Properties

Label 288.3.u.a.163.1
Level $288$
Weight $3$
Character 288.163
Analytic conductor $7.847$
Analytic rank $0$
Dimension $28$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 288 = 2^{5} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 288.u (of order \(8\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.84743161358\)
Analytic rank: \(0\)
Dimension: \(28\)
Relative dimension: \(7\) over \(\Q(\zeta_{8})\)
Twist minimal: no (minimal twist has level 32)
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 163.1
Character \(\chi\) \(=\) 288.163
Dual form 288.3.u.a.235.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.93931 + 0.488972i) q^{2} +(3.52181 - 1.89653i) q^{4} +(1.85856 + 4.48696i) q^{5} +(-5.27676 - 5.27676i) q^{7} +(-5.90252 + 5.40002i) q^{8} +O(q^{10})\) \(q+(-1.93931 + 0.488972i) q^{2} +(3.52181 - 1.89653i) q^{4} +(1.85856 + 4.48696i) q^{5} +(-5.27676 - 5.27676i) q^{7} +(-5.90252 + 5.40002i) q^{8} +(-5.79831 - 7.79280i) q^{10} +(-6.20050 - 14.9693i) q^{11} +(-4.22532 + 10.2008i) q^{13} +(12.8134 + 7.65307i) q^{14} +(8.80634 - 13.3585i) q^{16} +2.84356i q^{17} +(-12.4276 - 5.14768i) q^{19} +(15.0551 + 12.2774i) q^{20} +(19.3443 + 25.9983i) q^{22} +(1.43918 - 1.43918i) q^{23} +(0.999126 - 0.999126i) q^{25} +(3.20628 - 21.8486i) q^{26} +(-28.5913 - 8.57623i) q^{28} +(-36.9596 - 15.3092i) q^{29} -4.73823i q^{31} +(-10.5463 + 30.2122i) q^{32} +(-1.39042 - 5.51453i) q^{34} +(13.8694 - 33.4838i) q^{35} +(-6.68390 - 16.1364i) q^{37} +(26.6180 + 3.90618i) q^{38} +(-35.1998 - 16.4481i) q^{40} +(-40.4523 - 40.4523i) q^{41} +(-24.5000 - 59.1482i) q^{43} +(-50.2268 - 40.9598i) q^{44} +(-2.08729 + 3.49473i) q^{46} +16.5262 q^{47} +6.68842i q^{49} +(-1.44907 + 2.42615i) q^{50} +(4.46539 + 43.9389i) q^{52} +(46.9950 - 19.4659i) q^{53} +(55.6428 - 55.6428i) q^{55} +(59.6408 + 2.65160i) q^{56} +(79.1617 + 11.6170i) q^{58} +(-50.0578 + 20.7346i) q^{59} +(-54.3116 - 22.4966i) q^{61} +(2.31686 + 9.18889i) q^{62} +(5.67958 - 63.7475i) q^{64} -53.6237 q^{65} +(-25.5017 + 61.5665i) q^{67} +(5.39290 + 10.0145i) q^{68} +(-10.5245 + 71.7170i) q^{70} +(-7.12641 - 7.12641i) q^{71} +(55.3669 + 55.3669i) q^{73} +(20.8524 + 28.0251i) q^{74} +(-53.5304 + 5.44015i) q^{76} +(-46.2711 + 111.708i) q^{77} +11.0986 q^{79} +(76.3059 + 14.6862i) q^{80} +(98.2293 + 58.6693i) q^{82} +(29.9476 + 12.4047i) q^{83} +(-12.7589 + 5.28492i) q^{85} +(76.4348 + 102.727i) q^{86} +(117.433 + 54.8740i) q^{88} +(-16.7667 + 16.7667i) q^{89} +(76.1234 - 31.5313i) q^{91} +(2.33907 - 7.79797i) q^{92} +(-32.0494 + 8.08086i) q^{94} -65.3294i q^{95} -67.8301 q^{97} +(-3.27045 - 12.9709i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28q + 4q^{2} - 4q^{4} + 4q^{5} - 4q^{7} + 4q^{8} + O(q^{10}) \) \( 28q + 4q^{2} - 4q^{4} + 4q^{5} - 4q^{7} + 4q^{8} - 44q^{10} + 4q^{11} - 4q^{13} + 20q^{14} + 16q^{16} - 4q^{19} - 76q^{20} + 144q^{22} + 68q^{23} - 4q^{25} - 96q^{26} + 56q^{28} + 4q^{29} + 24q^{32} - 48q^{34} - 92q^{35} - 4q^{37} + 396q^{38} - 408q^{40} + 4q^{41} + 92q^{43} + 188q^{44} - 36q^{46} + 8q^{47} - 308q^{50} + 420q^{52} + 164q^{53} + 252q^{55} - 552q^{56} + 528q^{58} - 124q^{59} - 68q^{61} - 216q^{62} - 232q^{64} + 8q^{65} - 164q^{67} + 368q^{68} - 664q^{70} + 260q^{71} - 4q^{73} + 532q^{74} - 516q^{76} - 220q^{77} - 520q^{79} - 312q^{80} + 636q^{82} + 484q^{83} + 96q^{85} - 688q^{86} + 672q^{88} + 4q^{89} - 196q^{91} - 616q^{92} + 40q^{94} - 8q^{97} + 328q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/288\mathbb{Z}\right)^\times\).

\(n\) \(37\) \(65\) \(127\)
\(\chi(n)\) \(e\left(\frac{3}{8}\right)\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.93931 + 0.488972i −0.969653 + 0.244486i
\(3\) 0 0
\(4\) 3.52181 1.89653i 0.880453 0.474133i
\(5\) 1.85856 + 4.48696i 0.371712 + 0.897391i 0.993461 + 0.114175i \(0.0364224\pi\)
−0.621749 + 0.783217i \(0.713578\pi\)
\(6\) 0 0
\(7\) −5.27676 5.27676i −0.753823 0.753823i 0.221367 0.975190i \(-0.428948\pi\)
−0.975190 + 0.221367i \(0.928948\pi\)
\(8\) −5.90252 + 5.40002i −0.737816 + 0.675002i
\(9\) 0 0
\(10\) −5.79831 7.79280i −0.579831 0.779280i
\(11\) −6.20050 14.9693i −0.563682 1.36085i −0.906802 0.421557i \(-0.861484\pi\)
0.343120 0.939292i \(-0.388516\pi\)
\(12\) 0 0
\(13\) −4.22532 + 10.2008i −0.325025 + 0.784680i 0.673922 + 0.738802i \(0.264608\pi\)
−0.998947 + 0.0458772i \(0.985392\pi\)
\(14\) 12.8134 + 7.65307i 0.915246 + 0.546648i
\(15\) 0 0
\(16\) 8.80634 13.3585i 0.550396 0.834903i
\(17\) 2.84356i 0.167268i 0.996497 + 0.0836341i \(0.0266527\pi\)
−0.996497 + 0.0836341i \(0.973347\pi\)
\(18\) 0 0
\(19\) −12.4276 5.14768i −0.654084 0.270931i 0.0308626 0.999524i \(-0.490175\pi\)
−0.684947 + 0.728593i \(0.740175\pi\)
\(20\) 15.0551 + 12.2774i 0.752757 + 0.613871i
\(21\) 0 0
\(22\) 19.3443 + 25.9983i 0.879284 + 1.18174i
\(23\) 1.43918 1.43918i 0.0625730 0.0625730i −0.675128 0.737701i \(-0.735912\pi\)
0.737701 + 0.675128i \(0.235912\pi\)
\(24\) 0 0
\(25\) 0.999126 0.999126i 0.0399650 0.0399650i
\(26\) 3.20628 21.8486i 0.123318 0.840331i
\(27\) 0 0
\(28\) −28.5913 8.57623i −1.02112 0.306294i
\(29\) −36.9596 15.3092i −1.27447 0.527902i −0.360148 0.932895i \(-0.617274\pi\)
−0.914320 + 0.404993i \(0.867274\pi\)
\(30\) 0 0
\(31\) 4.73823i 0.152846i −0.997075 0.0764231i \(-0.975650\pi\)
0.997075 0.0764231i \(-0.0243500\pi\)
\(32\) −10.5463 + 30.2122i −0.329572 + 0.944131i
\(33\) 0 0
\(34\) −1.39042 5.51453i −0.0408947 0.162192i
\(35\) 13.8694 33.4838i 0.396269 0.956679i
\(36\) 0 0
\(37\) −6.68390 16.1364i −0.180646 0.436118i 0.807454 0.589930i \(-0.200845\pi\)
−0.988100 + 0.153812i \(0.950845\pi\)
\(38\) 26.6180 + 3.90618i 0.700473 + 0.102794i
\(39\) 0 0
\(40\) −35.1998 16.4481i −0.879996 0.411203i
\(41\) −40.4523 40.4523i −0.986641 0.986641i 0.0132711 0.999912i \(-0.495776\pi\)
−0.999912 + 0.0132711i \(0.995776\pi\)
\(42\) 0 0
\(43\) −24.5000 59.1482i −0.569767 1.37554i −0.901751 0.432255i \(-0.857718\pi\)
0.331984 0.943285i \(-0.392282\pi\)
\(44\) −50.2268 40.9598i −1.14152 0.930904i
\(45\) 0 0
\(46\) −2.08729 + 3.49473i −0.0453759 + 0.0759723i
\(47\) 16.5262 0.351622 0.175811 0.984424i \(-0.443745\pi\)
0.175811 + 0.984424i \(0.443745\pi\)
\(48\) 0 0
\(49\) 6.68842i 0.136498i
\(50\) −1.44907 + 2.42615i −0.0289813 + 0.0485231i
\(51\) 0 0
\(52\) 4.46539 + 43.9389i 0.0858729 + 0.844979i
\(53\) 46.9950 19.4659i 0.886697 0.367282i 0.107607 0.994194i \(-0.465681\pi\)
0.779090 + 0.626912i \(0.215681\pi\)
\(54\) 0 0
\(55\) 55.6428 55.6428i 1.01169 1.01169i
\(56\) 59.6408 + 2.65160i 1.06501 + 0.0473500i
\(57\) 0 0
\(58\) 79.1617 + 11.6170i 1.36486 + 0.200292i
\(59\) −50.0578 + 20.7346i −0.848437 + 0.351434i −0.764174 0.645010i \(-0.776853\pi\)
−0.0842623 + 0.996444i \(0.526853\pi\)
\(60\) 0 0
\(61\) −54.3116 22.4966i −0.890353 0.368796i −0.109850 0.993948i \(-0.535037\pi\)
−0.780503 + 0.625152i \(0.785037\pi\)
\(62\) 2.31686 + 9.18889i 0.0373687 + 0.148208i
\(63\) 0 0
\(64\) 5.67958 63.7475i 0.0887435 0.996055i
\(65\) −53.6237 −0.824980
\(66\) 0 0
\(67\) −25.5017 + 61.5665i −0.380622 + 0.918904i 0.611223 + 0.791458i \(0.290678\pi\)
−0.991846 + 0.127445i \(0.959322\pi\)
\(68\) 5.39290 + 10.0145i 0.0793073 + 0.147272i
\(69\) 0 0
\(70\) −10.5245 + 71.7170i −0.150349 + 1.02453i
\(71\) −7.12641 7.12641i −0.100372 0.100372i 0.655138 0.755510i \(-0.272611\pi\)
−0.755510 + 0.655138i \(0.772611\pi\)
\(72\) 0 0
\(73\) 55.3669 + 55.3669i 0.758451 + 0.758451i 0.976040 0.217590i \(-0.0698194\pi\)
−0.217590 + 0.976040i \(0.569819\pi\)
\(74\) 20.8524 + 28.0251i 0.281789 + 0.378718i
\(75\) 0 0
\(76\) −53.5304 + 5.44015i −0.704348 + 0.0715809i
\(77\) −46.2711 + 111.708i −0.600923 + 1.45076i
\(78\) 0 0
\(79\) 11.0986 0.140489 0.0702446 0.997530i \(-0.477622\pi\)
0.0702446 + 0.997530i \(0.477622\pi\)
\(80\) 76.3059 + 14.6862i 0.953824 + 0.183578i
\(81\) 0 0
\(82\) 98.2293 + 58.6693i 1.19792 + 0.715480i
\(83\) 29.9476 + 12.4047i 0.360814 + 0.149454i 0.555724 0.831367i \(-0.312441\pi\)
−0.194909 + 0.980821i \(0.562441\pi\)
\(84\) 0 0
\(85\) −12.7589 + 5.28492i −0.150105 + 0.0621755i
\(86\) 76.4348 + 102.727i 0.888777 + 1.19450i
\(87\) 0 0
\(88\) 117.433 + 54.8740i 1.33447 + 0.623569i
\(89\) −16.7667 + 16.7667i −0.188390 + 0.188390i −0.795000 0.606610i \(-0.792529\pi\)
0.606610 + 0.795000i \(0.292529\pi\)
\(90\) 0 0
\(91\) 76.1234 31.5313i 0.836521 0.346498i
\(92\) 2.33907 7.79797i 0.0254247 0.0847606i
\(93\) 0 0
\(94\) −32.0494 + 8.08086i −0.340951 + 0.0859666i
\(95\) 65.3294i 0.687678i
\(96\) 0 0
\(97\) −67.8301 −0.699280 −0.349640 0.936884i \(-0.613696\pi\)
−0.349640 + 0.936884i \(0.613696\pi\)
\(98\) −3.27045 12.9709i −0.0333719 0.132356i
\(99\) 0 0
\(100\) 1.62386 5.41361i 0.0162386 0.0541361i
\(101\) 45.6943 + 110.316i 0.452419 + 1.09224i 0.971400 + 0.237450i \(0.0763115\pi\)
−0.518981 + 0.854786i \(0.673689\pi\)
\(102\) 0 0
\(103\) 61.7093 + 61.7093i 0.599120 + 0.599120i 0.940078 0.340959i \(-0.110752\pi\)
−0.340959 + 0.940078i \(0.610752\pi\)
\(104\) −30.1446 83.0275i −0.289852 0.798341i
\(105\) 0 0
\(106\) −81.6193 + 60.7296i −0.769993 + 0.572921i
\(107\) −7.13652 17.2291i −0.0666965 0.161020i 0.887017 0.461737i \(-0.152774\pi\)
−0.953713 + 0.300718i \(0.902774\pi\)
\(108\) 0 0
\(109\) −75.1681 + 181.472i −0.689616 + 1.66488i 0.0559384 + 0.998434i \(0.482185\pi\)
−0.745554 + 0.666445i \(0.767815\pi\)
\(110\) −80.7006 + 135.116i −0.733642 + 1.22833i
\(111\) 0 0
\(112\) −116.958 + 24.0204i −1.04427 + 0.214468i
\(113\) 156.784i 1.38747i −0.720232 0.693734i \(-0.755965\pi\)
0.720232 0.693734i \(-0.244035\pi\)
\(114\) 0 0
\(115\) 9.13234 + 3.78274i 0.0794116 + 0.0328934i
\(116\) −159.199 + 16.1790i −1.37241 + 0.139474i
\(117\) 0 0
\(118\) 86.9387 64.6876i 0.736769 0.548200i
\(119\) 15.0048 15.0048i 0.126091 0.126091i
\(120\) 0 0
\(121\) −100.075 + 100.075i −0.827066 + 0.827066i
\(122\) 116.327 + 17.0710i 0.953499 + 0.139926i
\(123\) 0 0
\(124\) −8.98621 16.6872i −0.0724694 0.134574i
\(125\) 118.514 + 49.0901i 0.948111 + 0.392720i
\(126\) 0 0
\(127\) 192.971i 1.51946i −0.650240 0.759729i \(-0.725332\pi\)
0.650240 0.759729i \(-0.274668\pi\)
\(128\) 20.1563 + 126.403i 0.157471 + 0.987524i
\(129\) 0 0
\(130\) 103.993 26.2205i 0.799944 0.201696i
\(131\) −18.2599 + 44.0834i −0.139389 + 0.336515i −0.978123 0.208026i \(-0.933296\pi\)
0.838734 + 0.544541i \(0.183296\pi\)
\(132\) 0 0
\(133\) 38.4144 + 92.7406i 0.288830 + 0.697297i
\(134\) 19.3513 131.866i 0.144413 0.984074i
\(135\) 0 0
\(136\) −15.3553 16.7842i −0.112906 0.123413i
\(137\) 27.8671 + 27.8671i 0.203409 + 0.203409i 0.801459 0.598050i \(-0.204057\pi\)
−0.598050 + 0.801459i \(0.704057\pi\)
\(138\) 0 0
\(139\) 33.3447 + 80.5013i 0.239890 + 0.579146i 0.997271 0.0738274i \(-0.0235214\pi\)
−0.757381 + 0.652973i \(0.773521\pi\)
\(140\) −14.6574 144.227i −0.104696 1.03020i
\(141\) 0 0
\(142\) 17.3049 + 10.3357i 0.121866 + 0.0727865i
\(143\) 178.899 1.25104
\(144\) 0 0
\(145\) 194.289i 1.33992i
\(146\) −134.446 80.3005i −0.920864 0.550004i
\(147\) 0 0
\(148\) −54.1426 44.1531i −0.365828 0.298331i
\(149\) 125.860 52.1327i 0.844695 0.349884i 0.0819919 0.996633i \(-0.473872\pi\)
0.762703 + 0.646749i \(0.223872\pi\)
\(150\) 0 0
\(151\) 106.254 106.254i 0.703672 0.703672i −0.261525 0.965197i \(-0.584225\pi\)
0.965197 + 0.261525i \(0.0842254\pi\)
\(152\) 101.152 36.7250i 0.665472 0.241612i
\(153\) 0 0
\(154\) 35.1116 239.262i 0.227997 1.55365i
\(155\) 21.2603 8.80629i 0.137163 0.0568147i
\(156\) 0 0
\(157\) 209.345 + 86.7136i 1.33341 + 0.552316i 0.931626 0.363419i \(-0.118391\pi\)
0.401783 + 0.915735i \(0.368391\pi\)
\(158\) −21.5237 + 5.42692i −0.136226 + 0.0343476i
\(159\) 0 0
\(160\) −155.162 + 8.83036i −0.969760 + 0.0551897i
\(161\) −15.1884 −0.0943380
\(162\) 0 0
\(163\) −0.176018 + 0.424946i −0.00107987 + 0.00260703i −0.924419 0.381380i \(-0.875449\pi\)
0.923339 + 0.383987i \(0.125449\pi\)
\(164\) −219.184 65.7464i −1.33649 0.400893i
\(165\) 0 0
\(166\) −64.1431 9.41298i −0.386404 0.0567047i
\(167\) −96.7499 96.7499i −0.579341 0.579341i 0.355381 0.934722i \(-0.384351\pi\)
−0.934722 + 0.355381i \(0.884351\pi\)
\(168\) 0 0
\(169\) 33.2974 + 33.2974i 0.197026 + 0.197026i
\(170\) 22.1593 16.4878i 0.130349 0.0969872i
\(171\) 0 0
\(172\) −198.461 161.844i −1.15384 0.940954i
\(173\) −102.242 + 246.834i −0.590994 + 1.42678i 0.291551 + 0.956555i \(0.405829\pi\)
−0.882544 + 0.470229i \(0.844171\pi\)
\(174\) 0 0
\(175\) −10.5443 −0.0602531
\(176\) −254.571 48.9960i −1.44643 0.278386i
\(177\) 0 0
\(178\) 24.3174 40.7143i 0.136614 0.228732i
\(179\) −269.771 111.743i −1.50710 0.624262i −0.532144 0.846654i \(-0.678613\pi\)
−0.974957 + 0.222393i \(0.928613\pi\)
\(180\) 0 0
\(181\) −33.2079 + 13.7552i −0.183469 + 0.0759954i −0.472527 0.881316i \(-0.656658\pi\)
0.289058 + 0.957312i \(0.406658\pi\)
\(182\) −132.209 + 98.3711i −0.726421 + 0.540500i
\(183\) 0 0
\(184\) −0.723195 + 16.2664i −0.00393041 + 0.0884043i
\(185\) 59.9808 59.9808i 0.324220 0.324220i
\(186\) 0 0
\(187\) 42.5662 17.6315i 0.227627 0.0942861i
\(188\) 58.2023 31.3425i 0.309587 0.166715i
\(189\) 0 0
\(190\) 31.9442 + 126.694i 0.168127 + 0.666809i
\(191\) 47.7299i 0.249895i 0.992163 + 0.124947i \(0.0398762\pi\)
−0.992163 + 0.124947i \(0.960124\pi\)
\(192\) 0 0
\(193\) −302.171 −1.56565 −0.782827 0.622240i \(-0.786223\pi\)
−0.782827 + 0.622240i \(0.786223\pi\)
\(194\) 131.543 33.1670i 0.678059 0.170964i
\(195\) 0 0
\(196\) 12.6848 + 23.5554i 0.0647183 + 0.120180i
\(197\) −18.2996 44.1791i −0.0928913 0.224259i 0.870604 0.491984i \(-0.163728\pi\)
−0.963495 + 0.267725i \(0.913728\pi\)
\(198\) 0 0
\(199\) −94.2590 94.2590i −0.473663 0.473663i 0.429435 0.903098i \(-0.358713\pi\)
−0.903098 + 0.429435i \(0.858713\pi\)
\(200\) −0.502066 + 11.2927i −0.00251033 + 0.0564633i
\(201\) 0 0
\(202\) −142.556 191.593i −0.705725 0.948479i
\(203\) 114.244 + 275.810i 0.562779 + 1.35867i
\(204\) 0 0
\(205\) 106.325 256.691i 0.518657 1.25215i
\(206\) −149.847 89.4992i −0.727414 0.434462i
\(207\) 0 0
\(208\) 99.0577 + 146.276i 0.476239 + 0.703249i
\(209\) 217.951i 1.04283i
\(210\) 0 0
\(211\) −267.734 110.899i −1.26888 0.525589i −0.356259 0.934387i \(-0.615948\pi\)
−0.912625 + 0.408799i \(0.865948\pi\)
\(212\) 128.590 157.683i 0.606555 0.743787i
\(213\) 0 0
\(214\) 22.2644 + 29.9229i 0.104039 + 0.139827i
\(215\) 219.861 219.861i 1.02261 1.02261i
\(216\) 0 0
\(217\) −25.0025 + 25.0025i −0.115219 + 0.115219i
\(218\) 57.0394 388.684i 0.261648 1.78296i
\(219\) 0 0
\(220\) 90.4353 301.492i 0.411069 1.37042i
\(221\) −29.0067 12.0150i −0.131252 0.0543663i
\(222\) 0 0
\(223\) 408.363i 1.83123i 0.402061 + 0.915613i \(0.368294\pi\)
−0.402061 + 0.915613i \(0.631706\pi\)
\(224\) 215.073 103.772i 0.960146 0.463269i
\(225\) 0 0
\(226\) 76.6628 + 304.052i 0.339216 + 1.34536i
\(227\) −82.5132 + 199.204i −0.363494 + 0.877553i 0.631290 + 0.775547i \(0.282526\pi\)
−0.994784 + 0.102005i \(0.967474\pi\)
\(228\) 0 0
\(229\) 22.6069 + 54.5778i 0.0987200 + 0.238331i 0.965522 0.260321i \(-0.0838284\pi\)
−0.866802 + 0.498652i \(0.833828\pi\)
\(230\) −19.5600 2.87043i −0.0850437 0.0124801i
\(231\) 0 0
\(232\) 300.824 109.220i 1.29666 0.470775i
\(233\) −58.2826 58.2826i −0.250140 0.250140i 0.570888 0.821028i \(-0.306599\pi\)
−0.821028 + 0.570888i \(0.806599\pi\)
\(234\) 0 0
\(235\) 30.7150 + 74.1525i 0.130702 + 0.315543i
\(236\) −136.970 + 167.960i −0.580383 + 0.711693i
\(237\) 0 0
\(238\) −21.7619 + 36.4358i −0.0914368 + 0.153091i
\(239\) 367.366 1.53710 0.768548 0.639792i \(-0.220979\pi\)
0.768548 + 0.639792i \(0.220979\pi\)
\(240\) 0 0
\(241\) 312.345i 1.29604i −0.761624 0.648020i \(-0.775597\pi\)
0.761624 0.648020i \(-0.224403\pi\)
\(242\) 145.142 243.010i 0.599761 1.00417i
\(243\) 0 0
\(244\) −233.941 + 23.7748i −0.958773 + 0.0974375i
\(245\) −30.0106 + 12.4308i −0.122492 + 0.0507380i
\(246\) 0 0
\(247\) 105.021 105.021i 0.425187 0.425187i
\(248\) 25.5866 + 27.9675i 0.103172 + 0.112772i
\(249\) 0 0
\(250\) −253.838 37.2507i −1.01535 0.149003i
\(251\) −223.120 + 92.4192i −0.888923 + 0.368204i −0.779951 0.625841i \(-0.784756\pi\)
−0.108972 + 0.994045i \(0.534756\pi\)
\(252\) 0 0
\(253\) −30.4672 12.6199i −0.120424 0.0498811i
\(254\) 94.3574 + 374.230i 0.371486 + 1.47335i
\(255\) 0 0
\(256\) −100.897 235.278i −0.394127 0.919056i
\(257\) −178.176 −0.693293 −0.346646 0.937996i \(-0.612680\pi\)
−0.346646 + 0.937996i \(0.612680\pi\)
\(258\) 0 0
\(259\) −49.8784 + 120.417i −0.192581 + 0.464931i
\(260\) −188.853 + 101.699i −0.726357 + 0.391150i
\(261\) 0 0
\(262\) 13.8561 94.4198i 0.0528858 0.360381i
\(263\) 147.164 + 147.164i 0.559558 + 0.559558i 0.929182 0.369623i \(-0.120513\pi\)
−0.369623 + 0.929182i \(0.620513\pi\)
\(264\) 0 0
\(265\) 174.686 + 174.686i 0.659191 + 0.659191i
\(266\) −119.845 161.069i −0.450544 0.605522i
\(267\) 0 0
\(268\) 26.9506 + 265.191i 0.100562 + 0.989517i
\(269\) 138.119 333.450i 0.513455 1.23959i −0.428405 0.903587i \(-0.640924\pi\)
0.941861 0.336004i \(-0.109076\pi\)
\(270\) 0 0
\(271\) 218.643 0.806801 0.403400 0.915024i \(-0.367828\pi\)
0.403400 + 0.915024i \(0.367828\pi\)
\(272\) 37.9856 + 25.0414i 0.139653 + 0.0920638i
\(273\) 0 0
\(274\) −67.6690 40.4166i −0.246967 0.147506i
\(275\) −21.1513 8.76117i −0.0769139 0.0318588i
\(276\) 0 0
\(277\) 256.038 106.054i 0.924323 0.382867i 0.130801 0.991409i \(-0.458245\pi\)
0.793522 + 0.608541i \(0.208245\pi\)
\(278\) −104.028 139.812i −0.374203 0.502921i
\(279\) 0 0
\(280\) 98.9483 + 272.534i 0.353387 + 0.973336i
\(281\) 49.4126 49.4126i 0.175845 0.175845i −0.613697 0.789542i \(-0.710318\pi\)
0.789542 + 0.613697i \(0.210318\pi\)
\(282\) 0 0
\(283\) 118.290 48.9975i 0.417987 0.173136i −0.163770 0.986499i \(-0.552365\pi\)
0.581757 + 0.813363i \(0.302365\pi\)
\(284\) −38.6133 11.5824i −0.135962 0.0407832i
\(285\) 0 0
\(286\) −346.940 + 87.4765i −1.21308 + 0.305862i
\(287\) 426.914i 1.48751i
\(288\) 0 0
\(289\) 280.914 0.972021
\(290\) 95.0018 + 376.786i 0.327592 + 1.29926i
\(291\) 0 0
\(292\) 299.997 + 89.9869i 1.02739 + 0.308174i
\(293\) 100.203 + 241.910i 0.341988 + 0.825633i 0.997515 + 0.0704605i \(0.0224469\pi\)
−0.655526 + 0.755172i \(0.727553\pi\)
\(294\) 0 0
\(295\) −186.071 186.071i −0.630748 0.630748i
\(296\) 126.589 + 59.1521i 0.427664 + 0.199838i
\(297\) 0 0
\(298\) −218.589 + 162.643i −0.733519 + 0.545782i
\(299\) 8.59983 + 20.7618i 0.0287620 + 0.0694376i
\(300\) 0 0
\(301\) −182.830 + 441.392i −0.607410 + 1.46642i
\(302\) −154.104 + 258.015i −0.510280 + 0.854355i
\(303\) 0 0
\(304\) −178.207 + 120.681i −0.586206 + 0.396978i
\(305\) 285.505i 0.936081i
\(306\) 0 0
\(307\) −371.163 153.741i −1.20900 0.500784i −0.315103 0.949058i \(-0.602039\pi\)
−0.893896 + 0.448274i \(0.852039\pi\)
\(308\) 48.9000 + 481.170i 0.158766 + 1.56224i
\(309\) 0 0
\(310\) −36.9241 + 27.4737i −0.119110 + 0.0886250i
\(311\) 312.733 312.733i 1.00557 1.00557i 0.00558671 0.999984i \(-0.498222\pi\)
0.999984 0.00558671i \(-0.00177831\pi\)
\(312\) 0 0
\(313\) 358.245 358.245i 1.14455 1.14455i 0.156946 0.987607i \(-0.449835\pi\)
0.987607 0.156946i \(-0.0501649\pi\)
\(314\) −448.385 65.8004i −1.42798 0.209555i
\(315\) 0 0
\(316\) 39.0874 21.0489i 0.123694 0.0666105i
\(317\) −164.720 68.2292i −0.519621 0.215234i 0.107429 0.994213i \(-0.465738\pi\)
−0.627051 + 0.778979i \(0.715738\pi\)
\(318\) 0 0
\(319\) 648.185i 2.03193i
\(320\) 296.588 92.9944i 0.926838 0.290607i
\(321\) 0 0
\(322\) 29.4550 7.42670i 0.0914751 0.0230643i
\(323\) 14.6377 35.3386i 0.0453181 0.109407i
\(324\) 0 0
\(325\) 5.97029 + 14.4135i 0.0183701 + 0.0443494i
\(326\) 0.133567 0.910167i 0.000409714 0.00279192i
\(327\) 0 0
\(328\) 457.214 + 20.3275i 1.39394 + 0.0619740i
\(329\) −87.2050 87.2050i −0.265061 0.265061i
\(330\) 0 0
\(331\) 21.3130 + 51.4542i 0.0643898 + 0.155451i 0.952799 0.303601i \(-0.0981891\pi\)
−0.888409 + 0.459052i \(0.848189\pi\)
\(332\) 128.996 13.1095i 0.388541 0.0394864i
\(333\) 0 0
\(334\) 234.936 + 140.320i 0.703400 + 0.420119i
\(335\) −323.643 −0.966098
\(336\) 0 0
\(337\) 173.028i 0.513437i 0.966486 + 0.256718i \(0.0826413\pi\)
−0.966486 + 0.256718i \(0.917359\pi\)
\(338\) −80.8553 48.2924i −0.239217 0.142877i
\(339\) 0 0
\(340\) −34.9115 + 42.8102i −0.102681 + 0.125912i
\(341\) −70.9282 + 29.3794i −0.208001 + 0.0861567i
\(342\) 0 0
\(343\) −223.268 + 223.268i −0.650927 + 0.650927i
\(344\) 464.013 + 216.823i 1.34888 + 0.630301i
\(345\) 0 0
\(346\) 77.5836 528.679i 0.224230 1.52798i
\(347\) −48.9563 + 20.2784i −0.141085 + 0.0584391i −0.452109 0.891963i \(-0.649328\pi\)
0.311024 + 0.950402i \(0.399328\pi\)
\(348\) 0 0
\(349\) −222.227 92.0495i −0.636754 0.263752i 0.0408656 0.999165i \(-0.486988\pi\)
−0.677620 + 0.735412i \(0.736988\pi\)
\(350\) 20.4486 5.15586i 0.0584246 0.0147310i
\(351\) 0 0
\(352\) 517.649 29.4597i 1.47059 0.0836924i
\(353\) 75.1997 0.213030 0.106515 0.994311i \(-0.466031\pi\)
0.106515 + 0.994311i \(0.466031\pi\)
\(354\) 0 0
\(355\) 18.7310 45.2208i 0.0527635 0.127382i
\(356\) −27.2507 + 90.8479i −0.0765469 + 0.255191i
\(357\) 0 0
\(358\) 577.808 + 84.7931i 1.61399 + 0.236852i
\(359\) −369.532 369.532i −1.02934 1.02934i −0.999556 0.0297806i \(-0.990519\pi\)
−0.0297806 0.999556i \(-0.509481\pi\)
\(360\) 0 0
\(361\) −127.319 127.319i −0.352684 0.352684i
\(362\) 57.6744 42.9132i 0.159322 0.118545i
\(363\) 0 0
\(364\) 208.292 255.418i 0.572231 0.701697i
\(365\) −145.526 + 351.332i −0.398702 + 0.962552i
\(366\) 0 0
\(367\) −482.888 −1.31577 −0.657885 0.753118i \(-0.728549\pi\)
−0.657885 + 0.753118i \(0.728549\pi\)
\(368\) −6.55131 31.8991i −0.0178025 0.0866824i
\(369\) 0 0
\(370\) −86.9922 + 145.650i −0.235114 + 0.393648i
\(371\) −350.698 145.264i −0.945278 0.391547i
\(372\) 0 0
\(373\) 459.056 190.147i 1.23071 0.509778i 0.329913 0.944011i \(-0.392980\pi\)
0.900801 + 0.434233i \(0.142980\pi\)
\(374\) −73.9276 + 55.0065i −0.197667 + 0.147076i
\(375\) 0 0
\(376\) −97.5465 + 89.2420i −0.259432 + 0.237346i
\(377\) 312.332 312.332i 0.828468 0.828468i
\(378\) 0 0
\(379\) 209.167 86.6398i 0.551891 0.228601i −0.0892693 0.996008i \(-0.528453\pi\)
0.641161 + 0.767407i \(0.278453\pi\)
\(380\) −123.899 230.078i −0.326050 0.605468i
\(381\) 0 0
\(382\) −23.3386 92.5629i −0.0610958 0.242311i
\(383\) 243.083i 0.634682i −0.948312 0.317341i \(-0.897210\pi\)
0.948312 0.317341i \(-0.102790\pi\)
\(384\) 0 0
\(385\) −587.227 −1.52527
\(386\) 586.002 147.753i 1.51814 0.382780i
\(387\) 0 0
\(388\) −238.885 + 128.642i −0.615683 + 0.331551i
\(389\) −100.024 241.479i −0.257131 0.620768i 0.741616 0.670825i \(-0.234060\pi\)
−0.998746 + 0.0500566i \(0.984060\pi\)
\(390\) 0 0
\(391\) 4.09239 + 4.09239i 0.0104665 + 0.0104665i
\(392\) −36.1176 39.4786i −0.0921367 0.100711i
\(393\) 0 0
\(394\) 57.0908 + 76.7288i 0.144901 + 0.194743i
\(395\) 20.6275 + 49.7992i 0.0522215 + 0.126074i
\(396\) 0 0
\(397\) −177.617 + 428.806i −0.447399 + 1.08012i 0.525894 + 0.850550i \(0.323731\pi\)
−0.973293 + 0.229566i \(0.926269\pi\)
\(398\) 228.887 + 136.707i 0.575093 + 0.343485i
\(399\) 0 0
\(400\) −4.54813 22.1454i −0.0113703 0.0553636i
\(401\) 539.233i 1.34472i −0.740224 0.672360i \(-0.765281\pi\)
0.740224 0.672360i \(-0.234719\pi\)
\(402\) 0 0
\(403\) 48.3339 + 20.0206i 0.119935 + 0.0496788i
\(404\) 370.144 + 301.851i 0.916198 + 0.747156i
\(405\) 0 0
\(406\) −356.417 479.017i −0.877875 1.17984i
\(407\) −200.107 + 200.107i −0.491664 + 0.491664i
\(408\) 0 0
\(409\) 177.821 177.821i 0.434769 0.434769i −0.455478 0.890247i \(-0.650532\pi\)
0.890247 + 0.455478i \(0.150532\pi\)
\(410\) −80.6817 + 549.791i −0.196785 + 1.34095i
\(411\) 0 0
\(412\) 334.362 + 100.295i 0.811559 + 0.243435i
\(413\) 373.554 + 154.731i 0.904490 + 0.374652i
\(414\) 0 0
\(415\) 157.428i 0.379345i
\(416\) −263.628 235.237i −0.633721 0.565474i
\(417\) 0 0
\(418\) −106.572 422.674i −0.254957 1.01118i
\(419\) −55.0604 + 132.927i −0.131409 + 0.317249i −0.975865 0.218376i \(-0.929924\pi\)
0.844456 + 0.535625i \(0.179924\pi\)
\(420\) 0 0
\(421\) −292.384 705.877i −0.694498 1.67667i −0.735514 0.677509i \(-0.763059\pi\)
0.0410159 0.999158i \(-0.486941\pi\)
\(422\) 573.445 + 84.1530i 1.35888 + 0.199415i
\(423\) 0 0
\(424\) −172.272 + 368.672i −0.406303 + 0.869509i
\(425\) 2.84107 + 2.84107i 0.00668488 + 0.00668488i
\(426\) 0 0
\(427\) 167.880 + 405.298i 0.393162 + 0.949176i
\(428\) −57.8090 47.1430i −0.135068 0.110147i
\(429\) 0 0
\(430\) −318.872 + 533.883i −0.741562 + 1.24159i
\(431\) −810.711 −1.88100 −0.940500 0.339794i \(-0.889643\pi\)
−0.940500 + 0.339794i \(0.889643\pi\)
\(432\) 0 0
\(433\) 753.072i 1.73920i −0.493759 0.869599i \(-0.664378\pi\)
0.493759 0.869599i \(-0.335622\pi\)
\(434\) 36.2620 60.7131i 0.0835531 0.139892i
\(435\) 0 0
\(436\) 79.4389 + 781.669i 0.182199 + 1.79282i
\(437\) −25.2940 + 10.4771i −0.0578810 + 0.0239751i
\(438\) 0 0
\(439\) 504.938 504.938i 1.15020 1.15020i 0.163689 0.986512i \(-0.447661\pi\)
0.986512 0.163689i \(-0.0523392\pi\)
\(440\) −27.9608 + 628.905i −0.0635472 + 1.42933i
\(441\) 0 0
\(442\) 62.1278 + 9.11724i 0.140561 + 0.0206272i
\(443\) 697.291 288.827i 1.57402 0.651981i 0.586569 0.809899i \(-0.300478\pi\)
0.987452 + 0.157919i \(0.0504784\pi\)
\(444\) 0 0
\(445\) −106.394 44.0697i −0.239087 0.0990330i
\(446\) −199.678 791.942i −0.447709 1.77565i
\(447\) 0 0
\(448\) −366.350 + 306.410i −0.817746 + 0.683952i
\(449\) 294.056 0.654913 0.327457 0.944866i \(-0.393808\pi\)
0.327457 + 0.944866i \(0.393808\pi\)
\(450\) 0 0
\(451\) −354.719 + 856.368i −0.786517 + 1.89882i
\(452\) −297.345 552.163i −0.657843 1.22160i
\(453\) 0 0
\(454\) 62.6130 426.665i 0.137914 0.939791i
\(455\) 282.960 + 282.960i 0.621889 + 0.621889i
\(456\) 0 0
\(457\) 175.139 + 175.139i 0.383237 + 0.383237i 0.872267 0.489030i \(-0.162649\pi\)
−0.489030 + 0.872267i \(0.662649\pi\)
\(458\) −70.5287 94.7890i −0.153993 0.206963i
\(459\) 0 0
\(460\) 39.3365 3.99766i 0.0855141 0.00869056i
\(461\) 107.290 259.020i 0.232732 0.561866i −0.763765 0.645495i \(-0.776651\pi\)
0.996497 + 0.0836293i \(0.0266512\pi\)
\(462\) 0 0
\(463\) 53.7059 0.115996 0.0579978 0.998317i \(-0.481528\pi\)
0.0579978 + 0.998317i \(0.481528\pi\)
\(464\) −529.985 + 358.905i −1.14221 + 0.773502i
\(465\) 0 0
\(466\) 141.526 + 84.5292i 0.303704 + 0.181393i
\(467\) −101.550 42.0634i −0.217452 0.0900716i 0.271298 0.962495i \(-0.412547\pi\)
−0.488750 + 0.872424i \(0.662547\pi\)
\(468\) 0 0
\(469\) 459.438 190.306i 0.979613 0.405769i
\(470\) −95.8242 128.786i −0.203881 0.274012i
\(471\) 0 0
\(472\) 183.500 392.699i 0.388771 0.831990i
\(473\) −733.498 + 733.498i −1.55074 + 1.55074i
\(474\) 0 0
\(475\) −17.5599 + 7.27355i −0.0369682 + 0.0153127i
\(476\) 24.3870 81.3011i 0.0512332 0.170801i
\(477\) 0 0
\(478\) −712.435 + 179.632i −1.49045 + 0.375798i
\(479\) 40.7997i 0.0851769i 0.999093 + 0.0425884i \(0.0135604\pi\)
−0.999093 + 0.0425884i \(0.986440\pi\)
\(480\) 0 0
\(481\) 192.846 0.400927
\(482\) 152.728 + 605.733i 0.316863 + 1.25671i
\(483\) 0 0
\(484\) −162.650 + 542.241i −0.336054 + 1.12033i
\(485\) −126.066 304.351i −0.259931 0.627528i
\(486\) 0 0
\(487\) −143.660 143.660i −0.294989 0.294989i 0.544058 0.839047i \(-0.316887\pi\)
−0.839047 + 0.544058i \(0.816887\pi\)
\(488\) 442.057 160.497i 0.905855 0.328887i
\(489\) 0 0
\(490\) 52.1215 38.7815i 0.106370 0.0791459i
\(491\) −182.575 440.775i −0.371843 0.897709i −0.993438 0.114370i \(-0.963515\pi\)
0.621595 0.783339i \(-0.286485\pi\)
\(492\) 0 0
\(493\) 43.5325 105.097i 0.0883012 0.213178i
\(494\) −152.316 + 255.021i −0.308332 + 0.516236i
\(495\) 0 0
\(496\) −63.2955 41.7265i −0.127612 0.0841261i
\(497\) 75.2087i 0.151325i
\(498\) 0 0
\(499\) −409.850 169.766i −0.821343 0.340211i −0.0678733 0.997694i \(-0.521621\pi\)
−0.753470 + 0.657482i \(0.771621\pi\)
\(500\) 510.485 51.8792i 1.02097 0.103758i
\(501\) 0 0
\(502\) 387.507 288.328i 0.771926 0.574359i
\(503\) −453.715 + 453.715i −0.902019 + 0.902019i −0.995611 0.0935920i \(-0.970165\pi\)
0.0935920 + 0.995611i \(0.470165\pi\)
\(504\) 0 0
\(505\) −410.057 + 410.057i −0.811993 + 0.811993i
\(506\) 65.2560 + 9.57631i 0.128964 + 0.0189255i
\(507\) 0 0
\(508\) −365.976 679.608i −0.720425 1.33781i
\(509\) 71.5029 + 29.6175i 0.140477 + 0.0581876i 0.451815 0.892112i \(-0.350777\pi\)
−0.311337 + 0.950299i \(0.600777\pi\)
\(510\) 0 0
\(511\) 584.316i 1.14348i
\(512\) 310.714 + 406.941i 0.606863 + 0.794807i
\(513\) 0 0
\(514\) 345.538 87.1231i 0.672253 0.169500i
\(515\) −162.197 + 391.578i −0.314945 + 0.760345i
\(516\) 0 0
\(517\) −102.471 247.387i −0.198203 0.478504i
\(518\) 37.8489 257.915i 0.0730674 0.497905i
\(519\) 0 0
\(520\) 316.515 289.569i 0.608683 0.556864i
\(521\) 565.729 + 565.729i 1.08585 + 1.08585i 0.995951 + 0.0899020i \(0.0286554\pi\)
0.0899020 + 0.995951i \(0.471345\pi\)
\(522\) 0 0
\(523\) −1.50925 3.64366i −0.00288576 0.00696685i 0.922430 0.386164i \(-0.126200\pi\)
−0.925316 + 0.379197i \(0.876200\pi\)
\(524\) 19.2974 + 189.884i 0.0368271 + 0.362374i
\(525\) 0 0
\(526\) −357.355 213.437i −0.679381 0.405773i
\(527\) 13.4734 0.0255663
\(528\) 0 0
\(529\) 524.858i 0.992169i
\(530\) −424.185 253.353i −0.800350 0.478024i
\(531\) 0 0
\(532\) 311.174 + 253.761i 0.584913 + 0.476994i
\(533\) 583.571 241.723i 1.09488 0.453514i
\(534\) 0 0
\(535\) 64.0426 64.0426i 0.119706 0.119706i
\(536\) −181.936 501.108i −0.339433 0.934902i
\(537\) 0 0
\(538\) −104.808 + 714.198i −0.194811 + 1.32751i
\(539\) 100.121 41.4716i 0.185754 0.0769417i
\(540\) 0 0
\(541\) −746.681 309.286i −1.38019 0.571692i −0.435656 0.900113i \(-0.643483\pi\)
−0.944531 + 0.328421i \(0.893483\pi\)
\(542\) −424.016 + 106.910i −0.782317 + 0.197251i
\(543\) 0 0
\(544\) −85.9101 29.9890i −0.157923 0.0551268i
\(545\) −953.961 −1.75039
\(546\) 0 0
\(547\) 298.176 719.861i 0.545112 1.31602i −0.375964 0.926634i \(-0.622688\pi\)
0.921076 0.389383i \(-0.127312\pi\)
\(548\) 150.993 + 45.2919i 0.275535 + 0.0826494i
\(549\) 0 0
\(550\) 45.3029 + 6.64819i 0.0823688 + 0.0120876i
\(551\) 380.512 + 380.512i 0.690585 + 0.690585i
\(552\) 0 0
\(553\) −58.5649 58.5649i −0.105904 0.105904i
\(554\) −444.678 + 330.867i −0.802667 + 0.597232i
\(555\) 0 0
\(556\) 270.107 + 220.271i 0.485804 + 0.396171i
\(557\) −83.4142 + 201.380i −0.149756 + 0.361544i −0.980900 0.194515i \(-0.937687\pi\)
0.831143 + 0.556058i \(0.187687\pi\)
\(558\) 0 0
\(559\) 706.882 1.26455
\(560\) −325.152 480.144i −0.580629 0.857400i
\(561\) 0 0
\(562\) −71.6647 + 119.987i −0.127517 + 0.213501i
\(563\) 19.5811 + 8.11076i 0.0347800 + 0.0144063i 0.400006 0.916513i \(-0.369008\pi\)
−0.365226 + 0.930919i \(0.619008\pi\)
\(564\) 0 0
\(565\) 703.482 291.392i 1.24510 0.515738i
\(566\) −205.443 + 152.862i −0.362973 + 0.270074i
\(567\) 0 0
\(568\) 80.5466 + 3.58106i 0.141807 + 0.00630468i
\(569\) 366.760 366.760i 0.644569 0.644569i −0.307106 0.951675i \(-0.599361\pi\)
0.951675 + 0.307106i \(0.0993606\pi\)
\(570\) 0 0
\(571\) −121.285 + 50.2378i −0.212408 + 0.0879822i −0.486350 0.873764i \(-0.661672\pi\)
0.273943 + 0.961746i \(0.411672\pi\)
\(572\) 630.049 339.287i 1.10148 0.593159i
\(573\) 0 0
\(574\) −208.749 827.917i −0.363674 1.44236i
\(575\) 2.87584i 0.00500147i
\(576\) 0 0
\(577\) 464.948 0.805802 0.402901 0.915244i \(-0.368002\pi\)
0.402901 + 0.915244i \(0.368002\pi\)
\(578\) −544.778 + 137.359i −0.942523 + 0.237645i
\(579\) 0 0
\(580\) −368.475 684.250i −0.635302 1.17974i
\(581\) −92.5696 223.483i −0.159328 0.384652i
\(582\) 0 0
\(583\) −582.785 582.785i −0.999631 0.999631i
\(584\) −625.787 27.8221i −1.07155 0.0476407i
\(585\) 0 0
\(586\) −312.611 420.142i −0.533465 0.716966i
\(587\) −159.551 385.190i −0.271807 0.656201i 0.727753 0.685839i \(-0.240565\pi\)
−0.999561 + 0.0296380i \(0.990565\pi\)
\(588\) 0 0
\(589\) −24.3909 + 58.8849i −0.0414107 + 0.0999743i
\(590\) 451.831 + 269.865i 0.765815 + 0.457398i
\(591\) 0 0
\(592\) −274.418 52.8158i −0.463543 0.0892159i
\(593\) 470.422i 0.793292i −0.917972 0.396646i \(-0.870174\pi\)
0.917972 0.396646i \(-0.129826\pi\)
\(594\) 0 0
\(595\) 95.2131 + 39.4385i 0.160022 + 0.0662833i
\(596\) 344.383 422.298i 0.577823 0.708554i
\(597\) 0 0
\(598\) −26.8296 36.0585i −0.0448656 0.0602984i
\(599\) 506.817 506.817i 0.846105 0.846105i −0.143540 0.989645i \(-0.545849\pi\)
0.989645 + 0.143540i \(0.0458485\pi\)
\(600\) 0 0
\(601\) −261.398 + 261.398i −0.434939 + 0.434939i −0.890305 0.455366i \(-0.849509\pi\)
0.455366 + 0.890305i \(0.349509\pi\)
\(602\) 138.736 945.393i 0.230459 1.57042i
\(603\) 0 0
\(604\) 172.694 575.723i 0.285916 0.953184i
\(605\) −635.027 263.037i −1.04963 0.434772i
\(606\) 0 0
\(607\) 812.089i 1.33787i 0.743319 + 0.668937i \(0.233250\pi\)
−0.743319 + 0.668937i \(0.766750\pi\)
\(608\) 286.588 321.176i 0.471361 0.528250i
\(609\) 0 0
\(610\) 139.604 + 553.681i 0.228859 + 0.907674i
\(611\) −69.8287 + 168.581i −0.114286 + 0.275911i
\(612\) 0 0
\(613\) 105.168 + 253.898i 0.171563 + 0.414190i 0.986151 0.165850i \(-0.0530369\pi\)
−0.814588 + 0.580040i \(0.803037\pi\)
\(614\) 794.973 + 116.662i 1.29474 + 0.190003i
\(615\) 0 0
\(616\) −330.110 909.225i −0.535894 1.47601i
\(617\) 508.739 + 508.739i 0.824536 + 0.824536i 0.986755 0.162218i \(-0.0518649\pi\)
−0.162218 + 0.986755i \(0.551865\pi\)
\(618\) 0 0
\(619\) −6.64960 16.0536i −0.0107425 0.0259347i 0.918417 0.395613i \(-0.129468\pi\)
−0.929160 + 0.369678i \(0.879468\pi\)
\(620\) 58.1733 71.3348i 0.0938278 0.115056i
\(621\) 0 0
\(622\) −453.567 + 759.402i −0.729207 + 1.22090i
\(623\) 176.948 0.284026
\(624\) 0 0
\(625\) 587.679i 0.940287i
\(626\) −519.575 + 869.919i −0.829992 + 1.38965i
\(627\) 0 0
\(628\) 901.730 91.6403i 1.43588 0.145924i
\(629\) 45.8847 19.0061i 0.0729487 0.0302163i
\(630\) 0 0
\(631\) −177.518 + 177.518i −0.281329 + 0.281329i −0.833639 0.552310i \(-0.813746\pi\)
0.552310 + 0.833639i \(0.313746\pi\)
\(632\) −65.5100 + 59.9329i −0.103655 + 0.0948306i
\(633\) 0 0
\(634\) 352.804 + 51.7740i 0.556474 + 0.0816624i
\(635\) 865.853 358.648i 1.36355 0.564800i
\(636\) 0 0
\(637\) −68.2274 28.2607i −0.107107 0.0443654i
\(638\) −316.944 1257.03i −0.496777 1.97026i
\(639\) 0 0
\(640\) −529.703 + 325.368i −0.827662 + 0.508387i
\(641\) −334.058 −0.521151 −0.260575 0.965454i \(-0.583912\pi\)
−0.260575 + 0.965454i \(0.583912\pi\)
\(642\) 0 0
\(643\) −19.9758 + 48.2257i −0.0310665 + 0.0750011i −0.938651 0.344867i \(-0.887924\pi\)
0.907585 + 0.419869i \(0.137924\pi\)
\(644\) −53.4908 + 28.8053i −0.0830602 + 0.0447287i
\(645\) 0 0
\(646\) −11.1075 + 75.6898i −0.0171942 + 0.117167i
\(647\) −443.581 443.581i −0.685596 0.685596i 0.275659 0.961255i \(-0.411104\pi\)
−0.961255 + 0.275659i \(0.911104\pi\)
\(648\) 0 0
\(649\) 620.767 + 620.767i 0.956497 + 0.956497i
\(650\) −18.6260 25.0330i −0.0286554 0.0385123i
\(651\) 0 0
\(652\) 0.186019 + 1.83040i 0.000285305 + 0.00280737i
\(653\) 14.0746 33.9792i 0.0215538 0.0520355i −0.912736 0.408549i \(-0.866035\pi\)
0.934290 + 0.356514i \(0.116035\pi\)
\(654\) 0 0
\(655\) −231.737 −0.353798
\(656\) −896.617 + 184.143i −1.36679 + 0.280706i
\(657\) 0 0
\(658\) 211.758 + 126.476i 0.321821 + 0.192213i
\(659\) 845.778 + 350.333i 1.28343 + 0.531613i 0.917020 0.398842i \(-0.130588\pi\)
0.366407 + 0.930455i \(0.380588\pi\)
\(660\) 0 0
\(661\) −1022.39 + 423.490i −1.54674 + 0.640680i −0.982723 0.185083i \(-0.940745\pi\)
−0.564017 + 0.825763i \(0.690745\pi\)
\(662\) −66.4921 89.3640i −0.100441 0.134991i
\(663\) 0 0
\(664\) −243.752 + 88.4985i −0.367096 + 0.133281i
\(665\) −344.727 + 344.727i −0.518387 + 0.518387i
\(666\) 0 0
\(667\) −75.2241 + 31.1588i −0.112780 + 0.0467149i
\(668\) −524.224 157.246i −0.784767 0.235398i
\(669\) 0 0
\(670\) 627.642 158.252i 0.936780 0.236197i
\(671\) 952.498i 1.41952i
\(672\) 0 0
\(673\) −441.074 −0.655385 −0.327693 0.944784i \(-0.606271\pi\)
−0.327693 + 0.944784i \(0.606271\pi\)
\(674\) −84.6059 335.555i −0.125528 0.497856i
\(675\) 0 0
\(676\) 180.417 + 54.1177i 0.266889 + 0.0800558i
\(677\) 3.12869 + 7.55333i 0.00462140 + 0.0111571i 0.926173 0.377098i \(-0.123078\pi\)
−0.921552 + 0.388255i \(0.873078\pi\)
\(678\) 0 0
\(679\) 357.923 + 357.923i 0.527133 + 0.527133i
\(680\) 46.7712 100.093i 0.0687812 0.147195i
\(681\) 0 0
\(682\) 123.186 91.6576i 0.180624 0.134395i
\(683\) 198.853 + 480.073i 0.291146 + 0.702889i 0.999997 0.00246964i \(-0.000786112\pi\)
−0.708851 + 0.705358i \(0.750786\pi\)
\(684\) 0 0
\(685\) −73.2458 + 176.831i −0.106928 + 0.258147i
\(686\) 323.813 542.157i 0.472031 0.790316i
\(687\) 0 0
\(688\) −1005.88 193.598i −1.46204 0.281392i
\(689\) 561.638i 0.815149i
\(690\) 0 0
\(691\) 260.304 + 107.822i 0.376707 + 0.156037i 0.563000 0.826457i \(-0.309647\pi\)
−0.186293 + 0.982494i \(0.559647\pi\)
\(692\) 108.051 + 1063.21i 0.156143 + 1.53643i
\(693\) 0 0
\(694\) 85.0257 63.2642i 0.122515 0.0911588i
\(695\) −299.233 + 299.233i −0.430551 + 0.430551i
\(696\) 0 0
\(697\) 115.028 115.028i 0.165034 0.165034i
\(698\) 475.976 + 69.8494i 0.681914 + 0.100071i
\(699\) 0 0
\(700\) −37.1350 + 19.9976i −0.0530501 + 0.0285680i
\(701\) 487.328 + 201.858i 0.695189 + 0.287957i 0.702160 0.712019i \(-0.252219\pi\)
−0.00697111 + 0.999976i \(0.502219\pi\)
\(702\) 0 0
\(703\) 234.943i 0.334200i
\(704\) −989.474 + 310.247i −1.40550 + 0.440692i
\(705\) 0 0
\(706\) −145.835 + 36.7705i −0.206565 + 0.0520829i
\(707\) 340.992 823.228i 0.482309 1.16440i
\(708\) 0 0
\(709\) 260.932 + 629.945i 0.368028 + 0.888498i 0.994073 + 0.108711i \(0.0346724\pi\)
−0.626046 + 0.779786i \(0.715328\pi\)
\(710\) −14.2136 + 96.8558i −0.0200191 + 0.136417i
\(711\) 0 0
\(712\) 8.42537 189.507i 0.0118334 0.266161i
\(713\) −6.81917 6.81917i −0.00956405 0.00956405i
\(714\) 0 0
\(715\) 332.494 + 802.712i 0.465027 + 1.12267i
\(716\) −1162.01 + 118.092i −1.62291 + 0.164932i
\(717\) 0 0
\(718\) 897.326 + 535.945i 1.24976 + 0.746441i
\(719\) 349.854 0.486585 0.243292 0.969953i \(-0.421773\pi\)
0.243292 + 0.969953i \(0.421773\pi\)
\(720\) 0 0
\(721\) 651.251i 0.903261i
\(722\) 309.166 + 184.655i 0.428207 + 0.255755i
\(723\) 0 0
\(724\) −90.8650 + 111.423i −0.125504 + 0.153899i
\(725\) −52.2230 + 21.6315i −0.0720318 + 0.0298365i
\(726\) 0 0
\(727\) −58.3736 + 58.3736i −0.0802938 + 0.0802938i −0.746113 0.665819i \(-0.768082\pi\)
0.665819 + 0.746113i \(0.268082\pi\)
\(728\) −279.050 + 597.182i −0.383311 + 0.820305i
\(729\) 0 0
\(730\) 110.429 752.498i 0.151272 1.03082i
\(731\) 168.191 69.6672i 0.230084 0.0953040i
\(732\) 0 0
\(733\) 327.632 + 135.710i 0.446975 + 0.185143i 0.594805 0.803870i \(-0.297229\pi\)
−0.147831 + 0.989013i \(0.547229\pi\)
\(734\) 936.467 236.118i 1.27584 0.321687i
\(735\) 0 0
\(736\) 28.3027 + 58.6588i 0.0384548 + 0.0796994i
\(737\) 1079.73 1.46504
\(738\) 0 0
\(739\) 328.523 793.126i 0.444551 1.07324i −0.529783 0.848134i \(-0.677726\pi\)
0.974334 0.225108i \(-0.0722736\pi\)
\(740\) 97.4857 324.996i 0.131737 0.439184i
\(741\) 0 0
\(742\) 751.141 + 110.230i 1.01232 + 0.148558i
\(743\) −79.8532 79.8532i −0.107474 0.107474i 0.651325 0.758799i \(-0.274214\pi\)
−0.758799 + 0.651325i \(0.774214\pi\)
\(744\) 0 0
\(745\) 467.835 + 467.835i 0.627966 + 0.627966i
\(746\) −797.274 + 593.219i −1.06873 + 0.795200i
\(747\) 0 0
\(748\) 116.472 142.823i 0.155711 0.190940i
\(749\) −53.2561 + 128.572i −0.0711029 + 0.171658i
\(750\) 0 0
\(751\) −729.615 −0.971524 −0.485762 0.874091i \(-0.661458\pi\)
−0.485762 + 0.874091i \(0.661458\pi\)
\(752\) 145.536 220.765i 0.193532 0.293570i
\(753\) 0 0
\(754\) −452.986 + 758.429i −0.600778 + 1.00587i
\(755\) 674.239 + 279.279i 0.893032 + 0.369906i
\(756\) 0 0
\(757\) 565.974 234.434i 0.747654 0.309688i 0.0238700 0.999715i \(-0.492401\pi\)
0.723784 + 0.690027i \(0.242401\pi\)
\(758\) −363.274 + 270.298i −0.479253 + 0.356593i
\(759\) 0 0
\(760\) 352.780 + 385.608i 0.464184 + 0.507379i
\(761\) −186.563 + 186.563i −0.245155 + 0.245155i −0.818979 0.573824i \(-0.805459\pi\)
0.573824 + 0.818979i \(0.305459\pi\)
\(762\) 0 0
\(763\) 1354.23 560.940i 1.77487 0.735176i
\(764\) 90.5213 + 168.096i 0.118483 + 0.220021i
\(765\) 0 0
\(766\) 118.861 + 471.413i 0.155171 + 0.615421i
\(767\) 598.241i 0.779976i
\(768\) 0 0
\(769\) 134.178 0.174484 0.0872420 0.996187i \(-0.472195\pi\)
0.0872420 + 0.996187i \(0.472195\pi\)
\(770\) 1138.81 287.137i 1.47898 0.372906i
\(771\) 0 0
\(772\) −1064.19 + 573.077i −1.37849 + 0.742328i
\(773\) 155.016 + 374.241i 0.200538 + 0.484141i 0.991872 0.127243i \(-0.0406130\pi\)
−0.791334 + 0.611384i \(0.790613\pi\)
\(774\) 0 0
\(775\) −4.73409 4.73409i −0.00610851 0.00610851i
\(776\) 400.369 366.284i 0.515940 0.472016i
\(777\) 0 0
\(778\) 312.053 + 419.393i 0.401097 + 0.539065i
\(779\) 294.489 + 710.960i 0.378035 + 0.912657i
\(780\) 0 0
\(781\) −62.4903 + 150.865i −0.0800132 + 0.193169i
\(782\) −9.93746 5.93534i −0.0127078 0.00758994i
\(783\) 0 0
\(784\) 89.3469 + 58.9005i 0.113963 + 0.0751282i
\(785\) 1100.49i 1.40189i
\(786\) 0 0
\(787\) 464.245 + 192.297i 0.589892 + 0.244341i 0.657604 0.753364i \(-0.271570\pi\)
−0.0677120 + 0.997705i \(0.521570\pi\)