Properties

Label 1638.2.bj.f.127.4
Level $1638$
Weight $2$
Character 1638.127
Analytic conductor $13.079$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1638.bj (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(13.0794958511\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: 8.0.195105024.2
Defining polynomial: \( x^{8} - 4x^{7} + 5x^{6} + 4x^{5} - 20x^{4} + 12x^{3} + 45x^{2} - 108x + 81 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 546)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 127.4
Root \(0.560908 - 1.63871i\) of defining polynomial
Character \(\chi\) \(=\) 1638.127
Dual form 1638.2.bj.f.1135.3

$q$-expansion

\(f(q)\) \(=\) \(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +4.39924i q^{5} +(-0.866025 - 0.500000i) q^{7} -1.00000i q^{8} +O(q^{10})\) \(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +4.39924i q^{5} +(-0.866025 - 0.500000i) q^{7} -1.00000i q^{8} +(2.19962 + 3.80986i) q^{10} +(-0.971521 + 0.560908i) q^{11} +(-2.14345 + 2.89924i) q^{13} -1.00000 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-1.57781 + 2.73284i) q^{17} +(-6.99395 - 4.03796i) q^{19} +(3.80986 + 2.19962i) q^{20} +(-0.560908 + 0.971521i) q^{22} +(2.70436 + 4.68409i) q^{23} -14.3533 q^{25} +(-0.406663 + 3.58254i) q^{26} +(-0.866025 + 0.500000i) q^{28} +(-3.37076 - 5.83834i) q^{29} -5.58592i q^{31} +(-0.866025 - 0.500000i) q^{32} +3.15561i q^{34} +(2.19962 - 3.80986i) q^{35} +(6.59886 - 3.80986i) q^{37} -8.07591 q^{38} +4.39924 q^{40} +(1.78138 - 1.02848i) q^{41} +(0.792959 - 1.37344i) q^{43} +1.12182i q^{44} +(4.68409 + 2.70436i) q^{46} +7.58865i q^{47} +(0.500000 + 0.866025i) q^{49} +(-12.4304 + 7.17667i) q^{50} +(1.43909 + 3.30591i) q^{52} -8.44252 q^{53} +(-2.46757 - 4.27396i) q^{55} +(-0.500000 + 0.866025i) q^{56} +(-5.83834 - 3.37076i) q^{58} +(6.30380 + 3.63950i) q^{59} +(-5.20831 + 9.02106i) q^{61} +(-2.79296 - 4.83755i) q^{62} -1.00000 q^{64} +(-12.7545 - 9.42957i) q^{65} +(4.56902 - 2.63792i) q^{67} +(1.57781 + 2.73284i) q^{68} -4.39924i q^{70} +(-7.51422 - 4.33834i) q^{71} +12.7985i q^{73} +(3.80986 - 6.59886i) q^{74} +(-6.99395 + 4.03796i) q^{76} +1.12182 q^{77} -3.52106 q^{79} +(3.80986 - 2.19962i) q^{80} +(1.02848 - 1.78138i) q^{82} +11.1392i q^{83} +(-12.0224 - 6.94115i) q^{85} -1.58592i q^{86} +(0.560908 + 0.971521i) q^{88} +(-9.02707 + 5.21178i) q^{89} +(3.30591 - 1.43909i) q^{91} +5.40872 q^{92} +(3.79432 + 6.57196i) q^{94} +(17.7640 - 30.7681i) q^{95} +(1.06297 + 0.613704i) q^{97} +(0.866025 + 0.500000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 4 q^{4}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 4 q^{4} + 6 q^{10} - 6 q^{11} + 12 q^{13} - 8 q^{14} - 4 q^{16} - 2 q^{17} - 12 q^{19} + 6 q^{20} - 4 q^{22} - 8 q^{23} - 24 q^{25} - 6 q^{26} - 2 q^{29} + 6 q^{35} + 18 q^{37} + 4 q^{38} + 12 q^{40} - 12 q^{41} - 8 q^{43} + 18 q^{46} + 4 q^{49} - 12 q^{50} + 12 q^{52} + 12 q^{53} - 22 q^{55} - 4 q^{56} - 24 q^{58} - 18 q^{59} - 8 q^{61} - 8 q^{62} - 8 q^{64} - 46 q^{65} + 18 q^{67} + 2 q^{68} - 6 q^{71} + 6 q^{74} - 12 q^{76} + 8 q^{77} - 4 q^{79} + 6 q^{80} + 10 q^{82} - 54 q^{85} + 4 q^{88} + 18 q^{89} + 6 q^{91} - 16 q^{92} - 2 q^{94} + 50 q^{95} - 54 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1638\mathbb{Z}\right)^\times\).

\(n\) \(379\) \(703\) \(911\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(1\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.866025 0.500000i 0.612372 0.353553i
\(3\) 0 0
\(4\) 0.500000 0.866025i 0.250000 0.433013i
\(5\) 4.39924i 1.96740i 0.179814 + 0.983701i \(0.442451\pi\)
−0.179814 + 0.983701i \(0.557549\pi\)
\(6\) 0 0
\(7\) −0.866025 0.500000i −0.327327 0.188982i
\(8\) 1.00000i 0.353553i
\(9\) 0 0
\(10\) 2.19962 + 3.80986i 0.695581 + 1.20478i
\(11\) −0.971521 + 0.560908i −0.292925 + 0.169120i −0.639260 0.768991i \(-0.720759\pi\)
0.346335 + 0.938111i \(0.387426\pi\)
\(12\) 0 0
\(13\) −2.14345 + 2.89924i −0.594487 + 0.804105i
\(14\) −1.00000 −0.267261
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −1.57781 + 2.73284i −0.382674 + 0.662811i −0.991444 0.130536i \(-0.958330\pi\)
0.608769 + 0.793347i \(0.291663\pi\)
\(18\) 0 0
\(19\) −6.99395 4.03796i −1.60452 0.926371i −0.990567 0.137029i \(-0.956245\pi\)
−0.613954 0.789342i \(-0.710422\pi\)
\(20\) 3.80986 + 2.19962i 0.851910 + 0.491850i
\(21\) 0 0
\(22\) −0.560908 + 0.971521i −0.119586 + 0.207129i
\(23\) 2.70436 + 4.68409i 0.563898 + 0.976700i 0.997151 + 0.0754280i \(0.0240323\pi\)
−0.433253 + 0.901272i \(0.642634\pi\)
\(24\) 0 0
\(25\) −14.3533 −2.87067
\(26\) −0.406663 + 3.58254i −0.0797531 + 0.702595i
\(27\) 0 0
\(28\) −0.866025 + 0.500000i −0.163663 + 0.0944911i
\(29\) −3.37076 5.83834i −0.625935 1.08415i −0.988359 0.152138i \(-0.951384\pi\)
0.362424 0.932013i \(-0.381949\pi\)
\(30\) 0 0
\(31\) 5.58592i 1.00326i −0.865082 0.501630i \(-0.832734\pi\)
0.865082 0.501630i \(-0.167266\pi\)
\(32\) −0.866025 0.500000i −0.153093 0.0883883i
\(33\) 0 0
\(34\) 3.15561i 0.541183i
\(35\) 2.19962 3.80986i 0.371804 0.643983i
\(36\) 0 0
\(37\) 6.59886 3.80986i 1.08485 0.626337i 0.152647 0.988281i \(-0.451220\pi\)
0.932200 + 0.361944i \(0.117887\pi\)
\(38\) −8.07591 −1.31009
\(39\) 0 0
\(40\) 4.39924 0.695581
\(41\) 1.78138 1.02848i 0.278204 0.160621i −0.354406 0.935092i \(-0.615317\pi\)
0.632610 + 0.774470i \(0.281984\pi\)
\(42\) 0 0
\(43\) 0.792959 1.37344i 0.120925 0.209448i −0.799208 0.601055i \(-0.794747\pi\)
0.920133 + 0.391607i \(0.128081\pi\)
\(44\) 1.12182i 0.169120i
\(45\) 0 0
\(46\) 4.68409 + 2.70436i 0.690631 + 0.398736i
\(47\) 7.58865i 1.10692i 0.832876 + 0.553459i \(0.186692\pi\)
−0.832876 + 0.553459i \(0.813308\pi\)
\(48\) 0 0
\(49\) 0.500000 + 0.866025i 0.0714286 + 0.123718i
\(50\) −12.4304 + 7.17667i −1.75792 + 1.01493i
\(51\) 0 0
\(52\) 1.43909 + 3.30591i 0.199566 + 0.458447i
\(53\) −8.44252 −1.15967 −0.579834 0.814734i \(-0.696883\pi\)
−0.579834 + 0.814734i \(0.696883\pi\)
\(54\) 0 0
\(55\) −2.46757 4.27396i −0.332727 0.576300i
\(56\) −0.500000 + 0.866025i −0.0668153 + 0.115728i
\(57\) 0 0
\(58\) −5.83834 3.37076i −0.766611 0.442603i
\(59\) 6.30380 + 3.63950i 0.820685 + 0.473823i 0.850653 0.525728i \(-0.176207\pi\)
−0.0299675 + 0.999551i \(0.509540\pi\)
\(60\) 0 0
\(61\) −5.20831 + 9.02106i −0.666856 + 1.15503i 0.311923 + 0.950107i \(0.399027\pi\)
−0.978779 + 0.204921i \(0.934306\pi\)
\(62\) −2.79296 4.83755i −0.354706 0.614369i
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) −12.7545 9.42957i −1.58200 1.16959i
\(66\) 0 0
\(67\) 4.56902 2.63792i 0.558195 0.322274i −0.194226 0.980957i \(-0.562219\pi\)
0.752421 + 0.658683i \(0.228886\pi\)
\(68\) 1.57781 + 2.73284i 0.191337 + 0.331405i
\(69\) 0 0
\(70\) 4.39924i 0.525810i
\(71\) −7.51422 4.33834i −0.891773 0.514866i −0.0172513 0.999851i \(-0.505492\pi\)
−0.874522 + 0.484986i \(0.838825\pi\)
\(72\) 0 0
\(73\) 12.7985i 1.49795i 0.662599 + 0.748975i \(0.269454\pi\)
−0.662599 + 0.748975i \(0.730546\pi\)
\(74\) 3.80986 6.59886i 0.442887 0.767102i
\(75\) 0 0
\(76\) −6.99395 + 4.03796i −0.802261 + 0.463185i
\(77\) 1.12182 0.127843
\(78\) 0 0
\(79\) −3.52106 −0.396150 −0.198075 0.980187i \(-0.563469\pi\)
−0.198075 + 0.980187i \(0.563469\pi\)
\(80\) 3.80986 2.19962i 0.425955 0.245925i
\(81\) 0 0
\(82\) 1.02848 1.78138i 0.113576 0.196720i
\(83\) 11.1392i 1.22269i 0.791366 + 0.611343i \(0.209370\pi\)
−0.791366 + 0.611343i \(0.790630\pi\)
\(84\) 0 0
\(85\) −12.0224 6.94115i −1.30402 0.752873i
\(86\) 1.58592i 0.171014i
\(87\) 0 0
\(88\) 0.560908 + 0.971521i 0.0597930 + 0.103565i
\(89\) −9.02707 + 5.21178i −0.956867 + 0.552448i −0.895207 0.445650i \(-0.852973\pi\)
−0.0616598 + 0.998097i \(0.519639\pi\)
\(90\) 0 0
\(91\) 3.30591 1.43909i 0.346553 0.150858i
\(92\) 5.40872 0.563898
\(93\) 0 0
\(94\) 3.79432 + 6.57196i 0.391355 + 0.677846i
\(95\) 17.7640 30.7681i 1.82254 3.15674i
\(96\) 0 0
\(97\) 1.06297 + 0.613704i 0.107928 + 0.0623122i 0.552992 0.833186i \(-0.313486\pi\)
−0.445064 + 0.895499i \(0.646819\pi\)
\(98\) 0.866025 + 0.500000i 0.0874818 + 0.0505076i
\(99\) 0 0
\(100\) −7.17667 + 12.4304i −0.717667 + 1.24304i
\(101\) 5.40714 + 9.36545i 0.538031 + 0.931897i 0.999010 + 0.0444859i \(0.0141650\pi\)
−0.460979 + 0.887411i \(0.652502\pi\)
\(102\) 0 0
\(103\) 17.2910 1.70374 0.851868 0.523757i \(-0.175470\pi\)
0.851868 + 0.523757i \(0.175470\pi\)
\(104\) 2.89924 + 2.14345i 0.284294 + 0.210183i
\(105\) 0 0
\(106\) −7.31143 + 4.22126i −0.710149 + 0.410005i
\(107\) 7.10282 + 12.3024i 0.686655 + 1.18932i 0.972914 + 0.231169i \(0.0742550\pi\)
−0.286259 + 0.958152i \(0.592412\pi\)
\(108\) 0 0
\(109\) 3.43821i 0.329321i −0.986350 0.164660i \(-0.947347\pi\)
0.986350 0.164660i \(-0.0526528\pi\)
\(110\) −4.27396 2.46757i −0.407506 0.235274i
\(111\) 0 0
\(112\) 1.00000i 0.0944911i
\(113\) −3.01295 + 5.21858i −0.283434 + 0.490922i −0.972228 0.234035i \(-0.924807\pi\)
0.688794 + 0.724957i \(0.258140\pi\)
\(114\) 0 0
\(115\) −20.6065 + 11.8971i −1.92156 + 1.10941i
\(116\) −6.74153 −0.625935
\(117\) 0 0
\(118\) 7.27900 0.670087
\(119\) 2.73284 1.57781i 0.250519 0.144637i
\(120\) 0 0
\(121\) −4.87076 + 8.43641i −0.442797 + 0.766946i
\(122\) 10.4166i 0.943077i
\(123\) 0 0
\(124\) −4.83755 2.79296i −0.434425 0.250815i
\(125\) 41.1476i 3.68036i
\(126\) 0 0
\(127\) 4.87818 + 8.44926i 0.432869 + 0.749751i 0.997119 0.0758531i \(-0.0241680\pi\)
−0.564250 + 0.825604i \(0.690835\pi\)
\(128\) −0.866025 + 0.500000i −0.0765466 + 0.0441942i
\(129\) 0 0
\(130\) −15.7605 1.78901i −1.38229 0.156906i
\(131\) −7.62761 −0.666428 −0.333214 0.942851i \(-0.608133\pi\)
−0.333214 + 0.942851i \(0.608133\pi\)
\(132\) 0 0
\(133\) 4.03796 + 6.99395i 0.350135 + 0.606452i
\(134\) 2.63792 4.56902i 0.227882 0.394703i
\(135\) 0 0
\(136\) 2.73284 + 1.57781i 0.234339 + 0.135296i
\(137\) −6.36818 3.67667i −0.544070 0.314119i 0.202657 0.979250i \(-0.435042\pi\)
−0.746727 + 0.665131i \(0.768376\pi\)
\(138\) 0 0
\(139\) 4.29454 7.43835i 0.364258 0.630913i −0.624399 0.781106i \(-0.714656\pi\)
0.988657 + 0.150193i \(0.0479894\pi\)
\(140\) −2.19962 3.80986i −0.185902 0.321992i
\(141\) 0 0
\(142\) −8.67667 −0.728130
\(143\) 0.456201 4.01896i 0.0381494 0.336082i
\(144\) 0 0
\(145\) 25.6843 14.8288i 2.13296 1.23147i
\(146\) 6.39924 + 11.0838i 0.529605 + 0.917303i
\(147\) 0 0
\(148\) 7.61971i 0.626337i
\(149\) 3.01285 + 1.73947i 0.246822 + 0.142503i 0.618308 0.785936i \(-0.287818\pi\)
−0.371486 + 0.928439i \(0.621152\pi\)
\(150\) 0 0
\(151\) 16.2991i 1.32640i 0.748441 + 0.663202i \(0.230803\pi\)
−0.748441 + 0.663202i \(0.769197\pi\)
\(152\) −4.03796 + 6.99395i −0.327522 + 0.567284i
\(153\) 0 0
\(154\) 0.971521 0.560908i 0.0782874 0.0451993i
\(155\) 24.5738 1.97382
\(156\) 0 0
\(157\) −0.684571 −0.0546347 −0.0273174 0.999627i \(-0.508696\pi\)
−0.0273174 + 0.999627i \(0.508696\pi\)
\(158\) −3.04933 + 1.76053i −0.242591 + 0.140060i
\(159\) 0 0
\(160\) 2.19962 3.80986i 0.173895 0.301196i
\(161\) 5.40872i 0.426267i
\(162\) 0 0
\(163\) 12.1690 + 7.02580i 0.953153 + 0.550303i 0.894059 0.447949i \(-0.147846\pi\)
0.0590938 + 0.998252i \(0.481179\pi\)
\(164\) 2.05696i 0.160621i
\(165\) 0 0
\(166\) 5.56960 + 9.64683i 0.432285 + 0.748739i
\(167\) −0.421983 + 0.243632i −0.0326540 + 0.0188528i −0.516238 0.856445i \(-0.672668\pi\)
0.483584 + 0.875298i \(0.339335\pi\)
\(168\) 0 0
\(169\) −3.81122 12.4288i −0.293171 0.956060i
\(170\) −13.8823 −1.06472
\(171\) 0 0
\(172\) −0.792959 1.37344i −0.0604625 0.104724i
\(173\) 1.71910 2.97757i 0.130701 0.226381i −0.793246 0.608901i \(-0.791611\pi\)
0.923947 + 0.382521i \(0.124944\pi\)
\(174\) 0 0
\(175\) 12.4304 + 7.17667i 0.939647 + 0.542505i
\(176\) 0.971521 + 0.560908i 0.0732312 + 0.0422800i
\(177\) 0 0
\(178\) −5.21178 + 9.02707i −0.390639 + 0.676607i
\(179\) 1.08802 + 1.88451i 0.0813225 + 0.140855i 0.903818 0.427917i \(-0.140752\pi\)
−0.822496 + 0.568771i \(0.807419\pi\)
\(180\) 0 0
\(181\) 10.7188 0.796721 0.398361 0.917229i \(-0.369579\pi\)
0.398361 + 0.917229i \(0.369579\pi\)
\(182\) 2.14345 2.89924i 0.158883 0.214906i
\(183\) 0 0
\(184\) 4.68409 2.70436i 0.345316 0.199368i
\(185\) 16.7605 + 29.0300i 1.23226 + 2.13433i
\(186\) 0 0
\(187\) 3.54002i 0.258872i
\(188\) 6.57196 + 3.79432i 0.479310 + 0.276730i
\(189\) 0 0
\(190\) 35.5279i 2.57747i
\(191\) 7.62813 13.2123i 0.551952 0.956009i −0.446181 0.894943i \(-0.647216\pi\)
0.998134 0.0610668i \(-0.0194503\pi\)
\(192\) 0 0
\(193\) −12.2800 + 7.08987i −0.883935 + 0.510340i −0.871954 0.489588i \(-0.837147\pi\)
−0.0119809 + 0.999928i \(0.503814\pi\)
\(194\) 1.22741 0.0881228
\(195\) 0 0
\(196\) 1.00000 0.0714286
\(197\) −10.3662 + 5.98495i −0.738564 + 0.426410i −0.821547 0.570141i \(-0.806889\pi\)
0.0829831 + 0.996551i \(0.473555\pi\)
\(198\) 0 0
\(199\) −2.49684 + 4.32465i −0.176996 + 0.306566i −0.940850 0.338823i \(-0.889971\pi\)
0.763854 + 0.645389i \(0.223305\pi\)
\(200\) 14.3533i 1.01493i
\(201\) 0 0
\(202\) 9.36545 + 5.40714i 0.658951 + 0.380445i
\(203\) 6.74153i 0.473163i
\(204\) 0 0
\(205\) 4.52453 + 7.83671i 0.316007 + 0.547340i
\(206\) 14.9745 8.64551i 1.04332 0.602361i
\(207\) 0 0
\(208\) 3.58254 + 0.406663i 0.248405 + 0.0281970i
\(209\) 9.05969 0.626672
\(210\) 0 0
\(211\) 3.27743 + 5.67667i 0.225627 + 0.390798i 0.956507 0.291708i \(-0.0942235\pi\)
−0.730880 + 0.682506i \(0.760890\pi\)
\(212\) −4.22126 + 7.31143i −0.289917 + 0.502151i
\(213\) 0 0
\(214\) 12.3024 + 7.10282i 0.840977 + 0.485538i
\(215\) 6.04212 + 3.48842i 0.412069 + 0.237908i
\(216\) 0 0
\(217\) −2.79296 + 4.83755i −0.189598 + 0.328394i
\(218\) −1.71910 2.97757i −0.116432 0.201667i
\(219\) 0 0
\(220\) −4.93514 −0.332727
\(221\) −4.54121 10.4322i −0.305475 0.701743i
\(222\) 0 0
\(223\) 6.43757 3.71673i 0.431091 0.248891i −0.268720 0.963218i \(-0.586601\pi\)
0.699811 + 0.714328i \(0.253267\pi\)
\(224\) 0.500000 + 0.866025i 0.0334077 + 0.0578638i
\(225\) 0 0
\(226\) 6.02589i 0.400837i
\(227\) −10.1529 5.86177i −0.673870 0.389059i 0.123671 0.992323i \(-0.460533\pi\)
−0.797542 + 0.603264i \(0.793867\pi\)
\(228\) 0 0
\(229\) 9.70668i 0.641436i −0.947175 0.320718i \(-0.896076\pi\)
0.947175 0.320718i \(-0.103924\pi\)
\(230\) −11.8971 + 20.6065i −0.784474 + 1.35875i
\(231\) 0 0
\(232\) −5.83834 + 3.37076i −0.383305 + 0.221302i
\(233\) 11.8444 0.775952 0.387976 0.921670i \(-0.373174\pi\)
0.387976 + 0.921670i \(0.373174\pi\)
\(234\) 0 0
\(235\) −33.3843 −2.17775
\(236\) 6.30380 3.63950i 0.410343 0.236911i
\(237\) 0 0
\(238\) 1.57781 2.73284i 0.102274 0.177144i
\(239\) 1.50484i 0.0973397i −0.998815 0.0486698i \(-0.984502\pi\)
0.998815 0.0486698i \(-0.0154982\pi\)
\(240\) 0 0
\(241\) −2.56160 1.47894i −0.165007 0.0952669i 0.415222 0.909720i \(-0.363704\pi\)
−0.580229 + 0.814453i \(0.697037\pi\)
\(242\) 9.74153i 0.626209i
\(243\) 0 0
\(244\) 5.20831 + 9.02106i 0.333428 + 0.577514i
\(245\) −3.80986 + 2.19962i −0.243403 + 0.140529i
\(246\) 0 0
\(247\) 26.6982 11.6220i 1.69877 0.739489i
\(248\) −5.58592 −0.354706
\(249\) 0 0
\(250\) −20.5738 35.6349i −1.30120 2.25375i
\(251\) 3.81728 6.61172i 0.240944 0.417328i −0.720039 0.693933i \(-0.755876\pi\)
0.960984 + 0.276606i \(0.0892095\pi\)
\(252\) 0 0
\(253\) −5.25469 3.03380i −0.330359 0.190733i
\(254\) 8.44926 + 4.87818i 0.530154 + 0.306084i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 10.6616 + 18.4665i 0.665054 + 1.15191i 0.979271 + 0.202555i \(0.0649246\pi\)
−0.314217 + 0.949351i \(0.601742\pi\)
\(258\) 0 0
\(259\) −7.61971 −0.473466
\(260\) −14.5435 + 6.33092i −0.901949 + 0.392627i
\(261\) 0 0
\(262\) −6.60571 + 3.81381i −0.408102 + 0.235618i
\(263\) −2.65582 4.60002i −0.163765 0.283649i 0.772451 0.635074i \(-0.219031\pi\)
−0.936216 + 0.351425i \(0.885697\pi\)
\(264\) 0 0
\(265\) 37.1407i 2.28153i
\(266\) 6.99395 + 4.03796i 0.428826 + 0.247583i
\(267\) 0 0
\(268\) 5.27585i 0.322274i
\(269\) −1.01642 + 1.76048i −0.0619720 + 0.107339i −0.895347 0.445370i \(-0.853072\pi\)
0.833375 + 0.552708i \(0.186406\pi\)
\(270\) 0 0
\(271\) 1.22099 0.704938i 0.0741698 0.0428219i −0.462456 0.886642i \(-0.653032\pi\)
0.536626 + 0.843820i \(0.319699\pi\)
\(272\) 3.15561 0.191337
\(273\) 0 0
\(274\) −7.35334 −0.444232
\(275\) 13.9446 8.05090i 0.840889 0.485488i
\(276\) 0 0
\(277\) 11.7848 20.4119i 0.708080 1.22643i −0.257488 0.966281i \(-0.582895\pi\)
0.965568 0.260149i \(-0.0837718\pi\)
\(278\) 8.58907i 0.515138i
\(279\) 0 0
\(280\) −3.80986 2.19962i −0.227682 0.131453i
\(281\) 8.12593i 0.484753i 0.970182 + 0.242376i \(0.0779268\pi\)
−0.970182 + 0.242376i \(0.922073\pi\)
\(282\) 0 0
\(283\) −9.96358 17.2574i −0.592273 1.02585i −0.993926 0.110055i \(-0.964897\pi\)
0.401652 0.915792i \(-0.368436\pi\)
\(284\) −7.51422 + 4.33834i −0.445887 + 0.257433i
\(285\) 0 0
\(286\) −1.61440 3.70862i −0.0954613 0.219295i
\(287\) −2.05696 −0.121418
\(288\) 0 0
\(289\) 3.52106 + 6.09865i 0.207121 + 0.358744i
\(290\) 14.8288 25.6843i 0.870778 1.50823i
\(291\) 0 0
\(292\) 11.0838 + 6.39924i 0.648631 + 0.374487i
\(293\) −17.5078 10.1081i −1.02282 0.590523i −0.107898 0.994162i \(-0.534412\pi\)
−0.914918 + 0.403639i \(0.867745\pi\)
\(294\) 0 0
\(295\) −16.0111 + 27.7320i −0.932200 + 1.61462i
\(296\) −3.80986 6.59886i −0.221443 0.383551i
\(297\) 0 0
\(298\) 3.47894 0.201530
\(299\) −19.3770 2.19953i −1.12060 0.127202i
\(300\) 0 0
\(301\) −1.37344 + 0.792959i −0.0791641 + 0.0457054i
\(302\) 8.14956 + 14.1154i 0.468954 + 0.812253i
\(303\) 0 0
\(304\) 8.07591i 0.463185i
\(305\) −39.6858 22.9126i −2.27240 1.31197i
\(306\) 0 0
\(307\) 26.2764i 1.49967i −0.661624 0.749836i \(-0.730132\pi\)
0.661624 0.749836i \(-0.269868\pi\)
\(308\) 0.560908 0.971521i 0.0319607 0.0553576i
\(309\) 0 0
\(310\) 21.2815 12.2869i 1.20871 0.697849i
\(311\) −7.30017 −0.413954 −0.206977 0.978346i \(-0.566363\pi\)
−0.206977 + 0.978346i \(0.566363\pi\)
\(312\) 0 0
\(313\) 25.4414 1.43803 0.719015 0.694994i \(-0.244593\pi\)
0.719015 + 0.694994i \(0.244593\pi\)
\(314\) −0.592856 + 0.342286i −0.0334568 + 0.0193163i
\(315\) 0 0
\(316\) −1.76053 + 3.04933i −0.0990375 + 0.171538i
\(317\) 20.2153i 1.13540i −0.823234 0.567702i \(-0.807833\pi\)
0.823234 0.567702i \(-0.192167\pi\)
\(318\) 0 0
\(319\) 6.54954 + 3.78138i 0.366704 + 0.211716i
\(320\) 4.39924i 0.245925i
\(321\) 0 0
\(322\) −2.70436 4.68409i −0.150708 0.261034i
\(323\) 22.0702 12.7422i 1.22802 0.708996i
\(324\) 0 0
\(325\) 30.7657 41.6138i 1.70657 2.30832i
\(326\) 14.0516 0.778246
\(327\) 0 0
\(328\) −1.02848 1.78138i −0.0567882 0.0983601i
\(329\) 3.79432 6.57196i 0.209188 0.362324i
\(330\) 0 0
\(331\) −21.0120 12.1313i −1.15492 0.666796i −0.204842 0.978795i \(-0.565668\pi\)
−0.950083 + 0.311999i \(0.899002\pi\)
\(332\) 9.64683 + 5.56960i 0.529438 + 0.305671i
\(333\) 0 0
\(334\) −0.243632 + 0.421983i −0.0133310 + 0.0230899i
\(335\) 11.6049 + 20.1002i 0.634042 + 1.09819i
\(336\) 0 0
\(337\) 8.14035 0.443433 0.221717 0.975111i \(-0.428834\pi\)
0.221717 + 0.975111i \(0.428834\pi\)
\(338\) −9.51501 8.85803i −0.517548 0.481813i
\(339\) 0 0
\(340\) −12.0224 + 6.94115i −0.652008 + 0.376437i
\(341\) 3.13319 + 5.42684i 0.169672 + 0.293880i
\(342\) 0 0
\(343\) 1.00000i 0.0539949i
\(344\) −1.37344 0.792959i −0.0740512 0.0427535i
\(345\) 0 0
\(346\) 3.43821i 0.184839i
\(347\) −6.73894 + 11.6722i −0.361765 + 0.626596i −0.988251 0.152836i \(-0.951159\pi\)
0.626486 + 0.779433i \(0.284493\pi\)
\(348\) 0 0
\(349\) −5.64467 + 3.25895i −0.302152 + 0.174448i −0.643409 0.765522i \(-0.722481\pi\)
0.341257 + 0.939970i \(0.389147\pi\)
\(350\) 14.3533 0.767218
\(351\) 0 0
\(352\) 1.12182 0.0597930
\(353\) −20.7274 + 11.9669i −1.10321 + 0.636936i −0.937061 0.349165i \(-0.886465\pi\)
−0.166145 + 0.986101i \(0.553132\pi\)
\(354\) 0 0
\(355\) 19.0854 33.0569i 1.01295 1.75448i
\(356\) 10.4236i 0.552448i
\(357\) 0 0
\(358\) 1.88451 + 1.08802i 0.0995993 + 0.0575037i
\(359\) 7.32429i 0.386561i 0.981144 + 0.193281i \(0.0619128\pi\)
−0.981144 + 0.193281i \(0.938087\pi\)
\(360\) 0 0
\(361\) 23.1102 + 40.0280i 1.21633 + 2.10674i
\(362\) 9.28274 5.35939i 0.487890 0.281684i
\(363\) 0 0
\(364\) 0.406663 3.58254i 0.0213149 0.187776i
\(365\) −56.3037 −2.94707
\(366\) 0 0
\(367\) −5.11150 8.85339i −0.266818 0.462143i 0.701220 0.712945i \(-0.252639\pi\)
−0.968038 + 0.250802i \(0.919306\pi\)
\(368\) 2.70436 4.68409i 0.140975 0.244175i
\(369\) 0 0
\(370\) 29.0300 + 16.7605i 1.50920 + 0.871336i
\(371\) 7.31143 + 4.22126i 0.379591 + 0.219157i
\(372\) 0 0
\(373\) −0.781422 + 1.35346i −0.0404605 + 0.0700797i −0.885547 0.464551i \(-0.846216\pi\)
0.845086 + 0.534630i \(0.179549\pi\)
\(374\) −1.77001 3.06574i −0.0915249 0.158526i
\(375\) 0 0
\(376\) 7.58865 0.391355
\(377\) 24.1518 + 2.74153i 1.24388 + 0.141196i
\(378\) 0 0
\(379\) −7.26194 + 4.19268i −0.373021 + 0.215364i −0.674777 0.738021i \(-0.735760\pi\)
0.301757 + 0.953385i \(0.402427\pi\)
\(380\) −17.7640 30.7681i −0.911272 1.57837i
\(381\) 0 0
\(382\) 15.2563i 0.780578i
\(383\) −7.89645 4.55902i −0.403490 0.232955i 0.284499 0.958676i \(-0.408173\pi\)
−0.687989 + 0.725722i \(0.741506\pi\)
\(384\) 0 0
\(385\) 4.93514i 0.251518i
\(386\) −7.08987 + 12.2800i −0.360865 + 0.625036i
\(387\) 0 0
\(388\) 1.06297 0.613704i 0.0539639 0.0311561i
\(389\) −37.1923 −1.88572 −0.942862 0.333184i \(-0.891877\pi\)
−0.942862 + 0.333184i \(0.891877\pi\)
\(390\) 0 0
\(391\) −17.0678 −0.863157
\(392\) 0.866025 0.500000i 0.0437409 0.0252538i
\(393\) 0 0
\(394\) −5.98495 + 10.3662i −0.301517 + 0.522243i
\(395\) 15.4900i 0.779386i
\(396\) 0 0
\(397\) −27.4588 15.8533i −1.37812 0.795656i −0.386184 0.922422i \(-0.626207\pi\)
−0.991933 + 0.126765i \(0.959541\pi\)
\(398\) 4.99368i 0.250310i
\(399\) 0 0
\(400\) 7.17667 + 12.4304i 0.358834 + 0.621518i
\(401\) 23.3818 13.4995i 1.16763 0.674132i 0.214509 0.976722i \(-0.431185\pi\)
0.953121 + 0.302590i \(0.0978514\pi\)
\(402\) 0 0
\(403\) 16.1949 + 11.9731i 0.806727 + 0.596425i
\(404\) 10.8143 0.538031
\(405\) 0 0
\(406\) 3.37076 + 5.83834i 0.167288 + 0.289752i
\(407\) −4.27396 + 7.40271i −0.211852 + 0.366939i
\(408\) 0 0
\(409\) 8.94747 + 5.16583i 0.442424 + 0.255434i 0.704625 0.709580i \(-0.251115\pi\)
−0.262201 + 0.965013i \(0.584448\pi\)
\(410\) 7.83671 + 4.52453i 0.387028 + 0.223451i
\(411\) 0 0
\(412\) 8.64551 14.9745i 0.425934 0.737739i
\(413\) −3.63950 6.30380i −0.179088 0.310190i
\(414\) 0 0
\(415\) −49.0040 −2.40551
\(416\) 3.30591 1.43909i 0.162085 0.0705573i
\(417\) 0 0
\(418\) 7.84592 4.52984i 0.383757 0.221562i
\(419\) 12.7635 + 22.1070i 0.623536 + 1.08000i 0.988822 + 0.149101i \(0.0476380\pi\)
−0.365285 + 0.930896i \(0.619029\pi\)
\(420\) 0 0
\(421\) 4.31438i 0.210270i 0.994458 + 0.105135i \(0.0335274\pi\)
−0.994458 + 0.105135i \(0.966473\pi\)
\(422\) 5.67667 + 3.27743i 0.276336 + 0.159543i
\(423\) 0 0
\(424\) 8.44252i 0.410005i
\(425\) 22.6468 39.2254i 1.09853 1.90271i
\(426\) 0 0
\(427\) 9.02106 5.20831i 0.436560 0.252048i
\(428\) 14.2056 0.686655
\(429\) 0 0
\(430\) 6.97684 0.336453
\(431\) 6.37502 3.68062i 0.307074 0.177289i −0.338542 0.940951i \(-0.609934\pi\)
0.645616 + 0.763662i \(0.276601\pi\)
\(432\) 0 0
\(433\) −13.4103 + 23.2273i −0.644458 + 1.11623i 0.339969 + 0.940437i \(0.389584\pi\)
−0.984426 + 0.175797i \(0.943750\pi\)
\(434\) 5.58592i 0.268133i
\(435\) 0 0
\(436\) −2.97757 1.71910i −0.142600 0.0823301i
\(437\) 43.6804i 2.08952i
\(438\) 0 0
\(439\) 17.4346 + 30.1976i 0.832109 + 1.44125i 0.896363 + 0.443321i \(0.146200\pi\)
−0.0642541 + 0.997934i \(0.520467\pi\)
\(440\) −4.27396 + 2.46757i −0.203753 + 0.117637i
\(441\) 0 0
\(442\) −9.14888 6.76390i −0.435168 0.321726i
\(443\) 8.59832 0.408518 0.204259 0.978917i \(-0.434521\pi\)
0.204259 + 0.978917i \(0.434521\pi\)
\(444\) 0 0
\(445\) −22.9279 39.7123i −1.08689 1.88254i
\(446\) 3.71673 6.43757i 0.175992 0.304828i
\(447\) 0 0
\(448\) 0.866025 + 0.500000i 0.0409159 + 0.0236228i
\(449\) 27.1348 + 15.6663i 1.28057 + 0.739337i 0.976952 0.213458i \(-0.0684726\pi\)
0.303616 + 0.952794i \(0.401806\pi\)
\(450\) 0 0
\(451\) −1.15376 + 1.99838i −0.0543286 + 0.0940999i
\(452\) 3.01295 + 5.21858i 0.141717 + 0.245461i
\(453\) 0 0
\(454\) −11.7235 −0.550213
\(455\) 6.33092 + 14.5435i 0.296798 + 0.681809i
\(456\) 0 0
\(457\) 8.32180 4.80459i 0.389277 0.224749i −0.292570 0.956244i \(-0.594510\pi\)
0.681847 + 0.731495i \(0.261177\pi\)
\(458\) −4.85334 8.40623i −0.226782 0.392797i
\(459\) 0 0
\(460\) 23.7943i 1.10941i
\(461\) 11.5452 + 6.66562i 0.537713 + 0.310449i 0.744151 0.668011i \(-0.232854\pi\)
−0.206439 + 0.978460i \(0.566187\pi\)
\(462\) 0 0
\(463\) 5.55011i 0.257935i 0.991649 + 0.128968i \(0.0411664\pi\)
−0.991649 + 0.128968i \(0.958834\pi\)
\(464\) −3.37076 + 5.83834i −0.156484 + 0.271038i
\(465\) 0 0
\(466\) 10.2575 5.92219i 0.475171 0.274340i
\(467\) 16.9272 0.783299 0.391650 0.920114i \(-0.371905\pi\)
0.391650 + 0.920114i \(0.371905\pi\)
\(468\) 0 0
\(469\) −5.27585 −0.243616
\(470\) −28.9117 + 16.6922i −1.33360 + 0.769952i
\(471\) 0 0
\(472\) 3.63950 6.30380i 0.167522 0.290156i
\(473\) 1.77911i 0.0818035i
\(474\) 0 0
\(475\) 100.386 + 57.9582i 4.60605 + 2.65930i
\(476\) 3.15561i 0.144637i
\(477\) 0 0
\(478\) −0.752418 1.30323i −0.0344148 0.0596081i
\(479\) −16.7981 + 9.69840i −0.767526 + 0.443131i −0.831991 0.554789i \(-0.812799\pi\)
0.0644654 + 0.997920i \(0.479466\pi\)
\(480\) 0 0
\(481\) −3.09865 + 27.2980i −0.141286 + 1.24468i
\(482\) −2.95788 −0.134728
\(483\) 0 0
\(484\) 4.87076 + 8.43641i 0.221398 + 0.383473i
\(485\) −2.69983 + 4.67625i −0.122593 + 0.212337i
\(486\) 0 0
\(487\) −13.3417 7.70283i −0.604570 0.349049i 0.166267 0.986081i \(-0.446829\pi\)
−0.770837 + 0.637032i \(0.780162\pi\)
\(488\) 9.02106 + 5.20831i 0.408364 + 0.235769i
\(489\) 0 0
\(490\) −2.19962 + 3.80986i −0.0993688 + 0.172112i
\(491\) 4.87818 + 8.44926i 0.220149 + 0.381310i 0.954853 0.297078i \(-0.0960122\pi\)
−0.734704 + 0.678388i \(0.762679\pi\)
\(492\) 0 0
\(493\) 21.2736 0.958117
\(494\) 17.3103 23.4140i 0.778829 1.05345i
\(495\) 0 0
\(496\) −4.83755 + 2.79296i −0.217212 + 0.125408i
\(497\) 4.33834 + 7.51422i 0.194601 + 0.337059i
\(498\) 0 0
\(499\) 5.52642i 0.247397i 0.992320 + 0.123698i \(0.0394755\pi\)
−0.992320 + 0.123698i \(0.960525\pi\)
\(500\) −35.6349 20.5738i −1.59364 0.920089i
\(501\) 0 0
\(502\) 7.63455i 0.340747i
\(503\) 2.06759 3.58117i 0.0921893 0.159677i −0.816243 0.577709i \(-0.803947\pi\)
0.908432 + 0.418032i \(0.137280\pi\)
\(504\) 0 0
\(505\) −41.2009 + 23.7873i −1.83342 + 1.05852i
\(506\) −6.06759 −0.269737
\(507\) 0 0
\(508\) 9.75637 0.432869
\(509\) 7.70067 4.44599i 0.341326 0.197065i −0.319532 0.947575i \(-0.603526\pi\)
0.660858 + 0.750511i \(0.270192\pi\)
\(510\) 0 0
\(511\) 6.39924 11.0838i 0.283086 0.490319i
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) 18.4665 + 10.6616i 0.814521 + 0.470264i
\(515\) 76.0674i 3.35193i
\(516\) 0 0
\(517\) −4.25653 7.37253i −0.187202 0.324244i
\(518\) −6.59886 + 3.80986i −0.289937 + 0.167395i
\(519\) 0 0
\(520\) −9.42957 + 12.7545i −0.413514 + 0.559321i
\(521\) −8.17974 −0.358361 −0.179180 0.983816i \(-0.557345\pi\)
−0.179180 + 0.983816i \(0.557345\pi\)
\(522\) 0 0
\(523\) −3.12787 5.41763i −0.136772 0.236896i 0.789501 0.613749i \(-0.210339\pi\)
−0.926273 + 0.376853i \(0.877006\pi\)
\(524\) −3.81381 + 6.60571i −0.166607 + 0.288572i
\(525\) 0 0
\(526\) −4.60002 2.65582i −0.200570 0.115799i
\(527\) 15.2654 + 8.81349i 0.664972 + 0.383922i
\(528\) 0 0
\(529\) −3.12713 + 5.41635i −0.135962 + 0.235494i
\(530\) −18.5703 32.1648i −0.806644 1.39715i
\(531\) 0 0
\(532\) 8.07591 0.350135
\(533\) −0.836488 + 7.36914i −0.0362323 + 0.319193i
\(534\) 0 0
\(535\) −54.1214 + 31.2470i −2.33987 + 1.35093i
\(536\) −2.63792 4.56902i −0.113941 0.197352i
\(537\) 0 0
\(538\) 2.03283i 0.0876416i
\(539\) −0.971521 0.560908i −0.0418464 0.0241600i
\(540\) 0 0
\(541\) 35.8526i 1.54142i −0.637183 0.770712i \(-0.719901\pi\)
0.637183 0.770712i \(-0.280099\pi\)
\(542\) 0.704938 1.22099i 0.0302797 0.0524459i
\(543\) 0 0
\(544\) 2.73284 1.57781i 0.117170 0.0676479i
\(545\) 15.1255 0.647906
\(546\) 0 0
\(547\) 16.7073 0.714353 0.357177 0.934037i \(-0.383739\pi\)
0.357177 + 0.934037i \(0.383739\pi\)
\(548\) −6.36818 + 3.67667i −0.272035 + 0.157060i
\(549\) 0 0
\(550\) 8.05090 13.9446i 0.343292 0.594599i
\(551\) 54.4440i 2.31939i
\(552\) 0 0
\(553\) 3.04933 + 1.76053i 0.129671 + 0.0748653i
\(554\) 23.5696i 1.00138i
\(555\) 0 0
\(556\) −4.29454 7.43835i −0.182129 0.315456i
\(557\) 12.1384 7.00811i 0.514321 0.296943i −0.220287 0.975435i \(-0.570699\pi\)
0.734608 + 0.678492i \(0.237366\pi\)
\(558\) 0 0
\(559\) 2.28228 + 5.24289i 0.0965302 + 0.221751i
\(560\) −4.39924 −0.185902
\(561\) 0 0
\(562\) 4.06297 + 7.03726i 0.171386 + 0.296849i
\(563\) −13.4476 + 23.2919i −0.566747 + 0.981635i 0.430138 + 0.902763i \(0.358465\pi\)
−0.996885 + 0.0788716i \(0.974868\pi\)
\(564\) 0 0
\(565\) −22.9578 13.2547i −0.965842 0.557629i
\(566\) −17.2574 9.96358i −0.725383 0.418800i
\(567\) 0 0
\(568\) −4.33834 + 7.51422i −0.182033 + 0.315290i
\(569\) −3.92493 6.79817i −0.164541 0.284994i 0.771951 0.635682i \(-0.219281\pi\)
−0.936492 + 0.350688i \(0.885948\pi\)
\(570\) 0 0
\(571\) 7.24502 0.303195 0.151597 0.988442i \(-0.451558\pi\)
0.151597 + 0.988442i \(0.451558\pi\)
\(572\) −3.25242 2.40456i −0.135990 0.100540i
\(573\) 0 0
\(574\) −1.78138 + 1.02848i −0.0743533 + 0.0429279i
\(575\) −38.8166 67.2323i −1.61876 2.80378i
\(576\) 0 0
\(577\) 31.9688i 1.33088i −0.746451 0.665440i \(-0.768244\pi\)
0.746451 0.665440i \(-0.231756\pi\)
\(578\) 6.09865 + 3.52106i 0.253671 + 0.146457i
\(579\) 0 0
\(580\) 29.6576i 1.23147i
\(581\) 5.56960 9.64683i 0.231066 0.400218i
\(582\) 0 0
\(583\) 8.20208 4.73548i 0.339696 0.196123i
\(584\) 12.7985 0.529605
\(585\) 0 0
\(586\) −20.2163 −0.835126
\(587\) 3.59302 2.07443i 0.148300 0.0856210i −0.424014 0.905656i \(-0.639379\pi\)
0.572314 + 0.820035i \(0.306046\pi\)
\(588\) 0 0
\(589\) −22.5557 + 39.0676i −0.929391 + 1.60975i
\(590\) 32.0221i 1.31833i
\(591\) 0 0
\(592\) −6.59886 3.80986i −0.271212 0.156584i
\(593\) 21.0163i 0.863037i −0.902104 0.431519i \(-0.857978\pi\)
0.902104 0.431519i \(-0.142022\pi\)
\(594\) 0 0
\(595\) 6.94115 + 12.0224i 0.284559 + 0.492871i
\(596\) 3.01285 1.73947i 0.123411 0.0712515i
\(597\) 0 0
\(598\) −17.8807 + 7.78365i −0.731197 + 0.318297i
\(599\) 35.0575 1.43241 0.716205 0.697890i \(-0.245878\pi\)
0.716205 + 0.697890i \(0.245878\pi\)
\(600\) 0 0
\(601\) 15.7586 + 27.2947i 0.642806 + 1.11337i 0.984803 + 0.173672i \(0.0555634\pi\)
−0.341997 + 0.939701i \(0.611103\pi\)
\(602\) −0.792959 + 1.37344i −0.0323186 + 0.0559774i
\(603\) 0 0
\(604\) 14.1154 + 8.14956i 0.574349 + 0.331601i
\(605\) −37.1138 21.4277i −1.50889 0.871159i
\(606\) 0 0
\(607\) −16.9445 + 29.3488i −0.687757 + 1.19123i 0.284805 + 0.958586i \(0.408071\pi\)
−0.972562 + 0.232645i \(0.925262\pi\)
\(608\) 4.03796 + 6.99395i 0.163761 + 0.283642i
\(609\) 0 0
\(610\) −45.8253 −1.85541
\(611\) −22.0013 16.2659i −0.890079 0.658048i
\(612\) 0 0
\(613\) −7.08979 + 4.09329i −0.286354 + 0.165327i −0.636296 0.771445i \(-0.719534\pi\)
0.349942 + 0.936771i \(0.386201\pi\)
\(614\) −13.1382 22.7560i −0.530214 0.918358i
\(615\) 0 0
\(616\) 1.12182i 0.0451993i
\(617\) 31.4716 + 18.1701i 1.26700 + 0.731502i 0.974419 0.224739i \(-0.0721529\pi\)
0.292580 + 0.956241i \(0.405486\pi\)
\(618\) 0 0
\(619\) 38.2625i 1.53790i −0.639309 0.768950i \(-0.720780\pi\)
0.639309 0.768950i \(-0.279220\pi\)
\(620\) 12.2869 21.2815i 0.493454 0.854687i
\(621\) 0 0
\(622\) −6.32213 + 3.65008i −0.253494 + 0.146355i
\(623\) 10.4236 0.417611
\(624\) 0 0
\(625\) 109.252 4.37007
\(626\) 22.0329 12.7207i 0.880610 0.508421i
\(627\) 0 0
\(628\) −0.342286 + 0.592856i −0.0136587 + 0.0236575i
\(629\) 24.0449i 0.958731i
\(630\) 0 0
\(631\) −8.77412 5.06574i −0.349292 0.201664i 0.315081 0.949065i \(-0.397968\pi\)
−0.664374 + 0.747401i \(0.731302\pi\)
\(632\) 3.52106i 0.140060i
\(633\) 0 0
\(634\) −10.1077 17.5070i −0.401426 0.695290i
\(635\) −37.1704 + 21.4603i −1.47506 + 0.851627i
\(636\) 0 0
\(637\) −3.58254 0.406663i −0.141946 0.0161126i
\(638\) 7.56276 0.299412
\(639\) 0 0
\(640\) −2.19962 3.80986i −0.0869477 0.150598i
\(641\) −13.4520 + 23.2995i −0.531322 + 0.920276i 0.468010 + 0.883723i \(0.344971\pi\)
−0.999332 + 0.0365532i \(0.988362\pi\)
\(642\) 0 0
\(643\) −28.9459 16.7119i −1.14151 0.659053i −0.194708 0.980861i \(-0.562376\pi\)
−0.946805 + 0.321808i \(0.895709\pi\)
\(644\) −4.68409 2.70436i −0.184579 0.106567i
\(645\) 0 0
\(646\) 12.7422 22.0702i 0.501336 0.868339i
\(647\) 10.8789 + 18.8428i 0.427693 + 0.740786i 0.996668 0.0815693i \(-0.0259932\pi\)
−0.568975 + 0.822355i \(0.692660\pi\)
\(648\) 0 0
\(649\) −8.16570 −0.320532
\(650\) 5.83697 51.4215i 0.228945 2.01692i
\(651\) 0 0
\(652\) 12.1690 7.02580i 0.476576 0.275151i
\(653\) 3.21872 + 5.57498i 0.125958 + 0.218166i 0.922107 0.386935i \(-0.126466\pi\)
−0.796149 + 0.605101i \(0.793133\pi\)
\(654\) 0 0
\(655\) 33.5557i 1.31113i
\(656\) −1.78138 1.02848i −0.0695511 0.0401554i
\(657\) 0 0
\(658\) 7.58865i 0.295836i
\(659\) 4.51690 7.82350i 0.175953 0.304760i −0.764537 0.644579i \(-0.777033\pi\)
0.940491 + 0.339819i \(0.110366\pi\)
\(660\) 0 0
\(661\) −8.45556 + 4.88182i −0.328883 + 0.189881i −0.655345 0.755330i \(-0.727477\pi\)
0.326462 + 0.945210i \(0.394143\pi\)
\(662\) −24.2626 −0.942992
\(663\) 0 0
\(664\) 11.1392 0.432285
\(665\) −30.7681 + 17.7640i −1.19313 + 0.688857i
\(666\) 0 0
\(667\) 18.2315 31.5779i 0.705927 1.22270i
\(668\) 0.487264i 0.0188528i
\(669\) 0 0
\(670\) 20.1002 + 11.6049i 0.776540 + 0.448335i
\(671\) 11.6855i 0.451115i
\(672\) 0 0
\(673\) −20.3902 35.3169i −0.785985 1.36137i −0.928409 0.371559i \(-0.878823\pi\)
0.142425 0.989806i \(-0.454510\pi\)
\(674\) 7.04975 4.07017i 0.271546 0.156777i
\(675\) 0 0
\(676\) −12.6693 2.91377i −0.487279 0.112068i
\(677\) −28.6313 −1.10039 −0.550195 0.835036i \(-0.685447\pi\)
−0.550195 + 0.835036i \(0.685447\pi\)
\(678\) 0 0
\(679\) −0.613704 1.06297i −0.0235518 0.0407929i
\(680\) −6.94115 + 12.0224i −0.266181 + 0.461039i
\(681\) 0 0
\(682\) 5.42684 + 3.13319i 0.207804 + 0.119976i
\(683\) −34.7160 20.0433i −1.32837 0.766935i −0.343322 0.939218i \(-0.611552\pi\)
−0.985047 + 0.172283i \(0.944886\pi\)
\(684\) 0 0
\(685\) 16.1746 28.0152i 0.617998 1.07040i
\(686\) −0.500000 0.866025i −0.0190901 0.0330650i
\(687\) 0 0
\(688\) −1.58592 −0.0604625
\(689\) 18.0961 24.4769i 0.689408 0.932496i
\(690\) 0 0
\(691\) −24.3518 + 14.0595i −0.926385 + 0.534848i −0.885666 0.464322i \(-0.846298\pi\)
−0.0407184 + 0.999171i \(0.512965\pi\)
\(692\) −1.71910 2.97757i −0.0653505 0.113190i
\(693\) 0 0
\(694\) 13.4779i 0.511614i
\(695\) 32.7231 + 18.8927i 1.24126 + 0.716641i
\(696\) 0 0
\(697\) 6.49096i 0.245863i
\(698\) −3.25895 + 5.64467i −0.123353 + 0.213654i
\(699\) 0 0
\(700\) 12.4304 7.17667i 0.469823 0.271253i
\(701\) 3.59224 0.135677 0.0678385 0.997696i \(-0.478390\pi\)
0.0678385 + 0.997696i \(0.478390\pi\)
\(702\) 0 0
\(703\) −61.5361 −2.32088
\(704\) 0.971521 0.560908i 0.0366156 0.0211400i
\(705\) 0 0
\(706\) −11.9669 + 20.7274i −0.450382 + 0.780085i
\(707\) 10.8143i 0.406713i
\(708\) 0 0
\(709\) 7.28564 + 4.20637i 0.273618 + 0.157973i 0.630531 0.776164i \(-0.282837\pi\)
−0.356913 + 0.934138i \(0.616171\pi\)
\(710\) 38.1708i 1.43252i
\(711\) 0 0
\(712\) 5.21178 + 9.02707i 0.195320 + 0.338304i
\(713\) 26.1649 15.1063i 0.979885 0.565737i
\(714\) 0 0
\(715\) 17.6804 + 2.00694i 0.661208 + 0.0750552i
\(716\) 2.17604 0.0813225
\(717\) 0 0
\(718\) 3.66215 + 6.34302i 0.136670 + 0.236720i
\(719\) 24.1674 41.8591i 0.901290 1.56108i 0.0754696 0.997148i \(-0.475954\pi\)
0.825821 0.563933i \(-0.190712\pi\)
\(720\) 0 0
\(721\) −14.9745 8.64551i −0.557678 0.321976i
\(722\) 40.0280 + 23.1102i 1.48969 + 0.860072i
\(723\) 0 0
\(724\) 5.35939 9.28274i 0.199180 0.344990i
\(725\) 48.3817 + 83.7996i 1.79685 + 3.11224i
\(726\) 0 0
\(727\) 46.3297 1.71827 0.859137 0.511745i \(-0.171001\pi\)
0.859137 + 0.511745i \(0.171001\pi\)
\(728\) −1.43909 3.30591i −0.0533363 0.122525i
\(729\) 0 0
\(730\) −48.7604 + 28.1518i −1.80470 + 1.04195i
\(731\) 2.50227 + 4.33406i 0.0925498 + 0.160301i
\(732\) 0 0
\(733\) 17.1464i 0.633315i −0.948540 0.316658i \(-0.897439\pi\)
0.948540 0.316658i \(-0.102561\pi\)
\(734\) −8.85339 5.11150i −0.326784 0.188669i
\(735\) 0 0
\(736\) 5.40872i 0.199368i
\(737\) −2.95927 + 5.12560i −0.109006 + 0.188804i
\(738\) 0 0
\(739\) −13.0327 + 7.52443i −0.479416 + 0.276791i −0.720173 0.693795i \(-0.755938\pi\)
0.240757 + 0.970585i \(0.422604\pi\)
\(740\) 33.5210 1.23226
\(741\) 0 0
\(742\) 8.44252 0.309935
\(743\) −20.1776 + 11.6496i −0.740245 + 0.427381i −0.822158 0.569259i \(-0.807230\pi\)
0.0819132 + 0.996639i \(0.473897\pi\)
\(744\) 0 0
\(745\) −7.65235 + 13.2543i −0.280361 + 0.485599i
\(746\) 1.56284i 0.0572198i
\(747\) 0 0
\(748\) −3.06574 1.77001i −0.112095 0.0647179i
\(749\) 14.2056i 0.519062i
\(750\) 0 0
\(751\) 15.4534 + 26.7661i 0.563903 + 0.976709i 0.997151 + 0.0754344i \(0.0240343\pi\)
−0.433247 + 0.901275i \(0.642632\pi\)
\(752\) 6.57196 3.79432i 0.239655 0.138365i
\(753\) 0 0
\(754\) 22.2869 9.70168i 0.811640 0.353314i
\(755\) −71.7038 −2.60957
\(756\) 0 0
\(757\) −7.58518 13.1379i −0.275688 0.477506i 0.694620 0.719376i \(-0.255572\pi\)
−0.970308 + 0.241871i \(0.922239\pi\)
\(758\) −4.19268 + 7.26194i −0.152285 + 0.263766i
\(759\) 0 0
\(760\) −30.7681 17.7640i −1.11608 0.644366i
\(761\) −9.45208 5.45716i −0.342638 0.197822i 0.318800 0.947822i \(-0.396720\pi\)
−0.661438 + 0.750000i \(0.730053\pi\)
\(762\) 0 0
\(763\) −1.71910 + 2.97757i −0.0622357 + 0.107795i
\(764\) −7.62813 13.2123i −0.275976 0.478005i
\(765\) 0 0
\(766\) −9.11803 −0.329448
\(767\) −24.0637 + 10.4752i −0.868890 + 0.378236i
\(768\) 0 0
\(769\) −15.9112 + 9.18636i −0.573774 + 0.331269i −0.758655 0.651492i \(-0.774143\pi\)
0.184881 + 0.982761i \(0.440810\pi\)
\(770\) 2.46757 + 4.27396i 0.0889251 + 0.154023i
\(771\) 0 0
\(772\) 14.1797i 0.510340i
\(773\) 12.8159 + 7.39924i 0.460955 + 0.266132i 0.712446 0.701727i \(-0.247588\pi\)
−0.251491 + 0.967860i \(0.580921\pi\)
\(774\) 0 0
\(775\) 80.1766i 2.88003i
\(776\) 0.613704 1.06297i 0.0220307 0.0381583i
\(777\) 0 0
\(778\) −32.2095 + 18.5961i −1.15477 + 0.666704i
\(779\) −16.6118 −0.595180
\(780\) 0 0
\(781\) 9.73363 0.348297
\(782\) −14.7812 + 8.53391i −0.528573 + 0.305172i
\(783\) 0 0
\(784\) 0.500000 0.866025i 0.0178571 0.0309295i
\(785\) 3.01159i 0.107488i
\(786\) 0 0
\(787\) −36.8542 21.2778i −1.31371 0.758472i −0.331003 0.943630i \(-0.607387\pi\)
−0.982709 + 0.185158i \(0.940720\pi\)