Properties

Label 1340.1.bl.b.39.1
Level $1340$
Weight $1$
Character 1340.39
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 39.1
Root \(0.981929 + 0.189251i\) of defining polynomial
Character \(\chi\) \(=\) 1340.39
Dual form 1340.1.bl.b.859.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.928368 - 0.371662i) q^{2} +(-0.947890 - 1.09392i) q^{3} +(0.723734 - 0.690079i) q^{4} +(0.841254 + 0.540641i) q^{5} +(-1.28656 - 0.663268i) q^{6} +(0.514186 + 0.404360i) q^{7} +(0.415415 - 0.909632i) q^{8} +(-0.155858 + 1.08402i) q^{9} +O(q^{10})\) \(q+(0.928368 - 0.371662i) q^{2} +(-0.947890 - 1.09392i) q^{3} +(0.723734 - 0.690079i) q^{4} +(0.841254 + 0.540641i) q^{5} +(-1.28656 - 0.663268i) q^{6} +(0.514186 + 0.404360i) q^{7} +(0.415415 - 0.909632i) q^{8} +(-0.155858 + 1.08402i) q^{9} +(0.981929 + 0.189251i) q^{10} +(-1.44091 - 0.137591i) q^{12} +(0.627639 + 0.184291i) q^{14} +(-0.205996 - 1.43273i) q^{15} +(0.0475819 - 0.998867i) q^{16} +(0.258195 + 1.06429i) q^{18} +(0.981929 - 0.189251i) q^{20} +(-0.0450525 - 0.945768i) q^{21} +(0.327068 - 0.945001i) q^{23} +(-1.38884 + 0.407799i) q^{24} +(0.415415 + 0.909632i) q^{25} +(0.115880 - 0.0744714i) q^{27} +(0.651174 - 0.0621796i) q^{28} +(-0.981929 + 1.70075i) q^{29} +(-0.723734 - 1.25354i) q^{30} +(-0.327068 - 0.945001i) q^{32} +(0.213947 + 0.618159i) q^{35} +(0.635257 + 0.892094i) q^{36} +(0.841254 - 0.540641i) q^{40} +(0.273507 - 1.12741i) q^{41} +(-0.393332 - 0.861277i) q^{42} +(-0.452418 + 0.132842i) q^{43} +(-0.717180 + 0.827670i) q^{45} +(-0.0475819 - 0.998867i) q^{46} +(-1.95496 + 0.376789i) q^{47} +(-1.13779 + 0.894765i) q^{48} +(-0.134879 - 0.555979i) q^{49} +(0.723734 + 0.690079i) q^{50} +(0.0799009 - 0.112205i) q^{54} +(0.581419 - 0.299742i) q^{56} +(-0.279486 + 1.94387i) q^{58} +(-1.13779 - 0.894765i) q^{60} +(-1.49547 - 0.770969i) q^{61} +(-0.518473 + 0.494363i) q^{63} +(-0.654861 - 0.755750i) q^{64} +(0.235759 + 0.971812i) q^{67} +(-1.34378 + 0.537970i) q^{69} +(0.428368 + 0.494363i) q^{70} +(0.921310 + 0.592090i) q^{72} +(0.601300 - 1.31666i) q^{75} +(0.580057 - 0.814576i) q^{80} +(0.859495 + 0.252370i) q^{81} +(-0.165101 - 1.14831i) q^{82} +(-0.0748038 + 1.57033i) q^{83} +(-0.685261 - 0.653395i) q^{84} +(-0.370638 + 0.291473i) q^{86} +(2.79125 - 0.537970i) q^{87} +(0.186393 - 0.215109i) q^{89} +(-0.358193 + 1.03493i) q^{90} +(-0.415415 - 0.909632i) q^{92} +(-1.67489 + 1.07639i) q^{94} +(-0.723734 + 1.25354i) q^{96} +(-0.331854 - 0.466024i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20q + q^{2} + 2q^{3} + q^{4} - 2q^{5} - q^{6} - q^{7} - 2q^{8} + O(q^{10}) \) \( 20q + q^{2} + 2q^{3} + q^{4} - 2q^{5} - q^{6} - q^{7} - 2q^{8} + q^{10} - q^{12} + 2q^{14} + 2q^{15} + q^{16} + q^{20} - 10q^{21} - q^{23} - 9q^{24} - 2q^{25} - 2q^{27} - q^{28} - q^{29} - q^{30} + q^{32} + 21q^{35} - 2q^{40} - q^{41} + 20q^{42} - 9q^{43} - q^{46} - q^{47} - q^{48} + q^{50} + q^{54} - q^{56} + 2q^{58} - q^{60} - 9q^{61} - 11q^{63} - 2q^{64} + q^{67} + q^{69} - 9q^{70} - 11q^{72} + 2q^{75} + q^{80} + 2q^{81} + 2q^{82} - q^{83} + q^{84} - q^{86} + q^{87} - 4q^{89} + 2q^{92} + 2q^{94} - q^{96} + O(q^{100}) \)

Character values

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

\(n\) \(537\) \(671\) \(1141\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{29}{33}\right)\)

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:
<
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.928368 0.371662i 0.928368 0.371662i
\(3\) −0.947890 1.09392i −0.947890 1.09392i −0.995472 0.0950560i \(-0.969697\pi\)
0.0475819 0.998867i \(-0.484848\pi\)
\(4\) 0.723734 0.690079i 0.723734 0.690079i
\(5\) 0.841254 + 0.540641i 0.841254 + 0.540641i
\(6\) −1.28656 0.663268i −1.28656 0.663268i
\(7\) 0.514186 + 0.404360i 0.514186 + 0.404360i 0.841254 0.540641i \(-0.181818\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(8\) 0.415415 0.909632i 0.415415 0.909632i
\(9\) −0.155858 + 1.08402i −0.155858 + 1.08402i
\(10\) 0.981929 + 0.189251i 0.981929 + 0.189251i
\(11\) 0 0 0.888835 0.458227i \(-0.151515\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(12\) −1.44091 0.137591i −1.44091 0.137591i
\(13\) 0 0 0.580057 0.814576i \(-0.303030\pi\)
−0.580057 + 0.814576i \(0.696970\pi\)
\(14\) 0.627639 + 0.184291i 0.627639 + 0.184291i
\(15\) −0.205996 1.43273i −0.205996 1.43273i
\(16\) 0.0475819 0.998867i 0.0475819 0.998867i
\(17\) 0 0 −0.723734 0.690079i \(-0.757576\pi\)
0.723734 + 0.690079i \(0.242424\pi\)
\(18\) 0.258195 + 1.06429i 0.258195 + 1.06429i
\(19\) 0 0 0.786053 0.618159i \(-0.212121\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(20\) 0.981929 0.189251i 0.981929 0.189251i
\(21\) −0.0450525 0.945768i −0.0450525 0.945768i
\(22\) 0 0
\(23\) 0.327068 0.945001i 0.327068 0.945001i −0.654861 0.755750i \(-0.727273\pi\)
0.981929 0.189251i \(-0.0606061\pi\)
\(24\) −1.38884 + 0.407799i −1.38884 + 0.407799i
\(25\) 0.415415 + 0.909632i 0.415415 + 0.909632i
\(26\) 0 0
\(27\) 0.115880 0.0744714i 0.115880 0.0744714i
\(28\) 0.651174 0.0621796i 0.651174 0.0621796i
\(29\) −0.981929 + 1.70075i −0.981929 + 1.70075i −0.327068 + 0.945001i \(0.606061\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(30\) −0.723734 1.25354i −0.723734 1.25354i
\(31\) 0 0 −0.580057 0.814576i \(-0.696970\pi\)
0.580057 + 0.814576i \(0.303030\pi\)
\(32\) −0.327068 0.945001i −0.327068 0.945001i
\(33\) 0 0
\(34\) 0 0
\(35\) 0.213947 + 0.618159i 0.213947 + 0.618159i
\(36\) 0.635257 + 0.892094i 0.635257 + 0.892094i
\(37\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0.841254 0.540641i 0.841254 0.540641i
\(41\) 0.273507 1.12741i 0.273507 1.12741i −0.654861 0.755750i \(-0.727273\pi\)
0.928368 0.371662i \(-0.121212\pi\)
\(42\) −0.393332 0.861277i −0.393332 0.861277i
\(43\) −0.452418 + 0.132842i −0.452418 + 0.132842i −0.500000 0.866025i \(-0.666667\pi\)
0.0475819 + 0.998867i \(0.484848\pi\)
\(44\) 0 0
\(45\) −0.717180 + 0.827670i −0.717180 + 0.827670i
\(46\) −0.0475819 0.998867i −0.0475819 0.998867i
\(47\) −1.95496 + 0.376789i −1.95496 + 0.376789i −0.959493 + 0.281733i \(0.909091\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(48\) −1.13779 + 0.894765i −1.13779 + 0.894765i
\(49\) −0.134879 0.555979i −0.134879 0.555979i
\(50\) 0.723734 + 0.690079i 0.723734 + 0.690079i
\(51\) 0 0
\(52\) 0 0
\(53\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(54\) 0.0799009 0.112205i 0.0799009 0.112205i
\(55\) 0 0
\(56\) 0.581419 0.299742i 0.581419 0.299742i
\(57\) 0 0
\(58\) −0.279486 + 1.94387i −0.279486 + 1.94387i
\(59\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(60\) −1.13779 0.894765i −1.13779 0.894765i
\(61\) −1.49547 0.770969i −1.49547 0.770969i −0.500000 0.866025i \(-0.666667\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(62\) 0 0
\(63\) −0.518473 + 0.494363i −0.518473 + 0.494363i
\(64\) −0.654861 0.755750i −0.654861 0.755750i
\(65\) 0 0
\(66\) 0 0
\(67\) 0.235759 + 0.971812i 0.235759 + 0.971812i
\(68\) 0 0
\(69\) −1.34378 + 0.537970i −1.34378 + 0.537970i
\(70\) 0.428368 + 0.494363i 0.428368 + 0.494363i
\(71\) 0 0 0.723734 0.690079i \(-0.242424\pi\)
−0.723734 + 0.690079i \(0.757576\pi\)
\(72\) 0.921310 + 0.592090i 0.921310 + 0.592090i
\(73\) 0 0 −0.888835 0.458227i \(-0.848485\pi\)
0.888835 + 0.458227i \(0.151515\pi\)
\(74\) 0 0
\(75\) 0.601300 1.31666i 0.601300 1.31666i
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 −0.995472 0.0950560i \(-0.969697\pi\)
0.995472 + 0.0950560i \(0.0303030\pi\)
\(80\) 0.580057 0.814576i 0.580057 0.814576i
\(81\) 0.859495 + 0.252370i 0.859495 + 0.252370i
\(82\) −0.165101 1.14831i −0.165101 1.14831i
\(83\) −0.0748038 + 1.57033i −0.0748038 + 1.57033i 0.580057 + 0.814576i \(0.303030\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(84\) −0.685261 0.653395i −0.685261 0.653395i
\(85\) 0 0
\(86\) −0.370638 + 0.291473i −0.370638 + 0.291473i
\(87\) 2.79125 0.537970i 2.79125 0.537970i
\(88\) 0 0
\(89\) 0.186393 0.215109i 0.186393 0.215109i −0.654861 0.755750i \(-0.727273\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(90\) −0.358193 + 1.03493i −0.358193 + 1.03493i
\(91\) 0 0
\(92\) −0.415415 0.909632i −0.415415 0.909632i
\(93\) 0 0
\(94\) −1.67489 + 1.07639i −1.67489 + 1.07639i
\(95\) 0 0
\(96\) −0.723734 + 1.25354i −0.723734 + 1.25354i
\(97\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(98\) −0.331854 0.466024i −0.331854 0.466024i
\(99\) 0 0
\(100\) 0.928368 + 0.371662i 0.928368 + 0.371662i
\(101\) −0.264241 0.105786i −0.264241 0.105786i 0.235759 0.971812i \(-0.424242\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(102\) 0 0
\(103\) 1.07701 + 1.51245i 1.07701 + 1.51245i 0.841254 + 0.540641i \(0.181818\pi\)
0.235759 + 0.971812i \(0.424242\pi\)
\(104\) 0 0
\(105\) 0.473420 0.819988i 0.473420 0.819988i
\(106\) 0 0
\(107\) 0.698939 0.449181i 0.698939 0.449181i −0.142315 0.989821i \(-0.545455\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(108\) 0.0324750 0.133864i 0.0324750 0.133864i
\(109\) 0.771316 + 1.68895i 0.771316 + 1.68895i 0.723734 + 0.690079i \(0.242424\pi\)
0.0475819 + 0.998867i \(0.484848\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0.428368 0.494363i 0.428368 0.494363i
\(113\) 0 0 −0.0475819 0.998867i \(-0.515152\pi\)
0.0475819 + 0.998867i \(0.484848\pi\)
\(114\) 0 0
\(115\) 0.786053 0.618159i 0.786053 0.618159i
\(116\) 0.462997 + 1.90850i 0.462997 + 1.90850i
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) −1.38884 0.407799i −1.38884 0.407799i
\(121\) 0.580057 0.814576i 0.580057 0.814576i
\(122\) −1.67489 0.159932i −1.67489 0.159932i
\(123\) −1.49256 + 0.769467i −1.49256 + 0.769467i
\(124\) 0 0
\(125\) −0.142315 + 0.989821i −0.142315 + 0.989821i
\(126\) −0.297598 + 0.651648i −0.297598 + 0.651648i
\(127\) 1.39734 + 1.09888i 1.39734 + 1.09888i 0.981929 + 0.189251i \(0.0606061\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(128\) −0.888835 0.458227i −0.888835 0.458227i
\(129\) 0.574161 + 0.368991i 0.574161 + 0.368991i
\(130\) 0 0
\(131\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0.580057 + 0.814576i 0.580057 + 0.814576i
\(135\) 0.137747 0.137747
\(136\) 0 0
\(137\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(138\) −1.04758 + 0.998867i −1.04758 + 0.998867i
\(139\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(140\) 0.581419 + 0.299742i 0.581419 + 0.299742i
\(141\) 2.26527 + 1.78143i 2.26527 + 1.78143i
\(142\) 0 0
\(143\) 0 0
\(144\) 1.07537 + 0.207261i 1.07537 + 0.207261i
\(145\) −1.74555 + 0.899892i −1.74555 + 0.899892i
\(146\) 0 0
\(147\) −0.480348 + 0.674555i −0.480348 + 0.674555i
\(148\) 0 0
\(149\) −0.165101 1.14831i −0.165101 1.14831i −0.888835 0.458227i \(-0.848485\pi\)
0.723734 0.690079i \(-0.242424\pi\)
\(150\) 0.0688733 1.44583i 0.0688733 1.44583i
\(151\) 0 0 −0.723734 0.690079i \(-0.757576\pi\)
0.723734 + 0.690079i \(0.242424\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 0 0 0.327068 0.945001i \(-0.393939\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0.235759 0.971812i 0.235759 0.971812i
\(161\) 0.550294 0.353653i 0.550294 0.353653i
\(162\) 0.891724 0.0851493i 0.891724 0.0851493i
\(163\) 0.959493 1.66189i 0.959493 1.66189i 0.235759 0.971812i \(-0.424242\pi\)
0.723734 0.690079i \(-0.242424\pi\)
\(164\) −0.580057 1.00469i −0.580057 1.00469i
\(165\) 0 0
\(166\) 0.514186 + 1.48564i 0.514186 + 1.48564i
\(167\) −1.21590 0.486774i −1.21590 0.486774i −0.327068 0.945001i \(-0.606061\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(168\) −0.879017 0.351905i −0.879017 0.351905i
\(169\) −0.327068 0.945001i −0.327068 0.945001i
\(170\) 0 0
\(171\) 0 0
\(172\) −0.235759 + 0.408346i −0.235759 + 0.408346i
\(173\) 0 0 0.995472 0.0950560i \(-0.0303030\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(174\) 2.39136 1.53684i 2.39136 1.53684i
\(175\) −0.154218 + 0.635697i −0.154218 + 0.635697i
\(176\) 0 0
\(177\) 0 0
\(178\) 0.0930932 0.268975i 0.0930932 0.268975i
\(179\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(180\) 0.0521100 + 1.09392i 0.0521100 + 1.09392i
\(181\) −1.88431 + 0.363170i −1.88431 + 0.363170i −0.995472 0.0950560i \(-0.969697\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(182\) 0 0
\(183\) 0.574161 + 2.36673i 0.574161 + 2.36673i
\(184\) −0.723734 0.690079i −0.723734 0.690079i
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) −1.15486 + 1.62177i −1.15486 + 1.62177i
\(189\) 0.0896970 + 0.00856503i 0.0896970 + 0.00856503i
\(190\) 0 0
\(191\) 0 0 −0.981929 0.189251i \(-0.939394\pi\)
0.981929 + 0.189251i \(0.0606061\pi\)
\(192\) −0.205996 + 1.43273i −0.205996 + 1.43273i
\(193\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) −0.481286 0.309304i −0.481286 0.309304i
\(197\) 0 0 0.723734 0.690079i \(-0.242424\pi\)
−0.723734 + 0.690079i \(0.757576\pi\)
\(198\) 0 0
\(199\) 0 0 0.928368 0.371662i \(-0.121212\pi\)
−0.928368 + 0.371662i \(0.878788\pi\)
\(200\) 1.00000 1.00000
\(201\) 0.839614 1.17907i 0.839614 1.17907i
\(202\) −0.284630 −0.284630
\(203\) −1.19261 + 0.477449i −1.19261 + 0.477449i
\(204\) 0 0
\(205\) 0.839614 0.800570i 0.839614 0.800570i
\(206\) 1.56199 + 1.00383i 1.56199 + 1.00383i
\(207\) 0.973420 + 0.501833i 0.973420 + 0.501833i
\(208\) 0 0
\(209\) 0 0
\(210\) 0.134750 0.937203i 0.134750 0.937203i
\(211\) 0 0 −0.981929 0.189251i \(-0.939394\pi\)
0.981929 + 0.189251i \(0.0606061\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0.481929 0.676774i 0.481929 0.676774i
\(215\) −0.452418 0.132842i −0.452418 0.132842i
\(216\) −0.0196034 0.136345i −0.0196034 0.136345i
\(217\) 0 0
\(218\) 1.34378 + 1.28129i 1.34378 + 1.28129i
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) −1.10181 + 1.27155i −1.10181 + 1.27155i −0.142315 + 0.989821i \(0.545455\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(224\) 0.213947 0.618159i 0.213947 0.618159i
\(225\) −1.05080 + 0.308543i −1.05080 + 0.308543i
\(226\) 0 0
\(227\) −0.0671040 + 0.276606i −0.0671040 + 0.276606i −0.995472 0.0950560i \(-0.969697\pi\)
0.928368 + 0.371662i \(0.121212\pi\)
\(228\) 0 0
\(229\) 1.76962 0.168978i 1.76962 0.168978i 0.841254 0.540641i \(-0.181818\pi\)
0.928368 + 0.371662i \(0.121212\pi\)
\(230\) 0.500000 0.866025i 0.500000 0.866025i
\(231\) 0 0
\(232\) 1.13915 + 1.59971i 1.13915 + 1.59971i
\(233\) 0 0 −0.327068 0.945001i \(-0.606061\pi\)
0.327068 + 0.945001i \(0.393939\pi\)
\(234\) 0 0
\(235\) −1.84833 0.739959i −1.84833 0.739959i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(240\) −1.44091 + 0.137591i −1.44091 + 0.137591i
\(241\) 1.56199 1.00383i 1.56199 1.00383i 0.580057 0.814576i \(-0.303030\pi\)
0.981929 0.189251i \(-0.0606061\pi\)
\(242\) 0.235759 0.971812i 0.235759 0.971812i
\(243\) −0.595855 1.30474i −0.595855 1.30474i
\(244\) −1.61435 + 0.474017i −1.61435 + 0.474017i
\(245\) 0.187118 0.540641i 0.187118 0.540641i
\(246\) −1.09966 + 1.26908i −1.09966 + 1.26908i
\(247\) 0 0
\(248\) 0 0
\(249\) 1.78872 1.40667i 1.78872 1.40667i
\(250\) 0.235759 + 0.971812i 0.235759 + 0.971812i
\(251\) 0 0 −0.723734 0.690079i \(-0.757576\pi\)
0.723734 + 0.690079i \(0.242424\pi\)
\(252\) −0.0340870 + 0.715575i −0.0340870 + 0.715575i
\(253\) 0 0
\(254\) 1.70566 + 0.500828i 1.70566 + 0.500828i
\(255\) 0 0
\(256\) −0.995472 0.0950560i −0.995472 0.0950560i
\(257\) 0 0 0.888835 0.458227i \(-0.151515\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(258\) 0.670173 + 0.129165i 0.670173 + 0.129165i
\(259\) 0 0
\(260\) 0 0
\(261\) −1.69060 1.32950i −1.69060 1.32950i
\(262\) 0 0
\(263\) 0.0800569 + 0.0514495i 0.0800569 + 0.0514495i 0.580057 0.814576i \(-0.303030\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) −0.411992 −0.411992
\(268\) 0.841254 + 0.540641i 0.841254 + 0.540641i
\(269\) −1.91899 −1.91899 −0.959493 0.281733i \(-0.909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(270\) 0.127880 0.0511952i 0.127880 0.0511952i
\(271\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) −0.601300 + 1.31666i −0.601300 + 1.31666i
\(277\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0.651174 + 0.0621796i 0.651174 + 0.0621796i
\(281\) −1.15486 + 1.62177i −1.15486 + 1.62177i −0.500000 + 0.866025i \(0.666667\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(282\) 2.76509 + 0.811905i 2.76509 + 0.811905i
\(283\) −0.0135432 0.0941952i −0.0135432 0.0941952i 0.981929 0.189251i \(-0.0606061\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0.596514 0.469104i 0.596514 0.469104i
\(288\) 1.07537 0.207261i 1.07537 0.207261i
\(289\) 0.0475819 + 0.998867i 0.0475819 + 0.998867i
\(290\) −1.28605 + 1.48418i −1.28605 + 1.48418i
\(291\) 0 0
\(292\) 0 0
\(293\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(294\) −0.195233 + 0.804762i −0.195233 + 0.804762i
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) −0.580057 1.00469i −0.580057 1.00469i
\(299\) 0 0
\(300\) −0.473420 1.36786i −0.473420 1.36786i
\(301\) −0.286343 0.114634i −0.286343 0.114634i
\(302\) 0 0
\(303\) 0.134750 + 0.389333i 0.134750 + 0.389333i
\(304\) 0 0
\(305\) −0.841254 1.45709i −0.841254 1.45709i
\(306\) 0 0
\(307\) −0.827068 + 0.0789754i −0.827068 + 0.0789754i −0.500000 0.866025i \(-0.666667\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(308\) 0 0
\(309\) 0.633618 2.61181i 0.633618 2.61181i
\(310\) 0 0
\(311\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(312\) 0 0
\(313\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(314\) 0 0
\(315\) −0.703440 + 0.135577i −0.703440 + 0.135577i
\(316\) 0 0
\(317\) 0 0 −0.235759 0.971812i \(-0.575758\pi\)
0.235759 + 0.971812i \(0.424242\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) −0.142315 0.989821i −0.142315 0.989821i
\(321\) −1.15389 0.338812i −1.15389 0.338812i
\(322\) 0.379436 0.532843i 0.379436 0.532843i
\(323\) 0 0
\(324\) 0.796201 0.410470i 0.796201 0.410470i
\(325\) 0 0
\(326\) 0.273100 1.89945i 0.273100 1.89945i
\(327\) 1.11646 2.44470i 1.11646 2.44470i
\(328\) −0.911911 0.717135i −0.911911 0.717135i
\(329\) −1.15757 0.596770i −1.15757 0.596770i
\(330\) 0 0
\(331\) 0 0 0.723734 0.690079i \(-0.242424\pi\)
−0.723734 + 0.690079i \(0.757576\pi\)
\(332\) 1.02951 + 1.18812i 1.02951 + 1.18812i
\(333\) 0 0
\(334\) −1.30972 −1.30972
\(335\) −0.327068 + 0.945001i −0.327068 + 0.945001i
\(336\) −0.946841 −0.946841
\(337\) 0 0 0.928368 0.371662i \(-0.121212\pi\)
−0.928368 + 0.371662i \(0.878788\pi\)
\(338\) −0.654861 0.755750i −0.654861 0.755750i
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 0.427201 0.935439i 0.427201 0.935439i
\(344\) −0.0671040 + 0.466718i −0.0671040 + 0.466718i
\(345\) −1.42131 0.273935i −1.42131 0.273935i
\(346\) 0 0
\(347\) −1.67489 0.159932i −1.67489 0.159932i −0.786053 0.618159i \(-0.787879\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(348\) 1.64888 2.31553i 1.64888 2.31553i
\(349\) −0.452418 0.132842i −0.452418 0.132842i 0.0475819 0.998867i \(-0.484848\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(350\) 0.0930932 + 0.647478i 0.0930932 + 0.647478i
\(351\) 0 0
\(352\) 0 0
\(353\) 0 0 −0.235759 0.971812i \(-0.575758\pi\)
0.235759 + 0.971812i \(0.424242\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) −0.0135432 0.284307i −0.0135432 0.284307i
\(357\) 0 0
\(358\) 0 0
\(359\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(360\) 0.454947 + 0.996196i 0.454947 + 0.996196i
\(361\) 0.235759 0.971812i 0.235759 0.971812i
\(362\) −1.61435 + 1.03748i −1.61435 + 1.03748i
\(363\) −1.44091 + 0.137591i −1.44091 + 0.137591i
\(364\) 0 0
\(365\) 0 0
\(366\) 1.41266 + 1.98380i 1.41266 + 1.98380i
\(367\) −0.607279 1.75462i −0.607279 1.75462i −0.654861 0.755750i \(-0.727273\pi\)
0.0475819 0.998867i \(-0.484848\pi\)
\(368\) −0.928368 0.371662i −0.928368 0.371662i
\(369\) 1.17951 + 0.472203i 1.17951 + 0.472203i
\(370\) 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
\(375\) 1.21769 0.782560i 1.21769 0.782560i
\(376\) −0.469383 + 1.93482i −0.469383 + 1.93482i
\(377\) 0 0
\(378\) 0.0864551 0.0253855i 0.0864551 0.0253855i
\(379\) 0 0 0.327068 0.945001i \(-0.393939\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(380\) 0 0
\(381\) −0.122434 2.57021i −0.122434 2.57021i
\(382\) 0 0
\(383\) 1.56499 1.23072i 1.56499 1.23072i 0.723734 0.690079i \(-0.242424\pi\)
0.841254 0.540641i \(-0.181818\pi\)
\(384\) 0.341254 + 1.40667i 0.341254 + 1.40667i
\(385\) 0 0
\(386\) 0 0
\(387\) −0.0734899 0.511133i −0.0734899 0.511133i
\(388\) 0 0
\(389\) 1.07701 1.51245i 1.07701 1.51245i 0.235759 0.971812i \(-0.424242\pi\)
0.841254 0.540641i \(-0.181818\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) −0.561767 0.108272i −0.561767 0.108272i
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0.928368 0.371662i 0.928368 0.371662i
\(401\) −0.654136 −0.654136 −0.327068 0.945001i \(-0.606061\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(402\) 0.341254 1.40667i 0.341254 1.40667i
\(403\) 0 0
\(404\) −0.264241 + 0.105786i −0.264241 + 0.105786i
\(405\) 0.586611 + 0.676985i 0.586611 + 0.676985i
\(406\) −0.929730 + 0.886496i −0.929730 + 0.886496i
\(407\) 0 0
\(408\) 0 0
\(409\) 1.50842 + 1.18624i 1.50842 + 1.18624i 0.928368 + 0.371662i \(0.121212\pi\)
0.580057 + 0.814576i \(0.303030\pi\)
\(410\) 0.481929 1.05528i 0.481929 1.05528i
\(411\) 0 0
\(412\) 1.82318 + 0.351390i 1.82318 + 0.351390i
\(413\) 0 0
\(414\) 1.09020 + 0.104102i 1.09020 + 0.104102i
\(415\) −0.911911 + 1.28060i −0.911911 + 1.28060i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 0 0 −0.723734 0.690079i \(-0.757576\pi\)
0.723734 + 0.690079i \(0.242424\pi\)
\(420\) −0.223226 0.920151i −0.223226 0.920151i
\(421\) 1.02951 0.809616i 1.02951 0.809616i 0.0475819 0.998867i \(-0.484848\pi\)
0.981929 + 0.189251i \(0.0606061\pi\)
\(422\) 0 0
\(423\) −0.103748 2.17794i −0.103748 2.17794i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −0.457201 1.00113i −0.457201 1.00113i
\(428\) 0.195876 0.807410i 0.195876 0.807410i
\(429\) 0 0
\(430\) −0.469383 + 0.0448206i −0.469383 + 0.0448206i
\(431\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(432\) −0.0688733 0.119292i −0.0688733 0.119292i
\(433\) 0 0 −0.580057 0.814576i \(-0.696970\pi\)
0.580057 + 0.814576i \(0.303030\pi\)
\(434\) 0 0
\(435\) 2.63900 + 1.05650i 2.63900 + 1.05650i
\(436\) 1.72373 + 0.690079i 1.72373 + 0.690079i
\(437\) 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
\(441\) 0.623713 0.0595574i 0.623713 0.0595574i
\(442\) 0 0
\(443\) 0.462997 1.90850i 0.462997 1.90850i 0.0475819 0.998867i \(-0.484848\pi\)
0.415415 0.909632i \(-0.363636\pi\)
\(444\) 0 0
\(445\) 0.273100 0.0801894i 0.273100 0.0801894i
\(446\) −0.550294 + 1.58997i −0.550294 + 1.58997i
\(447\) −1.09966 + 1.26908i −1.09966 + 1.26908i
\(448\) −0.0311250 0.653395i −0.0311250 0.653395i
\(449\) −1.95496 + 0.376789i −1.95496 + 0.376789i −0.959493 + 0.281733i \(0.909091\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(450\) −0.860857 + 0.676985i −0.860857 + 0.676985i
\(451\) 0 0
\(452\) 0 0
\(453\) 0 0
\(454\) 0.0405070 + 0.281733i 0.0405070 + 0.281733i
\(455\) 0 0
\(456\) 0 0
\(457\) 0 0 −0.995472 0.0950560i \(-0.969697\pi\)
0.995472 + 0.0950560i \(0.0303030\pi\)
\(458\) 1.58006 0.814576i 1.58006 0.814576i
\(459\) 0 0
\(460\) 0.142315 0.989821i 0.142315 0.989821i
\(461\) −0.653077 + 1.43004i −0.653077 + 1.43004i 0.235759 + 0.971812i \(0.424242\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(462\) 0 0
\(463\) 1.70566 + 0.879330i 1.70566 + 0.879330i 0.981929 + 0.189251i \(0.0606061\pi\)
0.723734 + 0.690079i \(0.242424\pi\)
\(464\) 1.65210 + 1.06174i 1.65210 + 1.06174i
\(465\) 0 0
\(466\) 0 0
\(467\) −1.65033 + 0.660694i −1.65033 + 0.660694i −0.995472 0.0950560i \(-0.969697\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(468\) 0 0
\(469\) −0.271738 + 0.595023i −0.271738 + 0.595023i
\(470\) −1.99094 −1.99094
\(471\) 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 −0.981929 0.189251i \(-0.939394\pi\)
0.981929 + 0.189251i \(0.0606061\pi\)
\(480\) −1.28656 + 0.663268i −1.28656 + 0.663268i
\(481\) 0 0
\(482\) 1.07701 1.51245i 1.07701 1.51245i
\(483\) −0.908487 0.266756i −0.908487 0.266756i
\(484\) −0.142315 0.989821i −0.142315 0.989821i
\(485\) 0 0
\(486\) −1.03809 0.989821i −1.03809 0.989821i
\(487\) −0.370638 1.52779i −0.370638 1.52779i −0.786053 0.618159i \(-0.787879\pi\)
0.415415 0.909632i \(-0.363636\pi\)
\(488\) −1.32254 + 1.04006i −1.32254 + 1.04006i
\(489\) −2.72747 + 0.525678i −2.72747 + 0.525678i
\(490\) −0.0272219 0.571458i −0.0272219 0.571458i
\(491\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(492\) −0.549222 + 1.58687i −0.549222 + 1.58687i
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 1.13779 1.97070i 1.13779 1.97070i
\(499\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(500\) 0.580057 + 0.814576i 0.580057 + 0.814576i
\(501\) 0.620049 + 1.79151i 0.620049 + 1.79151i
\(502\) 0 0
\(503\) 1.07701 + 0.431171i 1.07701 + 0.431171i 0.841254 0.540641i \(-0.181818\pi\)
0.235759 + 0.971812i \(0.424242\pi\)
\(504\) 0.234307 + 0.676985i 0.234307 + 0.676985i
\(505\) −0.165101 0.231852i −0.165101 0.231852i
\(506\) 0 0
\(507\) −0.723734 + 1.25354i −0.723734 + 1.25354i
\(508\) 1.76962 0.168978i 1.76962 0.168978i
\(509\) −1.10181 + 0.708089i −1.10181 + 0.708089i −0.959493 0.281733i \(-0.909091\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −0.959493 + 0.281733i −0.959493 + 0.281733i
\(513\) 0 0
\(514\) 0 0
\(515\) 0.0883470 + 1.85463i 0.0883470 + 1.85463i
\(516\) 0.670173 0.129165i 0.670173 0.129165i
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 0.142315 + 0.989821i 0.142315 + 0.989821i 0.928368 + 0.371662i \(0.121212\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(522\) −2.06363 0.605935i −2.06363 0.605935i
\(523\) 0.273507 0.384087i 0.273507 0.384087i −0.654861 0.755750i \(-0.727273\pi\)
0.928368 + 0.371662i \(0.121212\pi\)
\(524\) 0 0
\(525\) 0.841586 0.433868i 0.841586 0.433868i
\(526\) 0.0934441 + 0.0180099i 0.0934441 + 0.0180099i
\(527\) 0 0
\(528\) 0 0
\(529\) 0 0
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) −0.382481 + 0.153122i −0.382481 + 0.153122i
\(535\) 0.830830 0.830830
\(536\) 0.981929 + 0.189251i 0.981929 + 0.189251i
\(537\) 0 0
\(538\) −1.78153 + 0.713215i −1.78153 + 0.713215i
\(539\) 0 0
\(540\) 0.0996919 0.0950560i 0.0996919 0.0950560i
\(541\) 0.396666 + 0.254922i 0.396666 + 0.254922i 0.723734 0.690079i \(-0.242424\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(542\) 0 0
\(543\) 2.18340 + 1.71704i 2.18340 + 1.71704i
\(544\) 0 0
\(545\) −0.264241 + 1.83784i −0.264241 + 1.83784i
\(546\) 0 0
\(547\) 1.58006 0.814576i 1.58006 0.814576i 0.580057 0.814576i \(-0.303030\pi\)
1.00000 \(0\)
\(548\) 0 0
\(549\) 1.06882 1.50095i 1.06882 1.50095i
\(550\) 0 0
\(551\) 0 0
\(552\) −0.0688733 + 1.44583i −0.0688733 + 1.44583i
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 0 0 −0.0475819 0.998867i \(-0.515152\pi\)
0.0475819 + 0.998867i \(0.484848\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0.627639 0.184291i 0.627639 0.184291i
\(561\) 0 0
\(562\) −0.469383 + 1.93482i −0.469383 + 1.93482i
\(563\) 0.396666 0.254922i 0.396666 0.254922i −0.327068 0.945001i \(-0.606061\pi\)
0.723734 + 0.690079i \(0.242424\pi\)
\(564\) 2.86878 0.273935i 2.86878 0.273935i
\(565\) 0 0
\(566\) −0.0475819 0.0824143i −0.0475819 0.0824143i
\(567\) 0.339891 + 0.477310i 0.339891 + 0.477310i
\(568\) 0 0
\(569\) −1.21590 0.486774i −1.21590 0.486774i −0.327068 0.945001i \(-0.606061\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(570\) 0 0
\(571\) 0 0 −0.327068 0.945001i \(-0.606061\pi\)
0.327068 + 0.945001i \(0.393939\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0.379436 0.657203i 0.379436 0.657203i
\(575\) 0.995472 0.0950560i 0.995472 0.0950560i
\(576\) 0.921310 0.592090i 0.921310 0.592090i
\(577\) 0 0 0.235759 0.971812i \(-0.424242\pi\)
−0.235759 + 0.971812i \(0.575758\pi\)
\(578\) 0.415415 + 0.909632i 0.415415 + 0.909632i
\(579\) 0 0
\(580\) −0.642315 + 1.85585i −0.642315 + 1.85585i
\(581\) −0.673440 + 0.777191i −0.673440 + 0.777191i
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 0.0395325 0.829889i 0.0395325 0.829889i −0.888835 0.458227i \(-0.848485\pi\)
0.928368 0.371662i \(-0.121212\pi\)
\(588\) 0.117852 + 0.819677i 0.117852 + 0.819677i
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 0 0 −0.981929 0.189251i \(-0.939394\pi\)
0.981929 + 0.189251i \(0.0606061\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −0.911911 0.717135i −0.911911 0.717135i
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 0.723734 0.690079i \(-0.242424\pi\)
−0.723734 + 0.690079i \(0.757576\pi\)
\(600\) −0.947890 1.09392i −0.947890 1.09392i
\(601\) 0.437742 0.175245i 0.437742 0.175245i −0.142315 0.989821i \(-0.545455\pi\)
0.580057 + 0.814576i \(0.303030\pi\)
\(602\) −0.308437 −0.308437
\(603\) −1.09020 + 0.104102i −1.09020 + 0.104102i
\(604\) 0 0
\(605\) 0.928368 0.371662i 0.928368 0.371662i
\(606\) 0.269798 + 0.311363i 0.269798 + 0.311363i
\(607\) −1.44091 + 1.37391i −1.44091 + 1.37391i −0.654861 + 0.755750i \(0.727273\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(608\) 0 0
\(609\) 1.65275 + 0.852054i 1.65275 + 0.852054i
\(610\) −1.32254 1.04006i −1.32254 1.04006i
\(611\) 0 0
\(612\) 0 0
\(613\) 0 0 −0.981929 0.189251i \(-0.939394\pi\)
0.981929 + 0.189251i \(0.0606061\pi\)
\(614\) −0.738471 + 0.380708i −0.738471 + 0.380708i
\(615\) −1.67162 0.159621i −1.67162 0.159621i
\(616\) 0 0
\(617\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(618\) −0.382481 2.66021i −0.382481 2.66021i
\(619\) 0 0 0.0475819 0.998867i \(-0.484848\pi\)
−0.0475819 + 0.998867i \(0.515152\pi\)
\(620\) 0 0
\(621\) −0.0324750 0.133864i −0.0324750 0.133864i
\(622\) 0 0
\(623\) 0.182822 0.0352360i 0.182822 0.0352360i
\(624\) 0 0
\(625\) −0.654861 + 0.755750i −0.654861 + 0.755750i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) −0.602662 + 0.387308i −0.602662 + 0.387308i
\(631\) 0 0 0.995472 0.0950560i \(-0.0303030\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 0.581419 + 1.67990i 0.581419 + 1.67990i
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) −0.500000 0.866025i −0.500000 0.866025i
\(641\) −0.0475819 + 0.0824143i −0.0475819 + 0.0824143i −0.888835 0.458227i \(-0.848485\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(642\) −1.19715 + 0.114314i −1.19715 + 0.114314i
\(643\) 1.65210 1.06174i 1.65210 1.06174i 0.723734 0.690079i \(-0.242424\pi\)
0.928368 0.371662i \(-0.121212\pi\)
\(644\) 0.154218 0.635697i 0.154218 0.635697i
\(645\) 0.283524 + 0.620830i 0.283524 + 0.620830i
\(646\) 0 0
\(647\) 0.651174 1.88144i 0.651174 1.88144i 0.235759 0.971812i \(-0.424242\pi\)
0.415415 0.909632i \(-0.363636\pi\)
\(648\) 0.586611 0.676985i 0.586611 0.676985i
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) −0.452418 1.86489i −0.452418 1.86489i
\(653\) 0 0 −0.723734 0.690079i \(-0.757576\pi\)
0.723734 + 0.690079i \(0.242424\pi\)
\(654\) 0.127880 2.68452i 0.127880 2.68452i
\(655\) 0 0
\(656\) −1.11312 0.326842i −1.11312 0.326842i
\(657\) 0 0
\(658\) −1.29645 0.123796i −1.29645 0.123796i
\(659\) 0 0 0.888835 0.458227i \(-0.151515\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(660\) 0 0
\(661\) 0.186393 1.29639i 0.186393 1.29639i −0.654861 0.755750i \(-0.727273\pi\)
0.841254 0.540641i \(-0.181818\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 1.39734 + 0.720381i 1.39734 + 0.720381i
\(665\) 0 0
\(666\) 0 0
\(667\) 1.28605 + 1.48418i 1.28605 + 1.48418i
\(668\) −1.21590 + 0.486774i −1.21590 + 0.486774i
\(669\) 2.43538 2.43538
\(670\) 0.0475819 + 0.998867i 0.0475819 + 0.998867i
\(671\) 0 0
\(672\) −0.879017 + 0.351905i −0.879017 + 0.351905i
\(673\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(674\) 0 0
\(675\) 0.115880 + 0.0744714i 0.115880 + 0.0744714i
\(676\) −0.888835 0.458227i −0.888835 0.458227i
\(677\) 0 0 −0.786053 0.618159i \(-0.787879\pi\)
0.786053 + 0.618159i \(0.212121\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0.366193 0.188786i 0.366193 0.188786i
\(682\) 0 0
\(683\) 0.481929 0.676774i 0.481929 0.676774i −0.500000 0.866025i \(-0.666667\pi\)
0.981929 + 0.189251i \(0.0606061\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0.0489319 1.02721i 0.0489319 1.02721i
\(687\) −1.86226 1.77566i −1.86226 1.77566i
\(688\) 0.111165 + 0.458227i 0.111165 + 0.458227i
\(689\) 0 0
\(690\) −1.42131 + 0.273935i −1.42131 + 0.273935i
\(691\) 0 0 −0.0475819 0.998867i \(-0.515152\pi\)
0.0475819 + 0.998867i \(0.484848\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) −1.61435 + 0.474017i −1.61435 + 0.474017i
\(695\) 0 0
\(696\) 0.670173 2.76249i 0.670173 2.76249i
\(697\) 0 0
\(698\) −0.469383 + 0.0448206i −0.469383 + 0.0448206i
\(699\) 0 0
\(700\) 0.327068 + 0.566498i 0.327068 + 0.566498i
\(701\) −0.580057 0.814576i −0.580057 0.814576i 0.415415 0.909632i \(-0.363636\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0 0
\(705\) 0.942554 + 2.72333i 0.942554 + 2.72333i
\(706\) 0 0
\(707\) −0.0930932 0.161242i −0.0930932 0.161242i
\(708\) 0 0
\(709\) 0.995472 0.0950560i 0.995472 0.0950560i 0.415415 0.909632i \(-0.363636\pi\)
0.580057 + 0.814576i \(0.303030\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) −0.118239 0.258908i −0.118239 0.258908i
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 −0.235759 0.971812i \(-0.575758\pi\)
0.235759 + 0.971812i \(0.424242\pi\)
\(720\) 0.792607 + 0.755750i 0.792607 + 0.755750i
\(721\) −0.0577910 + 1.21318i −0.0577910 + 1.21318i
\(722\) −0.142315 0.989821i −0.142315 0.989821i
\(723\) −2.57870 0.757175i −2.57870 0.757175i
\(724\) −1.11312 + 1.56316i −1.11312 + 1.56316i
\(725\) −1.95496 0.186677i −1.95496 0.186677i
\(726\) −1.28656 + 0.663268i −1.28656 + 0.663268i
\(727\) 1.13915 + 0.219553i 1.13915 + 0.219553i 0.723734 0.690079i \(-0.242424\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(728\) 0 0
\(729\) −0.490360 + 1.07374i −0.490360 + 1.07374i
\(730\) 0 0
\(731\) 0 0
\(732\) 2.04877 + 1.31666i 2.04877 + 1.31666i
\(733\) 0 0 0.723734 0.690079i \(-0.242424\pi\)
−0.723734 + 0.690079i \(0.757576\pi\)
\(734\) −1.21590 1.40323i −1.21590 1.40323i
\(735\) −0.768787 + 0.307776i −0.768787 + 0.307776i
\(736\) −1.00000 −1.00000
\(737\) 0 0
\(738\) 1.27051 1.27051
\(739\) 0 0 0.928368 0.371662i \(-0.121212\pi\)
−0.928368 + 0.371662i \(0.878788\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 1.70566 + 0.879330i 1.70566 + 0.879330i 0.981929 + 0.189251i \(0.0606061\pi\)
0.723734 + 0.690079i \(0.242424\pi\)
\(744\) 0 0
\(745\) 0.481929 1.05528i 0.481929 1.05528i
\(746\) 0 0
\(747\) −1.69060 0.325836i −1.69060 0.325836i
\(748\) 0 0
\(749\) 0.541015 + 0.0516607i 0.541015 + 0.0516607i
\(750\) 0.839614 1.17907i 0.839614 1.17907i
\(751\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(752\) 0.283341 + 1.97068i 0.283341 + 1.97068i
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 0.0708273 0.0556992i 0.0708273 0.0556992i
\(757\) 0 0 0.981929 0.189251i \(-0.0606061\pi\)
−0.981929 + 0.189251i \(0.939394\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 1.84125 0.540641i 1.84125 0.540641i 0.841254 0.540641i \(-0.181818\pi\)
1.00000 \(0\)
\(762\) −1.06891 2.34059i −1.06891 2.34059i
\(763\) −0.286343 + 1.18032i −0.286343 + 1.18032i
\(764\) 0 0
\(765\) 0 0
\(766\) 0.995472 1.72421i 0.995472 1.72421i
\(767\) 0 0
\(768\) 0.839614 + 1.17907i 0.839614 + 1.17907i
\(769\) −0.473420 1.36786i −0.473420 1.36786i −0.888835 0.458227i \(-0.848485\pi\)
0.415415 0.909632i \(-0.363636\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 0 0 −0.580057 0.814576i \(-0.696970\pi\)
0.580057 + 0.814576i \(0.303030\pi\)
\(774\) −0.258195 0.447206i −0.258195 0.447206i
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0.437742 1.80440i 0.437742 1.80440i
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0.0128716 + 0.270208i 0.0128716 + 0.270208i
\(784\) −0.561767 + 0.108272i −0.561767 + 0.108272i
\(785\) 0 0
\(786\) 0 0
\(787\) −1.28656 1.22673i −1.28656 1.22673i −0.959493 0.281733i \(-0.909091\pi\)
−0.327068 0.945001i \(-0.606061\pi\)
\(788\) 0 0
\(789\) −0.0196034 0.136345i −0.0196034 0.136345i
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0