Properties

Label 1340.1.bl.b.839.1
Level $1340$
Weight $1$
Character 1340.839
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 839.1
Root \(-0.786053 - 0.618159i\) of defining polynomial
Character \(\chi\) \(=\) 1340.839
Dual form 1340.1.bl.b.559.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.235759 - 0.971812i) q^{2} +(0.252989 + 1.75958i) q^{3} +(-0.888835 - 0.458227i) q^{4} +(0.415415 - 0.909632i) q^{5} +(1.76962 + 0.168978i) q^{6} +(1.34378 + 1.28129i) q^{7} +(-0.654861 + 0.755750i) q^{8} +(-2.07261 + 0.608574i) q^{9} +O(q^{10})\) \(q+(0.235759 - 0.971812i) q^{2} +(0.252989 + 1.75958i) q^{3} +(-0.888835 - 0.458227i) q^{4} +(0.415415 - 0.909632i) q^{5} +(1.76962 + 0.168978i) q^{6} +(1.34378 + 1.28129i) q^{7} +(-0.654861 + 0.755750i) q^{8} +(-2.07261 + 0.608574i) q^{9} +(-0.786053 - 0.618159i) q^{10} +(0.581419 - 1.67990i) q^{12} +(1.56199 - 1.00383i) q^{14} +(1.70566 + 0.500828i) q^{15} +(0.580057 + 0.814576i) q^{16} +(0.102782 + 2.15767i) q^{18} +(-0.786053 + 0.618159i) q^{20} +(-1.91457 + 2.68864i) q^{21} +(-0.928368 - 0.371662i) q^{23} +(-1.49547 - 0.961081i) q^{24} +(-0.654861 - 0.755750i) q^{25} +(-0.856711 - 1.87593i) q^{27} +(-0.607279 - 1.75462i) q^{28} +(0.786053 + 1.36148i) q^{29} +(0.888835 - 1.53951i) q^{30} +(0.928368 - 0.371662i) q^{32} +(1.72373 - 0.690079i) q^{35} +(2.12108 + 0.408804i) q^{36} +(0.415415 + 0.909632i) q^{40} +(0.0934441 - 1.96163i) q^{41} +(2.16148 + 2.49448i) q^{42} +(0.0800569 + 0.0514495i) q^{43} +(-0.307416 + 2.13813i) q^{45} +(-0.580057 + 0.814576i) q^{46} +(0.514186 - 0.404360i) q^{47} +(-1.28656 + 1.22673i) q^{48} +(0.116455 + 2.44470i) q^{49} +(-0.888835 + 0.458227i) q^{50} +(-2.02503 + 0.390293i) q^{54} +(-1.84833 + 0.176494i) q^{56} +(1.50842 - 0.442913i) q^{58} +(-1.28656 - 1.22673i) q^{60} +(-0.827068 - 0.0789754i) q^{61} +(-3.56491 - 1.83784i) q^{63} +(-0.142315 - 0.989821i) q^{64} +(0.0475819 + 0.998867i) q^{67} +(0.419102 - 1.72756i) q^{69} +(-0.264241 - 1.83784i) q^{70} +(0.897344 - 1.96491i) q^{72} +(1.16413 - 1.34347i) q^{75} +(0.981929 - 0.189251i) q^{80} +(1.26691 - 0.814193i) q^{81} +(-1.88431 - 0.553283i) q^{82} +(0.839614 + 1.17907i) q^{83} +(2.93375 - 1.51245i) q^{84} +(0.0688733 - 0.0656706i) q^{86} +(-2.19677 + 1.72756i) q^{87} +(0.273100 - 1.89945i) q^{89} +(2.00538 + 0.802833i) q^{90} +(0.654861 + 0.755750i) q^{92} +(-0.271738 - 0.595023i) q^{94} +(0.888835 + 1.53951i) q^{96} +(2.40324 + 0.463186i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20q + q^{2} + 2q^{3} + q^{4} - 2q^{5} - q^{6} - q^{7} - 2q^{8} + O(q^{10}) \) \( 20q + q^{2} + 2q^{3} + q^{4} - 2q^{5} - q^{6} - q^{7} - 2q^{8} + q^{10} - q^{12} + 2q^{14} + 2q^{15} + q^{16} + q^{20} - 10q^{21} - q^{23} - 9q^{24} - 2q^{25} - 2q^{27} - q^{28} - q^{29} - q^{30} + q^{32} + 21q^{35} - 2q^{40} - q^{41} + 20q^{42} - 9q^{43} - q^{46} - q^{47} - q^{48} + q^{50} + q^{54} - q^{56} + 2q^{58} - q^{60} - 9q^{61} - 11q^{63} - 2q^{64} + q^{67} + q^{69} - 9q^{70} - 11q^{72} + 2q^{75} + q^{80} + 2q^{81} + 2q^{82} - q^{83} + q^{84} - q^{86} + q^{87} - 4q^{89} + 2q^{92} + 2q^{94} - q^{96} + O(q^{100}) \)

Character values

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

\(n\) \(537\) \(671\) \(1141\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{19}{33}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.235759 0.971812i 0.235759 0.971812i
\(3\) 0.252989 + 1.75958i 0.252989 + 1.75958i 0.580057 + 0.814576i \(0.303030\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(4\) −0.888835 0.458227i −0.888835 0.458227i
\(5\) 0.415415 0.909632i 0.415415 0.909632i
\(6\) 1.76962 + 0.168978i 1.76962 + 0.168978i
\(7\) 1.34378 + 1.28129i 1.34378 + 1.28129i 0.928368 + 0.371662i \(0.121212\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(8\) −0.654861 + 0.755750i −0.654861 + 0.755750i
\(9\) −2.07261 + 0.608574i −2.07261 + 0.608574i
\(10\) −0.786053 0.618159i −0.786053 0.618159i
\(11\) 0 0 0.995472 0.0950560i \(-0.0303030\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(12\) 0.581419 1.67990i 0.581419 1.67990i
\(13\) 0 0 0.981929 0.189251i \(-0.0606061\pi\)
−0.981929 + 0.189251i \(0.939394\pi\)
\(14\) 1.56199 1.00383i 1.56199 1.00383i
\(15\) 1.70566 + 0.500828i 1.70566 + 0.500828i
\(16\) 0.580057 + 0.814576i 0.580057 + 0.814576i
\(17\) 0 0 0.888835 0.458227i \(-0.151515\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(18\) 0.102782 + 2.15767i 0.102782 + 2.15767i
\(19\) 0 0 0.723734 0.690079i \(-0.242424\pi\)
−0.723734 + 0.690079i \(0.757576\pi\)
\(20\) −0.786053 + 0.618159i −0.786053 + 0.618159i
\(21\) −1.91457 + 2.68864i −1.91457 + 2.68864i
\(22\) 0 0
\(23\) −0.928368 0.371662i −0.928368 0.371662i −0.142315 0.989821i \(-0.545455\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(24\) −1.49547 0.961081i −1.49547 0.961081i
\(25\) −0.654861 0.755750i −0.654861 0.755750i
\(26\) 0 0
\(27\) −0.856711 1.87593i −0.856711 1.87593i
\(28\) −0.607279 1.75462i −0.607279 1.75462i
\(29\) 0.786053 + 1.36148i 0.786053 + 1.36148i 0.928368 + 0.371662i \(0.121212\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(30\) 0.888835 1.53951i 0.888835 1.53951i
\(31\) 0 0 −0.981929 0.189251i \(-0.939394\pi\)
0.981929 + 0.189251i \(0.0606061\pi\)
\(32\) 0.928368 0.371662i 0.928368 0.371662i
\(33\) 0 0
\(34\) 0 0
\(35\) 1.72373 0.690079i 1.72373 0.690079i
\(36\) 2.12108 + 0.408804i 2.12108 + 0.408804i
\(37\) 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
\(41\) 0.0934441 1.96163i 0.0934441 1.96163i −0.142315 0.989821i \(-0.545455\pi\)
0.235759 0.971812i \(-0.424242\pi\)
\(42\) 2.16148 + 2.49448i 2.16148 + 2.49448i
\(43\) 0.0800569 + 0.0514495i 0.0800569 + 0.0514495i 0.580057 0.814576i \(-0.303030\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(44\) 0 0
\(45\) −0.307416 + 2.13813i −0.307416 + 2.13813i
\(46\) −0.580057 + 0.814576i −0.580057 + 0.814576i
\(47\) 0.514186 0.404360i 0.514186 0.404360i −0.327068 0.945001i \(-0.606061\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(48\) −1.28656 + 1.22673i −1.28656 + 1.22673i
\(49\) 0.116455 + 2.44470i 0.116455 + 2.44470i
\(50\) −0.888835 + 0.458227i −0.888835 + 0.458227i
\(51\) 0 0
\(52\) 0 0
\(53\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(54\) −2.02503 + 0.390293i −2.02503 + 0.390293i
\(55\) 0 0
\(56\) −1.84833 + 0.176494i −1.84833 + 0.176494i
\(57\) 0 0
\(58\) 1.50842 0.442913i 1.50842 0.442913i
\(59\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(60\) −1.28656 1.22673i −1.28656 1.22673i
\(61\) −0.827068 0.0789754i −0.827068 0.0789754i −0.327068 0.945001i \(-0.606061\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(62\) 0 0
\(63\) −3.56491 1.83784i −3.56491 1.83784i
\(64\) −0.142315 0.989821i −0.142315 0.989821i
\(65\) 0 0
\(66\) 0 0
\(67\) 0.0475819 + 0.998867i 0.0475819 + 0.998867i
\(68\) 0 0
\(69\) 0.419102 1.72756i 0.419102 1.72756i
\(70\) −0.264241 1.83784i −0.264241 1.83784i
\(71\) 0 0 −0.888835 0.458227i \(-0.848485\pi\)
0.888835 + 0.458227i \(0.151515\pi\)
\(72\) 0.897344 1.96491i 0.897344 1.96491i
\(73\) 0 0 −0.995472 0.0950560i \(-0.969697\pi\)
0.995472 + 0.0950560i \(0.0303030\pi\)
\(74\) 0 0
\(75\) 1.16413 1.34347i 1.16413 1.34347i
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 0.327068 0.945001i \(-0.393939\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(80\) 0.981929 0.189251i 0.981929 0.189251i
\(81\) 1.26691 0.814193i 1.26691 0.814193i
\(82\) −1.88431 0.553283i −1.88431 0.553283i
\(83\) 0.839614 + 1.17907i 0.839614 + 1.17907i 0.981929 + 0.189251i \(0.0606061\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(84\) 2.93375 1.51245i 2.93375 1.51245i
\(85\) 0 0
\(86\) 0.0688733 0.0656706i 0.0688733 0.0656706i
\(87\) −2.19677 + 1.72756i −2.19677 + 1.72756i
\(88\) 0 0
\(89\) 0.273100 1.89945i 0.273100 1.89945i −0.142315 0.989821i \(-0.545455\pi\)
0.415415 0.909632i \(-0.363636\pi\)
\(90\) 2.00538 + 0.802833i 2.00538 + 0.802833i
\(91\) 0 0
\(92\) 0.654861 + 0.755750i 0.654861 + 0.755750i
\(93\) 0 0
\(94\) −0.271738 0.595023i −0.271738 0.595023i
\(95\) 0 0
\(96\) 0.888835 + 1.53951i 0.888835 + 1.53951i
\(97\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(98\) 2.40324 + 0.463186i 2.40324 + 0.463186i
\(99\) 0 0
\(100\) 0.235759 + 0.971812i 0.235759 + 0.971812i
\(101\) −0.452418 1.86489i −0.452418 1.86489i −0.500000 0.866025i \(-0.666667\pi\)
0.0475819 0.998867i \(-0.484848\pi\)
\(102\) 0 0
\(103\) 0.462997 + 0.0892353i 0.462997 + 0.0892353i 0.415415 0.909632i \(-0.363636\pi\)
0.0475819 + 0.998867i \(0.484848\pi\)
\(104\) 0 0
\(105\) 1.65033 + 2.85846i 1.65033 + 2.85846i
\(106\) 0 0
\(107\) −0.544078 1.19136i −0.544078 1.19136i −0.959493 0.281733i \(-0.909091\pi\)
0.415415 0.909632i \(-0.363636\pi\)
\(108\) −0.0981282 + 2.05996i −0.0981282 + 2.05996i
\(109\) −0.308779 0.356349i −0.308779 0.356349i 0.580057 0.814576i \(-0.303030\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) −0.264241 + 1.83784i −0.264241 + 1.83784i
\(113\) 0 0 0.580057 0.814576i \(-0.303030\pi\)
−0.580057 + 0.814576i \(0.696970\pi\)
\(114\) 0 0
\(115\) −0.723734 + 0.690079i −0.723734 + 0.690079i
\(116\) −0.0748038 1.57033i −0.0748038 1.57033i
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) −1.49547 + 0.961081i −1.49547 + 0.961081i
\(121\) 0.981929 0.189251i 0.981929 0.189251i
\(122\) −0.271738 + 0.785135i −0.271738 + 0.785135i
\(123\) 3.47528 0.331849i 3.47528 0.331849i
\(124\) 0 0
\(125\) −0.959493 + 0.281733i −0.959493 + 0.281733i
\(126\) −2.62649 + 3.03113i −2.62649 + 3.03113i
\(127\) −1.44091 1.37391i −1.44091 1.37391i −0.786053 0.618159i \(-0.787879\pi\)
−0.654861 0.755750i \(-0.727273\pi\)
\(128\) −0.995472 0.0950560i −0.995472 0.0950560i
\(129\) −0.0702757 + 0.153882i −0.0702757 + 0.153882i
\(130\) 0 0
\(131\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0.981929 + 0.189251i 0.981929 + 0.189251i
\(135\) −2.06230 −2.06230
\(136\) 0 0
\(137\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(138\) −1.58006 0.814576i −1.58006 0.814576i
\(139\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(140\) −1.84833 0.176494i −1.84833 0.176494i
\(141\) 0.841586 + 0.802450i 0.841586 + 0.802450i
\(142\) 0 0
\(143\) 0 0
\(144\) −1.69796 1.33529i −1.69796 1.33529i
\(145\) 1.56499 0.149438i 1.56499 0.149438i
\(146\) 0 0
\(147\) −4.27217 + 0.823393i −4.27217 + 0.823393i
\(148\) 0 0
\(149\) −1.88431 0.553283i −1.88431 0.553283i −0.995472 0.0950560i \(-0.969697\pi\)
−0.888835 0.458227i \(-0.848485\pi\)
\(150\) −1.03115 1.44805i −1.03115 1.44805i
\(151\) 0 0 0.888835 0.458227i \(-0.151515\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 0 0 −0.928368 0.371662i \(-0.878788\pi\)
0.928368 + 0.371662i \(0.121212\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0.0475819 0.998867i 0.0475819 0.998867i
\(161\) −0.771316 1.68895i −0.771316 1.68895i
\(162\) −0.492557 1.42315i −0.492557 1.42315i
\(163\) −0.841254 1.45709i −0.841254 1.45709i −0.888835 0.458227i \(-0.848485\pi\)
0.0475819 0.998867i \(-0.484848\pi\)
\(164\) −0.981929 + 1.70075i −0.981929 + 1.70075i
\(165\) 0 0
\(166\) 1.34378 0.537970i 1.34378 0.537970i
\(167\) −0.0671040 0.276606i −0.0671040 0.276606i 0.928368 0.371662i \(-0.121212\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(168\) −0.778161 3.20762i −0.778161 3.20762i
\(169\) 0.928368 0.371662i 0.928368 0.371662i
\(170\) 0 0
\(171\) 0 0
\(172\) −0.0475819 0.0824143i −0.0475819 0.0824143i
\(173\) 0 0 −0.327068 0.945001i \(-0.606061\pi\)
0.327068 + 0.945001i \(0.393939\pi\)
\(174\) 1.16096 + 2.54214i 1.16096 + 2.54214i
\(175\) 0.0883470 1.85463i 0.0883470 1.85463i
\(176\) 0 0
\(177\) 0 0
\(178\) −1.78153 0.713215i −1.78153 0.713215i
\(179\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(180\) 1.25299 1.75958i 1.25299 1.75958i
\(181\) −1.32254 + 1.04006i −1.32254 + 1.04006i −0.327068 + 0.945001i \(0.606061\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(182\) 0 0
\(183\) −0.0702757 1.47527i −0.0702757 1.47527i
\(184\) 0.888835 0.458227i 0.888835 0.458227i
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) −0.642315 + 0.123796i −0.642315 + 0.123796i
\(189\) 1.25239 3.61855i 1.25239 3.61855i
\(190\) 0 0
\(191\) 0 0 −0.786053 0.618159i \(-0.787879\pi\)
0.786053 + 0.618159i \(0.212121\pi\)
\(192\) 1.70566 0.500828i 1.70566 0.500828i
\(193\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 1.01671 2.22630i 1.01671 2.22630i
\(197\) 0 0 −0.888835 0.458227i \(-0.848485\pi\)
0.888835 + 0.458227i \(0.151515\pi\)
\(198\) 0 0
\(199\) 0 0 0.235759 0.971812i \(-0.424242\pi\)
−0.235759 + 0.971812i \(0.575758\pi\)
\(200\) 1.00000 1.00000
\(201\) −1.74555 + 0.336426i −1.74555 + 0.336426i
\(202\) −1.91899 −1.91899
\(203\) −0.688177 + 2.83670i −0.688177 + 2.83670i
\(204\) 0 0
\(205\) −1.74555 0.899892i −1.74555 0.899892i
\(206\) 0.195876 0.428908i 0.195876 0.428908i
\(207\) 2.15033 + 0.205332i 2.15033 + 0.205332i
\(208\) 0 0
\(209\) 0 0
\(210\) 3.16697 0.929905i 3.16697 0.929905i
\(211\) 0 0 −0.786053 0.618159i \(-0.787879\pi\)
0.786053 + 0.618159i \(0.212121\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) −1.28605 + 0.247866i −1.28605 + 0.247866i
\(215\) 0.0800569 0.0514495i 0.0800569 0.0514495i
\(216\) 1.97876 + 0.581017i 1.97876 + 0.581017i
\(217\) 0 0
\(218\) −0.419102 + 0.216062i −0.419102 + 0.216062i
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) −0.118239 + 0.822373i −0.118239 + 0.822373i 0.841254 + 0.540641i \(0.181818\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(224\) 1.72373 + 0.690079i 1.72373 + 0.690079i
\(225\) 1.81720 + 1.16785i 1.81720 + 1.16785i
\(226\) 0 0
\(227\) −0.0913090 + 1.91681i −0.0913090 + 1.91681i 0.235759 + 0.971812i \(0.424242\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(228\) 0 0
\(229\) 0.651174 + 1.88144i 0.651174 + 1.88144i 0.415415 + 0.909632i \(0.363636\pi\)
0.235759 + 0.971812i \(0.424242\pi\)
\(230\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(231\) 0 0
\(232\) −1.54370 0.297523i −1.54370 0.297523i
\(233\) 0 0 0.928368 0.371662i \(-0.121212\pi\)
−0.928368 + 0.371662i \(0.878788\pi\)
\(234\) 0 0
\(235\) −0.154218 0.635697i −0.154218 0.635697i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(240\) 0.581419 + 1.67990i 0.581419 + 1.67990i
\(241\) 0.195876 + 0.428908i 0.195876 + 0.428908i 0.981929 0.189251i \(-0.0606061\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(242\) 0.0475819 0.998867i 0.0475819 0.998867i
\(243\) 0.402630 + 0.464659i 0.402630 + 0.464659i
\(244\) 0.698939 + 0.449181i 0.698939 + 0.449181i
\(245\) 2.27215 + 0.909632i 2.27215 + 0.909632i
\(246\) 0.496834 3.45556i 0.496834 3.45556i
\(247\) 0 0
\(248\) 0 0
\(249\) −1.86226 + 1.77566i −1.86226 + 1.77566i
\(250\) 0.0475819 + 0.998867i 0.0475819 + 0.998867i
\(251\) 0 0 0.888835 0.458227i \(-0.151515\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(252\) 2.32647 + 3.26707i 2.32647 + 3.26707i
\(253\) 0 0
\(254\) −1.67489 + 1.07639i −1.67489 + 1.07639i
\(255\) 0 0
\(256\) −0.327068 + 0.945001i −0.327068 + 0.945001i
\(257\) 0 0 0.995472 0.0950560i \(-0.0303030\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(258\) 0.132977 + 0.104574i 0.132977 + 0.104574i
\(259\) 0 0
\(260\) 0 0
\(261\) −2.45775 2.34346i −2.45775 2.34346i
\(262\) 0 0
\(263\) 0.481929 1.05528i 0.481929 1.05528i −0.500000 0.866025i \(-0.666667\pi\)
0.981929 0.189251i \(-0.0606061\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 3.41133 3.41133
\(268\) 0.415415 0.909632i 0.415415 0.909632i
\(269\) 1.68251 1.68251 0.841254 0.540641i \(-0.181818\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(270\) −0.486206 + 2.00417i −0.486206 + 2.00417i
\(271\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) −1.16413 + 1.34347i −1.16413 + 1.34347i
\(277\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) −0.607279 + 1.75462i −0.607279 + 1.75462i
\(281\) −0.642315 + 0.123796i −0.642315 + 0.123796i −0.500000 0.866025i \(-0.666667\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(282\) 0.978242 0.628678i 0.978242 0.628678i
\(283\) −1.11312 0.326842i −1.11312 0.326842i −0.327068 0.945001i \(-0.606061\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 2.63900 2.51628i 2.63900 2.51628i
\(288\) −1.69796 + 1.33529i −1.69796 + 1.33529i
\(289\) 0.580057 0.814576i 0.580057 0.814576i
\(290\) 0.223734 1.55610i 0.223734 1.55610i
\(291\) 0 0
\(292\) 0 0
\(293\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(294\) −0.207019 + 4.34586i −0.207019 + 4.34586i
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) −0.981929 + 1.70075i −0.981929 + 1.70075i
\(299\) 0 0
\(300\) −1.65033 + 0.660694i −1.65033 + 0.660694i
\(301\) 0.0416572 + 0.171713i 0.0416572 + 0.171713i
\(302\) 0 0
\(303\) 3.16697 1.26786i 3.16697 1.26786i
\(304\) 0 0
\(305\) −0.415415 + 0.719520i −0.415415 + 0.719520i
\(306\) 0 0
\(307\) 0.428368 + 1.23769i 0.428368 + 1.23769i 0.928368 + 0.371662i \(0.121212\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(308\) 0 0
\(309\) −0.0398833 + 0.837254i −0.0398833 + 0.837254i
\(310\) 0 0
\(311\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(312\) 0 0
\(313\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(314\) 0 0
\(315\) −3.15267 + 2.47929i −3.15267 + 2.47929i
\(316\) 0 0
\(317\) 0 0 −0.0475819 0.998867i \(-0.515152\pi\)
0.0475819 + 0.998867i \(0.484848\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) −0.959493 0.281733i −0.959493 0.281733i
\(321\) 1.95865 1.25875i 1.95865 1.25875i
\(322\) −1.82318 + 0.351390i −1.82318 + 0.351390i
\(323\) 0 0
\(324\) −1.49916 + 0.143152i −1.49916 + 0.143152i
\(325\) 0 0
\(326\) −1.61435 + 0.474017i −1.61435 + 0.474017i
\(327\) 0.548907 0.633472i 0.548907 0.633472i
\(328\) 1.42131 + 1.35522i 1.42131 + 1.35522i
\(329\) 1.20906 + 0.115451i 1.20906 + 0.115451i
\(330\) 0 0
\(331\) 0 0 −0.888835 0.458227i \(-0.848485\pi\)
0.888835 + 0.458227i \(0.151515\pi\)
\(332\) −0.205996 1.43273i −0.205996 1.43273i
\(333\) 0 0
\(334\) −0.284630 −0.284630
\(335\) 0.928368 + 0.371662i 0.928368 + 0.371662i
\(336\) −3.30067 −3.30067
\(337\) 0 0 0.235759 0.971812i \(-0.424242\pi\)
−0.235759 + 0.971812i \(0.575758\pi\)
\(338\) −0.142315 0.989821i −0.142315 0.989821i
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) −1.75998 + 2.03113i −1.75998 + 2.03113i
\(344\) −0.0913090 + 0.0268107i −0.0913090 + 0.0268107i
\(345\) −1.39734 1.09888i −1.39734 1.09888i
\(346\) 0 0
\(347\) −0.271738 + 0.785135i −0.271738 + 0.785135i 0.723734 + 0.690079i \(0.242424\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(348\) 2.74418 0.528898i 2.74418 0.528898i
\(349\) 0.0800569 0.0514495i 0.0800569 0.0514495i −0.500000 0.866025i \(-0.666667\pi\)
0.580057 + 0.814576i \(0.303030\pi\)
\(350\) −1.78153 0.523103i −1.78153 0.523103i
\(351\) 0 0
\(352\) 0 0
\(353\) 0 0 −0.0475819 0.998867i \(-0.515152\pi\)
0.0475819 + 0.998867i \(0.484848\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) −1.11312 + 1.56316i −1.11312 + 1.56316i
\(357\) 0 0
\(358\) 0 0
\(359\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(360\) −1.41457 1.63251i −1.41457 1.63251i
\(361\) 0.0475819 0.998867i 0.0475819 0.998867i
\(362\) 0.698939 + 1.53046i 0.698939 + 1.53046i
\(363\) 0.581419 + 1.67990i 0.581419 + 1.67990i
\(364\) 0 0
\(365\) 0 0
\(366\) −1.45025 0.279513i −1.45025 0.279513i
\(367\) 0.437742 0.175245i 0.437742 0.175245i −0.142315 0.989821i \(-0.545455\pi\)
0.580057 + 0.814576i \(0.303030\pi\)
\(368\) −0.235759 0.971812i −0.235759 0.971812i
\(369\) 1.00013 + 4.12258i 1.00013 + 4.12258i
\(370\) 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
\(375\) −0.738471 1.61703i −0.738471 1.61703i
\(376\) −0.0311250 + 0.653395i −0.0311250 + 0.653395i
\(377\) 0 0
\(378\) −3.22128 2.07019i −3.22128 2.07019i
\(379\) 0 0 −0.928368 0.371662i \(-0.878788\pi\)
0.928368 + 0.371662i \(0.121212\pi\)
\(380\) 0 0
\(381\) 2.05296 2.88298i 2.05296 2.88298i
\(382\) 0 0
\(383\) −0.473420 + 0.451405i −0.473420 + 0.451405i −0.888835 0.458227i \(-0.848485\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(384\) −0.0845850 1.77566i −0.0845850 1.77566i
\(385\) 0 0
\(386\) 0 0
\(387\) −0.197238 0.0579143i −0.197238 0.0579143i
\(388\) 0 0
\(389\) 0.462997 0.0892353i 0.462997 0.0892353i 0.0475819 0.998867i \(-0.484848\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) −1.92384 1.51292i −1.92384 1.51292i
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0.235759 0.971812i 0.235759 0.971812i
\(401\) 1.85674 1.85674 0.928368 0.371662i \(-0.121212\pi\)
0.928368 + 0.371662i \(0.121212\pi\)
\(402\) −0.0845850 + 1.77566i −0.0845850 + 1.77566i
\(403\) 0 0
\(404\) −0.452418 + 1.86489i −0.452418 + 1.86489i
\(405\) −0.214323 1.49065i −0.214323 1.49065i
\(406\) 2.59450 + 1.33756i 2.59450 + 1.33756i
\(407\) 0 0
\(408\) 0 0
\(409\) 1.21769 + 1.16106i 1.21769 + 1.16106i 0.981929 + 0.189251i \(0.0606061\pi\)
0.235759 + 0.971812i \(0.424242\pi\)
\(410\) −1.28605 + 1.48418i −1.28605 + 1.48418i
\(411\) 0 0
\(412\) −0.370638 0.291473i −0.370638 0.291473i
\(413\) 0 0
\(414\) 0.706504 2.04131i 0.706504 2.04131i
\(415\) 1.42131 0.273935i 1.42131 0.273935i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 0 0 0.888835 0.458227i \(-0.151515\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(420\) −0.157052 3.29693i −0.157052 3.29693i
\(421\) −0.205996 + 0.196417i −0.205996 + 0.196417i −0.786053 0.618159i \(-0.787879\pi\)
0.580057 + 0.814576i \(0.303030\pi\)
\(422\) 0 0
\(423\) −0.819625 + 1.15100i −0.819625 + 1.15100i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −1.01021 1.16584i −1.01021 1.16584i
\(428\) −0.0623191 + 1.30824i −0.0623191 + 1.30824i
\(429\) 0 0
\(430\) −0.0311250 0.0899299i −0.0311250 0.0899299i
\(431\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(432\) 1.03115 1.78600i 1.03115 1.78600i
\(433\) 0 0 −0.981929 0.189251i \(-0.939394\pi\)
0.981929 + 0.189251i \(0.0606061\pi\)
\(434\) 0 0
\(435\) 0.658873 + 2.71591i 0.658873 + 2.71591i
\(436\) 0.111165 + 0.458227i 0.111165 + 0.458227i
\(437\) 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
\(441\) −1.72915 4.99604i −1.72915 4.99604i
\(442\) 0 0
\(443\) −0.0748038 + 1.57033i −0.0748038 + 1.57033i 0.580057 + 0.814576i \(0.303030\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(444\) 0 0
\(445\) −1.61435 1.03748i −1.61435 1.03748i
\(446\) 0.771316 + 0.308788i 0.771316 + 0.308788i
\(447\) 0.496834 3.45556i 0.496834 3.45556i
\(448\) 1.07701 1.51245i 1.07701 1.51245i
\(449\) 0.514186 0.404360i 0.514186 0.404360i −0.327068 0.945001i \(-0.606061\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(450\) 1.56335 1.49065i 1.56335 1.49065i
\(451\) 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 0.327068 0.945001i \(-0.393939\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(458\) 1.98193 0.189251i 1.98193 0.189251i
\(459\) 0 0
\(460\) 0.959493 0.281733i 0.959493 0.281733i
\(461\) −0.947890 + 1.09392i −0.947890 + 1.09392i 0.0475819 + 0.998867i \(0.484848\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(462\) 0 0
\(463\) −1.67489 0.159932i −1.67489 0.159932i −0.786053 0.618159i \(-0.787879\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(464\) −0.653077 + 1.43004i −0.653077 + 1.43004i
\(465\) 0 0
\(466\) 0 0
\(467\) −0.469383 + 1.93482i −0.469383 + 1.93482i −0.142315 + 0.989821i \(0.545455\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(468\) 0 0
\(469\) −1.21590 + 1.40323i −1.21590 + 1.40323i
\(470\) −0.654136 −0.654136
\(471\) 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 −0.786053 0.618159i \(-0.787879\pi\)
0.786053 + 0.618159i \(0.212121\pi\)
\(480\) 1.76962 0.168978i 1.76962 0.168978i
\(481\) 0 0
\(482\) 0.462997 0.0892353i 0.462997 0.0892353i
\(483\) 2.77670 1.78447i 2.77670 1.78447i
\(484\) −0.959493 0.281733i −0.959493 0.281733i
\(485\) 0 0
\(486\) 0.546485 0.281733i 0.546485 0.281733i
\(487\) 0.0688733 + 1.44583i 0.0688733 + 1.44583i 0.723734 + 0.690079i \(0.242424\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(488\) 0.601300 0.573338i 0.601300 0.573338i
\(489\) 2.35104 1.84888i 2.35104 1.84888i
\(490\) 1.41967 1.99365i 1.41967 1.99365i
\(491\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(492\) −3.24102 1.29751i −3.24102 1.29751i
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 1.28656 + 2.22839i 1.28656 + 2.22839i
\(499\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(500\) 0.981929 + 0.189251i 0.981929 + 0.189251i
\(501\) 0.469734 0.188053i 0.469734 0.188053i
\(502\) 0 0
\(503\) 0.462997 + 1.90850i 0.462997 + 1.90850i 0.415415 + 0.909632i \(0.363636\pi\)
0.0475819 + 0.998867i \(0.484848\pi\)
\(504\) 3.72346 1.49065i 3.72346 1.49065i
\(505\) −1.88431 0.363170i −1.88431 0.363170i
\(506\) 0 0
\(507\) 0.888835 + 1.53951i 0.888835 + 1.53951i
\(508\) 0.651174 + 1.88144i 0.651174 + 1.88144i
\(509\) −0.118239 0.258908i −0.118239 0.258908i 0.841254 0.540641i \(-0.181818\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0.841254 + 0.540641i 0.841254 + 0.540641i
\(513\) 0 0
\(514\) 0 0
\(515\) 0.273507 0.384087i 0.273507 0.384087i
\(516\) 0.132977 0.104574i 0.132977 0.104574i
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 0.959493 + 0.281733i 0.959493 + 0.281733i 0.723734 0.690079i \(-0.242424\pi\)
0.235759 + 0.971812i \(0.424242\pi\)
\(522\) −2.85684 + 1.83598i −2.85684 + 1.83598i
\(523\) 0.0934441 0.0180099i 0.0934441 0.0180099i −0.142315 0.989821i \(-0.545455\pi\)
0.235759 + 0.971812i \(0.424242\pi\)
\(524\) 0 0
\(525\) 3.28572 0.313748i 3.28572 0.313748i
\(526\) −0.911911 0.717135i −0.911911 0.717135i
\(527\) 0 0
\(528\) 0 0
\(529\) 0 0
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) 0.804250 3.31517i 0.804250 3.31517i
\(535\) −1.30972 −1.30972
\(536\) −0.786053 0.618159i −0.786053 0.618159i
\(537\) 0 0
\(538\) 0.396666 1.63508i 0.396666 1.63508i
\(539\) 0 0
\(540\) 1.83305 + 0.945001i 1.83305 + 0.945001i
\(541\) 0.0395325 0.0865641i 0.0395325 0.0865641i −0.888835 0.458227i \(-0.848485\pi\)
0.928368 + 0.371662i \(0.121212\pi\)
\(542\) 0 0
\(543\) −2.16465 2.06399i −2.16465 2.06399i
\(544\) 0 0
\(545\) −0.452418 + 0.132842i −0.452418 + 0.132842i
\(546\) 0 0
\(547\) 1.98193 0.189251i 1.98193 0.189251i 0.981929 0.189251i \(-0.0606061\pi\)
1.00000 \(0\)
\(548\) 0 0
\(549\) 1.76226 0.339647i 1.76226 0.339647i
\(550\) 0 0
\(551\) 0 0
\(552\) 1.03115 + 1.44805i 1.03115 + 1.44805i
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 0 0 0.580057 0.814576i \(-0.303030\pi\)
−0.580057 + 0.814576i \(0.696970\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 1.56199 + 1.00383i 1.56199 + 1.00383i
\(561\) 0 0
\(562\) −0.0311250 + 0.653395i −0.0311250 + 0.653395i
\(563\) 0.0395325 + 0.0865641i 0.0395325 + 0.0865641i 0.928368 0.371662i \(-0.121212\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(564\) −0.380327 1.09888i −0.380327 1.09888i
\(565\) 0 0
\(566\) −0.580057 + 1.00469i −0.580057 + 1.00469i
\(567\) 2.74567 + 0.529185i 2.74567 + 0.529185i
\(568\) 0 0
\(569\) −0.0671040 0.276606i −0.0671040 0.276606i 0.928368 0.371662i \(-0.121212\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(570\) 0 0
\(571\) 0 0 0.928368 0.371662i \(-0.121212\pi\)
−0.928368 + 0.371662i \(0.878788\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) −1.82318 3.15784i −1.82318 3.15784i
\(575\) 0.327068 + 0.945001i 0.327068 + 0.945001i
\(576\) 0.897344 + 1.96491i 0.897344 + 1.96491i
\(577\) 0 0 0.0475819 0.998867i \(-0.484848\pi\)
−0.0475819 + 0.998867i \(0.515152\pi\)
\(578\) −0.654861 0.755750i −0.654861 0.755750i
\(579\) 0 0
\(580\) −1.45949 0.584293i −1.45949 0.584293i
\(581\) −0.382481 + 2.66021i −0.382481 + 2.66021i
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −0.759713 1.06687i −0.759713 1.06687i −0.995472 0.0950560i \(-0.969697\pi\)
0.235759 0.971812i \(-0.424242\pi\)
\(588\) 4.17456 + 1.22576i 4.17456 + 1.22576i
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 0 0 −0.786053 0.618159i \(-0.787879\pi\)
0.786053 + 0.618159i \(0.212121\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 1.42131 + 1.35522i 1.42131 + 1.35522i
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 −0.888835 0.458227i \(-0.848485\pi\)
0.888835 + 0.458227i \(0.151515\pi\)
\(600\) 0.252989 + 1.75958i 0.252989 + 1.75958i
\(601\) 0.0224357 0.0924813i 0.0224357 0.0924813i −0.959493 0.281733i \(-0.909091\pi\)
0.981929 + 0.189251i \(0.0606061\pi\)
\(602\) 0.176694 0.176694
\(603\) −0.706504 2.04131i −0.706504 2.04131i
\(604\) 0 0
\(605\) 0.235759 0.971812i 0.235759 0.971812i
\(606\) −0.485482 3.37660i −0.485482 3.37660i
\(607\) 0.581419 + 0.299742i 0.581419 + 0.299742i 0.723734 0.690079i \(-0.242424\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(608\) 0 0
\(609\) −5.16550 0.493245i −5.16550 0.493245i
\(610\) 0.601300 + 0.573338i 0.601300 + 0.573338i
\(611\) 0 0
\(612\) 0 0
\(613\) 0 0 −0.786053 0.618159i \(-0.787879\pi\)
0.786053 + 0.618159i \(0.212121\pi\)
\(614\) 1.30379 0.124497i 1.30379 0.124497i
\(615\) 1.14182 3.29908i 1.14182 3.29908i
\(616\) 0 0
\(617\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(618\) 0.804250 + 0.236149i 0.804250 + 0.236149i
\(619\) 0 0 −0.580057 0.814576i \(-0.696970\pi\)
0.580057 + 0.814576i \(0.303030\pi\)
\(620\) 0 0
\(621\) 0.0981282 + 2.05996i 0.0981282 + 2.05996i
\(622\) 0 0
\(623\) 2.80075 2.20253i 2.80075 2.20253i
\(624\) 0 0
\(625\) −0.142315 + 0.989821i −0.142315 + 0.989821i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) 1.66613 + 3.64832i 1.66613 + 3.64832i
\(631\) 0 0 −0.327068 0.945001i \(-0.606061\pi\)
0.327068 + 0.945001i \(0.393939\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −1.84833 + 0.739959i −1.84833 + 0.739959i
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(641\) −0.580057 1.00469i −0.580057 1.00469i −0.995472 0.0950560i \(-0.969697\pi\)
0.415415 0.909632i \(-0.363636\pi\)
\(642\) −0.761497 2.20020i −0.761497 2.20020i
\(643\) −0.653077 1.43004i −0.653077 1.43004i −0.888835 0.458227i \(-0.848485\pi\)
0.235759 0.971812i \(-0.424242\pi\)
\(644\) −0.0883470 + 1.85463i −0.0883470 + 1.85463i
\(645\) 0.110783 + 0.127850i 0.110783 + 0.127850i
\(646\) 0 0
\(647\) −0.607279 0.243118i −0.607279 0.243118i 0.0475819 0.998867i \(-0.484848\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(648\) −0.214323 + 1.49065i −0.214323 + 1.49065i
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) 0.0800569 + 1.68060i 0.0800569 + 1.68060i
\(653\) 0 0 0.888835 0.458227i \(-0.151515\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(654\) −0.486206 0.682780i −0.486206 0.682780i
\(655\) 0 0
\(656\) 1.65210 1.06174i 1.65210 1.06174i
\(657\) 0 0
\(658\) 0.397243 1.14776i 0.397243 1.14776i
\(659\) 0 0 0.995472 0.0950560i \(-0.0303030\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(660\) 0 0
\(661\) 0.273100 0.0801894i 0.273100 0.0801894i −0.142315 0.989821i \(-0.545455\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) −1.44091 0.137591i −1.44091 0.137591i
\(665\) 0 0
\(666\) 0 0
\(667\) −0.223734 1.55610i −0.223734 1.55610i
\(668\) −0.0671040 + 0.276606i −0.0671040 + 0.276606i
\(669\) −1.47694 −1.47694
\(670\) 0.580057 0.814576i 0.580057 0.814576i
\(671\) 0 0
\(672\) −0.778161 + 3.20762i −0.778161 + 3.20762i
\(673\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(674\) 0 0
\(675\) −0.856711 + 1.87593i −0.856711 + 1.87593i
\(676\) −0.995472 0.0950560i −0.995472 0.0950560i
\(677\) 0 0 −0.723734 0.690079i \(-0.757576\pi\)
0.723734 + 0.690079i \(0.242424\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) −3.39588 + 0.324267i −3.39588 + 0.324267i
\(682\) 0 0
\(683\) −1.28605 + 0.247866i −1.28605 + 0.247866i −0.786053 0.618159i \(-0.787879\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 1.55894 + 2.18923i 1.55894 + 2.18923i
\(687\) −3.14580 + 1.62177i −3.14580 + 1.62177i
\(688\) 0.00452808 + 0.0950560i 0.00452808 + 0.0950560i
\(689\) 0 0
\(690\) −1.39734 + 1.09888i −1.39734 + 1.09888i
\(691\) 0 0 0.580057 0.814576i \(-0.303030\pi\)
−0.580057 + 0.814576i \(0.696970\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0.698939 + 0.449181i 0.698939 + 0.449181i
\(695\) 0 0
\(696\) 0.132977 2.79152i 0.132977 2.79152i
\(697\) 0 0
\(698\) −0.0311250 0.0899299i −0.0311250 0.0899299i
\(699\) 0 0
\(700\) −0.928368 + 1.60798i −0.928368 + 1.60798i
\(701\) −0.981929 0.189251i −0.981929 0.189251i −0.327068 0.945001i \(-0.606061\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0 0
\(705\) 1.07954 0.432183i 1.07954 0.432183i
\(706\) 0 0
\(707\) 1.78153 3.08569i 1.78153 3.08569i
\(708\) 0 0
\(709\) 0.327068 + 0.945001i 0.327068 + 0.945001i 0.981929 + 0.189251i \(0.0606061\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(710\) 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 −0.0475819 0.998867i \(-0.515152\pi\)
0.0475819 + 0.998867i \(0.484848\pi\)
\(720\) −1.91999 + 0.989821i −1.91999 + 0.989821i
\(721\) 0.507831 + 0.713148i 0.507831 + 0.713148i
\(722\) −0.959493 0.281733i −0.959493 0.281733i
\(723\) −0.705142 + 0.453167i −0.705142 + 0.453167i
\(724\) 1.65210 0.318417i 1.65210 0.318417i
\(725\) 0.514186 1.48564i 0.514186 1.48564i
\(726\) 1.76962 0.168978i 1.76962 0.168978i
\(727\) −1.54370 1.21398i −1.54370 1.21398i −0.888835 0.458227i \(-0.848485\pi\)
−0.654861 0.755750i \(-0.727273\pi\)
\(728\) 0 0
\(729\) 0.270463 0.312131i 0.270463 0.312131i
\(730\) 0 0
\(731\) 0 0
\(732\) −0.613544 + 1.34347i −0.613544 + 1.34347i
\(733\) 0 0 −0.888835 0.458227i \(-0.848485\pi\)
0.888835 + 0.458227i \(0.151515\pi\)
\(734\) −0.0671040 0.466718i −0.0671040 0.466718i
\(735\) −1.02574 + 4.22815i −1.02574 + 4.22815i
\(736\) −1.00000 −1.00000
\(737\) 0 0
\(738\) 4.24216 4.24216
\(739\) 0 0 0.235759 0.971812i \(-0.424242\pi\)
−0.235759 + 0.971812i \(0.575758\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −1.67489 0.159932i −1.67489 0.159932i −0.786053 0.618159i \(-0.787879\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(744\) 0 0
\(745\) −1.28605 + 1.48418i −1.28605 + 1.48418i
\(746\) 0 0
\(747\) −2.45775 1.93280i −2.45775 1.93280i
\(748\) 0 0
\(749\) 0.795366 2.29806i 0.795366 2.29806i
\(750\) −1.74555 + 0.336426i −1.74555 + 0.336426i
\(751\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(752\) 0.627639 + 0.184291i 0.627639 + 0.184291i
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) −2.77128 + 2.64241i −2.77128 + 2.64241i
\(757\) 0 0 0.786053 0.618159i \(-0.212121\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 1.41542 + 0.909632i 1.41542 + 0.909632i 1.00000 \(0\)
0.415415 + 0.909632i \(0.363636\pi\)
\(762\) −2.31771 2.67478i −2.31771 2.67478i
\(763\) 0.0416572 0.874493i 0.0416572 0.874493i
\(764\) 0 0
\(765\) 0 0
\(766\) 0.327068 + 0.566498i 0.327068 + 0.566498i
\(767\) 0 0
\(768\) −1.74555 0.336426i −1.74555 0.336426i
\(769\) −1.65033 + 0.660694i −1.65033 + 0.660694i −0.995472 0.0950560i \(-0.969697\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 0 0 −0.981929 0.189251i \(-0.939394\pi\)
0.981929 + 0.189251i \(0.0606061\pi\)
\(774\) −0.102782 + 0.178024i −0.102782 + 0.178024i
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0.0224357 0.470984i 0.0224357 0.470984i
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 1.88063 2.64098i 1.88063 2.64098i
\(784\) −1.92384 + 1.51292i −1.92384 + 1.51292i
\(785\) 0 0
\(786\) 0 0
\(787\) 1.76962 0.912303i 1.76962 0.912303i 0.841254 0.540641i \(-0.181818\pi\)
0.928368 0.371662i \(-0.121212\pi\)
\(788\) 0 0
\(789\) 1.97876 + 0.581017i 1.97876 + 0.581017i
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0