Properties

Label 536.1.ba.a.83.1
Level $536$
Weight $1$
Character 536.83
Analytic conductor $0.267$
Analytic rank $0$
Dimension $20$
Projective image $D_{33}$
CM discriminant -8
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 536 = 2^{3} \cdot 67 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 536.ba (of order \(66\), degree \(20\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.267498846771\)
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 83.1
Root \(-0.327068 - 0.945001i\) of defining polynomial
Character \(\chi\) \(=\) 536.83
Dual form 536.1.ba.a.155.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.981929 + 0.189251i) q^{2} +(-0.738471 - 1.61703i) q^{3} +(0.928368 + 0.371662i) q^{4} +(-0.419102 - 1.72756i) q^{6} +(0.841254 + 0.540641i) q^{8} +(-1.41457 + 1.63251i) q^{9} +O(q^{10})\) \(q+(0.981929 + 0.189251i) q^{2} +(-0.738471 - 1.61703i) q^{3} +(0.928368 + 0.371662i) q^{4} +(-0.419102 - 1.72756i) q^{6} +(0.841254 + 0.540641i) q^{8} +(-1.41457 + 1.63251i) q^{9} +(0.396666 - 1.63508i) q^{11} +(-0.0845850 - 1.77566i) q^{12} +(0.723734 + 0.690079i) q^{16} +(-1.45949 + 0.584293i) q^{17} +(-1.69796 + 1.33529i) q^{18} +(-0.473420 + 1.36786i) q^{19} +(0.698939 - 1.53046i) q^{22} +(0.252989 - 1.75958i) q^{24} +(0.841254 - 0.540641i) q^{25} +(1.97876 + 0.581017i) q^{27} +(0.580057 + 0.814576i) q^{32} +(-2.93689 + 0.566040i) q^{33} +(-1.54370 + 0.297523i) q^{34} +(-1.91999 + 0.989821i) q^{36} +(-0.723734 + 1.25354i) q^{38} +(1.02951 + 0.809616i) q^{41} +(-0.0671040 + 0.466718i) q^{43} +(0.975950 - 1.37053i) q^{44} +(0.581419 - 1.67990i) q^{48} +(-0.786053 + 0.618159i) q^{49} +(0.928368 - 0.371662i) q^{50} +(2.02261 + 1.92856i) q^{51} +(1.83305 + 0.945001i) q^{54} +(2.56147 - 0.244591i) q^{57} +(0.0800569 + 0.0514495i) q^{59} +(0.415415 + 0.909632i) q^{64} -2.99094 q^{66} +(-0.959493 + 0.281733i) q^{67} -1.57211 q^{68} +(-2.07261 + 0.608574i) q^{72} +(0.437742 + 1.80440i) q^{73} +(-1.49547 - 0.961081i) q^{75} +(-0.947890 + 1.09392i) q^{76} +(-0.214323 - 1.49065i) q^{81} +(0.857685 + 0.989821i) q^{82} +(-1.38884 - 1.32425i) q^{83} +(-0.154218 + 0.445585i) q^{86} +(1.21769 - 1.16106i) q^{88} +(0.815816 - 1.78639i) q^{89} +(0.888835 - 1.53951i) q^{96} +(-0.928368 - 1.60798i) q^{97} +(-0.888835 + 0.458227i) q^{98} +(2.10816 + 2.96050i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20q + q^{2} + 2q^{3} + q^{4} - q^{6} - 2q^{8} + O(q^{10}) \) \( 20q + q^{2} + 2q^{3} + q^{4} - q^{6} - 2q^{8} + 2q^{11} - 12q^{12} + q^{16} - 12q^{17} - q^{19} - 4q^{22} + 2q^{24} - 2q^{25} - 2q^{27} + q^{32} - 2q^{33} - q^{34} - q^{38} + 2q^{41} + 2q^{43} + 2q^{44} - q^{48} + q^{49} + q^{50} + q^{51} + 23q^{54} + q^{57} - 9q^{59} - 2q^{64} - 18q^{66} - 2q^{67} + 2q^{68} - q^{73} - 9q^{75} + 2q^{76} + 2q^{81} + 18q^{82} - 9q^{83} - q^{86} + 2q^{88} + 2q^{89} - q^{96} - q^{97} + q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/536\mathbb{Z}\right)^\times\).

\(n\) \(135\) \(269\) \(337\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{2}{33}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.981929 + 0.189251i 0.981929 + 0.189251i
\(3\) −0.738471 1.61703i −0.738471 1.61703i −0.786053 0.618159i \(-0.787879\pi\)
0.0475819 0.998867i \(-0.484848\pi\)
\(4\) 0.928368 + 0.371662i 0.928368 + 0.371662i
\(5\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(6\) −0.419102 1.72756i −0.419102 1.72756i
\(7\) 0 0 −0.327068 0.945001i \(-0.606061\pi\)
0.327068 + 0.945001i \(0.393939\pi\)
\(8\) 0.841254 + 0.540641i 0.841254 + 0.540641i
\(9\) −1.41457 + 1.63251i −1.41457 + 1.63251i
\(10\) 0 0
\(11\) 0.396666 1.63508i 0.396666 1.63508i −0.327068 0.945001i \(-0.606061\pi\)
0.723734 0.690079i \(-0.242424\pi\)
\(12\) −0.0845850 1.77566i −0.0845850 1.77566i
\(13\) 0 0 −0.888835 0.458227i \(-0.848485\pi\)
0.888835 + 0.458227i \(0.151515\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0.723734 + 0.690079i 0.723734 + 0.690079i
\(17\) −1.45949 + 0.584293i −1.45949 + 0.584293i −0.959493 0.281733i \(-0.909091\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(18\) −1.69796 + 1.33529i −1.69796 + 1.33529i
\(19\) −0.473420 + 1.36786i −0.473420 + 1.36786i 0.415415 + 0.909632i \(0.363636\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0.698939 1.53046i 0.698939 1.53046i
\(23\) 0 0 0.580057 0.814576i \(-0.303030\pi\)
−0.580057 + 0.814576i \(0.696970\pi\)
\(24\) 0.252989 1.75958i 0.252989 1.75958i
\(25\) 0.841254 0.540641i 0.841254 0.540641i
\(26\) 0 0
\(27\) 1.97876 + 0.581017i 1.97876 + 0.581017i
\(28\) 0 0
\(29\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(30\) 0 0
\(31\) 0 0 0.888835 0.458227i \(-0.151515\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(32\) 0.580057 + 0.814576i 0.580057 + 0.814576i
\(33\) −2.93689 + 0.566040i −2.93689 + 0.566040i
\(34\) −1.54370 + 0.297523i −1.54370 + 0.297523i
\(35\) 0 0
\(36\) −1.91999 + 0.989821i −1.91999 + 0.989821i
\(37\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(38\) −0.723734 + 1.25354i −0.723734 + 1.25354i
\(39\) 0 0
\(40\) 0 0
\(41\) 1.02951 + 0.809616i 1.02951 + 0.809616i 0.981929 0.189251i \(-0.0606061\pi\)
0.0475819 + 0.998867i \(0.484848\pi\)
\(42\) 0 0
\(43\) −0.0671040 + 0.466718i −0.0671040 + 0.466718i 0.928368 + 0.371662i \(0.121212\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(44\) 0.975950 1.37053i 0.975950 1.37053i
\(45\) 0 0
\(46\) 0 0
\(47\) 0 0 −0.995472 0.0950560i \(-0.969697\pi\)
0.995472 + 0.0950560i \(0.0303030\pi\)
\(48\) 0.581419 1.67990i 0.581419 1.67990i
\(49\) −0.786053 + 0.618159i −0.786053 + 0.618159i
\(50\) 0.928368 0.371662i 0.928368 0.371662i
\(51\) 2.02261 + 1.92856i 2.02261 + 1.92856i
\(52\) 0 0
\(53\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(54\) 1.83305 + 0.945001i 1.83305 + 0.945001i
\(55\) 0 0
\(56\) 0 0
\(57\) 2.56147 0.244591i 2.56147 0.244591i
\(58\) 0 0
\(59\) 0.0800569 + 0.0514495i 0.0800569 + 0.0514495i 0.580057 0.814576i \(-0.303030\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(60\) 0 0
\(61\) 0 0 −0.235759 0.971812i \(-0.575758\pi\)
0.235759 + 0.971812i \(0.424242\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0.415415 + 0.909632i 0.415415 + 0.909632i
\(65\) 0 0
\(66\) −2.99094 −2.99094
\(67\) −0.959493 + 0.281733i −0.959493 + 0.281733i
\(68\) −1.57211 −1.57211
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 −0.928368 0.371662i \(-0.878788\pi\)
0.928368 + 0.371662i \(0.121212\pi\)
\(72\) −2.07261 + 0.608574i −2.07261 + 0.608574i
\(73\) 0.437742 + 1.80440i 0.437742 + 1.80440i 0.580057 + 0.814576i \(0.303030\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(74\) 0 0
\(75\) −1.49547 0.961081i −1.49547 0.961081i
\(76\) −0.947890 + 1.09392i −0.947890 + 1.09392i
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 −0.0475819 0.998867i \(-0.515152\pi\)
0.0475819 + 0.998867i \(0.484848\pi\)
\(80\) 0 0
\(81\) −0.214323 1.49065i −0.214323 1.49065i
\(82\) 0.857685 + 0.989821i 0.857685 + 0.989821i
\(83\) −1.38884 1.32425i −1.38884 1.32425i −0.888835 0.458227i \(-0.848485\pi\)
−0.500000 0.866025i \(-0.666667\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) −0.154218 + 0.445585i −0.154218 + 0.445585i
\(87\) 0 0
\(88\) 1.21769 1.16106i 1.21769 1.16106i
\(89\) 0.815816 1.78639i 0.815816 1.78639i 0.235759 0.971812i \(-0.424242\pi\)
0.580057 0.814576i \(-0.303030\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 0.888835 1.53951i 0.888835 1.53951i
\(97\) −0.928368 1.60798i −0.928368 1.60798i −0.786053 0.618159i \(-0.787879\pi\)
−0.142315 0.989821i \(-0.545455\pi\)
\(98\) −0.888835 + 0.458227i −0.888835 + 0.458227i
\(99\) 2.10816 + 2.96050i 2.10816 + 2.96050i
\(100\) 0.981929 0.189251i 0.981929 0.189251i
\(101\) 0 0 0.981929 0.189251i \(-0.0606061\pi\)
−0.981929 + 0.189251i \(0.939394\pi\)
\(102\) 1.62108 + 2.27649i 1.62108 + 2.27649i
\(103\) 0 0 0.888835 0.458227i \(-0.151515\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −0.797176 0.234072i −0.797176 0.234072i −0.142315 0.989821i \(-0.545455\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(108\) 1.62108 + 1.27483i 1.62108 + 1.27483i
\(109\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 0.0688733 0.0656706i 0.0688733 0.0656706i −0.654861 0.755750i \(-0.727273\pi\)
0.723734 + 0.690079i \(0.242424\pi\)
\(114\) 2.56147 + 0.244591i 2.56147 + 0.244591i
\(115\) 0 0
\(116\) 0 0
\(117\) 0 0
\(118\) 0.0688733 + 0.0656706i 0.0688733 + 0.0656706i
\(119\) 0 0
\(120\) 0 0
\(121\) −1.62731 0.838935i −1.62731 0.838935i
\(122\) 0 0
\(123\) 0.548907 2.26262i 0.548907 2.26262i
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 0 0 −0.327068 0.945001i \(-0.606061\pi\)
0.327068 + 0.945001i \(0.393939\pi\)
\(128\) 0.235759 + 0.971812i 0.235759 + 0.971812i
\(129\) 0.804250 0.236149i 0.804250 0.236149i
\(130\) 0 0
\(131\) −0.544078 1.19136i −0.544078 1.19136i −0.959493 0.281733i \(-0.909091\pi\)
0.415415 0.909632i \(-0.363636\pi\)
\(132\) −2.93689 0.566040i −2.93689 0.566040i
\(133\) 0 0
\(134\) −0.995472 + 0.0950560i −0.995472 + 0.0950560i
\(135\) 0 0
\(136\) −1.54370 0.297523i −1.54370 0.297523i
\(137\) −0.827068 1.81103i −0.827068 1.81103i −0.500000 0.866025i \(-0.666667\pi\)
−0.327068 0.945001i \(-0.606061\pi\)
\(138\) 0 0
\(139\) 0.959493 0.281733i 0.959493 0.281733i 0.235759 0.971812i \(-0.424242\pi\)
0.723734 + 0.690079i \(0.242424\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) −2.15033 + 0.205332i −2.15033 + 0.205332i
\(145\) 0 0
\(146\) 0.0883470 + 1.85463i 0.0883470 + 1.85463i
\(147\) 1.58006 + 0.814576i 1.58006 + 0.814576i
\(148\) 0 0
\(149\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(150\) −1.28656 1.22673i −1.28656 1.22673i
\(151\) 0 0 0.928368 0.371662i \(-0.121212\pi\)
−0.928368 + 0.371662i \(0.878788\pi\)
\(152\) −1.13779 + 0.894765i −1.13779 + 0.894765i
\(153\) 1.11070 3.20916i 1.11070 3.20916i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 0 0 0.580057 0.814576i \(-0.303030\pi\)
−0.580057 + 0.814576i \(0.696970\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) 0.0716573 1.50427i 0.0716573 1.50427i
\(163\) 0.327068 0.566498i 0.327068 0.566498i −0.654861 0.755750i \(-0.727273\pi\)
0.981929 + 0.189251i \(0.0606061\pi\)
\(164\) 0.654861 + 1.13425i 0.654861 + 1.13425i
\(165\) 0 0
\(166\) −1.11312 1.56316i −1.11312 1.56316i
\(167\) 0 0 0.981929 0.189251i \(-0.0606061\pi\)
−0.981929 + 0.189251i \(0.939394\pi\)
\(168\) 0 0
\(169\) 0.580057 + 0.814576i 0.580057 + 0.814576i
\(170\) 0 0
\(171\) −1.56335 2.70780i −1.56335 2.70780i
\(172\) −0.235759 + 0.408346i −0.235759 + 0.408346i
\(173\) 0 0 0.0475819 0.998867i \(-0.484848\pi\)
−0.0475819 + 0.998867i \(0.515152\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 1.41542 0.909632i 1.41542 0.909632i
\(177\) 0.0240754 0.167448i 0.0240754 0.167448i
\(178\) 1.13915 1.59971i 1.13915 1.59971i
\(179\) −0.797176 + 1.74557i −0.797176 + 1.74557i −0.142315 + 0.989821i \(0.545455\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(180\) 0 0
\(181\) 0 0 −0.995472 0.0950560i \(-0.969697\pi\)
0.995472 + 0.0950560i \(0.0303030\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 0.376434 + 2.61816i 0.376434 + 2.61816i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 0 0 0.995472 0.0950560i \(-0.0303030\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(192\) 1.16413 1.34347i 1.16413 1.34347i
\(193\) −0.239446 0.153882i −0.239446 0.153882i 0.415415 0.909632i \(-0.363636\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(194\) −0.607279 1.75462i −0.607279 1.75462i
\(195\) 0 0
\(196\) −0.959493 + 0.281733i −0.959493 + 0.281733i
\(197\) 0 0 −0.928368 0.371662i \(-0.878788\pi\)
0.928368 + 0.371662i \(0.121212\pi\)
\(198\) 1.50979 + 3.30597i 1.50979 + 3.30597i
\(199\) 0 0 −0.981929 0.189251i \(-0.939394\pi\)
0.981929 + 0.189251i \(0.0606061\pi\)
\(200\) 1.00000 1.00000
\(201\) 1.16413 + 1.34347i 1.16413 + 1.34347i
\(202\) 0 0
\(203\) 0 0
\(204\) 1.16096 + 2.54214i 1.16096 + 2.54214i
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 2.04877 + 1.31666i 2.04877 + 1.31666i
\(210\) 0 0
\(211\) −1.95496 + 0.186677i −1.95496 + 0.186677i −0.995472 0.0950560i \(-0.969697\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) −0.738471 0.380708i −0.738471 0.380708i
\(215\) 0 0
\(216\) 1.35052 + 1.55858i 1.35052 + 1.55858i
\(217\) 0 0
\(218\) 0 0
\(219\) 2.59450 2.04034i 2.59450 2.04034i
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(224\) 0 0
\(225\) −0.307416 + 2.13813i −0.307416 + 2.13813i
\(226\) 0.0800569 0.0514495i 0.0800569 0.0514495i
\(227\) 0.514186 + 0.404360i 0.514186 + 0.404360i 0.841254 0.540641i \(-0.181818\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(228\) 2.46889 + 0.724932i 2.46889 + 0.724932i
\(229\) 0 0 0.0475819 0.998867i \(-0.484848\pi\)
−0.0475819 + 0.998867i \(0.515152\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −0.580057 0.814576i −0.580057 0.814576i 0.415415 0.909632i \(-0.363636\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0.0552004 + 0.0775182i 0.0552004 + 0.0775182i
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(240\) 0 0
\(241\) 1.84125 + 0.540641i 1.84125 + 0.540641i 1.00000 \(0\)
0.841254 + 0.540641i \(0.181818\pi\)
\(242\) −1.43913 1.13174i −1.43913 1.13174i
\(243\) −0.517230 + 0.332404i −0.517230 + 0.332404i
\(244\) 0 0
\(245\) 0 0
\(246\) 0.967192 2.11785i 0.967192 2.11785i
\(247\) 0 0
\(248\) 0 0
\(249\) −1.11574 + 3.22371i −1.11574 + 3.22371i
\(250\) 0 0
\(251\) −0.607279 + 0.243118i −0.607279 + 0.243118i −0.654861 0.755750i \(-0.727273\pi\)
0.0475819 + 0.998867i \(0.484848\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) 0.0475819 + 0.998867i 0.0475819 + 0.998867i
\(257\) −0.0671040 + 0.276606i −0.0671040 + 0.276606i −0.995472 0.0950560i \(-0.969697\pi\)
0.928368 + 0.371662i \(0.121212\pi\)
\(258\) 0.834408 0.0796763i 0.834408 0.0796763i
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) −0.308779 1.27280i −0.308779 1.27280i
\(263\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(264\) −2.77670 1.11162i −2.77670 1.11162i
\(265\) 0 0
\(266\) 0 0
\(267\) −3.49109 −3.49109
\(268\) −0.995472 0.0950560i −0.995472 0.0950560i
\(269\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(270\) 0 0
\(271\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(272\) −1.45949 0.584293i −1.45949 0.584293i
\(273\) 0 0
\(274\) −0.469383 1.93482i −0.469383 1.93482i
\(275\) −0.550294 1.58997i −0.550294 1.58997i
\(276\) 0 0
\(277\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(278\) 0.995472 0.0950560i 0.995472 0.0950560i
\(279\) 0 0
\(280\) 0 0
\(281\) 1.39734 + 0.720381i 1.39734 + 0.720381i 0.981929 0.189251i \(-0.0606061\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(282\) 0 0
\(283\) 0.654861 + 0.755750i 0.654861 + 0.755750i 0.981929 0.189251i \(-0.0606061\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) −2.15033 0.205332i −2.15033 0.205332i
\(289\) 1.06499 1.01546i 1.06499 1.01546i
\(290\) 0 0
\(291\) −1.91457 + 2.68864i −1.91457 + 2.68864i
\(292\) −0.264241 + 1.83784i −0.264241 + 1.83784i
\(293\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(294\) 1.39734 + 1.09888i 1.39734 + 1.09888i
\(295\) 0 0
\(296\) 0 0
\(297\) 1.73492 3.00497i 1.73492 3.00497i
\(298\) 0 0
\(299\) 0 0
\(300\) −1.03115 1.44805i −1.03115 1.44805i
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) −1.28656 + 0.663268i −1.28656 + 0.663268i
\(305\) 0 0
\(306\) 1.69796 2.94096i 1.69796 2.94096i
\(307\) 0.0224357 0.470984i 0.0224357 0.470984i −0.959493 0.281733i \(-0.909091\pi\)
0.981929 0.189251i \(-0.0606061\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(312\) 0 0
\(313\) 0.601300 1.31666i 0.601300 1.31666i −0.327068 0.945001i \(-0.606061\pi\)
0.928368 0.371662i \(-0.121212\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 0 0 0.786053 0.618159i \(-0.212121\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 0.210191 + 1.46191i 0.210191 + 1.46191i
\(322\) 0 0
\(323\) −0.108276 2.27300i −0.108276 2.27300i
\(324\) 0.355048 1.46353i 0.355048 1.46353i
\(325\) 0 0
\(326\) 0.428368 0.494363i 0.428368 0.494363i
\(327\) 0 0
\(328\) 0.428368 + 1.23769i 0.428368 + 1.23769i
\(329\) 0 0
\(330\) 0 0
\(331\) 1.34378 + 0.537970i 1.34378 + 0.537970i 0.928368 0.371662i \(-0.121212\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(332\) −0.797176 1.74557i −0.797176 1.74557i
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −0.279486 0.0538665i −0.279486 0.0538665i 0.0475819 0.998867i \(-0.484848\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(338\) 0.415415 + 0.909632i 0.415415 + 0.909632i
\(339\) −0.157052 0.0628741i −0.157052 0.0628741i
\(340\) 0 0
\(341\) 0 0
\(342\) −1.02264 2.95473i −1.02264 2.95473i
\(343\) 0 0
\(344\) −0.308779 + 0.356349i −0.308779 + 0.356349i
\(345\) 0 0
\(346\) 0 0
\(347\) −0.0475819 0.998867i −0.0475819 0.998867i −0.888835 0.458227i \(-0.848485\pi\)
0.841254 0.540641i \(-0.181818\pi\)
\(348\) 0 0
\(349\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 1.56199 0.625325i 1.56199 0.625325i
\(353\) −0.653077 + 0.513585i −0.653077 + 0.513585i −0.888835 0.458227i \(-0.848485\pi\)
0.235759 + 0.971812i \(0.424242\pi\)
\(354\) 0.0553301 0.159866i 0.0553301 0.159866i
\(355\) 0 0
\(356\) 1.42131 1.35522i 1.42131 1.35522i
\(357\) 0 0
\(358\) −1.11312 + 1.56316i −1.11312 + 1.56316i
\(359\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(360\) 0 0
\(361\) −0.860857 0.676985i −0.860857 0.676985i
\(362\) 0 0
\(363\) −0.154861 + 3.25093i −0.154861 + 3.25093i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 0 0 −0.580057 0.814576i \(-0.696970\pi\)
0.580057 + 0.814576i \(0.303030\pi\)
\(368\) 0 0
\(369\) −2.77802 + 0.535420i −2.77802 + 0.535420i
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(374\) −0.125858 + 2.64208i −0.125858 + 2.64208i
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) −0.759713 + 1.06687i −0.759713 + 1.06687i 0.235759 + 0.971812i \(0.424242\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 0 0 0.327068 0.945001i \(-0.393939\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(384\) 1.39734 1.09888i 1.39734 1.09888i
\(385\) 0 0
\(386\) −0.205996 0.196417i −0.205996 0.196417i
\(387\) −0.666997 0.769755i −0.666997 0.769755i
\(388\) −0.264241 1.83784i −0.264241 1.83784i
\(389\) 0 0 −0.888835 0.458227i \(-0.848485\pi\)
0.888835 + 0.458227i \(0.151515\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) −0.995472 + 0.0950560i −0.995472 + 0.0950560i
\(393\) −1.52468 + 1.75958i −1.52468 + 1.75958i
\(394\) 0 0
\(395\) 0 0
\(396\) 0.856844 + 3.53196i 0.856844 + 3.53196i
\(397\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0.981929 + 0.189251i 0.981929 + 0.189251i
\(401\) −0.284630 −0.284630 −0.142315 0.989821i \(-0.545455\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(402\) 0.888835 + 1.53951i 0.888835 + 1.53951i
\(403\) 0 0
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 0.658873 + 2.71591i 0.658873 + 2.71591i
\(409\) −0.271738 0.785135i −0.271738 0.785135i −0.995472 0.0950560i \(-0.969697\pi\)
0.723734 0.690079i \(-0.242424\pi\)
\(410\) 0 0
\(411\) −2.31771 + 2.67478i −2.31771 + 2.67478i
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −1.16413 1.34347i −1.16413 1.34347i
\(418\) 1.76256 + 1.68060i 1.76256 + 1.68060i
\(419\) 1.72373 0.690079i 1.72373 0.690079i 0.723734 0.690079i \(-0.242424\pi\)
1.00000 \(0\)
\(420\) 0 0
\(421\) 0 0 0.327068 0.945001i \(-0.393939\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(422\) −1.95496 0.186677i −1.95496 0.186677i
\(423\) 0 0
\(424\) 0 0
\(425\) −0.911911 + 1.28060i −0.911911 + 1.28060i
\(426\) 0 0
\(427\) 0 0
\(428\) −0.653077 0.513585i −0.653077 0.513585i
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(432\) 1.03115 + 1.78600i 1.03115 + 1.78600i
\(433\) 1.76962 0.912303i 1.76962 0.912303i 0.841254 0.540641i \(-0.181818\pi\)
0.928368 0.371662i \(-0.121212\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) 2.93375 1.51245i 2.93375 1.51245i
\(439\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(440\) 0 0
\(441\) 0.102782 2.15767i 0.102782 2.15767i
\(442\) 0 0
\(443\) 1.23576 + 0.971812i 1.23576 + 0.971812i 1.00000 \(0\)
0.235759 + 0.971812i \(0.424242\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −1.67489 0.159932i −1.67489 0.159932i −0.786053 0.618159i \(-0.787879\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(450\) −0.706504 + 2.04131i −0.706504 + 2.04131i
\(451\) 1.73216 1.36218i 1.73216 1.36218i
\(452\) 0.0883470 0.0353688i 0.0883470 0.0353688i
\(453\) 0 0
\(454\) 0.428368 + 0.494363i 0.428368 + 0.494363i
\(455\) 0 0
\(456\) 2.28708 + 1.17907i 2.28708 + 1.17907i
\(457\) 0.0934441 + 1.96163i 0.0934441 + 1.96163i 0.235759 + 0.971812i \(0.424242\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(458\) 0 0
\(459\) −3.22747 + 0.308186i −3.22747 + 0.308186i
\(460\) 0 0
\(461\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(462\) 0 0
\(463\) 0 0 −0.235759 0.971812i \(-0.575758\pi\)
0.235759 + 0.971812i \(0.424242\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) −0.415415 0.909632i −0.415415 0.909632i
\(467\) 1.65210 + 0.318417i 1.65210 + 0.318417i 0.928368 0.371662i \(-0.121212\pi\)
0.723734 + 0.690079i \(0.242424\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 0.0395325 + 0.0865641i 0.0395325 + 0.0865641i
\(473\) 0.736504 + 0.294852i 0.736504 + 0.294852i
\(474\) 0 0
\(475\) 0.341254 + 1.40667i 0.341254 + 1.40667i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 0 0 0.995472 0.0950560i \(-0.0303030\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 1.70566 + 0.879330i 1.70566 + 0.879330i
\(483\) 0 0
\(484\) −1.19894 1.38365i −1.19894 1.38365i
\(485\) 0 0
\(486\) −0.570791 + 0.228510i −0.570791 + 0.228510i
\(487\) 0 0 0.786053 0.618159i \(-0.212121\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(488\) 0 0
\(489\) −1.15757 0.110535i −1.15757 0.110535i
\(490\) 0 0
\(491\) −0.415415 + 0.909632i −0.415415 + 0.909632i 0.580057 + 0.814576i \(0.303030\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(492\) 1.35052 1.89654i 1.35052 1.89654i
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) −1.70566 + 2.95429i −1.70566 + 2.95429i
\(499\) −0.580057 1.00469i −0.580057 1.00469i −0.995472 0.0950560i \(-0.969697\pi\)
0.415415 0.909632i \(-0.363636\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) −0.642315 + 0.123796i −0.642315 + 0.123796i
\(503\) 0 0 0.981929 0.189251i \(-0.0606061\pi\)
−0.981929 + 0.189251i \(0.939394\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 0.888835 1.53951i 0.888835 1.53951i
\(508\) 0 0
\(509\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −0.142315 + 0.989821i −0.142315 + 0.989821i
\(513\) −1.73154 + 2.43160i −1.73154 + 2.43160i
\(514\) −0.118239 + 0.258908i −0.118239 + 0.258908i
\(515\) 0 0
\(516\) 0.834408 + 0.0796763i 0.834408 + 0.0796763i
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −0.759713 0.876756i −0.759713 0.876756i 0.235759 0.971812i \(-0.424242\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(522\) 0 0
\(523\) 1.76962 + 0.912303i 1.76962 + 0.912303i 0.928368 + 0.371662i \(0.121212\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(524\) −0.0623191 1.30824i −0.0623191 1.30824i
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) −2.51614 1.61703i −2.51614 1.61703i
\(529\) −0.327068 0.945001i −0.327068 0.945001i
\(530\) 0 0
\(531\) −0.197238 + 0.0579143i −0.197238 + 0.0579143i
\(532\) 0 0
\(533\) 0 0
\(534\) −3.42800 0.660694i −3.42800 0.660694i
\(535\) 0 0
\(536\) −0.959493 0.281733i −0.959493 0.281733i
\(537\) 3.41133 3.41133
\(538\) 0 0
\(539\) 0.698939 + 1.53046i 0.698939 + 1.53046i
\(540\) 0 0
\(541\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) −1.32254 0.849945i −1.32254 0.849945i
\(545\) 0 0
\(546\) 0 0
\(547\) −0.452418 + 1.86489i −0.452418 + 1.86489i 0.0475819 + 0.998867i \(0.484848\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(548\) −0.0947329 1.98869i −0.0947329 1.98869i
\(549\) 0 0
\(550\) −0.239446 1.66538i −0.239446 1.66538i
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 0.995472 + 0.0950560i 0.995472 + 0.0950560i
\(557\) 0 0 0.723734 0.690079i \(-0.242424\pi\)
−0.723734 + 0.690079i \(0.757576\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 3.95564 2.54214i 3.95564 2.54214i
\(562\) 1.23576 + 0.971812i 1.23576 + 0.971812i
\(563\) −1.11312 0.326842i −1.11312 0.326842i −0.327068 0.945001i \(-0.606061\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(567\) 0 0
\(568\) 0 0
\(569\) 1.82318 0.351390i 1.82318 0.351390i 0.841254 0.540641i \(-0.181818\pi\)
0.981929 + 0.189251i \(0.0606061\pi\)
\(570\) 0 0
\(571\) −0.911911 1.28060i −0.911911 1.28060i −0.959493 0.281733i \(-0.909091\pi\)
0.0475819 0.998867i \(-0.484848\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) −2.07261 0.608574i −2.07261 0.608574i
\(577\) −1.54370 1.21398i −1.54370 1.21398i −0.888835 0.458227i \(-0.848485\pi\)
−0.654861 0.755750i \(-0.727273\pi\)
\(578\) 1.23792 0.795563i 1.23792 0.795563i
\(579\) −0.0720082 + 0.500828i −0.0720082 + 0.500828i
\(580\) 0 0
\(581\) 0 0
\(582\) −2.38880 + 2.27772i −2.38880 + 2.27772i
\(583\) 0 0
\(584\) −0.607279 + 1.75462i −0.607279 + 1.75462i
\(585\) 0 0
\(586\) 0 0
\(587\) 1.34378 + 1.28129i 1.34378 + 1.28129i 0.928368 + 0.371662i \(0.121212\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(588\) 1.16413 + 1.34347i 1.16413 + 1.34347i
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −1.84833 + 0.176494i −1.84833 + 0.176494i −0.959493 0.281733i \(-0.909091\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(594\) 2.27226 2.62233i 2.27226 2.62233i
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 −0.928368 0.371662i \(-0.878788\pi\)
0.928368 + 0.371662i \(0.121212\pi\)
\(600\) −0.738471 1.61703i −0.738471 1.61703i
\(601\) −0.642315 0.123796i −0.642315 0.123796i −0.142315 0.989821i \(-0.545455\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(602\) 0 0
\(603\) 0.897344 1.96491i 0.897344 1.96491i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 0 0 −0.928368 0.371662i \(-0.878788\pi\)
0.928368 + 0.371662i \(0.121212\pi\)
\(608\) −1.38884 + 0.407799i −1.38884 + 0.407799i
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 2.22386 2.56647i 2.22386 2.56647i
\(613\) 0 0 0.995472 0.0950560i \(-0.0303030\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(614\) 0.111165 0.458227i 0.111165 0.458227i
\(615\) 0 0
\(616\) 0 0
\(617\) 0.186393 + 1.29639i 0.186393 + 1.29639i 0.841254 + 0.540641i \(0.181818\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(618\) 0 0
\(619\) −1.44091 1.37391i −1.44091 1.37391i −0.786053 0.618159i \(-0.787879\pi\)
−0.654861 0.755750i \(-0.727273\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 0.415415 0.909632i 0.415415 0.909632i
\(626\) 0.839614 1.17907i 0.839614 1.17907i
\(627\) 0.616123 4.28523i 0.616123 4.28523i
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 0 0 0.0475819 0.998867i \(-0.484848\pi\)
−0.0475819 + 0.998867i \(0.515152\pi\)
\(632\) 0 0
\(633\) 1.74555 + 3.02337i 1.74555 + 3.02337i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 0.327068 0.566498i 0.327068 0.566498i −0.654861 0.755750i \(-0.727273\pi\)
0.981929 + 0.189251i \(0.0606061\pi\)
\(642\) −0.0702757 + 1.47527i −0.0702757 + 1.47527i
\(643\) −0.0913090 0.0268107i −0.0913090 0.0268107i 0.235759 0.971812i \(-0.424242\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0.323848 2.25241i 0.323848 2.25241i
\(647\) 0 0 0.580057 0.814576i \(-0.303030\pi\)
−0.580057 + 0.814576i \(0.696970\pi\)
\(648\) 0.625606 1.36989i 0.625606 1.36989i
\(649\) 0.115880 0.110491i 0.115880 0.110491i
\(650\) 0 0
\(651\) 0 0
\(652\) 0.514186 0.404360i 0.514186 0.404360i
\(653\) 0 0 0.928368 0.371662i \(-0.121212\pi\)
−0.928368 + 0.371662i \(0.878788\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0.186393 + 1.29639i 0.186393 + 1.29639i
\(657\) −3.56491 1.83784i −3.56491 1.83784i
\(658\) 0 0
\(659\) −0.235759 + 0.971812i −0.235759 + 0.971812i 0.723734 + 0.690079i \(0.242424\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(660\) 0 0
\(661\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(662\) 1.21769 + 0.782560i 1.21769 + 0.782560i
\(663\) 0 0
\(664\) −0.452418 1.86489i −0.452418 1.86489i
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 0.481929 + 1.05528i 0.481929 + 1.05528i 0.981929 + 0.189251i \(0.0606061\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(674\) −0.264241 0.105786i −0.264241 0.105786i
\(675\) 1.97876 0.581017i 1.97876 0.581017i
\(676\) 0.235759 + 0.971812i 0.235759 + 0.971812i
\(677\) 0 0 −0.327068 0.945001i \(-0.606061\pi\)
0.327068 + 0.945001i \(0.393939\pi\)
\(678\) −0.142315 0.0914602i −0.142315 0.0914602i
\(679\) 0 0
\(680\) 0 0
\(681\) 0.274150 1.13006i 0.274150 1.13006i
\(682\) 0 0
\(683\) 1.76962 + 0.912303i 1.76962 + 0.912303i 0.928368 + 0.371662i \(0.121212\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(684\) −0.444975 3.09487i −0.444975 3.09487i
\(685\) 0 0
\(686\) 0 0
\(687\) 0 0
\(688\) −0.370638 + 0.291473i −0.370638 + 0.291473i
\(689\) 0 0
\(690\) 0 0
\(691\) 0.601300 0.573338i 0.601300 0.573338i −0.327068 0.945001i \(-0.606061\pi\)
0.928368 + 0.371662i \(0.121212\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0.142315 0.989821i 0.142315 0.989821i
\(695\) 0 0
\(696\) 0 0
\(697\) −1.97562 0.580093i −1.97562 0.580093i
\(698\) 0 0
\(699\) −0.888835 + 1.53951i −0.888835 + 1.53951i
\(700\) 0 0
\(701\) 0 0 0.888835 0.458227i \(-0.151515\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 1.65210 0.318417i 1.65210 0.318417i
\(705\) 0 0
\(706\) −0.738471 + 0.380708i −0.738471 + 0.380708i
\(707\) 0 0
\(708\) 0.0845850 0.146505i 0.0845850 0.146505i
\(709\) 0 0 0.0475819 0.998867i \(-0.484848\pi\)
−0.0475819 + 0.998867i \(0.515152\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 1.65210 1.06174i 1.65210 1.06174i
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) −1.38884 + 1.32425i −1.38884 + 1.32425i
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 0.786053 0.618159i \(-0.212121\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −0.717180 0.827670i −0.717180 0.827670i
\(723\) −0.485482 3.37660i −0.485482 3.37660i
\(724\) 0 0
\(725\) 0 0
\(726\) −0.767304 + 3.16287i −0.767304 + 3.16287i
\(727\) 0 0 0.995472 0.0950560i \(-0.0303030\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(728\) 0 0
\(729\) −0.347444 0.223289i −0.347444 0.223289i
\(730\) 0 0
\(731\) −0.174762 0.720381i −0.174762 0.720381i
\(732\) 0 0
\(733\) 0 0 −0.928368 0.371662i \(-0.878788\pi\)
0.928368 + 0.371662i \(0.121212\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0.0800569 + 1.68060i 0.0800569 + 1.68060i
\(738\) −2.82915 −2.82915
\(739\) 0.0934441 + 0.0180099i 0.0934441 + 0.0180099i 0.235759 0.971812i \(-0.424242\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 −0.235759 0.971812i \(-0.575758\pi\)
0.235759 + 0.971812i \(0.424242\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 4.12646 0.394029i 4.12646 0.394029i
\(748\) −0.623601 + 2.57052i −0.623601 + 2.57052i
\(749\) 0 0
\(750\) 0 0
\(751\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(752\) 0 0
\(753\) 0.841586 + 0.802450i 0.841586 + 0.802450i
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 0 0 −0.995472 0.0950560i \(-0.969697\pi\)
0.995472 + 0.0950560i \(0.0303030\pi\)
\(758\) −0.947890 + 0.903811i −0.947890 + 0.903811i
\(759\) 0 0
\(760\) 0 0
\(761\) −0.118239 + 0.822373i −0.118239 + 0.822373i 0.841254 + 0.540641i \(0.181818\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 1.58006 0.814576i 1.58006 0.814576i
\(769\) −0.379436 0.532843i −0.379436 0.532843i 0.580057 0.814576i \(-0.303030\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(770\) 0 0
\(771\) 0.496834 0.0957569i 0.496834 0.0957569i
\(772\) −0.165101 0.231852i −0.165101 0.231852i
\(773\) 0 0 0.888835 0.458227i \(-0.151515\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(774\) −0.509266 0.882075i −0.509266 0.882075i
\(775\) 0 0
\(776\) 0.0883470 1.85463i 0.0883470 1.85463i
\(777\) 0 0
\(778\) 0 0
\(779\) −1.59483 + 1.02494i −1.59483 + 1.02494i
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) −0.995472 0.0950560i −0.995472 0.0950560i
\(785\) 0 0
\(786\) −1.83013 + 1.43923i −1.83013 + 1.43923i
\(787\) 0.771316 0.308788i 0.771316 0.308788i 0.0475819 0.998867i \(-0.484848\pi\)
0.723734 + 0.690079i \(0.242424\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0.172932 + 3.63029i 0.172932 + 3.63029i
\(793\) 0 0
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 0 0 −0.327068 0.945001i \(-0.606061\pi\)
0.327068 + 0.945001i \(0.393939\pi\)