Properties

Label 726.2.e.b.511.1
Level $726$
Weight $2$
Character 726.511
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 511.1
Root \(-0.309017 + 0.951057i\) of defining polynomial
Character \(\chi\) \(=\) 726.511
Dual form 726.2.e.b.493.1

$q$-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 \(\left(\mathbb{Z}/726\mathbb{Z}\right)^\times\).

\(n\) \(485\) \(607\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{5}\right)\)

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 \(-0.900000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(6\) 0.309017 0.951057i 0.126156 0.388267i
\(7\) 1.61803 1.17557i 0.611559 0.444324i −0.238404 0.971166i \(-0.576624\pi\)
0.849963 + 0.526842i \(0.176624\pi\)
\(8\) −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 0.962739 + 0.270434i \(0.0871670\pi\)
−0.619915 + 0.784669i \(0.712833\pi\)
\(14\) 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 −0.427576 0.903979i \(-0.640633\pi\)
0.877262 0.480011i \(-0.159367\pi\)
\(18\) −0.809017 + 0.587785i −0.190687 + 0.138542i
\(19\) −3.23607 2.35114i −0.742405 0.539389i 0.151058 0.988525i \(-0.451732\pi\)
−0.893463 + 0.449136i \(0.851732\pi\)
\(20\) 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 \(-0.511919\pi\)
0.938821 + 0.344405i \(0.111919\pi\)
\(30\) 0 0
\(31\) 2.47214 + 7.60845i 0.444009 + 1.36652i 0.883567 + 0.468304i \(0.155135\pi\)
−0.439558 + 0.898214i \(0.644865\pi\)
\(32\) 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 0.330267 0.943887i \(-0.392861\pi\)
0.999749 0.0224255i \(-0.00713887\pi\)
\(38\) 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 \(-0.144787\pi\)
−0.140238 + 0.990118i \(0.544787\pi\)
\(42\) −0.618034 1.90211i −0.0953647 0.293502i
\(43\) −8.00000 −1.21999 −0.609994 0.792406i \(-0.708828\pi\)
−0.609994 + 0.792406i \(0.708828\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 1.85410 + 5.70634i 0.273372 + 0.841354i
\(47\) 4.85410 + 3.52671i 0.708044 + 0.514424i 0.882542 0.470234i \(-0.155830\pi\)
−0.174498 + 0.984657i \(0.555830\pi\)
\(48\) −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 \(-0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(54\) 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 \(-0.700000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(60\) 0 0
\(61\) −2.47214 + 7.60845i −0.316525 + 0.974162i 0.658598 + 0.752495i \(0.271150\pi\)
−0.975122 + 0.221667i \(0.928850\pi\)
\(62\) −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 −0.778716 0.627377i \(-0.784129\pi\)
0.998757 0.0498409i \(-0.0158714\pi\)
\(72\) 0.309017 0.951057i 0.0364180 0.112083i
\(73\) 1.61803 1.17557i 0.189377 0.137590i −0.489057 0.872252i \(-0.662659\pi\)
0.678434 + 0.734662i \(0.262659\pi\)
\(74\) 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 −0.829445 0.558588i \(-0.811343\pi\)
0.342705 0.939443i \(-0.388657\pi\)
\(80\) 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 −0.512161 0.858889i \(-0.671155\pi\)
0.919190 0.393815i \(-0.128845\pi\)
\(84\) 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 0.888654 + 0.458577i \(0.151641\pi\)
−0.449392 + 0.893335i \(0.648359\pi\)
\(98\) −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 \(-0.196490\pi\)
−0.999939 + 0.0110267i \(0.996490\pi\)
\(102\) −4.85410 3.52671i −0.480628 0.349196i
\(103\) 3.23607 2.35114i 0.318859 0.231665i −0.416829 0.908985i \(-0.636859\pi\)
0.735689 + 0.677320i \(0.236859\pi\)
\(104\) 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 \(-0.496964\pi\)
−0.948066 + 0.318074i \(0.896964\pi\)
\(108\) 0.309017 + 0.951057i 0.0297352 + 0.0915155i
\(109\) 4.00000 0.383131 0.191565 0.981480i \(-0.438644\pi\)
0.191565 + 0.981480i \(0.438644\pi\)
\(110\) 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 −0.997744 0.0671276i \(-0.978617\pi\)
−0.372162 0.928168i \(-0.621383\pi\)
\(114\) −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 0.553390 + 0.832922i \(0.313334\pi\)
−0.937281 + 0.348574i \(0.886666\pi\)
\(128\) −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 \(-0.324356\pi\)
0.524222 + 0.851581i \(0.324356\pi\)
\(132\) 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 0.370441 + 0.928856i \(0.379207\pi\)
−0.845661 + 0.533720i \(0.820793\pi\)
\(138\) 1.85410 5.70634i 0.157832 0.485756i
\(139\) −3.23607 + 2.35114i −0.274480 + 0.199421i −0.716506 0.697581i \(-0.754260\pi\)
0.442026 + 0.897002i \(0.354260\pi\)
\(140\) 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 \(-0.820959\pi\)
0.997833 + 0.0657982i \(0.0209593\pi\)
\(150\) 4.04508 2.93893i 0.330280 0.239962i
\(151\) −8.09017 5.87785i −0.658369 0.478333i 0.207743 0.978183i \(-0.433388\pi\)
−0.866112 + 0.499851i \(0.833388\pi\)
\(152\) 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 0.521344 0.853347i \(-0.325431\pi\)
−0.650477 + 0.759526i \(0.725431\pi\)
\(158\) 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 0.890906 0.454187i \(-0.150070\pi\)
−0.987723 + 0.156217i \(0.950070\pi\)
\(164\) −6.00000 −0.468521
\(165\) 0 0
\(166\) 12.0000 0.931381
\(167\) −3.70820 11.4127i −0.286949 0.883140i −0.985808 0.167879i \(-0.946308\pi\)
0.698858 0.715260i \(-0.253692\pi\)
\(168\) 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 \(-0.226753\pi\)
−0.387767 + 0.921758i \(0.626753\pi\)
\(174\) −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 −0.985537 0.169460i \(-0.945798\pi\)
−0.465713 0.884936i \(-0.654202\pi\)
\(180\) 0 0
\(181\) −6.79837 + 20.9232i −0.505319 + 1.55521i 0.294914 + 0.955524i \(0.404709\pi\)
−0.800233 + 0.599689i \(0.795291\pi\)
\(182\) −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 −0.972911 0.231180i \(-0.925741\pi\)
−0.0807805 + 0.996732i \(0.525741\pi\)
\(192\) 0.309017 0.951057i 0.0223014 0.0686366i
\(193\) −4.32624 + 13.3148i −0.311409 + 0.958420i 0.665798 + 0.746132i \(0.268091\pi\)
−0.977207 + 0.212287i \(0.931909\pi\)
\(194\) −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 \(-0.568565\pi\)
−0.213741 + 0.976890i \(0.568565\pi\)
\(198\) 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 \(-0.188801\pi\)
−0.999381 + 0.0351760i \(0.988801\pi\)
\(212\) 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 0.929730 0.368243i \(-0.120040\pi\)
−0.0629172 + 0.998019i \(0.520040\pi\)
\(224\) 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 \(-0.830377\pi\)
0.216988 + 0.976174i \(0.430377\pi\)
\(228\) −3.23607 2.35114i −0.214314 0.155708i
\(229\) −6.79837 20.9232i −0.449249 1.38265i −0.877756 0.479108i \(-0.840960\pi\)
0.428507 0.903539i \(-0.359040\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −6.00000 −0.393919
\(233\) 5.56231 + 17.1190i 0.364399 + 1.12150i 0.950357 + 0.311163i \(0.100718\pi\)
−0.585958 + 0.810341i \(0.699282\pi\)
\(234\) −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 \(-0.426871\pi\)
−0.855697 + 0.517477i \(0.826871\pi\)
\(240\) 0 0
\(241\) 10.0000 0.644157 0.322078 0.946713i \(-0.395619\pi\)
0.322078 + 0.946713i \(0.395619\pi\)
\(242\) 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 \(-0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(252\) −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 0.549568 0.835449i \(-0.314792\pi\)
0.964385 0.264502i \(-0.0852075\pi\)
\(258\) −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 0.422221 + 0.906493i \(0.361251\pi\)
−0.874407 + 0.485193i \(0.838749\pi\)
\(270\) 0 0
\(271\) 1.61803 1.17557i 0.0982886 0.0714108i −0.537555 0.843228i \(-0.680652\pi\)
0.635844 + 0.771818i \(0.280652\pi\)
\(272\) −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 0.982517 + 0.186171i \(0.0596077\pi\)
−0.685445 + 0.728124i \(0.740392\pi\)
\(278\) −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 \(-0.842725\pi\)
0.991005 + 0.133822i \(0.0427251\pi\)
\(282\) 4.85410 3.52671i 0.289058 0.210013i
\(283\) 6.47214 + 4.70228i 0.384729 + 0.279522i 0.763292 0.646054i \(-0.223582\pi\)
−0.378563 + 0.925575i \(0.623582\pi\)
\(284\) 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 \(-0.756077\pi\)
0.436898 + 0.899511i \(0.356077\pi\)
\(294\) 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 \(-0.693340\pi\)
−0.570730 + 0.821138i \(0.693340\pi\)
\(308\) 0 0
\(309\) −4.00000 −0.227552
\(310\) 0 0
\(311\) 14.5623 + 10.5801i 0.825753 + 0.599944i 0.918354 0.395759i \(-0.129518\pi\)
−0.0926019 + 0.995703i \(0.529518\pi\)
\(312\) −3.23607 + 2.35114i −0.183206 + 0.133107i
\(313\) 8.03444 24.7275i 0.454134 1.39768i −0.418016 0.908440i \(-0.637274\pi\)
0.872149 0.489240i \(-0.162726\pi\)
\(314\) 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 0.999563 + 0.0295583i \(0.00941007\pi\)
−0.791290 + 0.611442i \(0.790590\pi\)
\(318\) 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 \(-0.682652\pi\)
0.630982 + 0.775797i \(0.282652\pi\)
\(338\) −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 −0.0537472 + 0.998555i \(0.517117\pi\)
−0.543453 + 0.839439i \(0.682883\pi\)
\(348\) 4.85410 3.52671i 0.260207 0.189052i
\(349\) −3.23607 2.35114i −0.173223 0.125854i 0.497796 0.867294i \(-0.334143\pi\)
−0.671019 + 0.741441i \(0.734143\pi\)
\(350\) 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 \(-0.802564\pi\)
0.301346 + 0.953515i \(0.402564\pi\)
\(360\) 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 −0.743751 0.668457i \(-0.766955\pi\)
0.405908 + 0.913914i \(0.366955\pi\)
\(368\) 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 \(-0.673242\pi\)
−0.517780 + 0.855514i \(0.673242\pi\)
\(374\) 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 −0.657266 0.753659i \(-0.728287\pi\)
0.974729 0.223391i \(-0.0717128\pi\)
\(380\) 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 0.987186 0.159575i \(-0.0510122\pi\)
−0.892446 + 0.451155i \(0.851012\pi\)
\(384\) 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 \(-0.700000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(390\) 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 −0.398599 0.917125i \(-0.630503\pi\)
0.861546 0.507679i \(-0.169497\pi\)
\(402\) −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 0.774910 + 0.632071i \(0.217795\pi\)
−0.255393 + 0.966837i \(0.582205\pi\)
\(410\) 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 0.767211 0.641394i \(-0.221644\pi\)
−0.372921 + 0.927863i \(0.621644\pi\)
\(422\) 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 \(-0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(432\) −0.809017 0.587785i −0.0389238 0.0282798i
\(433\) −21.0344 + 15.2824i −1.01085 + 0.734426i −0.964387 0.264494i \(-0.914795\pi\)
−0.0464634 + 0.998920i \(0.514795\pi\)
\(434\) −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 \(-0.423299\pi\)
0.238637 + 0.971109i \(0.423299\pi\)
\(440\) 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 0.944145 0.329529i \(-0.106890\pi\)
−0.0216440 + 0.999766i \(0.506890\pi\)
\(444\) 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 0.985227 0.171255i \(-0.0547822\pi\)
−0.897726 + 0.440554i \(0.854782\pi\)
\(450\) −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 \(-0.824854\pi\)
0.996953 + 0.0780031i \(0.0248544\pi\)
\(458\) 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 \(-0.933211\pi\)
−0.978068 + 0.208288i \(0.933211\pi\)
\(462\) 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 −0.999462 0.0328096i \(-0.989555\pi\)
0.827866 + 0.560925i \(0.189555\pi\)
\(468\) 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 −0.625923 0.779885i \(-0.715277\pi\)
0.964787 0.263032i \(-0.0847225\pi\)
\(480\) 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 0.157373 0.987539i \(-0.449697\pi\)
−0.890575 + 0.454837i \(0.849697\pi\)
\(488\) 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 \(-0.612720\pi\)
0.784890 + 0.619636i \(0.212720\pi\)
\(492\) 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 −0.512992 0.858394i \(-0.671463\pi\)
0.657858 + 0.753142i \(0.271463\pi\)
\(500\) 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 \(-0.213794\pi\)
−0.349927 + 0.936777i \(0.613794\pi\)
\(504\) −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 0.0674356 0.997724i \(-0.478518\pi\)
−0.928053 + 0.372449i \(0.878518\pi\)
\(510\) 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 −0.221172 0.975235i \(-0.570988\pi\)
0.859158 + 0.511711i \(0.170988\pi\)
\(522\) −1.85410 + 5.70634i −0.0811518 + 0.249760i
\(523\) 4.94427 15.2169i 0.216198 0.665389i −0.782868 0.622187i \(-0.786244\pi\)
0.999066 0.0432015i \(-0.0137558\pi\)
\(524\) −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 −0.991528 0.129892i \(-0.958537\pi\)
0.725815 0.687890i \(-0.241463\pi\)
\(542\) 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 \(-0.504275\pi\)
−0.955121 + 0.296217i \(0.904275\pi\)
\(548\) −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 \(-0.575462\pi\)
0.851881 + 0.523735i \(0.175462\pi\)
\(558\) −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 \(-0.0186256\pi\)
−0.842006 + 0.539468i \(0.818626\pi\)
\(564\) 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 \(-0.176853\pi\)
−0.239101 + 0.970995i \(0.576853\pi\)
\(570\) 0 0
\(571\) 28.0000 1.17176 0.585882 0.810397i \(-0.300748\pi\)
0.585882 + 0.810397i \(0.300748\pi\)
\(572\) 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 0.453218 + 0.891400i \(0.350276\pi\)
−0.890613 + 0.454762i \(0.849724\pi\)
\(578\) 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 −0.911325 0.411688i \(-0.864939\pi\)
0.109924 + 0.993940i \(0.464939\pi\)
\(588\) −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 \(-0.288762\pi\)
0.615976 + 0.787765i \(0.288762\pi\)
\(594\) 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 −0.562108 0.827064i \(-0.690010\pi\)
0.940891 0.338710i \(-0.109990\pi\)
\(600\) −1.54508 + 4.75528i −0.0630778 + 0.194134i
\(601\) −17.7984 + 12.9313i −0.726011 + 0.527478i −0.888299 0.459266i \(-0.848113\pi\)
0.162288 + 0.986743i \(0.448113\pi\)
\(602\) −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 \(-0.191702\pi\)
−0.999660 + 0.0260665i \(0.991702\pi\)
\(608\) −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 \(-0.404731\pi\)
−0.817663 + 0.575697i \(0.804731\pi\)
\(614\) −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 −0.989876 0.141937i \(-0.954667\pi\)
−0.440878 0.897567i \(-0.645333\pi\)
\(620\) 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 −0.299528 0.954087i \(-0.596829\pi\)
0.814832 + 0.579698i \(0.196829\pi\)
\(632\) −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 0.487781 0.872966i \(-0.337806\pi\)
−0.679507 + 0.733669i \(0.737806\pi\)
\(642\) −9.70820 + 7.05342i −0.383152 + 0.278376i
\(643\) −1.23607 + 3.80423i −0.0487458 + 0.150024i −0.972467 0.233042i \(-0.925132\pi\)
0.923721 + 0.383066i \(0.125132\pi\)
\(644\) −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 0.980865 0.194691i \(-0.0623703\pi\)
−0.907972 + 0.419030i \(0.862370\pi\)
\(648\) 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 0.152652 0.988280i \(-0.451219\pi\)
0.987082 + 0.160215i \(0.0512187\pi\)
\(654\) 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 \(-0.747343\pi\)
−0.701180 + 0.712984i \(0.747343\pi\)
\(660\) 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 \(-0.186968\pi\)
−0.999162 + 0.0409312i \(0.986968\pi\)
\(674\) 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 0.598960 + 0.800779i \(0.295581\pi\)
−0.955255 + 0.295783i \(0.904419\pi\)
\(678\) −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 0.997107 + 0.0760155i \(0.0242198\pi\)
−0.761995 + 0.647582i \(0.775780\pi\)
\(692\) −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 \(-0.336145\pi\)
−0.675668 + 0.737206i \(0.736145\pi\)
\(702\) 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 −0.679134 0.734014i \(-0.737644\pi\)
0.980874 0.194645i \(-0.0623555\pi\)
\(710\) 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 −0.939780 0.341779i \(-0.888971\pi\)
0.0346431 + 0.999400i \(0.488971\pi\)
\(720\) 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 \(-0.723536\pi\)
0.526416 + 0.850227i \(0.323536\pi\)
\(734\) −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 \(-0.147008\pi\)
−0.986174 + 0.165713i \(0.947008\pi\)
\(740\) 0 0
\(741\) −12.9443 + 9.40456i −0.475520 + 0.345485i
\(742\) 0 0
\(743\) −11.1246 + 34.2380i −0.408122 + 1.25607i 0.510137 + 0.860093i \(0.329595\pi\)
−0.918260 + 0.395979i \(0.870405\pi\)
\(744\) −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 0.463404 0.886147i \(-0.346628\pi\)
−0.699576 + 0.714558i \(0.746628\pi\)
\(752\) 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 −0.938727 0.344662i \(-0.887994\pi\)
0.556859 0.830607i \(-0.312006\pi\)
\(758\) 20.0000 0.726433
\(759\) 0 0
\(760\) 0 0
\(761\) −5.56231 17.1190i −0.201633 0.620564i −0.999835 0.0181732i \(-0.994215\pi\)
0.798201 0.602391i \(-0.205785\pi\)
\(762\) 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 \(-0.289948\pi\)
0.613036 + 0.790055i \(0.289948\pi\)
\(770\) 0 0
\(771\) −30.0000 −1.08042
\(772\) −4.32624 13.3148i −0.155705 0.479210i
\(773\) 0 0 0.587785 0.809017i \(-0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(774\) 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