Properties

Label 1340.1.bl.b.1279.1
Level $1340$
Weight $1$
Character 1340.1279
Analytic conductor $0.669$
Analytic rank $0$
Dimension $20$
Projective image $D_{33}$
CM discriminant -20
Inner twists $4$

Related objects

Downloads

Learn more

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 1279.1
Root \(0.580057 - 0.814576i\) of defining polynomial
Character \(\chi\) \(=\) 1340.1279
Dual form 1340.1.bl.b.659.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.327068 + 0.945001i) q^{2} +(-0.653077 + 1.43004i) q^{3} +(-0.786053 - 0.618159i) q^{4} +(-0.959493 - 0.281733i) q^{5} +(-1.13779 - 1.08488i) q^{6} +(-1.95496 + 0.376789i) q^{7} +(0.841254 - 0.540641i) q^{8} +(-0.963639 - 1.11210i) q^{9} +O(q^{10})\) \(q+(-0.327068 + 0.945001i) q^{2} +(-0.653077 + 1.43004i) q^{3} +(-0.786053 - 0.618159i) q^{4} +(-0.959493 - 0.281733i) q^{5} +(-1.13779 - 1.08488i) q^{6} +(-1.95496 + 0.376789i) q^{7} +(0.841254 - 0.540641i) q^{8} +(-0.963639 - 1.11210i) q^{9} +(0.580057 - 0.814576i) q^{10} +(1.39734 - 0.720381i) q^{12} +(0.283341 - 1.97068i) q^{14} +(1.02951 - 1.18812i) q^{15} +(0.235759 + 0.971812i) q^{16} +(1.36611 - 0.546908i) q^{18} +(0.580057 + 0.814576i) q^{20} +(0.737920 - 3.04175i) q^{21} +(0.995472 - 0.0950560i) q^{23} +(0.223734 + 1.55610i) q^{24} +(0.841254 + 0.540641i) q^{25} +(0.711249 - 0.208842i) q^{27} +(1.76962 + 0.912303i) q^{28} +(-0.580057 + 1.00469i) q^{29} +(0.786053 + 1.36148i) q^{30} +(-0.995472 - 0.0950560i) q^{32} +(1.98193 + 0.189251i) q^{35} +(0.0700176 + 1.46985i) q^{36} +(-0.959493 + 0.281733i) q^{40} +(0.0883470 + 0.0353688i) q^{41} +(2.63310 + 1.69219i) q^{42} +(-0.264241 - 1.83784i) q^{43} +(0.611291 + 1.33854i) q^{45} +(-0.235759 + 0.971812i) q^{46} +(-1.03115 - 1.44805i) q^{47} +(-1.54370 - 0.297523i) q^{48} +(2.75155 - 1.10155i) q^{49} +(-0.786053 + 0.618159i) q^{50} +(-0.0352713 + 0.740437i) q^{54} +(-1.44091 + 1.37391i) q^{56} +(-0.759713 - 0.876756i) q^{58} +(-1.54370 + 0.297523i) q^{60} +(-1.38884 - 1.32425i) q^{61} +(2.30291 + 1.81103i) q^{63} +(0.415415 - 0.909632i) q^{64} +(0.928368 - 0.371662i) q^{67} +(-0.514186 + 1.48564i) q^{69} +(-0.827068 + 1.81103i) q^{70} +(-1.41191 - 0.414574i) q^{72} +(-1.32254 + 0.849945i) q^{75} +(0.0475819 - 0.998867i) q^{80} +(0.0435701 - 0.303037i) q^{81} +(-0.0623191 + 0.0719200i) q^{82} +(0.462997 + 1.90850i) q^{83} +(-2.46033 + 1.93482i) q^{84} +(1.82318 + 0.351390i) q^{86} +(-1.05792 - 1.48564i) q^{87} +(-0.544078 - 1.19136i) q^{89} +(-1.46485 + 0.139877i) q^{90} +(-0.841254 - 0.540641i) q^{92} +(1.70566 - 0.500828i) q^{94} +(0.786053 - 1.36148i) q^{96} +(0.141026 + 2.96050i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20q + q^{2} + 2q^{3} + q^{4} - 2q^{5} - q^{6} - q^{7} - 2q^{8} + O(q^{10}) \) \( 20q + q^{2} + 2q^{3} + q^{4} - 2q^{5} - q^{6} - q^{7} - 2q^{8} + q^{10} - q^{12} + 2q^{14} + 2q^{15} + q^{16} + q^{20} - 10q^{21} - q^{23} - 9q^{24} - 2q^{25} - 2q^{27} - q^{28} - q^{29} - q^{30} + q^{32} + 21q^{35} - 2q^{40} - q^{41} + 20q^{42} - 9q^{43} - q^{46} - q^{47} - q^{48} + q^{50} + q^{54} - q^{56} + 2q^{58} - q^{60} - 9q^{61} - 11q^{63} - 2q^{64} + q^{67} + q^{69} - 9q^{70} - 11q^{72} + 2q^{75} + q^{80} + 2q^{81} + 2q^{82} - q^{83} + q^{84} - q^{86} + q^{87} - 4q^{89} + 2q^{92} + 2q^{94} - q^{96} + O(q^{100}) \)

Character values

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

\(n\) \(537\) \(671\) \(1141\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{20}{33}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.327068 + 0.945001i −0.327068 + 0.945001i
\(3\) −0.653077 + 1.43004i −0.653077 + 1.43004i 0.235759 + 0.971812i \(0.424242\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(4\) −0.786053 0.618159i −0.786053 0.618159i
\(5\) −0.959493 0.281733i −0.959493 0.281733i
\(6\) −1.13779 1.08488i −1.13779 1.08488i
\(7\) −1.95496 + 0.376789i −1.95496 + 0.376789i −0.959493 + 0.281733i \(0.909091\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(8\) 0.841254 0.540641i 0.841254 0.540641i
\(9\) −0.963639 1.11210i −0.963639 1.11210i
\(10\) 0.580057 0.814576i 0.580057 0.814576i
\(11\) 0 0 0.723734 0.690079i \(-0.242424\pi\)
−0.723734 + 0.690079i \(0.757576\pi\)
\(12\) 1.39734 0.720381i 1.39734 0.720381i
\(13\) 0 0 0.0475819 0.998867i \(-0.484848\pi\)
−0.0475819 + 0.998867i \(0.515152\pi\)
\(14\) 0.283341 1.97068i 0.283341 1.97068i
\(15\) 1.02951 1.18812i 1.02951 1.18812i
\(16\) 0.235759 + 0.971812i 0.235759 + 0.971812i
\(17\) 0 0 0.786053 0.618159i \(-0.212121\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(18\) 1.36611 0.546908i 1.36611 0.546908i
\(19\) 0 0 −0.981929 0.189251i \(-0.939394\pi\)
0.981929 + 0.189251i \(0.0606061\pi\)
\(20\) 0.580057 + 0.814576i 0.580057 + 0.814576i
\(21\) 0.737920 3.04175i 0.737920 3.04175i
\(22\) 0 0
\(23\) 0.995472 0.0950560i 0.995472 0.0950560i 0.415415 0.909632i \(-0.363636\pi\)
0.580057 + 0.814576i \(0.303030\pi\)
\(24\) 0.223734 + 1.55610i 0.223734 + 1.55610i
\(25\) 0.841254 + 0.540641i 0.841254 + 0.540641i
\(26\) 0 0
\(27\) 0.711249 0.208842i 0.711249 0.208842i
\(28\) 1.76962 + 0.912303i 1.76962 + 0.912303i
\(29\) −0.580057 + 1.00469i −0.580057 + 1.00469i 0.415415 + 0.909632i \(0.363636\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(30\) 0.786053 + 1.36148i 0.786053 + 1.36148i
\(31\) 0 0 −0.0475819 0.998867i \(-0.515152\pi\)
0.0475819 + 0.998867i \(0.484848\pi\)
\(32\) −0.995472 0.0950560i −0.995472 0.0950560i
\(33\) 0 0
\(34\) 0 0
\(35\) 1.98193 + 0.189251i 1.98193 + 0.189251i
\(36\) 0.0700176 + 1.46985i 0.0700176 + 1.46985i
\(37\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) −0.959493 + 0.281733i −0.959493 + 0.281733i
\(41\) 0.0883470 + 0.0353688i 0.0883470 + 0.0353688i 0.415415 0.909632i \(-0.363636\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(42\) 2.63310 + 1.69219i 2.63310 + 1.69219i
\(43\) −0.264241 1.83784i −0.264241 1.83784i −0.500000 0.866025i \(-0.666667\pi\)
0.235759 0.971812i \(-0.424242\pi\)
\(44\) 0 0
\(45\) 0.611291 + 1.33854i 0.611291 + 1.33854i
\(46\) −0.235759 + 0.971812i −0.235759 + 0.971812i
\(47\) −1.03115 1.44805i −1.03115 1.44805i −0.888835 0.458227i \(-0.848485\pi\)
−0.142315 0.989821i \(-0.545455\pi\)
\(48\) −1.54370 0.297523i −1.54370 0.297523i
\(49\) 2.75155 1.10155i 2.75155 1.10155i
\(50\) −0.786053 + 0.618159i −0.786053 + 0.618159i
\(51\) 0 0
\(52\) 0 0
\(53\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(54\) −0.0352713 + 0.740437i −0.0352713 + 0.740437i
\(55\) 0 0
\(56\) −1.44091 + 1.37391i −1.44091 + 1.37391i
\(57\) 0 0
\(58\) −0.759713 0.876756i −0.759713 0.876756i
\(59\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(60\) −1.54370 + 0.297523i −1.54370 + 0.297523i
\(61\) −1.38884 1.32425i −1.38884 1.32425i −0.888835 0.458227i \(-0.848485\pi\)
−0.500000 0.866025i \(-0.666667\pi\)
\(62\) 0 0
\(63\) 2.30291 + 1.81103i 2.30291 + 1.81103i
\(64\) 0.415415 0.909632i 0.415415 0.909632i
\(65\) 0 0
\(66\) 0 0
\(67\) 0.928368 0.371662i 0.928368 0.371662i
\(68\) 0 0
\(69\) −0.514186 + 1.48564i −0.514186 + 1.48564i
\(70\) −0.827068 + 1.81103i −0.827068 + 1.81103i
\(71\) 0 0 −0.786053 0.618159i \(-0.787879\pi\)
0.786053 + 0.618159i \(0.212121\pi\)
\(72\) −1.41191 0.414574i −1.41191 0.414574i
\(73\) 0 0 −0.723734 0.690079i \(-0.757576\pi\)
0.723734 + 0.690079i \(0.242424\pi\)
\(74\) 0 0
\(75\) −1.32254 + 0.849945i −1.32254 + 0.849945i
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 0.888835 0.458227i \(-0.151515\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(80\) 0.0475819 0.998867i 0.0475819 0.998867i
\(81\) 0.0435701 0.303037i 0.0435701 0.303037i
\(82\) −0.0623191 + 0.0719200i −0.0623191 + 0.0719200i
\(83\) 0.462997 + 1.90850i 0.462997 + 1.90850i 0.415415 + 0.909632i \(0.363636\pi\)
0.0475819 + 0.998867i \(0.484848\pi\)
\(84\) −2.46033 + 1.93482i −2.46033 + 1.93482i
\(85\) 0 0
\(86\) 1.82318 + 0.351390i 1.82318 + 0.351390i
\(87\) −1.05792 1.48564i −1.05792 1.48564i
\(88\) 0 0
\(89\) −0.544078 1.19136i −0.544078 1.19136i −0.959493 0.281733i \(-0.909091\pi\)
0.415415 0.909632i \(-0.363636\pi\)
\(90\) −1.46485 + 0.139877i −1.46485 + 0.139877i
\(91\) 0 0
\(92\) −0.841254 0.540641i −0.841254 0.540641i
\(93\) 0 0
\(94\) 1.70566 0.500828i 1.70566 0.500828i
\(95\) 0 0
\(96\) 0.786053 1.36148i 0.786053 1.36148i
\(97\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(98\) 0.141026 + 2.96050i 0.141026 + 2.96050i
\(99\) 0 0
\(100\) −0.327068 0.945001i −0.327068 0.945001i
\(101\) 0.428368 + 1.23769i 0.428368 + 1.23769i 0.928368 + 0.371662i \(0.121212\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(102\) 0 0
\(103\) −0.0311250 0.653395i −0.0311250 0.653395i −0.959493 0.281733i \(-0.909091\pi\)
0.928368 0.371662i \(-0.121212\pi\)
\(104\) 0 0
\(105\) −1.56499 + 2.71064i −1.56499 + 2.71064i
\(106\) 0 0
\(107\) −1.61435 + 0.474017i −1.61435 + 0.474017i −0.959493 0.281733i \(-0.909091\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(108\) −0.688177 0.275505i −0.688177 0.275505i
\(109\) −0.550294 0.353653i −0.550294 0.353653i 0.235759 0.971812i \(-0.424242\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) −0.827068 1.81103i −0.827068 1.81103i
\(113\) 0 0 0.235759 0.971812i \(-0.424242\pi\)
−0.235759 + 0.971812i \(0.575758\pi\)
\(114\) 0 0
\(115\) −0.981929 0.189251i −0.981929 0.189251i
\(116\) 1.07701 0.431171i 1.07701 0.431171i
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0.223734 1.55610i 0.223734 1.55610i
\(121\) 0.0475819 0.998867i 0.0475819 0.998867i
\(122\) 1.70566 0.879330i 1.70566 0.879330i
\(123\) −0.108276 + 0.103241i −0.108276 + 0.103241i
\(124\) 0 0
\(125\) −0.654861 0.755750i −0.654861 0.755750i
\(126\) −2.46463 + 1.58392i −2.46463 + 1.58392i
\(127\) 1.42131 0.273935i 1.42131 0.273935i 0.580057 0.814576i \(-0.303030\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(128\) 0.723734 + 0.690079i 0.723734 + 0.690079i
\(129\) 2.80075 + 0.822373i 2.80075 + 0.822373i
\(130\) 0 0
\(131\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0.0475819 + 0.998867i 0.0475819 + 0.998867i
\(135\) −0.741276 −0.741276
\(136\) 0 0
\(137\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(138\) −1.23576 0.971812i −1.23576 0.971812i
\(139\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(140\) −1.44091 1.37391i −1.44091 1.37391i
\(141\) 2.74418 0.528898i 2.74418 0.528898i
\(142\) 0 0
\(143\) 0 0
\(144\) 0.853564 1.19866i 0.853564 1.19866i
\(145\) 0.839614 0.800570i 0.839614 0.800570i
\(146\) 0 0
\(147\) −0.221708 + 4.65422i −0.221708 + 4.65422i
\(148\) 0 0
\(149\) −0.0623191 + 0.0719200i −0.0623191 + 0.0719200i −0.786053 0.618159i \(-0.787879\pi\)
0.723734 + 0.690079i \(0.242424\pi\)
\(150\) −0.370638 1.52779i −0.370638 1.52779i
\(151\) 0 0 0.786053 0.618159i \(-0.212121\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 0 0 0.995472 0.0950560i \(-0.0303030\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0.928368 + 0.371662i 0.928368 + 0.371662i
\(161\) −1.91030 + 0.560914i −1.91030 + 0.560914i
\(162\) 0.272120 + 0.140287i 0.272120 + 0.140287i
\(163\) 0.142315 0.246497i 0.142315 0.246497i −0.786053 0.618159i \(-0.787879\pi\)
0.928368 + 0.371662i \(0.121212\pi\)
\(164\) −0.0475819 0.0824143i −0.0475819 0.0824143i
\(165\) 0 0
\(166\) −1.95496 0.186677i −1.95496 0.186677i
\(167\) −0.271738 0.785135i −0.271738 0.785135i −0.995472 0.0950560i \(-0.969697\pi\)
0.723734 0.690079i \(-0.242424\pi\)
\(168\) −1.02371 2.95783i −1.02371 2.95783i
\(169\) −0.995472 0.0950560i −0.995472 0.0950560i
\(170\) 0 0
\(171\) 0 0
\(172\) −0.928368 + 1.60798i −0.928368 + 1.60798i
\(173\) 0 0 −0.888835 0.458227i \(-0.848485\pi\)
0.888835 + 0.458227i \(0.151515\pi\)
\(174\) 1.74994 0.513830i 1.74994 0.513830i
\(175\) −1.84833 0.739959i −1.84833 0.739959i
\(176\) 0 0
\(177\) 0 0
\(178\) 1.30379 0.124497i 1.30379 0.124497i
\(179\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(180\) 0.346923 1.43004i 0.346923 1.43004i
\(181\) −0.165101 0.231852i −0.165101 0.231852i 0.723734 0.690079i \(-0.242424\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(182\) 0 0
\(183\) 2.80075 1.12125i 2.80075 1.12125i
\(184\) 0.786053 0.618159i 0.786053 0.618159i
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) −0.0845850 + 1.77566i −0.0845850 + 1.77566i
\(189\) −1.31178 + 0.676269i −1.31178 + 0.676269i
\(190\) 0 0
\(191\) 0 0 0.580057 0.814576i \(-0.303030\pi\)
−0.580057 + 0.814576i \(0.696970\pi\)
\(192\) 1.02951 + 1.18812i 1.02951 + 1.18812i
\(193\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) −2.84380 0.835015i −2.84380 0.835015i
\(197\) 0 0 −0.786053 0.618159i \(-0.787879\pi\)
0.786053 + 0.618159i \(0.212121\pi\)
\(198\) 0 0
\(199\) 0 0 0.327068 0.945001i \(-0.393939\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(200\) 1.00000 1.00000
\(201\) −0.0748038 + 1.57033i −0.0748038 + 1.57033i
\(202\) −1.30972 −1.30972
\(203\) 0.755436 2.18269i 0.755436 2.18269i
\(204\) 0 0
\(205\) −0.0748038 0.0588264i −0.0748038 0.0588264i
\(206\) 0.627639 + 0.184291i 0.627639 + 0.184291i
\(207\) −1.06499 1.01546i −1.06499 1.01546i
\(208\) 0 0
\(209\) 0 0
\(210\) −2.04970 2.36548i −2.04970 2.36548i
\(211\) 0 0 0.580057 0.814576i \(-0.303030\pi\)
−0.580057 + 0.814576i \(0.696970\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0.0800569 1.68060i 0.0800569 1.68060i
\(215\) −0.264241 + 1.83784i −0.264241 + 1.83784i
\(216\) 0.485433 0.560219i 0.485433 0.560219i
\(217\) 0 0
\(218\) 0.514186 0.404360i 0.514186 0.404360i
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) −0.797176 1.74557i −0.797176 1.74557i −0.654861 0.755750i \(-0.727273\pi\)
−0.142315 0.989821i \(-0.545455\pi\)
\(224\) 1.98193 0.189251i 1.98193 0.189251i
\(225\) −0.209419 1.45654i −0.209419 1.45654i
\(226\) 0 0
\(227\) −1.21590 0.486774i −1.21590 0.486774i −0.327068 0.945001i \(-0.606061\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(228\) 0 0
\(229\) −1.28656 0.663268i −1.28656 0.663268i −0.327068 0.945001i \(-0.606061\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(230\) 0.500000 0.866025i 0.500000 0.866025i
\(231\) 0 0
\(232\) 0.0552004 + 1.15880i 0.0552004 + 1.15880i
\(233\) 0 0 −0.995472 0.0950560i \(-0.969697\pi\)
0.995472 + 0.0950560i \(0.0303030\pi\)
\(234\) 0 0
\(235\) 0.581419 + 1.67990i 0.581419 + 1.67990i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(240\) 1.39734 + 0.720381i 1.39734 + 0.720381i
\(241\) 0.627639 0.184291i 0.627639 0.184291i 0.0475819 0.998867i \(-0.484848\pi\)
0.580057 + 0.814576i \(0.303030\pi\)
\(242\) 0.928368 + 0.371662i 0.928368 + 0.371662i
\(243\) 1.02850 + 0.660977i 1.02850 + 0.660977i
\(244\) 0.273100 + 1.89945i 0.273100 + 1.89945i
\(245\) −2.95044 + 0.281733i −2.95044 + 0.281733i
\(246\) −0.0621493 0.136088i −0.0621493 0.136088i
\(247\) 0 0
\(248\) 0 0
\(249\) −3.03160 0.584293i −3.03160 0.584293i
\(250\) 0.928368 0.371662i 0.928368 0.371662i
\(251\) 0 0 0.786053 0.618159i \(-0.212121\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(252\) −0.690705 2.84713i −0.690705 2.84713i
\(253\) 0 0
\(254\) −0.205996 + 1.43273i −0.205996 + 1.43273i
\(255\) 0 0
\(256\) −0.888835 + 0.458227i −0.888835 + 0.458227i
\(257\) 0 0 0.723734 0.690079i \(-0.242424\pi\)
−0.723734 + 0.690079i \(0.757576\pi\)
\(258\) −1.69318 + 2.37774i −1.69318 + 2.37774i
\(259\) 0 0
\(260\) 0 0
\(261\) 1.67628 0.323076i 1.67628 0.323076i
\(262\) 0 0
\(263\) −0.452418 0.132842i −0.452418 0.132842i 0.0475819 0.998867i \(-0.484848\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 2.05902 2.05902
\(268\) −0.959493 0.281733i −0.959493 0.281733i
\(269\) −0.284630 −0.284630 −0.142315 0.989821i \(-0.545455\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(270\) 0.242448 0.700507i 0.242448 0.700507i
\(271\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) 1.32254 0.849945i 1.32254 0.849945i
\(277\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 1.76962 0.912303i 1.76962 0.912303i
\(281\) −0.0845850 + 1.77566i −0.0845850 + 1.77566i 0.415415 + 0.909632i \(0.363636\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(282\) −0.397725 + 2.76624i −0.397725 + 2.76624i
\(283\) −0.308779 + 0.356349i −0.308779 + 0.356349i −0.888835 0.458227i \(-0.848485\pi\)
0.580057 + 0.814576i \(0.303030\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −0.186042 0.0358566i −0.186042 0.0358566i
\(288\) 0.853564 + 1.19866i 0.853564 + 1.19866i
\(289\) 0.235759 0.971812i 0.235759 0.971812i
\(290\) 0.481929 + 1.05528i 0.481929 + 1.05528i
\(291\) 0 0
\(292\) 0 0
\(293\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(294\) −4.32573 1.73176i −4.32573 1.73176i
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) −0.0475819 0.0824143i −0.0475819 0.0824143i
\(299\) 0 0
\(300\) 1.56499 + 0.149438i 1.56499 + 0.149438i
\(301\) 1.20906 + 3.49334i 1.20906 + 3.49334i
\(302\) 0 0
\(303\) −2.04970 0.195722i −2.04970 0.195722i
\(304\) 0 0
\(305\) 0.959493 + 1.66189i 0.959493 + 1.66189i
\(306\) 0 0
\(307\) −1.49547 0.770969i −1.49547 0.770969i −0.500000 0.866025i \(-0.666667\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(308\) 0 0
\(309\) 0.954707 + 0.382207i 0.954707 + 0.382207i
\(310\) 0 0
\(311\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(312\) 0 0
\(313\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(314\) 0 0
\(315\) −1.69940 2.38647i −1.69940 2.38647i
\(316\) 0 0
\(317\) 0 0 0.928368 0.371662i \(-0.121212\pi\)
−0.928368 + 0.371662i \(0.878788\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) −0.654861 + 0.755750i −0.654861 + 0.755750i
\(321\) 0.376434 2.61816i 0.376434 2.61816i
\(322\) 0.0947329 1.98869i 0.0947329 1.98869i
\(323\) 0 0
\(324\) −0.221573 + 0.211270i −0.221573 + 0.211270i
\(325\) 0 0
\(326\) 0.186393 + 0.215109i 0.186393 + 0.215109i
\(327\) 0.865121 0.555979i 0.865121 0.555979i
\(328\) 0.0934441 0.0180099i 0.0934441 0.0180099i
\(329\) 2.56147 + 2.44236i 2.56147 + 2.44236i
\(330\) 0 0
\(331\) 0 0 −0.786053 0.618159i \(-0.787879\pi\)
0.786053 + 0.618159i \(0.212121\pi\)
\(332\) 0.815816 1.78639i 0.815816 1.78639i
\(333\) 0 0
\(334\) 0.830830 0.830830
\(335\) −0.995472 + 0.0950560i −0.995472 + 0.0950560i
\(336\) 3.12998 3.12998
\(337\) 0 0 0.327068 0.945001i \(-0.393939\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(338\) 0.415415 0.909632i 0.415415 0.909632i
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) −3.28924 + 2.11387i −3.28924 + 2.11387i
\(344\) −1.21590 1.40323i −1.21590 1.40323i
\(345\) 0.911911 1.28060i 0.911911 1.28060i
\(346\) 0 0
\(347\) 1.70566 0.879330i 1.70566 0.879330i 0.723734 0.690079i \(-0.242424\pi\)
0.981929 0.189251i \(-0.0606061\pi\)
\(348\) −0.0867810 + 1.82176i −0.0867810 + 1.82176i
\(349\) −0.264241 + 1.83784i −0.264241 + 1.83784i 0.235759 + 0.971812i \(0.424242\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(350\) 1.30379 1.50465i 1.30379 1.50465i
\(351\) 0 0
\(352\) 0 0
\(353\) 0 0 0.928368 0.371662i \(-0.121212\pi\)
−0.928368 + 0.371662i \(0.878788\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) −0.308779 + 1.27280i −0.308779 + 1.27280i
\(357\) 0 0
\(358\) 0 0
\(359\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(360\) 1.23792 + 0.795563i 1.23792 + 0.795563i
\(361\) 0.928368 + 0.371662i 0.928368 + 0.371662i
\(362\) 0.273100 0.0801894i 0.273100 0.0801894i
\(363\) 1.39734 + 0.720381i 1.39734 + 0.720381i
\(364\) 0 0
\(365\) 0 0
\(366\) 0.143547 + 3.01343i 0.143547 + 3.01343i
\(367\) 0.651174 + 0.0621796i 0.651174 + 0.0621796i 0.415415 0.909632i \(-0.363636\pi\)
0.235759 + 0.971812i \(0.424242\pi\)
\(368\) 0.327068 + 0.945001i 0.327068 + 0.945001i
\(369\) −0.0458011 0.132333i −0.0458011 0.132333i
\(370\) 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 0
\(375\) 1.50842 0.442913i 1.50842 0.442913i
\(376\) −1.65033 0.660694i −1.65033 0.660694i
\(377\) 0 0
\(378\) −0.210034 1.46082i −0.210034 1.46082i
\(379\) 0 0 0.995472 0.0950560i \(-0.0303030\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(380\) 0 0
\(381\) −0.536487 + 2.21143i −0.536487 + 2.21143i
\(382\) 0 0
\(383\) −1.74555 0.336426i −1.74555 0.336426i −0.786053 0.618159i \(-0.787879\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(384\) −1.45949 + 0.584293i −1.45949 + 0.584293i
\(385\) 0 0
\(386\) 0 0
\(387\) −1.78922 + 2.06487i −1.78922 + 2.06487i
\(388\) 0 0
\(389\) −0.0311250 + 0.653395i −0.0311250 + 0.653395i 0.928368 + 0.371662i \(0.121212\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 1.71921 2.41429i 1.71921 2.41429i
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) −0.327068 + 0.945001i −0.327068 + 0.945001i
\(401\) −1.99094 −1.99094 −0.995472 0.0950560i \(-0.969697\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(402\) −1.45949 0.584293i −1.45949 0.584293i
\(403\) 0 0
\(404\) 0.428368 1.23769i 0.428368 1.23769i
\(405\) −0.127181 + 0.278487i −0.127181 + 0.278487i
\(406\) 1.81556 + 1.42778i 1.81556 + 1.42778i
\(407\) 0 0
\(408\) 0 0
\(409\) −0.279486 + 0.0538665i −0.279486 + 0.0538665i −0.327068 0.945001i \(-0.606061\pi\)
0.0475819 + 0.998867i \(0.484848\pi\)
\(410\) 0.0800569 0.0514495i 0.0800569 0.0514495i
\(411\) 0 0
\(412\) −0.379436 + 0.532843i −0.379436 + 0.532843i
\(413\) 0 0
\(414\) 1.30794 0.674289i 1.30794 0.674289i
\(415\) 0.0934441 1.96163i 0.0934441 1.96163i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 0 0 0.786053 0.618159i \(-0.212121\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(420\) 2.90577 1.16329i 2.90577 1.16329i
\(421\) 0.815816 + 0.157236i 0.815816 + 0.157236i 0.580057 0.814576i \(-0.303030\pi\)
0.235759 + 0.971812i \(0.424242\pi\)
\(422\) 0 0
\(423\) −0.616716 + 2.54214i −0.616716 + 2.54214i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 3.21409 + 2.06557i 3.21409 + 2.06557i
\(428\) 1.56199 + 0.625325i 1.56199 + 0.625325i
\(429\) 0 0
\(430\) −1.65033 0.850806i −1.65033 0.850806i
\(431\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(432\) 0.370638 + 0.641964i 0.370638 + 0.641964i
\(433\) 0 0 −0.0475819 0.998867i \(-0.515152\pi\)
0.0475819 + 0.998867i \(0.484848\pi\)
\(434\) 0 0
\(435\) 0.596514 + 1.72351i 0.596514 + 1.72351i
\(436\) 0.213947 + 0.618159i 0.213947 + 0.618159i
\(437\) 0 0
\(438\) 0 0
\(439\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(440\) 0 0
\(441\) −3.87654 1.99850i −3.87654 1.99850i
\(442\) 0 0
\(443\) 1.07701 + 0.431171i 1.07701 + 0.431171i 0.841254 0.540641i \(-0.181818\pi\)
0.235759 + 0.971812i \(0.424242\pi\)
\(444\) 0 0
\(445\) 0.186393 + 1.29639i 0.186393 + 1.29639i
\(446\) 1.91030 0.182411i 1.91030 0.182411i
\(447\) −0.0621493 0.136088i −0.0621493 0.136088i
\(448\) −0.469383 + 1.93482i −0.469383 + 1.93482i
\(449\) −1.03115 1.44805i −1.03115 1.44805i −0.888835 0.458227i \(-0.848485\pi\)
−0.142315 0.989821i \(-0.545455\pi\)
\(450\) 1.44493 + 0.278487i 1.44493 + 0.278487i
\(451\) 0 0
\(452\) 0 0
\(453\) 0 0
\(454\) 0.857685 0.989821i 0.857685 0.989821i
\(455\) 0 0
\(456\) 0 0
\(457\) 0 0 0.888835 0.458227i \(-0.151515\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(458\) 1.04758 0.998867i 1.04758 0.998867i
\(459\) 0 0
\(460\) 0.654861 + 0.755750i 0.654861 + 0.755750i
\(461\) 1.65210 1.06174i 1.65210 1.06174i 0.723734 0.690079i \(-0.242424\pi\)
0.928368 0.371662i \(-0.121212\pi\)
\(462\) 0 0
\(463\) −0.205996 0.196417i −0.205996 0.196417i 0.580057 0.814576i \(-0.303030\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(464\) −1.11312 0.326842i −1.11312 0.326842i
\(465\) 0 0
\(466\) 0 0
\(467\) −0.473420 + 1.36786i −0.473420 + 1.36786i 0.415415 + 0.909632i \(0.363636\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(468\) 0 0
\(469\) −1.67489 + 1.07639i −1.67489 + 1.07639i
\(470\) −1.77767 −1.77767
\(471\) 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 0.580057 0.814576i \(-0.303030\pi\)
−0.580057 + 0.814576i \(0.696970\pi\)
\(480\) −1.13779 + 1.08488i −1.13779 + 1.08488i
\(481\) 0 0
\(482\) −0.0311250 + 0.653395i −0.0311250 + 0.653395i
\(483\) 0.445442 3.09812i 0.445442 3.09812i
\(484\) −0.654861 + 0.755750i −0.654861 + 0.755750i
\(485\) 0 0
\(486\) −0.961014 + 0.755750i −0.961014 + 0.755750i
\(487\) 1.82318 0.729892i 1.82318 0.729892i 0.841254 0.540641i \(-0.181818\pi\)
0.981929 0.189251i \(-0.0606061\pi\)
\(488\) −1.88431 0.363170i −1.88431 0.363170i
\(489\) 0.259557 + 0.364497i 0.259557 + 0.364497i
\(490\) 0.698756 2.88031i 0.698756 2.88031i
\(491\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(492\) 0.148930 0.0142211i 0.148930 0.0142211i
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 1.54370 2.67376i 1.54370 2.67376i
\(499\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(500\) 0.0475819 + 0.998867i 0.0475819 + 0.998867i
\(501\) 1.30024 + 0.124158i 1.30024 + 0.124158i
\(502\) 0 0
\(503\) −0.0311250 0.0899299i −0.0311250 0.0899299i 0.928368 0.371662i \(-0.121212\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(504\) 2.91644 + 0.278487i 2.91644 + 0.278487i
\(505\) −0.0623191 1.30824i −0.0623191 1.30824i
\(506\) 0 0
\(507\) 0.786053 1.36148i 0.786053 1.36148i
\(508\) −1.28656 0.663268i −1.28656 0.663268i
\(509\) −0.797176 + 0.234072i −0.797176 + 0.234072i −0.654861 0.755750i \(-0.727273\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −0.142315 0.989821i −0.142315 0.989821i
\(513\) 0 0
\(514\) 0 0
\(515\) −0.154218 + 0.635697i −0.154218 + 0.635697i
\(516\) −1.69318 2.37774i −1.69318 2.37774i
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 0.654861 0.755750i 0.654861 0.755750i −0.327068 0.945001i \(-0.606061\pi\)
0.981929 + 0.189251i \(0.0606061\pi\)
\(522\) −0.242950 + 1.68975i −0.242950 + 1.68975i
\(523\) 0.0883470 1.85463i 0.0883470 1.85463i −0.327068 0.945001i \(-0.606061\pi\)
0.415415 0.909632i \(-0.363636\pi\)
\(524\) 0 0
\(525\) 2.26527 2.15993i 2.26527 2.15993i
\(526\) 0.273507 0.384087i 0.273507 0.384087i
\(527\) 0 0
\(528\) 0 0
\(529\) 0 0
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) −0.673440 + 1.94578i −0.673440 + 1.94578i
\(535\) 1.68251 1.68251
\(536\) 0.580057 0.814576i 0.580057 0.814576i
\(537\) 0 0
\(538\) 0.0930932 0.268975i 0.0930932 0.268975i
\(539\) 0 0
\(540\) 0.582682 + 0.458227i 0.582682 + 0.458227i
\(541\) −1.78153 0.523103i −1.78153 0.523103i −0.786053 0.618159i \(-0.787879\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(542\) 0 0
\(543\) 0.439382 0.0846839i 0.439382 0.0846839i
\(544\) 0 0
\(545\) 0.428368 + 0.494363i 0.428368 + 0.494363i
\(546\) 0 0
\(547\) 1.04758 0.998867i 1.04758 0.998867i 0.0475819 0.998867i \(-0.484848\pi\)
1.00000 \(0\)
\(548\) 0 0
\(549\) −0.134363 + 2.82062i −0.134363 + 2.82062i
\(550\) 0 0
\(551\) 0 0
\(552\) 0.370638 + 1.52779i 0.370638 + 1.52779i
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 0 0 0.235759 0.971812i \(-0.424242\pi\)
−0.235759 + 0.971812i \(0.575758\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0.283341 + 1.97068i 0.283341 + 1.97068i
\(561\) 0 0
\(562\) −1.65033 0.660694i −1.65033 0.660694i
\(563\) −1.78153 + 0.523103i −1.78153 + 0.523103i −0.995472 0.0950560i \(-0.969697\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(564\) −2.48402 1.28060i −2.48402 1.28060i
\(565\) 0 0
\(566\) −0.235759 0.408346i −0.235759 0.408346i
\(567\) 0.0290028 + 0.608843i 0.0290028 + 0.608843i
\(568\) 0 0
\(569\) −0.271738 0.785135i −0.271738 0.785135i −0.995472 0.0950560i \(-0.969697\pi\)
0.723734 0.690079i \(-0.242424\pi\)
\(570\) 0 0
\(571\) 0 0 −0.995472 0.0950560i \(-0.969697\pi\)
0.995472 + 0.0950560i \(0.0303030\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0.0947329 0.164082i 0.0947329 0.164082i
\(575\) 0.888835 + 0.458227i 0.888835 + 0.458227i
\(576\) −1.41191 + 0.414574i −1.41191 + 0.414574i
\(577\) 0 0 −0.928368 0.371662i \(-0.878788\pi\)
0.928368 + 0.371662i \(0.121212\pi\)
\(578\) 0.841254 + 0.540641i 0.841254 + 0.540641i
\(579\) 0 0
\(580\) −1.15486 + 0.110276i −1.15486 + 0.110276i
\(581\) −1.62424 3.55660i −1.62424 3.55660i
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 0.396666 + 1.63508i 0.396666 + 1.63508i 0.723734 + 0.690079i \(0.242424\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(588\) 3.05132 3.52141i 3.05132 3.52141i
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 0 0 0.580057 0.814576i \(-0.303030\pi\)
−0.580057 + 0.814576i \(0.696970\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0.0934441 0.0180099i 0.0934441 0.0180099i
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 −0.786053 0.618159i \(-0.787879\pi\)
0.786053 + 0.618159i \(0.212121\pi\)
\(600\) −0.653077 + 1.43004i −0.653077 + 1.43004i
\(601\) −0.607279 + 1.75462i −0.607279 + 1.75462i 0.0475819 + 0.998867i \(0.484848\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(602\) −3.69666 −3.69666
\(603\) −1.30794 0.674289i −1.30794 0.674289i
\(604\) 0 0
\(605\) −0.327068 + 0.945001i −0.327068 + 0.945001i
\(606\) 0.855348 1.87295i 0.855348 1.87295i
\(607\) 1.39734 + 1.09888i 1.39734 + 1.09888i 0.981929 + 0.189251i \(0.0606061\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(608\) 0 0
\(609\) 2.62797 + 2.50576i 2.62797 + 2.50576i
\(610\) −1.88431 + 0.363170i −1.88431 + 0.363170i
\(611\) 0 0
\(612\) 0 0
\(613\) 0 0 0.580057 0.814576i \(-0.303030\pi\)
−0.580057 + 0.814576i \(0.696970\pi\)
\(614\) 1.21769 1.16106i 1.21769 1.16106i
\(615\) 0.132977 0.0685542i 0.132977 0.0685542i
\(616\) 0 0
\(617\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(618\) −0.673440 + 0.777191i −0.673440 + 0.777191i
\(619\) 0 0 −0.235759 0.971812i \(-0.575758\pi\)
0.235759 + 0.971812i \(0.424242\pi\)
\(620\) 0 0
\(621\) 0.688177 0.275505i 0.688177 0.275505i
\(622\) 0 0
\(623\) 1.51255 + 2.12407i 1.51255 + 2.12407i
\(624\) 0 0
\(625\) 0.415415 + 0.909632i 0.415415 + 0.909632i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) 2.81104 0.825395i 2.81104 0.825395i
\(631\) 0 0 −0.888835 0.458227i \(-0.848485\pi\)
0.888835 + 0.458227i \(0.151515\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −1.44091 0.137591i −1.44091 0.137591i
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) −0.500000 0.866025i −0.500000 0.866025i
\(641\) −0.235759 + 0.408346i −0.235759 + 0.408346i −0.959493 0.281733i \(-0.909091\pi\)
0.723734 + 0.690079i \(0.242424\pi\)
\(642\) 2.35104 + 1.21205i 2.35104 + 1.21205i
\(643\) −1.11312 + 0.326842i −1.11312 + 0.326842i −0.786053 0.618159i \(-0.787879\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(644\) 1.84833 + 0.739959i 1.84833 + 0.739959i
\(645\) −2.45561 1.57812i −2.45561 1.57812i
\(646\) 0 0
\(647\) 1.76962 0.168978i 1.76962 0.168978i 0.841254 0.540641i \(-0.181818\pi\)
0.928368 + 0.371662i \(0.121212\pi\)
\(648\) −0.127181 0.278487i −0.127181 0.278487i
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) −0.264241 + 0.105786i −0.264241 + 0.105786i
\(653\) 0 0 0.786053 0.618159i \(-0.212121\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(654\) 0.242448 + 0.999383i 0.242448 + 0.999383i
\(655\) 0 0
\(656\) −0.0135432 + 0.0941952i −0.0135432 + 0.0941952i
\(657\) 0 0
\(658\) −3.14580 + 1.62177i −3.14580 + 1.62177i
\(659\) 0 0 0.723734 0.690079i \(-0.242424\pi\)
−0.723734 + 0.690079i \(0.757576\pi\)
\(660\) 0 0
\(661\) −0.544078 0.627899i −0.544078 0.627899i 0.415415 0.909632i \(-0.363636\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 1.42131 + 1.35522i 1.42131 + 1.35522i
\(665\) 0 0
\(666\) 0 0
\(667\) −0.481929 + 1.05528i −0.481929 + 1.05528i
\(668\) −0.271738 + 0.785135i −0.271738 + 0.785135i
\(669\) 3.01685 3.01685
\(670\) 0.235759 0.971812i 0.235759 0.971812i
\(671\) 0 0
\(672\) −1.02371 + 2.95783i −1.02371 + 2.95783i
\(673\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(674\) 0 0
\(675\) 0.711249 + 0.208842i 0.711249 + 0.208842i
\(676\) 0.723734 + 0.690079i 0.723734 + 0.690079i
\(677\) 0 0 0.981929 0.189251i \(-0.0606061\pi\)
−0.981929 + 0.189251i \(0.939394\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 1.49018 1.42089i 1.49018 1.42089i
\(682\) 0 0
\(683\) 0.0800569 1.68060i 0.0800569 1.68060i −0.500000 0.866025i \(-0.666667\pi\)
0.580057 0.814576i \(-0.303030\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) −0.921801 3.79972i −0.921801 3.79972i
\(687\) 1.78872 1.40667i 1.78872 1.40667i
\(688\) 1.72373 0.690079i 1.72373 0.690079i
\(689\) 0 0
\(690\) 0.911911 + 1.28060i 0.911911 + 1.28060i
\(691\) 0 0 0.235759 0.971812i \(-0.424242\pi\)
−0.235759 + 0.971812i \(0.575758\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0.273100 + 1.89945i 0.273100 + 1.89945i
\(695\) 0 0
\(696\) −1.69318 0.677846i −1.69318 0.677846i
\(697\) 0 0
\(698\) −1.65033 0.850806i −1.65033 0.850806i
\(699\) 0 0
\(700\) 0.995472 + 1.72421i 0.995472 + 1.72421i
\(701\) −0.0475819 0.998867i −0.0475819 0.998867i −0.888835 0.458227i \(-0.848485\pi\)
0.841254 0.540641i \(-0.181818\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0 0
\(705\) −2.78203 0.265652i −2.78203 0.265652i
\(706\) 0 0
\(707\) −1.30379 2.25823i −1.30379 2.25823i
\(708\) 0 0
\(709\) 0.888835 + 0.458227i 0.888835 + 0.458227i 0.841254 0.540641i \(-0.181818\pi\)
0.0475819 + 0.998867i \(0.484848\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) −1.10181 0.708089i −1.10181 0.708089i
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 0.928368 0.371662i \(-0.121212\pi\)
−0.928368 + 0.371662i \(0.878788\pi\)
\(720\) −1.15669 + 0.909632i −1.15669 + 0.909632i
\(721\) 0.307040 + 1.26564i 0.307040 + 1.26564i
\(722\) −0.654861 + 0.755750i −0.654861 + 0.755750i
\(723\) −0.146352 + 1.01790i −0.146352 + 1.01790i
\(724\) −0.0135432 + 0.284307i −0.0135432 + 0.284307i
\(725\) −1.03115 + 0.531595i −1.03115 + 0.531595i
\(726\) −1.13779 + 1.08488i −1.13779 + 1.08488i
\(727\) 0.0552004 0.0775182i 0.0552004 0.0775182i −0.786053 0.618159i \(-0.787879\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(728\) 0 0
\(729\) −1.35936 + 0.873608i −1.35936 + 0.873608i
\(730\) 0 0
\(731\) 0 0
\(732\) −2.89465 0.849945i −2.89465 0.849945i
\(733\) 0 0 −0.786053 0.618159i \(-0.787879\pi\)
0.786053 + 0.618159i \(0.212121\pi\)
\(734\) −0.271738 + 0.595023i −0.271738 + 0.595023i
\(735\) 1.52397 4.40323i 1.52397 4.40323i
\(736\) −1.00000 −1.00000
\(737\) 0 0
\(738\) 0.140035 0.140035
\(739\) 0 0 0.327068 0.945001i \(-0.393939\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −0.205996 0.196417i −0.205996 0.196417i 0.580057 0.814576i \(-0.303030\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(744\) 0 0
\(745\) 0.0800569 0.0514495i 0.0800569 0.0514495i
\(746\) 0 0
\(747\) 1.67628 2.35400i 1.67628 2.35400i
\(748\) 0 0
\(749\) 2.97740 1.53496i 2.97740 1.53496i
\(750\) −0.0748038 + 1.57033i −0.0748038 + 1.57033i
\(751\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(752\) 1.16413 1.34347i 1.16413 1.34347i
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 1.44917 + 0.279304i 1.44917 + 0.279304i
\(757\) 0 0 −0.580057 0.814576i \(-0.696970\pi\)
0.580057 + 0.814576i \(0.303030\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 0.0405070 + 0.281733i 0.0405070 + 0.281733i 1.00000 \(0\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(762\) −1.91433 1.23027i −1.91433 1.23027i
\(763\) 1.20906 + 0.484034i 1.20906 + 0.484034i
\(764\) 0 0
\(765\) 0 0
\(766\) 0.888835 1.53951i 0.888835 1.53951i
\(767\) 0 0
\(768\) −0.0748038 1.57033i −0.0748038 1.57033i
\(769\) 1.56499 + 0.149438i 1.56499 + 0.149438i 0.841254 0.540641i \(-0.181818\pi\)
0.723734 + 0.690079i \(0.242424\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 0 0 −0.0475819 0.998867i \(-0.515152\pi\)
0.0475819 + 0.998867i \(0.484848\pi\)
\(774\) −1.36611 2.36617i −1.36611 2.36617i
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) −0.607279 0.243118i −0.607279 0.243118i
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) −0.202744 + 0.835724i −0.202744 + 0.835724i
\(784\) 1.71921 + 2.41429i 1.71921 + 2.41429i
\(785\) 0 0
\(786\) 0 0
\(787\) −1.13779 + 0.894765i −1.13779 + 0.894765i −0.995472 0.0950560i \(-0.969697\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(788\) 0 0
\(789\) 0.485433 0.560219i 0.485433 0.560219i
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0