\(393\) 0.0816206 + 0.0941952i 0.0816206 + 0.0941952i
\(394\) 0 0
\(395\) 0 0
\(396\) −1.20666 1.15055i −1.20666 1.15055i
\(397\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) −0.327068 + 0.945001i −0.327068 + 0.945001i
\(401\) −0.284630 −0.284630 −0.142315 0.989821i \(-0.545455\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(402\) −0.0475819 0.0824143i −0.0475819 0.0824143i
\(403\) 0 0
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 0.127880 + 0.121933i 0.127880 + 0.121933i
\(409\) 0.815816 0.157236i 0.815816 0.157236i 0.235759 0.971812i \(-0.424242\pi\)
0.580057 + 0.814576i \(0.303030\pi\)
\(410\) 0 0
\(411\) −0.0722972 0.0834354i −0.0722972 0.0834354i
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 0.0623191 0.0719200i 0.0623191 0.0719200i
\(418\) 0.187035 + 0.770969i 0.187035 + 0.770969i
\(419\) 1.23576 0.971812i 1.23576 0.971812i 0.235759 0.971812i \(-0.424242\pi\)
1.00000 \(0\)
\(420\) 0 0
\(421\) 0 0 −0.981929 0.189251i \(-0.939394\pi\)
0.981929 + 0.189251i \(0.0606061\pi\)
\(422\) −0.379436 0.532843i −0.379436 0.532843i
\(423\) 0 0
\(424\) 0 0
\(425\) −1.84833 + 0.176494i −1.84833 + 0.176494i
\(426\) 0 0
\(427\) 0 0
\(428\) 0.771316 + 0.308788i 0.771316 + 0.308788i
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(432\) 0.0947329 + 0.164082i 0.0947329 + 0.164082i
\(433\) 0.0552004 + 1.15880i 0.0552004 + 1.15880i 0.841254 + 0.540641i \(0.181818\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) −0.00711862 0.149438i −0.00711862 0.149438i
\(439\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(440\) 0 0
\(441\) 0.880786 + 0.454077i 0.880786 + 0.454077i
\(442\) 0 0
\(443\) 1.72373 + 0.690079i 1.72373 + 0.690079i 1.00000 \(0\)
0.723734 + 0.690079i \(0.242424\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 0.975950 + 1.37053i 0.975950 + 1.37053i 0.928368 + 0.371662i \(0.121212\pi\)
0.0475819 + 0.998867i \(0.484848\pi\)
\(450\) −0.973036 0.187537i −0.973036 0.187537i
\(451\) −2.04577 + 0.819001i −2.04577 + 0.819001i
\(452\) 1.39734 1.09888i 1.39734 1.09888i
\(453\) 0 0
\(454\) −1.28605 + 1.48418i −1.28605 + 1.48418i
\(455\) 0 0
\(456\) 0.00213507 0.0448206i 0.00213507 0.0448206i
\(457\) 0.581419 0.299742i 0.581419 0.299742i −0.142315 0.989821i \(-0.545455\pi\)
0.723734 + 0.690079i \(0.242424\pi\)
\(458\) 0 0
\(459\) −0.204057 + 0.286558i −0.204057 + 0.286558i
\(460\) 0 0
\(461\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(462\) 0 0
\(463\) 0 0 −0.723734 0.690079i \(-0.757576\pi\)
0.723734 + 0.690079i \(0.242424\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) −0.415415 + 0.909632i −0.415415 + 0.909632i
\(467\) −0.550294 + 1.58997i −0.550294 + 1.58997i 0.235759 + 0.971812i \(0.424242\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) −0.738471 + 1.61703i −0.738471 + 1.61703i
\(473\) −1.91433 1.50545i −1.91433 1.50545i
\(474\) 0 0
\(475\) 0.341254 + 0.325385i 0.341254 + 0.325385i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 0 0 0.580057 0.814576i \(-0.303030\pi\)
−0.580057 + 0.814576i \(0.696970\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) −0.0913090 + 1.91681i −0.0913090 + 1.91681i
\(483\) 0 0
\(484\) −1.19894 + 1.38365i −1.19894 + 1.38365i
\(485\) 0 0
\(486\) −0.221708 + 0.174353i −0.221708 + 0.174353i
\(487\) 0 0 0.928368 0.371662i \(-0.121212\pi\)
−0.928368 + 0.371662i \(0.878788\pi\)
\(488\) 0 0
\(489\) 0.108406 + 0.152235i 0.108406 + 0.152235i
\(490\) 0 0
\(491\) −0.415415 0.909632i −0.415415 0.909632i −0.995472 0.0950560i \(-0.969697\pi\)
0.580057 0.814576i \(-0.303030\pi\)
\(492\) 0.124074 0.0118476i 0.124074 0.0118476i
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0.0913090 0.158152i 0.0913090 0.158152i
\(499\) 0.995472 + 1.72421i 0.995472 + 1.72421i 0.580057 + 0.814576i \(0.303030\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) −0.642315 1.85585i −0.642315 1.85585i
\(503\) 0 0 −0.327068 0.945001i \(-0.606061\pi\)
0.327068 + 0.945001i \(0.393939\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −0.0475819 + 0.0824143i −0.0475819 + 0.0824143i
\(508\) 0 0
\(509\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −0.142315 0.989821i −0.142315 0.989821i
\(513\) 0.0889320 0.00849198i 0.0889320 0.00849198i
\(514\) −0.118239 0.258908i −0.118239 0.258908i
\(515\) 0 0
\(516\) 0.0799009 + 0.112205i 0.0799009 + 0.112205i
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 1.30379 1.50465i 1.30379 1.50465i 0.580057 0.814576i \(-0.303030\pi\)
0.723734 0.690079i \(-0.242424\pi\)
\(522\) 0 0
\(523\) 0.0552004 1.15880i 0.0552004 1.15880i −0.786053 0.618159i \(-0.787879\pi\)
0.841254 0.540641i \(-0.181818\pi\)
\(524\) 1.16413 0.600149i 1.16413 0.600149i
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 0.134696 0.0865641i 0.134696 0.0865641i
\(529\) 0.981929 0.189251i 0.981929 0.189251i
\(530\) 0 0
\(531\) −1.69022 0.496292i −1.69022 0.496292i
\(532\) 0 0
\(533\) 0 0
\(534\) 0.0203600 0.0588264i 0.0203600 0.0588264i
\(535\) 0 0
\(536\) −0.959493 + 0.281733i −0.959493 + 0.281733i
\(537\) −0.182618 −0.182618
\(538\) 0 0
\(539\) 0.698939 1.53046i 0.698939 1.53046i
\(540\) 0 0
\(541\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 1.56199 1.00383i 1.56199 1.00383i
\(545\) 0 0
\(546\) 0 0
\(547\) −1.38884 + 1.32425i −1.38884 + 1.32425i −0.500000 + 0.866025i \(0.666667\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(548\) −1.03115 + 0.531595i −1.03115 + 0.531595i
\(549\) 0 0
\(550\) −0.239446 + 1.66538i −0.239446 + 1.66538i
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) −0.580057 0.814576i −0.580057 0.814576i
\(557\) 0 0 0.235759 0.971812i \(-0.424242\pi\)
−0.235759 + 0.971812i \(0.575758\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0.250095 + 0.160727i 0.250095 + 0.160727i
\(562\) 1.72373 + 0.690079i 1.72373 + 0.690079i
\(563\) 1.91030 0.560914i 1.91030 0.560914i 0.928368 0.371662i \(-0.121212\pi\)
0.981929 0.189251i \(-0.0606061\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(567\) 0 0
\(568\) 0 0
\(569\) 0.514186 + 1.48564i 0.514186 + 1.48564i 0.841254 + 0.540641i \(0.181818\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(570\) 0 0
\(571\) −1.84833 0.176494i −1.84833 0.176494i −0.888835 0.458227i \(-0.848485\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 0.950804 0.279181i 0.950804 0.279181i
\(577\) −0.607279 0.243118i −0.607279 0.243118i 0.0475819 0.998867i \(-0.484848\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(578\) 2.05894 + 1.32320i 2.05894 + 1.32320i
\(579\) 0.00385480 + 0.0268107i 0.00385480 + 0.0268107i
\(580\) 0 0
\(581\) 0 0
\(582\) −0.0352713 + 0.145390i −0.0352713 + 0.145390i
\(583\) 0 0
\(584\) −1.54370 0.297523i −1.54370 0.297523i
\(585\) 0 0
\(586\) 0 0
\(587\) −0.370638 1.52779i −0.370638 1.52779i −0.786053 0.618159i \(-0.787879\pi\)
0.415415 0.909632i \(-0.363636\pi\)
\(588\) −0.0623191 + 0.0719200i −0.0623191 + 0.0719200i
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −0.911911 + 1.28060i −0.911911 + 1.28060i 0.0475819 + 0.998867i \(0.484848\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(594\) 0.208755 + 0.240916i 0.208755 + 0.240916i
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 −0.786053 0.618159i \(-0.787879\pi\)
0.786053 + 0.618159i \(0.212121\pi\)
\(600\) 0.0395325 0.0865641i 0.0395325 0.0865641i
\(601\) −0.642315 + 1.85585i −0.642315 + 1.85585i −0.142315 + 0.989821i \(0.545455\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(602\) 0 0
\(603\) −0.411653 0.901394i −0.411653 0.901394i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 0 0 −0.786053 0.618159i \(-0.787879\pi\)
0.786053 + 0.618159i \(0.212121\pi\)
\(608\) −0.452418 0.132842i −0.452418 0.132842i
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 1.20489 + 1.39052i 1.20489 + 1.39052i
\(613\) 0 0 0.580057 0.814576i \(-0.303030\pi\)
−0.580057 + 0.814576i \(0.696970\pi\)
\(614\) 1.04758 0.998867i 1.04758 0.998867i
\(615\) 0 0
\(616\) 0 0
\(617\) 0.186393 1.29639i 0.186393 1.29639i −0.654861 0.755750i \(-0.727273\pi\)
0.841254 0.540641i \(-0.181818\pi\)
\(618\) 0 0
\(619\) 0.273507 + 1.12741i 0.273507 + 1.12741i 0.928368 + 0.371662i \(0.121212\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 0.415415 + 0.909632i 0.415415 + 0.909632i
\(626\) −0.469383 + 0.0448206i −0.469383 + 0.0448206i
\(627\) −0.0107443 0.0747281i −0.0107443 0.0747281i
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 0 0 −0.888835 0.458227i \(-0.848485\pi\)
0.888835 + 0.458227i \(0.151515\pi\)
\(632\) 0 0
\(633\) 0.0311250 + 0.0539102i 0.0311250 + 0.0539102i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −0.981929 + 1.70075i −0.981929 + 1.70075i −0.327068 + 0.945001i \(0.606061\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(642\) −0.0702757 0.0362297i −0.0702757 0.0362297i
\(643\) 1.70566 0.500828i 1.70566 0.500828i 0.723734 0.690079i \(-0.242424\pi\)
0.981929 + 0.189251i \(0.0606061\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −0.124594 0.866573i −0.124594 0.866573i
\(647\) 0 0 0.995472 0.0950560i \(-0.0303030\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(648\) 0.404163 + 0.884993i 0.404163 + 0.884993i
\(649\) −0.705142 + 2.90663i −0.705142 + 2.90663i
\(650\) 0 0
\(651\) 0 0
\(652\) 1.82318 0.729892i 1.82318 0.729892i
\(653\) 0 0 0.786053 0.618159i \(-0.212121\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0.186393 1.29639i 0.186393 1.29639i
\(657\) 0.0741264 1.55610i 0.0741264 1.55610i
\(658\) 0 0
\(659\) −0.723734 + 0.690079i −0.723734 + 0.690079i −0.959493 0.281733i \(-0.909091\pi\)
0.235759 + 0.971812i \(0.424242\pi\)
\(660\) 0 0
\(661\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(662\) 0.396666 0.254922i 0.396666 0.254922i
\(663\) 0 0
\(664\) −1.38884 1.32425i −1.38884 1.32425i
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) −0.827068 + 1.81103i −0.827068 + 1.81103i −0.327068 + 0.945001i \(0.606061\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(674\) 0.223734 + 0.175946i 0.223734 + 0.175946i
\(675\) 0.181791 + 0.0533787i 0.181791 + 0.0533787i
\(676\) 0.723734 + 0.690079i 0.723734 + 0.690079i
\(677\) 0 0 0.981929 0.189251i \(-0.0606061\pi\)
−0.981929 + 0.189251i \(0.939394\pi\)
\(678\) −0.142315 + 0.0914602i −0.142315 + 0.0914602i
\(679\) 0 0
\(680\) 0 0
\(681\) 0.135257 0.128968i 0.135257 0.128968i
\(682\) 0 0
\(683\) 0.0552004 1.15880i 0.0552004 1.15880i −0.786053 0.618159i \(-0.787879\pi\)
0.841254 0.540641i \(-0.181818\pi\)
\(684\) 0.0664963 0.462492i 0.0664963 0.462492i
\(685\) 0 0
\(686\) 0 0
\(687\) 0 0
\(688\) 1.34378 0.537970i 1.34378 0.537970i
\(689\) 0 0
\(690\) 0 0
\(691\) 0.195876 0.807410i 0.195876 0.807410i −0.786053 0.618159i \(-0.787879\pi\)
0.981929 0.189251i \(-0.0606061\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0.142315 + 0.989821i 0.142315 + 0.989821i
\(695\) 0 0
\(696\) 0 0
\(697\) 2.33330 0.685119i 2.33330 0.685119i
\(698\) 0 0
\(699\) 0.0475819 0.0824143i 0.0475819 0.0824143i
\(700\) 0 0
\(701\) 0 0 −0.0475819 0.998867i \(-0.515152\pi\)
0.0475819 + 0.998867i \(0.484848\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) −0.550294 1.58997i −0.550294 1.58997i
\(705\) 0 0
\(706\) 0.0395325 + 0.829889i 0.0395325 + 0.829889i
\(707\) 0 0
\(708\) 0.0845850 0.146505i 0.0845850 0.146505i
\(709\) 0 0 −0.888835 0.458227i \(-0.848485\pi\)
0.888835 + 0.458227i \(0.151515\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) −0.550294 0.353653i −0.550294 0.353653i
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) −0.452418 + 1.86489i −0.452418 + 1.86489i
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 0.928368 0.371662i \(-0.121212\pi\)
−0.928368 + 0.371662i \(0.878788\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0.509266 0.587724i 0.509266 0.587724i
\(723\) 0.0259893 0.180759i 0.0259893 0.180759i
\(724\) 0 0
\(725\) 0 0
\(726\) 0.126095 0.120232i 0.126095 0.120232i
\(727\) 0 0 0.580057 0.814576i \(-0.303030\pi\)
−0.580057 + 0.814576i \(0.696970\pi\)
\(728\) 0 0
\(729\) −0.795887 + 0.511485i −0.795887 + 0.511485i
\(730\) 0 0
\(731\) 1.94508 + 1.85463i 1.94508 + 1.85463i
\(732\) 0 0
\(733\) 0 0 −0.786053 0.618159i \(-0.787879\pi\)
0.786053 + 0.618159i \(0.212121\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −1.49547 + 0.770969i −1.49547 + 0.770969i
\(738\) 1.29786 1.29786
\(739\) 0.581419 1.67990i 0.581419 1.67990i −0.142315 0.989821i \(-0.545455\pi\)
0.723734 0.690079i \(-0.242424\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 −0.723734 0.690079i \(-0.757576\pi\)
0.723734 + 0.690079i \(0.242424\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 1.10304 1.54900i 1.10304 1.54900i
\(748\) 2.26092 2.15579i 2.26092 2.15579i
\(749\) 0 0
\(750\) 0 0
\(751\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(752\) 0 0
\(753\) 0.0440606 + 0.181620i 0.0440606 + 0.181620i
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 0 0 −0.580057 0.814576i \(-0.696970\pi\)
0.580057 + 0.814576i \(0.303030\pi\)
\(758\) −0.308779 + 1.27280i −0.308779 + 1.27280i
\(759\) 0 0
\(760\) 0 0
\(761\) −0.118239 0.822373i −0.118239 0.822373i −0.959493 0.281733i \(-0.909091\pi\)
0.841254 0.540641i \(-0.181818\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 0.00452808 + 0.0950560i 0.00452808 + 0.0950560i
\(769\) −1.95496 0.186677i −1.95496 0.186677i −0.959493 0.281733i \(-0.909091\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(770\) 0 0
\(771\) 0.00885911 + 0.0255967i 0.00885911 + 0.0255967i
\(772\) 0.283341 + 0.0270558i 0.283341 + 0.0270558i
\(773\) 0 0 −0.0475819 0.998867i \(-0.515152\pi\)
0.0475819 + 0.998867i \(0.484848\pi\)
\(774\) 0.717180 + 1.24219i 0.717180 + 1.24219i
\(775\) 0 0
\(776\) 1.39734 + 0.720381i 1.39734 + 0.720381i
\(777\) 0 0
\(778\) 0 0
\(779\) −0.519522 0.333877i −0.519522 0.333877i
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 0.580057 + 0.814576i 0.580057 + 0.814576i
\(785\) 0 0
\(786\) −0.115710 + 0.0463233i −0.115710 + 0.0463233i
\(787\) −0.653077 + 0.513585i −0.653077 + 0.513585i −0.888835 0.458227i \(-0.848485\pi\)
0.235759 + 0.971812i \(0.424242\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 1.48193 0.763987i 1.48193 0.763987i
\(793\) 0 0
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 0 0 0.981929 0.189251i \(-0.0606061\pi\)