Properties

Label 1340.1.bl.b.199.1
Level $1340$
Weight $1$
Character 1340.199
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 199.1
Root \(0.723734 + 0.690079i\) of defining polynomial
Character \(\chi\) \(=\) 1340.199
Dual form 1340.1.bl.b.1239.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.0475819 - 0.998867i) q^{2} +(1.91030 + 0.560914i) q^{3} +(-0.995472 - 0.0950560i) q^{4} +(-0.654861 + 0.755750i) q^{5} +(0.651174 - 1.88144i) q^{6} +(-0.419102 + 0.216062i) q^{7} +(-0.142315 + 0.989821i) q^{8} +(2.49336 + 1.60238i) q^{9} +O(q^{10})\) \(q+(0.0475819 - 0.998867i) q^{2} +(1.91030 + 0.560914i) q^{3} +(-0.995472 - 0.0950560i) q^{4} +(-0.654861 + 0.755750i) q^{5} +(0.651174 - 1.88144i) q^{6} +(-0.419102 + 0.216062i) q^{7} +(-0.142315 + 0.989821i) q^{8} +(2.49336 + 1.60238i) q^{9} +(0.723734 + 0.690079i) q^{10} +(-1.84833 - 0.739959i) q^{12} +(0.195876 + 0.428908i) q^{14} +(-1.67489 + 1.07639i) q^{15} +(0.981929 + 0.189251i) q^{16} +(1.71921 - 2.41429i) q^{18} +(0.723734 - 0.690079i) q^{20} +(-0.921801 + 0.177663i) q^{21} +(-0.235759 - 0.971812i) q^{23} +(-0.827068 + 1.81103i) q^{24} +(-0.142315 - 0.989821i) q^{25} +(2.56046 + 2.95493i) q^{27} +(0.437742 - 0.175245i) q^{28} +(-0.723734 + 1.25354i) q^{29} +(0.995472 + 1.72421i) q^{30} +(0.235759 - 0.971812i) q^{32} +(0.111165 - 0.458227i) q^{35} +(-2.32975 - 1.83214i) q^{36} +(-0.654861 - 0.755750i) q^{40} +(-0.911911 - 1.28060i) q^{41} +(0.133600 + 0.929210i) q^{42} +(0.481929 - 1.05528i) q^{43} +(-2.84380 + 0.835015i) q^{45} +(-0.981929 + 0.189251i) q^{46} +(1.34378 - 1.28129i) q^{47} +(1.76962 + 0.912303i) q^{48} +(-0.451093 + 0.633472i) q^{49} +(-0.995472 + 0.0950560i) q^{50} +(3.07341 - 2.41696i) q^{54} +(-0.154218 - 0.445585i) q^{56} +(1.21769 + 0.782560i) q^{58} +(1.76962 - 0.912303i) q^{60} +(0.428368 - 1.23769i) q^{61} +(-1.39118 - 0.132842i) q^{63} +(-0.959493 - 0.281733i) q^{64} +(0.580057 - 0.814576i) q^{67} +(0.0947329 - 1.98869i) q^{69} +(-0.452418 - 0.132842i) q^{70} +(-1.94091 + 2.23993i) q^{72} +(0.283341 - 1.97068i) q^{75} +(-0.786053 + 0.618159i) q^{80} +(2.00255 + 4.38497i) q^{81} +(-1.32254 + 0.849945i) q^{82} +(-1.74555 - 0.336426i) q^{83} +(0.934515 - 0.0892353i) q^{84} +(-1.03115 - 0.531595i) q^{86} +(-2.08568 + 1.98869i) q^{87} +(-1.61435 + 0.474017i) q^{89} +(0.698756 + 2.88031i) q^{90} +(0.142315 + 0.989821i) q^{92} +(-1.21590 - 1.40323i) q^{94} +(0.995472 - 1.72421i) q^{96} +(0.611291 + 0.480724i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20q + q^{2} + 2q^{3} + q^{4} - 2q^{5} - q^{6} - q^{7} - 2q^{8} + O(q^{10}) \) \( 20q + q^{2} + 2q^{3} + q^{4} - 2q^{5} - q^{6} - q^{7} - 2q^{8} + q^{10} - q^{12} + 2q^{14} + 2q^{15} + q^{16} + q^{20} - 10q^{21} - q^{23} - 9q^{24} - 2q^{25} - 2q^{27} - q^{28} - q^{29} - q^{30} + q^{32} + 21q^{35} - 2q^{40} - q^{41} + 20q^{42} - 9q^{43} - q^{46} - q^{47} - q^{48} + q^{50} + q^{54} - q^{56} + 2q^{58} - q^{60} - 9q^{61} - 11q^{63} - 2q^{64} + q^{67} + q^{69} - 9q^{70} - 11q^{72} + 2q^{75} + q^{80} + 2q^{81} + 2q^{82} - q^{83} + q^{84} - q^{86} + q^{87} - 4q^{89} + 2q^{92} + 2q^{94} - q^{96} + O(q^{100}) \)

Character values

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

\(n\) \(537\) \(671\) \(1141\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{17}{33}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.0475819 0.998867i 0.0475819 0.998867i
\(3\) 1.91030 + 0.560914i 1.91030 + 0.560914i 0.981929 + 0.189251i \(0.0606061\pi\)
0.928368 + 0.371662i \(0.121212\pi\)
\(4\) −0.995472 0.0950560i −0.995472 0.0950560i
\(5\) −0.654861 + 0.755750i −0.654861 + 0.755750i
\(6\) 0.651174 1.88144i 0.651174 1.88144i
\(7\) −0.419102 + 0.216062i −0.419102 + 0.216062i −0.654861 0.755750i \(-0.727273\pi\)
0.235759 + 0.971812i \(0.424242\pi\)
\(8\) −0.142315 + 0.989821i −0.142315 + 0.989821i
\(9\) 2.49336 + 1.60238i 2.49336 + 1.60238i
\(10\) 0.723734 + 0.690079i 0.723734 + 0.690079i
\(11\) 0 0 −0.327068 0.945001i \(-0.606061\pi\)
0.327068 + 0.945001i \(0.393939\pi\)
\(12\) −1.84833 0.739959i −1.84833 0.739959i
\(13\) 0 0 0.786053 0.618159i \(-0.212121\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(14\) 0.195876 + 0.428908i 0.195876 + 0.428908i
\(15\) −1.67489 + 1.07639i −1.67489 + 1.07639i
\(16\) 0.981929 + 0.189251i 0.981929 + 0.189251i
\(17\) 0 0 0.995472 0.0950560i \(-0.0303030\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(18\) 1.71921 2.41429i 1.71921 2.41429i
\(19\) 0 0 −0.888835 0.458227i \(-0.848485\pi\)
0.888835 + 0.458227i \(0.151515\pi\)
\(20\) 0.723734 0.690079i 0.723734 0.690079i
\(21\) −0.921801 + 0.177663i −0.921801 + 0.177663i
\(22\) 0 0
\(23\) −0.235759 0.971812i −0.235759 0.971812i −0.959493 0.281733i \(-0.909091\pi\)
0.723734 0.690079i \(-0.242424\pi\)
\(24\) −0.827068 + 1.81103i −0.827068 + 1.81103i
\(25\) −0.142315 0.989821i −0.142315 0.989821i
\(26\) 0 0
\(27\) 2.56046 + 2.95493i 2.56046 + 2.95493i
\(28\) 0.437742 0.175245i 0.437742 0.175245i
\(29\) −0.723734 + 1.25354i −0.723734 + 1.25354i 0.235759 + 0.971812i \(0.424242\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(30\) 0.995472 + 1.72421i 0.995472 + 1.72421i
\(31\) 0 0 −0.786053 0.618159i \(-0.787879\pi\)
0.786053 + 0.618159i \(0.212121\pi\)
\(32\) 0.235759 0.971812i 0.235759 0.971812i
\(33\) 0 0
\(34\) 0 0
\(35\) 0.111165 0.458227i 0.111165 0.458227i
\(36\) −2.32975 1.83214i −2.32975 1.83214i
\(37\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) −0.654861 0.755750i −0.654861 0.755750i
\(41\) −0.911911 1.28060i −0.911911 1.28060i −0.959493 0.281733i \(-0.909091\pi\)
0.0475819 0.998867i \(-0.484848\pi\)
\(42\) 0.133600 + 0.929210i 0.133600 + 0.929210i
\(43\) 0.481929 1.05528i 0.481929 1.05528i −0.500000 0.866025i \(-0.666667\pi\)
0.981929 0.189251i \(-0.0606061\pi\)
\(44\) 0 0
\(45\) −2.84380 + 0.835015i −2.84380 + 0.835015i
\(46\) −0.981929 + 0.189251i −0.981929 + 0.189251i
\(47\) 1.34378 1.28129i 1.34378 1.28129i 0.415415 0.909632i \(-0.363636\pi\)
0.928368 0.371662i \(-0.121212\pi\)
\(48\) 1.76962 + 0.912303i 1.76962 + 0.912303i
\(49\) −0.451093 + 0.633472i −0.451093 + 0.633472i
\(50\) −0.995472 + 0.0950560i −0.995472 + 0.0950560i
\(51\) 0 0
\(52\) 0 0
\(53\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(54\) 3.07341 2.41696i 3.07341 2.41696i
\(55\) 0 0
\(56\) −0.154218 0.445585i −0.154218 0.445585i
\(57\) 0 0
\(58\) 1.21769 + 0.782560i 1.21769 + 0.782560i
\(59\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(60\) 1.76962 0.912303i 1.76962 0.912303i
\(61\) 0.428368 1.23769i 0.428368 1.23769i −0.500000 0.866025i \(-0.666667\pi\)
0.928368 0.371662i \(-0.121212\pi\)
\(62\) 0 0
\(63\) −1.39118 0.132842i −1.39118 0.132842i
\(64\) −0.959493 0.281733i −0.959493 0.281733i
\(65\) 0 0
\(66\) 0 0
\(67\) 0.580057 0.814576i 0.580057 0.814576i
\(68\) 0 0
\(69\) 0.0947329 1.98869i 0.0947329 1.98869i
\(70\) −0.452418 0.132842i −0.452418 0.132842i
\(71\) 0 0 −0.995472 0.0950560i \(-0.969697\pi\)
0.995472 + 0.0950560i \(0.0303030\pi\)
\(72\) −1.94091 + 2.23993i −1.94091 + 2.23993i
\(73\) 0 0 0.327068 0.945001i \(-0.393939\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(74\) 0 0
\(75\) 0.283341 1.97068i 0.283341 1.97068i
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 −0.928368 0.371662i \(-0.878788\pi\)
0.928368 + 0.371662i \(0.121212\pi\)
\(80\) −0.786053 + 0.618159i −0.786053 + 0.618159i
\(81\) 2.00255 + 4.38497i 2.00255 + 4.38497i
\(82\) −1.32254 + 0.849945i −1.32254 + 0.849945i
\(83\) −1.74555 0.336426i −1.74555 0.336426i −0.786053 0.618159i \(-0.787879\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(84\) 0.934515 0.0892353i 0.934515 0.0892353i
\(85\) 0 0
\(86\) −1.03115 0.531595i −1.03115 0.531595i
\(87\) −2.08568 + 1.98869i −2.08568 + 1.98869i
\(88\) 0 0
\(89\) −1.61435 + 0.474017i −1.61435 + 0.474017i −0.959493 0.281733i \(-0.909091\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(90\) 0.698756 + 2.88031i 0.698756 + 2.88031i
\(91\) 0 0
\(92\) 0.142315 + 0.989821i 0.142315 + 0.989821i
\(93\) 0 0
\(94\) −1.21590 1.40323i −1.21590 1.40323i
\(95\) 0 0
\(96\) 0.995472 1.72421i 0.995472 1.72421i
\(97\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(98\) 0.611291 + 0.480724i 0.611291 + 0.480724i
\(99\) 0 0
\(100\) 0.0475819 + 0.998867i 0.0475819 + 0.998867i
\(101\) 0.0800569 + 1.68060i 0.0800569 + 1.68060i 0.580057 + 0.814576i \(0.303030\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(102\) 0 0
\(103\) −0.0748038 0.0588264i −0.0748038 0.0588264i 0.580057 0.814576i \(-0.303030\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(104\) 0 0
\(105\) 0.469383 0.812995i 0.469383 0.812995i
\(106\) 0 0
\(107\) 0.186393 + 0.215109i 0.186393 + 0.215109i 0.841254 0.540641i \(-0.181818\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(108\) −2.26798 3.18493i −2.26798 3.18493i
\(109\) −0.0135432 0.0941952i −0.0135432 0.0941952i 0.981929 0.189251i \(-0.0606061\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) −0.452418 + 0.132842i −0.452418 + 0.132842i
\(113\) 0 0 0.981929 0.189251i \(-0.0606061\pi\)
−0.981929 + 0.189251i \(0.939394\pi\)
\(114\) 0 0
\(115\) 0.888835 + 0.458227i 0.888835 + 0.458227i
\(116\) 0.839614 1.17907i 0.839614 1.17907i
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) −0.827068 1.81103i −0.827068 1.81103i
\(121\) −0.786053 + 0.618159i −0.786053 + 0.618159i
\(122\) −1.21590 0.486774i −1.21590 0.486774i
\(123\) −1.02371 2.95783i −1.02371 2.95783i
\(124\) 0 0
\(125\) 0.841254 + 0.540641i 0.841254 + 0.540641i
\(126\) −0.198887 + 1.38329i −0.198887 + 1.38329i
\(127\) 0.581419 0.299742i 0.581419 0.299742i −0.142315 0.989821i \(-0.545455\pi\)
0.723734 + 0.690079i \(0.242424\pi\)
\(128\) −0.327068 + 0.945001i −0.327068 + 0.945001i
\(129\) 1.51255 1.74557i 1.51255 1.74557i
\(130\) 0 0
\(131\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −0.786053 0.618159i −0.786053 0.618159i
\(135\) −3.90993 −3.90993
\(136\) 0 0
\(137\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(138\) −1.98193 0.189251i −1.98193 0.189251i
\(139\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(140\) −0.154218 + 0.445585i −0.154218 + 0.445585i
\(141\) 3.28572 1.69391i 3.28572 1.69391i
\(142\) 0 0
\(143\) 0 0
\(144\) 2.14504 + 2.04530i 2.14504 + 2.04530i
\(145\) −0.473420 1.36786i −0.473420 1.36786i
\(146\) 0 0
\(147\) −1.21705 + 0.957095i −1.21705 + 0.957095i
\(148\) 0 0
\(149\) −1.32254 + 0.849945i −1.32254 + 0.849945i −0.995472 0.0950560i \(-0.969697\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(150\) −1.95496 0.376789i −1.95496 0.376789i
\(151\) 0 0 0.995472 0.0950560i \(-0.0303030\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 0 0 −0.235759 0.971812i \(-0.575758\pi\)
0.235759 + 0.971812i \(0.424242\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0.580057 + 0.814576i 0.580057 + 0.814576i
\(161\) 0.308779 + 0.356349i 0.308779 + 0.356349i
\(162\) 4.47528 1.79163i 4.47528 1.79163i
\(163\) −0.415415 + 0.719520i −0.415415 + 0.719520i −0.995472 0.0950560i \(-0.969697\pi\)
0.580057 + 0.814576i \(0.303030\pi\)
\(164\) 0.786053 + 1.36148i 0.786053 + 1.36148i
\(165\) 0 0
\(166\) −0.419102 + 1.72756i −0.419102 + 1.72756i
\(167\) −0.0913090 1.91681i −0.0913090 1.91681i −0.327068 0.945001i \(-0.606061\pi\)
0.235759 0.971812i \(-0.424242\pi\)
\(168\) −0.0446683 0.937702i −0.0446683 0.937702i
\(169\) 0.235759 0.971812i 0.235759 0.971812i
\(170\) 0 0
\(171\) 0 0
\(172\) −0.580057 + 1.00469i −0.580057 + 1.00469i
\(173\) 0 0 0.928368 0.371662i \(-0.121212\pi\)
−0.928368 + 0.371662i \(0.878788\pi\)
\(174\) 1.88720 + 2.17794i 1.88720 + 2.17794i
\(175\) 0.273507 + 0.384087i 0.273507 + 0.384087i
\(176\) 0 0
\(177\) 0 0
\(178\) 0.396666 + 1.63508i 0.396666 + 1.63508i
\(179\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(180\) 2.91030 0.560914i 2.91030 0.560914i
\(181\) 0.601300 0.573338i 0.601300 0.573338i −0.327068 0.945001i \(-0.606061\pi\)
0.928368 + 0.371662i \(0.121212\pi\)
\(182\) 0 0
\(183\) 1.51255 2.12407i 1.51255 2.12407i
\(184\) 0.995472 0.0950560i 0.995472 0.0950560i
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) −1.45949 + 1.14776i −1.45949 + 1.14776i
\(189\) −1.71154 0.685198i −1.71154 0.685198i
\(190\) 0 0
\(191\) 0 0 −0.723734 0.690079i \(-0.757576\pi\)
0.723734 + 0.690079i \(0.242424\pi\)
\(192\) −1.67489 1.07639i −1.67489 1.07639i
\(193\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0.509266 0.587724i 0.509266 0.587724i
\(197\) 0 0 −0.995472 0.0950560i \(-0.969697\pi\)
0.995472 + 0.0950560i \(0.0303030\pi\)
\(198\) 0 0
\(199\) 0 0 0.0475819 0.998867i \(-0.484848\pi\)
−0.0475819 + 0.998867i \(0.515152\pi\)
\(200\) 1.00000 1.00000
\(201\) 1.56499 1.23072i 1.56499 1.23072i
\(202\) 1.68251 1.68251
\(203\) 0.0324750 0.681734i 0.0324750 0.681734i
\(204\) 0 0
\(205\) 1.56499 + 0.149438i 1.56499 + 0.149438i
\(206\) −0.0623191 + 0.0719200i −0.0623191 + 0.0719200i
\(207\) 0.969383 2.80085i 0.969383 2.80085i
\(208\) 0 0
\(209\) 0 0
\(210\) −0.789740 0.507535i −0.789740 0.507535i
\(211\) 0 0 −0.723734 0.690079i \(-0.757576\pi\)
0.723734 + 0.690079i \(0.242424\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0.223734 0.175946i 0.223734 0.175946i
\(215\) 0.481929 + 1.05528i 0.481929 + 1.05528i
\(216\) −3.28924 + 2.11387i −3.28924 + 2.11387i
\(217\) 0 0
\(218\) −0.0947329 + 0.00904590i −0.0947329 + 0.00904590i
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 1.25667 0.368991i 1.25667 0.368991i 0.415415 0.909632i \(-0.363636\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(224\) 0.111165 + 0.458227i 0.111165 + 0.458227i
\(225\) 1.23123 2.69602i 1.23123 2.69602i
\(226\) 0 0
\(227\) 0.975950 + 1.37053i 0.975950 + 1.37053i 0.928368 + 0.371662i \(0.121212\pi\)
0.0475819 + 0.998867i \(0.484848\pi\)
\(228\) 0 0
\(229\) −0.607279 + 0.243118i −0.607279 + 0.243118i −0.654861 0.755750i \(-0.727273\pi\)
0.0475819 + 0.998867i \(0.484848\pi\)
\(230\) 0.500000 0.866025i 0.500000 0.866025i
\(231\) 0 0
\(232\) −1.13779 0.894765i −1.13779 0.894765i
\(233\) 0 0 0.235759 0.971812i \(-0.424242\pi\)
−0.235759 + 0.971812i \(0.575758\pi\)
\(234\) 0 0
\(235\) 0.0883470 + 1.85463i 0.0883470 + 1.85463i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(240\) −1.84833 + 0.739959i −1.84833 + 0.739959i
\(241\) −0.0623191 0.0719200i −0.0623191 0.0719200i 0.723734 0.690079i \(-0.242424\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(242\) 0.580057 + 0.814576i 0.580057 + 0.814576i
\(243\) 0.809430 + 5.62971i 0.809430 + 5.62971i
\(244\) −0.544078 + 1.19136i −0.544078 + 1.19136i
\(245\) −0.183343 0.755750i −0.183343 0.755750i
\(246\) −3.00319 + 0.881816i −3.00319 + 0.881816i
\(247\) 0 0
\(248\) 0 0
\(249\) −3.14580 1.62177i −3.14580 1.62177i
\(250\) 0.580057 0.814576i 0.580057 0.814576i
\(251\) 0 0 0.995472 0.0950560i \(-0.0303030\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(252\) 1.37226 + 0.264481i 1.37226 + 0.264481i
\(253\) 0 0
\(254\) −0.271738 0.595023i −0.271738 0.595023i
\(255\) 0 0
\(256\) 0.928368 + 0.371662i 0.928368 + 0.371662i
\(257\) 0 0 −0.327068 0.945001i \(-0.606061\pi\)
0.327068 + 0.945001i \(0.393939\pi\)
\(258\) −1.67162 1.59389i −1.67162 1.59389i
\(259\) 0 0
\(260\) 0 0
\(261\) −3.81318 + 1.96583i −3.81318 + 1.96583i
\(262\) 0 0
\(263\) −1.28605 + 1.48418i −1.28605 + 1.48418i −0.500000 + 0.866025i \(0.666667\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) −3.34978 −3.34978
\(268\) −0.654861 + 0.755750i −0.654861 + 0.755750i
\(269\) 0.830830 0.830830 0.415415 0.909632i \(-0.363636\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(270\) −0.186042 + 3.90550i −0.186042 + 3.90550i
\(271\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) −0.283341 + 1.97068i −0.283341 + 1.97068i
\(277\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0.437742 + 0.175245i 0.437742 + 0.175245i
\(281\) −1.45949 + 1.14776i −1.45949 + 1.14776i −0.500000 + 0.866025i \(0.666667\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(282\) −1.53565 3.36260i −1.53565 3.36260i
\(283\) 1.65210 1.06174i 1.65210 1.06174i 0.723734 0.690079i \(-0.242424\pi\)
0.928368 0.371662i \(-0.121212\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0.658873 + 0.339672i 0.658873 + 0.339672i
\(288\) 2.14504 2.04530i 2.14504 2.04530i
\(289\) 0.981929 0.189251i 0.981929 0.189251i
\(290\) −1.38884 + 0.407799i −1.38884 + 0.407799i
\(291\) 0 0
\(292\) 0 0
\(293\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(294\) 0.898102 + 1.26121i 0.898102 + 1.26121i
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) 0.786053 + 1.36148i 0.786053 + 1.36148i
\(299\) 0 0
\(300\) −0.469383 + 1.93482i −0.469383 + 1.93482i
\(301\) 0.0260280 + 0.546395i 0.0260280 + 0.546395i
\(302\) 0 0
\(303\) −0.789740 + 3.25535i −0.789740 + 3.25535i
\(304\) 0 0
\(305\) 0.654861 + 1.13425i 0.654861 + 1.13425i
\(306\) 0 0
\(307\) −0.264241 + 0.105786i −0.264241 + 0.105786i −0.500000 0.866025i \(-0.666667\pi\)
0.235759 + 0.971812i \(0.424242\pi\)
\(308\) 0 0
\(309\) −0.109901 0.154334i −0.109901 0.154334i
\(310\) 0 0
\(311\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(312\) 0 0
\(313\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(314\) 0 0
\(315\) 1.01143 0.964394i 1.01143 0.964394i
\(316\) 0 0
\(317\) 0 0 0.580057 0.814576i \(-0.303030\pi\)
−0.580057 + 0.814576i \(0.696970\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0.841254 0.540641i 0.841254 0.540641i
\(321\) 0.235408 + 0.515472i 0.235408 + 0.515472i
\(322\) 0.370638 0.291473i 0.370638 0.291473i
\(323\) 0 0
\(324\) −1.57666 4.55546i −1.57666 4.55546i
\(325\) 0 0
\(326\) 0.698939 + 0.449181i 0.698939 + 0.449181i
\(327\) 0.0269638 0.187537i 0.0269638 0.187537i
\(328\) 1.39734 0.720381i 1.39734 0.720381i
\(329\) −0.286343 + 0.827333i −0.286343 + 0.827333i
\(330\) 0 0
\(331\) 0 0 −0.995472 0.0950560i \(-0.969697\pi\)
0.995472 + 0.0950560i \(0.0303030\pi\)
\(332\) 1.70566 + 0.500828i 1.70566 + 0.500828i
\(333\) 0 0
\(334\) −1.91899 −1.91899
\(335\) 0.235759 + 0.971812i 0.235759 + 0.971812i
\(336\) −0.938766 −0.938766
\(337\) 0 0 0.0475819 0.998867i \(-0.484848\pi\)
−0.0475819 + 0.998867i \(0.515152\pi\)
\(338\) −0.959493 0.281733i −0.959493 0.281733i
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 0.119289 0.829672i 0.119289 0.829672i
\(344\) 0.975950 + 0.627205i 0.975950 + 0.627205i
\(345\) 1.44091 + 1.37391i 1.44091 + 1.37391i
\(346\) 0 0
\(347\) −1.21590 0.486774i −1.21590 0.486774i −0.327068 0.945001i \(-0.606061\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(348\) 2.26527 1.78143i 2.26527 1.78143i
\(349\) 0.481929 + 1.05528i 0.481929 + 1.05528i 0.981929 + 0.189251i \(0.0606061\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(350\) 0.396666 0.254922i 0.396666 0.254922i
\(351\) 0 0
\(352\) 0 0
\(353\) 0 0 0.580057 0.814576i \(-0.303030\pi\)
−0.580057 + 0.814576i \(0.696970\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 1.65210 0.318417i 1.65210 0.318417i
\(357\) 0 0
\(358\) 0 0
\(359\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(360\) −0.421801 2.93369i −0.421801 2.93369i
\(361\) 0.580057 + 0.814576i 0.580057 + 0.814576i
\(362\) −0.544078 0.627899i −0.544078 0.627899i
\(363\) −1.84833 + 0.739959i −1.84833 + 0.739959i
\(364\) 0 0
\(365\) 0 0
\(366\) −2.04970 1.61190i −2.04970 1.61190i
\(367\) 0.0224357 0.0924813i 0.0224357 0.0924813i −0.959493 0.281733i \(-0.909091\pi\)
0.981929 + 0.189251i \(0.0606061\pi\)
\(368\) −0.0475819 0.998867i −0.0475819 0.998867i
\(369\) −0.221708 4.65422i −0.221708 4.65422i
\(370\) 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
\(375\) 1.30379 + 1.50465i 1.30379 + 1.50465i
\(376\) 1.07701 + 1.51245i 1.07701 + 1.51245i
\(377\) 0 0
\(378\) −0.765860 + 1.67700i −0.765860 + 1.67700i
\(379\) 0 0 −0.235759 0.971812i \(-0.575758\pi\)
0.235759 + 0.971812i \(0.424242\pi\)
\(380\) 0 0
\(381\) 1.27881 0.246471i 1.27881 0.246471i
\(382\) 0 0
\(383\) −1.65033 0.850806i −1.65033 0.850806i −0.995472 0.0950560i \(-0.969697\pi\)
−0.654861 0.755750i \(-0.727273\pi\)
\(384\) −1.15486 + 1.62177i −1.15486 + 1.62177i
\(385\) 0 0
\(386\) 0 0
\(387\) 2.89258 1.85895i 2.89258 1.85895i
\(388\) 0 0
\(389\) −0.0748038 + 0.0588264i −0.0748038 + 0.0588264i −0.654861 0.755750i \(-0.727273\pi\)
0.580057 + 0.814576i \(0.303030\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) −0.562827 0.536654i −0.562827 0.536654i
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0.0475819 0.998867i 0.0475819 0.998867i
\(401\) 0.471518 0.471518 0.235759 0.971812i \(-0.424242\pi\)
0.235759 + 0.971812i \(0.424242\pi\)
\(402\) −1.15486 1.62177i −1.15486 1.62177i
\(403\) 0 0
\(404\) 0.0800569 1.68060i 0.0800569 1.68060i
\(405\) −4.62533 1.35812i −4.62533 1.35812i
\(406\) −0.679417 0.0648764i −0.679417 0.0648764i
\(407\) 0 0
\(408\) 0 0
\(409\) −0.738471 + 0.380708i −0.738471 + 0.380708i −0.786053 0.618159i \(-0.787879\pi\)
0.0475819 + 0.998867i \(0.484848\pi\)
\(410\) 0.223734 1.55610i 0.223734 1.55610i
\(411\) 0 0
\(412\) 0.0688733 + 0.0656706i 0.0688733 + 0.0656706i
\(413\) 0 0
\(414\) −2.75155 1.10155i −2.75155 1.10155i
\(415\) 1.39734 1.09888i 1.39734 1.09888i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 0 0 0.995472 0.0950560i \(-0.0303030\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(420\) −0.544537 + 0.764696i −0.544537 + 0.764696i
\(421\) 1.70566 + 0.879330i 1.70566 + 0.879330i 0.981929 + 0.189251i \(0.0606061\pi\)
0.723734 + 0.690079i \(0.242424\pi\)
\(422\) 0 0
\(423\) 5.40365 1.04147i 5.40365 1.04147i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 0.0878875 + 0.611271i 0.0878875 + 0.611271i
\(428\) −0.165101 0.231852i −0.165101 0.231852i
\(429\) 0 0
\(430\) 1.07701 0.431171i 1.07701 0.431171i
\(431\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(432\) 1.95496 + 3.38610i 1.95496 + 3.38610i
\(433\) 0 0 −0.786053 0.618159i \(-0.787879\pi\)
0.786053 + 0.618159i \(0.212121\pi\)
\(434\) 0 0
\(435\) −0.137123 2.87856i −0.137123 2.87856i
\(436\) 0.00452808 + 0.0950560i 0.00452808 + 0.0950560i
\(437\) 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
\(441\) −2.13980 + 0.856647i −2.13980 + 0.856647i
\(442\) 0 0
\(443\) 0.839614 + 1.17907i 0.839614 + 1.17907i 0.981929 + 0.189251i \(0.0606061\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(444\) 0 0
\(445\) 0.698939 1.53046i 0.698939 1.53046i
\(446\) −0.308779 1.27280i −0.308779 1.27280i
\(447\) −3.00319 + 0.881816i −3.00319 + 0.881816i
\(448\) 0.462997 0.0892353i 0.462997 0.0892353i
\(449\) 1.34378 1.28129i 1.34378 1.28129i 0.415415 0.909632i \(-0.363636\pi\)
0.928368 0.371662i \(-0.121212\pi\)
\(450\) −2.63438 1.35812i −2.63438 1.35812i
\(451\) 0 0
\(452\) 0 0
\(453\) 0 0
\(454\) 1.41542 0.909632i 1.41542 0.909632i
\(455\) 0 0
\(456\) 0 0
\(457\) 0 0 −0.928368 0.371662i \(-0.878788\pi\)
0.928368 + 0.371662i \(0.121212\pi\)
\(458\) 0.213947 + 0.618159i 0.213947 + 0.618159i
\(459\) 0 0
\(460\) −0.841254 0.540641i −0.841254 0.540641i
\(461\) 0.252989 1.75958i 0.252989 1.75958i −0.327068 0.945001i \(-0.606061\pi\)
0.580057 0.814576i \(-0.303030\pi\)
\(462\) 0 0
\(463\) −0.271738 + 0.785135i −0.271738 + 0.785135i 0.723734 + 0.690079i \(0.242424\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(464\) −0.947890 + 1.09392i −0.947890 + 1.09392i
\(465\) 0 0
\(466\) 0 0
\(467\) −0.0311250 + 0.653395i −0.0311250 + 0.653395i 0.928368 + 0.371662i \(0.121212\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(468\) 0 0
\(469\) −0.0671040 + 0.466718i −0.0671040 + 0.466718i
\(470\) 1.85674 1.85674
\(471\) 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 −0.723734 0.690079i \(-0.757576\pi\)
0.723734 + 0.690079i \(0.242424\pi\)
\(480\) 0.651174 + 1.88144i 0.651174 + 1.88144i
\(481\) 0 0
\(482\) −0.0748038 + 0.0588264i −0.0748038 + 0.0588264i
\(483\) 0.389977 + 0.853931i 0.389977 + 0.853931i
\(484\) 0.841254 0.540641i 0.841254 0.540641i
\(485\) 0 0
\(486\) 5.66185 0.540641i 5.66185 0.540641i
\(487\) −1.03115 + 1.44805i −1.03115 + 1.44805i −0.142315 + 0.989821i \(0.545455\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(488\) 1.16413 + 0.600149i 1.16413 + 0.600149i
\(489\) −1.19715 + 1.14148i −1.19715 + 1.14148i
\(490\) −0.763617 + 0.147175i −0.763617 + 0.147175i
\(491\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(492\) 0.737920 + 3.04175i 0.737920 + 3.04175i
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) −1.76962 + 3.06507i −1.76962 + 3.06507i
\(499\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(500\) −0.786053 0.618159i −0.786053 0.618159i
\(501\) 0.900739 3.71290i 0.900739 3.71290i
\(502\) 0 0
\(503\) −0.0748038 1.57033i −0.0748038 1.57033i −0.654861 0.755750i \(-0.727273\pi\)
0.580057 0.814576i \(-0.303030\pi\)
\(504\) 0.329476 1.35812i 0.329476 1.35812i
\(505\) −1.32254 1.04006i −1.32254 1.04006i
\(506\) 0 0
\(507\) 0.995472 1.72421i 0.995472 1.72421i
\(508\) −0.607279 + 0.243118i −0.607279 + 0.243118i
\(509\) 1.25667 + 1.45027i 1.25667 + 1.45027i 0.841254 + 0.540641i \(0.181818\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0.415415 0.909632i 0.415415 0.909632i
\(513\) 0 0
\(514\) 0 0
\(515\) 0.0934441 0.0180099i 0.0934441 0.0180099i
\(516\) −1.67162 + 1.59389i −1.67162 + 1.59389i
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −0.841254 + 0.540641i −0.841254 + 0.540641i −0.888835 0.458227i \(-0.848485\pi\)
0.0475819 + 0.998867i \(0.484848\pi\)
\(522\) 1.78217 + 3.90240i 1.78217 + 3.90240i
\(523\) −0.911911 + 0.717135i −0.911911 + 0.717135i −0.959493 0.281733i \(-0.909091\pi\)
0.0475819 + 0.998867i \(0.484848\pi\)
\(524\) 0 0
\(525\) 0.307040 + 0.887134i 0.307040 + 0.887134i
\(526\) 1.42131 + 1.35522i 1.42131 + 1.35522i
\(527\) 0 0
\(528\) 0 0
\(529\) 0 0
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) −0.159389 + 3.34598i −0.159389 + 3.34598i
\(535\) −0.284630 −0.284630
\(536\) 0.723734 + 0.690079i 0.723734 + 0.690079i
\(537\) 0 0
\(538\) 0.0395325 0.829889i 0.0395325 0.829889i
\(539\) 0 0
\(540\) 3.89223 + 0.371662i 3.89223 + 0.371662i
\(541\) −0.759713 + 0.876756i −0.759713 + 0.876756i −0.995472 0.0950560i \(-0.969697\pi\)
0.235759 + 0.971812i \(0.424242\pi\)
\(542\) 0 0
\(543\) 1.47025 0.757969i 1.47025 0.757969i
\(544\) 0 0
\(545\) 0.0800569 + 0.0514495i 0.0800569 + 0.0514495i
\(546\) 0 0
\(547\) 0.213947 + 0.618159i 0.213947 + 0.618159i 1.00000 \(0\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(548\) 0 0
\(549\) 3.05132 2.39959i 3.05132 2.39959i
\(550\) 0 0
\(551\) 0 0
\(552\) 1.95496 + 0.376789i 1.95496 + 0.376789i
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 0 0 0.981929 0.189251i \(-0.0606061\pi\)
−0.981929 + 0.189251i \(0.939394\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0.195876 0.428908i 0.195876 0.428908i
\(561\) 0 0
\(562\) 1.07701 + 1.51245i 1.07701 + 1.51245i
\(563\) −0.759713 0.876756i −0.759713 0.876756i 0.235759 0.971812i \(-0.424242\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(564\) −3.43186 + 1.37391i −3.43186 + 1.37391i
\(565\) 0 0
\(566\) −0.981929 1.70075i −0.981929 1.70075i
\(567\) −1.78670 1.40507i −1.78670 1.40507i
\(568\) 0 0
\(569\) −0.0913090 1.91681i −0.0913090 1.91681i −0.327068 0.945001i \(-0.606061\pi\)
0.235759 0.971812i \(-0.424242\pi\)
\(570\) 0 0
\(571\) 0 0 0.235759 0.971812i \(-0.424242\pi\)
−0.235759 + 0.971812i \(0.575758\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0.370638 0.641964i 0.370638 0.641964i
\(575\) −0.928368 + 0.371662i −0.928368 + 0.371662i
\(576\) −1.94091 2.23993i −1.94091 2.23993i
\(577\) 0 0 −0.580057 0.814576i \(-0.696970\pi\)
0.580057 + 0.814576i \(0.303030\pi\)
\(578\) −0.142315 0.989821i −0.142315 0.989821i
\(579\) 0 0
\(580\) 0.341254 + 1.40667i 0.341254 + 1.40667i
\(581\) 0.804250 0.236149i 0.804250 0.236149i
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −0.279486 0.0538665i −0.279486 0.0538665i 0.0475819 0.998867i \(-0.484848\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(588\) 1.30251 0.837074i 1.30251 0.837074i
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 0 0 −0.723734 0.690079i \(-0.757576\pi\)
0.723734 + 0.690079i \(0.242424\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 1.39734 0.720381i 1.39734 0.720381i
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 −0.995472 0.0950560i \(-0.969697\pi\)
0.995472 + 0.0950560i \(0.0303030\pi\)
\(600\) 1.91030 + 0.560914i 1.91030 + 0.560914i
\(601\) 0.0552004 1.15880i 0.0552004 1.15880i −0.786053 0.618159i \(-0.787879\pi\)
0.841254 0.540641i \(-0.181818\pi\)
\(602\) 0.547014 0.547014
\(603\) 2.75155 1.10155i 2.75155 1.10155i
\(604\) 0 0
\(605\) 0.0475819 0.998867i 0.0475819 0.998867i
\(606\) 3.21409 + 0.943741i 3.21409 + 0.943741i
\(607\) −1.84833 0.176494i −1.84833 0.176494i −0.888835 0.458227i \(-0.848485\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(608\) 0 0
\(609\) 0.444431 1.28410i 0.444431 1.28410i
\(610\) 1.16413 0.600149i 1.16413 0.600149i
\(611\) 0 0
\(612\) 0 0
\(613\) 0 0 −0.723734 0.690079i \(-0.757576\pi\)
0.723734 + 0.690079i \(0.242424\pi\)
\(614\) 0.0930932 + 0.268975i 0.0930932 + 0.268975i
\(615\) 2.90577 + 1.16329i 2.90577 + 1.16329i
\(616\) 0 0
\(617\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(618\) −0.159389 + 0.102433i −0.159389 + 0.102433i
\(619\) 0 0 −0.981929 0.189251i \(-0.939394\pi\)
0.981929 + 0.189251i \(0.0606061\pi\)
\(620\) 0 0
\(621\) 2.26798 3.18493i 2.26798 3.18493i
\(622\) 0 0
\(623\) 0.574161 0.547462i 0.574161 0.547462i
\(624\) 0 0
\(625\) −0.959493 + 0.281733i −0.959493 + 0.281733i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) −0.915176 1.05617i −0.915176 1.05617i
\(631\) 0 0 0.928368 0.371662i \(-0.121212\pi\)
−0.928368 + 0.371662i \(0.878788\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −0.154218 + 0.635697i −0.154218 + 0.635697i
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) −0.500000 0.866025i −0.500000 0.866025i
\(641\) −0.981929 + 1.70075i −0.981929 + 1.70075i −0.327068 + 0.945001i \(0.606061\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(642\) 0.526089 0.210614i 0.526089 0.210614i
\(643\) −0.947890 1.09392i −0.947890 1.09392i −0.995472 0.0950560i \(-0.969697\pi\)
0.0475819 0.998867i \(-0.484848\pi\)
\(644\) −0.273507 0.384087i −0.273507 0.384087i
\(645\) 0.328708 + 2.28621i 0.328708 + 2.28621i
\(646\) 0 0
\(647\) 0.437742 + 1.80440i 0.437742 + 1.80440i 0.580057 + 0.814576i \(0.303030\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(648\) −4.62533 + 1.35812i −4.62533 + 1.35812i
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) 0.481929 0.676774i 0.481929 0.676774i
\(653\) 0 0 0.995472 0.0950560i \(-0.0303030\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(654\) −0.186042 0.0358566i −0.186042 0.0358566i
\(655\) 0 0
\(656\) −0.653077 1.43004i −0.653077 1.43004i
\(657\) 0 0
\(658\) 0.812771 + 0.325385i 0.812771 + 0.325385i
\(659\) 0 0 −0.327068 0.945001i \(-0.606061\pi\)
0.327068 + 0.945001i \(0.393939\pi\)
\(660\) 0 0
\(661\) −1.61435 1.03748i −1.61435 1.03748i −0.959493 0.281733i \(-0.909091\pi\)
−0.654861 0.755750i \(-0.727273\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0.581419 1.67990i 0.581419 1.67990i
\(665\) 0 0
\(666\) 0 0
\(667\) 1.38884 + 0.407799i 1.38884 + 0.407799i
\(668\) −0.0913090 + 1.91681i −0.0913090 + 1.91681i
\(669\) 2.60758 2.60758
\(670\) 0.981929 0.189251i 0.981929 0.189251i
\(671\) 0 0
\(672\) −0.0446683 + 0.937702i −0.0446683 + 0.937702i
\(673\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(674\) 0 0
\(675\) 2.56046 2.95493i 2.56046 2.95493i
\(676\) −0.327068 + 0.945001i −0.327068 + 0.945001i
\(677\) 0 0 0.888835 0.458227i \(-0.151515\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 1.09560 + 3.16554i 1.09560 + 3.16554i
\(682\) 0 0
\(683\) 0.223734 0.175946i 0.223734 0.175946i −0.500000 0.866025i \(-0.666667\pi\)
0.723734 + 0.690079i \(0.242424\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) −0.823056 0.158631i −0.823056 0.158631i
\(687\) −1.29645 + 0.123796i −1.29645 + 0.123796i
\(688\) 0.672932 0.945001i 0.672932 0.945001i
\(689\) 0 0
\(690\) 1.44091 1.37391i 1.44091 1.37391i
\(691\) 0 0 0.981929 0.189251i \(-0.0606061\pi\)
−0.981929 + 0.189251i \(0.939394\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) −0.544078 + 1.19136i −0.544078 + 1.19136i
\(695\) 0 0
\(696\) −1.67162 2.34747i −1.67162 2.34747i
\(697\) 0 0
\(698\) 1.07701 0.431171i 1.07701 0.431171i
\(699\) 0 0
\(700\) −0.235759 0.408346i −0.235759 0.408346i
\(701\) 0.786053 + 0.618159i 0.786053 + 0.618159i 0.928368 0.371662i \(-0.121212\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0 0
\(705\) −0.871520 + 3.59245i −0.871520 + 3.59245i
\(706\) 0 0
\(707\) −0.396666 0.687046i −0.396666 0.687046i
\(708\) 0 0
\(709\) −0.928368 + 0.371662i −0.928368 + 0.371662i −0.786053 0.618159i \(-0.787879\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) −0.239446 1.66538i −0.239446 1.66538i
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 0.580057 0.814576i \(-0.303030\pi\)
−0.580057 + 0.814576i \(0.696970\pi\)
\(720\) −2.95044 + 0.281733i −2.95044 + 0.281733i
\(721\) 0.0440606 + 0.00849198i 0.0440606 + 0.00849198i
\(722\) 0.841254 0.540641i 0.841254 0.540641i
\(723\) −0.0787070 0.172344i −0.0787070 0.172344i
\(724\) −0.653077 + 0.513585i −0.653077 + 0.513585i
\(725\) 1.34378 + 0.537970i 1.34378 + 0.537970i
\(726\) 0.651174 + 1.88144i 0.651174 + 1.88144i
\(727\) −1.13779 1.08488i −1.13779 1.08488i −0.995472 0.0950560i \(-0.969697\pi\)
−0.142315 0.989821i \(-0.545455\pi\)
\(728\) 0 0
\(729\) −0.925488 + 6.43691i −0.925488 + 6.43691i
\(730\) 0 0
\(731\) 0 0
\(732\) −1.70760 + 1.97068i −1.70760 + 1.97068i
\(733\) 0 0 −0.995472 0.0950560i \(-0.969697\pi\)
0.995472 + 0.0950560i \(0.0303030\pi\)
\(734\) −0.0913090 0.0268107i −0.0913090 0.0268107i
\(735\) 0.0736710 1.54655i 0.0736710 1.54655i
\(736\) −1.00000 −1.00000
\(737\) 0 0
\(738\) −4.65950 −4.65950
\(739\) 0 0 0.0475819 0.998867i \(-0.484848\pi\)
−0.0475819 + 0.998867i \(0.515152\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −0.271738 + 0.785135i −0.271738 + 0.785135i 0.723734 + 0.690079i \(0.242424\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(744\) 0 0
\(745\) 0.223734 1.55610i 0.223734 1.55610i
\(746\) 0 0
\(747\) −3.81318 3.63586i −3.81318 3.63586i
\(748\) 0 0
\(749\) −0.124594 0.0498801i −0.124594 0.0498801i
\(750\) 1.56499 1.23072i 1.56499 1.23072i
\(751\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(752\) 1.56199 1.00383i 1.56199 1.00383i
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 1.63866 + 0.844787i 1.63866 + 0.844787i
\(757\) 0 0 0.723734 0.690079i \(-0.242424\pi\)
−0.723734 + 0.690079i \(0.757576\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 0.345139 0.755750i 0.345139 0.755750i −0.654861 0.755750i \(-0.727273\pi\)
1.00000 \(0\)
\(762\) −0.185343 1.28909i −0.185343 1.28909i
\(763\) 0.0260280 + 0.0365512i 0.0260280 + 0.0365512i
\(764\) 0 0
\(765\) 0 0
\(766\) −0.928368 + 1.60798i −0.928368 + 1.60798i
\(767\) 0 0
\(768\) 1.56499 + 1.23072i 1.56499 + 1.23072i
\(769\) −0.469383 + 1.93482i −0.469383 + 1.93482i −0.142315 + 0.989821i \(0.545455\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 0 0 −0.786053 0.618159i \(-0.787879\pi\)
0.786053 + 0.618159i \(0.212121\pi\)
\(774\) −1.71921 2.97775i −1.71921 2.97775i
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0.0552004 + 0.0775182i 0.0552004 + 0.0775182i
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) −5.55722 + 1.07107i −5.55722 + 1.07107i
\(784\) −0.562827 + 0.536654i −0.562827 + 0.536654i
\(785\) 0 0
\(786\) 0 0
\(787\) 0.651174 0.0621796i 0.651174 0.0621796i 0.235759 0.971812i \(-0.424242\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(788\) 0 0
\(789\) −3.28924 + 2.11387i −3.28924 + 2.11387i
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0