Properties

Label 1340.1.bl.b.1199.1
Level $1340$
Weight $1$
Character 1340.1199
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 1199.1
Root \(0.235759 - 0.971812i\) of defining polynomial
Character \(\chi\) \(=\) 1340.1199
Dual form 1340.1.bl.b.19.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.888835 + 0.458227i) q^{2} +(-1.11312 - 0.326842i) q^{3} +(0.580057 - 0.814576i) q^{4} +(-0.654861 + 0.755750i) q^{5} +(1.13915 - 0.219553i) q^{6} +(0.0688733 - 1.44583i) q^{7} +(-0.142315 + 0.989821i) q^{8} +(0.290959 + 0.186988i) q^{9} +O(q^{10})\) \(q+(-0.888835 + 0.458227i) q^{2} +(-1.11312 - 0.326842i) q^{3} +(0.580057 - 0.814576i) q^{4} +(-0.654861 + 0.755750i) q^{5} +(1.13915 - 0.219553i) q^{6} +(0.0688733 - 1.44583i) q^{7} +(-0.142315 + 0.989821i) q^{8} +(0.290959 + 0.186988i) q^{9} +(0.235759 - 0.971812i) q^{10} +(-0.911911 + 0.717135i) q^{12} +(0.601300 + 1.31666i) q^{14} +(0.975950 - 0.627205i) q^{15} +(-0.327068 - 0.945001i) q^{16} +(-0.344298 - 0.0328765i) q^{18} +(0.235759 + 0.971812i) q^{20} +(-0.549222 + 1.58687i) q^{21} +(-0.723734 + 0.690079i) q^{23} +(0.481929 - 1.05528i) q^{24} +(-0.142315 - 0.989821i) q^{25} +(0.496956 + 0.573517i) q^{27} +(-1.13779 - 0.894765i) q^{28} +(-0.235759 - 0.408346i) q^{29} +(-0.580057 + 1.00469i) q^{30} +(0.723734 + 0.690079i) q^{32} +(1.04758 + 0.998867i) q^{35} +(0.321089 - 0.128545i) q^{36} +(-0.654861 - 0.755750i) q^{40} +(-1.84833 + 0.176494i) q^{41} +(-0.238979 - 1.66214i) q^{42} +(-0.827068 + 1.81103i) q^{43} +(-0.331854 + 0.0974412i) q^{45} +(0.327068 - 0.945001i) q^{46} +(-0.370638 - 1.52779i) q^{47} +(0.0552004 + 1.15880i) q^{48} +(-1.09020 - 0.104102i) q^{49} +(0.580057 + 0.814576i) q^{50} +(-0.704513 - 0.282044i) q^{54} +(1.42131 + 0.273935i) q^{56} +(0.396666 + 0.254922i) q^{58} +(0.0552004 - 1.15880i) q^{60} +(-1.28605 + 0.247866i) q^{61} +(0.290392 - 0.407799i) q^{63} +(-0.959493 - 0.281733i) q^{64} +(-0.995472 - 0.0950560i) q^{67} +(1.03115 - 0.531595i) q^{69} +(-1.38884 - 0.407799i) q^{70} +(-0.226493 + 0.261387i) q^{72} +(-0.165101 + 1.14831i) q^{75} +(0.928368 + 0.371662i) q^{80} +(-0.509399 - 1.11543i) q^{81} +(1.56199 - 1.00383i) q^{82} +(-0.0311250 - 0.0899299i) q^{83} +(0.974048 + 1.36786i) q^{84} +(-0.0947329 - 1.98869i) q^{86} +(0.128964 + 0.531595i) q^{87} +(-1.61435 + 0.474017i) q^{89} +(0.250314 - 0.238674i) q^{90} +(0.142315 + 0.989821i) q^{92} +(1.02951 + 1.18812i) q^{94} +(-0.580057 - 1.00469i) q^{96} +(1.01671 - 0.407031i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20q + q^{2} + 2q^{3} + q^{4} - 2q^{5} - q^{6} - q^{7} - 2q^{8} + O(q^{10}) \) \( 20q + q^{2} + 2q^{3} + q^{4} - 2q^{5} - q^{6} - q^{7} - 2q^{8} + q^{10} - q^{12} + 2q^{14} + 2q^{15} + q^{16} + q^{20} - 10q^{21} - q^{23} - 9q^{24} - 2q^{25} - 2q^{27} - q^{28} - q^{29} - q^{30} + q^{32} + 21q^{35} - 2q^{40} - q^{41} + 20q^{42} - 9q^{43} - q^{46} - q^{47} - q^{48} + q^{50} + q^{54} - q^{56} + 2q^{58} - q^{60} - 9q^{61} - 11q^{63} - 2q^{64} + q^{67} + q^{69} - 9q^{70} - 11q^{72} + 2q^{75} + q^{80} + 2q^{81} + 2q^{82} - q^{83} + q^{84} - q^{86} + q^{87} - 4q^{89} + 2q^{92} + 2q^{94} - q^{96} + O(q^{100}) \)

Character values

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

\(n\) \(537\) \(671\) \(1141\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{28}{33}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.888835 + 0.458227i −0.888835 + 0.458227i
\(3\) −1.11312 0.326842i −1.11312 0.326842i −0.327068 0.945001i \(-0.606061\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(4\) 0.580057 0.814576i 0.580057 0.814576i
\(5\) −0.654861 + 0.755750i −0.654861 + 0.755750i
\(6\) 1.13915 0.219553i 1.13915 0.219553i
\(7\) 0.0688733 1.44583i 0.0688733 1.44583i −0.654861 0.755750i \(-0.727273\pi\)
0.723734 0.690079i \(-0.242424\pi\)
\(8\) −0.142315 + 0.989821i −0.142315 + 0.989821i
\(9\) 0.290959 + 0.186988i 0.290959 + 0.186988i
\(10\) 0.235759 0.971812i 0.235759 0.971812i
\(11\) 0 0 −0.981929 0.189251i \(-0.939394\pi\)
0.981929 + 0.189251i \(0.0606061\pi\)
\(12\) −0.911911 + 0.717135i −0.911911 + 0.717135i
\(13\) 0 0 −0.928368 0.371662i \(-0.878788\pi\)
0.928368 + 0.371662i \(0.121212\pi\)
\(14\) 0.601300 + 1.31666i 0.601300 + 1.31666i
\(15\) 0.975950 0.627205i 0.975950 0.627205i
\(16\) −0.327068 0.945001i −0.327068 0.945001i
\(17\) 0 0 −0.580057 0.814576i \(-0.696970\pi\)
0.580057 + 0.814576i \(0.303030\pi\)
\(18\) −0.344298 0.0328765i −0.344298 0.0328765i
\(19\) 0 0 −0.0475819 0.998867i \(-0.515152\pi\)
0.0475819 + 0.998867i \(0.484848\pi\)
\(20\) 0.235759 + 0.971812i 0.235759 + 0.971812i
\(21\) −0.549222 + 1.58687i −0.549222 + 1.58687i
\(22\) 0 0
\(23\) −0.723734 + 0.690079i −0.723734 + 0.690079i −0.959493 0.281733i \(-0.909091\pi\)
0.235759 + 0.971812i \(0.424242\pi\)
\(24\) 0.481929 1.05528i 0.481929 1.05528i
\(25\) −0.142315 0.989821i −0.142315 0.989821i
\(26\) 0 0
\(27\) 0.496956 + 0.573517i 0.496956 + 0.573517i
\(28\) −1.13779 0.894765i −1.13779 0.894765i
\(29\) −0.235759 0.408346i −0.235759 0.408346i 0.723734 0.690079i \(-0.242424\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(30\) −0.580057 + 1.00469i −0.580057 + 1.00469i
\(31\) 0 0 0.928368 0.371662i \(-0.121212\pi\)
−0.928368 + 0.371662i \(0.878788\pi\)
\(32\) 0.723734 + 0.690079i 0.723734 + 0.690079i
\(33\) 0 0
\(34\) 0 0
\(35\) 1.04758 + 0.998867i 1.04758 + 0.998867i
\(36\) 0.321089 0.128545i 0.321089 0.128545i
\(37\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) −0.654861 0.755750i −0.654861 0.755750i
\(41\) −1.84833 + 0.176494i −1.84833 + 0.176494i −0.959493 0.281733i \(-0.909091\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(42\) −0.238979 1.66214i −0.238979 1.66214i
\(43\) −0.827068 + 1.81103i −0.827068 + 1.81103i −0.327068 + 0.945001i \(0.606061\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(44\) 0 0
\(45\) −0.331854 + 0.0974412i −0.331854 + 0.0974412i
\(46\) 0.327068 0.945001i 0.327068 0.945001i
\(47\) −0.370638 1.52779i −0.370638 1.52779i −0.786053 0.618159i \(-0.787879\pi\)
0.415415 0.909632i \(-0.363636\pi\)
\(48\) 0.0552004 + 1.15880i 0.0552004 + 1.15880i
\(49\) −1.09020 0.104102i −1.09020 0.104102i
\(50\) 0.580057 + 0.814576i 0.580057 + 0.814576i
\(51\) 0 0
\(52\) 0 0
\(53\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(54\) −0.704513 0.282044i −0.704513 0.282044i
\(55\) 0 0
\(56\) 1.42131 + 0.273935i 1.42131 + 0.273935i
\(57\) 0 0
\(58\) 0.396666 + 0.254922i 0.396666 + 0.254922i
\(59\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(60\) 0.0552004 1.15880i 0.0552004 1.15880i
\(61\) −1.28605 + 0.247866i −1.28605 + 0.247866i −0.786053 0.618159i \(-0.787879\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(62\) 0 0
\(63\) 0.290392 0.407799i 0.290392 0.407799i
\(64\) −0.959493 0.281733i −0.959493 0.281733i
\(65\) 0 0
\(66\) 0 0
\(67\) −0.995472 0.0950560i −0.995472 0.0950560i
\(68\) 0 0
\(69\) 1.03115 0.531595i 1.03115 0.531595i
\(70\) −1.38884 0.407799i −1.38884 0.407799i
\(71\) 0 0 0.580057 0.814576i \(-0.303030\pi\)
−0.580057 + 0.814576i \(0.696970\pi\)
\(72\) −0.226493 + 0.261387i −0.226493 + 0.261387i
\(73\) 0 0 0.981929 0.189251i \(-0.0606061\pi\)
−0.981929 + 0.189251i \(0.939394\pi\)
\(74\) 0 0
\(75\) −0.165101 + 1.14831i −0.165101 + 1.14831i
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 0.786053 0.618159i \(-0.212121\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(80\) 0.928368 + 0.371662i 0.928368 + 0.371662i
\(81\) −0.509399 1.11543i −0.509399 1.11543i
\(82\) 1.56199 1.00383i 1.56199 1.00383i
\(83\) −0.0311250 0.0899299i −0.0311250 0.0899299i 0.928368 0.371662i \(-0.121212\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(84\) 0.974048 + 1.36786i 0.974048 + 1.36786i
\(85\) 0 0
\(86\) −0.0947329 1.98869i −0.0947329 1.98869i
\(87\) 0.128964 + 0.531595i 0.128964 + 0.531595i
\(88\) 0 0
\(89\) −1.61435 + 0.474017i −1.61435 + 0.474017i −0.959493 0.281733i \(-0.909091\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(90\) 0.250314 0.238674i 0.250314 0.238674i
\(91\) 0 0
\(92\) 0.142315 + 0.989821i 0.142315 + 0.989821i
\(93\) 0 0
\(94\) 1.02951 + 1.18812i 1.02951 + 1.18812i
\(95\) 0 0
\(96\) −0.580057 1.00469i −0.580057 1.00469i
\(97\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(98\) 1.01671 0.407031i 1.01671 0.407031i
\(99\) 0 0
\(100\) −0.888835 0.458227i −0.888835 0.458227i
\(101\) −1.49547 0.770969i −1.49547 0.770969i −0.500000 0.866025i \(-0.666667\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(102\) 0 0
\(103\) −1.65033 + 0.660694i −1.65033 + 0.660694i −0.995472 0.0950560i \(-0.969697\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(104\) 0 0
\(105\) −0.839614 1.45425i −0.839614 1.45425i
\(106\) 0 0
\(107\) 0.186393 + 0.215109i 0.186393 + 0.215109i 0.841254 0.540641i \(-0.181818\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(108\) 0.755436 0.0721354i 0.755436 0.0721354i
\(109\) 0.252989 + 1.75958i 0.252989 + 1.75958i 0.580057 + 0.814576i \(0.303030\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) −1.38884 + 0.407799i −1.38884 + 0.407799i
\(113\) 0 0 0.327068 0.945001i \(-0.393939\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(114\) 0 0
\(115\) −0.0475819 0.998867i −0.0475819 0.998867i
\(116\) −0.469383 0.0448206i −0.469383 0.0448206i
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0.481929 + 1.05528i 0.481929 + 1.05528i
\(121\) 0.928368 + 0.371662i 0.928368 + 0.371662i
\(122\) 1.02951 0.809616i 1.02951 0.809616i
\(123\) 2.11510 + 0.407652i 2.11510 + 0.407652i
\(124\) 0 0
\(125\) 0.841254 + 0.540641i 0.841254 + 0.540641i
\(126\) −0.0712467 + 0.495532i −0.0712467 + 0.495532i
\(127\) 0.0934441 1.96163i 0.0934441 1.96163i −0.142315 0.989821i \(-0.545455\pi\)
0.235759 0.971812i \(-0.424242\pi\)
\(128\) 0.981929 0.189251i 0.981929 0.189251i
\(129\) 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
\(134\) 0.928368 0.371662i 0.928368 0.371662i
\(135\) −0.758872 −0.758872
\(136\) 0 0
\(137\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(138\) −0.672932 + 0.945001i −0.672932 + 0.945001i
\(139\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(140\) 1.42131 0.273935i 1.42131 0.273935i
\(141\) −0.0867810 + 1.82176i −0.0867810 + 1.82176i
\(142\) 0 0
\(143\) 0 0
\(144\) 0.0815405 0.336115i 0.0815405 0.336115i
\(145\) 0.462997 + 0.0892353i 0.462997 + 0.0892353i
\(146\) 0 0
\(147\) 1.17951 + 0.472203i 1.17951 + 0.472203i
\(148\) 0 0
\(149\) 1.56199 1.00383i 1.56199 1.00383i 0.580057 0.814576i \(-0.303030\pi\)
0.981929 0.189251i \(-0.0606061\pi\)
\(150\) −0.379436 1.09631i −0.379436 1.09631i
\(151\) 0 0 −0.580057 0.814576i \(-0.696970\pi\)
0.580057 + 0.814576i \(0.303030\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 0 0 0.723734 0.690079i \(-0.242424\pi\)
−0.723734 + 0.690079i \(0.757576\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) −0.995472 + 0.0950560i −0.995472 + 0.0950560i
\(161\) 0.947890 + 1.09392i 0.947890 + 1.09392i
\(162\) 0.963891 + 0.758013i 0.963891 + 0.758013i
\(163\) −0.415415 0.719520i −0.415415 0.719520i 0.580057 0.814576i \(-0.303030\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(164\) −0.928368 + 1.60798i −0.928368 + 1.60798i
\(165\) 0 0
\(166\) 0.0688733 + 0.0656706i 0.0688733 + 0.0656706i
\(167\) 1.70566 + 0.879330i 1.70566 + 0.879330i 0.981929 + 0.189251i \(0.0606061\pi\)
0.723734 + 0.690079i \(0.242424\pi\)
\(168\) −1.49256 0.769467i −1.49256 0.769467i
\(169\) 0.723734 + 0.690079i 0.723734 + 0.690079i
\(170\) 0 0
\(171\) 0 0
\(172\) 0.995472 + 1.72421i 0.995472 + 1.72421i
\(173\) 0 0 −0.786053 0.618159i \(-0.787879\pi\)
0.786053 + 0.618159i \(0.212121\pi\)
\(174\) −0.358218 0.413406i −0.358218 0.413406i
\(175\) −1.44091 + 0.137591i −1.44091 + 0.137591i
\(176\) 0 0
\(177\) 0 0
\(178\) 1.21769 1.16106i 1.21769 1.16106i
\(179\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(180\) −0.113121 + 0.326842i −0.113121 + 0.326842i
\(181\) 0.195876 + 0.807410i 0.195876 + 0.807410i 0.981929 + 0.189251i \(0.0606061\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(182\) 0 0
\(183\) 1.51255 + 0.144431i 1.51255 + 0.144431i
\(184\) −0.580057 0.814576i −0.580057 0.814576i
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) −1.45949 0.584293i −1.45949 0.584293i
\(189\) 0.863435 0.679013i 0.863435 0.679013i
\(190\) 0 0
\(191\) 0 0 0.235759 0.971812i \(-0.424242\pi\)
−0.235759 + 0.971812i \(0.575758\pi\)
\(192\) 0.975950 + 0.627205i 0.975950 + 0.627205i
\(193\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) −0.717180 + 0.827670i −0.717180 + 0.827670i
\(197\) 0 0 0.580057 0.814576i \(-0.303030\pi\)
−0.580057 + 0.814576i \(0.696970\pi\)
\(198\) 0 0
\(199\) 0 0 0.888835 0.458227i \(-0.151515\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(200\) 1.00000 1.00000
\(201\) 1.07701 + 0.431171i 1.07701 + 0.431171i
\(202\) 1.68251 1.68251
\(203\) −0.606636 + 0.312743i −0.606636 + 0.312743i
\(204\) 0 0
\(205\) 1.07701 1.51245i 1.07701 1.51245i
\(206\) 1.16413 1.34347i 1.16413 1.34347i
\(207\) −0.339614 + 0.0654552i −0.339614 + 0.0654552i
\(208\) 0 0
\(209\) 0 0
\(210\) 1.41266 + 0.907859i 1.41266 + 0.907859i
\(211\) 0 0 0.235759 0.971812i \(-0.424242\pi\)
−0.235759 + 0.971812i \(0.575758\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) −0.264241 0.105786i −0.264241 0.105786i
\(215\) −0.827068 1.81103i −0.827068 1.81103i
\(216\) −0.638404 + 0.410277i −0.638404 + 0.410277i
\(217\) 0 0
\(218\) −1.03115 1.44805i −1.03115 1.44805i
\(219\) 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 \(0.181818\pi\)
\(224\) 1.04758 0.998867i 1.04758 0.998867i
\(225\) 0.143677 0.314609i 0.143677 0.314609i
\(226\) 0 0
\(227\) −1.67489 + 0.159932i −1.67489 + 0.159932i −0.888835 0.458227i \(-0.848485\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(228\) 0 0
\(229\) −1.54370 1.21398i −1.54370 1.21398i −0.888835 0.458227i \(-0.848485\pi\)
−0.654861 0.755750i \(-0.727273\pi\)
\(230\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(231\) 0 0
\(232\) 0.437742 0.175245i 0.437742 0.175245i
\(233\) 0 0 −0.723734 0.690079i \(-0.757576\pi\)
0.723734 + 0.690079i \(0.242424\pi\)
\(234\) 0 0
\(235\) 1.39734 + 0.720381i 1.39734 + 0.720381i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(240\) −0.911911 0.717135i −0.911911 0.717135i
\(241\) 1.16413 + 1.34347i 1.16413 + 1.34347i 0.928368 + 0.371662i \(0.121212\pi\)
0.235759 + 0.971812i \(0.424242\pi\)
\(242\) −0.995472 + 0.0950560i −0.995472 + 0.0950560i
\(243\) 0.0944555 + 0.656953i 0.0944555 + 0.656953i
\(244\) −0.544078 + 1.19136i −0.544078 + 1.19136i
\(245\) 0.792607 0.755750i 0.792607 0.755750i
\(246\) −2.06677 + 0.606859i −2.06677 + 0.606859i
\(247\) 0 0
\(248\) 0 0
\(249\) 0.00525309 + 0.110276i 0.00525309 + 0.110276i
\(250\) −0.995472 0.0950560i −0.995472 0.0950560i
\(251\) 0 0 −0.580057 0.814576i \(-0.696970\pi\)
0.580057 + 0.814576i \(0.303030\pi\)
\(252\) −0.163739 0.473093i −0.163739 0.473093i
\(253\) 0 0
\(254\) 0.815816 + 1.78639i 0.815816 + 1.78639i
\(255\) 0 0
\(256\) −0.786053 + 0.618159i −0.786053 + 0.618159i
\(257\) 0 0 −0.981929 0.189251i \(-0.939394\pi\)
0.981929 + 0.189251i \(0.0606061\pi\)
\(258\) −0.544537 + 2.24461i −0.544537 + 2.24461i
\(259\) 0 0
\(260\) 0 0
\(261\) 0.00775971 0.162896i 0.00775971 0.162896i
\(262\) 0 0
\(263\) 0.428368 0.494363i 0.428368 0.494363i −0.500000 0.866025i \(-0.666667\pi\)
0.928368 + 0.371662i \(0.121212\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 1.95190 1.95190
\(268\) −0.654861 + 0.755750i −0.654861 + 0.755750i
\(269\) 0.830830 0.830830 0.415415 0.909632i \(-0.363636\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(270\) 0.674512 0.347735i 0.674512 0.347735i
\(271\) 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
\(276\) 0.165101 1.14831i 0.165101 1.14831i
\(277\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) −1.13779 + 0.894765i −1.13779 + 0.894765i
\(281\) −1.45949 0.584293i −1.45949 0.584293i −0.500000 0.866025i \(-0.666667\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(282\) −0.757643 1.65901i −0.757643 1.65901i
\(283\) −0.550294 + 0.353653i −0.550294 + 0.353653i −0.786053 0.618159i \(-0.787879\pi\)
0.235759 + 0.971812i \(0.424242\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0.127880 + 2.68452i 0.127880 + 2.68452i
\(288\) 0.0815405 + 0.336115i 0.0815405 + 0.336115i
\(289\) −0.327068 + 0.945001i −0.327068 + 0.945001i
\(290\) −0.452418 + 0.132842i −0.452418 + 0.132842i
\(291\) 0 0
\(292\) 0 0
\(293\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(294\) −1.26476 + 0.120770i −1.26476 + 0.120770i
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) −0.928368 + 1.60798i −0.928368 + 1.60798i
\(299\) 0 0
\(300\) 0.839614 + 0.800570i 0.839614 + 0.800570i
\(301\) 2.56147 + 1.32053i 2.56147 + 1.32053i
\(302\) 0 0
\(303\) 1.41266 + 1.34697i 1.41266 + 1.34697i
\(304\) 0 0
\(305\) 0.654861 1.13425i 0.654861 1.13425i
\(306\) 0 0
\(307\) 0.223734 + 0.175946i 0.223734 + 0.175946i 0.723734 0.690079i \(-0.242424\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(308\) 0 0
\(309\) 2.05296 0.196034i 2.05296 0.196034i
\(310\) 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
\(315\) 0.118027 + 0.486515i 0.118027 + 0.486515i
\(316\) 0 0
\(317\) 0 0 −0.995472 0.0950560i \(-0.969697\pi\)
0.995472 + 0.0950560i \(0.0303030\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0.841254 0.540641i 0.841254 0.540641i
\(321\) −0.137171 0.300363i −0.137171 0.300363i
\(322\) −1.34378 0.537970i −1.34378 0.537970i
\(323\) 0 0
\(324\) −1.20408 0.232068i −1.20408 0.232068i
\(325\) 0 0
\(326\) 0.698939 + 0.449181i 0.698939 + 0.449181i
\(327\) 0.293496 2.04131i 0.293496 2.04131i
\(328\) 0.0883470 1.85463i 0.0883470 1.85463i
\(329\) −2.23445 + 0.430655i −2.23445 + 0.430655i
\(330\) 0 0
\(331\) 0 0 0.580057 0.814576i \(-0.303030\pi\)
−0.580057 + 0.814576i \(0.696970\pi\)
\(332\) −0.0913090 0.0268107i −0.0913090 0.0268107i
\(333\) 0 0
\(334\) −1.91899 −1.91899
\(335\) 0.723734 0.690079i 0.723734 0.690079i
\(336\) 1.67923 1.67923
\(337\) 0 0 0.888835 0.458227i \(-0.151515\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(338\) −0.959493 0.281733i −0.959493 0.281733i
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) −0.0196034 + 0.136345i −0.0196034 + 0.136345i
\(344\) −1.67489 1.07639i −1.67489 1.07639i
\(345\) −0.273507 + 1.12741i −0.273507 + 1.12741i
\(346\) 0 0
\(347\) 1.02951 0.809616i 1.02951 0.809616i 0.0475819 0.998867i \(-0.484848\pi\)
0.981929 + 0.189251i \(0.0606061\pi\)
\(348\) 0.507831 + 0.203305i 0.507831 + 0.203305i
\(349\) −0.827068 1.81103i −0.827068 1.81103i −0.500000 0.866025i \(-0.666667\pi\)
−0.327068 0.945001i \(-0.606061\pi\)
\(350\) 1.21769 0.782560i 1.21769 0.782560i
\(351\) 0 0
\(352\) 0 0
\(353\) 0 0 −0.995472 0.0950560i \(-0.969697\pi\)
0.995472 + 0.0950560i \(0.0303030\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) −0.550294 + 1.58997i −0.550294 + 1.58997i
\(357\) 0 0
\(358\) 0 0
\(359\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(360\) −0.0492216 0.342344i −0.0492216 0.342344i
\(361\) −0.995472 + 0.0950560i −0.995472 + 0.0950560i
\(362\) −0.544078 0.627899i −0.544078 0.627899i
\(363\) −0.911911 0.717135i −0.911911 0.717135i
\(364\) 0 0
\(365\) 0 0
\(366\) −1.41059 + 0.564714i −1.41059 + 0.564714i
\(367\) −1.28656 1.22673i −1.28656 1.22673i −0.959493 0.281733i \(-0.909091\pi\)
−0.327068 0.945001i \(-0.606061\pi\)
\(368\) 0.888835 + 0.458227i 0.888835 + 0.458227i
\(369\) −0.570791 0.294263i −0.570791 0.294263i
\(370\) 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
\(375\) −0.759713 0.876756i −0.759713 0.876756i
\(376\) 1.56499 0.149438i 1.56499 0.149438i
\(377\) 0 0
\(378\) −0.456310 + 0.999179i −0.456310 + 0.999179i
\(379\) 0 0 0.723734 0.690079i \(-0.242424\pi\)
−0.723734 + 0.690079i \(0.757576\pi\)
\(380\) 0 0
\(381\) −0.745158 + 2.15299i −0.745158 + 2.15299i
\(382\) 0 0
\(383\) −0.0748038 1.57033i −0.0748038 1.57033i −0.654861 0.755750i \(-0.727273\pi\)
0.580057 0.814576i \(-0.303030\pi\)
\(384\) −1.15486 0.110276i −1.15486 0.110276i
\(385\) 0 0
\(386\) 0 0
\(387\) −0.579284 + 0.372283i −0.579284 + 0.372283i
\(388\) 0 0
\(389\) −1.65033 0.660694i −1.65033 0.660694i −0.654861 0.755750i \(-0.727273\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0.258195 1.06429i 0.258195 1.06429i
\(393\) 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
\(400\) −0.888835 + 0.458227i −0.888835 + 0.458227i
\(401\) 1.44747 1.44747 0.723734 0.690079i \(-0.242424\pi\)
0.723734 + 0.690079i \(0.242424\pi\)
\(402\) −1.15486 + 0.110276i −1.15486 + 0.110276i
\(403\) 0 0
\(404\) −1.49547 + 0.770969i −1.49547 + 0.770969i
\(405\) 1.17657 + 0.345472i 1.17657 + 0.345472i
\(406\) 0.395893 0.555954i 0.395893 0.555954i
\(407\) 0 0
\(408\) 0 0
\(409\) 0.0395325 0.829889i 0.0395325 0.829889i −0.888835 0.458227i \(-0.848485\pi\)
0.928368 0.371662i \(-0.121212\pi\)
\(410\) −0.264241 + 1.83784i −0.264241 + 1.83784i
\(411\) 0 0
\(412\) −0.419102 + 1.72756i −0.419102 + 1.72756i
\(413\) 0 0
\(414\) 0.271868 0.213799i 0.271868 0.213799i
\(415\) 0.0883470 + 0.0353688i 0.0883470 + 0.0353688i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 0 0 −0.580057 0.814576i \(-0.696970\pi\)
0.580057 + 0.814576i \(0.303030\pi\)
\(420\) −1.67162 0.159621i −1.67162 0.159621i
\(421\) −0.0913090 1.91681i −0.0913090 1.91681i −0.327068 0.945001i \(-0.606061\pi\)
0.235759 0.971812i \(-0.424242\pi\)
\(422\) 0 0
\(423\) 0.177838 0.513830i 0.177838 0.513830i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 0.269798 + 1.87648i 0.269798 + 1.87648i
\(428\) 0.283341 0.0270558i 0.283341 0.0270558i
\(429\) 0 0
\(430\) 1.56499 + 1.23072i 1.56499 + 1.23072i
\(431\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(432\) 0.379436 0.657203i 0.379436 0.657203i
\(433\) 0 0 0.928368 0.371662i \(-0.121212\pi\)
−0.928368 + 0.371662i \(0.878788\pi\)
\(434\) 0 0
\(435\) −0.486206 0.250657i −0.486206 0.250657i
\(436\) 1.58006 + 0.814576i 1.58006 + 0.814576i
\(437\) 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
\(441\) −0.297739 0.234145i −0.297739 0.234145i
\(442\) 0 0
\(443\) −0.469383 + 0.0448206i −0.469383 + 0.0448206i −0.327068 0.945001i \(-0.606061\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(444\) 0 0
\(445\) 0.698939 1.53046i 0.698939 1.53046i
\(446\) −0.947890 + 0.903811i −0.947890 + 0.903811i
\(447\) −2.06677 + 0.606859i −2.06677 + 0.606859i
\(448\) −0.473420 + 1.36786i −0.473420 + 1.36786i
\(449\) −0.370638 1.52779i −0.370638 1.52779i −0.786053 0.618159i \(-0.787879\pi\)
0.415415 0.909632i \(-0.363636\pi\)
\(450\) 0.0164569 + 0.345472i 0.0164569 + 0.345472i
\(451\) 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 0.786053 0.618159i \(-0.212121\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(458\) 1.92837 + 0.371662i 1.92837 + 0.371662i
\(459\) 0 0
\(460\) −0.841254 0.540641i −0.841254 0.540641i
\(461\) −0.0135432 + 0.0941952i −0.0135432 + 0.0941952i −0.995472 0.0950560i \(-0.969697\pi\)
0.981929 + 0.189251i \(0.0606061\pi\)
\(462\) 0 0
\(463\) 0.815816 0.157236i 0.815816 0.157236i 0.235759 0.971812i \(-0.424242\pi\)
0.580057 + 0.814576i \(0.303030\pi\)
\(464\) −0.308779 + 0.356349i −0.308779 + 0.356349i
\(465\) 0 0
\(466\) 0 0
\(467\) −1.74555 + 0.899892i −1.74555 + 0.899892i −0.786053 + 0.618159i \(0.787879\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(468\) 0 0
\(469\) −0.205996 + 1.43273i −0.205996 + 1.43273i
\(470\) −1.57211 −1.57211
\(471\) 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 0.235759 0.971812i \(-0.424242\pi\)
−0.235759 + 0.971812i \(0.575758\pi\)
\(480\) 1.13915 + 0.219553i 1.13915 + 0.219553i
\(481\) 0 0
\(482\) −1.65033 0.660694i −1.65033 0.660694i
\(483\) −0.697576 1.52748i −0.697576 1.52748i
\(484\) 0.841254 0.540641i 0.841254 0.540641i
\(485\) 0 0
\(486\) −0.384989 0.540641i −0.384989 0.540641i
\(487\) −0.0947329 0.00904590i −0.0947329 0.00904590i 0.0475819 0.998867i \(-0.484848\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(488\) −0.0623191 1.30824i −0.0623191 1.30824i
\(489\) 0.227238 + 0.936688i 0.227238 + 0.936688i
\(490\) −0.358193 + 1.03493i −0.358193 + 1.03493i
\(491\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(492\) 1.55894 1.48645i 1.55894 1.48645i
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) −0.0552004 0.0956100i −0.0552004 0.0956100i
\(499\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(500\) 0.928368 0.371662i 0.928368 0.371662i
\(501\) −1.61121 1.53628i −1.61121 1.53628i
\(502\) 0 0
\(503\) −1.65033 0.850806i −1.65033 0.850806i −0.995472 0.0950560i \(-0.969697\pi\)
−0.654861 0.755750i \(-0.727273\pi\)
\(504\) 0.362321 + 0.345472i 0.362321 + 0.345472i
\(505\) 1.56199 0.625325i 1.56199 0.625325i
\(506\) 0 0
\(507\) −0.580057 1.00469i −0.580057 1.00469i
\(508\) −1.54370 1.21398i −1.54370 1.21398i
\(509\) 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
\(515\) 0.581419 1.67990i 0.581419 1.67990i
\(516\) −0.544537 2.24461i −0.544537 2.24461i
\(517\) 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 \(0.484848\pi\)
\(522\) 0.0677463 + 0.148344i 0.0677463 + 0.148344i
\(523\) −1.84833 0.739959i −1.84833 0.739959i −0.959493 0.281733i \(-0.909091\pi\)
−0.888835 0.458227i \(-0.848485\pi\)
\(524\) 0 0
\(525\) 1.64888 + 0.317796i 1.64888 + 0.317796i
\(526\) −0.154218 + 0.635697i −0.154218 + 0.635697i
\(527\) 0 0
\(528\) 0 0
\(529\) 0 0
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) −1.73492 + 0.894412i −1.73492 + 0.894412i
\(535\) −0.284630 −0.284630
\(536\) 0.235759 0.971812i 0.235759 0.971812i
\(537\) 0 0
\(538\) −0.738471 + 0.380708i −0.738471 + 0.380708i
\(539\) 0 0
\(540\) −0.440189 + 0.618159i −0.440189 + 0.618159i
\(541\) 1.30379 1.50465i 1.30379 1.50465i 0.580057 0.814576i \(-0.303030\pi\)
0.723734 0.690079i \(-0.242424\pi\)
\(542\) 0 0
\(543\) 0.0458622 0.962766i 0.0458622 0.962766i
\(544\) 0 0
\(545\) −1.49547 0.961081i −1.49547 0.961081i
\(546\) 0 0
\(547\) 1.92837 + 0.371662i 1.92837 + 0.371662i 1.00000 \(0\)
0.928368 + 0.371662i \(0.121212\pi\)
\(548\) 0 0
\(549\) −0.420537 0.168358i −0.420537 0.168358i
\(550\) 0 0
\(551\) 0 0
\(552\) 0.379436 + 1.09631i 0.379436 + 1.09631i
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 0 0 0.327068 0.945001i \(-0.393939\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0.601300 1.31666i 0.601300 1.31666i
\(561\) 0 0
\(562\) 1.56499 0.149438i 1.56499 0.149438i
\(563\) 1.30379 + 1.50465i 1.30379 + 1.50465i 0.723734 + 0.690079i \(0.242424\pi\)
0.580057 + 0.814576i \(0.303030\pi\)
\(564\) 1.43362 + 1.12741i 1.43362 + 1.12741i
\(565\) 0 0
\(566\) 0.327068 0.566498i 0.327068 0.566498i
\(567\) −1.64780 + 0.659681i −1.64780 + 0.659681i
\(568\) 0 0
\(569\) 1.70566 + 0.879330i 1.70566 + 0.879330i 0.981929 + 0.189251i \(0.0606061\pi\)
0.723734 + 0.690079i \(0.242424\pi\)
\(570\) 0 0
\(571\) 0 0 −0.723734 0.690079i \(-0.757576\pi\)
0.723734 + 0.690079i \(0.242424\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) −1.34378 2.32750i −1.34378 2.32750i
\(575\) 0.786053 + 0.618159i 0.786053 + 0.618159i
\(576\) −0.226493 0.261387i −0.226493 0.261387i
\(577\) 0 0 0.995472 0.0950560i \(-0.0303030\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(578\) −0.142315 0.989821i −0.142315 0.989821i
\(579\) 0 0
\(580\) 0.341254 0.325385i 0.341254 0.325385i
\(581\) −0.132167 + 0.0388077i −0.132167 + 0.0388077i
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 0.0930932 + 0.268975i 0.0930932 + 0.268975i 0.981929 0.189251i \(-0.0606061\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(588\) 1.06882 0.686892i 1.06882 0.686892i
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 0 0 0.235759 0.971812i \(-0.424242\pi\)
−0.235759 + 0.971812i \(0.575758\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0.0883470 1.85463i 0.0883470 1.85463i
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 0.580057 0.814576i \(-0.303030\pi\)
−0.580057 + 0.814576i \(0.696970\pi\)
\(600\) −1.11312 0.326842i −1.11312 0.326842i
\(601\) 1.76962 0.912303i 1.76962 0.912303i 0.841254 0.540641i \(-0.181818\pi\)
0.928368 0.371662i \(-0.121212\pi\)
\(602\) −2.88183 −2.88183
\(603\) −0.271868 0.213799i −0.271868 0.213799i
\(604\) 0 0
\(605\) −0.888835 + 0.458227i −0.888835 + 0.458227i
\(606\) −1.87283 0.549914i −1.87283 0.549914i
\(607\) −0.911911 + 1.28060i −0.911911 + 1.28060i 0.0475819 + 0.998867i \(0.484848\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(608\) 0 0
\(609\) 0.777477 0.149846i 0.777477 0.149846i
\(610\) −0.0623191 + 1.30824i −0.0623191 + 1.30824i
\(611\) 0 0
\(612\) 0 0
\(613\) 0 0 0.235759 0.971812i \(-0.424242\pi\)
−0.235759 + 0.971812i \(0.575758\pi\)
\(614\) −0.279486 0.0538665i −0.279486 0.0538665i
\(615\) −1.69318 + 1.33153i −1.69318 + 1.33153i
\(616\) 0 0
\(617\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(618\) −1.73492 + 1.11496i −1.73492 + 1.11496i
\(619\) 0 0 −0.327068 0.945001i \(-0.606061\pi\)
0.327068 + 0.945001i \(0.393939\pi\)
\(620\) 0 0
\(621\) −0.755436 0.0721354i −0.755436 0.0721354i
\(622\) 0 0
\(623\) 0.574161 + 2.36673i 0.574161 + 2.36673i
\(624\) 0 0
\(625\) −0.959493 + 0.281733i −0.959493 + 0.281733i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) −0.327841 0.378349i −0.327841 0.378349i
\(631\) 0 0 −0.786053 0.618159i \(-0.787879\pi\)
0.786053 + 0.618159i \(0.212121\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 1.42131 + 1.35522i 1.42131 + 1.35522i
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(641\) 0.327068 + 0.566498i 0.327068 + 0.566498i 0.981929 0.189251i \(-0.0606061\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(642\) 0.259557 + 0.204118i 0.259557 + 0.204118i
\(643\) −0.308779 0.356349i −0.308779 0.356349i 0.580057 0.814576i \(-0.303030\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(644\) 1.44091 0.137591i 1.44091 0.137591i
\(645\) 0.328708 + 2.28621i 0.328708 + 2.28621i
\(646\) 0 0
\(647\) −1.13779 + 1.08488i −1.13779 + 1.08488i −0.142315 + 0.989821i \(0.545455\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(648\) 1.17657 0.345472i 1.17657 0.345472i
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) −0.827068 0.0789754i −0.827068 0.0789754i
\(653\) 0 0 −0.580057 0.814576i \(-0.696970\pi\)
0.580057 + 0.814576i \(0.303030\pi\)
\(654\) 0.674512 + 1.94888i 0.674512 + 1.94888i
\(655\) 0 0
\(656\) 0.771316 + 1.68895i 0.771316 + 1.68895i
\(657\) 0 0
\(658\) 1.78872 1.40667i 1.78872 1.40667i
\(659\) 0 0 −0.981929 0.189251i \(-0.939394\pi\)
0.981929 + 0.189251i \(0.0606061\pi\)
\(660\) 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
\(664\) 0.0934441 0.0180099i 0.0934441 0.0180099i
\(665\) 0 0
\(666\) 0 0
\(667\) 0.452418 + 0.132842i 0.452418 + 0.132842i
\(668\) 1.70566 0.879330i 1.70566 0.879330i
\(669\) −1.51943 −1.51943
\(670\) −0.327068 + 0.945001i −0.327068 + 0.945001i
\(671\) 0 0
\(672\) −1.49256 + 0.769467i −1.49256 + 0.769467i
\(673\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(674\) 0 0
\(675\) 0.496956 0.573517i 0.496956 0.573517i
\(676\) 0.981929 0.189251i 0.981929 0.189251i
\(677\) 0 0 0.0475819 0.998867i \(-0.484848\pi\)
−0.0475819 + 0.998867i \(0.515152\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 1.91663 + 0.369399i 1.91663 + 0.369399i
\(682\) 0 0
\(683\) −0.264241 0.105786i −0.264241 0.105786i 0.235759 0.971812i \(-0.424242\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) −0.0450525 0.130171i −0.0450525 0.130171i
\(687\) 1.32154 + 1.85585i 1.32154 + 1.85585i
\(688\) 1.98193 + 0.189251i 1.98193 + 0.189251i
\(689\) 0 0
\(690\) −0.273507 1.12741i −0.273507 1.12741i
\(691\) 0 0 0.327068 0.945001i \(-0.393939\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) −0.544078 + 1.19136i −0.544078 + 1.19136i
\(695\) 0 0
\(696\) −0.544537 + 0.0519970i −0.544537 + 0.0519970i
\(697\) 0 0
\(698\) 1.56499 + 1.23072i 1.56499 + 1.23072i
\(699\) 0 0
\(700\) −0.723734 + 1.25354i −0.723734 + 1.25354i
\(701\) −0.928368 + 0.371662i −0.928368 + 0.371662i −0.786053 0.618159i \(-0.787879\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0 0
\(705\) −1.31996 1.25858i −1.31996 1.25858i
\(706\) 0 0
\(707\) −1.21769 + 2.10910i −1.21769 + 2.10910i
\(708\) 0 0
\(709\) 0.786053 + 0.618159i 0.786053 + 0.618159i 0.928368 0.371662i \(-0.121212\pi\)
−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 −0.995472 0.0950560i \(-0.969697\pi\)
0.995472 + 0.0950560i \(0.0303030\pi\)
\(720\) 0.200621 + 0.281733i 0.200621 + 0.281733i
\(721\) 0.841586 + 2.43160i 0.841586 + 2.43160i
\(722\) 0.841254 0.540641i 0.841254 0.540641i
\(723\) −0.856711 1.87593i −0.856711 1.87593i
\(724\) 0.771316 + 0.308788i 0.771316 + 0.308788i
\(725\) −0.370638 + 0.291473i −0.370638 + 0.291473i
\(726\) 1.13915 + 0.219553i 1.13915 + 0.219553i
\(727\) 0.437742 1.80440i 0.437742 1.80440i −0.142315 0.989821i \(-0.545455\pi\)
0.580057 0.814576i \(-0.303030\pi\)
\(728\) 0 0
\(729\) −0.0649333 + 0.451621i −0.0649333 + 0.451621i
\(730\) 0 0
\(731\) 0 0
\(732\) 0.995012 1.14831i 0.995012 1.14831i
\(733\) 0 0 0.580057 0.814576i \(-0.303030\pi\)
−0.580057 + 0.814576i \(0.696970\pi\)
\(734\) 1.70566 + 0.500828i 1.70566 + 0.500828i
\(735\) −1.12928 + 0.582184i −1.12928 + 0.582184i
\(736\) −1.00000 −1.00000
\(737\) 0 0
\(738\) 0.642178 0.642178
\(739\) 0 0 0.888835 0.458227i \(-0.151515\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 0.815816 0.157236i 0.815816 0.157236i 0.235759 0.971812i \(-0.424242\pi\)
0.580057 + 0.814576i \(0.303030\pi\)
\(744\) 0 0
\(745\) −0.264241 + 1.83784i −0.264241 + 1.83784i
\(746\) 0 0
\(747\) 0.00775971 0.0319860i 0.00775971 0.0319860i
\(748\) 0 0
\(749\) 0.323848 0.254677i 0.323848 0.254677i
\(750\) 1.07701 + 0.431171i 1.07701 + 0.431171i
\(751\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(752\) −1.32254 + 0.849945i −1.32254 + 0.849945i
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) −0.0522660 1.09720i −0.0522660 1.09720i
\(757\) 0 0 −0.235759 0.971812i \(-0.575758\pi\)
0.235759 + 0.971812i \(0.424242\pi\)
\(758\) 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 \(0\)
\(762\) −0.324236 2.25511i −0.324236 2.25511i
\(763\) 2.56147 0.244591i 2.56147 0.244591i
\(764\) 0 0
\(765\) 0 0
\(766\) 0.786053 + 1.36148i 0.786053 + 1.36148i
\(767\) 0 0
\(768\) 1.07701 0.431171i 1.07701 0.431171i
\(769\) 0.839614 + 0.800570i 0.839614 + 0.800570i 0.981929 0.189251i \(-0.0606061\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 0 0 0.928368 0.371662i \(-0.121212\pi\)
−0.928368 + 0.371662i \(0.878788\pi\)
\(774\) 0.344298 0.596342i 0.344298 0.596342i
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 1.76962 0.168978i 1.76962 0.168978i
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0.117032 0.338142i 0.117032 0.338142i
\(784\) 0.258195 + 1.06429i 0.258195 + 1.06429i
\(785\) 0 0
\(786\) 0 0
\(787\) 1.13915 + 1.59971i 1.13915 + 1.59971i 0.723734 + 0.690079i \(0.242424\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(788\) 0 0
\(789\) −0.638404 + 0.410277i −0.638404 + 0.410277i
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0