Properties

Label 1340.1.bl.b.639.1
Level $1340$
Weight $1$
Character 1340.639
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 639.1
Root \(-0.327068 - 0.945001i\) of defining polynomial
Character \(\chi\) \(=\) 1340.639
Dual form 1340.1.bl.b.1059.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.786053 - 0.618159i) q^{2} +(-0.308779 - 0.356349i) q^{3} +(0.235759 + 0.971812i) q^{4} +(0.841254 + 0.540641i) q^{5} +(0.0224357 + 0.470984i) q^{6} +(1.82318 - 0.729892i) q^{7} +(0.415415 - 0.909632i) q^{8} +(0.110674 - 0.769755i) q^{9} +O(q^{10})\) \(q+(-0.786053 - 0.618159i) q^{2} +(-0.308779 - 0.356349i) q^{3} +(0.235759 + 0.971812i) q^{4} +(0.841254 + 0.540641i) q^{5} +(0.0224357 + 0.470984i) q^{6} +(1.82318 - 0.729892i) q^{7} +(0.415415 - 0.909632i) q^{8} +(0.110674 - 0.769755i) q^{9} +(-0.327068 - 0.945001i) q^{10} +(0.273507 - 0.384087i) q^{12} +(-1.88431 - 0.553283i) q^{14} +(-0.0671040 - 0.466718i) q^{15} +(-0.888835 + 0.458227i) q^{16} +(-0.562827 + 0.536654i) q^{18} +(-0.327068 + 0.945001i) q^{20} +(-0.823056 - 0.424315i) q^{21} +(-0.981929 + 0.189251i) q^{23} +(-0.452418 + 0.132842i) q^{24} +(0.415415 + 0.909632i) q^{25} +(-0.705142 + 0.453167i) q^{27} +(1.13915 + 1.59971i) q^{28} +(0.327068 + 0.566498i) q^{29} +(-0.235759 + 0.408346i) q^{30} +(0.981929 + 0.189251i) q^{32} +(1.92837 + 0.371662i) q^{35} +(0.774150 - 0.0739223i) q^{36} +(0.841254 - 0.540641i) q^{40} +(-1.44091 - 1.37391i) q^{41} +(0.384672 + 0.842314i) q^{42} +(-1.38884 + 0.407799i) q^{43} +(0.509266 - 0.587724i) q^{45} +(0.888835 + 0.458227i) q^{46} +(-0.379436 + 1.09631i) q^{47} +(0.437742 + 0.175245i) q^{48} +(2.06752 - 1.97137i) q^{49} +(0.235759 - 0.971812i) q^{50} +(0.834408 + 0.0796763i) q^{54} +(0.0934441 - 1.96163i) q^{56} +(0.0930932 - 0.647478i) q^{58} +(0.437742 - 0.175245i) q^{60} +(0.0800569 + 1.68060i) q^{61} +(-0.360059 - 1.48418i) q^{63} +(-0.654861 - 0.755750i) q^{64} +(0.723734 - 0.690079i) q^{67} +(0.370638 + 0.291473i) q^{69} +(-1.28605 - 1.48418i) q^{70} +(-0.654218 - 0.420441i) q^{72} +(0.195876 - 0.428908i) q^{75} +(-0.995472 - 0.0950560i) q^{80} +(-0.366951 - 0.107747i) q^{81} +(0.283341 + 1.97068i) q^{82} +(-1.65033 + 0.850806i) q^{83} +(0.218311 - 0.899892i) q^{84} +(1.34378 + 0.537970i) q^{86} +(0.100880 - 0.291473i) q^{87} +(0.186393 - 0.215109i) q^{89} +(-0.763617 + 0.147175i) q^{90} +(-0.415415 - 0.909632i) q^{92} +(0.975950 - 0.627205i) q^{94} +(-0.235759 - 0.408346i) q^{96} +(-2.84380 + 0.271550i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20q + q^{2} + 2q^{3} + q^{4} - 2q^{5} - q^{6} - q^{7} - 2q^{8} + O(q^{10}) \) \( 20q + q^{2} + 2q^{3} + q^{4} - 2q^{5} - q^{6} - q^{7} - 2q^{8} + q^{10} - q^{12} + 2q^{14} + 2q^{15} + q^{16} + q^{20} - 10q^{21} - q^{23} - 9q^{24} - 2q^{25} - 2q^{27} - q^{28} - q^{29} - q^{30} + q^{32} + 21q^{35} - 2q^{40} - q^{41} + 20q^{42} - 9q^{43} - q^{46} - q^{47} - q^{48} + q^{50} + q^{54} - q^{56} + 2q^{58} - q^{60} - 9q^{61} - 11q^{63} - 2q^{64} + q^{67} + q^{69} - 9q^{70} - 11q^{72} + 2q^{75} + q^{80} + 2q^{81} + 2q^{82} - q^{83} + q^{84} - q^{86} + q^{87} - 4q^{89} + 2q^{92} + 2q^{94} - q^{96} + O(q^{100}) \)

Character values

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

\(n\) \(537\) \(671\) \(1141\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{7}{33}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.786053 0.618159i −0.786053 0.618159i
\(3\) −0.308779 0.356349i −0.308779 0.356349i 0.580057 0.814576i \(-0.303030\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(4\) 0.235759 + 0.971812i 0.235759 + 0.971812i
\(5\) 0.841254 + 0.540641i 0.841254 + 0.540641i
\(6\) 0.0224357 + 0.470984i 0.0224357 + 0.470984i
\(7\) 1.82318 0.729892i 1.82318 0.729892i 0.841254 0.540641i \(-0.181818\pi\)
0.981929 0.189251i \(-0.0606061\pi\)
\(8\) 0.415415 0.909632i 0.415415 0.909632i
\(9\) 0.110674 0.769755i 0.110674 0.769755i
\(10\) −0.327068 0.945001i −0.327068 0.945001i
\(11\) 0 0 0.0475819 0.998867i \(-0.484848\pi\)
−0.0475819 + 0.998867i \(0.515152\pi\)
\(12\) 0.273507 0.384087i 0.273507 0.384087i
\(13\) 0 0 −0.995472 0.0950560i \(-0.969697\pi\)
0.995472 + 0.0950560i \(0.0303030\pi\)
\(14\) −1.88431 0.553283i −1.88431 0.553283i
\(15\) −0.0671040 0.466718i −0.0671040 0.466718i
\(16\) −0.888835 + 0.458227i −0.888835 + 0.458227i
\(17\) 0 0 0.235759 0.971812i \(-0.424242\pi\)
−0.235759 + 0.971812i \(0.575758\pi\)
\(18\) −0.562827 + 0.536654i −0.562827 + 0.536654i
\(19\) 0 0 −0.928368 0.371662i \(-0.878788\pi\)
0.928368 + 0.371662i \(0.121212\pi\)
\(20\) −0.327068 + 0.945001i −0.327068 + 0.945001i
\(21\) −0.823056 0.424315i −0.823056 0.424315i
\(22\) 0 0
\(23\) −0.981929 + 0.189251i −0.981929 + 0.189251i −0.654861 0.755750i \(-0.727273\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(24\) −0.452418 + 0.132842i −0.452418 + 0.132842i
\(25\) 0.415415 + 0.909632i 0.415415 + 0.909632i
\(26\) 0 0
\(27\) −0.705142 + 0.453167i −0.705142 + 0.453167i
\(28\) 1.13915 + 1.59971i 1.13915 + 1.59971i
\(29\) 0.327068 + 0.566498i 0.327068 + 0.566498i 0.981929 0.189251i \(-0.0606061\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(30\) −0.235759 + 0.408346i −0.235759 + 0.408346i
\(31\) 0 0 0.995472 0.0950560i \(-0.0303030\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(32\) 0.981929 + 0.189251i 0.981929 + 0.189251i
\(33\) 0 0
\(34\) 0 0
\(35\) 1.92837 + 0.371662i 1.92837 + 0.371662i
\(36\) 0.774150 0.0739223i 0.774150 0.0739223i
\(37\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0.841254 0.540641i 0.841254 0.540641i
\(41\) −1.44091 1.37391i −1.44091 1.37391i −0.786053 0.618159i \(-0.787879\pi\)
−0.654861 0.755750i \(-0.727273\pi\)
\(42\) 0.384672 + 0.842314i 0.384672 + 0.842314i
\(43\) −1.38884 + 0.407799i −1.38884 + 0.407799i −0.888835 0.458227i \(-0.848485\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(44\) 0 0
\(45\) 0.509266 0.587724i 0.509266 0.587724i
\(46\) 0.888835 + 0.458227i 0.888835 + 0.458227i
\(47\) −0.379436 + 1.09631i −0.379436 + 1.09631i 0.580057 + 0.814576i \(0.303030\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(48\) 0.437742 + 0.175245i 0.437742 + 0.175245i
\(49\) 2.06752 1.97137i 2.06752 1.97137i
\(50\) 0.235759 0.971812i 0.235759 0.971812i
\(51\) 0 0
\(52\) 0 0
\(53\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(54\) 0.834408 + 0.0796763i 0.834408 + 0.0796763i
\(55\) 0 0
\(56\) 0.0934441 1.96163i 0.0934441 1.96163i
\(57\) 0 0
\(58\) 0.0930932 0.647478i 0.0930932 0.647478i
\(59\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(60\) 0.437742 0.175245i 0.437742 0.175245i
\(61\) 0.0800569 + 1.68060i 0.0800569 + 1.68060i 0.580057 + 0.814576i \(0.303030\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(62\) 0 0
\(63\) −0.360059 1.48418i −0.360059 1.48418i
\(64\) −0.654861 0.755750i −0.654861 0.755750i
\(65\) 0 0
\(66\) 0 0
\(67\) 0.723734 0.690079i 0.723734 0.690079i
\(68\) 0 0
\(69\) 0.370638 + 0.291473i 0.370638 + 0.291473i
\(70\) −1.28605 1.48418i −1.28605 1.48418i
\(71\) 0 0 −0.235759 0.971812i \(-0.575758\pi\)
0.235759 + 0.971812i \(0.424242\pi\)
\(72\) −0.654218 0.420441i −0.654218 0.420441i
\(73\) 0 0 −0.0475819 0.998867i \(-0.515152\pi\)
0.0475819 + 0.998867i \(0.484848\pi\)
\(74\) 0 0
\(75\) 0.195876 0.428908i 0.195876 0.428908i
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 0.580057 0.814576i \(-0.303030\pi\)
−0.580057 + 0.814576i \(0.696970\pi\)
\(80\) −0.995472 0.0950560i −0.995472 0.0950560i
\(81\) −0.366951 0.107747i −0.366951 0.107747i
\(82\) 0.283341 + 1.97068i 0.283341 + 1.97068i
\(83\) −1.65033 + 0.850806i −1.65033 + 0.850806i −0.654861 + 0.755750i \(0.727273\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(84\) 0.218311 0.899892i 0.218311 0.899892i
\(85\) 0 0
\(86\) 1.34378 + 0.537970i 1.34378 + 0.537970i
\(87\) 0.100880 0.291473i 0.100880 0.291473i
\(88\) 0 0
\(89\) 0.186393 0.215109i 0.186393 0.215109i −0.654861 0.755750i \(-0.727273\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(90\) −0.763617 + 0.147175i −0.763617 + 0.147175i
\(91\) 0 0
\(92\) −0.415415 0.909632i −0.415415 0.909632i
\(93\) 0 0
\(94\) 0.975950 0.627205i 0.975950 0.627205i
\(95\) 0 0
\(96\) −0.235759 0.408346i −0.235759 0.408346i
\(97\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(98\) −2.84380 + 0.271550i −2.84380 + 0.271550i
\(99\) 0 0
\(100\) −0.786053 + 0.618159i −0.786053 + 0.618159i
\(101\) 0.223734 0.175946i 0.223734 0.175946i −0.500000 0.866025i \(-0.666667\pi\)
0.723734 + 0.690079i \(0.242424\pi\)
\(102\) 0 0
\(103\) 1.56499 0.149438i 1.56499 0.149438i 0.723734 0.690079i \(-0.242424\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(104\) 0 0
\(105\) −0.462997 0.801934i −0.462997 0.801934i
\(106\) 0 0
\(107\) 0.698939 0.449181i 0.698939 0.449181i −0.142315 0.989821i \(-0.545455\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(108\) −0.606636 0.578427i −0.606636 0.578427i
\(109\) −0.653077 1.43004i −0.653077 1.43004i −0.888835 0.458227i \(-0.848485\pi\)
0.235759 0.971812i \(-0.424242\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) −1.28605 + 1.48418i −1.28605 + 1.48418i
\(113\) 0 0 −0.888835 0.458227i \(-0.848485\pi\)
0.888835 + 0.458227i \(0.151515\pi\)
\(114\) 0 0
\(115\) −0.928368 0.371662i −0.928368 0.371662i
\(116\) −0.473420 + 0.451405i −0.473420 + 0.451405i
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) −0.452418 0.132842i −0.452418 0.132842i
\(121\) −0.995472 0.0950560i −0.995472 0.0950560i
\(122\) 0.975950 1.37053i 0.975950 1.37053i
\(123\) −0.0446683 + 0.937702i −0.0446683 + 0.937702i
\(124\) 0 0
\(125\) −0.142315 + 0.989821i −0.142315 + 0.989821i
\(126\) −0.634436 + 1.38922i −0.634436 + 1.38922i
\(127\) 0.0883470 0.0353688i 0.0883470 0.0353688i −0.327068 0.945001i \(-0.606061\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(128\) 0.0475819 + 0.998867i 0.0475819 + 0.998867i
\(129\) 0.574161 + 0.368991i 0.574161 + 0.368991i
\(130\) 0 0
\(131\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −0.995472 + 0.0950560i −0.995472 + 0.0950560i
\(135\) −0.838204 −0.838204
\(136\) 0 0
\(137\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(138\) −0.111165 0.458227i −0.111165 0.458227i
\(139\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(140\) 0.0934441 + 1.96163i 0.0934441 + 1.96163i
\(141\) 0.507831 0.203305i 0.507831 0.203305i
\(142\) 0 0
\(143\) 0 0
\(144\) 0.254351 + 0.734900i 0.254351 + 0.734900i
\(145\) −0.0311250 + 0.653395i −0.0311250 + 0.653395i
\(146\) 0 0
\(147\) −1.34090 0.128041i −1.34090 0.128041i
\(148\) 0 0
\(149\) 0.283341 + 1.97068i 0.283341 + 1.97068i 0.235759 + 0.971812i \(0.424242\pi\)
0.0475819 + 0.998867i \(0.484848\pi\)
\(150\) −0.419102 + 0.216062i −0.419102 + 0.216062i
\(151\) 0 0 0.235759 0.971812i \(-0.424242\pi\)
−0.235759 + 0.971812i \(0.575758\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 0 0 0.981929 0.189251i \(-0.0606061\pi\)
−0.981929 + 0.189251i \(0.939394\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0.723734 + 0.690079i 0.723734 + 0.690079i
\(161\) −1.65210 + 1.06174i −1.65210 + 1.06174i
\(162\) 0.221839 + 0.311529i 0.221839 + 0.311529i
\(163\) 0.959493 + 1.66189i 0.959493 + 1.66189i 0.723734 + 0.690079i \(0.242424\pi\)
0.235759 + 0.971812i \(0.424242\pi\)
\(164\) 0.995472 1.72421i 0.995472 1.72421i
\(165\) 0 0
\(166\) 1.82318 + 0.351390i 1.82318 + 0.351390i
\(167\) 1.02951 0.809616i 1.02951 0.809616i 0.0475819 0.998867i \(-0.484848\pi\)
0.981929 + 0.189251i \(0.0606061\pi\)
\(168\) −0.727880 + 0.572411i −0.727880 + 0.572411i
\(169\) 0.981929 + 0.189251i 0.981929 + 0.189251i
\(170\) 0 0
\(171\) 0 0
\(172\) −0.723734 1.25354i −0.723734 1.25354i
\(173\) 0 0 −0.580057 0.814576i \(-0.696970\pi\)
0.580057 + 0.814576i \(0.303030\pi\)
\(174\) −0.259474 + 0.166754i −0.259474 + 0.166754i
\(175\) 1.42131 + 1.35522i 1.42131 + 1.35522i
\(176\) 0 0
\(177\) 0 0
\(178\) −0.279486 + 0.0538665i −0.279486 + 0.0538665i
\(179\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(180\) 0.691221 + 0.356349i 0.691221 + 0.356349i
\(181\) 0.627639 1.81344i 0.627639 1.81344i 0.0475819 0.998867i \(-0.484848\pi\)
0.580057 0.814576i \(-0.303030\pi\)
\(182\) 0 0
\(183\) 0.574161 0.547462i 0.574161 0.547462i
\(184\) −0.235759 + 0.971812i −0.235759 + 0.971812i
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) −1.15486 0.110276i −1.15486 0.110276i
\(189\) −0.954839 + 1.34088i −0.954839 + 1.34088i
\(190\) 0 0
\(191\) 0 0 −0.327068 0.945001i \(-0.606061\pi\)
0.327068 + 0.945001i \(0.393939\pi\)
\(192\) −0.0671040 + 0.466718i −0.0671040 + 0.466718i
\(193\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 2.40324 + 1.54447i 2.40324 + 1.54447i
\(197\) 0 0 −0.235759 0.971812i \(-0.575758\pi\)
0.235759 + 0.971812i \(0.424242\pi\)
\(198\) 0 0
\(199\) 0 0 −0.786053 0.618159i \(-0.787879\pi\)
0.786053 + 0.618159i \(0.212121\pi\)
\(200\) 1.00000 1.00000
\(201\) −0.469383 0.0448206i −0.469383 0.0448206i
\(202\) −0.284630 −0.284630
\(203\) 1.00979 + 0.794105i 1.00979 + 0.794105i
\(204\) 0 0
\(205\) −0.469383 1.93482i −0.469383 1.93482i
\(206\) −1.32254 0.849945i −1.32254 0.849945i
\(207\) 0.0370031 + 0.776790i 0.0370031 + 0.776790i
\(208\) 0 0
\(209\) 0 0
\(210\) −0.131783 + 0.916569i −0.131783 + 0.916569i
\(211\) 0 0 −0.327068 0.945001i \(-0.606061\pi\)
0.327068 + 0.945001i \(0.393939\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) −0.827068 0.0789754i −0.827068 0.0789754i
\(215\) −1.38884 0.407799i −1.38884 0.407799i
\(216\) 0.119289 + 0.829672i 0.119289 + 0.829672i
\(217\) 0 0
\(218\) −0.370638 + 1.52779i −0.370638 + 1.52779i
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) −1.10181 + 1.27155i −1.10181 + 1.27155i −0.142315 + 0.989821i \(0.545455\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(224\) 1.92837 0.371662i 1.92837 0.371662i
\(225\) 0.746170 0.219095i 0.746170 0.219095i
\(226\) 0 0
\(227\) −0.205996 0.196417i −0.205996 0.196417i 0.580057 0.814576i \(-0.303030\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(228\) 0 0
\(229\) 0.0552004 + 0.0775182i 0.0552004 + 0.0775182i 0.841254 0.540641i \(-0.181818\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(230\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(231\) 0 0
\(232\) 0.651174 0.0621796i 0.651174 0.0621796i
\(233\) 0 0 −0.981929 0.189251i \(-0.939394\pi\)
0.981929 + 0.189251i \(0.0606061\pi\)
\(234\) 0 0
\(235\) −0.911911 + 0.717135i −0.911911 + 0.717135i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(240\) 0.273507 + 0.384087i 0.273507 + 0.384087i
\(241\) −1.32254 + 0.849945i −1.32254 + 0.849945i −0.995472 0.0950560i \(-0.969697\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(242\) 0.723734 + 0.690079i 0.723734 + 0.690079i
\(243\) 0.423114 + 0.926490i 0.423114 + 0.926490i
\(244\) −1.61435 + 0.474017i −1.61435 + 0.474017i
\(245\) 2.80511 0.540641i 2.80511 0.540641i
\(246\) 0.614761 0.709472i 0.614761 0.709472i
\(247\) 0 0
\(248\) 0 0
\(249\) 0.812771 + 0.325385i 0.812771 + 0.325385i
\(250\) 0.723734 0.690079i 0.723734 0.690079i
\(251\) 0 0 0.235759 0.971812i \(-0.424242\pi\)
−0.235759 + 0.971812i \(0.575758\pi\)
\(252\) 1.35746 0.699819i 1.35746 0.699819i
\(253\) 0 0
\(254\) −0.0913090 0.0268107i −0.0913090 0.0268107i
\(255\) 0 0
\(256\) 0.580057 0.814576i 0.580057 0.814576i
\(257\) 0 0 0.0475819 0.998867i \(-0.484848\pi\)
−0.0475819 + 0.998867i \(0.515152\pi\)
\(258\) −0.223226 0.644970i −0.223226 0.644970i
\(259\) 0 0
\(260\) 0 0
\(261\) 0.472263 0.189066i 0.472263 0.189066i
\(262\) 0 0
\(263\) −1.49547 0.961081i −1.49547 0.961081i −0.995472 0.0950560i \(-0.969697\pi\)
−0.500000 0.866025i \(-0.666667\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) −0.134208 −0.134208
\(268\) 0.841254 + 0.540641i 0.841254 + 0.540641i
\(269\) −1.91899 −1.91899 −0.959493 0.281733i \(-0.909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(270\) 0.658873 + 0.518143i 0.658873 + 0.518143i
\(271\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) −0.195876 + 0.428908i −0.195876 + 0.428908i
\(277\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 1.13915 1.59971i 1.13915 1.59971i
\(281\) −1.15486 0.110276i −1.15486 0.110276i −0.500000 0.866025i \(-0.666667\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(282\) −0.524856 0.154112i −0.524856 0.154112i
\(283\) 0.252989 + 1.75958i 0.252989 + 1.75958i 0.580057 + 0.814576i \(0.303030\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −3.62985 1.45317i −3.62985 1.45317i
\(288\) 0.254351 0.734900i 0.254351 0.734900i
\(289\) −0.888835 0.458227i −0.888835 0.458227i
\(290\) 0.428368 0.494363i 0.428368 0.494363i
\(291\) 0 0
\(292\) 0 0
\(293\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(294\) 0.974871 + 0.929538i 0.974871 + 0.929538i
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) 0.995472 1.72421i 0.995472 1.72421i
\(299\) 0 0
\(300\) 0.462997 + 0.0892353i 0.462997 + 0.0892353i
\(301\) −2.23445 + 1.75719i −2.23445 + 1.75719i
\(302\) 0 0
\(303\) −0.131783 0.0253990i −0.131783 0.0253990i
\(304\) 0 0
\(305\) −0.841254 + 1.45709i −0.841254 + 1.45709i
\(306\) 0 0
\(307\) 0.481929 + 0.676774i 0.481929 + 0.676774i 0.981929 0.189251i \(-0.0606061\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(308\) 0 0
\(309\) −0.536487 0.511539i −0.536487 0.511539i
\(310\) 0 0
\(311\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(312\) 0 0
\(313\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(314\) 0 0
\(315\) 0.499510 1.44324i 0.499510 1.44324i
\(316\) 0 0
\(317\) 0 0 0.723734 0.690079i \(-0.242424\pi\)
−0.723734 + 0.690079i \(0.757576\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) −0.142315 0.989821i −0.142315 0.989821i
\(321\) −0.375883 0.110369i −0.375883 0.110369i
\(322\) 1.95496 + 0.186677i 1.95496 + 0.186677i
\(323\) 0 0
\(324\) 0.0181974 0.382010i 0.0181974 0.382010i
\(325\) 0 0
\(326\) 0.273100 1.89945i 0.273100 1.89945i
\(327\) −0.307937 + 0.674289i −0.307937 + 0.674289i
\(328\) −1.84833 + 0.739959i −1.84833 + 0.739959i
\(329\) 0.108406 + 2.27572i 0.108406 + 2.27572i
\(330\) 0 0
\(331\) 0 0 −0.235759 0.971812i \(-0.575758\pi\)
0.235759 + 0.971812i \(0.424242\pi\)
\(332\) −1.21590 1.40323i −1.21590 1.40323i
\(333\) 0 0
\(334\) −1.30972 −1.30972
\(335\) 0.981929 0.189251i 0.981929 0.189251i
\(336\) 0.925994 0.925994
\(337\) 0 0 −0.786053 0.618159i \(-0.787879\pi\)
0.786053 + 0.618159i \(0.212121\pi\)
\(338\) −0.654861 0.755750i −0.654861 0.755750i
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 1.51475 3.31685i 1.51475 3.31685i
\(344\) −0.205996 + 1.43273i −0.205996 + 1.43273i
\(345\) 0.154218 + 0.445585i 0.154218 + 0.445585i
\(346\) 0 0
\(347\) 0.975950 1.37053i 0.975950 1.37053i 0.0475819 0.998867i \(-0.484848\pi\)
0.928368 0.371662i \(-0.121212\pi\)
\(348\) 0.307040 + 0.0293188i 0.307040 + 0.0293188i
\(349\) −1.38884 0.407799i −1.38884 0.407799i −0.500000 0.866025i \(-0.666667\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(350\) −0.279486 1.94387i −0.279486 1.94387i
\(351\) 0 0
\(352\) 0 0
\(353\) 0 0 0.723734 0.690079i \(-0.242424\pi\)
−0.723734 + 0.690079i \(0.757576\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0.252989 + 0.130425i 0.252989 + 0.130425i
\(357\) 0 0
\(358\) 0 0
\(359\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(360\) −0.323056 0.707394i −0.323056 0.707394i
\(361\) 0.723734 + 0.690079i 0.723734 + 0.690079i
\(362\) −1.61435 + 1.03748i −1.61435 + 1.03748i
\(363\) 0.273507 + 0.384087i 0.273507 + 0.384087i
\(364\) 0 0
\(365\) 0 0
\(366\) −0.789740 + 0.0754110i −0.789740 + 0.0754110i
\(367\) −1.54370 0.297523i −1.54370 0.297523i −0.654861 0.755750i \(-0.727273\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(368\) 0.786053 0.618159i 0.786053 0.618159i
\(369\) −1.21705 + 0.957095i −1.21705 + 0.957095i
\(370\) 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
\(375\) 0.396666 0.254922i 0.396666 0.254922i
\(376\) 0.839614 + 0.800570i 0.839614 + 0.800570i
\(377\) 0 0
\(378\) 1.57943 0.463763i 1.57943 0.463763i
\(379\) 0 0 0.981929 0.189251i \(-0.0606061\pi\)
−0.981929 + 0.189251i \(0.939394\pi\)
\(380\) 0 0
\(381\) −0.0398833 0.0205613i −0.0398833 0.0205613i
\(382\) 0 0
\(383\) 1.07701 + 0.431171i 1.07701 + 0.431171i 0.841254 0.540641i \(-0.181818\pi\)
0.235759 + 0.971812i \(0.424242\pi\)
\(384\) 0.341254 0.325385i 0.341254 0.325385i
\(385\) 0 0
\(386\) 0 0
\(387\) 0.160197 + 1.11420i 0.160197 + 1.11420i
\(388\) 0 0
\(389\) 1.56499 + 0.149438i 1.56499 + 0.149438i 0.841254 0.540641i \(-0.181818\pi\)
0.723734 + 0.690079i \(0.242424\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) −0.934347 2.69962i −0.934347 2.69962i
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) −0.786053 0.618159i −0.786053 0.618159i
\(401\) 1.96386 1.96386 0.981929 0.189251i \(-0.0606061\pi\)
0.981929 + 0.189251i \(0.0606061\pi\)
\(402\) 0.341254 + 0.325385i 0.341254 + 0.325385i
\(403\) 0 0
\(404\) 0.223734 + 0.175946i 0.223734 + 0.175946i
\(405\) −0.250447 0.289031i −0.250447 0.289031i
\(406\) −0.302863 1.24842i −0.302863 1.24842i
\(407\) 0 0
\(408\) 0 0
\(409\) −1.78153 + 0.713215i −1.78153 + 0.713215i −0.786053 + 0.618159i \(0.787879\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(410\) −0.827068 + 1.81103i −0.827068 + 1.81103i
\(411\) 0 0
\(412\) 0.514186 + 1.48564i 0.514186 + 1.48564i
\(413\) 0 0
\(414\) 0.451093 0.633472i 0.451093 0.633472i
\(415\) −1.84833 0.176494i −1.84833 0.176494i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 0 0 0.235759 0.971812i \(-0.424242\pi\)
−0.235759 + 0.971812i \(0.575758\pi\)
\(420\) 0.670173 0.639009i 0.670173 0.639009i
\(421\) −1.21590 0.486774i −1.21590 0.486774i −0.327068 0.945001i \(-0.606061\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(422\) 0 0
\(423\) 0.801896 + 0.413406i 0.801896 + 0.413406i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 1.37262 + 3.00561i 1.37262 + 3.00561i
\(428\) 0.601300 + 0.573338i 0.601300 + 0.573338i
\(429\) 0 0
\(430\) 0.839614 + 1.17907i 0.839614 + 1.17907i
\(431\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(432\) 0.419102 0.725906i 0.419102 0.725906i
\(433\) 0 0 0.995472 0.0950560i \(-0.0303030\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(434\) 0 0
\(435\) 0.242448 0.190663i 0.242448 0.190663i
\(436\) 1.23576 0.971812i 1.23576 0.971812i
\(437\) 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
\(441\) −1.28865 1.80966i −1.28865 1.80966i
\(442\) 0 0
\(443\) −0.473420 0.451405i −0.473420 0.451405i 0.415415 0.909632i \(-0.363636\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(444\) 0 0
\(445\) 0.273100 0.0801894i 0.273100 0.0801894i
\(446\) 1.65210 0.318417i 1.65210 0.318417i
\(447\) 0.614761 0.709472i 0.614761 0.709472i
\(448\) −1.74555 0.899892i −1.74555 0.899892i
\(449\) −0.379436 + 1.09631i −0.379436 + 1.09631i 0.580057 + 0.814576i \(0.303030\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(450\) −0.721965 0.289031i −0.721965 0.289031i
\(451\) 0 0
\(452\) 0 0
\(453\) 0 0
\(454\) 0.0405070 + 0.281733i 0.0405070 + 0.281733i
\(455\) 0 0
\(456\) 0 0
\(457\) 0 0 0.580057 0.814576i \(-0.303030\pi\)
−0.580057 + 0.814576i \(0.696970\pi\)
\(458\) 0.00452808 0.0950560i 0.00452808 0.0950560i
\(459\) 0 0
\(460\) 0.142315 0.989821i 0.142315 0.989821i
\(461\) 0.771316 1.68895i 0.771316 1.68895i 0.0475819 0.998867i \(-0.484848\pi\)
0.723734 0.690079i \(-0.242424\pi\)
\(462\) 0 0
\(463\) −0.0913090 1.91681i −0.0913090 1.91681i −0.327068 0.945001i \(-0.606061\pi\)
0.235759 0.971812i \(-0.424242\pi\)
\(464\) −0.550294 0.353653i −0.550294 0.353653i
\(465\) 0 0
\(466\) 0 0
\(467\) −0.0748038 0.0588264i −0.0748038 0.0588264i 0.580057 0.814576i \(-0.303030\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(468\) 0 0
\(469\) 0.815816 1.78639i 0.815816 1.78639i
\(470\) 1.16011 1.16011
\(471\) 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 −0.327068 0.945001i \(-0.606061\pi\)
0.327068 + 0.945001i \(0.393939\pi\)
\(480\) 0.0224357 0.470984i 0.0224357 0.470984i
\(481\) 0 0
\(482\) 1.56499 + 0.149438i 1.56499 + 0.149438i
\(483\) 0.888485 + 0.260883i 0.888485 + 0.260883i
\(484\) −0.142315 0.989821i −0.142315 0.989821i
\(485\) 0 0
\(486\) 0.240128 0.989821i 0.240128 0.989821i
\(487\) 1.34378 1.28129i 1.34378 1.28129i 0.415415 0.909632i \(-0.363636\pi\)
0.928368 0.371662i \(-0.121212\pi\)
\(488\) 1.56199 + 0.625325i 1.56199 + 0.625325i
\(489\) 0.295943 0.855071i 0.295943 0.855071i
\(490\) −2.53917 1.30903i −2.53917 1.30903i
\(491\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(492\) −0.921801 + 0.177663i −0.921801 + 0.177663i
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) −0.437742 0.758192i −0.437742 0.758192i
\(499\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(500\) −0.995472 + 0.0950560i −0.995472 + 0.0950560i
\(501\) −0.606397 0.116873i −0.606397 0.116873i
\(502\) 0 0
\(503\) 1.56499 1.23072i 1.56499 1.23072i 0.723734 0.690079i \(-0.242424\pi\)
0.841254 0.540641i \(-0.181818\pi\)
\(504\) −1.49964 0.289031i −1.49964 0.289031i
\(505\) 0.283341 0.0270558i 0.283341 0.0270558i
\(506\) 0 0
\(507\) −0.235759 0.408346i −0.235759 0.408346i
\(508\) 0.0552004 + 0.0775182i 0.0552004 + 0.0775182i
\(509\) −1.10181 + 0.708089i −1.10181 + 0.708089i −0.959493 0.281733i \(-0.909091\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −0.959493 + 0.281733i −0.959493 + 0.281733i
\(513\) 0 0
\(514\) 0 0
\(515\) 1.39734 + 0.720381i 1.39734 + 0.720381i
\(516\) −0.223226 + 0.644970i −0.223226 + 0.644970i
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 0.142315 + 0.989821i 0.142315 + 0.989821i 0.928368 + 0.371662i \(0.121212\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(522\) −0.488096 0.143318i −0.488096 0.143318i
\(523\) −1.44091 0.137591i −1.44091 0.137591i −0.654861 0.755750i \(-0.727273\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(524\) 0 0
\(525\) 0.0440606 0.924945i 0.0440606 0.924945i
\(526\) 0.581419 + 1.67990i 0.581419 + 1.67990i
\(527\) 0 0
\(528\) 0 0
\(529\) 0 0
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) 0.105495 + 0.0829619i 0.105495 + 0.0829619i
\(535\) 0.830830 0.830830
\(536\) −0.327068 0.945001i −0.327068 0.945001i
\(537\) 0 0
\(538\) 1.50842 + 1.18624i 1.50842 + 1.18624i
\(539\) 0 0
\(540\) −0.197614 0.814576i −0.197614 0.814576i
\(541\) 1.21769 + 0.782560i 1.21769 + 0.782560i 0.981929 0.189251i \(-0.0606061\pi\)
0.235759 + 0.971812i \(0.424242\pi\)
\(542\) 0 0
\(543\) −0.840021 + 0.336294i −0.840021 + 0.336294i
\(544\) 0 0
\(545\) 0.223734 1.55610i 0.223734 1.55610i
\(546\) 0 0
\(547\) 0.00452808 0.0950560i 0.00452808 0.0950560i −0.995472 0.0950560i \(-0.969697\pi\)
1.00000 \(0\)
\(548\) 0 0
\(549\) 1.30251 + 0.124375i 1.30251 + 0.124375i
\(550\) 0 0
\(551\) 0 0
\(552\) 0.419102 0.216062i 0.419102 0.216062i
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 0 0 −0.888835 0.458227i \(-0.848485\pi\)
0.888835 + 0.458227i \(0.151515\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) −1.88431 + 0.553283i −1.88431 + 0.553283i
\(561\) 0 0
\(562\) 0.839614 + 0.800570i 0.839614 + 0.800570i
\(563\) 1.21769 0.782560i 1.21769 0.782560i 0.235759 0.971812i \(-0.424242\pi\)
0.981929 + 0.189251i \(0.0606061\pi\)
\(564\) 0.317299 + 0.445585i 0.317299 + 0.445585i
\(565\) 0 0
\(566\) 0.888835 1.53951i 0.888835 1.53951i
\(567\) −0.747662 + 0.0713931i −0.747662 + 0.0713931i
\(568\) 0 0
\(569\) 1.02951 0.809616i 1.02951 0.809616i 0.0475819 0.998867i \(-0.484848\pi\)
0.981929 + 0.189251i \(0.0606061\pi\)
\(570\) 0 0
\(571\) 0 0 −0.981929 0.189251i \(-0.939394\pi\)
0.981929 + 0.189251i \(0.0606061\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 1.95496 + 3.38610i 1.95496 + 3.38610i
\(575\) −0.580057 0.814576i −0.580057 0.814576i
\(576\) −0.654218 + 0.420441i −0.654218 + 0.420441i
\(577\) 0 0 −0.723734 0.690079i \(-0.757576\pi\)
0.723734 + 0.690079i \(0.242424\pi\)
\(578\) 0.415415 + 0.909632i 0.415415 + 0.909632i
\(579\) 0 0
\(580\) −0.642315 + 0.123796i −0.642315 + 0.123796i
\(581\) −2.38786 + 2.75574i −2.38786 + 2.75574i
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −0.738471 + 0.380708i −0.738471 + 0.380708i −0.786053 0.618159i \(-0.787879\pi\)
0.0475819 + 0.998867i \(0.484848\pi\)
\(588\) −0.191698 1.33329i −0.191698 1.33329i
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 0 0 −0.327068 0.945001i \(-0.606061\pi\)
0.327068 + 0.945001i \(0.393939\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −1.84833 + 0.739959i −1.84833 + 0.739959i
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 −0.235759 0.971812i \(-0.575758\pi\)
0.235759 + 0.971812i \(0.424242\pi\)
\(600\) −0.308779 0.356349i −0.308779 0.356349i
\(601\) −1.13779 0.894765i −1.13779 0.894765i −0.142315 0.989821i \(-0.545455\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(602\) 2.84262 2.84262
\(603\) −0.451093 0.633472i −0.451093 0.633472i
\(604\) 0 0
\(605\) −0.786053 0.618159i −0.786053 0.618159i
\(606\) 0.0878875 + 0.101428i 0.0878875 + 0.101428i
\(607\) 0.273507 + 1.12741i 0.273507 + 1.12741i 0.928368 + 0.371662i \(0.121212\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(608\) 0 0
\(609\) −0.0288216 0.605040i −0.0288216 0.605040i
\(610\) 1.56199 0.625325i 1.56199 0.625325i
\(611\) 0 0
\(612\) 0 0
\(613\) 0 0 −0.327068 0.945001i \(-0.606061\pi\)
0.327068 + 0.945001i \(0.393939\pi\)
\(614\) 0.0395325 0.829889i 0.0395325 0.829889i
\(615\) −0.544537 + 0.764696i −0.544537 + 0.764696i
\(616\) 0 0
\(617\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(618\) 0.105495 + 0.733731i 0.105495 + 0.733731i
\(619\) 0 0 0.888835 0.458227i \(-0.151515\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(620\) 0 0
\(621\) 0.606636 0.578427i 0.606636 0.578427i
\(622\) 0 0
\(623\) 0.182822 0.528229i 0.182822 0.528229i
\(624\) 0 0
\(625\) −0.654861 + 0.755750i −0.654861 + 0.755750i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) −1.28479 + 0.825685i −1.28479 + 0.825685i
\(631\) 0 0 −0.580057 0.814576i \(-0.696970\pi\)
0.580057 + 0.814576i \(0.303030\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 0.0934441 + 0.0180099i 0.0934441 + 0.0180099i
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(641\) 0.888835 + 1.53951i 0.888835 + 1.53951i 0.841254 + 0.540641i \(0.181818\pi\)
0.0475819 + 0.998867i \(0.484848\pi\)
\(642\) 0.227238 + 0.319111i 0.227238 + 0.319111i
\(643\) −0.550294 + 0.353653i −0.550294 + 0.353653i −0.786053 0.618159i \(-0.787879\pi\)
0.235759 + 0.971812i \(0.424242\pi\)
\(644\) −1.42131 1.35522i −1.42131 1.35522i
\(645\) 0.283524 + 0.620830i 0.283524 + 0.620830i
\(646\) 0 0
\(647\) 1.13915 0.219553i 1.13915 0.219553i 0.415415 0.909632i \(-0.363636\pi\)
0.723734 + 0.690079i \(0.242424\pi\)
\(648\) −0.250447 + 0.289031i −0.250447 + 0.289031i
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) −1.38884 + 1.32425i −1.38884 + 1.32425i
\(653\) 0 0 0.235759 0.971812i \(-0.424242\pi\)
−0.235759 + 0.971812i \(0.575758\pi\)
\(654\) 0.658873 0.339672i 0.658873 0.339672i
\(655\) 0 0
\(656\) 1.91030 + 0.560914i 1.91030 + 0.560914i
\(657\) 0 0
\(658\) 1.32154 1.85585i 1.32154 1.85585i
\(659\) 0 0 0.0475819 0.998867i \(-0.484848\pi\)
−0.0475819 + 0.998867i \(0.515152\pi\)
\(660\) 0 0
\(661\) 0.186393 1.29639i 0.186393 1.29639i −0.654861 0.755750i \(-0.727273\pi\)
0.841254 0.540641i \(-0.181818\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0.0883470 + 1.85463i 0.0883470 + 1.85463i
\(665\) 0 0
\(666\) 0 0
\(667\) −0.428368 0.494363i −0.428368 0.494363i
\(668\) 1.02951 + 0.809616i 1.02951 + 0.809616i
\(669\) 0.793332 0.793332
\(670\) −0.888835 0.458227i −0.888835 0.458227i
\(671\) 0 0
\(672\) −0.727880 0.572411i −0.727880 0.572411i
\(673\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(674\) 0 0
\(675\) −0.705142 0.453167i −0.705142 0.453167i
\(676\) 0.0475819 + 0.998867i 0.0475819 + 0.998867i
\(677\) 0 0 0.928368 0.371662i \(-0.121212\pi\)
−0.928368 + 0.371662i \(0.878788\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) −0.00638587 + 0.134056i −0.00638587 + 0.134056i
\(682\) 0 0
\(683\) −0.827068 0.0789754i −0.827068 0.0789754i −0.327068 0.945001i \(-0.606061\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) −3.24102 + 1.67086i −3.24102 + 1.67086i
\(687\) 0.0105788 0.0436066i 0.0105788 0.0436066i
\(688\) 1.04758 0.998867i 1.04758 0.998867i
\(689\) 0 0
\(690\) 0.154218 0.445585i 0.154218 0.445585i
\(691\) 0 0 −0.888835 0.458227i \(-0.848485\pi\)
0.888835 + 0.458227i \(0.151515\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) −1.61435 + 0.474017i −1.61435 + 0.474017i
\(695\) 0 0
\(696\) −0.223226 0.212846i −0.223226 0.212846i
\(697\) 0 0
\(698\) 0.839614 + 1.17907i 0.839614 + 1.17907i
\(699\) 0 0
\(700\) −0.981929 + 1.70075i −0.981929 + 1.70075i
\(701\) 0.995472 0.0950560i 0.995472 0.0950560i 0.415415 0.909632i \(-0.363636\pi\)
0.580057 + 0.814576i \(0.303030\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0 0
\(705\) 0.537129 + 0.103523i 0.537129 + 0.103523i
\(706\) 0 0
\(707\) 0.279486 0.484084i 0.279486 0.484084i
\(708\) 0 0
\(709\) −0.580057 0.814576i −0.580057 0.814576i 0.415415 0.909632i \(-0.363636\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) −0.118239 0.258908i −0.118239 0.258908i
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 0.723734 0.690079i \(-0.242424\pi\)
−0.723734 + 0.690079i \(0.757576\pi\)
\(720\) −0.183343 + 0.755750i −0.183343 + 0.755750i
\(721\) 2.74418 1.41473i 2.74418 1.41473i
\(722\) −0.142315 0.989821i −0.142315 0.989821i
\(723\) 0.711249 + 0.208842i 0.711249 + 0.208842i
\(724\) 1.91030 + 0.182411i 1.91030 + 0.182411i
\(725\) −0.379436 + 0.532843i −0.379436 + 0.532843i
\(726\) 0.0224357 0.470984i 0.0224357 0.470984i
\(727\) 0.651174 + 1.88144i 0.651174 + 1.88144i 0.415415 + 0.909632i \(0.363636\pi\)
0.235759 + 0.971812i \(0.424242\pi\)
\(728\) 0 0
\(729\) 0.0406331 0.0889741i 0.0406331 0.0889741i
\(730\) 0 0
\(731\) 0 0
\(732\) 0.667393 + 0.428908i 0.667393 + 0.428908i
\(733\) 0 0 −0.235759 0.971812i \(-0.575758\pi\)
0.235759 + 0.971812i \(0.424242\pi\)
\(734\) 1.02951 + 1.18812i 1.02951 + 1.18812i
\(735\) −1.05882 0.832661i −1.05882 0.832661i
\(736\) −1.00000 −1.00000
\(737\) 0 0
\(738\) 1.54830 1.54830
\(739\) 0 0 −0.786053 0.618159i \(-0.787879\pi\)
0.786053 + 0.618159i \(0.212121\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −0.0913090 1.91681i −0.0913090 1.91681i −0.327068 0.945001i \(-0.606061\pi\)
0.235759 0.971812i \(-0.424242\pi\)
\(744\) 0 0
\(745\) −0.827068 + 1.81103i −0.827068 + 1.81103i
\(746\) 0 0
\(747\) 0.472263 + 1.36451i 0.472263 + 1.36451i
\(748\) 0 0
\(749\) 0.946439 1.32909i 0.946439 1.32909i
\(750\) −0.469383 0.0448206i −0.469383 0.0448206i
\(751\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(752\) −0.165101 1.14831i −0.165101 1.14831i
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) −1.52820 0.611798i −1.52820 0.611798i
\(757\) 0 0 0.327068 0.945001i \(-0.393939\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 1.84125 0.540641i 1.84125 0.540641i 0.841254 0.540641i \(-0.181818\pi\)
1.00000 \(0\)
\(762\) 0.0186403 + 0.0408165i 0.0186403 + 0.0408165i
\(763\) −2.23445 2.13054i −2.23445 2.13054i
\(764\) 0 0
\(765\) 0 0
\(766\) −0.580057 1.00469i −0.580057 1.00469i
\(767\) 0 0
\(768\) −0.469383 + 0.0448206i −0.469383 + 0.0448206i
\(769\) 0.462997 + 0.0892353i 0.462997 + 0.0892353i 0.415415 0.909632i \(-0.363636\pi\)
0.0475819 + 0.998867i \(0.484848\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 0 0 0.995472 0.0950560i \(-0.0303030\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(774\) 0.562827 0.974845i 0.562827 0.974845i
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) −1.13779 1.08488i −1.13779 1.08488i
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) −0.487348 0.251245i −0.487348 0.251245i
\(784\) −0.934347 + 2.69962i −0.934347 + 2.69962i
\(785\) 0 0
\(786\) 0 0
\(787\) 0.0224357 0.0924813i 0.0224357 0.0924813i −0.959493 0.281733i \(-0.909091\pi\)
0.981929 + 0.189251i \(0.0606061\pi\)
\(788\) 0 0
\(789\) 0.119289 + 0.829672i 0.119289 + 0.829672i
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0