Properties

Label 1950.2.z.n.1849.3
Level $1950$
Weight $2$
Character 1950.1849
Analytic conductor $15.571$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1950.z (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(15.5708283941\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: 8.0.1731891456.1
Defining polynomial: \(x^{8} - 9 x^{6} + 65 x^{4} - 144 x^{2} + 256\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 390)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 1849.3
Root \(-2.21837 - 1.28078i\) of defining polynomial
Character \(\chi\) \(=\) 1950.1849
Dual form 1950.2.z.n.1699.3

$q$-expansion

\(f(q)\) \(=\) \(q+(0.866025 - 0.500000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{6} +(-3.08440 - 1.78078i) q^{7} -1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(0.866025 - 0.500000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{6} +(-3.08440 - 1.78078i) q^{7} -1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(2.06155 + 3.57071i) q^{11} +1.00000i q^{12} +(1.35234 + 3.34233i) q^{13} -3.56155 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-4.43674 - 2.56155i) q^{17} -1.00000i q^{18} +(-1.78078 + 3.08440i) q^{19} +3.56155 q^{21} +(3.57071 + 2.06155i) q^{22} +(6.65511 - 3.84233i) q^{23} +(0.500000 + 0.866025i) q^{24} +(2.84233 + 2.21837i) q^{26} +1.00000i q^{27} +(-3.08440 + 1.78078i) q^{28} +(3.28078 + 5.68247i) q^{29} +5.68466 q^{31} +(-0.866025 - 0.500000i) q^{32} +(-3.57071 - 2.06155i) q^{33} -5.12311 q^{34} +(-0.500000 - 0.866025i) q^{36} +(3.57071 - 2.06155i) q^{37} +3.56155i q^{38} +(-2.84233 - 2.21837i) q^{39} +(2.12311 + 3.67733i) q^{41} +(3.08440 - 1.78078i) q^{42} +(3.95042 + 2.28078i) q^{43} +4.12311 q^{44} +(3.84233 - 6.65511i) q^{46} +7.00000i q^{47} +(0.866025 + 0.500000i) q^{48} +(2.84233 + 4.92306i) q^{49} +5.12311 q^{51} +(3.57071 + 0.500000i) q^{52} -4.43845i q^{53} +(0.500000 + 0.866025i) q^{54} +(-1.78078 + 3.08440i) q^{56} -3.56155i q^{57} +(5.68247 + 3.28078i) q^{58} +(5.28078 - 9.14657i) q^{59} +(-3.00000 + 5.19615i) q^{61} +(4.92306 - 2.84233i) q^{62} +(-3.08440 + 1.78078i) q^{63} -1.00000 q^{64} -4.12311 q^{66} +(12.3376 - 7.12311i) q^{67} +(-4.43674 + 2.56155i) q^{68} +(-3.84233 + 6.65511i) q^{69} +(2.43845 - 4.22351i) q^{71} +(-0.866025 - 0.500000i) q^{72} +15.3693i q^{73} +(2.06155 - 3.57071i) q^{74} +(1.78078 + 3.08440i) q^{76} -14.6847i q^{77} +(-3.57071 - 0.500000i) q^{78} -7.43845 q^{79} +(-0.500000 - 0.866025i) q^{81} +(3.67733 + 2.12311i) q^{82} -1.12311i q^{83} +(1.78078 - 3.08440i) q^{84} +4.56155 q^{86} +(-5.68247 - 3.28078i) q^{87} +(3.57071 - 2.06155i) q^{88} +(0.903882 + 1.56557i) q^{89} +(1.78078 - 12.7173i) q^{91} -7.68466i q^{92} +(-4.92306 + 2.84233i) q^{93} +(3.50000 + 6.06218i) q^{94} +1.00000 q^{96} +(-0.972638 - 0.561553i) q^{97} +(4.92306 + 2.84233i) q^{98} +4.12311 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 4q^{4} - 4q^{6} + 4q^{9} + O(q^{10}) \) \( 8q + 4q^{4} - 4q^{6} + 4q^{9} - 12q^{14} - 4q^{16} - 6q^{19} + 12q^{21} + 4q^{24} - 2q^{26} + 18q^{29} - 4q^{31} - 8q^{34} - 4q^{36} + 2q^{39} - 16q^{41} + 6q^{46} - 2q^{49} + 8q^{51} + 4q^{54} - 6q^{56} + 34q^{59} - 24q^{61} - 8q^{64} - 6q^{69} + 36q^{71} + 6q^{76} - 76q^{79} - 4q^{81} + 6q^{84} + 20q^{86} - 34q^{89} + 6q^{91} + 28q^{94} + 8q^{96} + O(q^{100}) \)

Character values

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

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.866025 0.500000i 0.612372 0.353553i
\(3\) −0.866025 + 0.500000i −0.500000 + 0.288675i
\(4\) 0.500000 0.866025i 0.250000 0.433013i
\(5\) 0 0
\(6\) −0.500000 + 0.866025i −0.204124 + 0.353553i
\(7\) −3.08440 1.78078i −1.16579 0.673070i −0.213107 0.977029i \(-0.568358\pi\)
−0.952685 + 0.303959i \(0.901692\pi\)
\(8\) 1.00000i 0.353553i
\(9\) 0.500000 0.866025i 0.166667 0.288675i
\(10\) 0 0
\(11\) 2.06155 + 3.57071i 0.621582 + 1.07661i 0.989191 + 0.146631i \(0.0468429\pi\)
−0.367610 + 0.929980i \(0.619824\pi\)
\(12\) 1.00000i 0.288675i
\(13\) 1.35234 + 3.34233i 0.375073 + 0.926995i
\(14\) −3.56155 −0.951865
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −4.43674 2.56155i −1.07607 0.621268i −0.146235 0.989250i \(-0.546715\pi\)
−0.929833 + 0.367982i \(0.880049\pi\)
\(18\) 1.00000i 0.235702i
\(19\) −1.78078 + 3.08440i −0.408538 + 0.707609i −0.994726 0.102566i \(-0.967295\pi\)
0.586188 + 0.810175i \(0.300628\pi\)
\(20\) 0 0
\(21\) 3.56155 0.777195
\(22\) 3.57071 + 2.06155i 0.761279 + 0.439525i
\(23\) 6.65511 3.84233i 1.38769 0.801181i 0.394632 0.918839i \(-0.370872\pi\)
0.993054 + 0.117658i \(0.0375387\pi\)
\(24\) 0.500000 + 0.866025i 0.102062 + 0.176777i
\(25\) 0 0
\(26\) 2.84233 + 2.21837i 0.557427 + 0.435058i
\(27\) 1.00000i 0.192450i
\(28\) −3.08440 + 1.78078i −0.582896 + 0.336535i
\(29\) 3.28078 + 5.68247i 0.609225 + 1.05521i 0.991368 + 0.131105i \(0.0418527\pi\)
−0.382144 + 0.924103i \(0.624814\pi\)
\(30\) 0 0
\(31\) 5.68466 1.02099 0.510497 0.859879i \(-0.329461\pi\)
0.510497 + 0.859879i \(0.329461\pi\)
\(32\) −0.866025 0.500000i −0.153093 0.0883883i
\(33\) −3.57071 2.06155i −0.621582 0.358870i
\(34\) −5.12311 −0.878605
\(35\) 0 0
\(36\) −0.500000 0.866025i −0.0833333 0.144338i
\(37\) 3.57071 2.06155i 0.587022 0.338917i −0.176897 0.984229i \(-0.556606\pi\)
0.763919 + 0.645312i \(0.223273\pi\)
\(38\) 3.56155i 0.577760i
\(39\) −2.84233 2.21837i −0.455137 0.355223i
\(40\) 0 0
\(41\) 2.12311 + 3.67733i 0.331573 + 0.574302i 0.982821 0.184564i \(-0.0590872\pi\)
−0.651247 + 0.758866i \(0.725754\pi\)
\(42\) 3.08440 1.78078i 0.475933 0.274780i
\(43\) 3.95042 + 2.28078i 0.602433 + 0.347815i 0.769998 0.638046i \(-0.220257\pi\)
−0.167565 + 0.985861i \(0.553590\pi\)
\(44\) 4.12311 0.621582
\(45\) 0 0
\(46\) 3.84233 6.65511i 0.566521 0.981242i
\(47\) 7.00000i 1.02105i 0.859861 + 0.510527i \(0.170550\pi\)
−0.859861 + 0.510527i \(0.829450\pi\)
\(48\) 0.866025 + 0.500000i 0.125000 + 0.0721688i
\(49\) 2.84233 + 4.92306i 0.406047 + 0.703294i
\(50\) 0 0
\(51\) 5.12311 0.717378
\(52\) 3.57071 + 0.500000i 0.495169 + 0.0693375i
\(53\) 4.43845i 0.609668i −0.952406 0.304834i \(-0.901399\pi\)
0.952406 0.304834i \(-0.0986009\pi\)
\(54\) 0.500000 + 0.866025i 0.0680414 + 0.117851i
\(55\) 0 0
\(56\) −1.78078 + 3.08440i −0.237966 + 0.412170i
\(57\) 3.56155i 0.471739i
\(58\) 5.68247 + 3.28078i 0.746145 + 0.430787i
\(59\) 5.28078 9.14657i 0.687499 1.19078i −0.285146 0.958484i \(-0.592042\pi\)
0.972645 0.232298i \(-0.0746246\pi\)
\(60\) 0 0
\(61\) −3.00000 + 5.19615i −0.384111 + 0.665299i −0.991645 0.128994i \(-0.958825\pi\)
0.607535 + 0.794293i \(0.292159\pi\)
\(62\) 4.92306 2.84233i 0.625229 0.360976i
\(63\) −3.08440 + 1.78078i −0.388597 + 0.224357i
\(64\) −1.00000 −0.125000
\(65\) 0 0
\(66\) −4.12311 −0.507519
\(67\) 12.3376 7.12311i 1.50728 0.870226i 0.507311 0.861763i \(-0.330639\pi\)
0.999964 0.00846293i \(-0.00269387\pi\)
\(68\) −4.43674 + 2.56155i −0.538034 + 0.310634i
\(69\) −3.84233 + 6.65511i −0.462562 + 0.801181i
\(70\) 0 0
\(71\) 2.43845 4.22351i 0.289390 0.501239i −0.684274 0.729225i \(-0.739881\pi\)
0.973664 + 0.227986i \(0.0732141\pi\)
\(72\) −0.866025 0.500000i −0.102062 0.0589256i
\(73\) 15.3693i 1.79884i 0.437083 + 0.899421i \(0.356012\pi\)
−0.437083 + 0.899421i \(0.643988\pi\)
\(74\) 2.06155 3.57071i 0.239651 0.415087i
\(75\) 0 0
\(76\) 1.78078 + 3.08440i 0.204269 + 0.353804i
\(77\) 14.6847i 1.67347i
\(78\) −3.57071 0.500000i −0.404304 0.0566139i
\(79\) −7.43845 −0.836891 −0.418445 0.908242i \(-0.637425\pi\)
−0.418445 + 0.908242i \(0.637425\pi\)
\(80\) 0 0
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 3.67733 + 2.12311i 0.406093 + 0.234458i
\(83\) 1.12311i 0.123277i −0.998099 0.0616384i \(-0.980367\pi\)
0.998099 0.0616384i \(-0.0196326\pi\)
\(84\) 1.78078 3.08440i 0.194299 0.336535i
\(85\) 0 0
\(86\) 4.56155 0.491885
\(87\) −5.68247 3.28078i −0.609225 0.351736i
\(88\) 3.57071 2.06155i 0.380639 0.219762i
\(89\) 0.903882 + 1.56557i 0.0958113 + 0.165950i 0.909947 0.414725i \(-0.136122\pi\)
−0.814136 + 0.580675i \(0.802789\pi\)
\(90\) 0 0
\(91\) 1.78078 12.7173i 0.186676 1.33313i
\(92\) 7.68466i 0.801181i
\(93\) −4.92306 + 2.84233i −0.510497 + 0.294736i
\(94\) 3.50000 + 6.06218i 0.360997 + 0.625266i
\(95\) 0 0
\(96\) 1.00000 0.102062
\(97\) −0.972638 0.561553i −0.0987564 0.0570170i 0.449808 0.893125i \(-0.351492\pi\)
−0.548565 + 0.836108i \(0.684826\pi\)
\(98\) 4.92306 + 2.84233i 0.497304 + 0.287119i
\(99\) 4.12311 0.414388
\(100\) 0 0
\(101\) 8.56155 + 14.8290i 0.851906 + 1.47555i 0.879486 + 0.475925i \(0.157887\pi\)
−0.0275793 + 0.999620i \(0.508780\pi\)
\(102\) 4.43674 2.56155i 0.439303 0.253632i
\(103\) 0.438447i 0.0432015i −0.999767 0.0216007i \(-0.993124\pi\)
0.999767 0.0216007i \(-0.00687626\pi\)
\(104\) 3.34233 1.35234i 0.327742 0.132608i
\(105\) 0 0
\(106\) −2.21922 3.84381i −0.215550 0.373344i
\(107\) 1.73205 1.00000i 0.167444 0.0966736i −0.413936 0.910306i \(-0.635846\pi\)
0.581380 + 0.813632i \(0.302513\pi\)
\(108\) 0.866025 + 0.500000i 0.0833333 + 0.0481125i
\(109\) 20.2462 1.93924 0.969618 0.244625i \(-0.0786650\pi\)
0.969618 + 0.244625i \(0.0786650\pi\)
\(110\) 0 0
\(111\) −2.06155 + 3.57071i −0.195674 + 0.338917i
\(112\) 3.56155i 0.336535i
\(113\) −3.19101 1.84233i −0.300185 0.173312i 0.342341 0.939576i \(-0.388780\pi\)
−0.642526 + 0.766264i \(0.722113\pi\)
\(114\) −1.78078 3.08440i −0.166785 0.288880i
\(115\) 0 0
\(116\) 6.56155 0.609225
\(117\) 3.57071 + 0.500000i 0.330113 + 0.0462250i
\(118\) 10.5616i 0.972270i
\(119\) 9.12311 + 15.8017i 0.836314 + 1.44854i
\(120\) 0 0
\(121\) −3.00000 + 5.19615i −0.272727 + 0.472377i
\(122\) 6.00000i 0.543214i
\(123\) −3.67733 2.12311i −0.331573 0.191434i
\(124\) 2.84233 4.92306i 0.255249 0.442104i
\(125\) 0 0
\(126\) −1.78078 + 3.08440i −0.158644 + 0.274780i
\(127\) −3.84381 + 2.21922i −0.341083 + 0.196924i −0.660751 0.750605i \(-0.729762\pi\)
0.319668 + 0.947530i \(0.396429\pi\)
\(128\) −0.866025 + 0.500000i −0.0765466 + 0.0441942i
\(129\) −4.56155 −0.401622
\(130\) 0 0
\(131\) 6.12311 0.534978 0.267489 0.963561i \(-0.413806\pi\)
0.267489 + 0.963561i \(0.413806\pi\)
\(132\) −3.57071 + 2.06155i −0.310791 + 0.179435i
\(133\) 10.9852 6.34233i 0.952541 0.549950i
\(134\) 7.12311 12.3376i 0.615343 1.06580i
\(135\) 0 0
\(136\) −2.56155 + 4.43674i −0.219651 + 0.380447i
\(137\) 7.62775 + 4.40388i 0.651682 + 0.376249i 0.789101 0.614264i \(-0.210547\pi\)
−0.137418 + 0.990513i \(0.543880\pi\)
\(138\) 7.68466i 0.654162i
\(139\) 4.21922 7.30791i 0.357870 0.619849i −0.629735 0.776810i \(-0.716836\pi\)
0.987605 + 0.156961i \(0.0501698\pi\)
\(140\) 0 0
\(141\) −3.50000 6.06218i −0.294753 0.510527i
\(142\) 4.87689i 0.409260i
\(143\) −9.14657 + 11.7192i −0.764875 + 0.980011i
\(144\) −1.00000 −0.0833333
\(145\) 0 0
\(146\) 7.68466 + 13.3102i 0.635987 + 1.10156i
\(147\) −4.92306 2.84233i −0.406047 0.234431i
\(148\) 4.12311i 0.338917i
\(149\) −11.4039 + 19.7521i −0.934242 + 1.61816i −0.158263 + 0.987397i \(0.550589\pi\)
−0.775979 + 0.630758i \(0.782744\pi\)
\(150\) 0 0
\(151\) 9.36932 0.762464 0.381232 0.924479i \(-0.375500\pi\)
0.381232 + 0.924479i \(0.375500\pi\)
\(152\) 3.08440 + 1.78078i 0.250177 + 0.144440i
\(153\) −4.43674 + 2.56155i −0.358689 + 0.207089i
\(154\) −7.34233 12.7173i −0.591662 1.02479i
\(155\) 0 0
\(156\) −3.34233 + 1.35234i −0.267601 + 0.108274i
\(157\) 22.1231i 1.76562i 0.469734 + 0.882808i \(0.344350\pi\)
−0.469734 + 0.882808i \(0.655650\pi\)
\(158\) −6.44188 + 3.71922i −0.512489 + 0.295886i
\(159\) 2.21922 + 3.84381i 0.175996 + 0.304834i
\(160\) 0 0
\(161\) −27.3693 −2.15700
\(162\) −0.866025 0.500000i −0.0680414 0.0392837i
\(163\) −16.0748 9.28078i −1.25907 0.726927i −0.286179 0.958176i \(-0.592385\pi\)
−0.972894 + 0.231250i \(0.925719\pi\)
\(164\) 4.24621 0.331573
\(165\) 0 0
\(166\) −0.561553 0.972638i −0.0435850 0.0754913i
\(167\) −17.6403 + 10.1847i −1.36505 + 0.788113i −0.990291 0.139009i \(-0.955608\pi\)
−0.374760 + 0.927122i \(0.622275\pi\)
\(168\) 3.56155i 0.274780i
\(169\) −9.34233 + 9.03996i −0.718641 + 0.695382i
\(170\) 0 0
\(171\) 1.78078 + 3.08440i 0.136179 + 0.235870i
\(172\) 3.95042 2.28078i 0.301217 0.173908i
\(173\) −21.8040 12.5885i −1.65773 0.957089i −0.973760 0.227575i \(-0.926920\pi\)
−0.683966 0.729514i \(-0.739746\pi\)
\(174\) −6.56155 −0.497430
\(175\) 0 0
\(176\) 2.06155 3.57071i 0.155395 0.269153i
\(177\) 10.5616i 0.793855i
\(178\) 1.56557 + 0.903882i 0.117344 + 0.0677488i
\(179\) −0.157671 0.273094i −0.0117849 0.0204120i 0.860073 0.510171i \(-0.170418\pi\)
−0.871858 + 0.489759i \(0.837085\pi\)
\(180\) 0 0
\(181\) 11.1231 0.826774 0.413387 0.910555i \(-0.364346\pi\)
0.413387 + 0.910555i \(0.364346\pi\)
\(182\) −4.81645 11.9039i −0.357019 0.882374i
\(183\) 6.00000i 0.443533i
\(184\) −3.84233 6.65511i −0.283260 0.490621i
\(185\) 0 0
\(186\) −2.84233 + 4.92306i −0.208410 + 0.360976i
\(187\) 21.1231i 1.54467i
\(188\) 6.06218 + 3.50000i 0.442130 + 0.255264i
\(189\) 1.78078 3.08440i 0.129532 0.224357i
\(190\) 0 0
\(191\) −9.56155 + 16.5611i −0.691850 + 1.19832i 0.279381 + 0.960180i \(0.409871\pi\)
−0.971231 + 0.238139i \(0.923463\pi\)
\(192\) 0.866025 0.500000i 0.0625000 0.0360844i
\(193\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(194\) −1.12311 −0.0806343
\(195\) 0 0
\(196\) 5.68466 0.406047
\(197\) −6.76172 + 3.90388i −0.481753 + 0.278140i −0.721147 0.692782i \(-0.756385\pi\)
0.239394 + 0.970923i \(0.423051\pi\)
\(198\) 3.57071 2.06155i 0.253760 0.146508i
\(199\) 5.56155 9.63289i 0.394248 0.682858i −0.598757 0.800931i \(-0.704338\pi\)
0.993005 + 0.118073i \(0.0376718\pi\)
\(200\) 0 0
\(201\) −7.12311 + 12.3376i −0.502425 + 0.870226i
\(202\) 14.8290 + 8.56155i 1.04337 + 0.602389i
\(203\) 23.3693i 1.64020i
\(204\) 2.56155 4.43674i 0.179345 0.310634i
\(205\) 0 0
\(206\) −0.219224 0.379706i −0.0152740 0.0264554i
\(207\) 7.68466i 0.534121i
\(208\) 2.21837 2.84233i 0.153816 0.197080i
\(209\) −14.6847 −1.01576
\(210\) 0 0
\(211\) −3.46543 6.00231i −0.238570 0.413216i 0.721734 0.692171i \(-0.243345\pi\)
−0.960304 + 0.278955i \(0.910012\pi\)
\(212\) −3.84381 2.21922i −0.263994 0.152417i
\(213\) 4.87689i 0.334159i
\(214\) 1.00000 1.73205i 0.0683586 0.118401i
\(215\) 0 0
\(216\) 1.00000 0.0680414
\(217\) −17.5337 10.1231i −1.19027 0.687201i
\(218\) 17.5337 10.1231i 1.18753 0.685623i
\(219\) −7.68466 13.3102i −0.519281 0.899421i
\(220\) 0 0
\(221\) 2.56155 18.2931i 0.172309 1.23053i
\(222\) 4.12311i 0.276725i
\(223\) 22.7766 13.1501i 1.52524 0.880595i 0.525683 0.850680i \(-0.323810\pi\)
0.999552 0.0299151i \(-0.00952371\pi\)
\(224\) 1.78078 + 3.08440i 0.118983 + 0.206085i
\(225\) 0 0
\(226\) −3.68466 −0.245100
\(227\) 17.3205 + 10.0000i 1.14960 + 0.663723i 0.948790 0.315906i \(-0.102309\pi\)
0.200812 + 0.979630i \(0.435642\pi\)
\(228\) −3.08440 1.78078i −0.204269 0.117935i
\(229\) 7.75379 0.512385 0.256192 0.966626i \(-0.417532\pi\)
0.256192 + 0.966626i \(0.417532\pi\)
\(230\) 0 0
\(231\) 7.34233 + 12.7173i 0.483090 + 0.836736i
\(232\) 5.68247 3.28078i 0.373073 0.215394i
\(233\) 17.6847i 1.15856i 0.815128 + 0.579280i \(0.196666\pi\)
−0.815128 + 0.579280i \(0.803334\pi\)
\(234\) 3.34233 1.35234i 0.218495 0.0884055i
\(235\) 0 0
\(236\) −5.28078 9.14657i −0.343749 0.595391i
\(237\) 6.44188 3.71922i 0.418445 0.241590i
\(238\) 15.8017 + 9.12311i 1.02427 + 0.591363i
\(239\) −13.3693 −0.864789 −0.432395 0.901684i \(-0.642331\pi\)
−0.432395 + 0.901684i \(0.642331\pi\)
\(240\) 0 0
\(241\) 9.93845 17.2139i 0.640192 1.10884i −0.345198 0.938530i \(-0.612188\pi\)
0.985390 0.170315i \(-0.0544784\pi\)
\(242\) 6.00000i 0.385695i
\(243\) 0.866025 + 0.500000i 0.0555556 + 0.0320750i
\(244\) 3.00000 + 5.19615i 0.192055 + 0.332650i
\(245\) 0 0
\(246\) −4.24621 −0.270729
\(247\) −12.7173 1.78078i −0.809182 0.113308i
\(248\) 5.68466i 0.360976i
\(249\) 0.561553 + 0.972638i 0.0355870 + 0.0616384i
\(250\) 0 0
\(251\) −0.0615528 + 0.106613i −0.00388518 + 0.00672933i −0.867961 0.496632i \(-0.834570\pi\)
0.864076 + 0.503361i \(0.167903\pi\)
\(252\) 3.56155i 0.224357i
\(253\) 27.4397 + 15.8423i 1.72512 + 0.995999i
\(254\) −2.21922 + 3.84381i −0.139246 + 0.241182i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −1.24573 + 0.719224i −0.0777066 + 0.0448639i −0.538350 0.842721i \(-0.680952\pi\)
0.460643 + 0.887585i \(0.347619\pi\)
\(258\) −3.95042 + 2.28078i −0.245942 + 0.141995i
\(259\) −14.6847 −0.912460
\(260\) 0 0
\(261\) 6.56155 0.406150
\(262\) 5.30277 3.06155i 0.327606 0.189143i
\(263\) 11.2583 6.50000i 0.694218 0.400807i −0.110972 0.993824i \(-0.535396\pi\)
0.805190 + 0.593016i \(0.202063\pi\)
\(264\) −2.06155 + 3.57071i −0.126880 + 0.219762i
\(265\) 0 0
\(266\) 6.34233 10.9852i 0.388873 0.673548i
\(267\) −1.56557 0.903882i −0.0958113 0.0553167i
\(268\) 14.2462i 0.870226i
\(269\) −1.68466 + 2.91791i −0.102715 + 0.177908i −0.912803 0.408401i \(-0.866086\pi\)
0.810087 + 0.586310i \(0.199420\pi\)
\(270\) 0 0
\(271\) −16.0885 27.8662i −0.977309 1.69275i −0.672094 0.740466i \(-0.734605\pi\)
−0.305215 0.952283i \(-0.598728\pi\)
\(272\) 5.12311i 0.310634i
\(273\) 4.81645 + 11.9039i 0.291505 + 0.720456i
\(274\) 8.80776 0.532096
\(275\) 0 0
\(276\) 3.84233 + 6.65511i 0.231281 + 0.400591i
\(277\) 0.866025 + 0.500000i 0.0520344 + 0.0300421i 0.525792 0.850613i \(-0.323769\pi\)
−0.473757 + 0.880656i \(0.657103\pi\)
\(278\) 8.43845i 0.506104i
\(279\) 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 \(0.502338\pi\)
\(282\) −6.06218 3.50000i −0.360997 0.208422i
\(283\) −9.90599 + 5.71922i −0.588850 + 0.339973i −0.764643 0.644455i \(-0.777084\pi\)
0.175793 + 0.984427i \(0.443751\pi\)
\(284\) −2.43845 4.22351i −0.144695 0.250619i
\(285\) 0 0
\(286\) −2.06155 + 14.7224i −0.121902 + 0.870556i
\(287\) 15.1231i 0.892689i
\(288\) −0.866025 + 0.500000i −0.0510310 + 0.0294628i
\(289\) 4.62311 + 8.00745i 0.271947 + 0.471027i
\(290\) 0 0
\(291\) 1.12311 0.0658376
\(292\) 13.3102 + 7.68466i 0.778922 + 0.449711i
\(293\) −21.5908 12.4654i −1.26135 0.728238i −0.288011 0.957627i \(-0.592994\pi\)
−0.973335 + 0.229389i \(0.926327\pi\)
\(294\) −5.68466 −0.331536
\(295\) 0 0
\(296\) −2.06155 3.57071i −0.119825 0.207544i
\(297\) −3.57071 + 2.06155i −0.207194 + 0.119623i
\(298\) 22.8078i 1.32122i
\(299\) 21.8423 + 17.0474i 1.26317 + 0.985877i
\(300\) 0 0
\(301\) −8.12311 14.0696i −0.468208 0.810960i
\(302\) 8.11407 4.68466i 0.466912 0.269572i
\(303\) −14.8290 8.56155i −0.851906 0.491848i
\(304\) 3.56155 0.204269
\(305\) 0 0
\(306\) −2.56155 + 4.43674i −0.146434 + 0.253632i
\(307\) 15.6155i 0.891225i −0.895226 0.445613i \(-0.852986\pi\)
0.895226 0.445613i \(-0.147014\pi\)
\(308\) −12.7173 7.34233i −0.724635 0.418368i
\(309\) 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 \(0.678291\pi\)
\(312\) −2.21837 + 2.84233i −0.125590 + 0.160915i
\(313\) 6.63068i 0.374788i −0.982285 0.187394i \(-0.939996\pi\)
0.982285 0.187394i \(-0.0600042\pi\)
\(314\) 11.0616 + 19.1592i 0.624240 + 1.08121i
\(315\) 0 0
\(316\) −3.71922 + 6.44188i −0.209223 + 0.362384i
\(317\) 4.19224i 0.235459i −0.993046 0.117730i \(-0.962438\pi\)
0.993046 0.117730i \(-0.0375616\pi\)
\(318\) 3.84381 + 2.21922i 0.215550 + 0.124448i
\(319\) −13.5270 + 23.4294i −0.757366 + 1.31180i
\(320\) 0 0
\(321\) −1.00000 + 1.73205i −0.0558146 + 0.0966736i
\(322\) −23.7025 + 13.6847i −1.32089 + 0.762616i
\(323\) 15.8017 9.12311i 0.879229 0.507623i
\(324\) −1.00000 −0.0555556
\(325\) 0 0
\(326\) −18.5616 −1.02803
\(327\) −17.5337 + 10.1231i −0.969618 + 0.559809i
\(328\) 3.67733 2.12311i 0.203046 0.117229i
\(329\) 12.4654 21.5908i 0.687242 1.19034i
\(330\) 0 0
\(331\) 9.36932 16.2281i 0.514984 0.891979i −0.484865 0.874589i \(-0.661131\pi\)
0.999849 0.0173896i \(-0.00553556\pi\)
\(332\) −0.972638 0.561553i −0.0533804 0.0308192i
\(333\) 4.12311i 0.225945i
\(334\) −10.1847 + 17.6403i −0.557280 + 0.965237i
\(335\) 0 0
\(336\) −1.78078 3.08440i −0.0971493 0.168268i
\(337\) 6.00000i 0.326841i −0.986557 0.163420i \(-0.947747\pi\)
0.986557 0.163420i \(-0.0522527\pi\)
\(338\) −3.57071 + 12.5000i −0.194221 + 0.679910i
\(339\) 3.68466 0.200123
\(340\) 0 0
\(341\) 11.7192 + 20.2983i 0.634632 + 1.09921i
\(342\) 3.08440 + 1.78078i 0.166785 + 0.0962934i
\(343\) 4.68466i 0.252948i
\(344\) 2.28078 3.95042i 0.122971 0.212992i
\(345\) 0 0
\(346\) −25.1771 −1.35353
\(347\) −7.90084 4.56155i −0.424139 0.244877i 0.272707 0.962097i \(-0.412081\pi\)
−0.696847 + 0.717220i \(0.745414\pi\)
\(348\) −5.68247 + 3.28078i −0.304612 + 0.175868i
\(349\) −12.2462 21.2111i −0.655525 1.13540i −0.981762 0.190114i \(-0.939114\pi\)
0.326237 0.945288i \(-0.394219\pi\)
\(350\) 0 0
\(351\) −3.34233 + 1.35234i −0.178400 + 0.0721828i
\(352\) 4.12311i 0.219762i
\(353\) −27.5931 + 15.9309i −1.46863 + 0.847915i −0.999382 0.0351511i \(-0.988809\pi\)
−0.469249 + 0.883066i \(0.655475\pi\)
\(354\) 5.28078 + 9.14657i 0.280670 + 0.486135i
\(355\) 0 0
\(356\) 1.80776 0.0958113
\(357\) −15.8017 9.12311i −0.836314 0.482846i
\(358\) −0.273094 0.157671i −0.0144335 0.00833316i
\(359\) −4.87689 −0.257393 −0.128696 0.991684i \(-0.541079\pi\)
−0.128696 + 0.991684i \(0.541079\pi\)
\(360\) 0 0
\(361\) 3.15767 + 5.46925i 0.166193 + 0.287855i
\(362\) 9.63289 5.56155i 0.506294 0.292309i
\(363\) 6.00000i 0.314918i
\(364\) −10.1231 7.90084i −0.530595 0.414117i
\(365\) 0 0
\(366\) −3.00000 5.19615i −0.156813 0.271607i
\(367\) −17.7470 + 10.2462i −0.926384 + 0.534848i −0.885666 0.464323i \(-0.846298\pi\)
−0.0407177 + 0.999171i \(0.512964\pi\)
\(368\) −6.65511 3.84233i −0.346922 0.200295i
\(369\) 4.24621 0.221049
\(370\) 0 0
\(371\) −7.90388 + 13.6899i −0.410349 + 0.710746i
\(372\) 5.68466i 0.294736i
\(373\) −4.49661 2.59612i −0.232826 0.134422i 0.379049 0.925376i \(-0.376251\pi\)
−0.611875 + 0.790955i \(0.709584\pi\)
\(374\) −10.5616 18.2931i −0.546125 0.945916i
\(375\) 0 0
\(376\) 7.00000 0.360997
\(377\) −14.5560 + 18.6501i −0.749670 + 0.960529i
\(378\) 3.56155i 0.183187i
\(379\) −2.65767 4.60322i −0.136515 0.236452i 0.789660 0.613545i \(-0.210257\pi\)
−0.926175 + 0.377093i \(0.876924\pi\)
\(380\) 0 0
\(381\) 2.21922 3.84381i 0.113694 0.196924i
\(382\) 19.1231i 0.978423i
\(383\) 18.0201 + 10.4039i 0.920782 + 0.531614i 0.883884 0.467706i \(-0.154919\pi\)
0.0368973 + 0.999319i \(0.488253\pi\)
\(384\) 0.500000 0.866025i 0.0255155 0.0441942i
\(385\) 0 0
\(386\) 0 0
\(387\) 3.95042 2.28078i 0.200811 0.115938i
\(388\) −0.972638 + 0.561553i −0.0493782 + 0.0285085i
\(389\) −19.0540 −0.966075 −0.483037 0.875600i \(-0.660467\pi\)
−0.483037 + 0.875600i \(0.660467\pi\)
\(390\) 0 0
\(391\) −39.3693 −1.99099
\(392\) 4.92306 2.84233i 0.248652 0.143559i
\(393\) −5.30277 + 3.06155i −0.267489 + 0.154435i
\(394\) −3.90388 + 6.76172i −0.196675 + 0.340651i
\(395\) 0 0
\(396\) 2.06155 3.57071i 0.103597 0.179435i
\(397\) 10.2857 + 5.93845i 0.516224 + 0.298042i 0.735388 0.677646i \(-0.237000\pi\)
−0.219164 + 0.975688i \(0.570333\pi\)
\(398\) 11.1231i 0.557551i
\(399\) −6.34233 + 10.9852i −0.317514 + 0.549950i
\(400\) 0 0
\(401\) −6.34233 10.9852i −0.316721 0.548577i 0.663081 0.748548i \(-0.269248\pi\)
−0.979802 + 0.199971i \(0.935915\pi\)
\(402\) 14.2462i 0.710536i
\(403\) 7.68762 + 19.0000i 0.382947 + 0.946457i
\(404\) 17.1231 0.851906
\(405\) 0 0
\(406\) −11.6847 20.2384i −0.579900 1.00442i
\(407\) 14.7224 + 8.50000i 0.729764 + 0.421329i
\(408\) 5.12311i 0.253632i
\(409\) 0.903882 1.56557i 0.0446941 0.0774124i −0.842813 0.538207i \(-0.819102\pi\)
0.887507 + 0.460794i \(0.152435\pi\)
\(410\) 0 0
\(411\) −8.80776 −0.434455
\(412\) −0.379706 0.219224i −0.0187068 0.0108004i
\(413\) −32.5760 + 18.8078i −1.60296 + 0.925470i
\(414\) −3.84233 6.65511i −0.188840 0.327081i
\(415\) 0 0
\(416\) 0.500000 3.57071i 0.0245145 0.175069i
\(417\) 8.43845i 0.413233i
\(418\) −12.7173 + 7.34233i −0.622023 + 0.359125i
\(419\) −0.246211 0.426450i −0.0120282 0.0208335i 0.859949 0.510381i \(-0.170495\pi\)
−0.871977 + 0.489547i \(0.837162\pi\)
\(420\) 0 0
\(421\) 0.492423 0.0239992 0.0119996 0.999928i \(-0.496180\pi\)
0.0119996 + 0.999928i \(0.496180\pi\)
\(422\) −6.00231 3.46543i −0.292188 0.168695i
\(423\) 6.06218 + 3.50000i 0.294753 + 0.170176i
\(424\) −4.43845 −0.215550
\(425\) 0 0
\(426\) 2.43845 + 4.22351i 0.118143 + 0.204630i
\(427\) 18.5064 10.6847i 0.895586 0.517067i
\(428\) 2.00000i 0.0966736i
\(429\) 2.06155 14.7224i 0.0995327 0.710806i
\(430\) 0 0
\(431\) −13.3693 23.1563i −0.643977 1.11540i −0.984537 0.175178i \(-0.943950\pi\)
0.340559 0.940223i \(-0.389384\pi\)
\(432\) 0.866025 0.500000i 0.0416667 0.0240563i
\(433\) 26.6204 + 15.3693i 1.27930 + 0.738602i 0.976719 0.214523i \(-0.0688195\pi\)
0.302578 + 0.953125i \(0.402153\pi\)
\(434\) −20.2462 −0.971849
\(435\) 0 0
\(436\) 10.1231 17.5337i 0.484809 0.839714i
\(437\) 27.3693i 1.30925i
\(438\) −13.3102 7.68466i −0.635987 0.367187i
\(439\) 8.43845 + 14.6158i 0.402745 + 0.697575i 0.994056 0.108869i \(-0.0347228\pi\)
−0.591311 + 0.806444i \(0.701389\pi\)
\(440\) 0 0
\(441\) 5.68466 0.270698
\(442\) −6.92820 17.1231i −0.329541 0.814463i
\(443\) 4.87689i 0.231708i 0.993266 + 0.115854i \(0.0369605\pi\)
−0.993266 + 0.115854i \(0.963039\pi\)
\(444\) 2.06155 + 3.57071i 0.0978370 + 0.169459i
\(445\) 0 0
\(446\) 13.1501 22.7766i 0.622675 1.07850i
\(447\) 22.8078i 1.07877i
\(448\) 3.08440 + 1.78078i 0.145724 + 0.0841338i
\(449\) 12.5885 21.8040i 0.594090 1.02899i −0.399585 0.916696i \(-0.630846\pi\)
0.993675 0.112298i \(-0.0358210\pi\)
\(450\) 0 0
\(451\) −8.75379 + 15.1620i −0.412200 + 0.713951i
\(452\) −3.19101 + 1.84233i −0.150092 + 0.0866559i
\(453\) −8.11407 + 4.68466i −0.381232 + 0.220104i
\(454\) 20.0000 0.938647
\(455\) 0 0
\(456\) −3.56155 −0.166785
\(457\) 3.25088 1.87689i 0.152070 0.0877974i −0.422034 0.906580i \(-0.638684\pi\)
0.574104 + 0.818782i \(0.305351\pi\)
\(458\) 6.71498 3.87689i 0.313770 0.181155i
\(459\) 2.56155 4.43674i 0.119563 0.207089i
\(460\) 0 0
\(461\) −3.52699 + 6.10892i −0.164268 + 0.284521i −0.936395 0.350947i \(-0.885860\pi\)
0.772127 + 0.635468i \(0.219193\pi\)
\(462\) 12.7173 + 7.34233i 0.591662 + 0.341596i
\(463\) 33.6155i 1.56225i −0.624377 0.781123i \(-0.714647\pi\)
0.624377 0.781123i \(-0.285353\pi\)
\(464\) 3.28078 5.68247i 0.152306 0.263802i
\(465\) 0 0
\(466\) 8.84233 + 15.3154i 0.409613 + 0.709471i
\(467\) 39.8617i 1.84458i 0.386497 + 0.922291i \(0.373685\pi\)
−0.386497 + 0.922291i \(0.626315\pi\)
\(468\) 2.21837 2.84233i 0.102544 0.131387i
\(469\) −50.7386 −2.34289
\(470\) 0 0
\(471\) −11.0616 19.1592i −0.509689 0.882808i
\(472\) −9.14657 5.28078i −0.421005 0.243067i
\(473\) 18.8078i 0.864782i
\(474\) 3.71922 6.44188i 0.170830 0.295886i
\(475\) 0 0
\(476\) 18.2462 0.836314
\(477\) −3.84381 2.21922i −0.175996 0.101611i
\(478\) −11.5782 + 6.68466i −0.529573 + 0.305749i
\(479\) −10.8769 18.8393i −0.496978 0.860791i 0.503016 0.864277i \(-0.332224\pi\)
−0.999994 + 0.00348601i \(0.998890\pi\)
\(480\) 0 0
\(481\) 11.7192 + 9.14657i 0.534351 + 0.417048i
\(482\) 19.8769i 0.905368i
\(483\) 23.7025 13.6847i 1.07850 0.622674i
\(484\) 3.00000 + 5.19615i 0.136364 + 0.236189i
\(485\) 0 0
\(486\) 1.00000 0.0453609
\(487\) 20.8314 + 12.0270i 0.943959 + 0.544995i 0.891199 0.453612i \(-0.149865\pi\)
0.0527597 + 0.998607i \(0.483198\pi\)
\(488\) 5.19615 + 3.00000i 0.235219 + 0.135804i
\(489\) 18.5616 0.839382
\(490\) 0 0
\(491\) 10.7808 + 18.6729i 0.486530 + 0.842694i 0.999880 0.0154850i \(-0.00492923\pi\)
−0.513350 + 0.858179i \(0.671596\pi\)
\(492\) −3.67733 + 2.12311i −0.165787 + 0.0957170i
\(493\) 33.6155i 1.51397i
\(494\) −11.9039 + 4.81645i −0.535581 + 0.216702i
\(495\) 0 0
\(496\) −2.84233 4.92306i −0.127624 0.221052i
\(497\) −15.0423 + 8.68466i −0.674738 + 0.389560i
\(498\) 0.972638 + 0.561553i 0.0435850 + 0.0251638i
\(499\) −4.00000 −0.179065 −0.0895323 0.995984i \(-0.528537\pi\)
−0.0895323 + 0.995984i \(0.528537\pi\)
\(500\) 0 0
\(501\) 10.1847 17.6403i 0.455017 0.788113i
\(502\) 0.123106i 0.00549447i
\(503\) −5.14941 2.97301i −0.229601 0.132560i 0.380787 0.924663i \(-0.375653\pi\)
−0.610388 + 0.792103i \(0.708986\pi\)
\(504\) 1.78078 + 3.08440i 0.0793221 + 0.137390i
\(505\) 0 0
\(506\) 31.6847 1.40855
\(507\) 3.57071 12.5000i 0.158581 0.555144i
\(508\) 4.43845i 0.196924i
\(509\) −14.7732 25.5879i −0.654811 1.13417i −0.981941 0.189186i \(-0.939415\pi\)
0.327131 0.944979i \(-0.393918\pi\)
\(510\) 0 0
\(511\) 27.3693 47.4050i 1.21075 2.09708i
\(512\) 1.00000i 0.0441942i
\(513\) −3.08440 1.78078i −0.136179 0.0786232i
\(514\) −0.719224 + 1.24573i −0.0317236 + 0.0549469i
\(515\) 0 0
\(516\) −2.28078 + 3.95042i −0.100406 + 0.173908i
\(517\) −24.9950 + 14.4309i −1.09928 + 0.634669i
\(518\) −12.7173 + 7.34233i −0.558766 + 0.322603i
\(519\) 25.1771 1.10515
\(520\) 0 0
\(521\) −18.6847 −0.818590 −0.409295 0.912402i \(-0.634225\pi\)
−0.409295 + 0.912402i \(0.634225\pi\)
\(522\) 5.68247 3.28078i 0.248715 0.143596i
\(523\) 7.96071 4.59612i 0.348098 0.200974i −0.315749 0.948843i \(-0.602256\pi\)
0.663847 + 0.747868i \(0.268923\pi\)
\(524\) 3.06155 5.30277i 0.133745 0.231652i
\(525\) 0 0
\(526\) 6.50000 11.2583i 0.283413 0.490887i
\(527\) −25.2213 14.5616i −1.09866 0.634311i
\(528\) 4.12311i 0.179435i
\(529\) 18.0270 31.2237i 0.783782 1.35755i
\(530\) 0 0
\(531\) −5.28078 9.14657i −0.229166 0.396927i
\(532\) 12.6847i 0.549950i
\(533\) −9.41967 + 12.0691i −0.408011 + 0.522772i
\(534\) −1.80776 −0.0782296
\(535\) 0 0
\(536\) −7.12311 12.3376i −0.307671 0.532902i
\(537\) 0.273094 + 0.157671i 0.0117849 + 0.00680400i
\(538\) 3.36932i 0.145262i
\(539\) −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 \(0.518010\pi\)
\(542\) −27.8662 16.0885i −1.19695 0.691062i
\(543\) −9.63289 + 5.56155i −0.413387 + 0.238669i
\(544\) 2.56155 + 4.43674i 0.109826 + 0.190224i
\(545\) 0 0
\(546\) 10.1231 + 7.90084i 0.433229 + 0.338125i
\(547\) 35.6155i 1.52281i 0.648276 + 0.761405i \(0.275490\pi\)
−0.648276 + 0.761405i \(0.724510\pi\)
\(548\) 7.62775 4.40388i 0.325841 0.188125i
\(549\) 3.00000 + 5.19615i 0.128037 + 0.221766i
\(550\) 0 0
\(551\) −23.3693 −0.995566
\(552\) 6.65511 + 3.84233i 0.283260 + 0.163540i
\(553\) 22.9431 + 13.2462i 0.975640 + 0.563286i
\(554\) 1.00000 0.0424859
\(555\) 0 0
\(556\) −4.21922 7.30791i −0.178935 0.309924i
\(557\) −3.84381 + 2.21922i −0.162867 + 0.0940315i −0.579218 0.815172i \(-0.696642\pi\)
0.416351 + 0.909204i \(0.363309\pi\)
\(558\) 5.68466i 0.240651i
\(559\) −2.28078 + 16.2880i −0.0964666 + 0.688909i
\(560\) 0 0
\(561\) 10.5616 + 18.2931i 0.445909 + 0.772337i
\(562\) −0.213225 + 0.123106i −0.00899436 + 0.00519290i
\(563\) 28.5657 + 16.4924i 1.20390 + 0.695073i 0.961420 0.275083i \(-0.0887055\pi\)
0.242481 + 0.970156i \(0.422039\pi\)
\(564\) −7.00000 −0.294753
\(565\) 0 0
\(566\) −5.71922 + 9.90599i −0.240397 + 0.416380i
\(567\) 3.56155i 0.149571i
\(568\) −4.22351 2.43845i −0.177215 0.102315i
\(569\) −9.58854 16.6078i −0.401973 0.696237i 0.591991 0.805944i \(-0.298342\pi\)
−0.993964 + 0.109707i \(0.965009\pi\)
\(570\) 0 0
\(571\) 11.3153 0.473532 0.236766 0.971567i \(-0.423912\pi\)
0.236766 + 0.971567i \(0.423912\pi\)
\(572\) 5.57586 + 13.7808i 0.233138 + 0.576203i
\(573\) 19.1231i 0.798879i
\(574\) −7.56155 13.0970i −0.315613 0.546658i
\(575\) 0 0
\(576\) −0.500000 + 0.866025i −0.0208333 + 0.0360844i
\(577\) 8.73863i 0.363794i 0.983318 + 0.181897i \(0.0582238\pi\)
−0.983318 + 0.181897i \(0.941776\pi\)
\(578\) 8.00745 + 4.62311i 0.333066 + 0.192296i
\(579\) 0 0
\(580\) 0 0
\(581\) −2.00000 + 3.46410i −0.0829740 + 0.143715i
\(582\) 0.972638 0.561553i 0.0403171 0.0232771i
\(583\) 15.8484 9.15009i 0.656375 0.378958i
\(584\) 15.3693 0.635987
\(585\) 0 0
\(586\) −24.9309 −1.02988
\(587\) −20.5714 + 11.8769i −0.849072 + 0.490212i −0.860338 0.509725i \(-0.829747\pi\)
0.0112657 + 0.999937i \(0.496414\pi\)
\(588\) −4.92306 + 2.84233i −0.203024 + 0.117216i
\(589\) −10.1231 + 17.5337i −0.417115 + 0.722465i
\(590\) 0 0
\(591\) 3.90388 6.76172i 0.160584 0.278140i
\(592\) −3.57071 2.06155i −0.146755 0.0847293i
\(593\) 12.1771i 0.500053i 0.968239 + 0.250026i \(0.0804393\pi\)
−0.968239 + 0.250026i \(0.919561\pi\)
\(594\) −2.06155 + 3.57071i −0.0845865 + 0.146508i
\(595\) 0 0
\(596\) 11.4039 + 19.7521i 0.467121 + 0.809078i
\(597\) 11.1231i 0.455238i
\(598\) 27.4397 + 3.84233i 1.12209 + 0.157125i
\(599\) 14.0000 0.572024 0.286012 0.958226i \(-0.407670\pi\)
0.286012 + 0.958226i \(0.407670\pi\)
\(600\) 0 0
\(601\) 17.9924 + 31.1638i 0.733926 + 1.27120i 0.955193 + 0.295984i \(0.0956476\pi\)
−0.221267 + 0.975213i \(0.571019\pi\)
\(602\) −14.0696 8.12311i −0.573435 0.331073i
\(603\) 14.2462i 0.580151i
\(604\) 4.68466 8.11407i 0.190616 0.330157i
\(605\) 0 0
\(606\) −17.1231 −0.695579
\(607\) 25.4813 + 14.7116i 1.03425 + 0.597127i 0.918201 0.396116i \(-0.129642\pi\)
0.116054 + 0.993243i \(0.462975\pi\)
\(608\) 3.08440 1.78078i 0.125089 0.0722200i
\(609\) 11.6847 + 20.2384i 0.473486 + 0.820102i
\(610\) 0 0
\(611\) −23.3963 + 9.46641i −0.946513 + 0.382970i
\(612\) 5.12311i 0.207089i
\(613\) −24.3553 + 14.0616i −0.983702 + 0.567941i −0.903386 0.428829i \(-0.858926\pi\)
−0.0803164 + 0.996769i \(0.525593\pi\)
\(614\) −7.80776 13.5234i −0.315096 0.545762i
\(615\) 0 0
\(616\) −14.6847 −0.591662
\(617\) 36.1000 + 20.8423i 1.45333 + 0.839081i 0.998669 0.0515837i \(-0.0164269\pi\)
0.454662 + 0.890664i \(0.349760\pi\)
\(618\) 0.379706 + 0.219224i 0.0152740 + 0.00881847i
\(619\) 16.4384 0.660717 0.330358 0.943856i \(-0.392830\pi\)
0.330358 + 0.943856i \(0.392830\pi\)
\(620\) 0 0
\(621\) 3.84233 + 6.65511i 0.154187 + 0.267060i
\(622\) −16.2281 + 9.36932i −0.650689 + 0.375675i
\(623\) 6.43845i 0.257951i
\(624\) −0.500000 + 3.57071i −0.0200160 + 0.142943i
\(625\) 0 0
\(626\) −3.31534 5.74234i −0.132508 0.229510i
\(627\) 12.7173 7.34233i 0.507880 0.293224i
\(628\) 19.1592 + 11.0616i 0.764534 + 0.441404i
\(629\) −21.1231 −0.842233
\(630\) 0 0
\(631\) 15.1231 26.1940i 0.602041 1.04277i −0.390470 0.920616i \(-0.627688\pi\)
0.992512 0.122151i \(-0.0389791\pi\)
\(632\) 7.43845i 0.295886i
\(633\) 6.00231 + 3.46543i 0.238570 + 0.137739i
\(634\) −2.09612 3.63058i −0.0832475 0.144189i
\(635\) 0 0
\(636\) 4.43845 0.175996
\(637\) −12.6107 + 16.1577i −0.499653 + 0.640190i
\(638\) 27.0540i 1.07108i
\(639\) −2.43845 4.22351i −0.0964635 0.167080i
\(640\) 0 0
\(641\) 7.78078 13.4767i 0.307322 0.532298i −0.670453 0.741952i \(-0.733900\pi\)
0.977776 + 0.209654i \(0.0672337\pi\)
\(642\) 2.00000i 0.0789337i
\(643\) 33.1222 + 19.1231i 1.30621 + 0.754142i 0.981462 0.191658i \(-0.0613865\pi\)
0.324750 + 0.945800i \(0.394720\pi\)
\(644\) −13.6847 + 23.7025i −0.539251 + 0.934010i
\(645\) 0 0
\(646\) 9.12311 15.8017i 0.358944 0.621709i
\(647\) −1.77879 + 1.02699i −0.0699316 + 0.0403751i −0.534558 0.845132i \(-0.679522\pi\)
0.464626 + 0.885507i \(0.346189\pi\)
\(648\) −0.866025 + 0.500000i −0.0340207 + 0.0196419i
\(649\) 43.5464 1.70935
\(650\) 0 0
\(651\) 20.2462 0.793512
\(652\) −16.0748 + 9.28078i −0.629537 + 0.363463i
\(653\) 35.0207 20.2192i 1.37047 0.791239i 0.379480 0.925200i \(-0.376103\pi\)
0.990987 + 0.133961i \(0.0427695\pi\)
\(654\) −10.1231 + 17.5337i −0.395845 + 0.685623i
\(655\) 0 0
\(656\) 2.12311 3.67733i 0.0828933 0.143575i
\(657\) 13.3102 + 7.68466i 0.519281 + 0.299807i
\(658\) 24.9309i 0.971906i
\(659\) 15.5270 26.8935i 0.604846 1.04762i −0.387230 0.921983i \(-0.626568\pi\)
0.992076 0.125640i \(-0.0400985\pi\)
\(660\) 0 0
\(661\) 5.80776 + 10.0593i 0.225896 + 0.391263i 0.956588 0.291444i \(-0.0941358\pi\)
−0.730692 + 0.682707i \(0.760802\pi\)
\(662\) 18.7386i 0.728298i
\(663\) 6.92820 + 17.1231i 0.269069 + 0.665006i
\(664\) −1.12311 −0.0435850
\(665\) 0 0
\(666\) −2.06155 3.57071i −0.0798835 0.138362i
\(667\) 43.6679 + 25.2116i 1.69083 + 0.976199i
\(668\) 20.3693i 0.788113i
\(669\) −13.1501 + 22.7766i −0.508412 + 0.880595i
\(670\) 0 0
\(671\) −24.7386 −0.955024
\(672\) −3.08440 1.78078i −0.118983 0.0686949i
\(673\) −36.5863 + 21.1231i −1.41030 + 0.814236i −0.995416 0.0956394i \(-0.969510\pi\)
−0.414882 + 0.909875i \(0.636177\pi\)
\(674\) −3.00000 5.19615i −0.115556 0.200148i
\(675\) 0 0
\(676\) 3.15767 + 12.6107i 0.121449 + 0.485026i
\(677\) 28.8769i 1.10983i −0.831907 0.554915i \(-0.812751\pi\)
0.831907 0.554915i \(-0.187249\pi\)
\(678\) 3.19101 1.84233i 0.122550 0.0707542i
\(679\) 2.00000 + 3.46410i 0.0767530 + 0.132940i
\(680\) 0 0
\(681\) −20.0000 −0.766402
\(682\) 20.2983 + 11.7192i 0.777262 + 0.448752i
\(683\) 7.68762 + 4.43845i 0.294158 + 0.169832i 0.639816 0.768528i \(-0.279011\pi\)
−0.345657 + 0.938361i \(0.612344\pi\)
\(684\) 3.56155 0.136179
\(685\) 0 0
\(686\) 2.34233 + 4.05703i 0.0894305 + 0.154898i
\(687\) −6.71498 + 3.87689i −0.256192 + 0.147913i
\(688\) 4.56155i 0.173908i
\(689\) 14.8348 6.00231i 0.565159 0.228670i
\(690\) 0 0
\(691\) 8.21922 + 14.2361i 0.312674 + 0.541567i 0.978940 0.204147i \(-0.0654419\pi\)
−0.666266 + 0.745714i \(0.732109\pi\)
\(692\) −21.8040 + 12.5885i −0.828863 + 0.478545i
\(693\) −12.7173 7.34233i −0.483090 0.278912i
\(694\) −9.12311 −0.346308
\(695\) 0 0
\(696\) −3.28078 + 5.68247i −0.124358 + 0.215394i
\(697\) 21.7538i 0.823984i
\(698\) −21.2111 12.2462i −0.802850 0.463526i
\(699\) −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 \(0.394060\pi\)
\(702\) −2.21837 + 2.84233i −0.0837270 + 0.107277i
\(703\) 14.6847i 0.553842i
\(704\) −2.06155 3.57071i −0.0776977 0.134576i
\(705\) 0 0
\(706\) −15.9309 + 27.5931i −0.599566 + 1.03848i
\(707\) 60.9848i 2.29357i
\(708\) 9.14657 + 5.28078i 0.343749 + 0.198464i
\(709\) 8.87689 15.3752i 0.333379 0.577429i −0.649793 0.760111i \(-0.725145\pi\)
0.983172 + 0.182682i \(0.0584779\pi\)
\(710\) 0 0
\(711\) −3.71922 + 6.44188i −0.139482 + 0.241590i
\(712\) 1.56557 0.903882i 0.0586722 0.0338744i
\(713\) 37.8320 21.8423i 1.41682 0.818002i
\(714\) −18.2462 −0.682847
\(715\) 0 0
\(716\) −0.315342 −0.0117849
\(717\) 11.5782 6.68466i 0.432395 0.249643i
\(718\) −4.22351 + 2.43845i −0.157620 + 0.0910020i
\(719\) −10.4924 + 18.1734i −0.391301 + 0.677754i −0.992621 0.121254i \(-0.961308\pi\)
0.601320 + 0.799008i \(0.294642\pi\)
\(720\) 0 0
\(721\) −0.780776 + 1.35234i −0.0290776 + 0.0503639i
\(722\) 5.46925 + 3.15767i 0.203544 + 0.117516i
\(723\) 19.8769i 0.739230i
\(724\) 5.56155 9.63289i 0.206693 0.358004i
\(725\) 0 0
\(726\) −3.00000 5.19615i −0.111340 0.192847i
\(727\) 23.4233i 0.868722i −0.900739 0.434361i \(-0.856974\pi\)
0.900739 0.434361i \(-0.143026\pi\)
\(728\) −12.7173 1.78078i −0.471334 0.0660000i
\(729\) −1.00000 −0.0370370
\(730\) 0 0
\(731\) −11.6847 20.2384i −0.432173 0.748545i
\(732\) −5.19615 3.00000i −0.192055 0.110883i
\(733\) 48.9309i 1.80730i −0.428269 0.903651i \(-0.640876\pi\)
0.428269 0.903651i \(-0.359124\pi\)
\(734\) −10.2462 + 17.7470i −0.378195 + 0.655052i
\(735\) 0 0
\(736\) −7.68466 −0.283260
\(737\) 50.8691 + 29.3693i 1.87379 + 1.08183i
\(738\) 3.67733 2.12311i 0.135364 0.0781526i
\(739\) 21.2732 + 36.8463i 0.782547 + 1.35541i 0.930453 + 0.366410i \(0.119413\pi\)
−0.147906 + 0.989001i \(0.547253\pi\)
\(740\) 0 0
\(741\) 11.9039 4.81645i 0.437300 0.176937i
\(742\) 15.8078i 0.580321i
\(743\) 27.8662 16.0885i 1.02231 0.590231i 0.107538 0.994201i \(-0.465703\pi\)
0.914772 + 0.403970i \(0.132370\pi\)
\(744\) 2.84233 + 4.92306i 0.104205 + 0.180488i
\(745\) 0 0
\(746\) −5.19224 −0.190101
\(747\) −0.972638 0.561553i −0.0355870 0.0205461i
\(748\) −18.2931 10.5616i −0.668864 0.386169i
\(749\) −7.12311 −0.260273
\(750\) 0 0
\(751\) 1.59612 + 2.76456i 0.0582432 + 0.100880i 0.893677 0.448711i \(-0.148117\pi\)
−0.835434 + 0.549591i \(0.814783\pi\)
\(752\) 6.06218 3.50000i 0.221065 0.127632i
\(753\) 0.123106i 0.00448622i
\(754\) −3.28078 + 23.4294i −0.119479 + 0.853250i
\(755\) 0 0
\(756\) −1.78078 3.08440i −0.0647662 0.112178i
\(757\) 28.9454 16.7116i 1.05204 0.607395i 0.128820 0.991668i \(-0.458881\pi\)
0.923220 + 0.384273i \(0.125548\pi\)
\(758\) −4.60322 2.65767i −0.167197 0.0965309i
\(759\) −31.6847 −1.15008
\(760\) 0 0
\(761\) −5.46543 + 9.46641i −0.198122 + 0.343157i −0.947919 0.318510i \(-0.896818\pi\)
0.749798 + 0.661667i \(0.230151\pi\)
\(762\) 4.43845i 0.160788i
\(763\) −62.4473 36.0540i −2.26074 1.30524i
\(764\) 9.56155 + 16.5611i 0.345925 + 0.599159i
\(765\) 0 0
\(766\) 20.8078 0.751815
\(767\) 37.7123 + 5.28078i 1.36171 + 0.190678i
\(768\) 1.00000i 0.0360844i
\(769\) −22.8423 39.5641i −0.823715 1.42672i −0.902897 0.429857i \(-0.858564\pi\)
0.0791816 0.996860i \(-0.474769\pi\)
\(770\) 0 0
\(771\) 0.719224 1.24573i 0.0259022 0.0448639i
\(772\) 0 0
\(773\) −18.3399 10.5885i −0.659640 0.380843i 0.132500 0.991183i \(-0.457700\pi\)
−0.792140 + 0.610340i \(0.791033\pi\)
\(774\) 2.28078 3.95042i 0.0819808 0.141995i
\(775\) 0 0
\(776\) −0.561553 + 0.972638i −0.0201586 + 0.0349157i
\(777\) 12.7173 7.34233i 0.456230 0.263405i
\(778\) −16.5012 + 9.52699i −0.591598 + 0.341559i
\(779\) −15.1231 −0.541841
\(780\) 0 0
\(781\) 20.1080 0.719519
\(782\) −34.0948 + 19.6847i −1.21923 + 0.703922i
\(783\) −5.68247 + 3.28078i −0.203075 + 0.117245i
\(784\) 2.84233 4.92306i 0.101512 0.175824i
\(785\) 0 0