Properties

Label 950.2.e.m.501.3
Level $950$
Weight $2$
Character 950.501
Analytic conductor $7.586$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 950.e (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.58578819202\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: 8.0.39075800976.1
Defining polynomial: \(x^{8} - x^{7} + 12 x^{6} - 13 x^{5} + 125 x^{4} - 116 x^{3} + 232 x^{2} + 96 x + 64\)
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 501.3
Root \(-0.236942 - 0.410396i\) of defining polynomial
Character \(\chi\) \(=\) 950.501
Dual form 950.2.e.m.201.3

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{2} +(0.236942 + 0.410396i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.236942 + 0.410396i) q^{6} -2.19155 q^{7} -1.00000 q^{8} +(1.38772 - 2.40360i) q^{9} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{2} +(0.236942 + 0.410396i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.236942 + 0.410396i) q^{6} -2.19155 q^{7} -1.00000 q^{8} +(1.38772 - 2.40360i) q^{9} -4.96699 q^{11} -0.473885 q^{12} +(-1.14116 + 1.97656i) q^{13} +(-1.09578 - 1.89794i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-3.38772 - 5.86770i) q^{17} +2.77543 q^{18} +(-3.12466 - 3.03916i) q^{19} +(-0.519272 - 0.899406i) q^{21} +(-2.48349 - 4.30154i) q^{22} +(-3.84233 + 6.65511i) q^{23} +(-0.236942 - 0.410396i) q^{24} -2.28233 q^{26} +2.73689 q^{27} +(1.09578 - 1.89794i) q^{28} +(-0.983494 + 1.70346i) q^{29} +7.58388 q^{31} +(0.500000 - 0.866025i) q^{32} +(-1.17689 - 2.03843i) q^{33} +(3.38772 - 5.86770i) q^{34} +(1.38772 + 2.40360i) q^{36} -7.38864 q^{37} +(1.06966 - 4.22562i) q^{38} -1.08156 q^{39} +(-5.70393 - 9.87950i) q^{41} +(0.519272 - 0.899406i) q^{42} +(5.07927 + 8.79756i) q^{43} +(2.48349 - 4.30154i) q^{44} -7.68466 q^{46} +(-2.09578 + 3.62999i) q^{47} +(0.236942 - 0.410396i) q^{48} -2.19709 q^{49} +(1.60539 - 2.78061i) q^{51} +(-1.14116 - 1.97656i) q^{52} +(2.09578 - 3.62999i) q^{53} +(1.36844 + 2.37022i) q^{54} +2.19155 q^{56} +(0.506896 - 2.00245i) q^{57} -1.96699 q^{58} +(-1.72044 - 2.97988i) q^{59} +(2.36160 - 4.09041i) q^{61} +(3.79194 + 6.56783i) q^{62} +(-3.04126 + 5.26761i) q^{63} +1.00000 q^{64} +(1.17689 - 2.03843i) q^{66} +(-0.404223 + 0.700134i) q^{67} +6.77543 q^{68} -3.64164 q^{69} +(5.59854 + 9.69696i) q^{71} +(-1.38772 + 2.40360i) q^{72} +(2.42850 + 4.20628i) q^{73} +(-3.69432 - 6.39875i) q^{74} +(4.19432 - 1.18645i) q^{76} +10.8854 q^{77} +(-0.540781 - 0.936659i) q^{78} +(-7.63427 - 13.2229i) q^{79} +(-3.51467 - 6.08758i) q^{81} +(5.70393 - 9.87950i) q^{82} +12.7232 q^{83} +1.03854 q^{84} +(-5.07927 + 8.79756i) q^{86} -0.932126 q^{87} +4.96699 q^{88} +(1.78233 - 3.08709i) q^{89} +(2.50093 - 4.33173i) q^{91} +(-3.84233 - 6.65511i) q^{92} +(1.79694 + 3.11239i) q^{93} -4.19155 q^{94} +0.473885 q^{96} +(0.0861680 + 0.149247i) q^{97} +(-1.09854 - 1.90273i) q^{98} +(-6.89277 + 11.9386i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 4q^{2} - q^{3} - 4q^{4} + q^{6} - 12q^{7} - 8q^{8} - 11q^{9} + O(q^{10}) \) \( 8q + 4q^{2} - q^{3} - 4q^{4} + q^{6} - 12q^{7} - 8q^{8} - 11q^{9} + 10q^{11} + 2q^{12} - 9q^{13} - 6q^{14} - 4q^{16} - 5q^{17} - 22q^{18} - q^{21} + 5q^{22} - 6q^{23} + q^{24} - 18q^{26} - 16q^{27} + 6q^{28} + 17q^{29} + 22q^{31} + 4q^{32} + 4q^{33} + 5q^{34} - 11q^{36} + 8q^{37} - 36q^{39} + 7q^{41} + q^{42} + 13q^{43} - 5q^{44} - 12q^{46} - 14q^{47} - q^{48} + 44q^{49} - 9q^{51} - 9q^{52} + 14q^{53} - 8q^{54} + 12q^{56} + 48q^{57} + 34q^{58} + 14q^{59} - 9q^{61} + 11q^{62} + 45q^{63} + 8q^{64} - 4q^{66} - 6q^{67} + 10q^{68} + 54q^{69} + 14q^{71} + 11q^{72} + 11q^{73} + 4q^{74} + 10q^{77} - 18q^{78} - 17q^{79} - 36q^{81} - 7q^{82} + 46q^{83} + 2q^{84} - 13q^{86} + 2q^{87} - 10q^{88} + 14q^{89} - 25q^{91} - 6q^{92} - 13q^{93} - 28q^{94} - 2q^{96} + 17q^{97} + 22q^{98} - 60q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/950\mathbb{Z}\right)^\times\).

\(n\) \(77\) \(401\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 + 0.866025i 0.353553 + 0.612372i
\(3\) 0.236942 + 0.410396i 0.136799 + 0.236942i 0.926283 0.376828i \(-0.122985\pi\)
−0.789484 + 0.613771i \(0.789652\pi\)
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) 0 0
\(6\) −0.236942 + 0.410396i −0.0967313 + 0.167544i
\(7\) −2.19155 −0.828330 −0.414165 0.910202i \(-0.635926\pi\)
−0.414165 + 0.910202i \(0.635926\pi\)
\(8\) −1.00000 −0.353553
\(9\) 1.38772 2.40360i 0.462572 0.801199i
\(10\) 0 0
\(11\) −4.96699 −1.49760 −0.748802 0.662794i \(-0.769370\pi\)
−0.748802 + 0.662794i \(0.769370\pi\)
\(12\) −0.473885 −0.136799
\(13\) −1.14116 + 1.97656i −0.316502 + 0.548198i −0.979756 0.200197i \(-0.935842\pi\)
0.663253 + 0.748395i \(0.269175\pi\)
\(14\) −1.09578 1.89794i −0.292859 0.507246i
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −3.38772 5.86770i −0.821642 1.42313i −0.904459 0.426561i \(-0.859725\pi\)
0.0828169 0.996565i \(-0.473608\pi\)
\(18\) 2.77543 0.654176
\(19\) −3.12466 3.03916i −0.716846 0.697232i
\(20\) 0 0
\(21\) −0.519272 0.899406i −0.113314 0.196266i
\(22\) −2.48349 4.30154i −0.529483 0.917091i
\(23\) −3.84233 + 6.65511i −0.801181 + 1.38769i 0.117658 + 0.993054i \(0.462461\pi\)
−0.918839 + 0.394632i \(0.870872\pi\)
\(24\) −0.236942 0.410396i −0.0483656 0.0837718i
\(25\) 0 0
\(26\) −2.28233 −0.447602
\(27\) 2.73689 0.526715
\(28\) 1.09578 1.89794i 0.207082 0.358677i
\(29\) −0.983494 + 1.70346i −0.182630 + 0.316325i −0.942775 0.333428i \(-0.891794\pi\)
0.760145 + 0.649753i \(0.225128\pi\)
\(30\) 0 0
\(31\) 7.58388 1.36210 0.681052 0.732235i \(-0.261523\pi\)
0.681052 + 0.732235i \(0.261523\pi\)
\(32\) 0.500000 0.866025i 0.0883883 0.153093i
\(33\) −1.17689 2.03843i −0.204870 0.354846i
\(34\) 3.38772 5.86770i 0.580989 1.00630i
\(35\) 0 0
\(36\) 1.38772 + 2.40360i 0.231286 + 0.400599i
\(37\) −7.38864 −1.21469 −0.607343 0.794440i \(-0.707764\pi\)
−0.607343 + 0.794440i \(0.707764\pi\)
\(38\) 1.06966 4.22562i 0.173522 0.685485i
\(39\) −1.08156 −0.173188
\(40\) 0 0
\(41\) −5.70393 9.87950i −0.890804 1.54292i −0.838913 0.544266i \(-0.816808\pi\)
−0.0518913 0.998653i \(-0.516525\pi\)
\(42\) 0.519272 0.899406i 0.0801254 0.138781i
\(43\) 5.07927 + 8.79756i 0.774582 + 1.34161i 0.935029 + 0.354570i \(0.115373\pi\)
−0.160448 + 0.987044i \(0.551294\pi\)
\(44\) 2.48349 4.30154i 0.374401 0.648481i
\(45\) 0 0
\(46\) −7.68466 −1.13304
\(47\) −2.09578 + 3.62999i −0.305701 + 0.529489i −0.977417 0.211319i \(-0.932224\pi\)
0.671717 + 0.740808i \(0.265557\pi\)
\(48\) 0.236942 0.410396i 0.0341997 0.0592356i
\(49\) −2.19709 −0.313870
\(50\) 0 0
\(51\) 1.60539 2.78061i 0.224799 0.389364i
\(52\) −1.14116 1.97656i −0.158251 0.274099i
\(53\) 2.09578 3.62999i 0.287877 0.498618i −0.685426 0.728143i \(-0.740384\pi\)
0.973303 + 0.229525i \(0.0737172\pi\)
\(54\) 1.36844 + 2.37022i 0.186222 + 0.322545i
\(55\) 0 0
\(56\) 2.19155 0.292859
\(57\) 0.506896 2.00245i 0.0671401 0.265232i
\(58\) −1.96699 −0.258278
\(59\) −1.72044 2.97988i −0.223982 0.387948i 0.732032 0.681271i \(-0.238572\pi\)
−0.956013 + 0.293323i \(0.905239\pi\)
\(60\) 0 0
\(61\) 2.36160 4.09041i 0.302372 0.523724i −0.674301 0.738457i \(-0.735555\pi\)
0.976673 + 0.214733i \(0.0688882\pi\)
\(62\) 3.79194 + 6.56783i 0.481577 + 0.834115i
\(63\) −3.04126 + 5.26761i −0.383162 + 0.663657i
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 1.17689 2.03843i 0.144865 0.250914i
\(67\) −0.404223 + 0.700134i −0.0493836 + 0.0855350i −0.889661 0.456622i \(-0.849059\pi\)
0.840277 + 0.542157i \(0.182392\pi\)
\(68\) 6.77543 0.821642
\(69\) −3.64164 −0.438402
\(70\) 0 0
\(71\) 5.59854 + 9.69696i 0.664425 + 1.15082i 0.979441 + 0.201731i \(0.0646568\pi\)
−0.315016 + 0.949086i \(0.602010\pi\)
\(72\) −1.38772 + 2.40360i −0.163544 + 0.283266i
\(73\) 2.42850 + 4.20628i 0.284234 + 0.492308i 0.972423 0.233224i \(-0.0749274\pi\)
−0.688189 + 0.725531i \(0.741594\pi\)
\(74\) −3.69432 6.39875i −0.429456 0.743840i
\(75\) 0 0
\(76\) 4.19432 1.18645i 0.481122 0.136095i
\(77\) 10.8854 1.24051
\(78\) −0.540781 0.936659i −0.0612313 0.106056i
\(79\) −7.63427 13.2229i −0.858922 1.48770i −0.872958 0.487796i \(-0.837801\pi\)
0.0140356 0.999901i \(-0.495532\pi\)
\(80\) 0 0
\(81\) −3.51467 6.08758i −0.390518 0.676398i
\(82\) 5.70393 9.87950i 0.629894 1.09101i
\(83\) 12.7232 1.39655 0.698276 0.715828i \(-0.253951\pi\)
0.698276 + 0.715828i \(0.253951\pi\)
\(84\) 1.03854 0.113314
\(85\) 0 0
\(86\) −5.07927 + 8.79756i −0.547712 + 0.948665i
\(87\) −0.932126 −0.0999343
\(88\) 4.96699 0.529483
\(89\) 1.78233 3.08709i 0.188927 0.327230i −0.755966 0.654611i \(-0.772833\pi\)
0.944893 + 0.327380i \(0.106166\pi\)
\(90\) 0 0
\(91\) 2.50093 4.33173i 0.262168 0.454089i
\(92\) −3.84233 6.65511i −0.400591 0.693843i
\(93\) 1.79694 + 3.11239i 0.186334 + 0.322740i
\(94\) −4.19155 −0.432326
\(95\) 0 0
\(96\) 0.473885 0.0483656
\(97\) 0.0861680 + 0.149247i 0.00874903 + 0.0151538i 0.870367 0.492404i \(-0.163882\pi\)
−0.861618 + 0.507558i \(0.830548\pi\)
\(98\) −1.09854 1.90273i −0.110970 0.192205i
\(99\) −6.89277 + 11.9386i −0.692750 + 1.19988i
\(100\) 0 0
\(101\) −7.41199 + 12.8379i −0.737521 + 1.27742i 0.216088 + 0.976374i \(0.430670\pi\)
−0.953609 + 0.301049i \(0.902663\pi\)
\(102\) 3.21077 0.317914
\(103\) −14.6031 −1.43889 −0.719443 0.694552i \(-0.755603\pi\)
−0.719443 + 0.694552i \(0.755603\pi\)
\(104\) 1.14116 1.97656i 0.111900 0.193817i
\(105\) 0 0
\(106\) 4.19155 0.407120
\(107\) 0.363891 0.0351787 0.0175893 0.999845i \(-0.494401\pi\)
0.0175893 + 0.999845i \(0.494401\pi\)
\(108\) −1.36844 + 2.37022i −0.131679 + 0.228074i
\(109\) 6.61776 + 11.4623i 0.633867 + 1.09789i 0.986754 + 0.162224i \(0.0518666\pi\)
−0.352887 + 0.935666i \(0.614800\pi\)
\(110\) 0 0
\(111\) −1.75068 3.03227i −0.166167 0.287810i
\(112\) 1.09578 + 1.89794i 0.103541 + 0.179339i
\(113\) −17.4894 −1.64527 −0.822633 0.568572i \(-0.807496\pi\)
−0.822633 + 0.568572i \(0.807496\pi\)
\(114\) 1.98762 0.562242i 0.186158 0.0526588i
\(115\) 0 0
\(116\) −0.983494 1.70346i −0.0913151 0.158162i
\(117\) 3.16723 + 5.48580i 0.292810 + 0.507162i
\(118\) 1.72044 2.97988i 0.158379 0.274320i
\(119\) 7.42437 + 12.8594i 0.680591 + 1.17882i
\(120\) 0 0
\(121\) 13.6710 1.24282
\(122\) 4.72320 0.427619
\(123\) 2.70301 4.68174i 0.243722 0.422138i
\(124\) −3.79194 + 6.56783i −0.340526 + 0.589809i
\(125\) 0 0
\(126\) −6.08251 −0.541873
\(127\) −2.33272 + 4.04039i −0.206995 + 0.358527i −0.950767 0.309908i \(-0.899702\pi\)
0.743771 + 0.668434i \(0.233035\pi\)
\(128\) 0.500000 + 0.866025i 0.0441942 + 0.0765466i
\(129\) −2.40699 + 4.16903i −0.211924 + 0.367062i
\(130\) 0 0
\(131\) −0.449610 0.778747i −0.0392826 0.0680395i 0.845716 0.533634i \(-0.179174\pi\)
−0.884998 + 0.465594i \(0.845841\pi\)
\(132\) 2.35378 0.204870
\(133\) 6.84786 + 6.66049i 0.593785 + 0.577538i
\(134\) −0.808445 −0.0698390
\(135\) 0 0
\(136\) 3.38772 + 5.86770i 0.290494 + 0.503151i
\(137\) 3.73787 6.47418i 0.319348 0.553126i −0.661004 0.750382i \(-0.729870\pi\)
0.980352 + 0.197256i \(0.0632029\pi\)
\(138\) −1.82082 3.15375i −0.154999 0.268465i
\(139\) 3.00961 5.21280i 0.255272 0.442144i −0.709698 0.704506i \(-0.751168\pi\)
0.964969 + 0.262363i \(0.0845017\pi\)
\(140\) 0 0
\(141\) −1.98631 −0.167278
\(142\) −5.59854 + 9.69696i −0.469819 + 0.813751i
\(143\) 5.66815 9.81753i 0.473995 0.820983i
\(144\) −2.77543 −0.231286
\(145\) 0 0
\(146\) −2.42850 + 4.20628i −0.200984 + 0.348114i
\(147\) −0.520583 0.901676i −0.0429370 0.0743690i
\(148\) 3.69432 6.39875i 0.303671 0.525974i
\(149\) −2.99034 5.17942i −0.244978 0.424314i 0.717147 0.696921i \(-0.245447\pi\)
−0.962125 + 0.272607i \(0.912114\pi\)
\(150\) 0 0
\(151\) 6.06777 0.493788 0.246894 0.969042i \(-0.420590\pi\)
0.246894 + 0.969042i \(0.420590\pi\)
\(152\) 3.12466 + 3.03916i 0.253443 + 0.246509i
\(153\) −18.8048 −1.52028
\(154\) 5.44271 + 9.42706i 0.438586 + 0.759654i
\(155\) 0 0
\(156\) 0.540781 0.936659i 0.0432971 0.0749928i
\(157\) 0.954613 + 1.65344i 0.0761864 + 0.131959i 0.901602 0.432567i \(-0.142392\pi\)
−0.825415 + 0.564526i \(0.809059\pi\)
\(158\) 7.63427 13.2229i 0.607350 1.05196i
\(159\) 1.98631 0.157525
\(160\) 0 0
\(161\) 8.42068 14.5850i 0.663642 1.14946i
\(162\) 3.51467 6.08758i 0.276138 0.478285i
\(163\) −7.54533 −0.590996 −0.295498 0.955343i \(-0.595486\pi\)
−0.295498 + 0.955343i \(0.595486\pi\)
\(164\) 11.4079 0.890804
\(165\) 0 0
\(166\) 6.36160 + 11.0186i 0.493756 + 0.855211i
\(167\) 2.67782 4.63811i 0.207216 0.358908i −0.743621 0.668602i \(-0.766893\pi\)
0.950836 + 0.309694i \(0.100227\pi\)
\(168\) 0.519272 + 0.899406i 0.0400627 + 0.0693907i
\(169\) 3.89549 + 6.74718i 0.299653 + 0.519014i
\(170\) 0 0
\(171\) −11.6411 + 3.29292i −0.890214 + 0.251816i
\(172\) −10.1585 −0.774582
\(173\) −0.790099 1.36849i −0.0600701 0.104044i 0.834426 0.551119i \(-0.185799\pi\)
−0.894497 + 0.447075i \(0.852466\pi\)
\(174\) −0.466063 0.807244i −0.0353321 0.0611970i
\(175\) 0 0
\(176\) 2.48349 + 4.30154i 0.187200 + 0.324241i
\(177\) 0.815288 1.41212i 0.0612808 0.106142i
\(178\) 3.56466 0.267183
\(179\) −4.18155 −0.312544 −0.156272 0.987714i \(-0.549948\pi\)
−0.156272 + 0.987714i \(0.549948\pi\)
\(180\) 0 0
\(181\) 1.87350 3.24500i 0.139256 0.241199i −0.787959 0.615728i \(-0.788862\pi\)
0.927215 + 0.374529i \(0.122196\pi\)
\(182\) 5.00185 0.370762
\(183\) 2.23825 0.165456
\(184\) 3.84233 6.65511i 0.283260 0.490621i
\(185\) 0 0
\(186\) −1.79694 + 3.11239i −0.131758 + 0.228212i
\(187\) 16.8267 + 29.1448i 1.23049 + 2.13128i
\(188\) −2.09578 3.62999i −0.152850 0.264744i
\(189\) −5.99804 −0.436293
\(190\) 0 0
\(191\) −1.96699 −0.142326 −0.0711631 0.997465i \(-0.522671\pi\)
−0.0711631 + 0.997465i \(0.522671\pi\)
\(192\) 0.236942 + 0.410396i 0.0170998 + 0.0296178i
\(193\) 6.92621 + 11.9965i 0.498559 + 0.863530i 0.999999 0.00166273i \(-0.000529265\pi\)
−0.501439 + 0.865193i \(0.667196\pi\)
\(194\) −0.0861680 + 0.149247i −0.00618650 + 0.0107153i
\(195\) 0 0
\(196\) 1.09854 1.90273i 0.0784674 0.135910i
\(197\) −17.2218 −1.22701 −0.613503 0.789693i \(-0.710240\pi\)
−0.613503 + 0.789693i \(0.710240\pi\)
\(198\) −13.7855 −0.979696
\(199\) −4.60723 + 7.97995i −0.326598 + 0.565684i −0.981834 0.189740i \(-0.939236\pi\)
0.655237 + 0.755424i \(0.272569\pi\)
\(200\) 0 0
\(201\) −0.383110 −0.0270225
\(202\) −14.8240 −1.04301
\(203\) 2.15538 3.73323i 0.151278 0.262021i
\(204\) 1.60539 + 2.78061i 0.112400 + 0.194682i
\(205\) 0 0
\(206\) −7.30155 12.6467i −0.508723 0.881134i
\(207\) 10.6641 + 18.4708i 0.741208 + 1.28381i
\(208\) 2.28233 0.158251
\(209\) 15.5201 + 15.0955i 1.07355 + 1.04418i
\(210\) 0 0
\(211\) 5.89048 + 10.2026i 0.405518 + 0.702377i 0.994382 0.105855i \(-0.0337580\pi\)
−0.588864 + 0.808232i \(0.700425\pi\)
\(212\) 2.09578 + 3.62999i 0.143939 + 0.249309i
\(213\) −2.65306 + 4.59524i −0.181785 + 0.314861i
\(214\) 0.181945 + 0.315139i 0.0124375 + 0.0215424i
\(215\) 0 0
\(216\) −2.73689 −0.186222
\(217\) −16.6205 −1.12827
\(218\) −6.61776 + 11.4623i −0.448211 + 0.776325i
\(219\) −1.15083 + 1.99329i −0.0777657 + 0.134694i
\(220\) 0 0
\(221\) 15.4638 1.04021
\(222\) 1.75068 3.03227i 0.117498 0.203513i
\(223\) −0.298836 0.517599i −0.0200115 0.0346610i 0.855846 0.517230i \(-0.173037\pi\)
−0.875858 + 0.482569i \(0.839704\pi\)
\(224\) −1.09578 + 1.89794i −0.0732147 + 0.126812i
\(225\) 0 0
\(226\) −8.74471 15.1463i −0.581690 1.00752i
\(227\) −15.3364 −1.01791 −0.508957 0.860792i \(-0.669969\pi\)
−0.508957 + 0.860792i \(0.669969\pi\)
\(228\) 1.48073 + 1.44021i 0.0980636 + 0.0953804i
\(229\) 15.5802 1.02957 0.514784 0.857320i \(-0.327872\pi\)
0.514784 + 0.857320i \(0.327872\pi\)
\(230\) 0 0
\(231\) 2.57922 + 4.46734i 0.169700 + 0.293929i
\(232\) 0.983494 1.70346i 0.0645696 0.111838i
\(233\) −14.7310 25.5148i −0.965058 1.67153i −0.709459 0.704747i \(-0.751061\pi\)
−0.255599 0.966783i \(-0.582273\pi\)
\(234\) −3.16723 + 5.48580i −0.207048 + 0.358618i
\(235\) 0 0
\(236\) 3.44087 0.223982
\(237\) 3.61776 6.26615i 0.234999 0.407030i
\(238\) −7.42437 + 12.8594i −0.481250 + 0.833550i
\(239\) 1.34825 0.0872108 0.0436054 0.999049i \(-0.486116\pi\)
0.0436054 + 0.999049i \(0.486116\pi\)
\(240\) 0 0
\(241\) −13.9331 + 24.1328i −0.897507 + 1.55453i −0.0668355 + 0.997764i \(0.521290\pi\)
−0.830671 + 0.556763i \(0.812043\pi\)
\(242\) 6.83549 + 11.8394i 0.439402 + 0.761066i
\(243\) 5.77088 9.99546i 0.370202 0.641209i
\(244\) 2.36160 + 4.09041i 0.151186 + 0.261862i
\(245\) 0 0
\(246\) 5.40601 0.344675
\(247\) 9.57282 2.70788i 0.609104 0.172298i
\(248\) −7.58388 −0.481577
\(249\) 3.01467 + 5.22155i 0.191047 + 0.330902i
\(250\) 0 0
\(251\) −14.4166 + 24.9703i −0.909968 + 1.57611i −0.0958610 + 0.995395i \(0.530560\pi\)
−0.814107 + 0.580715i \(0.802773\pi\)
\(252\) −3.04126 5.26761i −0.191581 0.331828i
\(253\) 19.0848 33.0559i 1.19985 2.07820i
\(254\) −4.66544 −0.292736
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 1.65083 2.85932i 0.102976 0.178359i −0.809934 0.586522i \(-0.800497\pi\)
0.912909 + 0.408162i \(0.133830\pi\)
\(258\) −4.81398 −0.299705
\(259\) 16.1926 1.00616
\(260\) 0 0
\(261\) 2.72962 + 4.72784i 0.168959 + 0.292646i
\(262\) 0.449610 0.778747i 0.0277770 0.0481112i
\(263\) −5.59854 9.69696i −0.345221 0.597940i 0.640173 0.768231i \(-0.278863\pi\)
−0.985394 + 0.170291i \(0.945529\pi\)
\(264\) 1.17689 + 2.03843i 0.0724326 + 0.125457i
\(265\) 0 0
\(266\) −2.34422 + 9.26067i −0.143734 + 0.567808i
\(267\) 1.68924 0.103380
\(268\) −0.404223 0.700134i −0.0246918 0.0427675i
\(269\) 14.1998 + 24.5948i 0.865777 + 1.49957i 0.866273 + 0.499570i \(0.166509\pi\)
−0.000496384 1.00000i \(0.500158\pi\)
\(270\) 0 0
\(271\) −10.2850 17.8142i −0.624772 1.08214i −0.988585 0.150665i \(-0.951859\pi\)
0.363813 0.931472i \(-0.381475\pi\)
\(272\) −3.38772 + 5.86770i −0.205410 + 0.355781i
\(273\) 2.37030 0.143457
\(274\) 7.47574 0.451626
\(275\) 0 0
\(276\) 1.82082 3.15375i 0.109601 0.189834i
\(277\) −8.99447 −0.540425 −0.270213 0.962801i \(-0.587094\pi\)
−0.270213 + 0.962801i \(0.587094\pi\)
\(278\) 6.01922 0.361009
\(279\) 10.5243 18.2286i 0.630072 1.09132i
\(280\) 0 0
\(281\) 4.78233 8.28324i 0.285290 0.494137i −0.687390 0.726289i \(-0.741243\pi\)
0.972679 + 0.232152i \(0.0745768\pi\)
\(282\) −0.993157 1.72020i −0.0591416 0.102436i
\(283\) 1.25806 + 2.17902i 0.0747836 + 0.129529i 0.900992 0.433835i \(-0.142840\pi\)
−0.826209 + 0.563364i \(0.809507\pi\)
\(284\) −11.1971 −0.664425
\(285\) 0 0
\(286\) 11.3363 0.670330
\(287\) 12.5005 + 21.6515i 0.737880 + 1.27805i
\(288\) −1.38772 2.40360i −0.0817720 0.141633i
\(289\) −14.4532 + 25.0338i −0.850191 + 1.47257i
\(290\) 0 0
\(291\) −0.0408337 + 0.0707260i −0.00239371 + 0.00414603i
\(292\) −4.85699 −0.284234
\(293\) −0.406116 −0.0237256 −0.0118628 0.999930i \(-0.503776\pi\)
−0.0118628 + 0.999930i \(0.503776\pi\)
\(294\) 0.520583 0.901676i 0.0303610 0.0525868i
\(295\) 0 0
\(296\) 7.38864 0.429456
\(297\) −13.5941 −0.788809
\(298\) 2.99034 5.17942i 0.173226 0.300036i
\(299\) −8.76946 15.1892i −0.507151 0.878411i
\(300\) 0 0
\(301\) −11.1315 19.2803i −0.641609 1.11130i
\(302\) 3.03388 + 5.25484i 0.174580 + 0.302382i
\(303\) −7.02486 −0.403568
\(304\) −1.06966 + 4.22562i −0.0613493 + 0.242356i
\(305\) 0 0
\(306\) −9.40238 16.2854i −0.537498 0.930975i
\(307\) −10.4555 18.1095i −0.596729 1.03357i −0.993300 0.115561i \(-0.963133\pi\)
0.396571 0.918004i \(-0.370200\pi\)
\(308\) −5.44271 + 9.42706i −0.310127 + 0.537156i
\(309\) −3.46009 5.99305i −0.196838 0.340933i
\(310\) 0 0
\(311\) −9.92397 −0.562737 −0.281368 0.959600i \(-0.590788\pi\)
−0.281368 + 0.959600i \(0.590788\pi\)
\(312\) 1.08156 0.0612313
\(313\) 7.32766 12.6919i 0.414184 0.717388i −0.581158 0.813790i \(-0.697400\pi\)
0.995342 + 0.0964027i \(0.0307336\pi\)
\(314\) −0.954613 + 1.65344i −0.0538719 + 0.0933089i
\(315\) 0 0
\(316\) 15.2685 0.858922
\(317\) 17.5220 30.3490i 0.984133 1.70457i 0.338404 0.941001i \(-0.390113\pi\)
0.645729 0.763567i \(-0.276554\pi\)
\(318\) 0.993157 + 1.72020i 0.0556935 + 0.0964639i
\(319\) 4.88500 8.46107i 0.273508 0.473729i
\(320\) 0 0
\(321\) 0.0862211 + 0.149339i 0.00481239 + 0.00833531i
\(322\) 16.8414 0.938532
\(323\) −7.24742 + 28.6304i −0.403257 + 1.59304i
\(324\) 7.02933 0.390518
\(325\) 0 0
\(326\) −3.77267 6.53445i −0.208949 0.361910i
\(327\) −3.13606 + 5.43181i −0.173424 + 0.300380i
\(328\) 5.70393 + 9.87950i 0.314947 + 0.545504i
\(329\) 4.59301 7.95533i 0.253221 0.438591i
\(330\) 0 0
\(331\) 21.4464 1.17880 0.589401 0.807841i \(-0.299364\pi\)
0.589401 + 0.807841i \(0.299364\pi\)
\(332\) −6.36160 + 11.0186i −0.349138 + 0.604725i
\(333\) −10.2533 + 17.7593i −0.561880 + 0.973204i
\(334\) 5.35563 0.293047
\(335\) 0 0
\(336\) −0.519272 + 0.899406i −0.0283286 + 0.0490666i
\(337\) −14.8593 25.7371i −0.809438 1.40199i −0.913254 0.407392i \(-0.866438\pi\)
0.103815 0.994597i \(-0.466895\pi\)
\(338\) −3.89549 + 6.74718i −0.211886 + 0.366998i
\(339\) −4.14398 7.17759i −0.225070 0.389833i
\(340\) 0 0
\(341\) −37.6690 −2.03989
\(342\) −8.67228 8.43499i −0.468943 0.456112i
\(343\) 20.1559 1.08832
\(344\) −5.07927 8.79756i −0.273856 0.474332i
\(345\) 0 0
\(346\) 0.790099 1.36849i 0.0424760 0.0735705i
\(347\) 1.07651 + 1.86456i 0.0577898 + 0.100095i 0.893473 0.449117i \(-0.148261\pi\)
−0.835683 + 0.549212i \(0.814928\pi\)
\(348\) 0.466063 0.807244i 0.0249836 0.0432728i
\(349\) 17.5031 0.936920 0.468460 0.883485i \(-0.344809\pi\)
0.468460 + 0.883485i \(0.344809\pi\)
\(350\) 0 0
\(351\) −3.12324 + 5.40961i −0.166706 + 0.288744i
\(352\) −2.48349 + 4.30154i −0.132371 + 0.229273i
\(353\) 21.3171 1.13459 0.567297 0.823513i \(-0.307989\pi\)
0.567297 + 0.823513i \(0.307989\pi\)
\(354\) 1.63058 0.0866642
\(355\) 0 0
\(356\) 1.78233 + 3.08709i 0.0944633 + 0.163615i
\(357\) −3.51829 + 6.09386i −0.186208 + 0.322521i
\(358\) −2.09077 3.62133i −0.110501 0.191393i
\(359\) −12.8547 22.2650i −0.678445 1.17510i −0.975449 0.220226i \(-0.929321\pi\)
0.297004 0.954876i \(-0.404013\pi\)
\(360\) 0 0
\(361\) 0.526988 + 18.9927i 0.0277362 + 0.999615i
\(362\) 3.74700 0.196938
\(363\) 3.23923 + 5.61051i 0.170016 + 0.294476i
\(364\) 2.50093 + 4.33173i 0.131084 + 0.227044i
\(365\) 0 0
\(366\) 1.11913 + 1.93838i 0.0584977 + 0.101321i
\(367\) −7.17092 + 12.4204i −0.374319 + 0.648339i −0.990225 0.139480i \(-0.955457\pi\)
0.615906 + 0.787820i \(0.288790\pi\)
\(368\) 7.68466 0.400591
\(369\) −31.6618 −1.64825
\(370\) 0 0
\(371\) −4.59301 + 7.95533i −0.238457 + 0.413020i
\(372\) −3.59388 −0.186334
\(373\) −0.646114 −0.0334545 −0.0167273 0.999860i \(-0.505325\pi\)
−0.0167273 + 0.999860i \(0.505325\pi\)
\(374\) −16.8267 + 29.1448i −0.870090 + 1.50704i
\(375\) 0 0
\(376\) 2.09578 3.62999i 0.108081 0.187203i
\(377\) −2.24466 3.88786i −0.115606 0.200235i
\(378\) −2.99902 5.19446i −0.154253 0.267174i
\(379\) 13.1255 0.674213 0.337107 0.941466i \(-0.390552\pi\)
0.337107 + 0.941466i \(0.390552\pi\)
\(380\) 0 0
\(381\) −2.21088 −0.113267
\(382\) −0.983494 1.70346i −0.0503199 0.0871567i
\(383\) −5.59854 9.69696i −0.286072 0.495492i 0.686796 0.726850i \(-0.259016\pi\)
−0.972869 + 0.231358i \(0.925683\pi\)
\(384\) −0.236942 + 0.410396i −0.0120914 + 0.0209429i
\(385\) 0 0
\(386\) −6.92621 + 11.9965i −0.352535 + 0.610608i
\(387\) 28.1944 1.43320
\(388\) −0.172336 −0.00874903
\(389\) 11.0037 19.0590i 0.557909 0.966327i −0.439761 0.898115i \(-0.644937\pi\)
0.997671 0.0682127i \(-0.0217296\pi\)
\(390\) 0 0
\(391\) 52.0669 2.63314
\(392\) 2.19709 0.110970
\(393\) 0.213063 0.369036i 0.0107476 0.0186154i
\(394\) −8.61092 14.9145i −0.433812 0.751384i
\(395\) 0 0
\(396\) −6.89277 11.9386i −0.346375 0.599939i
\(397\) −4.78044 8.27996i −0.239923 0.415559i 0.720769 0.693176i \(-0.243789\pi\)
−0.960692 + 0.277616i \(0.910456\pi\)
\(398\) −9.21446 −0.461879
\(399\) −1.11089 + 4.38849i −0.0556141 + 0.219699i
\(400\) 0 0
\(401\) −7.71543 13.3635i −0.385290 0.667343i 0.606519 0.795069i \(-0.292565\pi\)
−0.991809 + 0.127726i \(0.959232\pi\)
\(402\) −0.191555 0.331783i −0.00955389 0.0165478i
\(403\) −8.65446 + 14.9900i −0.431109 + 0.746703i
\(404\) −7.41199 12.8379i −0.368760 0.638712i
\(405\) 0 0
\(406\) 4.31076 0.213940
\(407\) 36.6993 1.81912
\(408\) −1.60539 + 2.78061i −0.0794785 + 0.137661i
\(409\) 7.70164 13.3396i 0.380822 0.659602i −0.610358 0.792125i \(-0.708975\pi\)
0.991180 + 0.132523i \(0.0423079\pi\)
\(410\) 0 0
\(411\) 3.54264 0.174745
\(412\) 7.30155 12.6467i 0.359721 0.623056i
\(413\) 3.77043 + 6.53058i 0.185531 + 0.321349i
\(414\) −10.6641 + 18.4708i −0.524113 + 0.907791i
\(415\) 0 0
\(416\) 1.14116 + 1.97656i 0.0559502 + 0.0969086i
\(417\) 2.85242 0.139683
\(418\) −5.31300 + 20.9886i −0.259867 + 1.02659i
\(419\) −37.5581 −1.83484 −0.917418 0.397926i \(-0.869730\pi\)
−0.917418 + 0.397926i \(0.869730\pi\)
\(420\) 0 0
\(421\) 1.91844 + 3.32283i 0.0934990 + 0.161945i 0.908981 0.416837i \(-0.136861\pi\)
−0.815482 + 0.578782i \(0.803528\pi\)
\(422\) −5.89048 + 10.2026i −0.286744 + 0.496656i
\(423\) 5.81669 + 10.0748i 0.282817 + 0.489854i
\(424\) −2.09578 + 3.62999i −0.101780 + 0.176288i
\(425\) 0 0
\(426\) −5.30613 −0.257083
\(427\) −5.17558 + 8.96437i −0.250464 + 0.433816i
\(428\) −0.181945 + 0.315139i −0.00879466 + 0.0152328i
\(429\) 5.37210 0.259367
\(430\) 0 0
\(431\) −4.56282 + 7.90303i −0.219783 + 0.380676i −0.954742 0.297436i \(-0.903868\pi\)
0.734958 + 0.678112i \(0.237202\pi\)
\(432\) −1.36844 2.37022i −0.0658393 0.114037i
\(433\) 4.32766 7.49573i 0.207974 0.360222i −0.743102 0.669178i \(-0.766646\pi\)
0.951076 + 0.308956i \(0.0999796\pi\)
\(434\) −8.31024 14.3938i −0.398904 0.690923i
\(435\) 0 0
\(436\) −13.2355 −0.633867
\(437\) 32.2319 9.11749i 1.54186 0.436149i
\(438\) −2.30166 −0.109977
\(439\) 2.03757 + 3.52917i 0.0972477 + 0.168438i 0.910544 0.413411i \(-0.135663\pi\)
−0.813297 + 0.581849i \(0.802329\pi\)
\(440\) 0 0
\(441\) −3.04893 + 5.28091i −0.145187 + 0.251472i
\(442\) 7.73189 + 13.3920i 0.367768 + 0.636993i
\(443\) 1.37121 2.37501i 0.0651482 0.112840i −0.831612 0.555358i \(-0.812581\pi\)
0.896760 + 0.442518i \(0.145915\pi\)
\(444\) 3.50136 0.166167
\(445\) 0 0
\(446\) 0.298836 0.517599i 0.0141503 0.0245090i
\(447\) 1.41707 2.45445i 0.0670253 0.116091i
\(448\) −2.19155 −0.103541
\(449\) −20.7753 −0.980448 −0.490224 0.871596i \(-0.663085\pi\)
−0.490224 + 0.871596i \(0.663085\pi\)
\(450\) 0 0
\(451\) 28.3314 + 49.0713i 1.33407 + 2.31068i
\(452\) 8.74471 15.1463i 0.411317 0.712421i
\(453\) 1.43771 + 2.49019i 0.0675496 + 0.116999i
\(454\) −7.66821 13.2817i −0.359887 0.623342i
\(455\) 0 0
\(456\) −0.506896 + 2.00245i −0.0237376 + 0.0937735i
\(457\) 5.15669 0.241220 0.120610 0.992700i \(-0.461515\pi\)
0.120610 + 0.992700i \(0.461515\pi\)
\(458\) 7.79010 + 13.4928i 0.364007 + 0.630479i
\(459\) −9.27181 16.0592i −0.432771 0.749581i
\(460\) 0 0
\(461\) −17.7397 30.7261i −0.826221 1.43106i −0.900983 0.433855i \(-0.857153\pi\)
0.0747623 0.997201i \(-0.476180\pi\)
\(462\) −2.57922 + 4.46734i −0.119996 + 0.207839i
\(463\) 39.3280 1.82773 0.913865 0.406019i \(-0.133083\pi\)
0.913865 + 0.406019i \(0.133083\pi\)
\(464\) 1.96699 0.0913151
\(465\) 0 0
\(466\) 14.7310 25.5148i 0.682399 1.18195i
\(467\) −9.87174 −0.456810 −0.228405 0.973566i \(-0.573351\pi\)
−0.228405 + 0.973566i \(0.573351\pi\)
\(468\) −6.33445 −0.292810
\(469\) 0.885876 1.53438i 0.0409059 0.0708512i
\(470\) 0 0
\(471\) −0.452376 + 0.783539i −0.0208444 + 0.0361036i
\(472\) 1.72044 + 2.97988i 0.0791895 + 0.137160i
\(473\) −25.2287 43.6974i −1.16002 2.00921i
\(474\) 7.23553 0.332339
\(475\) 0 0
\(476\) −14.8487 −0.680591
\(477\) −5.81669 10.0748i −0.266328 0.461294i
\(478\) 0.674124 + 1.16762i 0.0308337 + 0.0534055i
\(479\) 9.36431 16.2195i 0.427866 0.741086i −0.568817 0.822464i \(-0.692599\pi\)
0.996683 + 0.0813778i \(0.0259320\pi\)
\(480\) 0 0
\(481\) 8.43166 14.6041i 0.384451 0.665888i
\(482\) −27.8661 −1.26927
\(483\) 7.98086 0.363142
\(484\) −6.83549 + 11.8394i −0.310704 + 0.538155i
\(485\) 0 0
\(486\) 11.5418 0.523545
\(487\) −17.9129 −0.811711 −0.405856 0.913937i \(-0.633026\pi\)
−0.405856 + 0.913937i \(0.633026\pi\)
\(488\) −2.36160 + 4.09041i −0.106905 + 0.185164i
\(489\) −1.78781 3.09658i −0.0808475 0.140032i
\(490\) 0 0
\(491\) −15.0101 25.9982i −0.677396 1.17328i −0.975762 0.218832i \(-0.929775\pi\)
0.298367 0.954451i \(-0.403558\pi\)
\(492\) 2.70301 + 4.68174i 0.121861 + 0.211069i
\(493\) 13.3272 0.600227
\(494\) 7.13150 + 6.93637i 0.320861 + 0.312082i
\(495\) 0 0
\(496\) −3.79194 6.56783i −0.170263 0.294904i
\(497\) −12.2695 21.2514i −0.550363 0.953257i
\(498\) −3.01467 + 5.22155i −0.135090 + 0.233983i
\(499\) −4.73966 8.20932i −0.212176 0.367500i 0.740219 0.672366i \(-0.234722\pi\)
−0.952395 + 0.304866i \(0.901388\pi\)
\(500\) 0 0
\(501\) 2.53795 0.113387
\(502\) −28.8332 −1.28689
\(503\) 2.43034 4.20947i 0.108363 0.187691i −0.806744 0.590901i \(-0.798772\pi\)
0.915107 + 0.403210i \(0.132106\pi\)
\(504\) 3.04126 5.26761i 0.135468 0.234638i
\(505\) 0 0
\(506\) 38.1696 1.69685
\(507\) −1.84601 + 3.19738i −0.0819842 + 0.142001i
\(508\) −2.33272 4.04039i −0.103498 0.179263i
\(509\) 14.5467 25.1957i 0.644773 1.11678i −0.339581 0.940577i \(-0.610285\pi\)
0.984354 0.176202i \(-0.0563813\pi\)
\(510\) 0 0
\(511\) −5.32218 9.21829i −0.235440 0.407793i
\(512\) −1.00000 −0.0441942
\(513\) −8.55185 8.31785i −0.377573 0.367242i
\(514\) 3.30166 0.145630
\(515\) 0 0
\(516\) −2.40699 4.16903i −0.105962 0.183531i
\(517\) 10.4097 18.0301i 0.457818 0.792964i
\(518\) 8.09631 + 14.0232i 0.355731 + 0.616145i
\(519\) 0.374416 0.648507i 0.0164350 0.0284663i
\(520\) 0 0
\(521\) −8.76175 −0.383859 −0.191930 0.981409i \(-0.561475\pi\)
−0.191930 + 0.981409i \(0.561475\pi\)
\(522\) −2.72962 + 4.72784i −0.119472 + 0.206932i
\(523\) 1.34733 2.33365i 0.0589147 0.102043i −0.835064 0.550153i \(-0.814569\pi\)
0.893978 + 0.448110i \(0.147903\pi\)
\(524\) 0.899220 0.0392826
\(525\) 0 0
\(526\) 5.59854 9.69696i 0.244108 0.422808i
\(527\) −25.6920 44.4999i −1.11916 1.93845i
\(528\) −1.17689 + 2.03843i −0.0512176 + 0.0887114i
\(529\) −18.0270 31.2237i −0.783782 1.35755i
\(530\) 0 0
\(531\) −9.54991 −0.414431
\(532\) −9.19208 + 2.60018i −0.398527 + 0.112732i
\(533\) 26.0365 1.12777
\(534\) 0.844619 + 1.46292i 0.0365502 + 0.0633068i
\(535\) 0 0
\(536\) 0.404223 0.700134i 0.0174598 0.0302412i
\(537\) −0.990786 1.71609i −0.0427556 0.0740548i
\(538\) −14.1998 + 24.5948i −0.612197 + 1.06036i
\(539\) 10.9129 0.470052
\(540\) 0 0
\(541\) 21.9890 38.0861i 0.945382 1.63745i 0.190398 0.981707i \(-0.439022\pi\)
0.754984 0.655743i \(-0.227644\pi\)
\(542\) 10.2850 17.8142i 0.441780 0.765186i
\(543\) 1.77565 0.0762003
\(544\) −6.77543 −0.290494
\(545\) 0 0
\(546\) 1.18515 + 2.05274i 0.0507197 + 0.0878492i
\(547\) −9.49121 + 16.4393i −0.405815 + 0.702892i −0.994416 0.105532i \(-0.966346\pi\)
0.588601 + 0.808424i \(0.299679\pi\)
\(548\) 3.73787 + 6.47418i 0.159674 + 0.276563i
\(549\) −6.55447 11.3527i −0.279738 0.484520i
\(550\) 0 0
\(551\) 8.25018 2.33374i 0.351469 0.0994206i
\(552\) 3.64164 0.154999
\(553\) 16.7309 + 28.9788i 0.711471 + 1.23230i
\(554\) −4.49723 7.78944i −0.191069 0.330941i
\(555\) 0 0
\(556\) 3.00961 + 5.21280i 0.127636 + 0.221072i
\(557\) −2.51927 + 4.36351i −0.106745 + 0.184888i −0.914450 0.404699i \(-0.867376\pi\)
0.807705 + 0.589587i \(0.200710\pi\)
\(558\) 21.0485 0.891056
\(559\) −23.1851 −0.980627
\(560\) 0 0
\(561\) −7.97394 + 13.8113i −0.336660 + 0.583112i
\(562\) 9.56466 0.403461
\(563\) 0.334560 0.0141000 0.00705002 0.999975i \(-0.497756\pi\)
0.00705002 + 0.999975i \(0.497756\pi\)
\(564\) 0.993157 1.72020i 0.0418194 0.0724334i
\(565\) 0 0
\(566\) −1.25806 + 2.17902i −0.0528800 + 0.0915909i
\(567\) 7.70258 + 13.3413i 0.323478 + 0.560280i
\(568\) −5.59854 9.69696i −0.234910 0.406875i
\(569\) 2.30155 0.0964859 0.0482430 0.998836i \(-0.484638\pi\)
0.0482430 + 0.998836i \(0.484638\pi\)
\(570\) 0 0
\(571\) −23.6131 −0.988178 −0.494089 0.869411i \(-0.664498\pi\)
−0.494089 + 0.869411i \(0.664498\pi\)
\(572\) 5.66815 + 9.81753i 0.236997 + 0.410491i
\(573\) −0.466063 0.807244i −0.0194701 0.0337231i
\(574\) −12.5005 + 21.6515i −0.521760 + 0.903715i
\(575\) 0 0
\(576\) 1.38772 2.40360i 0.0578215 0.100150i
\(577\) −1.59399 −0.0663587 −0.0331793 0.999449i \(-0.510563\pi\)
−0.0331793 + 0.999449i \(0.510563\pi\)
\(578\) −28.9065 −1.20235
\(579\) −3.28222 + 5.68498i −0.136405 + 0.236260i
\(580\) 0 0
\(581\) −27.8836 −1.15681
\(582\) −0.0816674 −0.00338522
\(583\) −10.4097 + 18.0301i −0.431126 + 0.746732i
\(584\) −2.42850 4.20628i −0.100492 0.174057i
\(585\) 0 0
\(586\) −0.203058 0.351707i −0.00838826 0.0145289i
\(587\) 4.86431 + 8.42524i 0.200772 + 0.347747i 0.948777 0.315946i \(-0.102322\pi\)
−0.748006 + 0.663692i \(0.768988\pi\)
\(588\) 1.04117 0.0429370
\(589\) −23.6970 23.0486i −0.976419 0.949702i
\(590\) 0 0
\(591\) −4.08058 7.06778i −0.167853 0.290729i
\(592\) 3.69432 + 6.39875i 0.151836 + 0.262987i
\(593\) −8.09757 + 14.0254i −0.332527 + 0.575954i −0.983007 0.183570i \(-0.941235\pi\)
0.650480 + 0.759524i \(0.274568\pi\)
\(594\) −6.79705 11.7728i −0.278886 0.483045i
\(595\) 0 0
\(596\) 5.98067 0.244978
\(597\) −4.36659 −0.178713
\(598\) 8.76946 15.1892i 0.358610 0.621131i
\(599\) −11.6159 + 20.1194i −0.474614 + 0.822055i −0.999577 0.0290696i \(-0.990746\pi\)
0.524964 + 0.851125i \(0.324079\pi\)
\(600\) 0 0
\(601\) 44.9899 1.83518 0.917588 0.397532i \(-0.130133\pi\)
0.917588 + 0.397532i \(0.130133\pi\)
\(602\) 11.1315 19.2803i 0.453686 0.785807i
\(603\) 1.12189 + 1.94318i 0.0456870 + 0.0791322i
\(604\) −3.03388 + 5.25484i −0.123447 + 0.213816i
\(605\) 0 0
\(606\) −3.51243 6.08371i −0.142683 0.247134i
\(607\) 36.6965 1.48947 0.744733 0.667363i \(-0.232577\pi\)
0.744733 + 0.667363i \(0.232577\pi\)
\(608\) −4.19432 + 1.18645i −0.170102 + 0.0481170i
\(609\) 2.04280 0.0827786
\(610\) 0 0
\(611\) −4.78326 8.28484i −0.193510 0.335169i
\(612\) 9.40238 16.2854i 0.380069 0.658298i
\(613\) −11.7090 20.2806i −0.472921 0.819124i 0.526598 0.850114i \(-0.323467\pi\)
−0.999520 + 0.0309903i \(0.990134\pi\)
\(614\) 10.4555 18.1095i 0.421951 0.730841i
\(615\) 0 0
\(616\) −10.8854 −0.438586
\(617\) −8.56777 + 14.8398i −0.344925 + 0.597428i −0.985340 0.170601i \(-0.945429\pi\)
0.640415 + 0.768029i \(0.278762\pi\)
\(618\) 3.46009 5.99305i 0.139185 0.241076i
\(619\) 25.3556 1.01913 0.509564 0.860433i \(-0.329807\pi\)
0.509564 + 0.860433i \(0.329807\pi\)
\(620\) 0 0
\(621\) −10.5160 + 18.2143i −0.421994 + 0.730915i
\(622\) −4.96199 8.59441i −0.198957 0.344604i
\(623\) −3.90607 + 6.76552i −0.156494 + 0.271055i
\(624\) 0.540781 + 0.936659i 0.0216485 + 0.0374964i
\(625\) 0 0
\(626\) 14.6553 0.585745
\(627\) −2.51775 + 9.94617i −0.100549 + 0.397212i
\(628\) −1.90923 −0.0761864
\(629\) 25.0306 + 43.3543i 0.998036 + 1.72865i
\(630\) 0 0
\(631\) −14.2956 + 24.7607i −0.569098 + 0.985707i 0.427557 + 0.903988i \(0.359374\pi\)
−0.996655 + 0.0817184i \(0.973959\pi\)
\(632\) 7.63427 + 13.2229i 0.303675 + 0.525980i
\(633\) −2.79141 + 4.83486i −0.110949 + 0.192169i
\(634\) 35.0440 1.39177
\(635\) 0 0
\(636\) −0.993157 + 1.72020i −0.0393812 + 0.0682103i
\(637\) 2.50724 4.34267i 0.0993404 0.172063i
\(638\) 9.77001 0.386798
\(639\) 31.0768 1.22938
\(640\) 0 0
\(641\) −1.82404 3.15932i −0.0720451 0.124786i 0.827752 0.561094i \(-0.189619\pi\)
−0.899797 + 0.436308i \(0.856286\pi\)
\(642\) −0.0862211 + 0.149339i −0.00340288 + 0.00589396i
\(643\) −14.9459 25.8870i −0.589408 1.02088i −0.994310 0.106524i \(-0.966028\pi\)
0.404902 0.914360i \(-0.367306\pi\)
\(644\) 8.42068 + 14.5850i 0.331821 + 0.574731i
\(645\) 0 0
\(646\) −28.4183 + 8.03873i −1.11810 + 0.316280i
\(647\) −30.0091 −1.17978 −0.589890 0.807483i \(-0.700829\pi\)
−0.589890 + 0.807483i \(0.700829\pi\)
\(648\) 3.51467 + 6.08758i 0.138069 + 0.239143i
\(649\) 8.54539 + 14.8010i 0.335436 + 0.580992i
\(650\) 0 0
\(651\) −3.93810 6.82098i −0.154346 0.267335i
\(652\) 3.77267 6.53445i 0.147749 0.255909i
\(653\) 26.4776 1.03615 0.518074 0.855336i \(-0.326649\pi\)
0.518074 + 0.855336i \(0.326649\pi\)
\(654\) −6.27211 −0.245259
\(655\) 0 0
\(656\) −5.70393 + 9.87950i −0.222701 + 0.385730i
\(657\) 13.4803 0.525915
\(658\) 9.18602 0.358108
\(659\) −0.581112 + 1.00652i −0.0226369 + 0.0392083i −0.877122 0.480268i \(-0.840540\pi\)
0.854485 + 0.519476i \(0.173873\pi\)
\(660\) 0 0
\(661\) −15.9899 + 27.6953i −0.621935 + 1.07722i 0.367190 + 0.930146i \(0.380320\pi\)
−0.989125 + 0.147077i \(0.953013\pi\)
\(662\) 10.7232 + 18.5731i 0.416769 + 0.721865i
\(663\) 3.66402 + 6.34627i 0.142299 + 0.246469i
\(664\) −12.7232 −0.493756
\(665\) 0 0
\(666\) −20.5067 −0.794618
\(667\) −7.55782 13.0905i −0.292640 0.506867i
\(668\) 2.67782 + 4.63811i 0.103608 + 0.179454i
\(669\) 0.141614 0.245282i 0.00547510 0.00948315i
\(670\) 0 0
\(671\) −11.7300 + 20.3170i −0.452833 + 0.784330i
\(672\) −1.03854 −0.0400627
\(673\) −48.3529 −1.86387 −0.931934 0.362629i \(-0.881879\pi\)
−0.931934 + 0.362629i \(0.881879\pi\)
\(674\) 14.8593 25.7371i 0.572359 0.991355i
\(675\) 0 0
\(676\) −7.79097 −0.299653
\(677\) −33.6964 −1.29506 −0.647529 0.762041i \(-0.724198\pi\)
−0.647529 + 0.762041i \(0.724198\pi\)
\(678\) 4.14398 7.17759i 0.159149 0.275654i
\(679\) −0.188842 0.327084i −0.00724708 0.0125523i
\(680\) 0 0
\(681\) −3.63384 6.29400i −0.139249 0.241187i
\(682\) −18.8345 32.6223i −0.721211 1.24917i
\(683\) −18.3886 −0.703622 −0.351811 0.936071i \(-0.614434\pi\)
−0.351811 + 0.936071i \(0.614434\pi\)
\(684\) 2.96878 11.7279i 0.113514 0.448428i
\(685\) 0 0
\(686\) 10.0780 + 17.4555i 0.384778 + 0.666456i
\(687\) 3.69161 + 6.39405i 0.140844 + 0.243948i
\(688\) 5.07927 8.79756i 0.193645 0.335404i
\(689\) 4.78326 + 8.28484i 0.182228 + 0.315627i
\(690\) 0 0
\(691\) 18.2779 0.695322 0.347661 0.937620i \(-0.386976\pi\)
0.347661 + 0.937620i \(0.386976\pi\)
\(692\) 1.58020 0.0600701
\(693\) 15.1059 26.1642i 0.573825 0.993895i
\(694\) −1.07651 + 1.86456i −0.0408636 + 0.0707778i
\(695\) 0 0
\(696\) 0.932126 0.0353321
\(697\) −38.6466 + 66.9379i −1.46384 + 2.53545i
\(698\) 8.75155 + 15.1581i 0.331251 + 0.573744i
\(699\) 6.98078 12.0911i 0.264037 0.457326i
\(700\) 0 0
\(701\) 4.80292 + 8.31891i 0.181404 + 0.314201i 0.942359 0.334604i \(-0.108603\pi\)
−0.760955 + 0.648805i \(0.775269\pi\)
\(702\) −6.24648 −0.235758
\(703\) 23.0870 + 22.4553i 0.870742 + 0.846917i
\(704\) −4.96699 −0.187200
\(705\) 0 0
\(706\) 10.6585 + 18.4611i 0.401140 + 0.694794i
\(707\) 16.2438 28.1351i 0.610910 1.05813i
\(708\) 0.815288 + 1.41212i 0.0306404 + 0.0530708i
\(709\) −10.2630 + 17.7760i −0.385435 + 0.667593i −0.991829 0.127571i \(-0.959282\pi\)
0.606394 + 0.795164i \(0.292615\pi\)
\(710\) 0 0
\(711\) −42.3768 −1.58925
\(712\) −1.78233 + 3.08709i −0.0667956 + 0.115693i
\(713\) −29.1398 + 50.4715i −1.09129 + 1.89017i
\(714\) −7.03659 −0.263338
\(715\) 0 0
\(716\) 2.09077 3.62133i 0.0781359 0.135335i
\(717\) 0.319457 + 0.553315i 0.0119303 + 0.0206639i
\(718\) 12.8547 22.2650i 0.479733 0.830922i
\(719\) 4.32220 + 7.48626i 0.161191 + 0.279190i 0.935296 0.353866i \(-0.115133\pi\)
−0.774105 + 0.633057i \(0.781800\pi\)
\(720\) 0 0
\(721\) 32.0035 1.19187
\(722\) −16.1847 + 9.95273i −0.602331 + 0.370402i
\(723\) −13.2053 −0.491111
\(724\) 1.87350 + 3.24500i 0.0696281 + 0.120599i
\(725\) 0 0
\(726\) −3.23923 + 5.61051i −0.120219 + 0.208226i
\(727\) −10.3547 17.9348i −0.384033 0.665164i 0.607602 0.794242i \(-0.292132\pi\)
−0.991634 + 0.129078i \(0.958798\pi\)
\(728\) −2.50093 + 4.33173i −0.0926905 + 0.160545i
\(729\) −15.6185 −0.578464
\(730\) 0 0
\(731\) 34.4143 59.6073i 1.27286 2.20465i
\(732\) −1.11913 + 1.93838i −0.0413641 + 0.0716447i
\(733\) 24.8157 0.916590 0.458295 0.888800i \(-0.348460\pi\)
0.458295 + 0.888800i \(0.348460\pi\)
\(734\) −14.3418 −0.529367
\(735\) 0 0
\(736\) 3.84233 + 6.65511i 0.141630 + 0.245311i
\(737\) 2.00777 3.47756i 0.0739571 0.128097i
\(738\) −15.8309 27.4199i −0.582743 1.00934i
\(739\) −2.07422 3.59265i −0.0763013 0.132158i 0.825350 0.564621i \(-0.190978\pi\)
−0.901651 + 0.432464i \(0.857644\pi\)
\(740\) 0 0
\(741\) 3.37951 + 3.28704i 0.124149 + 0.120752i
\(742\) −9.18602 −0.337229
\(743\) −0.401456 0.695343i −0.0147280 0.0255097i 0.858567 0.512701i \(-0.171355\pi\)
−0.873295 + 0.487191i \(0.838022\pi\)
\(744\) −1.79694 3.11239i −0.0658791 0.114106i
\(745\) 0 0
\(746\) −0.323057 0.559551i −0.0118280 0.0204866i
\(747\) 17.6562 30.5814i 0.646007 1.11892i
\(748\) −33.6535 −1.23049
\(749\) −0.797487 −0.0291395
\(750\) 0 0
\(751\) −16.1292 + 27.9366i −0.588563 + 1.01942i 0.405858 + 0.913936i \(0.366973\pi\)
−0.994421 + 0.105485i \(0.966360\pi\)
\(752\) 4.19155 0.152850
\(753\) −13.6636 −0.497930
\(754\) 2.24466 3.88786i 0.0817456 0.141588i
\(755\) 0 0
\(756\) 2.99902 5.19446i 0.109073 0.188921i
\(757\) 18.0531 + 31.2689i 0.656151 + 1.13649i 0.981604 + 0.190929i \(0.0611500\pi\)
−0.325453 + 0.945558i \(0.605517\pi\)
\(758\) 6.56277 + 11.3670i 0.238370 + 0.412870i
\(759\) 18.0880 0.656552
\(760\) 0 0
\(761\) 3.07513 0.111473 0.0557367 0.998446i \(-0.482249\pi\)
0.0557367 + 0.998446i \(0.482249\pi\)
\(762\) −1.10544 1.91468i −0.0400459 0.0693615i
\(763\) −14.5032 25.1203i −0.525051 0.909415i
\(764\) 0.983494 1.70346i 0.0355816 0.0616291i
\(765\) 0 0
\(766\) 5.59854 9.69696i 0.202284 0.350365i
\(767\) 7.85321 0.283563
\(768\) −0.473885 −0.0170998
\(769\) −0.423890 + 0.734199i −0.0152859 + 0.0264759i −0.873567 0.486704i \(-0.838199\pi\)
0.858281 + 0.513180i \(0.171533\pi\)
\(770\) 0 0
\(771\) 1.56460 0.0563478
\(772\) −13.8524 −0.498559
\(773\) 3.51743 6.09237i 0.126513 0.219127i −0.795810 0.605546i \(-0.792955\pi\)
0.922323 + 0.386419i \(0.126288\pi\)
\(774\) 14.0972 + 24.4170i 0.506713 + 0.877652i
\(775\) 0 0
\(776\) −0.0861680 0.149247i −0.00309325 0.00535767i
\(777\) 3.83672 + 6.64539i 0.137641 + 0.238402i
\(778\) 22.0074 0.789003
\(779\) −12.2026 + 48.2052i −0.437202 + 1.72713i
\(780\) 0 0
\(781\) −27.8079 48.1647i −0.995045 1.72347i
\(782\) 26.0334 + 45.0913i 0.930954 + 1.61246i
\(783\) −2.69171 + 4.66219i −0.0961940 + 0.166613i
\(784\) 1.09854 + 1.90273i 0.0392337 + 0.0679548i
\(785\) 0 0