Properties

Label 637.2.k.h.459.4
Level $637$
Weight $2$
Character 637.459
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.k (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: \( x^{12} - 5x^{10} - 2x^{9} + 15x^{8} + 2x^{7} - 30x^{6} + 4x^{5} + 60x^{4} - 16x^{3} - 80x^{2} + 64 \) Copy content Toggle raw display
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 459.4
Root \(1.34408 - 0.439820i\) of defining polynomial
Character \(\chi\) \(=\) 637.459
Dual form 637.2.k.h.569.3

$q$-expansion

\(f(q)\) \(=\) \(q+0.120360i q^{2} +(0.291146 + 0.504280i) q^{3} +1.98551 q^{4} +(-1.46199 + 0.844083i) q^{5} +(-0.0606950 + 0.0350423i) q^{6} +0.479696i q^{8} +(1.33047 - 2.30444i) q^{9} +O(q^{10})\) \(q+0.120360i q^{2} +(0.291146 + 0.504280i) q^{3} +1.98551 q^{4} +(-1.46199 + 0.844083i) 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} +(0.578074 + 1.00125i) q^{12} +(1.80124 + 3.12338i) q^{13} +(-0.851308 - 0.491503i) q^{15} +3.91329 q^{16} +3.18555 q^{17} +(0.277362 + 0.160135i) q^{18} +(-1.25046 - 0.721954i) q^{19} +(-2.90281 + 1.67594i) q^{20} +(0.0219427 + 0.0380059i) q^{22} +5.08321 q^{23} +(-0.241901 + 0.139662i) q^{24} +(-1.07505 + 1.86204i) q^{25} +(-0.375930 + 0.216797i) q^{26} +3.29632 q^{27} +(-4.09831 + 7.09848i) q^{29} +(0.0591572 - 0.102463i) q^{30} +(4.06838 + 2.34888i) q^{31} +1.43040i q^{32} +(0.183870 + 0.106157i) q^{33} +0.383412i q^{34} +(2.64166 - 4.57549i) q^{36} -6.31584i q^{37} +(0.0868943 - 0.150505i) q^{38} +(-1.05063 + 1.81769i) 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} +4.49210i q^{45} +0.611815i 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} +(3.57639 + 6.20152i) q^{52} +(-0.685548 + 1.18740i) q^{53} +0.396744i q^{54} +(-0.307768 + 0.533070i) q^{55} -0.840776i q^{57} +(-0.854372 - 0.493272i) q^{58} -9.36197i q^{59} +(-1.69028 - 0.975885i) q^{60} +(4.51242 - 7.81574i) q^{61} +(-0.282711 + 0.489669i) q^{62} +7.65442 q^{64} +(-5.26980 - 3.04597i) q^{65} +(-0.0127771 + 0.0221305i) q^{66} +(11.6705 - 6.73797i) q^{67} +6.32495 q^{68} +(1.47996 + 2.56336i) q^{69} +(-6.13246 + 3.54058i) q^{71} +(1.10543 + 0.638220i) q^{72} +(-1.87133 - 1.08041i) q^{73} +0.760173 q^{74} -1.25198 q^{75} +(-2.48281 - 1.43345i) q^{76} +(-0.218777 - 0.126454i) q^{78} +(3.44391 + 5.96502i) 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} +(0.0805861 - 0.0465264i) q^{86} -4.77282 q^{87} +(0.0874529 + 0.151473i) q^{88} +1.13893i q^{89} -0.540669 q^{90} +10.0928 q^{92} +2.73547i q^{93} +(-0.769734 - 1.33322i) q^{94} +2.43755 q^{95} +(-0.721319 + 0.416454i) q^{96} +(6.86572 - 3.96393i) q^{97} -0.970225i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 8 q^{4} + 6 q^{5} - 18 q^{6} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q - 8 q^{4} + 6 q^{5} - 18 q^{6} - 4 q^{9} + 12 q^{10} - 6 q^{11} + 2 q^{12} + 4 q^{13} + 6 q^{15} + 16 q^{16} + 8 q^{17} + 12 q^{18} - 12 q^{20} + 6 q^{22} + 24 q^{23} - 12 q^{24} + 10 q^{25} + 18 q^{26} + 12 q^{27} + 8 q^{29} + 8 q^{30} - 18 q^{31} + 30 q^{33} - 10 q^{36} - 2 q^{38} + 14 q^{39} - 46 q^{40} + 30 q^{41} + 2 q^{43} - 24 q^{44} - 42 q^{47} - 2 q^{48} - 18 q^{50} - 26 q^{51} - 28 q^{52} + 22 q^{53} - 6 q^{55} + 12 q^{58} - 66 q^{60} + 14 q^{61} - 4 q^{62} - 52 q^{64} - 18 q^{65} + 26 q^{66} + 24 q^{67} + 16 q^{68} + 4 q^{69} - 24 q^{71} - 60 q^{72} - 30 q^{73} - 12 q^{74} - 92 q^{75} - 18 q^{76} - 10 q^{78} + 28 q^{79} + 72 q^{80} + 2 q^{81} + 14 q^{82} - 48 q^{85} + 60 q^{86} + 4 q^{87} - 14 q^{88} + 24 q^{90} + 24 q^{92} + 4 q^{94} + 44 q^{95} - 6 q^{96} + 6 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(197\) \(248\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.120360i 0.0851073i 0.999094 + 0.0425536i \(0.0135493\pi\)
−0.999094 + 0.0425536i \(0.986451\pi\)
\(3\) 0.291146 + 0.504280i 0.168093 + 0.291146i 0.937749 0.347313i \(-0.112906\pi\)
−0.769656 + 0.638459i \(0.779572\pi\)
\(4\) 1.98551 0.992757
\(5\) −1.46199 + 0.844083i −0.653824 + 0.377485i −0.789920 0.613210i \(-0.789878\pi\)
0.136096 + 0.990696i \(0.456544\pi\)
\(6\) −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 −0.451640 0.892200i \(-0.649161\pi\)
0.546848 + 0.837232i \(0.315828\pi\)
\(12\) 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
\(16\) 3.91329 0.978323
\(17\) 3.18555 0.772609 0.386304 0.922371i \(-0.373751\pi\)
0.386304 + 0.922371i \(0.373751\pi\)
\(18\) 0.277362 + 0.160135i 0.0653748 + 0.0377442i
\(19\) −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
\(23\) 5.08321 1.05992 0.529962 0.848022i \(-0.322206\pi\)
0.529962 + 0.848022i \(0.322206\pi\)
\(24\) −0.241901 + 0.139662i −0.0493778 + 0.0285083i
\(25\) −1.07505 + 1.86204i −0.215010 + 0.372408i
\(26\) −0.375930 + 0.216797i −0.0737260 + 0.0425175i
\(27\) 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 \(0.891357\pi\)
\(30\) 0.0591572 0.102463i 0.0108006 0.0187071i
\(31\) 4.06838 + 2.34888i 0.730702 + 0.421871i 0.818679 0.574252i \(-0.194707\pi\)
−0.0879771 + 0.996122i \(0.528040\pi\)
\(32\) 1.43040i 0.252861i
\(33\) 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
\(37\) 6.31584i 1.03832i −0.854678 0.519159i \(-0.826245\pi\)
0.854678 0.519159i \(-0.173755\pi\)
\(38\) 0.0868943 0.150505i 0.0140961 0.0244152i
\(39\) −1.05063 + 1.81769i −0.168236 + 0.291063i
\(40\) −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
\(45\) 4.49210i 0.669643i
\(46\) 0.611815i 0.0902072i
\(47\) −11.0769 + 6.39527i −1.61574 + 0.932846i −0.627731 + 0.778430i \(0.716016\pi\)
−0.988006 + 0.154416i \(0.950650\pi\)
\(48\) 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
\(52\) 3.57639 + 6.20152i 0.495956 + 0.859996i
\(53\) −0.685548 + 1.18740i −0.0941672 + 0.163102i −0.909261 0.416227i \(-0.863352\pi\)
0.815094 + 0.579329i \(0.196685\pi\)
\(54\) 0.396744i 0.0539901i
\(55\) −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
\(59\) 9.36197i 1.21882i −0.792854 0.609412i \(-0.791405\pi\)
0.792854 0.609412i \(-0.208595\pi\)
\(60\) −1.69028 0.975885i −0.218215 0.125986i
\(61\) 4.51242 7.81574i 0.577756 1.00070i −0.417980 0.908456i \(-0.637262\pi\)
0.995736 0.0922469i \(-0.0294049\pi\)
\(62\) −0.282711 + 0.489669i −0.0359043 + 0.0621880i
\(63\) 0 0
\(64\) 7.65442 0.956802
\(65\) −5.26980 3.04597i −0.653638 0.377806i
\(66\) −0.0127771 + 0.0221305i −0.00157275 + 0.00272408i
\(67\) 11.6705 6.73797i 1.42578 0.823174i 0.428995 0.903307i \(-0.358868\pi\)
0.996784 + 0.0801330i \(0.0255345\pi\)
\(68\) 6.32495 0.767013
\(69\) 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 \(0.471370\pi\)
\(72\) 1.10543 + 0.638220i 0.130276 + 0.0752150i
\(73\) −1.87133 1.08041i −0.219023 0.126453i 0.386475 0.922300i \(-0.373693\pi\)
−0.605498 + 0.795847i \(0.707026\pi\)
\(74\) 0.760173 0.0883684
\(75\) −1.25198 −0.144567
\(76\) −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 0.992108 0.125382i \(-0.0400158\pi\)
−0.604639 + 0.796500i \(0.706682\pi\)
\(80\) −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
\(86\) 0.0805861 0.0465264i 0.00868982 0.00501707i
\(87\) −4.77282 −0.511700
\(88\) 0.0874529 + 0.151473i 0.00932251 + 0.0161471i
\(89\) 1.13893i 0.120727i 0.998176 + 0.0603634i \(0.0192260\pi\)
−0.998176 + 0.0603634i \(0.980774\pi\)
\(90\) −0.540669 −0.0569915
\(91\) 0 0
\(92\) 10.0928 1.05225
\(93\) 2.73547i 0.283655i
\(94\) −0.769734 1.33322i −0.0793920 0.137511i
\(95\) 2.43755 0.250088
\(96\) −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
\(100\) −2.13452 + 3.69710i −0.213452 + 0.369710i
\(101\) −7.77322 13.4636i −0.773465 1.33968i −0.935653 0.352920i \(-0.885189\pi\)
0.162189 0.986760i \(-0.448145\pi\)
\(102\) −0.193347 + 0.111629i −0.0191442 + 0.0110529i
\(103\) 5.14908 + 8.91847i 0.507354 + 0.878763i 0.999964 + 0.00851245i \(0.00270963\pi\)
−0.492610 + 0.870250i \(0.663957\pi\)
\(104\) −1.49827 + 0.864049i −0.146918 + 0.0847270i
\(105\) 0 0
\(106\) −0.142916 0.0825124i −0.0138812 0.00801432i
\(107\) −13.1244 −1.26878 −0.634391 0.773012i \(-0.718749\pi\)
−0.634391 + 0.773012i \(0.718749\pi\)
\(108\) 6.54488 0.629782
\(109\) −9.04641 5.22295i −0.866489 0.500268i −0.000309035 1.00000i \(-0.500098\pi\)
−0.866180 + 0.499732i \(0.833432\pi\)
\(110\) −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 0.725724 0.687986i \(-0.241505\pi\)
−0.958675 + 0.284502i \(0.908172\pi\)
\(114\) 0.101196 0.00947784
\(115\) −7.43163 + 4.29065i −0.693003 + 0.400105i
\(116\) −8.13725 + 14.0941i −0.755524 + 1.30861i
\(117\) 9.59414 + 0.00470779i 0.886979 + 0.000435235i
\(118\) 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
\(122\) 0.940702 + 0.543114i 0.0851671 + 0.0491713i
\(123\) 3.39320i 0.305955i
\(124\) 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 −0.629686 0.776850i \(-0.716816\pi\)
0.987615 + 0.156899i \(0.0501496\pi\)
\(128\) 3.78208i 0.334291i
\(129\) 0.225091 0.389870i 0.0198182 0.0343261i
\(130\) 0.366613 0.634273i 0.0321541 0.0556294i
\(131\) −9.45194 16.3712i −0.825820 1.43036i −0.901291 0.433214i \(-0.857380\pi\)
0.0754716 0.997148i \(-0.475954\pi\)
\(132\) 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
\(136\) 1.52809i 0.131033i
\(137\) 18.2255i 1.55711i 0.627577 + 0.778554i \(0.284047\pi\)
−0.627577 + 0.778554i \(0.715953\pi\)
\(138\) −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
\(143\) 1.13820 + 0.657883i 0.0951808 + 0.0550150i
\(144\) 5.20651 9.01794i 0.433876 0.751495i
\(145\) 13.8372i 1.14912i
\(146\) 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 0.133574 0.991039i \(-0.457354\pi\)
−0.791478 + 0.611198i \(0.790688\pi\)
\(150\) 0.150689i 0.0123037i
\(151\) −12.1358 7.00661i −0.987597 0.570189i −0.0830419 0.996546i \(-0.526464\pi\)
−0.904555 + 0.426357i \(0.859797\pi\)
\(152\) 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
\(156\) −2.08605 + 3.60905i −0.167017 + 0.288955i
\(157\) 8.59125 14.8805i 0.685656 1.18759i −0.287574 0.957759i \(-0.592849\pi\)
0.973230 0.229833i \(-0.0738180\pi\)
\(158\) −0.717949 + 0.414508i −0.0571170 + 0.0329765i
\(159\) −0.798378 −0.0633155
\(160\) −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 0.0435169 0.999053i \(-0.486144\pi\)
−0.843447 + 0.537213i \(0.819477\pi\)
\(164\) −10.0201 5.78511i −0.782439 0.451741i
\(165\) −0.358422 −0.0279031
\(166\) −0.0682898 −0.00530031
\(167\) 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
\(171\) −3.32739 + 1.92107i −0.254452 + 0.146908i
\(172\) −0.767522 1.32939i −0.0585230 0.101365i
\(173\) 6.25985 10.8424i 0.475928 0.824331i −0.523692 0.851908i \(-0.675446\pi\)
0.999620 + 0.0275769i \(0.00877910\pi\)
\(174\) 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
\(178\) −0.137082 −0.0102747
\(179\) −3.29767 5.71173i −0.246479 0.426915i 0.716067 0.698031i \(-0.245940\pi\)
−0.962547 + 0.271117i \(0.912607\pi\)
\(180\) 8.91913i 0.664792i
\(181\) −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
\(184\) 2.43840i 0.179761i
\(185\) 5.33109 + 9.23371i 0.391949 + 0.678876i
\(186\) −0.329240 −0.0241411
\(187\) 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
\(191\) −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 −0.625049 0.780586i \(-0.714921\pi\)
0.363482 + 0.931601i \(0.381588\pi\)
\(194\) 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 \(0.600596\pi\)
\(198\) 0.116776 0.00829893
\(199\) −11.9598 −0.847805 −0.423903 0.905708i \(-0.639340\pi\)
−0.423903 + 0.905708i \(0.639340\pi\)
\(200\) −0.893213 0.515697i −0.0631597 0.0364653i
\(201\) 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
\(205\) 9.83748 0.687079
\(206\) −1.07343 + 0.619743i −0.0747891 + 0.0431795i
\(207\) 6.76305 11.7139i 0.470065 0.814176i
\(208\) 7.04879 + 12.2227i 0.488746 + 0.847492i
\(209\) −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 \(0.0751738\pi\)
\(212\) −1.36116 + 2.35761i −0.0934851 + 0.161921i
\(213\) −3.57088 2.06165i −0.244673 0.141262i
\(214\) 1.57965i 0.107983i
\(215\) 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
\(219\) 1.25823i 0.0850234i
\(220\) −0.611077 + 1.05842i −0.0411988 + 0.0713584i
\(221\) 5.73795 + 9.94969i 0.385976 + 0.669288i
\(222\) 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
\(227\) 6.95467i 0.461598i −0.973002 0.230799i \(-0.925866\pi\)
0.973002 0.230799i \(-0.0741339\pi\)
\(228\) 1.66937i 0.110557i
\(229\) −23.7481 + 13.7110i −1.56932 + 0.906045i −0.573068 + 0.819508i \(0.694247\pi\)
−0.996249 + 0.0865377i \(0.972420\pi\)
\(230\) −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 0.731678 0.681651i \(-0.238738\pi\)
−0.956166 + 0.292826i \(0.905404\pi\)
\(234\) −0.000566629 1.15475i −3.70417e−5 0.0754883i
\(235\) 10.7963 18.6997i 0.704271 1.21983i
\(236\) 18.5883i 1.21000i
\(237\) −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 \(0.746895\pi\)
\(240\) −3.33141 1.92339i −0.215042 0.124154i
\(241\) 15.7971i 1.01758i 0.860890 + 0.508790i \(0.169907\pi\)
−0.860890 + 0.508790i \(0.830093\pi\)
\(242\) −1.13272 0.653979i −0.0728143 0.0420393i
\(243\) 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
\(247\) 0.00255459 5.20608i 0.000162545 0.331255i
\(248\) −1.12675 + 1.95158i −0.0715485 + 0.123926i
\(249\) −0.286118 + 0.165190i −0.0181320 + 0.0104685i
\(250\) 1.45281 0.0918838
\(251\) 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
\(254\) 0.840894 + 0.485490i 0.0527624 + 0.0304624i
\(255\) −2.71188 1.56570i −0.169825 0.0980483i
\(256\) 14.8536 0.928352
\(257\) −20.4129 −1.27332 −0.636660 0.771145i \(-0.719685\pi\)
−0.636660 + 0.771145i \(0.719685\pi\)
\(258\) 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
\(262\) 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
\(268\) 23.1719 13.3783i 1.41545 0.817211i
\(269\) 27.9163 1.70209 0.851043 0.525096i \(-0.175971\pi\)
0.851043 + 0.525096i \(0.175971\pi\)
\(270\) −0.334885 0.580038i −0.0203805 0.0353000i
\(271\) 29.4491i 1.78890i 0.447165 + 0.894451i \(0.352434\pi\)
−0.447165 + 0.894451i \(0.647566\pi\)
\(272\) 12.4660 0.755861
\(273\) 0 0
\(274\) −2.19362 −0.132521
\(275\) 0.783965i 0.0472748i
\(276\) 2.93847 + 5.08959i 0.176875 + 0.306357i
\(277\) −6.85854 −0.412090 −0.206045 0.978543i \(-0.566059\pi\)
−0.206045 + 0.978543i \(0.566059\pi\)
\(278\) 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 \(-0.334468\pi\)
\(282\) 0.448210 0.776323i 0.0266905 0.0462293i
\(283\) 5.80511 + 10.0547i 0.345078 + 0.597692i 0.985368 0.170441i \(-0.0545192\pi\)
−0.640290 + 0.768133i \(0.721186\pi\)
\(284\) −12.1761 + 7.02986i −0.722517 + 0.417146i
\(285\) 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
\(289\) −6.85229 −0.403076
\(290\) 1.66545 0.0977985
\(291\) 3.99786 + 2.30816i 0.234358 + 0.135307i
\(292\) −3.71555 2.14517i −0.217436 0.125537i
\(293\) −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
\(296\) 3.02968 0.176097
\(297\) 1.04087 0.600949i 0.0603976 0.0348706i
\(298\) 0.558054 0.966578i 0.0323272 0.0559924i
\(299\) 9.15610 + 15.8768i 0.529511 + 0.918180i
\(300\) −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
\(304\) −4.89341 2.82521i −0.280657 0.162037i
\(305\) 15.2354i 0.872378i
\(306\) 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
\(310\) 0.954525i 0.0542134i
\(311\) 0.785363 1.36029i 0.0445338 0.0771349i −0.842899 0.538071i \(-0.819153\pi\)
0.887433 + 0.460937i \(0.152486\pi\)
\(312\) −0.871939 0.503985i −0.0493638 0.0285325i
\(313\) −10.3116 17.8602i −0.582846 1.00952i −0.995140 0.0984686i \(-0.968606\pi\)
0.412294 0.911051i \(-0.364728\pi\)
\(314\) 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 \(-0.338530\pi\)
0.999867 + 0.0163255i \(0.00519681\pi\)
\(318\) 0.0960927i 0.00538861i
\(319\) 2.98863i 0.167331i
\(320\) −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
\(325\) −7.75229 0.00380400i −0.430019 0.000211008i
\(326\) 0.709687 1.22921i 0.0393059 0.0680799i
\(327\) 6.08256i 0.336366i
\(328\) 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 0.967162 0.254161i \(-0.0817992\pi\)
0.263472 + 0.964667i \(0.415132\pi\)
\(332\) 1.12654i 0.0618269i
\(333\) −14.5545 8.40302i −0.797579 0.460483i
\(334\) −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 \(0.698020\pi\)
\(338\) −1.35428 0.783669i −0.0736633 0.0426260i
\(339\) 1.44194 2.49750i 0.0783152 0.135646i
\(340\) −9.24704 + 5.33878i −0.501491 + 0.289536i
\(341\) 1.71289 0.0927580
\(342\) −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
\(346\) 1.30499 + 0.753435i 0.0701566 + 0.0405049i
\(347\) 2.20883 0.118576 0.0592882 0.998241i \(-0.481117\pi\)
0.0592882 + 0.998241i \(0.481117\pi\)
\(348\) −9.47651 −0.507994
\(349\) −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
\(353\) 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
\(359\) 16.7331 9.66089i 0.883142 0.509882i 0.0114488 0.999934i \(-0.496356\pi\)
0.871693 + 0.490052i \(0.163022\pi\)
\(360\) −2.15484 −0.113570
\(361\) −8.45757 14.6489i −0.445135 0.770997i
\(362\) 1.32585i 0.0696851i
\(363\) −6.32780 −0.332123
\(364\) 0 0
\(365\) 3.64783 0.190936
\(366\) 0.632502i 0.0330614i
\(367\) 1.86032 + 3.22218i 0.0971082 + 0.168196i 0.910487 0.413539i \(-0.135707\pi\)
−0.813378 + 0.581735i \(0.802374\pi\)
\(368\) 19.8921 1.03695
\(369\) −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
\(373\) 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
\(376\) −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 \(0.444564\pi\)
\(380\) 4.83980 0.248276
\(381\) 4.69753 0.240662
\(382\) −0.618333 0.356995i −0.0316367 0.0182655i
\(383\) 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
\(387\) −2.05723 −0.104575
\(388\) 13.6320 7.87043i 0.692059 0.399561i
\(389\) −6.66822 + 11.5497i −0.338092 + 0.585592i −0.984074 0.177760i \(-0.943115\pi\)
0.645982 + 0.763353i \(0.276448\pi\)
\(390\) 0.426589 0.000209325i 0.0216012 1.05996e-5i
\(391\) 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
\(395\) −10.0699 5.81388i −0.506674 0.292528i
\(396\) 1.92640i 0.0968050i
\(397\) 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
\(401\) 17.5605i 0.876930i −0.898748 0.438465i \(-0.855522\pi\)
0.898748 0.438465i \(-0.144478\pi\)
\(402\) −0.472228 + 0.817923i −0.0235526 + 0.0407943i
\(403\) −0.00831138 + 16.9380i −0.000414019 + 0.843742i
\(404\) −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
\(409\) 14.5282i 0.718373i 0.933266 + 0.359186i \(0.116946\pi\)
−0.933266 + 0.359186i \(0.883054\pi\)
\(410\) 1.18404i 0.0584755i
\(411\) −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
\(416\) −4.46767 + 2.57649i −0.219046 + 0.126323i
\(417\) 1.52876 2.64790i 0.0748639 0.129668i
\(418\) 0.0633664i 0.00309935i
\(419\) 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 \(-0.155547\pi\)
\(422\) 0.858468 + 0.495637i 0.0417896 + 0.0241272i
\(423\) 34.0348i 1.65483i
\(424\) −0.569593 0.328854i −0.0276619 0.0159706i
\(425\) −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
\(429\) −0.000375631 0.765510i −1.81357e−5 0.0369592i
\(430\) −0.0785443 + 0.136043i −0.00378774 + 0.00656056i
\(431\) 24.5649 14.1825i 1.18325 0.683149i 0.226485 0.974015i \(-0.427277\pi\)
0.956764 + 0.290865i \(0.0939432\pi\)
\(432\) 12.8995 0.620625
\(433\) −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
\(436\) −17.9618 10.3702i −0.860213 0.496644i
\(437\) −6.35636 3.66984i −0.304066 0.175552i
\(438\) 0.151441 0.00723611
\(439\) −31.7273 −1.51426 −0.757132 0.653262i \(-0.773400\pi\)
−0.757132 + 0.653262i \(0.773400\pi\)
\(440\) −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 0.844739 0.535179i \(-0.179756\pi\)
−0.885848 + 0.463976i \(0.846422\pi\)
\(444\) 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 −0.699961 0.714181i \(-0.746799\pi\)
0.268519 + 0.963274i \(0.413466\pi\)
\(450\) −0.596355 + 0.344306i −0.0281125 + 0.0162307i
\(451\) −2.12475 −0.100050
\(452\) −4.91675 8.51605i −0.231264 0.400561i
\(453\) 8.15978i 0.383380i
\(454\) 0.837063 0.0392853
\(455\) 0 0
\(456\) 0.403317 0.0188870
\(457\) 7.94894i 0.371836i 0.982565 + 0.185918i \(0.0595259\pi\)
−0.982565 + 0.185918i \(0.940474\pi\)
\(458\) −1.65025 2.85832i −0.0771111 0.133560i
\(459\) 10.5006 0.490125
\(460\) −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 \(-0.313040\pi\)
\(464\) −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
\(467\) 9.94917 + 17.2325i 0.460393 + 0.797423i 0.998980 0.0451460i \(-0.0143753\pi\)
−0.538588 + 0.842569i \(0.681042\pi\)
\(468\) 19.0493 + 0.00934738i 0.880554 + 0.000432083i
\(469\) 0 0
\(470\) 2.25069 + 1.29944i 0.103817 + 0.0599386i
\(471\) 10.0052 0.461017
\(472\) 4.49090 0.206710
\(473\) −0.244127 0.140947i −0.0112250 0.00648075i
\(474\) −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
\(478\) −2.65699 −0.121528
\(479\) −22.7680 + 13.1451i −1.04030 + 0.600615i −0.919917 0.392113i \(-0.871744\pi\)
−0.120379 + 0.992728i \(0.538411\pi\)
\(480\) 0.703043 1.21771i 0.0320894 0.0555804i
\(481\) 19.7268 11.3764i 0.899464 0.518717i
\(482\) −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
\(486\) 1.39879 + 0.807592i 0.0634504 + 0.0366331i
\(487\) 6.37962i 0.289088i 0.989498 + 0.144544i \(0.0461716\pi\)
−0.989498 + 0.144544i \(0.953828\pi\)
\(488\) 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 −0.897564 0.440885i \(-0.854665\pi\)
0.830599 + 0.556871i \(0.187998\pi\)
\(492\) 6.73725i 0.303739i
\(493\) −13.0554 + 22.6125i −0.587984 + 1.01842i
\(494\) 0.626603 0.000307471i 0.0281922 1.38338e-5i
\(495\) 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 \(-0.883491\pi\)
−0.156923 + 0.987611i \(0.550157\pi\)
\(500\) 23.9662i 1.07180i
\(501\) 2.51368i 0.112303i
\(502\) −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
\(507\) −7.56979 0.00742891i −0.336186 0.000329930i
\(508\) 8.00888 13.8718i 0.355336 0.615461i
\(509\) 13.5944i 0.602560i −0.953536 0.301280i \(-0.902586\pi\)
0.953536 0.301280i \(-0.0974139\pi\)
\(510\) 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
\(514\) 2.45689i 0.108369i
\(515\) −15.0558 8.69250i −0.663440 0.383037i
\(516\) 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
\(520\) 1.46114 2.52790i 0.0640752 0.110856i
\(521\) −4.39172 + 7.60669i −0.192405 + 0.333255i −0.946047 0.324030i \(-0.894962\pi\)
0.753642 + 0.657285i \(0.228295\pi\)
\(522\) −2.27343 + 1.31256i −0.0995053 + 0.0574494i
\(523\) 32.5698 1.42418 0.712088 0.702090i \(-0.247749\pi\)
0.712088 + 0.702090i \(0.247749\pi\)
\(524\) −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
\(528\) 0.719535 + 0.415424i 0.0313137 + 0.0180790i
\(529\) 2.83905 0.123437
\(530\) 0.278589 0.0121011
\(531\) −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
\(535\) 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
\(541\) −6.01775 + 3.47435i −0.258723 + 0.149374i −0.623752 0.781622i \(-0.714392\pi\)
0.365029 + 0.930996i \(0.381059\pi\)
\(542\) −3.54448 −0.152249
\(543\) −3.20718 5.55500i −0.137633 0.238388i
\(544\) 4.55659i 0.195362i
\(545\) 17.6344 0.755375
\(546\) 0 0
\(547\) 10.9095 0.466457 0.233229 0.972422i \(-0.425071\pi\)
0.233229 + 0.972422i \(0.425071\pi\)
\(548\) 36.1870i 1.54583i
\(549\) −12.0073 20.7972i −0.512457 0.887602i
\(550\) −0.0943579 −0.00402343
\(551\) 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
\(555\) −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 −0.975123 0.221662i \(-0.928852\pi\)
−0.295596 + 0.955313i \(0.595518\pi\)
\(558\) 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
\(562\) 3.50176 0.147713
\(563\) −9.13679 −0.385070 −0.192535 0.981290i \(-0.561671\pi\)
−0.192535 + 0.981290i \(0.561671\pi\)
\(564\) −12.8066 7.39388i −0.539254 0.311339i
\(565\) 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
\(569\) −18.3000 −0.767176 −0.383588 0.923504i \(-0.625312\pi\)
−0.383588 + 0.923504i \(0.625312\pi\)
\(570\) −0.147947 + 0.0854175i −0.00619684 + 0.00357775i
\(571\) 5.08954 8.81533i 0.212990 0.368910i −0.739659 0.672982i \(-0.765013\pi\)
0.952649 + 0.304072i \(0.0983464\pi\)
\(572\) 2.25991 + 1.30624i 0.0944914 + 0.0546165i
\(573\) −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
\(577\) −16.9018 9.75824i −0.703630 0.406241i 0.105068 0.994465i \(-0.466494\pi\)
−0.808698 + 0.588224i \(0.799827\pi\)
\(578\) 0.824740i 0.0343047i
\(579\) −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
\(583\) 0.499926i 0.0207048i
\(584\) 0.518270 0.897670i 0.0214462 0.0371458i
\(585\) −14.0306 + 8.09136i −0.580092 + 0.334537i
\(586\) −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
\(591\) 3.36852i 0.138562i
\(592\) 24.7157i 1.01581i
\(593\) −15.6648 + 9.04406i −0.643275 + 0.371395i −0.785875 0.618385i \(-0.787787\pi\)
0.142600 + 0.989780i \(0.454454\pi\)
\(594\) 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
\(598\) −1.91093 + 1.10203i −0.0781438 + 0.0450653i
\(599\) −4.52996 + 7.84612i −0.185089 + 0.320584i −0.943607 0.331069i \(-0.892591\pi\)
0.758517 + 0.651653i \(0.225924\pi\)
\(600\) 0.600572i 0.0245182i
\(601\) −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
\(604\) −24.0958 13.9117i −0.980444 0.566059i
\(605\) 18.3454i 0.745846i
\(606\) 0.943592 + 0.544783i 0.0383308 + 0.0221303i
\(607\) 19.6825 34.0911i 0.798887 1.38371i −0.121454 0.992597i \(-0.538756\pi\)
0.920341 0.391116i \(-0.127911\pi\)
\(608\) 1.03268 1.78865i 0.0418807 0.0725394i
\(609\) 0 0
\(610\) −1.83373 −0.0742457
\(611\) −39.9271 23.0781i −1.61528 0.933639i
\(612\) 8.41514 14.5755i 0.340162 0.589178i
\(613\) −4.79186 + 2.76658i −0.193541 + 0.111741i −0.593639 0.804731i \(-0.702309\pi\)
0.400098 + 0.916472i \(0.368976\pi\)
\(614\) −1.09283 −0.0441029
\(615\) 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 \(0.251832\pi\)
\(618\) −0.625047 0.360871i −0.0251431 0.0145164i
\(619\) −19.3950 11.1977i −0.779552 0.450075i 0.0567194 0.998390i \(-0.481936\pi\)
−0.836272 + 0.548316i \(0.815269\pi\)
\(620\) −15.7463 −0.632386
\(621\) 16.7559 0.672390
\(622\) 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
\(626\) 2.14965 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 −0.466029 0.884769i \(-0.654316\pi\)
0.533218 + 0.845978i \(0.320982\pi\)
\(632\) −2.86140 + 1.65203i −0.113820 + 0.0657142i
\(633\) 4.79570 0.190612
\(634\) 1.83811 + 3.18369i 0.0730005 + 0.126441i
\(635\) 13.6190i 0.540452i
\(636\) −1.58519 −0.0628569
\(637\) 0 0
\(638\) −0.359712 −0.0142411
\(639\) 18.8425i 0.745397i
\(640\) −3.19238 5.52937i −0.126190 0.218568i
\(641\) −10.4210 −0.411605 −0.205803 0.978594i \(-0.565981\pi\)
−0.205803 + 0.978594i \(0.565981\pi\)
\(642\) 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
\(646\) 0.276806 0.479442i 0.0108908 0.0188634i
\(647\) 8.75328 + 15.1611i 0.344127 + 0.596045i 0.985195 0.171439i \(-0.0548417\pi\)
−0.641068 + 0.767484i \(0.721508\pi\)
\(648\) 2.51891 1.45429i 0.0989520 0.0571300i
\(649\) −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
\(653\) −10.1834 −0.398506 −0.199253 0.979948i \(-0.563852\pi\)
−0.199253 + 0.979948i \(0.563852\pi\)
\(654\) 0.732096 0.0286272
\(655\) 27.6374 + 15.9564i 1.07988 + 0.623470i
\(656\) −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 0.877342 + 0.479866i \(0.159315\pi\)
−0.0230945 + 0.999733i \(0.507352\pi\)
\(660\) −0.711651 −0.0277010
\(661\) 28.5156 16.4635i 1.10913 0.640356i 0.170526 0.985353i \(-0.445453\pi\)
0.938604 + 0.344997i \(0.112120\pi\)
\(662\) −1.55584 + 2.69479i −0.0604693 + 0.104736i
\(663\) −3.34684 + 5.79034i −0.129981 + 0.224878i
\(664\) −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
\(668\) 7.42287 + 4.28560i 0.287200 + 0.165815i
\(669\) 8.90992i 0.344478i
\(670\) −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 −0.485555 0.874206i \(-0.661383\pi\)
0.999862 0.0165997i \(-0.00528409\pi\)
\(674\) 2.57515i 0.0991912i
\(675\) −3.54370 + 6.13787i −0.136397 + 0.236247i
\(676\) −12.9278 + 22.3409i −0.497222 + 0.859265i
\(677\) −14.7664 25.5761i −0.567519 0.982971i −0.996810 0.0798052i \(-0.974570\pi\)
0.429292 0.903166i \(-0.358763\pi\)
\(678\) 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
\(682\) 0.206163i 0.00789438i
\(683\) 18.2880i 0.699771i −0.936793 0.349885i \(-0.886221\pi\)
0.936793 0.349885i \(-0.113779\pi\)
\(684\) −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
\(689\) −4.94355 0.00242577i −0.188334 9.24146e-5i
\(690\) 0.300709 0.520843i 0.0114478 0.0198281i
\(691\) 10.3406i 0.393376i 0.980466 + 0.196688i \(0.0630186\pi\)
−0.980466 + 0.196688i \(0.936981\pi\)
\(692\) 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
\(696\) 2.28950i 0.0867834i
\(697\) −16.0762 9.28160i −0.608930 0.351566i
\(698\) 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 \(0.211419\pi\)
\(702\) −1.23918 + 0.714633i −0.0467700 + 0.0269721i
\(703\) −4.55974 + 7.89770i −0.171974 + 0.297867i
\(704\) 2.41702 1.39547i 0.0910951 0.0525938i
\(705\) 12.5732 0.473533
\(706\) 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 0.499822 0.866128i \(-0.333399\pi\)
−0.500178 + 0.865923i \(0.666732\pi\)
\(710\) 1.24604 + 0.719400i 0.0467630 + 0.0269986i
\(711\) 18.3280 0.687355
\(712\) −0.546342 −0.0204750
\(713\) 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
\(717\) −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 −0.999586 0.0287885i \(-0.990835\pi\)
0.524724 + 0.851272i \(0.324168\pi\)
\(720\) 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
\(724\) −21.8718 −0.812860
\(725\) −8.81176 15.2624i −0.327261 0.566832i
\(726\) 0.761613i 0.0282661i
\(727\) −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
\(730\) 0.439053i 0.0162501i
\(731\) −1.23141 2.13286i −0.0455453 0.0788867i
\(732\) 10.4341 0.385654
\(733\) 5.39750 3.11625i 0.199361 0.115101i −0.396996 0.917820i \(-0.629947\pi\)
0.596357 + 0.802719i \(0.296614\pi\)
\(734\) −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 −0.520520 0.853850i \(-0.674262\pi\)
0.479195 + 0.877708i \(0.340929\pi\)
\(740\) 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 \(0.631155\pi\)
\(744\) −1.31219 −0.0481073
\(745\) 15.6545 0.573537
\(746\) 0.366152 + 0.211398i 0.0134058 + 0.00773983i
\(747\) 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
\(751\) 36.6046 1.33572 0.667860 0.744287i \(-0.267210\pi\)
0.667860 + 0.744287i \(0.267210\pi\)
\(752\) −43.3473 + 25.0266i −1.58071 + 0.912625i
\(753\) −6.56728 + 11.3749i −0.239325 + 0.414523i
\(754\) 0.00174542 3.55703i 6.35643e−5 0.129540i
\(755\) 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 \(0.234747\pi\)
\(758\) −1.50548 + 2.60757i −0.0546815 + 0.0947111i
\(759\) 0.934648 + 0.539619i 0.0339256 + 0.0195869i
\(760\) 1.16928i 0.0424144i
\(761\) 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
\(765\) 14.3098i 0.517372i
\(766\) −1.35197 + 2.34167i −0.0488485 + 0.0846081i
\(767\) 29.2410 16.8632i 1.05583 0.608894i
\(768\) 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
\(773\) 12.7518i 0.458649i 0.973350 + 0.229324i \(0.0736517\pi\)
−0.973350 + 0.229324i \(0.926348\pi\)
\(774\) 0.247608i 0.00890007i
\(775\) −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