Properties

Label 390.2.i.g.211.1
Level $390$
Weight $2$
Character 390.211
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 211.1
Root \(1.28078 - 2.21837i\) of defining polynomial
Character \(\chi\) \(=\) 390.211
Dual form 390.2.i.g.61.1

$q$-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 \(\left(\mathbb{Z}/390\mathbb{Z}\right)^\times\).

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

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 0.303959 + 0.952685i \(0.401692\pi\)
−0.977029 + 0.213107i \(0.931642\pi\)
\(8\) 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 0.989191 + 0.146631i \(0.0468429\pi\)
−0.367610 + 0.929980i \(0.619824\pi\)
\(12\) 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 0.367982 + 0.929833i \(0.380049\pi\)
−0.989250 + 0.146235i \(0.953285\pi\)
\(18\) 1.00000 0.235702
\(19\) 1.78078 3.08440i 0.408538 0.707609i −0.586188 0.810175i \(-0.699372\pi\)
0.994726 + 0.102566i \(0.0327054\pi\)
\(20\) −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 0.918839 + 0.394632i \(0.129128\pi\)
−0.117658 + 0.993054i \(0.537539\pi\)
\(24\) −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 −0.991368 0.131105i \(-0.958147\pi\)
0.382144 0.924103i \(-0.375186\pi\)
\(30\) −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 0.645312 0.763919i \(-0.276727\pi\)
−0.984229 + 0.176897i \(0.943394\pi\)
\(38\) −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 0.982821 0.184564i \(-0.0590872\pi\)
−0.651247 + 0.758866i \(0.725754\pi\)
\(42\) −1.78078 3.08440i −0.274780 0.475933i
\(43\) −2.28078 + 3.95042i −0.347815 + 0.602433i −0.985861 0.167565i \(-0.946410\pi\)
0.638046 + 0.769998i \(0.279743\pi\)
\(44\) −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 0.285146 + 0.958484i \(0.407958\pi\)
−0.972645 + 0.232298i \(0.925375\pi\)
\(60\) 1.00000 0.129099
\(61\) −3.00000 + 5.19615i −0.384111 + 0.665299i −0.991645 0.128994i \(-0.958825\pi\)
0.607535 + 0.794293i \(0.292159\pi\)
\(62\) −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 −0.861763 0.507311i \(-0.830639\pi\)
−0.00846293 0.999964i \(-0.502694\pi\)
\(68\) −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 −0.684274 0.729225i \(-0.739881\pi\)
0.973664 + 0.227986i \(0.0732141\pi\)
\(72\) −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 0.814136 0.580675i \(-0.197211\pi\)
−0.909947 + 0.414725i \(0.863878\pi\)
\(90\) 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 −0.893125 0.449808i \(-0.851492\pi\)
0.836108 + 0.548565i \(0.184826\pi\)
\(98\) −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 0.879486 + 0.475925i \(0.157887\pi\)
−0.0275793 + 0.999620i \(0.508780\pi\)
\(102\) −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 0.813632 0.581380i \(-0.197487\pi\)
−0.910306 + 0.413936i \(0.864154\pi\)
\(108\) −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 −0.766264 0.642526i \(-0.777887\pi\)
0.939576 + 0.342341i \(0.111220\pi\)
\(114\) 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 0.947530 0.319668i \(-0.103571\pi\)
−0.750605 + 0.660751i \(0.770238\pi\)
\(128\) −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 −0.614264 0.789101i \(-0.710547\pi\)
0.990513 + 0.137418i \(0.0438804\pi\)
\(138\) −7.68466 −0.654162
\(139\) −4.21922 + 7.30791i −0.357870 + 0.619849i −0.987605 0.156961i \(-0.949830\pi\)
0.629735 + 0.776810i \(0.283164\pi\)
\(140\) −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 0.158263 0.987397i \(-0.449411\pi\)
0.775979 0.630758i \(-0.217256\pi\)
\(150\) −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 −0.231250 0.972894i \(-0.574281\pi\)
0.958176 0.286179i \(-0.0923853\pi\)
\(164\) −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 0.927122 + 0.374760i \(0.122275\pi\)
−0.139009 + 0.990291i \(0.544392\pi\)
\(168\) 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 0.227575 0.973760i \(-0.426920\pi\)
0.729514 0.683966i \(-0.239746\pi\)
\(174\) 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 0.871858 0.489759i \(-0.162915\pi\)
−0.860073 + 0.510171i \(0.829582\pi\)
\(180\) −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 0.279381 + 0.960180i \(0.409871\pi\)
−0.971231 + 0.238139i \(0.923463\pi\)
\(192\) −0.500000 0.866025i −0.0360844 0.0625000i
\(193\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(194\) 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 0.970923 0.239394i \(-0.0769487\pi\)
−0.692782 + 0.721147i \(0.743615\pi\)
\(198\) 2.06155 + 3.57071i 0.146508 + 0.253760i
\(199\) −5.56155 + 9.63289i −0.394248 + 0.682858i −0.993005 0.118073i \(-0.962328\pi\)
0.598757 + 0.800931i \(0.295662\pi\)
\(200\) 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 0.721734 0.692171i \(-0.243345\pi\)
−0.960304 + 0.278955i \(0.910012\pi\)
\(212\) −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 0.850680 + 0.525683i \(0.176190\pi\)
0.0299151 + 0.999552i \(0.490476\pi\)
\(224\) −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 −0.315906 0.948790i \(-0.602309\pi\)
0.979630 0.200812i \(-0.0643581\pi\)
\(228\) 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 −0.345198 0.938530i \(-0.612188\pi\)
0.985390 0.170315i \(-0.0544784\pi\)
\(242\) 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 −0.867961 0.496632i \(-0.834570\pi\)
0.864076 + 0.503361i \(0.167903\pi\)
\(252\) 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 0.887585 0.460643i \(-0.152381\pi\)
−0.842721 + 0.538350i \(0.819048\pi\)
\(258\) −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 0.993824 0.110972i \(-0.0353964\pi\)
−0.593016 + 0.805190i \(0.702063\pi\)
\(264\) 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 −0.810087 0.586310i \(-0.800580\pi\)
0.912803 + 0.408401i \(0.133914\pi\)
\(270\) −0.500000 0.866025i −0.0304290 0.0527046i
\(271\) −16.0885 27.8662i −0.977309 1.69275i −0.672094 0.740466i \(-0.734605\pi\)
−0.305215 0.952283i \(-0.598728\pi\)
\(272\) 5.12311 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 −0.850613 0.525792i \(-0.823769\pi\)
0.880656 + 0.473757i \(0.157103\pi\)
\(278\) 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 0.644455 0.764643i \(-0.277084\pi\)
−0.984427 + 0.175793i \(0.943751\pi\)
\(284\) 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 −0.229389 0.973335i \(-0.573673\pi\)
0.957627 0.288011i \(-0.0929940\pi\)
\(294\) 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 −0.484865 0.874589i \(-0.661131\pi\)
0.999849 0.0173896i \(-0.00553556\pi\)
\(332\) −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 −0.962097 0.272707i \(-0.912081\pi\)
0.717220 + 0.696847i \(0.245414\pi\)
\(348\) −3.28078 5.68247i −0.175868 0.304612i
\(349\) 12.2462 + 21.2111i 0.655525 + 1.13540i 0.981762 + 0.190114i \(0.0608858\pi\)
−0.326237 + 0.945288i \(0.605781\pi\)
\(350\) 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 −0.883066 0.469249i \(-0.844525\pi\)
0.0351511 0.999382i \(-0.488809\pi\)
\(354\) −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 0.999171 + 0.0407177i \(0.0129644\pi\)
−0.464323 + 0.885666i \(0.653702\pi\)
\(368\) 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 −0.790955 0.611875i \(-0.790416\pi\)
0.925376 + 0.379049i \(0.123749\pi\)
\(374\) 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 0.926175 0.377093i \(-0.123076\pi\)
−0.789660 + 0.613545i \(0.789743\pi\)
\(380\) 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 0.467706 + 0.883884i \(0.345081\pi\)
−0.999319 + 0.0368973i \(0.988253\pi\)
\(384\) −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 −0.677646 0.735388i \(-0.737000\pi\)
0.975688 + 0.219164i \(0.0703331\pi\)
\(398\) 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 0.663081 0.748548i \(-0.269248\pi\)
−0.979802 + 0.199971i \(0.935915\pi\)
\(402\) 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 −0.887507 0.460794i \(-0.847565\pi\)
0.842813 + 0.538207i \(0.180898\pi\)
\(410\) 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 0.871977 0.489547i \(-0.162838\pi\)
−0.859949 + 0.510381i \(0.829505\pi\)
\(420\) −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 −0.984537 0.175178i \(-0.943950\pi\)
0.340559 0.940223i \(-0.389384\pi\)
\(432\) −0.500000 0.866025i −0.0240563 0.0416667i
\(433\) −15.3693 + 26.6204i −0.738602 + 1.27930i 0.214523 + 0.976719i \(0.431180\pi\)
−0.953125 + 0.302578i \(0.902153\pi\)
\(434\) 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 0.591311 0.806444i \(-0.298611\pi\)
−0.994056 + 0.108869i \(0.965277\pi\)
\(440\) 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 0.399585 + 0.916696i \(0.369154\pi\)
−0.993675 + 0.112298i \(0.964179\pi\)
\(450\) 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 0.818782 0.574104i \(-0.194649\pi\)
−0.906580 + 0.422034i \(0.861316\pi\)
\(458\) 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 −0.936395 0.350947i \(-0.885860\pi\)
0.772127 + 0.635468i \(0.219193\pi\)
\(462\) 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 0.999994 0.00348601i \(-0.00110963\pi\)
−0.503016 + 0.864277i \(0.667776\pi\)
\(480\) 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 −0.453612 0.891199i \(-0.649865\pi\)
0.998607 0.0527597i \(-0.0168017\pi\)
\(488\) −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 0.999880 0.0154850i \(-0.00492923\pi\)
−0.513350 + 0.858179i \(0.671596\pi\)
\(492\) 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 −0.792103 0.610388i \(-0.791014\pi\)
0.924663 + 0.380787i \(0.124347\pi\)
\(504\) −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 0.981941 + 0.189186i \(0.0605849\pi\)
−0.327131 + 0.944979i \(0.606082\pi\)
\(510\) −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 0.948843 0.315749i \(-0.102256\pi\)
−0.747868 + 0.663847i \(0.768923\pi\)
\(524\) −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 0.909204 0.416351i \(-0.136691\pi\)
−0.815172 + 0.579218i \(0.803358\pi\)
\(558\) 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 0.275083 + 0.961420i \(0.411295\pi\)
−0.970156 + 0.242481i \(0.922039\pi\)
\(564\) 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 0.993964 0.109707i \(-0.0349914\pi\)
−0.591991 + 0.805944i \(0.701658\pi\)
\(570\) 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 0.999937 0.0112657i \(-0.00358606\pi\)
−0.509725 + 0.860338i \(0.670253\pi\)
\(588\) −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 0.955193 + 0.295984i \(0.0956476\pi\)
−0.221267 + 0.975213i \(0.571019\pi\)
\(602\) −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 −0.396116 0.918201i \(-0.629642\pi\)
0.993243 0.116054i \(-0.0370246\pi\)
\(608\) 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 −0.996769 0.0803164i \(-0.974407\pi\)
0.428829 0.903386i \(-0.358926\pi\)
\(614\) 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 −0.0515837 0.998669i \(-0.516427\pi\)
0.890664 0.454662i \(-0.150240\pi\)
\(618\) −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 −0.390470 0.920616i \(-0.627688\pi\)
0.992512 0.122151i \(-0.0389791\pi\)
\(632\) 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 −0.670453 0.741952i \(-0.733900\pi\)
0.977776 + 0.209654i \(0.0672337\pi\)
\(642\) 2.00000 0.0789337
\(643\) −19.1231 + 33.1222i −0.754142 + 1.30621i 0.191658 + 0.981462i \(0.438613\pi\)
−0.945800 + 0.324750i \(0.894720\pi\)
\(644\) 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 0.885507 0.464626i \(-0.153811\pi\)
−0.845132 + 0.534558i \(0.820478\pi\)
\(648\) −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 0.925200 + 0.379480i \(0.123897\pi\)
−0.133961 + 0.990987i \(0.542770\pi\)
\(654\) 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 0.387230 + 0.921983i \(0.373432\pi\)
−0.992076 + 0.125640i \(0.959902\pi\)
\(660\) 2.06155 + 3.57071i 0.0802458 + 0.138990i
\(661\) 5.80776 + 10.0593i 0.225896 + 0.391263i 0.956588 0.291444i \(-0.0941358\pi\)
−0.730692 + 0.682707i \(0.760802\pi\)
\(662\) −18.7386 −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 −0.909875 0.414882i \(-0.863823\pi\)
0.0956394 0.995416i \(-0.469510\pi\)
\(674\) 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 −0.938361 0.345657i \(-0.887656\pi\)
0.768528 + 0.639816i \(0.220989\pi\)
\(684\) −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 0.978940 0.204147i \(-0.0654419\pi\)
−0.666266 + 0.745714i \(0.732109\pi\)
\(692\) 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 −0.983172 0.182682i \(-0.941522\pi\)
0.649793 + 0.760111i \(0.274855\pi\)
\(710\) −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 −0.601320 0.799008i \(-0.705358\pi\)
0.992621 + 0.121254i \(0.0386917\pi\)
\(720\) 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 −0.930453 0.366410i \(-0.880587\pi\)
0.147906 0.989001i \(-0.452747\pi\)
\(740\) 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 0.994201 + 0.107538i \(0.0342968\pi\)
−0.403970 + 0.914772i \(0.632370\pi\)
\(744\) −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 0.893677 0.448711i \(-0.148117\pi\)
−0.835434 + 0.549591i \(0.814783\pi\)
\(752\) −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 −0.991668 0.128820i \(-0.958881\pi\)
0.384273 0.923220i \(-0.374452\pi\)
\(758\) 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 −0.947919 0.318510i \(-0.896818\pi\)
0.749798 + 0.661667i \(0.230151\pi\)
\(762\) −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 0.902897 + 0.429857i \(0.141436\pi\)
−0.0791816 + 0.996860i \(0.525231\pi\)
\(770\) 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 −0.610340 0.792140i \(-0.708967\pi\)
0.991183 + 0.132500i \(0.0423004\pi\)
\(774\) −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
\(778\)