Properties

Label 1170.2.i.o.991.1
Level $1170$
Weight $2$
Character 1170.991
Analytic conductor $9.342$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1170.i (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.34249703649\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{17})\)
Defining polynomial: \(x^{4} - x^{3} + 5 x^{2} + 4 x + 16\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 390)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 991.1
Root \(1.28078 - 2.21837i\) of defining polynomial
Character \(\chi\) \(=\) 1170.991
Dual form 1170.2.i.o.451.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} -1.00000 q^{5} +(-1.78078 + 3.08440i) q^{7} -1.00000 q^{8} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} -1.00000 q^{5} +(-1.78078 + 3.08440i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{10} +(-2.06155 - 3.57071i) q^{11} +(-3.34233 + 1.35234i) q^{13} -3.56155 q^{14} +(-0.500000 - 0.866025i) q^{16} +(2.56155 - 4.43674i) q^{17} +(1.78078 - 3.08440i) q^{19} +(0.500000 - 0.866025i) q^{20} +(2.06155 - 3.57071i) q^{22} +(-3.84233 - 6.65511i) q^{23} +1.00000 q^{25} +(-2.84233 - 2.21837i) q^{26} +(-1.78078 - 3.08440i) q^{28} +(3.28078 + 5.68247i) q^{29} +5.68466 q^{31} +(0.500000 - 0.866025i) q^{32} +5.12311 q^{34} +(1.78078 - 3.08440i) q^{35} +(-2.06155 - 3.57071i) q^{37} +3.56155 q^{38} +1.00000 q^{40} +(-2.12311 - 3.67733i) q^{41} +(-2.28078 + 3.95042i) q^{43} +4.12311 q^{44} +(3.84233 - 6.65511i) q^{46} -7.00000 q^{47} +(-2.84233 - 4.92306i) q^{49} +(0.500000 + 0.866025i) q^{50} +(0.500000 - 3.57071i) q^{52} -4.43845 q^{53} +(2.06155 + 3.57071i) q^{55} +(1.78078 - 3.08440i) q^{56} +(-3.28078 + 5.68247i) q^{58} +(5.28078 - 9.14657i) q^{59} +(-3.00000 + 5.19615i) q^{61} +(2.84233 + 4.92306i) q^{62} +1.00000 q^{64} +(3.34233 - 1.35234i) q^{65} +(-7.12311 - 12.3376i) q^{67} +(2.56155 + 4.43674i) q^{68} +3.56155 q^{70} +(-2.43845 + 4.22351i) q^{71} -15.3693 q^{73} +(2.06155 - 3.57071i) q^{74} +(1.78078 + 3.08440i) q^{76} +14.6847 q^{77} +7.43845 q^{79} +(0.500000 + 0.866025i) q^{80} +(2.12311 - 3.67733i) q^{82} -1.12311 q^{83} +(-2.56155 + 4.43674i) q^{85} -4.56155 q^{86} +(2.06155 + 3.57071i) q^{88} +(0.903882 + 1.56557i) q^{89} +(1.78078 - 12.7173i) q^{91} +7.68466 q^{92} +(-3.50000 - 6.06218i) q^{94} +(-1.78078 + 3.08440i) q^{95} +(-0.561553 + 0.972638i) q^{97} +(2.84233 - 4.92306i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 2q^{2} - 2q^{4} - 4q^{5} - 3q^{7} - 4q^{8} + O(q^{10}) \) \( 4q + 2q^{2} - 2q^{4} - 4q^{5} - 3q^{7} - 4q^{8} - 2q^{10} - q^{13} - 6q^{14} - 2q^{16} + 2q^{17} + 3q^{19} + 2q^{20} - 3q^{23} + 4q^{25} + q^{26} - 3q^{28} + 9q^{29} - 2q^{31} + 2q^{32} + 4q^{34} + 3q^{35} + 6q^{38} + 4q^{40} + 8q^{41} - 5q^{43} + 3q^{46} - 28q^{47} + q^{49} + 2q^{50} + 2q^{52} - 26q^{53} + 3q^{56} - 9q^{58} + 17q^{59} - 12q^{61} - q^{62} + 4q^{64} + q^{65} - 12q^{67} + 2q^{68} + 6q^{70} - 18q^{71} - 12q^{73} + 3q^{76} + 34q^{77} + 38q^{79} + 2q^{80} - 8q^{82} + 12q^{83} - 2q^{85} - 10q^{86} - 17q^{89} + 3q^{91} + 6q^{92} - 14q^{94} - 3q^{95} + 6q^{97} - q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1170\mathbb{Z}\right)^\times\).

\(n\) \(911\) \(937\) \(1081\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\)

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 0
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) −1.00000 −0.447214
\(6\) 0 0
\(7\) −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 0
\(10\) −0.500000 0.866025i −0.158114 0.273861i
\(11\) −2.06155 3.57071i −0.621582 1.07661i −0.989191 0.146631i \(-0.953157\pi\)
0.367610 0.929980i \(-0.380176\pi\)
\(12\) 0 0
\(13\) −3.34233 + 1.35234i −0.926995 + 0.375073i
\(14\) −3.56155 −0.951865
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 2.56155 4.43674i 0.621268 1.07607i −0.367982 0.929833i \(-0.619951\pi\)
0.989250 0.146235i \(-0.0467154\pi\)
\(18\) 0 0
\(19\) 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
\(21\) 0 0
\(22\) 2.06155 3.57071i 0.439525 0.761279i
\(23\) −3.84233 6.65511i −0.801181 1.38769i −0.918839 0.394632i \(-0.870872\pi\)
0.117658 0.993054i \(-0.462461\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) −2.84233 2.21837i −0.557427 0.435058i
\(27\) 0 0
\(28\) −1.78078 3.08440i −0.336535 0.582896i
\(29\) 3.28078 + 5.68247i 0.609225 + 1.05521i 0.991368 + 0.131105i \(0.0418527\pi\)
−0.382144 + 0.924103i \(0.624814\pi\)
\(30\) 0 0
\(31\) 5.68466 1.02099 0.510497 0.859879i \(-0.329461\pi\)
0.510497 + 0.859879i \(0.329461\pi\)
\(32\) 0.500000 0.866025i 0.0883883 0.153093i
\(33\) 0 0
\(34\) 5.12311 0.878605
\(35\) 1.78078 3.08440i 0.301006 0.521358i
\(36\) 0 0
\(37\) −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
\(39\) 0 0
\(40\) 1.00000 0.158114
\(41\) −2.12311 3.67733i −0.331573 0.574302i 0.651247 0.758866i \(-0.274246\pi\)
−0.982821 + 0.184564i \(0.940913\pi\)
\(42\) 0 0
\(43\) −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 0
\(46\) 3.84233 6.65511i 0.566521 0.981242i
\(47\) −7.00000 −1.02105 −0.510527 0.859861i \(-0.670550\pi\)
−0.510527 + 0.859861i \(0.670550\pi\)
\(48\) 0 0
\(49\) −2.84233 4.92306i −0.406047 0.703294i
\(50\) 0.500000 + 0.866025i 0.0707107 + 0.122474i
\(51\) 0 0
\(52\) 0.500000 3.57071i 0.0693375 0.495169i
\(53\) −4.43845 −0.609668 −0.304834 0.952406i \(-0.598601\pi\)
−0.304834 + 0.952406i \(0.598601\pi\)
\(54\) 0 0
\(55\) 2.06155 + 3.57071i 0.277980 + 0.481475i
\(56\) 1.78078 3.08440i 0.237966 0.412170i
\(57\) 0 0
\(58\) −3.28078 + 5.68247i −0.430787 + 0.746145i
\(59\) 5.28078 9.14657i 0.687499 1.19078i −0.285146 0.958484i \(-0.592042\pi\)
0.972645 0.232298i \(-0.0746246\pi\)
\(60\) 0 0
\(61\) −3.00000 + 5.19615i −0.384111 + 0.665299i −0.991645 0.128994i \(-0.958825\pi\)
0.607535 + 0.794293i \(0.292159\pi\)
\(62\) 2.84233 + 4.92306i 0.360976 + 0.625229i
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 3.34233 1.35234i 0.414565 0.167738i
\(66\) 0 0
\(67\) −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
\(69\) 0 0
\(70\) 3.56155 0.425687
\(71\) −2.43845 + 4.22351i −0.289390 + 0.501239i −0.973664 0.227986i \(-0.926786\pi\)
0.684274 + 0.729225i \(0.260119\pi\)
\(72\) 0 0
\(73\) −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 0
\(76\) 1.78078 + 3.08440i 0.204269 + 0.353804i
\(77\) 14.6847 1.67347
\(78\) 0 0
\(79\) 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 0
\(82\) 2.12311 3.67733i 0.234458 0.406093i
\(83\) −1.12311 −0.123277 −0.0616384 0.998099i \(-0.519633\pi\)
−0.0616384 + 0.998099i \(0.519633\pi\)
\(84\) 0 0
\(85\) −2.56155 + 4.43674i −0.277839 + 0.481232i
\(86\) −4.56155 −0.491885
\(87\) 0 0
\(88\) 2.06155 + 3.57071i 0.219762 + 0.380639i
\(89\) 0.903882 + 1.56557i 0.0958113 + 0.165950i 0.909947 0.414725i \(-0.136122\pi\)
−0.814136 + 0.580675i \(0.802789\pi\)
\(90\) 0 0
\(91\) 1.78078 12.7173i 0.186676 1.33313i
\(92\) 7.68466 0.801181
\(93\) 0 0
\(94\) −3.50000 6.06218i −0.360997 0.625266i
\(95\) −1.78078 + 3.08440i −0.182704 + 0.316452i
\(96\) 0 0
\(97\) −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
\(99\) 0 0
\(100\) −0.500000 + 0.866025i −0.0500000 + 0.0866025i
\(101\) −8.56155 14.8290i −0.851906 1.47555i −0.879486 0.475925i \(-0.842113\pi\)
0.0275793 0.999620i \(-0.491220\pi\)
\(102\) 0 0
\(103\) 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
\(105\) 0 0
\(106\) −2.21922 3.84381i −0.215550 0.373344i
\(107\) 1.00000 + 1.73205i 0.0966736 + 0.167444i 0.910306 0.413936i \(-0.135846\pi\)
−0.813632 + 0.581380i \(0.802513\pi\)
\(108\) 0 0
\(109\) −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
\(111\) 0 0
\(112\) 3.56155 0.336535
\(113\) −1.84233 + 3.19101i −0.173312 + 0.300185i −0.939576 0.342341i \(-0.888780\pi\)
0.766264 + 0.642526i \(0.222113\pi\)
\(114\) 0 0
\(115\) 3.84233 + 6.65511i 0.358299 + 0.620592i
\(116\) −6.56155 −0.609225
\(117\) 0 0
\(118\) 10.5616 0.972270
\(119\) 9.12311 + 15.8017i 0.836314 + 1.44854i
\(120\) 0 0
\(121\) −3.00000 + 5.19615i −0.272727 + 0.472377i
\(122\) −6.00000 −0.543214
\(123\) 0 0
\(124\) −2.84233 + 4.92306i −0.255249 + 0.442104i
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) 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
\(129\) 0 0
\(130\) 2.84233 + 2.21837i 0.249289 + 0.194564i
\(131\) −6.12311 −0.534978 −0.267489 0.963561i \(-0.586194\pi\)
−0.267489 + 0.963561i \(0.586194\pi\)
\(132\) 0 0
\(133\) 6.34233 + 10.9852i 0.549950 + 0.952541i
\(134\) 7.12311 12.3376i 0.615343 1.06580i
\(135\) 0 0
\(136\) −2.56155 + 4.43674i −0.219651 + 0.380447i
\(137\) −4.40388 + 7.62775i −0.376249 + 0.651682i −0.990513 0.137418i \(-0.956120\pi\)
0.614264 + 0.789101i \(0.289453\pi\)
\(138\) 0 0
\(139\) −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
\(141\) 0 0
\(142\) −4.87689 −0.409260
\(143\) 11.7192 + 9.14657i 0.980011 + 0.764875i
\(144\) 0 0
\(145\) −3.28078 5.68247i −0.272454 0.471904i
\(146\) −7.68466 13.3102i −0.635987 1.10156i
\(147\) 0 0
\(148\) 4.12311 0.338917
\(149\) −11.4039 + 19.7521i −0.934242 + 1.61816i −0.158263 + 0.987397i \(0.550589\pi\)
−0.775979 + 0.630758i \(0.782744\pi\)
\(150\) 0 0
\(151\) 9.36932 0.762464 0.381232 0.924479i \(-0.375500\pi\)
0.381232 + 0.924479i \(0.375500\pi\)
\(152\) −1.78078 + 3.08440i −0.144440 + 0.250177i
\(153\) 0 0
\(154\) 7.34233 + 12.7173i 0.591662 + 1.02479i
\(155\) −5.68466 −0.456603
\(156\) 0 0
\(157\) 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
\(159\) 0 0
\(160\) −0.500000 + 0.866025i −0.0395285 + 0.0684653i
\(161\) 27.3693 2.15700
\(162\) 0 0
\(163\) 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
\(165\) 0 0
\(166\) −0.561553 0.972638i −0.0435850 0.0754913i
\(167\) −10.1847 17.6403i −0.788113 1.36505i −0.927122 0.374760i \(-0.877725\pi\)
0.139009 0.990291i \(-0.455608\pi\)
\(168\) 0 0
\(169\) 9.34233 9.03996i 0.718641 0.695382i
\(170\) −5.12311 −0.392924
\(171\) 0 0
\(172\) −2.28078 3.95042i −0.173908 0.301217i
\(173\) −12.5885 + 21.8040i −0.957089 + 1.65773i −0.227575 + 0.973760i \(0.573080\pi\)
−0.729514 + 0.683966i \(0.760254\pi\)
\(174\) 0 0
\(175\) −1.78078 + 3.08440i −0.134614 + 0.233158i
\(176\) −2.06155 + 3.57071i −0.155395 + 0.269153i
\(177\) 0 0
\(178\) −0.903882 + 1.56557i −0.0677488 + 0.117344i
\(179\) −0.157671 0.273094i −0.0117849 0.0204120i 0.860073 0.510171i \(-0.170418\pi\)
−0.871858 + 0.489759i \(0.837085\pi\)
\(180\) 0 0
\(181\) 11.1231 0.826774 0.413387 0.910555i \(-0.364346\pi\)
0.413387 + 0.910555i \(0.364346\pi\)
\(182\) 11.9039 4.81645i 0.882374 0.357019i
\(183\) 0 0
\(184\) 3.84233 + 6.65511i 0.283260 + 0.490621i
\(185\) 2.06155 + 3.57071i 0.151568 + 0.262524i
\(186\) 0 0
\(187\) −21.1231 −1.54467
\(188\) 3.50000 6.06218i 0.255264 0.442130i
\(189\) 0 0
\(190\) −3.56155 −0.258382
\(191\) 9.56155 16.5611i 0.691850 1.19832i −0.279381 0.960180i \(-0.590129\pi\)
0.971231 0.238139i \(-0.0765373\pi\)
\(192\) 0 0
\(193\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(194\) −1.12311 −0.0806343
\(195\) 0 0
\(196\) 5.68466 0.406047
\(197\) −3.90388 6.76172i −0.278140 0.481753i 0.692782 0.721147i \(-0.256385\pi\)
−0.970923 + 0.239394i \(0.923051\pi\)
\(198\) 0 0
\(199\) −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
\(201\) 0 0
\(202\) 8.56155 14.8290i 0.602389 1.04337i
\(203\) −23.3693 −1.64020
\(204\) 0 0
\(205\) 2.12311 + 3.67733i 0.148284 + 0.256836i
\(206\) 0.219224 + 0.379706i 0.0152740 + 0.0264554i
\(207\) 0 0
\(208\) 2.84233 + 2.21837i 0.197080 + 0.153816i
\(209\) −14.6847 −1.01576
\(210\) 0 0
\(211\) −3.46543 6.00231i −0.238570 0.413216i 0.721734 0.692171i \(-0.243345\pi\)
−0.960304 + 0.278955i \(0.910012\pi\)
\(212\) 2.21922 3.84381i 0.152417 0.263994i
\(213\) 0 0
\(214\) −1.00000 + 1.73205i −0.0683586 + 0.118401i
\(215\) 2.28078 3.95042i 0.155548 0.269416i
\(216\) 0 0
\(217\) −10.1231 + 17.5337i −0.687201 + 1.19027i
\(218\) −10.1231 17.5337i −0.685623 1.18753i
\(219\) 0 0
\(220\) −4.12311 −0.277980
\(221\) −2.56155 + 18.2931i −0.172309 + 1.23053i
\(222\) 0 0
\(223\) 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 0
\(226\) −3.68466 −0.245100
\(227\) −10.0000 + 17.3205i −0.663723 + 1.14960i 0.315906 + 0.948790i \(0.397691\pi\)
−0.979630 + 0.200812i \(0.935642\pi\)
\(228\) 0 0
\(229\) −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
\(231\) 0 0
\(232\) −3.28078 5.68247i −0.215394 0.373073i
\(233\) 17.6847 1.15856 0.579280 0.815128i \(-0.303334\pi\)
0.579280 + 0.815128i \(0.303334\pi\)
\(234\) 0 0
\(235\) 7.00000 0.456630
\(236\) 5.28078 + 9.14657i 0.343749 + 0.595391i
\(237\) 0 0
\(238\) −9.12311 + 15.8017i −0.591363 + 1.02427i
\(239\) −13.3693 −0.864789 −0.432395 0.901684i \(-0.642331\pi\)
−0.432395 + 0.901684i \(0.642331\pi\)
\(240\) 0 0
\(241\) 9.93845 17.2139i 0.640192 1.10884i −0.345198 0.938530i \(-0.612188\pi\)
0.985390 0.170315i \(-0.0544784\pi\)
\(242\) −6.00000 −0.385695
\(243\) 0 0
\(244\) −3.00000 5.19615i −0.192055 0.332650i
\(245\) 2.84233 + 4.92306i 0.181590 + 0.314523i
\(246\) 0 0
\(247\) −1.78078 + 12.7173i −0.113308 + 0.809182i
\(248\) −5.68466 −0.360976
\(249\) 0 0
\(250\) −0.500000 0.866025i −0.0316228 0.0547723i
\(251\) 0.0615528 0.106613i 0.00388518 0.00672933i −0.864076 0.503361i \(-0.832097\pi\)
0.867961 + 0.496632i \(0.165430\pi\)
\(252\) 0 0
\(253\) −15.8423 + 27.4397i −0.995999 + 1.72512i
\(254\) −2.21922 + 3.84381i −0.139246 + 0.241182i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −0.719224 1.24573i −0.0448639 0.0777066i 0.842721 0.538350i \(-0.180952\pi\)
−0.887585 + 0.460643i \(0.847619\pi\)
\(258\) 0 0
\(259\) 14.6847 0.912460
\(260\) −0.500000 + 3.57071i −0.0310087 + 0.221446i
\(261\) 0 0
\(262\) −3.06155 5.30277i −0.189143 0.327606i
\(263\) −6.50000 11.2583i −0.400807 0.694218i 0.593016 0.805190i \(-0.297937\pi\)
−0.993824 + 0.110972i \(0.964604\pi\)
\(264\) 0 0
\(265\) 4.43845 0.272652
\(266\) −6.34233 + 10.9852i −0.388873 + 0.673548i
\(267\) 0 0
\(268\) 14.2462 0.870226
\(269\) −1.68466 + 2.91791i −0.102715 + 0.177908i −0.912803 0.408401i \(-0.866086\pi\)
0.810087 + 0.586310i \(0.199420\pi\)
\(270\) 0 0
\(271\) −16.0885 27.8662i −0.977309 1.69275i −0.672094 0.740466i \(-0.734605\pi\)
−0.305215 0.952283i \(-0.598728\pi\)
\(272\) −5.12311 −0.310634
\(273\) 0 0
\(274\) −8.80776 −0.532096
\(275\) −2.06155 3.57071i −0.124316 0.215322i
\(276\) 0 0
\(277\) 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
\(279\) 0 0
\(280\) −1.78078 + 3.08440i −0.106422 + 0.184328i
\(281\) 0.246211 0.0146877 0.00734387 0.999973i \(-0.497662\pi\)
0.00734387 + 0.999973i \(0.497662\pi\)
\(282\) 0 0
\(283\) −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
\(285\) 0 0
\(286\) −2.06155 + 14.7224i −0.121902 + 0.870556i
\(287\) 15.1231 0.892689
\(288\) 0 0
\(289\) −4.62311 8.00745i −0.271947 0.471027i
\(290\) 3.28078 5.68247i 0.192654 0.333686i
\(291\) 0 0
\(292\) 7.68466 13.3102i 0.449711 0.778922i
\(293\) −12.4654 + 21.5908i −0.728238 + 1.26135i 0.229389 + 0.973335i \(0.426327\pi\)
−0.957627 + 0.288011i \(0.907006\pi\)
\(294\) 0 0
\(295\) −5.28078 + 9.14657i −0.307459 + 0.532534i
\(296\) 2.06155 + 3.57071i 0.119825 + 0.207544i
\(297\) 0 0
\(298\) −22.8078 −1.32122
\(299\) 21.8423 + 17.0474i 1.26317 + 0.985877i
\(300\) 0 0
\(301\) −8.12311 14.0696i −0.468208 0.810960i
\(302\) 4.68466 + 8.11407i 0.269572 + 0.466912i
\(303\) 0 0
\(304\) −3.56155 −0.204269
\(305\) 3.00000 5.19615i 0.171780 0.297531i
\(306\) 0 0
\(307\) −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 0
\(310\) −2.84233 4.92306i −0.161433 0.279611i
\(311\) 18.7386 1.06257 0.531285 0.847193i \(-0.321709\pi\)
0.531285 + 0.847193i \(0.321709\pi\)
\(312\) 0 0
\(313\) 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
\(315\) 0 0
\(316\) −3.71922 + 6.44188i −0.209223 + 0.362384i
\(317\) 4.19224 0.235459 0.117730 0.993046i \(-0.462438\pi\)
0.117730 + 0.993046i \(0.462438\pi\)
\(318\) 0 0
\(319\) 13.5270 23.4294i 0.757366 1.31180i
\(320\) −1.00000 −0.0559017
\(321\) 0 0
\(322\) 13.6847 + 23.7025i 0.762616 + 1.32089i
\(323\) −9.12311 15.8017i −0.507623 0.879229i
\(324\) 0 0
\(325\) −3.34233 + 1.35234i −0.185399 + 0.0750146i
\(326\) 18.5616 1.02803
\(327\) 0 0
\(328\) 2.12311 + 3.67733i 0.117229 + 0.203046i
\(329\) 12.4654 21.5908i 0.687242 1.19034i
\(330\) 0 0
\(331\) 9.36932 16.2281i 0.514984 0.891979i −0.484865 0.874589i \(-0.661131\pi\)
0.999849 0.0173896i \(-0.00553556\pi\)
\(332\) 0.561553 0.972638i 0.0308192 0.0533804i
\(333\) 0 0
\(334\) 10.1847 17.6403i 0.557280 0.965237i
\(335\) 7.12311 + 12.3376i 0.389177 + 0.674074i
\(336\) 0 0
\(337\) −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
\(339\) 0 0
\(340\) −2.56155 4.43674i −0.138920 0.240616i
\(341\) −11.7192 20.2983i −0.634632 1.09921i
\(342\) 0 0
\(343\) −4.68466 −0.252948
\(344\) 2.28078 3.95042i 0.122971 0.212992i
\(345\) 0 0
\(346\) −25.1771 −1.35353
\(347\) 4.56155 7.90084i 0.244877 0.424139i −0.717220 0.696847i \(-0.754586\pi\)
0.962097 + 0.272707i \(0.0879191\pi\)
\(348\) 0 0
\(349\) 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
\(351\) 0 0
\(352\) −4.12311 −0.219762
\(353\) 15.9309 + 27.5931i 0.847915 + 1.46863i 0.883066 + 0.469249i \(0.155475\pi\)
−0.0351511 + 0.999382i \(0.511191\pi\)
\(354\) 0 0
\(355\) 2.43845 4.22351i 0.129419 0.224161i
\(356\) −1.80776 −0.0958113
\(357\) 0 0
\(358\) 0.157671 0.273094i 0.00833316 0.0144335i
\(359\) −4.87689 −0.257393 −0.128696 0.991684i \(-0.541079\pi\)
−0.128696 + 0.991684i \(0.541079\pi\)
\(360\) 0 0
\(361\) 3.15767 + 5.46925i 0.166193 + 0.287855i
\(362\) 5.56155 + 9.63289i 0.292309 + 0.506294i
\(363\) 0 0
\(364\) 10.1231 + 7.90084i 0.530595 + 0.414117i
\(365\) 15.3693 0.804467
\(366\) 0 0
\(367\) 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
\(369\) 0 0
\(370\) −2.06155 + 3.57071i −0.107175 + 0.185633i
\(371\) 7.90388 13.6899i 0.410349 0.710746i
\(372\) 0 0
\(373\) 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 0
\(376\) 7.00000 0.360997
\(377\) −18.6501 14.5560i −0.960529 0.749670i
\(378\) 0 0
\(379\) 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
\(381\) 0 0
\(382\) 19.1231 0.978423
\(383\) 10.4039 18.0201i 0.531614 0.920782i −0.467706 0.883884i \(-0.654919\pi\)
0.999319 0.0368973i \(-0.0117474\pi\)
\(384\) 0 0
\(385\) −14.6847 −0.748399
\(386\) 0 0
\(387\) 0 0
\(388\) −0.561553 0.972638i −0.0285085 0.0493782i
\(389\) −19.0540 −0.966075 −0.483037 0.875600i \(-0.660467\pi\)
−0.483037 + 0.875600i \(0.660467\pi\)
\(390\) 0 0
\(391\) −39.3693 −1.99099
\(392\) 2.84233 + 4.92306i 0.143559 + 0.248652i
\(393\) 0 0
\(394\) 3.90388 6.76172i 0.196675 0.340651i
\(395\) −7.43845 −0.374269
\(396\) 0 0
\(397\) 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
\(399\) 0 0
\(400\) −0.500000 0.866025i −0.0250000 0.0433013i
\(401\) 6.34233 + 10.9852i 0.316721 + 0.548577i 0.979802 0.199971i \(-0.0640848\pi\)
−0.663081 + 0.748548i \(0.730752\pi\)
\(402\) 0 0
\(403\) −19.0000 + 7.68762i −0.946457 + 0.382947i
\(404\) 17.1231 0.851906
\(405\) 0 0
\(406\) −11.6847 20.2384i −0.579900 1.00442i
\(407\) −8.50000 + 14.7224i −0.421329 + 0.729764i
\(408\) 0 0
\(409\) −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
\(411\) 0 0
\(412\) −0.219224 + 0.379706i −0.0108004 + 0.0187068i
\(413\) 18.8078 + 32.5760i 0.925470 + 1.60296i
\(414\) 0 0
\(415\) 1.12311 0.0551311
\(416\) −0.500000 + 3.57071i −0.0245145 + 0.175069i
\(417\) 0 0
\(418\) −7.34233 12.7173i −0.359125 0.622023i
\(419\) −0.246211 0.426450i −0.0120282 0.0208335i 0.859949 0.510381i \(-0.170495\pi\)
−0.871977 + 0.489547i \(0.837162\pi\)
\(420\) 0 0
\(421\) 0.492423 0.0239992 0.0119996 0.999928i \(-0.496180\pi\)
0.0119996 + 0.999928i \(0.496180\pi\)
\(422\) 3.46543 6.00231i 0.168695 0.292188i
\(423\) 0 0
\(424\) 4.43845 0.215550
\(425\) 2.56155 4.43674i 0.124254 0.215213i
\(426\) 0 0
\(427\) −10.6847 18.5064i −0.517067 0.895586i
\(428\) −2.00000 −0.0966736
\(429\) 0 0
\(430\) 4.56155 0.219978
\(431\) 13.3693 + 23.1563i 0.643977 + 1.11540i 0.984537 + 0.175178i \(0.0560502\pi\)
−0.340559 + 0.940223i \(0.610616\pi\)
\(432\) 0 0
\(433\) −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
\(435\) 0 0
\(436\) 10.1231 17.5337i 0.484809 0.839714i
\(437\) −27.3693 −1.30925
\(438\) 0 0
\(439\) −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
\(441\) 0 0
\(442\) −17.1231 + 6.92820i −0.814463 + 0.329541i
\(443\) 4.87689 0.231708 0.115854 0.993266i \(-0.463039\pi\)
0.115854 + 0.993266i \(0.463039\pi\)
\(444\) 0 0
\(445\) −0.903882 1.56557i −0.0428481 0.0742151i
\(446\) −13.1501 + 22.7766i −0.622675 + 1.07850i
\(447\) 0 0
\(448\) −1.78078 + 3.08440i −0.0841338 + 0.145724i
\(449\) 12.5885 21.8040i 0.594090 1.02899i −0.399585 0.916696i \(-0.630846\pi\)
0.993675 0.112298i \(-0.0358210\pi\)
\(450\) 0 0
\(451\) −8.75379 + 15.1620i −0.412200 + 0.713951i
\(452\) −1.84233 3.19101i −0.0866559 0.150092i
\(453\) 0 0
\(454\) −20.0000 −0.938647
\(455\) −1.78078 + 12.7173i −0.0834841 + 0.596196i
\(456\) 0 0
\(457\) −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
\(459\) 0 0
\(460\) −7.68466 −0.358299
\(461\) 3.52699 6.10892i 0.164268 0.284521i −0.772127 0.635468i \(-0.780807\pi\)
0.936395 + 0.350947i \(0.114140\pi\)
\(462\) 0 0
\(463\) 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
\(465\) 0 0
\(466\) 8.84233 + 15.3154i 0.409613 + 0.709471i
\(467\) −39.8617 −1.84458 −0.922291 0.386497i \(-0.873685\pi\)
−0.922291 + 0.386497i \(0.873685\pi\)
\(468\) 0 0
\(469\) 50.7386 2.34289
\(470\) 3.50000 + 6.06218i 0.161443 + 0.279627i
\(471\) 0 0
\(472\) −5.28078 + 9.14657i −0.243067 + 0.421005i
\(473\) 18.8078 0.864782
\(474\) 0 0
\(475\) 1.78078 3.08440i 0.0817076 0.141522i
\(476\) −18.2462 −0.836314
\(477\) 0 0
\(478\) −6.68466 11.5782i −0.305749 0.529573i
\(479\) −10.8769 18.8393i −0.496978 0.860791i 0.503016 0.864277i \(-0.332224\pi\)
−0.999994 + 0.00348601i \(0.998890\pi\)
\(480\) 0 0
\(481\) 11.7192 + 9.14657i 0.534351 + 0.417048i
\(482\) 19.8769 0.905368
\(483\) 0 0
\(484\) −3.00000 5.19615i −0.136364 0.236189i
\(485\) 0.561553 0.972638i 0.0254988 0.0441652i
\(486\) 0 0
\(487\) 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
\(489\) 0 0
\(490\) −2.84233 + 4.92306i −0.128403 + 0.222401i
\(491\) −10.7808 18.6729i −0.486530 0.842694i 0.513350 0.858179i \(-0.328404\pi\)
−0.999880 + 0.0154850i \(0.995071\pi\)
\(492\) 0 0
\(493\) 33.6155 1.51397
\(494\) −11.9039 + 4.81645i −0.535581 + 0.216702i
\(495\) 0 0
\(496\) −2.84233 4.92306i −0.127624 0.221052i
\(497\) −8.68466 15.0423i −0.389560 0.674738i
\(498\) 0 0
\(499\) 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
\(501\) 0 0
\(502\) 0.123106 0.00549447
\(503\) −2.97301 + 5.14941i −0.132560 + 0.229601i −0.924663 0.380787i \(-0.875653\pi\)
0.792103 + 0.610388i \(0.208986\pi\)
\(504\) 0 0
\(505\) 8.56155 + 14.8290i 0.380984 + 0.659884i
\(506\) −31.6847 −1.40855
\(507\) 0 0
\(508\) −4.43845 −0.196924
\(509\) −14.7732 25.5879i −0.654811 1.13417i −0.981941 0.189186i \(-0.939415\pi\)
0.327131 0.944979i \(-0.393918\pi\)
\(510\) 0 0
\(511\) 27.3693 47.4050i 1.21075 2.09708i
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) 0.719224 1.24573i 0.0317236 0.0549469i
\(515\) −0.438447 −0.0193203
\(516\) 0 0
\(517\) 14.4309 + 24.9950i 0.634669 + 1.09928i
\(518\) 7.34233 + 12.7173i 0.322603 + 0.558766i
\(519\) 0 0
\(520\) −3.34233 + 1.35234i −0.146571 + 0.0593042i
\(521\) 18.6847 0.818590 0.409295 0.912402i \(-0.365775\pi\)
0.409295 + 0.912402i \(0.365775\pi\)
\(522\) 0 0
\(523\) 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
\(525\) 0 0
\(526\) 6.50000 11.2583i 0.283413 0.490887i
\(527\) 14.5616 25.2213i 0.634311 1.09866i
\(528\) 0 0
\(529\) −18.0270 + 31.2237i −0.783782 + 1.35755i
\(530\) 2.21922 + 3.84381i 0.0963969 + 0.166964i
\(531\) 0 0
\(532\) −12.6847 −0.549950
\(533\) 12.0691 + 9.41967i 0.522772 + 0.408011i
\(534\) 0 0
\(535\) −1.00000 1.73205i −0.0432338 0.0748831i
\(536\) 7.12311 + 12.3376i 0.307671 + 0.532902i
\(537\) 0 0
\(538\) −3.36932 −0.145262
\(539\) −11.7192 + 20.2983i −0.504783 + 0.874309i
\(540\) 0 0
\(541\) −2.63068 −0.113102 −0.0565510 0.998400i \(-0.518010\pi\)
−0.0565510 + 0.998400i \(0.518010\pi\)
\(542\) 16.0885 27.8662i 0.691062 1.19695i
\(543\) 0 0
\(544\) −2.56155 4.43674i −0.109826 0.190224i
\(545\) 20.2462 0.867252
\(546\) 0 0
\(547\) 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
\(549\) 0 0
\(550\) 2.06155 3.57071i 0.0879049 0.152256i
\(551\) 23.3693 0.995566
\(552\) 0 0
\(553\) −13.2462 + 22.9431i −0.563286 + 0.975640i
\(554\) 1.00000 0.0424859
\(555\) 0 0
\(556\) −4.21922 7.30791i −0.178935 0.309924i
\(557\) −2.21922 3.84381i −0.0940315 0.162867i 0.815172 0.579218i \(-0.196642\pi\)
−0.909204 + 0.416351i \(0.863309\pi\)
\(558\) 0 0
\(559\) 2.28078 16.2880i 0.0964666 0.688909i
\(560\) −3.56155 −0.150503
\(561\) 0 0
\(562\) 0.123106 + 0.213225i 0.00519290 + 0.00899436i
\(563\) 16.4924 28.5657i 0.695073 1.20390i −0.275083 0.961420i \(-0.588705\pi\)
0.970156 0.242481i \(-0.0779612\pi\)
\(564\) 0 0
\(565\) 1.84233 3.19101i 0.0775074 0.134247i
\(566\) 5.71922 9.90599i 0.240397 0.416380i
\(567\) 0 0
\(568\) 2.43845 4.22351i 0.102315 0.177215i
\(569\) −9.58854 16.6078i −0.401973 0.696237i 0.591991 0.805944i \(-0.298342\pi\)
−0.993964 + 0.109707i \(0.965009\pi\)
\(570\) 0 0
\(571\) 11.3153 0.473532 0.236766 0.971567i \(-0.423912\pi\)
0.236766 + 0.971567i \(0.423912\pi\)
\(572\) −13.7808 + 5.57586i −0.576203 + 0.233138i
\(573\) 0 0
\(574\) 7.56155 + 13.0970i 0.315613 + 0.546658i
\(575\) −3.84233 6.65511i −0.160236 0.277537i
\(576\) 0 0
\(577\) 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 0
\(583\) 9.15009 + 15.8484i 0.378958 + 0.656375i
\(584\) 15.3693 0.635987
\(585\) 0 0
\(586\) −24.9309 −1.02988
\(587\) −11.8769 20.5714i −0.490212 0.849072i 0.509725 0.860338i \(-0.329747\pi\)
−0.999937 + 0.0112657i \(0.996414\pi\)
\(588\) 0 0
\(589\) 10.1231 17.5337i 0.417115 0.722465i
\(590\) −10.5616 −0.434812
\(591\) 0 0
\(592\) −2.06155 + 3.57071i −0.0847293 + 0.146755i
\(593\) 12.1771 0.500053 0.250026 0.968239i \(-0.419561\pi\)
0.250026 + 0.968239i \(0.419561\pi\)
\(594\) 0 0
\(595\) −9.12311 15.8017i −0.374011 0.647806i
\(596\) −11.4039 19.7521i −0.467121 0.809078i
\(597\) 0 0
\(598\) −3.84233 + 27.4397i −0.157125 + 1.12209i
\(599\) 14.0000 0.572024 0.286012 0.958226i \(-0.407670\pi\)
0.286012 + 0.958226i \(0.407670\pi\)
\(600\) 0 0
\(601\) 17.9924 + 31.1638i 0.733926 + 1.27120i 0.955193 + 0.295984i \(0.0956476\pi\)
−0.221267 + 0.975213i \(0.571019\pi\)
\(602\) 8.12311 14.0696i 0.331073 0.573435i
\(603\) 0 0
\(604\) −4.68466 + 8.11407i −0.190616 + 0.330157i
\(605\) 3.00000 5.19615i 0.121967 0.211254i
\(606\) 0 0
\(607\) 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
\(609\) 0 0
\(610\) 6.00000 0.242933
\(611\) 23.3963 9.46641i 0.946513 0.382970i
\(612\) 0 0
\(613\) −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
\(615\) 0 0
\(616\) −14.6847 −0.591662
\(617\) −20.8423 + 36.1000i −0.839081 + 1.45333i 0.0515837 + 0.998669i \(0.483573\pi\)
−0.890664 + 0.454662i \(0.849760\pi\)
\(618\) 0 0
\(619\) −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
\(621\) 0 0
\(622\) 9.36932 + 16.2281i 0.375675 + 0.650689i
\(623\) −6.43845 −0.257951
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 3.31534 + 5.74234i 0.132508 + 0.229510i
\(627\) 0 0
\(628\) −11.0616 + 19.1592i −0.441404 + 0.764534i
\(629\) −21.1231 −0.842233
\(630\) 0 0
\(631\) 15.1231 26.1940i 0.602041 1.04277i −0.390470 0.920616i \(-0.627688\pi\)
0.992512 0.122151i \(-0.0389791\pi\)
\(632\) −7.43845 −0.295886
\(633\) 0 0
\(634\) 2.09612 + 3.63058i 0.0832475 + 0.144189i
\(635\) −2.21922 3.84381i −0.0880672 0.152537i
\(636\) 0 0
\(637\) 16.1577 + 12.6107i 0.640190 + 0.499653i
\(638\) 27.0540 1.07108
\(639\) 0 0
\(640\) −0.500000 0.866025i −0.0197642 0.0342327i
\(641\) −7.78078 + 13.4767i −0.307322 + 0.532298i −0.977776 0.209654i \(-0.932766\pi\)
0.670453 + 0.741952i \(0.266100\pi\)
\(642\) 0 0
\(643\) −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
\(645\) 0 0
\(646\) 9.12311 15.8017i 0.358944 0.621709i
\(647\) −1.02699 1.77879i −0.0403751 0.0699316i 0.845132 0.534558i \(-0.179522\pi\)
−0.885507 + 0.464626i \(0.846189\pi\)
\(648\) 0 0
\(649\) −43.5464 −1.70935
\(650\) −2.84233 2.21837i −0.111485 0.0870116i
\(651\) 0 0
\(652\) 9.28078 + 16.0748i 0.363463 + 0.629537i
\(653\) −20.2192 35.0207i −0.791239 1.37047i −0.925200 0.379480i \(-0.876103\pi\)
0.133961 0.990987i \(-0.457230\pi\)
\(654\) 0 0
\(655\) 6.12311 0.239250
\(656\) −2.12311 + 3.67733i −0.0828933 + 0.143575i
\(657\) 0 0
\(658\) 24.9309 0.971906
\(659\) 15.5270 26.8935i 0.604846 1.04762i −0.387230 0.921983i \(-0.626568\pi\)
0.992076 0.125640i \(-0.0400985\pi\)
\(660\) 0 0
\(661\) 5.80776 + 10.0593i 0.225896 + 0.391263i 0.956588 0.291444i \(-0.0941358\pi\)
−0.730692 + 0.682707i \(0.760802\pi\)
\(662\) 18.7386 0.728298
\(663\) 0 0
\(664\) 1.12311 0.0435850
\(665\) −6.34233 10.9852i −0.245945 0.425989i
\(666\) 0 0
\(667\) 25.2116 43.6679i 0.976199 1.69083i
\(668\) 20.3693 0.788113
\(669\) 0 0
\(670\) −7.12311 + 12.3376i −0.275190 + 0.476642i
\(671\) 24.7386 0.955024
\(672\) 0 0
\(673\) −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
\(675\) 0 0
\(676\) 3.15767 + 12.6107i 0.121449 + 0.485026i
\(677\) 28.8769 1.10983 0.554915 0.831907i \(-0.312751\pi\)
0.554915 + 0.831907i \(0.312751\pi\)
\(678\) 0 0
\(679\) −2.00000 3.46410i −0.0767530 0.132940i
\(680\) 2.56155 4.43674i 0.0982311 0.170141i
\(681\) 0 0
\(682\) 11.7192 20.2983i 0.448752 0.777262i
\(683\) 4.43845 7.68762i 0.169832 0.294158i −0.768528 0.639816i \(-0.779011\pi\)
0.938361 + 0.345657i \(0.112344\pi\)
\(684\) 0 0
\(685\) 4.40388 7.62775i 0.168264 0.291441i
\(686\) −2.34233 4.05703i −0.0894305 0.154898i
\(687\) 0 0
\(688\) 4.56155 0.173908
\(689\) 14.8348 6.00231i 0.565159 0.228670i
\(690\) 0 0
\(691\) 8.21922 + 14.2361i 0.312674 + 0.541567i 0.978940 0.204147i \(-0.0654419\pi\)
−0.666266 + 0.745714i \(0.732109\pi\)
\(692\) −12.5885 21.8040i −0.478545 0.828863i
\(693\) 0 0
\(694\) 9.12311 0.346308
\(695\) 4.21922 7.30791i 0.160044 0.277205i
\(696\) 0 0
\(697\) −21.7538 −0.823984
\(698\) −12.2462 + 21.2111i −0.463526 + 0.802850i
\(699\) 0 0
\(700\) −1.78078 3.08440i −0.0673070 0.116579i
\(701\) −17.3002 −0.653419 −0.326710 0.945125i \(-0.605940\pi\)
−0.326710 + 0.945125i \(0.605940\pi\)
\(702\) 0 0
\(703\) −14.6847 −0.553842
\(704\) −2.06155 3.57071i −0.0776977 0.134576i
\(705\) 0 0
\(706\) −15.9309 + 27.5931i −0.599566 + 1.03848i
\(707\) 60.9848 2.29357
\(708\) 0 0
\(709\) −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
\(711\) 0 0
\(712\) −0.903882 1.56557i −0.0338744 0.0586722i
\(713\) −21.8423 37.8320i −0.818002 1.41682i
\(714\) 0 0
\(715\) −11.7192 9.14657i −0.438274 0.342062i
\(716\) 0.315342 0.0117849
\(717\) 0 0
\(718\) −2.43845 4.22351i −0.0910020 0.157620i
\(719\) −10.4924 + 18.1734i −0.391301 + 0.677754i −0.992621 0.121254i \(-0.961308\pi\)
0.601320 + 0.799008i \(0.294642\pi\)
\(720\) 0 0
\(721\) −0.780776 + 1.35234i −0.0290776 + 0.0503639i
\(722\) −3.15767 + 5.46925i −0.117516 + 0.203544i
\(723\) 0 0
\(724\) −5.56155 + 9.63289i −0.206693 + 0.358004i
\(725\) 3.28078 + 5.68247i 0.121845 + 0.211042i
\(726\) 0 0
\(727\) −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
\(729\) 0 0
\(730\) 7.68466 + 13.3102i 0.284422 + 0.492633i
\(731\) 11.6847 + 20.2384i 0.432173 + 0.748545i
\(732\) 0 0
\(733\) 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
\(735\) 0 0
\(736\) −7.68466 −0.283260
\(737\) −29.3693 + 50.8691i −1.08183 + 1.87379i
\(738\) 0 0
\(739\) −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
\(741\) 0 0
\(742\) 15.8078 0.580321
\(743\) −16.0885 27.8662i −0.590231 1.02231i −0.994201 0.107538i \(-0.965703\pi\)
0.403970 0.914772i \(-0.367630\pi\)
\(744\) 0 0
\(745\) 11.4039 19.7521i 0.417806 0.723661i
\(746\) 5.19224 0.190101
\(747\) 0 0
\(748\) 10.5616 18.2931i 0.386169 0.668864i
\(749\) −7.12311 −0.260273
\(750\) 0 0
\(751\) 1.59612 + 2.76456i 0.0582432 + 0.100880i 0.893677 0.448711i \(-0.148117\pi\)
−0.835434 + 0.549591i \(0.814783\pi\)
\(752\) 3.50000 + 6.06218i 0.127632 + 0.221065i
\(753\) 0 0
\(754\) 3.28078 23.4294i 0.119479 0.853250i
\(755\) −9.36932 −0.340984
\(756\) 0 0
\(757\) −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
\(759\) 0 0
\(760\) 1.78078 3.08440i 0.0645955 0.111883i
\(761\) 5.46543 9.46641i 0.198122 0.343157i −0.749798 0.661667i \(-0.769849\pi\)
0.947919 + 0.318510i \(0.103182\pi\)
\(762\) 0 0
\(763\) 36.0540 62.4473i 1.30524 2.26074i
\(764\) 9.56155 + 16.5611i 0.345925 + 0.599159i
\(765\) 0 0
\(766\) 20.8078 0.751815
\(767\) −5.28078 + 37.7123i −0.190678 + 1.36171i
\(768\) 0 0
\(769\) 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 0
\(772\) 0 0
\(773\) −10.5885 + 18.3399i −0.380843 + 0.659640i −0.991183 0.132500i \(-0.957700\pi\)
0.610340 + 0.792140i \(0.291033\pi\)
\(774\) 0 0
\(775\) 5.68466 0.204199
\(776\) 0.561553 0.972638i 0.0201586 0.0349157i
\(777\) 0 0
\(778\) −9.52699 16.5012i −0.341559 0.591598i
\(779\) −15.1231 −0.541841
\(780\) 0 0
\(781\) 20.1080 0.719519
\(782\) −19.6847 34.0948i −0.703922 1.21923i
\(783\) 0 0
\(784\) −2.84233 + 4.92306i −0.101512 + 0.175824i
\(785\) −22.1231 −0.789607
\(786\) 0 0
\(787\) −21.8423 + 37.8320i −0.778595 + 1.34857i 0.154157 + 0.988046i \(0.450734\pi\)
−0.932752 + 0.360520i \(0.882599\pi\)
\(788\) 7.80776 0.278140
\(789\) 0 0
\(790\) −3.71922 6.44188i