Properties

Label 405.2.r.a.368.16
Level $405$
Weight $2$
Character 405.368
Analytic conductor $3.234$
Analytic rank $0$
Dimension $192$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 405 = 3^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 405.r (of order \(36\), degree \(12\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.23394128186\)
Analytic rank: \(0\)
Dimension: \(192\)
Relative dimension: \(16\) over \(\Q(\zeta_{36})\)
Twist minimal: no (minimal twist has level 135)
Sato-Tate group: $\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label 368.16
Character \(\chi\) \(=\) 405.368
Dual form 405.2.r.a.197.16

$q$-expansion

\(f(q)\) \(=\) \(q+(2.71476 + 0.237511i) q^{2} +(5.34392 + 0.942278i) q^{4} +(-1.08230 - 1.95669i) q^{5} +(-1.29639 - 0.907744i) q^{7} +(9.01913 + 2.41667i) q^{8} +O(q^{10})\) \(q+(2.71476 + 0.237511i) q^{2} +(5.34392 + 0.942278i) q^{4} +(-1.08230 - 1.95669i) q^{5} +(-1.29639 - 0.907744i) q^{7} +(9.01913 + 2.41667i) q^{8} +(-2.47344 - 5.56901i) q^{10} +(-0.162954 + 0.447712i) q^{11} +(0.242081 + 2.76700i) q^{13} +(-3.30380 - 2.77222i) q^{14} +(13.7126 + 4.99098i) q^{16} +(-3.35386 + 0.898665i) q^{17} +(-1.97319 + 1.13922i) q^{19} +(-3.93995 - 11.4762i) q^{20} +(-0.548719 + 1.17673i) q^{22} +(0.230790 + 0.329603i) q^{23} +(-2.65727 + 4.23543i) q^{25} +7.56924i q^{26} +(-6.07248 - 6.07248i) q^{28} +(-4.29568 + 3.60450i) q^{29} +(0.908475 - 5.15222i) q^{31} +(19.1162 + 8.91403i) q^{32} +(-9.31839 + 1.64308i) q^{34} +(-0.373094 + 3.51909i) q^{35} +(-0.387140 - 1.44483i) q^{37} +(-5.62733 + 2.62407i) q^{38} +(-5.03269 - 20.2632i) q^{40} +(4.99389 - 5.95149i) q^{41} +(-0.501128 - 1.07467i) q^{43} +(-1.29268 + 2.23899i) q^{44} +(0.548257 + 0.949609i) q^{46} +(-6.94767 + 9.92230i) q^{47} +(-1.53751 - 4.22426i) q^{49} +(-8.21984 + 10.8671i) q^{50} +(-1.31362 + 15.0147i) q^{52} +(0.274270 - 0.274270i) q^{53} +(1.05240 - 0.165706i) q^{55} +(-9.49862 - 11.3200i) q^{56} +(-12.5179 + 8.76510i) q^{58} +(3.33385 - 1.21342i) q^{59} +(-1.59716 - 9.05792i) q^{61} +(3.69001 - 13.7713i) q^{62} +(24.5036 + 14.1471i) q^{64} +(5.15215 - 3.46838i) q^{65} +(13.1561 - 1.15101i) q^{67} +(-18.7696 + 1.64212i) q^{68} +(-1.84869 + 9.46488i) q^{70} +(13.8198 + 7.97886i) q^{71} +(2.07381 - 7.73957i) q^{73} +(-0.707832 - 4.01431i) q^{74} +(-11.6180 + 4.22862i) q^{76} +(0.617661 - 0.432491i) q^{77} +(-2.85683 - 3.40464i) q^{79} +(-5.07529 - 32.2331i) q^{80} +(14.9708 - 14.9708i) q^{82} +(-0.253902 + 2.90211i) q^{83} +(5.38828 + 5.58985i) q^{85} +(-1.10520 - 3.03651i) q^{86} +(-2.55168 + 3.64417i) q^{88} +(-3.50126 - 6.06435i) q^{89} +(2.19789 - 3.80686i) q^{91} +(0.922748 + 1.97884i) q^{92} +(-21.2179 + 25.2866i) q^{94} +(4.36468 + 2.62795i) q^{95} +(-6.86175 + 3.19969i) q^{97} +(-3.17066 - 11.8331i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8} - 6 q^{10} + 36 q^{11} - 12 q^{13} - 24 q^{16} + 18 q^{17} - 36 q^{20} - 12 q^{22} + 36 q^{23} - 30 q^{25} - 24 q^{28} - 24 q^{31} + 48 q^{32} - 36 q^{35} - 6 q^{37} - 12 q^{38} - 36 q^{40} - 24 q^{41} - 12 q^{43} - 12 q^{46} + 6 q^{47} - 36 q^{50} + 12 q^{52} - 24 q^{55} - 180 q^{56} - 12 q^{58} - 60 q^{61} + 18 q^{62} + 84 q^{65} + 24 q^{67} + 60 q^{68} - 12 q^{70} + 36 q^{71} - 6 q^{73} - 72 q^{76} - 132 q^{77} - 24 q^{82} - 48 q^{83} - 12 q^{85} - 12 q^{86} - 48 q^{88} - 12 q^{91} - 258 q^{92} - 18 q^{95} + 24 q^{97} - 324 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/405\mathbb{Z}\right)^\times\).

\(n\) \(82\) \(326\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(e\left(\frac{5}{18}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.71476 + 0.237511i 1.91963 + 0.167946i 0.983153 0.182786i \(-0.0585116\pi\)
0.936476 + 0.350732i \(0.114067\pi\)
\(3\) 0 0
\(4\) 5.34392 + 0.942278i 2.67196 + 0.471139i
\(5\) −1.08230 1.95669i −0.484017 0.875059i
\(6\) 0 0
\(7\) −1.29639 0.907744i −0.489990 0.343095i 0.302327 0.953204i \(-0.402237\pi\)
−0.792317 + 0.610109i \(0.791126\pi\)
\(8\) 9.01913 + 2.41667i 3.18874 + 0.854422i
\(9\) 0 0
\(10\) −2.47344 5.56901i −0.782171 1.76108i
\(11\) −0.162954 + 0.447712i −0.0491325 + 0.134990i −0.961832 0.273642i \(-0.911772\pi\)
0.912699 + 0.408632i \(0.133994\pi\)
\(12\) 0 0
\(13\) 0.242081 + 2.76700i 0.0671411 + 0.767427i 0.952901 + 0.303282i \(0.0980826\pi\)
−0.885760 + 0.464144i \(0.846362\pi\)
\(14\) −3.30380 2.77222i −0.882978 0.740907i
\(15\) 0 0
\(16\) 13.7126 + 4.99098i 3.42815 + 1.24775i
\(17\) −3.35386 + 0.898665i −0.813431 + 0.217958i −0.641473 0.767146i \(-0.721676\pi\)
−0.171959 + 0.985104i \(0.555010\pi\)
\(18\) 0 0
\(19\) −1.97319 + 1.13922i −0.452681 + 0.261356i −0.708962 0.705247i \(-0.750836\pi\)
0.256281 + 0.966602i \(0.417503\pi\)
\(20\) −3.93995 11.4762i −0.881001 2.56616i
\(21\) 0 0
\(22\) −0.548719 + 1.17673i −0.116987 + 0.250880i
\(23\) 0.230790 + 0.329603i 0.0481231 + 0.0687269i 0.842493 0.538708i \(-0.181087\pi\)
−0.794369 + 0.607435i \(0.792199\pi\)
\(24\) 0 0
\(25\) −2.65727 + 4.23543i −0.531455 + 0.847087i
\(26\) 7.56924i 1.48445i
\(27\) 0 0
\(28\) −6.07248 6.07248i −1.14759 1.14759i
\(29\) −4.29568 + 3.60450i −0.797687 + 0.669339i −0.947635 0.319355i \(-0.896534\pi\)
0.149948 + 0.988694i \(0.452089\pi\)
\(30\) 0 0
\(31\) 0.908475 5.15222i 0.163167 0.925366i −0.787767 0.615973i \(-0.788763\pi\)
0.950934 0.309393i \(-0.100126\pi\)
\(32\) 19.1162 + 8.91403i 3.37930 + 1.57579i
\(33\) 0 0
\(34\) −9.31839 + 1.64308i −1.59809 + 0.281787i
\(35\) −0.373094 + 3.51909i −0.0630645 + 0.594834i
\(36\) 0 0
\(37\) −0.387140 1.44483i −0.0636454 0.237528i 0.926774 0.375619i \(-0.122570\pi\)
−0.990420 + 0.138091i \(0.955903\pi\)
\(38\) −5.62733 + 2.62407i −0.912873 + 0.425680i
\(39\) 0 0
\(40\) −5.03269 20.2632i −0.795738 3.20389i
\(41\) 4.99389 5.95149i 0.779915 0.929467i −0.219015 0.975722i \(-0.570284\pi\)
0.998930 + 0.0462550i \(0.0147287\pi\)
\(42\) 0 0
\(43\) −0.501128 1.07467i −0.0764213 0.163886i 0.864385 0.502830i \(-0.167708\pi\)
−0.940806 + 0.338944i \(0.889930\pi\)
\(44\) −1.29268 + 2.23899i −0.194879 + 0.337541i
\(45\) 0 0
\(46\) 0.548257 + 0.949609i 0.0808361 + 0.140012i
\(47\) −6.94767 + 9.92230i −1.01342 + 1.44732i −0.122876 + 0.992422i \(0.539212\pi\)
−0.890546 + 0.454894i \(0.849677\pi\)
\(48\) 0 0
\(49\) −1.53751 4.22426i −0.219644 0.603466i
\(50\) −8.21984 + 10.8671i −1.16246 + 1.53684i
\(51\) 0 0
\(52\) −1.31362 + 15.0147i −0.182166 + 2.08217i
\(53\) 0.274270 0.274270i 0.0376738 0.0376738i −0.688019 0.725693i \(-0.741519\pi\)
0.725693 + 0.688019i \(0.241519\pi\)
\(54\) 0 0
\(55\) 1.05240 0.165706i 0.141905 0.0223439i
\(56\) −9.49862 11.3200i −1.26931 1.51270i
\(57\) 0 0
\(58\) −12.5179 + 8.76510i −1.64368 + 1.15091i
\(59\) 3.33385 1.21342i 0.434031 0.157974i −0.115759 0.993277i \(-0.536930\pi\)
0.549790 + 0.835303i \(0.314708\pi\)
\(60\) 0 0
\(61\) −1.59716 9.05792i −0.204495 1.15975i −0.898233 0.439520i \(-0.855149\pi\)
0.693738 0.720228i \(-0.255963\pi\)
\(62\) 3.69001 13.7713i 0.468631 1.74896i
\(63\) 0 0
\(64\) 24.5036 + 14.1471i 3.06294 + 1.76839i
\(65\) 5.15215 3.46838i 0.639046 0.430200i
\(66\) 0 0
\(67\) 13.1561 1.15101i 1.60727 0.140618i 0.752132 0.659012i \(-0.229025\pi\)
0.855142 + 0.518394i \(0.173470\pi\)
\(68\) −18.7696 + 1.64212i −2.27614 + 0.199137i
\(69\) 0 0
\(70\) −1.84869 + 9.46488i −0.220960 + 1.13127i
\(71\) 13.8198 + 7.97886i 1.64011 + 0.946916i 0.980794 + 0.195047i \(0.0624860\pi\)
0.659313 + 0.751869i \(0.270847\pi\)
\(72\) 0 0
\(73\) 2.07381 7.73957i 0.242721 0.905849i −0.731794 0.681526i \(-0.761317\pi\)
0.974515 0.224322i \(-0.0720168\pi\)
\(74\) −0.707832 4.01431i −0.0822838 0.466655i
\(75\) 0 0
\(76\) −11.6180 + 4.22862i −1.33268 + 0.485056i
\(77\) 0.617661 0.432491i 0.0703890 0.0492869i
\(78\) 0 0
\(79\) −2.85683 3.40464i −0.321418 0.383051i 0.581006 0.813899i \(-0.302659\pi\)
−0.902425 + 0.430848i \(0.858215\pi\)
\(80\) −5.07529 32.2331i −0.567434 3.60377i
\(81\) 0 0
\(82\) 14.9708 14.9708i 1.65325 1.65325i
\(83\) −0.253902 + 2.90211i −0.0278694 + 0.318548i 0.969445 + 0.245309i \(0.0788893\pi\)
−0.997314 + 0.0732395i \(0.976666\pi\)
\(84\) 0 0
\(85\) 5.38828 + 5.58985i 0.584441 + 0.606304i
\(86\) −1.10520 3.03651i −0.119177 0.327435i
\(87\) 0 0
\(88\) −2.55168 + 3.64417i −0.272010 + 0.388470i
\(89\) −3.50126 6.06435i −0.371132 0.642820i 0.618608 0.785700i \(-0.287697\pi\)
−0.989740 + 0.142880i \(0.954364\pi\)
\(90\) 0 0
\(91\) 2.19789 3.80686i 0.230402 0.399068i
\(92\) 0.922748 + 1.97884i 0.0962031 + 0.206308i
\(93\) 0 0
\(94\) −21.2179 + 25.2866i −2.18846 + 2.60811i
\(95\) 4.36468 + 2.62795i 0.447807 + 0.269622i
\(96\) 0 0
\(97\) −6.86175 + 3.19969i −0.696705 + 0.324879i −0.738506 0.674247i \(-0.764468\pi\)
0.0418007 + 0.999126i \(0.486691\pi\)
\(98\) −3.17066 11.8331i −0.320285 1.19532i
\(99\) 0 0
\(100\) −18.1912 + 20.1299i −1.81912 + 2.01299i
\(101\) −5.72678 + 1.00979i −0.569836 + 0.100477i −0.451140 0.892453i \(-0.648983\pi\)
−0.118696 + 0.992931i \(0.537871\pi\)
\(102\) 0 0
\(103\) −4.05522 1.89098i −0.399573 0.186324i 0.212436 0.977175i \(-0.431860\pi\)
−0.612009 + 0.790851i \(0.709638\pi\)
\(104\) −4.50356 + 25.5409i −0.441610 + 2.50450i
\(105\) 0 0
\(106\) 0.809720 0.679435i 0.0786469 0.0659926i
\(107\) −0.577939 0.577939i −0.0558714 0.0558714i 0.678619 0.734490i \(-0.262579\pi\)
−0.734490 + 0.678619i \(0.762579\pi\)
\(108\) 0 0
\(109\) 8.45996i 0.810317i 0.914246 + 0.405159i \(0.132784\pi\)
−0.914246 + 0.405159i \(0.867216\pi\)
\(110\) 2.89637 0.199898i 0.276158 0.0190595i
\(111\) 0 0
\(112\) −13.2464 18.9178i −1.25167 1.78757i
\(113\) 0.921497 1.97616i 0.0866871 0.185901i −0.858185 0.513340i \(-0.828408\pi\)
0.944872 + 0.327439i \(0.106186\pi\)
\(114\) 0 0
\(115\) 0.395147 0.808313i 0.0368477 0.0753756i
\(116\) −26.3522 + 15.2145i −2.44674 + 1.41263i
\(117\) 0 0
\(118\) 9.33883 2.50233i 0.859709 0.230358i
\(119\) 5.16368 + 1.87943i 0.473354 + 0.172287i
\(120\) 0 0
\(121\) 8.25260 + 6.92475i 0.750236 + 0.629523i
\(122\) −2.18454 24.9695i −0.197779 2.26063i
\(123\) 0 0
\(124\) 9.70964 26.6770i 0.871952 2.39567i
\(125\) 11.1634 + 0.615475i 0.998484 + 0.0550498i
\(126\) 0 0
\(127\) −3.44795 0.923874i −0.305956 0.0819806i 0.102575 0.994725i \(-0.467292\pi\)
−0.408530 + 0.912745i \(0.633959\pi\)
\(128\) 28.6056 + 20.0298i 2.52840 + 1.77040i
\(129\) 0 0
\(130\) 14.8107 8.19215i 1.29898 0.718499i
\(131\) 3.02885 + 0.534068i 0.264632 + 0.0466617i 0.304390 0.952548i \(-0.401548\pi\)
−0.0397579 + 0.999209i \(0.512659\pi\)
\(132\) 0 0
\(133\) 3.59215 + 0.314273i 0.311479 + 0.0272509i
\(134\) 35.9891 3.10899
\(135\) 0 0
\(136\) −32.4207 −2.78005
\(137\) −2.06926 0.181036i −0.176788 0.0154670i −0.00158226 0.999999i \(-0.500504\pi\)
−0.175206 + 0.984532i \(0.556059\pi\)
\(138\) 0 0
\(139\) 15.2015 + 2.68044i 1.28938 + 0.227352i 0.775957 0.630785i \(-0.217267\pi\)
0.513420 + 0.858137i \(0.328378\pi\)
\(140\) −5.30974 + 18.4542i −0.448755 + 1.55966i
\(141\) 0 0
\(142\) 35.6224 + 24.9431i 2.98937 + 2.09318i
\(143\) −1.27827 0.342511i −0.106894 0.0286422i
\(144\) 0 0
\(145\) 11.7021 + 4.50418i 0.971805 + 0.374051i
\(146\) 7.46815 20.5186i 0.618068 1.69813i
\(147\) 0 0
\(148\) −0.707419 8.08583i −0.0581495 0.664651i
\(149\) −12.0609 10.1203i −0.988065 0.829085i −0.00277827 0.999996i \(-0.500884\pi\)
−0.985286 + 0.170911i \(0.945329\pi\)
\(150\) 0 0
\(151\) −1.00956 0.367451i −0.0821571 0.0299027i 0.300615 0.953746i \(-0.402808\pi\)
−0.382772 + 0.923843i \(0.625030\pi\)
\(152\) −20.5496 + 5.50625i −1.66679 + 0.446616i
\(153\) 0 0
\(154\) 1.77953 1.02741i 0.143398 0.0827910i
\(155\) −11.0645 + 3.79862i −0.888725 + 0.305112i
\(156\) 0 0
\(157\) −7.27543 + 15.6022i −0.580643 + 1.24519i 0.368289 + 0.929711i \(0.379944\pi\)
−0.948932 + 0.315481i \(0.897834\pi\)
\(158\) −6.94698 9.92131i −0.552672 0.789297i
\(159\) 0 0
\(160\) −3.24737 47.0521i −0.256727 3.71979i
\(161\) 0.636793i 0.0501863i
\(162\) 0 0
\(163\) 2.47310 + 2.47310i 0.193708 + 0.193708i 0.797296 0.603588i \(-0.206263\pi\)
−0.603588 + 0.797296i \(0.706263\pi\)
\(164\) 32.2949 27.0987i 2.52181 2.11605i
\(165\) 0 0
\(166\) −1.37857 + 7.81825i −0.106998 + 0.606814i
\(167\) 5.97097 + 2.78431i 0.462048 + 0.215456i 0.639681 0.768640i \(-0.279066\pi\)
−0.177634 + 0.984097i \(0.556844\pi\)
\(168\) 0 0
\(169\) 5.20483 0.917752i 0.400372 0.0705963i
\(170\) 13.3003 + 16.4549i 1.02008 + 1.26203i
\(171\) 0 0
\(172\) −1.66535 6.21517i −0.126982 0.473902i
\(173\) 9.69016 4.51859i 0.736729 0.343542i −0.0177714 0.999842i \(-0.505657\pi\)
0.754500 + 0.656300i \(0.227879\pi\)
\(174\) 0 0
\(175\) 7.28956 3.07866i 0.551039 0.232725i
\(176\) −4.46905 + 5.32601i −0.336867 + 0.401463i
\(177\) 0 0
\(178\) −8.06473 17.2949i −0.604477 1.29631i
\(179\) 3.31311 5.73847i 0.247633 0.428913i −0.715235 0.698884i \(-0.753681\pi\)
0.962869 + 0.269970i \(0.0870139\pi\)
\(180\) 0 0
\(181\) −4.36897 7.56727i −0.324743 0.562471i 0.656717 0.754137i \(-0.271944\pi\)
−0.981460 + 0.191666i \(0.938611\pi\)
\(182\) 6.87094 9.81271i 0.509308 0.727367i
\(183\) 0 0
\(184\) 1.28499 + 3.53048i 0.0947306 + 0.260270i
\(185\) −2.40808 + 2.32124i −0.177045 + 0.170661i
\(186\) 0 0
\(187\) 0.144182 1.64801i 0.0105436 0.120514i
\(188\) −46.4773 + 46.4773i −3.38971 + 3.38971i
\(189\) 0 0
\(190\) 11.2249 + 8.17092i 0.814341 + 0.592781i
\(191\) 12.9658 + 15.4521i 0.938176 + 1.11807i 0.992826 + 0.119569i \(0.0381512\pi\)
−0.0546500 + 0.998506i \(0.517404\pi\)
\(192\) 0 0
\(193\) −15.3824 + 10.7709i −1.10725 + 0.775303i −0.976372 0.216096i \(-0.930668\pi\)
−0.130875 + 0.991399i \(0.541779\pi\)
\(194\) −19.3880 + 7.05665i −1.39198 + 0.506638i
\(195\) 0 0
\(196\) −4.23588 24.0229i −0.302563 1.71592i
\(197\) 1.29693 4.84019i 0.0924021 0.344849i −0.904211 0.427087i \(-0.859540\pi\)
0.996613 + 0.0822373i \(0.0262066\pi\)
\(198\) 0 0
\(199\) −14.4356 8.33443i −1.02332 0.590812i −0.108253 0.994123i \(-0.534526\pi\)
−0.915063 + 0.403312i \(0.867859\pi\)
\(200\) −34.2020 + 31.7782i −2.41844 + 2.24706i
\(201\) 0 0
\(202\) −15.7867 + 1.38116i −1.11075 + 0.0971779i
\(203\) 8.84085 0.773474i 0.620506 0.0542872i
\(204\) 0 0
\(205\) −17.0501 3.33023i −1.19083 0.232594i
\(206\) −10.5599 6.09673i −0.735740 0.424779i
\(207\) 0 0
\(208\) −10.4905 + 39.1510i −0.727384 + 2.71463i
\(209\) −0.188505 1.06906i −0.0130391 0.0739486i
\(210\) 0 0
\(211\) 9.81899 3.57382i 0.675967 0.246032i 0.0188522 0.999822i \(-0.493999\pi\)
0.657115 + 0.753790i \(0.271777\pi\)
\(212\) 1.72411 1.20724i 0.118413 0.0829134i
\(213\) 0 0
\(214\) −1.43170 1.70623i −0.0978690 0.116636i
\(215\) −1.56043 + 2.14367i −0.106421 + 0.146197i
\(216\) 0 0
\(217\) −5.85464 + 5.85464i −0.397439 + 0.397439i
\(218\) −2.00934 + 22.9668i −0.136089 + 1.55551i
\(219\) 0 0
\(220\) 5.78008 + 0.106130i 0.389693 + 0.00715525i
\(221\) −3.29851 9.06258i −0.221882 0.609615i
\(222\) 0 0
\(223\) −13.4550 + 19.2158i −0.901015 + 1.28678i 0.0565006 + 0.998403i \(0.482006\pi\)
−0.957516 + 0.288381i \(0.906883\pi\)
\(224\) −16.6904 28.9087i −1.11518 1.93154i
\(225\) 0 0
\(226\) 2.97101 5.14593i 0.197628 0.342302i
\(227\) 8.45994 + 18.1424i 0.561506 + 1.20415i 0.958173 + 0.286191i \(0.0923891\pi\)
−0.396667 + 0.917963i \(0.629833\pi\)
\(228\) 0 0
\(229\) 14.1827 16.9023i 0.937218 1.11693i −0.0557370 0.998445i \(-0.517751\pi\)
0.992955 0.118488i \(-0.0378047\pi\)
\(230\) 1.26472 2.10053i 0.0833929 0.138505i
\(231\) 0 0
\(232\) −47.4542 + 22.1282i −3.11552 + 1.45279i
\(233\) −4.83296 18.0369i −0.316618 1.18163i −0.922474 0.386059i \(-0.873836\pi\)
0.605856 0.795574i \(-0.292831\pi\)
\(234\) 0 0
\(235\) 26.9343 + 2.85558i 1.75700 + 0.186277i
\(236\) 18.9592 3.34302i 1.23414 0.217612i
\(237\) 0 0
\(238\) 13.5718 + 6.32863i 0.879729 + 0.410224i
\(239\) 3.38846 19.2169i 0.219181 1.24304i −0.654320 0.756218i \(-0.727045\pi\)
0.873502 0.486821i \(-0.161844\pi\)
\(240\) 0 0
\(241\) −3.76991 + 3.16333i −0.242841 + 0.203768i −0.756082 0.654476i \(-0.772889\pi\)
0.513241 + 0.858244i \(0.328445\pi\)
\(242\) 20.7592 + 20.7592i 1.33445 + 1.33445i
\(243\) 0 0
\(244\) 49.9098i 3.19515i
\(245\) −6.60154 + 7.58032i −0.421757 + 0.484289i
\(246\) 0 0
\(247\) −3.62990 5.18403i −0.230965 0.329852i
\(248\) 20.6449 44.2731i 1.31095 2.81134i
\(249\) 0 0
\(250\) 30.1598 + 4.32230i 1.90747 + 0.273366i
\(251\) 18.1080 10.4546i 1.14297 0.659892i 0.195803 0.980643i \(-0.437269\pi\)
0.947163 + 0.320752i \(0.103935\pi\)
\(252\) 0 0
\(253\) −0.185175 + 0.0496176i −0.0116419 + 0.00311943i
\(254\) −9.14093 3.32703i −0.573553 0.208756i
\(255\) 0 0
\(256\) 29.5507 + 24.7960i 1.84692 + 1.54975i
\(257\) 1.27235 + 14.5430i 0.0793667 + 0.907166i 0.926626 + 0.375986i \(0.122696\pi\)
−0.847259 + 0.531180i \(0.821749\pi\)
\(258\) 0 0
\(259\) −0.809647 + 2.22449i −0.0503090 + 0.138223i
\(260\) 30.8009 13.6800i 1.91019 0.848399i
\(261\) 0 0
\(262\) 8.09576 + 2.16925i 0.500158 + 0.134017i
\(263\) −25.0799 17.5612i −1.54650 1.08287i −0.962561 0.271067i \(-0.912624\pi\)
−0.583935 0.811801i \(-0.698488\pi\)
\(264\) 0 0
\(265\) −0.833501 0.239820i −0.0512016 0.0147320i
\(266\) 9.67721 + 1.70635i 0.593348 + 0.104623i
\(267\) 0 0
\(268\) 71.3898 + 6.24580i 4.36083 + 0.381523i
\(269\) −23.6912 −1.44448 −0.722239 0.691643i \(-0.756887\pi\)
−0.722239 + 0.691643i \(0.756887\pi\)
\(270\) 0 0
\(271\) 20.1164 1.22198 0.610991 0.791638i \(-0.290771\pi\)
0.610991 + 0.791638i \(0.290771\pi\)
\(272\) −50.4755 4.41603i −3.06052 0.267761i
\(273\) 0 0
\(274\) −5.57454 0.982943i −0.336771 0.0593817i
\(275\) −1.46324 1.87988i −0.0882368 0.113361i
\(276\) 0 0
\(277\) −12.4565 8.72217i −0.748441 0.524064i 0.136004 0.990708i \(-0.456574\pi\)
−0.884445 + 0.466644i \(0.845463\pi\)
\(278\) 40.6320 + 10.8873i 2.43694 + 0.652977i
\(279\) 0 0
\(280\) −11.8695 + 30.8375i −0.709336 + 1.84289i
\(281\) 8.16607 22.4361i 0.487147 1.33842i −0.416106 0.909316i \(-0.636606\pi\)
0.903253 0.429108i \(-0.141172\pi\)
\(282\) 0 0
\(283\) −0.0248657 0.284217i −0.00147811 0.0168949i 0.995420 0.0956001i \(-0.0304770\pi\)
−0.996898 + 0.0787051i \(0.974921\pi\)
\(284\) 66.3335 + 55.6605i 3.93617 + 3.30284i
\(285\) 0 0
\(286\) −3.38884 1.23344i −0.200387 0.0729347i
\(287\) −11.8765 + 3.18229i −0.701046 + 0.187845i
\(288\) 0 0
\(289\) −4.28164 + 2.47200i −0.251861 + 0.145412i
\(290\) 30.6986 + 15.0072i 1.80268 + 0.881250i
\(291\) 0 0
\(292\) 18.3751 39.4056i 1.07532 2.30604i
\(293\) 8.91694 + 12.7347i 0.520933 + 0.743969i 0.990287 0.139041i \(-0.0444019\pi\)
−0.469354 + 0.883010i \(0.655513\pi\)
\(294\) 0 0
\(295\) −5.98250 5.21003i −0.348315 0.303340i
\(296\) 13.9667i 0.811796i
\(297\) 0 0
\(298\) −30.3387 30.3387i −1.75748 1.75748i
\(299\) −0.856140 + 0.718387i −0.0495119 + 0.0415454i
\(300\) 0 0
\(301\) −0.325869 + 1.84809i −0.0187828 + 0.106522i
\(302\) −2.65345 1.23733i −0.152689 0.0712001i
\(303\) 0 0
\(304\) −32.7435 + 5.77355i −1.87797 + 0.331136i
\(305\) −15.9949 + 12.9285i −0.915868 + 0.740283i
\(306\) 0 0
\(307\) 2.72426 + 10.1671i 0.155482 + 0.580267i 0.999064 + 0.0432656i \(0.0137762\pi\)
−0.843582 + 0.537001i \(0.819557\pi\)
\(308\) 3.70826 1.72919i 0.211298 0.0985297i
\(309\) 0 0
\(310\) −30.9398 + 7.68440i −1.75726 + 0.436445i
\(311\) −2.06659 + 2.46287i −0.117186 + 0.139657i −0.821448 0.570283i \(-0.806833\pi\)
0.704262 + 0.709940i \(0.251278\pi\)
\(312\) 0 0
\(313\) 10.2775 + 22.0403i 0.580921 + 1.24579i 0.948789 + 0.315911i \(0.102310\pi\)
−0.367868 + 0.929878i \(0.619912\pi\)
\(314\) −23.4568 + 40.6283i −1.32374 + 2.29279i
\(315\) 0 0
\(316\) −12.0586 20.8860i −0.678347 1.17493i
\(317\) −11.9128 + 17.0133i −0.669092 + 0.955562i 0.330838 + 0.943688i \(0.392669\pi\)
−0.999929 + 0.0118742i \(0.996220\pi\)
\(318\) 0 0
\(319\) −0.913782 2.51060i −0.0511620 0.140566i
\(320\) 1.16148 63.2573i 0.0649289 3.53619i
\(321\) 0 0
\(322\) 0.151246 1.72874i 0.00842858 0.0963391i
\(323\) 5.59403 5.59403i 0.311260 0.311260i
\(324\) 0 0
\(325\) −12.3627 6.32735i −0.685759 0.350978i
\(326\) 6.12650 + 7.30128i 0.339315 + 0.404380i
\(327\) 0 0
\(328\) 59.4234 41.6087i 3.28111 2.29746i
\(329\) 18.0138 6.55649i 0.993134 0.361471i
\(330\) 0 0
\(331\) 1.03458 + 5.86738i 0.0568655 + 0.322500i 0.999949 0.0100545i \(-0.00320050\pi\)
−0.943084 + 0.332555i \(0.892089\pi\)
\(332\) −4.09143 + 15.2694i −0.224546 + 0.838018i
\(333\) 0 0
\(334\) 15.5485 + 8.97692i 0.850775 + 0.491195i
\(335\) −16.4910 24.4967i −0.900998 1.33840i
\(336\) 0 0
\(337\) −11.1098 + 0.971978i −0.605187 + 0.0529470i −0.385631 0.922653i \(-0.626016\pi\)
−0.219556 + 0.975600i \(0.570461\pi\)
\(338\) 14.3479 1.25528i 0.780421 0.0682780i
\(339\) 0 0
\(340\) 23.5273 + 34.9490i 1.27595 + 1.89537i
\(341\) 2.15867 + 1.24631i 0.116899 + 0.0674915i
\(342\) 0 0
\(343\) −4.70859 + 17.5727i −0.254240 + 0.948837i
\(344\) −1.92261 10.9037i −0.103660 0.587887i
\(345\) 0 0
\(346\) 27.3797 9.96540i 1.47194 0.535743i
\(347\) 19.4431 13.6142i 1.04376 0.730851i 0.0797793 0.996813i \(-0.474578\pi\)
0.963984 + 0.265962i \(0.0856896\pi\)
\(348\) 0 0
\(349\) −4.82633 5.75179i −0.258347 0.307886i 0.621243 0.783618i \(-0.286628\pi\)
−0.879591 + 0.475731i \(0.842183\pi\)
\(350\) 20.5207 6.62649i 1.09688 0.354201i
\(351\) 0 0
\(352\) −7.10598 + 7.10598i −0.378750 + 0.378750i
\(353\) −0.451688 + 5.16281i −0.0240409 + 0.274789i 0.974654 + 0.223717i \(0.0718192\pi\)
−0.998695 + 0.0510716i \(0.983736\pi\)
\(354\) 0 0
\(355\) 0.655066 35.6765i 0.0347673 1.89351i
\(356\) −12.9961 35.7066i −0.688793 1.89244i
\(357\) 0 0
\(358\) 10.3573 14.7917i 0.547398 0.781765i
\(359\) −6.82697 11.8247i −0.360314 0.624082i 0.627699 0.778457i \(-0.283997\pi\)
−0.988012 + 0.154375i \(0.950664\pi\)
\(360\) 0 0
\(361\) −6.90435 + 11.9587i −0.363387 + 0.629404i
\(362\) −10.0634 21.5810i −0.528921 1.13427i
\(363\) 0 0
\(364\) 15.3325 18.2725i 0.803641 0.957742i
\(365\) −17.3884 + 4.31869i −0.910152 + 0.226051i
\(366\) 0 0
\(367\) 19.5461 9.11448i 1.02030 0.475772i 0.160840 0.986981i \(-0.448580\pi\)
0.859457 + 0.511208i \(0.170802\pi\)
\(368\) 1.51970 + 5.67159i 0.0792197 + 0.295652i
\(369\) 0 0
\(370\) −7.08869 + 5.72968i −0.368523 + 0.297872i
\(371\) −0.604528 + 0.106595i −0.0313855 + 0.00553411i
\(372\) 0 0
\(373\) −11.9942 5.59299i −0.621037 0.289594i 0.0865206 0.996250i \(-0.472425\pi\)
−0.707557 + 0.706656i \(0.750203\pi\)
\(374\) 0.782840 4.43971i 0.0404797 0.229572i
\(375\) 0 0
\(376\) −86.6408 + 72.7003i −4.46816 + 3.74923i
\(377\) −11.0135 11.0135i −0.567226 0.567226i
\(378\) 0 0
\(379\) 27.4089i 1.40790i 0.710249 + 0.703951i \(0.248583\pi\)
−0.710249 + 0.703951i \(0.751417\pi\)
\(380\) 20.8483 + 18.1563i 1.06949 + 0.931398i
\(381\) 0 0
\(382\) 31.5292 + 45.0283i 1.61317 + 2.30385i
\(383\) −15.2701 + 32.7469i −0.780267 + 1.67329i −0.0416793 + 0.999131i \(0.513271\pi\)
−0.738588 + 0.674157i \(0.764507\pi\)
\(384\) 0 0
\(385\) −1.51474 0.740488i −0.0771984 0.0377388i
\(386\) −44.3177 + 25.5869i −2.25571 + 1.30234i
\(387\) 0 0
\(388\) −39.6836 + 10.6332i −2.01463 + 0.539819i
\(389\) 17.3733 + 6.32335i 0.880860 + 0.320607i 0.742557 0.669783i \(-0.233613\pi\)
0.138303 + 0.990390i \(0.455835\pi\)
\(390\) 0 0
\(391\) −1.07024 0.898039i −0.0541244 0.0454158i
\(392\) −3.65832 41.8148i −0.184773 2.11197i
\(393\) 0 0
\(394\) 4.67045 12.8320i 0.235294 0.646464i
\(395\) −3.56989 + 9.27475i −0.179620 + 0.466663i
\(396\) 0 0
\(397\) −29.1350 7.80671i −1.46224 0.391807i −0.561980 0.827151i \(-0.689960\pi\)
−0.900265 + 0.435343i \(0.856627\pi\)
\(398\) −37.2099 26.0546i −1.86516 1.30600i
\(399\) 0 0
\(400\) −57.5772 + 44.8165i −2.87886 + 2.24082i
\(401\) −34.2820 6.04485i −1.71196 0.301865i −0.770115 0.637905i \(-0.779801\pi\)
−0.941848 + 0.336040i \(0.890912\pi\)
\(402\) 0 0
\(403\) 14.4761 + 1.26649i 0.721106 + 0.0630886i
\(404\) −31.5550 −1.56992
\(405\) 0 0
\(406\) 24.1845 1.20026
\(407\) 0.709953 + 0.0621128i 0.0351911 + 0.00307882i
\(408\) 0 0
\(409\) −21.8207 3.84758i −1.07897 0.190251i −0.394208 0.919021i \(-0.628981\pi\)
−0.684758 + 0.728771i \(0.740092\pi\)
\(410\) −45.4960 13.0904i −2.24689 0.646488i
\(411\) 0 0
\(412\) −19.8890 13.9264i −0.979859 0.686105i
\(413\) −5.42346 1.45321i −0.266871 0.0715079i
\(414\) 0 0
\(415\) 5.95333 2.64413i 0.292238 0.129795i
\(416\) −20.0374 + 55.0524i −0.982415 + 2.69916i
\(417\) 0 0
\(418\) −0.257831 2.94703i −0.0126109 0.144144i
\(419\) 3.82900 + 3.21291i 0.187059 + 0.156961i 0.731508 0.681833i \(-0.238817\pi\)
−0.544449 + 0.838794i \(0.683261\pi\)
\(420\) 0 0
\(421\) 12.3825 + 4.50685i 0.603485 + 0.219651i 0.625650 0.780104i \(-0.284834\pi\)
−0.0221653 + 0.999754i \(0.507056\pi\)
\(422\) 27.5051 7.36996i 1.33893 0.358764i
\(423\) 0 0
\(424\) 3.13649 1.81086i 0.152322 0.0879429i
\(425\) 5.10590 16.5931i 0.247672 0.804882i
\(426\) 0 0
\(427\) −6.15173 + 13.1924i −0.297703 + 0.638426i
\(428\) −2.54388 3.63304i −0.122963 0.175609i
\(429\) 0 0
\(430\) −4.74535 + 5.44893i −0.228841 + 0.262771i
\(431\) 14.5168i 0.699251i −0.936890 0.349625i \(-0.886309\pi\)
0.936890 0.349625i \(-0.113691\pi\)
\(432\) 0 0
\(433\) −16.6348 16.6348i −0.799416 0.799416i 0.183587 0.983003i \(-0.441229\pi\)
−0.983003 + 0.183587i \(0.941229\pi\)
\(434\) −17.2845 + 14.5034i −0.829683 + 0.696187i
\(435\) 0 0
\(436\) −7.97163 + 45.2094i −0.381772 + 2.16514i
\(437\) −0.830884 0.387448i −0.0397466 0.0185341i
\(438\) 0 0
\(439\) −21.2894 + 3.75390i −1.01609 + 0.179164i −0.656801 0.754064i \(-0.728091\pi\)
−0.359287 + 0.933227i \(0.616980\pi\)
\(440\) 9.89218 + 1.04877i 0.471591 + 0.0499982i
\(441\) 0 0
\(442\) −6.80221 25.3862i −0.323548 1.20750i
\(443\) −10.8788 + 5.07285i −0.516866 + 0.241018i −0.663505 0.748172i \(-0.730932\pi\)
0.146640 + 0.989190i \(0.453154\pi\)
\(444\) 0 0
\(445\) −8.07667 + 13.4143i −0.382871 + 0.635898i
\(446\) −41.0912 + 48.9706i −1.94572 + 2.31882i
\(447\) 0 0
\(448\) −18.9243 40.5832i −0.894087 1.91738i
\(449\) −15.1373 + 26.2186i −0.714374 + 1.23733i 0.248826 + 0.968548i \(0.419955\pi\)
−0.963200 + 0.268784i \(0.913378\pi\)
\(450\) 0 0
\(451\) 1.85078 + 3.20565i 0.0871499 + 0.150948i
\(452\) 6.78649 9.69212i 0.319210 0.455879i
\(453\) 0 0
\(454\) 18.6577 + 51.2617i 0.875651 + 2.40583i
\(455\) −9.82762 0.180448i −0.460726 0.00845951i
\(456\) 0 0
\(457\) 3.62673 41.4537i 0.169651 1.93912i −0.143990 0.989579i \(-0.545993\pi\)
0.313642 0.949541i \(-0.398451\pi\)
\(458\) 42.5171 42.5171i 1.98670 1.98670i
\(459\) 0 0
\(460\) 2.87329 3.94722i 0.133968 0.184040i
\(461\) 11.0916 + 13.2184i 0.516586 + 0.615643i 0.959770 0.280788i \(-0.0905957\pi\)
−0.443184 + 0.896431i \(0.646151\pi\)
\(462\) 0 0
\(463\) −13.5021 + 9.45428i −0.627496 + 0.439378i −0.843585 0.536996i \(-0.819559\pi\)
0.216088 + 0.976374i \(0.430670\pi\)
\(464\) −76.8950 + 27.9875i −3.56976 + 1.29929i
\(465\) 0 0
\(466\) −8.83640 50.1137i −0.409338 2.32147i
\(467\) −1.03012 + 3.84448i −0.0476685 + 0.177901i −0.985656 0.168769i \(-0.946021\pi\)
0.937987 + 0.346670i \(0.112688\pi\)
\(468\) 0 0
\(469\) −18.1003 10.4502i −0.835795 0.482546i
\(470\) 72.4420 + 14.1494i 3.34150 + 0.652664i
\(471\) 0 0
\(472\) 33.0009 2.88720i 1.51899 0.132894i
\(473\) 0.562805 0.0492391i 0.0258778 0.00226402i
\(474\) 0 0
\(475\) 0.418210 11.3845i 0.0191888 0.522359i
\(476\) 25.8234 + 14.9091i 1.18361 + 0.683359i
\(477\) 0 0
\(478\) 13.7631 51.3646i 0.629510 2.34936i
\(479\) 0.246236 + 1.39648i 0.0112508 + 0.0638066i 0.989916 0.141654i \(-0.0452420\pi\)
−0.978665 + 0.205460i \(0.934131\pi\)
\(480\) 0 0
\(481\) 3.90411 1.42098i 0.178012 0.0647911i
\(482\) −10.9857 + 7.69230i −0.500387 + 0.350375i
\(483\) 0 0
\(484\) 37.5762 + 44.7816i 1.70801 + 2.03553i
\(485\) 13.6872 + 9.96332i 0.621505 + 0.452411i
\(486\) 0 0
\(487\) −5.92999 + 5.92999i −0.268714 + 0.268714i −0.828582 0.559868i \(-0.810852\pi\)
0.559868 + 0.828582i \(0.310852\pi\)
\(488\) 7.48504 85.5544i 0.338832 3.87286i
\(489\) 0 0
\(490\) −19.7220 + 19.0109i −0.890951 + 0.858823i
\(491\) 9.16760 + 25.1878i 0.413728 + 1.13671i 0.955193 + 0.295985i \(0.0956479\pi\)
−0.541464 + 0.840724i \(0.682130\pi\)
\(492\) 0 0
\(493\) 11.1679 15.9494i 0.502976 0.718324i
\(494\) −8.62305 14.9356i −0.387969 0.671983i
\(495\) 0 0
\(496\) 38.1722 66.1162i 1.71398 2.96871i
\(497\) −10.6731 22.8886i −0.478754 1.02669i
\(498\) 0 0
\(499\) 7.19594 8.57579i 0.322134 0.383905i −0.580538 0.814233i \(-0.697158\pi\)
0.902672 + 0.430328i \(0.141602\pi\)
\(500\) 59.0763 + 13.8081i 2.64197 + 0.617515i
\(501\) 0 0
\(502\) 51.6420 24.0811i 2.30490 1.07479i
\(503\) −3.44372 12.8521i −0.153548 0.573049i −0.999225 0.0393543i \(-0.987470\pi\)
0.845677 0.533694i \(-0.179197\pi\)
\(504\) 0 0
\(505\) 8.17391 + 10.1127i 0.363734 + 0.450007i
\(506\) −0.514493 + 0.0907189i −0.0228720 + 0.00403295i
\(507\) 0 0
\(508\) −17.5550 8.18603i −0.778877 0.363197i
\(509\) 1.12261 6.36664i 0.0497588 0.282196i −0.949768 0.312955i \(-0.898681\pi\)
0.999527 + 0.0307584i \(0.00979226\pi\)
\(510\) 0 0
\(511\) −9.71403 + 8.15104i −0.429723 + 0.360581i
\(512\) 24.9482 + 24.9482i 1.10257 + 1.10257i
\(513\) 0 0
\(514\) 39.7830i 1.75475i
\(515\) 0.688883 + 9.98142i 0.0303558 + 0.439834i
\(516\) 0 0
\(517\) −3.31019 4.72744i −0.145582 0.207912i
\(518\) −2.72634 + 5.84666i −0.119789 + 0.256887i
\(519\) 0 0
\(520\) 54.8499 18.8308i 2.40533 0.825784i
\(521\) 6.34977 3.66604i 0.278188 0.160612i −0.354415 0.935088i \(-0.615320\pi\)
0.632603 + 0.774476i \(0.281987\pi\)
\(522\) 0 0
\(523\) 12.5860 3.37240i 0.550346 0.147465i 0.0270787 0.999633i \(-0.491380\pi\)
0.523268 + 0.852168i \(0.324713\pi\)
\(524\) 15.6827 + 5.70803i 0.685101 + 0.249356i
\(525\) 0 0
\(526\) −63.9152 53.6312i −2.78683 2.33843i
\(527\) 1.58322 + 18.0963i 0.0689660 + 0.788285i
\(528\) 0 0
\(529\) 7.81109 21.4608i 0.339613 0.933078i
\(530\) −2.20580 0.849021i −0.0958139 0.0368791i
\(531\) 0 0
\(532\) 18.9001 + 5.06425i 0.819421 + 0.219563i
\(533\) 17.6767 + 12.3773i 0.765662 + 0.536122i
\(534\) 0 0
\(535\) −0.505347 + 1.75635i −0.0218480 + 0.0759335i
\(536\) 121.438 + 21.4128i 5.24534 + 0.924894i
\(537\) 0 0
\(538\) −64.3161 5.62693i −2.77286 0.242594i
\(539\) 2.14180 0.0922537
\(540\) 0 0
\(541\) −19.4815 −0.837576 −0.418788 0.908084i \(-0.637545\pi\)
−0.418788 + 0.908084i \(0.637545\pi\)
\(542\) 54.6112 + 4.77786i 2.34575 + 0.205227i
\(543\) 0 0
\(544\) −72.1238 12.7174i −3.09228 0.545253i
\(545\) 16.5535 9.15618i 0.709075 0.392207i
\(546\) 0 0
\(547\) 11.7626 + 8.23625i 0.502932 + 0.352157i 0.797347 0.603521i \(-0.206236\pi\)
−0.294415 + 0.955678i \(0.595125\pi\)
\(548\) −10.8874 2.91726i −0.465085 0.124619i
\(549\) 0 0
\(550\) −3.52587 5.45096i −0.150344 0.232430i
\(551\) 4.36986 12.0061i 0.186162 0.511477i
\(552\) 0 0
\(553\) 0.613034 + 7.00702i 0.0260689 + 0.297969i
\(554\) −31.7450 26.6372i −1.34871 1.13171i
\(555\) 0 0
\(556\) 78.7101 + 28.6481i 3.33805 + 1.21495i
\(557\) −22.3886 + 5.99902i −0.948637 + 0.254187i −0.699784 0.714355i \(-0.746720\pi\)
−0.248853 + 0.968541i \(0.580054\pi\)
\(558\) 0 0
\(559\) 2.85230 1.64678i 0.120640 0.0696513i
\(560\) −22.6798 + 46.3938i −0.958397 + 1.96049i
\(561\) 0 0
\(562\) 27.4978 58.9691i 1.15992 2.48746i
\(563\) 17.2788 + 24.6767i 0.728214 + 1.04000i 0.997046 + 0.0768099i \(0.0244735\pi\)
−0.268832 + 0.963187i \(0.586638\pi\)
\(564\) 0 0
\(565\) −4.86406 + 0.335700i −0.204632 + 0.0141230i
\(566\) 0.777487i 0.0326802i
\(567\) 0 0
\(568\) 105.360 + 105.360i 4.42082 + 4.42082i
\(569\) −14.2448 + 11.9528i −0.597173 + 0.501088i −0.890536 0.454913i \(-0.849670\pi\)
0.293362 + 0.956001i \(0.405226\pi\)
\(570\) 0 0
\(571\) 6.82003 38.6783i 0.285409 1.61864i −0.418410 0.908258i \(-0.637412\pi\)
0.703819 0.710379i \(-0.251476\pi\)
\(572\) −6.50822 3.03483i −0.272122 0.126893i
\(573\) 0 0
\(574\) −32.9977 + 5.81838i −1.37730 + 0.242854i
\(575\) −2.00928 + 0.101652i −0.0837929 + 0.00423918i
\(576\) 0 0
\(577\) 11.3255 + 42.2673i 0.471486 + 1.75961i 0.634436 + 0.772975i \(0.281232\pi\)
−0.162950 + 0.986634i \(0.552101\pi\)
\(578\) −12.2108 + 5.69397i −0.507901 + 0.236838i
\(579\) 0 0
\(580\) 58.2908 + 35.0966i 2.42039 + 1.45731i
\(581\) 2.96353 3.53180i 0.122948 0.146524i
\(582\) 0 0
\(583\) 0.0781006 + 0.167487i 0.00323460 + 0.00693661i
\(584\) 37.4080 64.7925i 1.54795 2.68113i
\(585\) 0 0
\(586\) 21.1828 + 36.6896i 0.875051 + 1.51563i
\(587\) 11.6046 16.5731i 0.478974 0.684046i −0.504845 0.863210i \(-0.668450\pi\)
0.983819 + 0.179164i \(0.0573394\pi\)
\(588\) 0 0
\(589\) 4.07693 + 11.2013i 0.167987 + 0.461540i
\(590\) −15.0037 15.5649i −0.617691 0.640798i
\(591\) 0 0
\(592\) 1.90240 21.7446i 0.0781883 0.893696i
\(593\) 2.27116 2.27116i 0.0932652 0.0932652i −0.658935 0.752200i \(-0.728993\pi\)
0.752200 + 0.658935i \(0.228993\pi\)
\(594\) 0 0
\(595\) −1.91117 12.1378i −0.0783504 0.497602i
\(596\) −54.9162 65.4466i −2.24946 2.68080i
\(597\) 0 0
\(598\) −2.49484 + 1.74691i −0.102022 + 0.0714364i
\(599\) −11.3910 + 4.14598i −0.465423 + 0.169400i −0.564078 0.825722i \(-0.690768\pi\)
0.0986548 + 0.995122i \(0.468546\pi\)
\(600\) 0 0
\(601\) 2.78962 + 15.8207i 0.113791 + 0.645340i 0.987342 + 0.158607i \(0.0507003\pi\)
−0.873551 + 0.486733i \(0.838189\pi\)
\(602\) −1.32360 + 4.93974i −0.0539459 + 0.201329i
\(603\) 0 0
\(604\) −5.04879 2.91492i −0.205432 0.118606i
\(605\) 4.61785 23.6424i 0.187742 0.961200i
\(606\) 0 0
\(607\) −12.6491 + 1.10665i −0.513412 + 0.0449177i −0.340918 0.940093i \(-0.610738\pi\)
−0.172494 + 0.985011i \(0.555182\pi\)
\(608\) −47.8750 + 4.18852i −1.94159 + 0.169867i
\(609\) 0 0
\(610\) −46.4932 + 31.2988i −1.88245 + 1.26725i
\(611\) −29.1369 16.8222i −1.17875 0.680552i
\(612\) 0 0
\(613\) 3.15725 11.7830i 0.127520 0.475912i −0.872397 0.488798i \(-0.837435\pi\)
0.999917 + 0.0128866i \(0.00410204\pi\)
\(614\) 4.98094 + 28.2483i 0.201014 + 1.14001i
\(615\) 0 0
\(616\) 6.61595 2.40801i 0.266564 0.0970215i
\(617\) −7.63591 + 5.34672i −0.307410 + 0.215251i −0.717094 0.696977i \(-0.754528\pi\)
0.409684 + 0.912228i \(0.365639\pi\)
\(618\) 0 0
\(619\) 10.1944 + 12.1492i 0.409748 + 0.488319i 0.930967 0.365104i \(-0.118967\pi\)
−0.521218 + 0.853423i \(0.674522\pi\)
\(620\) −62.7074 + 9.87365i −2.51839 + 0.396535i
\(621\) 0 0
\(622\) −6.19528 + 6.19528i −0.248408 + 0.248408i
\(623\) −0.965877 + 11.0400i −0.0386971 + 0.442309i
\(624\) 0 0
\(625\) −10.8778 22.5094i −0.435111 0.900377i
\(626\) 22.6663 + 62.2751i 0.905927 + 2.48901i
\(627\) 0 0
\(628\) −53.5809 + 76.5215i −2.13811 + 3.05354i
\(629\) 2.59683 + 4.49784i 0.103542 + 0.179341i
\(630\) 0 0
\(631\) −12.2239 + 21.1724i −0.486626 + 0.842861i −0.999882 0.0153745i \(-0.995106\pi\)
0.513256 + 0.858236i \(0.328439\pi\)
\(632\) −17.5382 37.6109i −0.697634 1.49608i
\(633\) 0 0
\(634\) −36.3814 + 43.3577i −1.44489 + 1.72195i
\(635\) 1.92396 + 7.74647i 0.0763500 + 0.307409i
\(636\) 0 0
\(637\) 11.3163 5.27689i 0.448369 0.209078i
\(638\) −1.88441 7.03271i −0.0746045 0.278428i
\(639\) 0 0
\(640\) 8.23251 77.6504i 0.325419 3.06940i
\(641\) 5.87001 1.03504i 0.231852 0.0408817i −0.0565151 0.998402i \(-0.517999\pi\)
0.288367 + 0.957520i \(0.406888\pi\)
\(642\) 0 0
\(643\) −29.1651 13.5999i −1.15016 0.536328i −0.248438 0.968648i \(-0.579917\pi\)
−0.901720 + 0.432320i \(0.857695\pi\)
\(644\) 0.600036 3.40297i 0.0236447 0.134096i
\(645\) 0 0
\(646\) 16.5151 13.8578i 0.649779 0.545229i
\(647\) 5.43613 + 5.43613i 0.213717 + 0.213717i 0.805844 0.592128i \(-0.201712\pi\)
−0.592128 + 0.805844i \(0.701712\pi\)
\(648\) 0 0
\(649\) 1.69034i 0.0663516i
\(650\) −32.0590 20.1136i −1.25746 0.788919i
\(651\) 0 0
\(652\) 10.8857 + 15.5464i 0.426317 + 0.608844i
\(653\) 6.80729 14.5983i 0.266390 0.571275i −0.726924 0.686717i \(-0.759051\pi\)
0.993314 + 0.115443i \(0.0368287\pi\)
\(654\) 0 0
\(655\) −2.23310 6.50454i −0.0872545 0.254153i
\(656\) 98.1831 56.6861i 3.83341 2.21322i
\(657\) 0 0
\(658\) 50.4605 13.5209i 1.96716 0.527098i
\(659\) 31.0994 + 11.3193i 1.21146 + 0.440936i 0.867210 0.497942i \(-0.165911\pi\)
0.344250 + 0.938878i \(0.388133\pi\)
\(660\) 0 0
\(661\) 22.7885 + 19.1218i 0.886369 + 0.743752i 0.967478 0.252954i \(-0.0814020\pi\)
−0.0811098 + 0.996705i \(0.525846\pi\)
\(662\) 1.41507 + 16.1743i 0.0549981 + 0.628631i
\(663\) 0 0
\(664\) −9.30342 + 25.5609i −0.361043 + 0.991957i
\(665\) −3.27284 7.36887i −0.126915 0.285752i
\(666\) 0 0
\(667\) −2.17945 0.583983i −0.0843888 0.0226119i
\(668\) 29.2848 + 20.5054i 1.13306 + 0.793379i
\(669\) 0 0
\(670\) −38.9509 70.4196i −1.50480 2.72055i
\(671\) 4.31561 + 0.760958i 0.166602 + 0.0293764i
\(672\) 0 0
\(673\) 34.6064 + 3.02767i 1.33398 + 0.116708i 0.731727 0.681598i \(-0.238715\pi\)
0.602252 + 0.798306i \(0.294270\pi\)
\(674\) −30.3912 −1.17063
\(675\) 0 0
\(676\) 28.6790 1.10304
\(677\) 17.3173 + 1.51507i 0.665560 + 0.0582289i 0.414929 0.909854i \(-0.363806\pi\)
0.250631 + 0.968083i \(0.419362\pi\)
\(678\) 0 0
\(679\) 11.8000 + 2.08066i 0.452843 + 0.0798485i
\(680\) 35.0888 + 63.4373i 1.34559 + 2.43271i
\(681\) 0 0
\(682\) 5.56428 + 3.89615i 0.213067 + 0.149191i
\(683\) 10.9763 + 2.94108i 0.419995 + 0.112537i 0.462626 0.886554i \(-0.346907\pi\)
−0.0426308 + 0.999091i \(0.513574\pi\)
\(684\) 0 0
\(685\) 1.88531 + 4.24483i 0.0720341 + 0.162187i
\(686\) −16.9564 + 46.5874i −0.647400 + 1.77872i
\(687\) 0 0
\(688\) −1.50810 17.2377i −0.0574959 0.657181i
\(689\) 0.825299 + 0.692508i 0.0314414 + 0.0263824i
\(690\) 0 0
\(691\) −22.0909 8.04044i −0.840378 0.305873i −0.114267 0.993450i \(-0.536452\pi\)
−0.726111 + 0.687577i \(0.758674\pi\)
\(692\) 56.0412 15.0162i 2.13037 0.570830i
\(693\) 0 0
\(694\) 56.0171 32.3415i 2.12638 1.22767i
\(695\) −11.2078 32.6457i −0.425134 1.23832i
\(696\) 0 0
\(697\) −11.4004 + 24.4483i −0.431822 + 0.926046i
\(698\) −11.7362 16.7611i −0.444223 0.634416i
\(699\) 0 0
\(700\) 41.8558 9.58333i 1.58200 0.362216i
\(701\) 44.6039i 1.68467i 0.538956 + 0.842334i \(0.318819\pi\)
−0.538956 + 0.842334i \(0.681181\pi\)
\(702\) 0 0
\(703\) 2.40988 + 2.40988i 0.0908903 + 0.0908903i
\(704\) −10.3268 + 8.66522i −0.389206 + 0.326583i
\(705\) 0 0
\(706\) −2.45245 + 13.9085i −0.0922992 + 0.523455i
\(707\) 8.34079 + 3.88937i 0.313688 + 0.146275i
\(708\) 0 0
\(709\) 36.4781 6.43207i 1.36996 0.241562i 0.560219 0.828344i \(-0.310717\pi\)
0.809744 + 0.586783i \(0.199606\pi\)
\(710\) 10.2519 96.6978i 0.384748 3.62900i
\(711\) 0 0
\(712\) −16.9228 63.1566i −0.634207 2.36689i
\(713\) 1.90785 0.889647i 0.0714497 0.0333175i
\(714\) 0 0
\(715\) 0.713275 + 2.87187i 0.0266750 + 0.107402i
\(716\) 23.1122 27.5441i 0.863744 1.02937i
\(717\) 0 0
\(718\) −15.7251 33.7227i −0.586857 1.25852i
\(719\) 19.2483 33.3390i 0.717839 1.24333i −0.244016 0.969771i \(-0.578465\pi\)
0.961854 0.273562i \(-0.0882018\pi\)
\(720\) 0 0
\(721\) 3.54064 + 6.13256i 0.131860 + 0.228389i
\(722\) −21.5840 + 30.8251i −0.803273 + 1.14719i
\(723\) 0 0
\(724\) −16.2169 44.5557i −0.602698 1.65590i
\(725\) −3.85183 27.7722i −0.143053 1.03143i
\(726\) 0 0
\(727\) −2.27381 + 25.9897i −0.0843308 + 0.963906i 0.829686 + 0.558230i \(0.188519\pi\)
−0.914017 + 0.405676i \(0.867036\pi\)
\(728\) 29.0230 29.0230i 1.07566 1.07566i
\(729\) 0 0
\(730\) −48.2312 + 7.59429i −1.78512 + 0.281077i
\(731\) 2.64649 + 3.15396i 0.0978838 + 0.116653i
\(732\) 0 0
\(733\) 39.9276 27.9576i 1.47476 1.03264i 0.487571 0.873083i \(-0.337883\pi\)
0.987189 0.159555i \(-0.0510060\pi\)
\(734\) 55.2278 20.1013i 2.03849 0.741951i
\(735\) 0 0
\(736\) 1.47374 + 8.35802i 0.0543230 + 0.308081i
\(737\) −1.62852 + 6.07772i −0.0599873 + 0.223876i
\(738\) 0 0
\(739\) 11.7531 + 6.78566i 0.432345 + 0.249614i 0.700345 0.713804i \(-0.253029\pi\)
−0.268000 + 0.963419i \(0.586363\pi\)
\(740\) −15.0558 + 10.1355i −0.553464 + 0.372587i
\(741\) 0 0
\(742\) −1.66647 + 0.145797i −0.0611780 + 0.00535238i
\(743\) 1.23767 0.108282i 0.0454055 0.00397247i −0.0644303 0.997922i \(-0.520523\pi\)
0.109836 + 0.993950i \(0.464967\pi\)
\(744\) 0 0
\(745\) −6.74882 + 34.5525i −0.247257 + 1.26591i
\(746\) −31.2331 18.0324i −1.14352 0.660214i
\(747\) 0 0
\(748\) 2.32338 8.67096i 0.0849511 0.317042i
\(749\) 0.224615 + 1.27386i 0.00820726 + 0.0465457i
\(750\) 0 0
\(751\) −8.15950 + 2.96982i −0.297745 + 0.108370i −0.486573 0.873640i \(-0.661753\pi\)
0.188828 + 0.982010i \(0.439531\pi\)
\(752\) −144.793 + 101.385i −5.28005 + 3.69713i
\(753\) 0 0
\(754\) −27.2833 32.5150i −0.993601 1.18413i
\(755\) 0.373658 + 2.37309i 0.0135988 + 0.0863657i
\(756\) 0 0
\(757\) 29.4262 29.4262i 1.06951 1.06951i 0.0721170 0.997396i \(-0.477025\pi\)
0.997396 0.0721170i \(-0.0229755\pi\)
\(758\) −6.50993 + 74.4088i −0.236451 + 2.70265i
\(759\) 0 0
\(760\) 33.0147 + 34.2498i 1.19757 + 1.24237i
\(761\) −14.0169 38.5111i −0.508112 1.39603i −0.883183 0.469029i \(-0.844604\pi\)
0.375071 0.926996i \(-0.377618\pi\)
\(762\) 0 0
\(763\) 7.67948 10.9674i 0.278016 0.397048i
\(764\) 54.7283 + 94.7922i 1.98000 + 3.42946i
\(765\) 0 0
\(766\) −49.2326 + 85.2733i −1.77884 + 3.08105i
\(767\) 4.16460 + 8.93101i 0.150375 + 0.322480i
\(768\) 0 0
\(769\) −3.94057 + 4.69619i −0.142100 + 0.169349i −0.832401 0.554174i \(-0.813034\pi\)
0.690300 + 0.723523i \(0.257479\pi\)
\(770\) −3.93629 2.37002i −0.141854 0.0854096i
\(771\) 0 0
\(772\) −92.3513 + 43.0641i −3.32380 + 1.54991i
\(773\) 2.46257 + 9.19044i 0.0885726 + 0.330557i 0.995967 0.0897234i \(-0.0285983\pi\)
−0.907394 + 0.420281i \(0.861932\pi\)
\(774\) 0 0
\(775\) 19.4078 + 17.5386i 0.697149 + 0.630007i
\(776\) −69.6196 + 12.2758i −2.49920 + 0.440676i
\(777\) 0 0
\(778\) 45.6625 + 21.2928i 1.63708 + 0.763382i
\(779\) −3.07383 + 17.4326i −0.110132 + 0.624587i
\(780\) 0 0
\(781\) −5.82422 + 4.88710i −0.208407 + 0.174874i
\(782\) −2.69216 2.69216i −0.0962714 0.0962714i
\(783\) 0 0
\(784\) 65.5994i 2.34283i
\(785\) 38.4029 2.65043i 1.37066 0.0945980i
\(786\) 0 0
\(787\) 4.85971 + 6.94038i