Properties

Label 637.2.u.h.30.4
Level $637$
Weight $2$
Character 637.30
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.u (of order \(6\), degree \(2\), not 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: \(\Z[a_1, a_2, a_3]\)
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 30.4
Root \(1.34408 + 0.439820i\) of defining polynomial
Character \(\chi\) \(=\) 637.30
Dual form 637.2.u.h.361.4

$q$-expansion

\(f(q)\) \(=\) \(q+(0.104235 - 0.0601799i) q^{2} -0.582292 q^{3} +(-0.992757 + 1.71951i) q^{4} +(1.46199 + 0.844083i) q^{5} +(-0.0606950 + 0.0350423i) q^{6} +0.479696i q^{8} -2.66094 q^{9} +O(q^{10})\) \(q+(0.104235 - 0.0601799i) q^{2} -0.582292 q^{3} +(-0.992757 + 1.71951i) q^{4} +(1.46199 + 0.844083i) q^{5} +(-0.0606950 + 0.0350423i) q^{6} +0.479696i q^{8} -2.66094 q^{9} +0.203187 q^{10} +0.364618i q^{11} +(0.578074 - 1.00125i) 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} +(-0.277362 + 0.160135i) q^{18} +1.44391i q^{19} +(-2.90281 + 1.67594i) q^{20} +(0.0219427 + 0.0380059i) q^{22} +(-2.54161 - 4.40219i) q^{23} -0.279323i q^{24} +(-1.07505 - 1.86204i) q^{25} +(0.375717 + 0.217166i) q^{26} +3.29632 q^{27} +(-4.09831 + 7.09848i) q^{29} -0.118314 q^{30} +(-4.06838 + 2.34888i) q^{31} +(-1.23876 - 0.715198i) q^{32} -0.212314i q^{33} +0.383412i q^{34} +(2.64166 - 4.57549i) q^{36} +(-5.46967 + 3.15792i) q^{37} +(0.0868943 + 0.150505i) q^{38} +(-1.04885 - 1.81872i) q^{39} +(-0.404903 + 0.701313i) q^{40} +(-5.04661 - 2.91366i) q^{41} +(-0.386561 - 0.669543i) q^{43} +(-0.626963 - 0.361977i) q^{44} +(-3.89027 - 2.24605i) q^{45} +(-0.529847 - 0.305907i) q^{46} +(11.0769 + 6.39527i) q^{47} +(1.13934 + 1.97339i) q^{48} +(-0.224115 - 0.129393i) q^{50} +(0.927459 - 1.60641i) q^{51} +(-7.15887 - 0.00351282i) q^{52} +(-0.685548 - 1.18740i) q^{53} +(0.343591 - 0.198372i) q^{54} +(-0.307768 + 0.533070i) q^{55} -0.840776i q^{57} +0.986544i q^{58} +(8.10770 + 4.68098i) q^{59} +(1.69028 - 0.975885i) q^{60} -9.02484 q^{61} +(-0.282711 + 0.489669i) q^{62} +7.65442 q^{64} +(-0.00298674 + 6.08677i) q^{65} +(-0.0127771 - 0.0221305i) q^{66} +13.4759i q^{67} +(-3.16247 - 5.47757i) q^{68} +(1.47996 + 2.56336i) q^{69} +(-6.13246 + 3.54058i) q^{71} -1.27644i q^{72} +(1.87133 - 1.08041i) 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} +(3.44391 - 5.96502i) q^{79} -6.60628i q^{80} +6.06339 q^{81} -0.701376 q^{82} +0.567380i q^{83} +(-4.65725 + 2.68887i) q^{85} +(-0.0805861 - 0.0465264i) q^{86} +(2.38641 - 4.13339i) q^{87} -0.174906 q^{88} +(0.986346 - 0.569467i) q^{89} -0.540669 q^{90} +10.0928 q^{92} +(2.36898 - 1.36773i) q^{93} +1.53947 q^{94} +(-1.21878 + 2.11098i) q^{95} +(0.721319 + 0.416454i) q^{96} +(6.86572 - 3.96393i) q^{97} -0.970225i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 4 q^{4} - 6 q^{5} - 18 q^{6} + 8 q^{9} + O(q^{10}) \) \( 12 q + 4 q^{4} - 6 q^{5} - 18 q^{6} + 8 q^{9} - 24 q^{10} + 2 q^{12} + 4 q^{13} + 6 q^{15} - 8 q^{16} - 4 q^{17} - 12 q^{18} - 12 q^{20} + 6 q^{22} - 12 q^{23} + 10 q^{25} + 24 q^{26} + 12 q^{27} + 8 q^{29} - 16 q^{30} + 18 q^{31} - 36 q^{32} - 10 q^{36} + 42 q^{37} - 2 q^{38} - 10 q^{39} - 46 q^{40} + 30 q^{41} + 2 q^{43} + 24 q^{44} - 12 q^{46} + 42 q^{47} - 2 q^{48} - 18 q^{50} - 26 q^{51} + 26 q^{52} + 22 q^{53} - 12 q^{54} - 6 q^{55} - 18 q^{59} + 66 q^{60} - 28 q^{61} - 4 q^{62} - 52 q^{64} - 42 q^{65} + 26 q^{66} - 8 q^{68} + 4 q^{69} - 24 q^{71} + 30 q^{73} + 6 q^{74} + 46 q^{75} - 18 q^{76} - 10 q^{78} + 28 q^{79} - 4 q^{81} - 28 q^{82} - 48 q^{85} - 60 q^{86} - 2 q^{87} + 28 q^{88} + 12 q^{89} + 24 q^{90} + 24 q^{92} + 18 q^{93} - 8 q^{94} - 22 q^{95} + 6 q^{96} + 6 q^{97} + O(q^{100}) \)

Character values

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

\(n\) \(197\) \(248\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.104235 0.0601799i 0.0737051 0.0425536i −0.462695 0.886518i \(-0.653117\pi\)
0.536400 + 0.843964i \(0.319784\pi\)
\(3\) −0.582292 −0.336186 −0.168093 0.985771i \(-0.553761\pi\)
−0.168093 + 0.985771i \(0.553761\pi\)
\(4\) −0.992757 + 1.71951i −0.496378 + 0.859753i
\(5\) 1.46199 + 0.844083i 0.653824 + 0.377485i 0.789920 0.613210i \(-0.210122\pi\)
−0.136096 + 0.990696i \(0.543456\pi\)
\(6\) −0.0606950 + 0.0350423i −0.0247786 + 0.0143060i
\(7\) 0 0
\(8\) 0.479696i 0.169598i
\(9\) −2.66094 −0.886979
\(10\) 0.203187 0.0642535
\(11\) 0.364618i 0.109936i 0.998488 + 0.0549682i \(0.0175058\pi\)
−0.998488 + 0.0549682i \(0.982494\pi\)
\(12\) 0.578074 1.00125i 0.166876 0.289037i
\(13\) 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 −0.991949 0.126636i \(-0.959582\pi\)
0.605645 + 0.795735i \(0.292915\pi\)
\(18\) −0.277362 + 0.160135i −0.0653748 + 0.0377442i
\(19\) 1.44391i 0.331255i 0.986188 + 0.165628i \(0.0529649\pi\)
−0.986188 + 0.165628i \(0.947035\pi\)
\(20\) −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 \(-0.344460\pi\)
\(24\) 0.279323i 0.0570166i
\(25\) −1.07505 1.86204i −0.215010 0.372408i
\(26\) 0.375717 + 0.217166i 0.0736842 + 0.0425898i
\(27\) 3.29632 0.634377
\(28\) 0 0
\(29\) −4.09831 + 7.09848i −0.761037 + 1.31815i 0.181280 + 0.983432i \(0.441976\pi\)
−0.942317 + 0.334723i \(0.891357\pi\)
\(30\) −0.118314 −0.0216012
\(31\) −4.06838 + 2.34888i −0.730702 + 0.421871i −0.818679 0.574252i \(-0.805293\pi\)
0.0879771 + 0.996122i \(0.471960\pi\)
\(32\) −1.23876 0.715198i −0.218984 0.126430i
\(33\) 0.212314i 0.0369592i
\(34\) 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 −0.876943 0.480594i \(-0.840421\pi\)
−0.0222655 + 0.999752i \(0.507088\pi\)
\(38\) 0.0868943 + 0.150505i 0.0140961 + 0.0244152i
\(39\) −1.04885 1.81872i −0.167950 0.291228i
\(40\) −0.404903 + 0.701313i −0.0640208 + 0.110887i
\(41\) −5.04661 2.91366i −0.788148 0.455037i 0.0511624 0.998690i \(-0.483707\pi\)
−0.839310 + 0.543653i \(0.817041\pi\)
\(42\) 0 0
\(43\) −0.386561 0.669543i −0.0589500 0.102104i 0.835044 0.550183i \(-0.185442\pi\)
−0.893994 + 0.448078i \(0.852109\pi\)
\(44\) −0.626963 0.361977i −0.0945182 0.0545701i
\(45\) −3.89027 2.24605i −0.579928 0.334821i
\(46\) −0.529847 0.305907i −0.0781217 0.0451036i
\(47\) 11.0769 + 6.39527i 1.61574 + 0.932846i 0.988006 + 0.154416i \(0.0493495\pi\)
0.627731 + 0.778430i \(0.283984\pi\)
\(48\) 1.13934 + 1.97339i 0.164449 + 0.284835i
\(49\) 0 0
\(50\) −0.224115 0.129393i −0.0316946 0.0182989i
\(51\) 0.927459 1.60641i 0.129870 0.224942i
\(52\) −7.15887 0.00351282i −0.992757 0.000487140i
\(53\) −0.685548 1.18740i −0.0941672 0.163102i 0.815094 0.579329i \(-0.196685\pi\)
−0.909261 + 0.416227i \(0.863352\pi\)
\(54\) 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
\(58\) 0.986544i 0.129540i
\(59\) 8.10770 + 4.68098i 1.05553 + 0.609412i 0.924193 0.381925i \(-0.124739\pi\)
0.131340 + 0.991337i \(0.458072\pi\)
\(60\) 1.69028 0.975885i 0.218215 0.125986i
\(61\) −9.02484 −1.15551 −0.577756 0.816209i \(-0.696072\pi\)
−0.577756 + 0.816209i \(0.696072\pi\)
\(62\) −0.282711 + 0.489669i −0.0359043 + 0.0621880i
\(63\) 0 0
\(64\) 7.65442 0.956802
\(65\) −0.00298674 + 6.08677i −0.000370460 + 0.754970i
\(66\) −0.0127771 0.0221305i −0.00157275 0.00272408i
\(67\) 13.4759i 1.64635i 0.567789 + 0.823174i \(0.307799\pi\)
−0.567789 + 0.823174i \(0.692201\pi\)
\(68\) −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 −0.817613 0.575769i \(-0.804703\pi\)
0.0898239 + 0.995958i \(0.471370\pi\)
\(72\) 1.27644i 0.150430i
\(73\) 1.87133 1.08041i 0.219023 0.126453i −0.386475 0.922300i \(-0.626307\pi\)
0.605498 + 0.795847i \(0.292974\pi\)
\(74\) −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
\(79\) 3.44391 5.96502i 0.387470 0.671117i −0.604639 0.796500i \(-0.706682\pi\)
0.992108 + 0.125382i \(0.0400158\pi\)
\(80\) 6.60628i 0.738605i
\(81\) 6.06339 0.673710
\(82\) −0.701376 −0.0774540
\(83\) 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
\(86\) −0.0805861 0.0465264i −0.00868982 0.00501707i
\(87\) 2.38641 4.13339i 0.255850 0.443146i
\(88\) −0.174906 −0.0186450
\(89\) 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
\(94\) 1.53947 0.158784
\(95\) −1.21878 + 2.11098i −0.125044 + 0.216582i
\(96\) 0.721319 + 0.416454i 0.0736193 + 0.0425041i
\(97\) 6.86572 3.96393i 0.697109 0.402476i −0.109161 0.994024i \(-0.534816\pi\)
0.806270 + 0.591548i \(0.201483\pi\)
\(98\) 0 0
\(99\) 0.970225i 0.0975113i
\(100\) 4.26905 0.426905
\(101\) 15.5464 1.54693 0.773465 0.633839i \(-0.218522\pi\)
0.773465 + 0.633839i \(0.218522\pi\)
\(102\) 0.223258i 0.0221058i
\(103\) 5.14908 8.91847i 0.507354 0.878763i −0.492610 0.870250i \(-0.663957\pi\)
0.999964 0.00851245i \(-0.00270963\pi\)
\(104\) −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
\(109\) 9.04641 5.22295i 0.866489 0.500268i 0.000309035 1.00000i \(-0.499902\pi\)
0.866180 + 0.499732i \(0.166568\pi\)
\(110\) 0.0740858i 0.00706380i
\(111\) 3.18495 1.83883i 0.302302 0.174534i
\(112\) 0 0
\(113\) −2.47631 4.28909i −0.232952 0.403484i 0.725724 0.687986i \(-0.241505\pi\)
−0.958675 + 0.284502i \(0.908172\pi\)
\(114\) −0.0505978 0.0876380i −0.00473892 0.00820805i
\(115\) 8.58130i 0.800211i
\(116\) −8.13725 14.0941i −0.755524 1.30861i
\(117\) −4.79299 8.31112i −0.443112 0.768364i
\(118\) 1.12681 0.103731
\(119\) 0 0
\(120\) 0.235772 0.408369i 0.0215229 0.0372788i
\(121\) 10.8671 0.987914
\(122\) −0.940702 + 0.543114i −0.0851671 + 0.0491713i
\(123\) 2.93860 + 1.69660i 0.264965 + 0.152977i
\(124\) 9.32746i 0.837630i
\(125\) 12.0705i 1.07962i
\(126\) 0 0
\(127\) 4.03366 6.98650i 0.357929 0.619951i −0.629686 0.776850i \(-0.716816\pi\)
0.987615 + 0.156899i \(0.0501496\pi\)
\(128\) 3.27537 1.89104i 0.289505 0.167146i
\(129\) 0.225091 + 0.389870i 0.0198182 + 0.0343261i
\(130\) 0.365990 + 0.634632i 0.0320994 + 0.0556609i
\(131\) −9.45194 + 16.3712i −0.825820 + 1.43036i 0.0754716 + 0.997148i \(0.475954\pi\)
−0.901291 + 0.433214i \(0.857380\pi\)
\(132\) 0.365075 + 0.210776i 0.0317757 + 0.0183457i
\(133\) 0 0
\(134\) 0.810981 + 1.40466i 0.0700581 + 0.121344i
\(135\) 4.81920 + 2.78236i 0.414770 + 0.239468i
\(136\) −1.32337 0.764047i −0.113478 0.0655165i
\(137\) −15.7837 9.11274i −1.34850 0.778554i −0.360459 0.932775i \(-0.617380\pi\)
−0.988036 + 0.154221i \(0.950713\pi\)
\(138\) 0.308526 + 0.178127i 0.0262635 + 0.0151632i
\(139\) −2.62542 4.54737i −0.222686 0.385703i 0.732937 0.680297i \(-0.238149\pi\)
−0.955623 + 0.294594i \(0.904816\pi\)
\(140\) 0 0
\(141\) −6.45001 3.72392i −0.543189 0.313610i
\(142\) −0.426143 + 0.738102i −0.0357612 + 0.0619401i
\(143\) −1.13884 + 0.656766i −0.0952348 + 0.0549215i
\(144\) 5.20651 + 9.01794i 0.433876 + 0.751495i
\(145\) −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
\(149\) 9.27309i 0.759681i 0.925052 + 0.379841i \(0.124021\pi\)
−0.925052 + 0.379841i \(0.875979\pi\)
\(150\) 0.130500 + 0.0753444i 0.0106553 + 0.00615184i
\(151\) 12.1358 7.00661i 0.987597 0.570189i 0.0830419 0.996546i \(-0.473536\pi\)
0.904555 + 0.426357i \(0.140203\pi\)
\(152\) −0.692636 −0.0561802
\(153\) 4.23827 7.34090i 0.342644 0.593476i
\(154\) 0 0
\(155\) −7.93059 −0.637000
\(156\) 4.16855 + 0.00204549i 0.333751 + 0.000163770i
\(157\) 8.59125 + 14.8805i 0.685656 + 1.18759i 0.973230 + 0.229833i \(0.0738180\pi\)
−0.287574 + 0.957759i \(0.592849\pi\)
\(158\) 0.829017i 0.0659530i
\(159\) 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
\(163\) 11.7927i 0.923679i 0.886963 + 0.461840i \(0.152810\pi\)
−0.886963 + 0.461840i \(0.847190\pi\)
\(164\) 10.0201 5.78511i 0.782439 0.451741i
\(165\) 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 \(-0.279917\pi\)
−0.348329 + 0.937372i \(0.613251\pi\)
\(168\) 0 0
\(169\) −6.51105 + 11.2519i −0.500850 + 0.865534i
\(170\) −0.323632 + 0.560546i −0.0248214 + 0.0429919i
\(171\) 3.84214i 0.293816i
\(172\) 1.53504 0.117046
\(173\) −12.5197 −0.951855 −0.475928 0.879484i \(-0.657888\pi\)
−0.475928 + 0.879484i \(0.657888\pi\)
\(174\) 0.574457i 0.0435494i
\(175\) 0 0
\(176\) 1.23569 0.713428i 0.0931440 0.0537767i
\(177\) −4.72105 2.72570i −0.354856 0.204876i
\(178\) 0.0685410 0.118717i 0.00513737 0.00889818i
\(179\) 6.59534 0.492959 0.246479 0.969148i \(-0.420726\pi\)
0.246479 + 0.969148i \(0.420726\pi\)
\(180\) 7.72419 4.45956i 0.575727 0.332396i
\(181\) −11.0157 −0.818791 −0.409395 0.912357i \(-0.634260\pi\)
−0.409395 + 0.912357i \(0.634260\pi\)
\(182\) 0 0
\(183\) 5.25509 0.388468
\(184\) 2.11171 1.21920i 0.155678 0.0898805i
\(185\) −10.6622 −0.783899
\(186\) 0.164620 0.285130i 0.0120705 0.0209068i
\(187\) −1.00590 0.580754i −0.0735584 0.0424690i
\(188\) −21.9934 + 12.6979i −1.60403 + 0.926089i
\(189\) 0 0
\(190\) 0.293384i 0.0212843i
\(191\) 5.93213 0.429234 0.214617 0.976698i \(-0.431150\pi\)
0.214617 + 0.976698i \(0.431150\pi\)
\(192\) −4.45711 −0.321664
\(193\) 4.19595i 0.302031i −0.988531 0.151016i \(-0.951746\pi\)
0.988531 0.151016i \(-0.0482544\pi\)
\(194\) 0.477098 0.826358i 0.0342536 0.0593290i
\(195\) 0.00173916 3.54428i 0.000124544 0.253811i
\(196\) 0 0
\(197\) 5.00990 + 2.89247i 0.356941 + 0.206080i 0.667738 0.744396i \(-0.267263\pi\)
−0.310797 + 0.950476i \(0.600596\pi\)
\(198\) −0.0583881 0.101131i −0.00414946 0.00718708i
\(199\) 5.97988 10.3575i 0.423903 0.734221i −0.572415 0.819964i \(-0.693993\pi\)
0.996317 + 0.0857435i \(0.0273266\pi\)
\(200\) 0.893213 0.515697i 0.0631597 0.0364653i
\(201\) 7.84693i 0.553480i
\(202\) 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
\(206\) 1.23949i 0.0863590i
\(207\) 6.76305 + 11.7139i 0.470065 + 0.814176i
\(208\) 7.06078 12.2158i 0.489577 0.847012i
\(209\) −0.526475 −0.0364170
\(210\) 0 0
\(211\) 4.11795 7.13251i 0.283492 0.491022i −0.688751 0.724998i \(-0.741840\pi\)
0.972242 + 0.233976i \(0.0751738\pi\)
\(212\) 2.72233 0.186970
\(213\) 3.57088 2.06165i 0.244673 0.141262i
\(214\) 1.36802 + 0.789825i 0.0935157 + 0.0539913i
\(215\) 1.30516i 0.0890110i
\(216\) 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
\(220\) −0.611077 1.05842i −0.0411988 0.0713584i
\(221\) −11.4857 0.00563595i −0.772609 0.000379115i
\(222\) 0.221321 0.383340i 0.0148541 0.0257281i
\(223\) 13.2515 + 7.65073i 0.887383 + 0.512331i 0.873086 0.487567i \(-0.162115\pi\)
0.0142977 + 0.999898i \(0.495449\pi\)
\(224\) 0 0
\(225\) 2.86064 + 4.95477i 0.190709 + 0.330318i
\(226\) −0.516235 0.298048i −0.0343394 0.0198259i
\(227\) 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
\(229\) 23.7481 + 13.7110i 1.56932 + 0.906045i 0.996249 + 0.0865377i \(0.0275803\pi\)
0.573068 + 0.819508i \(0.305753\pi\)
\(230\) −0.516422 0.894470i −0.0340519 0.0589796i
\(231\) 0 0
\(232\) −3.40511 1.96594i −0.223556 0.129070i
\(233\) −3.42666 + 5.93515i −0.224488 + 0.388825i −0.956166 0.292826i \(-0.905404\pi\)
0.731678 + 0.681651i \(0.238738\pi\)
\(234\) −0.999759 0.577866i −0.0653563 0.0377763i
\(235\) 10.7963 + 18.6997i 0.704271 + 1.21983i
\(236\) −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 \(0.253105\pi\)
−0.700177 + 0.713970i \(0.746895\pi\)
\(240\) 3.84679i 0.248309i
\(241\) −13.6807 7.89855i −0.881251 0.508790i −0.0101802 0.999948i \(-0.503241\pi\)
−0.871071 + 0.491158i \(0.836574\pi\)
\(242\) 1.13272 0.653979i 0.0728143 0.0420393i
\(243\) −13.4196 −0.860869
\(244\) 8.95947 15.5183i 0.573571 0.993455i
\(245\) 0 0
\(246\) 0.408405 0.0260390
\(247\) −4.50988 + 2.60083i −0.286957 + 0.165487i
\(248\) −1.12675 1.95158i −0.0715485 0.123926i
\(249\) 0.330381i 0.0209370i
\(250\) −0.726405 1.25817i −0.0459419 0.0795737i
\(251\) 11.2783 + 19.5346i 0.711882 + 1.23302i 0.964150 + 0.265359i \(0.0854903\pi\)
−0.252268 + 0.967658i \(0.581176\pi\)
\(252\) 0 0
\(253\) 1.60512 0.926716i 0.100913 0.0582621i
\(254\) 0.970981i 0.0609247i
\(255\) 2.71188 1.56570i 0.169825 0.0980483i
\(256\) −7.42681 + 12.8636i −0.464176 + 0.803976i
\(257\) 10.2064 + 17.6781i 0.636660 + 1.10273i 0.986161 + 0.165791i \(0.0530179\pi\)
−0.349501 + 0.936936i \(0.613649\pi\)
\(258\) 0.0469247 + 0.0270920i 0.00292140 + 0.00168667i
\(259\) 0 0
\(260\) −10.4633 6.04781i −0.648904 0.375069i
\(261\) 10.9053 18.8886i 0.675023 1.16917i
\(262\) 2.27527i 0.140567i
\(263\) −29.5402 −1.82153 −0.910764 0.412927i \(-0.864506\pi\)
−0.910764 + 0.412927i \(0.864506\pi\)
\(264\) 0.101846 0.00626820
\(265\) 2.31464i 0.142187i
\(266\) 0 0
\(267\) −0.574342 + 0.331596i −0.0351491 + 0.0202934i
\(268\) −23.1719 13.3783i −1.41545 0.817211i
\(269\) −13.9581 + 24.1762i −0.851043 + 1.47405i 0.0292252 + 0.999573i \(0.490696\pi\)
−0.880268 + 0.474477i \(0.842637\pi\)
\(270\) 0.669770 0.0407609
\(271\) 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
\(276\) −5.87695 −0.353751
\(277\) 3.42927 5.93967i 0.206045 0.356880i −0.744420 0.667711i \(-0.767274\pi\)
0.950465 + 0.310831i \(0.100607\pi\)
\(278\) −0.547321 0.315996i −0.0328261 0.0189522i
\(279\) 10.8257 6.25021i 0.648117 0.374190i
\(280\) 0 0
\(281\) 29.0940i 1.73561i −0.496909 0.867803i \(-0.665532\pi\)
0.496909 0.867803i \(-0.334468\pi\)
\(282\) −0.896420 −0.0533810
\(283\) −11.6102 −0.690156 −0.345078 0.938574i \(-0.612147\pi\)
−0.345078 + 0.938574i \(0.612147\pi\)
\(284\) 14.0597i 0.834291i
\(285\) 0.709684 1.22921i 0.0420381 0.0728121i
\(286\) −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
\(291\) −3.99786 + 2.30816i −0.234358 + 0.135307i
\(292\) 4.29035i 0.251074i
\(293\) −15.4054 + 8.89430i −0.899992 + 0.519610i −0.877197 0.480130i \(-0.840590\pi\)
−0.0227942 + 0.999740i \(0.507256\pi\)
\(294\) 0 0
\(295\) 7.90228 + 13.6871i 0.460088 + 0.796896i
\(296\) −1.51484 2.62378i −0.0880483 0.152504i
\(297\) 1.20190i 0.0697412i
\(298\) 0.558054 + 0.966578i 0.0323272 + 0.0559924i
\(299\) 9.17168 15.8678i 0.530412 0.917660i
\(300\) −2.48583 −0.143520
\(301\) 0 0
\(302\) 0.843314 1.46066i 0.0485273 0.0840517i
\(303\) −9.05257 −0.520057
\(304\) 4.89341 2.82521i 0.280657 0.162037i
\(305\) −13.1943 7.61771i −0.755501 0.436189i
\(306\) 1.02024i 0.0583230i
\(307\) 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
\(311\) 0.785363 + 1.36029i 0.0445338 + 0.0771349i 0.887433 0.460937i \(-0.152486\pi\)
−0.842899 + 0.538071i \(0.819153\pi\)
\(312\) 0.872433 0.503129i 0.0493918 0.0284841i
\(313\) −10.3116 + 17.8602i −0.582846 + 1.00952i 0.412294 + 0.911051i \(0.364728\pi\)
−0.995140 + 0.0984686i \(0.968606\pi\)
\(314\) 1.79101 + 1.03404i 0.101073 + 0.0583544i
\(315\) 0 0
\(316\) 6.83792 + 11.8436i 0.384663 + 0.666256i
\(317\) −26.4515 15.2718i −1.48566 0.857747i −0.485795 0.874073i \(-0.661470\pi\)
−0.999867 + 0.0163255i \(0.994803\pi\)
\(318\) 0.0832187 + 0.0480463i 0.00466667 + 0.00269430i
\(319\) −2.58823 1.49432i −0.144913 0.0836657i
\(320\) 11.1907 + 6.46096i 0.625580 + 0.361179i
\(321\) −3.82111 6.61836i −0.213274 0.369401i
\(322\) 0 0
\(323\) −3.98340 2.29982i −0.221642 0.127965i
\(324\) −6.01947 + 10.4260i −0.334415 + 0.579224i
\(325\) 3.87944 6.71177i 0.215192 0.372302i
\(326\) 0.709687 + 1.22921i 0.0393059 + 0.0680799i
\(327\) −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
\(331\) 25.8531i 1.42101i −0.703690 0.710507i \(-0.748466\pi\)
0.703690 0.710507i \(-0.251534\pi\)
\(332\) −0.975612 0.563270i −0.0535437 0.0309135i
\(333\) 14.5545 8.40302i 0.797579 0.460483i
\(334\) 0.519578 0.0284300
\(335\) −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 \(0.698020\pi\)
\(338\) −0.00153556 + 1.56468i −8.35233e−5 + 0.0851073i
\(339\) 1.44194 + 2.49750i 0.0783152 + 0.135646i
\(340\) 10.6776i 0.579072i
\(341\) −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
\(345\) 4.99682i 0.269020i
\(346\) −1.30499 + 0.753435i −0.0701566 + 0.0405049i
\(347\) −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 \(-0.431055\pi\)
−0.738336 + 0.674433i \(0.764388\pi\)
\(350\) 0 0
\(351\) 5.93747 + 10.2957i 0.316919 + 0.549542i
\(352\) 0.260774 0.451674i 0.0138993 0.0240743i
\(353\) 35.6433i 1.89710i 0.316623 + 0.948552i \(0.397451\pi\)
−0.316623 + 0.948552i \(0.602549\pi\)
\(354\) −0.656130 −0.0348729
\(355\) −11.9542 −0.634461
\(356\) 2.26137i 0.119852i
\(357\) 0 0
\(358\) 0.687464 0.396907i 0.0363336 0.0209772i
\(359\) −16.7331 9.66089i −0.883142 0.509882i −0.0114488 0.999934i \(-0.503644\pi\)
−0.871693 + 0.490052i \(0.836978\pi\)
\(360\) 1.07742 1.86615i 0.0567851 0.0983546i
\(361\) 16.9151 0.890270
\(362\) −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
\(367\) −3.72065 −0.194216 −0.0971082 0.995274i \(-0.530959\pi\)
−0.0971082 + 0.995274i \(0.530959\pi\)
\(368\) −9.94604 + 17.2271i −0.518473 + 0.898022i
\(369\) 13.4287 + 7.75306i 0.699070 + 0.403608i
\(370\) −1.11137 + 0.641649i −0.0577773 + 0.0333578i
\(371\) 0 0
\(372\) 5.43130i 0.281600i
\(373\) −3.51276 −0.181884 −0.0909420 0.995856i \(-0.528988\pi\)
−0.0909420 + 0.995856i \(0.528988\pi\)
\(374\) −0.139799 −0.00722884
\(375\) 7.02858i 0.362954i
\(376\) −3.06779 + 5.31356i −0.158209 + 0.274026i
\(377\) −29.5533 0.0145016i −1.52207 0.000746873i
\(378\) 0 0
\(379\) 21.6647 + 12.5081i 1.11284 + 0.642500i 0.939564 0.342373i \(-0.111230\pi\)
0.173279 + 0.984873i \(0.444564\pi\)
\(380\) −2.41990 4.19139i −0.124138 0.215014i
\(381\) −2.34877 + 4.06818i −0.120331 + 0.208419i
\(382\) 0.618333 0.356995i 0.0316367 0.0182655i
\(383\) 22.4654i 1.14793i −0.818881 0.573964i \(-0.805405\pi\)
0.818881 0.573964i \(-0.194595\pi\)
\(384\) −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
\(388\) 15.7409i 0.799121i
\(389\) −6.66822 11.5497i −0.338092 0.585592i 0.645982 0.763353i \(-0.276448\pi\)
−0.984074 + 0.177760i \(0.943115\pi\)
\(390\) −0.213113 0.369541i −0.0107914 0.0187124i
\(391\) 16.1928 0.818906
\(392\) 0 0
\(393\) 5.50379 9.53284i 0.277629 0.480868i
\(394\) 0.696274 0.0350778
\(395\) 10.0699 5.81388i 0.506674 0.292528i
\(396\) 1.66831 + 0.963198i 0.0838356 + 0.0484025i
\(397\) 25.8333i 1.29654i −0.761412 0.648268i \(-0.775494\pi\)
0.761412 0.648268i \(-0.224506\pi\)
\(398\) 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 −0.829096 0.559106i \(-0.811144\pi\)
0.0696524 + 0.997571i \(0.477811\pi\)
\(402\) −0.472228 0.817923i −0.0235526 0.0407943i
\(403\) −14.6646 8.47620i −0.730495 0.422229i
\(404\) −15.4338 + 26.7322i −0.767862 + 1.32998i
\(405\) 8.86464 + 5.11800i 0.440487 + 0.254316i
\(406\) 0 0
\(407\) −1.15143 1.99434i −0.0570745 0.0988559i
\(408\) 0.770587 + 0.444899i 0.0381497 + 0.0220258i
\(409\) −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
\(411\) 9.19074 + 5.30628i 0.453346 + 0.261739i
\(412\) 10.2236 + 17.7077i 0.503679 + 0.872398i
\(413\) 0 0
\(414\) 1.40989 + 0.814000i 0.0692923 + 0.0400059i
\(415\) −0.478915 + 0.829506i −0.0235090 + 0.0407188i
\(416\) 0.00253069 5.15736i 0.000124077 0.252861i
\(417\) 1.52876 + 2.64790i 0.0748639 + 0.129668i
\(418\) −0.0548769 + 0.0316832i −0.00268412 + 0.00154968i
\(419\) 2.30096 3.98538i 0.112409 0.194699i −0.804332 0.594180i \(-0.797477\pi\)
0.916741 + 0.399482i \(0.130810\pi\)
\(420\) 0 0
\(421\) 19.2645i 0.938895i −0.882960 0.469447i \(-0.844453\pi\)
0.882960 0.469447i \(-0.155547\pi\)
\(422\) 0.991273i 0.0482544i
\(423\) −29.4750 17.0174i −1.43312 0.827415i
\(424\) 0.569593 0.328854i 0.0276619 0.0159706i
\(425\) 6.84924 0.332237
\(426\) 0.248140 0.429791i 0.0120224 0.0208234i
\(427\) 0 0
\(428\) −26.0587 −1.25959
\(429\) 0.663139 0.382430i 0.0320166 0.0184639i
\(430\) −0.0785443 0.136043i −0.00378774 0.00656056i
\(431\) 28.3651i 1.36630i 0.730279 + 0.683149i \(0.239390\pi\)
−0.730279 + 0.683149i \(0.760610\pi\)
\(432\) −6.44973 11.1713i −0.310313 0.537477i
\(433\) −6.26014 10.8429i −0.300843 0.521076i 0.675484 0.737375i \(-0.263935\pi\)
−0.976327 + 0.216299i \(0.930601\pi\)
\(434\) 0 0
\(435\) 6.97784 4.02866i 0.334562 0.193159i
\(436\) 20.7405i 0.993288i
\(437\) 6.35636 3.66984i 0.304066 0.175552i
\(438\) −0.0757203 + 0.131151i −0.00361806 + 0.00626666i
\(439\) 15.8637 + 27.4767i 0.757132 + 1.31139i 0.944307 + 0.329064i \(0.106733\pi\)
−0.187176 + 0.982326i \(0.559933\pi\)
\(440\) −0.255711 0.147635i −0.0121906 0.00703822i
\(441\) 0 0
\(442\) −1.19754 + 0.690619i −0.0569613 + 0.0328494i
\(443\) −0.865241 + 1.49864i −0.0411088 + 0.0712026i −0.885848 0.463976i \(-0.846422\pi\)
0.844739 + 0.535179i \(0.179756\pi\)
\(444\) 7.30205i 0.346540i
\(445\) 1.92271 0.0911452
\(446\) 1.84168 0.0872062
\(447\) 5.39965i 0.255394i
\(448\) 0 0
\(449\) −9.14208 + 5.27818i −0.431442 + 0.249093i −0.699961 0.714181i \(-0.746799\pi\)
0.268519 + 0.963274i \(0.413466\pi\)
\(450\) 0.596355 + 0.344306i 0.0281125 + 0.0162307i
\(451\) 1.06237 1.84008i 0.0500252 0.0866462i
\(452\) 9.83349 0.462528
\(453\) −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 −0.330273 0.943885i \(-0.607141\pi\)
0.652292 + 0.757968i \(0.273807\pi\)
\(458\) 3.30050 0.154222
\(459\) −5.25029 + 9.09377i −0.245062 + 0.424461i
\(460\) 14.7556 + 8.51915i 0.687983 + 0.397207i
\(461\) 9.43262 5.44592i 0.439321 0.253642i −0.263989 0.964526i \(-0.585038\pi\)
0.703309 + 0.710884i \(0.251705\pi\)
\(462\) 0 0
\(463\) 35.8227i 1.66482i −0.554158 0.832411i \(-0.686960\pi\)
0.554158 0.832411i \(-0.313040\pi\)
\(464\) 32.0757 1.48908
\(465\) 4.61792 0.214151
\(466\) 0.824866i 0.0382112i
\(467\) 9.94917 17.2325i 0.460393 0.797423i −0.538588 0.842569i \(-0.681042\pi\)
0.998980 + 0.0451460i \(0.0143753\pi\)
\(468\) 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
\(473\) 0.244127 0.140947i 0.0112250 0.00648075i
\(474\) 0.482730i 0.0221725i
\(475\) 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
\(479\) 26.2902i 1.20123i −0.799538 0.600615i \(-0.794922\pi\)
0.799538 0.600615i \(-0.205078\pi\)
\(480\) 0.703043 + 1.21771i 0.0320894 + 0.0555804i
\(481\) −19.7156 11.3957i −0.898954 0.519600i
\(482\) −1.90134 −0.0866035
\(483\) 0 0
\(484\) −10.7883 + 18.6860i −0.490379 + 0.849362i
\(485\) 13.3835 0.607715
\(486\) −1.39879 + 0.807592i −0.0634504 + 0.0366331i
\(487\) −5.52491 3.18981i −0.250358 0.144544i 0.369570 0.929203i \(-0.379505\pi\)
−0.619928 + 0.784659i \(0.712838\pi\)
\(488\) 4.32918i 0.195973i
\(489\) 6.86682i 0.310528i
\(490\) 0 0
\(491\) −1.48384 + 2.57008i −0.0669647 + 0.115986i −0.897564 0.440885i \(-0.854665\pi\)
0.830599 + 0.556871i \(0.187998\pi\)
\(492\) −5.83463 + 3.36862i −0.263045 + 0.151869i
\(493\) −13.0554 22.6125i −0.587984 1.01842i
\(494\) −0.313568 + 0.542501i −0.0141081 + 0.0244083i
\(495\) 0.818951 1.41846i 0.0368091 0.0637552i
\(496\) 15.9207 + 9.19184i 0.714862 + 0.412726i
\(497\) 0 0
\(498\) −0.0198823 0.0344371i −0.000890947 0.00154316i
\(499\) 24.3639 + 14.0665i 1.09068 + 0.629704i 0.933757 0.357906i \(-0.116509\pi\)
0.156923 + 0.987611i \(0.449843\pi\)
\(500\) 20.7554 + 11.9831i 0.928208 + 0.535901i
\(501\) −2.17691 1.25684i −0.0972571 0.0561514i
\(502\) 2.35119 + 1.35746i 0.104939 + 0.0605864i
\(503\) 15.7688 + 27.3124i 0.703097 + 1.21780i 0.967374 + 0.253353i \(0.0815334\pi\)
−0.264277 + 0.964447i \(0.585133\pi\)
\(504\) 0 0
\(505\) 22.7288 + 13.1225i 1.01142 + 0.583943i
\(506\) 0.111539 0.193192i 0.00495853 0.00858843i
\(507\) 3.79133 6.55192i 0.168379 0.290981i
\(508\) 8.00888 + 13.8718i 0.355336 + 0.615461i
\(509\) −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
\(513\) 4.75958i 0.210140i
\(514\) 2.12773 + 1.22845i 0.0938502 + 0.0541844i
\(515\) 15.0558 8.69250i 0.663440 0.383037i
\(516\) −0.893844 −0.0393493
\(517\) −2.33183 + 4.03885i −0.102554 + 0.177628i
\(518\) 0 0
\(519\) 7.29012 0.320001
\(520\) −2.91980 0.00143273i −0.128042 6.28293e-5i
\(521\) −4.39172 7.60669i −0.192405 0.333255i 0.753642 0.657285i \(-0.228295\pi\)
−0.946047 + 0.324030i \(0.894962\pi\)
\(522\) 2.62513i 0.114899i
\(523\) −16.2849 28.2063i −0.712088 1.23337i −0.964072 0.265642i \(-0.914416\pi\)
0.251983 0.967732i \(-0.418917\pi\)
\(524\) −18.7670 32.5053i −0.819838 1.42000i
\(525\) 0 0
\(526\) −3.07912 + 1.77773i −0.134256 + 0.0775127i
\(527\) 14.9649i 0.651882i
\(528\) −0.719535 + 0.415424i −0.0313137 + 0.0180790i
\(529\) −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
\(534\) −0.0399109 + 0.0691277i −0.00172711 + 0.00299145i
\(535\) 22.1561i 0.957894i
\(536\) −6.46435 −0.279218
\(537\) −3.84041 −0.165726
\(538\) 3.36000i 0.144860i
\(539\) 0 0
\(540\) −9.56858 + 5.52442i −0.411766 + 0.237733i
\(541\) 6.01775 + 3.47435i 0.258723 + 0.149374i 0.623752 0.781622i \(-0.285608\pi\)
−0.365029 + 0.930996i \(0.618941\pi\)
\(542\) 1.77224 3.06961i 0.0761243 0.131851i
\(543\) 6.41436 0.275266
\(544\) 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
\(549\) 24.0145 1.02491
\(550\) 0.0471789 0.0817163i 0.00201172 0.00348440i
\(551\) −10.2495 5.91758i −0.436645 0.252097i
\(552\) −1.22963 + 0.709929i −0.0523367 + 0.0302166i
\(553\) 0 0
\(554\) 0.825493i 0.0350718i
\(555\) 6.20850 0.263536
\(556\) 10.4256 0.442145
\(557\) 34.6295i 1.46730i −0.679527 0.733650i \(-0.737815\pi\)
0.679527 0.733650i \(-0.262185\pi\)
\(558\) 0.752275 1.30298i 0.0318463 0.0551595i
\(559\) 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 −0.753555 0.657385i \(-0.771662\pi\)
0.946090 + 0.323905i \(0.104996\pi\)
\(564\) 12.8066 7.39388i 0.539254 0.311339i
\(565\) 8.36084i 0.351743i
\(566\) −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 \(0.708022\pi\)
\(570\) 0.170835i 0.00715549i
\(571\) 5.08954 + 8.81533i 0.212990 + 0.368910i 0.952649 0.304072i \(-0.0983464\pi\)
−0.739659 + 0.672982i \(0.765013\pi\)
\(572\) 0.00128084 2.61025i 5.35545e−5 0.109140i
\(573\) −3.45423 −0.144303
\(574\) 0 0
\(575\) −5.46470 + 9.46514i −0.227894 + 0.394724i
\(576\) −20.3679 −0.848663
\(577\) 16.9018 9.75824i 0.703630 0.406241i −0.105068 0.994465i \(-0.533506\pi\)
0.808698 + 0.588224i \(0.200173\pi\)
\(578\) 0.714246 + 0.412370i 0.0297087 + 0.0171523i
\(579\) 2.44327i 0.101539i
\(580\) 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
\(584\) 0.518270 + 0.897670i 0.0214462 + 0.0371458i
\(585\) 0.00794753 16.1965i 0.000328590 0.669643i
\(586\) −1.07052 + 1.85419i −0.0442226 + 0.0765959i
\(587\) −30.6486 17.6950i −1.26501 0.730351i −0.290967 0.956733i \(-0.593977\pi\)
−0.974039 + 0.226382i \(0.927310\pi\)
\(588\) 0 0
\(589\) −3.39156 5.87436i −0.139747 0.242049i
\(590\) 1.64738 + 0.951117i 0.0678217 + 0.0391569i
\(591\) −2.91723 1.68426i −0.119999 0.0692812i
\(592\) 21.4044 + 12.3579i 0.879716 + 0.507905i
\(593\) 15.6648 + 9.04406i 0.643275 + 0.371395i 0.785875 0.618385i \(-0.212213\pi\)
−0.142600 + 0.989780i \(0.545546\pi\)
\(594\) 0.0723301 + 0.125279i 0.00296774 + 0.00514028i
\(595\) 0 0
\(596\) −15.9451 9.20592i −0.653138 0.377089i
\(597\) −3.48204 + 6.03107i −0.142510 + 0.246835i
\(598\) 0.00108244 2.20593i 4.42642e−5 0.0902072i
\(599\) −4.52996 7.84612i −0.185089 0.320584i 0.758517 0.651653i \(-0.225924\pi\)
−0.943607 + 0.331069i \(0.892591\pi\)
\(600\) −0.520111 + 0.300286i −0.0212334 + 0.0122591i
\(601\) −14.6440 + 25.3642i −0.597343 + 1.03463i 0.395869 + 0.918307i \(0.370444\pi\)
−0.993212 + 0.116321i \(0.962890\pi\)
\(602\) 0 0
\(603\) 35.8586i 1.46028i
\(604\) 27.8234i 1.13212i
\(605\) 15.8876 + 9.17269i 0.645922 + 0.372923i
\(606\) −0.943592 + 0.544783i −0.0383308 + 0.0221303i
\(607\) −39.3650 −1.59777 −0.798887 0.601481i \(-0.794578\pi\)
−0.798887 + 0.601481i \(0.794578\pi\)
\(608\) 1.03268 1.78865i 0.0418807 0.0725394i
\(609\) 0 0
\(610\) −1.83373 −0.0742457
\(611\) −0.0226293 + 46.1170i −0.000915485 + 1.86569i
\(612\) 8.41514 + 14.5755i 0.340162 + 0.589178i
\(613\) 5.53316i 0.223482i −0.993737 0.111741i \(-0.964357\pi\)
0.993737 0.111741i \(-0.0356427\pi\)
\(614\) 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 −0.264373 0.964421i \(-0.585165\pi\)
0.703026 + 0.711164i \(0.251832\pi\)
\(618\) 0.721742i 0.0290327i
\(619\) 19.3950 11.1977i 0.779552 0.450075i −0.0567194 0.998390i \(-0.518064\pi\)
0.836272 + 0.548316i \(0.184731\pi\)
\(620\) 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
\(625\) 4.81330 8.33687i 0.192532 0.333475i
\(626\) 2.48221i 0.0992090i
\(627\) 0.306562 0.0122429
\(628\) −34.1161 −1.36138
\(629\) 20.1194i 0.802213i
\(630\) 0 0
\(631\) 1.68778 0.974439i 0.0671894 0.0387918i −0.466029 0.884769i \(-0.654316\pi\)
0.533218 + 0.845978i \(0.320982\pi\)
\(632\) 2.86140 + 1.65203i 0.113820 + 0.0657142i
\(633\) −2.39785 + 4.15320i −0.0953061 + 0.165075i
\(634\) −3.67621 −0.146001
\(635\) 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
\(640\) 6.38477 0.252380
\(641\) 5.21051 9.02487i 0.205803 0.356461i −0.744585 0.667527i \(-0.767353\pi\)
0.950388 + 0.311066i \(0.100686\pi\)
\(642\) −0.796586 0.459909i −0.0314387 0.0181512i
\(643\) 13.2247 7.63531i 0.521533 0.301107i −0.216029 0.976387i \(-0.569310\pi\)
0.737562 + 0.675280i \(0.235977\pi\)
\(644\) 0 0
\(645\) 0.759983i 0.0299243i
\(646\) −0.553612 −0.0217816
\(647\) −17.5066 −0.688254 −0.344127 0.938923i \(-0.611825\pi\)
−0.344127 + 0.938923i \(0.611825\pi\)
\(648\) 2.90858i 0.114260i
\(649\) −1.70677 + 2.95622i −0.0669966 + 0.116042i
\(650\) 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
\(655\) −27.6374 + 15.9564i −1.07988 + 0.623470i
\(656\) 22.8040i 0.890346i
\(657\) −4.97949 + 2.87491i −0.194268 + 0.112161i
\(658\) 0 0
\(659\) 21.9294 + 37.9828i 0.854247 + 1.47960i 0.877342 + 0.479866i \(0.159315\pi\)
−0.0230945 + 0.999733i \(0.507352\pi\)
\(660\) 0.355825 + 0.616308i 0.0138505 + 0.0239897i
\(661\) 32.9270i 1.28071i 0.768078 + 0.640356i \(0.221213\pi\)
−0.768078 + 0.640356i \(0.778787\pi\)
\(662\) −1.55584 2.69479i −0.0604693 0.104736i
\(663\) 6.68800 + 0.00328177i 0.259741 + 0.000127453i
\(664\) −0.272170 −0.0105622
\(665\) 0 0
\(666\) 1.01139 1.75177i 0.0391904 0.0678798i
\(667\) 41.6651 1.61328
\(668\) −7.42287 + 4.28560i −0.287200 + 0.165815i
\(669\) −7.71622 4.45496i −0.298326 0.172239i
\(670\) 2.73814i 0.105784i
\(671\) 3.29062i 0.127033i
\(672\) 0 0
\(673\) 13.3423 23.1095i 0.514307 0.890806i −0.485555 0.874206i \(-0.661383\pi\)
0.999862 0.0165997i \(-0.00528409\pi\)
\(674\) −2.23015 + 1.28758i −0.0859021 + 0.0495956i
\(675\) −3.54370 6.13787i −0.136397 0.236247i
\(676\) −12.8839 22.3662i −0.495534 0.860239i
\(677\) −14.7664 + 25.5761i −0.567519 + 0.982971i 0.429292 + 0.903166i \(0.358763\pi\)
−0.996810 + 0.0798052i \(0.974570\pi\)
\(678\) 0.300599 + 0.173551i 0.0115444 + 0.00666519i
\(679\) 0 0
\(680\) −1.28984 2.23406i −0.0494630 0.0856725i
\(681\) −3.50710 2.02482i −0.134392 0.0775914i
\(682\) −0.178542 0.103081i −0.00683674 0.00394719i
\(683\) 15.8379 + 9.14400i 0.606019 + 0.349885i 0.771406 0.636343i \(-0.219554\pi\)
−0.165387 + 0.986229i \(0.552887\pi\)
\(684\) 6.60659 + 3.81431i 0.252609 + 0.145844i
\(685\) −15.3838 26.6456i −0.587786 1.01807i
\(686\) 0 0
\(687\) −13.8283 7.98378i −0.527583 0.304600i
\(688\) −1.51272 + 2.62012i −0.0576721 + 0.0998910i
\(689\) 2.47388 4.28003i 0.0942472 0.163056i
\(690\) 0.300709 + 0.520843i 0.0114478 + 0.0198281i
\(691\) 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
\(695\) 8.86430i 0.336242i
\(696\) 1.98277 + 1.14475i 0.0751567 + 0.0433917i
\(697\) 16.0762 9.28160i 0.608930 0.351566i
\(698\) −1.35900 −0.0514390
\(699\) 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 \(0.211419\pi\)
\(702\) 1.23848 + 0.715849i 0.0467435 + 0.0270180i
\(703\) −4.55974 7.89770i −0.171974 0.297867i
\(704\) 2.79094i 0.105188i
\(705\) −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
\(709\) 0.0109463i 0.000411095i 1.00000 0.000205548i \(6.54279e-5\pi\)
−1.00000 0.000205548i \(0.999935\pi\)
\(710\) −1.24604 + 0.719400i −0.0467630 + 0.0269986i
\(711\) −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
\(716\) −6.54757 + 11.3407i −0.244694 + 0.423823i
\(717\) 12.8543i 0.480054i
\(718\) −2.32557 −0.0867894
\(719\) 25.4660 0.949722 0.474861 0.880061i \(-0.342498\pi\)
0.474861 + 0.880061i \(0.342498\pi\)
\(720\) 17.5789i 0.655127i
\(721\) 0 0
\(722\) 1.76314 1.01795i 0.0656174 0.0378842i
\(723\) 7.96616 + 4.59926i 0.296265 + 0.171048i
\(724\) 10.9359 18.9416i 0.406430 0.703957i
\(725\) 17.6235 0.654521
\(726\) −0.659576 + 0.380807i −0.0244792 + 0.0141331i
\(727\) −23.5565 −0.873663 −0.436831 0.899543i \(-0.643899\pi\)
−0.436831 + 0.899543i \(0.643899\pi\)
\(728\) 0 0
\(729\) −10.3760 −0.384297
\(730\) 0.380231 0.219526i 0.0140730 0.00812503i
\(731\) 2.46282 0.0910905
\(732\) −5.21703 + 9.03616i −0.192827 + 0.333986i
\(733\) −5.39750 3.11625i −0.199361 0.115101i 0.396996 0.917820i \(-0.370053\pi\)
−0.596357 + 0.802719i \(0.703386\pi\)
\(734\) −0.387821 + 0.223909i −0.0143147 + 0.00826461i
\(735\) 0 0
\(736\) 7.27100i 0.268013i
\(737\) −4.91357 −0.180994
\(738\) 1.86632 0.0687000
\(739\) 1.29718i 0.0477174i −0.999715 0.0238587i \(-0.992405\pi\)
0.999715 0.0238587i \(-0.00759517\pi\)
\(740\) 10.5849 18.3337i 0.389110 0.673959i
\(741\) 2.62606 1.51444i 0.0964709 0.0556344i
\(742\) 0 0
\(743\) 5.25627 + 3.03471i 0.192834 + 0.111333i 0.593309 0.804975i \(-0.297821\pi\)
−0.400475 + 0.916308i \(0.631155\pi\)
\(744\) 0.656096 + 1.13639i 0.0240536 + 0.0416621i
\(745\) −7.82725 + 13.5572i −0.286768 + 0.496697i
\(746\) −0.366152 + 0.211398i −0.0134058 + 0.00773983i
\(747\) 1.50976i 0.0552393i
\(748\) 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 \(-0.399456\pi\)
\(752\) 50.0531i 1.82525i
\(753\) −6.56728 11.3749i −0.239325 0.414523i
\(754\) −3.08135 + 1.77701i −0.112216 + 0.0647147i
\(755\) 23.6566 0.860952
\(756\) 0 0
\(757\) −5.83991 + 10.1150i −0.212255 + 0.367636i −0.952420 0.304789i \(-0.901414\pi\)
0.740165 + 0.672425i \(0.234747\pi\)
\(758\) 3.01096 0.109363
\(759\) −0.934648 + 0.539619i −0.0339256 + 0.0195869i
\(760\) −1.01263 0.584642i −0.0367320 0.0212072i
\(761\) 39.7688i 1.44162i −0.693133 0.720810i \(-0.743770\pi\)
0.693133 0.720810i \(-0.256230\pi\)
\(762\) 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
\(766\) −1.35197 2.34167i −0.0488485 0.0846081i
\(767\) −0.0165634 + 33.7551i −0.000598070 + 1.21882i
\(768\) 4.32457 7.49038i 0.156050 0.270286i
\(769\) −8.62507 4.97969i −0.311028 0.179572i 0.336358 0.941734i \(-0.390805\pi\)
−0.647386 + 0.762162i \(0.724138\pi\)
\(770\) 0 0
\(771\) −5.94313 10.2938i −0.214036 0.370722i
\(772\) 7.21496 + 4.16556i 0.259672 + 0.149922i
\(773\) −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
\(775\) 8.74740 + 5.05032i 0.314216 + 0.181413i
\(776\) 1.90148 + 3.29346i 0.0682592 + 0.118228i
\(777\) 0 0
\(778\) −1.39012 0.802586i −0.0498382 0.0287741i
\(779\) 4.20705 7.28683i 0.150733 0.261078i
\(780\) 6.09267 + 3.52159i