Properties

Label 1340.1.bl.b.1119.1
Level $1340$
Weight $1$
Character 1340.1119
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 1119.1
Root \(0.928368 + 0.371662i\) of defining polynomial
Character \(\chi\) \(=\) 1340.1119
Dual form 1340.1.bl.b.479.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.723734 - 0.690079i) q^{2} +(-0.0135432 + 0.0941952i) q^{3} +(0.0475819 - 0.998867i) q^{4} +(0.415415 + 0.909632i) q^{5} +(0.0552004 + 0.0775182i) q^{6} +(-0.370638 - 1.52779i) q^{7} +(-0.654861 - 0.755750i) q^{8} +(0.950804 + 0.279181i) q^{9} +O(q^{10})\) \(q+(0.723734 - 0.690079i) q^{2} +(-0.0135432 + 0.0941952i) q^{3} +(0.0475819 - 0.998867i) q^{4} +(0.415415 + 0.909632i) q^{5} +(0.0552004 + 0.0775182i) q^{6} +(-0.370638 - 1.52779i) q^{7} +(-0.654861 - 0.755750i) q^{8} +(0.950804 + 0.279181i) q^{9} +(0.928368 + 0.371662i) q^{10} +(0.0934441 + 0.0180099i) q^{12} +(-1.32254 - 0.849945i) q^{14} +(-0.0913090 + 0.0268107i) q^{15} +(-0.995472 - 0.0950560i) q^{16} +(0.880786 - 0.454077i) q^{18} +(0.928368 - 0.371662i) q^{20} +(0.148930 - 0.0142211i) q^{21} +(0.786053 + 0.618159i) q^{23} +(0.0800569 - 0.0514495i) q^{24} +(-0.654861 + 0.755750i) q^{25} +(-0.0787070 + 0.172344i) q^{27} +(-1.54370 + 0.297523i) q^{28} +(-0.928368 - 1.60798i) q^{29} +(-0.0475819 + 0.0824143i) q^{30} +(-0.786053 + 0.618159i) q^{32} +(1.23576 - 0.971812i) q^{35} +(0.324106 - 0.936443i) q^{36} +(0.415415 - 0.909632i) q^{40} +(0.581419 + 0.299742i) q^{41} +(0.0979722 - 0.113066i) q^{42} +(-1.49547 + 0.961081i) q^{43} +(0.141026 + 0.980857i) q^{45} +(0.995472 - 0.0950560i) q^{46} +(1.82318 - 0.729892i) q^{47} +(0.0224357 - 0.0924813i) q^{48} +(-1.30794 + 0.674289i) q^{49} +(0.0475819 + 0.998867i) q^{50} +(0.0619682 + 0.179045i) q^{54} +(-0.911911 + 1.28060i) q^{56} +(-1.78153 - 0.523103i) q^{58} +(0.0224357 + 0.0924813i) q^{60} +(0.481929 + 0.676774i) q^{61} +(0.0741264 - 1.55610i) q^{63} +(-0.142315 + 0.989821i) q^{64} +(-0.888835 + 0.458227i) q^{67} +(-0.0688733 + 0.0656706i) q^{69} +(0.223734 - 1.55610i) q^{70} +(-0.411653 - 0.901394i) q^{72} +(-0.0623191 - 0.0719200i) q^{75} +(-0.327068 - 0.945001i) q^{80} +(0.818467 + 0.525997i) q^{81} +(0.627639 - 0.184291i) q^{82} +(-0.469383 - 0.0448206i) q^{83} +(-0.00711862 - 0.149438i) q^{84} +(-0.419102 + 1.72756i) q^{86} +(0.164037 - 0.0656706i) q^{87} +(0.273100 + 1.89945i) q^{89} +(0.778934 + 0.612561i) q^{90} +(0.654861 - 0.755750i) q^{92} +(0.815816 - 1.78639i) q^{94} +(-0.0475819 - 0.0824143i) q^{96} +(-0.481286 + 1.39059i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20q + q^{2} + 2q^{3} + q^{4} - 2q^{5} - q^{6} - q^{7} - 2q^{8} + O(q^{10}) \) \( 20q + q^{2} + 2q^{3} + q^{4} - 2q^{5} - q^{6} - q^{7} - 2q^{8} + q^{10} - q^{12} + 2q^{14} + 2q^{15} + q^{16} + q^{20} - 10q^{21} - q^{23} - 9q^{24} - 2q^{25} - 2q^{27} - q^{28} - q^{29} - q^{30} + q^{32} + 21q^{35} - 2q^{40} - q^{41} + 20q^{42} - 9q^{43} - q^{46} - q^{47} - q^{48} + q^{50} + q^{54} - q^{56} + 2q^{58} - q^{60} - 9q^{61} - 11q^{63} - 2q^{64} + q^{67} + q^{69} - 9q^{70} - 11q^{72} + 2q^{75} + q^{80} + 2q^{81} + 2q^{82} - q^{83} + q^{84} - q^{86} + q^{87} - 4q^{89} + 2q^{92} + 2q^{94} - q^{96} + O(q^{100}) \)

Character values

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

\(n\) \(537\) \(671\) \(1141\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{25}{33}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.723734 0.690079i 0.723734 0.690079i
\(3\) −0.0135432 + 0.0941952i −0.0135432 + 0.0941952i −0.995472 0.0950560i \(-0.969697\pi\)
0.981929 + 0.189251i \(0.0606061\pi\)
\(4\) 0.0475819 0.998867i 0.0475819 0.998867i
\(5\) 0.415415 + 0.909632i 0.415415 + 0.909632i
\(6\) 0.0552004 + 0.0775182i 0.0552004 + 0.0775182i
\(7\) −0.370638 1.52779i −0.370638 1.52779i −0.786053 0.618159i \(-0.787879\pi\)
0.415415 0.909632i \(-0.363636\pi\)
\(8\) −0.654861 0.755750i −0.654861 0.755750i
\(9\) 0.950804 + 0.279181i 0.950804 + 0.279181i
\(10\) 0.928368 + 0.371662i 0.928368 + 0.371662i
\(11\) 0 0 0.580057 0.814576i \(-0.303030\pi\)
−0.580057 + 0.814576i \(0.696970\pi\)
\(12\) 0.0934441 + 0.0180099i 0.0934441 + 0.0180099i
\(13\) 0 0 −0.327068 0.945001i \(-0.606061\pi\)
0.327068 + 0.945001i \(0.393939\pi\)
\(14\) −1.32254 0.849945i −1.32254 0.849945i
\(15\) −0.0913090 + 0.0268107i −0.0913090 + 0.0268107i
\(16\) −0.995472 0.0950560i −0.995472 0.0950560i
\(17\) 0 0 −0.0475819 0.998867i \(-0.515152\pi\)
0.0475819 + 0.998867i \(0.484848\pi\)
\(18\) 0.880786 0.454077i 0.880786 0.454077i
\(19\) 0 0 0.235759 0.971812i \(-0.424242\pi\)
−0.235759 + 0.971812i \(0.575758\pi\)
\(20\) 0.928368 0.371662i 0.928368 0.371662i
\(21\) 0.148930 0.0142211i 0.148930 0.0142211i
\(22\) 0 0
\(23\) 0.786053 + 0.618159i 0.786053 + 0.618159i 0.928368 0.371662i \(-0.121212\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(24\) 0.0800569 0.0514495i 0.0800569 0.0514495i
\(25\) −0.654861 + 0.755750i −0.654861 + 0.755750i
\(26\) 0 0
\(27\) −0.0787070 + 0.172344i −0.0787070 + 0.172344i
\(28\) −1.54370 + 0.297523i −1.54370 + 0.297523i
\(29\) −0.928368 1.60798i −0.928368 1.60798i −0.786053 0.618159i \(-0.787879\pi\)
−0.142315 0.989821i \(-0.545455\pi\)
\(30\) −0.0475819 + 0.0824143i −0.0475819 + 0.0824143i
\(31\) 0 0 0.327068 0.945001i \(-0.393939\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(32\) −0.786053 + 0.618159i −0.786053 + 0.618159i
\(33\) 0 0
\(34\) 0 0
\(35\) 1.23576 0.971812i 1.23576 0.971812i
\(36\) 0.324106 0.936443i 0.324106 0.936443i
\(37\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0.415415 0.909632i 0.415415 0.909632i
\(41\) 0.581419 + 0.299742i 0.581419 + 0.299742i 0.723734 0.690079i \(-0.242424\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(42\) 0.0979722 0.113066i 0.0979722 0.113066i
\(43\) −1.49547 + 0.961081i −1.49547 + 0.961081i −0.500000 + 0.866025i \(0.666667\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(44\) 0 0
\(45\) 0.141026 + 0.980857i 0.141026 + 0.980857i
\(46\) 0.995472 0.0950560i 0.995472 0.0950560i
\(47\) 1.82318 0.729892i 1.82318 0.729892i 0.841254 0.540641i \(-0.181818\pi\)
0.981929 0.189251i \(-0.0606061\pi\)
\(48\) 0.0224357 0.0924813i 0.0224357 0.0924813i
\(49\) −1.30794 + 0.674289i −1.30794 + 0.674289i
\(50\) 0.0475819 + 0.998867i 0.0475819 + 0.998867i
\(51\) 0 0
\(52\) 0 0
\(53\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(54\) 0.0619682 + 0.179045i 0.0619682 + 0.179045i
\(55\) 0 0
\(56\) −0.911911 + 1.28060i −0.911911 + 1.28060i
\(57\) 0 0
\(58\) −1.78153 0.523103i −1.78153 0.523103i
\(59\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(60\) 0.0224357 + 0.0924813i 0.0224357 + 0.0924813i
\(61\) 0.481929 + 0.676774i 0.481929 + 0.676774i 0.981929 0.189251i \(-0.0606061\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(62\) 0 0
\(63\) 0.0741264 1.55610i 0.0741264 1.55610i
\(64\) −0.142315 + 0.989821i −0.142315 + 0.989821i
\(65\) 0 0
\(66\) 0 0
\(67\) −0.888835 + 0.458227i −0.888835 + 0.458227i
\(68\) 0 0
\(69\) −0.0688733 + 0.0656706i −0.0688733 + 0.0656706i
\(70\) 0.223734 1.55610i 0.223734 1.55610i
\(71\) 0 0 0.0475819 0.998867i \(-0.484848\pi\)
−0.0475819 + 0.998867i \(0.515152\pi\)
\(72\) −0.411653 0.901394i −0.411653 0.901394i
\(73\) 0 0 −0.580057 0.814576i \(-0.696970\pi\)
0.580057 + 0.814576i \(0.303030\pi\)
\(74\) 0 0
\(75\) −0.0623191 0.0719200i −0.0623191 0.0719200i
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 −0.981929 0.189251i \(-0.939394\pi\)
0.981929 + 0.189251i \(0.0606061\pi\)
\(80\) −0.327068 0.945001i −0.327068 0.945001i
\(81\) 0.818467 + 0.525997i 0.818467 + 0.525997i
\(82\) 0.627639 0.184291i 0.627639 0.184291i
\(83\) −0.469383 0.0448206i −0.469383 0.0448206i −0.142315 0.989821i \(-0.545455\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(84\) −0.00711862 0.149438i −0.00711862 0.149438i
\(85\) 0 0
\(86\) −0.419102 + 1.72756i −0.419102 + 1.72756i
\(87\) 0.164037 0.0656706i 0.164037 0.0656706i
\(88\) 0 0
\(89\) 0.273100 + 1.89945i 0.273100 + 1.89945i 0.415415 + 0.909632i \(0.363636\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(90\) 0.778934 + 0.612561i 0.778934 + 0.612561i
\(91\) 0 0
\(92\) 0.654861 0.755750i 0.654861 0.755750i
\(93\) 0 0
\(94\) 0.815816 1.78639i 0.815816 1.78639i
\(95\) 0 0
\(96\) −0.0475819 0.0824143i −0.0475819 0.0824143i
\(97\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(98\) −0.481286 + 1.39059i −0.481286 + 1.39059i
\(99\) 0 0
\(100\) 0.723734 + 0.690079i 0.723734 + 0.690079i
\(101\) −1.38884 1.32425i −1.38884 1.32425i −0.888835 0.458227i \(-0.848485\pi\)
−0.500000 0.866025i \(-0.666667\pi\)
\(102\) 0 0
\(103\) −0.473420 + 1.36786i −0.473420 + 1.36786i 0.415415 + 0.909632i \(0.363636\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(104\) 0 0
\(105\) 0.0748038 + 0.129564i 0.0748038 + 0.129564i
\(106\) 0 0
\(107\) −0.544078 + 1.19136i −0.544078 + 1.19136i 0.415415 + 0.909632i \(0.363636\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(108\) 0.168404 + 0.0868183i 0.168404 + 0.0868183i
\(109\) −0.947890 + 1.09392i −0.947890 + 1.09392i 0.0475819 + 0.998867i \(0.484848\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0.223734 + 1.55610i 0.223734 + 1.55610i
\(113\) 0 0 0.995472 0.0950560i \(-0.0303030\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(114\) 0 0
\(115\) −0.235759 + 0.971812i −0.235759 + 0.971812i
\(116\) −1.65033 + 0.850806i −1.65033 + 0.850806i
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0.0800569 + 0.0514495i 0.0800569 + 0.0514495i
\(121\) −0.327068 0.945001i −0.327068 0.945001i
\(122\) 0.815816 + 0.157236i 0.815816 + 0.157236i
\(123\) −0.0361086 + 0.0507074i −0.0361086 + 0.0507074i
\(124\) 0 0
\(125\) −0.959493 0.281733i −0.959493 0.281733i
\(126\) −1.02019 1.17736i −1.02019 1.17736i
\(127\) 0.273507 + 1.12741i 0.273507 + 1.12741i 0.928368 + 0.371662i \(0.121212\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(128\) 0.580057 + 0.814576i 0.580057 + 0.814576i
\(129\) −0.0702757 0.153882i −0.0702757 0.153882i
\(130\) 0 0
\(131\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −0.327068 + 0.945001i −0.327068 + 0.945001i
\(135\) −0.189466 −0.189466
\(136\) 0 0
\(137\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(138\) −0.00452808 + 0.0950560i −0.00452808 + 0.0950560i
\(139\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(140\) −0.911911 1.28060i −0.911911 1.28060i
\(141\) 0.0440606 + 0.181620i 0.0440606 + 0.181620i
\(142\) 0 0
\(143\) 0 0
\(144\) −0.919960 0.368297i −0.919960 0.368297i
\(145\) 1.07701 1.51245i 1.07701 1.51245i
\(146\) 0 0
\(147\) −0.0458011 0.132333i −0.0458011 0.132333i
\(148\) 0 0
\(149\) 0.627639 0.184291i 0.627639 0.184291i 0.0475819 0.998867i \(-0.484848\pi\)
0.580057 + 0.814576i \(0.303030\pi\)
\(150\) −0.0947329 0.00904590i −0.0947329 0.00904590i
\(151\) 0 0 −0.0475819 0.998867i \(-0.515152\pi\)
0.0475819 + 0.998867i \(0.484848\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 0 0 −0.786053 0.618159i \(-0.787879\pi\)
0.786053 + 0.618159i \(0.212121\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) −0.888835 0.458227i −0.888835 0.458227i
\(161\) 0.653077 1.43004i 0.653077 1.43004i
\(162\) 0.955332 0.184125i 0.955332 0.184125i
\(163\) −0.841254 1.45709i −0.841254 1.45709i −0.888835 0.458227i \(-0.848485\pi\)
0.0475819 0.998867i \(-0.484848\pi\)
\(164\) 0.327068 0.566498i 0.327068 0.566498i
\(165\) 0 0
\(166\) −0.370638 + 0.291473i −0.370638 + 0.291473i
\(167\) −0.205996 0.196417i −0.205996 0.196417i 0.580057 0.814576i \(-0.303030\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(168\) −0.108276 0.103241i −0.108276 0.103241i
\(169\) −0.786053 + 0.618159i −0.786053 + 0.618159i
\(170\) 0 0
\(171\) 0 0
\(172\) 0.888835 + 1.53951i 0.888835 + 1.53951i
\(173\) 0 0 0.981929 0.189251i \(-0.0606061\pi\)
−0.981929 + 0.189251i \(0.939394\pi\)
\(174\) 0.0734014 0.160727i 0.0734014 0.160727i
\(175\) 1.39734 + 0.720381i 1.39734 + 0.720381i
\(176\) 0 0
\(177\) 0 0
\(178\) 1.50842 + 1.18624i 1.50842 + 1.18624i
\(179\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(180\) 0.986457 0.0941952i 0.986457 0.0941952i
\(181\) 1.56199 0.625325i 1.56199 0.625325i 0.580057 0.814576i \(-0.303030\pi\)
0.981929 + 0.189251i \(0.0606061\pi\)
\(182\) 0 0
\(183\) −0.0702757 + 0.0362297i −0.0702757 + 0.0362297i
\(184\) −0.0475819 0.998867i −0.0475819 0.998867i
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) −0.642315 1.85585i −0.642315 1.85585i
\(189\) 0.292478 + 0.0563705i 0.292478 + 0.0563705i
\(190\) 0 0
\(191\) 0 0 −0.928368 0.371662i \(-0.878788\pi\)
0.928368 + 0.371662i \(0.121212\pi\)
\(192\) −0.0913090 0.0268107i −0.0913090 0.0268107i
\(193\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0.611291 + 1.33854i 0.611291 + 1.33854i
\(197\) 0 0 0.0475819 0.998867i \(-0.484848\pi\)
−0.0475819 + 0.998867i \(0.515152\pi\)
\(198\) 0 0
\(199\) 0 0 0.723734 0.690079i \(-0.242424\pi\)
−0.723734 + 0.690079i \(0.757576\pi\)
\(200\) 1.00000 1.00000
\(201\) −0.0311250 0.0899299i −0.0311250 0.0899299i
\(202\) −1.91899 −1.91899
\(203\) −2.11257 + 2.01433i −2.11257 + 2.01433i
\(204\) 0 0
\(205\) −0.0311250 + 0.653395i −0.0311250 + 0.653395i
\(206\) 0.601300 + 1.31666i 0.601300 + 1.31666i
\(207\) 0.574804 + 0.807199i 0.574804 + 0.807199i
\(208\) 0 0
\(209\) 0 0
\(210\) 0.143547 + 0.0421493i 0.143547 + 0.0421493i
\(211\) 0 0 −0.928368 0.371662i \(-0.878788\pi\)
0.928368 + 0.371662i \(0.121212\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0.428368 + 1.23769i 0.428368 + 1.23769i
\(215\) −1.49547 0.961081i −1.49547 0.961081i
\(216\) 0.181791 0.0533787i 0.181791 0.0533787i
\(217\) 0 0
\(218\) 0.0688733 + 1.44583i 0.0688733 + 1.44583i
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) −0.118239 0.822373i −0.118239 0.822373i −0.959493 0.281733i \(-0.909091\pi\)
0.841254 0.540641i \(-0.181818\pi\)
\(224\) 1.23576 + 0.971812i 1.23576 + 0.971812i
\(225\) −0.833635 + 0.535745i −0.833635 + 0.535745i
\(226\) 0 0
\(227\) 1.70566 + 0.879330i 1.70566 + 0.879330i 0.981929 + 0.189251i \(0.0606061\pi\)
0.723734 + 0.690079i \(0.242424\pi\)
\(228\) 0 0
\(229\) 1.13915 0.219553i 1.13915 0.219553i 0.415415 0.909632i \(-0.363636\pi\)
0.723734 + 0.690079i \(0.242424\pi\)
\(230\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(231\) 0 0
\(232\) −0.607279 + 1.75462i −0.607279 + 1.75462i
\(233\) 0 0 0.786053 0.618159i \(-0.212121\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(234\) 0 0
\(235\) 1.42131 + 1.35522i 1.42131 + 1.35522i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(240\) 0.0934441 0.0180099i 0.0934441 0.0180099i
\(241\) 0.601300 1.31666i 0.601300 1.31666i −0.327068 0.945001i \(-0.606061\pi\)
0.928368 0.371662i \(-0.121212\pi\)
\(242\) −0.888835 0.458227i −0.888835 0.458227i
\(243\) −0.184705 + 0.213161i −0.184705 + 0.213161i
\(244\) 0.698939 0.449181i 0.698939 0.449181i
\(245\) −1.15669 0.909632i −1.15669 0.909632i
\(246\) 0.00885911 + 0.0616165i 0.00885911 + 0.0616165i
\(247\) 0 0
\(248\) 0 0
\(249\) 0.0105788 0.0436066i 0.0105788 0.0436066i
\(250\) −0.888835 + 0.458227i −0.888835 + 0.458227i
\(251\) 0 0 −0.0475819 0.998867i \(-0.515152\pi\)
0.0475819 + 0.998867i \(0.484848\pi\)
\(252\) −1.55081 0.148085i −1.55081 0.148085i
\(253\) 0 0
\(254\) 0.975950 + 0.627205i 0.975950 + 0.627205i
\(255\) 0 0
\(256\) 0.981929 + 0.189251i 0.981929 + 0.189251i
\(257\) 0 0 0.580057 0.814576i \(-0.303030\pi\)
−0.580057 + 0.814576i \(0.696970\pi\)
\(258\) −0.157052 0.0628741i −0.157052 0.0628741i
\(259\) 0 0
\(260\) 0 0
\(261\) −0.433778 1.78806i −0.433778 1.78806i
\(262\) 0 0
\(263\) −0.827068 1.81103i −0.827068 1.81103i −0.500000 0.866025i \(-0.666667\pi\)
−0.327068 0.945001i \(-0.606061\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) −0.182618 −0.182618
\(268\) 0.415415 + 0.909632i 0.415415 + 0.909632i
\(269\) 1.68251 1.68251 0.841254 0.540641i \(-0.181818\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(270\) −0.137123 + 0.130746i −0.137123 + 0.130746i
\(271\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) 0.0623191 + 0.0719200i 0.0623191 + 0.0719200i
\(277\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) −1.54370 0.297523i −1.54370 0.297523i
\(281\) −0.642315 1.85585i −0.642315 1.85585i −0.500000 0.866025i \(-0.666667\pi\)
−0.142315 0.989821i \(-0.545455\pi\)
\(282\) 0.157220 + 0.101039i 0.157220 + 0.101039i
\(283\) 1.91030 0.560914i 1.91030 0.560914i 0.928368 0.371662i \(-0.121212\pi\)
0.981929 0.189251i \(-0.0606061\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0.242448 0.999383i 0.242448 0.999383i
\(288\) −0.919960 + 0.368297i −0.919960 + 0.368297i
\(289\) −0.995472 + 0.0950560i −0.995472 + 0.0950560i
\(290\) −0.264241 1.83784i −0.264241 1.83784i
\(291\) 0 0
\(292\) 0 0
\(293\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(294\) −0.124468 0.0641679i −0.124468 0.0641679i
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) 0.327068 0.566498i 0.327068 0.566498i
\(299\) 0 0
\(300\) −0.0748038 + 0.0588264i −0.0748038 + 0.0588264i
\(301\) 2.02261 + 1.92856i 2.02261 + 1.92856i
\(302\) 0 0
\(303\) 0.143547 0.112887i 0.143547 0.112887i
\(304\) 0 0
\(305\) −0.415415 + 0.719520i −0.415415 + 0.719520i
\(306\) 0 0
\(307\) −1.28605 + 0.247866i −1.28605 + 0.247866i −0.786053 0.618159i \(-0.787879\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(308\) 0 0
\(309\) −0.122434 0.0631191i −0.122434 0.0631191i
\(310\) 0 0
\(311\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(312\) 0 0
\(313\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(314\) 0 0
\(315\) 1.44628 0.579001i 1.44628 0.579001i
\(316\) 0 0
\(317\) 0 0 0.888835 0.458227i \(-0.151515\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) −0.959493 + 0.281733i −0.959493 + 0.281733i
\(321\) −0.104852 0.0673845i −0.104852 0.0673845i
\(322\) −0.514186 1.48564i −0.514186 1.48564i
\(323\) 0 0
\(324\) 0.564345 0.792512i 0.564345 0.792512i
\(325\) 0 0
\(326\) −1.61435 0.474017i −1.61435 0.474017i
\(327\) −0.0902048 0.104102i −0.0902048 0.104102i
\(328\) −0.154218 0.635697i −0.154218 0.635697i
\(329\) −1.79086 2.51492i −1.79086 2.51492i
\(330\) 0 0
\(331\) 0 0 0.0475819 0.998867i \(-0.484848\pi\)
−0.0475819 + 0.998867i \(0.515152\pi\)
\(332\) −0.0671040 + 0.466718i −0.0671040 + 0.466718i
\(333\) 0 0
\(334\) −0.284630 −0.284630
\(335\) −0.786053 0.618159i −0.786053 0.618159i
\(336\) −0.149608 −0.149608
\(337\) 0 0 0.723734 0.690079i \(-0.242424\pi\)
−0.723734 + 0.690079i \(0.757576\pi\)
\(338\) −0.142315 + 0.989821i −0.142315 + 0.989821i
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 0.485433 + 0.560219i 0.485433 + 0.560219i
\(344\) 1.70566 + 0.500828i 1.70566 + 0.500828i
\(345\) −0.0883470 0.0353688i −0.0883470 0.0353688i
\(346\) 0 0
\(347\) 0.815816 + 0.157236i 0.815816 + 0.157236i 0.580057 0.814576i \(-0.303030\pi\)
0.235759 + 0.971812i \(0.424242\pi\)
\(348\) −0.0577910 0.166976i −0.0577910 0.166976i
\(349\) −1.49547 0.961081i −1.49547 0.961081i −0.995472 0.0950560i \(-0.969697\pi\)
−0.500000 0.866025i \(-0.666667\pi\)
\(350\) 1.50842 0.442913i 1.50842 0.442913i
\(351\) 0 0
\(352\) 0 0
\(353\) 0 0 0.888835 0.458227i \(-0.151515\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 1.91030 0.182411i 1.91030 0.182411i
\(357\) 0 0
\(358\) 0 0
\(359\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(360\) 0.648930 0.748905i 0.648930 0.748905i
\(361\) −0.888835 0.458227i −0.888835 0.458227i
\(362\) 0.698939 1.53046i 0.698939 1.53046i
\(363\) 0.0934441 0.0180099i 0.0934441 0.0180099i
\(364\) 0 0
\(365\) 0 0
\(366\) −0.0258596 + 0.0747165i −0.0258596 + 0.0747165i
\(367\) −1.13779 + 0.894765i −1.13779 + 0.894765i −0.995472 0.0950560i \(-0.969697\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(368\) −0.723734 0.690079i −0.723734 0.690079i
\(369\) 0.469133 + 0.447317i 0.469133 + 0.447317i
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(374\) 0 0
\(375\) 0.0395325 0.0865641i 0.0395325 0.0865641i
\(376\) −1.74555 0.899892i −1.74555 0.899892i
\(377\) 0 0
\(378\) 0.250576 0.161036i 0.250576 0.161036i
\(379\) 0 0 −0.786053 0.618159i \(-0.787879\pi\)
0.786053 + 0.618159i \(0.212121\pi\)
\(380\) 0 0
\(381\) −0.109901 + 0.0104943i −0.109901 + 0.0104943i
\(382\) 0 0
\(383\) 0.462997 1.90850i 0.462997 1.90850i 0.0475819 0.998867i \(-0.484848\pi\)
0.415415 0.909632i \(-0.363636\pi\)
\(384\) −0.0845850 + 0.0436066i −0.0845850 + 0.0436066i
\(385\) 0 0
\(386\) 0 0
\(387\) −1.69022 + 0.496292i −1.69022 + 0.496292i
\(388\) 0 0
\(389\) −0.473420 1.36786i −0.473420 1.36786i −0.888835 0.458227i \(-0.848485\pi\)
0.415415 0.909632i \(-0.363636\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 1.36611 + 0.546908i 1.36611 + 0.546908i
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0.723734 0.690079i 0.723734 0.690079i
\(401\) −1.57211 −1.57211 −0.786053 0.618159i \(-0.787879\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(402\) −0.0845850 0.0436066i −0.0845850 0.0436066i
\(403\) 0 0
\(404\) −1.38884 + 1.32425i −1.38884 + 1.32425i
\(405\) −0.138460 + 0.963011i −0.138460 + 0.963011i
\(406\) −0.138891 + 2.91568i −0.138891 + 2.91568i
\(407\) 0 0
\(408\) 0 0
\(409\) 0.396666 + 1.63508i 0.396666 + 1.63508i 0.723734 + 0.690079i \(0.242424\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(410\) 0.428368 + 0.494363i 0.428368 + 0.494363i
\(411\) 0 0
\(412\) 1.34378 + 0.537970i 1.34378 + 0.537970i
\(413\) 0 0
\(414\) 0.973036 + 0.187537i 0.973036 + 0.187537i
\(415\) −0.154218 0.445585i −0.154218 0.445585i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 0 0 −0.0475819 0.998867i \(-0.515152\pi\)
0.0475819 + 0.998867i \(0.484848\pi\)
\(420\) 0.132977 0.0685542i 0.132977 0.0685542i
\(421\) −0.0671040 + 0.276606i −0.0671040 + 0.276606i −0.995472 0.0950560i \(-0.969697\pi\)
0.928368 + 0.371662i \(0.121212\pi\)
\(422\) 0 0
\(423\) 1.93726 0.184986i 1.93726 0.184986i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 0.855348 0.987125i 0.855348 0.987125i
\(428\) 1.16413 + 0.600149i 1.16413 + 0.600149i
\(429\) 0 0
\(430\) −1.74555 + 0.336426i −1.74555 + 0.336426i
\(431\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(432\) 0.0947329 0.164082i 0.0947329 0.164082i
\(433\) 0 0 0.327068 0.945001i \(-0.393939\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(434\) 0 0
\(435\) 0.127880 + 0.121933i 0.127880 + 0.121933i
\(436\) 1.04758 + 0.998867i 1.04758 + 0.998867i
\(437\) 0 0
\(438\) 0 0
\(439\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(440\) 0 0
\(441\) −1.43184 + 0.275965i −1.43184 + 0.275965i
\(442\) 0 0
\(443\) −1.65033 0.850806i −1.65033 0.850806i −0.995472 0.0950560i \(-0.969697\pi\)
−0.654861 0.755750i \(-0.727273\pi\)
\(444\) 0 0
\(445\) −1.61435 + 1.03748i −1.61435 + 1.03748i
\(446\) −0.653077 0.513585i −0.653077 0.513585i
\(447\) 0.00885911 + 0.0616165i 0.00885911 + 0.0616165i
\(448\) 1.56499 0.149438i 1.56499 0.149438i
\(449\) 1.82318 0.729892i 1.82318 0.729892i 0.841254 0.540641i \(-0.181818\pi\)
0.981929 0.189251i \(-0.0606061\pi\)
\(450\) −0.233624 + 0.963011i −0.233624 + 0.963011i
\(451\) 0 0
\(452\) 0 0
\(453\) 0 0
\(454\) 1.84125 0.540641i 1.84125 0.540641i
\(455\) 0 0
\(456\) 0 0
\(457\) 0 0 −0.981929 0.189251i \(-0.939394\pi\)
0.981929 + 0.189251i \(0.0606061\pi\)
\(458\) 0.672932 0.945001i 0.672932 0.945001i
\(459\) 0 0
\(460\) 0.959493 + 0.281733i 0.959493 + 0.281733i
\(461\) −0.308779 0.356349i −0.308779 0.356349i 0.580057 0.814576i \(-0.303030\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(462\) 0 0
\(463\) 0.975950 + 1.37053i 0.975950 + 1.37053i 0.928368 + 0.371662i \(0.121212\pi\)
0.0475819 + 0.998867i \(0.484848\pi\)
\(464\) 0.771316 + 1.68895i 0.771316 + 1.68895i
\(465\) 0 0
\(466\) 0 0
\(467\) 0.839614 0.800570i 0.839614 0.800570i −0.142315 0.989821i \(-0.545455\pi\)
0.981929 + 0.189251i \(0.0606061\pi\)
\(468\) 0 0
\(469\) 1.02951 + 1.18812i 1.02951 + 1.18812i
\(470\) 1.96386 1.96386
\(471\) 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 −0.928368 0.371662i \(-0.878788\pi\)
0.928368 + 0.371662i \(0.121212\pi\)
\(480\) 0.0552004 0.0775182i 0.0552004 0.0775182i
\(481\) 0 0
\(482\) −0.473420 1.36786i −0.473420 1.36786i
\(483\) 0.125858 + 0.0808840i 0.125858 + 0.0808840i
\(484\) −0.959493 + 0.281733i −0.959493 + 0.281733i
\(485\) 0 0
\(486\) 0.0134206 + 0.281733i 0.0134206 + 0.281733i
\(487\) −0.419102 + 0.216062i −0.419102 + 0.216062i −0.654861 0.755750i \(-0.727273\pi\)
0.235759 + 0.971812i \(0.424242\pi\)
\(488\) 0.195876 0.807410i 0.195876 0.807410i
\(489\) 0.148645 0.0595083i 0.148645 0.0595083i
\(490\) −1.46485 + 0.139877i −1.46485 + 0.139877i
\(491\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(492\) 0.0489319 + 0.0384804i 0.0489319 + 0.0384804i
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) −0.0224357 0.0388598i −0.0224357 0.0388598i
\(499\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(500\) −0.327068 + 0.945001i −0.327068 + 0.945001i
\(501\) 0.0212914 0.0167437i 0.0212914 0.0167437i
\(502\) 0 0
\(503\) −0.473420 0.451405i −0.473420 0.451405i 0.415415 0.909632i \(-0.363636\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(504\) −1.22457 + 0.963011i −1.22457 + 0.963011i
\(505\) 0.627639 1.81344i 0.627639 1.81344i
\(506\) 0 0
\(507\) −0.0475819 0.0824143i −0.0475819 0.0824143i
\(508\) 1.13915 0.219553i 1.13915 0.219553i
\(509\) −0.118239 + 0.258908i −0.118239 + 0.258908i −0.959493 0.281733i \(-0.909091\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0.841254 0.540641i 0.841254 0.540641i
\(513\) 0 0
\(514\) 0 0
\(515\) −1.44091 + 0.137591i −1.44091 + 0.137591i
\(516\) −0.157052 + 0.0628741i −0.157052 + 0.0628741i
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 0.959493 0.281733i 0.959493 0.281733i 0.235759 0.971812i \(-0.424242\pi\)
0.723734 + 0.690079i \(0.242424\pi\)
\(522\) −1.54784 0.994736i −1.54784 0.994736i
\(523\) 0.581419 + 1.67990i 0.581419 + 1.67990i 0.723734 + 0.690079i \(0.242424\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(524\) 0 0
\(525\) −0.0867810 + 0.121867i −0.0867810 + 0.121867i
\(526\) −1.84833 0.739959i −1.84833 0.739959i
\(527\) 0 0
\(528\) 0 0
\(529\) 0 0
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) −0.132167 + 0.126021i −0.132167 + 0.126021i
\(535\) −1.30972 −1.30972
\(536\) 0.928368 + 0.371662i 0.928368 + 0.371662i
\(537\) 0 0
\(538\) 1.21769 1.16106i 1.21769 1.16106i
\(539\) 0 0
\(540\) −0.00901515 + 0.189251i −0.00901515 + 0.189251i
\(541\) −0.738471 1.61703i −0.738471 1.61703i −0.786053 0.618159i \(-0.787879\pi\)
0.0475819 0.998867i \(-0.484848\pi\)
\(542\) 0 0
\(543\) 0.0377483 + 0.155600i 0.0377483 + 0.155600i
\(544\) 0 0
\(545\) −1.38884 0.407799i −1.38884 0.407799i
\(546\) 0 0
\(547\) 0.672932 0.945001i 0.672932 0.945001i −0.327068 0.945001i \(-0.606061\pi\)
1.00000 \(0\)
\(548\) 0 0
\(549\) 0.269277 + 0.778025i 0.269277 + 0.778025i
\(550\) 0 0
\(551\) 0 0
\(552\) 0.0947329 + 0.00904590i 0.0947329 + 0.00904590i
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 0 0 0.995472 0.0950560i \(-0.0303030\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) −1.32254 + 0.849945i −1.32254 + 0.849945i
\(561\) 0 0
\(562\) −1.74555 0.899892i −1.74555 0.899892i
\(563\) −0.738471 + 1.61703i −0.738471 + 1.61703i 0.0475819 + 0.998867i \(0.484848\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(564\) 0.183511 0.0353688i 0.183511 0.0353688i
\(565\) 0 0
\(566\) 0.995472 1.72421i 0.995472 1.72421i
\(567\) 0.500258 1.44540i 0.500258 1.44540i
\(568\) 0 0
\(569\) −0.205996 0.196417i −0.205996 0.196417i 0.580057 0.814576i \(-0.303030\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(570\) 0 0
\(571\) 0 0 0.786053 0.618159i \(-0.212121\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) −0.514186 0.890596i −0.514186 0.890596i
\(575\) −0.981929 + 0.189251i −0.981929 + 0.189251i
\(576\) −0.411653 + 0.901394i −0.411653 + 0.901394i
\(577\) 0 0 −0.888835 0.458227i \(-0.848485\pi\)
0.888835 + 0.458227i \(0.151515\pi\)
\(578\) −0.654861 + 0.755750i −0.654861 + 0.755750i
\(579\) 0 0
\(580\) −1.45949 1.14776i −1.45949 1.14776i
\(581\) 0.105495 + 0.733731i 0.105495 + 0.733731i
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 1.30379 + 0.124497i 1.30379 + 0.124497i 0.723734 0.690079i \(-0.242424\pi\)
0.580057 + 0.814576i \(0.303030\pi\)
\(588\) −0.134363 + 0.0394525i −0.134363 + 0.0394525i
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 0 0 −0.928368 0.371662i \(-0.878788\pi\)
0.928368 + 0.371662i \(0.121212\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −0.154218 0.635697i −0.154218 0.635697i
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 0.0475819 0.998867i \(-0.484848\pi\)
−0.0475819 + 0.998867i \(0.515152\pi\)
\(600\) −0.0135432 + 0.0941952i −0.0135432 + 0.0941952i
\(601\) −1.28656 + 1.22673i −1.28656 + 1.22673i −0.327068 + 0.945001i \(0.606061\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(602\) 2.79469 2.79469
\(603\) −0.973036 + 0.187537i −0.973036 + 0.187537i
\(604\) 0 0
\(605\) 0.723734 0.690079i 0.723734 0.690079i
\(606\) 0.0259893 0.180759i 0.0259893 0.180759i
\(607\) 0.0934441 1.96163i 0.0934441 1.96163i −0.142315 0.989821i \(-0.545455\pi\)
0.235759 0.971812i \(-0.424242\pi\)
\(608\) 0 0
\(609\) −0.161129 0.226274i −0.161129 0.226274i
\(610\) 0.195876 + 0.807410i 0.195876 + 0.807410i
\(611\) 0 0
\(612\) 0 0
\(613\) 0 0 −0.928368 0.371662i \(-0.878788\pi\)
0.928368 + 0.371662i \(0.121212\pi\)
\(614\) −0.759713 + 1.06687i −0.759713 + 1.06687i
\(615\) −0.0611251 0.0117809i −0.0611251 0.0117809i
\(616\) 0 0
\(617\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(618\) −0.132167 + 0.0388077i −0.132167 + 0.0388077i
\(619\) 0 0 −0.995472 0.0950560i \(-0.969697\pi\)
0.995472 + 0.0950560i \(0.0303030\pi\)
\(620\) 0 0
\(621\) −0.168404 + 0.0868183i −0.168404 + 0.0868183i
\(622\) 0 0
\(623\) 2.80075 1.12125i 2.80075 1.12125i
\(624\) 0 0
\(625\) −0.142315 0.989821i −0.142315 0.989821i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) 0.647162 1.41709i 0.647162 1.41709i
\(631\) 0 0 0.981929 0.189251i \(-0.0606061\pi\)
−0.981929 + 0.189251i \(0.939394\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −0.911911 + 0.717135i −0.911911 + 0.717135i
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(641\) 0.995472 + 1.72421i 0.995472 + 1.72421i 0.580057 + 0.814576i \(0.303030\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(642\) −0.122386 + 0.0235879i −0.122386 + 0.0235879i
\(643\) 0.771316 1.68895i 0.771316 1.68895i 0.0475819 0.998867i \(-0.484848\pi\)
0.723734 0.690079i \(-0.242424\pi\)
\(644\) −1.39734 0.720381i −1.39734 0.720381i
\(645\) 0.110783 0.127850i 0.110783 0.127850i
\(646\) 0 0
\(647\) −1.54370 1.21398i −1.54370 1.21398i −0.888835 0.458227i \(-0.848485\pi\)
−0.654861 0.755750i \(-0.727273\pi\)
\(648\) −0.138460 0.963011i −0.138460 0.963011i
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) −1.49547 + 0.770969i −1.49547 + 0.770969i
\(653\) 0 0 −0.0475819 0.998867i \(-0.515152\pi\)
0.0475819 + 0.998867i \(0.484848\pi\)
\(654\) −0.137123 0.0130936i −0.137123 0.0130936i
\(655\) 0 0
\(656\) −0.550294 0.353653i −0.550294 0.353653i
\(657\) 0 0
\(658\) −3.03160 0.584293i −3.03160 0.584293i
\(659\) 0 0 0.580057 0.814576i \(-0.303030\pi\)
−0.580057 + 0.814576i \(0.696970\pi\)
\(660\) 0 0
\(661\) 0.273100 + 0.0801894i 0.273100 + 0.0801894i 0.415415 0.909632i \(-0.363636\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0.273507 + 0.384087i 0.273507 + 0.384087i
\(665\) 0 0
\(666\) 0 0
\(667\) 0.264241 1.83784i 0.264241 1.83784i
\(668\) −0.205996 + 0.196417i −0.205996 + 0.196417i
\(669\) 0.0790650 0.0790650
\(670\) −0.995472 + 0.0950560i −0.995472 + 0.0950560i
\(671\) 0 0
\(672\) −0.108276 + 0.103241i −0.108276 + 0.103241i
\(673\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(674\) 0 0
\(675\) −0.0787070 0.172344i −0.0787070 0.172344i
\(676\) 0.580057 + 0.814576i 0.580057 + 0.814576i
\(677\) 0 0 −0.235759 0.971812i \(-0.575758\pi\)
0.235759 + 0.971812i \(0.424242\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) −0.105929 + 0.148756i −0.105929 + 0.148756i
\(682\) 0 0
\(683\) 0.428368 + 1.23769i 0.428368 + 1.23769i 0.928368 + 0.371662i \(0.121212\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0.737920 + 0.0704628i 0.737920 + 0.0704628i
\(687\) 0.00525309 + 0.110276i 0.00525309 + 0.110276i
\(688\) 1.58006 0.814576i 1.58006 0.814576i
\(689\) 0 0
\(690\) −0.0883470 + 0.0353688i −0.0883470 + 0.0353688i
\(691\) 0 0 0.995472 0.0950560i \(-0.0303030\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0.698939 0.449181i 0.698939 0.449181i
\(695\) 0 0
\(696\) −0.157052 0.0809659i −0.157052 0.0809659i
\(697\) 0 0
\(698\) −1.74555 + 0.336426i −1.74555 + 0.336426i
\(699\) 0 0
\(700\) 0.786053 1.36148i 0.786053 1.36148i
\(701\) 0.327068 0.945001i 0.327068 0.945001i −0.654861 0.755750i \(-0.727273\pi\)
0.981929 0.189251i \(-0.0606061\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0 0
\(705\) −0.146904 + 0.115527i −0.146904 + 0.115527i
\(706\) 0 0
\(707\) −1.50842 + 2.61267i −1.50842 + 2.61267i
\(708\) 0 0
\(709\) −0.981929 + 0.189251i −0.981929 + 0.189251i −0.654861 0.755750i \(-0.727273\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 1.25667 1.45027i 1.25667 1.45027i
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 0.888835 0.458227i \(-0.151515\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(720\) −0.0471510 0.989821i −0.0471510 0.989821i
\(721\) 2.26527 + 0.216307i 2.26527 + 0.216307i
\(722\) −0.959493 + 0.281733i −0.959493 + 0.281733i
\(723\) 0.115880 + 0.0744714i 0.115880 + 0.0744714i
\(724\) −0.550294 1.58997i −0.550294 1.58997i
\(725\) 1.82318 + 0.351390i 1.82318 + 0.351390i
\(726\) 0.0552004 0.0775182i 0.0552004 0.0775182i
\(727\) −0.607279 0.243118i −0.607279 0.243118i 0.0475819 0.998867i \(-0.484848\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(728\) 0 0
\(729\) 0.619546 + 0.714994i 0.619546 + 0.714994i
\(730\) 0 0
\(731\) 0 0
\(732\) 0.0328448 + 0.0719200i 0.0328448 + 0.0719200i
\(733\) 0 0 0.0475819 0.998867i \(-0.484848\pi\)
−0.0475819 + 0.998867i \(0.515152\pi\)
\(734\) −0.205996 + 1.43273i −0.205996 + 1.43273i
\(735\) 0.101348 0.0966354i 0.101348 0.0966354i
\(736\) −1.00000 −1.00000
\(737\) 0 0
\(738\) 0.648212 0.648212
\(739\) 0 0 0.723734 0.690079i \(-0.242424\pi\)
−0.723734 + 0.690079i \(0.757576\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 0.975950 + 1.37053i 0.975950 + 1.37053i 0.928368 + 0.371662i \(0.121212\pi\)
0.0475819 + 0.998867i \(0.484848\pi\)
\(744\) 0 0
\(745\) 0.428368 + 0.494363i 0.428368 + 0.494363i
\(746\) 0 0
\(747\) −0.433778 0.173658i −0.433778 0.173658i
\(748\) 0 0
\(749\) 2.02181 + 0.389672i 2.02181 + 0.389672i
\(750\) −0.0311250 0.0899299i −0.0311250 0.0899299i
\(751\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(752\) −1.88431 + 0.553283i −1.88431 + 0.553283i
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 0.0702233 0.289464i 0.0702233 0.289464i
\(757\) 0 0 0.928368 0.371662i \(-0.121212\pi\)
−0.928368 + 0.371662i \(0.878788\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 1.41542 0.909632i 1.41542 0.909632i 0.415415 0.909632i \(-0.363636\pi\)
1.00000 \(0\)
\(762\) −0.0722972 + 0.0834354i −0.0722972 + 0.0834354i
\(763\) 2.02261 + 1.04273i 2.02261 + 1.04273i
\(764\) 0 0
\(765\) 0 0
\(766\) −0.981929 1.70075i −0.981929 1.70075i
\(767\) 0 0
\(768\) −0.0311250 + 0.0899299i −0.0311250 + 0.0899299i
\(769\) −0.0748038 + 0.0588264i −0.0748038 + 0.0588264i −0.654861 0.755750i \(-0.727273\pi\)
0.580057 + 0.814576i \(0.303030\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 0 0 0.327068 0.945001i \(-0.393939\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(774\) −0.880786 + 1.52557i −0.880786 + 1.52557i
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) −1.28656 0.663268i −1.28656 0.663268i
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0.350195 0.0334396i 0.350195 0.0334396i
\(784\) 1.36611 0.546908i 1.36611 0.546908i
\(785\) 0 0
\(786\) 0 0
\(787\) 0.0552004 + 1.15880i 0.0552004 + 1.15880i 0.841254 + 0.540641i \(0.181818\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(788\) 0 0
\(789\) 0.181791 0.0533787i 0.181791 0.0533787i
\(790\) 0 0
\(791\) 0 0
\(792\)