Properties

Label 637.2.k.g.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.g.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 0.769656 0.638459i \(-0.220428\pi\)
−0.937749 + 0.347313i \(0.887094\pi\)
\(4\) 1.98551 0.992757
\(5\) 1.46199 0.844083i 0.653824 0.377485i −0.136096 0.990696i \(-0.543456\pi\)
0.789920 + 0.613210i \(0.210122\pi\)
\(6\) 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 \(-0.626249\pi\)
−0.386304 + 0.922371i \(0.626249\pi\)
\(18\) 0.277362 + 0.160135i 0.0653748 + 0.0377442i
\(19\) 1.25046 + 0.721954i 0.286875 + 0.165628i 0.636532 0.771250i \(-0.280368\pi\)
−0.349657 + 0.936878i \(0.613702\pi\)
\(20\) 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 0.0879771 0.996122i \(-0.471960\pi\)
−0.818679 + 0.574252i \(0.805293\pi\)
\(32\) 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 0.839310 0.543653i \(-0.182959\pi\)
−0.0511624 + 0.998690i \(0.516293\pi\)
\(42\) 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 \(-0.283984\pi\)
0.988006 0.154416i \(-0.0493495\pi\)
\(48\) −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 \(0.208595\pi\)
−0.792854 + 0.609412i \(0.791405\pi\)
\(60\) −1.69028 0.975885i −0.218215 0.125986i
\(61\) −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
\(65\) −5.26980 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 0.605498 0.795847i \(-0.292974\pi\)
−0.386475 + 0.922300i \(0.626307\pi\)
\(74\) 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 \(-0.990087\pi\)
0.999515 0.0311390i \(-0.00991345\pi\)
\(84\) 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 \(-0.980774\pi\)
0.998176 0.0603634i \(-0.0192260\pi\)
\(90\) 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 −0.806270 0.591548i \(-0.798517\pi\)
0.109161 + 0.994024i \(0.465184\pi\)
\(98\) 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
\(103\) −5.14908 8.91847i −0.507354 0.878763i −0.999964 0.00851245i \(-0.997290\pi\)
0.492610 0.870250i \(-0.336043\pi\)
\(104\) 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 \(0.142620\pi\)
−0.0754716 + 0.997148i \(0.524046\pi\)
\(132\) −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 0.955623 0.294594i \(-0.0951843\pi\)
−0.732937 + 0.680297i \(0.761851\pi\)
\(140\) 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 \(0.407151\pi\)
−0.973230 + 0.229833i \(0.926182\pi\)
\(158\) −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 0.348329 0.937372i \(-0.386749\pi\)
−0.637624 + 0.770348i \(0.720083\pi\)
\(168\) 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 −0.999620 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
\(177\) 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 \(-0.365740\pi\)
0.409395 + 0.912357i \(0.365740\pi\)
\(182\) 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 \(-0.360660\pi\)
0.423903 + 0.905708i \(0.360660\pi\)
\(200\) −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 −0.0142977 0.999898i \(-0.504551\pi\)
−0.873086 + 0.487567i \(0.837885\pi\)
\(224\) 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 \(0.0741339\pi\)
−0.973002 + 0.230799i \(0.925866\pi\)
\(228\) 1.66937i 0.110557i
\(229\) 23.7481 13.7110i 1.56932 0.906045i 0.573068 0.819508i \(-0.305753\pi\)
0.996249 0.0865377i \(-0.0275803\pi\)
\(230\) 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 \(-0.830093\pi\)
0.860890 0.508790i \(-0.169907\pi\)
\(242\) −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 \(-0.914510\pi\)
0.252268 0.967658i \(-0.418824\pi\)
\(252\) 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 \(-0.280315\pi\)
0.636660 + 0.771145i \(0.280315\pi\)
\(258\) −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 \(-0.824029\pi\)
−0.851043 + 0.525096i \(0.824029\pi\)
\(270\) −0.334885 0.580038i −0.0203805 0.0353000i
\(271\) 29.4491i 1.78890i −0.447165 0.894451i \(-0.647566\pi\)
0.447165 0.894451i \(-0.352434\pi\)
\(272\) −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 0.640290 0.768133i \(-0.278814\pi\)
−0.985368 + 0.170441i \(0.945481\pi\)
\(284\) −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 0.0227942 0.999740i \(-0.492744\pi\)
0.877197 + 0.480130i \(0.159410\pi\)
\(294\) 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 \(-0.916573\pi\)
0.965850 0.259102i \(-0.0834265\pi\)
\(308\) 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 −0.887433 0.460937i \(-0.847514\pi\)
0.842899 + 0.538071i \(0.180847\pi\)
\(312\) −0.871939 0.503985i −0.0493638 0.0285325i
\(313\) 10.3116 + 17.8602i 0.582846 + 1.00952i 0.995140 + 0.0984686i \(0.0313944\pi\)
−0.412294 + 0.911051i \(0.635272\pi\)
\(314\) −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 0.738336 0.674433i \(-0.235612\pi\)
−0.214908 + 0.976634i \(0.568945\pi\)
\(350\) 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 \(0.730784\pi\)
−0.979781 + 0.200072i \(0.935882\pi\)
\(354\) 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 0.813378 0.581735i \(-0.197626\pi\)
−0.910487 + 0.413539i \(0.864293\pi\)
\(368\) 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 −0.0876266 0.996153i \(-0.527928\pi\)
−0.906507 + 0.422190i \(0.861262\pi\)
\(384\) 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 −0.180710 0.983536i \(-0.557840\pi\)
−0.942123 + 0.335268i \(0.891173\pi\)
\(398\) 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 \(-0.883054\pi\)
0.933266 0.359186i \(-0.116946\pi\)
\(410\) 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 −0.916741 0.399482i \(-0.869190\pi\)
0.804332 + 0.594180i \(0.202523\pi\)
\(420\) 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 0.976327 0.216299i \(-0.0693986\pi\)
−0.675484 + 0.737375i \(0.736065\pi\)
\(434\) 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 \(-0.226600\pi\)
0.757132 + 0.653262i \(0.226600\pi\)
\(440\) 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 −0.703309 0.710884i \(-0.748295\pi\)
0.263989 + 0.964526i \(0.414962\pi\)
\(462\) 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 0.538588 0.842569i \(-0.318958\pi\)
−0.998980 + 0.0451460i \(0.985625\pi\)
\(468\) −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 0.120379 0.992728i \(-0.461589\pi\)
0.919917 + 0.392113i \(0.128256\pi\)
\(480\) 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 \(-0.918467\pi\)
0.264277 0.964447i \(-0.414867\pi\)
\(504\) 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 \(0.0974139\pi\)
−0.953536 + 0.301280i \(0.902586\pi\)
\(510\) −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 −0.753642 0.657285i \(-0.771705\pi\)
0.946047 + 0.324030i \(0.105038\pi\)
\(522\) −2.27343 + 1.31256i −0.0995053 + 0.0574494i
\(523\) −32.5698 −1.42418 −0.712088 0.702090i \(-0.752251\pi\)
−0.712088 + 0.702090i \(0.752251\pi\)
\(524\) 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 \(-0.438329\pi\)
0.192535 + 0.981290i \(0.438329\pi\)
\(564\) −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 0.808698 0.588224i \(-0.200173\pi\)
−0.105068 + 0.994465i \(0.533506\pi\)
\(578\) 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 0.974039 0.226382i \(-0.0726898\pi\)
0.290967 + 0.956733i \(0.406023\pi\)
\(588\) 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 −0.142600 0.989780i \(-0.545546\pi\)
0.785875 + 0.618385i \(0.212213\pi\)
\(594\) −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 \(-0.629556\pi\)
0.993212 0.116321i \(-0.0371102\pi\)
\(602\) 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 \(0.461244\pi\)
−0.920341 + 0.391116i \(0.872089\pi\)
\(608\) −1.03268 + 1.78865i −0.0418807 + 0.0725394i
\(609\) 0 0
\(610\) −1.83373 −0.0742457
\(611\) −39.9271 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 0.836272 0.548316i \(-0.184731\pi\)
−0.0567194 + 0.998390i \(0.518064\pi\)
\(620\) −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 −0.737562 0.675280i \(-0.764023\pi\)
0.216029 + 0.976387i \(0.430690\pi\)
\(644\) 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
\(649\) 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 −0.938604 0.344997i \(-0.887880\pi\)
−0.170526 + 0.985353i \(0.554547\pi\)
\(662\) −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 \(0.0254298\pi\)
−0.429292 + 0.903166i \(0.641237\pi\)
\(678\) −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 \(-0.936981\pi\)
0.980466 0.196688i \(-0.0630186\pi\)
\(692\) −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 −0.524724 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
\(723\) −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 \(-0.356101\pi\)
0.436831 + 0.899543i \(0.356101\pi\)
\(728\) 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 −0.596357 0.802719i \(-0.703386\pi\)
0.396996 + 0.917820i \(0.370053\pi\)
\(734\) 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 −0.277673 0.960676i \(-0.589563\pi\)
−0.970806 + 0.239866i \(0.922896\pi\)
\(762\) 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 0.647386 0.762162i \(-0.275862\pi\)
−0.336358 + 0.941734i \(0.609195\pi\)
\(770\) 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 \(-0.926348\pi\)
0.973350 0.229324i \(-0.0736517\pi\)
\(774\) 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
\(778\)