Properties

Label 536.1.ba.a.19.1
Level $536$
Weight $1$
Character 536.19
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 19.1
Root \(0.0475819 + 0.998867i\) of defining polynomial
Character \(\chi\) \(=\) 536.19
Dual form 536.1.ba.a.395.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.888835 - 0.458227i) q^{2} +(-1.78153 + 0.523103i) q^{3} +(0.580057 + 0.814576i) q^{4} +(1.82318 + 0.351390i) q^{6} +(-0.142315 - 0.989821i) q^{8} +(2.05894 - 1.32320i) q^{9} +O(q^{10})\) \(q+(-0.888835 - 0.458227i) q^{2} +(-1.78153 + 0.523103i) q^{3} +(0.580057 + 0.814576i) q^{4} +(1.82318 + 0.351390i) q^{6} +(-0.142315 - 0.989821i) q^{8} +(2.05894 - 1.32320i) q^{9} +(-0.279486 + 0.0538665i) q^{11} +(-1.45949 - 1.14776i) q^{12} +(-0.327068 + 0.945001i) q^{16} +(-1.15486 + 1.62177i) q^{17} +(-2.43639 + 0.232647i) q^{18} +(-0.0311250 + 0.653395i) q^{19} +(0.273100 + 0.0801894i) q^{22} +(0.771316 + 1.68895i) q^{24} +(-0.142315 + 0.989821i) q^{25} +(-1.75998 + 2.03113i) q^{27} +(0.723734 - 0.690079i) q^{32} +(0.469734 - 0.242165i) q^{33} +(1.76962 - 0.912303i) q^{34} +(2.27215 + 0.909632i) q^{36} +(0.327068 - 0.566498i) q^{38} +(-1.67489 - 0.159932i) q^{41} +(0.815816 + 1.78639i) q^{43} +(-0.205996 - 0.196417i) q^{44} +(0.0883470 - 1.85463i) q^{48} +(-0.995472 + 0.0950560i) q^{49} +(0.580057 - 0.814576i) q^{50} +(1.20906 - 3.49334i) q^{51} +(2.49505 - 0.998867i) q^{54} +(-0.286343 - 1.18032i) q^{57} +(0.223734 + 1.55610i) q^{59} +(-0.959493 + 0.281733i) q^{64} -0.528482 q^{66} +(-0.654861 - 0.755750i) q^{67} -1.99094 q^{68} +(-1.60275 - 1.84967i) q^{72} +(1.13915 + 0.219553i) q^{73} +(-0.264241 - 1.83784i) q^{75} +(-0.550294 + 0.353653i) q^{76} +(1.05625 - 2.31286i) q^{81} +(1.41542 + 0.909632i) q^{82} +(0.428368 - 1.23769i) q^{83} +(0.0934441 - 1.96163i) q^{86} +(0.0930932 + 0.268975i) q^{88} +(1.70566 + 0.500828i) q^{89} +(-0.928368 + 1.60798i) q^{96} +(-0.580057 - 1.00469i) q^{97} +(0.928368 + 0.371662i) q^{98} +(-0.504169 + 0.480724i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20q + q^{2} + 2q^{3} + q^{4} - q^{6} - 2q^{8} + O(q^{10}) \) \( 20q + q^{2} + 2q^{3} + q^{4} - q^{6} - 2q^{8} + 2q^{11} - 12q^{12} + q^{16} - 12q^{17} - q^{19} - 4q^{22} + 2q^{24} - 2q^{25} - 2q^{27} + q^{32} - 2q^{33} - q^{34} - q^{38} + 2q^{41} + 2q^{43} + 2q^{44} - q^{48} + q^{49} + q^{50} + q^{51} + 23q^{54} + q^{57} - 9q^{59} - 2q^{64} - 18q^{66} - 2q^{67} + 2q^{68} - q^{73} - 9q^{75} + 2q^{76} + 2q^{81} + 18q^{82} - 9q^{83} - q^{86} + 2q^{88} + 2q^{89} - q^{96} - q^{97} + q^{98} + O(q^{100}) \)

Character values

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

\(n\) \(135\) \(269\) \(337\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{5}{33}\right)\)

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
\(3\) −1.78153 + 0.523103i −1.78153 + 0.523103i −0.995472 0.0950560i \(-0.969697\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(4\) 0.580057 + 0.814576i 0.580057 + 0.814576i
\(5\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(6\) 1.82318 + 0.351390i 1.82318 + 0.351390i
\(7\) 0 0 −0.0475819 0.998867i \(-0.515152\pi\)
0.0475819 + 0.998867i \(0.484848\pi\)
\(8\) −0.142315 0.989821i −0.142315 0.989821i
\(9\) 2.05894 1.32320i 2.05894 1.32320i
\(10\) 0 0
\(11\) −0.279486 + 0.0538665i −0.279486 + 0.0538665i −0.327068 0.945001i \(-0.606061\pi\)
0.0475819 + 0.998867i \(0.484848\pi\)
\(12\) −1.45949 1.14776i −1.45949 1.14776i
\(13\) 0 0 0.928368 0.371662i \(-0.121212\pi\)
−0.928368 + 0.371662i \(0.878788\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −0.327068 + 0.945001i −0.327068 + 0.945001i
\(17\) −1.15486 + 1.62177i −1.15486 + 1.62177i −0.500000 + 0.866025i \(0.666667\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(18\) −2.43639 + 0.232647i −2.43639 + 0.232647i
\(19\) −0.0311250 + 0.653395i −0.0311250 + 0.653395i 0.928368 + 0.371662i \(0.121212\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0.273100 + 0.0801894i 0.273100 + 0.0801894i
\(23\) 0 0 −0.723734 0.690079i \(-0.757576\pi\)
0.723734 + 0.690079i \(0.242424\pi\)
\(24\) 0.771316 + 1.68895i 0.771316 + 1.68895i
\(25\) −0.142315 + 0.989821i −0.142315 + 0.989821i
\(26\) 0 0
\(27\) −1.75998 + 2.03113i −1.75998 + 2.03113i
\(28\) 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 −0.928368 0.371662i \(-0.878788\pi\)
0.928368 + 0.371662i \(0.121212\pi\)
\(32\) 0.723734 0.690079i 0.723734 0.690079i
\(33\) 0.469734 0.242165i 0.469734 0.242165i
\(34\) 1.76962 0.912303i 1.76962 0.912303i
\(35\) 0 0
\(36\) 2.27215 + 0.909632i 2.27215 + 0.909632i
\(37\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(38\) 0.327068 0.566498i 0.327068 0.566498i
\(39\) 0 0
\(40\) 0 0
\(41\) −1.67489 0.159932i −1.67489 0.159932i −0.786053 0.618159i \(-0.787879\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(42\) 0 0
\(43\) 0.815816 + 1.78639i 0.815816 + 1.78639i 0.580057 + 0.814576i \(0.303030\pi\)
0.235759 + 0.971812i \(0.424242\pi\)
\(44\) −0.205996 0.196417i −0.205996 0.196417i
\(45\) 0 0
\(46\) 0 0
\(47\) 0 0 0.235759 0.971812i \(-0.424242\pi\)
−0.235759 + 0.971812i \(0.575758\pi\)
\(48\) 0.0883470 1.85463i 0.0883470 1.85463i
\(49\) −0.995472 + 0.0950560i −0.995472 + 0.0950560i
\(50\) 0.580057 0.814576i 0.580057 0.814576i
\(51\) 1.20906 3.49334i 1.20906 3.49334i
\(52\) 0 0
\(53\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(54\) 2.49505 0.998867i 2.49505 0.998867i
\(55\) 0 0
\(56\) 0 0
\(57\) −0.286343 1.18032i −0.286343 1.18032i
\(58\) 0 0
\(59\) 0.223734 + 1.55610i 0.223734 + 1.55610i 0.723734 + 0.690079i \(0.242424\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(60\) 0 0
\(61\) 0 0 −0.981929 0.189251i \(-0.939394\pi\)
0.981929 + 0.189251i \(0.0606061\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) −0.959493 + 0.281733i −0.959493 + 0.281733i
\(65\) 0 0
\(66\) −0.528482 −0.528482
\(67\) −0.654861 0.755750i −0.654861 0.755750i
\(68\) −1.99094 −1.99094
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 −0.580057 0.814576i \(-0.696970\pi\)
0.580057 + 0.814576i \(0.303030\pi\)
\(72\) −1.60275 1.84967i −1.60275 1.84967i
\(73\) 1.13915 + 0.219553i 1.13915 + 0.219553i 0.723734 0.690079i \(-0.242424\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(74\) 0 0
\(75\) −0.264241 1.83784i −0.264241 1.83784i
\(76\) −0.550294 + 0.353653i −0.550294 + 0.353653i
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 −0.786053 0.618159i \(-0.787879\pi\)
0.786053 + 0.618159i \(0.212121\pi\)
\(80\) 0 0
\(81\) 1.05625 2.31286i 1.05625 2.31286i
\(82\) 1.41542 + 0.909632i 1.41542 + 0.909632i
\(83\) 0.428368 1.23769i 0.428368 1.23769i −0.500000 0.866025i \(-0.666667\pi\)
0.928368 0.371662i \(-0.121212\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0.0934441 1.96163i 0.0934441 1.96163i
\(87\) 0 0
\(88\) 0.0930932 + 0.268975i 0.0930932 + 0.268975i
\(89\) 1.70566 + 0.500828i 1.70566 + 0.500828i 0.981929 0.189251i \(-0.0606061\pi\)
0.723734 + 0.690079i \(0.242424\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) −0.928368 + 1.60798i −0.928368 + 1.60798i
\(97\) −0.580057 1.00469i −0.580057 1.00469i −0.995472 0.0950560i \(-0.969697\pi\)
0.415415 0.909632i \(-0.363636\pi\)
\(98\) 0.928368 + 0.371662i 0.928368 + 0.371662i
\(99\) −0.504169 + 0.480724i −0.504169 + 0.480724i
\(100\) −0.888835 + 0.458227i −0.888835 + 0.458227i
\(101\) 0 0 0.888835 0.458227i \(-0.151515\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(102\) −2.67540 + 2.55099i −2.67540 + 2.55099i
\(103\) 0 0 −0.928368 0.371662i \(-0.878788\pi\)
0.928368 + 0.371662i \(0.121212\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 1.25667 1.45027i 1.25667 1.45027i 0.415415 0.909632i \(-0.363636\pi\)
0.841254 0.540641i \(-0.181818\pi\)
\(108\) −2.67540 0.255469i −2.67540 0.255469i
\(109\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 0.514186 + 1.48564i 0.514186 + 1.48564i 0.841254 + 0.540641i \(0.181818\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(114\) −0.286343 + 1.18032i −0.286343 + 1.18032i
\(115\) 0 0
\(116\) 0 0
\(117\) 0 0
\(118\) 0.514186 1.48564i 0.514186 1.48564i
\(119\) 0 0
\(120\) 0 0
\(121\) −0.853157 + 0.341553i −0.853157 + 0.341553i
\(122\) 0 0
\(123\) 3.06752 0.591215i 3.06752 0.591215i
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 0 0 −0.0475819 0.998867i \(-0.515152\pi\)
0.0475819 + 0.998867i \(0.484848\pi\)
\(128\) 0.981929 + 0.189251i 0.981929 + 0.189251i
\(129\) −2.38786 2.75574i −2.38786 2.75574i
\(130\) 0 0
\(131\) −1.61435 + 0.474017i −1.61435 + 0.474017i −0.959493 0.281733i \(-0.909091\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(132\) 0.469734 + 0.242165i 0.469734 + 0.242165i
\(133\) 0 0
\(134\) 0.235759 + 0.971812i 0.235759 + 0.971812i
\(135\) 0 0
\(136\) 1.76962 + 0.912303i 1.76962 + 0.912303i
\(137\) −0.452418 + 0.132842i −0.452418 + 0.132842i −0.500000 0.866025i \(-0.666667\pi\)
0.0475819 + 0.998867i \(0.484848\pi\)
\(138\) 0 0
\(139\) 0.654861 + 0.755750i 0.654861 + 0.755750i 0.981929 0.189251i \(-0.0606061\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) 0.577012 + 2.37848i 0.577012 + 2.37848i
\(145\) 0 0
\(146\) −0.911911 0.717135i −0.911911 0.717135i
\(147\) 1.72373 0.690079i 1.72373 0.690079i
\(148\) 0 0
\(149\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(150\) −0.607279 + 1.75462i −0.607279 + 1.75462i
\(151\) 0 0 0.580057 0.814576i \(-0.303030\pi\)
−0.580057 + 0.814576i \(0.696970\pi\)
\(152\) 0.651174 0.0621796i 0.651174 0.0621796i
\(153\) −0.231856 + 4.86725i −0.231856 + 4.86725i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 0 0 −0.723734 0.690079i \(-0.757576\pi\)
0.723734 + 0.690079i \(0.242424\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) −1.99864 + 1.57175i −1.99864 + 1.57175i
\(163\) −0.0475819 + 0.0824143i −0.0475819 + 0.0824143i −0.888835 0.458227i \(-0.848485\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(164\) −0.841254 1.45709i −0.841254 1.45709i
\(165\) 0 0
\(166\) −0.947890 + 0.903811i −0.947890 + 0.903811i
\(167\) 0 0 0.888835 0.458227i \(-0.151515\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(168\) 0 0
\(169\) 0.723734 0.690079i 0.723734 0.690079i
\(170\) 0 0
\(171\) 0.800488 + 1.38649i 0.800488 + 1.38649i
\(172\) −0.981929 + 1.70075i −0.981929 + 1.70075i
\(173\) 0 0 0.786053 0.618159i \(-0.212121\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0.0405070 0.281733i 0.0405070 0.281733i
\(177\) −1.21259 2.65520i −1.21259 2.65520i
\(178\) −1.28656 1.22673i −1.28656 1.22673i
\(179\) 1.25667 + 0.368991i 1.25667 + 0.368991i 0.841254 0.540641i \(-0.181818\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(180\) 0 0
\(181\) 0 0 0.235759 0.971812i \(-0.424242\pi\)
−0.235759 + 0.971812i \(0.575758\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 0.235408 0.515472i 0.235408 0.515472i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 0 0 −0.235759 0.971812i \(-0.575758\pi\)
0.235759 + 0.971812i \(0.424242\pi\)
\(192\) 1.56199 1.00383i 1.56199 1.00383i
\(193\) −0.118239 0.822373i −0.118239 0.822373i −0.959493 0.281733i \(-0.909091\pi\)
0.841254 0.540641i \(-0.181818\pi\)
\(194\) 0.0552004 + 1.15880i 0.0552004 + 1.15880i
\(195\) 0 0
\(196\) −0.654861 0.755750i −0.654861 0.755750i
\(197\) 0 0 −0.580057 0.814576i \(-0.696970\pi\)
0.580057 + 0.814576i \(0.303030\pi\)
\(198\) 0.668404 0.196261i 0.668404 0.196261i
\(199\) 0 0 −0.888835 0.458227i \(-0.848485\pi\)
0.888835 + 0.458227i \(0.151515\pi\)
\(200\) 1.00000 1.00000
\(201\) 1.56199 + 1.00383i 1.56199 + 1.00383i
\(202\) 0 0
\(203\) 0 0
\(204\) 3.54692 1.04147i 3.54692 1.04147i
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −0.0264971 0.184291i −0.0264971 0.184291i
\(210\) 0 0
\(211\) −0.419102 1.72756i −0.419102 1.72756i −0.654861 0.755750i \(-0.727273\pi\)
0.235759 0.971812i \(-0.424242\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) −1.78153 + 0.713215i −1.78153 + 0.713215i
\(215\) 0 0
\(216\) 2.26092 + 1.45301i 2.26092 + 1.45301i
\(217\) 0 0
\(218\) 0 0
\(219\) −2.14427 + 0.204753i −2.14427 + 0.204753i
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(224\) 0 0
\(225\) 1.01671 + 2.22630i 1.01671 + 2.22630i
\(226\) 0.223734 1.55610i 0.223734 1.55610i
\(227\) −0.0947329 0.00904590i −0.0947329 0.00904590i 0.0475819 0.998867i \(-0.484848\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(228\) 0.795366 0.917901i 0.795366 0.917901i
\(229\) 0 0 0.786053 0.618159i \(-0.212121\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −0.723734 + 0.690079i −0.723734 + 0.690079i −0.959493 0.281733i \(-0.909091\pi\)
0.235759 + 0.971812i \(0.424242\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) −1.13779 + 1.08488i −1.13779 + 1.08488i
\(237\) 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
\(241\) 0.857685 0.989821i 0.857685 0.989821i −0.142315 0.989821i \(-0.545455\pi\)
1.00000 \(0\)
\(242\) 0.914825 + 0.0873552i 0.914825 + 0.0873552i
\(243\) −0.289387 + 2.01273i −0.289387 + 2.01273i
\(244\) 0 0
\(245\) 0 0
\(246\) −2.99743 0.880124i −2.99743 0.880124i
\(247\) 0 0
\(248\) 0 0
\(249\) −0.115710 + 2.42905i −0.115710 + 2.42905i
\(250\) 0 0
\(251\) 0.0552004 0.0775182i 0.0552004 0.0775182i −0.786053 0.618159i \(-0.787879\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) −0.786053 0.618159i −0.786053 0.618159i
\(257\) 0.815816 0.157236i 0.815816 0.157236i 0.235759 0.971812i \(-0.424242\pi\)
0.580057 + 0.814576i \(0.303030\pi\)
\(258\) 0.859663 + 3.54358i 0.859663 + 3.54358i
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) 1.65210 + 0.318417i 1.65210 + 0.318417i
\(263\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(264\) −0.306550 0.430489i −0.306550 0.430489i
\(265\) 0 0
\(266\) 0 0
\(267\) −3.30067 −3.30067
\(268\) 0.235759 0.971812i 0.235759 0.971812i
\(269\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(270\) 0 0
\(271\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(272\) −1.15486 1.62177i −1.15486 1.62177i
\(273\) 0 0
\(274\) 0.462997 + 0.0892353i 0.462997 + 0.0892353i
\(275\) −0.0135432 0.284307i −0.0135432 0.284307i
\(276\) 0 0
\(277\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(278\) −0.235759 0.971812i −0.235759 0.971812i
\(279\) 0 0
\(280\) 0 0
\(281\) −1.84833 + 0.739959i −1.84833 + 0.739959i −0.888835 + 0.458227i \(0.848485\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(282\) 0 0
\(283\) −0.841254 0.540641i −0.841254 0.540641i 0.0475819 0.998867i \(-0.484848\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0.577012 2.37848i 0.577012 2.37848i
\(289\) −0.969383 2.80085i −0.969383 2.80085i
\(290\) 0 0
\(291\) 1.55894 + 1.48645i 1.55894 + 1.48645i
\(292\) 0.481929 + 1.05528i 0.481929 + 1.05528i
\(293\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(294\) −1.84833 0.176494i −1.84833 0.176494i
\(295\) 0 0
\(296\) 0 0
\(297\) 0.382481 0.662476i 0.382481 0.662476i
\(298\) 0 0
\(299\) 0 0
\(300\) 1.34378 1.28129i 1.34378 1.28129i
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) −0.607279 0.243118i −0.607279 0.243118i
\(305\) 0 0
\(306\) 2.43639 4.21994i 2.43639 4.21994i
\(307\) −1.54370 + 1.21398i −1.54370 + 1.21398i −0.654861 + 0.755750i \(0.727273\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(312\) 0 0
\(313\) 0.627639 + 0.184291i 0.627639 + 0.184291i 0.580057 0.814576i \(-0.303030\pi\)
0.0475819 + 0.998867i \(0.484848\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 0 0 0.995472 0.0950560i \(-0.0303030\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) −1.48014 + 3.24106i −1.48014 + 3.24106i
\(322\) 0 0
\(323\) −1.02371 0.805058i −1.02371 0.805058i
\(324\) 2.49668 0.481196i 2.49668 0.481196i
\(325\) 0 0
\(326\) 0.0800569 0.0514495i 0.0800569 0.0514495i
\(327\) 0 0
\(328\) 0.0800569 + 1.68060i 0.0800569 + 1.68060i
\(329\) 0 0
\(330\) 0 0
\(331\) −0.379436 0.532843i −0.379436 0.532843i 0.580057 0.814576i \(-0.303030\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(332\) 1.25667 0.368991i 1.25667 0.368991i
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −0.738471 0.380708i −0.738471 0.380708i 0.0475819 0.998867i \(-0.484848\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(338\) −0.959493 + 0.281733i −0.959493 + 0.281733i
\(339\) −1.69318 2.37774i −1.69318 2.37774i
\(340\) 0 0
\(341\) 0 0
\(342\) −0.0761775 1.59916i −0.0761775 1.59916i
\(343\) 0 0
\(344\) 1.65210 1.06174i 1.65210 1.06174i
\(345\) 0 0
\(346\) 0 0
\(347\) 0.786053 + 0.618159i 0.786053 + 0.618159i 0.928368 0.371662i \(-0.121212\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(348\) 0 0
\(349\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −0.165101 + 0.231852i −0.165101 + 0.231852i
\(353\) 1.91030 0.182411i 1.91030 0.182411i 0.928368 0.371662i \(-0.121212\pi\)
0.981929 + 0.189251i \(0.0606061\pi\)
\(354\) −0.138891 + 2.91568i −0.138891 + 2.91568i
\(355\) 0 0
\(356\) 0.581419 + 1.67990i 0.581419 + 1.67990i
\(357\) 0 0
\(358\) −0.947890 0.903811i −0.947890 0.903811i
\(359\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(360\) 0 0
\(361\) 0.569516 + 0.0543822i 0.569516 + 0.0543822i
\(362\) 0 0
\(363\) 1.34125 1.05477i 1.34125 1.05477i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 0 0 0.723734 0.690079i \(-0.242424\pi\)
−0.723734 + 0.690079i \(0.757576\pi\)
\(368\) 0 0
\(369\) −3.66012 + 1.88692i −3.66012 + 1.88692i
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(374\) −0.445442 + 0.350299i −0.445442 + 0.350299i
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 1.21769 + 1.16106i 1.21769 + 1.16106i 0.981929 + 0.189251i \(0.0606061\pi\)
0.235759 + 0.971812i \(0.424242\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 0 0 0.0475819 0.998867i \(-0.484848\pi\)
−0.0475819 + 0.998867i \(0.515152\pi\)
\(384\) −1.84833 + 0.176494i −1.84833 + 0.176494i
\(385\) 0 0
\(386\) −0.271738 + 0.785135i −0.271738 + 0.785135i
\(387\) 4.04347 + 2.59858i 4.04347 + 2.59858i
\(388\) 0.481929 1.05528i 0.481929 1.05528i
\(389\) 0 0 0.928368 0.371662i \(-0.121212\pi\)
−0.928368 + 0.371662i \(0.878788\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0.235759 + 0.971812i 0.235759 + 0.971812i
\(393\) 2.62805 1.68895i 2.62805 1.68895i
\(394\) 0 0
\(395\) 0 0
\(396\) −0.684033 0.131837i −0.684033 0.131837i
\(397\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) −0.888835 0.458227i −0.888835 0.458227i
\(401\) 0.830830 0.830830 0.415415 0.909632i \(-0.363636\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(402\) −0.928368 1.60798i −0.928368 1.60798i
\(403\) 0 0
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) −3.62985 0.699597i −3.62985 0.699597i
\(409\) −0.0913090 1.91681i −0.0913090 1.91681i −0.327068 0.945001i \(-0.606061\pi\)
0.235759 0.971812i \(-0.424242\pi\)
\(410\) 0 0
\(411\) 0.736504 0.473322i 0.736504 0.473322i
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −1.56199 1.00383i −1.56199 1.00383i
\(418\) −0.0608956 + 0.175946i −0.0608956 + 0.175946i
\(419\) 0.672932 0.945001i 0.672932 0.945001i −0.327068 0.945001i \(-0.606061\pi\)
1.00000 \(0\)
\(420\) 0 0
\(421\) 0 0 0.0475819 0.998867i \(-0.484848\pi\)
−0.0475819 + 0.998867i \(0.515152\pi\)
\(422\) −0.419102 + 1.72756i −0.419102 + 1.72756i
\(423\) 0 0
\(424\) 0 0
\(425\) −1.44091 1.37391i −1.44091 1.37391i
\(426\) 0 0
\(427\) 0 0
\(428\) 1.91030 + 0.182411i 1.91030 + 0.182411i
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(432\) −1.34378 2.32750i −1.34378 2.32750i
\(433\) 0.437742 + 0.175245i 0.437742 + 0.175245i 0.580057 0.814576i \(-0.303030\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) 1.99973 + 0.800570i 1.99973 + 0.800570i
\(439\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(440\) 0 0
\(441\) −1.92384 + 1.51292i −1.92384 + 1.51292i
\(442\) 0 0
\(443\) 1.98193 + 0.189251i 1.98193 + 0.189251i 1.00000 \(0\)
0.981929 + 0.189251i \(0.0606061\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −0.0671040 + 0.276606i −0.0671040 + 0.276606i −0.995472 0.0950560i \(-0.969697\pi\)
0.928368 + 0.371662i \(0.121212\pi\)
\(450\) 0.116455 2.44470i 0.116455 2.44470i
\(451\) 0.476723 0.0455215i 0.476723 0.0455215i
\(452\) −0.911911 + 1.28060i −0.911911 + 1.28060i
\(453\) 0 0
\(454\) 0.0800569 + 0.0514495i 0.0800569 + 0.0514495i
\(455\) 0 0
\(456\) −1.12756 + 0.451405i −1.12756 + 0.451405i
\(457\) 1.39734 + 1.09888i 1.39734 + 1.09888i 0.981929 + 0.189251i \(0.0606061\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(458\) 0 0
\(459\) −1.26150 5.19996i −1.26150 5.19996i
\(460\) 0 0
\(461\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(462\) 0 0
\(463\) 0 0 −0.981929 0.189251i \(-0.939394\pi\)
0.981929 + 0.189251i \(0.0606061\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0.959493 0.281733i 0.959493 0.281733i
\(467\) 0.252989 + 0.130425i 0.252989 + 0.130425i 0.580057 0.814576i \(-0.303030\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 1.50842 0.442913i 1.50842 0.442913i
\(473\) −0.324236 0.455325i −0.324236 0.455325i
\(474\) 0 0
\(475\) −0.642315 0.123796i −0.642315 0.123796i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 0 0 −0.235759 0.971812i \(-0.575758\pi\)
0.235759 + 0.971812i \(0.424242\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) −1.21590 + 0.486774i −1.21590 + 0.486774i
\(483\) 0 0
\(484\) −0.773100 0.496841i −0.773100 0.496841i
\(485\) 0 0
\(486\) 1.17951 1.65638i 1.17951 1.65638i
\(487\) 0 0 0.995472 0.0950560i \(-0.0303030\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(488\) 0 0
\(489\) 0.0416572 0.171713i 0.0416572 0.171713i
\(490\) 0 0
\(491\) 0.959493 + 0.281733i 0.959493 + 0.281733i 0.723734 0.690079i \(-0.242424\pi\)
0.235759 + 0.971812i \(0.424242\pi\)
\(492\) 2.26092 + 2.15579i 2.26092 + 2.15579i
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 1.21590 2.10601i 1.21590 2.10601i
\(499\) −0.723734 1.25354i −0.723734 1.25354i −0.959493 0.281733i \(-0.909091\pi\)
0.235759 0.971812i \(-0.424242\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) −0.0845850 + 0.0436066i −0.0845850 + 0.0436066i
\(503\) 0 0 0.888835 0.458227i \(-0.151515\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −0.928368 + 1.60798i −0.928368 + 1.60798i
\(508\) 0 0
\(509\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0.415415 + 0.909632i 0.415415 + 0.909632i
\(513\) −1.27235 1.21318i −1.27235 1.21318i
\(514\) −0.797176 0.234072i −0.797176 0.234072i
\(515\) 0 0
\(516\) 0.859663 3.54358i 0.859663 3.54358i
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 1.21769 + 0.782560i 1.21769 + 0.782560i 0.981929 0.189251i \(-0.0606061\pi\)
0.235759 + 0.971812i \(0.424242\pi\)
\(522\) 0 0
\(523\) 0.437742 0.175245i 0.437742 0.175245i −0.142315 0.989821i \(-0.545455\pi\)
0.580057 + 0.814576i \(0.303030\pi\)
\(524\) −1.32254 1.04006i −1.32254 1.04006i
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 0.0752108 + 0.523103i 0.0752108 + 0.523103i
\(529\) 0.0475819 + 0.998867i 0.0475819 + 0.998867i
\(530\) 0 0
\(531\) 2.51969 + 2.90788i 2.51969 + 2.90788i
\(532\) 0 0
\(533\) 0 0
\(534\) 2.93375 + 1.51245i 2.93375 + 1.51245i
\(535\) 0 0
\(536\) −0.654861 + 0.755750i −0.654861 + 0.755750i
\(537\) −2.43181 −2.43181
\(538\) 0 0
\(539\) 0.273100 0.0801894i 0.273100 0.0801894i
\(540\) 0 0
\(541\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0.283341 + 1.97068i 0.283341 + 1.97068i
\(545\) 0 0
\(546\) 0 0
\(547\) −1.28605 + 0.247866i −1.28605 + 0.247866i −0.786053 0.618159i \(-0.787879\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(548\) −0.370638 0.291473i −0.370638 0.291473i
\(549\) 0 0
\(550\) −0.118239 + 0.258908i −0.118239 + 0.258908i
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) −0.235759 + 0.971812i −0.235759 + 0.971812i
\(557\) 0 0 −0.327068 0.945001i \(-0.606061\pi\)
0.327068 + 0.945001i \(0.393939\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) −0.149741 + 1.04147i −0.149741 + 1.04147i
\(562\) 1.98193 + 0.189251i 1.98193 + 0.189251i
\(563\) −0.947890 + 1.09392i −0.947890 + 1.09392i 0.0475819 + 0.998867i \(0.484848\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(567\) 0 0
\(568\) 0 0
\(569\) −1.03115 + 0.531595i −1.03115 + 0.531595i −0.888835 0.458227i \(-0.848485\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(570\) 0 0
\(571\) −1.44091 + 1.37391i −1.44091 + 1.37391i −0.654861 + 0.755750i \(0.727273\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) −1.60275 + 1.84967i −1.60275 + 1.84967i
\(577\) 1.76962 + 0.168978i 1.76962 + 0.168978i 0.928368 0.371662i \(-0.121212\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(578\) −0.421801 + 2.93369i −0.421801 + 2.93369i
\(579\) 0.640832 + 1.40323i 0.640832 + 1.40323i
\(580\) 0 0
\(581\) 0 0
\(582\) −0.704513 2.03556i −0.704513 2.03556i
\(583\) 0 0
\(584\) 0.0552004 1.15880i 0.0552004 1.15880i
\(585\) 0 0
\(586\) 0 0
\(587\) −0.379436 + 1.09631i −0.379436 + 1.09631i 0.580057 + 0.814576i \(0.303030\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(588\) 1.56199 + 1.00383i 1.56199 + 1.00383i
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 0.273507 + 1.12741i 0.273507 + 1.12741i 0.928368 + 0.371662i \(0.121212\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(594\) −0.643526 + 0.413569i −0.643526 + 0.413569i
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 −0.580057 0.814576i \(-0.696970\pi\)
0.580057 + 0.814576i \(0.303030\pi\)
\(600\) −1.78153 + 0.523103i −1.78153 + 0.523103i
\(601\) −0.0845850 0.0436066i −0.0845850 0.0436066i 0.415415 0.909632i \(-0.363636\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(602\) 0 0
\(603\) −2.34833 0.689531i −2.34833 0.689531i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 0 0 −0.580057 0.814576i \(-0.696970\pi\)
0.580057 + 0.814576i \(0.303030\pi\)
\(608\) 0.428368 + 0.494363i 0.428368 + 0.494363i
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) −4.09924 + 2.63442i −4.09924 + 2.63442i
\(613\) 0 0 −0.235759 0.971812i \(-0.575758\pi\)
0.235759 + 0.971812i \(0.424242\pi\)
\(614\) 1.92837 0.371662i 1.92837 0.371662i
\(615\) 0 0
\(616\) 0 0
\(617\) 0.698939 1.53046i 0.698939 1.53046i −0.142315 0.989821i \(-0.545455\pi\)
0.841254 0.540641i \(-0.181818\pi\)
\(618\) 0 0
\(619\) −0.154218 + 0.445585i −0.154218 + 0.445585i −0.995472 0.0950560i \(-0.969697\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −0.959493 0.281733i −0.959493 0.281733i
\(626\) −0.473420 0.451405i −0.473420 0.451405i
\(627\) 0.143609 + 0.314459i 0.143609 + 0.314459i
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 0 0 0.786053 0.618159i \(-0.212121\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(632\) 0 0
\(633\) 1.65033 + 2.85846i 1.65033 + 2.85846i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −0.0475819 + 0.0824143i −0.0475819 + 0.0824143i −0.888835 0.458227i \(-0.848485\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(642\) 2.80075 2.20253i 2.80075 2.20253i
\(643\) 1.02951 1.18812i 1.02951 1.18812i 0.0475819 0.998867i \(-0.484848\pi\)
0.981929 0.189251i \(-0.0606061\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0.541015 + 1.18466i 0.541015 + 1.18466i
\(647\) 0 0 −0.723734 0.690079i \(-0.757576\pi\)
0.723734 + 0.690079i \(0.242424\pi\)
\(648\) −2.43964 0.716342i −2.43964 0.716342i
\(649\) −0.146352 0.422858i −0.146352 0.422858i
\(650\) 0 0
\(651\) 0 0
\(652\) −0.0947329 + 0.00904590i −0.0947329 + 0.00904590i
\(653\) 0 0 0.580057 0.814576i \(-0.303030\pi\)
−0.580057 + 0.814576i \(0.696970\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0.698939 1.53046i 0.698939 1.53046i
\(657\) 2.63595 1.05528i 2.63595 1.05528i
\(658\) 0 0
\(659\) −0.981929 + 0.189251i −0.981929 + 0.189251i −0.654861 0.755750i \(-0.727273\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(660\) 0 0
\(661\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(662\) 0.0930932 + 0.647478i 0.0930932 + 0.647478i
\(663\) 0 0
\(664\) −1.28605 0.247866i −1.28605 0.247866i
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) −1.38884 + 0.407799i −1.38884 + 0.407799i −0.888835 0.458227i \(-0.848485\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(674\) 0.481929 + 0.676774i 0.481929 + 0.676774i
\(675\) −1.75998 2.03113i −1.75998 2.03113i
\(676\) 0.981929 + 0.189251i 0.981929 + 0.189251i
\(677\) 0 0 −0.0475819 0.998867i \(-0.515152\pi\)
0.0475819 + 0.998867i \(0.484848\pi\)
\(678\) 0.415415 + 2.88927i 0.415415 + 2.88927i
\(679\) 0 0
\(680\) 0 0
\(681\) 0.173501 0.0334396i 0.173501 0.0334396i
\(682\) 0 0
\(683\) 0.437742 0.175245i 0.437742 0.175245i −0.142315 0.989821i \(-0.545455\pi\)
0.580057 + 0.814576i \(0.303030\pi\)
\(684\) −0.665070 + 1.45630i −0.665070 + 1.45630i
\(685\) 0 0
\(686\) 0 0
\(687\) 0 0
\(688\) −1.95496 + 0.186677i −1.95496 + 0.186677i
\(689\) 0 0
\(690\) 0 0
\(691\) 0.627639 + 1.81344i 0.627639 + 1.81344i 0.580057 + 0.814576i \(0.303030\pi\)
0.0475819 + 0.998867i \(0.484848\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) −0.415415 0.909632i −0.415415 0.909632i
\(695\) 0 0
\(696\) 0 0
\(697\) 2.19364 2.53159i 2.19364 2.53159i
\(698\) 0 0
\(699\) 0.928368 1.60798i 0.928368 1.60798i
\(700\) 0 0
\(701\) 0 0 −0.928368 0.371662i \(-0.878788\pi\)
0.928368 + 0.371662i \(0.121212\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0.252989 0.130425i 0.252989 0.130425i
\(705\) 0 0
\(706\) −1.78153 0.713215i −1.78153 0.713215i
\(707\) 0 0
\(708\) 1.45949 2.52792i 1.45949 2.52792i
\(709\) 0 0 0.786053 0.618159i \(-0.212121\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0.252989 1.75958i 0.252989 1.75958i
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0.428368 + 1.23769i 0.428368 + 1.23769i
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 0.995472 0.0950560i \(-0.0303030\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −0.481286 0.309304i −0.481286 0.309304i
\(723\) −1.01021 + 2.21205i −1.01021 + 2.21205i
\(724\) 0 0
\(725\) 0 0
\(726\) −1.67548 + 0.322922i −1.67548 + 0.322922i
\(727\) 0 0 −0.235759 0.971812i \(-0.575758\pi\)
0.235759 + 0.971812i \(0.424242\pi\)
\(728\) 0 0
\(729\) −0.175461 1.22036i −0.175461 1.22036i
\(730\) 0 0
\(731\) −3.83927 0.739959i −3.83927 0.739959i
\(732\) 0 0
\(733\) 0 0 −0.580057 0.814576i \(-0.696970\pi\)
0.580057 + 0.814576i \(0.303030\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0.223734 + 0.175946i 0.223734 + 0.175946i
\(738\) 4.11788 4.11788
\(739\) 1.39734 + 0.720381i 1.39734 + 0.720381i 0.981929 0.189251i \(-0.0606061\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 −0.981929 0.189251i \(-0.939394\pi\)
0.981929 + 0.189251i \(0.0606061\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −0.755726 3.11514i −0.755726 3.11514i
\(748\) 0.556441 0.107245i 0.556441 0.107245i
\(749\) 0 0
\(750\) 0 0
\(751\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(752\) 0 0
\(753\) −0.0577910 + 0.166976i −0.0577910 + 0.166976i
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 0 0 0.235759 0.971812i \(-0.424242\pi\)
−0.235759 + 0.971812i \(0.575758\pi\)
\(758\) −0.550294 1.58997i −0.550294 1.58997i
\(759\) 0 0
\(760\) 0 0
\(761\) −0.797176 1.74557i −0.797176 1.74557i −0.654861 0.755750i \(-0.727273\pi\)
−0.142315 0.989821i \(-0.545455\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 1.72373 + 0.690079i 1.72373 + 0.690079i
\(769\) 0.0688733 0.0656706i 0.0688733 0.0656706i −0.654861 0.755750i \(-0.727273\pi\)
0.723734 + 0.690079i \(0.242424\pi\)
\(770\) 0 0
\(771\) −1.37115 + 0.706875i −1.37115 + 0.706875i
\(772\) 0.601300 0.573338i 0.601300 0.573338i
\(773\) 0 0 −0.928368 0.371662i \(-0.878788\pi\)
0.928368 + 0.371662i \(0.121212\pi\)
\(774\) −2.40324 4.16253i −2.40324 4.16253i
\(775\) 0 0
\(776\) −0.911911 + 0.717135i −0.911911 + 0.717135i
\(777\) 0 0
\(778\) 0 0
\(779\) 0.156630 1.08939i 0.156630 1.08939i
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 0.235759 0.971812i 0.235759 0.971812i
\(785\) 0 0
\(786\) −3.10983 + 0.296952i −3.10983 + 0.296952i
\(787\) −1.11312 + 1.56316i −1.11312 + 1.56316i −0.327068 + 0.945001i \(0.606061\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0.547582 + 0.430623i 0.547582 + 0.430623i
\(793\) 0 0
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 0 0 −0.0475819 0.998867i \(-0.515152\pi\)
0.0475819 + 0.998867i \(0.484848\pi\)