Properties

Label 950.2.e.m.201.3
Level $950$
Weight $2$
Character 950.201
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 201.3
Root \(-0.236942 + 0.410396i\) of defining polynomial
Character \(\chi\) \(=\) 950.201
Dual form 950.2.e.m.501.3

$q$-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 \(\left(\mathbb{Z}/950\mathbb{Z}\right)^\times\).

\(n\) \(77\) \(401\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 0.866025i 0.353553 0.612372i
\(3\) 0.236942 0.410396i 0.136799 0.236942i −0.789484 0.613771i \(-0.789652\pi\)
0.926283 + 0.376828i \(0.122985\pi\)
\(4\) −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 0.663253 0.748395i \(-0.269175\pi\)
−0.979756 + 0.200197i \(0.935842\pi\)
\(14\) −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 0.0828169 + 0.996565i \(0.473608\pi\)
−0.904459 + 0.426561i \(0.859725\pi\)
\(18\) 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 −0.918839 0.394632i \(-0.870872\pi\)
0.117658 0.993054i \(-0.462461\pi\)
\(24\) −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 0.760145 0.649753i \(-0.225128\pi\)
−0.942775 + 0.333428i \(0.891794\pi\)
\(30\) 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 −0.0518913 + 0.998653i \(0.516525\pi\)
−0.838913 + 0.544266i \(0.816808\pi\)
\(42\) 0.519272 + 0.899406i 0.0801254 + 0.138781i
\(43\) 5.07927 8.79756i 0.774582 1.34161i −0.160448 0.987044i \(-0.551294\pi\)
0.935029 0.354570i \(-0.115373\pi\)
\(44\) 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 0.671717 0.740808i \(-0.265557\pi\)
−0.977417 + 0.211319i \(0.932224\pi\)
\(48\) 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 0.973303 0.229525i \(-0.0737172\pi\)
−0.685426 + 0.728143i \(0.740384\pi\)
\(54\) 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 −0.956013 0.293323i \(-0.905239\pi\)
0.732032 + 0.681271i \(0.238572\pi\)
\(60\) 0 0
\(61\) 2.36160 + 4.09041i 0.302372 + 0.523724i 0.976673 0.214733i \(-0.0688882\pi\)
−0.674301 + 0.738457i \(0.735555\pi\)
\(62\) 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 0.840277 0.542157i \(-0.182392\pi\)
−0.889661 + 0.456622i \(0.849059\pi\)
\(68\) 6.77543 0.821642
\(69\) −3.64164 −0.438402
\(70\) 0 0
\(71\) 5.59854 9.69696i 0.664425 1.15082i −0.315016 0.949086i \(-0.602010\pi\)
0.979441 0.201731i \(-0.0646568\pi\)
\(72\) −1.38772 2.40360i −0.163544 0.283266i
\(73\) 2.42850 4.20628i 0.284234 0.492308i −0.688189 0.725531i \(-0.741594\pi\)
0.972423 + 0.233224i \(0.0749274\pi\)
\(74\) −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 0.0140356 + 0.999901i \(0.495532\pi\)
−0.872958 + 0.487796i \(0.837801\pi\)
\(80\) 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 0.944893 0.327380i \(-0.106166\pi\)
−0.755966 + 0.654611i \(0.772833\pi\)
\(90\) 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 −0.861618 0.507558i \(-0.830548\pi\)
0.870367 + 0.492404i \(0.163882\pi\)
\(98\) −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 −0.953609 0.301049i \(-0.902663\pi\)
0.216088 0.976374i \(-0.430670\pi\)
\(102\) 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 −0.352887 0.935666i \(-0.614800\pi\)
0.986754 0.162224i \(-0.0518666\pi\)
\(110\) 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 0.743771 0.668434i \(-0.233035\pi\)
−0.950767 + 0.309908i \(0.899702\pi\)
\(128\) 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 −0.884998 0.465594i \(-0.845841\pi\)
0.845716 + 0.533634i \(0.179174\pi\)
\(132\) 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 0.980352 0.197256i \(-0.0632029\pi\)
−0.661004 + 0.750382i \(0.729870\pi\)
\(138\) −1.82082 + 3.15375i −0.154999 + 0.268465i
\(139\) 3.00961 + 5.21280i 0.255272 + 0.442144i 0.964969 0.262363i \(-0.0845017\pi\)
−0.709698 + 0.704506i \(0.751168\pi\)
\(140\) 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 −0.962125 0.272607i \(-0.912114\pi\)
0.717147 + 0.696921i \(0.245447\pi\)
\(150\) 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 −0.825415 0.564526i \(-0.809059\pi\)
0.901602 + 0.432567i \(0.142392\pi\)
\(158\) 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 0.950836 0.309694i \(-0.100227\pi\)
−0.743621 + 0.668602i \(0.766893\pi\)
\(168\) 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 −0.894497 0.447075i \(-0.852466\pi\)
0.834426 + 0.551119i \(0.185799\pi\)
\(174\) −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 0.927215 0.374529i \(-0.122196\pi\)
−0.787959 + 0.615728i \(0.788862\pi\)
\(182\) 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 −0.501439 0.865193i \(-0.667196\pi\)
0.999999 + 0.00166273i \(0.000529265\pi\)
\(194\) −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 0.655237 0.755424i \(-0.272569\pi\)
−0.981834 + 0.189740i \(0.939236\pi\)
\(200\) 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 −0.588864 0.808232i \(-0.700425\pi\)
0.994382 + 0.105855i \(0.0337580\pi\)
\(212\) 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 −0.875858 0.482569i \(-0.839704\pi\)
0.855846 + 0.517230i \(0.173037\pi\)
\(224\) −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 −0.255599 + 0.966783i \(0.582273\pi\)
−0.709459 + 0.704747i \(0.751061\pi\)
\(234\) −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 −0.830671 0.556763i \(-0.812043\pi\)
−0.0668355 0.997764i \(-0.521290\pi\)
\(242\) 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 −0.814107 0.580715i \(-0.802773\pi\)
−0.0958610 0.995395i \(-0.530560\pi\)
\(252\) −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 0.912909 0.408162i \(-0.133830\pi\)
−0.809934 + 0.586522i \(0.800497\pi\)
\(258\) −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 −0.985394 0.170291i \(-0.945529\pi\)
0.640173 + 0.768231i \(0.278863\pi\)
\(264\) 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 −0.000496384 1.00000i \(-0.500158\pi\)
0.866273 0.499570i \(-0.166509\pi\)
\(270\) 0 0
\(271\) −10.2850 + 17.8142i −0.624772 + 1.08214i 0.363813 + 0.931472i \(0.381475\pi\)
−0.988585 + 0.150665i \(0.951859\pi\)
\(272\) −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 0.972679 0.232152i \(-0.0745768\pi\)
−0.687390 + 0.726289i \(0.741243\pi\)
\(282\) −0.993157 + 1.72020i −0.0591416 + 0.102436i
\(283\) 1.25806 2.17902i 0.0747836 0.129529i −0.826209 0.563364i \(-0.809507\pi\)
0.900992 + 0.433835i \(0.142840\pi\)
\(284\) −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 0.396571 + 0.918004i \(0.370200\pi\)
−0.993300 + 0.115561i \(0.963133\pi\)
\(308\) −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 0.995342 0.0964027i \(-0.0307336\pi\)
−0.581158 + 0.813790i \(0.697400\pi\)
\(314\) −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 0.645729 + 0.763567i \(0.276554\pi\)
0.338404 + 0.941001i \(0.390113\pi\)
\(318\) 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 0.103815 + 0.994597i \(0.466895\pi\)
−0.913254 + 0.407392i \(0.866438\pi\)
\(338\) −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 −0.835683 0.549212i \(-0.814928\pi\)
0.893473 + 0.449117i \(0.148261\pi\)
\(348\) 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 0.297004 + 0.954876i \(0.404013\pi\)
−0.975449 + 0.220226i \(0.929321\pi\)
\(360\) 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 0.615906 0.787820i \(-0.288790\pi\)
−0.990225 + 0.139480i \(0.955457\pi\)
\(368\) 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 −0.972869 0.231358i \(-0.925683\pi\)
0.686796 + 0.726850i \(0.259016\pi\)
\(384\) −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 0.997671 + 0.0682127i \(0.0217296\pi\)
−0.439761 + 0.898115i \(0.644937\pi\)
\(390\) 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 −0.960692 0.277616i \(-0.910456\pi\)
0.720769 + 0.693176i \(0.243789\pi\)
\(398\) −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 −0.991809 0.127726i \(-0.959232\pi\)
0.606519 + 0.795069i \(0.292565\pi\)
\(402\) −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 0.991180 0.132523i \(-0.0423079\pi\)
−0.610358 + 0.792125i \(0.708975\pi\)
\(410\) 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 −0.815482 0.578782i \(-0.803528\pi\)
0.908981 + 0.416837i \(0.136861\pi\)
\(422\) −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 0.734958 0.678112i \(-0.237202\pi\)
−0.954742 + 0.297436i \(0.903868\pi\)
\(432\) −1.36844 + 2.37022i −0.0658393 + 0.114037i
\(433\) 4.32766 + 7.49573i 0.207974 + 0.360222i 0.951076 0.308956i \(-0.0999796\pi\)
−0.743102 + 0.669178i \(0.766646\pi\)
\(434\) −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 −0.813297 0.581849i \(-0.802329\pi\)
0.910544 + 0.413411i \(0.135663\pi\)
\(440\) 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 0.896760 0.442518i \(-0.145915\pi\)
−0.831612 + 0.555358i \(0.812581\pi\)
\(444\) 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 0.0747623 + 0.997201i \(0.476180\pi\)
−0.900983 + 0.433855i \(0.857153\pi\)
\(462\) −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 0.996683 0.0813778i \(-0.0259320\pi\)
−0.568817 + 0.822464i \(0.692599\pi\)
\(480\) 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 0.298367 + 0.954451i \(0.403558\pi\)
−0.975762 + 0.218832i \(0.929775\pi\)
\(492\) 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 −0.952395 0.304866i \(-0.901388\pi\)
0.740219 + 0.672366i \(0.234722\pi\)
\(500\) 0 0
\(501\) 2.53795 0.113387
\(502\) −28.8332 −1.28689
\(503\) 2.43034 + 4.20947i 0.108363 + 0.187691i 0.915107 0.403210i \(-0.132106\pi\)
−0.806744 + 0.590901i \(0.798772\pi\)
\(504\) 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 0.984354 + 0.176202i \(0.0563813\pi\)
−0.339581 + 0.940577i \(0.610285\pi\)
\(510\) 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 0.893978 0.448110i \(-0.147903\pi\)
−0.835064 + 0.550153i \(0.814569\pi\)
\(524\) 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 0.754984 + 0.655743i \(0.227644\pi\)
0.190398 + 0.981707i \(0.439022\pi\)
\(542\) 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 0.588601 0.808424i \(-0.299679\pi\)
−0.994416 + 0.105532i \(0.966346\pi\)
\(548\) 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 0.807705 0.589587i \(-0.200710\pi\)
−0.914450 + 0.404699i \(0.867376\pi\)
\(558\) 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 −0.748006 0.663692i \(-0.768988\pi\)
0.948777 + 0.315946i \(0.102322\pi\)
\(588\) 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 0.650480 0.759524i \(-0.274568\pi\)
−0.983007 + 0.183570i \(0.941235\pi\)
\(594\) −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 0.524964 0.851125i \(-0.324079\pi\)
−0.999577 + 0.0290696i \(0.990746\pi\)
\(600\) 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 −0.999520 0.0309903i \(-0.990134\pi\)
0.526598 + 0.850114i \(0.323467\pi\)
\(614\) 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 0.640415 0.768029i \(-0.278762\pi\)
−0.985340 + 0.170601i \(0.945429\pi\)
\(618\) 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 −0.996655 0.0817184i \(-0.973959\pi\)
0.427557 0.903988i \(-0.359374\pi\)
\(632\) 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 −0.899797 0.436308i \(-0.856286\pi\)
0.827752 + 0.561094i \(0.189619\pi\)
\(642\) −0.0862211 0.149339i −0.00340288 0.00589396i
\(643\) −14.9459 + 25.8870i −0.589408 + 1.02088i 0.404902 + 0.914360i \(0.367306\pi\)
−0.994310 + 0.106524i \(0.966028\pi\)
\(644\) 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 0.854485 0.519476i \(-0.173873\pi\)
−0.877122 + 0.480268i \(0.840540\pi\)
\(660\) 0 0
\(661\) −15.9899 27.6953i −0.621935 1.07722i −0.989125 0.147077i \(-0.953013\pi\)
0.367190 0.930146i \(-0.380320\pi\)
\(662\) 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 −0.760955 0.648805i \(-0.775269\pi\)
0.942359 + 0.334604i \(0.108603\pi\)
\(702\) −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 0.606394 0.795164i \(-0.292615\pi\)
−0.991829 + 0.127571i \(0.959282\pi\)
\(710\) 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 −0.774105 0.633057i \(-0.781800\pi\)
0.935296 + 0.353866i \(0.115133\pi\)
\(720\) 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 −0.991634 0.129078i \(-0.958798\pi\)
0.607602 + 0.794242i \(0.292132\pi\)
\(728\) −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 −0.901651 0.432464i \(-0.857644\pi\)
0.825350 + 0.564621i \(0.190978\pi\)
\(740\) 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 −0.873295 0.487191i \(-0.838022\pi\)
0.858567 + 0.512701i \(0.171355\pi\)
\(744\) −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 −0.994421 0.105485i \(-0.966360\pi\)
0.405858 0.913936i \(-0.366973\pi\)
\(752\) 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 −0.325453 0.945558i \(-0.605517\pi\)
0.981604 0.190929i \(-0.0611500\pi\)
\(758\) 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 0.858281 0.513180i \(-0.171533\pi\)
−0.873567 + 0.486704i \(0.838199\pi\)
\(770\) 0 0
\(771\) 1.56460 0.0563478
\(772\) −13.8524 −0.498559
\(773\) 3.51743 + 6.09237i 0.126513 + 0.219127i 0.922323 0.386419i \(-0.126288\pi\)
−0.795810 + 0.605546i \(0.792955\pi\)
\(774\) 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