Properties

Label 1950.2.i.bi.451.2
Level $1950$
Weight $2$
Character 1950.451
Analytic conductor $15.571$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1950.i (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(15.5708283941\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{17})\)
Defining polynomial: \(x^{4} - x^{3} + 5 x^{2} + 4 x + 16\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 390)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 451.2
Root \(1.28078 + 2.21837i\) of defining polynomial
Character \(\chi\) \(=\) 1950.451
Dual form 1950.2.i.bi.601.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{6} +(1.78078 + 3.08440i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{6} +(1.78078 + 3.08440i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(2.06155 - 3.57071i) q^{11} -1.00000 q^{12} +(3.34233 + 1.35234i) q^{13} +3.56155 q^{14} +(-0.500000 + 0.866025i) q^{16} +(2.56155 + 4.43674i) q^{17} -1.00000 q^{18} +(1.78078 + 3.08440i) q^{19} +3.56155 q^{21} +(-2.06155 - 3.57071i) q^{22} +(-3.84233 + 6.65511i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(2.84233 - 2.21837i) q^{26} -1.00000 q^{27} +(1.78078 - 3.08440i) q^{28} +(-3.28078 + 5.68247i) q^{29} +5.68466 q^{31} +(0.500000 + 0.866025i) q^{32} +(-2.06155 - 3.57071i) q^{33} +5.12311 q^{34} +(-0.500000 + 0.866025i) q^{36} +(2.06155 - 3.57071i) q^{37} +3.56155 q^{38} +(2.84233 - 2.21837i) q^{39} +(2.12311 - 3.67733i) q^{41} +(1.78078 - 3.08440i) q^{42} +(2.28078 + 3.95042i) q^{43} -4.12311 q^{44} +(3.84233 + 6.65511i) q^{46} -7.00000 q^{47} +(0.500000 + 0.866025i) q^{48} +(-2.84233 + 4.92306i) q^{49} +5.12311 q^{51} +(-0.500000 - 3.57071i) q^{52} -4.43845 q^{53} +(-0.500000 + 0.866025i) q^{54} +(-1.78078 - 3.08440i) q^{56} +3.56155 q^{57} +(3.28078 + 5.68247i) q^{58} +(-5.28078 - 9.14657i) q^{59} +(-3.00000 - 5.19615i) q^{61} +(2.84233 - 4.92306i) q^{62} +(1.78078 - 3.08440i) q^{63} +1.00000 q^{64} -4.12311 q^{66} +(7.12311 - 12.3376i) q^{67} +(2.56155 - 4.43674i) q^{68} +(3.84233 + 6.65511i) q^{69} +(2.43845 + 4.22351i) q^{71} +(0.500000 + 0.866025i) q^{72} +15.3693 q^{73} +(-2.06155 - 3.57071i) q^{74} +(1.78078 - 3.08440i) q^{76} +14.6847 q^{77} +(-0.500000 - 3.57071i) q^{78} +7.43845 q^{79} +(-0.500000 + 0.866025i) q^{81} +(-2.12311 - 3.67733i) q^{82} -1.12311 q^{83} +(-1.78078 - 3.08440i) q^{84} +4.56155 q^{86} +(3.28078 + 5.68247i) q^{87} +(-2.06155 + 3.57071i) q^{88} +(-0.903882 + 1.56557i) q^{89} +(1.78078 + 12.7173i) q^{91} +7.68466 q^{92} +(2.84233 - 4.92306i) q^{93} +(-3.50000 + 6.06218i) q^{94} +1.00000 q^{96} +(0.561553 + 0.972638i) q^{97} +(2.84233 + 4.92306i) q^{98} -4.12311 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 2q^{2} + 2q^{3} - 2q^{4} - 2q^{6} + 3q^{7} - 4q^{8} - 2q^{9} + O(q^{10}) \) \( 4q + 2q^{2} + 2q^{3} - 2q^{4} - 2q^{6} + 3q^{7} - 4q^{8} - 2q^{9} - 4q^{12} + q^{13} + 6q^{14} - 2q^{16} + 2q^{17} - 4q^{18} + 3q^{19} + 6q^{21} - 3q^{23} - 2q^{24} - q^{26} - 4q^{27} + 3q^{28} - 9q^{29} - 2q^{31} + 2q^{32} + 4q^{34} - 2q^{36} + 6q^{38} - q^{39} - 8q^{41} + 3q^{42} + 5q^{43} + 3q^{46} - 28q^{47} + 2q^{48} + q^{49} + 4q^{51} - 2q^{52} - 26q^{53} - 2q^{54} - 3q^{56} + 6q^{57} + 9q^{58} - 17q^{59} - 12q^{61} - q^{62} + 3q^{63} + 4q^{64} + 12q^{67} + 2q^{68} + 3q^{69} + 18q^{71} + 2q^{72} + 12q^{73} + 3q^{76} + 34q^{77} - 2q^{78} + 38q^{79} - 2q^{81} + 8q^{82} + 12q^{83} - 3q^{84} + 10q^{86} + 9q^{87} + 17q^{89} + 3q^{91} + 6q^{92} - q^{93} - 14q^{94} + 4q^{96} - 6q^{97} - q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1950\mathbb{Z}\right)^\times\).

\(n\) \(301\) \(1301\) \(1327\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 0.866025i 0.353553 0.612372i
\(3\) 0.500000 0.866025i 0.288675 0.500000i
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) 0 0
\(6\) −0.500000 0.866025i −0.204124 0.353553i
\(7\) 1.78078 + 3.08440i 0.673070 + 1.16579i 0.977029 + 0.213107i \(0.0683582\pi\)
−0.303959 + 0.952685i \(0.598308\pi\)
\(8\) −1.00000 −0.353553
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) 0 0
\(11\) 2.06155 3.57071i 0.621582 1.07661i −0.367610 0.929980i \(-0.619824\pi\)
0.989191 0.146631i \(-0.0468429\pi\)
\(12\) −1.00000 −0.288675
\(13\) 3.34233 + 1.35234i 0.926995 + 0.375073i
\(14\) 3.56155 0.951865
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 2.56155 + 4.43674i 0.621268 + 1.07607i 0.989250 + 0.146235i \(0.0467154\pi\)
−0.367982 + 0.929833i \(0.619951\pi\)
\(18\) −1.00000 −0.235702
\(19\) 1.78078 + 3.08440i 0.408538 + 0.707609i 0.994726 0.102566i \(-0.0327054\pi\)
−0.586188 + 0.810175i \(0.699372\pi\)
\(20\) 0 0
\(21\) 3.56155 0.777195
\(22\) −2.06155 3.57071i −0.439525 0.761279i
\(23\) −3.84233 + 6.65511i −0.801181 + 1.38769i 0.117658 + 0.993054i \(0.462461\pi\)
−0.918839 + 0.394632i \(0.870872\pi\)
\(24\) −0.500000 + 0.866025i −0.102062 + 0.176777i
\(25\) 0 0
\(26\) 2.84233 2.21837i 0.557427 0.435058i
\(27\) −1.00000 −0.192450
\(28\) 1.78078 3.08440i 0.336535 0.582896i
\(29\) −3.28078 + 5.68247i −0.609225 + 1.05521i 0.382144 + 0.924103i \(0.375186\pi\)
−0.991368 + 0.131105i \(0.958147\pi\)
\(30\) 0 0
\(31\) 5.68466 1.02099 0.510497 0.859879i \(-0.329461\pi\)
0.510497 + 0.859879i \(0.329461\pi\)
\(32\) 0.500000 + 0.866025i 0.0883883 + 0.153093i
\(33\) −2.06155 3.57071i −0.358870 0.621582i
\(34\) 5.12311 0.878605
\(35\) 0 0
\(36\) −0.500000 + 0.866025i −0.0833333 + 0.144338i
\(37\) 2.06155 3.57071i 0.338917 0.587022i −0.645312 0.763919i \(-0.723273\pi\)
0.984229 + 0.176897i \(0.0566060\pi\)
\(38\) 3.56155 0.577760
\(39\) 2.84233 2.21837i 0.455137 0.355223i
\(40\) 0 0
\(41\) 2.12311 3.67733i 0.331573 0.574302i −0.651247 0.758866i \(-0.725754\pi\)
0.982821 + 0.184564i \(0.0590872\pi\)
\(42\) 1.78078 3.08440i 0.274780 0.475933i
\(43\) 2.28078 + 3.95042i 0.347815 + 0.602433i 0.985861 0.167565i \(-0.0535903\pi\)
−0.638046 + 0.769998i \(0.720257\pi\)
\(44\) −4.12311 −0.621582
\(45\) 0 0
\(46\) 3.84233 + 6.65511i 0.566521 + 0.981242i
\(47\) −7.00000 −1.02105 −0.510527 0.859861i \(-0.670550\pi\)
−0.510527 + 0.859861i \(0.670550\pi\)
\(48\) 0.500000 + 0.866025i 0.0721688 + 0.125000i
\(49\) −2.84233 + 4.92306i −0.406047 + 0.703294i
\(50\) 0 0
\(51\) 5.12311 0.717378
\(52\) −0.500000 3.57071i −0.0693375 0.495169i
\(53\) −4.43845 −0.609668 −0.304834 0.952406i \(-0.598601\pi\)
−0.304834 + 0.952406i \(0.598601\pi\)
\(54\) −0.500000 + 0.866025i −0.0680414 + 0.117851i
\(55\) 0 0
\(56\) −1.78078 3.08440i −0.237966 0.412170i
\(57\) 3.56155 0.471739
\(58\) 3.28078 + 5.68247i 0.430787 + 0.746145i
\(59\) −5.28078 9.14657i −0.687499 1.19078i −0.972645 0.232298i \(-0.925375\pi\)
0.285146 0.958484i \(-0.407958\pi\)
\(60\) 0 0
\(61\) −3.00000 5.19615i −0.384111 0.665299i 0.607535 0.794293i \(-0.292159\pi\)
−0.991645 + 0.128994i \(0.958825\pi\)
\(62\) 2.84233 4.92306i 0.360976 0.625229i
\(63\) 1.78078 3.08440i 0.224357 0.388597i
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) −4.12311 −0.507519
\(67\) 7.12311 12.3376i 0.870226 1.50728i 0.00846293 0.999964i \(-0.497306\pi\)
0.861763 0.507311i \(-0.169361\pi\)
\(68\) 2.56155 4.43674i 0.310634 0.538034i
\(69\) 3.84233 + 6.65511i 0.462562 + 0.801181i
\(70\) 0 0
\(71\) 2.43845 + 4.22351i 0.289390 + 0.501239i 0.973664 0.227986i \(-0.0732141\pi\)
−0.684274 + 0.729225i \(0.739881\pi\)
\(72\) 0.500000 + 0.866025i 0.0589256 + 0.102062i
\(73\) 15.3693 1.79884 0.899421 0.437083i \(-0.143988\pi\)
0.899421 + 0.437083i \(0.143988\pi\)
\(74\) −2.06155 3.57071i −0.239651 0.415087i
\(75\) 0 0
\(76\) 1.78078 3.08440i 0.204269 0.353804i
\(77\) 14.6847 1.67347
\(78\) −0.500000 3.57071i −0.0566139 0.404304i
\(79\) 7.43845 0.836891 0.418445 0.908242i \(-0.362575\pi\)
0.418445 + 0.908242i \(0.362575\pi\)
\(80\) 0 0
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) −2.12311 3.67733i −0.234458 0.406093i
\(83\) −1.12311 −0.123277 −0.0616384 0.998099i \(-0.519633\pi\)
−0.0616384 + 0.998099i \(0.519633\pi\)
\(84\) −1.78078 3.08440i −0.194299 0.336535i
\(85\) 0 0
\(86\) 4.56155 0.491885
\(87\) 3.28078 + 5.68247i 0.351736 + 0.609225i
\(88\) −2.06155 + 3.57071i −0.219762 + 0.380639i
\(89\) −0.903882 + 1.56557i −0.0958113 + 0.165950i −0.909947 0.414725i \(-0.863878\pi\)
0.814136 + 0.580675i \(0.197211\pi\)
\(90\) 0 0
\(91\) 1.78078 + 12.7173i 0.186676 + 1.33313i
\(92\) 7.68466 0.801181
\(93\) 2.84233 4.92306i 0.294736 0.510497i
\(94\) −3.50000 + 6.06218i −0.360997 + 0.625266i
\(95\) 0 0
\(96\) 1.00000 0.102062
\(97\) 0.561553 + 0.972638i 0.0570170 + 0.0987564i 0.893125 0.449808i \(-0.148508\pi\)
−0.836108 + 0.548565i \(0.815174\pi\)
\(98\) 2.84233 + 4.92306i 0.287119 + 0.497304i
\(99\) −4.12311 −0.414388
\(100\) 0 0
\(101\) 8.56155 14.8290i 0.851906 1.47555i −0.0275793 0.999620i \(-0.508780\pi\)
0.879486 0.475925i \(-0.157887\pi\)
\(102\) 2.56155 4.43674i 0.253632 0.439303i
\(103\) −0.438447 −0.0432015 −0.0216007 0.999767i \(-0.506876\pi\)
−0.0216007 + 0.999767i \(0.506876\pi\)
\(104\) −3.34233 1.35234i −0.327742 0.132608i
\(105\) 0 0
\(106\) −2.21922 + 3.84381i −0.215550 + 0.373344i
\(107\) 1.00000 1.73205i 0.0966736 0.167444i −0.813632 0.581380i \(-0.802513\pi\)
0.910306 + 0.413936i \(0.135846\pi\)
\(108\) 0.500000 + 0.866025i 0.0481125 + 0.0833333i
\(109\) −20.2462 −1.93924 −0.969618 0.244625i \(-0.921335\pi\)
−0.969618 + 0.244625i \(0.921335\pi\)
\(110\) 0 0
\(111\) −2.06155 3.57071i −0.195674 0.338917i
\(112\) −3.56155 −0.336535
\(113\) −1.84233 3.19101i −0.173312 0.300185i 0.766264 0.642526i \(-0.222113\pi\)
−0.939576 + 0.342341i \(0.888780\pi\)
\(114\) 1.78078 3.08440i 0.166785 0.288880i
\(115\) 0 0
\(116\) 6.56155 0.609225
\(117\) −0.500000 3.57071i −0.0462250 0.330113i
\(118\) −10.5616 −0.972270
\(119\) −9.12311 + 15.8017i −0.836314 + 1.44854i
\(120\) 0 0
\(121\) −3.00000 5.19615i −0.272727 0.472377i
\(122\) −6.00000 −0.543214
\(123\) −2.12311 3.67733i −0.191434 0.331573i
\(124\) −2.84233 4.92306i −0.255249 0.442104i
\(125\) 0 0
\(126\) −1.78078 3.08440i −0.158644 0.274780i
\(127\) −2.21922 + 3.84381i −0.196924 + 0.341083i −0.947530 0.319668i \(-0.896429\pi\)
0.750605 + 0.660751i \(0.229762\pi\)
\(128\) 0.500000 0.866025i 0.0441942 0.0765466i
\(129\) 4.56155 0.401622
\(130\) 0 0
\(131\) 6.12311 0.534978 0.267489 0.963561i \(-0.413806\pi\)
0.267489 + 0.963561i \(0.413806\pi\)
\(132\) −2.06155 + 3.57071i −0.179435 + 0.310791i
\(133\) −6.34233 + 10.9852i −0.549950 + 0.952541i
\(134\) −7.12311 12.3376i −0.615343 1.06580i
\(135\) 0 0
\(136\) −2.56155 4.43674i −0.219651 0.380447i
\(137\) −4.40388 7.62775i −0.376249 0.651682i 0.614264 0.789101i \(-0.289453\pi\)
−0.990513 + 0.137418i \(0.956120\pi\)
\(138\) 7.68466 0.654162
\(139\) −4.21922 7.30791i −0.357870 0.619849i 0.629735 0.776810i \(-0.283164\pi\)
−0.987605 + 0.156961i \(0.949830\pi\)
\(140\) 0 0
\(141\) −3.50000 + 6.06218i −0.294753 + 0.510527i
\(142\) 4.87689 0.409260
\(143\) 11.7192 9.14657i 0.980011 0.764875i
\(144\) 1.00000 0.0833333
\(145\) 0 0
\(146\) 7.68466 13.3102i 0.635987 1.10156i
\(147\) 2.84233 + 4.92306i 0.234431 + 0.406047i
\(148\) −4.12311 −0.338917
\(149\) 11.4039 + 19.7521i 0.934242 + 1.61816i 0.775979 + 0.630758i \(0.217256\pi\)
0.158263 + 0.987397i \(0.449411\pi\)
\(150\) 0 0
\(151\) 9.36932 0.762464 0.381232 0.924479i \(-0.375500\pi\)
0.381232 + 0.924479i \(0.375500\pi\)
\(152\) −1.78078 3.08440i −0.144440 0.250177i
\(153\) 2.56155 4.43674i 0.207089 0.358689i
\(154\) 7.34233 12.7173i 0.591662 1.02479i
\(155\) 0 0
\(156\) −3.34233 1.35234i −0.267601 0.108274i
\(157\) −22.1231 −1.76562 −0.882808 0.469734i \(-0.844350\pi\)
−0.882808 + 0.469734i \(0.844350\pi\)
\(158\) 3.71922 6.44188i 0.295886 0.512489i
\(159\) −2.21922 + 3.84381i −0.175996 + 0.304834i
\(160\) 0 0
\(161\) −27.3693 −2.15700
\(162\) 0.500000 + 0.866025i 0.0392837 + 0.0680414i
\(163\) −9.28078 16.0748i −0.726927 1.25907i −0.958176 0.286179i \(-0.907615\pi\)
0.231250 0.972894i \(-0.425719\pi\)
\(164\) −4.24621 −0.331573
\(165\) 0 0
\(166\) −0.561553 + 0.972638i −0.0435850 + 0.0754913i
\(167\) −10.1847 + 17.6403i −0.788113 + 1.36505i 0.139009 + 0.990291i \(0.455608\pi\)
−0.927122 + 0.374760i \(0.877725\pi\)
\(168\) −3.56155 −0.274780
\(169\) 9.34233 + 9.03996i 0.718641 + 0.695382i
\(170\) 0 0
\(171\) 1.78078 3.08440i 0.136179 0.235870i
\(172\) 2.28078 3.95042i 0.173908 0.301217i
\(173\) −12.5885 21.8040i −0.957089 1.65773i −0.729514 0.683966i \(-0.760254\pi\)
−0.227575 0.973760i \(-0.573080\pi\)
\(174\) 6.56155 0.497430
\(175\) 0 0
\(176\) 2.06155 + 3.57071i 0.155395 + 0.269153i
\(177\) −10.5616 −0.793855
\(178\) 0.903882 + 1.56557i 0.0677488 + 0.117344i
\(179\) 0.157671 0.273094i 0.0117849 0.0204120i −0.860073 0.510171i \(-0.829582\pi\)
0.871858 + 0.489759i \(0.162915\pi\)
\(180\) 0 0
\(181\) 11.1231 0.826774 0.413387 0.910555i \(-0.364346\pi\)
0.413387 + 0.910555i \(0.364346\pi\)
\(182\) 11.9039 + 4.81645i 0.882374 + 0.357019i
\(183\) −6.00000 −0.443533
\(184\) 3.84233 6.65511i 0.283260 0.490621i
\(185\) 0 0
\(186\) −2.84233 4.92306i −0.208410 0.360976i
\(187\) 21.1231 1.54467
\(188\) 3.50000 + 6.06218i 0.255264 + 0.442130i
\(189\) −1.78078 3.08440i −0.129532 0.224357i
\(190\) 0 0
\(191\) −9.56155 16.5611i −0.691850 1.19832i −0.971231 0.238139i \(-0.923463\pi\)
0.279381 0.960180i \(-0.409871\pi\)
\(192\) 0.500000 0.866025i 0.0360844 0.0625000i
\(193\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(194\) 1.12311 0.0806343
\(195\) 0 0
\(196\) 5.68466 0.406047
\(197\) −3.90388 + 6.76172i −0.278140 + 0.481753i −0.970923 0.239394i \(-0.923051\pi\)
0.692782 + 0.721147i \(0.256385\pi\)
\(198\) −2.06155 + 3.57071i −0.146508 + 0.253760i
\(199\) −5.56155 9.63289i −0.394248 0.682858i 0.598757 0.800931i \(-0.295662\pi\)
−0.993005 + 0.118073i \(0.962328\pi\)
\(200\) 0 0
\(201\) −7.12311 12.3376i −0.502425 0.870226i
\(202\) −8.56155 14.8290i −0.602389 1.04337i
\(203\) −23.3693 −1.64020
\(204\) −2.56155 4.43674i −0.179345 0.310634i
\(205\) 0 0
\(206\) −0.219224 + 0.379706i −0.0152740 + 0.0264554i
\(207\) 7.68466 0.534121
\(208\) −2.84233 + 2.21837i −0.197080 + 0.153816i
\(209\) 14.6847 1.01576
\(210\) 0 0
\(211\) −3.46543 + 6.00231i −0.238570 + 0.413216i −0.960304 0.278955i \(-0.910012\pi\)
0.721734 + 0.692171i \(0.243345\pi\)
\(212\) 2.21922 + 3.84381i 0.152417 + 0.263994i
\(213\) 4.87689 0.334159
\(214\) −1.00000 1.73205i −0.0683586 0.118401i
\(215\) 0 0
\(216\) 1.00000 0.0680414
\(217\) 10.1231 + 17.5337i 0.687201 + 1.19027i
\(218\) −10.1231 + 17.5337i −0.685623 + 1.18753i
\(219\) 7.68466 13.3102i 0.519281 0.899421i
\(220\) 0 0
\(221\) 2.56155 + 18.2931i 0.172309 + 1.23053i
\(222\) −4.12311 −0.276725
\(223\) −13.1501 + 22.7766i −0.880595 + 1.52524i −0.0299151 + 0.999552i \(0.509524\pi\)
−0.850680 + 0.525683i \(0.823810\pi\)
\(224\) −1.78078 + 3.08440i −0.118983 + 0.206085i
\(225\) 0 0
\(226\) −3.68466 −0.245100
\(227\) −10.0000 17.3205i −0.663723 1.14960i −0.979630 0.200812i \(-0.935642\pi\)
0.315906 0.948790i \(-0.397691\pi\)
\(228\) −1.78078 3.08440i −0.117935 0.204269i
\(229\) −7.75379 −0.512385 −0.256192 0.966626i \(-0.582468\pi\)
−0.256192 + 0.966626i \(0.582468\pi\)
\(230\) 0 0
\(231\) 7.34233 12.7173i 0.483090 0.836736i
\(232\) 3.28078 5.68247i 0.215394 0.373073i
\(233\) 17.6847 1.15856 0.579280 0.815128i \(-0.303334\pi\)
0.579280 + 0.815128i \(0.303334\pi\)
\(234\) −3.34233 1.35234i −0.218495 0.0884055i
\(235\) 0 0
\(236\) −5.28078 + 9.14657i −0.343749 + 0.595391i
\(237\) 3.71922 6.44188i 0.241590 0.418445i
\(238\) 9.12311 + 15.8017i 0.591363 + 1.02427i
\(239\) 13.3693 0.864789 0.432395 0.901684i \(-0.357669\pi\)
0.432395 + 0.901684i \(0.357669\pi\)
\(240\) 0 0
\(241\) 9.93845 + 17.2139i 0.640192 + 1.10884i 0.985390 + 0.170315i \(0.0544784\pi\)
−0.345198 + 0.938530i \(0.612188\pi\)
\(242\) −6.00000 −0.385695
\(243\) 0.500000 + 0.866025i 0.0320750 + 0.0555556i
\(244\) −3.00000 + 5.19615i −0.192055 + 0.332650i
\(245\) 0 0
\(246\) −4.24621 −0.270729
\(247\) 1.78078 + 12.7173i 0.113308 + 0.809182i
\(248\) −5.68466 −0.360976
\(249\) −0.561553 + 0.972638i −0.0355870 + 0.0616384i
\(250\) 0 0
\(251\) −0.0615528 0.106613i −0.00388518 0.00672933i 0.864076 0.503361i \(-0.167903\pi\)
−0.867961 + 0.496632i \(0.834570\pi\)
\(252\) −3.56155 −0.224357
\(253\) 15.8423 + 27.4397i 0.995999 + 1.72512i
\(254\) 2.21922 + 3.84381i 0.139246 + 0.241182i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −0.719224 + 1.24573i −0.0448639 + 0.0777066i −0.887585 0.460643i \(-0.847619\pi\)
0.842721 + 0.538350i \(0.180952\pi\)
\(258\) 2.28078 3.95042i 0.141995 0.245942i
\(259\) 14.6847 0.912460
\(260\) 0 0
\(261\) 6.56155 0.406150
\(262\) 3.06155 5.30277i 0.189143 0.327606i
\(263\) −6.50000 + 11.2583i −0.400807 + 0.694218i −0.993824 0.110972i \(-0.964604\pi\)
0.593016 + 0.805190i \(0.297937\pi\)
\(264\) 2.06155 + 3.57071i 0.126880 + 0.219762i
\(265\) 0 0
\(266\) 6.34233 + 10.9852i 0.388873 + 0.673548i
\(267\) 0.903882 + 1.56557i 0.0553167 + 0.0958113i
\(268\) −14.2462 −0.870226
\(269\) 1.68466 + 2.91791i 0.102715 + 0.177908i 0.912803 0.408401i \(-0.133914\pi\)
−0.810087 + 0.586310i \(0.800580\pi\)
\(270\) 0 0
\(271\) −16.0885 + 27.8662i −0.977309 + 1.69275i −0.305215 + 0.952283i \(0.598728\pi\)
−0.672094 + 0.740466i \(0.734605\pi\)
\(272\) −5.12311 −0.310634
\(273\) 11.9039 + 4.81645i 0.720456 + 0.291505i
\(274\) −8.80776 −0.532096
\(275\) 0 0
\(276\) 3.84233 6.65511i 0.231281 0.400591i
\(277\) −0.500000 0.866025i −0.0300421 0.0520344i 0.850613 0.525792i \(-0.176231\pi\)
−0.880656 + 0.473757i \(0.842897\pi\)
\(278\) −8.43845 −0.506104
\(279\) −2.84233 4.92306i −0.170166 0.294736i
\(280\) 0 0
\(281\) −0.246211 −0.0146877 −0.00734387 0.999973i \(-0.502338\pi\)
−0.00734387 + 0.999973i \(0.502338\pi\)
\(282\) 3.50000 + 6.06218i 0.208422 + 0.360997i
\(283\) 5.71922 9.90599i 0.339973 0.588850i −0.644455 0.764643i \(-0.722916\pi\)
0.984427 + 0.175793i \(0.0562489\pi\)
\(284\) 2.43845 4.22351i 0.144695 0.250619i
\(285\) 0 0
\(286\) −2.06155 14.7224i −0.121902 0.870556i
\(287\) 15.1231 0.892689
\(288\) 0.500000 0.866025i 0.0294628 0.0510310i
\(289\) −4.62311 + 8.00745i −0.271947 + 0.471027i
\(290\) 0 0
\(291\) 1.12311 0.0658376
\(292\) −7.68466 13.3102i −0.449711 0.778922i
\(293\) −12.4654 21.5908i −0.728238 1.26135i −0.957627 0.288011i \(-0.907006\pi\)
0.229389 0.973335i \(-0.426327\pi\)
\(294\) 5.68466 0.331536
\(295\) 0 0
\(296\) −2.06155 + 3.57071i −0.119825 + 0.207544i
\(297\) −2.06155 + 3.57071i −0.119623 + 0.207194i
\(298\) 22.8078 1.32122
\(299\) −21.8423 + 17.0474i −1.26317 + 0.985877i
\(300\) 0 0
\(301\) −8.12311 + 14.0696i −0.468208 + 0.810960i
\(302\) 4.68466 8.11407i 0.269572 0.466912i
\(303\) −8.56155 14.8290i −0.491848 0.851906i
\(304\) −3.56155 −0.204269
\(305\) 0 0
\(306\) −2.56155 4.43674i −0.146434 0.253632i
\(307\) 15.6155 0.891225 0.445613 0.895226i \(-0.352986\pi\)
0.445613 + 0.895226i \(0.352986\pi\)
\(308\) −7.34233 12.7173i −0.418368 0.724635i
\(309\) −0.219224 + 0.379706i −0.0124712 + 0.0216007i
\(310\) 0 0
\(311\) −18.7386 −1.06257 −0.531285 0.847193i \(-0.678291\pi\)
−0.531285 + 0.847193i \(0.678291\pi\)
\(312\) −2.84233 + 2.21837i −0.160915 + 0.125590i
\(313\) −6.63068 −0.374788 −0.187394 0.982285i \(-0.560004\pi\)
−0.187394 + 0.982285i \(0.560004\pi\)
\(314\) −11.0616 + 19.1592i −0.624240 + 1.08121i
\(315\) 0 0
\(316\) −3.71922 6.44188i −0.209223 0.362384i
\(317\) 4.19224 0.235459 0.117730 0.993046i \(-0.462438\pi\)
0.117730 + 0.993046i \(0.462438\pi\)
\(318\) 2.21922 + 3.84381i 0.124448 + 0.215550i
\(319\) 13.5270 + 23.4294i 0.757366 + 1.31180i
\(320\) 0 0
\(321\) −1.00000 1.73205i −0.0558146 0.0966736i
\(322\) −13.6847 + 23.7025i −0.762616 + 1.32089i
\(323\) −9.12311 + 15.8017i −0.507623 + 0.879229i
\(324\) 1.00000 0.0555556
\(325\) 0 0
\(326\) −18.5616 −1.02803
\(327\) −10.1231 + 17.5337i −0.559809 + 0.969618i
\(328\) −2.12311 + 3.67733i −0.117229 + 0.203046i
\(329\) −12.4654 21.5908i −0.687242 1.19034i
\(330\) 0 0
\(331\) 9.36932 + 16.2281i 0.514984 + 0.891979i 0.999849 + 0.0173896i \(0.00553556\pi\)
−0.484865 + 0.874589i \(0.661131\pi\)
\(332\) 0.561553 + 0.972638i 0.0308192 + 0.0533804i
\(333\) −4.12311 −0.225945
\(334\) 10.1847 + 17.6403i 0.557280 + 0.965237i
\(335\) 0 0
\(336\) −1.78078 + 3.08440i −0.0971493 + 0.168268i
\(337\) 6.00000 0.326841 0.163420 0.986557i \(-0.447747\pi\)
0.163420 + 0.986557i \(0.447747\pi\)
\(338\) 12.5000 3.57071i 0.679910 0.194221i
\(339\) −3.68466 −0.200123
\(340\) 0 0
\(341\) 11.7192 20.2983i 0.634632 1.09921i
\(342\) −1.78078 3.08440i −0.0962934 0.166785i
\(343\) 4.68466 0.252948
\(344\) −2.28078 3.95042i −0.122971 0.212992i
\(345\) 0 0
\(346\) −25.1771 −1.35353
\(347\) 4.56155 + 7.90084i 0.244877 + 0.424139i 0.962097 0.272707i \(-0.0879191\pi\)
−0.717220 + 0.696847i \(0.754586\pi\)
\(348\) 3.28078 5.68247i 0.175868 0.304612i
\(349\) 12.2462 21.2111i 0.655525 1.13540i −0.326237 0.945288i \(-0.605781\pi\)
0.981762 0.190114i \(-0.0608858\pi\)
\(350\) 0 0
\(351\) −3.34233 1.35234i −0.178400 0.0721828i
\(352\) 4.12311 0.219762
\(353\) 15.9309 27.5931i 0.847915 1.46863i −0.0351511 0.999382i \(-0.511191\pi\)
0.883066 0.469249i \(-0.155475\pi\)
\(354\) −5.28078 + 9.14657i −0.280670 + 0.486135i
\(355\) 0 0
\(356\) 1.80776 0.0958113
\(357\) 9.12311 + 15.8017i 0.482846 + 0.836314i
\(358\) −0.157671 0.273094i −0.00833316 0.0144335i
\(359\) 4.87689 0.257393 0.128696 0.991684i \(-0.458921\pi\)
0.128696 + 0.991684i \(0.458921\pi\)
\(360\) 0 0
\(361\) 3.15767 5.46925i 0.166193 0.287855i
\(362\) 5.56155 9.63289i 0.292309 0.506294i
\(363\) −6.00000 −0.314918
\(364\) 10.1231 7.90084i 0.530595 0.414117i
\(365\) 0 0
\(366\) −3.00000 + 5.19615i −0.156813 + 0.271607i
\(367\) −10.2462 + 17.7470i −0.534848 + 0.926384i 0.464323 + 0.885666i \(0.346298\pi\)
−0.999171 + 0.0407177i \(0.987036\pi\)
\(368\) −3.84233 6.65511i −0.200295 0.346922i
\(369\) −4.24621 −0.221049
\(370\) 0 0
\(371\) −7.90388 13.6899i −0.410349 0.710746i
\(372\) −5.68466 −0.294736
\(373\) −2.59612 4.49661i −0.134422 0.232826i 0.790955 0.611875i \(-0.209584\pi\)
−0.925376 + 0.379049i \(0.876251\pi\)
\(374\) 10.5616 18.2931i 0.546125 0.945916i
\(375\) 0 0
\(376\) 7.00000 0.360997
\(377\) −18.6501 + 14.5560i −0.960529 + 0.749670i
\(378\) −3.56155 −0.183187
\(379\) 2.65767 4.60322i 0.136515 0.236452i −0.789660 0.613545i \(-0.789743\pi\)
0.926175 + 0.377093i \(0.123076\pi\)
\(380\) 0 0
\(381\) 2.21922 + 3.84381i 0.113694 + 0.196924i
\(382\) −19.1231 −0.978423
\(383\) 10.4039 + 18.0201i 0.531614 + 0.920782i 0.999319 + 0.0368973i \(0.0117474\pi\)
−0.467706 + 0.883884i \(0.654919\pi\)
\(384\) −0.500000 0.866025i −0.0255155 0.0441942i
\(385\) 0 0
\(386\) 0 0
\(387\) 2.28078 3.95042i 0.115938 0.200811i
\(388\) 0.561553 0.972638i 0.0285085 0.0493782i
\(389\) 19.0540 0.966075 0.483037 0.875600i \(-0.339533\pi\)
0.483037 + 0.875600i \(0.339533\pi\)
\(390\) 0 0
\(391\) −39.3693 −1.99099
\(392\) 2.84233 4.92306i 0.143559 0.248652i
\(393\) 3.06155 5.30277i 0.154435 0.267489i
\(394\) 3.90388 + 6.76172i 0.196675 + 0.340651i
\(395\) 0 0
\(396\) 2.06155 + 3.57071i 0.103597 + 0.179435i
\(397\) −5.93845 10.2857i −0.298042 0.516224i 0.677646 0.735388i \(-0.263000\pi\)
−0.975688 + 0.219164i \(0.929667\pi\)
\(398\) −11.1231 −0.557551
\(399\) 6.34233 + 10.9852i 0.317514 + 0.549950i
\(400\) 0 0
\(401\) −6.34233 + 10.9852i −0.316721 + 0.548577i −0.979802 0.199971i \(-0.935915\pi\)
0.663081 + 0.748548i \(0.269248\pi\)
\(402\) −14.2462 −0.710536
\(403\) 19.0000 + 7.68762i 0.946457 + 0.382947i
\(404\) −17.1231 −0.851906
\(405\) 0 0
\(406\) −11.6847 + 20.2384i −0.579900 + 1.00442i
\(407\) −8.50000 14.7224i −0.421329 0.729764i
\(408\) −5.12311 −0.253632
\(409\) −0.903882 1.56557i −0.0446941 0.0774124i 0.842813 0.538207i \(-0.180898\pi\)
−0.887507 + 0.460794i \(0.847565\pi\)
\(410\) 0 0
\(411\) −8.80776 −0.434455
\(412\) 0.219224 + 0.379706i 0.0108004 + 0.0187068i
\(413\) 18.8078 32.5760i 0.925470 1.60296i
\(414\) 3.84233 6.65511i 0.188840 0.327081i
\(415\) 0 0
\(416\) 0.500000 + 3.57071i 0.0245145 + 0.175069i
\(417\) −8.43845 −0.413233
\(418\) 7.34233 12.7173i 0.359125 0.622023i
\(419\) 0.246211 0.426450i 0.0120282 0.0208335i −0.859949 0.510381i \(-0.829505\pi\)
0.871977 + 0.489547i \(0.162838\pi\)
\(420\) 0 0
\(421\) 0.492423 0.0239992 0.0119996 0.999928i \(-0.496180\pi\)
0.0119996 + 0.999928i \(0.496180\pi\)
\(422\) 3.46543 + 6.00231i 0.168695 + 0.292188i
\(423\) 3.50000 + 6.06218i 0.170176 + 0.294753i
\(424\) 4.43845 0.215550
\(425\) 0 0
\(426\) 2.43845 4.22351i 0.118143 0.204630i
\(427\) 10.6847 18.5064i 0.517067 0.895586i
\(428\) −2.00000 −0.0966736
\(429\) −2.06155 14.7224i −0.0995327 0.710806i
\(430\) 0 0
\(431\) −13.3693 + 23.1563i −0.643977 + 1.11540i 0.340559 + 0.940223i \(0.389384\pi\)
−0.984537 + 0.175178i \(0.943950\pi\)
\(432\) 0.500000 0.866025i 0.0240563 0.0416667i
\(433\) 15.3693 + 26.6204i 0.738602 + 1.27930i 0.953125 + 0.302578i \(0.0978471\pi\)
−0.214523 + 0.976719i \(0.568820\pi\)
\(434\) 20.2462 0.971849
\(435\) 0 0
\(436\) 10.1231 + 17.5337i 0.484809 + 0.839714i
\(437\) −27.3693 −1.30925
\(438\) −7.68466 13.3102i −0.367187 0.635987i
\(439\) −8.43845 + 14.6158i −0.402745 + 0.697575i −0.994056 0.108869i \(-0.965277\pi\)
0.591311 + 0.806444i \(0.298611\pi\)
\(440\) 0 0
\(441\) 5.68466 0.270698
\(442\) 17.1231 + 6.92820i 0.814463 + 0.329541i
\(443\) 4.87689 0.231708 0.115854 0.993266i \(-0.463039\pi\)
0.115854 + 0.993266i \(0.463039\pi\)
\(444\) −2.06155 + 3.57071i −0.0978370 + 0.169459i
\(445\) 0 0
\(446\) 13.1501 + 22.7766i 0.622675 + 1.07850i
\(447\) 22.8078 1.07877
\(448\) 1.78078 + 3.08440i 0.0841338 + 0.145724i
\(449\) −12.5885 21.8040i −0.594090 1.02899i −0.993675 0.112298i \(-0.964179\pi\)
0.399585 0.916696i \(-0.369154\pi\)
\(450\) 0 0
\(451\) −8.75379 15.1620i −0.412200 0.713951i
\(452\) −1.84233 + 3.19101i −0.0866559 + 0.150092i
\(453\) 4.68466 8.11407i 0.220104 0.381232i
\(454\) −20.0000 −0.938647
\(455\) 0 0
\(456\) −3.56155 −0.166785
\(457\) 1.87689 3.25088i 0.0877974 0.152070i −0.818782 0.574104i \(-0.805351\pi\)
0.906580 + 0.422034i \(0.138684\pi\)
\(458\) −3.87689 + 6.71498i −0.181155 + 0.313770i
\(459\) −2.56155 4.43674i −0.119563 0.207089i
\(460\) 0 0
\(461\) −3.52699 6.10892i −0.164268 0.284521i 0.772127 0.635468i \(-0.219193\pi\)
−0.936395 + 0.350947i \(0.885860\pi\)
\(462\) −7.34233 12.7173i −0.341596 0.591662i
\(463\) −33.6155 −1.56225 −0.781123 0.624377i \(-0.785353\pi\)
−0.781123 + 0.624377i \(0.785353\pi\)
\(464\) −3.28078 5.68247i −0.152306 0.263802i
\(465\) 0 0
\(466\) 8.84233 15.3154i 0.409613 0.709471i
\(467\) −39.8617 −1.84458 −0.922291 0.386497i \(-0.873685\pi\)
−0.922291 + 0.386497i \(0.873685\pi\)
\(468\) −2.84233 + 2.21837i −0.131387 + 0.102544i
\(469\) 50.7386 2.34289
\(470\) 0 0
\(471\) −11.0616 + 19.1592i −0.509689 + 0.882808i
\(472\) 5.28078 + 9.14657i 0.243067 + 0.421005i
\(473\) 18.8078 0.864782
\(474\) −3.71922 6.44188i −0.170830 0.295886i
\(475\) 0 0
\(476\) 18.2462 0.836314
\(477\) 2.21922 + 3.84381i 0.101611 + 0.175996i
\(478\) 6.68466 11.5782i 0.305749 0.529573i
\(479\) 10.8769 18.8393i 0.496978 0.860791i −0.503016 0.864277i \(-0.667776\pi\)
0.999994 + 0.00348601i \(0.00110963\pi\)
\(480\) 0 0
\(481\) 11.7192 9.14657i 0.534351 0.417048i
\(482\) 19.8769 0.905368
\(483\) −13.6847 + 23.7025i −0.622674 + 1.07850i
\(484\) −3.00000 + 5.19615i −0.136364 + 0.236189i
\(485\) 0 0
\(486\) 1.00000 0.0453609
\(487\) −12.0270 20.8314i −0.544995 0.943959i −0.998607 0.0527597i \(-0.983198\pi\)
0.453612 0.891199i \(-0.350135\pi\)
\(488\) 3.00000 + 5.19615i 0.135804 + 0.235219i
\(489\) −18.5616 −0.839382
\(490\) 0 0
\(491\) 10.7808 18.6729i 0.486530 0.842694i −0.513350 0.858179i \(-0.671596\pi\)
0.999880 + 0.0154850i \(0.00492923\pi\)
\(492\) −2.12311 + 3.67733i −0.0957170 + 0.165787i
\(493\) −33.6155 −1.51397
\(494\) 11.9039 + 4.81645i 0.535581 + 0.216702i
\(495\) 0 0
\(496\) −2.84233 + 4.92306i −0.127624 + 0.221052i
\(497\) −8.68466 + 15.0423i −0.389560 + 0.674738i
\(498\) 0.561553 + 0.972638i 0.0251638 + 0.0435850i
\(499\) 4.00000 0.179065 0.0895323 0.995984i \(-0.471463\pi\)
0.0895323 + 0.995984i \(0.471463\pi\)
\(500\) 0 0
\(501\) 10.1847 + 17.6403i 0.455017 + 0.788113i
\(502\) −0.123106 −0.00549447
\(503\) −2.97301 5.14941i −0.132560 0.229601i 0.792103 0.610388i \(-0.208986\pi\)
−0.924663 + 0.380787i \(0.875653\pi\)
\(504\) −1.78078 + 3.08440i −0.0793221 + 0.137390i
\(505\) 0 0
\(506\) 31.6847 1.40855
\(507\) 12.5000 3.57071i 0.555144 0.158581i
\(508\) 4.43845 0.196924
\(509\) 14.7732 25.5879i 0.654811 1.13417i −0.327131 0.944979i \(-0.606082\pi\)
0.981941 0.189186i \(-0.0605849\pi\)
\(510\) 0 0
\(511\) 27.3693 + 47.4050i 1.21075 + 2.09708i
\(512\) −1.00000 −0.0441942
\(513\) −1.78078 3.08440i −0.0786232 0.136179i
\(514\) 0.719224 + 1.24573i 0.0317236 + 0.0549469i
\(515\) 0 0
\(516\) −2.28078 3.95042i −0.100406 0.173908i
\(517\) −14.4309 + 24.9950i −0.634669 + 1.09928i
\(518\) 7.34233 12.7173i 0.322603 0.558766i
\(519\) −25.1771 −1.10515
\(520\) 0 0
\(521\) −18.6847 −0.818590 −0.409295 0.912402i \(-0.634225\pi\)
−0.409295 + 0.912402i \(0.634225\pi\)
\(522\) 3.28078 5.68247i 0.143596 0.248715i
\(523\) −4.59612 + 7.96071i −0.200974 + 0.348098i −0.948843 0.315749i \(-0.897744\pi\)
0.747868 + 0.663847i \(0.231077\pi\)
\(524\) −3.06155 5.30277i −0.133745 0.231652i
\(525\) 0 0
\(526\) 6.50000 + 11.2583i 0.283413 + 0.490887i
\(527\) 14.5616 + 25.2213i 0.634311 + 1.09866i
\(528\) 4.12311 0.179435
\(529\) −18.0270 31.2237i −0.783782 1.35755i
\(530\) 0 0
\(531\) −5.28078 + 9.14657i −0.229166 + 0.396927i
\(532\) 12.6847 0.549950
\(533\) 12.0691 9.41967i 0.522772 0.408011i
\(534\) 1.80776 0.0782296
\(535\) 0 0
\(536\) −7.12311 + 12.3376i −0.307671 + 0.532902i
\(537\) −0.157671 0.273094i −0.00680400 0.0117849i
\(538\) 3.36932 0.145262
\(539\) 11.7192 + 20.2983i 0.504783 + 0.874309i
\(540\) 0 0
\(541\) −2.63068 −0.113102 −0.0565510 0.998400i \(-0.518010\pi\)
−0.0565510 + 0.998400i \(0.518010\pi\)
\(542\) 16.0885 + 27.8662i 0.691062 + 1.19695i
\(543\) 5.56155 9.63289i 0.238669 0.413387i
\(544\) −2.56155 + 4.43674i −0.109826 + 0.190224i
\(545\) 0 0
\(546\) 10.1231 7.90084i 0.433229 0.338125i
\(547\) −35.6155 −1.52281 −0.761405 0.648276i \(-0.775490\pi\)
−0.761405 + 0.648276i \(0.775490\pi\)
\(548\) −4.40388 + 7.62775i −0.188125 + 0.325841i
\(549\) −3.00000 + 5.19615i −0.128037 + 0.221766i
\(550\) 0 0
\(551\) −23.3693 −0.995566
\(552\) −3.84233 6.65511i −0.163540 0.283260i
\(553\) 13.2462 + 22.9431i 0.563286 + 0.975640i
\(554\) −1.00000 −0.0424859
\(555\) 0 0
\(556\) −4.21922 + 7.30791i −0.178935 + 0.309924i
\(557\) −2.21922 + 3.84381i −0.0940315 + 0.162867i −0.909204 0.416351i \(-0.863309\pi\)
0.815172 + 0.579218i \(0.196642\pi\)
\(558\) −5.68466 −0.240651
\(559\) 2.28078 + 16.2880i 0.0964666 + 0.688909i
\(560\) 0 0
\(561\) 10.5616 18.2931i 0.445909 0.772337i
\(562\) −0.123106 + 0.213225i −0.00519290 + 0.00899436i
\(563\) 16.4924 + 28.5657i 0.695073 + 1.20390i 0.970156 + 0.242481i \(0.0779612\pi\)
−0.275083 + 0.961420i \(0.588705\pi\)
\(564\) 7.00000 0.294753
\(565\) 0 0
\(566\) −5.71922 9.90599i −0.240397 0.416380i
\(567\) −3.56155 −0.149571
\(568\) −2.43845 4.22351i −0.102315 0.177215i
\(569\) 9.58854 16.6078i 0.401973 0.696237i −0.591991 0.805944i \(-0.701658\pi\)
0.993964 + 0.109707i \(0.0349914\pi\)
\(570\) 0 0
\(571\) 11.3153 0.473532 0.236766 0.971567i \(-0.423912\pi\)
0.236766 + 0.971567i \(0.423912\pi\)
\(572\) −13.7808 5.57586i −0.576203 0.233138i
\(573\) −19.1231 −0.798879
\(574\) 7.56155 13.0970i 0.315613 0.546658i
\(575\) 0 0
\(576\) −0.500000 0.866025i −0.0208333 0.0360844i
\(577\) −8.73863 −0.363794 −0.181897 0.983318i \(-0.558224\pi\)
−0.181897 + 0.983318i \(0.558224\pi\)
\(578\) 4.62311 + 8.00745i 0.192296 + 0.333066i
\(579\) 0 0
\(580\) 0 0
\(581\) −2.00000 3.46410i −0.0829740 0.143715i
\(582\) 0.561553 0.972638i 0.0232771 0.0403171i
\(583\) −9.15009 + 15.8484i −0.378958 + 0.656375i
\(584\) −15.3693 −0.635987
\(585\) 0 0
\(586\) −24.9309 −1.02988
\(587\) −11.8769 + 20.5714i −0.490212 + 0.849072i −0.999937 0.0112657i \(-0.996414\pi\)
0.509725 + 0.860338i \(0.329747\pi\)
\(588\) 2.84233 4.92306i 0.117216 0.203024i
\(589\) 10.1231 + 17.5337i 0.417115 + 0.722465i
\(590\) 0 0
\(591\) 3.90388 + 6.76172i 0.160584 + 0.278140i
\(592\) 2.06155 + 3.57071i 0.0847293 + 0.146755i
\(593\) 12.1771 0.500053 0.250026 0.968239i \(-0.419561\pi\)
0.250026 + 0.968239i \(0.419561\pi\)
\(594\) 2.06155 + 3.57071i 0.0845865 + 0.146508i
\(595\) 0 0
\(596\) 11.4039 19.7521i 0.467121 0.809078i
\(597\) −11.1231 −0.455238
\(598\) 3.84233 + 27.4397i 0.157125 + 1.12209i
\(599\) −14.0000 −0.572024 −0.286012 0.958226i \(-0.592330\pi\)
−0.286012 + 0.958226i \(0.592330\pi\)
\(600\) 0 0
\(601\) 17.9924 31.1638i 0.733926 1.27120i −0.221267 0.975213i \(-0.571019\pi\)
0.955193 0.295984i \(-0.0956476\pi\)
\(602\) 8.12311 + 14.0696i 0.331073 + 0.573435i
\(603\) −14.2462 −0.580151
\(604\) −4.68466 8.11407i −0.190616 0.330157i
\(605\) 0 0
\(606\) −17.1231 −0.695579
\(607\) −14.7116 25.4813i −0.597127 1.03425i −0.993243 0.116054i \(-0.962975\pi\)
0.396116 0.918201i \(-0.370358\pi\)
\(608\) −1.78078 + 3.08440i −0.0722200 + 0.125089i
\(609\) −11.6847 + 20.2384i −0.473486 + 0.820102i
\(610\) 0 0
\(611\) −23.3963 9.46641i −0.946513 0.382970i
\(612\) −5.12311 −0.207089
\(613\) 14.0616 24.3553i 0.567941 0.983702i −0.428829 0.903386i \(-0.641074\pi\)
0.996769 0.0803164i \(-0.0255931\pi\)
\(614\) 7.80776 13.5234i 0.315096 0.545762i
\(615\) 0 0
\(616\) −14.6847 −0.591662
\(617\) −20.8423 36.1000i −0.839081 1.45333i −0.890664 0.454662i \(-0.849760\pi\)
0.0515837 0.998669i \(-0.483573\pi\)
\(618\) 0.219224 + 0.379706i 0.00881847 + 0.0152740i
\(619\) −16.4384 −0.660717 −0.330358 0.943856i \(-0.607170\pi\)
−0.330358 + 0.943856i \(0.607170\pi\)
\(620\) 0 0
\(621\) 3.84233 6.65511i 0.154187 0.267060i
\(622\) −9.36932 + 16.2281i −0.375675 + 0.650689i
\(623\) −6.43845 −0.257951
\(624\) 0.500000 + 3.57071i 0.0200160 + 0.142943i
\(625\) 0 0
\(626\) −3.31534 + 5.74234i −0.132508 + 0.229510i
\(627\) 7.34233 12.7173i 0.293224 0.507880i
\(628\) 11.0616 + 19.1592i 0.441404 + 0.764534i
\(629\) 21.1231 0.842233
\(630\) 0 0
\(631\) 15.1231 + 26.1940i 0.602041 + 1.04277i 0.992512 + 0.122151i \(0.0389791\pi\)
−0.390470 + 0.920616i \(0.627688\pi\)
\(632\) −7.43845 −0.295886
\(633\) 3.46543 + 6.00231i 0.137739 + 0.238570i
\(634\) 2.09612 3.63058i 0.0832475 0.144189i
\(635\) 0 0
\(636\) 4.43845 0.175996
\(637\) −16.1577 + 12.6107i −0.640190 + 0.499653i
\(638\) 27.0540 1.07108
\(639\) 2.43845 4.22351i 0.0964635 0.167080i
\(640\) 0 0
\(641\) 7.78078 + 13.4767i 0.307322 + 0.532298i 0.977776 0.209654i \(-0.0672337\pi\)
−0.670453 + 0.741952i \(0.733900\pi\)
\(642\) −2.00000 −0.0789337
\(643\) 19.1231 + 33.1222i 0.754142 + 1.30621i 0.945800 + 0.324750i \(0.105280\pi\)
−0.191658 + 0.981462i \(0.561387\pi\)
\(644\) 13.6847 + 23.7025i 0.539251 + 0.934010i
\(645\) 0 0
\(646\) 9.12311 + 15.8017i 0.358944 + 0.621709i
\(647\) −1.02699 + 1.77879i −0.0403751 + 0.0699316i −0.885507 0.464626i \(-0.846189\pi\)
0.845132 + 0.534558i \(0.179522\pi\)
\(648\) 0.500000 0.866025i 0.0196419 0.0340207i
\(649\) −43.5464 −1.70935
\(650\) 0 0
\(651\) 20.2462 0.793512
\(652\) −9.28078 + 16.0748i −0.363463 + 0.629537i
\(653\) −20.2192 + 35.0207i −0.791239 + 1.37047i 0.133961 + 0.990987i \(0.457230\pi\)
−0.925200 + 0.379480i \(0.876103\pi\)
\(654\) 10.1231 + 17.5337i 0.395845 + 0.685623i
\(655\) 0 0
\(656\) 2.12311 + 3.67733i 0.0828933 + 0.143575i
\(657\) −7.68466 13.3102i −0.299807 0.519281i
\(658\) −24.9309 −0.971906
\(659\) −15.5270 26.8935i −0.604846 1.04762i −0.992076 0.125640i \(-0.959902\pi\)
0.387230 0.921983i \(-0.373432\pi\)
\(660\) 0 0
\(661\) 5.80776 10.0593i 0.225896 0.391263i −0.730692 0.682707i \(-0.760802\pi\)
0.956588 + 0.291444i \(0.0941358\pi\)
\(662\) 18.7386 0.728298
\(663\) 17.1231 + 6.92820i 0.665006 + 0.269069i
\(664\) 1.12311 0.0435850
\(665\) 0 0
\(666\) −2.06155 + 3.57071i −0.0798835 + 0.138362i
\(667\) −25.2116 43.6679i −0.976199 1.69083i
\(668\) 20.3693 0.788113
\(669\) 13.1501 + 22.7766i 0.508412 + 0.880595i
\(670\) 0 0
\(671\) −24.7386 −0.955024
\(672\) 1.78078 + 3.08440i 0.0686949 + 0.118983i
\(673\) 21.1231 36.5863i 0.814236 1.41030i −0.0956394 0.995416i \(-0.530490\pi\)
0.909875 0.414882i \(-0.136177\pi\)
\(674\) 3.00000 5.19615i 0.115556 0.200148i
\(675\) 0 0
\(676\) 3.15767 12.6107i 0.121449 0.485026i
\(677\) 28.8769 1.10983 0.554915 0.831907i \(-0.312751\pi\)
0.554915 + 0.831907i \(0.312751\pi\)
\(678\) −1.84233 + 3.19101i −0.0707542 + 0.122550i
\(679\) −2.00000 + 3.46410i −0.0767530 + 0.132940i
\(680\) 0 0
\(681\) −20.0000 −0.766402
\(682\) −11.7192 20.2983i −0.448752 0.777262i
\(683\) 4.43845 + 7.68762i 0.169832 + 0.294158i 0.938361 0.345657i \(-0.112344\pi\)
−0.768528 + 0.639816i \(0.779011\pi\)
\(684\) −3.56155 −0.136179
\(685\) 0 0
\(686\) 2.34233 4.05703i 0.0894305 0.154898i
\(687\) −3.87689 + 6.71498i −0.147913 + 0.256192i
\(688\) −4.56155 −0.173908
\(689\) −14.8348 6.00231i −0.565159 0.228670i
\(690\) 0 0
\(691\) 8.21922 14.2361i 0.312674 0.541567i −0.666266 0.745714i \(-0.732109\pi\)
0.978940 + 0.204147i \(0.0654419\pi\)
\(692\) −12.5885 + 21.8040i −0.478545 + 0.828863i
\(693\) −7.34233 12.7173i −0.278912 0.483090i
\(694\) 9.12311 0.346308
\(695\) 0 0
\(696\) −3.28078 5.68247i −0.124358 0.215394i
\(697\) 21.7538 0.823984
\(698\) −12.2462 21.2111i −0.463526 0.802850i
\(699\) 8.84233 15.3154i 0.334448 0.579280i
\(700\) 0 0
\(701\) 17.3002 0.653419 0.326710 0.945125i \(-0.394060\pi\)
0.326710 + 0.945125i \(0.394060\pi\)
\(702\) −2.84233 + 2.21837i −0.107277 + 0.0837270i
\(703\) 14.6847 0.553842
\(704\) 2.06155 3.57071i 0.0776977 0.134576i
\(705\) 0 0
\(706\) −15.9309 27.5931i −0.599566 1.03848i
\(707\) 60.9848 2.29357
\(708\) 5.28078 + 9.14657i 0.198464 + 0.343749i
\(709\) −8.87689 15.3752i −0.333379 0.577429i 0.649793 0.760111i \(-0.274855\pi\)
−0.983172 + 0.182682i \(0.941522\pi\)
\(710\) 0 0
\(711\) −3.71922 6.44188i −0.139482 0.241590i
\(712\) 0.903882 1.56557i 0.0338744 0.0586722i
\(713\) −21.8423 + 37.8320i −0.818002 + 1.41682i
\(714\) 18.2462 0.682847
\(715\) 0 0
\(716\) −0.315342 −0.0117849
\(717\) 6.68466 11.5782i 0.249643 0.432395i
\(718\) 2.43845 4.22351i 0.0910020 0.157620i
\(719\) 10.4924 + 18.1734i 0.391301 + 0.677754i 0.992621 0.121254i \(-0.0386917\pi\)
−0.601320 + 0.799008i \(0.705358\pi\)
\(720\) 0 0
\(721\) −0.780776 1.35234i −0.0290776 0.0503639i
\(722\) −3.15767 5.46925i −0.117516 0.203544i
\(723\) 19.8769 0.739230
\(724\) −5.56155 9.63289i −0.206693 0.358004i
\(725\) 0 0
\(726\) −3.00000 + 5.19615i −0.111340 + 0.192847i
\(727\) 23.4233 0.868722 0.434361 0.900739i \(-0.356974\pi\)
0.434361 + 0.900739i \(0.356974\pi\)
\(728\) −1.78078 12.7173i −0.0660000 0.471334i
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −11.6847 + 20.2384i −0.432173 + 0.748545i
\(732\) 3.00000 + 5.19615i 0.110883 + 0.192055i
\(733\) −48.9309 −1.80730 −0.903651 0.428269i \(-0.859124\pi\)
−0.903651 + 0.428269i \(0.859124\pi\)
\(734\) 10.2462 + 17.7470i 0.378195 + 0.655052i
\(735\) 0 0
\(736\) −7.68466 −0.283260
\(737\) −29.3693 50.8691i −1.08183 1.87379i
\(738\) −2.12311 + 3.67733i −0.0781526 + 0.135364i
\(739\) −21.2732 + 36.8463i −0.782547 + 1.35541i 0.147906 + 0.989001i \(0.452747\pi\)
−0.930453 + 0.366410i \(0.880587\pi\)
\(740\) 0 0
\(741\) 11.9039 + 4.81645i 0.437300 + 0.176937i
\(742\) −15.8078 −0.580321
\(743\) −16.0885 + 27.8662i −0.590231 + 1.02231i 0.403970 + 0.914772i \(0.367630\pi\)
−0.994201 + 0.107538i \(0.965703\pi\)
\(744\) −2.84233 + 4.92306i −0.104205 + 0.180488i
\(745\) 0 0
\(746\) −5.19224 −0.190101
\(747\) 0.561553 + 0.972638i 0.0205461 + 0.0355870i
\(748\) −10.5616 18.2931i −0.386169 0.668864i
\(749\) 7.12311 0.260273
\(750\) 0 0
\(751\) 1.59612 2.76456i 0.0582432 0.100880i −0.835434 0.549591i \(-0.814783\pi\)
0.893677 + 0.448711i \(0.148117\pi\)
\(752\) 3.50000 6.06218i 0.127632 0.221065i
\(753\) −0.123106 −0.00448622
\(754\) 3.28078 + 23.4294i 0.119479 + 0.853250i
\(755\) 0 0
\(756\) −1.78078 + 3.08440i −0.0647662 + 0.112178i
\(757\) 16.7116 28.9454i 0.607395 1.05204i −0.384273 0.923220i \(-0.625548\pi\)
0.991668 0.128820i \(-0.0411188\pi\)
\(758\) −2.65767 4.60322i −0.0965309 0.167197i
\(759\) 31.6847 1.15008
\(760\) 0 0
\(761\) −5.46543 9.46641i −0.198122 0.343157i 0.749798 0.661667i \(-0.230151\pi\)
−0.947919 + 0.318510i \(0.896818\pi\)
\(762\) 4.43845 0.160788
\(763\) −36.0540 62.4473i −1.30524 2.26074i
\(764\) −9.56155 + 16.5611i −0.345925 + 0.599159i
\(765\) 0 0
\(766\) 20.8078 0.751815
\(767\) −5.28078 37.7123i −0.190678 1.36171i
\(768\) −1.00000 −0.0360844
\(769\) 22.8423 39.5641i 0.823715 1.42672i −0.0791816 0.996860i \(-0.525231\pi\)
0.902897 0.429857i \(-0.141436\pi\)
\(770\) 0 0
\(771\) 0.719224 + 1.24573i 0.0259022 + 0.0448639i
\(772\) 0 0
\(773\) −10.5885 18.3399i −0.380843 0.659640i 0.610340 0.792140i \(-0.291033\pi\)
−0.991183 + 0.132500i \(0.957700\pi\)
\(774\) −2.28078 3.95042i −0.0819808 0.141995i
\(775\) 0 0
\(776\) −0.561553 0.972638i −0.0201586 0.0349157i
\(777\) 7.34233 12.7173i 0.263405 0.456230i
\(778\) 9.52699 16.5012i 0.341559 0.591598i
\(779\) 15.1231 0.541841
\(780\) 0 0
\(781\) 20.1080 0.719519
\(782\) −19.6847 + 34.0948i −0.703922 + 1.21923i
\(783\) 3.28078 5.68247i 0.117245 0.203075i
\(784\) −2.84233 4.92306i −0.101512 0.175824i
\(785\) 0 0
\(786\) −3.06155 5.30277i −0.109202 0.189143i