Properties

Label 536.1.ba.a.451.1
Level $536$
Weight $1$
Character 536.451
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 451.1
Root \(-0.995472 - 0.0950560i\) of defining polynomial
Character \(\chi\) \(=\) 536.451
Dual form 536.1.ba.a.227.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.580057 - 0.814576i) q^{2} +(1.21769 + 0.782560i) q^{3} +(-0.327068 - 0.945001i) q^{4} +(1.34378 - 0.537970i) q^{6} +(-0.959493 - 0.281733i) q^{8} +(0.454947 + 0.996196i) q^{9} +O(q^{10})\) \(q+(0.580057 - 0.814576i) q^{2} +(1.21769 + 0.782560i) q^{3} +(-0.327068 - 0.945001i) q^{4} +(1.34378 - 0.537970i) q^{6} +(-0.959493 - 0.281733i) q^{8} +(0.454947 + 0.996196i) q^{9} +(-1.78153 - 0.713215i) q^{11} +(0.341254 - 1.40667i) q^{12} +(-0.786053 + 0.618159i) q^{16} +(-0.642315 + 1.85585i) q^{17} +(1.07537 + 0.207261i) q^{18} +(1.56499 - 0.149438i) q^{19} +(-1.61435 + 1.03748i) q^{22} +(-0.947890 - 1.09392i) q^{24} +(-0.959493 + 0.281733i) q^{25} +(-0.0196034 + 0.136345i) q^{27} +(0.0475819 + 0.998867i) q^{32} +(-1.61121 - 2.26262i) q^{33} +(1.13915 + 1.59971i) q^{34} +(0.792607 - 0.755750i) q^{36} +(0.786053 - 1.36148i) q^{38} +(0.815816 - 0.157236i) q^{41} +(-1.21590 - 1.40323i) q^{43} +(-0.0913090 + 1.91681i) q^{44} +(-1.44091 + 0.137591i) q^{48} +(0.981929 + 0.189251i) q^{49} +(-0.327068 + 0.945001i) q^{50} +(-2.23445 + 1.75719i) q^{51} +(0.0996919 + 0.0950560i) q^{54} +(2.02261 + 1.04273i) q^{57} +(-0.452418 - 0.132842i) q^{59} +(0.841254 + 0.540641i) q^{64} -2.77767 q^{66} +(-0.142315 - 0.989821i) q^{67} +1.96386 q^{68} +(-0.155858 - 1.08402i) q^{72} +(-0.607279 + 0.243118i) q^{73} +(-1.38884 - 0.407799i) q^{75} +(-0.653077 - 1.43004i) q^{76} +(0.586611 - 0.676985i) q^{81} +(0.345139 - 0.755750i) q^{82} +(0.223734 - 0.175946i) q^{83} +(-1.84833 + 0.176494i) q^{86} +(1.50842 + 1.18624i) q^{88} +(0.975950 - 0.627205i) q^{89} +(-0.723734 + 1.25354i) q^{96} +(0.327068 + 0.566498i) q^{97} +(0.723734 - 0.690079i) q^{98} +(-0.0999983 - 2.09922i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20q + q^{2} + 2q^{3} + q^{4} - q^{6} - 2q^{8} + O(q^{10}) \) \( 20q + q^{2} + 2q^{3} + q^{4} - q^{6} - 2q^{8} + 2q^{11} - 12q^{12} + q^{16} - 12q^{17} - q^{19} - 4q^{22} + 2q^{24} - 2q^{25} - 2q^{27} + q^{32} - 2q^{33} - q^{34} - q^{38} + 2q^{41} + 2q^{43} + 2q^{44} - q^{48} + q^{49} + q^{50} + q^{51} + 23q^{54} + q^{57} - 9q^{59} - 2q^{64} - 18q^{66} - 2q^{67} + 2q^{68} - q^{73} - 9q^{75} + 2q^{76} + 2q^{81} + 18q^{82} - 9q^{83} - q^{86} + 2q^{88} + 2q^{89} - q^{96} - q^{97} + q^{98} + O(q^{100}) \)

Character values

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

\(n\) \(135\) \(269\) \(337\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{23}{33}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.580057 0.814576i 0.580057 0.814576i
\(3\) 1.21769 + 0.782560i 1.21769 + 0.782560i 0.981929 0.189251i \(-0.0606061\pi\)
0.235759 + 0.971812i \(0.424242\pi\)
\(4\) −0.327068 0.945001i −0.327068 0.945001i
\(5\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(6\) 1.34378 0.537970i 1.34378 0.537970i
\(7\) 0 0 −0.995472 0.0950560i \(-0.969697\pi\)
0.995472 + 0.0950560i \(0.0303030\pi\)
\(8\) −0.959493 0.281733i −0.959493 0.281733i
\(9\) 0.454947 + 0.996196i 0.454947 + 0.996196i
\(10\) 0 0
\(11\) −1.78153 0.713215i −1.78153 0.713215i −0.995472 0.0950560i \(-0.969697\pi\)
−0.786053 0.618159i \(-0.787879\pi\)
\(12\) 0.341254 1.40667i 0.341254 1.40667i
\(13\) 0 0 −0.723734 0.690079i \(-0.757576\pi\)
0.723734 + 0.690079i \(0.242424\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −0.786053 + 0.618159i −0.786053 + 0.618159i
\(17\) −0.642315 + 1.85585i −0.642315 + 1.85585i −0.142315 + 0.989821i \(0.545455\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(18\) 1.07537 + 0.207261i 1.07537 + 0.207261i
\(19\) 1.56499 0.149438i 1.56499 0.149438i 0.723734 0.690079i \(-0.242424\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) −1.61435 + 1.03748i −1.61435 + 1.03748i
\(23\) 0 0 0.0475819 0.998867i \(-0.484848\pi\)
−0.0475819 + 0.998867i \(0.515152\pi\)
\(24\) −0.947890 1.09392i −0.947890 1.09392i
\(25\) −0.959493 + 0.281733i −0.959493 + 0.281733i
\(26\) 0 0
\(27\) −0.0196034 + 0.136345i −0.0196034 + 0.136345i
\(28\) 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 0.723734 0.690079i \(-0.242424\pi\)
−0.723734 + 0.690079i \(0.757576\pi\)
\(32\) 0.0475819 + 0.998867i 0.0475819 + 0.998867i
\(33\) −1.61121 2.26262i −1.61121 2.26262i
\(34\) 1.13915 + 1.59971i 1.13915 + 1.59971i
\(35\) 0 0
\(36\) 0.792607 0.755750i 0.792607 0.755750i
\(37\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(38\) 0.786053 1.36148i 0.786053 1.36148i
\(39\) 0 0
\(40\) 0 0
\(41\) 0.815816 0.157236i 0.815816 0.157236i 0.235759 0.971812i \(-0.424242\pi\)
0.580057 + 0.814576i \(0.303030\pi\)
\(42\) 0 0
\(43\) −1.21590 1.40323i −1.21590 1.40323i −0.888835 0.458227i \(-0.848485\pi\)
−0.327068 0.945001i \(-0.606061\pi\)
\(44\) −0.0913090 + 1.91681i −0.0913090 + 1.91681i
\(45\) 0 0
\(46\) 0 0
\(47\) 0 0 0.888835 0.458227i \(-0.151515\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(48\) −1.44091 + 0.137591i −1.44091 + 0.137591i
\(49\) 0.981929 + 0.189251i 0.981929 + 0.189251i
\(50\) −0.327068 + 0.945001i −0.327068 + 0.945001i
\(51\) −2.23445 + 1.75719i −2.23445 + 1.75719i
\(52\) 0 0
\(53\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(54\) 0.0996919 + 0.0950560i 0.0996919 + 0.0950560i
\(55\) 0 0
\(56\) 0 0
\(57\) 2.02261 + 1.04273i 2.02261 + 1.04273i
\(58\) 0 0
\(59\) −0.452418 0.132842i −0.452418 0.132842i 0.0475819 0.998867i \(-0.484848\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(60\) 0 0
\(61\) 0 0 0.928368 0.371662i \(-0.121212\pi\)
−0.928368 + 0.371662i \(0.878788\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0.841254 + 0.540641i 0.841254 + 0.540641i
\(65\) 0 0
\(66\) −2.77767 −2.77767
\(67\) −0.142315 0.989821i −0.142315 0.989821i
\(68\) 1.96386 1.96386
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 −0.327068 0.945001i \(-0.606061\pi\)
0.327068 + 0.945001i \(0.393939\pi\)
\(72\) −0.155858 1.08402i −0.155858 1.08402i
\(73\) −0.607279 + 0.243118i −0.607279 + 0.243118i −0.654861 0.755750i \(-0.727273\pi\)
0.0475819 + 0.998867i \(0.484848\pi\)
\(74\) 0 0
\(75\) −1.38884 0.407799i −1.38884 0.407799i
\(76\) −0.653077 1.43004i −0.653077 1.43004i
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 0.235759 0.971812i \(-0.424242\pi\)
−0.235759 + 0.971812i \(0.575758\pi\)
\(80\) 0 0
\(81\) 0.586611 0.676985i 0.586611 0.676985i
\(82\) 0.345139 0.755750i 0.345139 0.755750i
\(83\) 0.223734 0.175946i 0.223734 0.175946i −0.500000 0.866025i \(-0.666667\pi\)
0.723734 + 0.690079i \(0.242424\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) −1.84833 + 0.176494i −1.84833 + 0.176494i
\(87\) 0 0
\(88\) 1.50842 + 1.18624i 1.50842 + 1.18624i
\(89\) 0.975950 0.627205i 0.975950 0.627205i 0.0475819 0.998867i \(-0.484848\pi\)
0.928368 + 0.371662i \(0.121212\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) −0.723734 + 1.25354i −0.723734 + 1.25354i
\(97\) 0.327068 + 0.566498i 0.327068 + 0.566498i 0.981929 0.189251i \(-0.0606061\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(98\) 0.723734 0.690079i 0.723734 0.690079i
\(99\) −0.0999983 2.09922i −0.0999983 2.09922i
\(100\) 0.580057 + 0.814576i 0.580057 + 0.814576i
\(101\) 0 0 −0.580057 0.814576i \(-0.696970\pi\)
0.580057 + 0.814576i \(0.303030\pi\)
\(102\) 0.135257 + 2.83940i 0.135257 + 2.83940i
\(103\) 0 0 0.723734 0.690079i \(-0.242424\pi\)
−0.723734 + 0.690079i \(0.757576\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −0.239446 + 1.66538i −0.239446 + 1.66538i 0.415415 + 0.909632i \(0.363636\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(108\) 0.135257 0.0260687i 0.135257 0.0260687i
\(109\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −0.370638 0.291473i −0.370638 0.291473i 0.415415 0.909632i \(-0.363636\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(114\) 2.02261 1.04273i 2.02261 1.04273i
\(115\) 0 0
\(116\) 0 0
\(117\) 0 0
\(118\) −0.370638 + 0.291473i −0.370638 + 0.291473i
\(119\) 0 0
\(120\) 0 0
\(121\) 1.94142 + 1.85114i 1.94142 + 1.85114i
\(122\) 0 0
\(123\) 1.11646 + 0.446961i 1.11646 + 0.446961i
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 0 0 −0.995472 0.0950560i \(-0.969697\pi\)
0.995472 + 0.0950560i \(0.0303030\pi\)
\(128\) 0.928368 0.371662i 0.928368 0.371662i
\(129\) −0.382481 2.66021i −0.382481 2.66021i
\(130\) 0 0
\(131\) 0.698939 + 0.449181i 0.698939 + 0.449181i 0.841254 0.540641i \(-0.181818\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(132\) −1.61121 + 2.26262i −1.61121 + 2.26262i
\(133\) 0 0
\(134\) −0.888835 0.458227i −0.888835 0.458227i
\(135\) 0 0
\(136\) 1.13915 1.59971i 1.13915 1.59971i
\(137\) −1.49547 0.961081i −1.49547 0.961081i −0.995472 0.0950560i \(-0.969697\pi\)
−0.500000 0.866025i \(-0.666667\pi\)
\(138\) 0 0
\(139\) 0.142315 + 0.989821i 0.142315 + 0.989821i 0.928368 + 0.371662i \(0.121212\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) −0.973420 0.501833i −0.973420 0.501833i
\(145\) 0 0
\(146\) −0.154218 + 0.635697i −0.154218 + 0.635697i
\(147\) 1.04758 + 0.998867i 1.04758 + 0.998867i
\(148\) 0 0
\(149\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(150\) −1.13779 + 0.894765i −1.13779 + 0.894765i
\(151\) 0 0 0.327068 0.945001i \(-0.393939\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(152\) −1.54370 0.297523i −1.54370 0.297523i
\(153\) −2.14101 + 0.204441i −2.14101 + 0.204441i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 0 0 0.0475819 0.998867i \(-0.484848\pi\)
−0.0475819 + 0.998867i \(0.515152\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) −0.211188 0.870529i −0.211188 0.870529i
\(163\) 0.995472 1.72421i 0.995472 1.72421i 0.415415 0.909632i \(-0.363636\pi\)
0.580057 0.814576i \(-0.303030\pi\)
\(164\) −0.415415 0.719520i −0.415415 0.719520i
\(165\) 0 0
\(166\) −0.0135432 0.284307i −0.0135432 0.284307i
\(167\) 0 0 −0.580057 0.814576i \(-0.696970\pi\)
0.580057 + 0.814576i \(0.303030\pi\)
\(168\) 0 0
\(169\) 0.0475819 + 0.998867i 0.0475819 + 0.998867i
\(170\) 0 0
\(171\) 0.860857 + 1.49105i 0.860857 + 1.49105i
\(172\) −0.928368 + 1.60798i −0.928368 + 1.60798i
\(173\) 0 0 −0.235759 0.971812i \(-0.575758\pi\)
0.235759 + 0.971812i \(0.424242\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 1.84125 0.540641i 1.84125 0.540641i
\(177\) −0.446947 0.515804i −0.446947 0.515804i
\(178\) 0.0552004 1.15880i 0.0552004 1.15880i
\(179\) −0.239446 + 0.153882i −0.239446 + 0.153882i −0.654861 0.755750i \(-0.727273\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(180\) 0 0
\(181\) 0 0 0.888835 0.458227i \(-0.151515\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 2.46792 2.84813i 2.46792 2.84813i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 0 0 −0.888835 0.458227i \(-0.848485\pi\)
0.888835 + 0.458227i \(0.151515\pi\)
\(192\) 0.601300 + 1.31666i 0.601300 + 1.31666i
\(193\) 1.25667 + 0.368991i 1.25667 + 0.368991i 0.841254 0.540641i \(-0.181818\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(194\) 0.651174 + 0.0621796i 0.651174 + 0.0621796i
\(195\) 0 0
\(196\) −0.142315 0.989821i −0.142315 0.989821i
\(197\) 0 0 −0.327068 0.945001i \(-0.606061\pi\)
0.327068 + 0.945001i \(0.393939\pi\)
\(198\) −1.76798 1.13621i −1.76798 1.13621i
\(199\) 0 0 0.580057 0.814576i \(-0.303030\pi\)
−0.580057 + 0.814576i \(0.696970\pi\)
\(200\) 1.00000 1.00000
\(201\) 0.601300 1.31666i 0.601300 1.31666i
\(202\) 0 0
\(203\) 0 0
\(204\) 2.39136 + 1.53684i 2.39136 + 1.53684i
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −2.89465 0.849945i −2.89465 0.849945i
\(210\) 0 0
\(211\) −1.03115 0.531595i −1.03115 0.531595i −0.142315 0.989821i \(-0.545455\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 1.21769 + 1.16106i 1.21769 + 1.16106i
\(215\) 0 0
\(216\) 0.0572220 0.125299i 0.0572220 0.125299i
\(217\) 0 0
\(218\) 0 0
\(219\) −0.929730 0.179191i −0.929730 0.179191i
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(224\) 0 0
\(225\) −0.717180 0.827670i −0.717180 0.827670i
\(226\) −0.452418 + 0.132842i −0.452418 + 0.132842i
\(227\) −1.95496 + 0.376789i −1.95496 + 0.376789i −0.959493 + 0.281733i \(0.909091\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(228\) 0.323848 2.25241i 0.323848 2.25241i
\(229\) 0 0 −0.235759 0.971812i \(-0.575758\pi\)
0.235759 + 0.971812i \(0.424242\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −0.0475819 0.998867i −0.0475819 0.998867i −0.888835 0.458227i \(-0.848485\pi\)
0.841254 0.540641i \(-0.181818\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0.0224357 + 0.470984i 0.0224357 + 0.470984i
\(237\) 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
\(241\) 0.0405070 0.281733i 0.0405070 0.281733i −0.959493 0.281733i \(-0.909091\pi\)
1.00000 \(0\)
\(242\) 2.63403 0.507668i 2.63403 0.507668i
\(243\) 1.37626 0.404106i 1.37626 0.404106i
\(244\) 0 0
\(245\) 0 0
\(246\) 1.01169 0.650175i 1.01169 0.650175i
\(247\) 0 0
\(248\) 0 0
\(249\) 0.410127 0.0391624i 0.410127 0.0391624i
\(250\) 0 0
\(251\) 0.651174 1.88144i 0.651174 1.88144i 0.235759 0.971812i \(-0.424242\pi\)
0.415415 0.909632i \(-0.363636\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) 0.235759 0.971812i 0.235759 0.971812i
\(257\) −1.21590 0.486774i −1.21590 0.486774i −0.327068 0.945001i \(-0.606061\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(258\) −2.38880 1.23151i −2.38880 1.23151i
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) 0.771316 0.308788i 0.771316 0.308788i
\(263\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(264\) 0.908487 + 2.62490i 0.908487 + 2.62490i
\(265\) 0 0
\(266\) 0 0
\(267\) 1.67923 1.67923
\(268\) −0.888835 + 0.458227i −0.888835 + 0.458227i
\(269\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(270\) 0 0
\(271\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(272\) −0.642315 1.85585i −0.642315 1.85585i
\(273\) 0 0
\(274\) −1.65033 + 0.660694i −1.65033 + 0.660694i
\(275\) 1.91030 + 0.182411i 1.91030 + 0.182411i
\(276\) 0 0
\(277\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(278\) 0.888835 + 0.458227i 0.888835 + 0.458227i
\(279\) 0 0
\(280\) 0 0
\(281\) 1.42131 + 1.35522i 1.42131 + 1.35522i 0.841254 + 0.540641i \(0.181818\pi\)
0.580057 + 0.814576i \(0.303030\pi\)
\(282\) 0 0
\(283\) −0.415415 + 0.909632i −0.415415 + 0.909632i 0.580057 + 0.814576i \(0.303030\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) −0.973420 + 0.501833i −0.973420 + 0.501833i
\(289\) −2.24555 1.76592i −2.24555 1.76592i
\(290\) 0 0
\(291\) −0.0450525 + 0.945768i −0.0450525 + 0.945768i
\(292\) 0.428368 + 0.494363i 0.428368 + 0.494363i
\(293\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(294\) 1.42131 0.273935i 1.42131 0.273935i
\(295\) 0 0
\(296\) 0 0
\(297\) 0.132167 0.228920i 0.132167 0.228920i
\(298\) 0 0
\(299\) 0 0
\(300\) 0.0688733 + 1.44583i 0.0688733 + 1.44583i
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) −1.13779 + 1.08488i −1.13779 + 1.08488i
\(305\) 0 0
\(306\) −1.07537 + 1.86260i −1.07537 + 1.86260i
\(307\) 0.437742 + 1.80440i 0.437742 + 1.80440i 0.580057 + 0.814576i \(0.303030\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(312\) 0 0
\(313\) −1.32254 + 0.849945i −1.32254 + 0.849945i −0.995472 0.0950560i \(-0.969697\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 0 0 −0.981929 0.189251i \(-0.939394\pi\)
0.981929 + 0.189251i \(0.0606061\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) −1.59483 + 1.84053i −1.59483 + 1.84053i
\(322\) 0 0
\(323\) −0.727880 + 3.00036i −0.727880 + 3.00036i
\(324\) −0.831613 0.332928i −0.831613 0.332928i
\(325\) 0 0
\(326\) −0.827068 1.81103i −0.827068 1.81103i
\(327\) 0 0
\(328\) −0.827068 0.0789754i −0.827068 0.0789754i
\(329\) 0 0
\(330\) 0 0
\(331\) 0.514186 + 1.48564i 0.514186 + 1.48564i 0.841254 + 0.540641i \(0.181818\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(332\) −0.239446 0.153882i −0.239446 0.153882i
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −0.759713 + 1.06687i −0.759713 + 1.06687i 0.235759 + 0.971812i \(0.424242\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(338\) 0.841254 + 0.540641i 0.841254 + 0.540641i
\(339\) −0.223226 0.644970i −0.223226 0.644970i
\(340\) 0 0
\(341\) 0 0
\(342\) 1.71392 + 0.163659i 1.71392 + 0.163659i
\(343\) 0 0
\(344\) 0.771316 + 1.68895i 0.771316 + 1.68895i
\(345\) 0 0
\(346\) 0 0
\(347\) −0.235759 + 0.971812i −0.235759 + 0.971812i 0.723734 + 0.690079i \(0.242424\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(348\) 0 0
\(349\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0.627639 1.81344i 0.627639 1.81344i
\(353\) 1.65210 + 0.318417i 1.65210 + 0.318417i 0.928368 0.371662i \(-0.121212\pi\)
0.723734 + 0.690079i \(0.242424\pi\)
\(354\) −0.679417 + 0.0648764i −0.679417 + 0.0648764i
\(355\) 0 0
\(356\) −0.911911 0.717135i −0.911911 0.717135i
\(357\) 0 0
\(358\) −0.0135432 + 0.284307i −0.0135432 + 0.284307i
\(359\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(360\) 0 0
\(361\) 1.44493 0.278487i 1.44493 0.278487i
\(362\) 0 0
\(363\) 0.915415 + 3.77339i 0.915415 + 3.77339i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 0 0 −0.0475819 0.998867i \(-0.515152\pi\)
0.0475819 + 0.998867i \(0.484848\pi\)
\(368\) 0 0
\(369\) 0.527791 + 0.741179i 0.527791 + 0.741179i
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(374\) −0.888485 3.66238i −0.888485 3.66238i
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 0.0395325 0.829889i 0.0395325 0.829889i −0.888835 0.458227i \(-0.848485\pi\)
0.928368 0.371662i \(-0.121212\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 0 0 0.995472 0.0950560i \(-0.0303030\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(384\) 1.42131 + 0.273935i 1.42131 + 0.273935i
\(385\) 0 0
\(386\) 1.02951 0.809616i 1.02951 0.809616i
\(387\) 0.844717 1.84967i 0.844717 1.84967i
\(388\) 0.428368 0.494363i 0.428368 0.494363i
\(389\) 0 0 −0.723734 0.690079i \(-0.757576\pi\)
0.723734 + 0.690079i \(0.242424\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) −0.888835 0.458227i −0.888835 0.458227i
\(393\) 0.499578 + 1.09392i 0.499578 + 1.09392i
\(394\) 0 0
\(395\) 0 0
\(396\) −1.95106 + 0.781087i −1.95106 + 0.781087i
\(397\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0.580057 0.814576i 0.580057 0.814576i
\(401\) −1.30972 −1.30972 −0.654861 0.755750i \(-0.727273\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(402\) −0.723734 1.25354i −0.723734 1.25354i
\(403\) 0 0
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 2.63900 1.05650i 2.63900 1.05650i
\(409\) −1.67489 0.159932i −1.67489 0.159932i −0.786053 0.618159i \(-0.787879\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(410\) 0 0
\(411\) −1.06891 2.34059i −1.06891 2.34059i
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −0.601300 + 1.31666i −0.601300 + 1.31666i
\(418\) −2.37140 + 1.86489i −2.37140 + 1.86489i
\(419\) 0.213947 0.618159i 0.213947 0.618159i −0.786053 0.618159i \(-0.787879\pi\)
1.00000 \(0\)
\(420\) 0 0
\(421\) 0 0 0.995472 0.0950560i \(-0.0303030\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(422\) −1.03115 + 0.531595i −1.03115 + 0.531595i
\(423\) 0 0
\(424\) 0 0
\(425\) 0.0934441 1.96163i 0.0934441 1.96163i
\(426\) 0 0
\(427\) 0 0
\(428\) 1.65210 0.318417i 1.65210 0.318417i
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(432\) −0.0688733 0.119292i −0.0688733 0.119292i
\(433\) −1.28656 + 1.22673i −1.28656 + 1.22673i −0.327068 + 0.945001i \(0.606061\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) −0.685261 + 0.653395i −0.685261 + 0.653395i
\(439\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(440\) 0 0
\(441\) 0.258195 + 1.06429i 0.258195 + 1.06429i
\(442\) 0 0
\(443\) 1.92837 0.371662i 1.92837 0.371662i 0.928368 0.371662i \(-0.121212\pi\)
1.00000 \(0\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 1.70566 0.879330i 1.70566 0.879330i 0.723734 0.690079i \(-0.242424\pi\)
0.981929 0.189251i \(-0.0606061\pi\)
\(450\) −1.09020 + 0.104102i −1.09020 + 0.104102i
\(451\) −1.56554 0.301733i −1.56554 0.301733i
\(452\) −0.154218 + 0.445585i −0.154218 + 0.445585i
\(453\) 0 0
\(454\) −0.827068 + 1.81103i −0.827068 + 1.81103i
\(455\) 0 0
\(456\) −1.64691 1.57033i −1.64691 1.57033i
\(457\) 0.273507 1.12741i 0.273507 1.12741i −0.654861 0.755750i \(-0.727273\pi\)
0.928368 0.371662i \(-0.121212\pi\)
\(458\) 0 0
\(459\) −0.240443 0.123957i −0.240443 0.123957i
\(460\) 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 0.928368 0.371662i \(-0.121212\pi\)
−0.928368 + 0.371662i \(0.878788\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) −0.841254 0.540641i −0.841254 0.540641i
\(467\) −1.11312 + 1.56316i −1.11312 + 1.56316i −0.327068 + 0.945001i \(0.606061\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 0.396666 + 0.254922i 0.396666 + 0.254922i
\(473\) 1.16536 + 3.36709i 1.16536 + 3.36709i
\(474\) 0 0
\(475\) −1.45949 + 0.584293i −1.45949 + 0.584293i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 0 0 −0.888835 0.458227i \(-0.848485\pi\)
0.888835 + 0.458227i \(0.151515\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) −0.205996 0.196417i −0.205996 0.196417i
\(483\) 0 0
\(484\) 1.11435 2.44009i 1.11435 2.44009i
\(485\) 0 0
\(486\) 0.469133 1.35547i 0.469133 1.35547i
\(487\) 0 0 −0.981929 0.189251i \(-0.939394\pi\)
0.981929 + 0.189251i \(0.0606061\pi\)
\(488\) 0 0
\(489\) 2.56147 1.32053i 2.56147 1.32053i
\(490\) 0 0
\(491\) −0.841254 + 0.540641i −0.841254 + 0.540641i −0.888835 0.458227i \(-0.848485\pi\)
0.0475819 + 0.998867i \(0.484848\pi\)
\(492\) 0.0572220 1.20124i 0.0572220 1.20124i
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0.205996 0.356796i 0.205996 0.356796i
\(499\) −0.0475819 0.0824143i −0.0475819 0.0824143i 0.841254 0.540641i \(-0.181818\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) −1.15486 1.62177i −1.15486 1.62177i
\(503\) 0 0 −0.580057 0.814576i \(-0.696970\pi\)
0.580057 + 0.814576i \(0.303030\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −0.723734 + 1.25354i −0.723734 + 1.25354i
\(508\) 0 0
\(509\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −0.654861 0.755750i −0.654861 0.755750i
\(513\) −0.0103040 + 0.216307i −0.0103040 + 0.216307i
\(514\) −1.10181 + 0.708089i −1.10181 + 0.708089i
\(515\) 0 0
\(516\) −2.38880 + 1.23151i −2.38880 + 1.23151i
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 0.0395325 0.0865641i 0.0395325 0.0865641i −0.888835 0.458227i \(-0.848485\pi\)
0.928368 + 0.371662i \(0.121212\pi\)
\(522\) 0 0
\(523\) −1.28656 1.22673i −1.28656 1.22673i −0.959493 0.281733i \(-0.909091\pi\)
−0.327068 0.945001i \(-0.606061\pi\)
\(524\) 0.195876 0.807410i 0.195876 0.807410i
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 2.66516 + 0.782560i 2.66516 + 0.782560i
\(529\) −0.995472 0.0950560i −0.995472 0.0950560i
\(530\) 0 0
\(531\) −0.0734899 0.511133i −0.0734899 0.511133i
\(532\) 0 0
\(533\) 0 0
\(534\) 0.974048 1.36786i 0.974048 1.36786i
\(535\) 0 0
\(536\) −0.142315 + 0.989821i −0.142315 + 0.989821i
\(537\) −0.411992 −0.411992
\(538\) 0 0
\(539\) −1.61435 1.03748i −1.61435 1.03748i
\(540\) 0 0
\(541\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) −1.88431 0.553283i −1.88431 0.553283i
\(545\) 0 0
\(546\) 0 0
\(547\) −0.264241 0.105786i −0.264241 0.105786i 0.235759 0.971812i \(-0.424242\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(548\) −0.419102 + 1.72756i −0.419102 + 1.72756i
\(549\) 0 0
\(550\) 1.25667 1.45027i 1.25667 1.45027i
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 0.888835 0.458227i 0.888835 0.458227i
\(557\) 0 0 −0.786053 0.618159i \(-0.787879\pi\)
0.786053 + 0.618159i \(0.212121\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 5.23399 1.53684i 5.23399 1.53684i
\(562\) 1.92837 0.371662i 1.92837 0.371662i
\(563\) −0.0135432 + 0.0941952i −0.0135432 + 0.0941952i −0.995472 0.0950560i \(-0.969697\pi\)
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
\(569\) −0.379436 0.532843i −0.379436 0.532843i 0.580057 0.814576i \(-0.303030\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(570\) 0 0
\(571\) 0.0934441 + 1.96163i 0.0934441 + 1.96163i 0.235759 + 0.971812i \(0.424242\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) −0.155858 + 1.08402i −0.155858 + 1.08402i
\(577\) 1.13915 0.219553i 1.13915 0.219553i 0.415415 0.909632i \(-0.363636\pi\)
0.723734 + 0.690079i \(0.242424\pi\)
\(578\) −2.74102 + 0.804835i −2.74102 + 0.804835i
\(579\) 1.24147 + 1.43273i 1.24147 + 1.43273i
\(580\) 0 0
\(581\) 0 0
\(582\) 0.744267 + 0.585298i 0.744267 + 0.585298i
\(583\) 0 0
\(584\) 0.651174 0.0621796i 0.651174 0.0621796i
\(585\) 0 0
\(586\) 0 0
\(587\) 0.514186 0.404360i 0.514186 0.404360i −0.327068 0.945001i \(-0.606061\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(588\) 0.601300 1.31666i 0.601300 1.31666i
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 0.581419 + 0.299742i 0.581419 + 0.299742i 0.723734 0.690079i \(-0.242424\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(594\) −0.109808 0.240446i −0.109808 0.240446i
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 −0.327068 0.945001i \(-0.606061\pi\)
0.327068 + 0.945001i \(0.393939\pi\)
\(600\) 1.21769 + 0.782560i 1.21769 + 0.782560i
\(601\) −1.15486 + 1.62177i −1.15486 + 1.62177i −0.500000 + 0.866025i \(0.666667\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(602\) 0 0
\(603\) 0.921310 0.592090i 0.921310 0.592090i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 0 0 −0.327068 0.945001i \(-0.606061\pi\)
0.327068 + 0.945001i \(0.393939\pi\)
\(608\) 0.223734 + 1.55610i 0.223734 + 1.55610i
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0.893452 + 1.95639i 0.893452 + 1.95639i
\(613\) 0 0 −0.888835 0.458227i \(-0.848485\pi\)
0.888835 + 0.458227i \(0.151515\pi\)
\(614\) 1.72373 + 0.690079i 1.72373 + 0.690079i
\(615\) 0 0
\(616\) 0 0
\(617\) −0.544078 + 0.627899i −0.544078 + 0.627899i −0.959493 0.281733i \(-0.909091\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(618\) 0 0
\(619\) 1.39734 1.09888i 1.39734 1.09888i 0.415415 0.909632i \(-0.363636\pi\)
0.981929 0.189251i \(-0.0606061\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 0.841254 0.540641i 0.841254 0.540641i
\(626\) −0.0748038 + 1.57033i −0.0748038 + 1.57033i
\(627\) −2.85964 3.30020i −2.85964 3.30020i
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 0 0 −0.235759 0.971812i \(-0.575758\pi\)
0.235759 + 0.971812i \(0.424242\pi\)
\(632\) 0 0
\(633\) −0.839614 1.45425i −0.839614 1.45425i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 0.995472 1.72421i 0.995472 1.72421i 0.415415 0.909632i \(-0.363636\pi\)
0.580057 0.814576i \(-0.303030\pi\)
\(642\) 0.574161 + 2.36673i 0.574161 + 2.36673i
\(643\) −0.0671040 + 0.466718i −0.0671040 + 0.466718i 0.928368 + 0.371662i \(0.121212\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 2.02181 + 2.33330i 2.02181 + 2.33330i
\(647\) 0 0 0.0475819 0.998867i \(-0.484848\pi\)
−0.0475819 + 0.998867i \(0.515152\pi\)
\(648\) −0.753578 + 0.484295i −0.753578 + 0.484295i
\(649\) 0.711249 + 0.559333i 0.711249 + 0.559333i
\(650\) 0 0
\(651\) 0 0
\(652\) −1.95496 0.376789i −1.95496 0.376789i
\(653\) 0 0 0.327068 0.945001i \(-0.393939\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) −0.544078 + 0.627899i −0.544078 + 0.627899i
\(657\) −0.518473 0.494363i −0.518473 0.494363i
\(658\) 0 0
\(659\) −0.928368 0.371662i −0.928368 0.371662i −0.142315 0.989821i \(-0.545455\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(660\) 0 0
\(661\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(662\) 1.50842 + 0.442913i 1.50842 + 0.442913i
\(663\) 0 0
\(664\) −0.264241 + 0.105786i −0.264241 + 0.105786i
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 0.0800569 + 0.0514495i 0.0800569 + 0.0514495i 0.580057 0.814576i \(-0.303030\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(674\) 0.428368 + 1.23769i 0.428368 + 1.23769i
\(675\) −0.0196034 0.136345i −0.0196034 0.136345i
\(676\) 0.928368 0.371662i 0.928368 0.371662i
\(677\) 0 0 −0.995472 0.0950560i \(-0.969697\pi\)
0.995472 + 0.0950560i \(0.0303030\pi\)
\(678\) −0.654861 0.192284i −0.654861 0.192284i
\(679\) 0 0
\(680\) 0 0
\(681\) −2.67540 1.07107i −2.67540 1.07107i
\(682\) 0 0
\(683\) −1.28656 1.22673i −1.28656 1.22673i −0.959493 0.281733i \(-0.909091\pi\)
−0.327068 0.945001i \(-0.606061\pi\)
\(684\) 1.12748 1.30118i 1.12748 1.30118i
\(685\) 0 0
\(686\) 0 0
\(687\) 0 0
\(688\) 1.82318 + 0.351390i 1.82318 + 0.351390i
\(689\) 0 0
\(690\) 0 0
\(691\) −1.32254 1.04006i −1.32254 1.04006i −0.995472 0.0950560i \(-0.969697\pi\)
−0.327068 0.945001i \(-0.606061\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0.654861 + 0.755750i 0.654861 + 0.755750i
\(695\) 0 0
\(696\) 0 0
\(697\) −0.232205 + 1.61502i −0.232205 + 1.61502i
\(698\) 0 0
\(699\) 0.723734 1.25354i 0.723734 1.25354i
\(700\) 0 0
\(701\) 0 0 0.723734 0.690079i \(-0.242424\pi\)
−0.723734 + 0.690079i \(0.757576\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) −1.11312 1.56316i −1.11312 1.56316i
\(705\) 0 0
\(706\) 1.21769 1.16106i 1.21769 1.16106i
\(707\) 0 0
\(708\) −0.341254 + 0.591068i −0.341254 + 0.591068i
\(709\) 0 0 −0.235759 0.971812i \(-0.575758\pi\)
0.235759 + 0.971812i \(0.424242\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) −1.11312 + 0.326842i −1.11312 + 0.326842i
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0.223734 + 0.175946i 0.223734 + 0.175946i
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 −0.981929 0.189251i \(-0.939394\pi\)
0.981929 + 0.189251i \(0.0606061\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0.611291 1.33854i 0.611291 1.33854i
\(723\) 0.269798 0.311363i 0.269798 0.311363i
\(724\) 0 0
\(725\) 0 0
\(726\) 3.60471 + 1.44311i 3.60471 + 1.44311i
\(727\) 0 0 −0.888835 0.458227i \(-0.848485\pi\)
0.888835 + 0.458227i \(0.151515\pi\)
\(728\) 0 0
\(729\) 1.13259 + 0.332560i 1.13259 + 0.332560i
\(730\) 0 0
\(731\) 3.38517 1.35522i 3.38517 1.35522i
\(732\) 0 0
\(733\) 0 0 −0.327068 0.945001i \(-0.606061\pi\)
0.327068 + 0.945001i \(0.393939\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −0.452418 + 1.86489i −0.452418 + 1.86489i
\(738\) 0.909895 0.909895
\(739\) 0.273507 0.384087i 0.273507 0.384087i −0.654861 0.755750i \(-0.727273\pi\)
0.928368 + 0.371662i \(0.121212\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 0.928368 0.371662i \(-0.121212\pi\)
−0.928368 + 0.371662i \(0.878788\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 0.277064 + 0.142837i 0.277064 + 0.142837i
\(748\) −3.49866 1.40065i −3.49866 1.40065i
\(749\) 0 0
\(750\) 0 0
\(751\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(752\) 0 0
\(753\) 2.26527 1.78143i 2.26527 1.78143i
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 0 0 0.888835 0.458227i \(-0.151515\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(758\) −0.653077 0.513585i −0.653077 0.513585i
\(759\) 0 0
\(760\) 0 0
\(761\) −1.10181 1.27155i −1.10181 1.27155i −0.959493 0.281733i \(-0.909091\pi\)
−0.142315 0.989821i \(-0.545455\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 1.04758 0.998867i 1.04758 0.998867i
\(769\) −0.0947329 1.98869i −0.0947329 1.98869i −0.142315 0.989821i \(-0.545455\pi\)
0.0475819 0.998867i \(-0.484848\pi\)
\(770\) 0 0
\(771\) −1.09966 1.54426i −1.09966 1.54426i
\(772\) −0.0623191 1.30824i −0.0623191 1.30824i
\(773\) 0 0 0.723734 0.690079i \(-0.242424\pi\)
−0.723734 + 0.690079i \(0.757576\pi\)
\(774\) −1.01671 1.76100i −1.01671 1.76100i
\(775\) 0 0
\(776\) −0.154218 0.635697i −0.154218 0.635697i
\(777\) 0 0
\(778\) 0 0
\(779\) 1.25324 0.367986i 1.25324 0.367986i
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) −0.888835 + 0.458227i −0.888835 + 0.458227i
\(785\) 0 0
\(786\) 1.18087 + 0.227594i 1.18087 + 0.227594i
\(787\) −0.550294 + 1.58997i −0.550294 + 1.58997i 0.235759 + 0.971812i \(0.424242\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) −0.495472 + 2.04236i −0.495472 + 2.04236i
\(793\) 0 0
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 0 0 −0.995472 0.0950560i \(-0.969697\pi\)