Properties

Label 1323.2.g.b.361.3
Level $1323$
Weight $2$
Character 1323.361
Analytic conductor $10.564$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 1323 = 3^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1323.g (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(10.5642081874\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.309123.1
Defining polynomial: \(x^{6} - 3 x^{5} + 10 x^{4} - 15 x^{3} + 19 x^{2} - 12 x + 3\)
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 63)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 361.3
Root \(0.500000 + 0.224437i\) of defining polynomial
Character \(\chi\) \(=\) 1323.361
Dual form 1323.2.g.b.667.3

$q$-expansion

\(f(q)\) \(=\) \(q+(0.849814 - 1.47192i) q^{2} +(-0.444368 - 0.769668i) q^{4} -3.58836 q^{5} +1.88874 q^{8} +O(q^{10})\) \(q+(0.849814 - 1.47192i) q^{2} +(-0.444368 - 0.769668i) q^{4} -3.58836 q^{5} +1.88874 q^{8} +(-3.04944 + 5.28179i) q^{10} +2.81089 q^{11} +(0.500000 - 0.866025i) q^{13} +(2.49381 - 4.31941i) q^{16} +(2.05563 - 3.56046i) q^{17} +(-0.444368 - 0.769668i) q^{19} +(1.59455 + 2.76185i) q^{20} +(2.38874 - 4.13741i) q^{22} -5.87636 q^{23} +7.87636 q^{25} +(-0.849814 - 1.47192i) q^{26} +(-0.849814 - 1.47192i) q^{29} +(-3.49381 - 6.05146i) q^{31} +(-2.34981 - 4.07000i) q^{32} +(-3.49381 - 6.05146i) q^{34} +(-2.38255 - 4.12669i) q^{37} -1.51052 q^{38} -6.77747 q^{40} +(2.70582 - 4.68661i) q^{41} +(-2.60507 - 4.51212i) q^{43} +(-1.24907 - 2.16345i) q^{44} +(-4.99381 + 8.64953i) q^{46} +(1.33310 - 2.30900i) q^{47} +(6.69344 - 11.5934i) q^{50} -0.888736 q^{52} +(-0.0618219 + 0.107079i) q^{53} -10.0865 q^{55} -2.88874 q^{58} +(4.43818 + 7.68715i) q^{59} +(1.93818 - 3.35702i) q^{61} -11.8764 q^{62} +1.98762 q^{64} +(-1.79418 + 3.10761i) q^{65} +(-6.15452 - 10.6599i) q^{67} -3.65383 q^{68} +2.87636 q^{71} +(-5.32072 + 9.21576i) q^{73} -8.09888 q^{74} +(-0.394926 + 0.684031i) q^{76} +(3.54325 - 6.13709i) q^{79} +(-8.94870 + 15.4996i) q^{80} +(-4.59888 - 7.96550i) q^{82} +(2.05563 + 3.56046i) q^{83} +(-7.37636 + 12.7762i) q^{85} -8.85532 q^{86} +5.30903 q^{88} +(-4.80470 - 8.32199i) q^{89} +(2.61126 + 4.52284i) q^{92} +(-2.26578 - 3.92445i) q^{94} +(1.59455 + 2.76185i) q^{95} +(3.66071 + 6.34053i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q - q^{2} - 3q^{4} - 10q^{5} + 12q^{8} + O(q^{10}) \) \( 6q - q^{2} - 3q^{4} - 10q^{5} + 12q^{8} + 4q^{11} + 3q^{13} - 3q^{16} + 12q^{17} - 3q^{19} + 16q^{20} + 15q^{22} + 12q^{25} + q^{26} + q^{29} - 3q^{31} - 8q^{32} - 3q^{34} + 3q^{37} + 16q^{38} - 42q^{40} + 22q^{41} + 3q^{43} + 23q^{44} - 12q^{46} + 9q^{47} + 10q^{50} - 6q^{52} - 18q^{53} + 12q^{55} - 18q^{58} + 9q^{59} - 6q^{61} - 36q^{62} - 24q^{64} - 5q^{65} + 12q^{68} - 18q^{71} + 3q^{73} - 12q^{74} - 21q^{76} - 15q^{79} - 11q^{80} + 9q^{82} + 12q^{83} - 9q^{85} - 68q^{86} - 42q^{88} + 2q^{89} + 15q^{92} + 24q^{94} + 16q^{95} + 3q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times\).

\(n\) \(785\) \(1081\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.849814 1.47192i 0.600909 1.04081i −0.391774 0.920061i \(-0.628139\pi\)
0.992684 0.120744i \(-0.0385280\pi\)
\(3\) 0 0
\(4\) −0.444368 0.769668i −0.222184 0.384834i
\(5\) −3.58836 −1.60477 −0.802383 0.596810i \(-0.796435\pi\)
−0.802383 + 0.596810i \(0.796435\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 1.88874 0.667769
\(9\) 0 0
\(10\) −3.04944 + 5.28179i −0.964318 + 1.67025i
\(11\) 2.81089 0.847516 0.423758 0.905775i \(-0.360711\pi\)
0.423758 + 0.905775i \(0.360711\pi\)
\(12\) 0 0
\(13\) 0.500000 0.866025i 0.138675 0.240192i −0.788320 0.615265i \(-0.789049\pi\)
0.926995 + 0.375073i \(0.122382\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 2.49381 4.31941i 0.623453 1.07985i
\(17\) 2.05563 3.56046i 0.498564 0.863538i −0.501435 0.865196i \(-0.667194\pi\)
0.999999 + 0.00165734i \(0.000527549\pi\)
\(18\) 0 0
\(19\) −0.444368 0.769668i −0.101945 0.176574i 0.810541 0.585682i \(-0.199173\pi\)
−0.912486 + 0.409108i \(0.865840\pi\)
\(20\) 1.59455 + 2.76185i 0.356553 + 0.617568i
\(21\) 0 0
\(22\) 2.38874 4.13741i 0.509280 0.882099i
\(23\) −5.87636 −1.22530 −0.612652 0.790352i \(-0.709897\pi\)
−0.612652 + 0.790352i \(0.709897\pi\)
\(24\) 0 0
\(25\) 7.87636 1.57527
\(26\) −0.849814 1.47192i −0.166662 0.288667i
\(27\) 0 0
\(28\) 0 0
\(29\) −0.849814 1.47192i −0.157807 0.273329i 0.776271 0.630399i \(-0.217109\pi\)
−0.934077 + 0.357071i \(0.883776\pi\)
\(30\) 0 0
\(31\) −3.49381 6.05146i −0.627507 1.08687i −0.988050 0.154131i \(-0.950742\pi\)
0.360544 0.932742i \(-0.382591\pi\)
\(32\) −2.34981 4.07000i −0.415392 0.719481i
\(33\) 0 0
\(34\) −3.49381 6.05146i −0.599183 1.03782i
\(35\) 0 0
\(36\) 0 0
\(37\) −2.38255 4.12669i −0.391688 0.678424i 0.600984 0.799261i \(-0.294775\pi\)
−0.992672 + 0.120837i \(0.961442\pi\)
\(38\) −1.51052 −0.245039
\(39\) 0 0
\(40\) −6.77747 −1.07161
\(41\) 2.70582 4.68661i 0.422578 0.731926i −0.573613 0.819126i \(-0.694459\pi\)
0.996191 + 0.0872002i \(0.0277920\pi\)
\(42\) 0 0
\(43\) −2.60507 4.51212i −0.397270 0.688092i 0.596118 0.802897i \(-0.296709\pi\)
−0.993388 + 0.114805i \(0.963376\pi\)
\(44\) −1.24907 2.16345i −0.188304 0.326153i
\(45\) 0 0
\(46\) −4.99381 + 8.64953i −0.736297 + 1.27530i
\(47\) 1.33310 2.30900i 0.194453 0.336803i −0.752268 0.658857i \(-0.771040\pi\)
0.946721 + 0.322055i \(0.104373\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 6.69344 11.5934i 0.946595 1.63955i
\(51\) 0 0
\(52\) −0.888736 −0.123245
\(53\) −0.0618219 + 0.107079i −0.00849190 + 0.0147084i −0.870240 0.492628i \(-0.836036\pi\)
0.861748 + 0.507336i \(0.169370\pi\)
\(54\) 0 0
\(55\) −10.0865 −1.36006
\(56\) 0 0
\(57\) 0 0
\(58\) −2.88874 −0.379310
\(59\) 4.43818 + 7.68715i 0.577802 + 1.00078i 0.995731 + 0.0923022i \(0.0294226\pi\)
−0.417929 + 0.908479i \(0.637244\pi\)
\(60\) 0 0
\(61\) 1.93818 3.35702i 0.248158 0.429823i −0.714857 0.699271i \(-0.753508\pi\)
0.963015 + 0.269448i \(0.0868414\pi\)
\(62\) −11.8764 −1.50830
\(63\) 0 0
\(64\) 1.98762 0.248453
\(65\) −1.79418 + 3.10761i −0.222541 + 0.385452i
\(66\) 0 0
\(67\) −6.15452 10.6599i −0.751894 1.30232i −0.946904 0.321517i \(-0.895807\pi\)
0.195010 0.980801i \(-0.437526\pi\)
\(68\) −3.65383 −0.443092
\(69\) 0 0
\(70\) 0 0
\(71\) 2.87636 0.341361 0.170680 0.985326i \(-0.445403\pi\)
0.170680 + 0.985326i \(0.445403\pi\)
\(72\) 0 0
\(73\) −5.32072 + 9.21576i −0.622744 + 1.07862i 0.366229 + 0.930525i \(0.380649\pi\)
−0.988973 + 0.148099i \(0.952685\pi\)
\(74\) −8.09888 −0.941476
\(75\) 0 0
\(76\) −0.394926 + 0.684031i −0.0453011 + 0.0784638i
\(77\) 0 0
\(78\) 0 0
\(79\) 3.54325 6.13709i 0.398647 0.690477i −0.594912 0.803791i \(-0.702813\pi\)
0.993559 + 0.113314i \(0.0361465\pi\)
\(80\) −8.94870 + 15.4996i −1.00049 + 1.73291i
\(81\) 0 0
\(82\) −4.59888 7.96550i −0.507862 0.879642i
\(83\) 2.05563 + 3.56046i 0.225635 + 0.390811i 0.956510 0.291700i \(-0.0942210\pi\)
−0.730875 + 0.682512i \(0.760888\pi\)
\(84\) 0 0
\(85\) −7.37636 + 12.7762i −0.800078 + 1.38578i
\(86\) −8.85532 −0.954893
\(87\) 0 0
\(88\) 5.30903 0.565945
\(89\) −4.80470 8.32199i −0.509297 0.882129i −0.999942 0.0107692i \(-0.996572\pi\)
0.490645 0.871360i \(-0.336761\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 2.61126 + 4.52284i 0.272243 + 0.471539i
\(93\) 0 0
\(94\) −2.26578 3.92445i −0.233697 0.404776i
\(95\) 1.59455 + 2.76185i 0.163598 + 0.283360i
\(96\) 0 0
\(97\) 3.66071 + 6.34053i 0.371688 + 0.643783i 0.989825 0.142287i \(-0.0454456\pi\)
−0.618137 + 0.786070i \(0.712112\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −3.50000 6.06218i −0.350000 0.606218i
\(101\) 3.46472 0.344753 0.172376 0.985031i \(-0.444856\pi\)
0.172376 + 0.985031i \(0.444856\pi\)
\(102\) 0 0
\(103\) 15.8764 1.56434 0.782172 0.623063i \(-0.214112\pi\)
0.782172 + 0.623063i \(0.214112\pi\)
\(104\) 0.944368 1.63569i 0.0926029 0.160393i
\(105\) 0 0
\(106\) 0.105074 + 0.181994i 0.0102057 + 0.0176768i
\(107\) −2.67673 4.63623i −0.258769 0.448201i 0.707143 0.707070i \(-0.249984\pi\)
−0.965912 + 0.258869i \(0.916650\pi\)
\(108\) 0 0
\(109\) 9.43199 16.3367i 0.903421 1.56477i 0.0803973 0.996763i \(-0.474381\pi\)
0.823023 0.568008i \(-0.192286\pi\)
\(110\) −8.57165 + 14.8465i −0.817275 + 1.41556i
\(111\) 0 0
\(112\) 0 0
\(113\) −9.27561 + 16.0658i −0.872576 + 1.51135i −0.0132538 + 0.999912i \(0.504219\pi\)
−0.859322 + 0.511434i \(0.829114\pi\)
\(114\) 0 0
\(115\) 21.0865 1.96633
\(116\) −0.755260 + 1.30815i −0.0701242 + 0.121459i
\(117\) 0 0
\(118\) 15.0865 1.38883
\(119\) 0 0
\(120\) 0 0
\(121\) −3.09888 −0.281717
\(122\) −3.29418 5.70569i −0.298241 0.516569i
\(123\) 0 0
\(124\) −3.10507 + 5.37815i −0.278844 + 0.482972i
\(125\) −10.3214 −0.923175
\(126\) 0 0
\(127\) 9.98762 0.886258 0.443129 0.896458i \(-0.353868\pi\)
0.443129 + 0.896458i \(0.353868\pi\)
\(128\) 6.38874 11.0656i 0.564690 0.978071i
\(129\) 0 0
\(130\) 3.04944 + 5.28179i 0.267454 + 0.463244i
\(131\) 16.0531 1.40256 0.701282 0.712884i \(-0.252611\pi\)
0.701282 + 0.712884i \(0.252611\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −20.9208 −1.80728
\(135\) 0 0
\(136\) 3.88255 6.72477i 0.332926 0.576644i
\(137\) 12.9876 1.10961 0.554804 0.831981i \(-0.312793\pi\)
0.554804 + 0.831981i \(0.312793\pi\)
\(138\) 0 0
\(139\) 0.555632 0.962383i 0.0471281 0.0816283i −0.841499 0.540259i \(-0.818326\pi\)
0.888627 + 0.458630i \(0.151660\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 2.44437 4.23377i 0.205127 0.355290i
\(143\) 1.40545 2.43430i 0.117529 0.203567i
\(144\) 0 0
\(145\) 3.04944 + 5.28179i 0.253242 + 0.438629i
\(146\) 9.04325 + 15.6634i 0.748425 + 1.29631i
\(147\) 0 0
\(148\) −2.11745 + 3.66754i −0.174054 + 0.301470i
\(149\) −8.43268 −0.690832 −0.345416 0.938450i \(-0.612262\pi\)
−0.345416 + 0.938450i \(0.612262\pi\)
\(150\) 0 0
\(151\) −14.8516 −1.20861 −0.604303 0.796755i \(-0.706548\pi\)
−0.604303 + 0.796755i \(0.706548\pi\)
\(152\) −0.839294 1.45370i −0.0680757 0.117911i
\(153\) 0 0
\(154\) 0 0
\(155\) 12.5371 + 21.7148i 1.00700 + 1.74418i
\(156\) 0 0
\(157\) 1.44437 + 2.50172i 0.115273 + 0.199659i 0.917889 0.396837i \(-0.129892\pi\)
−0.802616 + 0.596496i \(0.796559\pi\)
\(158\) −6.02221 10.4308i −0.479101 0.829828i
\(159\) 0 0
\(160\) 8.43199 + 14.6046i 0.666607 + 1.15460i
\(161\) 0 0
\(162\) 0 0
\(163\) 5.15452 + 8.92788i 0.403733 + 0.699286i 0.994173 0.107796i \(-0.0343792\pi\)
−0.590440 + 0.807081i \(0.701046\pi\)
\(164\) −4.80951 −0.375560
\(165\) 0 0
\(166\) 6.98762 0.542345
\(167\) −6.07598 + 10.5239i −0.470174 + 0.814365i −0.999418 0.0341045i \(-0.989142\pi\)
0.529244 + 0.848469i \(0.322475\pi\)
\(168\) 0 0
\(169\) 6.00000 + 10.3923i 0.461538 + 0.799408i
\(170\) 12.5371 + 21.7148i 0.961549 + 1.66545i
\(171\) 0 0
\(172\) −2.31522 + 4.01008i −0.176534 + 0.305766i
\(173\) 3.30470 5.72391i 0.251252 0.435181i −0.712619 0.701551i \(-0.752491\pi\)
0.963871 + 0.266370i \(0.0858244\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 7.00983 12.1414i 0.528386 0.915191i
\(177\) 0 0
\(178\) −16.3324 −1.22417
\(179\) −1.92147 + 3.32808i −0.143617 + 0.248752i −0.928856 0.370440i \(-0.879207\pi\)
0.785239 + 0.619193i \(0.212540\pi\)
\(180\) 0 0
\(181\) −18.5426 −1.37826 −0.689129 0.724639i \(-0.742007\pi\)
−0.689129 + 0.724639i \(0.742007\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −11.0989 −0.818221
\(185\) 8.54944 + 14.8081i 0.628567 + 1.08871i
\(186\) 0 0
\(187\) 5.77816 10.0081i 0.422541 0.731862i
\(188\) −2.36955 −0.172818
\(189\) 0 0
\(190\) 5.42030 0.393230
\(191\) 2.31708 4.01330i 0.167658 0.290392i −0.769938 0.638119i \(-0.779713\pi\)
0.937596 + 0.347726i \(0.113046\pi\)
\(192\) 0 0
\(193\) 12.6483 + 21.9075i 0.910446 + 1.57694i 0.813435 + 0.581656i \(0.197595\pi\)
0.0970118 + 0.995283i \(0.469072\pi\)
\(194\) 12.4437 0.893404
\(195\) 0 0
\(196\) 0 0
\(197\) −10.7207 −0.763816 −0.381908 0.924200i \(-0.624733\pi\)
−0.381908 + 0.924200i \(0.624733\pi\)
\(198\) 0 0
\(199\) −4.38323 + 7.59199i −0.310719 + 0.538182i −0.978518 0.206160i \(-0.933903\pi\)
0.667799 + 0.744342i \(0.267237\pi\)
\(200\) 14.8764 1.05192
\(201\) 0 0
\(202\) 2.94437 5.09979i 0.207165 0.358820i
\(203\) 0 0
\(204\) 0 0
\(205\) −9.70946 + 16.8173i −0.678138 + 1.17457i
\(206\) 13.4920 23.3687i 0.940029 1.62818i
\(207\) 0 0
\(208\) −2.49381 4.31941i −0.172915 0.299497i
\(209\) −1.24907 2.16345i −0.0864000 0.149649i
\(210\) 0 0
\(211\) −5.26509 + 9.11941i −0.362464 + 0.627806i −0.988366 0.152096i \(-0.951398\pi\)
0.625902 + 0.779902i \(0.284731\pi\)
\(212\) 0.109887 0.00754705
\(213\) 0 0
\(214\) −9.09888 −0.621987
\(215\) 9.34795 + 16.1911i 0.637525 + 1.10423i
\(216\) 0 0
\(217\) 0 0
\(218\) −16.0309 27.7663i −1.08575 1.88057i
\(219\) 0 0
\(220\) 4.48212 + 7.76326i 0.302184 + 0.523399i
\(221\) −2.05563 3.56046i −0.138277 0.239502i
\(222\) 0 0
\(223\) −2.83379 4.90827i −0.189765 0.328682i 0.755407 0.655256i \(-0.227439\pi\)
−0.945172 + 0.326574i \(0.894106\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 15.7651 + 27.3059i 1.04868 + 1.81636i
\(227\) −11.0989 −0.736659 −0.368329 0.929695i \(-0.620070\pi\)
−0.368329 + 0.929695i \(0.620070\pi\)
\(228\) 0 0
\(229\) −19.6428 −1.29803 −0.649017 0.760774i \(-0.724820\pi\)
−0.649017 + 0.760774i \(0.724820\pi\)
\(230\) 17.9196 31.0377i 1.18158 2.04656i
\(231\) 0 0
\(232\) −1.60507 2.78007i −0.105378 0.182521i
\(233\) 4.48143 + 7.76207i 0.293588 + 0.508510i 0.974656 0.223711i \(-0.0718172\pi\)
−0.681067 + 0.732221i \(0.738484\pi\)
\(234\) 0 0
\(235\) −4.78366 + 8.28554i −0.312052 + 0.540489i
\(236\) 3.94437 6.83185i 0.256756 0.444715i
\(237\) 0 0
\(238\) 0 0
\(239\) 5.61126 9.71899i 0.362963 0.628670i −0.625484 0.780237i \(-0.715099\pi\)
0.988447 + 0.151567i \(0.0484320\pi\)
\(240\) 0 0
\(241\) 6.98624 0.450023 0.225012 0.974356i \(-0.427758\pi\)
0.225012 + 0.974356i \(0.427758\pi\)
\(242\) −2.63348 + 4.56131i −0.169286 + 0.293212i
\(243\) 0 0
\(244\) −3.44506 −0.220547
\(245\) 0 0
\(246\) 0 0
\(247\) −0.888736 −0.0565489
\(248\) −6.59888 11.4296i −0.419030 0.725781i
\(249\) 0 0
\(250\) −8.77128 + 15.1923i −0.554745 + 0.960846i
\(251\) 4.62041 0.291638 0.145819 0.989311i \(-0.453418\pi\)
0.145819 + 0.989311i \(0.453418\pi\)
\(252\) 0 0
\(253\) −16.5178 −1.03847
\(254\) 8.48762 14.7010i 0.532561 0.922422i
\(255\) 0 0
\(256\) −8.87085 15.3648i −0.554428 0.960298i
\(257\) −1.42402 −0.0888277 −0.0444138 0.999013i \(-0.514142\pi\)
−0.0444138 + 0.999013i \(0.514142\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 3.18911 0.197780
\(261\) 0 0
\(262\) 13.6421 23.6289i 0.842814 1.45980i
\(263\) −16.2632 −1.00283 −0.501417 0.865206i \(-0.667188\pi\)
−0.501417 + 0.865206i \(0.667188\pi\)
\(264\) 0 0
\(265\) 0.221840 0.384237i 0.0136275 0.0236035i
\(266\) 0 0
\(267\) 0 0
\(268\) −5.46974 + 9.47387i −0.334118 + 0.578709i
\(269\) 9.32691 16.1547i 0.568672 0.984969i −0.428026 0.903767i \(-0.640791\pi\)
0.996698 0.0812022i \(-0.0258759\pi\)
\(270\) 0 0
\(271\) 1.98143 + 3.43194i 0.120363 + 0.208475i 0.919911 0.392127i \(-0.128261\pi\)
−0.799548 + 0.600603i \(0.794927\pi\)
\(272\) −10.2527 17.7582i −0.621662 1.07675i
\(273\) 0 0
\(274\) 11.0371 19.1168i 0.666773 1.15489i
\(275\) 22.1396 1.33507
\(276\) 0 0
\(277\) −2.33379 −0.140224 −0.0701120 0.997539i \(-0.522336\pi\)
−0.0701120 + 0.997539i \(0.522336\pi\)
\(278\) −0.944368 1.63569i −0.0566394 0.0981024i
\(279\) 0 0
\(280\) 0 0
\(281\) 13.9975 + 24.2443i 0.835018 + 1.44629i 0.894016 + 0.448035i \(0.147876\pi\)
−0.0589978 + 0.998258i \(0.518790\pi\)
\(282\) 0 0
\(283\) 5.16002 + 8.93741i 0.306731 + 0.531274i 0.977645 0.210261i \(-0.0674314\pi\)
−0.670914 + 0.741535i \(0.734098\pi\)
\(284\) −1.27816 2.21384i −0.0758449 0.131367i
\(285\) 0 0
\(286\) −2.38874 4.13741i −0.141249 0.244650i
\(287\) 0 0
\(288\) 0 0
\(289\) 0.0487535 + 0.0844436i 0.00286785 + 0.00496727i
\(290\) 10.3658 0.608703
\(291\) 0 0
\(292\) 9.45744 0.553455
\(293\) 15.3480 26.5834i 0.896637 1.55302i 0.0648718 0.997894i \(-0.479336\pi\)
0.831765 0.555127i \(-0.187330\pi\)
\(294\) 0 0
\(295\) −15.9258 27.5843i −0.927236 1.60602i
\(296\) −4.50000 7.79423i −0.261557 0.453030i
\(297\) 0 0
\(298\) −7.16621 + 12.4122i −0.415127 + 0.719021i
\(299\) −2.93818 + 5.08907i −0.169919 + 0.294309i
\(300\) 0 0
\(301\) 0 0
\(302\) −12.6211 + 21.8604i −0.726262 + 1.25792i
\(303\) 0 0
\(304\) −4.43268 −0.254231
\(305\) −6.95489 + 12.0462i −0.398236 + 0.689765i
\(306\) 0 0
\(307\) 11.4437 0.653125 0.326563 0.945176i \(-0.394110\pi\)
0.326563 + 0.945176i \(0.394110\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 42.6167 2.42047
\(311\) −5.98143 10.3601i −0.339176 0.587470i 0.645102 0.764096i \(-0.276815\pi\)
−0.984278 + 0.176627i \(0.943481\pi\)
\(312\) 0 0
\(313\) −6.77197 + 11.7294i −0.382774 + 0.662985i −0.991458 0.130429i \(-0.958365\pi\)
0.608683 + 0.793413i \(0.291698\pi\)
\(314\) 4.90978 0.277075
\(315\) 0 0
\(316\) −6.29803 −0.354292
\(317\) −14.9814 + 25.9486i −0.841441 + 1.45742i 0.0472355 + 0.998884i \(0.484959\pi\)
−0.888676 + 0.458535i \(0.848374\pi\)
\(318\) 0 0
\(319\) −2.38874 4.13741i −0.133744 0.231651i
\(320\) −7.13231 −0.398708
\(321\) 0 0
\(322\) 0 0
\(323\) −3.65383 −0.203304
\(324\) 0 0
\(325\) 3.93818 6.82112i 0.218451 0.378368i
\(326\) 17.5215 0.970427
\(327\) 0 0
\(328\) 5.11058 8.85178i 0.282184 0.488758i
\(329\) 0 0
\(330\) 0 0
\(331\) −1.04325 + 1.80697i −0.0573423 + 0.0993198i −0.893272 0.449517i \(-0.851596\pi\)
0.835929 + 0.548837i \(0.184929\pi\)
\(332\) 1.82691 3.16431i 0.100265 0.173664i
\(333\) 0 0
\(334\) 10.3269 + 17.8867i 0.565064 + 0.978719i
\(335\) 22.0846 + 38.2517i 1.20661 + 2.08992i
\(336\) 0 0
\(337\) 8.10439 14.0372i 0.441474 0.764655i −0.556325 0.830965i \(-0.687789\pi\)
0.997799 + 0.0663093i \(0.0211224\pi\)
\(338\) 20.3955 1.10937
\(339\) 0 0
\(340\) 13.1113 0.711058
\(341\) −9.82072 17.0100i −0.531822 0.921143i
\(342\) 0 0
\(343\) 0 0
\(344\) −4.92030 8.52220i −0.265285 0.459486i
\(345\) 0 0
\(346\) −5.61677 9.72852i −0.301959 0.523009i
\(347\) 5.63348 + 9.75747i 0.302421 + 0.523808i 0.976684 0.214683i \(-0.0688719\pi\)
−0.674263 + 0.738491i \(0.735539\pi\)
\(348\) 0 0
\(349\) −0.0988844 0.171273i −0.00529316 0.00916803i 0.863367 0.504577i \(-0.168352\pi\)
−0.868660 + 0.495409i \(0.835018\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −6.60507 11.4403i −0.352052 0.609771i
\(353\) −12.5019 −0.665407 −0.332703 0.943032i \(-0.607961\pi\)
−0.332703 + 0.943032i \(0.607961\pi\)
\(354\) 0 0
\(355\) −10.3214 −0.547804
\(356\) −4.27011 + 7.39605i −0.226315 + 0.391990i
\(357\) 0 0
\(358\) 3.26578 + 5.65650i 0.172602 + 0.298955i
\(359\) 10.0098 + 17.3375i 0.528299 + 0.915040i 0.999456 + 0.0329908i \(0.0105032\pi\)
−0.471157 + 0.882049i \(0.656163\pi\)
\(360\) 0 0
\(361\) 9.10507 15.7705i 0.479214 0.830024i
\(362\) −15.7577 + 27.2932i −0.828208 + 1.43450i
\(363\) 0 0
\(364\) 0 0
\(365\) 19.0927 33.0695i 0.999357 1.73094i
\(366\) 0 0
\(367\) −30.0727 −1.56978 −0.784892 0.619632i \(-0.787282\pi\)
−0.784892 + 0.619632i \(0.787282\pi\)
\(368\) −14.6545 + 25.3824i −0.763919 + 1.32315i
\(369\) 0 0
\(370\) 29.0617 1.51085
\(371\) 0 0
\(372\) 0 0
\(373\) 7.01238 0.363087 0.181544 0.983383i \(-0.441891\pi\)
0.181544 + 0.983383i \(0.441891\pi\)
\(374\) −9.82072 17.0100i −0.507818 0.879566i
\(375\) 0 0
\(376\) 2.51788 4.36110i 0.129850 0.224906i
\(377\) −1.69963 −0.0875353
\(378\) 0 0
\(379\) −19.0741 −0.979772 −0.489886 0.871787i \(-0.662962\pi\)
−0.489886 + 0.871787i \(0.662962\pi\)
\(380\) 1.41714 2.45455i 0.0726976 0.125916i
\(381\) 0 0
\(382\) −3.93818 6.82112i −0.201495 0.348999i
\(383\) 3.21015 0.164031 0.0820155 0.996631i \(-0.473864\pi\)
0.0820155 + 0.996631i \(0.473864\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 42.9949 2.18838
\(387\) 0 0
\(388\) 3.25340 5.63506i 0.165166 0.286077i
\(389\) −5.13602 −0.260407 −0.130203 0.991487i \(-0.541563\pi\)
−0.130203 + 0.991487i \(0.541563\pi\)
\(390\) 0 0
\(391\) −12.0796 + 20.9225i −0.610893 + 1.05810i
\(392\) 0 0
\(393\) 0 0
\(394\) −9.11058 + 15.7800i −0.458984 + 0.794984i
\(395\) −12.7145 + 22.0221i −0.639735 + 1.10805i
\(396\) 0 0
\(397\) 11.4691 + 19.8650i 0.575615 + 0.996995i 0.995975 + 0.0896370i \(0.0285707\pi\)
−0.420359 + 0.907358i \(0.638096\pi\)
\(398\) 7.44987 + 12.9036i 0.373428 + 0.646797i
\(399\) 0 0
\(400\) 19.6421 34.0212i 0.982107 1.70106i
\(401\) 18.2101 0.909371 0.454686 0.890652i \(-0.349752\pi\)
0.454686 + 0.890652i \(0.349752\pi\)
\(402\) 0 0
\(403\) −6.98762 −0.348078
\(404\) −1.53961 2.66668i −0.0765985 0.132672i
\(405\) 0 0
\(406\) 0 0
\(407\) −6.69708 11.5997i −0.331962 0.574975i
\(408\) 0 0
\(409\) −7.66621 13.2783i −0.379070 0.656568i 0.611858 0.790968i \(-0.290423\pi\)
−0.990927 + 0.134400i \(0.957089\pi\)
\(410\) 16.5025 + 28.5831i 0.814999 + 1.41162i
\(411\) 0 0
\(412\) −7.05494 12.2195i −0.347572 0.602013i
\(413\) 0 0
\(414\) 0 0
\(415\) −7.37636 12.7762i −0.362091 0.627160i
\(416\) −4.69963 −0.230418
\(417\) 0 0
\(418\) −4.24591 −0.207674
\(419\) −5.28435 + 9.15276i −0.258157 + 0.447142i −0.965748 0.259481i \(-0.916449\pi\)
0.707591 + 0.706622i \(0.249782\pi\)
\(420\) 0 0
\(421\) 18.0858 + 31.3256i 0.881449 + 1.52671i 0.849731 + 0.527217i \(0.176765\pi\)
0.0317181 + 0.999497i \(0.489902\pi\)
\(422\) 8.94870 + 15.4996i 0.435616 + 0.754509i
\(423\) 0 0
\(424\) −0.116765 + 0.202243i −0.00567062 + 0.00982181i
\(425\) 16.1909 28.0434i 0.785374 1.36031i
\(426\) 0 0
\(427\) 0 0
\(428\) −2.37890 + 4.12038i −0.114989 + 0.199166i
\(429\) 0 0
\(430\) 31.7761 1.53238
\(431\) 17.5494 30.3965i 0.845327 1.46415i −0.0400101 0.999199i \(-0.512739\pi\)
0.885337 0.464950i \(-0.153928\pi\)
\(432\) 0 0
\(433\) 41.1730 1.97865 0.989324 0.145731i \(-0.0465533\pi\)
0.989324 + 0.145731i \(0.0465533\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −16.7651 −0.802902
\(437\) 2.61126 + 4.52284i 0.124914 + 0.216357i
\(438\) 0 0
\(439\) −2.33929 + 4.05178i −0.111648 + 0.193381i −0.916435 0.400184i \(-0.868946\pi\)
0.804787 + 0.593564i \(0.202280\pi\)
\(440\) −19.0507 −0.908209
\(441\) 0 0
\(442\) −6.98762 −0.332367
\(443\) 15.0865 26.1306i 0.716781 1.24150i −0.245487 0.969400i \(-0.578948\pi\)
0.962268 0.272102i \(-0.0877188\pi\)
\(444\) 0 0
\(445\) 17.2410 + 29.8623i 0.817303 + 1.41561i
\(446\) −9.63279 −0.456126
\(447\) 0 0
\(448\) 0 0
\(449\) −0.333792 −0.0157526 −0.00787632 0.999969i \(-0.502507\pi\)
−0.00787632 + 0.999969i \(0.502507\pi\)
\(450\) 0 0
\(451\) 7.60576 13.1736i 0.358141 0.620319i
\(452\) 16.4871 0.775490
\(453\) 0 0
\(454\) −9.43199 + 16.3367i −0.442665 + 0.766719i
\(455\) 0 0
\(456\) 0 0
\(457\) 9.65452 16.7221i 0.451619 0.782227i −0.546868 0.837219i \(-0.684180\pi\)
0.998487 + 0.0549917i \(0.0175132\pi\)
\(458\) −16.6927 + 28.9127i −0.780001 + 1.35100i
\(459\) 0 0
\(460\) −9.37017 16.2296i −0.436886 0.756709i
\(461\) −19.5538 33.8681i −0.910710 1.57740i −0.813064 0.582175i \(-0.802202\pi\)
−0.0976463 0.995221i \(-0.531131\pi\)
\(462\) 0 0
\(463\) −10.9382 + 18.9455i −0.508340 + 0.880471i 0.491613 + 0.870814i \(0.336407\pi\)
−0.999953 + 0.00965741i \(0.996926\pi\)
\(464\) −8.47710 −0.393539
\(465\) 0 0
\(466\) 15.2335 0.705680
\(467\) 6.16002 + 10.6695i 0.285052 + 0.493724i 0.972622 0.232394i \(-0.0746559\pi\)
−0.687570 + 0.726118i \(0.741323\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 8.13045 + 14.0823i 0.375029 + 0.649570i
\(471\) 0 0
\(472\) 8.38255 + 14.5190i 0.385838 + 0.668291i
\(473\) −7.32258 12.6831i −0.336693 0.583169i
\(474\) 0 0
\(475\) −3.50000 6.06218i −0.160591 0.278152i
\(476\) 0 0
\(477\) 0 0
\(478\) −9.53706 16.5187i −0.436215 0.755547i
\(479\) 13.4895 0.616350 0.308175 0.951330i \(-0.400282\pi\)
0.308175 + 0.951330i \(0.400282\pi\)
\(480\) 0 0
\(481\) −4.76509 −0.217269
\(482\) 5.93701 10.2832i 0.270423 0.468387i
\(483\) 0 0
\(484\) 1.37704 + 2.38511i 0.0625929 + 0.108414i
\(485\) −13.1359 22.7521i −0.596473 1.03312i
\(486\) 0 0
\(487\) −3.77197 + 6.53324i −0.170924 + 0.296050i −0.938743 0.344617i \(-0.888009\pi\)
0.767819 + 0.640667i \(0.221342\pi\)
\(488\) 3.66071 6.34053i 0.165712 0.287022i
\(489\) 0 0
\(490\) 0 0
\(491\) −8.06979 + 13.9773i −0.364185 + 0.630786i −0.988645 0.150270i \(-0.951986\pi\)
0.624460 + 0.781057i \(0.285319\pi\)
\(492\) 0 0
\(493\) −6.98762 −0.314707
\(494\) −0.755260 + 1.30815i −0.0339808 + 0.0588564i
\(495\) 0 0
\(496\) −34.8516 −1.56488
\(497\) 0 0
\(498\) 0 0
\(499\) −30.8654 −1.38172 −0.690862 0.722987i \(-0.742769\pi\)
−0.690862 + 0.722987i \(0.742769\pi\)
\(500\) 4.58650 + 7.94406i 0.205115 + 0.355269i
\(501\) 0 0
\(502\) 3.92649 6.80088i 0.175248 0.303538i
\(503\) 24.6304 1.09822 0.549109 0.835751i \(-0.314967\pi\)
0.549109 + 0.835751i \(0.314967\pi\)
\(504\) 0 0
\(505\) −12.4327 −0.553247
\(506\) −14.0371 + 24.3129i −0.624024 + 1.08084i
\(507\) 0 0
\(508\) −4.43818 7.68715i −0.196912 0.341062i
\(509\) 13.5897 0.602355 0.301177 0.953568i \(-0.402620\pi\)
0.301177 + 0.953568i \(0.402620\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −4.59937 −0.203265
\(513\) 0 0
\(514\) −1.21015 + 2.09604i −0.0533774 + 0.0924523i
\(515\) −56.9701 −2.51040
\(516\) 0 0
\(517\) 3.74721 6.49036i 0.164802 0.285446i
\(518\) 0 0
\(519\) 0 0
\(520\) −3.38874 + 5.86946i −0.148606 + 0.257393i
\(521\) 19.5865 33.9248i 0.858100 1.48627i −0.0156383 0.999878i \(-0.504978\pi\)
0.873739 0.486396i \(-0.161689\pi\)
\(522\) 0 0
\(523\) 9.56182 + 16.5616i 0.418109 + 0.724187i 0.995749 0.0921051i \(-0.0293596\pi\)
−0.577640 + 0.816292i \(0.696026\pi\)
\(524\) −7.13348 12.3555i −0.311627 0.539754i
\(525\) 0 0
\(526\) −13.8207 + 23.9382i −0.602612 + 1.04375i
\(527\) −28.7280 −1.25141
\(528\) 0 0
\(529\) 11.5316 0.501372
\(530\) −0.377045 0.653061i −0.0163778 0.0283671i
\(531\) 0 0
\(532\) 0 0
\(533\) −2.70582 4.68661i −0.117202 0.203000i
\(534\) 0 0
\(535\) 9.60507 + 16.6365i 0.415264 + 0.719258i
\(536\) −11.6243 20.1338i −0.502091 0.869648i
\(537\) 0 0
\(538\) −15.8523 27.4570i −0.683441 1.18375i
\(539\) 0 0
\(540\) 0 0
\(541\) −1.26509 2.19120i −0.0543906 0.0942072i 0.837548 0.546363i \(-0.183988\pi\)
−0.891939 + 0.452156i \(0.850655\pi\)
\(542\) 6.73539 0.289310
\(543\) 0 0
\(544\) −19.3214 −0.828399
\(545\) −33.8454 + 58.6220i −1.44978 + 2.51109i
\(546\) 0 0
\(547\) −8.92580 15.4599i −0.381640 0.661019i 0.609657 0.792665i \(-0.291307\pi\)
−0.991297 + 0.131646i \(0.957974\pi\)
\(548\) −5.77128 9.99615i −0.246537 0.427015i
\(549\) 0 0
\(550\) 18.8145 32.5877i 0.802254 1.38955i
\(551\) −0.755260 + 1.30815i −0.0321752 + 0.0557290i
\(552\) 0 0
\(553\) 0 0
\(554\) −1.98329 + 3.43516i −0.0842619 + 0.145946i
\(555\) 0 0
\(556\) −0.987620 −0.0418844
\(557\) 20.6804 35.8195i 0.876255 1.51772i 0.0208360 0.999783i \(-0.493367\pi\)
0.855419 0.517936i \(-0.173299\pi\)
\(558\) 0 0
\(559\) −5.21015 −0.220366
\(560\) 0 0
\(561\) 0 0
\(562\) 47.5809 2.00708
\(563\) 10.3683 + 17.9584i 0.436972 + 0.756858i 0.997454 0.0713087i \(-0.0227175\pi\)
−0.560482 + 0.828166i \(0.689384\pi\)
\(564\) 0 0
\(565\) 33.2843 57.6501i 1.40028 2.42536i
\(566\) 17.5402 0.737271
\(567\) 0 0
\(568\) 5.43268 0.227950
\(569\) −0.134164 + 0.232379i −0.00562446 + 0.00974185i −0.868824 0.495121i \(-0.835124\pi\)
0.863199 + 0.504863i \(0.168457\pi\)
\(570\) 0 0
\(571\) −17.9684 31.1221i −0.751953 1.30242i −0.946875 0.321601i \(-0.895779\pi\)
0.194923 0.980819i \(-0.437554\pi\)
\(572\) −2.49814 −0.104453
\(573\) 0 0
\(574\) 0 0
\(575\) −46.2843 −1.93019
\(576\) 0 0
\(577\) 2.71565 4.70364i 0.113054 0.195815i −0.803946 0.594702i \(-0.797270\pi\)
0.917000 + 0.398887i \(0.130603\pi\)
\(578\) 0.165726 0.00689328
\(579\) 0 0
\(580\) 2.71015 4.69412i 0.112533 0.194913i
\(581\) 0 0
\(582\) 0 0
\(583\) −0.173775 + 0.300987i −0.00719702 + 0.0124656i
\(584\) −10.0494 + 17.4061i −0.415849 + 0.720271i
\(585\) 0 0
\(586\) −26.0858 45.1820i −1.07760 1.86645i
\(587\) −17.5822 30.4532i −0.725694 1.25694i −0.958688 0.284461i \(-0.908185\pi\)
0.232994 0.972478i \(-0.425148\pi\)
\(588\) 0 0
\(589\) −3.10507 + 5.37815i −0.127942 + 0.221603i
\(590\) −54.1359 −2.22874
\(591\) 0 0
\(592\) −23.7665 −0.976796
\(593\) 16.7534 + 29.0177i 0.687980 + 1.19162i 0.972490 + 0.232943i \(0.0748355\pi\)
−0.284511 + 0.958673i \(0.591831\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 3.74721 + 6.49036i 0.153492 + 0.265856i
\(597\) 0 0
\(598\) 4.99381 + 8.64953i 0.204212 + 0.353706i
\(599\) 3.12364 + 5.41031i 0.127629 + 0.221059i 0.922757 0.385381i \(-0.125930\pi\)
−0.795129 + 0.606441i \(0.792597\pi\)
\(600\) 0 0
\(601\) 11.2040 + 19.4058i 0.457019 + 0.791580i 0.998802 0.0489384i \(-0.0155838\pi\)
−0.541783 + 0.840519i \(0.682250\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 6.59957 + 11.4308i 0.268533 + 0.465112i
\(605\) 11.1199 0.452089
\(606\) 0 0
\(607\) −14.9505 −0.606821 −0.303411 0.952860i \(-0.598125\pi\)
−0.303411 + 0.952860i \(0.598125\pi\)
\(608\) −2.08836 + 3.61715i −0.0846943 + 0.146695i
\(609\) 0 0
\(610\) 11.8207 + 20.4741i 0.478607 + 0.828972i
\(611\) −1.33310 2.30900i −0.0539316 0.0934123i
\(612\) 0 0
\(613\) −17.5989 + 30.4822i −0.710812 + 1.23116i 0.253740 + 0.967272i \(0.418339\pi\)
−0.964553 + 0.263891i \(0.914994\pi\)
\(614\) 9.72500 16.8442i 0.392469 0.679776i
\(615\) 0 0
\(616\) 0 0
\(617\) −1.00619 + 1.74277i −0.0405077 + 0.0701614i −0.885568 0.464509i \(-0.846231\pi\)
0.845061 + 0.534670i \(0.179564\pi\)
\(618\) 0 0
\(619\) −39.3818 −1.58289 −0.791444 0.611242i \(-0.790670\pi\)
−0.791444 + 0.611242i \(0.790670\pi\)
\(620\) 11.1421 19.2987i 0.447479 0.775056i
\(621\) 0 0
\(622\) −20.3324 −0.815256
\(623\) 0 0
\(624\) 0 0
\(625\) −2.34479 −0.0937918
\(626\) 11.5098 + 19.9356i 0.460025 + 0.796787i
\(627\) 0 0
\(628\) 1.28366 2.22337i 0.0512237 0.0887220i
\(629\) −19.5906 −0.781126
\(630\) 0 0
\(631\) 44.3832 1.76687 0.883433 0.468558i \(-0.155226\pi\)
0.883433 + 0.468558i \(0.155226\pi\)
\(632\) 6.69227 11.5913i 0.266204 0.461079i
\(633\) 0 0
\(634\) 25.4629 + 44.1030i 1.01126 + 1.75155i
\(635\) −35.8392 −1.42224
\(636\) 0 0
\(637\) 0 0
\(638\) −8.11993 −0.321471
\(639\) 0 0
\(640\) −22.9251 + 39.7075i −0.906195 + 1.56957i
\(641\) 14.9862 0.591921 0.295961 0.955200i \(-0.404360\pi\)
0.295961 + 0.955200i \(0.404360\pi\)
\(642\) 0 0
\(643\) −5.32691 + 9.22649i −0.210073 + 0.363857i −0.951737 0.306914i \(-0.900703\pi\)
0.741664 + 0.670771i \(0.234037\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −3.10507 + 5.37815i −0.122168 + 0.211600i
\(647\) −1.06478 + 1.84424i −0.0418606 + 0.0725047i −0.886197 0.463309i \(-0.846662\pi\)
0.844336 + 0.535814i \(0.179995\pi\)
\(648\) 0 0
\(649\) 12.4752 + 21.6078i 0.489696 + 0.848178i
\(650\) −6.69344 11.5934i −0.262538 0.454730i
\(651\) 0 0
\(652\) 4.58100 7.93453i 0.179406 0.310740i
\(653\) −11.1716 −0.437180 −0.218590 0.975817i \(-0.570146\pi\)
−0.218590 + 0.975817i \(0.570146\pi\)
\(654\) 0 0
\(655\) −57.6043 −2.25079
\(656\) −13.4956 23.3751i −0.526914 0.912642i
\(657\) 0 0
\(658\) 0 0
\(659\) −5.65452 9.79391i −0.220269 0.381517i 0.734621 0.678478i \(-0.237360\pi\)
−0.954890 + 0.296961i \(0.904027\pi\)
\(660\) 0 0
\(661\) 16.1785 + 28.0220i 0.629271 + 1.08993i 0.987698 + 0.156372i \(0.0499798\pi\)
−0.358427 + 0.933558i \(0.616687\pi\)
\(662\) 1.77314 + 3.07117i 0.0689151 + 0.119364i
\(663\) 0 0
\(664\) 3.88255 + 6.72477i 0.150672 + 0.260972i
\(665\) 0 0
\(666\) 0 0
\(667\) 4.99381 + 8.64953i 0.193361 + 0.334911i
\(668\) 10.7999 0.417860
\(669\) 0 0
\(670\) 75.0714 2.90026
\(671\) 5.44801 9.43623i 0.210318 0.364282i
\(672\) 0 0
\(673\) 12.0803 + 20.9237i 0.465662 + 0.806550i 0.999231 0.0392063i \(-0.0124830\pi\)
−0.533569 + 0.845756i \(0.679150\pi\)
\(674\) −13.7744 23.8580i −0.530572 0.918977i
\(675\) 0 0
\(676\) 5.33242 9.23601i 0.205093 0.355231i
\(677\) −12.5371 + 21.7148i −0.481838 + 0.834569i −0.999783 0.0208457i \(-0.993364\pi\)
0.517944 + 0.855414i \(0.326697\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) −13.9320 + 24.1309i −0.534267 + 0.925378i
\(681\) 0 0
\(682\) −33.3832 −1.27831
\(683\) −23.8392 + 41.2907i −0.912182 + 1.57995i −0.101207 + 0.994865i \(0.532271\pi\)
−0.810975 + 0.585081i \(0.801063\pi\)
\(684\) 0 0
\(685\) −46.6043 −1.78066
\(686\) 0 0
\(687\) 0 0
\(688\) −25.9862 −0.990716
\(689\) 0.0618219 + 0.107079i 0.00235523 + 0.00407937i
\(690\) 0 0
\(691\) −12.3400 + 21.3735i −0.469435 + 0.813085i −0.999389 0.0349408i \(-0.988876\pi\)
0.529954 + 0.848026i \(0.322209\pi\)
\(692\) −5.87402 −0.223297
\(693\) 0 0
\(694\) 19.1496 0.726910
\(695\) −1.99381 + 3.45338i −0.0756295 + 0.130994i
\(696\) 0 0
\(697\) −11.1243 19.2679i −0.421364 0.729824i
\(698\) −0.336134 −0.0127228
\(699\) 0 0
\(700\) 0 0
\(701\) 29.6784 1.12094 0.560469 0.828175i \(-0.310621\pi\)
0.560469 + 0.828175i \(0.310621\pi\)
\(702\) 0 0
\(703\) −2.11745 + 3.66754i −0.0798613 + 0.138324i
\(704\) 5.58699 0.210567
\(705\) 0 0
\(706\) −10.6243 + 18.4018i −0.399849 + 0.692559i
\(707\) 0 0
\(708\) 0 0
\(709\) 14.6291 25.3383i 0.549406 0.951599i −0.448909 0.893577i \(-0.648187\pi\)
0.998315 0.0580220i \(-0.0184794\pi\)
\(710\) −8.77128 + 15.1923i −0.329180 + 0.570157i
\(711\) 0 0
\(712\) −9.07481 15.7180i −0.340093 0.589058i
\(713\) 20.5309 + 35.5605i 0.768887 + 1.33175i
\(714\) 0 0
\(715\) −5.04325 + 8.73517i −0.188607 + 0.326677i
\(716\) 3.41535 0.127638
\(717\) 0 0
\(718\) 34.0260 1.26984
\(719\) −0.537063 0.930220i −0.0200291 0.0346913i 0.855837 0.517245i \(-0.173043\pi\)
−0.875866 + 0.482554i \(0.839709\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −15.4752 26.8039i −0.575929 0.997538i
\(723\) 0 0
\(724\) 8.23972 + 14.2716i 0.306227 + 0.530400i
\(725\) −6.69344 11.5934i −0.248588 0.430567i
\(726\) 0 0
\(727\) 12.7163 + 22.0253i 0.471623 + 0.816875i 0.999473 0.0324628i \(-0.0103350\pi\)
−0.527850 + 0.849338i \(0.677002\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) −32.4505 56.2059i −1.20105 2.08027i
\(731\) −21.4203 −0.792258
\(732\) 0 0
\(733\) 11.3955 0.420904 0.210452 0.977604i \(-0.432506\pi\)
0.210452 + 0.977604i \(0.432506\pi\)
\(734\) −25.5562 + 44.2647i −0.943298 + 1.63384i
\(735\) 0 0
\(736\) 13.8083 + 23.9168i 0.508982 + 0.881583i
\(737\) −17.2997 29.9639i −0.637242 1.10374i
\(738\) 0 0
\(739\) 14.9697 25.9283i 0.550671 0.953790i −0.447556 0.894256i \(-0.647705\pi\)
0.998226 0.0595336i \(-0.0189613\pi\)
\(740\) 7.59820 13.1605i 0.279315 0.483788i
\(741\) 0 0
\(742\) 0 0
\(743\) −9.50069 + 16.4557i −0.348546 + 0.603700i −0.985991 0.166796i \(-0.946658\pi\)
0.637445 + 0.770496i \(0.279991\pi\)
\(744\) 0 0
\(745\) 30.2595 1.10862
\(746\) 5.95922 10.3217i 0.218183 0.377903i
\(747\) 0 0
\(748\) −10.2705 −0.375527
\(749\) 0 0
\(750\) 0 0
\(751\) 0.0261368 0.000953747 0.000476873 1.00000i \(-0.499848\pi\)
0.000476873 1.00000i \(0.499848\pi\)
\(752\) −6.64902 11.5164i −0.242465 0.419961i
\(753\) 0 0
\(754\) −1.44437 + 2.50172i −0.0526008 + 0.0911072i
\(755\) 53.2929 1.93953
\(756\) 0 0
\(757\) −13.6910 −0.497607 −0.248803 0.968554i \(-0.580037\pi\)
−0.248803 + 0.968554i \(0.580037\pi\)
\(758\) −16.2095 + 28.0756i −0.588754 + 1.01975i
\(759\) 0 0
\(760\) 3.01169 + 5.21640i 0.109246 + 0.189219i
\(761\) −14.6428 −0.530802 −0.265401 0.964138i \(-0.585504\pi\)
−0.265401 + 0.964138i \(0.585504\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −4.11855 −0.149004
\(765\) 0 0
\(766\) 2.72803 4.72509i 0.0985677 0.170724i
\(767\) 8.87636 0.320507
\(768\) 0 0
\(769\) 24.5672 42.5517i 0.885918 1.53445i 0.0412592 0.999148i \(-0.486863\pi\)
0.844658 0.535306i \(-0.179804\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 11.2410 19.4700i 0.404573 0.700741i
\(773\) −6.22067 + 10.7745i −0.223742 + 0.387532i −0.955941 0.293558i \(-0.905161\pi\)
0.732199 + 0.681090i \(0.238494\pi\)
\(774\) 0 0
\(775\) −27.5185 47.6634i −0.988493 1.71212i
\(776\) 6.91411 + 11.9756i 0.248202 + 0.429898i
\(777\) 0 0
\(778\) −4.36467 + 7.55982i −0.156481 + 0.271033i
\(779\) −4.80951 −0.172319
\(780\) 0 0
\(781\) 8.08513 0.289309
\(782\) 20.5309 + 35.5605i 0.734183 + 1.27164i
\(783\) 0 0
\(784\) 0 0
\(785\) −5.18292 8.97708i −0.184986 0.320406i
\(786\) 0 0
\(787\) −16.4567 28.5038i −0.586617 1.01605i −0.994672 0.103093i \(-0.967126\pi\)
0.408055 0.912957i \(-0.366207\pi\)
\(788\) 4.76392 + 8.25135i 0.169708 + 0.293942i
\(789\) 0 0
\(790\) 21.6099 + 37.4294i 0.768845 + 1.33168i
\(791\) 0 0
\(792\) 0 0
\(793\) −1.93818 3.35702i −0.0688267 0.119211i
\(794\)