Properties

Label 726.2.e.k.493.1
Level $726$
Weight $2$
Character 726.493
Analytic conductor $5.797$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 726 = 2 \cdot 3 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 726.e (of order \(5\), degree \(4\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.79713918674\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{10})\)
Defining polynomial: \( x^{4} - x^{3} + x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 66)
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 493.1
Root \(-0.309017 - 0.951057i\) of defining polynomial
Character \(\chi\) \(=\) 726.493
Dual form 726.2.e.k.511.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.309017 + 0.951057i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-0.309017 - 0.951057i) q^{6} +(-1.61803 - 1.17557i) q^{7} +(0.809017 - 0.587785i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})\) \(q+(-0.309017 + 0.951057i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-0.309017 - 0.951057i) q^{6} +(-1.61803 - 1.17557i) q^{7} +(0.809017 - 0.587785i) q^{8} +(0.309017 - 0.951057i) q^{9} +1.00000 q^{12} +(-1.23607 + 3.80423i) q^{13} +(1.61803 - 1.17557i) q^{14} +(0.309017 + 0.951057i) q^{16} +(-1.85410 - 5.70634i) q^{17} +(0.809017 + 0.587785i) q^{18} +(3.23607 - 2.35114i) q^{19} +2.00000 q^{21} +6.00000 q^{23} +(-0.309017 + 0.951057i) q^{24} +(4.04508 - 2.93893i) q^{25} +(-3.23607 - 2.35114i) q^{26} +(0.309017 + 0.951057i) q^{27} +(0.618034 + 1.90211i) q^{28} +(-4.85410 - 3.52671i) q^{29} +(2.47214 - 7.60845i) q^{31} -1.00000 q^{32} +6.00000 q^{34} +(-0.809017 + 0.587785i) q^{36} +(8.09017 + 5.87785i) q^{37} +(1.23607 + 3.80423i) q^{38} +(-1.23607 - 3.80423i) q^{39} +(-4.85410 + 3.52671i) q^{41} +(-0.618034 + 1.90211i) q^{42} +8.00000 q^{43} +(-1.85410 + 5.70634i) q^{46} +(4.85410 - 3.52671i) q^{47} +(-0.809017 - 0.587785i) q^{48} +(-0.927051 - 2.85317i) q^{49} +(1.54508 + 4.75528i) q^{50} +(4.85410 + 3.52671i) q^{51} +(3.23607 - 2.35114i) q^{52} -1.00000 q^{54} -2.00000 q^{56} +(-1.23607 + 3.80423i) q^{57} +(4.85410 - 3.52671i) q^{58} +(2.47214 + 7.60845i) q^{61} +(6.47214 + 4.70228i) q^{62} +(-1.61803 + 1.17557i) q^{63} +(0.309017 - 0.951057i) q^{64} -4.00000 q^{67} +(-1.85410 + 5.70634i) q^{68} +(-4.85410 + 3.52671i) q^{69} +(1.85410 + 5.70634i) q^{71} +(-0.309017 - 0.951057i) q^{72} +(-1.61803 - 1.17557i) q^{73} +(-8.09017 + 5.87785i) q^{74} +(-1.54508 + 4.75528i) q^{75} -4.00000 q^{76} +4.00000 q^{78} +(4.32624 - 13.3148i) q^{79} +(-0.809017 - 0.587785i) q^{81} +(-1.85410 - 5.70634i) q^{82} +(-3.70820 - 11.4127i) q^{83} +(-1.61803 - 1.17557i) q^{84} +(-2.47214 + 7.60845i) q^{86} +6.00000 q^{87} -6.00000 q^{89} +(6.47214 - 4.70228i) q^{91} +(-4.85410 - 3.52671i) q^{92} +(2.47214 + 7.60845i) q^{93} +(1.85410 + 5.70634i) q^{94} +(0.809017 - 0.587785i) q^{96} +(4.32624 - 13.3148i) q^{97} +3.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + q^{2} - q^{3} - q^{4} + q^{6} - 2 q^{7} + q^{8} - q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + q^{2} - q^{3} - q^{4} + q^{6} - 2 q^{7} + q^{8} - q^{9} + 4 q^{12} + 4 q^{13} + 2 q^{14} - q^{16} + 6 q^{17} + q^{18} + 4 q^{19} + 8 q^{21} + 24 q^{23} + q^{24} + 5 q^{25} - 4 q^{26} - q^{27} - 2 q^{28} - 6 q^{29} - 8 q^{31} - 4 q^{32} + 24 q^{34} - q^{36} + 10 q^{37} - 4 q^{38} + 4 q^{39} - 6 q^{41} + 2 q^{42} + 32 q^{43} + 6 q^{46} + 6 q^{47} - q^{48} + 3 q^{49} - 5 q^{50} + 6 q^{51} + 4 q^{52} - 4 q^{54} - 8 q^{56} + 4 q^{57} + 6 q^{58} - 8 q^{61} + 8 q^{62} - 2 q^{63} - q^{64} - 16 q^{67} + 6 q^{68} - 6 q^{69} - 6 q^{71} + q^{72} - 2 q^{73} - 10 q^{74} + 5 q^{75} - 16 q^{76} + 16 q^{78} - 14 q^{79} - q^{81} + 6 q^{82} + 12 q^{83} - 2 q^{84} + 8 q^{86} + 24 q^{87} - 24 q^{89} + 8 q^{91} - 6 q^{92} - 8 q^{93} - 6 q^{94} + q^{96} - 14 q^{97} + 12 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/726\mathbb{Z}\right)^\times\).

\(n\) \(485\) \(607\)
\(\chi(n)\) \(1\) \(e\left(\frac{3}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.309017 + 0.951057i −0.218508 + 0.672499i
\(3\) −0.809017 + 0.587785i −0.467086 + 0.339358i
\(4\) −0.809017 0.587785i −0.404508 0.293893i
\(5\) 0 0 0.951057 0.309017i \(-0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(6\) −0.309017 0.951057i −0.126156 0.388267i
\(7\) −1.61803 1.17557i −0.611559 0.444324i 0.238404 0.971166i \(-0.423376\pi\)
−0.849963 + 0.526842i \(0.823376\pi\)
\(8\) 0.809017 0.587785i 0.286031 0.207813i
\(9\) 0.309017 0.951057i 0.103006 0.317019i
\(10\) 0 0
\(11\) 0 0
\(12\) 1.00000 0.288675
\(13\) −1.23607 + 3.80423i −0.342824 + 1.05510i 0.619915 + 0.784669i \(0.287167\pi\)
−0.962739 + 0.270434i \(0.912833\pi\)
\(14\) 1.61803 1.17557i 0.432438 0.314184i
\(15\) 0 0
\(16\) 0.309017 + 0.951057i 0.0772542 + 0.237764i
\(17\) −1.85410 5.70634i −0.449686 1.38399i −0.877262 0.480011i \(-0.840633\pi\)
0.427576 0.903979i \(-0.359367\pi\)
\(18\) 0.809017 + 0.587785i 0.190687 + 0.138542i
\(19\) 3.23607 2.35114i 0.742405 0.539389i −0.151058 0.988525i \(-0.548268\pi\)
0.893463 + 0.449136i \(0.148268\pi\)
\(20\) 0 0
\(21\) 2.00000 0.436436
\(22\) 0 0
\(23\) 6.00000 1.25109 0.625543 0.780189i \(-0.284877\pi\)
0.625543 + 0.780189i \(0.284877\pi\)
\(24\) −0.309017 + 0.951057i −0.0630778 + 0.194134i
\(25\) 4.04508 2.93893i 0.809017 0.587785i
\(26\) −3.23607 2.35114i −0.634645 0.461097i
\(27\) 0.309017 + 0.951057i 0.0594703 + 0.183031i
\(28\) 0.618034 + 1.90211i 0.116797 + 0.359466i
\(29\) −4.85410 3.52671i −0.901384 0.654894i 0.0374370 0.999299i \(-0.488081\pi\)
−0.938821 + 0.344405i \(0.888081\pi\)
\(30\) 0 0
\(31\) 2.47214 7.60845i 0.444009 1.36652i −0.439558 0.898214i \(-0.644865\pi\)
0.883567 0.468304i \(-0.155135\pi\)
\(32\) −1.00000 −0.176777
\(33\) 0 0
\(34\) 6.00000 1.02899
\(35\) 0 0
\(36\) −0.809017 + 0.587785i −0.134836 + 0.0979642i
\(37\) 8.09017 + 5.87785i 1.33002 + 0.966313i 0.999749 + 0.0224255i \(0.00713887\pi\)
0.330267 + 0.943887i \(0.392861\pi\)
\(38\) 1.23607 + 3.80423i 0.200517 + 0.617127i
\(39\) −1.23607 3.80423i −0.197929 0.609164i
\(40\) 0 0
\(41\) −4.85410 + 3.52671i −0.758083 + 0.550780i −0.898322 0.439338i \(-0.855213\pi\)
0.140238 + 0.990118i \(0.455213\pi\)
\(42\) −0.618034 + 1.90211i −0.0953647 + 0.293502i
\(43\) 8.00000 1.21999 0.609994 0.792406i \(-0.291172\pi\)
0.609994 + 0.792406i \(0.291172\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) −1.85410 + 5.70634i −0.273372 + 0.841354i
\(47\) 4.85410 3.52671i 0.708044 0.514424i −0.174498 0.984657i \(-0.555830\pi\)
0.882542 + 0.470234i \(0.155830\pi\)
\(48\) −0.809017 0.587785i −0.116772 0.0848395i
\(49\) −0.927051 2.85317i −0.132436 0.407596i
\(50\) 1.54508 + 4.75528i 0.218508 + 0.672499i
\(51\) 4.85410 + 3.52671i 0.679710 + 0.493838i
\(52\) 3.23607 2.35114i 0.448762 0.326045i
\(53\) 0 0 −0.951057 0.309017i \(-0.900000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(54\) −1.00000 −0.136083
\(55\) 0 0
\(56\) −2.00000 −0.267261
\(57\) −1.23607 + 3.80423i −0.163721 + 0.503882i
\(58\) 4.85410 3.52671i 0.637375 0.463080i
\(59\) 0 0 0.587785 0.809017i \(-0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(60\) 0 0
\(61\) 2.47214 + 7.60845i 0.316525 + 0.974162i 0.975122 + 0.221667i \(0.0711499\pi\)
−0.658598 + 0.752495i \(0.728850\pi\)
\(62\) 6.47214 + 4.70228i 0.821962 + 0.597190i
\(63\) −1.61803 + 1.17557i −0.203853 + 0.148108i
\(64\) 0.309017 0.951057i 0.0386271 0.118882i
\(65\) 0 0
\(66\) 0 0
\(67\) −4.00000 −0.488678 −0.244339 0.969690i \(-0.578571\pi\)
−0.244339 + 0.969690i \(0.578571\pi\)
\(68\) −1.85410 + 5.70634i −0.224843 + 0.691995i
\(69\) −4.85410 + 3.52671i −0.584365 + 0.424566i
\(70\) 0 0
\(71\) 1.85410 + 5.70634i 0.220041 + 0.677218i 0.998757 + 0.0498409i \(0.0158714\pi\)
−0.778716 + 0.627377i \(0.784129\pi\)
\(72\) −0.309017 0.951057i −0.0364180 0.112083i
\(73\) −1.61803 1.17557i −0.189377 0.137590i 0.489057 0.872252i \(-0.337341\pi\)
−0.678434 + 0.734662i \(0.737341\pi\)
\(74\) −8.09017 + 5.87785i −0.940463 + 0.683286i
\(75\) −1.54508 + 4.75528i −0.178411 + 0.549093i
\(76\) −4.00000 −0.458831
\(77\) 0 0
\(78\) 4.00000 0.452911
\(79\) 4.32624 13.3148i 0.486740 1.49803i −0.342705 0.939443i \(-0.611343\pi\)
0.829445 0.558588i \(-0.188657\pi\)
\(80\) 0 0
\(81\) −0.809017 0.587785i −0.0898908 0.0653095i
\(82\) −1.85410 5.70634i −0.204751 0.630160i
\(83\) −3.70820 11.4127i −0.407028 1.25270i −0.919190 0.393815i \(-0.871155\pi\)
0.512161 0.858889i \(-0.328845\pi\)
\(84\) −1.61803 1.17557i −0.176542 0.128265i
\(85\) 0 0
\(86\) −2.47214 + 7.60845i −0.266577 + 0.820440i
\(87\) 6.00000 0.643268
\(88\) 0 0
\(89\) −6.00000 −0.635999 −0.317999 0.948091i \(-0.603011\pi\)
−0.317999 + 0.948091i \(0.603011\pi\)
\(90\) 0 0
\(91\) 6.47214 4.70228i 0.678464 0.492933i
\(92\) −4.85410 3.52671i −0.506075 0.367685i
\(93\) 2.47214 + 7.60845i 0.256349 + 0.788960i
\(94\) 1.85410 + 5.70634i 0.191236 + 0.588564i
\(95\) 0 0
\(96\) 0.809017 0.587785i 0.0825700 0.0599906i
\(97\) 4.32624 13.3148i 0.439263 1.35191i −0.449392 0.893335i \(-0.648359\pi\)
0.888654 0.458577i \(-0.151641\pi\)
\(98\) 3.00000 0.303046
\(99\) 0 0
\(100\) −5.00000 −0.500000
\(101\) 1.85410 5.70634i 0.184490 0.567802i −0.815449 0.578829i \(-0.803510\pi\)
0.999939 + 0.0110267i \(0.00350999\pi\)
\(102\) −4.85410 + 3.52671i −0.480628 + 0.349196i
\(103\) 3.23607 + 2.35114i 0.318859 + 0.231665i 0.735689 0.677320i \(-0.236859\pi\)
−0.416829 + 0.908985i \(0.636859\pi\)
\(104\) 1.23607 + 3.80423i 0.121206 + 0.373035i
\(105\) 0 0
\(106\) 0 0
\(107\) 9.70820 7.05342i 0.938527 0.681880i −0.00953827 0.999955i \(-0.503036\pi\)
0.948066 + 0.318074i \(0.103036\pi\)
\(108\) 0.309017 0.951057i 0.0297352 0.0915155i
\(109\) −4.00000 −0.383131 −0.191565 0.981480i \(-0.561356\pi\)
−0.191565 + 0.981480i \(0.561356\pi\)
\(110\) 0 0
\(111\) −10.0000 −0.949158
\(112\) 0.618034 1.90211i 0.0583987 0.179733i
\(113\) −14.5623 + 10.5801i −1.36991 + 0.995295i −0.372162 + 0.928168i \(0.621383\pi\)
−0.997744 + 0.0671276i \(0.978617\pi\)
\(114\) −3.23607 2.35114i −0.303086 0.220205i
\(115\) 0 0
\(116\) 1.85410 + 5.70634i 0.172149 + 0.529820i
\(117\) 3.23607 + 2.35114i 0.299175 + 0.217363i
\(118\) 0 0
\(119\) −3.70820 + 11.4127i −0.339930 + 1.04620i
\(120\) 0 0
\(121\) 0 0
\(122\) −8.00000 −0.724286
\(123\) 1.85410 5.70634i 0.167179 0.514523i
\(124\) −6.47214 + 4.70228i −0.581215 + 0.422277i
\(125\) 0 0
\(126\) −0.618034 1.90211i −0.0550588 0.169454i
\(127\) 4.32624 + 13.3148i 0.383892 + 1.18150i 0.937281 + 0.348574i \(0.113334\pi\)
−0.553390 + 0.832922i \(0.686666\pi\)
\(128\) 0.809017 + 0.587785i 0.0715077 + 0.0519534i
\(129\) −6.47214 + 4.70228i −0.569840 + 0.414013i
\(130\) 0 0
\(131\) −12.0000 −1.04844 −0.524222 0.851581i \(-0.675644\pi\)
−0.524222 + 0.851581i \(0.675644\pi\)
\(132\) 0 0
\(133\) −8.00000 −0.693688
\(134\) 1.23607 3.80423i 0.106780 0.328635i
\(135\) 0 0
\(136\) −4.85410 3.52671i −0.416236 0.302413i
\(137\) −5.56231 17.1190i −0.475220 1.46258i −0.845661 0.533720i \(-0.820793\pi\)
0.370441 0.928856i \(-0.379207\pi\)
\(138\) −1.85410 5.70634i −0.157832 0.485756i
\(139\) 3.23607 + 2.35114i 0.274480 + 0.199421i 0.716506 0.697581i \(-0.245740\pi\)
−0.442026 + 0.897002i \(0.645740\pi\)
\(140\) 0 0
\(141\) −1.85410 + 5.70634i −0.156144 + 0.480560i
\(142\) −6.00000 −0.503509
\(143\) 0 0
\(144\) 1.00000 0.0833333
\(145\) 0 0
\(146\) 1.61803 1.17557i 0.133909 0.0972909i
\(147\) 2.42705 + 1.76336i 0.200180 + 0.145439i
\(148\) −3.09017 9.51057i −0.254010 0.781764i
\(149\) −1.85410 5.70634i −0.151894 0.467482i 0.845939 0.533280i \(-0.179041\pi\)
−0.997833 + 0.0657982i \(0.979041\pi\)
\(150\) −4.04508 2.93893i −0.330280 0.239962i
\(151\) 8.09017 5.87785i 0.658369 0.478333i −0.207743 0.978183i \(-0.566612\pi\)
0.866112 + 0.499851i \(0.166612\pi\)
\(152\) 1.23607 3.80423i 0.100258 0.308563i
\(153\) −6.00000 −0.485071
\(154\) 0 0
\(155\) 0 0
\(156\) −1.23607 + 3.80423i −0.0989646 + 0.304582i
\(157\) −1.61803 + 1.17557i −0.129133 + 0.0938207i −0.650477 0.759526i \(-0.725431\pi\)
0.521344 + 0.853347i \(0.325431\pi\)
\(158\) 11.3262 + 8.22899i 0.901067 + 0.654664i
\(159\) 0 0
\(160\) 0 0
\(161\) −9.70820 7.05342i −0.765114 0.555888i
\(162\) 0.809017 0.587785i 0.0635624 0.0461808i
\(163\) −1.23607 + 3.80423i −0.0968163 + 0.297970i −0.987723 0.156217i \(-0.950070\pi\)
0.890906 + 0.454187i \(0.150070\pi\)
\(164\) 6.00000 0.468521
\(165\) 0 0
\(166\) 12.0000 0.931381
\(167\) 3.70820 11.4127i 0.286949 0.883140i −0.698858 0.715260i \(-0.746308\pi\)
0.985808 0.167879i \(-0.0536919\pi\)
\(168\) 1.61803 1.17557i 0.124834 0.0906972i
\(169\) −2.42705 1.76336i −0.186696 0.135643i
\(170\) 0 0
\(171\) −1.23607 3.80423i −0.0945245 0.290916i
\(172\) −6.47214 4.70228i −0.493496 0.358546i
\(173\) −4.85410 + 3.52671i −0.369051 + 0.268131i −0.756817 0.653627i \(-0.773247\pi\)
0.387767 + 0.921758i \(0.373247\pi\)
\(174\) −1.85410 + 5.70634i −0.140559 + 0.432596i
\(175\) −10.0000 −0.755929
\(176\) 0 0
\(177\) 0 0
\(178\) 1.85410 5.70634i 0.138971 0.427708i
\(179\) −19.4164 + 14.1068i −1.45125 + 1.05440i −0.465713 + 0.884936i \(0.654202\pi\)
−0.985537 + 0.169460i \(0.945798\pi\)
\(180\) 0 0
\(181\) −6.79837 20.9232i −0.505319 1.55521i −0.800233 0.599689i \(-0.795291\pi\)
0.294914 0.955524i \(-0.404709\pi\)
\(182\) 2.47214 + 7.60845i 0.183247 + 0.563976i
\(183\) −6.47214 4.70228i −0.478434 0.347603i
\(184\) 4.85410 3.52671i 0.357849 0.259993i
\(185\) 0 0
\(186\) −8.00000 −0.586588
\(187\) 0 0
\(188\) −6.00000 −0.437595
\(189\) 0.618034 1.90211i 0.0449554 0.138358i
\(190\) 0 0
\(191\) −14.5623 10.5801i −1.05369 0.765552i −0.0807805 0.996732i \(-0.525741\pi\)
−0.972911 + 0.231180i \(0.925741\pi\)
\(192\) 0.309017 + 0.951057i 0.0223014 + 0.0686366i
\(193\) 4.32624 + 13.3148i 0.311409 + 0.958420i 0.977207 + 0.212287i \(0.0680913\pi\)
−0.665798 + 0.746132i \(0.731909\pi\)
\(194\) 11.3262 + 8.22899i 0.813176 + 0.590807i
\(195\) 0 0
\(196\) −0.927051 + 2.85317i −0.0662179 + 0.203798i
\(197\) 6.00000 0.427482 0.213741 0.976890i \(-0.431435\pi\)
0.213741 + 0.976890i \(0.431435\pi\)
\(198\) 0 0
\(199\) −4.00000 −0.283552 −0.141776 0.989899i \(-0.545281\pi\)
−0.141776 + 0.989899i \(0.545281\pi\)
\(200\) 1.54508 4.75528i 0.109254 0.336249i
\(201\) 3.23607 2.35114i 0.228255 0.165837i
\(202\) 4.85410 + 3.52671i 0.341533 + 0.248139i
\(203\) 3.70820 + 11.4127i 0.260265 + 0.801013i
\(204\) −1.85410 5.70634i −0.129813 0.399524i
\(205\) 0 0
\(206\) −3.23607 + 2.35114i −0.225468 + 0.163812i
\(207\) 1.85410 5.70634i 0.128869 0.396618i
\(208\) −4.00000 −0.277350
\(209\) 0 0
\(210\) 0 0
\(211\) 2.47214 7.60845i 0.170189 0.523787i −0.829192 0.558963i \(-0.811199\pi\)
0.999381 + 0.0351760i \(0.0111992\pi\)
\(212\) 0 0
\(213\) −4.85410 3.52671i −0.332598 0.241646i
\(214\) 3.70820 + 11.4127i 0.253488 + 0.780155i
\(215\) 0 0
\(216\) 0.809017 + 0.587785i 0.0550466 + 0.0399937i
\(217\) −12.9443 + 9.40456i −0.878714 + 0.638423i
\(218\) 1.23607 3.80423i 0.0837171 0.257655i
\(219\) 2.00000 0.135147
\(220\) 0 0
\(221\) 24.0000 1.61441
\(222\) 3.09017 9.51057i 0.207399 0.638307i
\(223\) 12.9443 9.40456i 0.866813 0.629776i −0.0629172 0.998019i \(-0.520040\pi\)
0.929730 + 0.368243i \(0.120040\pi\)
\(224\) 1.61803 + 1.17557i 0.108109 + 0.0785461i
\(225\) −1.54508 4.75528i −0.103006 0.317019i
\(226\) −5.56231 17.1190i −0.369999 1.13874i
\(227\) 9.70820 + 7.05342i 0.644356 + 0.468152i 0.861344 0.508022i \(-0.169623\pi\)
−0.216988 + 0.976174i \(0.569623\pi\)
\(228\) 3.23607 2.35114i 0.214314 0.155708i
\(229\) −6.79837 + 20.9232i −0.449249 + 1.38265i 0.428507 + 0.903539i \(0.359040\pi\)
−0.877756 + 0.479108i \(0.840960\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −6.00000 −0.393919
\(233\) −5.56231 + 17.1190i −0.364399 + 1.12150i 0.585958 + 0.810341i \(0.300718\pi\)
−0.950357 + 0.311163i \(0.899282\pi\)
\(234\) −3.23607 + 2.35114i −0.211548 + 0.153699i
\(235\) 0 0
\(236\) 0 0
\(237\) 4.32624 + 13.3148i 0.281019 + 0.864889i
\(238\) −9.70820 7.05342i −0.629289 0.457206i
\(239\) 9.70820 7.05342i 0.627972 0.456248i −0.227725 0.973725i \(-0.573129\pi\)
0.855697 + 0.517477i \(0.173129\pi\)
\(240\) 0 0
\(241\) −10.0000 −0.644157 −0.322078 0.946713i \(-0.604381\pi\)
−0.322078 + 0.946713i \(0.604381\pi\)
\(242\) 0 0
\(243\) 1.00000 0.0641500
\(244\) 2.47214 7.60845i 0.158262 0.487081i
\(245\) 0 0
\(246\) 4.85410 + 3.52671i 0.309486 + 0.224855i
\(247\) 4.94427 + 15.2169i 0.314596 + 0.968228i
\(248\) −2.47214 7.60845i −0.156981 0.483137i
\(249\) 9.70820 + 7.05342i 0.615232 + 0.446993i
\(250\) 0 0
\(251\) 0 0 −0.951057 0.309017i \(-0.900000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(252\) 2.00000 0.125988
\(253\) 0 0
\(254\) −14.0000 −0.878438
\(255\) 0 0
\(256\) −0.809017 + 0.587785i −0.0505636 + 0.0367366i
\(257\) 24.2705 + 17.6336i 1.51395 + 1.09995i 0.964385 + 0.264502i \(0.0852075\pi\)
0.549568 + 0.835449i \(0.314792\pi\)
\(258\) −2.47214 7.60845i −0.153908 0.473682i
\(259\) −6.18034 19.0211i −0.384028 1.18192i
\(260\) 0 0
\(261\) −4.85410 + 3.52671i −0.300461 + 0.218298i
\(262\) 3.70820 11.4127i 0.229094 0.705078i
\(263\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 2.47214 7.60845i 0.151576 0.466504i
\(267\) 4.85410 3.52671i 0.297066 0.215831i
\(268\) 3.23607 + 2.35114i 0.197674 + 0.143619i
\(269\) −7.41641 22.8254i −0.452186 1.39169i −0.874407 0.485193i \(-0.838749\pi\)
0.422221 0.906493i \(-0.361251\pi\)
\(270\) 0 0
\(271\) −1.61803 1.17557i −0.0982886 0.0714108i 0.537555 0.843228i \(-0.319348\pi\)
−0.635844 + 0.771818i \(0.719348\pi\)
\(272\) 4.85410 3.52671i 0.294323 0.213838i
\(273\) −2.47214 + 7.60845i −0.149620 + 0.460484i
\(274\) 18.0000 1.08742
\(275\) 0 0
\(276\) 6.00000 0.361158
\(277\) −4.94427 + 15.2169i −0.297073 + 0.914295i 0.685445 + 0.728124i \(0.259608\pi\)
−0.982517 + 0.186171i \(0.940392\pi\)
\(278\) −3.23607 + 2.35114i −0.194086 + 0.141012i
\(279\) −6.47214 4.70228i −0.387477 0.281518i
\(280\) 0 0
\(281\) −1.85410 5.70634i −0.110606 0.340412i 0.880399 0.474234i \(-0.157275\pi\)
−0.991005 + 0.133822i \(0.957275\pi\)
\(282\) −4.85410 3.52671i −0.289058 0.210013i
\(283\) −6.47214 + 4.70228i −0.384729 + 0.279522i −0.763292 0.646054i \(-0.776418\pi\)
0.378563 + 0.925575i \(0.376418\pi\)
\(284\) 1.85410 5.70634i 0.110021 0.338609i
\(285\) 0 0
\(286\) 0 0
\(287\) 12.0000 0.708338
\(288\) −0.309017 + 0.951057i −0.0182090 + 0.0560415i
\(289\) −15.3713 + 11.1679i −0.904195 + 0.656936i
\(290\) 0 0
\(291\) 4.32624 + 13.3148i 0.253609 + 0.780527i
\(292\) 0.618034 + 1.90211i 0.0361677 + 0.111313i
\(293\) 4.85410 + 3.52671i 0.283580 + 0.206033i 0.720477 0.693479i \(-0.243923\pi\)
−0.436898 + 0.899511i \(0.643923\pi\)
\(294\) −2.42705 + 1.76336i −0.141548 + 0.102841i
\(295\) 0 0
\(296\) 10.0000 0.581238
\(297\) 0 0
\(298\) 6.00000 0.347571
\(299\) −7.41641 + 22.8254i −0.428902 + 1.32002i
\(300\) 4.04508 2.93893i 0.233543 0.169679i
\(301\) −12.9443 9.40456i −0.746095 0.542070i
\(302\) 3.09017 + 9.51057i 0.177819 + 0.547272i
\(303\) 1.85410 + 5.70634i 0.106515 + 0.327821i
\(304\) 3.23607 + 2.35114i 0.185601 + 0.134847i
\(305\) 0 0
\(306\) 1.85410 5.70634i 0.105992 0.326210i
\(307\) 20.0000 1.14146 0.570730 0.821138i \(-0.306660\pi\)
0.570730 + 0.821138i \(0.306660\pi\)
\(308\) 0 0
\(309\) −4.00000 −0.227552
\(310\) 0 0
\(311\) 14.5623 10.5801i 0.825753 0.599944i −0.0926019 0.995703i \(-0.529518\pi\)
0.918354 + 0.395759i \(0.129518\pi\)
\(312\) −3.23607 2.35114i −0.183206 0.133107i
\(313\) 8.03444 + 24.7275i 0.454134 + 1.39768i 0.872149 + 0.489240i \(0.162726\pi\)
−0.418016 + 0.908440i \(0.637274\pi\)
\(314\) −0.618034 1.90211i −0.0348777 0.107342i
\(315\) 0 0
\(316\) −11.3262 + 8.22899i −0.637151 + 0.462917i
\(317\) 3.70820 11.4127i 0.208273 0.641000i −0.791290 0.611442i \(-0.790590\pi\)
0.999563 0.0295583i \(-0.00941007\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) −3.70820 + 11.4127i −0.206972 + 0.636994i
\(322\) 9.70820 7.05342i 0.541017 0.393072i
\(323\) −19.4164 14.1068i −1.08036 0.784926i
\(324\) 0.309017 + 0.951057i 0.0171676 + 0.0528365i
\(325\) 6.18034 + 19.0211i 0.342824 + 1.05510i
\(326\) −3.23607 2.35114i −0.179229 0.130218i
\(327\) 3.23607 2.35114i 0.178955 0.130018i
\(328\) −1.85410 + 5.70634i −0.102376 + 0.315080i
\(329\) −12.0000 −0.661581
\(330\) 0 0
\(331\) −4.00000 −0.219860 −0.109930 0.993939i \(-0.535063\pi\)
−0.109930 + 0.993939i \(0.535063\pi\)
\(332\) −3.70820 + 11.4127i −0.203514 + 0.626352i
\(333\) 8.09017 5.87785i 0.443339 0.322104i
\(334\) 9.70820 + 7.05342i 0.531209 + 0.385946i
\(335\) 0 0
\(336\) 0.618034 + 1.90211i 0.0337165 + 0.103769i
\(337\) −1.61803 1.17557i −0.0881399 0.0640374i 0.542843 0.839834i \(-0.317348\pi\)
−0.630982 + 0.775797i \(0.717348\pi\)
\(338\) 2.42705 1.76336i 0.132014 0.0959139i
\(339\) 5.56231 17.1190i 0.302103 0.929777i
\(340\) 0 0
\(341\) 0 0
\(342\) 4.00000 0.216295
\(343\) −6.18034 + 19.0211i −0.333707 + 1.02704i
\(344\) 6.47214 4.70228i 0.348954 0.253530i
\(345\) 0 0
\(346\) −1.85410 5.70634i −0.0996771 0.306775i
\(347\) 11.1246 + 34.2380i 0.597200 + 1.83799i 0.543453 + 0.839439i \(0.317117\pi\)
0.0537472 + 0.998555i \(0.482883\pi\)
\(348\) −4.85410 3.52671i −0.260207 0.189052i
\(349\) 3.23607 2.35114i 0.173223 0.125854i −0.497796 0.867294i \(-0.665857\pi\)
0.671019 + 0.741441i \(0.265857\pi\)
\(350\) 3.09017 9.51057i 0.165177 0.508361i
\(351\) −4.00000 −0.213504
\(352\) 0 0
\(353\) −6.00000 −0.319348 −0.159674 0.987170i \(-0.551044\pi\)
−0.159674 + 0.987170i \(0.551044\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 4.85410 + 3.52671i 0.257267 + 0.186915i
\(357\) −3.70820 11.4127i −0.196259 0.604023i
\(358\) −7.41641 22.8254i −0.391969 1.20636i
\(359\) 9.70820 + 7.05342i 0.512379 + 0.372265i 0.813725 0.581249i \(-0.197436\pi\)
−0.301346 + 0.953515i \(0.597436\pi\)
\(360\) 0 0
\(361\) −0.927051 + 2.85317i −0.0487922 + 0.150167i
\(362\) 22.0000 1.15629
\(363\) 0 0
\(364\) −8.00000 −0.419314
\(365\) 0 0
\(366\) 6.47214 4.70228i 0.338304 0.245792i
\(367\) −6.47214 4.70228i −0.337843 0.245457i 0.405908 0.913914i \(-0.366955\pi\)
−0.743751 + 0.668457i \(0.766955\pi\)
\(368\) 1.85410 + 5.70634i 0.0966517 + 0.297463i
\(369\) 1.85410 + 5.70634i 0.0965207 + 0.297060i
\(370\) 0 0
\(371\) 0 0
\(372\) 2.47214 7.60845i 0.128174 0.394480i
\(373\) 20.0000 1.03556 0.517780 0.855514i \(-0.326758\pi\)
0.517780 + 0.855514i \(0.326758\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 1.85410 5.70634i 0.0956180 0.294282i
\(377\) 19.4164 14.1068i 0.999996 0.726540i
\(378\) 1.61803 + 1.17557i 0.0832227 + 0.0604648i
\(379\) 6.18034 + 19.0211i 0.317463 + 0.977050i 0.974729 + 0.223391i \(0.0717128\pi\)
−0.657266 + 0.753659i \(0.728287\pi\)
\(380\) 0 0
\(381\) −11.3262 8.22899i −0.580261 0.421584i
\(382\) 14.5623 10.5801i 0.745072 0.541327i
\(383\) 1.85410 5.70634i 0.0947402 0.291580i −0.892446 0.451155i \(-0.851012\pi\)
0.987186 + 0.159575i \(0.0510122\pi\)
\(384\) −1.00000 −0.0510310
\(385\) 0 0
\(386\) −14.0000 −0.712581
\(387\) 2.47214 7.60845i 0.125666 0.386759i
\(388\) −11.3262 + 8.22899i −0.575003 + 0.417764i
\(389\) 0 0 0.587785 0.809017i \(-0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(390\) 0 0
\(391\) −11.1246 34.2380i −0.562596 1.73149i
\(392\) −2.42705 1.76336i −0.122585 0.0890629i
\(393\) 9.70820 7.05342i 0.489714 0.355798i
\(394\) −1.85410 + 5.70634i −0.0934083 + 0.287481i
\(395\) 0 0
\(396\) 0 0
\(397\) 26.0000 1.30490 0.652451 0.757831i \(-0.273741\pi\)
0.652451 + 0.757831i \(0.273741\pi\)
\(398\) 1.23607 3.80423i 0.0619585 0.190689i
\(399\) 6.47214 4.70228i 0.324012 0.235409i
\(400\) 4.04508 + 2.93893i 0.202254 + 0.146946i
\(401\) 9.27051 + 28.5317i 0.462947 + 1.42480i 0.861546 + 0.507679i \(0.169497\pi\)
−0.398599 + 0.917125i \(0.630503\pi\)
\(402\) 1.23607 + 3.80423i 0.0616495 + 0.189738i
\(403\) 25.8885 + 18.8091i 1.28960 + 0.936949i
\(404\) −4.85410 + 3.52671i −0.241501 + 0.175460i
\(405\) 0 0
\(406\) −12.0000 −0.595550
\(407\) 0 0
\(408\) 6.00000 0.297044
\(409\) −10.5066 + 32.3359i −0.519517 + 1.59891i 0.255393 + 0.966837i \(0.417795\pi\)
−0.774910 + 0.632071i \(0.782205\pi\)
\(410\) 0 0
\(411\) 14.5623 + 10.5801i 0.718306 + 0.521880i
\(412\) −1.23607 3.80423i −0.0608967 0.187421i
\(413\) 0 0
\(414\) 4.85410 + 3.52671i 0.238566 + 0.173328i
\(415\) 0 0
\(416\) 1.23607 3.80423i 0.0606032 0.186518i
\(417\) −4.00000 −0.195881
\(418\) 0 0
\(419\) 24.0000 1.17248 0.586238 0.810139i \(-0.300608\pi\)
0.586238 + 0.810139i \(0.300608\pi\)
\(420\) 0 0
\(421\) 8.09017 5.87785i 0.394291 0.286469i −0.372921 0.927863i \(-0.621644\pi\)
0.767211 + 0.641394i \(0.221644\pi\)
\(422\) 6.47214 + 4.70228i 0.315059 + 0.228904i
\(423\) −1.85410 5.70634i −0.0901495 0.277452i
\(424\) 0 0
\(425\) −24.2705 17.6336i −1.17729 0.855353i
\(426\) 4.85410 3.52671i 0.235182 0.170870i
\(427\) 4.94427 15.2169i 0.239270 0.736398i
\(428\) −12.0000 −0.580042
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 −0.951057 0.309017i \(-0.900000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(432\) −0.809017 + 0.587785i −0.0389238 + 0.0282798i
\(433\) −21.0344 15.2824i −1.01085 0.734426i −0.0464634 0.998920i \(-0.514795\pi\)
−0.964387 + 0.264494i \(0.914795\pi\)
\(434\) −4.94427 15.2169i −0.237333 0.730435i
\(435\) 0 0
\(436\) 3.23607 + 2.35114i 0.154980 + 0.112599i
\(437\) 19.4164 14.1068i 0.928813 0.674822i
\(438\) −0.618034 + 1.90211i −0.0295308 + 0.0908865i
\(439\) −10.0000 −0.477274 −0.238637 0.971109i \(-0.576701\pi\)
−0.238637 + 0.971109i \(0.576701\pi\)
\(440\) 0 0
\(441\) −3.00000 −0.142857
\(442\) −7.41641 + 22.8254i −0.352763 + 1.08569i
\(443\) 19.4164 14.1068i 0.922501 0.670236i −0.0216440 0.999766i \(-0.506890\pi\)
0.944145 + 0.329529i \(0.106890\pi\)
\(444\) 8.09017 + 5.87785i 0.383942 + 0.278951i
\(445\) 0 0
\(446\) 4.94427 + 15.2169i 0.234118 + 0.720541i
\(447\) 4.85410 + 3.52671i 0.229591 + 0.166808i
\(448\) −1.61803 + 1.17557i −0.0764449 + 0.0555405i
\(449\) 1.85410 5.70634i 0.0875005 0.269299i −0.897726 0.440554i \(-0.854782\pi\)
0.985227 + 0.171255i \(0.0547822\pi\)
\(450\) 5.00000 0.235702
\(451\) 0 0
\(452\) 18.0000 0.846649
\(453\) −3.09017 + 9.51057i −0.145189 + 0.446845i
\(454\) −9.70820 + 7.05342i −0.455629 + 0.331034i
\(455\) 0 0
\(456\) 1.23607 + 3.80423i 0.0578842 + 0.178149i
\(457\) −3.09017 9.51057i −0.144552 0.444885i 0.852401 0.522889i \(-0.175146\pi\)
−0.996953 + 0.0780031i \(0.975146\pi\)
\(458\) −17.7984 12.9313i −0.831663 0.604239i
\(459\) 4.85410 3.52671i 0.226570 0.164613i
\(460\) 0 0
\(461\) 42.0000 1.95614 0.978068 0.208288i \(-0.0667892\pi\)
0.978068 + 0.208288i \(0.0667892\pi\)
\(462\) 0 0
\(463\) −4.00000 −0.185896 −0.0929479 0.995671i \(-0.529629\pi\)
−0.0929479 + 0.995671i \(0.529629\pi\)
\(464\) 1.85410 5.70634i 0.0860745 0.264910i
\(465\) 0 0
\(466\) −14.5623 10.5801i −0.674586 0.490115i
\(467\) −3.70820 11.4127i −0.171595 0.528116i 0.827866 0.560925i \(-0.189555\pi\)
−0.999462 + 0.0328096i \(0.989555\pi\)
\(468\) −1.23607 3.80423i −0.0571373 0.175850i
\(469\) 6.47214 + 4.70228i 0.298855 + 0.217131i
\(470\) 0 0
\(471\) 0.618034 1.90211i 0.0284775 0.0876447i
\(472\) 0 0
\(473\) 0 0
\(474\) −14.0000 −0.643041
\(475\) 6.18034 19.0211i 0.283573 0.872749i
\(476\) 9.70820 7.05342i 0.444975 0.323293i
\(477\) 0 0
\(478\) 3.70820 + 11.4127i 0.169609 + 0.522004i
\(479\) −7.41641 22.8254i −0.338864 1.04292i −0.964787 0.263032i \(-0.915277\pi\)
0.625923 0.779885i \(-0.284723\pi\)
\(480\) 0 0
\(481\) −32.3607 + 23.5114i −1.47552 + 1.07203i
\(482\) 3.09017 9.51057i 0.140753 0.433194i
\(483\) 12.0000 0.546019
\(484\) 0 0
\(485\) 0 0
\(486\) −0.309017 + 0.951057i −0.0140173 + 0.0431408i
\(487\) −16.1803 + 11.7557i −0.733201 + 0.532702i −0.890575 0.454837i \(-0.849697\pi\)
0.157373 + 0.987539i \(0.449697\pi\)
\(488\) 6.47214 + 4.70228i 0.292980 + 0.212862i
\(489\) −1.23607 3.80423i −0.0558969 0.172033i
\(490\) 0 0
\(491\) −9.70820 7.05342i −0.438125 0.318317i 0.346764 0.937952i \(-0.387280\pi\)
−0.784890 + 0.619636i \(0.787280\pi\)
\(492\) −4.85410 + 3.52671i −0.218840 + 0.158996i
\(493\) −11.1246 + 34.2380i −0.501027 + 1.54200i
\(494\) −16.0000 −0.719874
\(495\) 0 0
\(496\) 8.00000 0.359211
\(497\) 3.70820 11.4127i 0.166336 0.511929i
\(498\) −9.70820 + 7.05342i −0.435035 + 0.316071i
\(499\) 3.23607 + 2.35114i 0.144866 + 0.105252i 0.657858 0.753142i \(-0.271463\pi\)
−0.512992 + 0.858394i \(0.671463\pi\)
\(500\) 0 0
\(501\) 3.70820 + 11.4127i 0.165670 + 0.509881i
\(502\) 0 0
\(503\) −9.70820 + 7.05342i −0.432867 + 0.314497i −0.782794 0.622280i \(-0.786206\pi\)
0.349927 + 0.936777i \(0.386206\pi\)
\(504\) −0.618034 + 1.90211i −0.0275294 + 0.0847268i
\(505\) 0 0
\(506\) 0 0
\(507\) 3.00000 0.133235
\(508\) 4.32624 13.3148i 0.191946 0.590748i
\(509\) −19.4164 + 14.1068i −0.860617 + 0.625275i −0.928053 0.372449i \(-0.878518\pi\)
0.0674356 + 0.997724i \(0.478518\pi\)
\(510\) 0 0
\(511\) 1.23607 + 3.80423i 0.0546804 + 0.168289i
\(512\) −0.309017 0.951057i −0.0136568 0.0420312i
\(513\) 3.23607 + 2.35114i 0.142876 + 0.103805i
\(514\) −24.2705 + 17.6336i −1.07053 + 0.777783i
\(515\) 0 0
\(516\) 8.00000 0.352180
\(517\) 0 0
\(518\) 20.0000 0.878750
\(519\) 1.85410 5.70634i 0.0813860 0.250480i
\(520\) 0 0
\(521\) 14.5623 + 10.5801i 0.637986 + 0.463524i 0.859158 0.511711i \(-0.170988\pi\)
−0.221172 + 0.975235i \(0.570988\pi\)
\(522\) −1.85410 5.70634i −0.0811518 0.249760i
\(523\) −4.94427 15.2169i −0.216198 0.665389i −0.999066 0.0432015i \(-0.986244\pi\)
0.782868 0.622187i \(-0.213756\pi\)
\(524\) 9.70820 + 7.05342i 0.424105 + 0.308130i
\(525\) 8.09017 5.87785i 0.353084 0.256531i
\(526\) 0 0
\(527\) −48.0000 −2.09091
\(528\) 0 0
\(529\) 13.0000 0.565217
\(530\) 0 0
\(531\) 0 0
\(532\) 6.47214 + 4.70228i 0.280603 + 0.203870i
\(533\) −7.41641 22.8254i −0.321240 0.988676i
\(534\) 1.85410 + 5.70634i 0.0802348 + 0.246937i
\(535\) 0 0
\(536\) −3.23607 + 2.35114i −0.139777 + 0.101554i
\(537\) 7.41641 22.8254i 0.320042 0.984987i
\(538\) 24.0000 1.03471
\(539\) 0 0
\(540\) 0 0
\(541\) 6.18034 19.0211i 0.265714 0.817782i −0.725815 0.687890i \(-0.758537\pi\)
0.991528 0.129892i \(-0.0414630\pi\)
\(542\) 1.61803 1.17557i 0.0695005 0.0504951i
\(543\) 17.7984 + 12.9313i 0.763801 + 0.554934i
\(544\) 1.85410 + 5.70634i 0.0794940 + 0.244657i
\(545\) 0 0
\(546\) −6.47214 4.70228i −0.276982 0.201239i
\(547\) 22.6525 16.4580i 0.968550 0.703693i 0.0134293 0.999910i \(-0.495725\pi\)
0.955121 + 0.296217i \(0.0957252\pi\)
\(548\) −5.56231 + 17.1190i −0.237610 + 0.731288i
\(549\) 8.00000 0.341432
\(550\) 0 0
\(551\) −24.0000 −1.02243
\(552\) −1.85410 + 5.70634i −0.0789158 + 0.242878i
\(553\) −22.6525 + 16.4580i −0.963281 + 0.699865i
\(554\) −12.9443 9.40456i −0.549949 0.399562i
\(555\) 0 0
\(556\) −1.23607 3.80423i −0.0524210 0.161335i
\(557\) −14.5623 10.5801i −0.617025 0.448295i 0.234856 0.972030i \(-0.424538\pi\)
−0.851881 + 0.523735i \(0.824538\pi\)
\(558\) 6.47214 4.70228i 0.273987 0.199063i
\(559\) −9.88854 + 30.4338i −0.418241 + 1.28721i
\(560\) 0 0
\(561\) 0 0
\(562\) 6.00000 0.253095
\(563\) −3.70820 + 11.4127i −0.156282 + 0.480987i −0.998289 0.0584805i \(-0.981374\pi\)
0.842006 + 0.539468i \(0.181374\pi\)
\(564\) 4.85410 3.52671i 0.204395 0.148501i
\(565\) 0 0
\(566\) −2.47214 7.60845i −0.103912 0.319807i
\(567\) 0.618034 + 1.90211i 0.0259550 + 0.0798812i
\(568\) 4.85410 + 3.52671i 0.203674 + 0.147978i
\(569\) −14.5623 + 10.5801i −0.610484 + 0.443542i −0.849585 0.527452i \(-0.823147\pi\)
0.239101 + 0.970995i \(0.423147\pi\)
\(570\) 0 0
\(571\) −28.0000 −1.17176 −0.585882 0.810397i \(-0.699252\pi\)
−0.585882 + 0.810397i \(0.699252\pi\)
\(572\) 0 0
\(573\) 18.0000 0.751961
\(574\) −3.70820 + 11.4127i −0.154777 + 0.476356i
\(575\) 24.2705 17.6336i 1.01215 0.735370i
\(576\) −0.809017 0.587785i −0.0337090 0.0244911i
\(577\) −10.5066 32.3359i −0.437395 1.34616i −0.890613 0.454762i \(-0.849724\pi\)
0.453218 0.891400i \(-0.350276\pi\)
\(578\) −5.87132 18.0701i −0.244215 0.751616i
\(579\) −11.3262 8.22899i −0.470702 0.341985i
\(580\) 0 0
\(581\) −7.41641 + 22.8254i −0.307684 + 0.946955i
\(582\) −14.0000 −0.580319
\(583\) 0 0
\(584\) −2.00000 −0.0827606
\(585\) 0 0
\(586\) −4.85410 + 3.52671i −0.200521 + 0.145687i
\(587\) −19.4164 14.1068i −0.801401 0.582252i 0.109924 0.993940i \(-0.464939\pi\)
−0.911325 + 0.411688i \(0.864939\pi\)
\(588\) −0.927051 2.85317i −0.0382309 0.117663i
\(589\) −9.88854 30.4338i −0.407450 1.25400i
\(590\) 0 0
\(591\) −4.85410 + 3.52671i −0.199671 + 0.145070i
\(592\) −3.09017 + 9.51057i −0.127005 + 0.390882i
\(593\) −30.0000 −1.23195 −0.615976 0.787765i \(-0.711238\pi\)
−0.615976 + 0.787765i \(0.711238\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −1.85410 + 5.70634i −0.0759470 + 0.233741i
\(597\) 3.23607 2.35114i 0.132443 0.0962258i
\(598\) −19.4164 14.1068i −0.793996 0.576872i
\(599\) 9.27051 + 28.5317i 0.378783 + 1.16577i 0.940891 + 0.338710i \(0.109990\pi\)
−0.562108 + 0.827064i \(0.690010\pi\)
\(600\) 1.54508 + 4.75528i 0.0630778 + 0.194134i
\(601\) 17.7984 + 12.9313i 0.726011 + 0.527478i 0.888299 0.459266i \(-0.151887\pi\)
−0.162288 + 0.986743i \(0.551887\pi\)
\(602\) 12.9443 9.40456i 0.527569 0.383301i
\(603\) −1.23607 + 3.80423i −0.0503366 + 0.154920i
\(604\) −10.0000 −0.406894
\(605\) 0 0
\(606\) −6.00000 −0.243733
\(607\) 4.32624 13.3148i 0.175597 0.540431i −0.824064 0.566497i \(-0.808298\pi\)
0.999660 + 0.0260665i \(0.00829818\pi\)
\(608\) −3.23607 + 2.35114i −0.131240 + 0.0953514i
\(609\) −9.70820 7.05342i −0.393396 0.285819i
\(610\) 0 0
\(611\) 7.41641 + 22.8254i 0.300036 + 0.923415i
\(612\) 4.85410 + 3.52671i 0.196215 + 0.142559i
\(613\) 12.9443 9.40456i 0.522814 0.379847i −0.294849 0.955544i \(-0.595269\pi\)
0.817663 + 0.575697i \(0.195269\pi\)
\(614\) −6.18034 + 19.0211i −0.249418 + 0.767630i
\(615\) 0 0
\(616\) 0 0
\(617\) −30.0000 −1.20775 −0.603877 0.797077i \(-0.706378\pi\)
−0.603877 + 0.797077i \(0.706378\pi\)
\(618\) 1.23607 3.80423i 0.0497219 0.153028i
\(619\) −35.5967 + 25.8626i −1.43075 + 1.03950i −0.440878 + 0.897567i \(0.645333\pi\)
−0.989876 + 0.141937i \(0.954667\pi\)
\(620\) 0 0
\(621\) 1.85410 + 5.70634i 0.0744025 + 0.228988i
\(622\) 5.56231 + 17.1190i 0.223028 + 0.686410i
\(623\) 9.70820 + 7.05342i 0.388951 + 0.282589i
\(624\) 3.23607 2.35114i 0.129546 0.0941210i
\(625\) 7.72542 23.7764i 0.309017 0.951057i
\(626\) −26.0000 −1.03917
\(627\) 0 0
\(628\) 2.00000 0.0798087
\(629\) 18.5410 57.0634i 0.739279 2.27527i
\(630\) 0 0
\(631\) 12.9443 + 9.40456i 0.515303 + 0.374390i 0.814832 0.579698i \(-0.196829\pi\)
−0.299528 + 0.954087i \(0.596829\pi\)
\(632\) −4.32624 13.3148i −0.172089 0.529634i
\(633\) 2.47214 + 7.60845i 0.0982586 + 0.302409i
\(634\) 9.70820 + 7.05342i 0.385562 + 0.280127i
\(635\) 0 0
\(636\) 0 0
\(637\) 12.0000 0.475457
\(638\) 0 0
\(639\) 6.00000 0.237356
\(640\) 0 0
\(641\) −4.85410 + 3.52671i −0.191726 + 0.139297i −0.679507 0.733669i \(-0.737806\pi\)
0.487781 + 0.872966i \(0.337806\pi\)
\(642\) −9.70820 7.05342i −0.383152 0.278376i
\(643\) −1.23607 3.80423i −0.0487458 0.150024i 0.923721 0.383066i \(-0.125132\pi\)
−0.972467 + 0.233042i \(0.925132\pi\)
\(644\) 3.70820 + 11.4127i 0.146124 + 0.449723i
\(645\) 0 0
\(646\) 19.4164 14.1068i 0.763928 0.555026i
\(647\) 1.85410 5.70634i 0.0728923 0.224339i −0.907972 0.419030i \(-0.862370\pi\)
0.980865 + 0.194691i \(0.0623703\pi\)
\(648\) −1.00000 −0.0392837
\(649\) 0 0
\(650\) −20.0000 −0.784465
\(651\) 4.94427 15.2169i 0.193781 0.596397i
\(652\) 3.23607 2.35114i 0.126734 0.0920778i
\(653\) 29.1246 + 21.1603i 1.13973 + 0.828065i 0.987082 0.160215i \(-0.0512187\pi\)
0.152652 + 0.988280i \(0.451219\pi\)
\(654\) 1.23607 + 3.80423i 0.0483341 + 0.148757i
\(655\) 0 0
\(656\) −4.85410 3.52671i −0.189521 0.137695i
\(657\) −1.61803 + 1.17557i −0.0631255 + 0.0458634i
\(658\) 3.70820 11.4127i 0.144561 0.444913i
\(659\) 36.0000 1.40236 0.701180 0.712984i \(-0.252657\pi\)
0.701180 + 0.712984i \(0.252657\pi\)
\(660\) 0 0
\(661\) −22.0000 −0.855701 −0.427850 0.903850i \(-0.640729\pi\)
−0.427850 + 0.903850i \(0.640729\pi\)
\(662\) 1.23607 3.80423i 0.0480411 0.147855i
\(663\) −19.4164 + 14.1068i −0.754071 + 0.547865i
\(664\) −9.70820 7.05342i −0.376751 0.273726i
\(665\) 0 0
\(666\) 3.09017 + 9.51057i 0.119742 + 0.368527i
\(667\) −29.1246 21.1603i −1.12771 0.819329i
\(668\) −9.70820 + 7.05342i −0.375622 + 0.272905i
\(669\) −4.94427 + 15.2169i −0.191157 + 0.588320i
\(670\) 0 0
\(671\) 0 0
\(672\) −2.00000 −0.0771517
\(673\) 4.32624 13.3148i 0.166764 0.513247i −0.832398 0.554179i \(-0.813032\pi\)
0.999162 + 0.0409312i \(0.0130324\pi\)
\(674\) 1.61803 1.17557i 0.0623243 0.0452813i
\(675\) 4.04508 + 2.93893i 0.155695 + 0.113119i
\(676\) 0.927051 + 2.85317i 0.0356558 + 0.109737i
\(677\) 9.27051 + 28.5317i 0.356295 + 1.09656i 0.955255 + 0.295783i \(0.0955807\pi\)
−0.598960 + 0.800779i \(0.704419\pi\)
\(678\) 14.5623 + 10.5801i 0.559262 + 0.406328i
\(679\) −22.6525 + 16.4580i −0.869322 + 0.631600i
\(680\) 0 0
\(681\) −12.0000 −0.459841
\(682\) 0 0
\(683\) −24.0000 −0.918334 −0.459167 0.888350i \(-0.651852\pi\)
−0.459167 + 0.888350i \(0.651852\pi\)
\(684\) −1.23607 + 3.80423i −0.0472622 + 0.145458i
\(685\) 0 0
\(686\) −16.1803 11.7557i −0.617768 0.448835i
\(687\) −6.79837 20.9232i −0.259374 0.798272i
\(688\) 2.47214 + 7.60845i 0.0942493 + 0.290070i
\(689\) 0 0
\(690\) 0 0
\(691\) 6.18034 19.0211i 0.235111 0.723598i −0.761995 0.647582i \(-0.775780\pi\)
0.997107 0.0760155i \(-0.0242198\pi\)
\(692\) 6.00000 0.228086
\(693\) 0 0
\(694\) −36.0000 −1.36654
\(695\) 0 0
\(696\) 4.85410 3.52671i 0.183994 0.133680i
\(697\) 29.1246 + 21.1603i 1.10317 + 0.801502i
\(698\) 1.23607 + 3.80423i 0.0467859 + 0.143992i
\(699\) −5.56231 17.1190i −0.210386 0.647501i
\(700\) 8.09017 + 5.87785i 0.305780 + 0.222162i
\(701\) 4.85410 3.52671i 0.183337 0.133202i −0.492331 0.870408i \(-0.663855\pi\)
0.675668 + 0.737206i \(0.263855\pi\)
\(702\) 1.23607 3.80423i 0.0466524 0.143581i
\(703\) 40.0000 1.50863
\(704\) 0 0
\(705\) 0 0
\(706\) 1.85410 5.70634i 0.0697800 0.214761i
\(707\) −9.70820 + 7.05342i −0.365115 + 0.265271i
\(708\) 0 0
\(709\) 8.03444 + 24.7275i 0.301740 + 0.928660i 0.980874 + 0.194645i \(0.0623555\pi\)
−0.679134 + 0.734014i \(0.737644\pi\)
\(710\) 0 0
\(711\) −11.3262 8.22899i −0.424767 0.308611i
\(712\) −4.85410 + 3.52671i −0.181915 + 0.132169i
\(713\) 14.8328 45.6507i 0.555493 1.70963i
\(714\) 12.0000 0.449089
\(715\) 0 0
\(716\) 24.0000 0.896922
\(717\) −3.70820 + 11.4127i −0.138485 + 0.426214i
\(718\) −9.70820 + 7.05342i −0.362307 + 0.263231i
\(719\) −24.2705 17.6336i −0.905137 0.657621i 0.0346431 0.999400i \(-0.488971\pi\)
−0.939780 + 0.341779i \(0.888971\pi\)
\(720\) 0 0
\(721\) −2.47214 7.60845i −0.0920672 0.283354i
\(722\) −2.42705 1.76336i −0.0903255 0.0656253i
\(723\) 8.09017 5.87785i 0.300877 0.218600i
\(724\) −6.79837 + 20.9232i −0.252660 + 0.777606i
\(725\) −30.0000 −1.11417
\(726\) 0 0
\(727\) −28.0000 −1.03846 −0.519231 0.854634i \(-0.673782\pi\)
−0.519231 + 0.854634i \(0.673782\pi\)
\(728\) 2.47214 7.60845i 0.0916235 0.281988i
\(729\) −0.809017 + 0.587785i −0.0299636 + 0.0217698i
\(730\) 0 0
\(731\) −14.8328 45.6507i −0.548612 1.68845i
\(732\) 2.47214 + 7.60845i 0.0913728 + 0.281216i
\(733\) 3.23607 + 2.35114i 0.119527 + 0.0868414i 0.645943 0.763386i \(-0.276464\pi\)
−0.526416 + 0.850227i \(0.676464\pi\)
\(734\) 6.47214 4.70228i 0.238891 0.173564i
\(735\) 0 0
\(736\) −6.00000 −0.221163
\(737\) 0 0
\(738\) −6.00000 −0.220863
\(739\) 2.47214 7.60845i 0.0909390 0.279881i −0.895235 0.445594i \(-0.852992\pi\)
0.986174 + 0.165713i \(0.0529924\pi\)
\(740\) 0 0
\(741\) −12.9443 9.40456i −0.475520 0.345485i
\(742\) 0 0
\(743\) 11.1246 + 34.2380i 0.408122 + 1.25607i 0.918260 + 0.395979i \(0.129595\pi\)
−0.510137 + 0.860093i \(0.670405\pi\)
\(744\) 6.47214 + 4.70228i 0.237280 + 0.172394i
\(745\) 0 0
\(746\) −6.18034 + 19.0211i −0.226278 + 0.696413i
\(747\) −12.0000 −0.439057
\(748\) 0 0
\(749\) −24.0000 −0.876941
\(750\) 0 0
\(751\) −6.47214 + 4.70228i −0.236172 + 0.171589i −0.699576 0.714558i \(-0.746628\pi\)
0.463404 + 0.886147i \(0.346628\pi\)
\(752\) 4.85410 + 3.52671i 0.177011 + 0.128606i
\(753\) 0 0
\(754\) 7.41641 + 22.8254i 0.270090 + 0.831250i
\(755\) 0 0
\(756\) −1.61803 + 1.17557i −0.0588473 + 0.0427551i
\(757\) −10.5066 + 32.3359i −0.381868 + 1.17527i 0.556859 + 0.830607i \(0.312006\pi\)
−0.938727 + 0.344662i \(0.887994\pi\)
\(758\) −20.0000 −0.726433
\(759\) 0 0
\(760\) 0 0
\(761\) 5.56231 17.1190i 0.201633 0.620564i −0.798201 0.602391i \(-0.794215\pi\)
0.999835 0.0181732i \(-0.00578504\pi\)
\(762\) 11.3262 8.22899i 0.410306 0.298105i
\(763\) 6.47214 + 4.70228i 0.234307 + 0.170234i
\(764\) 5.56231 + 17.1190i 0.201237 + 0.619344i
\(765\) 0 0
\(766\) 4.85410 + 3.52671i 0.175386 + 0.127425i
\(767\) 0 0
\(768\) 0.309017 0.951057i 0.0111507 0.0343183i
\(769\) −34.0000 −1.22607 −0.613036 0.790055i \(-0.710052\pi\)
−0.613036 + 0.790055i \(0.710052\pi\)
\(770\) 0 0
\(771\) −30.0000 −1.08042
\(772\) 4.32624 13.3148i 0.155705 0.479210i
\(773\) 0 0 −0.587785 0.809017i \(-0.700000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(774\) 6.47214 + 4.70228i 0.232636 + 0.169020i
\(775\) −12.3607 38.0423i −0.444009 1.36652i
\(776\) −4.32624 13.3148i −0.155303 0.477973i
\(777\) 16.1803 + 11.7557i 0.580466 + 0.421734i
\(778\) 0 0
\(779\) −7.41641 + 22.8254i −0.265720 + 0.817803i
\(780\) 0 0
\(781\) 0 0
\(782\) 36.0000 1.28736
\(783\) 1.85410 5.70634i 0.0662602 0.203928i
\(784\) 2.42705 1.76336i 0.0866804 0.0629770i