Properties

Label 441.2.f.g.148.3
Level $441$
Weight $2$
Character 441.148
Analytic conductor $3.521$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 441.f (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.52140272914\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Defining polynomial: \(x^{12} - 7 x^{10} + 37 x^{8} - 78 x^{6} + 123 x^{4} - 36 x^{2} + 9\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 3^{3} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 148.3
Root \(-1.29589 + 0.748185i\) of defining polynomial
Character \(\chi\) \(=\) 441.148
Dual form 441.2.f.g.295.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.119562 - 0.207087i) q^{2} +(-1.12441 + 1.31746i) q^{3} +(0.971410 - 1.68253i) q^{4} +(1.29589 - 2.24456i) q^{5} +(0.407265 + 0.0753324i) q^{6} -0.942820 q^{8} +(-0.471410 - 2.96273i) q^{9} +O(q^{10})\) \(q+(-0.119562 - 0.207087i) q^{2} +(-1.12441 + 1.31746i) q^{3} +(0.971410 - 1.68253i) q^{4} +(1.29589 - 2.24456i) q^{5} +(0.407265 + 0.0753324i) q^{6} -0.942820 q^{8} +(-0.471410 - 2.96273i) q^{9} -0.619757 q^{10} +(-2.09097 - 3.62167i) q^{11} +(1.12441 + 3.17165i) q^{12} +(-1.84155 + 3.18966i) q^{13} +(1.50000 + 4.23109i) q^{15} +(-1.83009 - 3.16982i) q^{16} +1.71107 q^{17} +(-0.557180 + 0.451852i) q^{18} -7.15561 q^{19} +(-2.51769 - 4.36077i) q^{20} +(-0.500000 + 0.866025i) q^{22} +(2.56238 - 4.43818i) q^{23} +(1.06012 - 1.24213i) q^{24} +(-0.858685 - 1.48729i) q^{25} +0.880716 q^{26} +(4.43334 + 2.71026i) q^{27} +(1.06238 + 1.84010i) q^{29} +(0.696860 - 0.816506i) q^{30} +(3.26793 - 5.66021i) q^{31} +(-1.38044 + 2.39099i) q^{32} +(7.12252 + 1.31746i) q^{33} +(-0.204579 - 0.354341i) q^{34} +(-5.44282 - 2.08486i) q^{36} +1.66019 q^{37} +(0.855536 + 1.48183i) q^{38} +(-2.13160 - 6.01266i) q^{39} +(-1.22180 + 2.11621i) q^{40} +(5.10948 - 8.84988i) q^{41} +(0.830095 + 1.43777i) q^{43} -8.12476 q^{44} +(-7.26091 - 2.78128i) q^{45} -1.22545 q^{46} +(-4.66912 - 8.08715i) q^{47} +(6.23389 + 1.15309i) q^{48} +(-0.205332 + 0.355645i) q^{50} +(-1.92395 + 2.25427i) q^{51} +(3.57780 + 6.19694i) q^{52} +10.6465 q^{53} +(0.0312007 - 1.24213i) q^{54} -10.8387 q^{55} +(8.04583 - 9.42724i) q^{57} +(0.254040 - 0.440011i) q^{58} +(-3.03215 + 5.25183i) q^{59} +(8.57605 + 1.58632i) q^{60} +(3.99298 + 6.91605i) q^{61} -1.56287 q^{62} -6.66019 q^{64} +(4.77292 + 8.26693i) q^{65} +(-0.578751 - 1.63250i) q^{66} +(-4.13160 + 7.15614i) q^{67} +(1.66215 - 2.87893i) q^{68} +(2.96596 + 8.36616i) q^{69} +6.23912 q^{71} +(0.444455 + 2.79332i) q^{72} +7.15561 q^{73} +(-0.198495 - 0.343803i) q^{74} +(2.92495 + 0.541033i) q^{75} +(-6.95103 + 12.0395i) q^{76} +(-0.990285 + 1.16031i) q^{78} +(4.91423 + 8.51170i) q^{79} -9.48644 q^{80} +(-8.55555 + 2.79332i) q^{81} -2.44359 q^{82} +(-3.44733 - 5.97094i) q^{83} +(2.21737 - 3.84060i) q^{85} +(0.198495 - 0.343803i) q^{86} +(-3.61881 - 0.669376i) q^{87} +(1.97141 + 3.41458i) q^{88} -5.03538 q^{89} +(0.292160 + 1.83617i) q^{90} +(-4.97825 - 8.62258i) q^{92} +(3.78263 + 10.6698i) q^{93} +(-1.11650 + 1.93383i) q^{94} +(-9.27292 + 16.0612i) q^{95} +(-1.59786 - 4.50712i) q^{96} +(-1.53167 - 2.65294i) q^{97} +(-9.74433 + 7.90228i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q - 2q^{2} - 6q^{4} + 24q^{8} + 12q^{9} + O(q^{10}) \) \( 12q - 2q^{2} - 6q^{4} + 24q^{8} + 12q^{9} - 8q^{11} + 18q^{15} - 6q^{16} - 42q^{18} - 6q^{22} - 4q^{23} - 12q^{25} - 22q^{29} - 48q^{30} - 16q^{32} - 30q^{36} - 12q^{37} + 24q^{39} - 6q^{43} - 28q^{44} + 24q^{46} - 56q^{50} - 18q^{51} + 56q^{53} - 6q^{57} - 18q^{58} + 108q^{60} - 48q^{64} + 6q^{65} + 76q^{71} + 60q^{72} - 36q^{74} + 36q^{78} + 6q^{79} - 48q^{81} + 30q^{85} + 36q^{86} + 6q^{88} - 62q^{92} + 42q^{93} - 60q^{95} - 48q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(344\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.119562 0.207087i −0.0845428 0.146433i 0.820653 0.571426i \(-0.193610\pi\)
−0.905196 + 0.424994i \(0.860276\pi\)
\(3\) −1.12441 + 1.31746i −0.649178 + 0.760637i
\(4\) 0.971410 1.68253i 0.485705 0.841266i
\(5\) 1.29589 2.24456i 0.579542 1.00380i −0.415990 0.909369i \(-0.636565\pi\)
0.995532 0.0944264i \(-0.0301017\pi\)
\(6\) 0.407265 + 0.0753324i 0.166265 + 0.0307543i
\(7\) 0 0
\(8\) −0.942820 −0.333337
\(9\) −0.471410 2.96273i −0.157137 0.987577i
\(10\) −0.619757 −0.195984
\(11\) −2.09097 3.62167i −0.630452 1.09197i −0.987459 0.157873i \(-0.949536\pi\)
0.357008 0.934101i \(-0.383797\pi\)
\(12\) 1.12441 + 3.17165i 0.324589 + 0.915576i
\(13\) −1.84155 + 3.18966i −0.510755 + 0.884653i 0.489168 + 0.872190i \(0.337301\pi\)
−0.999922 + 0.0124633i \(0.996033\pi\)
\(14\) 0 0
\(15\) 1.50000 + 4.23109i 0.387298 + 1.09246i
\(16\) −1.83009 3.16982i −0.457524 0.792454i
\(17\) 1.71107 0.414996 0.207498 0.978235i \(-0.433468\pi\)
0.207498 + 0.978235i \(0.433468\pi\)
\(18\) −0.557180 + 0.451852i −0.131329 + 0.106502i
\(19\) −7.15561 −1.64161 −0.820805 0.571209i \(-0.806475\pi\)
−0.820805 + 0.571209i \(0.806475\pi\)
\(20\) −2.51769 4.36077i −0.562973 0.975097i
\(21\) 0 0
\(22\) −0.500000 + 0.866025i −0.106600 + 0.184637i
\(23\) 2.56238 4.43818i 0.534294 0.925424i −0.464904 0.885361i \(-0.653911\pi\)
0.999197 0.0400622i \(-0.0127556\pi\)
\(24\) 1.06012 1.24213i 0.216395 0.253549i
\(25\) −0.858685 1.48729i −0.171737 0.297457i
\(26\) 0.880716 0.172723
\(27\) 4.43334 + 2.71026i 0.853197 + 0.521589i
\(28\) 0 0
\(29\) 1.06238 + 1.84010i 0.197279 + 0.341698i 0.947645 0.319325i \(-0.103456\pi\)
−0.750366 + 0.661023i \(0.770123\pi\)
\(30\) 0.696860 0.816506i 0.127229 0.149073i
\(31\) 3.26793 5.66021i 0.586937 1.01660i −0.407694 0.913119i \(-0.633667\pi\)
0.994631 0.103486i \(-0.0329997\pi\)
\(32\) −1.38044 + 2.39099i −0.244029 + 0.422671i
\(33\) 7.12252 + 1.31746i 1.23987 + 0.229341i
\(34\) −0.204579 0.354341i −0.0350850 0.0607689i
\(35\) 0 0
\(36\) −5.44282 2.08486i −0.907137 0.347477i
\(37\) 1.66019 0.272934 0.136467 0.990645i \(-0.456425\pi\)
0.136467 + 0.990645i \(0.456425\pi\)
\(38\) 0.855536 + 1.48183i 0.138786 + 0.240385i
\(39\) −2.13160 6.01266i −0.341329 0.962796i
\(40\) −1.22180 + 2.11621i −0.193183 + 0.334602i
\(41\) 5.10948 8.84988i 0.797967 1.38212i −0.122972 0.992410i \(-0.539242\pi\)
0.920938 0.389708i \(-0.127424\pi\)
\(42\) 0 0
\(43\) 0.830095 + 1.43777i 0.126588 + 0.219257i 0.922353 0.386349i \(-0.126264\pi\)
−0.795764 + 0.605606i \(0.792931\pi\)
\(44\) −8.12476 −1.22485
\(45\) −7.26091 2.78128i −1.08239 0.414609i
\(46\) −1.22545 −0.180683
\(47\) −4.66912 8.08715i −0.681061 1.17963i −0.974657 0.223703i \(-0.928185\pi\)
0.293596 0.955930i \(-0.405148\pi\)
\(48\) 6.23389 + 1.15309i 0.899784 + 0.166434i
\(49\) 0 0
\(50\) −0.205332 + 0.355645i −0.0290383 + 0.0502958i
\(51\) −1.92395 + 2.25427i −0.269406 + 0.315661i
\(52\) 3.57780 + 6.19694i 0.496152 + 0.859361i
\(53\) 10.6465 1.46241 0.731206 0.682157i \(-0.238958\pi\)
0.731206 + 0.682157i \(0.238958\pi\)
\(54\) 0.0312007 1.24213i 0.00424588 0.169032i
\(55\) −10.8387 −1.46149
\(56\) 0 0
\(57\) 8.04583 9.42724i 1.06570 1.24867i
\(58\) 0.254040 0.440011i 0.0333571 0.0577762i
\(59\) −3.03215 + 5.25183i −0.394752 + 0.683730i −0.993069 0.117529i \(-0.962503\pi\)
0.598318 + 0.801259i \(0.295836\pi\)
\(60\) 8.57605 + 1.58632i 1.10716 + 0.204794i
\(61\) 3.99298 + 6.91605i 0.511249 + 0.885509i 0.999915 + 0.0130384i \(0.00415038\pi\)
−0.488666 + 0.872471i \(0.662516\pi\)
\(62\) −1.56287 −0.198485
\(63\) 0 0
\(64\) −6.66019 −0.832524
\(65\) 4.77292 + 8.26693i 0.592007 + 1.02539i
\(66\) −0.578751 1.63250i −0.0712393 0.200947i
\(67\) −4.13160 + 7.15614i −0.504755 + 0.874262i 0.495230 + 0.868762i \(0.335084\pi\)
−0.999985 + 0.00549964i \(0.998249\pi\)
\(68\) 1.66215 2.87893i 0.201566 0.349122i
\(69\) 2.96596 + 8.36616i 0.357060 + 1.00717i
\(70\) 0 0
\(71\) 6.23912 0.740448 0.370224 0.928943i \(-0.379281\pi\)
0.370224 + 0.928943i \(0.379281\pi\)
\(72\) 0.444455 + 2.79332i 0.0523795 + 0.329196i
\(73\) 7.15561 0.837501 0.418750 0.908101i \(-0.362468\pi\)
0.418750 + 0.908101i \(0.362468\pi\)
\(74\) −0.198495 0.343803i −0.0230746 0.0399663i
\(75\) 2.92495 + 0.541033i 0.337745 + 0.0624731i
\(76\) −6.95103 + 12.0395i −0.797338 + 1.38103i
\(77\) 0 0
\(78\) −0.990285 + 1.16031i −0.112128 + 0.131379i
\(79\) 4.91423 + 8.51170i 0.552894 + 0.957641i 0.998064 + 0.0621945i \(0.0198099\pi\)
−0.445170 + 0.895446i \(0.646857\pi\)
\(80\) −9.48644 −1.06062
\(81\) −8.55555 + 2.79332i −0.950616 + 0.310369i
\(82\) −2.44359 −0.269849
\(83\) −3.44733 5.97094i −0.378393 0.655396i 0.612436 0.790521i \(-0.290190\pi\)
−0.990829 + 0.135124i \(0.956857\pi\)
\(84\) 0 0
\(85\) 2.21737 3.84060i 0.240508 0.416571i
\(86\) 0.198495 0.343803i 0.0214043 0.0370733i
\(87\) −3.61881 0.669376i −0.387977 0.0717647i
\(88\) 1.97141 + 3.41458i 0.210153 + 0.363996i
\(89\) −5.03538 −0.533749 −0.266875 0.963731i \(-0.585991\pi\)
−0.266875 + 0.963731i \(0.585991\pi\)
\(90\) 0.292160 + 1.83617i 0.0307963 + 0.193550i
\(91\) 0 0
\(92\) −4.97825 8.62258i −0.519018 0.898966i
\(93\) 3.78263 + 10.6698i 0.392240 + 1.10640i
\(94\) −1.11650 + 1.93383i −0.115158 + 0.199459i
\(95\) −9.27292 + 16.0612i −0.951381 + 1.64784i
\(96\) −1.59786 4.50712i −0.163081 0.460006i
\(97\) −1.53167 2.65294i −0.155518 0.269365i 0.777730 0.628599i \(-0.216371\pi\)
−0.933247 + 0.359234i \(0.883038\pi\)
\(98\) 0 0
\(99\) −9.74433 + 7.90228i −0.979342 + 0.794209i
\(100\) −3.33654 −0.333654
\(101\) 5.54984 + 9.61260i 0.552229 + 0.956489i 0.998113 + 0.0613986i \(0.0195561\pi\)
−0.445884 + 0.895091i \(0.647111\pi\)
\(102\) 0.696860 + 0.128899i 0.0689994 + 0.0127629i
\(103\) −3.99298 + 6.91605i −0.393440 + 0.681459i −0.992901 0.118946i \(-0.962049\pi\)
0.599460 + 0.800404i \(0.295382\pi\)
\(104\) 1.73625 3.00728i 0.170254 0.294888i
\(105\) 0 0
\(106\) −1.27292 2.20475i −0.123636 0.214145i
\(107\) 3.95649 0.382489 0.191244 0.981542i \(-0.438748\pi\)
0.191244 + 0.981542i \(0.438748\pi\)
\(108\) 8.86668 4.82647i 0.853197 0.464427i
\(109\) 7.26320 0.695688 0.347844 0.937552i \(-0.386914\pi\)
0.347844 + 0.937552i \(0.386914\pi\)
\(110\) 1.29589 + 2.24456i 0.123559 + 0.214010i
\(111\) −1.86673 + 2.18724i −0.177182 + 0.207603i
\(112\) 0 0
\(113\) −3.46457 + 6.00082i −0.325920 + 0.564509i −0.981698 0.190444i \(-0.939007\pi\)
0.655778 + 0.754953i \(0.272341\pi\)
\(114\) −2.91423 0.539049i −0.272943 0.0504866i
\(115\) −6.64115 11.5028i −0.619291 1.07264i
\(116\) 4.12803 0.383278
\(117\) 10.3182 + 3.95238i 0.953921 + 0.365398i
\(118\) 1.45011 0.133494
\(119\) 0 0
\(120\) −1.41423 3.98916i −0.129101 0.364158i
\(121\) −3.24433 + 5.61934i −0.294939 + 0.510849i
\(122\) 0.954815 1.65379i 0.0864449 0.149727i
\(123\) 5.91423 + 16.6824i 0.533268 + 1.50420i
\(124\) −6.34899 10.9968i −0.570156 0.987540i
\(125\) 8.50788 0.760968
\(126\) 0 0
\(127\) 9.11109 0.808479 0.404239 0.914653i \(-0.367536\pi\)
0.404239 + 0.914653i \(0.367536\pi\)
\(128\) 3.55718 + 6.16122i 0.314413 + 0.544580i
\(129\) −2.82757 0.523019i −0.248954 0.0460493i
\(130\) 1.14132 1.97682i 0.100100 0.173378i
\(131\) 2.15143 3.72639i 0.187971 0.325576i −0.756602 0.653875i \(-0.773142\pi\)
0.944574 + 0.328299i \(0.106475\pi\)
\(132\) 9.13555 10.7041i 0.795148 0.931669i
\(133\) 0 0
\(134\) 1.97592 0.170694
\(135\) 11.8285 6.43867i 1.01803 0.554153i
\(136\) −1.61323 −0.138334
\(137\) −10.2947 17.8309i −0.879533 1.52340i −0.851854 0.523779i \(-0.824522\pi\)
−0.0276785 0.999617i \(-0.508811\pi\)
\(138\) 1.37791 1.61448i 0.117295 0.137434i
\(139\) 7.88067 13.6497i 0.668429 1.15775i −0.309914 0.950765i \(-0.600300\pi\)
0.978343 0.206989i \(-0.0663665\pi\)
\(140\) 0 0
\(141\) 15.9045 + 2.94188i 1.33940 + 0.247751i
\(142\) −0.745960 1.29204i −0.0625996 0.108426i
\(143\) 15.4025 1.28802
\(144\) −8.52859 + 6.91636i −0.710716 + 0.576364i
\(145\) 5.50694 0.457326
\(146\) −0.855536 1.48183i −0.0708047 0.122637i
\(147\) 0 0
\(148\) 1.61273 2.79332i 0.132565 0.229610i
\(149\) −3.03379 + 5.25468i −0.248538 + 0.430480i −0.963120 0.269071i \(-0.913283\pi\)
0.714582 + 0.699551i \(0.246617\pi\)
\(150\) −0.237672 0.670406i −0.0194058 0.0547385i
\(151\) −2.24433 3.88728i −0.182641 0.316343i 0.760138 0.649761i \(-0.225131\pi\)
−0.942779 + 0.333418i \(0.891798\pi\)
\(152\) 6.74645 0.547210
\(153\) −0.806617 5.06945i −0.0652111 0.409841i
\(154\) 0 0
\(155\) −8.46978 14.6701i −0.680309 1.17833i
\(156\) −12.1871 2.25427i −0.975753 0.180486i
\(157\) −0.514457 + 0.891066i −0.0410582 + 0.0711148i −0.885824 0.464021i \(-0.846406\pi\)
0.844766 + 0.535136i \(0.179740\pi\)
\(158\) 1.17511 2.03534i 0.0934865 0.161923i
\(159\) −11.9710 + 14.0264i −0.949365 + 1.11236i
\(160\) 3.57780 + 6.19694i 0.282850 + 0.489911i
\(161\) 0 0
\(162\) 1.60138 + 1.43777i 0.125816 + 0.112962i
\(163\) 6.82846 0.534846 0.267423 0.963579i \(-0.413828\pi\)
0.267423 + 0.963579i \(0.413828\pi\)
\(164\) −9.92680 17.1937i −0.775153 1.34260i
\(165\) 12.1871 14.2796i 0.948768 1.11166i
\(166\) −0.824336 + 1.42779i −0.0639809 + 0.110818i
\(167\) −8.99716 + 15.5835i −0.696221 + 1.20589i 0.273546 + 0.961859i \(0.411803\pi\)
−0.969767 + 0.244032i \(0.921530\pi\)
\(168\) 0 0
\(169\) −0.282630 0.489530i −0.0217408 0.0376561i
\(170\) −1.06045 −0.0813328
\(171\) 3.37323 + 21.2001i 0.257957 + 1.62122i
\(172\) 3.22545 0.245938
\(173\) 0.415178 + 0.719110i 0.0315654 + 0.0546729i 0.881377 0.472414i \(-0.156617\pi\)
−0.849811 + 0.527087i \(0.823284\pi\)
\(174\) 0.294052 + 0.829440i 0.0222920 + 0.0628797i
\(175\) 0 0
\(176\) −7.65335 + 13.2560i −0.576893 + 0.999208i
\(177\) −3.50972 9.89994i −0.263806 0.744125i
\(178\) 0.602038 + 1.04276i 0.0451247 + 0.0781582i
\(179\) 7.57893 0.566476 0.283238 0.959050i \(-0.408591\pi\)
0.283238 + 0.959050i \(0.408591\pi\)
\(180\) −11.7329 + 9.51495i −0.874520 + 0.709202i
\(181\) 0.409157 0.0304124 0.0152062 0.999884i \(-0.495160\pi\)
0.0152062 + 0.999884i \(0.495160\pi\)
\(182\) 0 0
\(183\) −13.6014 2.51586i −1.00544 0.185978i
\(184\) −2.41586 + 4.18440i −0.178100 + 0.308478i
\(185\) 2.15143 3.72639i 0.158176 0.273969i
\(186\) 1.75731 2.05903i 0.128852 0.150975i
\(187\) −3.57780 6.19694i −0.261635 0.453165i
\(188\) −18.1425 −1.32318
\(189\) 0 0
\(190\) 4.43474 0.321730
\(191\) −8.01204 13.8773i −0.579731 1.00412i −0.995510 0.0946575i \(-0.969824\pi\)
0.415779 0.909466i \(-0.363509\pi\)
\(192\) 7.48878 8.77454i 0.540456 0.633248i
\(193\) 6.18715 10.7164i 0.445360 0.771387i −0.552717 0.833369i \(-0.686409\pi\)
0.998077 + 0.0619822i \(0.0197422\pi\)
\(194\) −0.366259 + 0.634379i −0.0262959 + 0.0455458i
\(195\) −16.2581 3.00728i −1.16426 0.215356i
\(196\) 0 0
\(197\) 23.1021 1.64595 0.822977 0.568075i \(-0.192312\pi\)
0.822977 + 0.568075i \(0.192312\pi\)
\(198\) 2.80150 + 1.07311i 0.199094 + 0.0762628i
\(199\) −6.74645 −0.478243 −0.239122 0.970990i \(-0.576859\pi\)
−0.239122 + 0.970990i \(0.576859\pi\)
\(200\) 0.809585 + 1.40224i 0.0572463 + 0.0991536i
\(201\) −4.78233 13.4897i −0.337320 0.951487i
\(202\) 1.32710 2.29860i 0.0933741 0.161729i
\(203\) 0 0
\(204\) 1.92395 + 5.42692i 0.134703 + 0.379961i
\(205\) −13.2427 22.9370i −0.924910 1.60199i
\(206\) 1.90963 0.133050
\(207\) −14.3571 5.49945i −0.997884 0.382238i
\(208\) 13.4809 0.934730
\(209\) 14.9622 + 25.9153i 1.03496 + 1.79260i
\(210\) 0 0
\(211\) −8.44282 + 14.6234i −0.581228 + 1.00672i 0.414106 + 0.910228i \(0.364094\pi\)
−0.995334 + 0.0964875i \(0.969239\pi\)
\(212\) 10.3421 17.9131i 0.710301 1.23028i
\(213\) −7.01532 + 8.21981i −0.480682 + 0.563212i
\(214\) −0.473045 0.819338i −0.0323367 0.0560088i
\(215\) 4.30286 0.293453
\(216\) −4.17984 2.55528i −0.284402 0.173865i
\(217\) 0 0
\(218\) −0.868400 1.50411i −0.0588155 0.101871i
\(219\) −8.04583 + 9.42724i −0.543687 + 0.637034i
\(220\) −10.5288 + 18.2365i −0.709854 + 1.22950i
\(221\) −3.15103 + 5.45774i −0.211961 + 0.367128i
\(222\) 0.676137 + 0.125066i 0.0453794 + 0.00839388i
\(223\) 2.25071 + 3.89834i 0.150719 + 0.261052i 0.931492 0.363762i \(-0.118508\pi\)
−0.780773 + 0.624815i \(0.785175\pi\)
\(224\) 0 0
\(225\) −4.00163 + 3.24517i −0.266776 + 0.216345i
\(226\) 1.65692 0.110217
\(227\) 3.03215 + 5.25183i 0.201251 + 0.348576i 0.948932 0.315482i \(-0.102166\pi\)
−0.747681 + 0.664058i \(0.768833\pi\)
\(228\) −8.04583 22.6951i −0.532848 1.50302i
\(229\) 5.52466 9.56899i 0.365080 0.632336i −0.623709 0.781656i \(-0.714375\pi\)
0.988789 + 0.149320i \(0.0477084\pi\)
\(230\) −1.58805 + 2.75059i −0.104713 + 0.181369i
\(231\) 0 0
\(232\) −1.00163 1.73488i −0.0657605 0.113901i
\(233\) −8.13844 −0.533167 −0.266583 0.963812i \(-0.585895\pi\)
−0.266583 + 0.963812i \(0.585895\pi\)
\(234\) −0.415178 2.60932i −0.0271411 0.170577i
\(235\) −24.2028 −1.57881
\(236\) 5.89092 + 10.2034i 0.383466 + 0.664183i
\(237\) −16.7394 3.09632i −1.08734 0.201127i
\(238\) 0 0
\(239\) −10.5813 + 18.3273i −0.684445 + 1.18549i 0.289166 + 0.957279i \(0.406622\pi\)
−0.973611 + 0.228214i \(0.926711\pi\)
\(240\) 10.6666 12.4980i 0.688528 0.806744i
\(241\) −6.84573 11.8572i −0.440972 0.763786i 0.556790 0.830654i \(-0.312033\pi\)
−0.997762 + 0.0668671i \(0.978700\pi\)
\(242\) 1.55159 0.0997398
\(243\) 5.93984 14.4124i 0.381041 0.924558i
\(244\) 15.5153 0.993265
\(245\) 0 0
\(246\) 2.74759 3.21934i 0.175180 0.205257i
\(247\) 13.1774 22.8240i 0.838460 1.45225i
\(248\) −3.08107 + 5.33656i −0.195648 + 0.338872i
\(249\) 11.7427 + 2.17206i 0.744163 + 0.137649i
\(250\) −1.01722 1.76187i −0.0643344 0.111430i
\(251\) 15.2040 0.959667 0.479833 0.877360i \(-0.340697\pi\)
0.479833 + 0.877360i \(0.340697\pi\)
\(252\) 0 0
\(253\) −21.4315 −1.34738
\(254\) −1.08934 1.88679i −0.0683511 0.118388i
\(255\) 2.56661 + 7.23970i 0.160727 + 0.453368i
\(256\) −5.80959 + 10.0625i −0.363099 + 0.628906i
\(257\) −12.8107 + 22.1889i −0.799112 + 1.38410i 0.121082 + 0.992642i \(0.461363\pi\)
−0.920195 + 0.391461i \(0.871970\pi\)
\(258\) 0.229758 + 0.648085i 0.0143041 + 0.0403480i
\(259\) 0 0
\(260\) 18.5458 1.15016
\(261\) 4.95090 4.01499i 0.306453 0.248522i
\(262\) −1.02891 −0.0635665
\(263\) −3.55034 6.14938i −0.218924 0.379187i 0.735556 0.677464i \(-0.236921\pi\)
−0.954479 + 0.298278i \(0.903588\pi\)
\(264\) −6.71525 1.24213i −0.413295 0.0764478i
\(265\) 13.7968 23.8967i 0.847528 1.46796i
\(266\) 0 0
\(267\) 5.66182 6.63392i 0.346498 0.405989i
\(268\) 8.02696 + 13.9031i 0.490324 + 0.849267i
\(269\) −16.4314 −1.00184 −0.500922 0.865493i \(-0.667006\pi\)
−0.500922 + 0.865493i \(0.667006\pi\)
\(270\) −2.74759 1.67970i −0.167213 0.102223i
\(271\) 12.6980 0.771348 0.385674 0.922635i \(-0.373969\pi\)
0.385674 + 0.922635i \(0.373969\pi\)
\(272\) −3.13143 5.42379i −0.189871 0.328865i
\(273\) 0 0
\(274\) −2.46169 + 4.26378i −0.148716 + 0.257584i
\(275\) −3.59097 + 6.21975i −0.216544 + 0.375065i
\(276\) 16.9575 + 3.13665i 1.02072 + 0.188804i
\(277\) 0.414230 + 0.717468i 0.0248887 + 0.0431084i 0.878201 0.478291i \(-0.158744\pi\)
−0.853313 + 0.521399i \(0.825410\pi\)
\(278\) −3.76890 −0.226044
\(279\) −18.3102 7.01370i −1.09620 0.419899i
\(280\) 0 0
\(281\) −2.60985 4.52039i −0.155690 0.269664i 0.777620 0.628735i \(-0.216427\pi\)
−0.933310 + 0.359071i \(0.883094\pi\)
\(282\) −1.29235 3.64535i −0.0769580 0.217078i
\(283\) 3.67708 6.36890i 0.218580 0.378592i −0.735794 0.677205i \(-0.763191\pi\)
0.954374 + 0.298614i \(0.0965242\pi\)
\(284\) 6.06075 10.4975i 0.359639 0.622913i
\(285\) −10.7334 30.2760i −0.635793 1.79340i
\(286\) −1.84155 3.18966i −0.108893 0.188609i
\(287\) 0 0
\(288\) 7.73461 + 2.96273i 0.455766 + 0.174581i
\(289\) −14.0722 −0.827778
\(290\) −0.658419 1.14041i −0.0386637 0.0669674i
\(291\) 5.21737 + 0.965064i 0.305848 + 0.0565731i
\(292\) 6.95103 12.0395i 0.406778 0.704561i
\(293\) −3.91286 + 6.77728i −0.228592 + 0.395933i −0.957391 0.288795i \(-0.906745\pi\)
0.728799 + 0.684728i \(0.240079\pi\)
\(294\) 0 0
\(295\) 7.85868 + 13.6116i 0.457550 + 0.792500i
\(296\) −1.56526 −0.0909789
\(297\) 0.545658 21.7232i 0.0316623 1.26051i
\(298\) 1.45090 0.0840484
\(299\) 9.43752 + 16.3463i 0.545786 + 0.945329i
\(300\) 3.75164 4.39576i 0.216601 0.253790i
\(301\) 0 0
\(302\) −0.536670 + 0.929540i −0.0308819 + 0.0534890i
\(303\) −18.9045 3.49679i −1.08604 0.200886i
\(304\) 13.0954 + 22.6820i 0.751075 + 1.30090i
\(305\) 20.6979 1.18516
\(306\) −0.953375 + 0.773151i −0.0545008 + 0.0441981i
\(307\) 22.6709 1.29390 0.646948 0.762534i \(-0.276045\pi\)
0.646948 + 0.762534i \(0.276045\pi\)
\(308\) 0 0
\(309\) −4.62188 13.0371i −0.262930 0.741653i
\(310\) −2.02532 + 3.50796i −0.115030 + 0.199239i
\(311\) 16.1588 27.9879i 0.916281 1.58705i 0.111266 0.993791i \(-0.464509\pi\)
0.805015 0.593255i \(-0.202157\pi\)
\(312\) 2.00972 + 5.66886i 0.113778 + 0.320936i
\(313\) 12.1598 + 21.0614i 0.687312 + 1.19046i 0.972704 + 0.232048i \(0.0745428\pi\)
−0.285392 + 0.958411i \(0.592124\pi\)
\(314\) 0.246037 0.0138847
\(315\) 0 0
\(316\) 19.0949 1.07417
\(317\) −2.56922 4.45002i −0.144302 0.249938i 0.784811 0.619736i \(-0.212760\pi\)
−0.929112 + 0.369798i \(0.879427\pi\)
\(318\) 4.33595 + 0.802027i 0.243148 + 0.0449755i
\(319\) 4.44282 7.69519i 0.248750 0.430848i
\(320\) −8.63090 + 14.9492i −0.482482 + 0.835684i
\(321\) −4.44872 + 5.21253i −0.248303 + 0.290935i
\(322\) 0 0
\(323\) −12.2438 −0.681262
\(324\) −3.61109 + 17.1084i −0.200616 + 0.950469i
\(325\) 6.32525 0.350862
\(326\) −0.816422 1.41408i −0.0452174 0.0783189i
\(327\) −8.16681 + 9.56899i −0.451625 + 0.529166i
\(328\) −4.81732 + 8.34384i −0.265992 + 0.460712i
\(329\) 0 0
\(330\) −4.41423 0.816506i −0.242995 0.0449472i
\(331\) 5.84897 + 10.1307i 0.321488 + 0.556834i 0.980795 0.195040i \(-0.0624835\pi\)
−0.659307 + 0.751874i \(0.729150\pi\)
\(332\) −13.3951 −0.735150
\(333\) −0.782630 4.91870i −0.0428879 0.269543i
\(334\) 4.30286 0.235442
\(335\) 10.7082 + 18.5472i 0.585053 + 1.01334i
\(336\) 0 0
\(337\) 16.8473 29.1804i 0.917733 1.58956i 0.114883 0.993379i \(-0.463351\pi\)
0.802850 0.596181i \(-0.203316\pi\)
\(338\) −0.0675835 + 0.117058i −0.00367606 + 0.00636711i
\(339\) −4.01025 11.3118i −0.217807 0.614373i
\(340\) −4.30795 7.46159i −0.233631 0.404661i
\(341\) −27.3326 −1.48014
\(342\) 3.98696 3.23327i 0.215590 0.174835i
\(343\) 0 0
\(344\) −0.782630 1.35556i −0.0421966 0.0730866i
\(345\) 22.6219 + 4.18440i 1.21792 + 0.225281i
\(346\) 0.0992788 0.171956i 0.00533726 0.00924441i
\(347\) −13.6557 + 23.6523i −0.733075 + 1.26972i 0.222488 + 0.974936i \(0.428582\pi\)
−0.955563 + 0.294788i \(0.904751\pi\)
\(348\) −4.64160 + 5.43852i −0.248816 + 0.291536i
\(349\) −11.4585 19.8467i −0.613358 1.06237i −0.990670 0.136281i \(-0.956485\pi\)
0.377312 0.926086i \(-0.376848\pi\)
\(350\) 0 0
\(351\) −16.8090 + 9.14978i −0.897200 + 0.488379i
\(352\) 11.5458 0.615395
\(353\) −5.13466 8.89349i −0.273290 0.473353i 0.696412 0.717642i \(-0.254779\pi\)
−0.969702 + 0.244289i \(0.921445\pi\)
\(354\) −1.63052 + 1.91047i −0.0866612 + 0.101540i
\(355\) 8.08525 14.0041i 0.429120 0.743258i
\(356\) −4.89142 + 8.47218i −0.259245 + 0.449025i
\(357\) 0 0
\(358\) −0.906150 1.56950i −0.0478915 0.0829505i
\(359\) 10.1007 0.533094 0.266547 0.963822i \(-0.414117\pi\)
0.266547 + 0.963822i \(0.414117\pi\)
\(360\) 6.84573 + 2.62225i 0.360802 + 0.138205i
\(361\) 32.2028 1.69488
\(362\) −0.0489195 0.0847311i −0.00257115 0.00445337i
\(363\) −3.75531 10.5927i −0.197103 0.555973i
\(364\) 0 0
\(365\) 9.27292 16.0612i 0.485367 0.840680i
\(366\) 1.10520 + 3.11747i 0.0577697 + 0.162953i
\(367\) 3.88768 + 6.73367i 0.202935 + 0.351494i 0.949473 0.313849i \(-0.101619\pi\)
−0.746538 + 0.665343i \(0.768285\pi\)
\(368\) −18.7576 −0.977808
\(369\) −28.6285 10.9661i −1.49034 0.570872i
\(370\) −1.02891 −0.0534907
\(371\) 0 0
\(372\) 21.6267 + 4.00032i 1.12129 + 0.207407i
\(373\) −12.0555 + 20.8808i −0.624212 + 1.08117i 0.364480 + 0.931211i \(0.381247\pi\)
−0.988693 + 0.149957i \(0.952087\pi\)
\(374\) −0.855536 + 1.48183i −0.0442387 + 0.0766237i
\(375\) −9.56634 + 11.2088i −0.494004 + 0.578821i
\(376\) 4.40214 + 7.62473i 0.227023 + 0.393215i
\(377\) −7.82573 −0.403045
\(378\) 0 0
\(379\) −13.3581 −0.686161 −0.343081 0.939306i \(-0.611470\pi\)
−0.343081 + 0.939306i \(0.611470\pi\)
\(380\) 18.0156 + 31.2039i 0.924181 + 1.60073i
\(381\) −10.2446 + 12.0035i −0.524846 + 0.614959i
\(382\) −1.91586 + 3.31838i −0.0980242 + 0.169783i
\(383\) 4.62020 8.00242i 0.236081 0.408905i −0.723505 0.690319i \(-0.757470\pi\)
0.959586 + 0.281414i \(0.0908035\pi\)
\(384\) −12.1169 2.24128i −0.618337 0.114375i
\(385\) 0 0
\(386\) −2.95898 −0.150608
\(387\) 3.86840 3.13713i 0.196642 0.159469i
\(388\) −5.95153 −0.302143
\(389\) −5.22421 9.04859i −0.264878 0.458782i 0.702654 0.711532i \(-0.251998\pi\)
−0.967532 + 0.252750i \(0.918665\pi\)
\(390\) 1.32107 + 3.72639i 0.0668952 + 0.188693i
\(391\) 4.38442 7.59404i 0.221730 0.384047i
\(392\) 0 0
\(393\) 2.49028 + 7.02441i 0.125618 + 0.354335i
\(394\) −2.76212 4.78413i −0.139154 0.241021i
\(395\) 25.4733 1.28170
\(396\) 3.83009 + 24.0715i 0.192470 + 1.20964i
\(397\) −0.409157 −0.0205350 −0.0102675 0.999947i \(-0.503268\pi\)
−0.0102675 + 0.999947i \(0.503268\pi\)
\(398\) 0.806617 + 1.39710i 0.0404321 + 0.0700304i
\(399\) 0 0
\(400\) −3.14295 + 5.44375i −0.157147 + 0.272187i
\(401\) −7.62640 + 13.2093i −0.380844 + 0.659641i −0.991183 0.132499i \(-0.957700\pi\)
0.610339 + 0.792140i \(0.291033\pi\)
\(402\) −2.22175 + 2.60320i −0.110811 + 0.129836i
\(403\) 12.0361 + 20.8472i 0.599562 + 1.03847i
\(404\) 21.5647 1.07288
\(405\) −4.81732 + 22.8232i −0.239375 + 1.13410i
\(406\) 0 0
\(407\) −3.47141 6.01266i −0.172071 0.298036i
\(408\) 1.81393 2.12537i 0.0898031 0.105222i
\(409\) 3.06335 5.30587i 0.151473 0.262359i −0.780296 0.625410i \(-0.784932\pi\)
0.931769 + 0.363051i \(0.118265\pi\)
\(410\) −3.16664 + 5.48477i −0.156389 + 0.270874i
\(411\) 35.0669 + 6.48638i 1.72972 + 0.319949i
\(412\) 7.75765 + 13.4366i 0.382192 + 0.661976i
\(413\) 0 0
\(414\) 0.577690 + 3.63068i 0.0283919 + 0.178438i
\(415\) −17.8695 −0.877178
\(416\) −5.08430 8.80626i −0.249278 0.431763i
\(417\) 9.12188 + 25.7303i 0.446701 + 1.26002i
\(418\) 3.57780 6.19694i 0.174996 0.303102i
\(419\) −0.781437 + 1.35349i −0.0381757 + 0.0661223i −0.884482 0.466574i \(-0.845488\pi\)
0.846306 + 0.532697i \(0.178821\pi\)
\(420\) 0 0
\(421\) −11.6316 20.1465i −0.566889 0.981881i −0.996871 0.0790438i \(-0.974813\pi\)
0.429982 0.902838i \(-0.358520\pi\)
\(422\) 4.03775 0.196555
\(423\) −21.7590 + 17.6457i −1.05796 + 0.857964i
\(424\) −10.0377 −0.487476
\(425\) −1.46927 2.54485i −0.0712702 0.123444i
\(426\) 2.54098 + 0.470008i 0.123111 + 0.0227720i
\(427\) 0 0
\(428\) 3.84338 6.65692i 0.185777 0.321775i
\(429\) −17.3187 + 20.2922i −0.836157 + 0.979719i
\(430\) −0.514457 0.891066i −0.0248093 0.0429710i
\(431\) 1.00576 0.0484456 0.0242228 0.999707i \(-0.492289\pi\)
0.0242228 + 0.999707i \(0.492289\pi\)
\(432\) 0.477580 19.0129i 0.0229776 0.914759i
\(433\) 13.1071 0.629889 0.314945 0.949110i \(-0.398014\pi\)
0.314945 + 0.949110i \(0.398014\pi\)
\(434\) 0 0
\(435\) −6.19205 + 7.25518i −0.296886 + 0.347859i
\(436\) 7.05555 12.2206i 0.337899 0.585259i
\(437\) −18.3354 + 31.7579i −0.877101 + 1.51918i
\(438\) 2.91423 + 0.539049i 0.139247 + 0.0257568i
\(439\) −9.30704 16.1203i −0.444201 0.769378i 0.553795 0.832653i \(-0.313179\pi\)
−0.997996 + 0.0632744i \(0.979846\pi\)
\(440\) 10.2190 0.487170
\(441\) 0 0
\(442\) 1.50697 0.0716792
\(443\) 0.559503 + 0.969088i 0.0265828 + 0.0460427i 0.879011 0.476802i \(-0.158204\pi\)
−0.852428 + 0.522845i \(0.824871\pi\)
\(444\) 1.86673 + 5.26554i 0.0885912 + 0.249891i
\(445\) −6.52532 + 11.3022i −0.309330 + 0.535775i
\(446\) 0.538197 0.932185i 0.0254844 0.0441402i
\(447\) −3.51162 9.90531i −0.166094 0.468505i
\(448\) 0 0
\(449\) −39.4419 −1.86138 −0.930689 0.365813i \(-0.880791\pi\)
−0.930689 + 0.365813i \(0.880791\pi\)
\(450\) 1.15047 + 0.440688i 0.0542339 + 0.0207742i
\(451\) −42.7351 −2.01232
\(452\) 6.73104 + 11.6585i 0.316602 + 0.548370i
\(453\) 7.64489 + 1.41409i 0.359188 + 0.0664395i
\(454\) 0.725057 1.25584i 0.0340286 0.0589393i
\(455\) 0 0
\(456\) −7.58577 + 8.88819i −0.355236 + 0.416228i
\(457\) 17.1202 + 29.6531i 0.800852 + 1.38712i 0.919056 + 0.394126i \(0.128953\pi\)
−0.118205 + 0.992989i \(0.537714\pi\)
\(458\) −2.64215 −0.123459
\(459\) 7.58577 + 4.63744i 0.354073 + 0.216457i
\(460\) −25.8051 −1.20317
\(461\) −10.1938 17.6561i −0.474772 0.822328i 0.524811 0.851219i \(-0.324136\pi\)
−0.999583 + 0.0288903i \(0.990803\pi\)
\(462\) 0 0
\(463\) −3.40451 + 5.89679i −0.158221 + 0.274047i −0.934227 0.356678i \(-0.883909\pi\)
0.776006 + 0.630725i \(0.217243\pi\)
\(464\) 3.88852 6.73511i 0.180520 0.312670i
\(465\) 28.8508 + 5.33656i 1.33792 + 0.247477i
\(466\) 0.973045 + 1.68536i 0.0450754 + 0.0780729i
\(467\) 24.7911 1.14720 0.573598 0.819137i \(-0.305547\pi\)
0.573598 + 0.819137i \(0.305547\pi\)
\(468\) 16.6733 13.5214i 0.770721 0.625026i
\(469\) 0 0
\(470\) 2.89372 + 5.01207i 0.133477 + 0.231190i
\(471\) −0.595485 1.67970i −0.0274385 0.0773965i
\(472\) 2.85877 4.95153i 0.131586 0.227913i
\(473\) 3.47141 6.01266i 0.159616 0.276462i
\(474\) 1.36019 + 3.83672i 0.0624755 + 0.176226i
\(475\) 6.14441 + 10.6424i 0.281925 + 0.488309i
\(476\) 0 0
\(477\) −5.01887 31.5428i −0.229798 1.44424i
\(478\) 5.06045 0.231460
\(479\) 5.54984 + 9.61260i 0.253579 + 0.439211i 0.964508 0.264052i \(-0.0850590\pi\)
−0.710930 + 0.703263i \(0.751726\pi\)
\(480\) −12.1871 2.25427i −0.556265 0.102893i
\(481\) −3.05733 + 5.29545i −0.139402 + 0.241452i
\(482\) −1.63697 + 2.83532i −0.0745621 + 0.129145i
\(483\) 0 0
\(484\) 6.30314 + 10.9174i 0.286506 + 0.496244i
\(485\) −7.93955 −0.360516
\(486\) −3.69480 + 0.493113i −0.167600 + 0.0223681i
\(487\) −10.0377 −0.454854 −0.227427 0.973795i \(-0.573031\pi\)
−0.227427 + 0.973795i \(0.573031\pi\)
\(488\) −3.76466 6.52059i −0.170418 0.295173i
\(489\) −7.67798 + 8.99623i −0.347210 + 0.406824i
\(490\) 0 0
\(491\) 6.19398 10.7283i 0.279530 0.484161i −0.691738 0.722149i \(-0.743155\pi\)
0.971268 + 0.237988i \(0.0764879\pi\)
\(492\) 33.8138 + 6.25459i 1.52445 + 0.281979i
\(493\) 1.81781 + 3.14854i 0.0818702 + 0.141803i
\(494\) −6.30206 −0.283543
\(495\) 5.10948 + 32.1122i 0.229654 + 1.44334i
\(496\) −23.9225 −1.07415
\(497\) 0 0
\(498\) −0.954170 2.69145i −0.0427574 0.120607i
\(499\) −5.11109 + 8.85267i −0.228804 + 0.396300i −0.957454 0.288586i \(-0.906815\pi\)
0.728650 + 0.684886i \(0.240148\pi\)
\(500\) 8.26464 14.3148i 0.369606 0.640177i
\(501\) −10.4142 29.3757i −0.465273 1.31241i
\(502\) −1.81781 3.14854i −0.0811329 0.140526i
\(503\) −8.45753 −0.377102 −0.188551 0.982063i \(-0.560379\pi\)
−0.188551 + 0.982063i \(0.560379\pi\)
\(504\) 0 0
\(505\) 28.7680 1.28016
\(506\) 2.56238 + 4.43818i 0.113912 + 0.197301i
\(507\) 0.962729 + 0.178077i 0.0427563 + 0.00790869i
\(508\) 8.85060 15.3297i 0.392682 0.680145i
\(509\) 5.28286 9.15018i 0.234159 0.405574i −0.724869 0.688886i \(-0.758100\pi\)
0.959028 + 0.283312i \(0.0914332\pi\)
\(510\) 1.19238 1.39710i 0.0527994 0.0618647i
\(511\) 0 0
\(512\) 17.0071 0.751616
\(513\) −31.7233 19.3935i −1.40062 0.856245i
\(514\) 6.12670 0.270237
\(515\) 10.3490 + 17.9249i 0.456030 + 0.789867i
\(516\) −3.62672 + 4.24941i −0.159658 + 0.187070i
\(517\) −19.5260 + 33.8200i −0.858752 + 1.48740i
\(518\) 0 0
\(519\) −1.41423 0.261592i −0.0620778 0.0114826i
\(520\) −4.50000 7.79423i −0.197338 0.341800i
\(521\) 19.7558 0.865515 0.432758 0.901510i \(-0.357541\pi\)
0.432758 + 0.901510i \(0.357541\pi\)
\(522\) −1.42339 0.545227i −0.0623001 0.0238639i
\(523\) −32.5282 −1.42236 −0.711179 0.703011i \(-0.751839\pi\)
−0.711179 + 0.703011i \(0.751839\pi\)
\(524\) −4.17984 7.23970i −0.182597 0.316268i
\(525\) 0 0
\(526\) −0.848970 + 1.47046i −0.0370168 + 0.0641150i
\(527\) 5.59166 9.68504i 0.243577 0.421887i
\(528\) −8.85877 24.9882i −0.385528 1.08747i
\(529\) −1.63160 2.82601i −0.0709391 0.122870i
\(530\) −6.59825 −0.286610
\(531\) 16.9891 + 6.50767i 0.737266 + 0.282409i
\(532\) 0 0
\(533\) 18.8187 + 32.5950i 0.815130 + 1.41185i
\(534\) −2.05073 0.379327i −0.0887440 0.0164151i
\(535\) 5.12720 8.88057i 0.221668 0.383940i
\(536\) 3.89536 6.74695i 0.168254 0.291424i
\(537\) −8.52182 + 9.98495i −0.367744 + 0.430883i
\(538\) 1.96457 + 3.40274i 0.0846987 + 0.146702i
\(539\) 0 0
\(540\) 0.657014 26.1563i 0.0282734 1.12559i
\(541\) 15.2222 0.654453 0.327226 0.944946i \(-0.393886\pi\)
0.327226 + 0.944946i \(0.393886\pi\)
\(542\) −1.51819 2.62959i −0.0652119 0.112950i
\(543\) −0.460060 + 0.539049i −0.0197431 + 0.0231328i
\(544\) −2.36203 + 4.09116i −0.101271 + 0.175407i
\(545\) 9.41234 16.3027i 0.403180 0.698329i
\(546\) 0 0
\(547\) −11.6871 20.2427i −0.499706 0.865517i 0.500294 0.865856i \(-0.333225\pi\)
−1.00000 0.000339172i \(0.999892\pi\)
\(548\) −40.0014 −1.70877
\(549\) 18.6081 15.0904i 0.794173 0.644044i
\(550\) 1.71737 0.0732289
\(551\) −7.60199 13.1670i −0.323856 0.560934i
\(552\) −2.79637 7.88779i −0.119021 0.335726i
\(553\) 0 0
\(554\) 0.0990521 0.171563i 0.00420832 0.00728902i
\(555\) 2.49028 + 7.02441i 0.105707 + 0.298170i
\(556\) −15.3107 26.5189i −0.649319 1.12465i
\(557\) 27.6673 1.17230 0.586151 0.810202i \(-0.300643\pi\)
0.586151 + 0.810202i \(0.300643\pi\)
\(558\) 0.736755 + 4.63038i 0.0311893 + 0.196019i
\(559\) −6.11465 −0.258622
\(560\) 0 0
\(561\) 12.1871 + 2.25427i 0.514542 + 0.0951755i
\(562\) −0.624075 + 1.08093i −0.0263250 + 0.0455963i
\(563\) 4.27912 7.41166i 0.180343 0.312364i −0.761654 0.647984i \(-0.775612\pi\)
0.941998 + 0.335620i \(0.108946\pi\)
\(564\) 20.3996 23.9021i 0.858979 1.00646i
\(565\) 8.97944 + 15.5529i 0.377768 + 0.654313i
\(566\) −1.75855 −0.0739175
\(567\) 0 0
\(568\) −5.88237 −0.246819
\(569\) −6.86389 11.8886i −0.287749 0.498396i 0.685523 0.728051i \(-0.259574\pi\)
−0.973272 + 0.229655i \(0.926240\pi\)
\(570\) −4.98646 + 5.84260i −0.208860 + 0.244720i
\(571\) −5.35868 + 9.28151i −0.224254 + 0.388419i −0.956095 0.293056i \(-0.905328\pi\)
0.731841 + 0.681475i \(0.238661\pi\)
\(572\) 14.9622 25.9153i 0.625600 1.08357i
\(573\) 27.2916 + 5.04816i 1.14012 + 0.210890i
\(574\) 0 0
\(575\) −8.80111 −0.367032
\(576\) 3.13968 + 19.7323i 0.130820 + 0.822181i
\(577\) 45.6353 1.89982 0.949912 0.312518i \(-0.101173\pi\)
0.949912 + 0.312518i \(0.101173\pi\)
\(578\) 1.68250 + 2.91417i 0.0699827 + 0.121214i
\(579\) 7.16163 + 20.2010i 0.297627 + 0.839525i
\(580\) 5.34950 9.26560i 0.222126 0.384733i
\(581\) 0 0
\(582\) −0.423945 1.19583i −0.0175731 0.0495689i
\(583\) −22.2616 38.5582i −0.921980 1.59692i
\(584\) −6.74645 −0.279170
\(585\) 22.2427 18.0380i 0.919622 0.745779i
\(586\) 1.87131 0.0773032
\(587\) −5.10948 8.84988i −0.210891 0.365274i 0.741103 0.671392i \(-0.234303\pi\)
−0.951994 + 0.306118i \(0.900970\pi\)
\(588\) 0 0
\(589\) −23.3840 + 40.5023i −0.963521 + 1.66887i
\(590\) 1.87919 3.25486i 0.0773652 0.134000i
\(591\) −25.9762 + 30.4361i −1.06852 + 1.25197i
\(592\) −3.03831 5.26250i −0.124874 0.216287i
\(593\) −11.3961 −0.467981 −0.233990 0.972239i \(-0.575178\pi\)
−0.233990 + 0.972239i \(0.575178\pi\)
\(594\) −4.56382 + 2.48426i −0.187256 + 0.101930i
\(595\) 0 0
\(596\) 5.89411 + 10.2089i 0.241432 + 0.418173i
\(597\) 7.58577 8.88819i 0.310465 0.363769i
\(598\) 2.25673 3.90877i 0.0922846 0.159842i
\(599\) 17.2873 29.9424i 0.706339 1.22341i −0.259867 0.965644i \(-0.583679\pi\)
0.966206 0.257771i \(-0.0829879\pi\)
\(600\) −2.75771 0.510097i −0.112583 0.0208246i
\(601\) −19.4207 33.6376i −0.792187 1.37211i −0.924610 0.380915i \(-0.875609\pi\)
0.132423 0.991193i \(-0.457724\pi\)
\(602\) 0 0
\(603\) 23.1494 + 8.86734i 0.942716 + 0.361106i
\(604\) −8.72064 −0.354838
\(605\) 8.40861 + 14.5641i 0.341858 + 0.592116i
\(606\) 1.53611 + 4.33296i 0.0624004 + 0.176014i
\(607\) −20.6662 + 35.7950i −0.838817 + 1.45287i 0.0520683 + 0.998644i \(0.483419\pi\)
−0.890885 + 0.454229i \(0.849915\pi\)
\(608\) 9.87788 17.1090i 0.400601 0.693861i
\(609\) 0 0
\(610\) −2.47468 4.28627i −0.100197 0.173546i
\(611\) 34.3937 1.39142
\(612\) −9.31306 3.56735i −0.376458 0.144202i
\(613\) −28.6569 −1.15744 −0.578721 0.815526i \(-0.696448\pi\)
−0.578721 + 0.815526i \(0.696448\pi\)
\(614\) −2.71057 4.69485i −0.109390 0.189469i
\(615\) 45.1088 + 8.34384i 1.81896 + 0.336456i
\(616\) 0 0
\(617\) 16.8518 29.1883i 0.678430 1.17508i −0.297024 0.954870i \(-0.595994\pi\)
0.975454 0.220205i \(-0.0706726\pi\)
\(618\) −2.14721 + 2.51586i −0.0863733 + 0.101203i
\(619\) 0.719036 + 1.24541i 0.0289005 + 0.0500571i 0.880114 0.474763i \(-0.157466\pi\)
−0.851213 + 0.524820i \(0.824133\pi\)
\(620\) −32.9105 −1.32172
\(621\) 23.3885 12.7312i 0.938548 0.510887i
\(622\) −7.72789 −0.309860
\(623\) 0 0
\(624\) −15.1580 + 17.7605i −0.606806 + 0.710990i
\(625\) 15.3187 26.5328i 0.612750 1.06131i
\(626\) 2.90769 5.03626i 0.116215 0.201290i
\(627\) −50.9660 9.42724i −2.03538 0.376488i
\(628\) 0.999498 + 1.73118i 0.0398843 + 0.0690816i
\(629\) 2.84071 0.113266
\(630\) 0 0
\(631\) −30.7680 −1.22486 −0.612428 0.790527i \(-0.709807\pi\)
−0.612428 + 0.790527i \(0.709807\pi\)
\(632\) −4.63323 8.02500i −0.184300 0.319217i
\(633\) −9.77258 27.5658i −0.388425 1.09564i
\(634\) −0.614360 + 1.06410i −0.0243993 + 0.0422609i
\(635\) 11.8070 20.4503i 0.468547 0.811547i
\(636\) 11.9710 + 33.7670i 0.474682 + 1.33895i
\(637\) 0 0
\(638\) −2.12476 −0.0841202
\(639\) −2.94119 18.4848i −0.116351 0.731249i
\(640\) 18.4389 0.728862
\(641\) −4.61956 8.00132i −0.182462 0.316033i 0.760257 0.649623i \(-0.225073\pi\)
−0.942718 + 0.333590i \(0.891740\pi\)
\(642\) 1.61134 + 0.298052i 0.0635946 + 0.0117632i
\(643\) −12.7795 + 22.1348i −0.503976 + 0.872912i 0.496013 + 0.868315i \(0.334797\pi\)
−0.999989 + 0.00459728i \(0.998537\pi\)
\(644\) 0 0
\(645\) −4.83818 + 5.66886i −0.190503 + 0.223211i
\(646\) 1.46389 + 2.53552i 0.0575958 + 0.0997588i
\(647\) −28.3111 −1.11302 −0.556512 0.830839i \(-0.687861\pi\)
−0.556512 + 0.830839i \(0.687861\pi\)
\(648\) 8.06634 2.63360i 0.316876 0.103458i
\(649\) 25.3605 0.995488
\(650\) −0.756258 1.30988i −0.0296629 0.0513776i
\(651\) 0 0
\(652\) 6.63323 11.4891i 0.259778 0.449948i
\(653\) 4.17511 7.23150i 0.163385 0.282990i −0.772696 0.634776i \(-0.781092\pi\)
0.936080 + 0.351786i \(0.114426\pi\)
\(654\) 2.95805 + 0.547154i 0.115669 + 0.0213954i
\(655\) −5.57605 9.65801i −0.217874 0.377370i
\(656\) −37.4033 −1.46035
\(657\) −3.37323 21.2001i −0.131602 0.827096i
\(658\) 0 0
\(659\) 16.7862 + 29.0745i 0.653897 + 1.13258i 0.982169 + 0.188000i \(0.0602005\pi\)
−0.328272 + 0.944583i \(0.606466\pi\)
\(660\) −12.1871 34.3766i −0.474384 1.33811i
\(661\) −8.47668 + 14.6820i −0.329705 + 0.571065i −0.982453 0.186509i \(-0.940283\pi\)
0.652748 + 0.757575i \(0.273616\pi\)
\(662\) 1.39862 2.42249i 0.0543591 0.0941527i
\(663\) −3.64732 10.2881i −0.141650 0.399557i
\(664\) 3.25021 + 5.62952i 0.126133 + 0.218468i
\(665\) 0 0
\(666\) −0.925025 + 0.750160i −0.0358440 + 0.0290681i
\(667\) 10.8889 0.421620
\(668\) 17.4799 + 30.2760i 0.676316 + 1.17141i
\(669\) −7.66664 1.41811i −0.296409 0.0548272i
\(670\) 2.56059 4.43507i 0.0989242 0.171342i
\(671\) 16.6984 28.9225i 0.644636 1.11654i
\(672\) 0 0
\(673\) 22.2157 + 38.4788i 0.856354 + 1.48325i 0.875384 + 0.483429i \(0.160609\pi\)
−0.0190299 + 0.999819i \(0.506058\pi\)
\(674\) −8.05718 −0.310351
\(675\) 0.224082 8.92090i 0.00862490 0.343366i
\(676\) −1.09820 −0.0422384
\(677\) −7.18681 12.4479i −0.276212 0.478412i 0.694229 0.719755i \(-0.255746\pi\)
−0.970440 + 0.241342i \(0.922412\pi\)
\(678\) −1.86306 + 2.18293i −0.0715502 + 0.0838349i
\(679\) 0 0
\(680\) −2.09058 + 3.62099i −0.0801701 + 0.138859i
\(681\) −10.3285 1.91047i −0.395787 0.0732093i
\(682\) 3.26793 + 5.66021i 0.125135 + 0.216741i
\(683\) −32.3092 −1.23628 −0.618138 0.786069i \(-0.712113\pi\)
−0.618138 + 0.786069i \(0.712113\pi\)
\(684\) 38.9467 + 14.9185i 1.48916 + 0.570422i
\(685\) −53.3632 −2.03890
\(686\) 0 0
\(687\) 6.39480 + 18.0380i 0.243977 + 0.688192i
\(688\) 3.03831 5.26250i 0.115834 0.200631i
\(689\) −19.6061 + 33.9588i −0.746934 + 1.29373i
\(690\) −1.83818 5.18499i −0.0699781 0.197389i
\(691\) −14.4981 25.1114i −0.551533 0.955283i −0.998164 0.0605650i \(-0.980710\pi\)
0.446631 0.894718i \(-0.352624\pi\)
\(692\) 1.61323 0.0613259
\(693\) 0 0
\(694\) 6.53078 0.247905
\(695\) −20.4250 35.3772i −0.774765 1.34193i
\(696\) 3.41189 + 0.631101i 0.129327 + 0.0239218i
\(697\) 8.74269 15.1428i 0.331153 0.573574i
\(698\) −2.73999 + 4.74580i −0.103710 + 0.179631i
\(699\) 9.15093 10.7221i 0.346120 0.405546i
\(700\) 0 0
\(701\) −26.3912 −0.996783 −0.498392 0.866952i \(-0.666076\pi\)
−0.498392 + 0.866952i \(0.666076\pi\)
\(702\) 3.90451 + 2.38697i 0.147366 + 0.0900902i
\(703\) −11.8797 −0.448050
\(704\) 13.9263 + 24.1210i 0.524866 + 0.909095i
\(705\) 27.2138 31.8862i 1.02493 1.20090i
\(706\) −1.22782 + 2.12664i −0.0462095 + 0.0800372i
\(707\) 0 0
\(708\) −20.0663 3.71170i −0.754139 0.139494i
\(709\) 3.94282 + 6.82916i 0.148076 + 0.256475i 0.930516 0.366251i \(-0.119359\pi\)
−0.782441 + 0.622725i \(0.786025\pi\)
\(710\) −3.86674 −0.145116
\(711\) 22.9012 18.5720i 0.858864 0.696506i
\(712\) 4.74746 0.177918
\(713\) −16.7473 29.0073i −0.627193 1.08633i
\(714\) 0 0
\(715\) 19.9601 34.5718i 0.746464 1.29291i
\(716\) 7.36225 12.7518i 0.275140 0.476557i
\(717\) −12.2478 34.5477i −0.457403 1.29021i
\(718\) −1.20765 2.09172i −0.0450693 0.0780623i
\(719\) 33.1508 1.23632 0.618159 0.786053i \(-0.287879\pi\)
0.618159 + 0.786053i \(0.287879\pi\)
\(720\) 4.47200 + 28.1058i 0.166662 + 1.04744i
\(721\) 0 0
\(722\) −3.85021 6.66877i −0.143290 0.248186i
\(723\) 23.3187 + 4.31330i 0.867233 + 0.160413i
\(724\) 0.397460 0.688420i 0.0147715 0.0255849i
\(725\) 1.82450 3.16013i 0.0677603 0.117364i
\(726\) −1.74462 + 2.04416i −0.0647489 + 0.0758658i
\(727\) 16.5502 + 28.6658i 0.613814 + 1.06316i 0.990591 + 0.136853i \(0.0436989\pi\)
−0.376777 + 0.926304i \(0.622968\pi\)
\(728\) 0 0
\(729\) 12.3090 + 24.0310i 0.455890 + 0.890036i
\(730\) −4.43474 −0.164137
\(731\) 1.42035 + 2.46012i 0.0525337 + 0.0909910i
\(732\) −17.4455 + 20.4408i −0.644805 + 0.755514i
\(733\) −22.2795 + 38.5892i −0.822911 + 1.42532i 0.0805946 + 0.996747i \(0.474318\pi\)
−0.903505 + 0.428577i \(0.859015\pi\)
\(734\) 0.929636 1.61018i 0.0343135 0.0594327i
\(735\) 0 0
\(736\) 7.07442 + 12.2533i 0.260767 + 0.451661i
\(737\) 34.5562 1.27290
\(738\) 1.15193 + 7.23970i 0.0424032 + 0.266497i
\(739\) 39.8090 1.46440 0.732199 0.681090i \(-0.238494\pi\)
0.732199 + 0.681090i \(0.238494\pi\)
\(740\) −4.17984 7.23970i −0.153654 0.266137i
\(741\) 15.2529 + 43.0242i 0.560329 + 1.58053i
\(742\) 0 0
\(743\) −5.37072 + 9.30237i −0.197033 + 0.341271i −0.947565 0.319563i \(-0.896464\pi\)
0.750532 + 0.660834i \(0.229797\pi\)
\(744\) −3.56634 10.0597i −0.130748 0.368805i
\(745\) 7.86295 + 13.6190i 0.288076 + 0.498962i
\(746\) 5.76552 0.211091
\(747\) −16.0652 + 13.0283i −0.587795 + 0.476679i
\(748\) −13.9021 −0.508310
\(749\) 0 0
\(750\) 3.46496 + 0.640919i 0.126523 + 0.0234031i
\(751\) −9.85705 + 17.0729i −0.359689 + 0.622999i −0.987909 0.155036i \(-0.950450\pi\)
0.628220 + 0.778036i \(0.283784\pi\)
\(752\) −17.0899 + 29.6005i −0.623203 + 1.07942i
\(753\) −17.0955 + 20.0307i −0.622994 + 0.729958i
\(754\) 0.935657 + 1.62060i 0.0340746 + 0.0590189i
\(755\) −11.6336 −0.423391
\(756\) 0 0
\(757\) 35.3549 1.28499 0.642497 0.766288i \(-0.277898\pi\)
0.642497 + 0.766288i \(0.277898\pi\)
\(758\) 1.59712 + 2.76629i 0.0580100 + 0.100476i
\(759\) 24.0977 28.2351i 0.874692 1.02487i
\(760\) 8.74269 15.1428i 0.317131 0.549286i
\(761\) −19.5572 + 33.8741i −0.708948 + 1.22793i 0.256300 + 0.966597i \(0.417497\pi\)
−0.965248 + 0.261336i \(0.915837\pi\)
\(762\) 3.71063 + 0.686360i 0.134422 + 0.0248642i
\(763\) 0 0
\(764\) −31.1319 −1.12631
\(765\) −12.4239 4.75897i −0.449189 0.172061i
\(766\) −2.20960 −0.0798359
\(767\) −11.1677 19.3430i −0.403243 0.698437i
\(768\) −6.72460 18.9683i −0.242653 0.684458i
\(769\) −18.9240 + 32.7773i −0.682415 + 1.18198i 0.291826 + 0.956471i \(0.405737\pi\)
−0.974242 + 0.225507i \(0.927596\pi\)
\(770\) 0 0
\(771\) −14.8285 41.8270i −0.534034 1.50636i
\(772\) −12.0205 20.8201i −0.432628 0.749333i
\(773\) −29.8265 −1.07279 −0.536393 0.843969i \(-0.680213\pi\)
−0.536393 + 0.843969i \(0.680213\pi\)
\(774\) −1.11217 0.426015i −0.0399761 0.0153128i
\(775\) −11.2245 −0.403195
\(776\) 1.44409 + 2.50124i 0.0518399 + 0.0897894i
\(777\) 0 0
\(778\) −1.24923 + 2.16373i −0.0447870 + 0.0775734i
\(779\) −36.5614 + 63.3263i −1.30995 + 2.26890i
\(780\) −20.8531 + 24.4334i −0.746661 + 0.874857i
\(781\) −13.0458 22.5960i −0.466817