Properties

Label 864.2.v.b.109.14
Level $864$
Weight $2$
Character 864.109
Analytic conductor $6.899$
Analytic rank $0$
Dimension $128$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 864 = 2^{5} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 864.v (of order \(8\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.89907473464\)
Analytic rank: \(0\)
Dimension: \(128\)
Relative dimension: \(32\) over \(\Q(\zeta_{8})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 109.14
Character \(\chi\) \(=\) 864.109
Dual form 864.2.v.b.325.14

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.322202 - 1.37702i) q^{2} +(-1.79237 + 0.887359i) q^{4} +(1.57161 - 0.650984i) q^{5} +(3.07534 - 3.07534i) q^{7} +(1.79942 + 2.18222i) q^{8} +O(q^{10})\) \(q+(-0.322202 - 1.37702i) q^{2} +(-1.79237 + 0.887359i) q^{4} +(1.57161 - 0.650984i) q^{5} +(3.07534 - 3.07534i) q^{7} +(1.79942 + 2.18222i) q^{8} +(-1.40280 - 1.95440i) q^{10} +(-1.10590 - 2.66989i) q^{11} +(4.29788 + 1.78024i) q^{13} +(-5.22569 - 3.24393i) q^{14} +(2.42519 - 3.18095i) q^{16} +5.78176i q^{17} +(1.92883 + 0.798948i) q^{19} +(-2.23926 + 2.56139i) q^{20} +(-3.32016 + 2.38309i) q^{22} +(-0.525810 - 0.525810i) q^{23} +(-1.48934 + 1.48934i) q^{25} +(1.06664 - 6.49187i) q^{26} +(-2.78322 + 8.24109i) q^{28} +(1.72922 - 4.17470i) q^{29} +6.80754 q^{31} +(-5.16164 - 2.31462i) q^{32} +(7.96160 - 1.86290i) q^{34} +(2.83125 - 6.83525i) q^{35} +(-1.09955 + 0.455448i) q^{37} +(0.478693 - 2.91346i) q^{38} +(4.24858 + 2.25822i) q^{40} +(-7.20426 - 7.20426i) q^{41} +(0.960366 + 2.31853i) q^{43} +(4.35133 + 3.80409i) q^{44} +(-0.554634 + 0.893469i) q^{46} -5.24257i q^{47} -11.9155i q^{49} +(2.53072 + 1.57099i) q^{50} +(-9.28311 + 0.622911i) q^{52} +(-0.00485782 - 0.0117278i) q^{53} +(-3.47611 - 3.47611i) q^{55} +(12.2449 + 1.17726i) q^{56} +(-6.30580 - 1.03607i) q^{58} +(-8.86095 + 3.67033i) q^{59} +(0.439229 - 1.06039i) q^{61} +(-2.19341 - 9.37412i) q^{62} +(-1.52419 + 7.85346i) q^{64} +7.91352 q^{65} +(-1.17849 + 2.84512i) q^{67} +(-5.13049 - 10.3631i) q^{68} +(-10.3245 - 1.69636i) q^{70} +(7.54709 - 7.54709i) q^{71} +(-9.04188 - 9.04188i) q^{73} +(0.981439 + 1.36735i) q^{74} +(-4.16613 + 0.279554i) q^{76} +(-11.6118 - 4.80978i) q^{77} -8.85007i q^{79} +(1.74071 - 6.57799i) q^{80} +(-7.59918 + 12.2416i) q^{82} +(13.0846 + 5.41983i) q^{83} +(3.76383 + 9.08669i) q^{85} +(2.88323 - 2.06948i) q^{86} +(3.83630 - 7.21756i) q^{88} +(-12.4152 + 12.4152i) q^{89} +(18.6923 - 7.74261i) q^{91} +(1.40903 + 0.475865i) q^{92} +(-7.21913 + 1.68917i) q^{94} +3.55148 q^{95} +9.47707 q^{97} +(-16.4078 + 3.83919i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 128 q+O(q^{10}) \) Copy content Toggle raw display \( 128 q + 16 q^{10} - 32 q^{16} - 16 q^{22} - 32 q^{40} - 32 q^{46} - 80 q^{52} + 32 q^{55} - 32 q^{58} + 64 q^{61} + 48 q^{64} + 64 q^{67} - 96 q^{70} + 32 q^{76} - 80 q^{82} - 80 q^{88} + 96 q^{91} - 48 q^{94}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/864\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(353\) \(703\)
\(\chi(n)\) \(e\left(\frac{7}{8}\right)\) \(1\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.322202 1.37702i −0.227832 0.973701i
\(3\) 0 0
\(4\) −1.79237 + 0.887359i −0.896186 + 0.443679i
\(5\) 1.57161 0.650984i 0.702847 0.291129i −0.00249383 0.999997i \(-0.500794\pi\)
0.705341 + 0.708868i \(0.250794\pi\)
\(6\) 0 0
\(7\) 3.07534 3.07534i 1.16237 1.16237i 0.178415 0.983955i \(-0.442903\pi\)
0.983955 0.178415i \(-0.0570969\pi\)
\(8\) 1.79942 + 2.18222i 0.636190 + 0.771532i
\(9\) 0 0
\(10\) −1.40280 1.95440i −0.443603 0.618035i
\(11\) −1.10590 2.66989i −0.333442 0.805001i −0.998314 0.0580432i \(-0.981514\pi\)
0.664872 0.746957i \(-0.268486\pi\)
\(12\) 0 0
\(13\) 4.29788 + 1.78024i 1.19202 + 0.493750i 0.888412 0.459047i \(-0.151809\pi\)
0.303606 + 0.952798i \(0.401809\pi\)
\(14\) −5.22569 3.24393i −1.39663 0.866976i
\(15\) 0 0
\(16\) 2.42519 3.18095i 0.606297 0.795238i
\(17\) 5.78176i 1.40228i 0.713022 + 0.701141i \(0.247326\pi\)
−0.713022 + 0.701141i \(0.752674\pi\)
\(18\) 0 0
\(19\) 1.92883 + 0.798948i 0.442504 + 0.183291i 0.592800 0.805350i \(-0.298023\pi\)
−0.150296 + 0.988641i \(0.548023\pi\)
\(20\) −2.23926 + 2.56139i −0.500714 + 0.572744i
\(21\) 0 0
\(22\) −3.32016 + 2.38309i −0.707861 + 0.508077i
\(23\) −0.525810 0.525810i −0.109639 0.109639i 0.650159 0.759798i \(-0.274702\pi\)
−0.759798 + 0.650159i \(0.774702\pi\)
\(24\) 0 0
\(25\) −1.48934 + 1.48934i −0.297868 + 0.297868i
\(26\) 1.06664 6.49187i 0.209185 1.27316i
\(27\) 0 0
\(28\) −2.78322 + 8.24109i −0.525980 + 1.55742i
\(29\) 1.72922 4.17470i 0.321107 0.775222i −0.678083 0.734985i \(-0.737189\pi\)
0.999190 0.0402362i \(-0.0128110\pi\)
\(30\) 0 0
\(31\) 6.80754 1.22267 0.611335 0.791372i \(-0.290633\pi\)
0.611335 + 0.791372i \(0.290633\pi\)
\(32\) −5.16164 2.31462i −0.912457 0.409172i
\(33\) 0 0
\(34\) 7.96160 1.86290i 1.36540 0.319484i
\(35\) 2.83125 6.83525i 0.478569 1.15537i
\(36\) 0 0
\(37\) −1.09955 + 0.455448i −0.180765 + 0.0748752i −0.471230 0.882010i \(-0.656190\pi\)
0.290465 + 0.956885i \(0.406190\pi\)
\(38\) 0.478693 2.91346i 0.0776543 0.472626i
\(39\) 0 0
\(40\) 4.24858 + 2.25822i 0.671760 + 0.357056i
\(41\) −7.20426 7.20426i −1.12512 1.12512i −0.990960 0.134156i \(-0.957168\pi\)
−0.134156 0.990960i \(-0.542832\pi\)
\(42\) 0 0
\(43\) 0.960366 + 2.31853i 0.146455 + 0.353572i 0.980035 0.198826i \(-0.0637128\pi\)
−0.833580 + 0.552398i \(0.813713\pi\)
\(44\) 4.35133 + 3.80409i 0.655988 + 0.573489i
\(45\) 0 0
\(46\) −0.554634 + 0.893469i −0.0817764 + 0.131735i
\(47\) 5.24257i 0.764708i −0.924016 0.382354i \(-0.875114\pi\)
0.924016 0.382354i \(-0.124886\pi\)
\(48\) 0 0
\(49\) 11.9155i 1.70221i
\(50\) 2.53072 + 1.57099i 0.357898 + 0.222171i
\(51\) 0 0
\(52\) −9.28311 + 0.622911i −1.28734 + 0.0863822i
\(53\) −0.00485782 0.0117278i −0.000667273 0.00161094i 0.923546 0.383489i \(-0.125278\pi\)
−0.924213 + 0.381878i \(0.875278\pi\)
\(54\) 0 0
\(55\) −3.47611 3.47611i −0.468718 0.468718i
\(56\) 12.2449 + 1.17726i 1.63629 + 0.157318i
\(57\) 0 0
\(58\) −6.30580 1.03607i −0.827992 0.136042i
\(59\) −8.86095 + 3.67033i −1.15360 + 0.477836i −0.875738 0.482786i \(-0.839625\pi\)
−0.277859 + 0.960622i \(0.589625\pi\)
\(60\) 0 0
\(61\) 0.439229 1.06039i 0.0562375 0.135769i −0.893263 0.449534i \(-0.851590\pi\)
0.949501 + 0.313764i \(0.101590\pi\)
\(62\) −2.19341 9.37412i −0.278563 1.19051i
\(63\) 0 0
\(64\) −1.52419 + 7.85346i −0.190524 + 0.981683i
\(65\) 7.91352 0.981552
\(66\) 0 0
\(67\) −1.17849 + 2.84512i −0.143975 + 0.347587i −0.979374 0.202058i \(-0.935237\pi\)
0.835398 + 0.549645i \(0.185237\pi\)
\(68\) −5.13049 10.3631i −0.622164 1.25671i
\(69\) 0 0
\(70\) −10.3245 1.69636i −1.23402 0.202754i
\(71\) 7.54709 7.54709i 0.895675 0.895675i −0.0993754 0.995050i \(-0.531684\pi\)
0.995050 + 0.0993754i \(0.0316845\pi\)
\(72\) 0 0
\(73\) −9.04188 9.04188i −1.05827 1.05827i −0.998194 0.0600782i \(-0.980865\pi\)
−0.0600782 0.998194i \(-0.519135\pi\)
\(74\) 0.981439 + 1.36735i 0.114090 + 0.158952i
\(75\) 0 0
\(76\) −4.16613 + 0.279554i −0.477888 + 0.0320670i
\(77\) −11.6118 4.80978i −1.32329 0.548126i
\(78\) 0 0
\(79\) 8.85007i 0.995711i −0.867260 0.497855i \(-0.834121\pi\)
0.867260 0.497855i \(-0.165879\pi\)
\(80\) 1.74071 6.57799i 0.194618 0.735442i
\(81\) 0 0
\(82\) −7.59918 + 12.2416i −0.839189 + 1.35186i
\(83\) 13.0846 + 5.41983i 1.43622 + 0.594903i 0.958880 0.283813i \(-0.0915997\pi\)
0.477344 + 0.878717i \(0.341600\pi\)
\(84\) 0 0
\(85\) 3.76383 + 9.08669i 0.408245 + 0.985590i
\(86\) 2.88323 2.06948i 0.310907 0.223158i
\(87\) 0 0
\(88\) 3.83630 7.21756i 0.408951 0.769395i
\(89\) −12.4152 + 12.4152i −1.31601 + 1.31601i −0.399108 + 0.916904i \(0.630680\pi\)
−0.916904 + 0.399108i \(0.869320\pi\)
\(90\) 0 0
\(91\) 18.6923 7.74261i 1.95949 0.811646i
\(92\) 1.40903 + 0.475865i 0.146901 + 0.0496123i
\(93\) 0 0
\(94\) −7.21913 + 1.68917i −0.744597 + 0.174225i
\(95\) 3.55148 0.364374
\(96\) 0 0
\(97\) 9.47707 0.962250 0.481125 0.876652i \(-0.340228\pi\)
0.481125 + 0.876652i \(0.340228\pi\)
\(98\) −16.4078 + 3.83919i −1.65744 + 0.387817i
\(99\) 0 0
\(100\) 1.34787 3.99103i 0.134787 0.399103i
\(101\) −15.7033 + 6.50453i −1.56254 + 0.647225i −0.985528 0.169511i \(-0.945781\pi\)
−0.577011 + 0.816736i \(0.695781\pi\)
\(102\) 0 0
\(103\) −9.78095 + 9.78095i −0.963746 + 0.963746i −0.999365 0.0356196i \(-0.988660\pi\)
0.0356196 + 0.999365i \(0.488660\pi\)
\(104\) 3.84880 + 12.5823i 0.377406 + 1.23380i
\(105\) 0 0
\(106\) −0.0145842 + 0.0104681i −0.00141655 + 0.00101675i
\(107\) −1.84303 4.44946i −0.178172 0.430145i 0.809411 0.587242i \(-0.199786\pi\)
−0.987583 + 0.157097i \(0.949786\pi\)
\(108\) 0 0
\(109\) 14.1918 + 5.87844i 1.35933 + 0.563052i 0.938874 0.344262i \(-0.111871\pi\)
0.420454 + 0.907314i \(0.361871\pi\)
\(110\) −3.66666 + 5.90668i −0.349602 + 0.563180i
\(111\) 0 0
\(112\) −2.32423 17.2408i −0.219619 1.62910i
\(113\) 13.1265i 1.23483i 0.786636 + 0.617417i \(0.211821\pi\)
−0.786636 + 0.617417i \(0.788179\pi\)
\(114\) 0 0
\(115\) −1.16867 0.484077i −0.108979 0.0451404i
\(116\) 0.605057 + 9.01704i 0.0561781 + 0.837211i
\(117\) 0 0
\(118\) 7.90913 + 11.0191i 0.728095 + 1.01439i
\(119\) 17.7809 + 17.7809i 1.62997 + 1.62997i
\(120\) 0 0
\(121\) 1.87291 1.87291i 0.170264 0.170264i
\(122\) −1.60170 0.263166i −0.145011 0.0238259i
\(123\) 0 0
\(124\) −12.2016 + 6.04073i −1.09574 + 0.542474i
\(125\) −4.62605 + 11.1683i −0.413767 + 0.998921i
\(126\) 0 0
\(127\) −16.0709 −1.42607 −0.713033 0.701131i \(-0.752679\pi\)
−0.713033 + 0.701131i \(0.752679\pi\)
\(128\) 11.3055 0.431559i 0.999272 0.0381448i
\(129\) 0 0
\(130\) −2.54976 10.8971i −0.223628 0.955738i
\(131\) 3.38930 8.18249i 0.296124 0.714907i −0.703865 0.710333i \(-0.748544\pi\)
0.999990 0.00457365i \(-0.00145584\pi\)
\(132\) 0 0
\(133\) 8.38885 3.47478i 0.727406 0.301301i
\(134\) 4.29750 + 0.706097i 0.371248 + 0.0609975i
\(135\) 0 0
\(136\) −12.6171 + 10.4038i −1.08191 + 0.892118i
\(137\) −9.96122 9.96122i −0.851044 0.851044i 0.139218 0.990262i \(-0.455541\pi\)
−0.990262 + 0.139218i \(0.955541\pi\)
\(138\) 0 0
\(139\) 1.78163 + 4.30123i 0.151116 + 0.364826i 0.981250 0.192737i \(-0.0617365\pi\)
−0.830135 + 0.557563i \(0.811737\pi\)
\(140\) 0.990662 + 14.7636i 0.0837263 + 1.24776i
\(141\) 0 0
\(142\) −12.8242 7.96081i −1.07618 0.668056i
\(143\) 13.4436i 1.12421i
\(144\) 0 0
\(145\) 7.68670i 0.638346i
\(146\) −9.53754 + 15.3642i −0.789332 + 1.27155i
\(147\) 0 0
\(148\) 1.56665 1.79203i 0.128778 0.147304i
\(149\) 4.12035 + 9.94741i 0.337552 + 0.814923i 0.997949 + 0.0640068i \(0.0203879\pi\)
−0.660397 + 0.750916i \(0.729612\pi\)
\(150\) 0 0
\(151\) 3.44757 + 3.44757i 0.280559 + 0.280559i 0.833332 0.552773i \(-0.186430\pi\)
−0.552773 + 0.833332i \(0.686430\pi\)
\(152\) 1.72729 + 5.64678i 0.140102 + 0.458014i
\(153\) 0 0
\(154\) −2.88181 + 17.5395i −0.232222 + 1.41337i
\(155\) 10.6988 4.43160i 0.859351 0.355955i
\(156\) 0 0
\(157\) −6.79910 + 16.4145i −0.542627 + 1.31002i 0.380236 + 0.924890i \(0.375843\pi\)
−0.922863 + 0.385129i \(0.874157\pi\)
\(158\) −12.1867 + 2.85151i −0.969524 + 0.226854i
\(159\) 0 0
\(160\) −9.61889 0.277553i −0.760440 0.0219425i
\(161\) −3.23409 −0.254882
\(162\) 0 0
\(163\) 7.18090 17.3362i 0.562452 1.35788i −0.345348 0.938475i \(-0.612239\pi\)
0.907800 0.419404i \(-0.137761\pi\)
\(164\) 19.3055 + 6.51994i 1.50750 + 0.509122i
\(165\) 0 0
\(166\) 3.24732 19.7641i 0.252041 1.53399i
\(167\) 6.69386 6.69386i 0.517986 0.517986i −0.398975 0.916962i \(-0.630634\pi\)
0.916962 + 0.398975i \(0.130634\pi\)
\(168\) 0 0
\(169\) 6.11015 + 6.11015i 0.470012 + 0.470012i
\(170\) 11.2998 8.11063i 0.866659 0.622057i
\(171\) 0 0
\(172\) −3.77870 3.30348i −0.288123 0.251888i
\(173\) 12.5160 + 5.18430i 0.951575 + 0.394155i 0.803822 0.594869i \(-0.202796\pi\)
0.147752 + 0.989024i \(0.452796\pi\)
\(174\) 0 0
\(175\) 9.16047i 0.692467i
\(176\) −11.1748 2.95715i −0.842332 0.222904i
\(177\) 0 0
\(178\) 21.0962 + 13.0958i 1.58123 + 0.981573i
\(179\) 8.07265 + 3.34380i 0.603378 + 0.249928i 0.663394 0.748270i \(-0.269115\pi\)
−0.0600160 + 0.998197i \(0.519115\pi\)
\(180\) 0 0
\(181\) −2.61334 6.30916i −0.194248 0.468956i 0.796505 0.604631i \(-0.206680\pi\)
−0.990753 + 0.135675i \(0.956680\pi\)
\(182\) −16.6844 23.2450i −1.23673 1.72304i
\(183\) 0 0
\(184\) 0.201283 2.09359i 0.0148388 0.154341i
\(185\) −1.43158 + 1.43158i −0.105252 + 0.105252i
\(186\) 0 0
\(187\) 15.4366 6.39406i 1.12884 0.467580i
\(188\) 4.65204 + 9.39664i 0.339285 + 0.685320i
\(189\) 0 0
\(190\) −1.14430 4.89046i −0.0830159 0.354791i
\(191\) −3.99365 −0.288970 −0.144485 0.989507i \(-0.546153\pi\)
−0.144485 + 0.989507i \(0.546153\pi\)
\(192\) 0 0
\(193\) 2.43219 0.175073 0.0875366 0.996161i \(-0.472101\pi\)
0.0875366 + 0.996161i \(0.472101\pi\)
\(194\) −3.05353 13.0501i −0.219231 0.936944i
\(195\) 0 0
\(196\) 10.5733 + 21.3569i 0.755235 + 1.52550i
\(197\) 10.1588 4.20791i 0.723783 0.299801i 0.00978883 0.999952i \(-0.496884\pi\)
0.713995 + 0.700151i \(0.246884\pi\)
\(198\) 0 0
\(199\) −10.5481 + 10.5481i −0.747737 + 0.747737i −0.974054 0.226316i \(-0.927332\pi\)
0.226316 + 0.974054i \(0.427332\pi\)
\(200\) −5.93002 0.570128i −0.419316 0.0403141i
\(201\) 0 0
\(202\) 14.0165 + 19.5280i 0.986199 + 1.37399i
\(203\) −7.52069 18.1566i −0.527849 1.27434i
\(204\) 0 0
\(205\) −16.0122 6.63246i −1.11834 0.463231i
\(206\) 16.6200 + 10.3171i 1.15797 + 0.718828i
\(207\) 0 0
\(208\) 16.0860 9.35394i 1.11537 0.648579i
\(209\) 6.03331i 0.417333i
\(210\) 0 0
\(211\) 9.72448 + 4.02801i 0.669461 + 0.277300i 0.691414 0.722459i \(-0.256988\pi\)
−0.0219526 + 0.999759i \(0.506988\pi\)
\(212\) 0.0191138 + 0.0167100i 0.00131274 + 0.00114765i
\(213\) 0 0
\(214\) −5.53317 + 3.97151i −0.378240 + 0.271487i
\(215\) 3.01865 + 3.01865i 0.205870 + 0.205870i
\(216\) 0 0
\(217\) 20.9355 20.9355i 1.42120 1.42120i
\(218\) 3.52209 21.4364i 0.238546 1.45186i
\(219\) 0 0
\(220\) 9.31502 + 3.14592i 0.628019 + 0.212098i
\(221\) −10.2929 + 24.8493i −0.692377 + 1.67155i
\(222\) 0 0
\(223\) −22.9813 −1.53894 −0.769470 0.638683i \(-0.779480\pi\)
−0.769470 + 0.638683i \(0.779480\pi\)
\(224\) −22.9921 + 8.75554i −1.53622 + 0.585004i
\(225\) 0 0
\(226\) 18.0754 4.22938i 1.20236 0.281334i
\(227\) −11.4882 + 27.7350i −0.762500 + 1.84084i −0.301355 + 0.953512i \(0.597439\pi\)
−0.461145 + 0.887325i \(0.652561\pi\)
\(228\) 0 0
\(229\) −17.5270 + 7.25994i −1.15822 + 0.479750i −0.877282 0.479976i \(-0.840646\pi\)
−0.280938 + 0.959726i \(0.590646\pi\)
\(230\) −0.290037 + 1.76525i −0.0191245 + 0.116397i
\(231\) 0 0
\(232\) 12.2217 3.73849i 0.802394 0.245444i
\(233\) 12.2771 + 12.2771i 0.804300 + 0.804300i 0.983764 0.179464i \(-0.0574364\pi\)
−0.179464 + 0.983764i \(0.557436\pi\)
\(234\) 0 0
\(235\) −3.41283 8.23930i −0.222629 0.537473i
\(236\) 12.6252 14.4414i 0.821832 0.940057i
\(237\) 0 0
\(238\) 18.7556 30.2137i 1.21575 1.95846i
\(239\) 18.7789i 1.21470i 0.794433 + 0.607351i \(0.207768\pi\)
−0.794433 + 0.607351i \(0.792232\pi\)
\(240\) 0 0
\(241\) 5.58803i 0.359956i 0.983671 + 0.179978i \(0.0576027\pi\)
−0.983671 + 0.179978i \(0.942397\pi\)
\(242\) −3.18249 1.97558i −0.204578 0.126995i
\(243\) 0 0
\(244\) 0.153687 + 2.29037i 0.00983881 + 0.146626i
\(245\) −7.75678 18.7265i −0.495562 1.19639i
\(246\) 0 0
\(247\) 6.86757 + 6.86757i 0.436973 + 0.436973i
\(248\) 12.2496 + 14.8556i 0.777851 + 0.943330i
\(249\) 0 0
\(250\) 16.8695 + 2.77172i 1.06692 + 0.175299i
\(251\) 12.1377 5.02760i 0.766125 0.317339i 0.0348230 0.999393i \(-0.488913\pi\)
0.731302 + 0.682054i \(0.238913\pi\)
\(252\) 0 0
\(253\) −0.822358 + 1.98535i −0.0517012 + 0.124818i
\(254\) 5.17810 + 22.1300i 0.324903 + 1.38856i
\(255\) 0 0
\(256\) −4.23692 15.4288i −0.264807 0.964301i
\(257\) 18.1239 1.13054 0.565268 0.824907i \(-0.308773\pi\)
0.565268 + 0.824907i \(0.308773\pi\)
\(258\) 0 0
\(259\) −1.98083 + 4.78215i −0.123083 + 0.297148i
\(260\) −14.1840 + 7.02213i −0.879653 + 0.435494i
\(261\) 0 0
\(262\) −12.3595 2.03071i −0.763572 0.125458i
\(263\) 3.62779 3.62779i 0.223699 0.223699i −0.586355 0.810054i \(-0.699438\pi\)
0.810054 + 0.586355i \(0.199438\pi\)
\(264\) 0 0
\(265\) −0.0152692 0.0152692i −0.000937982 0.000937982i
\(266\) −7.48775 10.4320i −0.459103 0.639629i
\(267\) 0 0
\(268\) −0.412356 6.14526i −0.0251886 0.375381i
\(269\) 12.7398 + 5.27701i 0.776761 + 0.321745i 0.735607 0.677408i \(-0.236897\pi\)
0.0411532 + 0.999153i \(0.486897\pi\)
\(270\) 0 0
\(271\) 17.2728i 1.04925i −0.851335 0.524623i \(-0.824206\pi\)
0.851335 0.524623i \(-0.175794\pi\)
\(272\) 18.3915 + 14.0219i 1.11515 + 0.850200i
\(273\) 0 0
\(274\) −10.5073 + 16.9263i −0.634768 + 1.02256i
\(275\) 5.62344 + 2.32931i 0.339106 + 0.140462i
\(276\) 0 0
\(277\) 0.284800 + 0.687567i 0.0171119 + 0.0413119i 0.932205 0.361932i \(-0.117883\pi\)
−0.915093 + 0.403244i \(0.867883\pi\)
\(278\) 5.34884 3.83921i 0.320802 0.230260i
\(279\) 0 0
\(280\) 20.0107 6.12105i 1.19587 0.365802i
\(281\) −12.6479 + 12.6479i −0.754513 + 0.754513i −0.975318 0.220805i \(-0.929131\pi\)
0.220805 + 0.975318i \(0.429131\pi\)
\(282\) 0 0
\(283\) −4.05155 + 1.67821i −0.240840 + 0.0997591i −0.499839 0.866118i \(-0.666607\pi\)
0.258999 + 0.965878i \(0.416607\pi\)
\(284\) −6.83021 + 20.2242i −0.405298 + 1.20008i
\(285\) 0 0
\(286\) −18.5122 + 4.33157i −1.09465 + 0.256131i
\(287\) −44.3111 −2.61560
\(288\) 0 0
\(289\) −16.4287 −0.966396
\(290\) −10.5848 + 2.47667i −0.621558 + 0.145435i
\(291\) 0 0
\(292\) 24.2298 + 8.18301i 1.41794 + 0.478875i
\(293\) 0.690177 0.285881i 0.0403206 0.0167013i −0.362432 0.932010i \(-0.618054\pi\)
0.402753 + 0.915309i \(0.368054\pi\)
\(294\) 0 0
\(295\) −11.5367 + 11.5367i −0.671691 + 0.671691i
\(296\) −2.97244 1.57992i −0.172769 0.0918309i
\(297\) 0 0
\(298\) 12.3702 8.87889i 0.716586 0.514340i
\(299\) −1.32380 3.19594i −0.0765574 0.184826i
\(300\) 0 0
\(301\) 10.0837 + 4.17682i 0.581217 + 0.240748i
\(302\) 3.63656 5.85819i 0.209261 0.337101i
\(303\) 0 0
\(304\) 7.21919 4.19792i 0.414049 0.240767i
\(305\) 1.95246i 0.111797i
\(306\) 0 0
\(307\) 5.14989 + 2.13316i 0.293920 + 0.121746i 0.524771 0.851243i \(-0.324151\pi\)
−0.230851 + 0.972989i \(0.574151\pi\)
\(308\) 25.0807 1.68295i 1.42911 0.0958952i
\(309\) 0 0
\(310\) −9.54959 13.3046i −0.542380 0.755652i
\(311\) −22.2089 22.2089i −1.25935 1.25935i −0.951404 0.307945i \(-0.900359\pi\)
−0.307945 0.951404i \(-0.599641\pi\)
\(312\) 0 0
\(313\) −19.6341 + 19.6341i −1.10978 + 1.10978i −0.116607 + 0.993178i \(0.537202\pi\)
−0.993178 + 0.116607i \(0.962798\pi\)
\(314\) 24.7938 + 4.07372i 1.39919 + 0.229893i
\(315\) 0 0
\(316\) 7.85319 + 15.8626i 0.441776 + 0.892342i
\(317\) −3.77085 + 9.10363i −0.211792 + 0.511311i −0.993699 0.112085i \(-0.964247\pi\)
0.781907 + 0.623395i \(0.214247\pi\)
\(318\) 0 0
\(319\) −13.0583 −0.731125
\(320\) 2.71703 + 13.3348i 0.151887 + 0.745440i
\(321\) 0 0
\(322\) 1.04203 + 4.45341i 0.0580702 + 0.248179i
\(323\) −4.61932 + 11.1520i −0.257026 + 0.620515i
\(324\) 0 0
\(325\) −9.05241 + 3.74963i −0.502137 + 0.207992i
\(326\) −26.1861 4.30247i −1.45031 0.238292i
\(327\) 0 0
\(328\) 2.75783 28.6848i 0.152276 1.58385i
\(329\) −16.1227 16.1227i −0.888874 0.888874i
\(330\) 0 0
\(331\) 8.74068 + 21.1019i 0.480431 + 1.15986i 0.959404 + 0.282034i \(0.0910090\pi\)
−0.478973 + 0.877829i \(0.658991\pi\)
\(332\) −28.2618 + 1.89641i −1.55107 + 0.104079i
\(333\) 0 0
\(334\) −11.3744 7.06080i −0.622377 0.386350i
\(335\) 5.23861i 0.286216i
\(336\) 0 0
\(337\) 8.93510i 0.486726i −0.969935 0.243363i \(-0.921749\pi\)
0.969935 0.243363i \(-0.0782506\pi\)
\(338\) 6.44510 10.3825i 0.350567 0.564734i
\(339\) 0 0
\(340\) −14.8093 12.9469i −0.803149 0.702142i
\(341\) −7.52848 18.1753i −0.407690 0.984250i
\(342\) 0 0
\(343\) −15.1167 15.1167i −0.816227 0.816227i
\(344\) −3.33145 + 6.26774i −0.179620 + 0.337934i
\(345\) 0 0
\(346\) 3.10620 18.9052i 0.166990 1.01635i
\(347\) 24.5023 10.1492i 1.31535 0.544838i 0.388912 0.921275i \(-0.372851\pi\)
0.926442 + 0.376437i \(0.122851\pi\)
\(348\) 0 0
\(349\) −6.18100 + 14.9223i −0.330861 + 0.798770i 0.667663 + 0.744464i \(0.267295\pi\)
−0.998524 + 0.0543063i \(0.982705\pi\)
\(350\) 12.6142 2.95153i 0.674255 0.157766i
\(351\) 0 0
\(352\) −0.471511 + 16.3407i −0.0251316 + 0.870964i
\(353\) −4.43676 −0.236145 −0.118072 0.993005i \(-0.537671\pi\)
−0.118072 + 0.993005i \(0.537671\pi\)
\(354\) 0 0
\(355\) 6.94808 16.7741i 0.368766 0.890279i
\(356\) 11.2359 33.2695i 0.595504 1.76328i
\(357\) 0 0
\(358\) 2.00346 12.1936i 0.105886 0.644451i
\(359\) 15.5906 15.5906i 0.822841 0.822841i −0.163674 0.986515i \(-0.552334\pi\)
0.986515 + 0.163674i \(0.0523344\pi\)
\(360\) 0 0
\(361\) −10.3530 10.3530i −0.544893 0.544893i
\(362\) −7.84582 + 5.63145i −0.412367 + 0.295982i
\(363\) 0 0
\(364\) −26.6331 + 30.4644i −1.39595 + 1.59677i
\(365\) −20.0965 8.32423i −1.05190 0.435710i
\(366\) 0 0
\(367\) 26.8476i 1.40143i 0.713440 + 0.700717i \(0.247136\pi\)
−0.713440 + 0.700717i \(0.752864\pi\)
\(368\) −2.94777 + 0.397388i −0.153663 + 0.0207153i
\(369\) 0 0
\(370\) 2.43257 + 1.51005i 0.126463 + 0.0785040i
\(371\) −0.0510065 0.0211276i −0.00264813 0.00109689i
\(372\) 0 0
\(373\) 8.30515 + 20.0504i 0.430024 + 1.03817i 0.979279 + 0.202515i \(0.0649116\pi\)
−0.549255 + 0.835655i \(0.685088\pi\)
\(374\) −13.7785 19.1964i −0.712468 0.992621i
\(375\) 0 0
\(376\) 11.4405 9.43358i 0.589997 0.486500i
\(377\) 14.8639 14.8639i 0.765532 0.765532i
\(378\) 0 0
\(379\) −13.2366 + 5.48277i −0.679917 + 0.281631i −0.695792 0.718243i \(-0.744947\pi\)
0.0158750 + 0.999874i \(0.494947\pi\)
\(380\) −6.36557 + 3.15144i −0.326547 + 0.161665i
\(381\) 0 0
\(382\) 1.28676 + 5.49934i 0.0658366 + 0.281371i
\(383\) 12.0126 0.613816 0.306908 0.951739i \(-0.400706\pi\)
0.306908 + 0.951739i \(0.400706\pi\)
\(384\) 0 0
\(385\) −21.3804 −1.08965
\(386\) −0.783659 3.34918i −0.0398872 0.170469i
\(387\) 0 0
\(388\) −16.9864 + 8.40956i −0.862355 + 0.426931i
\(389\) 24.5778 10.1804i 1.24614 0.516169i 0.340513 0.940240i \(-0.389399\pi\)
0.905629 + 0.424071i \(0.139399\pi\)
\(390\) 0 0
\(391\) 3.04011 3.04011i 0.153745 0.153745i
\(392\) 26.0022 21.4409i 1.31331 1.08293i
\(393\) 0 0
\(394\) −9.06756 12.6331i −0.456817 0.636444i
\(395\) −5.76125 13.9089i −0.289880 0.699833i
\(396\) 0 0
\(397\) −8.40317 3.48071i −0.421743 0.174692i 0.161710 0.986838i \(-0.448299\pi\)
−0.583453 + 0.812147i \(0.698299\pi\)
\(398\) 17.9236 + 11.1264i 0.898430 + 0.557714i
\(399\) 0 0
\(400\) 1.12559 + 8.34946i 0.0562795 + 0.417473i
\(401\) 19.5746i 0.977508i 0.872422 + 0.488754i \(0.162548\pi\)
−0.872422 + 0.488754i \(0.837452\pi\)
\(402\) 0 0
\(403\) 29.2580 + 12.1191i 1.45745 + 0.603694i
\(404\) 22.3743 25.5930i 1.11316 1.27330i
\(405\) 0 0
\(406\) −22.5788 + 16.2062i −1.12057 + 0.804302i
\(407\) 2.43199 + 2.43199i 0.120549 + 0.120549i
\(408\) 0 0
\(409\) 6.92958 6.92958i 0.342645 0.342645i −0.514716 0.857361i \(-0.672102\pi\)
0.857361 + 0.514716i \(0.172102\pi\)
\(410\) −3.97387 + 24.1861i −0.196256 + 1.19447i
\(411\) 0 0
\(412\) 8.85188 26.2103i 0.436101 1.29129i
\(413\) −15.9629 + 38.5380i −0.785485 + 1.89633i
\(414\) 0 0
\(415\) 24.0922 1.18264
\(416\) −18.0635 19.1369i −0.885637 0.938266i
\(417\) 0 0
\(418\) −8.30800 + 1.94395i −0.406357 + 0.0950816i
\(419\) −2.24489 + 5.41965i −0.109670 + 0.264767i −0.969181 0.246351i \(-0.920768\pi\)
0.859511 + 0.511118i \(0.170768\pi\)
\(420\) 0 0
\(421\) 0.0698584 0.0289363i 0.00340469 0.00141027i −0.380980 0.924583i \(-0.624413\pi\)
0.384385 + 0.923173i \(0.374413\pi\)
\(422\) 2.41340 14.6886i 0.117483 0.715032i
\(423\) 0 0
\(424\) 0.0168515 0.0317041i 0.000818379 0.00153969i
\(425\) −8.61102 8.61102i −0.417696 0.417696i
\(426\) 0 0
\(427\) −1.91029 4.61185i −0.0924454 0.223183i
\(428\) 7.25165 + 6.33966i 0.350522 + 0.306439i
\(429\) 0 0
\(430\) 3.18413 5.12936i 0.153552 0.247360i
\(431\) 3.28812i 0.158383i −0.996859 0.0791915i \(-0.974766\pi\)
0.996859 0.0791915i \(-0.0252339\pi\)
\(432\) 0 0
\(433\) 21.9752i 1.05606i −0.849225 0.528031i \(-0.822930\pi\)
0.849225 0.528031i \(-0.177070\pi\)
\(434\) −35.5741 22.0832i −1.70761 1.06003i
\(435\) 0 0
\(436\) −30.6533 + 2.05688i −1.46802 + 0.0985066i
\(437\) −0.594104 1.43429i −0.0284198 0.0686116i
\(438\) 0 0
\(439\) −23.5627 23.5627i −1.12459 1.12459i −0.991043 0.133544i \(-0.957364\pi\)
−0.133544 0.991043i \(-0.542636\pi\)
\(440\) 1.33067 13.8406i 0.0634373 0.659825i
\(441\) 0 0
\(442\) 37.5344 + 6.16706i 1.78533 + 0.293337i
\(443\) 10.4663 4.33528i 0.497268 0.205975i −0.119931 0.992782i \(-0.538267\pi\)
0.617199 + 0.786807i \(0.288267\pi\)
\(444\) 0 0
\(445\) −11.4298 + 27.5941i −0.541826 + 1.30808i
\(446\) 7.40462 + 31.6457i 0.350619 + 1.49847i
\(447\) 0 0
\(448\) 19.4647 + 28.8395i 0.919619 + 1.36254i
\(449\) −1.27254 −0.0600548 −0.0300274 0.999549i \(-0.509559\pi\)
−0.0300274 + 0.999549i \(0.509559\pi\)
\(450\) 0 0
\(451\) −11.2673 + 27.2017i −0.530558 + 1.28088i
\(452\) −11.6479 23.5275i −0.547870 1.10664i
\(453\) 0 0
\(454\) 41.8932 + 6.88322i 1.96615 + 0.323046i
\(455\) 24.3368 24.3368i 1.14093 1.14093i
\(456\) 0 0
\(457\) −15.8452 15.8452i −0.741205 0.741205i 0.231605 0.972810i \(-0.425602\pi\)
−0.972810 + 0.231605i \(0.925602\pi\)
\(458\) 15.6443 + 21.7959i 0.731012 + 1.01846i
\(459\) 0 0
\(460\) 2.52423 0.169380i 0.117693 0.00789737i
\(461\) −24.1001 9.98258i −1.12245 0.464935i −0.257244 0.966347i \(-0.582814\pi\)
−0.865209 + 0.501411i \(0.832814\pi\)
\(462\) 0 0
\(463\) 6.51158i 0.302619i 0.988486 + 0.151309i \(0.0483490\pi\)
−0.988486 + 0.151309i \(0.951651\pi\)
\(464\) −9.08584 15.6250i −0.421799 0.725371i
\(465\) 0 0
\(466\) 12.9501 20.8615i 0.599903 0.966393i
\(467\) 0.271505 + 0.112461i 0.0125637 + 0.00520407i 0.388956 0.921256i \(-0.372836\pi\)
−0.376393 + 0.926460i \(0.622836\pi\)
\(468\) 0 0
\(469\) 5.12547 + 12.3740i 0.236672 + 0.571377i
\(470\) −10.2461 + 7.35426i −0.472616 + 0.339227i
\(471\) 0 0
\(472\) −23.9540 12.7321i −1.10257 0.586043i
\(473\) 5.12814 5.12814i 0.235792 0.235792i
\(474\) 0 0
\(475\) −4.06259 + 1.68278i −0.186405 + 0.0772113i
\(476\) −47.6480 16.0919i −2.18394 0.737572i
\(477\) 0 0
\(478\) 25.8589 6.05059i 1.18276 0.276748i
\(479\) −13.5118 −0.617369 −0.308685 0.951164i \(-0.599889\pi\)
−0.308685 + 0.951164i \(0.599889\pi\)
\(480\) 0 0
\(481\) −5.53654 −0.252444
\(482\) 7.69483 1.80048i 0.350490 0.0820094i
\(483\) 0 0
\(484\) −1.69501 + 5.01889i −0.0770457 + 0.228131i
\(485\) 14.8943 6.16942i 0.676315 0.280139i
\(486\) 0 0
\(487\) 1.42751 1.42751i 0.0646866 0.0646866i −0.674023 0.738710i \(-0.735435\pi\)
0.738710 + 0.674023i \(0.235435\pi\)
\(488\) 3.10437 0.949593i 0.140528 0.0429860i
\(489\) 0 0
\(490\) −23.2875 + 16.7150i −1.05202 + 0.755105i
\(491\) 0.0538443 + 0.129992i 0.00242996 + 0.00586645i 0.925090 0.379748i \(-0.123989\pi\)
−0.922660 + 0.385615i \(0.873989\pi\)
\(492\) 0 0
\(493\) 24.1371 + 9.99791i 1.08708 + 0.450283i
\(494\) 7.24403 11.6695i 0.325924 0.525037i
\(495\) 0 0
\(496\) 16.5096 21.6545i 0.741302 0.972314i
\(497\) 46.4198i 2.08221i
\(498\) 0 0
\(499\) −31.1157 12.8885i −1.39293 0.576970i −0.445023 0.895519i \(-0.646804\pi\)
−0.947906 + 0.318549i \(0.896804\pi\)
\(500\) −1.61867 24.1227i −0.0723890 1.07880i
\(501\) 0 0
\(502\) −10.8339 15.0940i −0.483541 0.673676i
\(503\) −2.25575 2.25575i −0.100579 0.100579i 0.655027 0.755606i \(-0.272657\pi\)
−0.755606 + 0.655027i \(0.772657\pi\)
\(504\) 0 0
\(505\) −20.4452 + 20.4452i −0.909801 + 0.909801i
\(506\) 2.99883 + 0.492720i 0.133314 + 0.0219041i
\(507\) 0 0
\(508\) 28.8051 14.2607i 1.27802 0.632716i
\(509\) 0.0379139 0.0915322i 0.00168050 0.00405709i −0.923037 0.384711i \(-0.874301\pi\)
0.924718 + 0.380654i \(0.124301\pi\)
\(510\) 0 0
\(511\) −55.6137 −2.46021
\(512\) −19.8807 + 10.8055i −0.878609 + 0.477541i
\(513\) 0 0
\(514\) −5.83956 24.9570i −0.257572 1.10080i
\(515\) −9.00464 + 21.7391i −0.396792 + 0.957940i
\(516\) 0 0
\(517\) −13.9971 + 5.79778i −0.615590 + 0.254986i
\(518\) 7.22334 + 1.18682i 0.317376 + 0.0521461i
\(519\) 0 0
\(520\) 14.2397 + 17.2691i 0.624454 + 0.757299i
\(521\) −6.98279 6.98279i −0.305922 0.305922i 0.537403 0.843325i \(-0.319405\pi\)
−0.843325 + 0.537403i \(0.819405\pi\)
\(522\) 0 0
\(523\) −8.43255 20.3580i −0.368730 0.890192i −0.993959 0.109751i \(-0.964995\pi\)
0.625229 0.780441i \(-0.285005\pi\)
\(524\) 1.18592 + 17.6736i 0.0518073 + 0.772074i
\(525\) 0 0
\(526\) −6.16443 3.82666i −0.268782 0.166850i
\(527\) 39.3595i 1.71453i
\(528\) 0 0
\(529\) 22.4470i 0.975959i
\(530\) −0.0161063 + 0.0259459i −0.000699612 + 0.00112702i
\(531\) 0 0
\(532\) −11.9526 + 13.6720i −0.518209 + 0.592757i
\(533\) −18.1377 43.7884i −0.785633 1.89668i
\(534\) 0 0
\(535\) −5.79305 5.79305i −0.250456 0.250456i
\(536\) −8.32928 + 2.54784i −0.359770 + 0.110050i
\(537\) 0 0
\(538\) 3.16175 19.2433i 0.136313 0.829636i
\(539\) −31.8129 + 13.1773i −1.37028 + 0.567588i
\(540\) 0 0
\(541\) −3.66278 + 8.84273i −0.157475 + 0.380179i −0.982850 0.184406i \(-0.940964\pi\)
0.825375 + 0.564585i \(0.190964\pi\)
\(542\) −23.7850 + 5.56533i −1.02165 + 0.239051i
\(543\) 0 0
\(544\) 13.3826 29.8433i 0.573774 1.27952i
\(545\) 26.1308 1.11932
\(546\) 0 0
\(547\) 16.0012 38.6303i 0.684162 1.65171i −0.0720628 0.997400i \(-0.522958\pi\)
0.756224 0.654312i \(-0.227042\pi\)
\(548\) 26.6934 + 9.01503i 1.14028 + 0.385103i
\(549\) 0 0
\(550\) 1.39561 8.49410i 0.0595092 0.362190i
\(551\) 6.67073 6.67073i 0.284183 0.284183i
\(552\) 0 0
\(553\) −27.2170 27.2170i −1.15738 1.15738i
\(554\) 0.855031 0.613711i 0.0363268 0.0260741i
\(555\) 0 0
\(556\) −7.01007 6.12846i −0.297293 0.259905i
\(557\) 7.60439 + 3.14984i 0.322209 + 0.133463i 0.537925 0.842993i \(-0.319209\pi\)
−0.215716 + 0.976456i \(0.569209\pi\)
\(558\) 0 0
\(559\) 11.6745i 0.493777i
\(560\) −14.8763 25.5829i −0.628638 1.08107i
\(561\) 0 0
\(562\) 21.4917 + 13.3413i 0.906571 + 0.562768i
\(563\) 11.3013 + 4.68115i 0.476293 + 0.197287i 0.607898 0.794015i \(-0.292013\pi\)
−0.131605 + 0.991302i \(0.542013\pi\)
\(564\) 0 0
\(565\) 8.54512 + 20.6297i 0.359496 + 0.867899i
\(566\) 3.61635 + 5.03835i 0.152006 + 0.211778i
\(567\) 0 0
\(568\) 30.0498 + 2.88906i 1.26086 + 0.121222i
\(569\) 5.04807 5.04807i 0.211626 0.211626i −0.593332 0.804958i \(-0.702188\pi\)
0.804958 + 0.593332i \(0.202188\pi\)
\(570\) 0 0
\(571\) −12.9612 + 5.36872i −0.542411 + 0.224674i −0.637029 0.770840i \(-0.719837\pi\)
0.0946181 + 0.995514i \(0.469837\pi\)
\(572\) 11.9293 + 24.0960i 0.498790 + 1.00750i
\(573\) 0 0
\(574\) 14.2772 + 61.0173i 0.595917 + 2.54681i
\(575\) 1.56622 0.0653160
\(576\) 0 0
\(577\) 7.48115 0.311444 0.155722 0.987801i \(-0.450230\pi\)
0.155722 + 0.987801i \(0.450230\pi\)
\(578\) 5.29338 + 22.6227i 0.220175 + 0.940980i
\(579\) 0 0
\(580\) 6.82086 + 13.7774i 0.283221 + 0.572077i
\(581\) 56.9075 23.5719i 2.36092 0.977925i
\(582\) 0 0
\(583\) −0.0259396 + 0.0259396i −0.00107431 + 0.00107431i
\(584\) 3.46128 36.0015i 0.143229 1.48975i
\(585\) 0 0
\(586\) −0.616040 0.858276i −0.0254484 0.0354551i
\(587\) −8.24039 19.8941i −0.340117 0.821116i −0.997703 0.0677363i \(-0.978422\pi\)
0.657586 0.753380i \(-0.271578\pi\)
\(588\) 0 0
\(589\) 13.1306 + 5.43887i 0.541036 + 0.224105i
\(590\) 19.6034 + 12.1691i 0.807058 + 0.500994i
\(591\) 0 0
\(592\) −1.21786 + 4.60216i −0.0500535 + 0.189148i
\(593\) 40.6667i 1.66998i 0.550264 + 0.834991i \(0.314527\pi\)
−0.550264 + 0.834991i \(0.685473\pi\)
\(594\) 0 0
\(595\) 39.5198 + 16.3696i 1.62015 + 0.671089i
\(596\) −16.2121 14.1732i −0.664074 0.580557i
\(597\) 0 0
\(598\) −3.97434 + 2.85264i −0.162523 + 0.116653i
\(599\) −7.41576 7.41576i −0.303000 0.303000i 0.539187 0.842186i \(-0.318732\pi\)
−0.842186 + 0.539187i \(0.818732\pi\)
\(600\) 0 0
\(601\) 27.4592 27.4592i 1.12008 1.12008i 0.128354 0.991728i \(-0.459030\pi\)
0.991728 0.128354i \(-0.0409695\pi\)
\(602\) 2.50256 15.2313i 0.101997 0.620781i
\(603\) 0 0
\(604\) −9.23856 3.12009i −0.375912 0.126955i
\(605\) 1.72426 4.16272i 0.0701010 0.169239i
\(606\) 0 0
\(607\) 35.3994 1.43682 0.718409 0.695621i \(-0.244871\pi\)
0.718409 + 0.695621i \(0.244871\pi\)
\(608\) −8.10666 8.58840i −0.328768 0.348305i
\(609\) 0 0
\(610\) −2.68857 + 0.629087i −0.108857 + 0.0254710i
\(611\) 9.33305 22.5320i 0.377575 0.911546i
\(612\) 0 0
\(613\) 19.0395 7.88644i 0.769000 0.318530i 0.0365328 0.999332i \(-0.488369\pi\)
0.732467 + 0.680802i \(0.238369\pi\)
\(614\) 1.27809 7.77882i 0.0515796 0.313928i
\(615\) 0 0
\(616\) −10.3985 33.9944i −0.418969 1.36967i
\(617\) −9.37922 9.37922i −0.377593 0.377593i 0.492640 0.870233i \(-0.336032\pi\)
−0.870233 + 0.492640i \(0.836032\pi\)
\(618\) 0 0
\(619\) 12.9078 + 31.1622i 0.518808 + 1.25251i 0.938636 + 0.344910i \(0.112090\pi\)
−0.419828 + 0.907604i \(0.637910\pi\)
\(620\) −15.2439 + 17.4368i −0.612208 + 0.700278i
\(621\) 0 0
\(622\) −23.4263 + 37.7378i −0.939310 + 1.51315i
\(623\) 76.3622i 3.05939i
\(624\) 0 0
\(625\) 10.0325i 0.401299i
\(626\) 33.3627 + 20.7104i 1.33344 + 0.827754i
\(627\) 0 0
\(628\) −2.37902 35.4541i −0.0949333 1.41477i
\(629\) −2.63329 6.35733i −0.104996 0.253483i
\(630\) 0 0
\(631\) 4.80900 + 4.80900i 0.191443 + 0.191443i 0.796319 0.604876i \(-0.206777\pi\)
−0.604876 + 0.796319i \(0.706777\pi\)
\(632\) 19.3128 15.9250i 0.768223 0.633461i
\(633\) 0 0
\(634\) 13.7509 + 2.25932i 0.546116 + 0.0897291i
\(635\) −25.2573 + 10.4619i −1.00231 + 0.415169i
\(636\) 0 0
\(637\) 21.2124 51.2113i 0.840466 2.02906i
\(638\) 4.20742 + 17.9816i 0.166573 + 0.711896i
\(639\) 0 0
\(640\) 17.4869 8.03793i 0.691231 0.317727i
\(641\) 9.67074 0.381971 0.190986 0.981593i \(-0.438832\pi\)
0.190986 + 0.981593i \(0.438832\pi\)
\(642\) 0 0
\(643\) −16.0445 + 38.7348i −0.632733 + 1.52755i 0.203440 + 0.979087i \(0.434788\pi\)
−0.836173 + 0.548466i \(0.815212\pi\)
\(644\) 5.79670 2.86980i 0.228422 0.113086i
\(645\) 0 0
\(646\) 16.8449 + 2.76769i 0.662755 + 0.108893i
\(647\) −17.1946 + 17.1946i −0.675988 + 0.675988i −0.959090 0.283102i \(-0.908637\pi\)
0.283102 + 0.959090i \(0.408637\pi\)
\(648\) 0 0
\(649\) 19.5987 + 19.5987i 0.769316 + 0.769316i
\(650\) 8.08002 + 11.2572i 0.316925 + 0.441544i
\(651\) 0 0
\(652\) 2.51262 + 37.4450i 0.0984016 + 1.46646i
\(653\) 44.0250 + 18.2358i 1.72283 + 0.713620i 0.999738 + 0.0228702i \(0.00728045\pi\)
0.723094 + 0.690750i \(0.242720\pi\)
\(654\) 0 0
\(655\) 15.0661i 0.588681i
\(656\) −40.3881 + 5.44472i −1.57689 + 0.212580i
\(657\) 0 0
\(658\) −17.0065 + 27.3961i −0.662983 + 1.06801i
\(659\) −19.5624 8.10302i −0.762044 0.315649i −0.0323990 0.999475i \(-0.510315\pi\)
−0.729645 + 0.683826i \(0.760315\pi\)
\(660\) 0 0
\(661\) 15.7189 + 37.9488i 0.611394 + 1.47604i 0.861469 + 0.507810i \(0.169545\pi\)
−0.250075 + 0.968226i \(0.580455\pi\)
\(662\) 26.2414 18.8352i 1.01990 0.732049i
\(663\) 0 0
\(664\) 11.7174 + 38.3061i 0.454724 + 1.48656i
\(665\) 10.9220 10.9220i 0.423538 0.423538i
\(666\) 0 0
\(667\) −3.10434 + 1.28586i −0.120200 + 0.0497887i
\(668\) −6.05802 + 17.9377i −0.234392 + 0.694032i
\(669\) 0 0
\(670\) 7.21368 1.68789i 0.278689 0.0652090i
\(671\) −3.31687 −0.128046
\(672\) 0 0
\(673\) −1.41731 −0.0546334 −0.0273167 0.999627i \(-0.508696\pi\)
−0.0273167 + 0.999627i \(0.508696\pi\)
\(674\) −12.3038 + 2.87891i −0.473925 + 0.110892i
\(675\) 0 0
\(676\) −16.3736 5.52976i −0.629752 0.212683i
\(677\) 18.8465 7.80647i 0.724329 0.300027i 0.0101096 0.999949i \(-0.496782\pi\)
0.714219 + 0.699922i \(0.246782\pi\)
\(678\) 0 0
\(679\) 29.1452 29.1452i 1.11849 1.11849i
\(680\) −13.0565 + 24.5643i −0.500693 + 0.941997i
\(681\) 0 0
\(682\) −22.6021 + 16.2230i −0.865480 + 0.621211i
\(683\) −15.8135 38.1772i −0.605087 1.46081i −0.868284 0.496067i \(-0.834777\pi\)
0.263197 0.964742i \(-0.415223\pi\)
\(684\) 0 0
\(685\) −22.1398 9.17060i −0.845918 0.350391i
\(686\) −15.9454 + 25.6867i −0.608799 + 0.980723i
\(687\) 0 0
\(688\) 9.70420 + 2.56799i 0.369969 + 0.0979038i
\(689\) 0.0590529i 0.00224974i
\(690\) 0 0
\(691\) −0.368324 0.152565i −0.0140117 0.00580384i 0.375667 0.926755i \(-0.377414\pi\)
−0.389678 + 0.920951i \(0.627414\pi\)
\(692\) −27.0337 + 1.81400i −1.02767 + 0.0689579i
\(693\) 0 0
\(694\) −21.8704 30.4701i −0.830188 1.15663i
\(695\) 5.60007 + 5.60007i 0.212423 + 0.212423i
\(696\) 0 0
\(697\) 41.6533 41.6533i 1.57773 1.57773i
\(698\) 22.5398 + 3.70338i 0.853143 + 0.140175i
\(699\) 0 0
\(700\) −8.12863 16.4190i −0.307233 0.620579i
\(701\) −17.5964 + 42.4815i −0.664607 + 1.60450i 0.125895 + 0.992044i \(0.459820\pi\)
−0.790502 + 0.612459i \(0.790180\pi\)
\(702\) 0 0
\(703\) −2.48472 −0.0937131
\(704\) 22.6534 4.61574i 0.853784 0.173962i
\(705\) 0 0
\(706\) 1.42953 + 6.10951i 0.0538012 + 0.229934i
\(707\) −28.2895 + 68.2968i −1.06393 + 2.56856i
\(708\) 0 0
\(709\) 35.8877 14.8652i 1.34779 0.558274i 0.412115 0.911132i \(-0.364790\pi\)
0.935677 + 0.352858i \(0.114790\pi\)
\(710\) −25.3370 4.16298i −0.950882 0.156234i
\(711\) 0 0
\(712\) −49.4330 4.75262i −1.85258 0.178112i
\(713\) −3.57947 3.57947i −0.134052 0.134052i
\(714\) 0 0
\(715\) −8.75159 21.1282i −0.327291 0.790150i
\(716\) −17.4363 + 1.17000i −0.651627 + 0.0437251i
\(717\) 0 0
\(718\) −26.4919 16.4453i −0.988670 0.613732i
\(719\) 41.8039i 1.55902i −0.626388 0.779511i \(-0.715467\pi\)
0.626388 0.779511i \(-0.284533\pi\)
\(720\) 0 0
\(721\) 60.1596i 2.24046i
\(722\) −10.9205 + 17.5920i −0.406419 + 0.654706i
\(723\) 0 0
\(724\) 10.2826 + 8.98939i 0.382148 + 0.334088i
\(725\) 3.64216 + 8.79294i 0.135266 + 0.326562i
\(726\) 0 0
\(727\) −4.55220 4.55220i −0.168832 0.168832i 0.617634 0.786466i \(-0.288091\pi\)
−0.786466 + 0.617634i \(0.788091\pi\)
\(728\) 50.5314 + 26.8586i 1.87282 + 0.995446i
\(729\) 0 0
\(730\) −4.98750 + 30.3553i −0.184596 + 1.12350i
\(731\) −13.4052 + 5.55261i −0.495808 + 0.205371i
\(732\) 0 0
\(733\) 3.21856 7.77030i 0.118880 0.287003i −0.853227 0.521540i \(-0.825358\pi\)
0.972107 + 0.234538i \(0.0753576\pi\)
\(734\) 36.9697 8.65036i 1.36458 0.319291i
\(735\) 0 0
\(736\) 1.49699 + 3.93110i 0.0551798 + 0.144902i
\(737\) 8.89944 0.327815
\(738\) 0 0
\(739\) −6.56067 + 15.8389i −0.241338 + 0.582642i −0.997416 0.0718394i \(-0.977113\pi\)
0.756078 + 0.654482i \(0.227113\pi\)
\(740\) 1.29560 3.83624i 0.0476270 0.141023i
\(741\) 0 0
\(742\) −0.0126587 + 0.0770444i −0.000464716 + 0.00282839i
\(743\) −13.8972 + 13.8972i −0.509838 + 0.509838i −0.914477 0.404639i \(-0.867397\pi\)
0.404639 + 0.914477i \(0.367397\pi\)
\(744\) 0 0
\(745\) 12.9512 + 12.9512i 0.474495 + 0.474495i
\(746\) 24.9339 17.8966i 0.912894 0.655243i
\(747\) 0 0
\(748\) −21.9943 + 25.1584i −0.804193 + 0.919881i
\(749\) −19.3515 8.01567i −0.707090 0.292886i
\(750\) 0 0
\(751\) 16.1406i 0.588977i 0.955655 + 0.294489i \(0.0951493\pi\)
−0.955655 + 0.294489i \(0.904851\pi\)
\(752\) −16.6764 12.7142i −0.608125 0.463640i
\(753\) 0 0
\(754\) −25.2571 15.6787i −0.919811 0.570986i
\(755\) 7.66257 + 3.17394i 0.278869 + 0.115511i
\(756\) 0 0
\(757\) −8.62137 20.8138i −0.313349 0.756492i −0.999576 0.0291046i \(-0.990734\pi\)
0.686227 0.727387i \(-0.259266\pi\)
\(758\) 11.8147 + 16.4605i 0.429131 + 0.597871i
\(759\) 0 0
\(760\) 6.39059 + 7.75012i 0.231811 + 0.281126i
\(761\) −22.0688 + 22.0688i −0.799993 + 0.799993i −0.983094 0.183101i \(-0.941387\pi\)
0.183101 + 0.983094i \(0.441387\pi\)
\(762\) 0 0
\(763\) 61.7229 25.5664i 2.23452 0.925567i
\(764\) 7.15810 3.54380i 0.258971 0.128210i
\(765\) 0 0
\(766\) −3.87049 16.5416i −0.139847 0.597673i
\(767\) −44.6174 −1.61104
\(768\) 0 0
\(769\) 8.43463 0.304160 0.152080 0.988368i \(-0.451403\pi\)
0.152080 + 0.988368i \(0.451403\pi\)
\(770\) 6.88883 + 29.4413i 0.248256 + 1.06099i
\(771\) 0 0
\(772\) −4.35939 + 2.15823i −0.156898 + 0.0776763i
\(773\) 13.8656 5.74334i 0.498712 0.206573i −0.119125 0.992879i \(-0.538009\pi\)
0.617837 + 0.786306i \(0.288009\pi\)
\(774\) 0 0
\(775\) −10.1388 + 10.1388i −0.364195 + 0.364195i
\(776\) 17.0532 + 20.6811i 0.612174 + 0.742407i
\(777\) 0 0
\(778\) −21.9377 30.5639i −0.786505 1.09577i
\(779\) −8.13996 19.6516i −0.291644 0.704092i
\(780\) 0 0
\(781\) −28.4962 11.8035i −1.01967 0.422363i
\(782\) −5.16582 3.20676i −0.184729 0.114674i
\(783\) 0 0
\(784\) −37.9025 28.8973i −1.35366 1.03204i
\(785\) 30.2233i 1.07872i
\(786\) 0 0
\(787\) −22.1687 9.18256i −0.790227 0.327323i −0.0491923 0.998789i \(-0.515665\pi\)
−0.741035 + 0.671466i \(0.765665\pi\)
\(788\) −14.4744 + 16.5566i −0.515629 + 0.589805i
\(789\)