Properties

Label 1340.1.bl.b.619.1
Level $1340$
Weight $1$
Character 1340.619
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 619.1
Root \(-0.995472 + 0.0950560i\) of defining polynomial
Character \(\chi\) \(=\) 1340.619
Dual form 1340.1.bl.b.959.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.981929 + 0.189251i) q^{2} +(0.771316 + 1.68895i) q^{3} +(0.928368 + 0.371662i) q^{4} +(-0.959493 + 0.281733i) q^{5} +(0.437742 + 1.80440i) q^{6} +(-0.379436 - 1.09631i) q^{7} +(0.841254 + 0.540641i) q^{8} +(-1.60275 + 1.84967i) q^{9} +O(q^{10})\) \(q+(0.981929 + 0.189251i) q^{2} +(0.771316 + 1.68895i) q^{3} +(0.928368 + 0.371662i) q^{4} +(-0.959493 + 0.281733i) q^{5} +(0.437742 + 1.80440i) q^{6} +(-0.379436 - 1.09631i) q^{7} +(0.841254 + 0.540641i) q^{8} +(-1.60275 + 1.84967i) q^{9} +(-0.995472 + 0.0950560i) q^{10} +(0.0883470 + 1.85463i) q^{12} +(-0.165101 - 1.14831i) q^{14} +(-1.21590 - 1.40323i) q^{15} +(0.723734 + 0.690079i) q^{16} +(-1.92384 + 1.51292i) q^{18} +(-0.995472 - 0.0950560i) q^{20} +(1.55894 - 1.48645i) q^{21} +(-0.580057 + 0.814576i) q^{23} +(-0.264241 + 1.83784i) q^{24} +(0.841254 - 0.540641i) q^{25} +(-2.57870 - 0.757175i) q^{27} +(0.0552004 - 1.15880i) q^{28} +(0.995472 - 1.72421i) q^{29} +(-0.928368 - 1.60798i) q^{30} +(0.580057 + 0.814576i) q^{32} +(0.672932 + 0.945001i) q^{35} +(-2.17540 + 1.12149i) q^{36} +(-0.959493 - 0.281733i) q^{40} +(1.39734 + 1.09888i) q^{41} +(1.81208 - 1.16455i) q^{42} +(0.223734 - 1.55610i) q^{43} +(1.01671 - 2.22630i) q^{45} +(-0.723734 + 0.690079i) q^{46} +(-0.0947329 - 0.00904590i) q^{47} +(-0.607279 + 1.75462i) q^{48} +(-0.271868 + 0.213799i) q^{49} +(0.928368 - 0.371662i) q^{50} +(-2.38880 - 1.23151i) q^{54} +(0.273507 - 1.12741i) q^{56} +(1.30379 - 1.50465i) q^{58} +(-0.607279 - 1.75462i) q^{60} +(-0.452418 - 1.86489i) q^{61} +(2.63595 + 1.05528i) q^{63} +(0.415415 + 0.909632i) q^{64} +(-0.786053 + 0.618159i) q^{67} +(-1.82318 - 0.351390i) q^{69} +(0.481929 + 1.05528i) q^{70} +(-2.34833 + 0.689531i) q^{72} +(1.56199 + 1.00383i) q^{75} +(-0.888835 - 0.458227i) q^{80} +(-0.361854 - 2.51675i) q^{81} +(1.16413 + 1.34347i) q^{82} +(-0.473420 - 0.451405i) q^{83} +(1.99973 - 0.800570i) q^{84} +(0.514186 - 1.48564i) q^{86} +(3.67992 + 0.351390i) q^{87} +(-0.544078 + 1.19136i) q^{89} +(1.41967 - 1.99365i) q^{90} +(-0.841254 + 0.540641i) q^{92} +(-0.0913090 - 0.0268107i) q^{94} +(-0.928368 + 1.60798i) q^{96} +(-0.307416 + 0.158484i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20q + q^{2} + 2q^{3} + q^{4} - 2q^{5} - q^{6} - q^{7} - 2q^{8} + O(q^{10}) \) \( 20q + q^{2} + 2q^{3} + q^{4} - 2q^{5} - q^{6} - q^{7} - 2q^{8} + q^{10} - q^{12} + 2q^{14} + 2q^{15} + q^{16} + q^{20} - 10q^{21} - q^{23} - 9q^{24} - 2q^{25} - 2q^{27} - q^{28} - q^{29} - q^{30} + q^{32} + 21q^{35} - 2q^{40} - q^{41} + 20q^{42} - 9q^{43} - q^{46} - q^{47} - q^{48} + q^{50} + q^{54} - q^{56} + 2q^{58} - q^{60} - 9q^{61} - 11q^{63} - 2q^{64} + q^{67} + q^{69} - 9q^{70} - 11q^{72} + 2q^{75} + q^{80} + 2q^{81} + 2q^{82} - q^{83} + q^{84} - q^{86} + q^{87} - 4q^{89} + 2q^{92} + 2q^{94} - q^{96} + O(q^{100}) \)

Character values

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

\(n\) \(537\) \(671\) \(1141\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{2}{33}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.981929 + 0.189251i 0.981929 + 0.189251i
\(3\) 0.771316 + 1.68895i 0.771316 + 1.68895i 0.723734 + 0.690079i \(0.242424\pi\)
0.0475819 + 0.998867i \(0.484848\pi\)
\(4\) 0.928368 + 0.371662i 0.928368 + 0.371662i
\(5\) −0.959493 + 0.281733i −0.959493 + 0.281733i
\(6\) 0.437742 + 1.80440i 0.437742 + 1.80440i
\(7\) −0.379436 1.09631i −0.379436 1.09631i −0.959493 0.281733i \(-0.909091\pi\)
0.580057 0.814576i \(-0.303030\pi\)
\(8\) 0.841254 + 0.540641i 0.841254 + 0.540641i
\(9\) −1.60275 + 1.84967i −1.60275 + 1.84967i
\(10\) −0.995472 + 0.0950560i −0.995472 + 0.0950560i
\(11\) 0 0 0.235759 0.971812i \(-0.424242\pi\)
−0.235759 + 0.971812i \(0.575758\pi\)
\(12\) 0.0883470 + 1.85463i 0.0883470 + 1.85463i
\(13\) 0 0 −0.888835 0.458227i \(-0.848485\pi\)
0.888835 + 0.458227i \(0.151515\pi\)
\(14\) −0.165101 1.14831i −0.165101 1.14831i
\(15\) −1.21590 1.40323i −1.21590 1.40323i
\(16\) 0.723734 + 0.690079i 0.723734 + 0.690079i
\(17\) 0 0 0.928368 0.371662i \(-0.121212\pi\)
−0.928368 + 0.371662i \(0.878788\pi\)
\(18\) −1.92384 + 1.51292i −1.92384 + 1.51292i
\(19\) 0 0 0.327068 0.945001i \(-0.393939\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(20\) −0.995472 0.0950560i −0.995472 0.0950560i
\(21\) 1.55894 1.48645i 1.55894 1.48645i
\(22\) 0 0
\(23\) −0.580057 + 0.814576i −0.580057 + 0.814576i −0.995472 0.0950560i \(-0.969697\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(24\) −0.264241 + 1.83784i −0.264241 + 1.83784i
\(25\) 0.841254 0.540641i 0.841254 0.540641i
\(26\) 0 0
\(27\) −2.57870 0.757175i −2.57870 0.757175i
\(28\) 0.0552004 1.15880i 0.0552004 1.15880i
\(29\) 0.995472 1.72421i 0.995472 1.72421i 0.415415 0.909632i \(-0.363636\pi\)
0.580057 0.814576i \(-0.303030\pi\)
\(30\) −0.928368 1.60798i −0.928368 1.60798i
\(31\) 0 0 0.888835 0.458227i \(-0.151515\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(32\) 0.580057 + 0.814576i 0.580057 + 0.814576i
\(33\) 0 0
\(34\) 0 0
\(35\) 0.672932 + 0.945001i 0.672932 + 0.945001i
\(36\) −2.17540 + 1.12149i −2.17540 + 1.12149i
\(37\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) −0.959493 0.281733i −0.959493 0.281733i
\(41\) 1.39734 + 1.09888i 1.39734 + 1.09888i 0.981929 + 0.189251i \(0.0606061\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(42\) 1.81208 1.16455i 1.81208 1.16455i
\(43\) 0.223734 1.55610i 0.223734 1.55610i −0.500000 0.866025i \(-0.666667\pi\)
0.723734 0.690079i \(-0.242424\pi\)
\(44\) 0 0
\(45\) 1.01671 2.22630i 1.01671 2.22630i
\(46\) −0.723734 + 0.690079i −0.723734 + 0.690079i
\(47\) −0.0947329 0.00904590i −0.0947329 0.00904590i 0.0475819 0.998867i \(-0.484848\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(48\) −0.607279 + 1.75462i −0.607279 + 1.75462i
\(49\) −0.271868 + 0.213799i −0.271868 + 0.213799i
\(50\) 0.928368 0.371662i 0.928368 0.371662i
\(51\) 0 0
\(52\) 0 0
\(53\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(54\) −2.38880 1.23151i −2.38880 1.23151i
\(55\) 0 0
\(56\) 0.273507 1.12741i 0.273507 1.12741i
\(57\) 0 0
\(58\) 1.30379 1.50465i 1.30379 1.50465i
\(59\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(60\) −0.607279 1.75462i −0.607279 1.75462i
\(61\) −0.452418 1.86489i −0.452418 1.86489i −0.500000 0.866025i \(-0.666667\pi\)
0.0475819 0.998867i \(-0.484848\pi\)
\(62\) 0 0
\(63\) 2.63595 + 1.05528i 2.63595 + 1.05528i
\(64\) 0.415415 + 0.909632i 0.415415 + 0.909632i
\(65\) 0 0
\(66\) 0 0
\(67\) −0.786053 + 0.618159i −0.786053 + 0.618159i
\(68\) 0 0
\(69\) −1.82318 0.351390i −1.82318 0.351390i
\(70\) 0.481929 + 1.05528i 0.481929 + 1.05528i
\(71\) 0 0 −0.928368 0.371662i \(-0.878788\pi\)
0.928368 + 0.371662i \(0.121212\pi\)
\(72\) −2.34833 + 0.689531i −2.34833 + 0.689531i
\(73\) 0 0 −0.235759 0.971812i \(-0.575758\pi\)
0.235759 + 0.971812i \(0.424242\pi\)
\(74\) 0 0
\(75\) 1.56199 + 1.00383i 1.56199 + 1.00383i
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 −0.0475819 0.998867i \(-0.515152\pi\)
0.0475819 + 0.998867i \(0.484848\pi\)
\(80\) −0.888835 0.458227i −0.888835 0.458227i
\(81\) −0.361854 2.51675i −0.361854 2.51675i
\(82\) 1.16413 + 1.34347i 1.16413 + 1.34347i
\(83\) −0.473420 0.451405i −0.473420 0.451405i 0.415415 0.909632i \(-0.363636\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(84\) 1.99973 0.800570i 1.99973 0.800570i
\(85\) 0 0
\(86\) 0.514186 1.48564i 0.514186 1.48564i
\(87\) 3.67992 + 0.351390i 3.67992 + 0.351390i
\(88\) 0 0
\(89\) −0.544078 + 1.19136i −0.544078 + 1.19136i 0.415415 + 0.909632i \(0.363636\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(90\) 1.41967 1.99365i 1.41967 1.99365i
\(91\) 0 0
\(92\) −0.841254 + 0.540641i −0.841254 + 0.540641i
\(93\) 0 0
\(94\) −0.0913090 0.0268107i −0.0913090 0.0268107i
\(95\) 0 0
\(96\) −0.928368 + 1.60798i −0.928368 + 1.60798i
\(97\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(98\) −0.307416 + 0.158484i −0.307416 + 0.158484i
\(99\) 0 0
\(100\) 0.981929 0.189251i 0.981929 0.189251i
\(101\) −1.28605 + 0.247866i −1.28605 + 0.247866i −0.786053 0.618159i \(-0.787879\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(102\) 0 0
\(103\) −1.74555 + 0.899892i −1.74555 + 0.899892i −0.786053 + 0.618159i \(0.787879\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(104\) 0 0
\(105\) −1.07701 + 1.86544i −1.07701 + 1.86544i
\(106\) 0 0
\(107\) −1.61435 0.474017i −1.61435 0.474017i −0.654861 0.755750i \(-0.727273\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(108\) −2.11257 1.66134i −2.11257 1.66134i
\(109\) 1.65210 1.06174i 1.65210 1.06174i 0.723734 0.690079i \(-0.242424\pi\)
0.928368 0.371662i \(-0.121212\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0.481929 1.05528i 0.481929 1.05528i
\(113\) 0 0 0.723734 0.690079i \(-0.242424\pi\)
−0.723734 + 0.690079i \(0.757576\pi\)
\(114\) 0 0
\(115\) 0.327068 0.945001i 0.327068 0.945001i
\(116\) 1.56499 1.23072i 1.56499 1.23072i
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) −0.264241 1.83784i −0.264241 1.83784i
\(121\) −0.888835 0.458227i −0.888835 0.458227i
\(122\) −0.0913090 1.91681i −0.0913090 1.91681i
\(123\) −0.778161 + 3.20762i −0.778161 + 3.20762i
\(124\) 0 0
\(125\) −0.654861 + 0.755750i −0.654861 + 0.755750i
\(126\) 2.38861 + 1.53506i 2.38861 + 1.53506i
\(127\) −0.154218 0.445585i −0.154218 0.445585i 0.841254 0.540641i \(-0.181818\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(128\) 0.235759 + 0.971812i 0.235759 + 0.971812i
\(129\) 2.80075 0.822373i 2.80075 0.822373i
\(130\) 0 0
\(131\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −0.888835 + 0.458227i −0.888835 + 0.458227i
\(135\) 2.68757 2.68757
\(136\) 0 0
\(137\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(138\) −1.72373 0.690079i −1.72373 0.690079i
\(139\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(140\) 0.273507 + 1.12741i 0.273507 + 1.12741i
\(141\) −0.0577910 0.166976i −0.0577910 0.166976i
\(142\) 0 0
\(143\) 0 0
\(144\) −2.43639 + 0.232647i −2.43639 + 0.232647i
\(145\) −0.469383 + 1.93482i −0.469383 + 1.93482i
\(146\) 0 0
\(147\) −0.570791 0.294263i −0.570791 0.294263i
\(148\) 0 0
\(149\) 1.16413 + 1.34347i 1.16413 + 1.34347i 0.928368 + 0.371662i \(0.121212\pi\)
0.235759 + 0.971812i \(0.424242\pi\)
\(150\) 1.34378 + 1.28129i 1.34378 + 1.28129i
\(151\) 0 0 0.928368 0.371662i \(-0.121212\pi\)
−0.928368 + 0.371662i \(0.878788\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 0 0 0.580057 0.814576i \(-0.303030\pi\)
−0.580057 + 0.814576i \(0.696970\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) −0.786053 0.618159i −0.786053 0.618159i
\(161\) 1.11312 + 0.326842i 1.11312 + 0.326842i
\(162\) 0.120983 2.53975i 0.120983 2.53975i
\(163\) 0.142315 0.246497i 0.142315 0.246497i −0.786053 0.618159i \(-0.787879\pi\)
0.928368 + 0.371662i \(0.121212\pi\)
\(164\) 0.888835 + 1.53951i 0.888835 + 1.53951i
\(165\) 0 0
\(166\) −0.379436 0.532843i −0.379436 0.532843i
\(167\) 0.815816 0.157236i 0.815816 0.157236i 0.235759 0.971812i \(-0.424242\pi\)
0.580057 + 0.814576i \(0.303030\pi\)
\(168\) 2.11510 0.407652i 2.11510 0.407652i
\(169\) 0.580057 + 0.814576i 0.580057 + 0.814576i
\(170\) 0 0
\(171\) 0 0
\(172\) 0.786053 1.36148i 0.786053 1.36148i
\(173\) 0 0 0.0475819 0.998867i \(-0.484848\pi\)
−0.0475819 + 0.998867i \(0.515152\pi\)
\(174\) 3.54692 + 1.04147i 3.54692 + 1.04147i
\(175\) −0.911911 0.717135i −0.911911 0.717135i
\(176\) 0 0
\(177\) 0 0
\(178\) −0.759713 + 1.06687i −0.759713 + 1.06687i
\(179\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(180\) 1.77132 1.68895i 1.77132 1.68895i
\(181\) 0.283341 + 0.0270558i 0.283341 + 0.0270558i 0.235759 0.971812i \(-0.424242\pi\)
0.0475819 + 0.998867i \(0.484848\pi\)
\(182\) 0 0
\(183\) 2.80075 2.20253i 2.80075 2.20253i
\(184\) −0.928368 + 0.371662i −0.928368 + 0.371662i
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) −0.0845850 0.0436066i −0.0845850 0.0436066i
\(189\) 0.148355 + 3.11435i 0.148355 + 3.11435i
\(190\) 0 0
\(191\) 0 0 0.995472 0.0950560i \(-0.0303030\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(192\) −1.21590 + 1.40323i −1.21590 + 1.40323i
\(193\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) −0.331854 + 0.0974412i −0.331854 + 0.0974412i
\(197\) 0 0 −0.928368 0.371662i \(-0.878788\pi\)
0.928368 + 0.371662i \(0.121212\pi\)
\(198\) 0 0
\(199\) 0 0 −0.981929 0.189251i \(-0.939394\pi\)
0.981929 + 0.189251i \(0.0606061\pi\)
\(200\) 1.00000 1.00000
\(201\) −1.65033 0.850806i −1.65033 0.850806i
\(202\) −1.30972 −1.30972
\(203\) −2.26798 0.437118i −2.26798 0.437118i
\(204\) 0 0
\(205\) −1.65033 0.660694i −1.65033 0.660694i
\(206\) −1.88431 + 0.553283i −1.88431 + 0.553283i
\(207\) −0.577012 2.37848i −0.577012 2.37848i
\(208\) 0 0
\(209\) 0 0
\(210\) −1.41059 + 1.62790i −1.41059 + 1.62790i
\(211\) 0 0 0.995472 0.0950560i \(-0.0303030\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) −1.49547 0.770969i −1.49547 0.770969i
\(215\) 0.223734 + 1.55610i 0.223734 + 1.55610i
\(216\) −1.75998 2.03113i −1.75998 2.03113i
\(217\) 0 0
\(218\) 1.82318 0.729892i 1.82318 0.729892i
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) −0.797176 + 1.74557i −0.797176 + 1.74557i −0.142315 + 0.989821i \(0.545455\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(224\) 0.672932 0.945001i 0.672932 0.945001i
\(225\) −0.348311 + 2.42256i −0.348311 + 2.42256i
\(226\) 0 0
\(227\) 1.02951 + 0.809616i 1.02951 + 0.809616i 0.981929 0.189251i \(-0.0606061\pi\)
0.0475819 + 0.998867i \(0.484848\pi\)
\(228\) 0 0
\(229\) 0.0224357 0.470984i 0.0224357 0.470984i −0.959493 0.281733i \(-0.909091\pi\)
0.981929 0.189251i \(-0.0606061\pi\)
\(230\) 0.500000 0.866025i 0.500000 0.866025i
\(231\) 0 0
\(232\) 1.76962 0.912303i 1.76962 0.912303i
\(233\) 0 0 −0.580057 0.814576i \(-0.696970\pi\)
0.580057 + 0.814576i \(0.303030\pi\)
\(234\) 0 0
\(235\) 0.0934441 0.0180099i 0.0934441 0.0180099i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(240\) 0.0883470 1.85463i 0.0883470 1.85463i
\(241\) −1.88431 0.553283i −1.88431 0.553283i −0.995472 0.0950560i \(-0.969697\pi\)
−0.888835 0.458227i \(-0.848485\pi\)
\(242\) −0.786053 0.618159i −0.786053 0.618159i
\(243\) 1.71063 1.09936i 1.71063 1.09936i
\(244\) 0.273100 1.89945i 0.273100 1.89945i
\(245\) 0.200621 0.281733i 0.200621 0.281733i
\(246\) −1.37115 + 3.00239i −1.37115 + 3.00239i
\(247\) 0 0
\(248\) 0 0
\(249\) 0.397243 1.14776i 0.397243 1.14776i
\(250\) −0.786053 + 0.618159i −0.786053 + 0.618159i
\(251\) 0 0 0.928368 0.371662i \(-0.121212\pi\)
−0.928368 + 0.371662i \(0.878788\pi\)
\(252\) 2.05493 + 1.95937i 2.05493 + 1.95937i
\(253\) 0 0
\(254\) −0.0671040 0.466718i −0.0671040 0.466718i
\(255\) 0 0
\(256\) 0.0475819 + 0.998867i 0.0475819 + 0.998867i
\(257\) 0 0 0.235759 0.971812i \(-0.424242\pi\)
−0.235759 + 0.971812i \(0.575758\pi\)
\(258\) 2.90577 0.277467i 2.90577 0.277467i
\(259\) 0 0
\(260\) 0 0
\(261\) 1.59373 + 4.60477i 1.59373 + 4.60477i
\(262\) 0 0
\(263\) −1.38884 + 0.407799i −1.38884 + 0.407799i −0.888835 0.458227i \(-0.848485\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) −2.43181 −2.43181
\(268\) −0.959493 + 0.281733i −0.959493 + 0.281733i
\(269\) −0.284630 −0.284630 −0.142315 0.989821i \(-0.545455\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(270\) 2.63900 + 0.508625i 2.63900 + 0.508625i
\(271\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) −1.56199 1.00383i −1.56199 1.00383i
\(277\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0.0552004 + 1.15880i 0.0552004 + 1.15880i
\(281\) −0.0845850 0.0436066i −0.0845850 0.0436066i 0.415415 0.909632i \(-0.363636\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(282\) −0.0251462 0.174896i −0.0251462 0.174896i
\(283\) −0.947890 1.09392i −0.947890 1.09392i −0.995472 0.0950560i \(-0.969697\pi\)
0.0475819 0.998867i \(-0.484848\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0.674512 1.94888i 0.674512 1.94888i
\(288\) −2.43639 0.232647i −2.43639 0.232647i
\(289\) 0.723734 0.690079i 0.723734 0.690079i
\(290\) −0.827068 + 1.81103i −0.827068 + 1.81103i
\(291\) 0 0
\(292\) 0 0
\(293\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(294\) −0.504786 0.396968i −0.504786 0.396968i
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) 0.888835 + 1.53951i 0.888835 + 1.53951i
\(299\) 0 0
\(300\) 1.07701 + 1.51245i 1.07701 + 1.51245i
\(301\) −1.79086 + 0.345161i −1.79086 + 0.345161i
\(302\) 0 0
\(303\) −1.41059 1.98089i −1.41059 1.98089i
\(304\) 0 0
\(305\) 0.959493 + 1.66189i 0.959493 + 1.66189i
\(306\) 0 0
\(307\) 0.0800569 1.68060i 0.0800569 1.68060i −0.500000 0.866025i \(-0.666667\pi\)
0.580057 0.814576i \(-0.303030\pi\)
\(308\) 0 0
\(309\) −2.86624 2.25403i −2.86624 2.25403i
\(310\) 0 0
\(311\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(312\) 0 0
\(313\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(314\) 0 0
\(315\) −2.82648 0.269897i −2.82648 0.269897i
\(316\) 0 0
\(317\) 0 0 0.786053 0.618159i \(-0.212121\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) −0.654861 0.755750i −0.654861 0.755750i
\(321\) −0.444587 3.09217i −0.444587 3.09217i
\(322\) 1.03115 + 0.531595i 1.03115 + 0.531595i
\(323\) 0 0
\(324\) 0.599448 2.47096i 0.599448 2.47096i
\(325\) 0 0
\(326\) 0.186393 0.215109i 0.186393 0.215109i
\(327\) 3.06752 + 1.97137i 3.06752 + 1.97137i
\(328\) 0.581419 + 1.67990i 0.581419 + 1.67990i
\(329\) 0.0260280 + 0.107289i 0.0260280 + 0.107289i
\(330\) 0 0
\(331\) 0 0 −0.928368 0.371662i \(-0.878788\pi\)
0.928368 + 0.371662i \(0.121212\pi\)
\(332\) −0.271738 0.595023i −0.271738 0.595023i
\(333\) 0 0
\(334\) 0.830830 0.830830
\(335\) 0.580057 0.814576i 0.580057 0.814576i
\(336\) 2.15402 2.15402
\(337\) 0 0 −0.981929 0.189251i \(-0.939394\pi\)
0.981929 + 0.189251i \(0.0606061\pi\)
\(338\) 0.415415 + 0.909632i 0.415415 + 0.909632i
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) −0.638404 0.410277i −0.638404 0.410277i
\(344\) 1.02951 1.18812i 1.02951 1.18812i
\(345\) 1.84833 0.176494i 1.84833 0.176494i
\(346\) 0 0
\(347\) −0.0913090 1.91681i −0.0913090 1.91681i −0.327068 0.945001i \(-0.606061\pi\)
0.235759 0.971812i \(-0.424242\pi\)
\(348\) 3.28572 + 1.69391i 3.28572 + 1.69391i
\(349\) 0.223734 + 1.55610i 0.223734 + 1.55610i 0.723734 + 0.690079i \(0.242424\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(350\) −0.759713 0.876756i −0.759713 0.876756i
\(351\) 0 0
\(352\) 0 0
\(353\) 0 0 0.786053 0.618159i \(-0.212121\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) −0.947890 + 0.903811i −0.947890 + 0.903811i
\(357\) 0 0
\(358\) 0 0
\(359\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(360\) 2.05894 1.32320i 2.05894 1.32320i
\(361\) −0.786053 0.618159i −0.786053 0.618159i
\(362\) 0.273100 + 0.0801894i 0.273100 + 0.0801894i
\(363\) 0.0883470 1.85463i 0.0883470 1.85463i
\(364\) 0 0
\(365\) 0 0
\(366\) 3.16697 1.63268i 3.16697 1.63268i
\(367\) 1.13915 + 1.59971i 1.13915 + 1.59971i 0.723734 + 0.690079i \(0.242424\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(368\) −0.981929 + 0.189251i −0.981929 + 0.189251i
\(369\) −4.27217 + 0.823393i −4.27217 + 0.823393i
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(374\) 0 0
\(375\) −1.78153 0.523103i −1.78153 0.523103i
\(376\) −0.0748038 0.0588264i −0.0748038 0.0588264i
\(377\) 0 0
\(378\) −0.443721 + 3.08615i −0.443721 + 3.08615i
\(379\) 0 0 0.580057 0.814576i \(-0.303030\pi\)
−0.580057 + 0.814576i \(0.696970\pi\)
\(380\) 0 0
\(381\) 0.633618 0.604153i 0.633618 0.604153i
\(382\) 0 0
\(383\) −0.0311250 + 0.0899299i −0.0311250 + 0.0899299i −0.959493 0.281733i \(-0.909091\pi\)
0.928368 + 0.371662i \(0.121212\pi\)
\(384\) −1.45949 + 1.14776i −1.45949 + 1.14776i
\(385\) 0 0
\(386\) 0 0
\(387\) 2.51969 + 2.90788i 2.51969 + 2.90788i
\(388\) 0 0
\(389\) −1.74555 0.899892i −1.74555 0.899892i −0.959493 0.281733i \(-0.909091\pi\)
−0.786053 0.618159i \(-0.787879\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) −0.344298 + 0.0328765i −0.344298 + 0.0328765i
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0.981929 + 0.189251i 0.981929 + 0.189251i
\(401\) 1.16011 1.16011 0.580057 0.814576i \(-0.303030\pi\)
0.580057 + 0.814576i \(0.303030\pi\)
\(402\) −1.45949 1.14776i −1.45949 1.14776i
\(403\) 0 0
\(404\) −1.28605 0.247866i −1.28605 0.247866i
\(405\) 1.05625 + 2.31286i 1.05625 + 2.31286i
\(406\) −2.14427 0.858437i −2.14427 0.858437i
\(407\) 0 0
\(408\) 0 0
\(409\) 0.0930932 + 0.268975i 0.0930932 + 0.268975i 0.981929 0.189251i \(-0.0606061\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(410\) −1.49547 0.961081i −1.49547 0.961081i
\(411\) 0 0
\(412\) −1.95496 + 0.186677i −1.95496 + 0.186677i
\(413\) 0 0
\(414\) −0.116455 2.44470i −0.116455 2.44470i
\(415\) 0.581419 + 0.299742i 0.581419 + 0.299742i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 0 0 0.928368 0.371662i \(-0.121212\pi\)
−0.928368 + 0.371662i \(0.878788\pi\)
\(420\) −1.69318 + 1.33153i −1.69318 + 1.33153i
\(421\) −0.271738 + 0.785135i −0.271738 + 0.785135i 0.723734 + 0.690079i \(0.242424\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(422\) 0 0
\(423\) 0.168565 0.160727i 0.168565 0.160727i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −1.87283 + 1.20360i −1.87283 + 1.20360i
\(428\) −1.32254 1.04006i −1.32254 1.04006i
\(429\) 0 0
\(430\) −0.0748038 + 1.57033i −0.0748038 + 1.57033i
\(431\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(432\) −1.34378 2.32750i −1.34378 2.32750i
\(433\) 0 0 0.888835 0.458227i \(-0.151515\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(434\) 0 0
\(435\) −3.62985 + 0.699597i −3.62985 + 0.699597i
\(436\) 1.92837 0.371662i 1.92837 0.371662i
\(437\) 0 0
\(438\) 0 0
\(439\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(440\) 0 0
\(441\) 0.0402777 0.845532i 0.0402777 0.845532i
\(442\) 0 0
\(443\) 1.56499 + 1.23072i 1.56499 + 1.23072i 0.841254 + 0.540641i \(0.181818\pi\)
0.723734 + 0.690079i \(0.242424\pi\)
\(444\) 0 0
\(445\) 0.186393 1.29639i 0.186393 1.29639i
\(446\) −1.11312 + 1.56316i −1.11312 + 1.56316i
\(447\) −1.37115 + 3.00239i −1.37115 + 3.00239i
\(448\) 0.839614 0.800570i 0.839614 0.800570i
\(449\) −0.0947329 0.00904590i −0.0947329 0.00904590i 0.0475819 0.998867i \(-0.484848\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(450\) −0.800488 + 2.31286i −0.800488 + 2.31286i
\(451\) 0 0
\(452\) 0 0
\(453\) 0 0
\(454\) 0.857685 + 0.989821i 0.857685 + 0.989821i
\(455\) 0 0
\(456\) 0 0
\(457\) 0 0 −0.0475819 0.998867i \(-0.515152\pi\)
0.0475819 + 0.998867i \(0.484848\pi\)
\(458\) 0.111165 0.458227i 0.111165 0.458227i
\(459\) 0 0
\(460\) 0.654861 0.755750i 0.654861 0.755750i
\(461\) −0.550294 0.353653i −0.550294 0.353653i 0.235759 0.971812i \(-0.424242\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(462\) 0 0
\(463\) −0.0671040 0.276606i −0.0671040 0.276606i 0.928368 0.371662i \(-0.121212\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(464\) 1.91030 0.560914i 1.91030 0.560914i
\(465\) 0 0
\(466\) 0 0
\(467\) 0.462997 + 0.0892353i 0.462997 + 0.0892353i 0.415415 0.909632i \(-0.363636\pi\)
0.0475819 + 0.998867i \(0.484848\pi\)
\(468\) 0 0
\(469\) 0.975950 + 0.627205i 0.975950 + 0.627205i
\(470\) 0.0951638 0.0951638
\(471\) 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 0.995472 0.0950560i \(-0.0303030\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(480\) 0.437742 1.80440i 0.437742 1.80440i
\(481\) 0 0
\(482\) −1.74555 0.899892i −1.74555 0.899892i
\(483\) 0.306550 + 2.13210i 0.306550 + 2.13210i
\(484\) −0.654861 0.755750i −0.654861 0.755750i
\(485\) 0 0
\(486\) 1.88777 0.755750i 1.88777 0.755750i
\(487\) 0.514186 0.404360i 0.514186 0.404360i −0.327068 0.945001i \(-0.606061\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(488\) 0.627639 1.81344i 0.627639 1.81344i
\(489\) 0.526089 + 0.0502354i 0.526089 + 0.0502354i
\(490\) 0.250314 0.238674i 0.250314 0.238674i
\(491\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(492\) −1.91457 + 2.68864i −1.91457 + 2.68864i
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0.607279 1.05184i 0.607279 1.05184i
\(499\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(500\) −0.888835 + 0.458227i −0.888835 + 0.458227i
\(501\) 0.894814 + 1.25659i 0.894814 + 1.25659i
\(502\) 0 0
\(503\) −1.74555 + 0.336426i −1.74555 + 0.336426i −0.959493 0.281733i \(-0.909091\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(504\) 1.64698 + 2.31286i 1.64698 + 2.31286i
\(505\) 1.16413 0.600149i 1.16413 0.600149i
\(506\) 0 0
\(507\) −0.928368 + 1.60798i −0.928368 + 1.60798i
\(508\) 0.0224357 0.470984i 0.0224357 0.470984i
\(509\) −0.797176 0.234072i −0.797176 0.234072i −0.142315 0.989821i \(-0.545455\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −0.142315 + 0.989821i −0.142315 + 0.989821i
\(513\) 0 0
\(514\) 0 0
\(515\) 1.42131 1.35522i 1.42131 1.35522i
\(516\) 2.90577 + 0.277467i 2.90577 + 0.277467i
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 0.654861 + 0.755750i 0.654861 + 0.755750i 0.981929 0.189251i \(-0.0606061\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(522\) 0.693468 + 4.82317i 0.693468 + 4.82317i
\(523\) 1.39734 + 0.720381i 1.39734 + 0.720381i 0.981929 0.189251i \(-0.0606061\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(524\) 0 0
\(525\) 0.507831 2.09331i 0.507831 2.09331i
\(526\) −1.44091 + 0.137591i −1.44091 + 0.137591i
\(527\) 0 0
\(528\) 0 0
\(529\) 0 0
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) −2.38786 0.460222i −2.38786 0.460222i
\(535\) 1.68251 1.68251
\(536\) −0.995472 + 0.0950560i −0.995472 + 0.0950560i
\(537\) 0 0
\(538\) −0.279486 0.0538665i −0.279486 0.0538665i
\(539\) 0 0
\(540\) 2.49505 + 0.998867i 2.49505 + 0.998867i
\(541\) 1.50842 0.442913i 1.50842 0.442913i 0.580057 0.814576i \(-0.303030\pi\)
0.928368 + 0.371662i \(0.121212\pi\)
\(542\) 0 0
\(543\) 0.172850 + 0.499416i 0.172850 + 0.499416i
\(544\) 0 0
\(545\) −1.28605 + 1.48418i −1.28605 + 1.48418i
\(546\) 0 0
\(547\) 0.111165 0.458227i 0.111165 0.458227i −0.888835 0.458227i \(-0.848485\pi\)
1.00000 \(0\)
\(548\) 0 0
\(549\) 4.17456 + 2.15213i 4.17456 + 2.15213i
\(550\) 0 0
\(551\) 0 0
\(552\) −1.34378 1.28129i −1.34378 1.28129i
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 0 0 0.723734 0.690079i \(-0.242424\pi\)
−0.723734 + 0.690079i \(0.757576\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) −0.165101 + 1.14831i −0.165101 + 1.14831i
\(561\) 0 0
\(562\) −0.0748038 0.0588264i −0.0748038 0.0588264i
\(563\) 1.50842 + 0.442913i 1.50842 + 0.442913i 0.928368 0.371662i \(-0.121212\pi\)
0.580057 + 0.814576i \(0.303030\pi\)
\(564\) 0.00840744 0.176494i 0.00840744 0.176494i
\(565\) 0 0
\(566\) −0.723734 1.25354i −0.723734 1.25354i
\(567\) −2.62184 + 1.35165i −2.62184 + 1.35165i
\(568\) 0 0
\(569\) 0.815816 0.157236i 0.815816 0.157236i 0.235759 0.971812i \(-0.424242\pi\)
0.580057 + 0.814576i \(0.303030\pi\)
\(570\) 0 0
\(571\) 0 0 −0.580057 0.814576i \(-0.696970\pi\)
0.580057 + 0.814576i \(0.303030\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 1.03115 1.78600i 1.03115 1.78600i
\(575\) −0.0475819 + 0.998867i −0.0475819 + 0.998867i
\(576\) −2.34833 0.689531i −2.34833 0.689531i
\(577\) 0 0 −0.786053 0.618159i \(-0.787879\pi\)
0.786053 + 0.618159i \(0.212121\pi\)
\(578\) 0.841254 0.540641i 0.841254 0.540641i
\(579\) 0 0
\(580\) −1.15486 + 1.62177i −1.15486 + 1.62177i
\(581\) −0.315247 + 0.690294i −0.315247 + 0.690294i
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 1.21769 + 1.16106i 1.21769 + 1.16106i 0.981929 + 0.189251i \(0.0606061\pi\)
0.235759 + 0.971812i \(0.424242\pi\)
\(588\) −0.420537 0.485326i −0.420537 0.485326i
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 0 0 0.995472 0.0950560i \(-0.0303030\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0.581419 + 1.67990i 0.581419 + 1.67990i
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 −0.928368 0.371662i \(-0.878788\pi\)
0.928368 + 0.371662i \(0.121212\pi\)
\(600\) 0.771316 + 1.68895i 0.771316 + 1.68895i
\(601\) −1.54370 0.297523i −1.54370 0.297523i −0.654861 0.755750i \(-0.727273\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(602\) −1.82382 −1.82382
\(603\) 0.116455 2.44470i 0.116455 2.44470i
\(604\) 0 0
\(605\) 0.981929 + 0.189251i 0.981929 + 0.189251i
\(606\) −1.01021 2.21205i −1.01021 2.21205i
\(607\) 0.0883470 + 0.0353688i 0.0883470 + 0.0353688i 0.415415 0.909632i \(-0.363636\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(608\) 0 0
\(609\) −1.01106 4.16766i −1.01106 4.16766i
\(610\) 0.627639 + 1.81344i 0.627639 + 1.81344i
\(611\) 0 0
\(612\) 0 0
\(613\) 0 0 0.995472 0.0950560i \(-0.0303030\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(614\) 0.396666 1.63508i 0.396666 1.63508i
\(615\) −0.157052 3.29693i −0.157052 3.29693i
\(616\) 0 0
\(617\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(618\) −2.38786 2.75574i −2.38786 2.75574i
\(619\) 0 0 −0.723734 0.690079i \(-0.757576\pi\)
0.723734 + 0.690079i \(0.242424\pi\)
\(620\) 0 0
\(621\) 2.11257 1.66134i 2.11257 1.66134i
\(622\) 0 0
\(623\) 1.51255 + 0.144431i 1.51255 + 0.144431i
\(624\) 0 0
\(625\) 0.415415 0.909632i 0.415415 0.909632i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) −2.72433 0.799935i −2.72433 0.799935i
\(631\) 0 0 0.0475819 0.998867i \(-0.484848\pi\)
−0.0475819 + 0.998867i \(0.515152\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 0.273507 + 0.384087i 0.273507 + 0.384087i
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) −0.500000 0.866025i −0.500000 0.866025i
\(641\) −0.723734 + 1.25354i −0.723734 + 1.25354i 0.235759 + 0.971812i \(0.424242\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(642\) 0.148645 3.12043i 0.148645 3.12043i
\(643\) 1.91030 + 0.560914i 1.91030 + 0.560914i 0.981929 + 0.189251i \(0.0606061\pi\)
0.928368 + 0.371662i \(0.121212\pi\)
\(644\) 0.911911 + 0.717135i 0.911911 + 0.717135i
\(645\) −2.45561 + 1.57812i −2.45561 + 1.57812i
\(646\) 0 0
\(647\) 0.0552004 0.0775182i 0.0552004 0.0775182i −0.786053 0.618159i \(-0.787879\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(648\) 1.05625 2.31286i 1.05625 2.31286i
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) 0.223734 0.175946i 0.223734 0.175946i
\(653\) 0 0 0.928368 0.371662i \(-0.121212\pi\)
−0.928368 + 0.371662i \(0.878788\pi\)
\(654\) 2.63900 + 2.51628i 2.63900 + 2.51628i
\(655\) 0 0
\(656\) 0.252989 + 1.75958i 0.252989 + 1.75958i
\(657\) 0 0
\(658\) 0.00525309 + 0.110276i 0.00525309 + 0.110276i
\(659\) 0 0 0.235759 0.971812i \(-0.424242\pi\)
−0.235759 + 0.971812i \(0.575758\pi\)
\(660\) 0 0
\(661\) −0.544078 + 0.627899i −0.544078 + 0.627899i −0.959493 0.281733i \(-0.909091\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) −0.154218 0.635697i −0.154218 0.635697i
\(665\) 0 0
\(666\) 0 0
\(667\) 0.827068 + 1.81103i 0.827068 + 1.81103i
\(668\) 0.815816 + 0.157236i 0.815816 + 0.157236i
\(669\) −3.56305 −3.56305
\(670\) 0.723734 0.690079i 0.723734 0.690079i
\(671\) 0 0
\(672\) 2.11510 + 0.407652i 2.11510 + 0.407652i
\(673\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(674\) 0 0
\(675\) −2.57870 + 0.757175i −2.57870 + 0.757175i
\(676\) 0.235759 + 0.971812i 0.235759 + 0.971812i
\(677\) 0 0 −0.327068 0.945001i \(-0.606061\pi\)
0.327068 + 0.945001i \(0.393939\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) −0.573320 + 2.36326i −0.573320 + 2.36326i
\(682\) 0 0
\(683\) −1.49547 0.770969i −1.49547 0.770969i −0.500000 0.866025i \(-0.666667\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) −0.549222 0.523682i −0.549222 0.523682i
\(687\) 0.812771 0.325385i 0.812771 0.325385i
\(688\) 1.23576 0.971812i 1.23576 0.971812i
\(689\) 0 0
\(690\) 1.84833 + 0.176494i 1.84833 + 0.176494i
\(691\) 0 0 0.723734 0.690079i \(-0.242424\pi\)
−0.723734 + 0.690079i \(0.757576\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0.273100 1.89945i 0.273100 1.89945i
\(695\) 0 0
\(696\) 2.90577 + 2.28512i 2.90577 + 2.28512i
\(697\) 0 0
\(698\) −0.0748038 + 1.57033i −0.0748038 + 1.57033i
\(699\) 0 0
\(700\) −0.580057 1.00469i −0.580057 1.00469i
\(701\) 0.888835 0.458227i 0.888835 0.458227i 0.0475819 0.998867i \(-0.484848\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0 0
\(705\) 0.102493 + 0.143931i 0.102493 + 0.143931i
\(706\) 0 0
\(707\) 0.759713 + 1.31586i 0.759713 + 1.31586i
\(708\) 0 0
\(709\) −0.0475819 + 0.998867i −0.0475819 + 0.998867i 0.841254 + 0.540641i \(0.181818\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) −1.10181 + 0.708089i −1.10181 + 0.708089i
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 0.786053 0.618159i \(-0.212121\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(720\) 2.27215 0.909632i 2.27215 0.909632i
\(721\) 1.64888 + 1.57221i 1.64888 + 1.57221i
\(722\) −0.654861 0.755750i −0.654861 0.755750i
\(723\) −0.518932 3.60925i −0.518932 3.60925i
\(724\) 0.252989 + 0.130425i 0.252989 + 0.130425i
\(725\) −0.0947329 1.98869i −0.0947329 1.98869i
\(726\) 0.437742 1.80440i 0.437742 1.80440i
\(727\) 1.76962 0.168978i 1.76962 0.168978i 0.841254 0.540641i \(-0.181818\pi\)
0.928368 + 0.371662i \(0.121212\pi\)
\(728\) 0 0
\(729\) 1.03719 + 0.666562i 1.03719 + 0.666562i
\(730\) 0 0
\(731\) 0 0
\(732\) 3.41872 1.00383i 3.41872 1.00383i
\(733\) 0 0 −0.928368 0.371662i \(-0.878788\pi\)
0.928368 + 0.371662i \(0.121212\pi\)
\(734\) 0.815816 + 1.78639i 0.815816 + 1.78639i
\(735\) 0.630573 + 0.121533i 0.630573 + 0.121533i
\(736\) −1.00000 −1.00000
\(737\) 0 0
\(738\) −4.35079 −4.35079
\(739\) 0 0 −0.981929 0.189251i \(-0.939394\pi\)
0.981929 + 0.189251i \(0.0606061\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −0.0671040 0.276606i −0.0671040 0.276606i 0.928368 0.371662i \(-0.121212\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(744\) 0 0
\(745\) −1.49547 0.961081i −1.49547 0.961081i
\(746\) 0 0
\(747\) 1.59373 0.152183i 1.59373 0.152183i
\(748\) 0 0
\(749\) 0.0928751 + 1.94969i 0.0928751 + 1.94969i
\(750\) −1.65033 0.850806i −1.65033 0.850806i
\(751\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(752\) −0.0623191 0.0719200i −0.0623191 0.0719200i
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) −1.01976 + 2.94640i −1.01976 + 2.94640i
\(757\) 0 0 −0.995472 0.0950560i \(-0.969697\pi\)
0.995472 + 0.0950560i \(0.0303030\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 0.0405070 0.281733i 0.0405070 0.281733i −0.959493 0.281733i \(-0.909091\pi\)
1.00000 \(0\)
\(762\) 0.736504 0.473322i 0.736504 0.473322i
\(763\) −1.79086 1.40835i −1.79086 1.40835i
\(764\) 0 0
\(765\) 0 0
\(766\) −0.0475819 + 0.0824143i −0.0475819 + 0.0824143i
\(767\) 0 0
\(768\) −1.65033 + 0.850806i −1.65033 + 0.850806i
\(769\) 1.07701 + 1.51245i 1.07701 + 1.51245i 0.841254 + 0.540641i \(0.181818\pi\)
0.235759 + 0.971812i \(0.424242\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 0 0 0.888835 0.458227i \(-0.151515\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(774\) 1.92384 + 3.33219i 1.92384 + 3.33219i
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) −1.54370 1.21398i −1.54370 1.21398i
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) −3.87255 + 3.69247i −3.87255 + 3.69247i
\(784\) −0.344298 0.0328765i −0.344298 0.0328765i
\(785\) 0 0
\(786\) 0 0
\(787\) 0.437742 0.175245i 0.437742 0.175245i −0.142315 0.989821i \(-0.545455\pi\)
0.580057 + 0.814576i \(0.303030\pi\)
\(788\) 0 0
\(789\) −1.75998 2.03113i −1.75998 2.03113i
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0