Properties

Label 637.2.q.h.491.3
Level $637$
Weight $2$
Character 637.491
Analytic conductor $5.086$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 637 = 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 637.q (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.08647060876\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{6})\)
Coefficient field: 12.0.58891012706304.1
Defining polynomial: \(x^{12} - 5 x^{10} - 2 x^{9} + 15 x^{8} + 2 x^{7} - 30 x^{6} + 4 x^{5} + 60 x^{4} - 16 x^{3} - 80 x^{2} + 64\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{4} \)
Twist minimal: no (minimal twist has level 91)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 491.3
Root \(1.34408 + 0.439820i\) of defining polynomial
Character \(\chi\) \(=\) 637.491
Dual form 637.2.q.h.589.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.104235 + 0.0601799i) q^{2} +(-0.291146 - 0.504280i) q^{3} +(-0.992757 + 1.71951i) q^{4} -1.68817i q^{5} +(0.0606950 + 0.0350423i) q^{6} -0.479696i q^{8} +(1.33047 - 2.30444i) q^{9} +O(q^{10})\) \(q+(-0.104235 + 0.0601799i) q^{2} +(-0.291146 - 0.504280i) q^{3} +(-0.992757 + 1.71951i) q^{4} -1.68817i q^{5} +(0.0606950 + 0.0350423i) q^{6} -0.479696i q^{8} +(1.33047 - 2.30444i) q^{9} +(0.101594 + 0.175965i) q^{10} +(-0.315769 + 0.182309i) q^{11} +1.15615 q^{12} +(-1.80124 + 3.12338i) q^{13} +(-0.851308 + 0.491503i) q^{15} +(-1.95665 - 3.38901i) q^{16} +(1.59277 - 2.75877i) q^{17} +0.320270i q^{18} +(-1.25046 - 0.721954i) q^{19} +(2.90281 + 1.67594i) q^{20} +(0.0219427 - 0.0380059i) q^{22} +(-2.54161 - 4.40219i) q^{23} +(-0.241901 + 0.139662i) q^{24} +2.15010 q^{25} +(-0.000212944 - 0.433964i) q^{26} -3.29632 q^{27} +(-4.09831 - 7.09848i) q^{29} +(0.0591572 - 0.102463i) q^{30} -4.69775i q^{31} +(1.23876 + 0.715198i) q^{32} +(0.183870 + 0.106157i) q^{33} +0.383412i q^{34} +(2.64166 + 4.57549i) q^{36} +(5.46967 - 3.15792i) q^{37} +0.173789 q^{38} +(2.09948 - 0.00103020i) q^{39} -0.809806 q^{40} +(5.04661 - 2.91366i) q^{41} +(-0.386561 + 0.669543i) q^{43} -0.723954i q^{44} +(-3.89027 - 2.24605i) q^{45} +(0.529847 + 0.305907i) q^{46} -12.7905i q^{47} +(-1.13934 + 1.97339i) q^{48} +(-0.224115 + 0.129393i) q^{50} -1.85492 q^{51} +(-3.58248 - 6.19801i) q^{52} +1.37110 q^{53} +(0.343591 - 0.198372i) q^{54} +(0.307768 + 0.533070i) q^{55} +0.840776i q^{57} +(0.854372 + 0.493272i) q^{58} +(8.10770 + 4.68098i) q^{59} -1.95177i q^{60} +(-4.51242 + 7.81574i) q^{61} +(0.282711 + 0.489669i) q^{62} +7.65442 q^{64} +(5.27279 + 3.04080i) q^{65} -0.0255541 q^{66} +(-11.6705 + 6.73797i) q^{67} +(3.16247 + 5.47757i) q^{68} +(-1.47996 + 2.56336i) q^{69} +(-6.13246 - 3.54058i) q^{71} +(-1.10543 - 0.638220i) q^{72} +2.16083i q^{73} +(-0.380087 + 0.658329i) q^{74} +(-0.625992 - 1.08425i) q^{75} +(2.48281 - 1.43345i) q^{76} +(-0.218777 + 0.126454i) q^{78} -6.88781 q^{79} +(-5.72121 + 3.30314i) q^{80} +(-3.03169 - 5.25105i) q^{81} +(-0.350688 + 0.607409i) q^{82} +0.567380i q^{83} +(-4.65725 - 2.68887i) q^{85} -0.0930528i q^{86} +(-2.38641 + 4.13339i) q^{87} +(0.0874529 + 0.151473i) q^{88} +(0.986346 - 0.569467i) q^{89} +0.540669 q^{90} +10.0928 q^{92} +(-2.36898 + 1.36773i) q^{93} +(0.769734 + 1.33322i) q^{94} +(-1.21878 + 2.11098i) q^{95} -0.832908i q^{96} +(-6.86572 - 3.96393i) q^{97} +0.970225i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 4 q^{4} + 18 q^{6} - 4 q^{9} + O(q^{10}) \) \( 12 q + 4 q^{4} + 18 q^{6} - 4 q^{9} - 12 q^{10} + 6 q^{11} + 4 q^{12} - 4 q^{13} + 6 q^{15} - 8 q^{16} + 4 q^{17} + 12 q^{20} + 6 q^{22} - 12 q^{23} - 12 q^{24} - 20 q^{25} + 42 q^{26} - 12 q^{27} + 8 q^{29} + 8 q^{30} + 36 q^{32} + 30 q^{33} - 10 q^{36} - 42 q^{37} - 4 q^{38} - 4 q^{39} - 92 q^{40} - 30 q^{41} + 2 q^{43} + 12 q^{46} + 2 q^{48} - 18 q^{50} + 52 q^{51} - 2 q^{52} - 44 q^{53} - 12 q^{54} + 6 q^{55} - 12 q^{58} - 18 q^{59} - 14 q^{61} + 4 q^{62} - 52 q^{64} + 60 q^{65} + 52 q^{66} - 24 q^{67} + 8 q^{68} - 4 q^{69} - 24 q^{71} + 60 q^{72} + 6 q^{74} - 46 q^{75} + 18 q^{76} - 10 q^{78} - 56 q^{79} + 72 q^{80} + 2 q^{81} - 14 q^{82} - 48 q^{85} + 2 q^{87} - 14 q^{88} + 12 q^{89} - 24 q^{90} + 24 q^{92} - 18 q^{93} - 4 q^{94} - 22 q^{95} - 6 q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(248\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.104235 + 0.0601799i −0.0737051 + 0.0425536i −0.536400 0.843964i \(-0.680216\pi\)
0.462695 + 0.886518i \(0.346883\pi\)
\(3\) −0.291146 0.504280i −0.168093 0.291146i 0.769656 0.638459i \(-0.220428\pi\)
−0.937749 + 0.347313i \(0.887094\pi\)
\(4\) −0.992757 + 1.71951i −0.496378 + 0.859753i
\(5\) 1.68817i 0.754971i −0.926016 0.377485i \(-0.876789\pi\)
0.926016 0.377485i \(-0.123211\pi\)
\(6\) 0.0606950 + 0.0350423i 0.0247786 + 0.0143060i
\(7\) 0 0
\(8\) 0.479696i 0.169598i
\(9\) 1.33047 2.30444i 0.443489 0.768146i
\(10\) 0.101594 + 0.175965i 0.0321267 + 0.0556452i
\(11\) −0.315769 + 0.182309i −0.0952078 + 0.0549682i −0.546848 0.837232i \(-0.684172\pi\)
0.451640 + 0.892200i \(0.350839\pi\)
\(12\) 1.15615 0.333751
\(13\) −1.80124 + 3.12338i −0.499575 + 0.866271i
\(14\) 0 0
\(15\) −0.851308 + 0.491503i −0.219807 + 0.126905i
\(16\) −1.95665 3.38901i −0.489161 0.847252i
\(17\) 1.59277 2.75877i 0.386304 0.669099i −0.605645 0.795735i \(-0.707085\pi\)
0.991949 + 0.126636i \(0.0404181\pi\)
\(18\) 0.320270i 0.0754884i
\(19\) −1.25046 0.721954i −0.286875 0.165628i 0.349657 0.936878i \(-0.386298\pi\)
−0.636532 + 0.771250i \(0.719632\pi\)
\(20\) 2.90281 + 1.67594i 0.649088 + 0.374751i
\(21\) 0 0
\(22\) 0.0219427 0.0380059i 0.00467820 0.00810288i
\(23\) −2.54161 4.40219i −0.529962 0.917920i −0.999389 0.0349493i \(-0.988873\pi\)
0.469428 0.882971i \(-0.344460\pi\)
\(24\) −0.241901 + 0.139662i −0.0493778 + 0.0285083i
\(25\) 2.15010 0.430020
\(26\) −0.000212944 0.433964i −4.17617e−5 0.0851073i
\(27\) −3.29632 −0.634377
\(28\) 0 0
\(29\) −4.09831 7.09848i −0.761037 1.31815i −0.942317 0.334723i \(-0.891357\pi\)
0.181280 0.983432i \(-0.441976\pi\)
\(30\) 0.0591572 0.102463i 0.0108006 0.0187071i
\(31\) 4.69775i 0.843742i −0.906656 0.421871i \(-0.861374\pi\)
0.906656 0.421871i \(-0.138626\pi\)
\(32\) 1.23876 + 0.715198i 0.218984 + 0.126430i
\(33\) 0.183870 + 0.106157i 0.0320076 + 0.0184796i
\(34\) 0.383412i 0.0657546i
\(35\) 0 0
\(36\) 2.64166 + 4.57549i 0.440277 + 0.762582i
\(37\) 5.46967 3.15792i 0.899209 0.519159i 0.0222655 0.999752i \(-0.492912\pi\)
0.876943 + 0.480594i \(0.159579\pi\)
\(38\) 0.173789 0.0281922
\(39\) 2.09948 0.00103020i 0.336186 0.000164965i
\(40\) −0.809806 −0.128042
\(41\) 5.04661 2.91366i 0.788148 0.455037i −0.0511624 0.998690i \(-0.516293\pi\)
0.839310 + 0.543653i \(0.182959\pi\)
\(42\) 0 0
\(43\) −0.386561 + 0.669543i −0.0589500 + 0.102104i −0.893994 0.448078i \(-0.852109\pi\)
0.835044 + 0.550183i \(0.185442\pi\)
\(44\) 0.723954i 0.109140i
\(45\) −3.89027 2.24605i −0.579928 0.334821i
\(46\) 0.529847 + 0.305907i 0.0781217 + 0.0451036i
\(47\) 12.7905i 1.86569i −0.360275 0.932846i \(-0.617317\pi\)
0.360275 0.932846i \(-0.382683\pi\)
\(48\) −1.13934 + 1.97339i −0.164449 + 0.284835i
\(49\) 0 0
\(50\) −0.224115 + 0.129393i −0.0316946 + 0.0182989i
\(51\) −1.85492 −0.259741
\(52\) −3.58248 6.19801i −0.496800 0.859509i
\(53\) 1.37110 0.188334 0.0941672 0.995556i \(-0.469981\pi\)
0.0941672 + 0.995556i \(0.469981\pi\)
\(54\) 0.343591 0.198372i 0.0467568 0.0269950i
\(55\) 0.307768 + 0.533070i 0.0414994 + 0.0718791i
\(56\) 0 0
\(57\) 0.840776i 0.111363i
\(58\) 0.854372 + 0.493272i 0.112185 + 0.0647698i
\(59\) 8.10770 + 4.68098i 1.05553 + 0.609412i 0.924193 0.381925i \(-0.124739\pi\)
0.131340 + 0.991337i \(0.458072\pi\)
\(60\) 1.95177i 0.251972i
\(61\) −4.51242 + 7.81574i −0.577756 + 1.00070i 0.417980 + 0.908456i \(0.362738\pi\)
−0.995736 + 0.0922469i \(0.970595\pi\)
\(62\) 0.282711 + 0.489669i 0.0359043 + 0.0621880i
\(63\) 0 0
\(64\) 7.65442 0.956802
\(65\) 5.27279 + 3.04080i 0.654009 + 0.377164i
\(66\) −0.0255541 −0.00314549
\(67\) −11.6705 + 6.73797i −1.42578 + 0.823174i −0.996784 0.0801330i \(-0.974466\pi\)
−0.428995 + 0.903307i \(0.641132\pi\)
\(68\) 3.16247 + 5.47757i 0.383506 + 0.664252i
\(69\) −1.47996 + 2.56336i −0.178166 + 0.308592i
\(70\) 0 0
\(71\) −6.13246 3.54058i −0.727789 0.420189i 0.0898239 0.995958i \(-0.471370\pi\)
−0.817613 + 0.575769i \(0.804703\pi\)
\(72\) −1.10543 0.638220i −0.130276 0.0752150i
\(73\) 2.16083i 0.252906i 0.991973 + 0.126453i \(0.0403592\pi\)
−0.991973 + 0.126453i \(0.959641\pi\)
\(74\) −0.380087 + 0.658329i −0.0441842 + 0.0765292i
\(75\) −0.625992 1.08425i −0.0722834 0.125198i
\(76\) 2.48281 1.43345i 0.284797 0.164428i
\(77\) 0 0
\(78\) −0.218777 + 0.126454i −0.0247716 + 0.0143181i
\(79\) −6.88781 −0.774940 −0.387470 0.921882i \(-0.626651\pi\)
−0.387470 + 0.921882i \(0.626651\pi\)
\(80\) −5.72121 + 3.30314i −0.639651 + 0.369302i
\(81\) −3.03169 5.25105i −0.336855 0.583450i
\(82\) −0.350688 + 0.607409i −0.0387270 + 0.0670771i
\(83\) 0.567380i 0.0622780i 0.999515 + 0.0311390i \(0.00991345\pi\)
−0.999515 + 0.0311390i \(0.990087\pi\)
\(84\) 0 0
\(85\) −4.65725 2.68887i −0.505150 0.291648i
\(86\) 0.0930528i 0.0100341i
\(87\) −2.38641 + 4.13339i −0.255850 + 0.443146i
\(88\) 0.0874529 + 0.151473i 0.00932251 + 0.0161471i
\(89\) 0.986346 0.569467i 0.104553 0.0603634i −0.446812 0.894628i \(-0.647441\pi\)
0.551364 + 0.834264i \(0.314107\pi\)
\(90\) 0.540669 0.0569915
\(91\) 0 0
\(92\) 10.0928 1.05225
\(93\) −2.36898 + 1.36773i −0.245652 + 0.141827i
\(94\) 0.769734 + 1.33322i 0.0793920 + 0.137511i
\(95\) −1.21878 + 2.11098i −0.125044 + 0.216582i
\(96\) 0.832908i 0.0850083i
\(97\) −6.86572 3.96393i −0.697109 0.402476i 0.109161 0.994024i \(-0.465184\pi\)
−0.806270 + 0.591548i \(0.798517\pi\)
\(98\) 0 0
\(99\) 0.970225i 0.0975113i
\(100\) −2.13452 + 3.69710i −0.213452 + 0.369710i
\(101\) 7.77322 + 13.4636i 0.773465 + 1.33968i 0.935653 + 0.352920i \(0.114811\pi\)
−0.162189 + 0.986760i \(0.551855\pi\)
\(102\) 0.193347 0.111629i 0.0191442 0.0110529i
\(103\) 10.2982 1.01471 0.507354 0.861738i \(-0.330624\pi\)
0.507354 + 0.861738i \(0.330624\pi\)
\(104\) 1.49827 + 0.864049i 0.146918 + 0.0847270i
\(105\) 0 0
\(106\) −0.142916 + 0.0825124i −0.0138812 + 0.00801432i
\(107\) 6.56220 + 11.3661i 0.634391 + 1.09880i 0.986644 + 0.162893i \(0.0520826\pi\)
−0.352252 + 0.935905i \(0.614584\pi\)
\(108\) 3.27244 5.66804i 0.314891 0.545407i
\(109\) 10.4459i 1.00054i −0.865871 0.500268i \(-0.833235\pi\)
0.865871 0.500268i \(-0.166765\pi\)
\(110\) −0.0641602 0.0370429i −0.00611743 0.00353190i
\(111\) −3.18495 1.83883i −0.302302 0.174534i
\(112\) 0 0
\(113\) −2.47631 + 4.28909i −0.232952 + 0.403484i −0.958675 0.284502i \(-0.908172\pi\)
0.725724 + 0.687986i \(0.241505\pi\)
\(114\) −0.0505978 0.0876380i −0.00473892 0.00820805i
\(115\) −7.43163 + 4.29065i −0.693003 + 0.400105i
\(116\) 16.2745 1.51105
\(117\) 4.80115 + 8.30642i 0.443866 + 0.767928i
\(118\) −1.12681 −0.103731
\(119\) 0 0
\(120\) 0.235772 + 0.408369i 0.0215229 + 0.0372788i
\(121\) −5.43353 + 9.41114i −0.493957 + 0.855559i
\(122\) 1.08623i 0.0983425i
\(123\) −2.93860 1.69660i −0.264965 0.152977i
\(124\) 8.07781 + 4.66373i 0.725409 + 0.418815i
\(125\) 12.0705i 1.07962i
\(126\) 0 0
\(127\) 4.03366 + 6.98650i 0.357929 + 0.619951i 0.987615 0.156899i \(-0.0501496\pi\)
−0.629686 + 0.776850i \(0.716816\pi\)
\(128\) −3.27537 + 1.89104i −0.289505 + 0.167146i
\(129\) 0.450183 0.0396364
\(130\) −0.732603 0.000359484i −0.0642535 3.15288e-5i
\(131\) −18.9039 −1.65164 −0.825820 0.563934i \(-0.809287\pi\)
−0.825820 + 0.563934i \(0.809287\pi\)
\(132\) −0.365075 + 0.210776i −0.0317757 + 0.0183457i
\(133\) 0 0
\(134\) 0.810981 1.40466i 0.0700581 0.121344i
\(135\) 5.56473i 0.478936i
\(136\) −1.32337 0.764047i −0.113478 0.0655165i
\(137\) 15.7837 + 9.11274i 1.34850 + 0.778554i 0.988036 0.154221i \(-0.0492867\pi\)
0.360459 + 0.932775i \(0.382620\pi\)
\(138\) 0.356255i 0.0303264i
\(139\) 2.62542 4.54737i 0.222686 0.385703i −0.732937 0.680297i \(-0.761851\pi\)
0.955623 + 0.294594i \(0.0951843\pi\)
\(140\) 0 0
\(141\) −6.45001 + 3.72392i −0.543189 + 0.313610i
\(142\) 0.852287 0.0715223
\(143\) −0.000645091 1.31465i −5.39452e−5 0.109936i
\(144\) −10.4130 −0.867751
\(145\) −11.9834 + 6.91862i −0.995167 + 0.574560i
\(146\) −0.130038 0.225233i −0.0107621 0.0186404i
\(147\) 0 0
\(148\) 12.5402i 1.03080i
\(149\) 8.03073 + 4.63654i 0.657903 + 0.379841i 0.791478 0.611198i \(-0.209312\pi\)
−0.133574 + 0.991039i \(0.542646\pi\)
\(150\) 0.130500 + 0.0753444i 0.0106553 + 0.00615184i
\(151\) 14.0132i 1.14038i −0.821513 0.570189i \(-0.806870\pi\)
0.821513 0.570189i \(-0.193130\pi\)
\(152\) −0.346318 + 0.599841i −0.0280901 + 0.0486535i
\(153\) −4.23827 7.34090i −0.342644 0.593476i
\(154\) 0 0
\(155\) −7.93059 −0.637000
\(156\) −2.08250 + 3.61110i −0.166734 + 0.289119i
\(157\) 17.1825 1.37131 0.685656 0.727925i \(-0.259515\pi\)
0.685656 + 0.727925i \(0.259515\pi\)
\(158\) 0.717949 0.414508i 0.0571170 0.0329765i
\(159\) −0.399189 0.691415i −0.0316577 0.0548328i
\(160\) 1.20737 2.09123i 0.0954511 0.165326i
\(161\) 0 0
\(162\) 0.632016 + 0.364894i 0.0496558 + 0.0286688i
\(163\) 10.2128 + 5.89637i 0.799930 + 0.461840i 0.843447 0.537213i \(-0.180523\pi\)
−0.0435169 + 0.999053i \(0.513856\pi\)
\(164\) 11.5702i 0.903482i
\(165\) 0.179211 0.310402i 0.0139515 0.0241648i
\(166\) −0.0341449 0.0591407i −0.00265016 0.00459021i
\(167\) −3.73852 + 2.15843i −0.289295 + 0.167025i −0.637624 0.770348i \(-0.720083\pi\)
0.348329 + 0.937372i \(0.386749\pi\)
\(168\) 0 0
\(169\) −6.51105 11.2519i −0.500850 0.865534i
\(170\) 0.647263 0.0496428
\(171\) −3.32739 + 1.92107i −0.254452 + 0.146908i
\(172\) −0.767522 1.32939i −0.0585230 0.101365i
\(173\) −6.25985 + 10.8424i −0.475928 + 0.824331i −0.999620 0.0275769i \(-0.991221\pi\)
0.523692 + 0.851908i \(0.324554\pi\)
\(174\) 0.574457i 0.0435494i
\(175\) 0 0
\(176\) 1.23569 + 0.713428i 0.0931440 + 0.0537767i
\(177\) 5.45140i 0.409752i
\(178\) −0.0685410 + 0.118717i −0.00513737 + 0.00889818i
\(179\) −3.29767 5.71173i −0.246479 0.426915i 0.716067 0.698031i \(-0.245940\pi\)
−0.962547 + 0.271117i \(0.912607\pi\)
\(180\) 7.72419 4.45956i 0.575727 0.332396i
\(181\) 11.0157 0.818791 0.409395 0.912357i \(-0.365740\pi\)
0.409395 + 0.912357i \(0.365740\pi\)
\(182\) 0 0
\(183\) 5.25509 0.388468
\(184\) −2.11171 + 1.21920i −0.155678 + 0.0898805i
\(185\) −5.33109 9.23371i −0.391949 0.678876i
\(186\) 0.164620 0.285130i 0.0120705 0.0209068i
\(187\) 1.16151i 0.0849379i
\(188\) 21.9934 + 12.6979i 1.60403 + 0.926089i
\(189\) 0 0
\(190\) 0.293384i 0.0212843i
\(191\) −2.96606 + 5.13737i −0.214617 + 0.371727i −0.953154 0.302486i \(-0.902184\pi\)
0.738537 + 0.674213i \(0.235517\pi\)
\(192\) −2.22855 3.85997i −0.160832 0.278569i
\(193\) 3.63380 2.09798i 0.261567 0.151016i −0.363482 0.931601i \(-0.618412\pi\)
0.625049 + 0.780586i \(0.285079\pi\)
\(194\) 0.954196 0.0685073
\(195\) −0.00173916 3.54428i −0.000124544 0.253811i
\(196\) 0 0
\(197\) 5.00990 2.89247i 0.356941 0.206080i −0.310797 0.950476i \(-0.600596\pi\)
0.667738 + 0.744396i \(0.267263\pi\)
\(198\) −0.0583881 0.101131i −0.00414946 0.00718708i
\(199\) −5.97988 + 10.3575i −0.423903 + 0.734221i −0.996317 0.0857435i \(-0.972673\pi\)
0.572415 + 0.819964i \(0.306007\pi\)
\(200\) 1.03139i 0.0729305i
\(201\) 6.79564 + 3.92347i 0.479328 + 0.276740i
\(202\) −1.62048 0.935584i −0.114017 0.0658275i
\(203\) 0 0
\(204\) 1.84148 3.18954i 0.128930 0.223313i
\(205\) −4.91874 8.51951i −0.343540 0.595028i
\(206\) −1.07343 + 0.619743i −0.0747891 + 0.0431795i
\(207\) −13.5261 −0.940129
\(208\) 14.1096 0.00692349i 0.978323 0.000480057i
\(209\) 0.526475 0.0364170
\(210\) 0 0
\(211\) 4.11795 + 7.13251i 0.283492 + 0.491022i 0.972242 0.233976i \(-0.0751738\pi\)
−0.688751 + 0.724998i \(0.741840\pi\)
\(212\) −1.36116 + 2.35761i −0.0934851 + 0.161921i
\(213\) 4.12330i 0.282524i
\(214\) −1.36802 0.789825i −0.0935157 0.0539913i
\(215\) 1.13030 + 0.652579i 0.0770858 + 0.0445055i
\(216\) 1.58123i 0.107589i
\(217\) 0 0
\(218\) 0.628633 + 1.08882i 0.0425764 + 0.0737445i
\(219\) 1.08966 0.629116i 0.0736325 0.0425117i
\(220\) −1.22215 −0.0823976
\(221\) 5.74771 + 9.94405i 0.386633 + 0.668909i
\(222\) 0.442643 0.0297082
\(223\) −13.2515 + 7.65073i −0.887383 + 0.512331i −0.873086 0.487567i \(-0.837885\pi\)
−0.0142977 + 0.999898i \(0.504551\pi\)
\(224\) 0 0
\(225\) 2.86064 4.95477i 0.190709 0.330318i
\(226\) 0.596097i 0.0396518i
\(227\) 6.02292 + 3.47733i 0.399755 + 0.230799i 0.686378 0.727245i \(-0.259199\pi\)
−0.286623 + 0.958043i \(0.592533\pi\)
\(228\) −1.44572 0.834686i −0.0957450 0.0552784i
\(229\) 27.4219i 1.81209i −0.423180 0.906045i \(-0.639086\pi\)
0.423180 0.906045i \(-0.360914\pi\)
\(230\) 0.516422 0.894470i 0.0340519 0.0589796i
\(231\) 0 0
\(232\) −3.40511 + 1.96594i −0.223556 + 0.129070i
\(233\) 6.85333 0.448976 0.224488 0.974477i \(-0.427929\pi\)
0.224488 + 0.974477i \(0.427929\pi\)
\(234\) −1.00033 0.576884i −0.0653933 0.0377121i
\(235\) −21.5926 −1.40854
\(236\) −16.0980 + 9.29416i −1.04789 + 0.604998i
\(237\) 2.00536 + 3.47338i 0.130262 + 0.225621i
\(238\) 0 0
\(239\) 22.0754i 1.42794i −0.700177 0.713970i \(-0.746895\pi\)
0.700177 0.713970i \(-0.253105\pi\)
\(240\) 3.33141 + 1.92339i 0.215042 + 0.124154i
\(241\) −13.6807 7.89855i −0.881251 0.508790i −0.0101802 0.999948i \(-0.503241\pi\)
−0.871071 + 0.491158i \(0.836574\pi\)
\(242\) 1.30796i 0.0840787i
\(243\) −6.70981 + 11.6217i −0.430434 + 0.745534i
\(244\) −8.95947 15.5183i −0.573571 0.993455i
\(245\) 0 0
\(246\) 0.408405 0.0260390
\(247\) 4.50732 2.60525i 0.286794 0.165768i
\(248\) −2.25349 −0.143097
\(249\) 0.286118 0.165190i 0.0181320 0.0104685i
\(250\) 0.726405 + 1.25817i 0.0459419 + 0.0795737i
\(251\) −11.2783 + 19.5346i −0.711882 + 1.23302i 0.252268 + 0.967658i \(0.418824\pi\)
−0.964150 + 0.265359i \(0.914510\pi\)
\(252\) 0 0
\(253\) 1.60512 + 0.926716i 0.100913 + 0.0582621i
\(254\) −0.840894 0.485490i −0.0527624 0.0304624i
\(255\) 3.13141i 0.196097i
\(256\) −7.42681 + 12.8636i −0.464176 + 0.803976i
\(257\) −10.2064 17.6781i −0.636660 1.10273i −0.986161 0.165791i \(-0.946982\pi\)
0.349501 0.936936i \(-0.386351\pi\)
\(258\) −0.0469247 + 0.0270920i −0.00292140 + 0.00168667i
\(259\) 0 0
\(260\) −10.4633 + 6.04781i −0.648904 + 0.375069i
\(261\) −21.8107 −1.35005
\(262\) 1.97044 1.13763i 0.121734 0.0702833i
\(263\) 14.7701 + 25.5826i 0.910764 + 1.57749i 0.812987 + 0.582281i \(0.197840\pi\)
0.0977768 + 0.995208i \(0.468827\pi\)
\(264\) 0.0509231 0.0882015i 0.00313410 0.00542842i
\(265\) 2.31464i 0.142187i
\(266\) 0 0
\(267\) −0.574342 0.331596i −0.0351491 0.0202934i
\(268\) 26.7567i 1.63442i
\(269\) 13.9581 24.1762i 0.851043 1.47405i −0.0292252 0.999573i \(-0.509304\pi\)
0.880268 0.474477i \(-0.157363\pi\)
\(270\) −0.334885 0.580038i −0.0203805 0.0353000i
\(271\) 25.5036 14.7245i 1.54924 0.894451i 0.551035 0.834482i \(-0.314233\pi\)
0.998200 0.0599690i \(-0.0191002\pi\)
\(272\) −12.4660 −0.755861
\(273\) 0 0
\(274\) −2.19362 −0.132521
\(275\) −0.678933 + 0.391982i −0.0409412 + 0.0236374i
\(276\) −2.93847 5.08959i −0.176875 0.306357i
\(277\) 3.42927 5.93967i 0.206045 0.356880i −0.744420 0.667711i \(-0.767274\pi\)
0.950465 + 0.310831i \(0.100607\pi\)
\(278\) 0.631992i 0.0379043i
\(279\) −10.8257 6.25021i −0.648117 0.374190i
\(280\) 0 0
\(281\) 29.0940i 1.73561i 0.496909 + 0.867803i \(0.334468\pi\)
−0.496909 + 0.867803i \(0.665532\pi\)
\(282\) 0.448210 0.776323i 0.0266905 0.0462293i
\(283\) −5.80511 10.0547i −0.345078 0.597692i 0.640290 0.768133i \(-0.278814\pi\)
−0.985368 + 0.170441i \(0.945481\pi\)
\(284\) 12.1761 7.02986i 0.722517 0.417146i
\(285\) 1.41937 0.0840761
\(286\) 0.0791828 + 0.136993i 0.00468217 + 0.00810058i
\(287\) 0 0
\(288\) 3.29626 1.90310i 0.194234 0.112141i
\(289\) 3.42614 + 5.93425i 0.201538 + 0.349074i
\(290\) 0.832724 1.44232i 0.0488993 0.0846960i
\(291\) 4.61633i 0.270614i
\(292\) −3.71555 2.14517i −0.217436 0.125537i
\(293\) 15.4054 + 8.89430i 0.899992 + 0.519610i 0.877197 0.480130i \(-0.159410\pi\)
0.0227942 + 0.999740i \(0.492744\pi\)
\(294\) 0 0
\(295\) 7.90228 13.6871i 0.460088 0.796896i
\(296\) −1.51484 2.62378i −0.0880483 0.152504i
\(297\) 1.04087 0.600949i 0.0603976 0.0348706i
\(298\) −1.11611 −0.0646544
\(299\) 18.3278 0.00899334i 1.05992 0.000520098i
\(300\) 2.48583 0.143520
\(301\) 0 0
\(302\) 0.843314 + 1.46066i 0.0485273 + 0.0840517i
\(303\) 4.52629 7.83976i 0.260028 0.450382i
\(304\) 5.65043i 0.324074i
\(305\) 13.1943 + 7.61771i 0.755501 + 0.436189i
\(306\) 0.883550 + 0.510118i 0.0505092 + 0.0291615i
\(307\) 9.07966i 0.518204i 0.965850 + 0.259102i \(0.0834265\pi\)
−0.965850 + 0.259102i \(0.916573\pi\)
\(308\) 0 0
\(309\) −2.99827 5.19315i −0.170566 0.295428i
\(310\) 0.826643 0.477262i 0.0469501 0.0271067i
\(311\) 1.57073 0.0890677 0.0445338 0.999008i \(-0.485820\pi\)
0.0445338 + 0.999008i \(0.485820\pi\)
\(312\) −0.000494185 1.00711i −2.79777e−5 0.0570166i
\(313\) −20.6232 −1.16569 −0.582846 0.812582i \(-0.698061\pi\)
−0.582846 + 0.812582i \(0.698061\pi\)
\(314\) −1.79101 + 1.03404i −0.101073 + 0.0583544i
\(315\) 0 0
\(316\) 6.83792 11.8436i 0.384663 0.666256i
\(317\) 30.5435i 1.71549i −0.514072 0.857747i \(-0.671863\pi\)
0.514072 0.857747i \(-0.328137\pi\)
\(318\) 0.0832187 + 0.0480463i 0.00466667 + 0.00269430i
\(319\) 2.58823 + 1.49432i 0.144913 + 0.0836657i
\(320\) 12.9219i 0.722358i
\(321\) 3.82111 6.61836i 0.213274 0.369401i
\(322\) 0 0
\(323\) −3.98340 + 2.29982i −0.221642 + 0.127965i
\(324\) 12.0389 0.668830
\(325\) −3.87285 + 6.71558i −0.214827 + 0.372513i
\(326\) −1.41937 −0.0786118
\(327\) −5.26765 + 3.04128i −0.291302 + 0.168183i
\(328\) −1.39767 2.42084i −0.0771735 0.133668i
\(329\) 0 0
\(330\) 0.0431396i 0.00237476i
\(331\) −22.3894 12.9265i −1.23063 0.710507i −0.263472 0.964667i \(-0.584868\pi\)
−0.967162 + 0.254161i \(0.918201\pi\)
\(332\) −0.975612 0.563270i −0.0535437 0.0309135i
\(333\) 16.8060i 0.920965i
\(334\) 0.259789 0.449967i 0.0142150 0.0246211i
\(335\) 11.3748 + 19.7017i 0.621472 + 1.07642i
\(336\) 0 0
\(337\) −21.3954 −1.16548 −0.582742 0.812657i \(-0.698020\pi\)
−0.582742 + 0.812657i \(0.698020\pi\)
\(338\) 1.35582 + 0.781009i 0.0737468 + 0.0424813i
\(339\) 2.88387 0.156630
\(340\) 9.24704 5.33878i 0.501491 0.289536i
\(341\) 0.856443 + 1.48340i 0.0463790 + 0.0803308i
\(342\) 0.231220 0.400485i 0.0125029 0.0216557i
\(343\) 0 0
\(344\) 0.321177 + 0.185432i 0.0173167 + 0.00999781i
\(345\) 4.32738 + 2.49841i 0.232978 + 0.134510i
\(346\) 1.50687i 0.0810098i
\(347\) −1.10442 + 1.91291i −0.0592882 + 0.102690i −0.894146 0.447775i \(-0.852216\pi\)
0.834858 + 0.550466i \(0.185550\pi\)
\(348\) −4.73825 8.20689i −0.253997 0.439936i
\(349\) 9.77843 5.64558i 0.523427 0.302201i −0.214908 0.976634i \(-0.568945\pi\)
0.738336 + 0.674433i \(0.235612\pi\)
\(350\) 0 0
\(351\) 5.93747 10.2957i 0.316919 0.549542i
\(352\) −0.521548 −0.0277986
\(353\) 30.8680 17.8217i 1.64294 0.948552i 0.663158 0.748479i \(-0.269216\pi\)
0.979781 0.200072i \(-0.0641177\pi\)
\(354\) 0.328065 + 0.568225i 0.0174365 + 0.0302008i
\(355\) −5.97708 + 10.3526i −0.317230 + 0.549459i
\(356\) 2.26137i 0.119852i
\(357\) 0 0
\(358\) 0.687464 + 0.396907i 0.0363336 + 0.0209772i
\(359\) 19.3218i 1.01976i −0.860244 0.509882i \(-0.829689\pi\)
0.860244 0.509882i \(-0.170311\pi\)
\(360\) −1.07742 + 1.86615i −0.0567851 + 0.0983546i
\(361\) −8.45757 14.6489i −0.445135 0.770997i
\(362\) −1.14822 + 0.662924i −0.0603490 + 0.0348425i
\(363\) 6.32780 0.332123
\(364\) 0 0
\(365\) 3.64783 0.190936
\(366\) −0.547763 + 0.316251i −0.0286320 + 0.0165307i
\(367\) −1.86032 3.22218i −0.0971082 0.168196i 0.813378 0.581735i \(-0.197626\pi\)
−0.910487 + 0.413539i \(0.864293\pi\)
\(368\) −9.94604 + 17.2271i −0.518473 + 0.898022i
\(369\) 15.5061i 0.807217i
\(370\) 1.11137 + 0.641649i 0.0577773 + 0.0333578i
\(371\) 0 0
\(372\) 5.43130i 0.281600i
\(373\) 1.75638 3.04214i 0.0909420 0.157516i −0.816966 0.576686i \(-0.804346\pi\)
0.907908 + 0.419170i \(0.137679\pi\)
\(374\) −0.0698995 0.121070i −0.00361442 0.00626035i
\(375\) −6.08693 + 3.51429i −0.314328 + 0.181477i
\(376\) −6.13557 −0.316418
\(377\) 29.5533 0.0145016i 1.52207 0.000746873i
\(378\) 0 0
\(379\) 21.6647 12.5081i 1.11284 0.642500i 0.173279 0.984873i \(-0.444564\pi\)
0.939564 + 0.342373i \(0.111230\pi\)
\(380\) −2.41990 4.19139i −0.124138 0.215014i
\(381\) 2.34877 4.06818i 0.120331 0.208419i
\(382\) 0.713990i 0.0365309i
\(383\) 19.4556 + 11.2327i 0.994134 + 0.573964i 0.906507 0.422190i \(-0.138738\pi\)
0.0876266 + 0.996153i \(0.472072\pi\)
\(384\) 1.90722 + 1.10114i 0.0973276 + 0.0561921i
\(385\) 0 0
\(386\) −0.252512 + 0.437364i −0.0128525 + 0.0222612i
\(387\) 1.02861 + 1.78161i 0.0522874 + 0.0905644i
\(388\) 13.6320 7.87043i 0.692059 0.399561i
\(389\) 13.3364 0.676184 0.338092 0.941113i \(-0.390219\pi\)
0.338092 + 0.941113i \(0.390219\pi\)
\(390\) 0.213476 + 0.369332i 0.0108098 + 0.0187018i
\(391\) −16.1928 −0.818906
\(392\) 0 0
\(393\) 5.50379 + 9.53284i 0.277629 + 0.480868i
\(394\) −0.348137 + 0.602991i −0.0175389 + 0.0303783i
\(395\) 11.6278i 0.585057i
\(396\) −1.66831 0.963198i −0.0838356 0.0484025i
\(397\) 22.3723 + 12.9166i 1.12283 + 0.648268i 0.942123 0.335268i \(-0.108827\pi\)
0.180710 + 0.983536i \(0.442160\pi\)
\(398\) 1.43948i 0.0721544i
\(399\) 0 0
\(400\) −4.20698 7.28670i −0.210349 0.364335i
\(401\) 15.2078 8.78025i 0.759443 0.438465i −0.0696524 0.997571i \(-0.522189\pi\)
0.829096 + 0.559106i \(0.188856\pi\)
\(402\) −0.944456 −0.0471052
\(403\) 14.6729 + 8.46180i 0.730909 + 0.421512i
\(404\) −30.8677 −1.53572
\(405\) −8.86464 + 5.11800i −0.440487 + 0.254316i
\(406\) 0 0
\(407\) −1.15143 + 1.99434i −0.0570745 + 0.0988559i
\(408\) 0.889797i 0.0440515i
\(409\) −12.5818 7.26410i −0.622129 0.359186i 0.155568 0.987825i \(-0.450279\pi\)
−0.777698 + 0.628639i \(0.783612\pi\)
\(410\) 1.02541 + 0.592019i 0.0506412 + 0.0292377i
\(411\) 10.6126i 0.523479i
\(412\) −10.2236 + 17.7077i −0.503679 + 0.872398i
\(413\) 0 0
\(414\) 1.40989 0.814000i 0.0692923 0.0400059i
\(415\) 0.957831 0.0470181
\(416\) −4.46514 + 2.58087i −0.218922 + 0.126538i
\(417\) −3.05753 −0.149728
\(418\) −0.0548769 + 0.0316832i −0.00268412 + 0.00154968i
\(419\) −2.30096 3.98538i −0.112409 0.194699i 0.804332 0.594180i \(-0.202523\pi\)
−0.916741 + 0.399482i \(0.869190\pi\)
\(420\) 0 0
\(421\) 19.2645i 0.938895i 0.882960 + 0.469447i \(0.155547\pi\)
−0.882960 + 0.469447i \(0.844453\pi\)
\(422\) −0.858468 0.495637i −0.0417896 0.0241272i
\(423\) −29.4750 17.0174i −1.43312 0.827415i
\(424\) 0.657709i 0.0319412i
\(425\) 3.42462 5.93161i 0.166118 0.287726i
\(426\) −0.248140 0.429791i −0.0120224 0.0208234i
\(427\) 0 0
\(428\) −26.0587 −1.25959
\(429\) −0.662763 + 0.383080i −0.0319985 + 0.0184953i
\(430\) −0.157089 −0.00757548
\(431\) −24.5649 + 14.1825i −1.18325 + 0.683149i −0.956764 0.290865i \(-0.906057\pi\)
−0.226485 + 0.974015i \(0.572723\pi\)
\(432\) 6.44973 + 11.1713i 0.310313 + 0.537477i
\(433\) 6.26014 10.8429i 0.300843 0.521076i −0.675484 0.737375i \(-0.736065\pi\)
0.976327 + 0.216299i \(0.0693986\pi\)
\(434\) 0 0
\(435\) 6.97784 + 4.02866i 0.334562 + 0.193159i
\(436\) 17.9618 + 10.3702i 0.860213 + 0.496644i
\(437\) 7.33969i 0.351105i
\(438\) −0.0757203 + 0.131151i −0.00361806 + 0.00626666i
\(439\) −15.8637 27.4767i −0.757132 1.31139i −0.944307 0.329064i \(-0.893267\pi\)
0.187176 0.982326i \(-0.440067\pi\)
\(440\) 0.255711 0.147635i 0.0121906 0.00703822i
\(441\) 0 0
\(442\) −1.19754 0.690619i −0.0569613 0.0328494i
\(443\) 1.73048 0.0822177 0.0411088 0.999155i \(-0.486911\pi\)
0.0411088 + 0.999155i \(0.486911\pi\)
\(444\) 6.32376 3.65102i 0.300112 0.173270i
\(445\) −0.961355 1.66512i −0.0455726 0.0789341i
\(446\) 0.920842 1.59494i 0.0436031 0.0755228i
\(447\) 5.39965i 0.255394i
\(448\) 0 0
\(449\) −9.14208 5.27818i −0.431442 0.249093i 0.268519 0.963274i \(-0.413466\pi\)
−0.699961 + 0.714181i \(0.746799\pi\)
\(450\) 0.688612i 0.0324615i
\(451\) −1.06237 + 1.84008i −0.0500252 + 0.0866462i
\(452\) −4.91675 8.51605i −0.231264 0.400561i
\(453\) −7.06658 + 4.07989i −0.332017 + 0.191690i
\(454\) −0.837063 −0.0392853
\(455\) 0 0
\(456\) 0.403317 0.0188870
\(457\) −6.88399 + 3.97447i −0.322019 + 0.185918i −0.652292 0.757968i \(-0.726193\pi\)
0.330273 + 0.943885i \(0.392859\pi\)
\(458\) 1.65025 + 2.85832i 0.0771111 + 0.133560i
\(459\) −5.25029 + 9.09377i −0.245062 + 0.424461i
\(460\) 17.0383i 0.794415i
\(461\) −9.43262 5.44592i −0.439321 0.253642i 0.263989 0.964526i \(-0.414962\pi\)
−0.703309 + 0.710884i \(0.748295\pi\)
\(462\) 0 0
\(463\) 35.8227i 1.66482i 0.554158 + 0.832411i \(0.313040\pi\)
−0.554158 + 0.832411i \(0.686960\pi\)
\(464\) −16.0379 + 27.7784i −0.744539 + 1.28958i
\(465\) 2.30896 + 3.99923i 0.107075 + 0.185460i
\(466\) −0.714355 + 0.412433i −0.0330918 + 0.0191056i
\(467\) 19.8983 0.920785 0.460393 0.887715i \(-0.347709\pi\)
0.460393 + 0.887715i \(0.347709\pi\)
\(468\) −19.0493 + 0.00934738i −0.880554 + 0.000432083i
\(469\) 0 0
\(470\) 2.25069 1.29944i 0.103817 0.0599386i
\(471\) −5.00262 8.66479i −0.230508 0.399252i
\(472\) 2.24545 3.88923i 0.103355 0.179016i
\(473\) 0.281894i 0.0129615i
\(474\) −0.418056 0.241365i −0.0192020 0.0110863i
\(475\) −2.68861 1.55227i −0.123362 0.0712231i
\(476\) 0 0
\(477\) 1.82420 3.15960i 0.0835243 0.144668i
\(478\) 1.32850 + 2.30102i 0.0607640 + 0.105246i
\(479\) −22.7680 + 13.1451i −1.04030 + 0.600615i −0.919917 0.392113i \(-0.871744\pi\)
−0.120379 + 0.992728i \(0.538411\pi\)
\(480\) −1.40609 −0.0641788
\(481\) 0.0111741 + 22.7721i 0.000509496 + 1.03832i
\(482\) 1.90134 0.0866035
\(483\) 0 0
\(484\) −10.7883 18.6860i −0.490379 0.849362i
\(485\) −6.69177 + 11.5905i −0.303857 + 0.526296i
\(486\) 1.61518i 0.0732662i
\(487\) 5.52491 + 3.18981i 0.250358 + 0.144544i 0.619928 0.784659i \(-0.287162\pi\)
−0.369570 + 0.929203i \(0.620495\pi\)
\(488\) 3.74918 + 2.16459i 0.169717 + 0.0979864i
\(489\) 6.86682i 0.310528i
\(490\) 0 0
\(491\) −1.48384 2.57008i −0.0669647 0.115986i 0.830599 0.556871i \(-0.187998\pi\)
−0.897564 + 0.440885i \(0.854665\pi\)
\(492\) 5.83463 3.36862i 0.263045 0.151869i
\(493\) −26.1107 −1.17597
\(494\) −0.313035 + 0.542808i −0.0140841 + 0.0244221i
\(495\) 1.63790 0.0736182
\(496\) −15.9207 + 9.19184i −0.714862 + 0.412726i
\(497\) 0 0
\(498\) −0.0198823 + 0.0344371i −0.000890947 + 0.00154316i
\(499\) 28.1331i 1.25941i 0.776835 + 0.629704i \(0.216824\pi\)
−0.776835 + 0.629704i \(0.783176\pi\)
\(500\) 20.7554 + 11.9831i 0.928208 + 0.535901i
\(501\) 2.17691 + 1.25684i 0.0972571 + 0.0561514i
\(502\) 2.71492i 0.121173i
\(503\) −15.7688 + 27.3124i −0.703097 + 1.21780i 0.264277 + 0.964447i \(0.414867\pi\)
−0.967374 + 0.253353i \(0.918467\pi\)
\(504\) 0 0
\(505\) 22.7288 13.1225i 1.01142 0.583943i
\(506\) −0.223079 −0.00991706
\(507\) −3.77846 + 6.55935i −0.167807 + 0.291311i
\(508\) −16.0178 −0.710673
\(509\) −11.7731 + 6.79719i −0.521832 + 0.301280i −0.737684 0.675146i \(-0.764081\pi\)
0.215852 + 0.976426i \(0.430747\pi\)
\(510\) −0.188448 0.326402i −0.00834462 0.0144533i
\(511\) 0 0
\(512\) 9.35193i 0.413301i
\(513\) 4.12191 + 2.37979i 0.181987 + 0.105070i
\(514\) 2.12773 + 1.22845i 0.0938502 + 0.0541844i
\(515\) 17.3850i 0.766074i
\(516\) −0.446922 + 0.774091i −0.0196746 + 0.0340775i
\(517\) 2.33183 + 4.03885i 0.102554 + 0.177628i
\(518\) 0 0
\(519\) 7.29012 0.320001
\(520\) 1.45866 2.52933i 0.0639664 0.110919i
\(521\) −8.78344 −0.384810 −0.192405 0.981316i \(-0.561629\pi\)
−0.192405 + 0.981316i \(0.561629\pi\)
\(522\) 2.27343 1.31256i 0.0995053 0.0574494i
\(523\) 16.2849 + 28.2063i 0.712088 + 1.23337i 0.964072 + 0.265642i \(0.0855839\pi\)
−0.251983 + 0.967732i \(0.581083\pi\)
\(524\) 18.7670 32.5053i 0.819838 1.42000i
\(525\) 0 0
\(526\) −3.07912 1.77773i −0.134256 0.0775127i
\(527\) −12.9600 7.48246i −0.564547 0.325941i
\(528\) 0.830847i 0.0361580i
\(529\) −1.41953 + 2.45869i −0.0617185 + 0.106900i
\(530\) 0.139295 + 0.241265i 0.00605057 + 0.0104799i
\(531\) 21.5741 12.4558i 0.936235 0.540536i
\(532\) 0 0
\(533\) 0.0103098 + 21.0107i 0.000446568 + 0.910074i
\(534\) 0.0798218 0.00345423
\(535\) 19.1878 11.0781i 0.829560 0.478947i
\(536\) 3.23218 + 5.59829i 0.139609 + 0.241809i
\(537\) −1.92021 + 3.32590i −0.0828631 + 0.143523i
\(538\) 3.36000i 0.144860i
\(539\) 0 0
\(540\) −9.56858 5.52442i −0.411766 0.237733i
\(541\) 6.94870i 0.298748i 0.988781 + 0.149374i \(0.0477258\pi\)
−0.988781 + 0.149374i \(0.952274\pi\)
\(542\) −1.77224 + 3.06961i −0.0761243 + 0.131851i
\(543\) −3.20718 5.55500i −0.137633 0.238388i
\(544\) 3.94612 2.27830i 0.169189 0.0976811i
\(545\) −17.6344 −0.755375
\(546\) 0 0
\(547\) 10.9095 0.466457 0.233229 0.972422i \(-0.425071\pi\)
0.233229 + 0.972422i \(0.425071\pi\)
\(548\) −31.3388 + 18.0935i −1.33873 + 0.772915i
\(549\) 12.0073 + 20.7972i 0.512457 + 0.887602i
\(550\) 0.0471789 0.0817163i 0.00201172 0.00348440i
\(551\) 11.8352i 0.504194i
\(552\) 1.22963 + 0.709929i 0.0523367 + 0.0302166i
\(553\) 0 0
\(554\) 0.825493i 0.0350718i
\(555\) −3.10425 + 5.37672i −0.131768 + 0.228229i
\(556\) 5.21282 + 9.02886i 0.221073 + 0.382909i
\(557\) 29.9901 17.3148i 1.27072 0.733650i 0.295596 0.955313i \(-0.404482\pi\)
0.975123 + 0.221662i \(0.0711483\pi\)
\(558\) 1.50455 0.0636927
\(559\) −1.39495 2.41339i −0.0590001 0.102075i
\(560\) 0 0
\(561\) 0.585725 0.338169i 0.0247293 0.0142775i
\(562\) −1.75088 3.03261i −0.0738563 0.127923i
\(563\) −4.56839 + 7.91269i −0.192535 + 0.333480i −0.946090 0.323905i \(-0.895004\pi\)
0.753555 + 0.657385i \(0.228338\pi\)
\(564\) 14.7878i 0.622677i
\(565\) 7.24070 + 4.18042i 0.304618 + 0.175872i
\(566\) 1.21019 + 0.698702i 0.0508680 + 0.0293686i
\(567\) 0 0
\(568\) −1.69840 + 2.94172i −0.0712633 + 0.123432i
\(569\) 9.15000 + 15.8483i 0.383588 + 0.664394i 0.991572 0.129555i \(-0.0413549\pi\)
−0.607984 + 0.793949i \(0.708022\pi\)
\(570\) −0.147947 + 0.0854175i −0.00619684 + 0.00357775i
\(571\) −10.1791 −0.425981 −0.212990 0.977054i \(-0.568320\pi\)
−0.212990 + 0.977054i \(0.568320\pi\)
\(572\) 2.26119 + 1.30402i 0.0945450 + 0.0545237i
\(573\) 3.45423 0.144303
\(574\) 0 0
\(575\) −5.46470 9.46514i −0.227894 0.394724i
\(576\) 10.1840 17.6391i 0.424332 0.734964i
\(577\) 19.5165i 0.812482i 0.913766 + 0.406241i \(0.133161\pi\)
−0.913766 + 0.406241i \(0.866839\pi\)
\(578\) −0.714246 0.412370i −0.0297087 0.0171523i
\(579\) −2.11593 1.22163i −0.0879352 0.0507694i
\(580\) 27.4740i 1.14080i
\(581\) 0 0
\(582\) −0.277810 0.481182i −0.0115156 0.0199456i
\(583\) −0.432949 + 0.249963i −0.0179309 + 0.0103524i
\(584\) 1.03654 0.0428923
\(585\) 14.0226 8.10513i 0.579763 0.335106i
\(586\) −2.14103 −0.0884453
\(587\) 30.6486 17.6950i 1.26501 0.730351i 0.290967 0.956733i \(-0.406023\pi\)
0.974039 + 0.226382i \(0.0726898\pi\)
\(588\) 0 0
\(589\) −3.39156 + 5.87436i −0.139747 + 0.242049i
\(590\) 1.90223i 0.0783137i
\(591\) −2.91723 1.68426i −0.119999 0.0692812i
\(592\) −21.4044 12.3579i −0.879716 0.507905i
\(593\) 18.0881i 0.742790i −0.928475 0.371395i \(-0.878880\pi\)
0.928475 0.371395i \(-0.121120\pi\)
\(594\) −0.0723301 + 0.125279i −0.00296774 + 0.00514028i
\(595\) 0 0
\(596\) −15.9451 + 9.20592i −0.653138 + 0.377089i
\(597\) 6.96407 0.285021
\(598\) −1.90985 + 1.10390i −0.0780996 + 0.0451419i
\(599\) 9.05992 0.370178 0.185089 0.982722i \(-0.440743\pi\)
0.185089 + 0.982722i \(0.440743\pi\)
\(600\) −0.520111 + 0.300286i −0.0212334 + 0.0122591i
\(601\) 14.6440 + 25.3642i 0.597343 + 1.03463i 0.993212 + 0.116321i \(0.0371102\pi\)
−0.395869 + 0.918307i \(0.629556\pi\)
\(602\) 0 0
\(603\) 35.8586i 1.46028i
\(604\) 24.0958 + 13.9117i 0.980444 + 0.566059i
\(605\) 15.8876 + 9.17269i 0.645922 + 0.372923i
\(606\) 1.08957i 0.0442606i
\(607\) −19.6825 + 34.0911i −0.798887 + 1.38371i 0.121454 + 0.992597i \(0.461244\pi\)
−0.920341 + 0.391116i \(0.872089\pi\)
\(608\) −1.03268 1.78865i −0.0418807 0.0725394i
\(609\) 0 0
\(610\) −1.83373 −0.0742457
\(611\) 39.9498 + 23.0389i 1.61619 + 0.932053i
\(612\) 16.8303 0.680324
\(613\) 4.79186 2.76658i 0.193541 0.111741i −0.400098 0.916472i \(-0.631024\pi\)
0.593639 + 0.804731i \(0.297691\pi\)
\(614\) −0.546413 0.946416i −0.0220514 0.0381942i
\(615\) −2.86414 + 4.96084i −0.115493 + 0.200040i
\(616\) 0 0
\(617\) 10.8959 + 6.29077i 0.438654 + 0.253257i 0.703026 0.711164i \(-0.251832\pi\)
−0.264373 + 0.964421i \(0.585165\pi\)
\(618\) 0.625047 + 0.360871i 0.0251431 + 0.0145164i
\(619\) 22.3955i 0.900149i 0.892991 + 0.450075i \(0.148603\pi\)
−0.892991 + 0.450075i \(0.851397\pi\)
\(620\) 7.87314 13.6367i 0.316193 0.547662i
\(621\) 8.37794 + 14.5110i 0.336195 + 0.582307i
\(622\) −0.163724 + 0.0945262i −0.00656474 + 0.00379015i
\(623\) 0 0
\(624\) −4.11144 7.11315i −0.164589 0.284754i
\(625\) −9.62659 −0.385064
\(626\) 2.14965 1.24110i 0.0859175 0.0496045i
\(627\) −0.153281 0.265491i −0.00612145 0.0106027i
\(628\) −17.0580 + 29.5454i −0.680690 + 1.17899i
\(629\) 20.1194i 0.802213i
\(630\) 0 0
\(631\) 1.68778 + 0.974439i 0.0671894 + 0.0387918i 0.533218 0.845978i \(-0.320982\pi\)
−0.466029 + 0.884769i \(0.654316\pi\)
\(632\) 3.30406i 0.131428i
\(633\) 2.39785 4.15320i 0.0953061 0.165075i
\(634\) 1.83811 + 3.18369i 0.0730005 + 0.126441i
\(635\) 11.7944 6.80948i 0.468045 0.270226i
\(636\) 1.58519 0.0628569
\(637\) 0 0
\(638\) −0.359712 −0.0142411
\(639\) −16.3181 + 9.42125i −0.645533 + 0.372699i
\(640\) 3.19238 + 5.52937i 0.126190 + 0.218568i
\(641\) 5.21051 9.02487i 0.205803 0.356461i −0.744585 0.667527i \(-0.767353\pi\)
0.950388 + 0.311066i \(0.100686\pi\)
\(642\) 0.919818i 0.0363023i
\(643\) −13.2247 7.63531i −0.521533 0.301107i 0.216029 0.976387i \(-0.430690\pi\)
−0.737562 + 0.675280i \(0.764023\pi\)
\(644\) 0 0
\(645\) 0.759983i 0.0299243i
\(646\) 0.276806 0.479442i 0.0108908 0.0188634i
\(647\) −8.75328 15.1611i −0.344127 0.596045i 0.641068 0.767484i \(-0.278492\pi\)
−0.985195 + 0.171439i \(0.945158\pi\)
\(648\) −2.51891 + 1.45429i −0.0989520 + 0.0571300i
\(649\) −3.41354 −0.133993
\(650\) −0.000457849 0.933064i −1.79583e−5 0.0365978i
\(651\) 0 0
\(652\) −20.2777 + 11.7073i −0.794136 + 0.458494i
\(653\) 5.09169 + 8.81906i 0.199253 + 0.345117i 0.948287 0.317416i \(-0.102815\pi\)
−0.749033 + 0.662532i \(0.769482\pi\)
\(654\) 0.366048 0.634014i 0.0143136 0.0247919i
\(655\) 31.9129i 1.24694i
\(656\) −19.7488 11.4020i −0.771063 0.445173i
\(657\) 4.97949 + 2.87491i 0.194268 + 0.112161i
\(658\) 0 0
\(659\) 21.9294 37.9828i 0.854247 1.47960i −0.0230945 0.999733i \(-0.507352\pi\)
0.877342 0.479866i \(-0.159315\pi\)
\(660\) 0.355825 + 0.616308i 0.0138505 + 0.0239897i
\(661\) 28.5156 16.4635i 1.10913 0.640356i 0.170526 0.985353i \(-0.445453\pi\)
0.938604 + 0.344997i \(0.112120\pi\)
\(662\) 3.11167 0.120939
\(663\) 3.34116 5.79362i 0.129760 0.225006i
\(664\) 0.272170 0.0105622
\(665\) 0 0
\(666\) 1.01139 + 1.75177i 0.0391904 + 0.0678798i
\(667\) −20.8326 + 36.0831i −0.806640 + 1.39714i
\(668\) 8.57120i 0.331630i
\(669\) 7.71622 + 4.45496i 0.298326 + 0.172239i
\(670\) −2.37130 1.36907i −0.0916113 0.0528918i
\(671\) 3.29062i 0.127033i
\(672\) 0 0
\(673\) 13.3423 + 23.1095i 0.514307 + 0.890806i 0.999862 + 0.0165997i \(0.00528409\pi\)
−0.485555 + 0.874206i \(0.661383\pi\)
\(674\) 2.23015 1.28758i 0.0859021 0.0495956i
\(675\) −7.08740 −0.272794
\(676\) 25.8117 0.0253313i 0.992756 0.000974280i
\(677\) −29.5328 −1.13504 −0.567519 0.823361i \(-0.692096\pi\)
−0.567519 + 0.823361i \(0.692096\pi\)
\(678\) −0.300599 + 0.173551i −0.0115444 + 0.00666519i
\(679\) 0 0
\(680\) −1.28984 + 2.23406i −0.0494630 + 0.0856725i
\(681\) 4.04965i 0.155183i
\(682\) −0.178542 0.103081i −0.00683674 0.00394719i
\(683\) −15.8379 9.14400i −0.606019 0.349885i 0.165387 0.986229i \(-0.447113\pi\)
−0.771406 + 0.636343i \(0.780446\pi\)
\(684\) 7.62863i 0.291688i
\(685\) 15.3838 26.6456i 0.587786 1.01807i
\(686\) 0 0
\(687\) −13.8283 + 7.98378i −0.527583 + 0.304600i
\(688\) 3.02545 0.115344
\(689\) −2.46968 + 4.28246i −0.0940872 + 0.163149i
\(690\) −0.601417 −0.0228956
\(691\) 8.95525 5.17031i 0.340674 0.196688i −0.319896 0.947453i \(-0.603648\pi\)
0.660570 + 0.750765i \(0.270315\pi\)
\(692\) −12.4290 21.5277i −0.472480 0.818360i
\(693\) 0 0
\(694\) 0.265855i 0.0100917i
\(695\) −7.67671 4.43215i −0.291194 0.168121i
\(696\) 1.98277 + 1.14475i 0.0751567 + 0.0433917i
\(697\) 18.5632i 0.703131i
\(698\) −0.679501 + 1.17693i −0.0257195 + 0.0445475i
\(699\) −1.99532 3.45599i −0.0754699 0.130718i
\(700\) 0 0
\(701\) 41.6959 1.57483 0.787415 0.616423i \(-0.211419\pi\)
0.787415 + 0.616423i \(0.211419\pi\)
\(702\) 0.000701930 1.43048i 2.64926e−5 0.0539901i
\(703\) −9.11948 −0.343948
\(704\) −2.41702 + 1.39547i −0.0910951 + 0.0525938i
\(705\) 6.28659 + 10.8887i 0.236766 + 0.410092i
\(706\) −2.14501 + 3.71527i −0.0807287 + 0.139826i
\(707\) 0 0
\(708\) 9.37371 + 5.41191i 0.352286 + 0.203392i
\(709\) 0.00947974 + 0.00547313i 0.000356019 + 0.000205548i 0.500178 0.865923i \(-0.333268\pi\)
−0.499822 + 0.866128i \(0.666601\pi\)
\(710\) 1.43880i 0.0539972i
\(711\) −9.16402 + 15.8725i −0.343677 + 0.595267i
\(712\) −0.273171 0.473146i −0.0102375 0.0177319i
\(713\) −20.6804 + 11.9398i −0.774488 + 0.447151i
\(714\) 0 0
\(715\) −2.21935 + 0.00108902i −0.0829988 + 4.07271e-5i
\(716\) 13.0951 0.489388
\(717\) −11.1322 + 6.42717i −0.415739 + 0.240027i
\(718\) 1.16278 + 2.01400i 0.0433947 + 0.0751618i
\(719\) 12.7330 22.0542i 0.474861 0.822484i −0.524724 0.851272i \(-0.675832\pi\)
0.999586 + 0.0287885i \(0.00916494\pi\)
\(720\) 17.5789i 0.655127i
\(721\) 0 0
\(722\) 1.76314 + 1.01795i 0.0656174 + 0.0378842i
\(723\) 9.19853i 0.342097i
\(724\) −10.9359 + 18.9416i −0.406430 + 0.703957i
\(725\) −8.81176 15.2624i −0.327261 0.566832i
\(726\) −0.659576 + 0.380807i −0.0244792 + 0.0141331i
\(727\) 23.5565 0.873663 0.436831 0.899543i \(-0.356101\pi\)
0.436831 + 0.899543i \(0.356101\pi\)
\(728\) 0 0
\(729\) −10.3760 −0.384297
\(730\) −0.380231 + 0.219526i −0.0140730 + 0.00812503i
\(731\) 1.23141 + 2.13286i 0.0455453 + 0.0788867i
\(732\) −5.21703 + 9.03616i −0.192827 + 0.333986i
\(733\) 6.23249i 0.230202i 0.993354 + 0.115101i \(0.0367192\pi\)
−0.993354 + 0.115101i \(0.963281\pi\)
\(734\) 0.387821 + 0.223909i 0.0143147 + 0.00826461i
\(735\) 0 0
\(736\) 7.27100i 0.268013i
\(737\) 2.45679 4.25528i 0.0904969 0.156745i
\(738\) 0.933158 + 1.61628i 0.0343500 + 0.0594960i
\(739\) 1.12339 0.648588i 0.0413244 0.0238587i −0.479195 0.877708i \(-0.659071\pi\)
0.520520 + 0.853850i \(0.325738\pi\)
\(740\) 21.1699 0.778221
\(741\) −2.62606 1.51444i −0.0964709 0.0556344i
\(742\) 0 0
\(743\) 5.25627 3.03471i 0.192834 0.111333i −0.400475 0.916308i \(-0.631155\pi\)
0.593309 + 0.804975i \(0.297821\pi\)
\(744\) 0.656096 + 1.13639i 0.0240536 + 0.0416621i
\(745\) 7.82725 13.5572i 0.286768 0.496697i
\(746\) 0.422796i 0.0154797i
\(747\) 1.30749 + 0.754880i 0.0478386 + 0.0276196i
\(748\) −1.99722 1.15310i −0.0730256 0.0421613i
\(749\) 0 0
\(750\) 0.422980 0.732622i 0.0154450 0.0267516i
\(751\) −18.3023 31.7005i −0.667860 1.15677i −0.978501 0.206241i \(-0.933877\pi\)
0.310641 0.950527i \(-0.399456\pi\)
\(752\) −43.3473 + 25.0266i −1.58071 + 0.912625i
\(753\) 13.1346 0.478650
\(754\) −3.07961 + 1.78003i −0.112153 + 0.0648248i
\(755\) −23.6566 −0.860952
\(756\) 0 0
\(757\) −5.83991 10.1150i −0.212255 0.367636i 0.740165 0.672425i \(-0.234747\pi\)
−0.952420 + 0.304789i \(0.901414\pi\)
\(758\) −1.50548 + 2.60757i −0.0546815 + 0.0947111i
\(759\) 1.07924i 0.0391739i
\(760\) 1.01263 + 0.584642i 0.0367320 + 0.0212072i
\(761\) 34.4408 + 19.8844i 1.24848 + 0.720810i 0.970806 0.239866i \(-0.0771035\pi\)
0.277673 + 0.960676i \(0.410437\pi\)
\(762\) 0.565394i 0.0204821i
\(763\) 0 0
\(764\) −5.88916 10.2003i −0.213062 0.369035i
\(765\) −12.3926 + 7.15490i −0.448057 + 0.258686i
\(766\) −2.70393 −0.0976970
\(767\) −29.2245 + 16.8919i −1.05523 + 0.609930i
\(768\) 8.64915 0.312099
\(769\) 8.62507 4.97969i 0.311028 0.179572i −0.336358 0.941734i \(-0.609195\pi\)
0.647386 + 0.762162i \(0.275862\pi\)
\(770\) 0 0
\(771\) −5.94313 + 10.2938i −0.214036 + 0.370722i
\(772\) 8.33112i 0.299843i
\(773\) −11.0433 6.37588i −0.397201 0.229324i 0.288074 0.957608i \(-0.406985\pi\)
−0.685276 + 0.728284i \(0.740318\pi\)
\(774\) −0.214435 0.123804i −0.00770769 0.00445004i
\(775\) 10.1006i 0.362825i
\(776\) −1.90148 + 3.29346i −0.0682592 + 0.118228i
\(777\) 0 0
\(778\) −1.39012 + 0.802586i −0.0498382 + 0.0287741i
\(779\) −8.41411 −0.301467
\(780\) 6.09613 + 3.51561i 0.218276