Properties

Label 390.2.i.g.61.1
Level $390$
Weight $2$
Character 390.61
Analytic conductor $3.114$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 390 = 2 \cdot 3 \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 390.i (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.11416567883\)
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: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 61.1
Root \(1.28078 + 2.21837i\) of defining polynomial
Character \(\chi\) \(=\) 390.61
Dual form 390.2.i.g.211.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +1.00000 q^{5} +(-0.500000 - 0.866025i) q^{6} +(-1.78078 - 3.08440i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +1.00000 q^{5} +(-0.500000 - 0.866025i) q^{6} +(-1.78078 - 3.08440i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.500000 + 0.866025i) q^{10} +(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^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.56155 - 4.43674i) q^{17} +1.00000 q^{18} +(1.78078 + 3.08440i) q^{19} +(-0.500000 - 0.866025i) q^{20} +3.56155 q^{21} +(2.06155 + 3.57071i) q^{22} +(3.84233 - 6.65511i) q^{23} +(-0.500000 + 0.866025i) q^{24} +1.00000 q^{25} +(2.84233 - 2.21837i) q^{26} +1.00000 q^{27} +(-1.78078 + 3.08440i) q^{28} +(-3.28078 + 5.68247i) q^{29} +(-0.500000 - 0.866025i) q^{30} +5.68466 q^{31} +(-0.500000 - 0.866025i) q^{32} +(2.06155 + 3.57071i) q^{33} +5.12311 q^{34} +(-1.78078 - 3.08440i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(-2.06155 + 3.57071i) q^{37} -3.56155 q^{38} +(2.84233 - 2.21837i) q^{39} +1.00000 q^{40} +(2.12311 - 3.67733i) q^{41} +(-1.78078 + 3.08440i) q^{42} +(-2.28078 - 3.95042i) q^{43} -4.12311 q^{44} +(-0.500000 - 0.866025i) q^{45} +(3.84233 + 6.65511i) q^{46} +7.00000 q^{47} +(-0.500000 - 0.866025i) q^{48} +(-2.84233 + 4.92306i) q^{49} +(-0.500000 + 0.866025i) q^{50} +5.12311 q^{51} +(0.500000 + 3.57071i) q^{52} +4.43845 q^{53} +(-0.500000 + 0.866025i) q^{54} +(2.06155 - 3.57071i) q^{55} +(-1.78078 - 3.08440i) q^{56} -3.56155 q^{57} +(-3.28078 - 5.68247i) q^{58} +(-5.28078 - 9.14657i) q^{59} +1.00000 q^{60} +(-3.00000 - 5.19615i) q^{61} +(-2.84233 + 4.92306i) q^{62} +(-1.78078 + 3.08440i) q^{63} +1.00000 q^{64} +(-3.34233 - 1.35234i) q^{65} -4.12311 q^{66} +(-7.12311 + 12.3376i) q^{67} +(-2.56155 + 4.43674i) q^{68} +(3.84233 + 6.65511i) q^{69} +3.56155 q^{70} +(2.43845 + 4.22351i) q^{71} +(-0.500000 - 0.866025i) q^{72} -15.3693 q^{73} +(-2.06155 - 3.57071i) q^{74} +(-0.500000 + 0.866025i) q^{75} +(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^{80} +(-0.500000 + 0.866025i) q^{81} +(2.12311 + 3.67733i) q^{82} +1.12311 q^{83} +(-1.78078 - 3.08440i) q^{84} +(-2.56155 - 4.43674i) q^{85} +4.56155 q^{86} +(-3.28078 - 5.68247i) q^{87} +(2.06155 - 3.57071i) q^{88} +(-0.903882 + 1.56557i) q^{89} +1.00000 q^{90} +(1.78078 + 12.7173i) q^{91} -7.68466 q^{92} +(-2.84233 + 4.92306i) q^{93} +(-3.50000 + 6.06218i) q^{94} +(1.78078 + 3.08440i) q^{95} +1.00000 q^{96} +(-0.561553 - 0.972638i) q^{97} +(-2.84233 - 4.92306i) q^{98} -4.12311 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 2q^{2} - 2q^{3} - 2q^{4} + 4q^{5} - 2q^{6} - 3q^{7} + 4q^{8} - 2q^{9} + O(q^{10}) \) \( 4q - 2q^{2} - 2q^{3} - 2q^{4} + 4q^{5} - 2q^{6} - 3q^{7} + 4q^{8} - 2q^{9} - 2q^{10} + 4q^{12} - q^{13} + 6q^{14} - 2q^{15} - 2q^{16} - 2q^{17} + 4q^{18} + 3q^{19} - 2q^{20} + 6q^{21} + 3q^{23} - 2q^{24} + 4q^{25} - q^{26} + 4q^{27} - 3q^{28} - 9q^{29} - 2q^{30} - 2q^{31} - 2q^{32} + 4q^{34} - 3q^{35} - 2q^{36} - 6q^{38} - q^{39} + 4q^{40} - 8q^{41} - 3q^{42} - 5q^{43} - 2q^{45} + 3q^{46} + 28q^{47} - 2q^{48} + q^{49} - 2q^{50} + 4q^{51} + 2q^{52} + 26q^{53} - 2q^{54} - 3q^{56} - 6q^{57} - 9q^{58} - 17q^{59} + 4q^{60} - 12q^{61} + q^{62} - 3q^{63} + 4q^{64} - q^{65} - 12q^{67} - 2q^{68} + 3q^{69} + 6q^{70} + 18q^{71} - 2q^{72} - 12q^{73} - 2q^{75} + 3q^{76} - 34q^{77} + 2q^{78} + 38q^{79} - 2q^{80} - 2q^{81} - 8q^{82} - 12q^{83} - 3q^{84} - 2q^{85} + 10q^{86} - 9q^{87} + 17q^{89} + 4q^{90} + 3q^{91} - 6q^{92} + q^{93} - 14q^{94} + 3q^{95} + 4q^{96} + 6q^{97} + q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/390\mathbb{Z}\right)^\times\).

\(n\) \(131\) \(157\) \(301\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 + 0.866025i −0.353553 + 0.612372i
\(3\) −0.500000 + 0.866025i −0.288675 + 0.500000i
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) 1.00000 0.447214
\(6\) −0.500000 0.866025i −0.204124 0.353553i
\(7\) −1.78078 3.08440i −0.673070 1.16579i −0.977029 0.213107i \(-0.931642\pi\)
0.303959 0.952685i \(-0.401692\pi\)
\(8\) 1.00000 0.353553
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) −0.500000 + 0.866025i −0.158114 + 0.273861i
\(11\) 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
\(15\) −0.500000 + 0.866025i −0.129099 + 0.223607i
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −2.56155 4.43674i −0.621268 1.07607i −0.989250 0.146235i \(-0.953285\pi\)
0.367982 0.929833i \(-0.380049\pi\)
\(18\) 1.00000 0.235702
\(19\) 1.78078 + 3.08440i 0.408538 + 0.707609i 0.994726 0.102566i \(-0.0327054\pi\)
−0.586188 + 0.810175i \(0.699372\pi\)
\(20\) −0.500000 0.866025i −0.111803 0.193649i
\(21\) 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 \(-0.537539\pi\)
0.918839 0.394632i \(-0.129128\pi\)
\(24\) −0.500000 + 0.866025i −0.102062 + 0.176777i
\(25\) 1.00000 0.200000
\(26\) 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 \(0.958147\pi\)
\(30\) −0.500000 0.866025i −0.0912871 0.158114i
\(31\) 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
\(35\) −1.78078 3.08440i −0.301006 0.521358i
\(36\) −0.500000 + 0.866025i −0.0833333 + 0.144338i
\(37\) −2.06155 + 3.57071i −0.338917 + 0.587022i −0.984229 0.176897i \(-0.943394\pi\)
0.645312 + 0.763919i \(0.276727\pi\)
\(38\) −3.56155 −0.577760
\(39\) 2.84233 2.21837i 0.455137 0.355223i
\(40\) 1.00000 0.158114
\(41\) 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 0.638046 0.769998i \(-0.279743\pi\)
−0.985861 + 0.167565i \(0.946410\pi\)
\(44\) −4.12311 −0.621582
\(45\) −0.500000 0.866025i −0.0745356 0.129099i
\(46\) 3.84233 + 6.65511i 0.566521 + 0.981242i
\(47\) 7.00000 1.02105 0.510527 0.859861i \(-0.329450\pi\)
0.510527 + 0.859861i \(0.329450\pi\)
\(48\) −0.500000 0.866025i −0.0721688 0.125000i
\(49\) −2.84233 + 4.92306i −0.406047 + 0.703294i
\(50\) −0.500000 + 0.866025i −0.0707107 + 0.122474i
\(51\) 5.12311 0.717378
\(52\) 0.500000 + 3.57071i 0.0693375 + 0.495169i
\(53\) 4.43845 0.609668 0.304834 0.952406i \(-0.401399\pi\)
0.304834 + 0.952406i \(0.401399\pi\)
\(54\) −0.500000 + 0.866025i −0.0680414 + 0.117851i
\(55\) 2.06155 3.57071i 0.277980 0.481475i
\(56\) −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 \(-0.407958\pi\)
\(60\) 1.00000 0.129099
\(61\) −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
\(65\) −3.34233 1.35234i −0.414565 0.167738i
\(66\) −4.12311 −0.507519
\(67\) −7.12311 + 12.3376i −0.870226 + 1.50728i −0.00846293 + 0.999964i \(0.502694\pi\)
−0.861763 + 0.507311i \(0.830639\pi\)
\(68\) −2.56155 + 4.43674i −0.310634 + 0.538034i
\(69\) 3.84233 + 6.65511i 0.462562 + 0.801181i
\(70\) 3.56155 0.425687
\(71\) 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 \(-0.856012\pi\)
−0.899421 + 0.437083i \(0.856012\pi\)
\(74\) −2.06155 3.57071i −0.239651 0.415087i
\(75\) −0.500000 + 0.866025i −0.0577350 + 0.100000i
\(76\) 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 \(0.362575\pi\)
\(80\) −0.500000 + 0.866025i −0.0559017 + 0.0968246i
\(81\) −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 \(-0.480367\pi\)
0.0616384 + 0.998099i \(0.480367\pi\)
\(84\) −1.78078 3.08440i −0.194299 0.336535i
\(85\) −2.56155 4.43674i −0.277839 0.481232i
\(86\) 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 \(0.197211\pi\)
\(90\) 1.00000 0.105409
\(91\) 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
\(95\) 1.78078 + 3.08440i 0.182704 + 0.316452i
\(96\) 1.00000 0.102062
\(97\) −0.561553 0.972638i −0.0570170 0.0987564i 0.836108 0.548565i \(-0.184826\pi\)
−0.893125 + 0.449808i \(0.851492\pi\)
\(98\) −2.84233 4.92306i −0.287119 0.497304i
\(99\) −4.12311 −0.414388
\(100\) −0.500000 0.866025i −0.0500000 0.0866025i
\(101\) 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 \(-0.493124\pi\)
0.0216007 + 0.999767i \(0.493124\pi\)
\(104\) −3.34233 1.35234i −0.327742 0.132608i
\(105\) 3.56155 0.347572
\(106\) −2.21922 + 3.84381i −0.215550 + 0.373344i
\(107\) −1.00000 + 1.73205i −0.0966736 + 0.167444i −0.910306 0.413936i \(-0.864154\pi\)
0.813632 + 0.581380i \(0.197487\pi\)
\(108\) −0.500000 0.866025i −0.0481125 0.0833333i
\(109\) −20.2462 −1.93924 −0.969618 0.244625i \(-0.921335\pi\)
−0.969618 + 0.244625i \(0.921335\pi\)
\(110\) 2.06155 + 3.57071i 0.196561 + 0.340454i
\(111\) −2.06155 3.57071i −0.195674 0.338917i
\(112\) 3.56155 0.336535
\(113\) 1.84233 + 3.19101i 0.173312 + 0.300185i 0.939576 0.342341i \(-0.111220\pi\)
−0.766264 + 0.642526i \(0.777887\pi\)
\(114\) 1.78078 3.08440i 0.166785 0.288880i
\(115\) 3.84233 6.65511i 0.358299 0.620592i
\(116\) 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
\(120\) −0.500000 + 0.866025i −0.0456435 + 0.0790569i
\(121\) −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
\(125\) 1.00000 0.0894427
\(126\) −1.78078 3.08440i −0.158644 0.274780i
\(127\) 2.21922 3.84381i 0.196924 0.341083i −0.750605 0.660751i \(-0.770238\pi\)
0.947530 + 0.319668i \(0.103571\pi\)
\(128\) −0.500000 + 0.866025i −0.0441942 + 0.0765466i
\(129\) 4.56155 0.401622
\(130\) 2.84233 2.21837i 0.249289 0.194564i
\(131\) 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
\(135\) 1.00000 0.0860663
\(136\) −2.56155 4.43674i −0.219651 0.380447i
\(137\) 4.40388 + 7.62775i 0.376249 + 0.651682i 0.990513 0.137418i \(-0.0438804\pi\)
−0.614264 + 0.789101i \(0.710547\pi\)
\(138\) −7.68466 −0.654162
\(139\) −4.21922 7.30791i −0.357870 0.619849i 0.629735 0.776810i \(-0.283164\pi\)
−0.987605 + 0.156961i \(0.949830\pi\)
\(140\) −1.78078 + 3.08440i −0.150503 + 0.260679i
\(141\) −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
\(145\) −3.28078 + 5.68247i −0.272454 + 0.471904i
\(146\) 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 \(0.449411\pi\)
\(150\) −0.500000 0.866025i −0.0408248 0.0707107i
\(151\) 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
\(155\) 5.68466 0.456603
\(156\) −3.34233 1.35234i −0.267601 0.108274i
\(157\) 22.1231 1.76562 0.882808 0.469734i \(-0.155650\pi\)
0.882808 + 0.469734i \(0.155650\pi\)
\(158\) −3.71922 + 6.44188i −0.295886 + 0.512489i
\(159\) −2.21922 + 3.84381i −0.175996 + 0.304834i
\(160\) −0.500000 0.866025i −0.0395285 0.0684653i
\(161\) −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 \(0.0923853\pi\)
−0.231250 + 0.972894i \(0.574281\pi\)
\(164\) −4.24621 −0.331573
\(165\) 2.06155 + 3.57071i 0.160492 + 0.277980i
\(166\) −0.561553 + 0.972638i −0.0435850 + 0.0754913i
\(167\) 10.1847 17.6403i 0.788113 1.36505i −0.139009 0.990291i \(-0.544392\pi\)
0.927122 0.374760i \(-0.122275\pi\)
\(168\) 3.56155 0.274780
\(169\) 9.34233 + 9.03996i 0.718641 + 0.695382i
\(170\) 5.12311 0.392924
\(171\) 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 \(0.239746\pi\)
0.227575 + 0.973760i \(0.426920\pi\)
\(174\) 6.56155 0.497430
\(175\) −1.78078 3.08440i −0.134614 0.233158i
\(176\) 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 \(0.162915\pi\)
\(180\) −0.500000 + 0.866025i −0.0372678 + 0.0645497i
\(181\) 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
\(185\) −2.06155 + 3.57071i −0.151568 + 0.262524i
\(186\) −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
\(190\) −3.56155 −0.258382
\(191\) −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
\(195\) 2.84233 2.21837i 0.203543 0.158861i
\(196\) 5.68466 0.406047
\(197\) 3.90388 6.76172i 0.278140 0.481753i −0.692782 0.721147i \(-0.743615\pi\)
0.970923 + 0.239394i \(0.0769487\pi\)
\(198\) 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 \(0.962328\pi\)
\(200\) 1.00000 0.0707107
\(201\) −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
\(205\) 2.12311 3.67733i 0.148284 0.256836i
\(206\) −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
\(210\) −1.78078 + 3.08440i −0.122885 + 0.212843i
\(211\) −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
\(215\) −2.28078 3.95042i −0.155548 0.269416i
\(216\) 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
\(220\) −4.12311 −0.277980
\(221\) 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 \(-0.490476\pi\)
0.850680 0.525683i \(-0.176190\pi\)
\(224\) −1.78078 + 3.08440i −0.118983 + 0.206085i
\(225\) −0.500000 0.866025i −0.0333333 0.0577350i
\(226\) −3.68466 −0.245100
\(227\) 10.0000 + 17.3205i 0.663723 + 1.14960i 0.979630 + 0.200812i \(0.0643581\pi\)
−0.315906 + 0.948790i \(0.602309\pi\)
\(228\) 1.78078 + 3.08440i 0.117935 + 0.204269i
\(229\) −7.75379 −0.512385 −0.256192 0.966626i \(-0.582468\pi\)
−0.256192 + 0.966626i \(0.582468\pi\)
\(230\) 3.84233 + 6.65511i 0.253356 + 0.438825i
\(231\) 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 \(-0.696666\pi\)
−0.579280 + 0.815128i \(0.696666\pi\)
\(234\) −3.34233 1.35234i −0.218495 0.0884055i
\(235\) 7.00000 0.456630
\(236\) −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 \(0.357669\pi\)
\(240\) −0.500000 0.866025i −0.0322749 0.0559017i
\(241\) 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
\(245\) −2.84233 + 4.92306i −0.181590 + 0.314523i
\(246\) −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
\(250\) −0.500000 + 0.866025i −0.0316228 + 0.0547723i
\(251\) −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
\(255\) 5.12311 0.320821
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 0.719224 1.24573i 0.0448639 0.0777066i −0.842721 0.538350i \(-0.819048\pi\)
0.887585 + 0.460643i \(0.152381\pi\)
\(258\) −2.28078 + 3.95042i −0.141995 + 0.245942i
\(259\) 14.6847 0.912460
\(260\) 0.500000 + 3.57071i 0.0310087 + 0.221446i
\(261\) 6.56155 0.406150
\(262\) −3.06155 + 5.30277i −0.189143 + 0.327606i
\(263\) 6.50000 11.2583i 0.400807 0.694218i −0.593016 0.805190i \(-0.702063\pi\)
0.993824 + 0.110972i \(0.0353964\pi\)
\(264\) 2.06155 + 3.57071i 0.126880 + 0.219762i
\(265\) 4.43845 0.272652
\(266\) 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 \(0.800580\pi\)
\(270\) −0.500000 + 0.866025i −0.0304290 + 0.0527046i
\(271\) −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
\(275\) 2.06155 3.57071i 0.124316 0.215322i
\(276\) 3.84233 6.65511i 0.231281 0.400591i
\(277\) 0.500000 + 0.866025i 0.0300421 + 0.0520344i 0.880656 0.473757i \(-0.157103\pi\)
−0.850613 + 0.525792i \(0.823769\pi\)
\(278\) 8.43845 0.506104
\(279\) −2.84233 4.92306i −0.170166 0.294736i
\(280\) −1.78078 3.08440i −0.106422 0.184328i
\(281\) −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 −0.984427 0.175793i \(-0.943751\pi\)
0.644455 + 0.764643i \(0.277084\pi\)
\(284\) 2.43845 4.22351i 0.144695 0.250619i
\(285\) −3.56155 −0.210968
\(286\) −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
\(290\) −3.28078 5.68247i −0.192654 0.333686i
\(291\) 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 \(0.0929940\pi\)
−0.229389 + 0.973335i \(0.573673\pi\)
\(294\) 5.68466 0.331536
\(295\) −5.28078 9.14657i −0.307459 0.532534i
\(296\) −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
\(300\) 1.00000 0.0577350
\(301\) −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
\(305\) −3.00000 5.19615i −0.171780 0.297531i
\(306\) −2.56155 4.43674i −0.146434 0.253632i
\(307\) −15.6155 −0.891225 −0.445613 0.895226i \(-0.647014\pi\)
−0.445613 + 0.895226i \(0.647014\pi\)
\(308\) 7.34233 + 12.7173i 0.418368 + 0.724635i
\(309\) −0.219224 + 0.379706i −0.0124712 + 0.0216007i
\(310\) −2.84233 + 4.92306i −0.161433 + 0.279611i
\(311\) −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 \(-0.439996\pi\)
0.187394 + 0.982285i \(0.439996\pi\)
\(314\) −11.0616 + 19.1592i −0.624240 + 1.08121i
\(315\) −1.78078 + 3.08440i −0.100335 + 0.173786i
\(316\) −3.71922 6.44188i −0.209223 0.362384i
\(317\) −4.19224 −0.235459 −0.117730 0.993046i \(-0.537562\pi\)
−0.117730 + 0.993046i \(0.537562\pi\)
\(318\) −2.21922 3.84381i −0.124448 0.215550i
\(319\) 13.5270 + 23.4294i 0.757366 + 1.31180i
\(320\) 1.00000 0.0559017
\(321\) −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
\(325\) −3.34233 1.35234i −0.185399 0.0750146i
\(326\) −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
\(330\) −4.12311 −0.226969
\(331\) 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
\(335\) −7.12311 + 12.3376i −0.389177 + 0.674074i
\(336\) −1.78078 + 3.08440i −0.0971493 + 0.168268i
\(337\) −6.00000 −0.326841 −0.163420 0.986557i \(-0.552253\pi\)
−0.163420 + 0.986557i \(0.552253\pi\)
\(338\) −12.5000 + 3.57071i −0.679910 + 0.194221i
\(339\) −3.68466 −0.200123
\(340\) −2.56155 + 4.43674i −0.138920 + 0.240616i
\(341\) 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
\(345\) 3.84233 + 6.65511i 0.206864 + 0.358299i
\(346\) −25.1771 −1.35353
\(347\) −4.56155 7.90084i −0.244877 0.424139i 0.717220 0.696847i \(-0.245414\pi\)
−0.962097 + 0.272707i \(0.912081\pi\)
\(348\) −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 \(-0.0608858\pi\)
\(350\) 3.56155 0.190373
\(351\) −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 \(0.488809\pi\)
−0.883066 + 0.469249i \(0.844525\pi\)
\(354\) −5.28078 + 9.14657i −0.280670 + 0.486135i
\(355\) 2.43845 + 4.22351i 0.129419 + 0.224161i
\(356\) 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 \(0.458921\pi\)
\(360\) −0.500000 0.866025i −0.0263523 0.0456435i
\(361\) 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
\(365\) −15.3693 −0.804467
\(366\) −3.00000 + 5.19615i −0.156813 + 0.271607i
\(367\) 10.2462 17.7470i 0.534848 0.926384i −0.464323 0.885666i \(-0.653702\pi\)
0.999171 0.0407177i \(-0.0129644\pi\)
\(368\) 3.84233 + 6.65511i 0.200295 + 0.346922i
\(369\) −4.24621 −0.221049
\(370\) −2.06155 3.57071i −0.107175 0.185633i
\(371\) −7.90388 13.6899i −0.410349 0.710746i
\(372\) 5.68466 0.294736
\(373\) 2.59612 + 4.49661i 0.134422 + 0.232826i 0.925376 0.379049i \(-0.123749\pi\)
−0.790955 + 0.611875i \(0.790416\pi\)
\(374\) 10.5616 18.2931i 0.546125 0.945916i
\(375\) −0.500000 + 0.866025i −0.0258199 + 0.0447214i
\(376\) 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 \(0.123076\pi\)
\(380\) 1.78078 3.08440i 0.0913519 0.158226i
\(381\) 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 \(-0.988253\pi\)
0.467706 0.883884i \(-0.345081\pi\)
\(384\) −0.500000 0.866025i −0.0255155 0.0441942i
\(385\) −14.6847 −0.748399
\(386\) 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 \(0.339533\pi\)
\(390\) 0.500000 + 3.57071i 0.0253185 + 0.180810i
\(391\) −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
\(395\) 7.43845 0.374269
\(396\) 2.06155 + 3.57071i 0.103597 + 0.179435i
\(397\) 5.93845 + 10.2857i 0.298042 + 0.516224i 0.975688 0.219164i \(-0.0703331\pi\)
−0.677646 + 0.735388i \(0.737000\pi\)
\(398\) 11.1231 0.557551
\(399\) 6.34233 + 10.9852i 0.317514 + 0.549950i
\(400\) −0.500000 + 0.866025i −0.0250000 + 0.0433013i
\(401\) −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
\(405\) −0.500000 + 0.866025i −0.0248452 + 0.0430331i
\(406\) −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 \(0.847565\pi\)
\(410\) 2.12311 + 3.67733i 0.104853 + 0.181610i
\(411\) −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
\(415\) 1.12311 0.0551311
\(416\) 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 \(0.162838\pi\)
\(420\) −1.78078 3.08440i −0.0868930 0.150503i
\(421\) 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
\(425\) −2.56155 4.43674i −0.124254 0.215213i
\(426\) 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
\(430\) 4.56155 0.219978
\(431\) −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 \(-0.902153\pi\)
0.214523 0.976719i \(-0.431180\pi\)
\(434\) 20.2462 0.971849
\(435\) −3.28078 5.68247i −0.157301 0.272454i
\(436\) 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 \(0.298611\pi\)
\(440\) 2.06155 3.57071i 0.0982807 0.170227i
\(441\) 5.68466 0.270698
\(442\) −17.1231 6.92820i −0.814463 0.329541i
\(443\) −4.87689 −0.231708 −0.115854 0.993266i \(-0.536961\pi\)
−0.115854 + 0.993266i \(0.536961\pi\)
\(444\) −2.06155 + 3.57071i −0.0978370 + 0.169459i
\(445\) −0.903882 + 1.56557i −0.0428481 + 0.0742151i
\(446\) 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 \(-0.369154\pi\)
\(450\) 1.00000 0.0471405
\(451\) −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
\(455\) 1.78078 + 12.7173i 0.0834841 + 0.596196i
\(456\) −3.56155 −0.166785
\(457\) −1.87689 + 3.25088i −0.0877974 + 0.152070i −0.906580 0.422034i \(-0.861316\pi\)
0.818782 + 0.574104i \(0.194649\pi\)
\(458\) 3.87689 6.71498i 0.181155 0.313770i
\(459\) −2.56155 4.43674i −0.119563 0.207089i
\(460\) −7.68466 −0.358299
\(461\) −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 \(-0.214647\pi\)
0.781123 + 0.624377i \(0.214647\pi\)
\(464\) −3.28078 5.68247i −0.152306 0.263802i
\(465\) −2.84233 + 4.92306i −0.131810 + 0.228301i
\(466\) 8.84233 15.3154i 0.409613 0.709471i
\(467\) 39.8617 1.84458 0.922291 0.386497i \(-0.126315\pi\)
0.922291 + 0.386497i \(0.126315\pi\)
\(468\) 2.84233 2.21837i 0.131387 0.102544i
\(469\) 50.7386 2.34289
\(470\) −3.50000 + 6.06218i −0.161443 + 0.279627i
\(471\) −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
\(475\) 1.78078 + 3.08440i 0.0817076 + 0.141522i
\(476\) 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 \(0.00110963\pi\)
\(480\) 1.00000 0.0456435
\(481\) 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
\(485\) −0.561553 0.972638i −0.0254988 0.0441652i
\(486\) 1.00000 0.0453609
\(487\) 12.0270 + 20.8314i 0.544995 + 0.943959i 0.998607 + 0.0527597i \(0.0168017\pi\)
−0.453612 + 0.891199i \(0.649865\pi\)
\(488\) −3.00000 5.19615i −0.135804 0.235219i
\(489\) −18.5616 −0.839382
\(490\) −2.84233 4.92306i −0.128403 0.222401i
\(491\) 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
\(495\) −4.12311 −0.185320
\(496\) −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 \(0.471463\pi\)
\(500\) −0.500000 0.866025i −0.0223607 0.0387298i
\(501\) 10.1847 + 17.6403i 0.455017 + 0.788113i
\(502\) 0.123106 0.00549447
\(503\) 2.97301 + 5.14941i 0.132560 + 0.229601i 0.924663 0.380787i \(-0.124347\pi\)
−0.792103 + 0.610388i \(0.791014\pi\)
\(504\) −1.78078 + 3.08440i −0.0793221 + 0.137390i
\(505\) 8.56155 14.8290i 0.380984 0.659884i
\(506\) 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 \(-0.0605849\pi\)
\(510\) −2.56155 + 4.43674i −0.113427 + 0.196462i
\(511\) 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
\(515\) 0.438447 0.0193203
\(516\) −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
\(520\) −3.34233 1.35234i −0.146571 0.0593042i
\(521\) −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 −0.747868 0.663847i \(-0.768923\pi\)
0.948843 + 0.315749i \(0.102256\pi\)
\(524\) −3.06155 5.30277i −0.133745 0.231652i
\(525\) 3.56155 0.155439
\(526\) 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
\(530\) −2.21922 + 3.84381i −0.0963969 + 0.166964i
\(531\) −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
\(535\) −1.00000 + 1.73205i −0.0432338 + 0.0748831i
\(536\) −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
\(540\) −0.500000 0.866025i −0.0215166 0.0372678i
\(541\) −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
\(545\) −20.2462 −0.867252
\(546\) 10.1231 7.90084i 0.433229 0.338125i
\(547\) 35.6155 1.52281 0.761405 0.648276i \(-0.224510\pi\)
0.761405 + 0.648276i \(0.224510\pi\)
\(548\) 4.40388 7.62775i 0.188125 0.325841i
\(549\) −3.00000 + 5.19615i −0.128037 + 0.221766i
\(550\) 2.06155 + 3.57071i 0.0879049 + 0.152256i
\(551\) −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
\(555\) −2.06155 3.57071i −0.0875080 0.151568i
\(556\) −4.21922 + 7.30791i −0.178935 + 0.309924i
\(557\) 2.21922 3.84381i 0.0940315 0.162867i −0.815172 0.579218i \(-0.803358\pi\)
0.909204 + 0.416351i \(0.136691\pi\)
\(558\) 5.68466 0.240651
\(559\) 2.28078 + 16.2880i 0.0964666 + 0.688909i
\(560\) 3.56155 0.150503
\(561\) 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 \(-0.922039\pi\)
0.275083 0.961420i \(-0.411295\pi\)
\(564\) 7.00000 0.294753
\(565\) 1.84233 + 3.19101i 0.0775074 + 0.134247i
\(566\) −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 \(0.0349914\pi\)
\(570\) 1.78078 3.08440i 0.0745885 0.129191i
\(571\) 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
\(575\) 3.84233 6.65511i 0.160236 0.277537i
\(576\) −0.500000 0.866025i −0.0208333 0.0360844i
\(577\) 8.73863 0.363794 0.181897 0.983318i \(-0.441776\pi\)
0.181897 + 0.983318i \(0.441776\pi\)
\(578\) −4.62311 8.00745i −0.192296 0.333066i
\(579\) 0 0
\(580\) 6.56155 0.272454
\(581\) −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
\(585\) 0.500000 + 3.57071i 0.0206725 + 0.147631i
\(586\) −24.9309 −1.02988
\(587\) 11.8769 20.5714i 0.490212 0.849072i −0.509725 0.860338i \(-0.670253\pi\)
0.999937 + 0.0112657i \(0.00358606\pi\)
\(588\) −2.84233 + 4.92306i −0.117216 + 0.203024i
\(589\) 10.1231 + 17.5337i 0.417115 + 0.722465i
\(590\) 10.5616 0.434812
\(591\) 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 \(-0.580439\pi\)
−0.250026 + 0.968239i \(0.580439\pi\)
\(594\) 2.06155 + 3.57071i 0.0845865 + 0.146508i
\(595\) −9.12311 + 15.8017i −0.374011 + 0.647806i
\(596\) 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 \(0.592330\pi\)
\(600\) −0.500000 + 0.866025i −0.0204124 + 0.0353553i
\(601\) 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
\(605\) −3.00000 5.19615i −0.121967 0.211254i
\(606\) −17.1231 −0.695579
\(607\) 14.7116 + 25.4813i 0.597127 + 1.03425i 0.993243 + 0.116054i \(0.0370246\pi\)
−0.396116 + 0.918201i \(0.629642\pi\)
\(608\) 1.78078 3.08440i 0.0722200 0.125089i
\(609\) −11.6847 + 20.2384i −0.473486 + 0.820102i
\(610\) 6.00000 0.242933
\(611\) −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 \(0.358926\pi\)
−0.996769 + 0.0803164i \(0.974407\pi\)
\(614\) 7.80776 13.5234i 0.315096 0.545762i
\(615\) 2.12311 + 3.67733i 0.0856119 + 0.148284i
\(616\) −14.6847 −0.591662
\(617\) 20.8423 + 36.1000i 0.839081 + 1.45333i 0.890664 + 0.454662i \(0.150240\pi\)
−0.0515837 + 0.998669i \(0.516427\pi\)
\(618\) −0.219224 0.379706i −0.00881847 0.0152740i
\(619\) −16.4384 −0.660717 −0.330358 0.943856i \(-0.607170\pi\)
−0.330358 + 0.943856i \(0.607170\pi\)
\(620\) −2.84233 4.92306i −0.114151 0.197715i
\(621\) 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
\(625\) 1.00000 0.0400000
\(626\) −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
\(630\) −1.78078 3.08440i −0.0709478 0.122885i
\(631\) 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
\(635\) 2.21922 3.84381i 0.0880672 0.152537i
\(636\) 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
\(640\) −0.500000 + 0.866025i −0.0197642 + 0.0342327i
\(641\) 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 \(-0.894720\pi\)
0.191658 0.981462i \(-0.438613\pi\)
\(644\) 13.6847 + 23.7025i 0.539251 + 0.934010i
\(645\) 4.56155 0.179611
\(646\) 9.12311 + 15.8017i 0.358944 + 0.621709i
\(647\) 1.02699 1.77879i 0.0403751 0.0699316i −0.845132 0.534558i \(-0.820478\pi\)
0.885507 + 0.464626i \(0.153811\pi\)
\(648\) −0.500000 + 0.866025i −0.0196419 + 0.0340207i
\(649\) −43.5464 −1.70935
\(650\) 2.84233 2.21837i 0.111485 0.0870116i
\(651\) 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 \(-0.542770\pi\)
0.925200 0.379480i \(-0.123897\pi\)
\(654\) 10.1231 + 17.5337i 0.395845 + 0.685623i
\(655\) 6.12311 0.239250
\(656\) 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 \(-0.373432\pi\)
\(660\) 2.06155 3.57071i 0.0802458 0.138990i
\(661\) 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
\(665\) 6.34233 10.9852i 0.245945 0.425989i
\(666\) −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
\(670\) −7.12311 12.3376i −0.275190 0.476642i
\(671\) −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 \(0.469510\pi\)
−0.909875 + 0.414882i \(0.863823\pi\)
\(674\) 3.00000 5.19615i 0.115556 0.200148i
\(675\) 1.00000 0.0384900
\(676\) 3.15767 12.6107i 0.121449 0.485026i
\(677\) −28.8769 −1.10983 −0.554915 0.831907i \(-0.687249\pi\)
−0.554915 + 0.831907i \(0.687249\pi\)
\(678\) 1.84233 3.19101i 0.0707542 0.122550i
\(679\) −2.00000 + 3.46410i −0.0767530 + 0.132940i
\(680\) −2.56155 4.43674i −0.0982311 0.170141i
\(681\) −20.0000 −0.766402
\(682\) 11.7192 + 20.2983i 0.448752 + 0.777262i
\(683\) −4.43845 7.68762i −0.169832 0.294158i 0.768528 0.639816i \(-0.220989\pi\)
−0.938361 + 0.345657i \(0.887656\pi\)
\(684\) −3.56155 −0.136179
\(685\) 4.40388 + 7.62775i 0.168264 + 0.291441i
\(686\) 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
\(690\) −7.68466 −0.292550
\(691\) 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
\(695\) −4.21922 7.30791i −0.160044 0.277205i
\(696\) −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
\(700\) −1.78078 + 3.08440i −0.0673070 + 0.116579i
\(701\) 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
\(705\) −3.50000 + 6.06218i −0.131818 + 0.228315i
\(706\) −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 \(0.941522\pi\)
\(710\) −4.87689 −0.183027
\(711\) −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
\(715\) −11.7192 + 9.14657i −0.438274 + 0.342062i
\(716\) −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 \(0.705358\pi\)
\(720\) 1.00000 0.0372678
\(721\) −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
\(725\) −3.28078 + 5.68247i −0.121845 + 0.211042i
\(726\) −3.00000 + 5.19615i −0.111340 + 0.192847i
\(727\) −23.4233 −0.868722 −0.434361 0.900739i \(-0.643026\pi\)
−0.434361 + 0.900739i \(0.643026\pi\)
\(728\) 1.78078 + 12.7173i 0.0660000 + 0.471334i
\(729\) 1.00000 0.0370370
\(730\) 7.68466 13.3102i 0.284422 0.492633i
\(731\) −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 \(-0.140876\pi\)
0.903651 + 0.428269i \(0.140876\pi\)
\(734\) 10.2462 + 17.7470i 0.378195 + 0.655052i
\(735\) −2.84233 4.92306i −0.104841 0.181590i
\(736\) −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 \(0.880587\pi\)
\(740\) 4.12311 0.151568
\(741\) 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 \(-0.632370\pi\)
0.994201 0.107538i \(-0.0342968\pi\)
\(744\) −2.84233 + 4.92306i −0.104205 + 0.180488i
\(745\) 11.4039 + 19.7521i 0.417806 + 0.723661i
\(746\) −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
\(750\) −0.500000 0.866025i −0.0182574 0.0316228i
\(751\) 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
\(755\) 9.36932 0.340984
\(756\) −1.78078 + 3.08440i −0.0647662 + 0.112178i
\(757\) −16.7116 + 28.9454i −0.607395 + 1.05204i 0.384273 + 0.923220i \(0.374452\pi\)
−0.991668 + 0.128820i \(0.958881\pi\)
\(758\) 2.65767 + 4.60322i 0.0965309 + 0.167197i
\(759\) 31.6847 1.15008
\(760\) 1.78078 + 3.08440i 0.0645955 + 0.111883i
\(761\) −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
\(765\) −2.56155 + 4.43674i −0.0926131 + 0.160411i
\(766\) 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 \(-0.141436\pi\)
\(770\) 7.34233 12.7173i 0.264599 0.458299i
\(771\) 0.719224 + 1.24573i 0.0259022 + 0.0448639i
\(772\) 0 0
\(773\) 10.5885 + 18.3399i 0.380843 + 0.659640i 0.991183 0.132500i \(-0.0423004\pi\)
−0.610340 + 0.792140i \(0.708967\pi\)
\(774\) −2.28078 3.95042i −0.0819808 0.141995i
\(775\) 5.68466 0.204199
\(776\) −0.561553 0.972638i −0.0201586 0.0349157i
\(777\) −7.34233 + 12.7173i −0.263405 + 0.456230i
\(778\)