Properties

Label 1340.1.bl.b.1299.1
Level $1340$
Weight $1$
Character 1340.1299
Analytic conductor $0.669$
Analytic rank $0$
Dimension $20$
Projective image $D_{33}$
CM discriminant -20
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1340 = 2^{2} \cdot 5 \cdot 67 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1340.bl (of order \(66\), degree \(20\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.668747116928\)
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 1299.1
Root \(-0.888835 + 0.458227i\) of defining polynomial
Character \(\chi\) \(=\) 1340.1299
Dual form 1340.1.bl.b.719.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.580057 + 0.814576i) q^{2} +(-0.550294 + 0.353653i) q^{3} +(-0.327068 + 0.945001i) q^{4} +(-0.142315 + 0.989821i) q^{5} +(-0.607279 - 0.243118i) q^{6} +(-0.0947329 + 0.00904590i) q^{7} +(-0.959493 + 0.281733i) q^{8} +(-0.237662 + 0.520406i) q^{9} +O(q^{10})\) \(q+(0.580057 + 0.814576i) q^{2} +(-0.550294 + 0.353653i) q^{3} +(-0.327068 + 0.945001i) q^{4} +(-0.142315 + 0.989821i) q^{5} +(-0.607279 - 0.243118i) q^{6} +(-0.0947329 + 0.00904590i) q^{7} +(-0.959493 + 0.281733i) q^{8} +(-0.237662 + 0.520406i) q^{9} +(-0.888835 + 0.458227i) q^{10} +(-0.154218 - 0.635697i) q^{12} +(-0.0623191 - 0.0719200i) q^{14} +(-0.271738 - 0.595023i) q^{15} +(-0.786053 - 0.618159i) q^{16} +(-0.561767 + 0.108272i) q^{18} +(-0.888835 - 0.458227i) q^{20} +(0.0489319 - 0.0384804i) q^{21} +(-0.0475819 - 0.998867i) q^{23} +(0.428368 - 0.494363i) q^{24} +(-0.959493 - 0.281733i) q^{25} +(-0.146352 - 1.01790i) q^{27} +(0.0224357 - 0.0924813i) q^{28} +(0.888835 + 1.53951i) q^{29} +(0.327068 - 0.566498i) q^{30} +(0.0475819 - 0.998867i) q^{32} +(0.00452808 - 0.0950560i) q^{35} +(-0.414053 - 0.394798i) q^{36} +(-0.142315 - 0.989821i) q^{40} +(1.42131 + 0.273935i) q^{41} +(0.0597285 + 0.0175379i) q^{42} +(-1.28605 + 1.48418i) q^{43} +(-0.481286 - 0.309304i) q^{45} +(0.786053 - 0.618159i) q^{46} +(-0.419102 - 0.216062i) q^{47} +(0.651174 + 0.0621796i) q^{48} +(-0.973036 + 0.187537i) q^{49} +(-0.327068 - 0.945001i) q^{50} +(0.744267 - 0.709657i) q^{54} +(0.0883470 - 0.0353688i) q^{56} +(-0.738471 + 1.61703i) q^{58} +(0.651174 - 0.0621796i) q^{60} +(-0.264241 - 0.105786i) q^{61} +(0.0178068 - 0.0514495i) q^{63} +(0.841254 - 0.540641i) q^{64} +(0.981929 - 0.189251i) q^{67} +(0.379436 + 0.532843i) q^{69} +(0.0800569 - 0.0514495i) q^{70} +(0.0814192 - 0.566283i) q^{72} +(0.627639 - 0.184291i) q^{75} +(0.723734 - 0.690079i) q^{80} +(0.0658713 + 0.0760196i) q^{81} +(0.601300 + 1.31666i) q^{82} +(1.56499 + 1.23072i) q^{83} +(0.0203600 + 0.0588264i) q^{84} +(-1.95496 - 0.186677i) q^{86} +(-1.03357 - 0.532843i) q^{87} +(0.698939 + 0.449181i) q^{89} +(-0.0272219 - 0.571458i) q^{90} +(0.959493 + 0.281733i) q^{92} +(-0.0671040 - 0.466718i) q^{94} +(0.327068 + 0.566498i) q^{96} +(-0.717180 - 0.683830i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20q + q^{2} + 2q^{3} + q^{4} - 2q^{5} - q^{6} - q^{7} - 2q^{8} + O(q^{10}) \) \( 20q + q^{2} + 2q^{3} + q^{4} - 2q^{5} - q^{6} - q^{7} - 2q^{8} + q^{10} - q^{12} + 2q^{14} + 2q^{15} + q^{16} + q^{20} - 10q^{21} - q^{23} - 9q^{24} - 2q^{25} - 2q^{27} - q^{28} - q^{29} - q^{30} + q^{32} + 21q^{35} - 2q^{40} - q^{41} + 20q^{42} - 9q^{43} - q^{46} - q^{47} - q^{48} + q^{50} + q^{54} - q^{56} + 2q^{58} - q^{60} - 9q^{61} - 11q^{63} - 2q^{64} + q^{67} + q^{69} - 9q^{70} - 11q^{72} + 2q^{75} + q^{80} + 2q^{81} + 2q^{82} - q^{83} + q^{84} - q^{86} + q^{87} - 4q^{89} + 2q^{92} + 2q^{94} - q^{96} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1340\mathbb{Z}\right)^\times\).

\(n\) \(537\) \(671\) \(1141\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{10}{33}\right)\)

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
\(3\) −0.550294 + 0.353653i −0.550294 + 0.353653i −0.786053 0.618159i \(-0.787879\pi\)
0.235759 + 0.971812i \(0.424242\pi\)
\(4\) −0.327068 + 0.945001i −0.327068 + 0.945001i
\(5\) −0.142315 + 0.989821i −0.142315 + 0.989821i
\(6\) −0.607279 0.243118i −0.607279 0.243118i
\(7\) −0.0947329 + 0.00904590i −0.0947329 + 0.00904590i −0.142315 0.989821i \(-0.545455\pi\)
0.0475819 + 0.998867i \(0.484848\pi\)
\(8\) −0.959493 + 0.281733i −0.959493 + 0.281733i
\(9\) −0.237662 + 0.520406i −0.237662 + 0.520406i
\(10\) −0.888835 + 0.458227i −0.888835 + 0.458227i
\(11\) 0 0 0.928368 0.371662i \(-0.121212\pi\)
−0.928368 + 0.371662i \(0.878788\pi\)
\(12\) −0.154218 0.635697i −0.154218 0.635697i
\(13\) 0 0 0.723734 0.690079i \(-0.242424\pi\)
−0.723734 + 0.690079i \(0.757576\pi\)
\(14\) −0.0623191 0.0719200i −0.0623191 0.0719200i
\(15\) −0.271738 0.595023i −0.271738 0.595023i
\(16\) −0.786053 0.618159i −0.786053 0.618159i
\(17\) 0 0 −0.327068 0.945001i \(-0.606061\pi\)
0.327068 + 0.945001i \(0.393939\pi\)
\(18\) −0.561767 + 0.108272i −0.561767 + 0.108272i
\(19\) 0 0 −0.995472 0.0950560i \(-0.969697\pi\)
0.995472 + 0.0950560i \(0.0303030\pi\)
\(20\) −0.888835 0.458227i −0.888835 0.458227i
\(21\) 0.0489319 0.0384804i 0.0489319 0.0384804i
\(22\) 0 0
\(23\) −0.0475819 0.998867i −0.0475819 0.998867i −0.888835 0.458227i \(-0.848485\pi\)
0.841254 0.540641i \(-0.181818\pi\)
\(24\) 0.428368 0.494363i 0.428368 0.494363i
\(25\) −0.959493 0.281733i −0.959493 0.281733i
\(26\) 0 0
\(27\) −0.146352 1.01790i −0.146352 1.01790i
\(28\) 0.0224357 0.0924813i 0.0224357 0.0924813i
\(29\) 0.888835 + 1.53951i 0.888835 + 1.53951i 0.841254 + 0.540641i \(0.181818\pi\)
0.0475819 + 0.998867i \(0.484848\pi\)
\(30\) 0.327068 0.566498i 0.327068 0.566498i
\(31\) 0 0 −0.723734 0.690079i \(-0.757576\pi\)
0.723734 + 0.690079i \(0.242424\pi\)
\(32\) 0.0475819 0.998867i 0.0475819 0.998867i
\(33\) 0 0
\(34\) 0 0
\(35\) 0.00452808 0.0950560i 0.00452808 0.0950560i
\(36\) −0.414053 0.394798i −0.414053 0.394798i
\(37\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) −0.142315 0.989821i −0.142315 0.989821i
\(41\) 1.42131 + 0.273935i 1.42131 + 0.273935i 0.841254 0.540641i \(-0.181818\pi\)
0.580057 + 0.814576i \(0.303030\pi\)
\(42\) 0.0597285 + 0.0175379i 0.0597285 + 0.0175379i
\(43\) −1.28605 + 1.48418i −1.28605 + 1.48418i −0.500000 + 0.866025i \(0.666667\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(44\) 0 0
\(45\) −0.481286 0.309304i −0.481286 0.309304i
\(46\) 0.786053 0.618159i 0.786053 0.618159i
\(47\) −0.419102 0.216062i −0.419102 0.216062i 0.235759 0.971812i \(-0.424242\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(48\) 0.651174 + 0.0621796i 0.651174 + 0.0621796i
\(49\) −0.973036 + 0.187537i −0.973036 + 0.187537i
\(50\) −0.327068 0.945001i −0.327068 0.945001i
\(51\) 0 0
\(52\) 0 0
\(53\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(54\) 0.744267 0.709657i 0.744267 0.709657i
\(55\) 0 0
\(56\) 0.0883470 0.0353688i 0.0883470 0.0353688i
\(57\) 0 0
\(58\) −0.738471 + 1.61703i −0.738471 + 1.61703i
\(59\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(60\) 0.651174 0.0621796i 0.651174 0.0621796i
\(61\) −0.264241 0.105786i −0.264241 0.105786i 0.235759 0.971812i \(-0.424242\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(62\) 0 0
\(63\) 0.0178068 0.0514495i 0.0178068 0.0514495i
\(64\) 0.841254 0.540641i 0.841254 0.540641i
\(65\) 0 0
\(66\) 0 0
\(67\) 0.981929 0.189251i 0.981929 0.189251i
\(68\) 0 0
\(69\) 0.379436 + 0.532843i 0.379436 + 0.532843i
\(70\) 0.0800569 0.0514495i 0.0800569 0.0514495i
\(71\) 0 0 0.327068 0.945001i \(-0.393939\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(72\) 0.0814192 0.566283i 0.0814192 0.566283i
\(73\) 0 0 −0.928368 0.371662i \(-0.878788\pi\)
0.928368 + 0.371662i \(0.121212\pi\)
\(74\) 0 0
\(75\) 0.627639 0.184291i 0.627639 0.184291i
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 −0.235759 0.971812i \(-0.575758\pi\)
0.235759 + 0.971812i \(0.424242\pi\)
\(80\) 0.723734 0.690079i 0.723734 0.690079i
\(81\) 0.0658713 + 0.0760196i 0.0658713 + 0.0760196i
\(82\) 0.601300 + 1.31666i 0.601300 + 1.31666i
\(83\) 1.56499 + 1.23072i 1.56499 + 1.23072i 0.841254 + 0.540641i \(0.181818\pi\)
0.723734 + 0.690079i \(0.242424\pi\)
\(84\) 0.0203600 + 0.0588264i 0.0203600 + 0.0588264i
\(85\) 0 0
\(86\) −1.95496 0.186677i −1.95496 0.186677i
\(87\) −1.03357 0.532843i −1.03357 0.532843i
\(88\) 0 0
\(89\) 0.698939 + 0.449181i 0.698939 + 0.449181i 0.841254 0.540641i \(-0.181818\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(90\) −0.0272219 0.571458i −0.0272219 0.571458i
\(91\) 0 0
\(92\) 0.959493 + 0.281733i 0.959493 + 0.281733i
\(93\) 0 0
\(94\) −0.0671040 0.466718i −0.0671040 0.466718i
\(95\) 0 0
\(96\) 0.327068 + 0.566498i 0.327068 + 0.566498i
\(97\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(98\) −0.717180 0.683830i −0.717180 0.683830i
\(99\) 0 0
\(100\) 0.580057 0.814576i 0.580057 0.814576i
\(101\) 0.481929 0.676774i 0.481929 0.676774i −0.500000 0.866025i \(-0.666667\pi\)
0.981929 + 0.189251i \(0.0606061\pi\)
\(102\) 0 0
\(103\) 0.839614 + 0.800570i 0.839614 + 0.800570i 0.981929 0.189251i \(-0.0606061\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(104\) 0 0
\(105\) 0.0311250 + 0.0539102i 0.0311250 + 0.0539102i
\(106\) 0 0
\(107\) 0.273100 + 1.89945i 0.273100 + 1.89945i 0.415415 + 0.909632i \(0.363636\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(108\) 1.00979 + 0.194621i 1.00979 + 0.194621i
\(109\) −1.11312 0.326842i −1.11312 0.326842i −0.327068 0.945001i \(-0.606061\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0.0800569 + 0.0514495i 0.0800569 + 0.0514495i
\(113\) 0 0 0.786053 0.618159i \(-0.212121\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(114\) 0 0
\(115\) 0.995472 + 0.0950560i 0.995472 + 0.0950560i
\(116\) −1.74555 + 0.336426i −1.74555 + 0.336426i
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0.428368 + 0.494363i 0.428368 + 0.494363i
\(121\) 0.723734 0.690079i 0.723734 0.690079i
\(122\) −0.0671040 0.276606i −0.0671040 0.276606i
\(123\) −0.879017 + 0.351905i −0.879017 + 0.351905i
\(124\) 0 0
\(125\) 0.415415 0.909632i 0.415415 0.909632i
\(126\) 0.0522385 0.0153386i 0.0522385 0.0153386i
\(127\) −1.84833 + 0.176494i −1.84833 + 0.176494i −0.959493 0.281733i \(-0.909091\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(128\) 0.928368 + 0.371662i 0.928368 + 0.371662i
\(129\) 0.182822 1.27155i 0.182822 1.27155i
\(130\) 0 0
\(131\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0.723734 + 0.690079i 0.723734 + 0.690079i
\(135\) 1.02837 1.02837
\(136\) 0 0
\(137\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(138\) −0.213947 + 0.618159i −0.213947 + 0.618159i
\(139\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(140\) 0.0883470 + 0.0353688i 0.0883470 + 0.0353688i
\(141\) 0.307040 0.0293188i 0.307040 0.0293188i
\(142\) 0 0
\(143\) 0 0
\(144\) 0.508508 0.262154i 0.508508 0.262154i
\(145\) −1.65033 + 0.660694i −1.65033 + 0.660694i
\(146\) 0 0
\(147\) 0.469133 0.447317i 0.469133 0.447317i
\(148\) 0 0
\(149\) 0.601300 + 1.31666i 0.601300 + 1.31666i 0.928368 + 0.371662i \(0.121212\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(150\) 0.514186 + 0.404360i 0.514186 + 0.404360i
\(151\) 0 0 −0.327068 0.945001i \(-0.606061\pi\)
0.327068 + 0.945001i \(0.393939\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 0 0 −0.0475819 0.998867i \(-0.515152\pi\)
0.0475819 + 0.998867i \(0.484848\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0.981929 + 0.189251i 0.981929 + 0.189251i
\(161\) 0.0135432 + 0.0941952i 0.0135432 + 0.0941952i
\(162\) −0.0237146 + 0.0977529i −0.0237146 + 0.0977529i
\(163\) 0.654861 + 1.13425i 0.654861 + 1.13425i 0.981929 + 0.189251i \(0.0606061\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(164\) −0.723734 + 1.25354i −0.723734 + 1.25354i
\(165\) 0 0
\(166\) −0.0947329 + 1.98869i −0.0947329 + 1.98869i
\(167\) 0.975950 1.37053i 0.975950 1.37053i 0.0475819 0.998867i \(-0.484848\pi\)
0.928368 0.371662i \(-0.121212\pi\)
\(168\) −0.0361086 + 0.0507074i −0.0361086 + 0.0507074i
\(169\) 0.0475819 0.998867i 0.0475819 0.998867i
\(170\) 0 0
\(171\) 0 0
\(172\) −0.981929 1.70075i −0.981929 1.70075i
\(173\) 0 0 0.235759 0.971812i \(-0.424242\pi\)
−0.235759 + 0.971812i \(0.575758\pi\)
\(174\) −0.165489 1.15100i −0.165489 1.15100i
\(175\) 0.0934441 + 0.0180099i 0.0934441 + 0.0180099i
\(176\) 0 0
\(177\) 0 0
\(178\) 0.0395325 + 0.829889i 0.0395325 + 0.829889i
\(179\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(180\) 0.449706 0.353653i 0.449706 0.353653i
\(181\) 1.16413 + 0.600149i 1.16413 + 0.600149i 0.928368 0.371662i \(-0.121212\pi\)
0.235759 + 0.971812i \(0.424242\pi\)
\(182\) 0 0
\(183\) 0.182822 0.0352360i 0.182822 0.0352360i
\(184\) 0.327068 + 0.945001i 0.327068 + 0.945001i
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0.341254 0.325385i 0.341254 0.325385i
\(189\) 0.0230723 + 0.0951051i 0.0230723 + 0.0951051i
\(190\) 0 0
\(191\) 0 0 0.888835 0.458227i \(-0.151515\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(192\) −0.271738 + 0.595023i −0.271738 + 0.595023i
\(193\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0.141026 0.980857i 0.141026 0.980857i
\(197\) 0 0 0.327068 0.945001i \(-0.393939\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(198\) 0 0
\(199\) 0 0 −0.580057 0.814576i \(-0.696970\pi\)
0.580057 + 0.814576i \(0.303030\pi\)
\(200\) 1.00000 1.00000
\(201\) −0.473420 + 0.451405i −0.473420 + 0.451405i
\(202\) 0.830830 0.830830
\(203\) −0.0981282 0.137802i −0.0981282 0.137802i
\(204\) 0 0
\(205\) −0.473420 + 1.36786i −0.473420 + 1.36786i
\(206\) −0.165101 + 1.14831i −0.165101 + 1.14831i
\(207\) 0.531125 + 0.212630i 0.531125 + 0.212630i
\(208\) 0 0
\(209\) 0 0
\(210\) −0.0258596 + 0.0566247i −0.0258596 + 0.0566247i
\(211\) 0 0 0.888835 0.458227i \(-0.151515\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) −1.38884 + 1.32425i −1.38884 + 1.32425i
\(215\) −1.28605 1.48418i −1.28605 1.48418i
\(216\) 0.427201 + 0.935439i 0.427201 + 0.935439i
\(217\) 0 0
\(218\) −0.379436 1.09631i −0.379436 1.09631i
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) −0.239446 0.153882i −0.239446 0.153882i 0.415415 0.909632i \(-0.363636\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(224\) 0.00452808 + 0.0950560i 0.00452808 + 0.0950560i
\(225\) 0.374650 0.432369i 0.374650 0.432369i
\(226\) 0 0
\(227\) 0.815816 + 0.157236i 0.815816 + 0.157236i 0.580057 0.814576i \(-0.303030\pi\)
0.235759 + 0.971812i \(0.424242\pi\)
\(228\) 0 0
\(229\) 0.437742 1.80440i 0.437742 1.80440i −0.142315 0.989821i \(-0.545455\pi\)
0.580057 0.814576i \(-0.303030\pi\)
\(230\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(231\) 0 0
\(232\) −1.28656 1.22673i −1.28656 1.22673i
\(233\) 0 0 0.0475819 0.998867i \(-0.484848\pi\)
−0.0475819 + 0.998867i \(0.515152\pi\)
\(234\) 0 0
\(235\) 0.273507 0.384087i 0.273507 0.384087i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(240\) −0.154218 + 0.635697i −0.154218 + 0.635697i
\(241\) −0.165101 1.14831i −0.165101 1.14831i −0.888835 0.458227i \(-0.848485\pi\)
0.723734 0.690079i \(-0.242424\pi\)
\(242\) 0.981929 + 0.189251i 0.981929 + 0.189251i
\(243\) 0.923582 + 0.271188i 0.923582 + 0.271188i
\(244\) 0.186393 0.215109i 0.186393 0.215109i
\(245\) −0.0471510 0.989821i −0.0471510 0.989821i
\(246\) −0.796533 0.511901i −0.796533 0.511901i
\(247\) 0 0
\(248\) 0 0
\(249\) −1.29645 0.123796i −1.29645 0.123796i
\(250\) 0.981929 0.189251i 0.981929 0.189251i
\(251\) 0 0 −0.327068 0.945001i \(-0.606061\pi\)
0.327068 + 0.945001i \(0.393939\pi\)
\(252\) 0.0427957 + 0.0336549i 0.0427957 + 0.0336549i
\(253\) 0 0
\(254\) −1.21590 1.40323i −1.21590 1.40323i
\(255\) 0 0
\(256\) 0.235759 + 0.971812i 0.235759 + 0.971812i
\(257\) 0 0 0.928368 0.371662i \(-0.121212\pi\)
−0.928368 + 0.371662i \(0.878788\pi\)
\(258\) 1.14182 0.588651i 1.14182 0.588651i
\(259\) 0 0
\(260\) 0 0
\(261\) −1.01241 + 0.0966736i −1.01241 + 0.0966736i
\(262\) 0 0
\(263\) 0.223734 1.55610i 0.223734 1.55610i −0.500000 0.866025i \(-0.666667\pi\)
0.723734 0.690079i \(-0.242424\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) −0.543476 −0.543476
\(268\) −0.142315 + 0.989821i −0.142315 + 0.989821i
\(269\) −1.30972 −1.30972 −0.654861 0.755750i \(-0.727273\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(270\) 0.596514 + 0.837686i 0.596514 + 0.837686i
\(271\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) −0.627639 + 0.184291i −0.627639 + 0.184291i
\(277\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0.0224357 + 0.0924813i 0.0224357 + 0.0924813i
\(281\) 0.341254 0.325385i 0.341254 0.325385i −0.500000 0.866025i \(-0.666667\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(282\) 0.201983 + 0.233101i 0.201983 + 0.233101i
\(283\) −0.653077 1.43004i −0.653077 1.43004i −0.888835 0.458227i \(-0.848485\pi\)
0.235759 0.971812i \(-0.424242\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −0.137123 0.0130936i −0.137123 0.0130936i
\(288\) 0.508508 + 0.262154i 0.508508 + 0.262154i
\(289\) −0.786053 + 0.618159i −0.786053 + 0.618159i
\(290\) −1.49547 0.961081i −1.49547 0.961081i
\(291\) 0 0
\(292\) 0 0
\(293\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(294\) 0.636498 + 0.122675i 0.636498 + 0.122675i
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) −0.723734 + 1.25354i −0.723734 + 1.25354i
\(299\) 0 0
\(300\) −0.0311250 + 0.653395i −0.0311250 + 0.653395i
\(301\) 0.108406 0.152235i 0.108406 0.152235i
\(302\) 0 0
\(303\) −0.0258596 + 0.542860i −0.0258596 + 0.542860i
\(304\) 0 0
\(305\) 0.142315 0.246497i 0.142315 0.246497i
\(306\) 0 0
\(307\) −0.452418 + 1.86489i −0.452418 + 1.86489i 0.0475819 + 0.998867i \(0.484848\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(308\) 0 0
\(309\) −0.745158 0.143617i −0.745158 0.143617i
\(310\) 0 0
\(311\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(312\) 0 0
\(313\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(314\) 0 0
\(315\) 0.0483916 + 0.0249476i 0.0483916 + 0.0249476i
\(316\) 0 0
\(317\) 0 0 0.981929 0.189251i \(-0.0606061\pi\)
−0.981929 + 0.189251i \(0.939394\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0.415415 + 0.909632i 0.415415 + 0.909632i
\(321\) −0.822032 0.948676i −0.822032 0.948676i
\(322\) −0.0688733 + 0.0656706i −0.0688733 + 0.0656706i
\(323\) 0 0
\(324\) −0.0933830 + 0.0373849i −0.0933830 + 0.0373849i
\(325\) 0 0
\(326\) −0.544078 + 1.19136i −0.544078 + 1.19136i
\(327\) 0.728132 0.213799i 0.728132 0.213799i
\(328\) −1.44091 + 0.137591i −1.44091 + 0.137591i
\(329\) 0.0416572 + 0.0166770i 0.0416572 + 0.0166770i
\(330\) 0 0
\(331\) 0 0 0.327068 0.945001i \(-0.393939\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(332\) −1.67489 + 1.07639i −1.67489 + 1.07639i
\(333\) 0 0
\(334\) 1.68251 1.68251
\(335\) 0.0475819 + 0.998867i 0.0475819 + 0.998867i
\(336\) −0.0622501 −0.0622501
\(337\) 0 0 −0.580057 0.814576i \(-0.696970\pi\)
0.580057 + 0.814576i \(0.303030\pi\)
\(338\) 0.841254 0.540641i 0.841254 0.540641i
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 0.181791 0.0533787i 0.181791 0.0533787i
\(344\) 0.815816 1.78639i 0.815816 1.78639i
\(345\) −0.581419 + 0.299742i −0.581419 + 0.299742i
\(346\) 0 0
\(347\) −0.0671040 0.276606i −0.0671040 0.276606i 0.928368 0.371662i \(-0.121212\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(348\) 0.841586 0.802450i 0.841586 0.802450i
\(349\) −1.28605 1.48418i −1.28605 1.48418i −0.786053 0.618159i \(-0.787879\pi\)
−0.500000 0.866025i \(-0.666667\pi\)
\(350\) 0.0395325 + 0.0865641i 0.0395325 + 0.0865641i
\(351\) 0 0
\(352\) 0 0
\(353\) 0 0 0.981929 0.189251i \(-0.0606061\pi\)
−0.981929 + 0.189251i \(0.939394\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) −0.653077 + 0.513585i −0.653077 + 0.513585i
\(357\) 0 0
\(358\) 0 0
\(359\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(360\) 0.548932 + 0.161181i 0.548932 + 0.161181i
\(361\) 0.981929 + 0.189251i 0.981929 + 0.189251i
\(362\) 0.186393 + 1.29639i 0.186393 + 1.29639i
\(363\) −0.154218 + 0.635697i −0.154218 + 0.635697i
\(364\) 0 0
\(365\) 0 0
\(366\) 0.134750 + 0.128483i 0.134750 + 0.128483i
\(367\) 0.0552004 1.15880i 0.0552004 1.15880i −0.786053 0.618159i \(-0.787879\pi\)
0.841254 0.540641i \(-0.181818\pi\)
\(368\) −0.580057 + 0.814576i −0.580057 + 0.814576i
\(369\) −0.480348 + 0.674555i −0.480348 + 0.674555i
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(374\) 0 0
\(375\) 0.0930932 + 0.647478i 0.0930932 + 0.647478i
\(376\) 0.462997 + 0.0892353i 0.462997 + 0.0892353i
\(377\) 0 0
\(378\) −0.0640871 + 0.0739605i −0.0640871 + 0.0739605i
\(379\) 0 0 −0.0475819 0.998867i \(-0.515152\pi\)
0.0475819 + 0.998867i \(0.484848\pi\)
\(380\) 0 0
\(381\) 0.954707 0.750790i 0.954707 0.750790i
\(382\) 0 0
\(383\) −0.469383 0.0448206i −0.469383 0.0448206i −0.142315 0.989821i \(-0.545455\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(384\) −0.642315 + 0.123796i −0.642315 + 0.123796i
\(385\) 0 0
\(386\) 0 0
\(387\) −0.466733 1.02200i −0.466733 1.02200i
\(388\) 0 0
\(389\) 0.839614 0.800570i 0.839614 0.800570i −0.142315 0.989821i \(-0.545455\pi\)
0.981929 + 0.189251i \(0.0606061\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0.880786 0.454077i 0.880786 0.454077i
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0.580057 + 0.814576i 0.580057 + 0.814576i
\(401\) 0.0951638 0.0951638 0.0475819 0.998867i \(-0.484848\pi\)
0.0475819 + 0.998867i \(0.484848\pi\)
\(402\) −0.642315 0.123796i −0.642315 0.123796i
\(403\) 0 0
\(404\) 0.481929 + 0.676774i 0.481929 + 0.676774i
\(405\) −0.0846203 + 0.0543822i −0.0846203 + 0.0543822i
\(406\) 0.0553301 0.159866i 0.0553301 0.159866i
\(407\) 0 0
\(408\) 0 0
\(409\) 1.30379 0.124497i 1.30379 0.124497i 0.580057 0.814576i \(-0.303030\pi\)
0.723734 + 0.690079i \(0.242424\pi\)
\(410\) −1.38884 + 0.407799i −1.38884 + 0.407799i
\(411\) 0 0
\(412\) −1.03115 + 0.531595i −1.03115 + 0.531595i
\(413\) 0 0
\(414\) 0.134879 + 0.555979i 0.134879 + 0.555979i
\(415\) −1.44091 + 1.37391i −1.44091 + 1.37391i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 0 0 −0.327068 0.945001i \(-0.606061\pi\)
0.327068 + 0.945001i \(0.393939\pi\)
\(420\) −0.0611251 + 0.0117809i −0.0611251 + 0.0117809i
\(421\) −1.67489 0.159932i −1.67489 0.159932i −0.786053 0.618159i \(-0.787879\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(422\) 0 0
\(423\) 0.212044 0.166754i 0.212044 0.166754i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 0.0259893 + 0.00763113i 0.0259893 + 0.00763113i
\(428\) −1.88431 0.363170i −1.88431 0.363170i
\(429\) 0 0
\(430\) 0.462997 1.90850i 0.462997 1.90850i
\(431\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(432\) −0.514186 + 0.890596i −0.514186 + 0.890596i
\(433\) 0 0 −0.723734 0.690079i \(-0.757576\pi\)
0.723734 + 0.690079i \(0.242424\pi\)
\(434\) 0 0
\(435\) 0.674512 0.947220i 0.674512 0.947220i
\(436\) 0.672932 0.945001i 0.672932 0.945001i
\(437\) 0 0
\(438\) 0 0
\(439\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(440\) 0 0
\(441\) 0.133658 0.550944i 0.133658 0.550944i
\(442\) 0 0
\(443\) −1.74555 0.336426i −1.74555 0.336426i −0.786053 0.618159i \(-0.787879\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(444\) 0 0
\(445\) −0.544078 + 0.627899i −0.544078 + 0.627899i
\(446\) −0.0135432 0.284307i −0.0135432 0.284307i
\(447\) −0.796533 0.511901i −0.796533 0.511901i
\(448\) −0.0748038 + 0.0588264i −0.0748038 + 0.0588264i
\(449\) −0.419102 0.216062i −0.419102 0.216062i 0.235759 0.971812i \(-0.424242\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(450\) 0.569516 + 0.0543822i 0.569516 + 0.0543822i
\(451\) 0 0
\(452\) 0 0
\(453\) 0 0
\(454\) 0.345139 + 0.755750i 0.345139 + 0.755750i
\(455\) 0 0
\(456\) 0 0
\(457\) 0 0 −0.235759 0.971812i \(-0.575758\pi\)
0.235759 + 0.971812i \(0.424242\pi\)
\(458\) 1.72373 0.690079i 1.72373 0.690079i
\(459\) 0 0
\(460\) −0.415415 + 0.909632i −0.415415 + 0.909632i
\(461\) 1.91030 0.560914i 1.91030 0.560914i 0.928368 0.371662i \(-0.121212\pi\)
0.981929 0.189251i \(-0.0606061\pi\)
\(462\) 0 0
\(463\) −1.21590 0.486774i −1.21590 0.486774i −0.327068 0.945001i \(-0.606061\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(464\) 0.252989 1.75958i 0.252989 1.75958i
\(465\) 0 0
\(466\) 0 0
\(467\) 1.07701 + 1.51245i 1.07701 + 1.51245i 0.841254 + 0.540641i \(0.181818\pi\)
0.235759 + 0.971812i \(0.424242\pi\)
\(468\) 0 0
\(469\) −0.0913090 + 0.0268107i −0.0913090 + 0.0268107i
\(470\) 0.471518 0.471518
\(471\) 0 0
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 0 0 0.888835 0.458227i \(-0.151515\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(480\) −0.607279 + 0.243118i −0.607279 + 0.243118i
\(481\) 0 0
\(482\) 0.839614 0.800570i 0.839614 0.800570i
\(483\) −0.0407651 0.0470455i −0.0407651 0.0470455i
\(484\) 0.415415 + 0.909632i 0.415415 + 0.909632i
\(485\) 0 0
\(486\) 0.314827 + 0.909632i 0.314827 + 0.909632i
\(487\) −1.95496 + 0.376789i −1.95496 + 0.376789i −0.959493 + 0.281733i \(0.909091\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(488\) 0.283341 + 0.0270558i 0.283341 + 0.0270558i
\(489\) −0.761497 0.392579i −0.761497 0.392579i
\(490\) 0.778934 0.612561i 0.778934 0.612561i
\(491\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(492\) −0.0450525 0.945768i −0.0450525 0.945768i
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) −0.651174 1.12787i −0.651174 1.12787i
\(499\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(500\) 0.723734 + 0.690079i 0.723734 + 0.690079i
\(501\) −0.0523681 + 1.09934i −0.0523681 + 1.09934i
\(502\) 0 0
\(503\) 0.839614 1.17907i 0.839614 1.17907i −0.142315 0.989821i \(-0.545455\pi\)
0.981929 0.189251i \(-0.0606061\pi\)
\(504\) −0.00259054 + 0.0543822i −0.00259054 + 0.0543822i
\(505\) 0.601300 + 0.573338i 0.601300 + 0.573338i
\(506\) 0 0
\(507\) 0.327068 + 0.566498i 0.327068 + 0.566498i
\(508\) 0.437742 1.80440i 0.437742 1.80440i
\(509\) −0.239446 1.66538i −0.239446 1.66538i −0.654861 0.755750i \(-0.727273\pi\)
0.415415 0.909632i \(-0.363636\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −0.654861 + 0.755750i −0.654861 + 0.755750i
\(513\) 0 0
\(514\) 0 0
\(515\) −0.911911 + 0.717135i −0.911911 + 0.717135i
\(516\) 1.14182 + 0.588651i 1.14182 + 0.588651i
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −0.415415 0.909632i −0.415415 0.909632i −0.995472 0.0950560i \(-0.969697\pi\)
0.580057 0.814576i \(-0.303030\pi\)
\(522\) −0.666004 0.768610i −0.666004 0.768610i
\(523\) 1.42131 1.35522i 1.42131 1.35522i 0.580057 0.814576i \(-0.303030\pi\)
0.841254 0.540641i \(-0.181818\pi\)
\(524\) 0 0
\(525\) −0.0577910 + 0.0231360i −0.0577910 + 0.0231360i
\(526\) 1.39734 0.720381i 1.39734 0.720381i
\(527\) 0 0
\(528\) 0 0
\(529\) 0 0
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) −0.315247 0.442702i −0.315247 0.442702i
\(535\) −1.91899 −1.91899
\(536\) −0.888835 + 0.458227i −0.888835 + 0.458227i
\(537\) 0 0
\(538\) −0.759713 1.06687i −0.759713 1.06687i
\(539\) 0 0
\(540\) −0.336347 + 0.971812i −0.336347 + 0.971812i
\(541\) −0.279486 + 1.94387i −0.279486 + 1.94387i 0.0475819 + 0.998867i \(0.484848\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(542\) 0 0
\(543\) −0.852856 + 0.0814379i −0.852856 + 0.0814379i
\(544\) 0 0
\(545\) 0.481929 1.05528i 0.481929 1.05528i
\(546\) 0 0
\(547\) 1.72373 0.690079i 1.72373 0.690079i 0.723734 0.690079i \(-0.242424\pi\)
1.00000 \(0\)
\(548\) 0 0
\(549\) 0.117852 0.112371i 0.117852 0.112371i
\(550\) 0 0
\(551\) 0 0
\(552\) −0.514186 0.404360i −0.514186 0.404360i
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 0 0 0.786053 0.618159i \(-0.212121\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) −0.0623191 + 0.0719200i −0.0623191 + 0.0719200i
\(561\) 0 0
\(562\) 0.462997 + 0.0892353i 0.462997 + 0.0892353i
\(563\) −0.279486 1.94387i −0.279486 1.94387i −0.327068 0.945001i \(-0.606061\pi\)
0.0475819 0.998867i \(-0.484848\pi\)
\(564\) −0.0727167 + 0.299742i −0.0727167 + 0.299742i
\(565\) 0 0
\(566\) 0.786053 1.36148i 0.786053 1.36148i
\(567\) −0.00692785 0.00660569i −0.00692785 0.00660569i
\(568\) 0 0
\(569\) 0.975950 1.37053i 0.975950 1.37053i 0.0475819 0.998867i \(-0.484848\pi\)
0.928368 0.371662i \(-0.121212\pi\)
\(570\) 0 0
\(571\) 0 0 0.0475819 0.998867i \(-0.484848\pi\)
−0.0475819 + 0.998867i \(0.515152\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) −0.0688733 0.119292i −0.0688733 0.119292i
\(575\) −0.235759 + 0.971812i −0.235759 + 0.971812i
\(576\) 0.0814192 + 0.566283i 0.0814192 + 0.566283i
\(577\) 0 0 −0.981929 0.189251i \(-0.939394\pi\)
0.981929 + 0.189251i \(0.0606061\pi\)
\(578\) −0.959493 0.281733i −0.959493 0.281733i
\(579\) 0 0
\(580\) −0.0845850 1.77566i −0.0845850 1.77566i
\(581\) −0.159389 0.102433i −0.159389 0.102433i
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 1.50842 + 1.18624i 1.50842 + 1.18624i 0.928368 + 0.371662i \(0.121212\pi\)
0.580057 + 0.814576i \(0.303030\pi\)
\(588\) 0.269277 + 0.589634i 0.269277 + 0.589634i
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 0 0 0.888835 0.458227i \(-0.151515\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −1.44091 + 0.137591i −1.44091 + 0.137591i
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 0.327068 0.945001i \(-0.393939\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(600\) −0.550294 + 0.353653i −0.550294 + 0.353653i
\(601\) 1.13915 + 1.59971i 1.13915 + 1.59971i 0.723734 + 0.690079i \(0.242424\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(602\) 0.186888 0.186888
\(603\) −0.134879 + 0.555979i −0.134879 + 0.555979i
\(604\) 0 0
\(605\) 0.580057 + 0.814576i 0.580057 + 0.814576i
\(606\) −0.457201 + 0.293825i −0.457201 + 0.293825i
\(607\) −0.154218 + 0.445585i −0.154218 + 0.445585i −0.995472 0.0950560i \(-0.969697\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(608\) 0 0
\(609\) 0.102733 + 0.0411282i 0.102733 + 0.0411282i
\(610\) 0.283341 0.0270558i 0.283341 0.0270558i
\(611\) 0 0
\(612\) 0 0
\(613\) 0 0 0.888835 0.458227i \(-0.151515\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(614\) −1.78153 + 0.713215i −1.78153 + 0.713215i
\(615\) −0.223226 0.920151i −0.223226 0.920151i
\(616\) 0 0
\(617\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(618\) −0.315247 0.690294i −0.315247 0.690294i
\(619\) 0 0 −0.786053 0.618159i \(-0.787879\pi\)
0.786053 + 0.618159i \(0.212121\pi\)
\(620\) 0 0
\(621\) −1.00979 + 0.194621i −1.00979 + 0.194621i
\(622\) 0 0
\(623\) −0.0702757 0.0362297i −0.0702757 0.0362297i
\(624\) 0 0
\(625\) 0.841254 + 0.540641i 0.841254 + 0.540641i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) 0.00774816 + 0.0538897i 0.00774816 + 0.0538897i
\(631\) 0 0 0.235759 0.971812i \(-0.424242\pi\)
−0.235759 + 0.971812i \(0.575758\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 0.0883470 1.85463i 0.0883470 1.85463i
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(641\) 0.786053 + 1.36148i 0.786053 + 1.36148i 0.928368 + 0.371662i \(0.121212\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(642\) 0.295943 1.21989i 0.295943 1.21989i
\(643\) 0.252989 + 1.75958i 0.252989 + 1.75958i 0.580057 + 0.814576i \(0.303030\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(644\) −0.0934441 0.0180099i −0.0934441 0.0180099i
\(645\) 1.23259 + 0.361922i 1.23259 + 0.361922i
\(646\) 0 0
\(647\) 0.0224357 + 0.470984i 0.0224357 + 0.470984i 0.981929 + 0.189251i \(0.0606061\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(648\) −0.0846203 0.0543822i −0.0846203 0.0543822i
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) −1.28605 + 0.247866i −1.28605 + 0.247866i
\(653\) 0 0 −0.327068 0.945001i \(-0.606061\pi\)
0.327068 + 0.945001i \(0.393939\pi\)
\(654\) 0.596514 + 0.469104i 0.596514 + 0.469104i
\(655\) 0 0
\(656\) −0.947890 1.09392i −0.947890 1.09392i
\(657\) 0 0
\(658\) 0.0105788 + 0.0436066i 0.0105788 + 0.0436066i
\(659\) 0 0 0.928368 0.371662i \(-0.121212\pi\)
−0.928368 + 0.371662i \(0.878788\pi\)
\(660\) 0 0
\(661\) 0.698939 1.53046i 0.698939 1.53046i −0.142315 0.989821i \(-0.545455\pi\)
0.841254 0.540641i \(-0.181818\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) −1.84833 0.739959i −1.84833 0.739959i
\(665\) 0 0
\(666\) 0 0
\(667\) 1.49547 0.961081i 1.49547 0.961081i
\(668\) 0.975950 + 1.37053i 0.975950 + 1.37053i
\(669\) 0.186186 0.186186
\(670\) −0.786053 + 0.618159i −0.786053 + 0.618159i
\(671\) 0 0
\(672\) −0.0361086 0.0507074i −0.0361086 0.0507074i
\(673\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(674\) 0 0
\(675\) −0.146352 + 1.01790i −0.146352 + 1.01790i
\(676\) 0.928368 + 0.371662i 0.928368 + 0.371662i
\(677\) 0 0 0.995472 0.0950560i \(-0.0303030\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) −0.504545 + 0.201990i −0.504545 + 0.201990i
\(682\) 0 0
\(683\) −1.38884 + 1.32425i −1.38884 + 1.32425i −0.500000 + 0.866025i \(0.666667\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0.148930 + 0.117120i 0.148930 + 0.117120i
\(687\) 0.397243 + 1.14776i 0.397243 + 1.14776i
\(688\) 1.92837 0.371662i 1.92837 0.371662i
\(689\) 0 0
\(690\) −0.581419 0.299742i −0.581419 0.299742i
\(691\) 0 0 0.786053 0.618159i \(-0.212121\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0.186393 0.215109i 0.186393 0.215109i
\(695\) 0 0
\(696\) 1.14182 + 0.220069i 1.14182 + 0.220069i
\(697\) 0 0
\(698\) 0.462997 1.90850i 0.462997 1.90850i
\(699\) 0 0
\(700\) −0.0475819 + 0.0824143i −0.0475819 + 0.0824143i
\(701\) −0.723734 0.690079i −0.723734 0.690079i 0.235759 0.971812i \(-0.424242\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0 0
\(705\) −0.0146760 + 0.308087i −0.0146760 + 0.308087i
\(706\) 0 0
\(707\) −0.0395325 + 0.0684723i −0.0395325 + 0.0684723i
\(708\) 0 0
\(709\) −0.235759 + 0.971812i −0.235759 + 0.971812i 0.723734 + 0.690079i \(0.242424\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) −0.797176 0.234072i −0.797176 0.234072i
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 0.981929 0.189251i \(-0.0606061\pi\)
−0.981929 + 0.189251i \(0.939394\pi\)
\(720\) 0.187118 + 0.540641i 0.187118 + 0.540641i
\(721\) −0.0867810 0.0682453i −0.0867810 0.0682453i
\(722\) 0.415415 + 0.909632i 0.415415 + 0.909632i
\(723\) 0.496956 + 0.573517i 0.496956 + 0.573517i
\(724\) −0.947890 + 0.903811i −0.947890 + 0.903811i
\(725\) −0.419102 1.72756i −0.419102 1.72756i
\(726\) −0.607279 + 0.243118i −0.607279 + 0.243118i
\(727\) −1.28656 + 0.663268i −1.28656 + 0.663268i −0.959493 0.281733i \(-0.909091\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(728\) 0 0
\(729\) −0.700662 + 0.205733i −0.700662 + 0.205733i
\(730\) 0 0
\(731\) 0 0
\(732\) −0.0264971 + 0.184291i −0.0264971 + 0.184291i
\(733\) 0 0 0.327068 0.945001i \(-0.393939\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(734\) 0.975950 0.627205i 0.975950 0.627205i
\(735\) 0.376000 + 0.528018i 0.376000 + 0.528018i
\(736\) −1.00000 −1.00000
\(737\) 0 0
\(738\) −0.828105 −0.828105
\(739\) 0 0 −0.580057 0.814576i \(-0.696970\pi\)
0.580057 + 0.814576i \(0.303030\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −1.21590 0.486774i −1.21590 0.486774i −0.327068 0.945001i \(-0.606061\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(744\) 0 0
\(745\) −1.38884 + 0.407799i −1.38884 + 0.407799i
\(746\) 0 0
\(747\) −1.01241 + 0.521934i −1.01241 + 0.521934i
\(748\) 0 0
\(749\) −0.0430538 0.177470i −0.0430538 0.177470i
\(750\) −0.473420 + 0.451405i −0.473420 + 0.451405i
\(751\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(752\) 0.195876 + 0.428908i 0.195876 + 0.428908i
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) −0.0974206 0.00930254i −0.0974206 0.00930254i
\(757\) 0 0 −0.888835 0.458227i \(-0.848485\pi\)
0.888835 + 0.458227i \(0.151515\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 0.857685 0.989821i 0.857685 0.989821i −0.142315 0.989821i \(-0.545455\pi\)
1.00000 \(0\)
\(762\) 1.16536 + 0.342180i 1.16536 + 0.342180i
\(763\) 0.108406 + 0.0208935i 0.108406 + 0.0208935i
\(764\) 0 0
\(765\) 0 0
\(766\) −0.235759 0.408346i −0.235759 0.408346i
\(767\) 0 0
\(768\) −0.473420 0.451405i −0.473420 0.451405i
\(769\) −0.0311250 + 0.653395i −0.0311250 + 0.653395i 0.928368 + 0.371662i \(0.121212\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 0 0 −0.723734 0.690079i \(-0.757576\pi\)
0.723734 + 0.690079i \(0.242424\pi\)
\(774\) 0.561767 0.973010i 0.561767 0.973010i
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 1.13915 + 0.219553i 1.13915 + 0.219553i
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 1.43699 1.13006i 1.43699 1.13006i
\(784\) 0.880786 + 0.454077i 0.880786 + 0.454077i
\(785\) 0 0
\(786\) 0 0
\(787\) −0.607279 1.75462i −0.607279 1.75462i −0.654861 0.755750i \(-0.727273\pi\)
0.0475819 0.998867i \(-0.484848\pi\)
\(788\) 0 0
\(789\) 0.427201 + 0.935439i 0.427201 + 0.935439i
\(790\) 0 0
\(791\) 0 0
\(792\) 0