Properties

Label 140.2.g.a.111.1
Level $140$
Weight $2$
Character 140.111
Analytic conductor $1.118$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 140 = 2^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 140.g (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.11790562830\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{12})\)
Defining polynomial: \( x^{4} - x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 111.1
Root \(0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 140.111
Dual form 140.2.g.a.111.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.36603 - 0.366025i) q^{2} +1.73205 q^{3} +(1.73205 + 1.00000i) q^{4} +1.00000i q^{5} +(-2.36603 - 0.633975i) q^{6} +(1.73205 + 2.00000i) q^{7} +(-2.00000 - 2.00000i) q^{8} +O(q^{10})\) \(q+(-1.36603 - 0.366025i) q^{2} +1.73205 q^{3} +(1.73205 + 1.00000i) q^{4} +1.00000i q^{5} +(-2.36603 - 0.633975i) q^{6} +(1.73205 + 2.00000i) q^{7} +(-2.00000 - 2.00000i) q^{8} +(0.366025 - 1.36603i) q^{10} +3.73205i q^{11} +(3.00000 + 1.73205i) q^{12} -6.46410i q^{13} +(-1.63397 - 3.36603i) q^{14} +1.73205i q^{15} +(2.00000 + 3.46410i) q^{16} -0.464102i q^{17} +6.00000 q^{19} +(-1.00000 + 1.73205i) q^{20} +(3.00000 + 3.46410i) q^{21} +(1.36603 - 5.09808i) q^{22} -5.46410i q^{23} +(-3.46410 - 3.46410i) q^{24} -1.00000 q^{25} +(-2.36603 + 8.83013i) q^{26} -5.19615 q^{27} +(1.00000 + 5.19615i) q^{28} -5.92820 q^{29} +(0.633975 - 2.36603i) q^{30} -6.00000 q^{31} +(-1.46410 - 5.46410i) q^{32} +6.46410i q^{33} +(-0.169873 + 0.633975i) q^{34} +(-2.00000 + 1.73205i) q^{35} -2.53590 q^{37} +(-8.19615 - 2.19615i) q^{38} -11.1962i q^{39} +(2.00000 - 2.00000i) q^{40} -3.46410i q^{41} +(-2.83013 - 5.83013i) q^{42} +2.00000i q^{43} +(-3.73205 + 6.46410i) q^{44} +(-2.00000 + 7.46410i) q^{46} -1.73205 q^{47} +(3.46410 + 6.00000i) q^{48} +(-1.00000 + 6.92820i) q^{49} +(1.36603 + 0.366025i) q^{50} -0.803848i q^{51} +(6.46410 - 11.1962i) q^{52} +2.00000 q^{53} +(7.09808 + 1.90192i) q^{54} -3.73205 q^{55} +(0.535898 - 7.46410i) q^{56} +10.3923 q^{57} +(8.09808 + 2.16987i) q^{58} +3.46410 q^{59} +(-1.73205 + 3.00000i) q^{60} -2.53590i q^{61} +(8.19615 + 2.19615i) q^{62} +8.00000i q^{64} +6.46410 q^{65} +(2.36603 - 8.83013i) q^{66} +3.46410i q^{67} +(0.464102 - 0.803848i) q^{68} -9.46410i q^{69} +(3.36603 - 1.63397i) q^{70} +0.535898i q^{71} +0.928203i q^{73} +(3.46410 + 0.928203i) q^{74} -1.73205 q^{75} +(10.3923 + 6.00000i) q^{76} +(-7.46410 + 6.46410i) q^{77} +(-4.09808 + 15.2942i) q^{78} -2.66025i q^{79} +(-3.46410 + 2.00000i) q^{80} -9.00000 q^{81} +(-1.26795 + 4.73205i) q^{82} +8.53590 q^{83} +(1.73205 + 9.00000i) q^{84} +0.464102 q^{85} +(0.732051 - 2.73205i) q^{86} -10.2679 q^{87} +(7.46410 - 7.46410i) q^{88} -9.46410i q^{89} +(12.9282 - 11.1962i) q^{91} +(5.46410 - 9.46410i) q^{92} -10.3923 q^{93} +(2.36603 + 0.633975i) q^{94} +6.00000i q^{95} +(-2.53590 - 9.46410i) q^{96} -7.39230i q^{97} +(3.90192 - 9.09808i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 2 q^{2} - 6 q^{6} - 8 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 2 q^{2} - 6 q^{6} - 8 q^{8} - 2 q^{10} + 12 q^{12} - 10 q^{14} + 8 q^{16} + 24 q^{19} - 4 q^{20} + 12 q^{21} + 2 q^{22} - 4 q^{25} - 6 q^{26} + 4 q^{28} + 4 q^{29} + 6 q^{30} - 24 q^{31} + 8 q^{32} - 18 q^{34} - 8 q^{35} - 24 q^{37} - 12 q^{38} + 8 q^{40} + 6 q^{42} - 8 q^{44} - 8 q^{46} - 4 q^{49} + 2 q^{50} + 12 q^{52} + 8 q^{53} + 18 q^{54} - 8 q^{55} + 16 q^{56} + 22 q^{58} + 12 q^{62} + 12 q^{65} + 6 q^{66} - 12 q^{68} + 10 q^{70} - 16 q^{77} - 6 q^{78} - 36 q^{81} - 12 q^{82} + 48 q^{83} - 12 q^{85} - 4 q^{86} - 48 q^{87} + 16 q^{88} + 24 q^{91} + 8 q^{92} + 6 q^{94} - 24 q^{96} + 26 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/140\mathbb{Z}\right)^\times\).

\(n\) \(57\) \(71\) \(101\)
\(\chi(n)\) \(1\) \(-1\) \(-1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.36603 0.366025i −0.965926 0.258819i
\(3\) 1.73205 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(4\) 1.73205 + 1.00000i 0.866025 + 0.500000i
\(5\) 1.00000i 0.447214i
\(6\) −2.36603 0.633975i −0.965926 0.258819i
\(7\) 1.73205 + 2.00000i 0.654654 + 0.755929i
\(8\) −2.00000 2.00000i −0.707107 0.707107i
\(9\) 0 0
\(10\) 0.366025 1.36603i 0.115747 0.431975i
\(11\) 3.73205i 1.12526i 0.826710 + 0.562628i \(0.190210\pi\)
−0.826710 + 0.562628i \(0.809790\pi\)
\(12\) 3.00000 + 1.73205i 0.866025 + 0.500000i
\(13\) 6.46410i 1.79282i −0.443227 0.896410i \(-0.646166\pi\)
0.443227 0.896410i \(-0.353834\pi\)
\(14\) −1.63397 3.36603i −0.436698 0.899608i
\(15\) 1.73205i 0.447214i
\(16\) 2.00000 + 3.46410i 0.500000 + 0.866025i
\(17\) 0.464102i 0.112561i −0.998415 0.0562806i \(-0.982076\pi\)
0.998415 0.0562806i \(-0.0179241\pi\)
\(18\) 0 0
\(19\) 6.00000 1.37649 0.688247 0.725476i \(-0.258380\pi\)
0.688247 + 0.725476i \(0.258380\pi\)
\(20\) −1.00000 + 1.73205i −0.223607 + 0.387298i
\(21\) 3.00000 + 3.46410i 0.654654 + 0.755929i
\(22\) 1.36603 5.09808i 0.291238 1.08691i
\(23\) 5.46410i 1.13934i −0.821872 0.569672i \(-0.807070\pi\)
0.821872 0.569672i \(-0.192930\pi\)
\(24\) −3.46410 3.46410i −0.707107 0.707107i
\(25\) −1.00000 −0.200000
\(26\) −2.36603 + 8.83013i −0.464016 + 1.73173i
\(27\) −5.19615 −1.00000
\(28\) 1.00000 + 5.19615i 0.188982 + 0.981981i
\(29\) −5.92820 −1.10084 −0.550420 0.834888i \(-0.685532\pi\)
−0.550420 + 0.834888i \(0.685532\pi\)
\(30\) 0.633975 2.36603i 0.115747 0.431975i
\(31\) −6.00000 −1.07763 −0.538816 0.842424i \(-0.681128\pi\)
−0.538816 + 0.842424i \(0.681128\pi\)
\(32\) −1.46410 5.46410i −0.258819 0.965926i
\(33\) 6.46410i 1.12526i
\(34\) −0.169873 + 0.633975i −0.0291330 + 0.108726i
\(35\) −2.00000 + 1.73205i −0.338062 + 0.292770i
\(36\) 0 0
\(37\) −2.53590 −0.416899 −0.208450 0.978033i \(-0.566842\pi\)
−0.208450 + 0.978033i \(0.566842\pi\)
\(38\) −8.19615 2.19615i −1.32959 0.356263i
\(39\) 11.1962i 1.79282i
\(40\) 2.00000 2.00000i 0.316228 0.316228i
\(41\) 3.46410i 0.541002i −0.962720 0.270501i \(-0.912811\pi\)
0.962720 0.270501i \(-0.0871893\pi\)
\(42\) −2.83013 5.83013i −0.436698 0.899608i
\(43\) 2.00000i 0.304997i 0.988304 + 0.152499i \(0.0487319\pi\)
−0.988304 + 0.152499i \(0.951268\pi\)
\(44\) −3.73205 + 6.46410i −0.562628 + 0.974500i
\(45\) 0 0
\(46\) −2.00000 + 7.46410i −0.294884 + 1.10052i
\(47\) −1.73205 −0.252646 −0.126323 0.991989i \(-0.540318\pi\)
−0.126323 + 0.991989i \(0.540318\pi\)
\(48\) 3.46410 + 6.00000i 0.500000 + 0.866025i
\(49\) −1.00000 + 6.92820i −0.142857 + 0.989743i
\(50\) 1.36603 + 0.366025i 0.193185 + 0.0517638i
\(51\) 0.803848i 0.112561i
\(52\) 6.46410 11.1962i 0.896410 1.55263i
\(53\) 2.00000 0.274721 0.137361 0.990521i \(-0.456138\pi\)
0.137361 + 0.990521i \(0.456138\pi\)
\(54\) 7.09808 + 1.90192i 0.965926 + 0.258819i
\(55\) −3.73205 −0.503230
\(56\) 0.535898 7.46410i 0.0716124 0.997433i
\(57\) 10.3923 1.37649
\(58\) 8.09808 + 2.16987i 1.06333 + 0.284918i
\(59\) 3.46410 0.450988 0.225494 0.974245i \(-0.427600\pi\)
0.225494 + 0.974245i \(0.427600\pi\)
\(60\) −1.73205 + 3.00000i −0.223607 + 0.387298i
\(61\) 2.53590i 0.324689i −0.986734 0.162344i \(-0.948094\pi\)
0.986734 0.162344i \(-0.0519055\pi\)
\(62\) 8.19615 + 2.19615i 1.04091 + 0.278912i
\(63\) 0 0
\(64\) 8.00000i 1.00000i
\(65\) 6.46410 0.801773
\(66\) 2.36603 8.83013i 0.291238 1.08691i
\(67\) 3.46410i 0.423207i 0.977356 + 0.211604i \(0.0678686\pi\)
−0.977356 + 0.211604i \(0.932131\pi\)
\(68\) 0.464102 0.803848i 0.0562806 0.0974808i
\(69\) 9.46410i 1.13934i
\(70\) 3.36603 1.63397i 0.402317 0.195297i
\(71\) 0.535898i 0.0635994i 0.999494 + 0.0317997i \(0.0101239\pi\)
−0.999494 + 0.0317997i \(0.989876\pi\)
\(72\) 0 0
\(73\) 0.928203i 0.108638i 0.998524 + 0.0543190i \(0.0172988\pi\)
−0.998524 + 0.0543190i \(0.982701\pi\)
\(74\) 3.46410 + 0.928203i 0.402694 + 0.107901i
\(75\) −1.73205 −0.200000
\(76\) 10.3923 + 6.00000i 1.19208 + 0.688247i
\(77\) −7.46410 + 6.46410i −0.850613 + 0.736653i
\(78\) −4.09808 + 15.2942i −0.464016 + 1.73173i
\(79\) 2.66025i 0.299302i −0.988739 0.149651i \(-0.952185\pi\)
0.988739 0.149651i \(-0.0478150\pi\)
\(80\) −3.46410 + 2.00000i −0.387298 + 0.223607i
\(81\) −9.00000 −1.00000
\(82\) −1.26795 + 4.73205i −0.140022 + 0.522568i
\(83\) 8.53590 0.936937 0.468468 0.883480i \(-0.344806\pi\)
0.468468 + 0.883480i \(0.344806\pi\)
\(84\) 1.73205 + 9.00000i 0.188982 + 0.981981i
\(85\) 0.464102 0.0503389
\(86\) 0.732051 2.73205i 0.0789391 0.294605i
\(87\) −10.2679 −1.10084
\(88\) 7.46410 7.46410i 0.795676 0.795676i
\(89\) 9.46410i 1.00319i −0.865102 0.501596i \(-0.832746\pi\)
0.865102 0.501596i \(-0.167254\pi\)
\(90\) 0 0
\(91\) 12.9282 11.1962i 1.35524 1.17368i
\(92\) 5.46410 9.46410i 0.569672 0.986701i
\(93\) −10.3923 −1.07763
\(94\) 2.36603 + 0.633975i 0.244037 + 0.0653895i
\(95\) 6.00000i 0.615587i
\(96\) −2.53590 9.46410i −0.258819 0.965926i
\(97\) 7.39230i 0.750575i −0.926908 0.375287i \(-0.877544\pi\)
0.926908 0.375287i \(-0.122456\pi\)
\(98\) 3.90192 9.09808i 0.394154 0.919044i
\(99\) 0 0
\(100\) −1.73205 1.00000i −0.173205 0.100000i
\(101\) 8.53590i 0.849354i 0.905345 + 0.424677i \(0.139612\pi\)
−0.905345 + 0.424677i \(0.860388\pi\)
\(102\) −0.294229 + 1.09808i −0.0291330 + 0.108726i
\(103\) −17.1962 −1.69439 −0.847194 0.531284i \(-0.821710\pi\)
−0.847194 + 0.531284i \(0.821710\pi\)
\(104\) −12.9282 + 12.9282i −1.26771 + 1.26771i
\(105\) −3.46410 + 3.00000i −0.338062 + 0.292770i
\(106\) −2.73205 0.732051i −0.265360 0.0711031i
\(107\) 18.3923i 1.77805i 0.457857 + 0.889026i \(0.348617\pi\)
−0.457857 + 0.889026i \(0.651383\pi\)
\(108\) −9.00000 5.19615i −0.866025 0.500000i
\(109\) 15.9282 1.52565 0.762823 0.646608i \(-0.223813\pi\)
0.762823 + 0.646608i \(0.223813\pi\)
\(110\) 5.09808 + 1.36603i 0.486082 + 0.130245i
\(111\) −4.39230 −0.416899
\(112\) −3.46410 + 10.0000i −0.327327 + 0.944911i
\(113\) −1.46410 −0.137731 −0.0688655 0.997626i \(-0.521938\pi\)
−0.0688655 + 0.997626i \(0.521938\pi\)
\(114\) −14.1962 3.80385i −1.32959 0.356263i
\(115\) 5.46410 0.509530
\(116\) −10.2679 5.92820i −0.953355 0.550420i
\(117\) 0 0
\(118\) −4.73205 1.26795i −0.435621 0.116724i
\(119\) 0.928203 0.803848i 0.0850883 0.0736886i
\(120\) 3.46410 3.46410i 0.316228 0.316228i
\(121\) −2.92820 −0.266200
\(122\) −0.928203 + 3.46410i −0.0840356 + 0.313625i
\(123\) 6.00000i 0.541002i
\(124\) −10.3923 6.00000i −0.933257 0.538816i
\(125\) 1.00000i 0.0894427i
\(126\) 0 0
\(127\) 8.53590i 0.757438i −0.925512 0.378719i \(-0.876365\pi\)
0.925512 0.378719i \(-0.123635\pi\)
\(128\) 2.92820 10.9282i 0.258819 0.965926i
\(129\) 3.46410i 0.304997i
\(130\) −8.83013 2.36603i −0.774453 0.207514i
\(131\) 9.46410 0.826882 0.413441 0.910531i \(-0.364327\pi\)
0.413441 + 0.910531i \(0.364327\pi\)
\(132\) −6.46410 + 11.1962i −0.562628 + 0.974500i
\(133\) 10.3923 + 12.0000i 0.901127 + 1.04053i
\(134\) 1.26795 4.73205i 0.109534 0.408787i
\(135\) 5.19615i 0.447214i
\(136\) −0.928203 + 0.928203i −0.0795928 + 0.0795928i
\(137\) −0.392305 −0.0335169 −0.0167584 0.999860i \(-0.505335\pi\)
−0.0167584 + 0.999860i \(0.505335\pi\)
\(138\) −3.46410 + 12.9282i −0.294884 + 1.10052i
\(139\) −6.92820 −0.587643 −0.293821 0.955860i \(-0.594927\pi\)
−0.293821 + 0.955860i \(0.594927\pi\)
\(140\) −5.19615 + 1.00000i −0.439155 + 0.0845154i
\(141\) −3.00000 −0.252646
\(142\) 0.196152 0.732051i 0.0164607 0.0614323i
\(143\) 24.1244 2.01738
\(144\) 0 0
\(145\) 5.92820i 0.492310i
\(146\) 0.339746 1.26795i 0.0281176 0.104936i
\(147\) −1.73205 + 12.0000i −0.142857 + 0.989743i
\(148\) −4.39230 2.53590i −0.361045 0.208450i
\(149\) 16.9282 1.38681 0.693406 0.720547i \(-0.256109\pi\)
0.693406 + 0.720547i \(0.256109\pi\)
\(150\) 2.36603 + 0.633975i 0.193185 + 0.0517638i
\(151\) 4.80385i 0.390932i 0.980711 + 0.195466i \(0.0626219\pi\)
−0.980711 + 0.195466i \(0.937378\pi\)
\(152\) −12.0000 12.0000i −0.973329 0.973329i
\(153\) 0 0
\(154\) 12.5622 6.09808i 1.01229 0.491397i
\(155\) 6.00000i 0.481932i
\(156\) 11.1962 19.3923i 0.896410 1.55263i
\(157\) 19.8564i 1.58471i 0.610058 + 0.792357i \(0.291146\pi\)
−0.610058 + 0.792357i \(0.708854\pi\)
\(158\) −0.973721 + 3.63397i −0.0774650 + 0.289103i
\(159\) 3.46410 0.274721
\(160\) 5.46410 1.46410i 0.431975 0.115747i
\(161\) 10.9282 9.46410i 0.861263 0.745876i
\(162\) 12.2942 + 3.29423i 0.965926 + 0.258819i
\(163\) 20.7846i 1.62798i 0.580881 + 0.813988i \(0.302708\pi\)
−0.580881 + 0.813988i \(0.697292\pi\)
\(164\) 3.46410 6.00000i 0.270501 0.468521i
\(165\) −6.46410 −0.503230
\(166\) −11.6603 3.12436i −0.905011 0.242497i
\(167\) 5.19615 0.402090 0.201045 0.979582i \(-0.435566\pi\)
0.201045 + 0.979582i \(0.435566\pi\)
\(168\) 0.928203 12.9282i 0.0716124 0.997433i
\(169\) −28.7846 −2.21420
\(170\) −0.633975 0.169873i −0.0486236 0.0130287i
\(171\) 0 0
\(172\) −2.00000 + 3.46410i −0.152499 + 0.264135i
\(173\) 20.3205i 1.54494i −0.635051 0.772470i \(-0.719021\pi\)
0.635051 0.772470i \(-0.280979\pi\)
\(174\) 14.0263 + 3.75833i 1.06333 + 0.284918i
\(175\) −1.73205 2.00000i −0.130931 0.151186i
\(176\) −12.9282 + 7.46410i −0.974500 + 0.562628i
\(177\) 6.00000 0.450988
\(178\) −3.46410 + 12.9282i −0.259645 + 0.969010i
\(179\) 14.3923i 1.07573i 0.843031 + 0.537866i \(0.180769\pi\)
−0.843031 + 0.537866i \(0.819231\pi\)
\(180\) 0 0
\(181\) 12.9282i 0.960946i −0.877010 0.480473i \(-0.840465\pi\)
0.877010 0.480473i \(-0.159535\pi\)
\(182\) −21.7583 + 10.5622i −1.61283 + 0.782921i
\(183\) 4.39230i 0.324689i
\(184\) −10.9282 + 10.9282i −0.805638 + 0.805638i
\(185\) 2.53590i 0.186443i
\(186\) 14.1962 + 3.80385i 1.04091 + 0.278912i
\(187\) 1.73205 0.126660
\(188\) −3.00000 1.73205i −0.218797 0.126323i
\(189\) −9.00000 10.3923i −0.654654 0.755929i
\(190\) 2.19615 8.19615i 0.159326 0.594611i
\(191\) 3.19615i 0.231265i −0.993292 0.115633i \(-0.963110\pi\)
0.993292 0.115633i \(-0.0368896\pi\)
\(192\) 13.8564i 1.00000i
\(193\) −2.53590 −0.182538 −0.0912690 0.995826i \(-0.529092\pi\)
−0.0912690 + 0.995826i \(0.529092\pi\)
\(194\) −2.70577 + 10.0981i −0.194263 + 0.725000i
\(195\) 11.1962 0.801773
\(196\) −8.66025 + 11.0000i −0.618590 + 0.785714i
\(197\) 21.3205 1.51902 0.759512 0.650494i \(-0.225438\pi\)
0.759512 + 0.650494i \(0.225438\pi\)
\(198\) 0 0
\(199\) −3.46410 −0.245564 −0.122782 0.992434i \(-0.539182\pi\)
−0.122782 + 0.992434i \(0.539182\pi\)
\(200\) 2.00000 + 2.00000i 0.141421 + 0.141421i
\(201\) 6.00000i 0.423207i
\(202\) 3.12436 11.6603i 0.219829 0.820413i
\(203\) −10.2679 11.8564i −0.720669 0.832157i
\(204\) 0.803848 1.39230i 0.0562806 0.0974808i
\(205\) 3.46410 0.241943
\(206\) 23.4904 + 6.29423i 1.63665 + 0.438540i
\(207\) 0 0
\(208\) 22.3923 12.9282i 1.55263 0.896410i
\(209\) 22.3923i 1.54891i
\(210\) 5.83013 2.83013i 0.402317 0.195297i
\(211\) 7.19615i 0.495404i −0.968836 0.247702i \(-0.920325\pi\)
0.968836 0.247702i \(-0.0796753\pi\)
\(212\) 3.46410 + 2.00000i 0.237915 + 0.137361i
\(213\) 0.928203i 0.0635994i
\(214\) 6.73205 25.1244i 0.460194 1.71747i
\(215\) −2.00000 −0.136399
\(216\) 10.3923 + 10.3923i 0.707107 + 0.707107i
\(217\) −10.3923 12.0000i −0.705476 0.814613i
\(218\) −21.7583 5.83013i −1.47366 0.394866i
\(219\) 1.60770i 0.108638i
\(220\) −6.46410 3.73205i −0.435810 0.251615i
\(221\) −3.00000 −0.201802
\(222\) 6.00000 + 1.60770i 0.402694 + 0.107901i
\(223\) −10.2679 −0.687593 −0.343796 0.939044i \(-0.611713\pi\)
−0.343796 + 0.939044i \(0.611713\pi\)
\(224\) 8.39230 12.3923i 0.560734 0.827996i
\(225\) 0 0
\(226\) 2.00000 + 0.535898i 0.133038 + 0.0356474i
\(227\) 3.33975 0.221667 0.110833 0.993839i \(-0.464648\pi\)
0.110833 + 0.993839i \(0.464648\pi\)
\(228\) 18.0000 + 10.3923i 1.19208 + 0.688247i
\(229\) 15.4641i 1.02190i 0.859611 + 0.510948i \(0.170706\pi\)
−0.859611 + 0.510948i \(0.829294\pi\)
\(230\) −7.46410 2.00000i −0.492168 0.131876i
\(231\) −12.9282 + 11.1962i −0.850613 + 0.736653i
\(232\) 11.8564 + 11.8564i 0.778411 + 0.778411i
\(233\) −22.9282 −1.50208 −0.751038 0.660259i \(-0.770447\pi\)
−0.751038 + 0.660259i \(0.770447\pi\)
\(234\) 0 0
\(235\) 1.73205i 0.112987i
\(236\) 6.00000 + 3.46410i 0.390567 + 0.225494i
\(237\) 4.60770i 0.299302i
\(238\) −1.56218 + 0.758330i −0.101261 + 0.0491552i
\(239\) 27.9808i 1.80993i 0.425491 + 0.904963i \(0.360101\pi\)
−0.425491 + 0.904963i \(0.639899\pi\)
\(240\) −6.00000 + 3.46410i −0.387298 + 0.223607i
\(241\) 4.39230i 0.282933i 0.989943 + 0.141467i \(0.0451818\pi\)
−0.989943 + 0.141467i \(0.954818\pi\)
\(242\) 4.00000 + 1.07180i 0.257130 + 0.0688977i
\(243\) 0 0
\(244\) 2.53590 4.39230i 0.162344 0.281189i
\(245\) −6.92820 1.00000i −0.442627 0.0638877i
\(246\) −2.19615 + 8.19615i −0.140022 + 0.522568i
\(247\) 38.7846i 2.46781i
\(248\) 12.0000 + 12.0000i 0.762001 + 0.762001i
\(249\) 14.7846 0.936937
\(250\) −0.366025 + 1.36603i −0.0231495 + 0.0863950i
\(251\) 1.85641 0.117175 0.0585877 0.998282i \(-0.481340\pi\)
0.0585877 + 0.998282i \(0.481340\pi\)
\(252\) 0 0
\(253\) 20.3923 1.28205
\(254\) −3.12436 + 11.6603i −0.196040 + 0.731629i
\(255\) 0.803848 0.0503389
\(256\) −8.00000 + 13.8564i −0.500000 + 0.866025i
\(257\) 6.00000i 0.374270i −0.982334 0.187135i \(-0.940080\pi\)
0.982334 0.187135i \(-0.0599201\pi\)
\(258\) 1.26795 4.73205i 0.0789391 0.294605i
\(259\) −4.39230 5.07180i −0.272925 0.315146i
\(260\) 11.1962 + 6.46410i 0.694356 + 0.400887i
\(261\) 0 0
\(262\) −12.9282 3.46410i −0.798707 0.214013i
\(263\) 4.53590i 0.279695i −0.990173 0.139848i \(-0.955339\pi\)
0.990173 0.139848i \(-0.0446613\pi\)
\(264\) 12.9282 12.9282i 0.795676 0.795676i
\(265\) 2.00000i 0.122859i
\(266\) −9.80385 20.1962i −0.601112 1.23831i
\(267\) 16.3923i 1.00319i
\(268\) −3.46410 + 6.00000i −0.211604 + 0.366508i
\(269\) 12.0000i 0.731653i 0.930683 + 0.365826i \(0.119214\pi\)
−0.930683 + 0.365826i \(0.880786\pi\)
\(270\) −1.90192 + 7.09808i −0.115747 + 0.431975i
\(271\) 2.53590 0.154045 0.0770224 0.997029i \(-0.475459\pi\)
0.0770224 + 0.997029i \(0.475459\pi\)
\(272\) 1.60770 0.928203i 0.0974808 0.0562806i
\(273\) 22.3923 19.3923i 1.35524 1.17368i
\(274\) 0.535898 + 0.143594i 0.0323748 + 0.00867480i
\(275\) 3.73205i 0.225051i
\(276\) 9.46410 16.3923i 0.569672 0.986701i
\(277\) −24.7846 −1.48916 −0.744581 0.667532i \(-0.767351\pi\)
−0.744581 + 0.667532i \(0.767351\pi\)
\(278\) 9.46410 + 2.53590i 0.567619 + 0.152093i
\(279\) 0 0
\(280\) 7.46410 + 0.535898i 0.446065 + 0.0320261i
\(281\) 5.92820 0.353647 0.176823 0.984243i \(-0.443418\pi\)
0.176823 + 0.984243i \(0.443418\pi\)
\(282\) 4.09808 + 1.09808i 0.244037 + 0.0653895i
\(283\) −12.1244 −0.720718 −0.360359 0.932814i \(-0.617346\pi\)
−0.360359 + 0.932814i \(0.617346\pi\)
\(284\) −0.535898 + 0.928203i −0.0317997 + 0.0550787i
\(285\) 10.3923i 0.615587i
\(286\) −32.9545 8.83013i −1.94864 0.522136i
\(287\) 6.92820 6.00000i 0.408959 0.354169i
\(288\) 0 0
\(289\) 16.7846 0.987330
\(290\) −2.16987 + 8.09808i −0.127419 + 0.475535i
\(291\) 12.8038i 0.750575i
\(292\) −0.928203 + 1.60770i −0.0543190 + 0.0940832i
\(293\) 14.3205i 0.836613i 0.908306 + 0.418307i \(0.137376\pi\)
−0.908306 + 0.418307i \(0.862624\pi\)
\(294\) 6.75833 15.7583i 0.394154 0.919044i
\(295\) 3.46410i 0.201688i
\(296\) 5.07180 + 5.07180i 0.294792 + 0.294792i
\(297\) 19.3923i 1.12526i
\(298\) −23.1244 6.19615i −1.33956 0.358933i
\(299\) −35.3205 −2.04264
\(300\) −3.00000 1.73205i −0.173205 0.100000i
\(301\) −4.00000 + 3.46410i −0.230556 + 0.199667i
\(302\) 1.75833 6.56218i 0.101181 0.377611i
\(303\) 14.7846i 0.849354i
\(304\) 12.0000 + 20.7846i 0.688247 + 1.19208i
\(305\) 2.53590 0.145205
\(306\) 0 0
\(307\) −1.73205 −0.0988534 −0.0494267 0.998778i \(-0.515739\pi\)
−0.0494267 + 0.998778i \(0.515739\pi\)
\(308\) −19.3923 + 3.73205i −1.10498 + 0.212653i
\(309\) −29.7846 −1.69439
\(310\) −2.19615 + 8.19615i −0.124733 + 0.465510i
\(311\) −19.8564 −1.12595 −0.562977 0.826473i \(-0.690344\pi\)
−0.562977 + 0.826473i \(0.690344\pi\)
\(312\) −22.3923 + 22.3923i −1.26771 + 1.26771i
\(313\) 24.4641i 1.38279i 0.722476 + 0.691396i \(0.243004\pi\)
−0.722476 + 0.691396i \(0.756996\pi\)
\(314\) 7.26795 27.1244i 0.410154 1.53072i
\(315\) 0 0
\(316\) 2.66025 4.60770i 0.149651 0.259203i
\(317\) −16.9282 −0.950783 −0.475391 0.879774i \(-0.657694\pi\)
−0.475391 + 0.879774i \(0.657694\pi\)
\(318\) −4.73205 1.26795i −0.265360 0.0711031i
\(319\) 22.1244i 1.23873i
\(320\) −8.00000 −0.447214
\(321\) 31.8564i 1.77805i
\(322\) −18.3923 + 8.92820i −1.02496 + 0.497549i
\(323\) 2.78461i 0.154940i
\(324\) −15.5885 9.00000i −0.866025 0.500000i
\(325\) 6.46410i 0.358564i
\(326\) 7.60770 28.3923i 0.421351 1.57250i
\(327\) 27.5885 1.52565
\(328\) −6.92820 + 6.92820i −0.382546 + 0.382546i
\(329\) −3.00000 3.46410i −0.165395 0.190982i
\(330\) 8.83013 + 2.36603i 0.486082 + 0.130245i
\(331\) 5.60770i 0.308227i −0.988053 0.154113i \(-0.950748\pi\)
0.988053 0.154113i \(-0.0492521\pi\)
\(332\) 14.7846 + 8.53590i 0.811411 + 0.468468i
\(333\) 0 0
\(334\) −7.09808 1.90192i −0.388389 0.104069i
\(335\) −3.46410 −0.189264
\(336\) −6.00000 + 17.3205i −0.327327 + 0.944911i
\(337\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(338\) 39.3205 + 10.5359i 2.13875 + 0.573077i
\(339\) −2.53590 −0.137731
\(340\) 0.803848 + 0.464102i 0.0435948 + 0.0251694i
\(341\) 22.3923i 1.21261i
\(342\) 0 0
\(343\) −15.5885 + 10.0000i −0.841698 + 0.539949i
\(344\) 4.00000 4.00000i 0.215666 0.215666i
\(345\) 9.46410 0.509530
\(346\) −7.43782 + 27.7583i −0.399860 + 1.49230i
\(347\) 14.2487i 0.764911i −0.923974 0.382455i \(-0.875079\pi\)
0.923974 0.382455i \(-0.124921\pi\)
\(348\) −17.7846 10.2679i −0.953355 0.550420i
\(349\) 29.3205i 1.56949i −0.619818 0.784745i \(-0.712794\pi\)
0.619818 0.784745i \(-0.287206\pi\)
\(350\) 1.63397 + 3.36603i 0.0873396 + 0.179922i
\(351\) 33.5885i 1.79282i
\(352\) 20.3923 5.46410i 1.08691 0.291238i
\(353\) 13.3923i 0.712800i −0.934333 0.356400i \(-0.884004\pi\)
0.934333 0.356400i \(-0.115996\pi\)
\(354\) −8.19615 2.19615i −0.435621 0.116724i
\(355\) −0.535898 −0.0284425
\(356\) 9.46410 16.3923i 0.501596 0.868790i
\(357\) 1.60770 1.39230i 0.0850883 0.0736886i
\(358\) 5.26795 19.6603i 0.278420 1.03908i
\(359\) 9.32051i 0.491918i −0.969280 0.245959i \(-0.920897\pi\)
0.969280 0.245959i \(-0.0791028\pi\)
\(360\) 0 0
\(361\) 17.0000 0.894737
\(362\) −4.73205 + 17.6603i −0.248711 + 0.928202i
\(363\) −5.07180 −0.266200
\(364\) 33.5885 6.46410i 1.76051 0.338811i
\(365\) −0.928203 −0.0485844
\(366\) −1.60770 + 6.00000i −0.0840356 + 0.313625i
\(367\) 36.1244 1.88568 0.942838 0.333251i \(-0.108146\pi\)
0.942838 + 0.333251i \(0.108146\pi\)
\(368\) 18.9282 10.9282i 0.986701 0.569672i
\(369\) 0 0
\(370\) −0.928203 + 3.46410i −0.0482550 + 0.180090i
\(371\) 3.46410 + 4.00000i 0.179847 + 0.207670i
\(372\) −18.0000 10.3923i −0.933257 0.538816i
\(373\) −24.3923 −1.26299 −0.631493 0.775382i \(-0.717557\pi\)
−0.631493 + 0.775382i \(0.717557\pi\)
\(374\) −2.36603 0.633975i −0.122344 0.0327820i
\(375\) 1.73205i 0.0894427i
\(376\) 3.46410 + 3.46410i 0.178647 + 0.178647i
\(377\) 38.3205i 1.97361i
\(378\) 8.49038 + 17.4904i 0.436698 + 0.899608i
\(379\) 26.3923i 1.35568i 0.735209 + 0.677841i \(0.237084\pi\)
−0.735209 + 0.677841i \(0.762916\pi\)
\(380\) −6.00000 + 10.3923i −0.307794 + 0.533114i
\(381\) 14.7846i 0.757438i
\(382\) −1.16987 + 4.36603i −0.0598559 + 0.223385i
\(383\) 20.5359 1.04934 0.524668 0.851307i \(-0.324190\pi\)
0.524668 + 0.851307i \(0.324190\pi\)
\(384\) 5.07180 18.9282i 0.258819 0.965926i
\(385\) −6.46410 7.46410i −0.329441 0.380406i
\(386\) 3.46410 + 0.928203i 0.176318 + 0.0472443i
\(387\) 0 0
\(388\) 7.39230 12.8038i 0.375287 0.650017i
\(389\) 6.85641 0.347634 0.173817 0.984778i \(-0.444390\pi\)
0.173817 + 0.984778i \(0.444390\pi\)
\(390\) −15.2942 4.09808i −0.774453 0.207514i
\(391\) −2.53590 −0.128246
\(392\) 15.8564 11.8564i 0.800869 0.598839i
\(393\) 16.3923 0.826882
\(394\) −29.1244 7.80385i −1.46726 0.393152i
\(395\) 2.66025 0.133852
\(396\) 0 0
\(397\) 5.53590i 0.277839i −0.990304 0.138919i \(-0.955637\pi\)
0.990304 0.138919i \(-0.0443629\pi\)
\(398\) 4.73205 + 1.26795i 0.237196 + 0.0635566i
\(399\) 18.0000 + 20.7846i 0.901127 + 1.04053i
\(400\) −2.00000 3.46410i −0.100000 0.173205i
\(401\) −23.9282 −1.19492 −0.597459 0.801900i \(-0.703823\pi\)
−0.597459 + 0.801900i \(0.703823\pi\)
\(402\) 2.19615 8.19615i 0.109534 0.408787i
\(403\) 38.7846i 1.93200i
\(404\) −8.53590 + 14.7846i −0.424677 + 0.735562i
\(405\) 9.00000i 0.447214i
\(406\) 9.68653 + 19.9545i 0.480735 + 0.990324i
\(407\) 9.46410i 0.469118i
\(408\) −1.60770 + 1.60770i −0.0795928 + 0.0795928i
\(409\) 31.8564i 1.57520i −0.616188 0.787599i \(-0.711324\pi\)
0.616188 0.787599i \(-0.288676\pi\)
\(410\) −4.73205 1.26795i −0.233699 0.0626195i
\(411\) −0.679492 −0.0335169
\(412\) −29.7846 17.1962i −1.46738 0.847194i
\(413\) 6.00000 + 6.92820i 0.295241 + 0.340915i
\(414\) 0 0
\(415\) 8.53590i 0.419011i
\(416\) −35.3205 + 9.46410i −1.73173 + 0.464016i
\(417\) −12.0000 −0.587643
\(418\) 8.19615 30.5885i 0.400887 1.49613i
\(419\) 24.2487 1.18463 0.592314 0.805708i \(-0.298215\pi\)
0.592314 + 0.805708i \(0.298215\pi\)
\(420\) −9.00000 + 1.73205i −0.439155 + 0.0845154i
\(421\) 19.0000 0.926003 0.463002 0.886357i \(-0.346772\pi\)
0.463002 + 0.886357i \(0.346772\pi\)
\(422\) −2.63397 + 9.83013i −0.128220 + 0.478523i
\(423\) 0 0
\(424\) −4.00000 4.00000i −0.194257 0.194257i
\(425\) 0.464102i 0.0225122i
\(426\) 0.339746 1.26795i 0.0164607 0.0614323i
\(427\) 5.07180 4.39230i 0.245441 0.212559i
\(428\) −18.3923 + 31.8564i −0.889026 + 1.53984i
\(429\) 41.7846 2.01738
\(430\) 2.73205 + 0.732051i 0.131751 + 0.0353026i
\(431\) 17.5885i 0.847206i 0.905848 + 0.423603i \(0.139235\pi\)
−0.905848 + 0.423603i \(0.860765\pi\)
\(432\) −10.3923 18.0000i −0.500000 0.866025i
\(433\) 4.14359i 0.199128i 0.995031 + 0.0995642i \(0.0317449\pi\)
−0.995031 + 0.0995642i \(0.968255\pi\)
\(434\) 9.80385 + 20.1962i 0.470600 + 0.969446i
\(435\) 10.2679i 0.492310i
\(436\) 27.5885 + 15.9282i 1.32125 + 0.762823i
\(437\) 32.7846i 1.56830i
\(438\) 0.588457 2.19615i 0.0281176 0.104936i
\(439\) 15.7128 0.749932 0.374966 0.927039i \(-0.377654\pi\)
0.374966 + 0.927039i \(0.377654\pi\)
\(440\) 7.46410 + 7.46410i 0.355837 + 0.355837i
\(441\) 0 0
\(442\) 4.09808 + 1.09808i 0.194926 + 0.0522302i
\(443\) 26.0000i 1.23530i −0.786454 0.617649i \(-0.788085\pi\)
0.786454 0.617649i \(-0.211915\pi\)
\(444\) −7.60770 4.39230i −0.361045 0.208450i
\(445\) 9.46410 0.448641
\(446\) 14.0263 + 3.75833i 0.664164 + 0.177962i
\(447\) 29.3205 1.38681
\(448\) −16.0000 + 13.8564i −0.755929 + 0.654654i
\(449\) −1.92820 −0.0909975 −0.0454988 0.998964i \(-0.514488\pi\)
−0.0454988 + 0.998964i \(0.514488\pi\)
\(450\) 0 0
\(451\) 12.9282 0.608765
\(452\) −2.53590 1.46410i −0.119279 0.0688655i
\(453\) 8.32051i 0.390932i
\(454\) −4.56218 1.22243i −0.214114 0.0573716i
\(455\) 11.1962 + 12.9282i 0.524884 + 0.606084i
\(456\) −20.7846 20.7846i −0.973329 0.973329i
\(457\) 27.4641 1.28472 0.642358 0.766405i \(-0.277956\pi\)
0.642358 + 0.766405i \(0.277956\pi\)
\(458\) 5.66025 21.1244i 0.264486 0.987076i
\(459\) 2.41154i 0.112561i
\(460\) 9.46410 + 5.46410i 0.441266 + 0.254765i
\(461\) 27.7128i 1.29071i 0.763881 + 0.645357i \(0.223291\pi\)
−0.763881 + 0.645357i \(0.776709\pi\)
\(462\) 21.7583 10.5622i 1.01229 0.491397i
\(463\) 4.39230i 0.204128i 0.994778 + 0.102064i \(0.0325446\pi\)
−0.994778 + 0.102064i \(0.967455\pi\)
\(464\) −11.8564 20.5359i −0.550420 0.953355i
\(465\) 10.3923i 0.481932i
\(466\) 31.3205 + 8.39230i 1.45089 + 0.388766i
\(467\) −22.5167 −1.04195 −0.520973 0.853573i \(-0.674431\pi\)
−0.520973 + 0.853573i \(0.674431\pi\)
\(468\) 0 0
\(469\) −6.92820 + 6.00000i −0.319915 + 0.277054i
\(470\) −0.633975 + 2.36603i −0.0292431 + 0.109137i
\(471\) 34.3923i 1.58471i
\(472\) −6.92820 6.92820i −0.318896 0.318896i
\(473\) −7.46410 −0.343200
\(474\) −1.68653 + 6.29423i −0.0774650 + 0.289103i
\(475\) −6.00000 −0.275299
\(476\) 2.41154 0.464102i 0.110533 0.0212721i
\(477\) 0 0
\(478\) 10.2417 38.2224i 0.468443 1.74825i
\(479\) −37.1769 −1.69866 −0.849328 0.527865i \(-0.822993\pi\)
−0.849328 + 0.527865i \(0.822993\pi\)
\(480\) 9.46410 2.53590i 0.431975 0.115747i
\(481\) 16.3923i 0.747425i
\(482\) 1.60770 6.00000i 0.0732285 0.273293i
\(483\) 18.9282 16.3923i 0.861263 0.745876i
\(484\) −5.07180 2.92820i −0.230536 0.133100i
\(485\) 7.39230 0.335667
\(486\) 0 0
\(487\) 28.7846i 1.30436i 0.758066 + 0.652178i \(0.226144\pi\)
−0.758066 + 0.652178i \(0.773856\pi\)
\(488\) −5.07180 + 5.07180i −0.229589 + 0.229589i
\(489\) 36.0000i 1.62798i
\(490\) 9.09808 + 3.90192i 0.411009 + 0.176271i
\(491\) 34.1244i 1.54001i −0.638037 0.770005i \(-0.720254\pi\)
0.638037 0.770005i \(-0.279746\pi\)
\(492\) 6.00000 10.3923i 0.270501 0.468521i
\(493\) 2.75129i 0.123912i
\(494\) −14.1962 + 52.9808i −0.638715 + 2.38372i
\(495\) 0 0
\(496\) −12.0000 20.7846i −0.538816 0.933257i
\(497\) −1.07180 + 0.928203i −0.0480767 + 0.0416356i
\(498\) −20.1962 5.41154i −0.905011 0.242497i
\(499\) 5.58846i 0.250174i −0.992146 0.125087i \(-0.960079\pi\)
0.992146 0.125087i \(-0.0399210\pi\)
\(500\) 1.00000 1.73205i 0.0447214 0.0774597i
\(501\) 9.00000 0.402090
\(502\) −2.53590 0.679492i −0.113183 0.0303272i
\(503\) 15.5885 0.695055 0.347527 0.937670i \(-0.387021\pi\)
0.347527 + 0.937670i \(0.387021\pi\)
\(504\) 0 0
\(505\) −8.53590 −0.379842
\(506\) −27.8564 7.46410i −1.23837 0.331820i
\(507\) −49.8564 −2.21420
\(508\) 8.53590 14.7846i 0.378719 0.655961i
\(509\) 1.85641i 0.0822838i 0.999153 + 0.0411419i \(0.0130996\pi\)
−0.999153 + 0.0411419i \(0.986900\pi\)
\(510\) −1.09808 0.294229i −0.0486236 0.0130287i
\(511\) −1.85641 + 1.60770i −0.0821226 + 0.0711202i
\(512\) 16.0000 16.0000i 0.707107 0.707107i
\(513\) −31.1769 −1.37649
\(514\) −2.19615 + 8.19615i −0.0968681 + 0.361517i
\(515\) 17.1962i 0.757753i
\(516\) −3.46410 + 6.00000i −0.152499 + 0.264135i
\(517\) 6.46410i 0.284291i
\(518\) 4.14359 + 8.53590i 0.182059 + 0.375046i
\(519\) 35.1962i 1.54494i
\(520\) −12.9282 12.9282i −0.566939 0.566939i
\(521\) 34.3923i 1.50675i −0.657589 0.753377i \(-0.728424\pi\)
0.657589 0.753377i \(-0.271576\pi\)
\(522\) 0 0
\(523\) 24.2487 1.06032 0.530161 0.847897i \(-0.322131\pi\)
0.530161 + 0.847897i \(0.322131\pi\)
\(524\) 16.3923 + 9.46410i 0.716101 + 0.413441i
\(525\) −3.00000 3.46410i −0.130931 0.151186i
\(526\) −1.66025 + 6.19615i −0.0723905 + 0.270165i
\(527\) 2.78461i 0.121300i
\(528\) −22.3923 + 12.9282i −0.974500 + 0.562628i
\(529\) −6.85641 −0.298105
\(530\) 0.732051 2.73205i 0.0317983 0.118673i
\(531\) 0 0
\(532\) 6.00000 + 31.1769i 0.260133 + 1.35169i
\(533\) −22.3923 −0.969918
\(534\) −6.00000 + 22.3923i −0.259645 + 0.969010i
\(535\) −18.3923 −0.795169
\(536\) 6.92820 6.92820i 0.299253 0.299253i
\(537\) 24.9282i 1.07573i
\(538\) 4.39230 16.3923i 0.189366 0.706722i
\(539\) −25.8564 3.73205i −1.11371 0.160751i
\(540\) 5.19615 9.00000i 0.223607 0.387298i
\(541\) −33.7846 −1.45251 −0.726257 0.687423i \(-0.758742\pi\)
−0.726257 + 0.687423i \(0.758742\pi\)
\(542\) −3.46410 0.928203i −0.148796 0.0398697i
\(543\) 22.3923i 0.960946i
\(544\) −2.53590 + 0.679492i −0.108726 + 0.0291330i
\(545\) 15.9282i 0.682289i
\(546\) −37.6865 + 18.2942i −1.61283 + 0.782921i
\(547\) 14.5359i 0.621510i 0.950490 + 0.310755i \(0.100582\pi\)
−0.950490 + 0.310755i \(0.899418\pi\)
\(548\) −0.679492 0.392305i −0.0290265 0.0167584i
\(549\) 0 0
\(550\) −1.36603 + 5.09808i −0.0582475 + 0.217383i
\(551\) −35.5692 −1.51530
\(552\) −18.9282 + 18.9282i −0.805638 + 0.805638i
\(553\) 5.32051 4.60770i 0.226251 0.195939i
\(554\) 33.8564 + 9.07180i 1.43842 + 0.385424i
\(555\) 4.39230i 0.186443i
\(556\) −12.0000 6.92820i −0.508913 0.293821i
\(557\) 5.85641 0.248144 0.124072 0.992273i \(-0.460405\pi\)
0.124072 + 0.992273i \(0.460405\pi\)
\(558\) 0 0
\(559\) 12.9282 0.546805
\(560\) −10.0000 3.46410i −0.422577 0.146385i
\(561\) 3.00000 0.126660
\(562\) −8.09808 2.16987i −0.341597 0.0915306i
\(563\) −43.1769 −1.81969 −0.909845 0.414948i \(-0.863800\pi\)
−0.909845 + 0.414948i \(0.863800\pi\)
\(564\) −5.19615 3.00000i −0.218797 0.126323i
\(565\) 1.46410i 0.0615952i
\(566\) 16.5622 + 4.43782i 0.696160 + 0.186536i
\(567\) −15.5885 18.0000i −0.654654 0.755929i
\(568\) 1.07180 1.07180i 0.0449716 0.0449716i
\(569\) 20.9282 0.877356 0.438678 0.898644i \(-0.355447\pi\)
0.438678 + 0.898644i \(0.355447\pi\)
\(570\) 3.80385 14.1962i 0.159326 0.594611i
\(571\) 41.3205i 1.72921i −0.502453 0.864605i \(-0.667569\pi\)
0.502453 0.864605i \(-0.332431\pi\)
\(572\) 41.7846 + 24.1244i 1.74710 + 1.00869i
\(573\) 5.53590i 0.231265i
\(574\) −11.6603 + 5.66025i −0.486690 + 0.236254i
\(575\) 5.46410i 0.227869i
\(576\) 0 0
\(577\) 1.39230i 0.0579624i 0.999580 + 0.0289812i \(0.00922630\pi\)
−0.999580 + 0.0289812i \(0.990774\pi\)
\(578\) −22.9282 6.14359i −0.953688 0.255540i
\(579\) −4.39230 −0.182538
\(580\) 5.92820 10.2679i 0.246155 0.426353i
\(581\) 14.7846 + 17.0718i 0.613369 + 0.708257i
\(582\) −4.68653 + 17.4904i −0.194263 + 0.725000i
\(583\) 7.46410i 0.309132i
\(584\) 1.85641 1.85641i 0.0768186 0.0768186i
\(585\) 0 0
\(586\) 5.24167 19.5622i 0.216531 0.808106i
\(587\) −27.4641 −1.13356 −0.566782 0.823868i \(-0.691812\pi\)
−0.566782 + 0.823868i \(0.691812\pi\)
\(588\) −15.0000 + 19.0526i −0.618590 + 0.785714i
\(589\) −36.0000 −1.48335
\(590\) 1.26795 4.73205i 0.0522006 0.194815i
\(591\) 36.9282 1.51902
\(592\) −5.07180 8.78461i −0.208450 0.361045i
\(593\) 23.5359i 0.966504i −0.875481 0.483252i \(-0.839456\pi\)
0.875481 0.483252i \(-0.160544\pi\)
\(594\) −7.09808 + 26.4904i −0.291238 + 1.08691i
\(595\) 0.803848 + 0.928203i 0.0329545 + 0.0380526i
\(596\) 29.3205 + 16.9282i 1.20101 + 0.693406i
\(597\) −6.00000 −0.245564
\(598\) 48.2487 + 12.9282i 1.97304 + 0.528674i
\(599\) 14.1244i 0.577106i 0.957464 + 0.288553i \(0.0931741\pi\)
−0.957464 + 0.288553i \(0.906826\pi\)
\(600\) 3.46410 + 3.46410i 0.141421 + 0.141421i
\(601\) 26.7846i 1.09257i −0.837600 0.546284i \(-0.816042\pi\)
0.837600 0.546284i \(-0.183958\pi\)
\(602\) 6.73205 3.26795i 0.274378 0.133192i
\(603\) 0 0
\(604\) −4.80385 + 8.32051i −0.195466 + 0.338557i
\(605\) 2.92820i 0.119048i
\(606\) 5.41154 20.1962i 0.219829 0.820413i
\(607\) −18.8038 −0.763225 −0.381612 0.924322i \(-0.624631\pi\)
−0.381612 + 0.924322i \(0.624631\pi\)
\(608\) −8.78461 32.7846i −0.356263 1.32959i
\(609\) −17.7846 20.5359i −0.720669 0.832157i
\(610\) −3.46410 0.928203i −0.140257 0.0375819i
\(611\) 11.1962i 0.452948i
\(612\) 0 0
\(613\) −10.0000 −0.403896 −0.201948 0.979396i \(-0.564727\pi\)
−0.201948 + 0.979396i \(0.564727\pi\)
\(614\) 2.36603 + 0.633975i 0.0954850 + 0.0255851i
\(615\) 6.00000 0.241943
\(616\) 27.8564 + 2.00000i 1.12237 + 0.0805823i
\(617\) −9.07180 −0.365217 −0.182608 0.983186i \(-0.558454\pi\)
−0.182608 + 0.983186i \(0.558454\pi\)
\(618\) 40.6865 + 10.9019i 1.63665 + 0.438540i
\(619\) 35.3205 1.41965 0.709826 0.704378i \(-0.248774\pi\)
0.709826 + 0.704378i \(0.248774\pi\)
\(620\) 6.00000 10.3923i 0.240966 0.417365i
\(621\) 28.3923i 1.13934i
\(622\) 27.1244 + 7.26795i 1.08759 + 0.291418i
\(623\) 18.9282 16.3923i 0.758342 0.656744i
\(624\) 38.7846 22.3923i 1.55263 0.896410i
\(625\) 1.00000 0.0400000
\(626\) 8.95448 33.4186i 0.357893 1.33568i
\(627\) 38.7846i 1.54891i
\(628\) −19.8564 + 34.3923i −0.792357 + 1.37240i
\(629\) 1.17691i 0.0469267i
\(630\) 0 0
\(631\) 26.9090i 1.07123i −0.844463 0.535614i \(-0.820080\pi\)
0.844463 0.535614i \(-0.179920\pi\)
\(632\) −5.32051 + 5.32051i −0.211638 + 0.211638i
\(633\) 12.4641i 0.495404i
\(634\) 23.1244 + 6.19615i 0.918385 + 0.246081i
\(635\) 8.53590 0.338737
\(636\) 6.00000 + 3.46410i 0.237915 + 0.137361i
\(637\) 44.7846 + 6.46410i 1.77443 + 0.256117i
\(638\) −8.09808 + 30.2224i −0.320606 + 1.19652i
\(639\) 0 0
\(640\) 10.9282 + 2.92820i 0.431975 + 0.115747i
\(641\) −4.92820 −0.194652 −0.0973262 0.995253i \(-0.531029\pi\)
−0.0973262 + 0.995253i \(0.531029\pi\)
\(642\) 11.6603 43.5167i 0.460194 1.71747i
\(643\) −31.0526 −1.22459 −0.612297 0.790628i \(-0.709754\pi\)
−0.612297 + 0.790628i \(0.709754\pi\)
\(644\) 28.3923 5.46410i 1.11881 0.215316i
\(645\) −3.46410 −0.136399
\(646\) −1.01924 + 3.80385i −0.0401014 + 0.149660i
\(647\) 10.3923 0.408564 0.204282 0.978912i \(-0.434514\pi\)
0.204282 + 0.978912i \(0.434514\pi\)
\(648\) 18.0000 + 18.0000i 0.707107 + 0.707107i
\(649\) 12.9282i 0.507476i
\(650\) 2.36603 8.83013i 0.0928032 0.346346i
\(651\) −18.0000 20.7846i −0.705476 0.814613i
\(652\) −20.7846 + 36.0000i −0.813988 + 1.40987i
\(653\) 38.3923 1.50241 0.751203 0.660071i \(-0.229474\pi\)
0.751203 + 0.660071i \(0.229474\pi\)
\(654\) −37.6865 10.0981i −1.47366 0.394866i
\(655\) 9.46410i 0.369793i
\(656\) 12.0000 6.92820i 0.468521 0.270501i
\(657\) 0 0
\(658\) 2.83013 + 5.83013i 0.110330 + 0.227282i
\(659\) 20.8038i 0.810403i −0.914227 0.405201i \(-0.867201\pi\)
0.914227 0.405201i \(-0.132799\pi\)
\(660\) −11.1962 6.46410i −0.435810 0.251615i
\(661\) 15.7128i 0.611158i 0.952167 + 0.305579i \(0.0988499\pi\)
−0.952167 + 0.305579i \(0.901150\pi\)
\(662\) −2.05256 + 7.66025i −0.0797750 + 0.297724i
\(663\) −5.19615 −0.201802
\(664\) −17.0718 17.0718i −0.662514 0.662514i
\(665\) −12.0000 + 10.3923i −0.465340 + 0.402996i
\(666\) 0 0
\(667\) 32.3923i 1.25424i
\(668\) 9.00000 + 5.19615i 0.348220 + 0.201045i
\(669\) −17.7846 −0.687593
\(670\) 4.73205 + 1.26795i 0.182815 + 0.0489852i
\(671\) 9.46410 0.365358
\(672\) 14.5359 21.4641i 0.560734 0.827996i
\(673\) 49.1769 1.89563 0.947815 0.318820i \(-0.103286\pi\)
0.947815 + 0.318820i \(0.103286\pi\)
\(674\) 0 0
\(675\) 5.19615 0.200000
\(676\) −49.8564 28.7846i −1.91755 1.10710i
\(677\) 4.60770i 0.177088i 0.996072 + 0.0885441i \(0.0282214\pi\)
−0.996072 + 0.0885441i \(0.971779\pi\)
\(678\) 3.46410 + 0.928203i 0.133038 + 0.0356474i
\(679\) 14.7846 12.8038i 0.567381 0.491367i
\(680\) −0.928203 0.928203i −0.0355950 0.0355950i
\(681\) 5.78461 0.221667
\(682\) −8.19615 + 30.5885i −0.313847 + 1.17129i
\(683\) 27.3205i 1.04539i −0.852520 0.522695i \(-0.824927\pi\)
0.852520 0.522695i \(-0.175073\pi\)
\(684\) 0 0
\(685\) 0.392305i 0.0149892i
\(686\) 24.9545 7.95448i 0.952767 0.303704i
\(687\) 26.7846i 1.02190i
\(688\) −6.92820 + 4.00000i −0.264135 + 0.152499i
\(689\) 12.9282i 0.492525i
\(690\) −12.9282 3.46410i −0.492168 0.131876i
\(691\) 46.6410 1.77431 0.887154 0.461474i \(-0.152679\pi\)
0.887154 + 0.461474i \(0.152679\pi\)
\(692\) 20.3205 35.1962i 0.772470 1.33796i
\(693\) 0 0
\(694\) −5.21539 + 19.4641i −0.197974 + 0.738847i
\(695\) 6.92820i 0.262802i
\(696\) 20.5359 + 20.5359i 0.778411 + 0.778411i
\(697\) −1.60770 −0.0608958
\(698\) −10.7321 + 40.0526i −0.406214 + 1.51601i
\(699\) −39.7128 −1.50208
\(700\) −1.00000 5.19615i −0.0377964 0.196396i
\(701\) 3.78461 0.142943 0.0714714 0.997443i \(-0.477231\pi\)
0.0714714 + 0.997443i \(0.477231\pi\)
\(702\) 12.2942 45.8827i 0.464016 1.73173i
\(703\) −15.2154 −0.573859
\(704\) −29.8564 −1.12526
\(705\) 3.00000i 0.112987i
\(706\) −4.90192 + 18.2942i −0.184486 + 0.688512i
\(707\) −17.0718 + 14.7846i −0.642051 + 0.556032i
\(708\) 10.3923 + 6.00000i 0.390567 + 0.225494i
\(709\) 21.0000 0.788672 0.394336 0.918966i \(-0.370975\pi\)
0.394336 + 0.918966i \(0.370975\pi\)
\(710\) 0.732051 + 0.196152i 0.0274734 + 0.00736147i
\(711\) 0 0
\(712\) −18.9282 + 18.9282i −0.709364 + 0.709364i
\(713\) 32.7846i 1.22779i
\(714\) −2.70577 + 1.31347i −0.101261 + 0.0491552i
\(715\) 24.1244i 0.902200i
\(716\) −14.3923 + 24.9282i −0.537866 + 0.931611i
\(717\) 48.4641i 1.80993i
\(718\) −3.41154 + 12.7321i −0.127318 + 0.475156i
\(719\) 45.4641 1.69552 0.847762 0.530376i \(-0.177949\pi\)
0.847762 + 0.530376i \(0.177949\pi\)
\(720\) 0 0
\(721\) −29.7846 34.3923i −1.10924 1.28084i
\(722\) −23.2224 6.22243i −0.864249 0.231575i
\(723\) 7.60770i 0.282933i
\(724\) 12.9282 22.3923i 0.480473 0.832203i
\(725\) 5.92820 0.220168
\(726\) 6.92820 + 1.85641i 0.257130 + 0.0688977i
\(727\) −34.3923 −1.27554 −0.637770 0.770227i \(-0.720143\pi\)
−0.637770 + 0.770227i \(0.720143\pi\)
\(728\) −48.2487 3.46410i −1.78822 0.128388i
\(729\) 27.0000 1.00000
\(730\) 1.26795 + 0.339746i 0.0469289 + 0.0125746i
\(731\) 0.928203 0.0343308
\(732\) 4.39230 7.60770i 0.162344 0.281189i
\(733\) 18.4641i 0.681987i −0.940066 0.340994i \(-0.889237\pi\)
0.940066 0.340994i \(-0.110763\pi\)
\(734\) −49.3468 13.2224i −1.82142 0.488049i
\(735\) −12.0000 1.73205i −0.442627 0.0638877i
\(736\) −29.8564 + 8.00000i −1.10052 + 0.294884i
\(737\) −12.9282 −0.476216
\(738\) 0 0
\(739\) 7.73205i 0.284428i −0.989836 0.142214i \(-0.954578\pi\)
0.989836 0.142214i \(-0.0454221\pi\)
\(740\) 2.53590 4.39230i 0.0932215 0.161464i
\(741\) 67.1769i 2.46781i
\(742\) −3.26795 6.73205i −0.119970 0.247141i
\(743\) 9.60770i 0.352472i 0.984348 + 0.176236i \(0.0563922\pi\)
−0.984348 + 0.176236i \(0.943608\pi\)
\(744\) 20.7846 + 20.7846i 0.762001 + 0.762001i
\(745\) 16.9282i 0.620201i
\(746\) 33.3205 + 8.92820i 1.21995 + 0.326885i
\(747\) 0 0
\(748\) 3.00000 + 1.73205i 0.109691 + 0.0633300i
\(749\) −36.7846 + 31.8564i −1.34408 + 1.16401i
\(750\) −0.633975 + 2.36603i −0.0231495 + 0.0863950i
\(751\) 5.58846i 0.203926i 0.994788 + 0.101963i \(0.0325123\pi\)
−0.994788 + 0.101963i \(0.967488\pi\)
\(752\) −3.46410 6.00000i −0.126323 0.218797i
\(753\) 3.21539 0.117175
\(754\) 14.0263 52.3468i 0.510807 1.90636i
\(755\) −4.80385 −0.174830
\(756\) −5.19615 27.0000i −0.188982 0.981981i
\(757\) 10.1436 0.368675 0.184338 0.982863i \(-0.440986\pi\)
0.184338 + 0.982863i \(0.440986\pi\)
\(758\) 9.66025 36.0526i 0.350876 1.30949i
\(759\) 35.3205 1.28205
\(760\) 12.0000 12.0000i 0.435286 0.435286i
\(761\) 6.24871i 0.226516i −0.993566 0.113258i \(-0.963871\pi\)
0.993566 0.113258i \(-0.0361286\pi\)
\(762\) −5.41154 + 20.1962i −0.196040 + 0.731629i
\(763\) 27.5885 + 31.8564i 0.998769 + 1.15328i
\(764\) 3.19615 5.53590i 0.115633 0.200282i
\(765\) 0 0
\(766\) −28.0526 7.51666i −1.01358 0.271588i
\(767\) 22.3923i 0.808539i
\(768\) −13.8564 + 24.0000i −0.500000 + 0.866025i
\(769\) 18.0000i 0.649097i −0.945869 0.324548i \(-0.894788\pi\)
0.945869 0.324548i \(-0.105212\pi\)
\(770\) 6.09808 + 12.5622i 0.219759 + 0.452709i
\(771\) 10.3923i 0.374270i
\(772\) −4.39230 2.53590i −0.158083 0.0912690i
\(773\) 12.4641i 0.448303i 0.974554 + 0.224151i \(0.0719610\pi\)
−0.974554 + 0.224151i \(0.928039\pi\)
\(774\) 0 0
\(775\) 6.00000 0.215526
\(776\) −14.7846 + 14.7846i −0.530737 + 0.530737i
\(777\) −7.60770 8.78461i −0.272925 0.315146i
\(778\) −9.36603 2.50962i −0.335788 0.0899742i
\(779\) 20.7846i 0.744686i