Properties

Label 1340.1.bl.b.419.1
Level $1340$
Weight $1$
Character 1340.419
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 419.1
Root \(0.0475819 - 0.998867i\) of defining polynomial
Character \(\chi\) \(=\) 1340.419
Dual form 1340.1.bl.b.339.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.995472 + 0.0950560i) q^{2} +(1.65210 - 1.06174i) q^{3} +(0.981929 - 0.189251i) q^{4} +(-0.142315 + 0.989821i) q^{5} +(-1.54370 + 1.21398i) q^{6} +(-1.03115 - 1.44805i) q^{7} +(-0.959493 + 0.281733i) q^{8} +(1.18673 - 2.59858i) q^{9} +O(q^{10})\) \(q+(-0.995472 + 0.0950560i) q^{2} +(1.65210 - 1.06174i) q^{3} +(0.981929 - 0.189251i) q^{4} +(-0.142315 + 0.989821i) q^{5} +(-1.54370 + 1.21398i) q^{6} +(-1.03115 - 1.44805i) q^{7} +(-0.959493 + 0.281733i) q^{8} +(1.18673 - 2.59858i) q^{9} +(0.0475819 - 0.998867i) q^{10} +(1.42131 - 1.35522i) q^{12} +(1.16413 + 1.34347i) q^{14} +(0.815816 + 1.78639i) q^{15} +(0.928368 - 0.371662i) q^{16} +(-0.934347 + 2.69962i) q^{18} +(0.0475819 + 0.998867i) q^{20} +(-3.24102 - 1.29751i) q^{21} +(0.888835 + 0.458227i) q^{23} +(-1.28605 + 1.48418i) q^{24} +(-0.959493 - 0.281733i) q^{25} +(-0.518932 - 3.60925i) q^{27} +(-1.28656 - 1.22673i) q^{28} +(-0.0475819 + 0.0824143i) q^{29} +(-0.981929 - 1.70075i) q^{30} +(-0.888835 + 0.458227i) q^{32} +(1.58006 - 0.814576i) q^{35} +(0.673501 - 2.77621i) q^{36} +(-0.142315 - 0.989821i) q^{40} +(-0.154218 - 0.445585i) q^{41} +(3.34968 + 0.983554i) q^{42} +(0.428368 - 0.494363i) q^{43} +(2.40324 + 1.54447i) q^{45} +(-0.928368 - 0.371662i) q^{46} +(0.0688733 + 1.44583i) q^{47} +(1.13915 - 1.59971i) q^{48} +(-0.706504 + 2.04131i) q^{49} +(0.981929 + 0.189251i) q^{50} +(0.859663 + 3.54358i) q^{54} +(1.39734 + 1.09888i) q^{56} +(0.0395325 - 0.0865641i) q^{58} +(1.13915 + 1.59971i) q^{60} +(0.223734 - 0.175946i) q^{61} +(-4.98656 + 0.961081i) q^{63} +(0.841254 - 0.540641i) q^{64} +(-0.327068 + 0.945001i) q^{67} +(1.95496 - 0.186677i) q^{69} +(-1.49547 + 0.961081i) q^{70} +(-0.406556 + 2.82766i) q^{72} +(-1.88431 + 0.553283i) q^{75} +(0.235759 + 0.971812i) q^{80} +(-2.81865 - 3.25290i) q^{81} +(0.195876 + 0.428908i) q^{82} +(1.07701 - 0.431171i) q^{83} +(-3.42800 - 0.660694i) q^{84} +(-0.379436 + 0.532843i) q^{86} +(0.00889250 + 0.186677i) q^{87} +(0.698939 + 0.449181i) q^{89} +(-2.53917 - 1.30903i) q^{90} +(0.959493 + 0.281733i) q^{92} +(-0.205996 - 1.43273i) q^{94} +(-0.981929 + 1.70075i) q^{96} +(0.509266 - 2.09922i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20q + q^{2} + 2q^{3} + q^{4} - 2q^{5} - q^{6} - q^{7} - 2q^{8} + O(q^{10}) \) \( 20q + q^{2} + 2q^{3} + q^{4} - 2q^{5} - q^{6} - q^{7} - 2q^{8} + q^{10} - q^{12} + 2q^{14} + 2q^{15} + q^{16} + q^{20} - 10q^{21} - q^{23} - 9q^{24} - 2q^{25} - 2q^{27} - q^{28} - q^{29} - q^{30} + q^{32} + 21q^{35} - 2q^{40} - q^{41} + 20q^{42} - 9q^{43} - q^{46} - q^{47} - q^{48} + q^{50} + q^{54} - q^{56} + 2q^{58} - q^{60} - 9q^{61} - 11q^{63} - 2q^{64} + q^{67} + q^{69} - 9q^{70} - 11q^{72} + 2q^{75} + q^{80} + 2q^{81} + 2q^{82} - q^{83} + q^{84} - q^{86} + q^{87} - 4q^{89} + 2q^{92} + 2q^{94} - q^{96} + O(q^{100}) \)

Character values

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

\(n\) \(537\) \(671\) \(1141\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{32}{33}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.995472 + 0.0950560i −0.995472 + 0.0950560i
\(3\) 1.65210 1.06174i 1.65210 1.06174i 0.723734 0.690079i \(-0.242424\pi\)
0.928368 0.371662i \(-0.121212\pi\)
\(4\) 0.981929 0.189251i 0.981929 0.189251i
\(5\) −0.142315 + 0.989821i −0.142315 + 0.989821i
\(6\) −1.54370 + 1.21398i −1.54370 + 1.21398i
\(7\) −1.03115 1.44805i −1.03115 1.44805i −0.888835 0.458227i \(-0.848485\pi\)
−0.142315 0.989821i \(-0.545455\pi\)
\(8\) −0.959493 + 0.281733i −0.959493 + 0.281733i
\(9\) 1.18673 2.59858i 1.18673 2.59858i
\(10\) 0.0475819 0.998867i 0.0475819 0.998867i
\(11\) 0 0 −0.786053 0.618159i \(-0.787879\pi\)
0.786053 + 0.618159i \(0.212121\pi\)
\(12\) 1.42131 1.35522i 1.42131 1.35522i
\(13\) 0 0 −0.235759 0.971812i \(-0.575758\pi\)
0.235759 + 0.971812i \(0.424242\pi\)
\(14\) 1.16413 + 1.34347i 1.16413 + 1.34347i
\(15\) 0.815816 + 1.78639i 0.815816 + 1.78639i
\(16\) 0.928368 0.371662i 0.928368 0.371662i
\(17\) 0 0 −0.981929 0.189251i \(-0.939394\pi\)
0.981929 + 0.189251i \(0.0606061\pi\)
\(18\) −0.934347 + 2.69962i −0.934347 + 2.69962i
\(19\) 0 0 0.580057 0.814576i \(-0.303030\pi\)
−0.580057 + 0.814576i \(0.696970\pi\)
\(20\) 0.0475819 + 0.998867i 0.0475819 + 0.998867i
\(21\) −3.24102 1.29751i −3.24102 1.29751i
\(22\) 0 0
\(23\) 0.888835 + 0.458227i 0.888835 + 0.458227i 0.841254 0.540641i \(-0.181818\pi\)
0.0475819 + 0.998867i \(0.484848\pi\)
\(24\) −1.28605 + 1.48418i −1.28605 + 1.48418i
\(25\) −0.959493 0.281733i −0.959493 0.281733i
\(26\) 0 0
\(27\) −0.518932 3.60925i −0.518932 3.60925i
\(28\) −1.28656 1.22673i −1.28656 1.22673i
\(29\) −0.0475819 + 0.0824143i −0.0475819 + 0.0824143i −0.888835 0.458227i \(-0.848485\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(30\) −0.981929 1.70075i −0.981929 1.70075i
\(31\) 0 0 0.235759 0.971812i \(-0.424242\pi\)
−0.235759 + 0.971812i \(0.575758\pi\)
\(32\) −0.888835 + 0.458227i −0.888835 + 0.458227i
\(33\) 0 0
\(34\) 0 0
\(35\) 1.58006 0.814576i 1.58006 0.814576i
\(36\) 0.673501 2.77621i 0.673501 2.77621i
\(37\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) −0.142315 0.989821i −0.142315 0.989821i
\(41\) −0.154218 0.445585i −0.154218 0.445585i 0.841254 0.540641i \(-0.181818\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(42\) 3.34968 + 0.983554i 3.34968 + 0.983554i
\(43\) 0.428368 0.494363i 0.428368 0.494363i −0.500000 0.866025i \(-0.666667\pi\)
0.928368 + 0.371662i \(0.121212\pi\)
\(44\) 0 0
\(45\) 2.40324 + 1.54447i 2.40324 + 1.54447i
\(46\) −0.928368 0.371662i −0.928368 0.371662i
\(47\) 0.0688733 + 1.44583i 0.0688733 + 1.44583i 0.723734 + 0.690079i \(0.242424\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(48\) 1.13915 1.59971i 1.13915 1.59971i
\(49\) −0.706504 + 2.04131i −0.706504 + 2.04131i
\(50\) 0.981929 + 0.189251i 0.981929 + 0.189251i
\(51\) 0 0
\(52\) 0 0
\(53\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(54\) 0.859663 + 3.54358i 0.859663 + 3.54358i
\(55\) 0 0
\(56\) 1.39734 + 1.09888i 1.39734 + 1.09888i
\(57\) 0 0
\(58\) 0.0395325 0.0865641i 0.0395325 0.0865641i
\(59\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(60\) 1.13915 + 1.59971i 1.13915 + 1.59971i
\(61\) 0.223734 0.175946i 0.223734 0.175946i −0.500000 0.866025i \(-0.666667\pi\)
0.723734 + 0.690079i \(0.242424\pi\)
\(62\) 0 0
\(63\) −4.98656 + 0.961081i −4.98656 + 0.961081i
\(64\) 0.841254 0.540641i 0.841254 0.540641i
\(65\) 0 0
\(66\) 0 0
\(67\) −0.327068 + 0.945001i −0.327068 + 0.945001i
\(68\) 0 0
\(69\) 1.95496 0.186677i 1.95496 0.186677i
\(70\) −1.49547 + 0.961081i −1.49547 + 0.961081i
\(71\) 0 0 0.981929 0.189251i \(-0.0606061\pi\)
−0.981929 + 0.189251i \(0.939394\pi\)
\(72\) −0.406556 + 2.82766i −0.406556 + 2.82766i
\(73\) 0 0 0.786053 0.618159i \(-0.212121\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(74\) 0 0
\(75\) −1.88431 + 0.553283i −1.88431 + 0.553283i
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 0.723734 0.690079i \(-0.242424\pi\)
−0.723734 + 0.690079i \(0.757576\pi\)
\(80\) 0.235759 + 0.971812i 0.235759 + 0.971812i
\(81\) −2.81865 3.25290i −2.81865 3.25290i
\(82\) 0.195876 + 0.428908i 0.195876 + 0.428908i
\(83\) 1.07701 0.431171i 1.07701 0.431171i 0.235759 0.971812i \(-0.424242\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(84\) −3.42800 0.660694i −3.42800 0.660694i
\(85\) 0 0
\(86\) −0.379436 + 0.532843i −0.379436 + 0.532843i
\(87\) 0.00889250 + 0.186677i 0.00889250 + 0.186677i
\(88\) 0 0
\(89\) 0.698939 + 0.449181i 0.698939 + 0.449181i 0.841254 0.540641i \(-0.181818\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(90\) −2.53917 1.30903i −2.53917 1.30903i
\(91\) 0 0
\(92\) 0.959493 + 0.281733i 0.959493 + 0.281733i
\(93\) 0 0
\(94\) −0.205996 1.43273i −0.205996 1.43273i
\(95\) 0 0
\(96\) −0.981929 + 1.70075i −0.981929 + 1.70075i
\(97\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(98\) 0.509266 2.09922i 0.509266 2.09922i
\(99\) 0 0
\(100\) −0.995472 0.0950560i −0.995472 0.0950560i
\(101\) −0.827068 0.0789754i −0.827068 0.0789754i −0.327068 0.945001i \(-0.606061\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(102\) 0 0
\(103\) −0.469383 + 1.93482i −0.469383 + 1.93482i −0.142315 + 0.989821i \(0.545455\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(104\) 0 0
\(105\) 1.74555 3.02337i 1.74555 3.02337i
\(106\) 0 0
\(107\) 0.273100 + 1.89945i 0.273100 + 1.89945i 0.415415 + 0.909632i \(0.363636\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(108\) −1.19261 3.44582i −1.19261 3.44582i
\(109\) 1.91030 + 0.560914i 1.91030 + 0.560914i 0.981929 + 0.189251i \(0.0606061\pi\)
0.928368 + 0.371662i \(0.121212\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) −1.49547 0.961081i −1.49547 0.961081i
\(113\) 0 0 −0.928368 0.371662i \(-0.878788\pi\)
0.928368 + 0.371662i \(0.121212\pi\)
\(114\) 0 0
\(115\) −0.580057 + 0.814576i −0.580057 + 0.814576i
\(116\) −0.0311250 + 0.0899299i −0.0311250 + 0.0899299i
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) −1.28605 1.48418i −1.28605 1.48418i
\(121\) 0.235759 + 0.971812i 0.235759 + 0.971812i
\(122\) −0.205996 + 0.196417i −0.205996 + 0.196417i
\(123\) −0.727880 0.572411i −0.727880 0.572411i
\(124\) 0 0
\(125\) 0.415415 0.909632i 0.415415 0.909632i
\(126\) 4.87263 1.43073i 4.87263 1.43073i
\(127\) −0.911911 1.28060i −0.911911 1.28060i −0.959493 0.281733i \(-0.909091\pi\)
0.0475819 0.998867i \(-0.484848\pi\)
\(128\) −0.786053 + 0.618159i −0.786053 + 0.618159i
\(129\) 0.182822 1.27155i 0.182822 1.27155i
\(130\) 0 0
\(131\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0.235759 0.971812i 0.235759 0.971812i
\(135\) 3.64636 3.64636
\(136\) 0 0
\(137\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(138\) −1.92837 + 0.371662i −1.92837 + 0.371662i
\(139\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(140\) 1.39734 1.09888i 1.39734 1.09888i
\(141\) 1.64888 + 2.31553i 1.64888 + 2.31553i
\(142\) 0 0
\(143\) 0 0
\(144\) 0.135929 2.85350i 0.135929 2.85350i
\(145\) −0.0748038 0.0588264i −0.0748038 0.0588264i
\(146\) 0 0
\(147\) 1.00013 + 4.12258i 1.00013 + 4.12258i
\(148\) 0 0
\(149\) 0.195876 + 0.428908i 0.195876 + 0.428908i 0.981929 0.189251i \(-0.0606061\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(150\) 1.82318 0.729892i 1.82318 0.729892i
\(151\) 0 0 −0.981929 0.189251i \(-0.939394\pi\)
0.981929 + 0.189251i \(0.0606061\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 0 0 −0.888835 0.458227i \(-0.848485\pi\)
0.888835 + 0.458227i \(0.151515\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) −0.327068 0.945001i −0.327068 0.945001i
\(161\) −0.252989 1.75958i −0.252989 1.75958i
\(162\) 3.11510 + 2.97024i 3.11510 + 2.97024i
\(163\) 0.654861 1.13425i 0.654861 1.13425i −0.327068 0.945001i \(-0.606061\pi\)
0.981929 0.189251i \(-0.0606061\pi\)
\(164\) −0.235759 0.408346i −0.235759 0.408346i
\(165\) 0 0
\(166\) −1.03115 + 0.531595i −1.03115 + 0.531595i
\(167\) −1.67489 0.159932i −1.67489 0.159932i −0.786053 0.618159i \(-0.787879\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(168\) 3.47528 + 0.331849i 3.47528 + 0.331849i
\(169\) −0.888835 + 0.458227i −0.888835 + 0.458227i
\(170\) 0 0
\(171\) 0 0
\(172\) 0.327068 0.566498i 0.327068 0.566498i
\(173\) 0 0 −0.723734 0.690079i \(-0.757576\pi\)
0.723734 + 0.690079i \(0.242424\pi\)
\(174\) −0.0265970 0.184986i −0.0265970 0.184986i
\(175\) 0.581419 + 1.67990i 0.581419 + 1.67990i
\(176\) 0 0
\(177\) 0 0
\(178\) −0.738471 0.380708i −0.738471 0.380708i
\(179\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(180\) 2.65210 + 1.06174i 2.65210 + 1.06174i
\(181\) −0.0623191 1.30824i −0.0623191 1.30824i −0.786053 0.618159i \(-0.787879\pi\)
0.723734 0.690079i \(-0.242424\pi\)
\(182\) 0 0
\(183\) 0.182822 0.528229i 0.182822 0.528229i
\(184\) −0.981929 0.189251i −0.981929 0.189251i
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0.341254 + 1.40667i 0.341254 + 1.40667i
\(189\) −4.69127 + 4.47312i −4.69127 + 4.47312i
\(190\) 0 0
\(191\) 0 0 0.0475819 0.998867i \(-0.484848\pi\)
−0.0475819 + 0.998867i \(0.515152\pi\)
\(192\) 0.815816 1.78639i 0.815816 1.78639i
\(193\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) −0.307416 + 2.13813i −0.307416 + 2.13813i
\(197\) 0 0 0.981929 0.189251i \(-0.0606061\pi\)
−0.981929 + 0.189251i \(0.939394\pi\)
\(198\) 0 0
\(199\) 0 0 0.995472 0.0950560i \(-0.0303030\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(200\) 1.00000 1.00000
\(201\) 0.462997 + 1.90850i 0.462997 + 1.90850i
\(202\) 0.830830 0.830830
\(203\) 0.168404 0.0160806i 0.168404 0.0160806i
\(204\) 0 0
\(205\) 0.462997 0.0892353i 0.462997 0.0892353i
\(206\) 0.283341 1.97068i 0.283341 1.97068i
\(207\) 2.24555 1.76592i 2.24555 1.76592i
\(208\) 0 0
\(209\) 0 0
\(210\) −1.45025 + 3.17561i −1.45025 + 3.17561i
\(211\) 0 0 0.0475819 0.998867i \(-0.484848\pi\)
−0.0475819 + 0.998867i \(0.515152\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) −0.452418 1.86489i −0.452418 1.86489i
\(215\) 0.428368 + 0.494363i 0.428368 + 0.494363i
\(216\) 1.51475 + 3.31685i 1.51475 + 3.31685i
\(217\) 0 0
\(218\) −1.95496 0.376789i −1.95496 0.376789i
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) −0.239446 0.153882i −0.239446 0.153882i 0.415415 0.909632i \(-0.363636\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(224\) 1.58006 + 0.814576i 1.58006 + 0.814576i
\(225\) −1.87076 + 2.15898i −1.87076 + 2.15898i
\(226\) 0 0
\(227\) −0.271738 0.785135i −0.271738 0.785135i −0.995472 0.0950560i \(-0.969697\pi\)
0.723734 0.690079i \(-0.242424\pi\)
\(228\) 0 0
\(229\) −1.13779 1.08488i −1.13779 1.08488i −0.995472 0.0950560i \(-0.969697\pi\)
−0.142315 0.989821i \(-0.545455\pi\)
\(230\) 0.500000 0.866025i 0.500000 0.866025i
\(231\) 0 0
\(232\) 0.0224357 0.0924813i 0.0224357 0.0924813i
\(233\) 0 0 0.888835 0.458227i \(-0.151515\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(234\) 0 0
\(235\) −1.44091 0.137591i −1.44091 0.137591i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(240\) 1.42131 + 1.35522i 1.42131 + 1.35522i
\(241\) 0.283341 + 1.97068i 0.283341 + 1.97068i 0.235759 + 0.971812i \(0.424242\pi\)
0.0475819 + 0.998867i \(0.484848\pi\)
\(242\) −0.327068 0.945001i −0.327068 0.945001i
\(243\) −4.61178 1.35414i −4.61178 1.35414i
\(244\) 0.186393 0.215109i 0.186393 0.215109i
\(245\) −1.91999 0.989821i −1.91999 0.989821i
\(246\) 0.778996 + 0.500630i 0.778996 + 0.500630i
\(247\) 0 0
\(248\) 0 0
\(249\) 1.32154 1.85585i 1.32154 1.85585i
\(250\) −0.327068 + 0.945001i −0.327068 + 0.945001i
\(251\) 0 0 −0.981929 0.189251i \(-0.939394\pi\)
0.981929 + 0.189251i \(0.0606061\pi\)
\(252\) −4.71456 + 1.88743i −4.71456 + 1.88743i
\(253\) 0 0
\(254\) 1.02951 + 1.18812i 1.02951 + 1.18812i
\(255\) 0 0
\(256\) 0.723734 0.690079i 0.723734 0.690079i
\(257\) 0 0 −0.786053 0.618159i \(-0.787879\pi\)
0.786053 + 0.618159i \(0.212121\pi\)
\(258\) −0.0611251 + 1.28317i −0.0611251 + 1.28317i
\(259\) 0 0
\(260\) 0 0
\(261\) 0.157693 + 0.221449i 0.157693 + 0.221449i
\(262\) 0 0
\(263\) −0.264241 + 1.83784i −0.264241 + 1.83784i 0.235759 + 0.971812i \(0.424242\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 1.63163 1.63163
\(268\) −0.142315 + 0.989821i −0.142315 + 0.989821i
\(269\) −1.30972 −1.30972 −0.654861 0.755750i \(-0.727273\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(270\) −3.62985 + 0.346609i −3.62985 + 0.346609i
\(271\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) 1.88431 0.553283i 1.88431 0.553283i
\(277\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) −1.28656 + 1.22673i −1.28656 + 1.22673i
\(281\) 0.341254 + 1.40667i 0.341254 + 1.40667i 0.841254 + 0.540641i \(0.181818\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(282\) −1.86152 2.14831i −1.86152 2.14831i
\(283\) 0.771316 + 1.68895i 0.771316 + 1.68895i 0.723734 + 0.690079i \(0.242424\pi\)
0.0475819 + 0.998867i \(0.484848\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −0.486206 + 0.682780i −0.486206 + 0.682780i
\(288\) 0.135929 + 2.85350i 0.135929 + 2.85350i
\(289\) 0.928368 + 0.371662i 0.928368 + 0.371662i
\(290\) 0.0800569 + 0.0514495i 0.0800569 + 0.0514495i
\(291\) 0 0
\(292\) 0 0
\(293\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(294\) −1.38747 4.00884i −1.38747 4.00884i
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) −0.235759 0.408346i −0.235759 0.408346i
\(299\) 0 0
\(300\) −1.74555 + 0.899892i −1.74555 + 0.899892i
\(301\) −1.15757 0.110535i −1.15757 0.110535i
\(302\) 0 0
\(303\) −1.45025 + 0.747657i −1.45025 + 0.747657i
\(304\) 0 0
\(305\) 0.142315 + 0.246497i 0.142315 + 0.246497i
\(306\) 0 0
\(307\) −1.38884 1.32425i −1.38884 1.32425i −0.888835 0.458227i \(-0.848485\pi\)
−0.500000 0.866025i \(-0.666667\pi\)
\(308\) 0 0
\(309\) 1.27881 + 3.69489i 1.27881 + 3.69489i
\(310\) 0 0
\(311\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(312\) 0 0
\(313\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(314\) 0 0
\(315\) −0.241637 5.07258i −0.241637 5.07258i
\(316\) 0 0
\(317\) 0 0 0.327068 0.945001i \(-0.393939\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0.415415 + 0.909632i 0.415415 + 0.909632i
\(321\) 2.46792 + 2.84813i 2.46792 + 2.84813i
\(322\) 0.419102 + 1.72756i 0.419102 + 1.72756i
\(323\) 0 0
\(324\) −3.38333 2.66068i −3.38333 2.66068i
\(325\) 0 0
\(326\) −0.544078 + 1.19136i −0.544078 + 1.19136i
\(327\) 3.75155 1.10155i 3.75155 1.10155i
\(328\) 0.273507 + 0.384087i 0.273507 + 0.384087i
\(329\) 2.02261 1.59060i 2.02261 1.59060i
\(330\) 0 0
\(331\) 0 0 0.981929 0.189251i \(-0.0606061\pi\)
−0.981929 + 0.189251i \(0.939394\pi\)
\(332\) 0.975950 0.627205i 0.975950 0.627205i
\(333\) 0 0
\(334\) 1.68251 1.68251
\(335\) −0.888835 0.458227i −0.888835 0.458227i
\(336\) −3.49109 −3.49109
\(337\) 0 0 0.995472 0.0950560i \(-0.0303030\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(338\) 0.841254 0.540641i 0.841254 0.540641i
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 1.97876 0.581017i 1.97876 0.581017i
\(344\) −0.271738 + 0.595023i −0.271738 + 0.595023i
\(345\) −0.0934441 + 1.96163i −0.0934441 + 1.96163i
\(346\) 0 0
\(347\) −0.205996 + 0.196417i −0.205996 + 0.196417i −0.786053 0.618159i \(-0.787879\pi\)
0.580057 + 0.814576i \(0.303030\pi\)
\(348\) 0.0440606 + 0.181620i 0.0440606 + 0.181620i
\(349\) 0.428368 + 0.494363i 0.428368 + 0.494363i 0.928368 0.371662i \(-0.121212\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(350\) −0.738471 1.61703i −0.738471 1.61703i
\(351\) 0 0
\(352\) 0 0
\(353\) 0 0 0.327068 0.945001i \(-0.393939\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0.771316 + 0.308788i 0.771316 + 0.308788i
\(357\) 0 0
\(358\) 0 0
\(359\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(360\) −2.74102 0.804835i −2.74102 0.804835i
\(361\) −0.327068 0.945001i −0.327068 0.945001i
\(362\) 0.186393 + 1.29639i 0.186393 + 1.29639i
\(363\) 1.42131 + 1.35522i 1.42131 + 1.35522i
\(364\) 0 0
\(365\) 0 0
\(366\) −0.131783 + 0.543216i −0.131783 + 0.543216i
\(367\) 1.76962 0.912303i 1.76962 0.912303i 0.841254 0.540641i \(-0.181818\pi\)
0.928368 0.371662i \(-0.121212\pi\)
\(368\) 0.995472 + 0.0950560i 0.995472 + 0.0950560i
\(369\) −1.34090 0.128041i −1.34090 0.128041i
\(370\) 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
\(375\) −0.279486 1.94387i −0.279486 1.94387i
\(376\) −0.473420 1.36786i −0.473420 1.36786i
\(377\) 0 0
\(378\) 4.24483 4.89880i 4.24483 4.89880i
\(379\) 0 0 −0.888835 0.458227i \(-0.848485\pi\)
0.888835 + 0.458227i \(0.151515\pi\)
\(380\) 0 0
\(381\) −2.86624 1.14747i −2.86624 1.14747i
\(382\) 0 0
\(383\) 0.839614 1.17907i 0.839614 1.17907i −0.142315 0.989821i \(-0.545455\pi\)
0.981929 0.189251i \(-0.0606061\pi\)
\(384\) −0.642315 + 1.85585i −0.642315 + 1.85585i
\(385\) 0 0
\(386\) 0 0
\(387\) −0.776283 1.69982i −0.776283 1.69982i
\(388\) 0 0
\(389\) −0.469383 1.93482i −0.469383 1.93482i −0.327068 0.945001i \(-0.606061\pi\)
−0.142315 0.989821i \(-0.545455\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0.102782 2.15767i 0.102782 2.15767i
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) −0.995472 + 0.0950560i −0.995472 + 0.0950560i
\(401\) −1.77767 −1.77767 −0.888835 0.458227i \(-0.848485\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(402\) −0.642315 1.85585i −0.642315 1.85585i
\(403\) 0 0
\(404\) −0.827068 + 0.0789754i −0.827068 + 0.0789754i
\(405\) 3.62093 2.32703i 3.62093 2.32703i
\(406\) −0.166113 + 0.0320156i −0.166113 + 0.0320156i
\(407\) 0 0
\(408\) 0 0
\(409\) −0.759713 1.06687i −0.759713 1.06687i −0.995472 0.0950560i \(-0.969697\pi\)
0.235759 0.971812i \(-0.424242\pi\)
\(410\) −0.452418 + 0.132842i −0.452418 + 0.132842i
\(411\) 0 0
\(412\) −0.0947329 + 1.98869i −0.0947329 + 1.98869i
\(413\) 0 0
\(414\) −2.06752 + 1.97137i −2.06752 + 1.97137i
\(415\) 0.273507 + 1.12741i 0.273507 + 1.12741i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 0 0 −0.981929 0.189251i \(-0.939394\pi\)
0.981929 + 0.189251i \(0.0606061\pi\)
\(420\) 1.14182 3.29908i 1.14182 3.29908i
\(421\) 0.975950 1.37053i 0.975950 1.37053i 0.0475819 0.998867i \(-0.484848\pi\)
0.928368 0.371662i \(-0.121212\pi\)
\(422\) 0 0
\(423\) 3.83883 + 1.53684i 3.83883 + 1.53684i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −0.485482 0.142550i −0.485482 0.142550i
\(428\) 0.627639 + 1.81344i 0.627639 + 1.81344i
\(429\) 0 0
\(430\) −0.473420 0.451405i −0.473420 0.451405i
\(431\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(432\) −1.82318 3.15784i −1.82318 3.15784i
\(433\) 0 0 0.235759 0.971812i \(-0.424242\pi\)
−0.235759 + 0.971812i \(0.575758\pi\)
\(434\) 0 0
\(435\) −0.186042 0.0177649i −0.186042 0.0177649i
\(436\) 1.98193 + 0.189251i 1.98193 + 0.189251i
\(437\) 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
\(441\) 4.46607 + 4.25839i 4.46607 + 4.25839i
\(442\) 0 0
\(443\) −0.0311250 0.0899299i −0.0311250 0.0899299i 0.928368 0.371662i \(-0.121212\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(444\) 0 0
\(445\) −0.544078 + 0.627899i −0.544078 + 0.627899i
\(446\) 0.252989 + 0.130425i 0.252989 + 0.130425i
\(447\) 0.778996 + 0.500630i 0.778996 + 0.500630i
\(448\) −1.65033 0.660694i −1.65033 0.660694i
\(449\) 0.0688733 + 1.44583i 0.0688733 + 1.44583i 0.723734 + 0.690079i \(0.242424\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(450\) 1.65707 2.32703i 1.65707 2.32703i
\(451\) 0 0
\(452\) 0 0
\(453\) 0 0
\(454\) 0.345139 + 0.755750i 0.345139 + 0.755750i
\(455\) 0 0
\(456\) 0 0
\(457\) 0 0 0.723734 0.690079i \(-0.242424\pi\)
−0.723734 + 0.690079i \(0.757576\pi\)
\(458\) 1.23576 + 0.971812i 1.23576 + 0.971812i
\(459\) 0 0
\(460\) −0.415415 + 0.909632i −0.415415 + 0.909632i
\(461\) −1.11312 + 0.326842i −1.11312 + 0.326842i −0.786053 0.618159i \(-0.787879\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(462\) 0 0
\(463\) 1.02951 0.809616i 1.02951 0.809616i 0.0475819 0.998867i \(-0.484848\pi\)
0.981929 + 0.189251i \(0.0606061\pi\)
\(464\) −0.0135432 + 0.0941952i −0.0135432 + 0.0941952i
\(465\) 0 0
\(466\) 0 0
\(467\) 1.56499 0.149438i 1.56499 0.149438i 0.723734 0.690079i \(-0.242424\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(468\) 0 0
\(469\) 1.70566 0.500828i 1.70566 0.500828i
\(470\) 1.44747 1.44747
\(471\) 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 0.0475819 0.998867i \(-0.484848\pi\)
−0.0475819 + 0.998867i \(0.515152\pi\)
\(480\) −1.54370 1.21398i −1.54370 1.21398i
\(481\) 0 0
\(482\) −0.469383 1.93482i −0.469383 1.93482i
\(483\) −2.28618 2.63839i −2.28618 2.63839i
\(484\) 0.415415 + 0.909632i 0.415415 + 0.909632i
\(485\) 0 0
\(486\) 4.71962 + 0.909632i 4.71962 + 0.909632i
\(487\) −0.379436 + 1.09631i −0.379436 + 1.09631i 0.580057 + 0.814576i \(0.303030\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(488\) −0.165101 + 0.231852i −0.165101 + 0.231852i
\(489\) −0.122386 2.56919i −0.122386 2.56919i
\(490\) 2.00538 + 0.802833i 2.00538 + 0.802833i
\(491\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(492\) −0.823056 0.424315i −0.823056 0.424315i
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) −1.13915 + 1.97306i −1.13915 + 1.97306i
\(499\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(500\) 0.235759 0.971812i 0.235759 0.971812i
\(501\) −2.93689 + 1.51407i −2.93689 + 1.51407i
\(502\) 0 0
\(503\) −0.469383 0.0448206i −0.469383 0.0448206i −0.142315 0.989821i \(-0.545455\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(504\) 4.51381 2.32703i 4.51381 2.32703i
\(505\) 0.195876 0.807410i 0.195876 0.807410i
\(506\) 0 0
\(507\) −0.981929 + 1.70075i −0.981929 + 1.70075i
\(508\) −1.13779 1.08488i −1.13779 1.08488i
\(509\) −0.239446 1.66538i −0.239446 1.66538i −0.654861 0.755750i \(-0.727273\pi\)
0.415415 0.909632i \(-0.363636\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −0.654861 + 0.755750i −0.654861 + 0.755750i
\(513\) 0 0
\(514\) 0 0
\(515\) −1.84833 0.739959i −1.84833 0.739959i
\(516\) −0.0611251 1.28317i −0.0611251 1.28317i
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −0.415415 0.909632i −0.415415 0.909632i −0.995472 0.0950560i \(-0.969697\pi\)
0.580057 0.814576i \(-0.303030\pi\)
\(522\) −0.178029 0.205457i −0.178029 0.205457i
\(523\) −0.154218 0.635697i −0.154218 0.635697i −0.995472 0.0950560i \(-0.969697\pi\)
0.841254 0.540641i \(-0.181818\pi\)
\(524\) 0 0
\(525\) 2.74418 + 2.15805i 2.74418 + 2.15805i
\(526\) 0.0883470 1.85463i 0.0883470 1.85463i
\(527\) 0 0
\(528\) 0 0
\(529\) 0 0
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) −1.62424 + 0.155096i −1.62424 + 0.155096i
\(535\) −1.91899 −1.91899
\(536\) 0.0475819 0.998867i 0.0475819 0.998867i
\(537\) 0 0
\(538\) 1.30379 0.124497i 1.30379 0.124497i
\(539\) 0 0
\(540\) 3.58047 0.690079i 3.58047 0.690079i
\(541\) 0.0930932 0.647478i 0.0930932 0.647478i −0.888835 0.458227i \(-0.848485\pi\)
0.981929 0.189251i \(-0.0606061\pi\)
\(542\) 0 0
\(543\) −1.49197 2.09518i −1.49197 2.09518i
\(544\) 0 0
\(545\) −0.827068 + 1.81103i −0.827068 + 1.81103i
\(546\) 0 0
\(547\) 1.23576 + 0.971812i 1.23576 + 0.971812i 1.00000 \(0\)
0.235759 + 0.971812i \(0.424242\pi\)
\(548\) 0 0
\(549\) −0.191698 0.790191i −0.191698 0.790191i
\(550\) 0 0
\(551\) 0 0
\(552\) −1.82318 + 0.729892i −1.82318 + 0.729892i
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 0 0 −0.928368 0.371662i \(-0.878788\pi\)
0.928368 + 0.371662i \(0.121212\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 1.16413 1.34347i 1.16413 1.34347i
\(561\) 0 0
\(562\) −0.473420 1.36786i −0.473420 1.36786i
\(563\) 0.0930932 + 0.647478i 0.0930932 + 0.647478i 0.981929 + 0.189251i \(0.0606061\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(564\) 2.05730 + 1.96163i 2.05730 + 1.96163i
\(565\) 0 0
\(566\) −0.928368 1.60798i −0.928368 1.60798i
\(567\) −1.80390 + 7.43578i −1.80390 + 7.43578i
\(568\) 0 0
\(569\) −1.67489 0.159932i −1.67489 0.159932i −0.786053 0.618159i \(-0.787879\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(570\) 0 0
\(571\) 0 0 0.888835 0.458227i \(-0.151515\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0.419102 0.725906i 0.419102 0.725906i
\(575\) −0.723734 0.690079i −0.723734 0.690079i
\(576\) −0.406556 2.82766i −0.406556 2.82766i
\(577\) 0 0 −0.327068 0.945001i \(-0.606061\pi\)
0.327068 + 0.945001i \(0.393939\pi\)
\(578\) −0.959493 0.281733i −0.959493 0.281733i
\(579\) 0 0
\(580\) −0.0845850 0.0436066i −0.0845850 0.0436066i
\(581\) −1.73492 1.11496i −1.73492 1.11496i
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −1.78153 + 0.713215i −1.78153 + 0.713215i −0.786053 + 0.618159i \(0.787879\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(588\) 1.76226 + 3.85880i 1.76226 + 3.85880i
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 0 0 0.0475819 0.998867i \(-0.484848\pi\)
−0.0475819 + 0.998867i \(0.515152\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0.273507 + 0.384087i 0.273507 + 0.384087i
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 0.981929 0.189251i \(-0.0606061\pi\)
−0.981929 + 0.189251i \(0.939394\pi\)
\(600\) 1.65210 1.06174i 1.65210 1.06174i
\(601\) 0.651174 0.0621796i 0.651174 0.0621796i 0.235759 0.971812i \(-0.424242\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(602\) 1.16284 1.16284
\(603\) 2.06752 + 1.97137i 2.06752 + 1.97137i
\(604\) 0 0
\(605\) −0.995472 + 0.0950560i −0.995472 + 0.0950560i
\(606\) 1.37262 0.882127i 1.37262 0.882127i
\(607\) 1.42131 0.273935i 1.42131 0.273935i 0.580057 0.814576i \(-0.303030\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(608\) 0 0
\(609\) 0.261147 0.205368i 0.261147 0.205368i
\(610\) −0.165101 0.231852i −0.165101 0.231852i
\(611\) 0 0
\(612\) 0 0
\(613\) 0 0 0.0475819 0.998867i \(-0.484848\pi\)
−0.0475819 + 0.998867i \(0.515152\pi\)
\(614\) 1.50842 + 1.18624i 1.50842 + 1.18624i
\(615\) 0.670173 0.639009i 0.670173 0.639009i
\(616\) 0 0
\(617\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(618\) −1.62424 3.55660i −1.62424 3.55660i
\(619\) 0 0 0.928368 0.371662i \(-0.121212\pi\)
−0.928368 + 0.371662i \(0.878788\pi\)
\(620\) 0 0
\(621\) 1.19261 3.44582i 1.19261 3.44582i
\(622\) 0 0
\(623\) −0.0702757 1.47527i −0.0702757 1.47527i
\(624\) 0 0
\(625\) 0.841254 + 0.540641i 0.841254 + 0.540641i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) 0.722723 + 5.02665i 0.722723 + 5.02665i
\(631\) 0 0 −0.723734 0.690079i \(-0.757576\pi\)
0.723734 + 0.690079i \(0.242424\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 1.39734 0.720381i 1.39734 0.720381i
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) −0.500000 0.866025i −0.500000 0.866025i
\(641\) −0.928368 + 1.60798i −0.928368 + 1.60798i −0.142315 + 0.989821i \(0.545455\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(642\) −2.72747 2.60064i −2.72747 2.60064i
\(643\) −0.0135432 0.0941952i −0.0135432 0.0941952i 0.981929 0.189251i \(-0.0606061\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(644\) −0.581419 1.67990i −0.581419 1.67990i
\(645\) 1.23259 + 0.361922i 1.23259 + 0.361922i
\(646\) 0 0
\(647\) −1.28656 0.663268i −1.28656 0.663268i −0.327068 0.945001i \(-0.606061\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(648\) 3.62093 + 2.32703i 3.62093 + 2.32703i
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) 0.428368 1.23769i 0.428368 1.23769i
\(653\) 0 0 −0.981929 0.189251i \(-0.939394\pi\)
0.981929 + 0.189251i \(0.0606061\pi\)
\(654\) −3.62985 + 1.45317i −3.62985 + 1.45317i
\(655\) 0 0
\(656\) −0.308779 0.356349i −0.308779 0.356349i
\(657\) 0 0
\(658\) −1.86226 + 1.77566i −1.86226 + 1.77566i
\(659\) 0 0 −0.786053 0.618159i \(-0.787879\pi\)
0.786053 + 0.618159i \(0.212121\pi\)
\(660\) 0 0
\(661\) 0.698939 1.53046i 0.698939 1.53046i −0.142315 0.989821i \(-0.545455\pi\)
0.841254 0.540641i \(-0.181818\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) −0.911911 + 0.717135i −0.911911 + 0.717135i
\(665\) 0 0
\(666\) 0 0
\(667\) −0.0800569 + 0.0514495i −0.0800569 + 0.0514495i
\(668\) −1.67489 + 0.159932i −1.67489 + 0.159932i
\(669\) −0.558972 −0.558972
\(670\) 0.928368 + 0.371662i 0.928368 + 0.371662i
\(671\) 0 0
\(672\) 3.47528 0.331849i 3.47528 0.331849i
\(673\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(674\) 0 0
\(675\) −0.518932 + 3.60925i −0.518932 + 3.60925i
\(676\) −0.786053 + 0.618159i −0.786053 + 0.618159i
\(677\) 0 0 −0.580057 0.814576i \(-0.696970\pi\)
0.580057 + 0.814576i \(0.303030\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) −1.28255 1.00861i −1.28255 1.00861i
\(682\) 0 0
\(683\) −0.452418 1.86489i −0.452418 1.86489i −0.500000 0.866025i \(-0.666667\pi\)
0.0475819 0.998867i \(-0.484848\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) −1.91457 + 0.766480i −1.91457 + 0.766480i
\(687\) −3.03160 0.584293i −3.03160 0.584293i
\(688\) 0.213947 0.618159i 0.213947 0.618159i
\(689\) 0 0
\(690\) −0.0934441 1.96163i −0.0934441 1.96163i
\(691\) 0 0 −0.928368 0.371662i \(-0.878788\pi\)
0.928368 + 0.371662i \(0.121212\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0.186393 0.215109i 0.186393 0.215109i
\(695\) 0 0
\(696\) −0.0611251 0.176609i −0.0611251 0.176609i
\(697\) 0 0
\(698\) −0.473420 0.451405i −0.473420 0.451405i
\(699\) 0 0
\(700\) 0.888835 + 1.53951i 0.888835 + 1.53951i
\(701\) −0.235759 + 0.971812i −0.235759 + 0.971812i 0.723734 + 0.690079i \(0.242424\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0 0
\(705\) −2.52662 + 1.30256i −2.52662 + 1.30256i
\(706\) 0 0
\(707\) 0.738471 + 1.27907i 0.738471 + 1.27907i
\(708\) 0 0
\(709\) −0.723734 0.690079i −0.723734 0.690079i 0.235759 0.971812i \(-0.424242\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) −0.797176 0.234072i −0.797176 0.234072i
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 0.327068 0.945001i \(-0.393939\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(720\) 2.80511 + 0.540641i 2.80511 + 0.540641i
\(721\) 3.28572 1.31540i 3.28572 1.31540i
\(722\) 0.415415 + 0.909632i 0.415415 + 0.909632i
\(723\) 2.56046 + 2.95493i 2.56046 + 2.95493i
\(724\) −0.308779 1.27280i −0.308779 1.27280i
\(725\) 0.0688733 0.0656706i 0.0688733 0.0656706i
\(726\) −1.54370 1.21398i −1.54370 1.21398i
\(727\) 0.0224357 0.470984i 0.0224357 0.470984i −0.959493 0.281733i \(-0.909091\pi\)
0.981929 0.189251i \(-0.0606061\pi\)
\(728\) 0 0
\(729\) −4.92703 + 1.44671i −4.92703 + 1.44671i
\(730\) 0 0
\(731\) 0 0
\(732\) 0.0795500 0.553283i 0.0795500 0.553283i
\(733\) 0 0 0.981929 0.189251i \(-0.0606061\pi\)
−0.981929 + 0.189251i \(0.939394\pi\)
\(734\) −1.67489 + 1.07639i −1.67489 + 1.07639i
\(735\) −4.22295 + 0.403243i −4.22295 + 0.403243i
\(736\) −1.00000 −1.00000
\(737\) 0 0
\(738\) 1.34700 1.34700
\(739\) 0 0 0.995472 0.0950560i \(-0.0303030\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 1.02951 0.809616i 1.02951 0.809616i 0.0475819 0.998867i \(-0.484848\pi\)
0.981929 + 0.189251i \(0.0606061\pi\)
\(744\) 0 0
\(745\) −0.452418 + 0.132842i −0.452418 + 0.132842i
\(746\) 0 0
\(747\) 0.157693 3.31038i 0.157693 3.31038i
\(748\) 0 0
\(749\) 2.46889 2.35408i 2.46889 2.35408i
\(750\) 0.462997 + 1.90850i 0.462997 + 1.90850i
\(751\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(752\) 0.601300 + 1.31666i 0.601300 + 1.31666i
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) −3.75995 + 5.28011i −3.75995 + 5.28011i
\(757\) 0 0 −0.0475819 0.998867i \(-0.515152\pi\)
0.0475819 + 0.998867i \(0.484848\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 0.857685 0.989821i 0.857685 0.989821i −0.142315 0.989821i \(-0.545455\pi\)
1.00000 \(0\)
\(762\) 2.96233 + 0.869819i 2.96233 + 0.869819i
\(763\) −1.15757 3.34459i −1.15757 3.34459i
\(764\) 0 0
\(765\) 0 0
\(766\) −0.723734 + 1.25354i −0.723734 + 1.25354i
\(767\) 0 0
\(768\) 0.462997 1.90850i 0.462997 1.90850i
\(769\) −1.74555 + 0.899892i −1.74555 + 0.899892i −0.786053 + 0.618159i \(0.787879\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 0 0 0.235759 0.971812i \(-0.424242\pi\)
−0.235759 + 0.971812i \(0.575758\pi\)
\(774\) 0.934347 + 1.61834i 0.934347 + 1.61834i
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0.651174 + 1.88144i 0.651174 + 1.88144i
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0.322146 + 0.128968i 0.322146 + 0.128968i
\(784\) 0.102782 + 2.15767i 0.102782 + 2.15767i
\(785\) 0 0
\(786\) 0 0
\(787\) −1.54370 0.297523i −1.54370 0.297523i −0.654861 0.755750i \(-0.727273\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(788\) 0 0
\(789\) 1.51475 + 3.31685i 1.51475 + 3.31685i
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0