Properties

Label 536.1.ba.a.291.1
Level $536$
Weight $1$
Character 536.291
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 291.1
Root \(0.723734 - 0.690079i\) of defining polynomial
Character \(\chi\) \(=\) 536.291
Dual form 536.1.ba.a.35.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.235759 + 0.971812i) q^{2} +(-0.279486 + 1.94387i) q^{3} +(-0.888835 + 0.458227i) q^{4} +(-1.95496 + 0.186677i) q^{6} +(-0.654861 - 0.755750i) q^{8} +(-2.74102 - 0.804835i) q^{9} +O(q^{10})\) \(q+(0.235759 + 0.971812i) q^{2} +(-0.279486 + 1.94387i) q^{3} +(-0.888835 + 0.458227i) q^{4} +(-1.95496 + 0.186677i) q^{6} +(-0.654861 - 0.755750i) q^{8} +(-2.74102 - 0.804835i) q^{9} +(1.30379 + 0.124497i) q^{11} +(-0.642315 - 1.85585i) q^{12} +(0.580057 - 0.814576i) q^{16} +(-0.0845850 - 0.0436066i) q^{17} +(0.135929 - 2.85350i) q^{18} +(0.839614 + 0.800570i) q^{19} +(0.186393 + 1.29639i) q^{22} +(1.65210 - 1.06174i) q^{24} +(-0.654861 + 0.755750i) q^{25} +(1.51475 - 3.31685i) q^{27} +(0.928368 + 0.371662i) q^{32} +(-0.606397 + 2.49960i) q^{33} +(0.0224357 - 0.0924813i) q^{34} +(2.80511 - 0.540641i) q^{36} +(-0.580057 + 1.00469i) q^{38} +(-0.0913090 - 1.91681i) q^{41} +(-1.67489 + 1.07639i) q^{43} +(-1.21590 + 0.486774i) q^{44} +(1.42131 + 1.35522i) q^{48} +(0.0475819 - 0.998867i) q^{49} +(-0.888835 - 0.458227i) q^{50} +(0.108406 - 0.152235i) q^{51} +(3.58047 + 0.690079i) q^{54} +(-1.79086 + 1.40835i) q^{57} +(0.428368 + 0.494363i) q^{59} +(-0.142315 + 0.989821i) q^{64} -2.57211 q^{66} +(0.415415 + 0.909632i) q^{67} +0.0951638 q^{68} +(1.18673 + 2.59858i) q^{72} +(1.76962 - 0.168978i) q^{73} +(-1.28605 - 1.48418i) q^{75} +(-1.11312 - 0.326842i) q^{76} +(3.62093 + 2.32703i) q^{81} +(1.84125 - 0.540641i) q^{82} +(0.481929 - 0.676774i) q^{83} +(-1.44091 - 1.37391i) q^{86} +(-0.759713 - 1.06687i) q^{88} +(-0.0671040 - 0.466718i) q^{89} +(-0.981929 + 1.70075i) q^{96} +(0.888835 + 1.53951i) q^{97} +(0.981929 - 0.189251i) q^{98} +(-3.47351 - 1.39059i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20q + q^{2} + 2q^{3} + q^{4} - q^{6} - 2q^{8} + O(q^{10}) \) \( 20q + q^{2} + 2q^{3} + q^{4} - q^{6} - 2q^{8} + 2q^{11} - 12q^{12} + q^{16} - 12q^{17} - q^{19} - 4q^{22} + 2q^{24} - 2q^{25} - 2q^{27} + q^{32} - 2q^{33} - q^{34} - q^{38} + 2q^{41} + 2q^{43} + 2q^{44} - q^{48} + q^{49} + q^{50} + q^{51} + 23q^{54} + q^{57} - 9q^{59} - 2q^{64} - 18q^{66} - 2q^{67} + 2q^{68} - q^{73} - 9q^{75} + 2q^{76} + 2q^{81} + 18q^{82} - 9q^{83} - q^{86} + 2q^{88} + 2q^{89} - q^{96} - q^{97} + q^{98} + O(q^{100}) \)

Character values

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

\(n\) \(135\) \(269\) \(337\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{14}{33}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.235759 + 0.971812i 0.235759 + 0.971812i
\(3\) −0.279486 + 1.94387i −0.279486 + 1.94387i 0.0475819 + 0.998867i \(0.484848\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(4\) −0.888835 + 0.458227i −0.888835 + 0.458227i
\(5\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(6\) −1.95496 + 0.186677i −1.95496 + 0.186677i
\(7\) 0 0 0.723734 0.690079i \(-0.242424\pi\)
−0.723734 + 0.690079i \(0.757576\pi\)
\(8\) −0.654861 0.755750i −0.654861 0.755750i
\(9\) −2.74102 0.804835i −2.74102 0.804835i
\(10\) 0 0
\(11\) 1.30379 + 0.124497i 1.30379 + 0.124497i 0.723734 0.690079i \(-0.242424\pi\)
0.580057 + 0.814576i \(0.303030\pi\)
\(12\) −0.642315 1.85585i −0.642315 1.85585i
\(13\) 0 0 −0.981929 0.189251i \(-0.939394\pi\)
0.981929 + 0.189251i \(0.0606061\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0.580057 0.814576i 0.580057 0.814576i
\(17\) −0.0845850 0.0436066i −0.0845850 0.0436066i 0.415415 0.909632i \(-0.363636\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(18\) 0.135929 2.85350i 0.135929 2.85350i
\(19\) 0.839614 + 0.800570i 0.839614 + 0.800570i 0.981929 0.189251i \(-0.0606061\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0.186393 + 1.29639i 0.186393 + 1.29639i
\(23\) 0 0 0.928368 0.371662i \(-0.121212\pi\)
−0.928368 + 0.371662i \(0.878788\pi\)
\(24\) 1.65210 1.06174i 1.65210 1.06174i
\(25\) −0.654861 + 0.755750i −0.654861 + 0.755750i
\(26\) 0 0
\(27\) 1.51475 3.31685i 1.51475 3.31685i
\(28\) 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 0.981929 0.189251i \(-0.0606061\pi\)
−0.981929 + 0.189251i \(0.939394\pi\)
\(32\) 0.928368 + 0.371662i 0.928368 + 0.371662i
\(33\) −0.606397 + 2.49960i −0.606397 + 2.49960i
\(34\) 0.0224357 0.0924813i 0.0224357 0.0924813i
\(35\) 0 0
\(36\) 2.80511 0.540641i 2.80511 0.540641i
\(37\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(38\) −0.580057 + 1.00469i −0.580057 + 1.00469i
\(39\) 0 0
\(40\) 0 0
\(41\) −0.0913090 1.91681i −0.0913090 1.91681i −0.327068 0.945001i \(-0.606061\pi\)
0.235759 0.971812i \(-0.424242\pi\)
\(42\) 0 0
\(43\) −1.67489 + 1.07639i −1.67489 + 1.07639i −0.786053 + 0.618159i \(0.787879\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(44\) −1.21590 + 0.486774i −1.21590 + 0.486774i
\(45\) 0 0
\(46\) 0 0
\(47\) 0 0 −0.786053 0.618159i \(-0.787879\pi\)
0.786053 + 0.618159i \(0.212121\pi\)
\(48\) 1.42131 + 1.35522i 1.42131 + 1.35522i
\(49\) 0.0475819 0.998867i 0.0475819 0.998867i
\(50\) −0.888835 0.458227i −0.888835 0.458227i
\(51\) 0.108406 0.152235i 0.108406 0.152235i
\(52\) 0 0
\(53\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(54\) 3.58047 + 0.690079i 3.58047 + 0.690079i
\(55\) 0 0
\(56\) 0 0
\(57\) −1.79086 + 1.40835i −1.79086 + 1.40835i
\(58\) 0 0
\(59\) 0.428368 + 0.494363i 0.428368 + 0.494363i 0.928368 0.371662i \(-0.121212\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(60\) 0 0
\(61\) 0 0 0.995472 0.0950560i \(-0.0303030\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) −0.142315 + 0.989821i −0.142315 + 0.989821i
\(65\) 0 0
\(66\) −2.57211 −2.57211
\(67\) 0.415415 + 0.909632i 0.415415 + 0.909632i
\(68\) 0.0951638 0.0951638
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 0.888835 0.458227i \(-0.151515\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(72\) 1.18673 + 2.59858i 1.18673 + 2.59858i
\(73\) 1.76962 0.168978i 1.76962 0.168978i 0.841254 0.540641i \(-0.181818\pi\)
0.928368 + 0.371662i \(0.121212\pi\)
\(74\) 0 0
\(75\) −1.28605 1.48418i −1.28605 1.48418i
\(76\) −1.11312 0.326842i −1.11312 0.326842i
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 −0.327068 0.945001i \(-0.606061\pi\)
0.327068 + 0.945001i \(0.393939\pi\)
\(80\) 0 0
\(81\) 3.62093 + 2.32703i 3.62093 + 2.32703i
\(82\) 1.84125 0.540641i 1.84125 0.540641i
\(83\) 0.481929 0.676774i 0.481929 0.676774i −0.500000 0.866025i \(-0.666667\pi\)
0.981929 + 0.189251i \(0.0606061\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) −1.44091 1.37391i −1.44091 1.37391i
\(87\) 0 0
\(88\) −0.759713 1.06687i −0.759713 1.06687i
\(89\) −0.0671040 0.466718i −0.0671040 0.466718i −0.995472 0.0950560i \(-0.969697\pi\)
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
\(96\) −0.981929 + 1.70075i −0.981929 + 1.70075i
\(97\) 0.888835 + 1.53951i 0.888835 + 1.53951i 0.841254 + 0.540641i \(0.181818\pi\)
0.0475819 + 0.998867i \(0.484848\pi\)
\(98\) 0.981929 0.189251i 0.981929 0.189251i
\(99\) −3.47351 1.39059i −3.47351 1.39059i
\(100\) 0.235759 0.971812i 0.235759 0.971812i
\(101\) 0 0 0.235759 0.971812i \(-0.424242\pi\)
−0.235759 + 0.971812i \(0.575758\pi\)
\(102\) 0.173501 + 0.0694593i 0.173501 + 0.0694593i
\(103\) 0 0 0.981929 0.189251i \(-0.0606061\pi\)
−0.981929 + 0.189251i \(0.939394\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −0.118239 + 0.258908i −0.118239 + 0.258908i −0.959493 0.281733i \(-0.909091\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(108\) 0.173501 + 3.64223i 0.173501 + 3.64223i
\(109\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −0.379436 0.532843i −0.379436 0.532843i 0.580057 0.814576i \(-0.303030\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(114\) −1.79086 1.40835i −1.79086 1.40835i
\(115\) 0 0
\(116\) 0 0
\(117\) 0 0
\(118\) −0.379436 + 0.532843i −0.379436 + 0.532843i
\(119\) 0 0
\(120\) 0 0
\(121\) 0.702443 + 0.135385i 0.702443 + 0.135385i
\(122\) 0 0
\(123\) 3.75155 + 0.358230i 3.75155 + 0.358230i
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 0 0 0.723734 0.690079i \(-0.242424\pi\)
−0.723734 + 0.690079i \(0.757576\pi\)
\(128\) −0.995472 + 0.0950560i −0.995472 + 0.0950560i
\(129\) −1.62424 3.55660i −1.62424 3.55660i
\(130\) 0 0
\(131\) 0.273100 1.89945i 0.273100 1.89945i −0.142315 0.989821i \(-0.545455\pi\)
0.415415 0.909632i \(-0.363636\pi\)
\(132\) −0.606397 2.49960i −0.606397 2.49960i
\(133\) 0 0
\(134\) −0.786053 + 0.618159i −0.786053 + 0.618159i
\(135\) 0 0
\(136\) 0.0224357 + 0.0924813i 0.0224357 + 0.0924813i
\(137\) 0.223734 1.55610i 0.223734 1.55610i −0.500000 0.866025i \(-0.666667\pi\)
0.723734 0.690079i \(-0.242424\pi\)
\(138\) 0 0
\(139\) −0.415415 0.909632i −0.415415 0.909632i −0.995472 0.0950560i \(-0.969697\pi\)
0.580057 0.814576i \(-0.303030\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) −2.24555 + 1.76592i −2.24555 + 1.76592i
\(145\) 0 0
\(146\) 0.581419 + 1.67990i 0.581419 + 1.67990i
\(147\) 1.92837 + 0.371662i 1.92837 + 0.371662i
\(148\) 0 0
\(149\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(150\) 1.13915 1.59971i 1.13915 1.59971i
\(151\) 0 0 −0.888835 0.458227i \(-0.848485\pi\)
0.888835 + 0.458227i \(0.151515\pi\)
\(152\) 0.0552004 1.15880i 0.0552004 1.15880i
\(153\) 0.196753 + 0.187603i 0.196753 + 0.187603i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 0 0 0.928368 0.371662i \(-0.121212\pi\)
−0.928368 + 0.371662i \(0.878788\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) −1.40777 + 4.06748i −1.40777 + 4.06748i
\(163\) −0.723734 + 1.25354i −0.723734 + 1.25354i 0.235759 + 0.971812i \(0.424242\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(164\) 0.959493 + 1.66189i 0.959493 + 1.66189i
\(165\) 0 0
\(166\) 0.771316 + 0.308788i 0.771316 + 0.308788i
\(167\) 0 0 0.235759 0.971812i \(-0.424242\pi\)
−0.235759 + 0.971812i \(0.575758\pi\)
\(168\) 0 0
\(169\) 0.928368 + 0.371662i 0.928368 + 0.371662i
\(170\) 0 0
\(171\) −1.65707 2.87013i −1.65707 2.87013i
\(172\) 0.995472 1.72421i 0.995472 1.72421i
\(173\) 0 0 0.327068 0.945001i \(-0.393939\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0.857685 0.989821i 0.857685 0.989821i
\(177\) −1.08070 + 0.694523i −1.08070 + 0.694523i
\(178\) 0.437742 0.175245i 0.437742 0.175245i
\(179\) −0.118239 0.822373i −0.118239 0.822373i −0.959493 0.281733i \(-0.909091\pi\)
0.841254 0.540641i \(-0.181818\pi\)
\(180\) 0 0
\(181\) 0 0 −0.786053 0.618159i \(-0.787879\pi\)
0.786053 + 0.618159i \(0.212121\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −0.104852 0.0673845i −0.104852 0.0673845i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 0 0 0.786053 0.618159i \(-0.212121\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(192\) −1.88431 0.553283i −1.88431 0.553283i
\(193\) −1.10181 1.27155i −1.10181 1.27155i −0.959493 0.281733i \(-0.909091\pi\)
−0.142315 0.989821i \(-0.545455\pi\)
\(194\) −1.28656 + 1.22673i −1.28656 + 1.22673i
\(195\) 0 0
\(196\) 0.415415 + 0.909632i 0.415415 + 0.909632i
\(197\) 0 0 0.888835 0.458227i \(-0.151515\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(198\) 0.532475 3.70344i 0.532475 3.70344i
\(199\) 0 0 −0.235759 0.971812i \(-0.575758\pi\)
0.235759 + 0.971812i \(0.424242\pi\)
\(200\) 1.00000 1.00000
\(201\) −1.88431 + 0.553283i −1.88431 + 0.553283i
\(202\) 0 0
\(203\) 0 0
\(204\) −0.0265970 + 0.184986i −0.0265970 + 0.184986i
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 0.995012 + 1.14831i 0.995012 + 1.14831i
\(210\) 0 0
\(211\) −0.370638 + 0.291473i −0.370638 + 0.291473i −0.786053 0.618159i \(-0.787879\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) −0.279486 0.0538665i −0.279486 0.0538665i
\(215\) 0 0
\(216\) −3.49866 + 1.02730i −3.49866 + 1.02730i
\(217\) 0 0
\(218\) 0 0
\(219\) −0.166113 + 3.48714i −0.166113 + 3.48714i
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(224\) 0 0
\(225\) 2.40324 1.54447i 2.40324 1.54447i
\(226\) 0.428368 0.494363i 0.428368 0.494363i
\(227\) 0.0688733 + 1.44583i 0.0688733 + 1.44583i 0.723734 + 0.690079i \(0.242424\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(228\) 0.946439 2.07241i 0.946439 2.07241i
\(229\) 0 0 0.327068 0.945001i \(-0.393939\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −0.928368 0.371662i −0.928368 0.371662i −0.142315 0.989821i \(-0.545455\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) −0.607279 0.243118i −0.607279 0.243118i
\(237\) 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
\(241\) 0.345139 0.755750i 0.345139 0.755750i −0.654861 0.755750i \(-0.727273\pi\)
1.00000 \(0\)
\(242\) 0.0340387 + 0.714560i 0.0340387 + 0.714560i
\(243\) −3.14757 + 3.63249i −3.14757 + 3.63249i
\(244\) 0 0
\(245\) 0 0
\(246\) 0.536330 + 3.73026i 0.536330 + 3.73026i
\(247\) 0 0
\(248\) 0 0
\(249\) 1.18087 + 1.12595i 1.18087 + 1.12595i
\(250\) 0 0
\(251\) −1.28656 0.663268i −1.28656 0.663268i −0.327068 0.945001i \(-0.606061\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) −0.327068 0.945001i −0.327068 0.945001i
\(257\) −1.67489 0.159932i −1.67489 0.159932i −0.786053 0.618159i \(-0.787879\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(258\) 3.07341 2.41696i 3.07341 2.41696i
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) 1.91030 0.182411i 1.91030 0.182411i
\(263\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(264\) 2.28618 1.17861i 2.28618 1.17861i
\(265\) 0 0
\(266\) 0 0
\(267\) 0.925994 0.925994
\(268\) −0.786053 0.618159i −0.786053 0.618159i
\(269\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(270\) 0 0
\(271\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(272\) −0.0845850 + 0.0436066i −0.0845850 + 0.0436066i
\(273\) 0 0
\(274\) 1.56499 0.149438i 1.56499 0.149438i
\(275\) −0.947890 + 0.903811i −0.947890 + 0.903811i
\(276\) 0 0
\(277\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(278\) 0.786053 0.618159i 0.786053 0.618159i
\(279\) 0 0
\(280\) 0 0
\(281\) 0.0934441 + 0.0180099i 0.0934441 + 0.0180099i 0.235759 0.971812i \(-0.424242\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(282\) 0 0
\(283\) 0.959493 0.281733i 0.959493 0.281733i 0.235759 0.971812i \(-0.424242\pi\)
0.723734 + 0.690079i \(0.242424\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) −2.24555 1.76592i −2.24555 1.76592i
\(289\) −0.574804 0.807199i −0.574804 0.807199i
\(290\) 0 0
\(291\) −3.24102 + 1.29751i −3.24102 + 1.29751i
\(292\) −1.49547 + 0.961081i −1.49547 + 0.961081i
\(293\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(294\) 0.0934441 + 1.96163i 0.0934441 + 1.96163i
\(295\) 0 0
\(296\) 0 0
\(297\) 2.38786 4.13590i 2.38786 4.13590i
\(298\) 0 0
\(299\) 0 0
\(300\) 1.82318 + 0.729892i 1.82318 + 0.729892i
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) 1.13915 0.219553i 1.13915 0.219553i
\(305\) 0 0
\(306\) −0.135929 + 0.235436i −0.135929 + 0.235436i
\(307\) 0.651174 1.88144i 0.651174 1.88144i 0.235759 0.971812i \(-0.424242\pi\)
0.415415 0.909632i \(-0.363636\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(312\) 0 0
\(313\) −0.165101 1.14831i −0.165101 1.14831i −0.888835 0.458227i \(-0.848485\pi\)
0.723734 0.690079i \(-0.242424\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 0 0 0.0475819 0.998867i \(-0.484848\pi\)
−0.0475819 + 0.998867i \(0.515152\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) −0.470237 0.302203i −0.470237 0.302203i
\(322\) 0 0
\(323\) −0.0361086 0.104329i −0.0361086 0.104329i
\(324\) −4.28471 0.409141i −4.28471 0.409141i
\(325\) 0 0
\(326\) −1.38884 0.407799i −1.38884 0.407799i
\(327\) 0 0
\(328\) −1.38884 + 1.32425i −1.38884 + 1.32425i
\(329\) 0 0
\(330\) 0 0
\(331\) −1.03115 + 0.531595i −1.03115 + 0.531595i −0.888835 0.458227i \(-0.848485\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(332\) −0.118239 + 0.822373i −0.118239 + 0.822373i
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 0.396666 + 1.63508i 0.396666 + 1.63508i 0.723734 + 0.690079i \(0.242424\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(338\) −0.142315 + 0.989821i −0.142315 + 0.989821i
\(339\) 1.14182 0.588651i 1.14182 0.588651i
\(340\) 0 0
\(341\) 0 0
\(342\) 2.39856 2.28702i 2.39856 2.28702i
\(343\) 0 0
\(344\) 1.91030 + 0.560914i 1.91030 + 0.560914i
\(345\) 0 0
\(346\) 0 0
\(347\) 0.327068 + 0.945001i 0.327068 + 0.945001i 0.981929 + 0.189251i \(0.0606061\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(348\) 0 0
\(349\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 1.16413 + 0.600149i 1.16413 + 0.600149i
\(353\) −0.0135432 + 0.284307i −0.0135432 + 0.284307i 0.981929 + 0.189251i \(0.0606061\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(354\) −0.929730 0.886496i −0.929730 0.886496i
\(355\) 0 0
\(356\) 0.273507 + 0.384087i 0.273507 + 0.384087i
\(357\) 0 0
\(358\) 0.771316 0.308788i 0.771316 0.308788i
\(359\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(360\) 0 0
\(361\) 0.0164569 + 0.345472i 0.0164569 + 0.345472i
\(362\) 0 0
\(363\) −0.459493 + 1.32762i −0.459493 + 1.32762i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 0 0 −0.928368 0.371662i \(-0.878788\pi\)
0.928368 + 0.371662i \(0.121212\pi\)
\(368\) 0 0
\(369\) −1.29244 + 5.32751i −1.29244 + 5.32751i
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(374\) 0.0407651 0.117783i 0.0407651 0.117783i
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) −1.78153 + 0.713215i −1.78153 + 0.713215i −0.786053 + 0.618159i \(0.787879\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 0 0 −0.723734 0.690079i \(-0.757576\pi\)
0.723734 + 0.690079i \(0.242424\pi\)
\(384\) 0.0934441 1.96163i 0.0934441 1.96163i
\(385\) 0 0
\(386\) 0.975950 1.37053i 0.975950 1.37053i
\(387\) 5.45721 1.60238i 5.45721 1.60238i
\(388\) −1.49547 0.961081i −1.49547 0.961081i
\(389\) 0 0 −0.981929 0.189251i \(-0.939394\pi\)
0.981929 + 0.189251i \(0.0606061\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) −0.786053 + 0.618159i −0.786053 + 0.618159i
\(393\) 3.61596 + 1.06174i 3.61596 + 1.06174i
\(394\) 0 0
\(395\) 0 0
\(396\) 3.72459 0.355655i 3.72459 0.355655i
\(397\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0.235759 + 0.971812i 0.235759 + 0.971812i
\(401\) 1.68251 1.68251 0.841254 0.540641i \(-0.181818\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(402\) −0.981929 1.70075i −0.981929 1.70075i
\(403\) 0 0
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) −0.186042 + 0.0177649i −0.186042 + 0.0177649i
\(409\) −0.205996 + 0.196417i −0.205996 + 0.196417i −0.786053 0.618159i \(-0.787879\pi\)
0.580057 + 0.814576i \(0.303030\pi\)
\(410\) 0 0
\(411\) 2.96233 + 0.869819i 2.96233 + 0.869819i
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 1.88431 0.553283i 1.88431 0.553283i
\(418\) −0.881354 + 1.23769i −0.881354 + 1.23769i
\(419\) 1.58006 + 0.814576i 1.58006 + 0.814576i 1.00000 \(0\)
0.580057 + 0.814576i \(0.303030\pi\)
\(420\) 0 0
\(421\) 0 0 −0.723734 0.690079i \(-0.757576\pi\)
0.723734 + 0.690079i \(0.242424\pi\)
\(422\) −0.370638 0.291473i −0.370638 0.291473i
\(423\) 0 0
\(424\) 0 0
\(425\) 0.0883470 0.0353688i 0.0883470 0.0353688i
\(426\) 0 0
\(427\) 0 0
\(428\) −0.0135432 0.284307i −0.0135432 0.284307i
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(432\) −1.82318 3.15784i −1.82318 3.15784i
\(433\) −1.54370 + 0.297523i −1.54370 + 0.297523i −0.888835 0.458227i \(-0.848485\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) −3.42800 + 0.660694i −3.42800 + 0.660694i
\(439\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(440\) 0 0
\(441\) −0.934347 + 2.69962i −0.934347 + 2.69962i
\(442\) 0 0
\(443\) 0.00452808 + 0.0950560i 0.00452808 + 0.0950560i 1.00000 \(0\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 1.02951 + 0.809616i 1.02951 + 0.809616i 0.981929 0.189251i \(-0.0606061\pi\)
0.0475819 + 0.998867i \(0.484848\pi\)
\(450\) 2.06752 + 1.97137i 2.06752 + 1.97137i
\(451\) 0.119589 2.51049i 0.119589 2.51049i
\(452\) 0.581419 + 0.299742i 0.581419 + 0.299742i
\(453\) 0 0
\(454\) −1.38884 + 0.407799i −1.38884 + 0.407799i
\(455\) 0 0
\(456\) 2.23713 + 0.431171i 2.23713 + 0.431171i
\(457\) −0.154218 0.445585i −0.154218 0.445585i 0.841254 0.540641i \(-0.181818\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(458\) 0 0
\(459\) −0.272762 + 0.214502i −0.272762 + 0.214502i
\(460\) 0 0
\(461\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(462\) 0 0
\(463\) 0 0 0.995472 0.0950560i \(-0.0303030\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0.142315 0.989821i 0.142315 0.989821i
\(467\) −0.308779 1.27280i −0.308779 1.27280i −0.888835 0.458227i \(-0.848485\pi\)
0.580057 0.814576i \(-0.303030\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 0.0930932 0.647478i 0.0930932 0.647478i
\(473\) −2.31771 + 1.19486i −2.31771 + 1.19486i
\(474\) 0 0
\(475\) −1.15486 + 0.110276i −1.15486 + 0.110276i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 0 0 0.786053 0.618159i \(-0.212121\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0.815816 + 0.157236i 0.815816 + 0.157236i
\(483\) 0 0
\(484\) −0.686393 + 0.201543i −0.686393 + 0.201543i
\(485\) 0 0
\(486\) −4.27217 2.20246i −4.27217 2.20246i
\(487\) 0 0 0.0475819 0.998867i \(-0.484848\pi\)
−0.0475819 + 0.998867i \(0.515152\pi\)
\(488\) 0 0
\(489\) −2.23445 1.75719i −2.23445 1.75719i
\(490\) 0 0
\(491\) 0.142315 + 0.989821i 0.142315 + 0.989821i 0.928368 + 0.371662i \(0.121212\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(492\) −3.49866 + 1.40065i −3.49866 + 1.40065i
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) −0.815816 + 1.41303i −0.815816 + 1.41303i
\(499\) −0.928368 1.60798i −0.928368 1.60798i −0.786053 0.618159i \(-0.787879\pi\)
−0.142315 0.989821i \(-0.545455\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0.341254 1.40667i 0.341254 1.40667i
\(503\) 0 0 0.235759 0.971812i \(-0.424242\pi\)
−0.235759 + 0.971812i \(0.575758\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −0.981929 + 1.70075i −0.981929 + 1.70075i
\(508\) 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
\(512\) 0.841254 0.540641i 0.841254 0.540641i
\(513\) 3.92718 1.57221i 3.92718 1.57221i
\(514\) −0.239446 1.66538i −0.239446 1.66538i
\(515\) 0 0
\(516\) 3.07341 + 2.41696i 3.07341 + 2.41696i
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −1.78153 + 0.523103i −1.78153 + 0.523103i −0.995472 0.0950560i \(-0.969697\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(522\) 0 0
\(523\) −1.54370 0.297523i −1.54370 0.297523i −0.654861 0.755750i \(-0.727273\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(524\) 0.627639 + 1.81344i 0.627639 + 1.81344i
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 1.68437 + 1.94387i 1.68437 + 1.94387i
\(529\) 0.723734 0.690079i 0.723734 0.690079i
\(530\) 0 0
\(531\) −0.776283 1.69982i −0.776283 1.69982i
\(532\) 0 0
\(533\) 0 0
\(534\) 0.218311 + 0.899892i 0.218311 + 0.899892i
\(535\) 0 0
\(536\) 0.415415 0.909632i 0.415415 0.909632i
\(537\) 1.63163 1.63163
\(538\) 0 0
\(539\) 0.186393 1.29639i 0.186393 1.29639i
\(540\) 0 0
\(541\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) −0.0623191 0.0719200i −0.0623191 0.0719200i
\(545\) 0 0
\(546\) 0 0
\(547\) −0.827068 0.0789754i −0.827068 0.0789754i −0.327068 0.945001i \(-0.606061\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(548\) 0.514186 + 1.48564i 0.514186 + 1.48564i
\(549\) 0 0
\(550\) −1.10181 0.708089i −1.10181 0.708089i
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 0.786053 + 0.618159i 0.786053 + 0.618159i
\(557\) 0 0 −0.580057 0.814576i \(-0.696970\pi\)
0.580057 + 0.814576i \(0.303030\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0.160291 0.184986i 0.160291 0.184986i
\(562\) 0.00452808 + 0.0950560i 0.00452808 + 0.0950560i
\(563\) 0.771316 1.68895i 0.771316 1.68895i 0.0475819 0.998867i \(-0.484848\pi\)
0.723734 0.690079i \(-0.242424\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(567\) 0 0
\(568\) 0 0
\(569\) −0.419102 + 1.72756i −0.419102 + 1.72756i 0.235759 + 0.971812i \(0.424242\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(570\) 0 0
\(571\) 0.0883470 + 0.0353688i 0.0883470 + 0.0353688i 0.415415 0.909632i \(-0.363636\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 1.18673 2.59858i 1.18673 2.59858i
\(577\) 0.0224357 + 0.470984i 0.0224357 + 0.470984i 0.981929 + 0.189251i \(0.0606061\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(578\) 0.648930 0.748905i 0.648930 0.748905i
\(579\) 2.77967 1.78639i 2.77967 1.78639i
\(580\) 0 0
\(581\) 0 0
\(582\) −2.02503 2.84376i −2.02503 2.84376i
\(583\) 0 0
\(584\) −1.28656 1.22673i −1.28656 1.22673i
\(585\) 0 0
\(586\) 0 0
\(587\) −1.03115 + 1.44805i −1.03115 + 1.44805i −0.142315 + 0.989821i \(0.545455\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(588\) −1.88431 + 0.553283i −1.88431 + 0.553283i
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 1.39734 1.09888i 1.39734 1.09888i 0.415415 0.909632i \(-0.363636\pi\)
0.981929 0.189251i \(-0.0606061\pi\)
\(594\) 4.58227 + 1.34548i 4.58227 + 1.34548i
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 0.888835 0.458227i \(-0.151515\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(600\) −0.279486 + 1.94387i −0.279486 + 1.94387i
\(601\) 0.341254 + 1.40667i 0.341254 + 1.40667i 0.841254 + 0.540641i \(0.181818\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(602\) 0 0
\(603\) −0.406556 2.82766i −0.406556 2.82766i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 0 0 0.888835 0.458227i \(-0.151515\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(608\) 0.481929 + 1.05528i 0.481929 + 1.05528i
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) −0.260846 0.0765912i −0.260846 0.0765912i
\(613\) 0 0 0.786053 0.618159i \(-0.212121\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(614\) 1.98193 + 0.189251i 1.98193 + 0.189251i
\(615\) 0 0
\(616\) 0 0
\(617\) −1.61435 1.03748i −1.61435 1.03748i −0.959493 0.281733i \(-0.909091\pi\)
−0.654861 0.755750i \(-0.727273\pi\)
\(618\) 0 0
\(619\) −0.911911 + 1.28060i −0.911911 + 1.28060i 0.0475819 + 0.998867i \(0.484848\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −0.142315 0.989821i −0.142315 0.989821i
\(626\) 1.07701 0.431171i 1.07701 0.431171i
\(627\) −2.51025 + 1.61324i −2.51025 + 1.61324i
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 0 0 0.327068 0.945001i \(-0.393939\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(632\) 0 0
\(633\) −0.462997 0.801934i −0.462997 0.801934i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −0.723734 + 1.25354i −0.723734 + 1.25354i 0.235759 + 0.971812i \(0.424242\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(642\) 0.182822 0.528229i 0.182822 0.528229i
\(643\) −0.271738 + 0.595023i −0.271738 + 0.595023i −0.995472 0.0950560i \(-0.969697\pi\)
0.723734 + 0.690079i \(0.242424\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0.0928751 0.0596872i 0.0928751 0.0596872i
\(647\) 0 0 0.928368 0.371662i \(-0.121212\pi\)
−0.928368 + 0.371662i \(0.878788\pi\)
\(648\) −0.612552 4.26039i −0.612552 4.26039i
\(649\) 0.496956 + 0.697876i 0.496956 + 0.697876i
\(650\) 0 0
\(651\) 0 0
\(652\) 0.0688733 1.44583i 0.0688733 1.44583i
\(653\) 0 0 −0.888835 0.458227i \(-0.848485\pi\)
0.888835 + 0.458227i \(0.151515\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) −1.61435 1.03748i −1.61435 1.03748i
\(657\) −4.98656 0.961081i −4.98656 0.961081i
\(658\) 0 0
\(659\) 0.995472 + 0.0950560i 0.995472 + 0.0950560i 0.580057 0.814576i \(-0.303030\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(660\) 0 0
\(661\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(662\) −0.759713 0.876756i −0.759713 0.876756i
\(663\) 0 0
\(664\) −0.827068 + 0.0789754i −0.827068 + 0.0789754i
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) −0.264241 + 1.83784i −0.264241 + 1.83784i 0.235759 + 0.971812i \(0.424242\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(674\) −1.49547 + 0.770969i −1.49547 + 0.770969i
\(675\) 1.51475 + 3.31685i 1.51475 + 3.31685i
\(676\) −0.995472 + 0.0950560i −0.995472 + 0.0950560i
\(677\) 0 0 0.723734 0.690079i \(-0.242424\pi\)
−0.723734 + 0.690079i \(0.757576\pi\)
\(678\) 0.841254 + 0.970858i 0.841254 + 0.970858i
\(679\) 0 0
\(680\) 0 0
\(681\) −2.82975 0.270208i −2.82975 0.270208i
\(682\) 0 0
\(683\) −1.54370 0.297523i −1.54370 0.297523i −0.654861 0.755750i \(-0.727273\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(684\) 2.78803 + 1.79176i 2.78803 + 1.79176i
\(685\) 0 0
\(686\) 0 0
\(687\) 0 0
\(688\) −0.0947329 + 1.98869i −0.0947329 + 1.98869i
\(689\) 0 0
\(690\) 0 0
\(691\) −0.165101 0.231852i −0.165101 0.231852i 0.723734 0.690079i \(-0.242424\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) −0.841254 + 0.540641i −0.841254 + 0.540641i
\(695\) 0 0
\(696\) 0 0
\(697\) −0.0758623 + 0.166115i −0.0758623 + 0.166115i
\(698\) 0 0
\(699\) 0.981929 1.70075i 0.981929 1.70075i
\(700\) 0 0
\(701\) 0 0 0.981929 0.189251i \(-0.0606061\pi\)
−0.981929 + 0.189251i \(0.939394\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) −0.308779 + 1.27280i −0.308779 + 1.27280i
\(705\) 0 0
\(706\) −0.279486 + 0.0538665i −0.279486 + 0.0538665i
\(707\) 0 0
\(708\) 0.642315 1.11252i 0.642315 1.11252i
\(709\) 0 0 0.327068 0.945001i \(-0.393939\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) −0.308779 + 0.356349i −0.308779 + 0.356349i
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0.481929 + 0.676774i 0.481929 + 0.676774i
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 0.0475819 0.998867i \(-0.484848\pi\)
−0.0475819 + 0.998867i \(0.515152\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −0.331854 + 0.0974412i −0.331854 + 0.0974412i
\(723\) 1.37262 + 0.882127i 1.37262 + 0.882127i
\(724\) 0 0
\(725\) 0 0
\(726\) −1.39852 0.133543i −1.39852 0.133543i
\(727\) 0 0 0.786053 0.618159i \(-0.212121\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(728\) 0 0
\(729\) −3.36273 3.88080i −3.36273 3.88080i
\(730\) 0 0
\(731\) 0.188608 0.0180099i 0.188608 0.0180099i
\(732\) 0 0
\(733\) 0 0 0.888835 0.458227i \(-0.151515\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0.428368 + 1.23769i 0.428368 + 1.23769i
\(738\) −5.48204 −5.48204
\(739\) −0.154218 0.635697i −0.154218 0.635697i −0.995472 0.0950560i \(-0.969697\pi\)
0.841254 0.540641i \(-0.181818\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 0.995472 0.0950560i \(-0.0303030\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −1.86567 + 1.46718i −1.86567 + 1.46718i
\(748\) 0.124074 + 0.0118476i 0.124074 + 0.0118476i
\(749\) 0 0
\(750\) 0 0
\(751\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(752\) 0 0
\(753\) 1.64888 2.31553i 1.64888 2.31553i
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 0 0 −0.786053 0.618159i \(-0.787879\pi\)
0.786053 + 0.618159i \(0.212121\pi\)
\(758\) −1.11312 1.56316i −1.11312 1.56316i
\(759\) 0 0
\(760\) 0 0
\(761\) −0.239446 + 0.153882i −0.239446 + 0.153882i −0.654861 0.755750i \(-0.727273\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 1.92837 0.371662i 1.92837 0.371662i
\(769\) 1.34378 + 0.537970i 1.34378 + 0.537970i 0.928368 0.371662i \(-0.121212\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(770\) 0 0
\(771\) 0.778996 3.21106i 0.778996 3.21106i
\(772\) 1.56199 + 0.625325i 1.56199 + 0.625325i
\(773\) 0 0 0.981929 0.189251i \(-0.0606061\pi\)
−0.981929 + 0.189251i \(0.939394\pi\)
\(774\) 2.84380 + 4.92561i 2.84380 + 4.92561i
\(775\) 0 0
\(776\) 0.581419 1.67990i 0.581419 1.67990i
\(777\) 0 0
\(778\) 0 0
\(779\) 1.45788 1.68248i 1.45788 1.68248i
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) −0.786053 0.618159i −0.786053 0.618159i
\(785\) 0 0
\(786\) −0.179318 + 3.76435i −0.179318 + 3.76435i
\(787\) 0.252989 + 0.130425i 0.252989 + 0.130425i 0.580057 0.814576i \(-0.303030\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 1.22373 + 3.53575i 1.22373 + 3.53575i
\(793\) 0 0
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 0 0 0.723734 0.690079i \(-0.242424\pi\)
−0.723734 + 0.690079i