Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [74,2,Mod(47,74)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(74, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("74.47");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 74 = 2 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 74.c (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(0.590892974957\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 6.0.4406832.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} + 6x^{4} + 7x^{3} + 24x^{2} + 5x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 47.3 | ||
Root | \(-0.827721 - 1.43366i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 74.47 |
Dual form | 74.2.c.c.63.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/74\mathbb{Z}\right)^\times\).
\(n\) | \(39\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | + | 0.866025i | −0.353553 | + | 0.612372i | ||||
\(3\) | 1.52569 | + | 2.64257i | 0.880856 | + | 1.52569i | 0.850391 | + | 0.526151i | \(0.176365\pi\) |
0.0304649 | + | 0.999536i | \(0.490301\pi\) | |||||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | −0.629755 | − | 1.09077i | −0.281635 | − | 0.487806i | 0.690153 | − | 0.723664i | \(-0.257543\pi\) |
−0.971788 | + | 0.235858i | \(0.924210\pi\) | |||||||
\(6\) | −3.05137 | −1.24572 | ||||||||
\(7\) | −1.52569 | − | 2.64257i | −0.576656 | − | 0.998797i | −0.995860 | − | 0.0909046i | \(-0.971024\pi\) |
0.419204 | − | 0.907892i | \(-0.362309\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −3.15544 | + | 5.46539i | −1.05181 | + | 1.82180i | ||||
\(10\) | 1.25951 | 0.398292 | ||||||||
\(11\) | 5.31088 | 1.60129 | 0.800646 | − | 0.599138i | \(-0.204490\pi\) | ||||
0.800646 | + | 0.599138i | \(0.204490\pi\) | |||||||
\(12\) | 1.52569 | − | 2.64257i | 0.440428 | − | 0.762844i | ||||
\(13\) | −1.00000 | − | 1.73205i | −0.277350 | − | 0.480384i | 0.693375 | − | 0.720577i | \(-0.256123\pi\) |
−0.970725 | + | 0.240192i | \(0.922790\pi\) | |||||||
\(14\) | 3.05137 | 0.815514 | ||||||||
\(15\) | 1.92162 | − | 3.32834i | 0.496160 | − | 0.859374i | ||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | −2.55137 | + | 4.41911i | −0.618799 | + | 1.07179i | 0.370906 | + | 0.928670i | \(0.379047\pi\) |
−0.989705 | + | 0.143121i | \(0.954286\pi\) | |||||||
\(18\) | −3.15544 | − | 5.46539i | −0.743745 | − | 1.28820i | ||||
\(19\) | −2.39593 | − | 4.14988i | −0.549664 | − | 0.952047i | −0.998297 | − | 0.0583306i | \(-0.981422\pi\) |
0.448633 | − | 0.893716i | \(-0.351911\pi\) | |||||||
\(20\) | −0.629755 | + | 1.09077i | −0.140818 | + | 0.243903i | ||||
\(21\) | 4.65544 | − | 8.06346i | 1.01590 | − | 1.75959i | ||||
\(22\) | −2.65544 | + | 4.59936i | −0.566142 | + | 0.980587i | ||||
\(23\) | 1.74049 | 0.362917 | 0.181459 | − | 0.983399i | \(-0.441918\pi\) | ||||
0.181459 | + | 0.983399i | \(0.441918\pi\) | |||||||
\(24\) | 1.52569 | + | 2.64257i | 0.311430 | + | 0.539412i | ||||
\(25\) | 1.70682 | − | 2.95629i | 0.341363 | − | 0.591259i | ||||
\(26\) | 2.00000 | 0.392232 | ||||||||
\(27\) | −10.1027 | −1.94427 | ||||||||
\(28\) | −1.52569 | + | 2.64257i | −0.288328 | + | 0.499398i | ||||
\(29\) | −4.05137 | −0.752321 | −0.376161 | − | 0.926554i | \(-0.622756\pi\) | ||||
−0.376161 | + | 0.926554i | \(0.622756\pi\) | |||||||
\(30\) | 1.92162 | + | 3.32834i | 0.350838 | + | 0.607669i | ||||
\(31\) | −0.791864 | −0.142223 | −0.0711115 | − | 0.997468i | \(-0.522655\pi\) | ||||
−0.0711115 | + | 0.997468i | \(0.522655\pi\) | |||||||
\(32\) | −0.500000 | − | 0.866025i | −0.0883883 | − | 0.153093i | ||||
\(33\) | 8.10275 | + | 14.0344i | 1.41051 | + | 2.44307i | ||||
\(34\) | −2.55137 | − | 4.41911i | −0.437557 | − | 0.757871i | ||||
\(35\) | −1.92162 | + | 3.32834i | −0.324813 | + | 0.562592i | ||||
\(36\) | 6.31088 | 1.05181 | ||||||||
\(37\) | −1.37024 | + | 5.92642i | −0.225267 | + | 0.974297i | ||||
\(38\) | 4.79186 | 0.777343 | ||||||||
\(39\) | 3.05137 | − | 5.28514i | 0.488611 | − | 0.846299i | ||||
\(40\) | −0.629755 | − | 1.09077i | −0.0995730 | − | 0.172466i | ||||
\(41\) | 0.104068 | + | 0.180251i | 0.0162527 | + | 0.0281505i | 0.874037 | − | 0.485859i | \(-0.161493\pi\) |
−0.857785 | + | 0.514009i | \(0.828160\pi\) | |||||||
\(42\) | 4.65544 | + | 8.06346i | 0.718350 | + | 1.24422i | ||||
\(43\) | −4.36226 | −0.665238 | −0.332619 | − | 0.943061i | \(-0.607932\pi\) | ||||
−0.332619 | + | 0.943061i | \(0.607932\pi\) | |||||||
\(44\) | −2.65544 | − | 4.59936i | −0.400323 | − | 0.693380i | ||||
\(45\) | 7.94863 | 1.18491 | ||||||||
\(46\) | −0.870245 | + | 1.50731i | −0.128311 | + | 0.222240i | ||||
\(47\) | −3.20814 | −0.467955 | −0.233977 | − | 0.972242i | \(-0.575174\pi\) | ||||
−0.233977 | + | 0.972242i | \(0.575174\pi\) | |||||||
\(48\) | −3.05137 | −0.440428 | ||||||||
\(49\) | −1.15544 | + | 2.00128i | −0.165063 | + | 0.285898i | ||||
\(50\) | 1.70682 | + | 2.95629i | 0.241380 | + | 0.418083i | ||||
\(51\) | −15.5704 | −2.18029 | ||||||||
\(52\) | −1.00000 | + | 1.73205i | −0.138675 | + | 0.240192i | ||||
\(53\) | −5.65544 | + | 9.79551i | −0.776835 | + | 1.34552i | 0.156923 | + | 0.987611i | \(0.449843\pi\) |
−0.933757 | + | 0.357906i | \(0.883491\pi\) | |||||||
\(54\) | 5.05137 | − | 8.74924i | 0.687405 | − | 1.19062i | ||||
\(55\) | −3.34456 | − | 5.79294i | −0.450980 | − | 0.781120i | ||||
\(56\) | −1.52569 | − | 2.64257i | −0.203879 | − | 0.353128i | ||||
\(57\) | 7.31088 | − | 12.6628i | 0.968350 | − | 1.67723i | ||||
\(58\) | 2.02569 | − | 3.50859i | 0.265986 | − | 0.460701i | ||||
\(59\) | 6.36226 | − | 11.0198i | 0.828296 | − | 1.43465i | −0.0710788 | − | 0.997471i | \(-0.522644\pi\) |
0.899374 | − | 0.437179i | \(-0.144022\pi\) | |||||||
\(60\) | −3.84324 | −0.496160 | ||||||||
\(61\) | −3.02569 | − | 5.24064i | −0.387400 | − | 0.670996i | 0.604699 | − | 0.796454i | \(-0.293293\pi\) |
−0.992099 | + | 0.125458i | \(0.959960\pi\) | |||||||
\(62\) | 0.395932 | − | 0.685774i | 0.0502834 | − | 0.0870934i | ||||
\(63\) | 19.2569 | 2.42614 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −1.25951 | + | 2.18154i | −0.156223 | + | 0.270586i | ||||
\(66\) | −16.2055 | −1.99476 | ||||||||
\(67\) | 4.65544 | + | 8.06346i | 0.568753 | + | 0.985109i | 0.996690 | + | 0.0813001i | \(0.0259072\pi\) |
−0.427937 | + | 0.903809i | \(0.640759\pi\) | |||||||
\(68\) | 5.10275 | 0.618799 | ||||||||
\(69\) | 2.65544 | + | 4.59936i | 0.319678 | + | 0.553698i | ||||
\(70\) | −1.92162 | − | 3.32834i | −0.229677 | − | 0.397813i | ||||
\(71\) | 3.52569 | + | 6.10667i | 0.418422 | + | 0.724728i | 0.995781 | − | 0.0917622i | \(-0.0292500\pi\) |
−0.577359 | + | 0.816491i | \(0.695917\pi\) | |||||||
\(72\) | −3.15544 | + | 5.46539i | −0.371872 | + | 0.644102i | ||||
\(73\) | −3.31088 | −0.387510 | −0.193755 | − | 0.981050i | \(-0.562067\pi\) | ||||
−0.193755 | + | 0.981050i | \(0.562067\pi\) | |||||||
\(74\) | −4.44731 | − | 4.14988i | −0.516989 | − | 0.482413i | ||||
\(75\) | 10.4163 | 1.20277 | ||||||||
\(76\) | −2.39593 | + | 4.14988i | −0.274832 | + | 0.476023i | ||||
\(77\) | −8.10275 | − | 14.0344i | −0.923394 | − | 1.59937i | ||||
\(78\) | 3.05137 | + | 5.28514i | 0.345500 | + | 0.598424i | ||||
\(79\) | 5.70682 | + | 9.88450i | 0.642067 | + | 1.11209i | 0.984971 | + | 0.172722i | \(0.0552563\pi\) |
−0.342904 | + | 0.939371i | \(0.611410\pi\) | |||||||
\(80\) | 1.25951 | 0.140818 | ||||||||
\(81\) | −5.94731 | − | 10.3010i | −0.660812 | − | 1.14456i | ||||
\(82\) | −0.208136 | −0.0229848 | ||||||||
\(83\) | 1.78520 | − | 3.09205i | 0.195951 | − | 0.339397i | −0.751261 | − | 0.660005i | \(-0.770554\pi\) |
0.947212 | + | 0.320608i | \(0.103887\pi\) | |||||||
\(84\) | −9.31088 | −1.01590 | ||||||||
\(85\) | 6.42697 | 0.697102 | ||||||||
\(86\) | 2.18113 | − | 3.77783i | 0.235197 | − | 0.407374i | ||||
\(87\) | −6.18113 | − | 10.7060i | −0.662687 | − | 1.14781i | ||||
\(88\) | 5.31088 | 0.566142 | ||||||||
\(89\) | −1.63642 | + | 2.83436i | −0.173460 | + | 0.300442i | −0.939627 | − | 0.342199i | \(-0.888828\pi\) |
0.766167 | + | 0.642641i | \(0.222162\pi\) | |||||||
\(90\) | −3.97431 | + | 6.88371i | −0.418929 | + | 0.725607i | ||||
\(91\) | −3.05137 | + | 5.28514i | −0.319871 | + | 0.554033i | ||||
\(92\) | −0.870245 | − | 1.50731i | −0.0907293 | − | 0.157148i | ||||
\(93\) | −1.20814 | − | 2.09255i | −0.125278 | − | 0.216988i | ||||
\(94\) | 1.60407 | − | 2.77833i | 0.165447 | − | 0.286563i | ||||
\(95\) | −3.01770 | + | 5.22681i | −0.309610 | + | 0.536260i | ||||
\(96\) | 1.52569 | − | 2.64257i | 0.155715 | − | 0.269706i | ||||
\(97\) | 2.20814 | 0.224202 | 0.112101 | − | 0.993697i | \(-0.464242\pi\) | ||||
0.112101 | + | 0.993697i | \(0.464242\pi\) | |||||||
\(98\) | −1.15544 | − | 2.00128i | −0.116717 | − | 0.202160i | ||||
\(99\) | −16.7582 | + | 29.0260i | −1.68426 | + | 2.91723i | ||||
\(100\) | −3.41363 | −0.341363 | ||||||||
\(101\) | 3.36226 | 0.334557 | 0.167279 | − | 0.985910i | \(-0.446502\pi\) | ||||
0.167279 | + | 0.985910i | \(0.446502\pi\) | |||||||
\(102\) | 7.78520 | − | 13.4844i | 0.770849 | − | 1.33515i | ||||
\(103\) | 17.1541 | 1.69025 | 0.845123 | − | 0.534572i | \(-0.179527\pi\) | ||||
0.845123 | + | 0.534572i | \(0.179527\pi\) | |||||||
\(104\) | −1.00000 | − | 1.73205i | −0.0980581 | − | 0.169842i | ||||
\(105\) | −11.7272 | −1.14445 | ||||||||
\(106\) | −5.65544 | − | 9.79551i | −0.549305 | − | 0.951424i | ||||
\(107\) | −0.181130 | − | 0.313726i | −0.0175104 | − | 0.0303290i | 0.857137 | − | 0.515088i | \(-0.172241\pi\) |
−0.874648 | + | 0.484759i | \(0.838907\pi\) | |||||||
\(108\) | 5.05137 | + | 8.74924i | 0.486069 | + | 0.841896i | ||||
\(109\) | −0.233823 | + | 0.404994i | −0.0223962 | + | 0.0387914i | −0.877006 | − | 0.480479i | \(-0.840463\pi\) |
0.854610 | + | 0.519270i | \(0.173796\pi\) | |||||||
\(110\) | 6.68912 | 0.637782 | ||||||||
\(111\) | −17.7515 | + | 5.42090i | −1.68490 | + | 0.514529i | ||||
\(112\) | 3.05137 | 0.288328 | ||||||||
\(113\) | 0.344558 | − | 0.596791i | 0.0324133 | − | 0.0561414i | −0.849364 | − | 0.527808i | \(-0.823014\pi\) |
0.881777 | + | 0.471667i | \(0.156347\pi\) | |||||||
\(114\) | 7.31088 | + | 12.6628i | 0.684727 | + | 1.18598i | ||||
\(115\) | −1.09608 | − | 1.89847i | −0.102210 | − | 0.177033i | ||||
\(116\) | 2.02569 | + | 3.50859i | 0.188080 | + | 0.325765i | ||||
\(117\) | 12.6218 | 1.16688 | ||||||||
\(118\) | 6.36226 | + | 11.0198i | 0.585693 | + | 1.01445i | ||||
\(119\) | 15.5704 | 1.42734 | ||||||||
\(120\) | 1.92162 | − | 3.32834i | 0.175419 | − | 0.303835i | ||||
\(121\) | 17.2055 | 1.56414 | ||||||||
\(122\) | 6.05137 | 0.547866 | ||||||||
\(123\) | −0.317551 | + | 0.550014i | −0.0286326 | + | 0.0495931i | ||||
\(124\) | 0.395932 | + | 0.685774i | 0.0355557 | + | 0.0615843i | ||||
\(125\) | −10.5971 | −0.947830 | ||||||||
\(126\) | −9.62844 | + | 16.6769i | −0.857769 | + | 1.48570i | ||||
\(127\) | 7.49201 | − | 12.9765i | 0.664809 | − | 1.15148i | −0.314528 | − | 0.949248i | \(-0.601846\pi\) |
0.979337 | − | 0.202234i | \(-0.0648203\pi\) | |||||||
\(128\) | −0.500000 | + | 0.866025i | −0.0441942 | + | 0.0765466i | ||||
\(129\) | −6.65544 | − | 11.5276i | −0.585979 | − | 1.01495i | ||||
\(130\) | −1.25951 | − | 2.18154i | −0.110466 | − | 0.191333i | ||||
\(131\) | −6.04471 | + | 10.4697i | −0.528129 | + | 0.914746i | 0.471334 | + | 0.881955i | \(0.343773\pi\) |
−0.999462 | + | 0.0327906i | \(0.989561\pi\) | |||||||
\(132\) | 8.10275 | − | 14.0344i | 0.705254 | − | 1.22154i | ||||
\(133\) | −7.31088 | + | 12.6628i | −0.633934 | + | 1.09801i | ||||
\(134\) | −9.31088 | −0.804338 | ||||||||
\(135\) | 6.36226 | + | 11.0198i | 0.547576 | + | 0.948430i | ||||
\(136\) | −2.55137 | + | 4.41911i | −0.218779 | + | 0.378936i | ||||
\(137\) | −16.6865 | −1.42562 | −0.712811 | − | 0.701356i | \(-0.752578\pi\) | ||||
−0.712811 | + | 0.701356i | \(0.752578\pi\) | |||||||
\(138\) | −5.31088 | −0.452093 | ||||||||
\(139\) | 9.09608 | − | 15.7549i | 0.771520 | − | 1.33631i | −0.165210 | − | 0.986258i | \(-0.552830\pi\) |
0.936730 | − | 0.350053i | \(-0.113836\pi\) | |||||||
\(140\) | 3.84324 | 0.324813 | ||||||||
\(141\) | −4.89461 | − | 8.47772i | −0.412201 | − | 0.713953i | ||||
\(142\) | −7.05137 | −0.591738 | ||||||||
\(143\) | −5.31088 | − | 9.19872i | −0.444118 | − | 0.769236i | ||||
\(144\) | −3.15544 | − | 5.46539i | −0.262954 | − | 0.455449i | ||||
\(145\) | 2.55137 | + | 4.41911i | 0.211880 | + | 0.366987i | ||||
\(146\) | 1.65544 | − | 2.86731i | 0.137005 | − | 0.237300i | ||||
\(147\) | −7.05137 | −0.581588 | ||||||||
\(148\) | 5.81755 | − | 1.77654i | 0.478200 | − | 0.146031i | ||||
\(149\) | 13.5324 | 1.10861 | 0.554307 | − | 0.832312i | \(-0.312983\pi\) | ||||
0.554307 | + | 0.832312i | \(0.312983\pi\) | |||||||
\(150\) | −5.20814 | + | 9.02076i | −0.425243 | + | 0.736542i | ||||
\(151\) | −0.610734 | − | 1.05782i | −0.0497008 | − | 0.0860844i | 0.840105 | − | 0.542424i | \(-0.182493\pi\) |
−0.889806 | + | 0.456340i | \(0.849160\pi\) | |||||||
\(152\) | −2.39593 | − | 4.14988i | −0.194336 | − | 0.336599i | ||||
\(153\) | −16.1014 | − | 27.8885i | −1.30172 | − | 2.25465i | ||||
\(154\) | 16.2055 | 1.30588 | ||||||||
\(155\) | 0.498680 | + | 0.863740i | 0.0400550 | + | 0.0693772i | ||||
\(156\) | −6.10275 | −0.488611 | ||||||||
\(157\) | −9.38795 | + | 16.2604i | −0.749240 | + | 1.29772i | 0.198948 | + | 0.980010i | \(0.436248\pi\) |
−0.948188 | + | 0.317711i | \(0.897086\pi\) | |||||||
\(158\) | −11.4136 | −0.908020 | ||||||||
\(159\) | −34.5137 | −2.73712 | ||||||||
\(160\) | −0.629755 | + | 1.09077i | −0.0497865 | + | 0.0862328i | ||||
\(161\) | −2.65544 | − | 4.59936i | −0.209278 | − | 0.362480i | ||||
\(162\) | 11.8946 | 0.934529 | ||||||||
\(163\) | 3.92162 | − | 6.79244i | 0.307165 | − | 0.532025i | −0.670576 | − | 0.741841i | \(-0.733953\pi\) |
0.977741 | + | 0.209816i | \(0.0672863\pi\) | |||||||
\(164\) | 0.104068 | − | 0.180251i | 0.00812636 | − | 0.0140753i | ||||
\(165\) | 10.2055 | − | 17.6764i | 0.794497 | − | 1.37611i | ||||
\(166\) | 1.78520 | + | 3.09205i | 0.138558 | + | 0.239990i | ||||
\(167\) | 6.00000 | + | 10.3923i | 0.464294 | + | 0.804181i | 0.999169 | − | 0.0407502i | \(-0.0129748\pi\) |
−0.534875 | + | 0.844931i | \(0.679641\pi\) | |||||||
\(168\) | 4.65544 | − | 8.06346i | 0.359175 | − | 0.622110i | ||||
\(169\) | 4.50000 | − | 7.79423i | 0.346154 | − | 0.599556i | ||||
\(170\) | −3.21348 | + | 5.56592i | −0.246463 | + | 0.426886i | ||||
\(171\) | 30.2409 | 2.31258 | ||||||||
\(172\) | 2.18113 | + | 3.77783i | 0.166310 | + | 0.288057i | ||||
\(173\) | −2.23382 | + | 3.86910i | −0.169834 | + | 0.294162i | −0.938362 | − | 0.345655i | \(-0.887657\pi\) |
0.768527 | + | 0.639817i | \(0.220990\pi\) | |||||||
\(174\) | 12.3623 | 0.937180 | ||||||||
\(175\) | −10.4163 | −0.787396 | ||||||||
\(176\) | −2.65544 | + | 4.59936i | −0.200162 | + | 0.346690i | ||||
\(177\) | 38.8273 | 2.91844 | ||||||||
\(178\) | −1.63642 | − | 2.83436i | −0.122655 | − | 0.212445i | ||||
\(179\) | −14.1027 | −1.05409 | −0.527044 | − | 0.849838i | \(-0.676700\pi\) | ||||
−0.527044 | + | 0.849838i | \(0.676700\pi\) | |||||||
\(180\) | −3.97431 | − | 6.88371i | −0.296228 | − | 0.513082i | ||||
\(181\) | −6.73250 | − | 11.6610i | −0.500423 | − | 0.866758i | −1.00000 | 0.000488579i | \(-0.999844\pi\) | |
0.499577 | − | 0.866270i | \(-0.333489\pi\) | |||||||
\(182\) | −3.05137 | − | 5.28514i | −0.226183 | − | 0.391760i | ||||
\(183\) | 9.23250 | − | 15.9912i | 0.682486 | − | 1.18210i | ||||
\(184\) | 1.74049 | 0.128311 | ||||||||
\(185\) | 7.32727 | − | 2.23757i | 0.538711 | − | 0.164510i | ||||
\(186\) | 2.41627 | 0.177170 | ||||||||
\(187\) | −13.5501 | + | 23.4694i | −0.990878 | + | 1.71625i | ||||
\(188\) | 1.60407 | + | 2.77833i | 0.116989 | + | 0.202630i | ||||
\(189\) | 15.4136 | + | 26.6972i | 1.12118 | + | 1.94194i | ||||
\(190\) | −3.01770 | − | 5.22681i | −0.218927 | − | 0.379193i | ||||
\(191\) | 9.42697 | 0.682111 | 0.341056 | − | 0.940043i | \(-0.389216\pi\) | ||||
0.341056 | + | 0.940043i | \(0.389216\pi\) | |||||||
\(192\) | 1.52569 | + | 2.64257i | 0.110107 | + | 0.190711i | ||||
\(193\) | 2.48098 | 0.178585 | 0.0892924 | − | 0.996005i | \(-0.471539\pi\) | ||||
0.0892924 | + | 0.996005i | \(0.471539\pi\) | |||||||
\(194\) | −1.10407 | + | 1.91230i | −0.0792675 | + | 0.137295i | ||||
\(195\) | −7.68648 | −0.550440 | ||||||||
\(196\) | 2.31088 | 0.165063 | ||||||||
\(197\) | 0.974313 | − | 1.68756i | 0.0694169 | − | 0.120234i | −0.829228 | − | 0.558911i | \(-0.811219\pi\) |
0.898645 | + | 0.438677i | \(0.144553\pi\) | |||||||
\(198\) | −16.7582 | − | 29.0260i | −1.19095 | − | 2.06279i | ||||
\(199\) | −1.98667 | −0.140831 | −0.0704156 | − | 0.997518i | \(-0.522433\pi\) | ||||
−0.0704156 | + | 0.997518i | \(0.522433\pi\) | |||||||
\(200\) | 1.70682 | − | 2.95629i | 0.120690 | − | 0.209041i | ||||
\(201\) | −14.2055 | + | 24.6046i | −1.00198 | + | 1.73548i | ||||
\(202\) | −1.68113 | + | 2.91180i | −0.118284 | + | 0.204874i | ||||
\(203\) | 6.18113 | + | 10.7060i | 0.433830 | + | 0.751416i | ||||
\(204\) | 7.78520 | + | 13.4844i | 0.545073 | + | 0.944094i | ||||
\(205\) | 0.131075 | − | 0.227028i | 0.00915467 | − | 0.0158564i | ||||
\(206\) | −8.57706 | + | 14.8559i | −0.597592 | + | 1.03506i | ||||
\(207\) | −5.49201 | + | 9.51245i | −0.381721 | + | 0.661161i | ||||
\(208\) | 2.00000 | 0.138675 | ||||||||
\(209\) | −12.7245 | − | 22.0395i | −0.880173 | − | 1.52450i | ||||
\(210\) | 5.86358 | − | 10.1560i | 0.404625 | − | 0.700832i | ||||
\(211\) | −17.0868 | −1.17630 | −0.588151 | − | 0.808751i | \(-0.700144\pi\) | ||||
−0.588151 | + | 0.808751i | \(0.700144\pi\) | |||||||
\(212\) | 11.3109 | 0.776835 | ||||||||
\(213\) | −10.7582 | + | 18.6337i | −0.737139 | + | 1.27676i | ||||
\(214\) | 0.362259 | 0.0247635 | ||||||||
\(215\) | 2.74716 | + | 4.75821i | 0.187354 | + | 0.324507i | ||||
\(216\) | −10.1027 | −0.687405 | ||||||||
\(217\) | 1.20814 | + | 2.09255i | 0.0820136 | + | 0.142052i | ||||
\(218\) | −0.233823 | − | 0.404994i | −0.0158365 | − | 0.0274297i | ||||
\(219\) | −5.05137 | − | 8.74924i | −0.341340 | − | 0.591219i | ||||
\(220\) | −3.34456 | + | 5.79294i | −0.225490 | + | 0.390560i | ||||
\(221\) | 10.2055 | 0.686496 | ||||||||
\(222\) | 4.18113 | − | 18.0837i | 0.280619 | − | 1.21370i | ||||
\(223\) | 1.94599 | 0.130313 | 0.0651564 | − | 0.997875i | \(-0.479245\pi\) | ||||
0.0651564 | + | 0.997875i | \(0.479245\pi\) | |||||||
\(224\) | −1.52569 | + | 2.64257i | −0.101939 | + | 0.176564i | ||||
\(225\) | 10.7715 | + | 18.6568i | 0.718102 | + | 1.24379i | ||||
\(226\) | 0.344558 | + | 0.596791i | 0.0229196 | + | 0.0396980i | ||||
\(227\) | −2.29318 | − | 3.97191i | −0.152204 | − | 0.263625i | 0.779833 | − | 0.625987i | \(-0.215304\pi\) |
−0.932037 | + | 0.362362i | \(0.881970\pi\) | |||||||
\(228\) | −14.6218 | −0.968350 | ||||||||
\(229\) | 0.817551 | + | 1.41604i | 0.0540253 | + | 0.0935745i | 0.891773 | − | 0.452483i | \(-0.149462\pi\) |
−0.837748 | + | 0.546057i | \(0.816128\pi\) | |||||||
\(230\) | 2.19216 | 0.144547 | ||||||||
\(231\) | 24.7245 | − | 42.8241i | 1.62675 | − | 2.81762i | ||||
\(232\) | −4.05137 | −0.265986 | ||||||||
\(233\) | 8.03804 | 0.526590 | 0.263295 | − | 0.964715i | \(-0.415191\pi\) | ||||
0.263295 | + | 0.964715i | \(0.415191\pi\) | |||||||
\(234\) | −6.31088 | + | 10.9308i | −0.412555 | + | 0.714567i | ||||
\(235\) | 2.02034 | + | 3.49933i | 0.131792 | + | 0.228271i | ||||
\(236\) | −12.7245 | −0.828296 | ||||||||
\(237\) | −17.4136 | + | 30.1613i | −1.13114 | + | 1.95919i | ||||
\(238\) | −7.78520 | + | 13.4844i | −0.504639 | + | 0.874061i | ||||
\(239\) | −0.317551 | + | 0.550014i | −0.0205407 | + | 0.0355775i | −0.876113 | − | 0.482106i | \(-0.839872\pi\) |
0.855572 | + | 0.517683i | \(0.173205\pi\) | |||||||
\(240\) | 1.92162 | + | 3.32834i | 0.124040 | + | 0.214844i | ||||
\(241\) | 3.75819 | + | 6.50938i | 0.242086 | + | 0.419306i | 0.961308 | − | 0.275474i | \(-0.0888349\pi\) |
−0.719222 | + | 0.694780i | \(0.755502\pi\) | |||||||
\(242\) | −8.60275 | + | 14.9004i | −0.553006 | + | 0.957834i | ||||
\(243\) | 2.99333 | − | 5.18461i | 0.192022 | − | 0.332593i | ||||
\(244\) | −3.02569 | + | 5.24064i | −0.193700 | + | 0.335498i | ||||
\(245\) | 2.91058 | 0.185950 | ||||||||
\(246\) | −0.317551 | − | 0.550014i | −0.0202463 | − | 0.0350676i | ||||
\(247\) | −4.79186 | + | 8.29975i | −0.304899 | + | 0.528101i | ||||
\(248\) | −0.791864 | −0.0502834 | ||||||||
\(249\) | 10.8946 | 0.690418 | ||||||||
\(250\) | 5.29853 | − | 9.17732i | 0.335108 | − | 0.580425i | ||||
\(251\) | −8.88128 | −0.560581 | −0.280291 | − | 0.959915i | \(-0.590431\pi\) | ||||
−0.280291 | + | 0.959915i | \(0.590431\pi\) | |||||||
\(252\) | −9.62844 | − | 16.6769i | −0.606534 | − | 1.05055i | ||||
\(253\) | 9.24354 | 0.581136 | ||||||||
\(254\) | 7.49201 | + | 12.9765i | 0.470091 | + | 0.814221i | ||||
\(255\) | 9.80554 | + | 16.9837i | 0.614047 | + | 1.06356i | ||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 6.05005 | − | 10.4790i | 0.377392 | − | 0.653662i | −0.613290 | − | 0.789858i | \(-0.710154\pi\) |
0.990682 | + | 0.136196i | \(0.0434876\pi\) | |||||||
\(258\) | 13.3109 | 0.828699 | ||||||||
\(259\) | 17.7515 | − | 5.42090i | 1.10303 | − | 0.336838i | ||||
\(260\) | 2.51902 | 0.156223 | ||||||||
\(261\) | 12.7839 | − | 22.1423i | 0.791302 | − | 1.37058i | ||||
\(262\) | −6.04471 | − | 10.4697i | −0.373443 | − | 0.646823i | ||||
\(263\) | 9.57040 | + | 16.5764i | 0.590136 | + | 1.02215i | 0.994214 | + | 0.107421i | \(0.0342592\pi\) |
−0.404078 | + | 0.914725i | \(0.632408\pi\) | |||||||
\(264\) | 8.10275 | + | 14.0344i | 0.498690 | + | 0.863756i | ||||
\(265\) | 14.2462 | 0.875136 | ||||||||
\(266\) | −7.31088 | − | 12.6628i | −0.448259 | − | 0.776408i | ||||
\(267\) | −9.98667 | −0.611174 | ||||||||
\(268\) | 4.65544 | − | 8.06346i | 0.284376 | − | 0.492554i | ||||
\(269\) | −15.7892 | −0.962686 | −0.481343 | − | 0.876532i | \(-0.659851\pi\) | ||||
−0.481343 | + | 0.876532i | \(0.659851\pi\) | |||||||
\(270\) | −12.7245 | −0.774390 | ||||||||
\(271\) | 9.55005 | − | 16.5412i | 0.580125 | − | 1.00481i | −0.415340 | − | 0.909666i | \(-0.636337\pi\) |
0.995464 | − | 0.0951386i | \(-0.0303294\pi\) | |||||||
\(272\) | −2.55137 | − | 4.41911i | −0.154700 | − | 0.267948i | ||||
\(273\) | −18.6218 | −1.12704 | ||||||||
\(274\) | 8.34324 | − | 14.4509i | 0.504033 | − | 0.873012i | ||||
\(275\) | 9.06471 | − | 15.7005i | 0.546622 | − | 0.946778i | ||||
\(276\) | 2.65544 | − | 4.59936i | 0.159839 | − | 0.276849i | ||||
\(277\) | −8.20015 | − | 14.2031i | −0.492699 | − | 0.853380i | 0.507265 | − | 0.861790i | \(-0.330656\pi\) |
−0.999965 | + | 0.00840971i | \(0.997323\pi\) | |||||||
\(278\) | 9.09608 | + | 15.7549i | 0.545547 | + | 0.944915i | ||||
\(279\) | 2.49868 | − | 4.32784i | 0.149592 | − | 0.259101i | ||||
\(280\) | −1.92162 | + | 3.32834i | −0.114839 | + | 0.198906i | ||||
\(281\) | 2.39725 | − | 4.15216i | 0.143008 | − | 0.247697i | −0.785620 | − | 0.618709i | \(-0.787656\pi\) |
0.928628 | + | 0.371012i | \(0.120989\pi\) | |||||||
\(282\) | 9.78922 | 0.582940 | ||||||||
\(283\) | −12.9730 | − | 22.4699i | −0.771164 | − | 1.33570i | −0.936925 | − | 0.349530i | \(-0.886341\pi\) |
0.165761 | − | 0.986166i | \(-0.446992\pi\) | |||||||
\(284\) | 3.52569 | − | 6.10667i | 0.209211 | − | 0.362364i | ||||
\(285\) | −18.4163 | −1.09089 | ||||||||
\(286\) | 10.6218 | 0.628078 | ||||||||
\(287\) | 0.317551 | − | 0.550014i | 0.0187444 | − | 0.0324663i | ||||
\(288\) | 6.31088 | 0.371872 | ||||||||
\(289\) | −4.51902 | − | 7.82717i | −0.265825 | − | 0.460422i | ||||
\(290\) | −5.10275 | −0.299644 | ||||||||
\(291\) | 3.36893 | + | 5.83515i | 0.197490 | + | 0.342063i | ||||
\(292\) | 1.65544 | + | 2.86731i | 0.0968774 | + | 0.167797i | ||||
\(293\) | −11.0257 | − | 19.0971i | −0.644128 | − | 1.11566i | −0.984502 | − | 0.175372i | \(-0.943887\pi\) |
0.340375 | − | 0.940290i | \(-0.389446\pi\) | |||||||
\(294\) | 3.52569 | − | 6.10667i | 0.205622 | − | 0.356148i | ||||
\(295\) | −16.0267 | −0.933108 | ||||||||
\(296\) | −1.37024 | + | 5.92642i | −0.0796439 | + | 0.344466i | ||||
\(297\) | −53.6545 | −3.11335 | ||||||||
\(298\) | −6.76618 | + | 11.7194i | −0.391954 | + | 0.678884i | ||||
\(299\) | −1.74049 | − | 3.01462i | −0.100655 | − | 0.174340i | ||||
\(300\) | −5.20814 | − | 9.02076i | −0.300692 | − | 0.520814i | ||||
\(301\) | 6.65544 | + | 11.5276i | 0.383613 | + | 0.664438i | ||||
\(302\) | 1.22147 | 0.0702876 | ||||||||
\(303\) | 5.12976 | + | 8.88500i | 0.294697 | + | 0.510430i | ||||
\(304\) | 4.79186 | 0.274832 | ||||||||
\(305\) | −3.81088 | + | 6.60065i | −0.218211 | + | 0.377952i | ||||
\(306\) | 32.2029 | 1.84091 | ||||||||
\(307\) | −5.74049 | −0.327627 | −0.163814 | − | 0.986491i | \(-0.552380\pi\) | ||||
−0.163814 | + | 0.986491i | \(0.552380\pi\) | |||||||
\(308\) | −8.10275 | + | 14.0344i | −0.461697 | + | 0.799683i | ||||
\(309\) | 26.1718 | + | 45.3309i | 1.48886 | + | 2.57879i | ||||
\(310\) | −0.997361 | −0.0566463 | ||||||||
\(311\) | 5.26618 | − | 9.12129i | 0.298617 | − | 0.517221i | −0.677202 | − | 0.735797i | \(-0.736808\pi\) |
0.975820 | + | 0.218576i | \(0.0701412\pi\) | |||||||
\(312\) | 3.05137 | − | 5.28514i | 0.172750 | − | 0.299212i | ||||
\(313\) | −12.4150 | + | 21.5033i | −0.701735 | + | 1.21544i | 0.266122 | + | 0.963939i | \(0.414257\pi\) |
−0.967857 | + | 0.251501i | \(0.919076\pi\) | |||||||
\(314\) | −9.38795 | − | 16.2604i | −0.529792 | − | 0.917627i | ||||
\(315\) | −12.1271 | − | 21.0048i | −0.683286 | − | 1.18349i | ||||
\(316\) | 5.70682 | − | 9.88450i | 0.321034 | − | 0.556046i | ||||
\(317\) | 13.1461 | − | 22.7698i | 0.738361 | − | 1.27888i | −0.214873 | − | 0.976642i | \(-0.568934\pi\) |
0.953233 | − | 0.302236i | \(-0.0977331\pi\) | |||||||
\(318\) | 17.2569 | − | 29.8898i | 0.967717 | − | 1.67614i | ||||
\(319\) | −21.5164 | −1.20469 | ||||||||
\(320\) | −0.629755 | − | 1.09077i | −0.0352044 | − | 0.0609758i | ||||
\(321\) | 0.552694 | − | 0.957294i | 0.0308484 | − | 0.0534309i | ||||
\(322\) | 5.31088 | 0.295964 | ||||||||
\(323\) | 24.4517 | 1.36053 | ||||||||
\(324\) | −5.94731 | + | 10.3010i | −0.330406 | + | 0.572280i | ||||
\(325\) | −6.82727 | −0.378709 | ||||||||
\(326\) | 3.92162 | + | 6.79244i | 0.217198 | + | 0.376199i | ||||
\(327\) | −1.42697 | −0.0789114 | ||||||||
\(328\) | 0.104068 | + | 0.180251i | 0.00574620 | + | 0.00995271i | ||||
\(329\) | 4.89461 | + | 8.47772i | 0.269849 | + | 0.467392i | ||||
\(330\) | 10.2055 | + | 17.6764i | 0.561794 | + | 0.973056i | ||||
\(331\) | −14.8946 | + | 25.7982i | −0.818682 | + | 1.41800i | 0.0879717 | + | 0.996123i | \(0.471961\pi\) |
−0.906654 | + | 0.421876i | \(0.861372\pi\) | |||||||
\(332\) | −3.57040 | −0.195951 | ||||||||
\(333\) | −28.0664 | − | 26.1894i | −1.53803 | − | 1.43517i | ||||
\(334\) | −12.0000 | −0.656611 | ||||||||
\(335\) | 5.86358 | − | 10.1560i | 0.320362 | − | 0.554882i | ||||
\(336\) | 4.65544 | + | 8.06346i | 0.253975 | + | 0.439898i | ||||
\(337\) | 6.36358 | + | 11.0220i | 0.346646 | + | 0.600409i | 0.985651 | − | 0.168794i | \(-0.0539871\pi\) |
−0.639005 | + | 0.769202i | \(0.720654\pi\) | |||||||
\(338\) | 4.50000 | + | 7.79423i | 0.244768 | + | 0.423950i | ||||
\(339\) | 2.10275 | 0.114206 | ||||||||
\(340\) | −3.21348 | − | 5.56592i | −0.174276 | − | 0.301854i | ||||
\(341\) | −4.20550 | −0.227740 | ||||||||
\(342\) | −15.1204 | + | 26.1894i | −0.817620 | + | 1.41616i | ||||
\(343\) | −14.3082 | −0.772573 | ||||||||
\(344\) | −4.36226 | −0.235197 | ||||||||
\(345\) | 3.34456 | − | 5.79294i | 0.180065 | − | 0.311882i | ||||
\(346\) | −2.23382 | − | 3.86910i | −0.120091 | − | 0.208004i | ||||
\(347\) | 29.5651 | 1.58714 | 0.793569 | − | 0.608480i | \(-0.208220\pi\) | ||||
0.793569 | + | 0.608480i | \(0.208220\pi\) | |||||||
\(348\) | −6.18113 | + | 10.7060i | −0.331343 | + | 0.573903i | ||||
\(349\) | 16.2515 | − | 28.1485i | 0.869924 | − | 1.50675i | 0.00785093 | − | 0.999969i | \(-0.497501\pi\) |
0.862073 | − | 0.506784i | \(-0.169166\pi\) | |||||||
\(350\) | 5.20814 | − | 9.02076i | 0.278387 | − | 0.482180i | ||||
\(351\) | 10.1027 | + | 17.4985i | 0.539245 | + | 0.933999i | ||||
\(352\) | −2.65544 | − | 4.59936i | −0.141536 | − | 0.245147i | ||||
\(353\) | −2.05269 | + | 3.55537i | −0.109254 | + | 0.189233i | −0.915468 | − | 0.402390i | \(-0.868179\pi\) |
0.806214 | + | 0.591624i | \(0.201513\pi\) | |||||||
\(354\) | −19.4136 | + | 33.6254i | −1.03182 | + | 1.78717i | ||||
\(355\) | 4.44064 | − | 7.69141i | 0.235685 | − | 0.408218i | ||||
\(356\) | 3.27284 | 0.173460 | ||||||||
\(357\) | 23.7556 | + | 41.1458i | 1.25728 | + | 2.17767i | ||||
\(358\) | 7.05137 | − | 12.2133i | 0.372677 | − | 0.645495i | ||||
\(359\) | −28.2055 | −1.48863 | −0.744315 | − | 0.667829i | \(-0.767224\pi\) | ||||
−0.744315 | + | 0.667829i | \(0.767224\pi\) | |||||||
\(360\) | 7.94863 | 0.418929 | ||||||||
\(361\) | −1.98098 | + | 3.43116i | −0.104262 | + | 0.180587i | ||||
\(362\) | 13.4650 | 0.707705 | ||||||||
\(363\) | 26.2502 | + | 45.4667i | 1.37778 | + | 2.38638i | ||||
\(364\) | 6.10275 | 0.319871 | ||||||||
\(365\) | 2.08505 | + | 3.61141i | 0.109136 | + | 0.189030i | ||||
\(366\) | 9.23250 | + | 15.9912i | 0.482591 | + | 0.835872i | ||||
\(367\) | 2.00000 | + | 3.46410i | 0.104399 | + | 0.180825i | 0.913493 | − | 0.406855i | \(-0.133375\pi\) |
−0.809093 | + | 0.587680i | \(0.800041\pi\) | |||||||
\(368\) | −0.870245 | + | 1.50731i | −0.0453646 | + | 0.0785739i | ||||
\(369\) | −1.31352 | −0.0683793 | ||||||||
\(370\) | −1.72584 | + | 7.46439i | −0.0897220 | + | 0.388055i | ||||
\(371\) | 34.5137 | 1.79186 | ||||||||
\(372\) | −1.20814 | + | 2.09255i | −0.0626389 | + | 0.108494i | ||||
\(373\) | −18.6785 | − | 32.3521i | −0.967136 | − | 1.67513i | −0.703765 | − | 0.710433i | \(-0.748499\pi\) |
−0.263371 | − | 0.964695i | \(-0.584834\pi\) | |||||||
\(374\) | −13.5501 | − | 23.4694i | −0.700657 | − | 1.21357i | ||||
\(375\) | −16.1678 | − | 28.0034i | −0.834901 | − | 1.44609i | ||||
\(376\) | −3.20814 | −0.165447 | ||||||||
\(377\) | 4.05137 | + | 7.01719i | 0.208656 | + | 0.361403i | ||||
\(378\) | −30.8273 | −1.58558 | ||||||||
\(379\) | 2.45397 | − | 4.25040i | 0.126052 | − | 0.218329i | −0.796092 | − | 0.605176i | \(-0.793103\pi\) |
0.922144 | + | 0.386848i | \(0.126436\pi\) | |||||||
\(380\) | 6.03540 | 0.309610 | ||||||||
\(381\) | 45.7219 | 2.34240 | ||||||||
\(382\) | −4.71348 | + | 8.16399i | −0.241163 | + | 0.417706i | ||||
\(383\) | −10.3042 | − | 17.8474i | −0.526521 | − | 0.911961i | −0.999522 | − | 0.0308995i | \(-0.990163\pi\) |
0.473002 | − | 0.881062i | \(-0.343171\pi\) | |||||||
\(384\) | −3.05137 | −0.155715 | ||||||||
\(385\) | −10.2055 | + | 17.6764i | −0.520120 | + | 0.900875i | ||||
\(386\) | −1.24049 | + | 2.14859i | −0.0631393 | + | 0.109360i | ||||
\(387\) | 13.7649 | − | 23.8414i | 0.699707 | − | 1.21193i | ||||
\(388\) | −1.10407 | − | 1.91230i | −0.0560506 | − | 0.0970824i | ||||
\(389\) | 12.7839 | + | 22.1423i | 0.648168 | + | 1.12266i | 0.983560 | + | 0.180582i | \(0.0577980\pi\) |
−0.335392 | + | 0.942079i | \(0.608869\pi\) | |||||||
\(390\) | 3.84324 | − | 6.65668i | 0.194610 | − | 0.337074i | ||||
\(391\) | −4.44064 | + | 7.69141i | −0.224573 | + | 0.388972i | ||||
\(392\) | −1.15544 | + | 2.00128i | −0.0583587 | + | 0.101080i | ||||
\(393\) | −36.8893 | −1.86082 | ||||||||
\(394\) | 0.974313 | + | 1.68756i | 0.0490852 | + | 0.0850180i | ||||
\(395\) | 7.18780 | − | 12.4496i | 0.361657 | − | 0.626409i | ||||
\(396\) | 33.5164 | 1.68426 | ||||||||
\(397\) | −30.2923 | −1.52033 | −0.760163 | − | 0.649733i | \(-0.774881\pi\) | ||||
−0.760163 | + | 0.649733i | \(0.774881\pi\) | |||||||
\(398\) | 0.993334 | − | 1.72050i | 0.0497913 | − | 0.0862411i | ||||
\(399\) | −44.6165 | −2.23362 | ||||||||
\(400\) | 1.70682 | + | 2.95629i | 0.0853408 | + | 0.147815i | ||||
\(401\) | 27.5164 | 1.37410 | 0.687051 | − | 0.726609i | \(-0.258905\pi\) | ||||
0.687051 | + | 0.726609i | \(0.258905\pi\) | |||||||
\(402\) | −14.2055 | − | 24.6046i | −0.708506 | − | 1.22717i | ||||
\(403\) | 0.791864 | + | 1.37155i | 0.0394455 | + | 0.0683217i | ||||
\(404\) | −1.68113 | − | 2.91180i | −0.0836393 | − | 0.144868i | ||||
\(405\) | −7.49069 | + | 12.9743i | −0.372216 | + | 0.644696i | ||||
\(406\) | −12.3623 | −0.613529 | ||||||||
\(407\) | −7.27721 | + | 31.4745i | −0.360718 | + | 1.56013i | ||||
\(408\) | −15.5704 | −0.770849 | ||||||||
\(409\) | −3.62309 | + | 6.27537i | −0.179150 | + | 0.310297i | −0.941590 | − | 0.336762i | \(-0.890668\pi\) |
0.762439 | + | 0.647060i | \(0.224001\pi\) | |||||||
\(410\) | 0.131075 | + | 0.227028i | 0.00647333 | + | 0.0112121i | ||||
\(411\) | −25.4583 | − | 44.0951i | −1.25577 | − | 2.17505i | ||||
\(412\) | −8.57706 | − | 14.8559i | −0.422561 | − | 0.731898i | ||||
\(413\) | −38.8273 | −1.91056 | ||||||||
\(414\) | −5.49201 | − | 9.51245i | −0.269918 | − | 0.467511i | ||||
\(415\) | −4.49695 | −0.220747 | ||||||||
\(416\) | −1.00000 | + | 1.73205i | −0.0490290 | + | 0.0849208i | ||||
\(417\) | 55.5111 | 2.71839 | ||||||||
\(418\) | 25.4490 | 1.24475 | ||||||||
\(419\) | 2.28388 | − | 3.95579i | 0.111575 | − | 0.193253i | −0.804831 | − | 0.593505i | \(-0.797744\pi\) |
0.916405 | + | 0.400251i | \(0.131077\pi\) | |||||||
\(420\) | 5.86358 | + | 10.1560i | 0.286113 | + | 0.495563i | ||||
\(421\) | 26.8432 | 1.30826 | 0.654130 | − | 0.756382i | \(-0.273035\pi\) | ||||
0.654130 | + | 0.756382i | \(0.273035\pi\) | |||||||
\(422\) | 8.54339 | − | 14.7976i | 0.415886 | − | 0.720335i | ||||
\(423\) | 10.1231 | − | 17.5337i | 0.492201 | − | 0.852518i | ||||
\(424\) | −5.65544 | + | 9.79551i | −0.274653 | + | 0.475712i | ||||
\(425\) | 8.70946 | + | 15.0852i | 0.422471 | + | 0.731741i | ||||
\(426\) | −10.7582 | − | 18.6337i | −0.521236 | − | 0.902807i | ||||
\(427\) | −9.23250 | + | 15.9912i | −0.446792 | + | 0.773867i | ||||
\(428\) | −0.181130 | + | 0.313726i | −0.00875522 | + | 0.0151645i | ||||
\(429\) | 16.2055 | − | 28.0687i | 0.782409 | − | 1.35517i | ||||
\(430\) | −5.49431 | −0.264959 | ||||||||
\(431\) | 10.3959 | + | 18.0063i | 0.500754 | + | 0.867332i | 1.00000 | 0.000871345i | \(0.000277358\pi\) | |
−0.499245 | + | 0.866461i | \(0.666389\pi\) | |||||||
\(432\) | 5.05137 | − | 8.74924i | 0.243034 | − | 0.420948i | ||||
\(433\) | 27.6572 | 1.32912 | 0.664559 | − | 0.747235i | \(-0.268619\pi\) | ||||
0.664559 | + | 0.747235i | \(0.268619\pi\) | |||||||
\(434\) | −2.41627 | −0.115985 | ||||||||
\(435\) | −7.78520 | + | 13.4844i | −0.373272 | + | 0.646525i | ||||
\(436\) | 0.467647 | 0.0223962 | ||||||||
\(437\) | −4.17009 | − | 7.22282i | −0.199483 | − | 0.345514i | ||||
\(438\) | 10.1027 | 0.482728 | ||||||||
\(439\) | 3.46765 | + | 6.00614i | 0.165502 | + | 0.286657i | 0.936833 | − | 0.349776i | \(-0.113742\pi\) |
−0.771332 | + | 0.636433i | \(0.780409\pi\) | |||||||
\(440\) | −3.34456 | − | 5.79294i | −0.159446 | − | 0.276168i | ||||
\(441\) | −7.29186 | − | 12.6299i | −0.347232 | − | 0.601423i | ||||
\(442\) | −5.10275 | + | 8.83822i | −0.242713 | + | 0.420391i | ||||
\(443\) | −19.8653 | −0.943829 | −0.471915 | − | 0.881644i | \(-0.656437\pi\) | ||||
−0.471915 | + | 0.881644i | \(0.656437\pi\) | |||||||
\(444\) | 13.5704 | + | 12.6628i | 0.644022 | + | 0.600951i | ||||
\(445\) | 4.12218 | 0.195410 | ||||||||
\(446\) | −0.972993 | + | 1.68527i | −0.0460726 | + | 0.0798000i | ||||
\(447\) | 20.6461 | + | 35.7602i | 0.976529 | + | 1.69140i | ||||
\(448\) | −1.52569 | − | 2.64257i | −0.0720819 | − | 0.124850i | ||||
\(449\) | 13.0691 | + | 22.6363i | 0.616768 | + | 1.06827i | 0.990072 | + | 0.140564i | \(0.0448916\pi\) |
−0.373304 | + | 0.927709i | \(0.621775\pi\) | |||||||
\(450\) | −21.5430 | −1.01555 | ||||||||
\(451\) | 0.552694 | + | 0.957294i | 0.0260253 | + | 0.0450772i | ||||
\(452\) | −0.689115 | −0.0324133 | ||||||||
\(453\) | 1.86358 | − | 3.22781i | 0.0875586 | − | 0.151656i | ||||
\(454\) | 4.58637 | 0.215249 | ||||||||
\(455\) | 7.68648 | 0.360348 | ||||||||
\(456\) | 7.31088 | − | 12.6628i | 0.342364 | − | 0.592991i | ||||
\(457\) | 10.3432 | + | 17.9150i | 0.483836 | + | 0.838029i | 0.999828 | − | 0.0185648i | \(-0.00590969\pi\) |
−0.515991 | + | 0.856594i | \(0.672576\pi\) | |||||||
\(458\) | −1.63510 | −0.0764033 | ||||||||
\(459\) | 25.7759 | − | 44.6452i | 1.20312 | − | 2.08386i | ||||
\(460\) | −1.09608 | + | 1.89847i | −0.0511051 | + | 0.0885166i | ||||
\(461\) | −11.1027 | + | 19.2305i | −0.517107 | + | 0.895655i | 0.482696 | + | 0.875788i | \(0.339658\pi\) |
−0.999803 | + | 0.0198669i | \(0.993676\pi\) | |||||||
\(462\) | 24.7245 | + | 42.8241i | 1.15029 | + | 1.99236i | ||||
\(463\) | −11.0961 | − | 19.2190i | −0.515679 | − | 0.893182i | −0.999834 | − | 0.0181998i | \(-0.994207\pi\) |
0.484156 | − | 0.874982i | \(-0.339127\pi\) | |||||||
\(464\) | 2.02569 | − | 3.50859i | 0.0940402 | − | 0.162882i | ||||
\(465\) | −1.52166 | + | 2.63559i | −0.0705653 | + | 0.122223i | ||||
\(466\) | −4.01902 | + | 6.96115i | −0.186178 | + | 0.322469i | ||||
\(467\) | −11.8920 | −0.550295 | −0.275147 | − | 0.961402i | \(-0.588727\pi\) | ||||
−0.275147 | + | 0.961402i | \(0.588727\pi\) | |||||||
\(468\) | −6.31088 | − | 10.9308i | −0.291721 | − | 0.505275i | ||||
\(469\) | 14.2055 | − | 24.6046i | 0.655949 | − | 1.13614i | ||||
\(470\) | −4.04068 | −0.186383 | ||||||||
\(471\) | −57.2923 | −2.63989 | ||||||||
\(472\) | 6.36226 | − | 11.0198i | 0.292847 | − | 0.507225i | ||||
\(473\) | −23.1675 | −1.06524 | ||||||||
\(474\) | −17.4136 | − | 30.1613i | −0.799835 | − | 1.38535i | ||||
\(475\) | −16.3577 | −0.750541 | ||||||||
\(476\) | −7.78520 | − | 13.4844i | −0.356834 | − | 0.618055i | ||||
\(477\) | −35.6908 | − | 61.8184i | −1.63417 | − | 2.83047i | ||||
\(478\) | −0.317551 | − | 0.550014i | −0.0145244 | − | 0.0251571i | ||||
\(479\) | −16.5678 | + | 28.6962i | −0.757000 | + | 1.31116i | 0.187374 | + | 0.982289i | \(0.440002\pi\) |
−0.944374 | + | 0.328874i | \(0.893331\pi\) | |||||||
\(480\) | −3.84324 | −0.175419 | ||||||||
\(481\) | 11.6351 | − | 3.55308i | 0.530515 | − | 0.162007i | ||||
\(482\) | −7.51638 | −0.342362 | ||||||||
\(483\) | 8.10275 | − | 14.0344i | 0.368688 | − | 0.638586i | ||||
\(484\) | −8.60275 | − | 14.9004i | −0.391034 | − | 0.677291i | ||||
\(485\) | −1.39059 | − | 2.40856i | −0.0631432 | − | 0.109367i | ||||
\(486\) | 2.99333 | + | 5.18461i | 0.135780 | + | 0.235179i | ||||
\(487\) | 19.6377 | 0.889871 | 0.444935 | − | 0.895563i | \(-0.353227\pi\) | ||||
0.444935 | + | 0.895563i | \(0.353227\pi\) | |||||||
\(488\) | −3.02569 | − | 5.24064i | −0.136966 | − | 0.237233i | ||||
\(489\) | 23.9327 | 1.08227 | ||||||||
\(490\) | −1.45529 | + | 2.52064i | −0.0657434 | + | 0.113871i | ||||
\(491\) | −5.31088 | −0.239677 | −0.119838 | − | 0.992793i | \(-0.538238\pi\) | ||||
−0.119838 | + | 0.992793i | \(0.538238\pi\) | |||||||
\(492\) | 0.635102 | 0.0286326 | ||||||||
\(493\) | 10.3366 | − | 17.9035i | 0.465536 | − | 0.806332i | ||||
\(494\) | −4.79186 | − | 8.29975i | −0.215596 | − | 0.373423i | ||||
\(495\) | 42.2142 | 1.89739 | ||||||||
\(496\) | 0.395932 | − | 0.685774i | 0.0177779 | − | 0.0307922i | ||||
\(497\) | 10.7582 | − | 18.6337i | 0.482571 | − | 0.835837i | ||||
\(498\) | −5.44731 | + | 9.43501i | −0.244100 | + | 0.422793i | ||||
\(499\) | −11.1878 | − | 19.3778i | −0.500835 | − | 0.867471i | −1.00000 | 0.000963882i | \(-0.999693\pi\) | |
0.499165 | − | 0.866507i | \(-0.333640\pi\) | |||||||
\(500\) | 5.29853 | + | 9.17732i | 0.236957 | + | 0.410422i | ||||
\(501\) | −18.3082 | + | 31.7108i | −0.817952 | + | 1.41673i | ||||
\(502\) | 4.44064 | − | 7.69141i | 0.198195 | − | 0.343285i | ||||
\(503\) | −11.8636 | + | 20.5483i | −0.528971 | + | 0.916204i | 0.470458 | + | 0.882422i | \(0.344089\pi\) |
−0.999429 | + | 0.0337822i | \(0.989245\pi\) | |||||||
\(504\) | 19.2569 | 0.857769 | ||||||||
\(505\) | −2.11740 | − | 3.66744i | −0.0942231 | − | 0.163199i | ||||
\(506\) | −4.62177 | + | 8.00514i | −0.205463 | + | 0.355872i | ||||
\(507\) | 27.4624 | 1.21965 | ||||||||
\(508\) | −14.9840 | −0.664809 | ||||||||
\(509\) | 3.62976 | − | 6.28692i | 0.160886 | − | 0.278663i | −0.774301 | − | 0.632818i | \(-0.781898\pi\) |
0.935187 | + | 0.354155i | \(0.115231\pi\) | |||||||
\(510\) | −19.6111 | −0.868393 | ||||||||
\(511\) | 5.05137 | + | 8.74924i | 0.223460 | + | 0.387043i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 24.2055 | + | 41.9252i | 1.06870 | + | 1.85104i | ||||
\(514\) | 6.05005 | + | 10.4790i | 0.266856 | + | 0.462209i | ||||
\(515\) | −10.8029 | − | 18.7112i | −0.476033 | − | 0.824513i | ||||
\(516\) | −6.65544 | + | 11.5276i | −0.292990 | + | 0.507473i | ||||
\(517\) | −17.0380 | −0.749332 | ||||||||
\(518\) | −4.18113 | + | 18.0837i | −0.183708 | + | 0.794553i | ||||
\(519\) | −13.6325 | −0.598399 | ||||||||
\(520\) | −1.25951 | + | 2.18154i | −0.0552332 | + | 0.0956667i | ||||
\(521\) | −1.03367 | − | 1.79037i | −0.0452860 | − | 0.0784377i | 0.842494 | − | 0.538706i | \(-0.181087\pi\) |
−0.887780 | + | 0.460268i | \(0.847753\pi\) | |||||||
\(522\) | 12.7839 | + | 22.1423i | 0.559535 | + | 0.969143i | ||||
\(523\) | 18.6125 | + | 32.2377i | 0.813866 | + | 1.40966i | 0.910139 | + | 0.414303i | \(0.135975\pi\) |
−0.0962729 | + | 0.995355i | \(0.530692\pi\) | |||||||
\(524\) | 12.0894 | 0.528129 | ||||||||
\(525\) | −15.8920 | − | 27.5257i | −0.693583 | − | 1.20132i | ||||
\(526\) | −19.1408 | −0.834578 | ||||||||
\(527\) | 2.02034 | − | 3.49933i | 0.0880074 | − | 0.152433i | ||||
\(528\) | −16.2055 | −0.705254 | ||||||||
\(529\) | −19.9707 | −0.868291 | ||||||||
\(530\) | −7.12309 | + | 12.3376i | −0.309407 | + | 0.535909i | ||||
\(531\) | 40.1515 | + | 69.5444i | 1.74243 | + | 3.01797i | ||||
\(532\) | 14.6218 | 0.633934 | ||||||||
\(533\) | 0.208136 | − | 0.360503i | 0.00901538 | − | 0.0156151i | ||||
\(534\) | 4.99333 | − | 8.64871i | 0.216083 | − | 0.374266i | ||||
\(535\) | −0.228135 | + | 0.395141i | −0.00986312 | + | 0.0170834i | ||||
\(536\) | 4.65544 | + | 8.06346i | 0.201084 | + | 0.348289i | ||||
\(537\) | −21.5164 | − | 37.2675i | −0.928500 | − | 1.60821i | ||||
\(538\) | 7.89461 | − | 13.6739i | 0.340361 | − | 0.589522i | ||||
\(539\) | −6.13642 | + | 10.6286i | −0.264314 | + | 0.457806i | ||||
\(540\) | 6.36226 | − | 11.0198i | 0.273788 | − | 0.474215i | ||||
\(541\) | −1.74313 | −0.0749430 | −0.0374715 | − | 0.999298i | \(-0.511930\pi\) | ||||
−0.0374715 | + | 0.999298i | \(0.511930\pi\) | |||||||
\(542\) | 9.55005 | + | 16.5412i | 0.410210 | + | 0.710505i | ||||
\(543\) | 20.5434 | − | 35.5822i | 0.881601 | − | 1.52698i | ||||
\(544\) | 5.10275 | 0.218779 | ||||||||
\(545\) | 0.589006 | 0.0252302 | ||||||||
\(546\) | 9.31088 | − | 16.1269i | 0.398469 | − | 0.690169i | ||||
\(547\) | 31.6191 | 1.35194 | 0.675968 | − | 0.736931i | \(-0.263726\pi\) | ||||
0.675968 | + | 0.736931i | \(0.263726\pi\) | |||||||
\(548\) | 8.34324 | + | 14.4509i | 0.356405 | + | 0.617312i | ||||
\(549\) | 38.1895 | 1.62989 | ||||||||
\(550\) | 9.06471 | + | 15.7005i | 0.386520 | + | 0.669473i | ||||
\(551\) | 9.70682 | + | 16.8127i | 0.413524 | + | 0.716245i | ||||
\(552\) | 2.65544 | + | 4.59936i | 0.113023 | + | 0.195762i | ||||
\(553\) | 17.4136 | − | 30.1613i | 0.740503 | − | 1.28259i | ||||
\(554\) | 16.4003 | 0.696782 | ||||||||
\(555\) | 17.0921 | + | 15.9490i | 0.725517 | + | 0.676996i | ||||
\(556\) | −18.1922 | −0.771520 | ||||||||
\(557\) | 11.3702 | − | 19.6938i | 0.481773 | − | 0.834455i | −0.518008 | − | 0.855376i | \(-0.673326\pi\) |
0.999781 | + | 0.0209207i | \(0.00665974\pi\) | |||||||
\(558\) | 2.49868 | + | 4.32784i | 0.105778 | + | 0.183212i | ||||
\(559\) | 4.36226 | + | 7.55565i | 0.184504 | + | 0.319570i | ||||
\(560\) | −1.92162 | − | 3.32834i | −0.0812032 | − | 0.140648i | ||||
\(561\) | −82.6926 | −3.49128 | ||||||||
\(562\) | 2.39725 | + | 4.15216i | 0.101122 | + | 0.175148i | ||||
\(563\) | −13.4676 | −0.567594 | −0.283797 | − | 0.958884i | \(-0.591594\pi\) | ||||
−0.283797 | + | 0.958884i | \(0.591594\pi\) | |||||||
\(564\) | −4.89461 | + | 8.47772i | −0.206100 | + | 0.356976i | ||||
\(565\) | −0.867948 | −0.0365148 | ||||||||
\(566\) | 25.9460 | 1.09059 | ||||||||
\(567\) | −18.1475 | + | 31.4323i | −0.762122 | + | 1.32003i | ||||
\(568\) | 3.52569 | + | 6.10667i | 0.147935 | + | 0.256230i | ||||
\(569\) | −41.8627 | −1.75497 | −0.877487 | − | 0.479600i | \(-0.840782\pi\) | ||||
−0.877487 | + | 0.479600i | \(0.840782\pi\) | |||||||
\(570\) | 9.20814 | − | 15.9490i | 0.385686 | − | 0.668028i | ||||
\(571\) | −14.2502 | + | 24.6821i | −0.596353 | + | 1.03291i | 0.397002 | + | 0.917818i | \(0.370051\pi\) |
−0.993354 | + | 0.115095i | \(0.963283\pi\) | |||||||
\(572\) | −5.31088 | + | 9.19872i | −0.222059 | + | 0.384618i | ||||
\(573\) | 14.3826 | + | 24.9114i | 0.600842 | + | 1.04069i | ||||
\(574\) | 0.317551 | + | 0.550014i | 0.0132543 | + | 0.0229571i | ||||
\(575\) | 2.97070 | − | 5.14540i | 0.123887 | − | 0.214578i | ||||
\(576\) | −3.15544 | + | 5.46539i | −0.131477 | + | 0.227724i | ||||
\(577\) | −12.1675 | + | 21.0747i | −0.506538 | + | 0.877349i | 0.493434 | + | 0.869783i | \(0.335742\pi\) |
−0.999971 | + | 0.00756570i | \(0.997592\pi\) | |||||||
\(578\) | 9.03804 | 0.375933 | ||||||||
\(579\) | 3.78520 | + | 6.55615i | 0.157307 | + | 0.272464i | ||||
\(580\) | 2.55137 | − | 4.41911i | 0.105940 | − | 0.183494i | ||||
\(581\) | −10.8946 | −0.451985 | ||||||||
\(582\) | −6.73785 | −0.279293 | ||||||||
\(583\) | −30.0354 | + | 52.0228i | −1.24394 | + | 2.15457i | ||||
\(584\) | −3.31088 | −0.137005 | ||||||||
\(585\) | −7.94863 | − | 13.7674i | −0.328635 | − | 0.569213i | ||||
\(586\) | 22.0514 | 0.910934 | ||||||||
\(587\) | −22.5230 | − | 39.0111i | −0.929626 | − | 1.61016i | −0.783948 | − | 0.620827i | \(-0.786797\pi\) |
−0.145678 | − | 0.989332i | \(-0.546536\pi\) | |||||||
\(588\) | 3.52569 | + | 6.10667i | 0.145397 | + | 0.251835i | ||||
\(589\) | 1.89725 | + | 3.28614i | 0.0781749 | + | 0.135403i | ||||
\(590\) | 8.01333 | − | 13.8795i | 0.329904 | − | 0.571410i | ||||
\(591\) | 5.94599 | 0.244585 | ||||||||
\(592\) | −4.44731 | − | 4.14988i | −0.182783 | − | 0.170559i | ||||
\(593\) | 6.93265 | 0.284690 | 0.142345 | − | 0.989817i | \(-0.454536\pi\) | ||||
0.142345 | + | 0.989817i | \(0.454536\pi\) | |||||||
\(594\) | 26.8273 | − | 46.4662i | 1.10074 | − | 1.90653i | ||||
\(595\) | −9.80554 | − | 16.9837i | −0.401988 | − | 0.696263i | ||||
\(596\) | −6.76618 | − | 11.7194i | −0.277153 | − | 0.480044i | ||||
\(597\) | −3.03103 | − | 5.24990i | −0.124052 | − | 0.214864i | ||||
\(598\) | 3.48098 | 0.142348 | ||||||||
\(599\) | 16.7582 | + | 29.0260i | 0.684721 | + | 1.18597i | 0.973524 | + | 0.228583i | \(0.0734093\pi\) |
−0.288803 | + | 0.957388i | \(0.593257\pi\) | |||||||
\(600\) | 10.4163 | 0.425243 | ||||||||
\(601\) | −4.08637 | + | 7.07779i | −0.166686 | + | 0.288709i | −0.937253 | − | 0.348650i | \(-0.886640\pi\) |
0.770566 | + | 0.637360i | \(0.219973\pi\) | |||||||
\(602\) | −13.3109 | −0.542511 | ||||||||
\(603\) | −58.7599 | −2.39289 | ||||||||
\(604\) | −0.610734 | + | 1.05782i | −0.0248504 | + | 0.0430422i | ||||
\(605\) | −10.8353 | − | 18.7672i | −0.440516 | − | 0.762995i | ||||
\(606\) | −10.2595 | −0.416764 | ||||||||
\(607\) | 21.2772 | − | 36.8532i | 0.863615 | − | 1.49583i | −0.00480007 | − | 0.999988i | \(-0.501528\pi\) |
0.868415 | − | 0.495837i | \(-0.165139\pi\) | |||||||
\(608\) | −2.39593 | + | 4.14988i | −0.0971679 | + | 0.168300i | ||||
\(609\) | −18.8609 | + | 32.6681i | −0.764284 | + | 1.32378i | ||||
\(610\) | −3.81088 | − | 6.60065i | −0.154298 | − | 0.267252i | ||||
\(611\) | 3.20814 | + | 5.55666i | 0.129787 | + | 0.224798i | ||||
\(612\) | −16.1014 | + | 27.8885i | −0.650862 | + | 1.12733i | ||||
\(613\) | −20.1461 | + | 34.8941i | −0.813695 | + | 1.40936i | 0.0965665 | + | 0.995327i | \(0.469214\pi\) |
−0.910261 | + | 0.414034i | \(0.864119\pi\) | |||||||
\(614\) | 2.87024 | − | 4.97141i | 0.115834 | − | 0.200630i | ||||
\(615\) | 0.799917 | 0.0322558 | ||||||||
\(616\) | −8.10275 | − | 14.0344i | −0.326469 | − | 0.565461i | ||||
\(617\) | 10.5501 | − | 18.2732i | 0.424729 | − | 0.735653i | −0.571666 | − | 0.820487i | \(-0.693703\pi\) |
0.996395 | + | 0.0848339i | \(0.0270360\pi\) | |||||||
\(618\) | −52.3436 | −2.10557 | ||||||||
\(619\) | 47.9140 | 1.92583 | 0.962914 | − | 0.269808i | \(-0.0869604\pi\) | ||||
0.962914 | + | 0.269808i | \(0.0869604\pi\) | |||||||
\(620\) | 0.498680 | − | 0.863740i | 0.0200275 | − | 0.0346886i | ||||
\(621\) | −17.5837 | −0.705611 | ||||||||
\(622\) | 5.26618 | + | 9.12129i | 0.211154 | + | 0.365730i | ||||
\(623\) | 9.98667 | 0.400107 | ||||||||
\(624\) | 3.05137 | + | 5.28514i | 0.122153 | + | 0.211575i | ||||
\(625\) | −1.86053 | − | 3.22253i | −0.0744212 | − | 0.128901i | ||||
\(626\) | −12.4150 | − | 21.5033i | −0.496201 | − | 0.859446i | ||||
\(627\) | 38.8273 | − | 67.2508i | 1.55061 | − | 2.68574i | ||||
\(628\) | 18.7759 | 0.749240 | ||||||||
\(629\) | −22.6935 | − | 21.1758i | −0.904848 | − | 0.844333i | ||||
\(630\) | 24.2542 | 0.966312 | ||||||||
\(631\) | 15.5053 | − | 26.8560i | 0.617258 | − | 1.06912i | −0.372726 | − | 0.927942i | \(-0.621577\pi\) |
0.989984 | − | 0.141181i | \(-0.0450899\pi\) | |||||||
\(632\) | 5.70682 | + | 9.88450i | 0.227005 | + | 0.393184i | ||||
\(633\) | −26.0691 | − | 45.1530i | −1.03615 | − | 1.79467i | ||||
\(634\) | 13.1461 | + | 22.7698i | 0.522100 | + | 0.904303i | ||||
\(635\) | −18.8725 | −0.748934 | ||||||||
\(636\) | 17.2569 | + | 29.8898i | 0.684279 | + | 1.18521i | ||||
\(637\) | 4.62177 | 0.183121 | ||||||||
\(638\) | 10.7582 | − | 18.6337i | 0.425921 | − | 0.737717i | ||||
\(639\) | −44.5004 | −1.76041 | ||||||||
\(640\) | 1.25951 | 0.0497865 | ||||||||
\(641\) | 16.3096 | − | 28.2490i | 0.644189 | − | 1.11577i | −0.340299 | − | 0.940317i | \(-0.610528\pi\) |
0.984488 | − | 0.175451i | \(-0.0561384\pi\) | |||||||
\(642\) | 0.552694 | + | 0.957294i | 0.0218131 | + | 0.0377814i | ||||
\(643\) | 18.1701 | 0.716559 | 0.358279 | − | 0.933614i | \(-0.383364\pi\) | ||||
0.358279 | + | 0.933614i | \(0.383364\pi\) | |||||||
\(644\) | −2.65544 | + | 4.59936i | −0.104639 | + | 0.181240i | ||||
\(645\) | −8.38260 | + | 14.5191i | −0.330065 | + | 0.571689i | ||||
\(646\) | −12.2258 | + | 21.1758i | −0.481019 | + | 0.833150i | ||||
\(647\) | 13.0067 | + | 22.5282i | 0.511345 | + | 0.885675i | 0.999914 | + | 0.0131498i | \(0.00418582\pi\) |
−0.488569 | + | 0.872525i | \(0.662481\pi\) | |||||||
\(648\) | −5.94731 | − | 10.3010i | −0.233632 | − | 0.404663i | ||||
\(649\) | 33.7892 | − | 58.5247i | 1.32634 | − | 2.29729i | ||||
\(650\) | 3.41363 | − | 5.91259i | 0.133894 | − | 0.231911i | ||||
\(651\) | −3.68648 | + | 6.38516i | −0.144484 | + | 0.250254i | ||||
\(652\) | −7.84324 | −0.307165 | ||||||||
\(653\) | 3.62976 | + | 6.28692i | 0.142043 | + | 0.246026i | 0.928266 | − | 0.371917i | \(-0.121299\pi\) |
−0.786223 | + | 0.617943i | \(0.787966\pi\) | |||||||
\(654\) | 0.713483 | − | 1.23579i | 0.0278994 | − | 0.0483231i | ||||
\(655\) | 15.2267 | 0.594958 | ||||||||
\(656\) | −0.208136 | −0.00812636 | ||||||||
\(657\) | 10.4473 | − | 18.0953i | 0.407588 | − | 0.705964i | ||||
\(658\) | −9.78922 | −0.381624 | ||||||||
\(659\) | −3.06471 | − | 5.30823i | −0.119384 | − | 0.206779i | 0.800140 | − | 0.599814i | \(-0.204759\pi\) |
−0.919524 | + | 0.393034i | \(0.871425\pi\) | |||||||
\(660\) | −20.4110 | −0.794497 | ||||||||
\(661\) | 16.9406 | + | 29.3420i | 0.658915 | + | 1.14127i | 0.980897 | + | 0.194528i | \(0.0623175\pi\) |
−0.321982 | + | 0.946746i | \(0.604349\pi\) | |||||||
\(662\) | −14.8946 | − | 25.7982i | −0.578896 | − | 1.00268i | ||||
\(663\) | 15.5704 | + | 26.9687i | 0.604704 | + | 1.04738i | ||||
\(664\) | 1.78520 | − | 3.09205i | 0.0692791 | − | 0.119995i | ||||
\(665\) | 18.4163 | 0.714152 | ||||||||
\(666\) | 36.7139 | − | 11.2116i | 1.42263 | − | 0.434439i | ||||
\(667\) | −7.05137 | −0.273030 | ||||||||
\(668\) | 6.00000 | − | 10.3923i | 0.232147 | − | 0.402090i | ||||
\(669\) | 2.96897 | + | 5.14240i | 0.114787 | + | 0.198817i | ||||
\(670\) | 5.86358 | + | 10.1560i | 0.226530 | + | 0.392361i | ||||
\(671\) | −16.0691 | − | 27.8325i | −0.620340 | − | 1.07446i | ||||
\(672\) | −9.31088 | −0.359175 | ||||||||
\(673\) | 12.8229 | + | 22.2099i | 0.494286 | + | 0.856129i | 0.999978 | − | 0.00658502i | \(-0.00209609\pi\) |
−0.505692 | + | 0.862714i | \(0.668763\pi\) | |||||||
\(674\) | −12.7272 | −0.490232 | ||||||||
\(675\) | −17.2435 | + | 29.8667i | −0.663704 | + | 1.14957i | ||||
\(676\) | −9.00000 | −0.346154 | ||||||||
\(677\) | 10.7759 | 0.414151 | 0.207076 | − | 0.978325i | \(-0.433605\pi\) | ||||
0.207076 | + | 0.978325i | \(0.433605\pi\) | |||||||
\(678\) | −1.05137 | + | 1.82103i | −0.0403778 | + | 0.0699364i | ||||
\(679\) | −3.36893 | − | 5.83515i | −0.129287 | − | 0.223932i | ||||
\(680\) | 6.42697 | 0.246463 | ||||||||
\(681\) | 6.99736 | − | 12.1198i | 0.268139 | − | 0.464431i | ||||
\(682\) | 2.10275 | − | 3.64207i | 0.0805184 | − | 0.139462i | ||||
\(683\) | 15.2458 | − | 26.4066i | 0.583366 | − | 1.01042i | −0.411711 | − | 0.911314i | \(-0.635069\pi\) |
0.995077 | − | 0.0991047i | \(-0.0315979\pi\) | |||||||
\(684\) | −15.1204 | − | 26.1894i | −0.578145 | − | 1.00138i | ||||
\(685\) | 10.5084 | + | 18.2011i | 0.401505 | + | 0.695427i | ||||
\(686\) | 7.15412 | − | 12.3913i | 0.273146 | − | 0.473102i | ||||
\(687\) | −2.49465 | + | 4.32087i | −0.0951770 | + | 0.164851i | ||||
\(688\) | 2.18113 | − | 3.77783i | 0.0831548 | − | 0.144028i | ||||
\(689\) | 22.6218 | 0.861821 | ||||||||
\(690\) | 3.34456 | + | 5.79294i | 0.127325 | + | 0.220534i | ||||
\(691\) | −4.49868 | + | 7.79194i | −0.171138 | + | 0.296419i | −0.938818 | − | 0.344414i | \(-0.888078\pi\) |
0.767680 | + | 0.640833i | \(0.221411\pi\) | |||||||
\(692\) | 4.46765 | 0.169834 | ||||||||
\(693\) | 102.271 | 3.88495 | ||||||||
\(694\) | −14.7826 | + | 25.6041i | −0.561138 | + | 0.971920i | ||||
\(695\) | −22.9132 | −0.869148 | ||||||||
\(696\) | −6.18113 | − | 10.7060i | −0.234295 | − | 0.405811i | ||||
\(697\) | −1.06207 | −0.0402287 | ||||||||
\(698\) | 16.2515 | + | 28.1485i | 0.615129 | + | 1.06544i | ||||
\(699\) | 12.2635 | + | 21.2411i | 0.463850 | + | 0.803411i | ||||
\(700\) | 5.20814 | + | 9.02076i | 0.196849 | + | 0.340953i | ||||
\(701\) | −17.3756 | + | 30.0954i | −0.656267 | + | 1.13669i | 0.325308 | + | 0.945608i | \(0.394532\pi\) |
−0.981575 | + | 0.191080i | \(0.938801\pi\) | |||||||
\(702\) | −20.2055 | −0.762607 | ||||||||
\(703\) | 27.8769 | − | 8.51295i | 1.05140 | − | 0.321072i | ||||
\(704\) | 5.31088 | 0.200162 | ||||||||
\(705\) | −6.16482 | + | 10.6778i | −0.232180 | + | 0.402148i | ||||
\(706\) | −2.05269 | − | 3.55537i | −0.0772542 | − | 0.133808i | ||||
\(707\) | −5.12976 | − | 8.88500i | −0.192924 | − | 0.334155i | ||||
\(708\) | −19.4136 | − | 33.6254i | −0.729609 | − | 1.26372i | ||||
\(709\) | 39.9947 | 1.50203 | 0.751017 | − | 0.660283i | \(-0.229564\pi\) | ||||
0.751017 | + | 0.660283i | \(0.229564\pi\) | |||||||
\(710\) | 4.44064 | + | 7.69141i | 0.166654 | + | 0.288654i | ||||
\(711\) | −72.0301 | −2.70134 | ||||||||
\(712\) | −1.63642 | + | 2.83436i | −0.0613275 | + | 0.106222i | ||||
\(713\) | −1.37823 | −0.0516151 | ||||||||
\(714\) | −47.5111 | −1.77806 | ||||||||
\(715\) | −6.68912 | + | 11.5859i | −0.250159 | + | 0.433288i | ||||
\(716\) | 7.05137 | + | 12.2133i | 0.263522 | + | 0.456434i | ||||
\(717\) | −1.93793 | −0.0723734 | ||||||||
\(718\) | 14.1027 | − | 24.4267i | 0.526310 | − | 0.911595i | ||||
\(719\) | −1.50535 | + | 2.60734i | −0.0561399 | + | 0.0972372i | −0.892730 | − | 0.450593i | \(-0.851213\pi\) |
0.836590 | + | 0.547830i | \(0.184546\pi\) | |||||||
\(720\) | −3.97431 | + | 6.88371i | −0.148114 | + | 0.256541i | ||||
\(721\) | −26.1718 | − | 45.3309i | −0.974690 | − | 1.68821i | ||||
\(722\) | −1.98098 | − | 3.43116i | −0.0737244 | − | 0.127694i | ||||
\(723\) | −11.4676 | + | 19.8625i | −0.426486 | + | 0.738696i | ||||
\(724\) | −6.73250 | + | 11.6610i | −0.250212 | + | 0.433379i | ||||
\(725\) | −6.91495 | + | 11.9770i | −0.256815 | + | 0.444816i | ||||
\(726\) | −52.5004 | −1.94847 | ||||||||
\(727\) | −26.7112 | − | 46.2651i | −0.990663 | − | 1.71588i | −0.613399 | − | 0.789773i | \(-0.710198\pi\) |
−0.377264 | − | 0.926106i | \(-0.623135\pi\) | |||||||
\(728\) | −3.05137 | + | 5.28514i | −0.113091 | + | 0.195880i | ||||
\(729\) | −17.4163 | −0.645047 | ||||||||
\(730\) | −4.17009 | −0.154342 | ||||||||
\(731\) | 11.1298 | − | 19.2773i | 0.411649 | − | 0.712997i | ||||
\(732\) | −18.4650 | −0.682486 | ||||||||
\(733\) | −2.82991 | − | 4.90154i | −0.104525 | − | 0.181043i | 0.809019 | − | 0.587782i | \(-0.199999\pi\) |
−0.913544 | + | 0.406740i | \(0.866666\pi\) | |||||||
\(734\) | −4.00000 | −0.147643 | ||||||||
\(735\) | 4.44064 | + | 7.69141i | 0.163795 | + | 0.283702i | ||||
\(736\) | −0.870245 | − | 1.50731i | −0.0320776 | − | 0.0555601i | ||||
\(737\) | 24.7245 | + | 42.8241i | 0.910739 | + | 1.57745i | ||||
\(738\) | 0.656762 | − | 1.13755i | 0.0241757 | − | 0.0418736i | ||||
\(739\) | 2.21883 | 0.0816209 | 0.0408105 | − | 0.999167i | \(-0.487006\pi\) | ||||
0.0408105 | + | 0.999167i | \(0.487006\pi\) | |||||||
\(740\) | −5.60143 | − | 5.22681i | −0.205913 | − | 0.192141i | ||||
\(741\) | −29.2435 | −1.07429 | ||||||||
\(742\) | −17.2569 | + | 29.8898i | −0.633520 | + | 1.09729i | ||||
\(743\) | −3.43397 | − | 5.94782i | −0.125980 | − | 0.218204i | 0.796135 | − | 0.605119i | \(-0.206874\pi\) |
−0.922116 | + | 0.386914i | \(0.873541\pi\) | |||||||
\(744\) | −1.20814 | − | 2.09255i | −0.0442924 | − | 0.0767167i | ||||
\(745\) | −8.52207 | − | 14.7607i | −0.312225 | − | 0.540789i | ||||
\(746\) | 37.3570 | 1.36774 | ||||||||
\(747\) | 11.2662 | + | 19.5136i | 0.412208 | + | 0.713965i | ||||
\(748\) | 27.1001 | 0.990878 | ||||||||
\(749\) | −0.552694 | + | 0.957294i | −0.0201950 | + | 0.0349788i | ||||
\(750\) | 32.3356 | 1.18073 | ||||||||
\(751\) | −3.80256 | −0.138757 | −0.0693786 | − | 0.997590i | \(-0.522102\pi\) | ||||
−0.0693786 | + | 0.997590i | \(0.522102\pi\) | |||||||
\(752\) | 1.60407 | − | 2.77833i | 0.0584943 | − | 0.101315i | ||||
\(753\) | −13.5501 | − | 23.4694i | −0.493791 | − | 0.855272i | ||||
\(754\) | −8.10275 | −0.295085 | ||||||||
\(755\) | −0.769226 | + | 1.33234i | −0.0279950 | + | 0.0484888i | ||||
\(756\) | 15.4136 | − | 26.6972i | 0.560588 | − | 0.970968i | ||||
\(757\) | 1.59608 | − | 2.76450i | 0.0580106 | − | 0.100477i | −0.835562 | − | 0.549397i | \(-0.814858\pi\) |
0.893572 | + | 0.448919i | \(0.148191\pi\) | |||||||
\(758\) | 2.45397 | + | 4.25040i | 0.0891323 | + | 0.154382i | ||||
\(759\) | 14.1027 | + | 24.4267i | 0.511897 | + | 0.886632i | ||||
\(760\) | −3.01770 | + | 5.22681i | −0.109464 | + | 0.189596i | ||||
\(761\) | −19.0297 | + | 32.9604i | −0.689827 | + | 1.19481i | 0.282067 | + | 0.959395i | \(0.408980\pi\) |
−0.971894 | + | 0.235420i | \(0.924353\pi\) | |||||||
\(762\) | −22.8609 | + | 39.5963i | −0.828164 | + | 1.43442i | ||||
\(763\) | 1.42697 | 0.0516596 | ||||||||
\(764\) | −4.71348 | − | 8.16399i | −0.170528 | − | 0.295363i | ||||
\(765\) | −20.2799 | + | 35.1259i | −0.733222 | + | 1.26998i | ||||
\(766\) | 20.6084 | 0.744613 | ||||||||
\(767\) | −25.4490 | −0.918911 | ||||||||
\(768\) | 1.52569 | − | 2.64257i | 0.0550535 | − | 0.0953554i | ||||
\(769\) | −2.76520 | −0.0997156 | −0.0498578 | − | 0.998756i | \(-0.515877\pi\) | ||||
−0.0498578 | + | 0.998756i | \(0.515877\pi\) | |||||||
\(770\) | −10.2055 | − | 17.6764i | −0.367781 | − | 0.637015i | ||||
\(771\) | 36.9220 | 1.32971 | ||||||||
\(772\) | −1.24049 | − | 2.14859i | −0.0446462 | − | 0.0773295i | ||||
\(773\) | −14.4527 | − | 25.0327i | −0.519826 | − | 0.900365i | −0.999734 | − | 0.0230462i | \(-0.992664\pi\) |
0.479909 | − | 0.877318i | \(-0.340670\pi\) | |||||||
\(774\) | 13.7649 | + | 23.8414i | 0.494768 | + | 0.856963i | ||||
\(775\) | −1.35157 | + | 2.34098i | −0.0485497 | + | 0.0840905i | ||||
\(776\) | 2.20814 | 0.0792675 | ||||||||
\(777\) | 41.4084 | + | 38.6390i | 1.48552 | + | 1.38617i | ||||
\(778\) | −25.5678 | −0.916648 | ||||||||
\(779\) | 0.498680 | − | 0.863740i | 0.0178671 | − | 0.0309467i | ||||
\(780\) | 3.84324 | + | 6.65668i | 0.137610 | + | 0.238348i | ||||
\(781\) | 18.7245 | + | 32.4318i | 0.670016 | + | 1.16050i | ||||
\(782\) | −4.44064 | − | 7.69141i | −0.158797 | − | 0.275044i | ||||
\(783\) | 40.9300 | 1.46272 | ||||||||
\(784\) | −1.15544 | − | 2.00128i | −0.0412658 | − | 0.0714745i | ||||
\(785\) | 23.6484 | 0.844049 | ||||||||
\(786\) | 18.4447 | − | 31.9471i | 0.657899 | − | 1.13952i | ||||
\(787\) | 10.2816 | 0.366499 | 0.183249 | − | 0.983066i | \(-0.441338\pi\) | ||||
0.183249 | + | 0.983066i | \(0.441338\pi\) | |||||||
\(788\) | −1.94863 | −0.0694169 | ||||||||
\(789\) | −29.2029 | + | 50.5808i | −1.03965 | + | 1.80073i | ||||
\(790\) | 7.18780 | + | 12.4496i | 0.255730 | + | 0.442938i | ||||
\(791\) | −2.10275 | −0.0747651 | ||||||||
\(792\) | −16.7582 | + | 29.0260i | −0.595476 | + | 1.03140i | ||||
\(793\) | −6.05137 | + | 10.4813i | −0.214891 | + | 0.372201i | ||||
\(794\) | 15.1461 | − | 26.2339i | 0.537516 | − | 0.931006i | ||||
\(795\) | 21.7352 | + | 37.6465i | 0.770868 | + | 1.33518i | ||||
\(796\) | 0.993334 | + | 1.72050i | 0.0352078 | + | 0.0609817i | ||||
\(797\) | −26.3463 | + | 45.6331i | −0.933233 | + | 1.61641i | −0.155479 | + | 0.987839i | \(0.549692\pi\) |
−0.777754 | + | 0.628568i | \(0.783641\pi\) | |||||||
\(798\) | 22.3082 | − | 38.6390i | 0.789703 | − | 1.36781i | ||||
\(799\) | 8.18516 | − | 14.1771i | 0.289570 | − | 0.501550i | ||||
\(800\) | −3.41363 | −0.120690 | ||||||||
\(801\) | −10.3273 | − | 17.8874i | −0.364896 | − | 0.632018i | ||||
\(802\) | −13.7582 | + | 23.8299i | −0.485819 | + | 0.841463i | ||||
\(803\) | −17.5837 | −0.620516 | ||||||||
\(804\) | 28.4110 | 1.00198 | ||||||||
\(805\) | −3.34456 | + | 5.79294i | −0.117880 | + | 0.204174i | ||||
\(806\) | −1.58373 | −0.0557844 | ||||||||
\(807\) | −24.0894 | − | 41.7241i | −0.847988 | − | 1.46876i | ||||
\(808\) | 3.36226 | 0.118284 | ||||||||
\(809\) | −0.0717149 | − | 0.124214i | −0.00252136 | − | 0.00436713i | 0.864762 | − | 0.502182i | \(-0.167469\pi\) |
−0.867283 | + | 0.497815i | \(0.834136\pi\) | |||||||
\(810\) | −7.49069 | − | 12.9743i | −0.263196 | − | 0.455869i | ||||
\(811\) | 14.3082 | + | 24.7826i | 0.502430 | + | 0.870235i | 0.999996 | + | 0.00280872i | \(0.000894045\pi\) |
−0.497566 | + | 0.867426i | \(0.665773\pi\) | |||||||
\(812\) | 6.18113 | − | 10.7060i | 0.216915 | − | 0.375708i | ||||
\(813\) | 58.2816 | 2.04402 | ||||||||
\(814\) | −23.6191 | − | 22.0395i | −0.827850 | − | 0.772484i | ||||
\(815\) | −9.87864 | −0.346034 | ||||||||
\(816\) | 7.78520 | − | 13.4844i | 0.272536 | − | 0.472047i | ||||
\(817\) | 10.4517 | + | 18.1028i | 0.365658 | + | 0.633338i | ||||
\(818\) | −3.62309 | − | 6.27537i | −0.126678 | − | 0.219413i | ||||
\(819\) | −19.2569 | − | 33.3539i | −0.672890 | − | 1.16548i | ||||
\(820\) | −0.262150 | −0.00915467 | ||||||||
\(821\) | −13.8946 | − | 24.0662i | −0.484925 | − | 0.839915i | 0.514925 | − | 0.857235i | \(-0.327820\pi\) |
−0.999850 | + | 0.0173201i | \(0.994487\pi\) | |||||||
\(822\) | 50.9167 | 1.77592 | ||||||||
\(823\) | −16.2705 | + | 28.1814i | −0.567156 | + | 0.982342i | 0.429690 | + | 0.902976i | \(0.358623\pi\) |
−0.996846 | + | 0.0793658i | \(0.974710\pi\) | |||||||
\(824\) | 17.1541 | 0.597592 | ||||||||
\(825\) | 55.3196 | 1.92598 | ||||||||
\(826\) | 19.4136 | − | 33.6254i | 0.675487 | − | 1.16998i | ||||
\(827\) | −22.4783 | − | 38.9336i | −0.781648 | − | 1.35385i | −0.930981 | − | 0.365068i | \(-0.881046\pi\) |
0.149332 | − | 0.988787i | \(-0.452288\pi\) | |||||||
\(828\) | 10.9840 | 0.381721 | ||||||||
\(829\) | −22.2435 | + | 38.5269i | −0.772550 | + | 1.33810i | 0.163611 | + | 0.986525i | \(0.447686\pi\) |
−0.936161 | + | 0.351571i | \(0.885648\pi\) | |||||||
\(830\) | 2.24848 | − | 3.89447i | 0.0780457 | − | 0.135179i | ||||
\(831\) | 25.0217 | − | 43.3389i | 0.867994 | − | 1.50341i | ||||
\(832\) | −1.00000 | − | 1.73205i | −0.0346688 | − | 0.0600481i | ||||
\(833\) | −5.89593 | − | 10.2121i | −0.204282 | − | 0.353827i | ||||
\(834\) | −27.7556 | + | 48.0740i | −0.961096 | + | 1.66467i | ||||
\(835\) | 7.55706 | − | 13.0892i | 0.261523 | − | 0.452971i | ||||
\(836\) | −12.7245 | + | 22.0395i | −0.440087 | + | 0.762252i | ||||
\(837\) | 8.00000 | 0.276520 | ||||||||
\(838\) | 2.28388 | + | 3.95579i | 0.0788953 | + | 0.136651i | ||||
\(839\) | −13.0891 | + | 22.6709i | −0.451885 | + | 0.782688i | −0.998503 | − | 0.0546942i | \(-0.982582\pi\) |
0.546618 | + | 0.837382i | \(0.315915\pi\) | |||||||
\(840\) | −11.7272 | −0.404625 | ||||||||
\(841\) | −12.5864 | −0.434013 | ||||||||
\(842\) | −13.4216 | + | 23.2469i | −0.462540 | + | 0.801142i | ||||
\(843\) | 14.6298 | 0.503878 | ||||||||
\(844\) | 8.54339 | + | 14.7976i | 0.294076 | + | 0.509354i | ||||
\(845\) | −11.3356 | −0.389956 | ||||||||
\(846\) | 10.1231 | + | 17.5337i | 0.348039 | + | 0.602821i | ||||
\(847\) | −26.2502 | − | 45.4667i | −0.901968 | − | 1.56225i | ||||
\(848\) | −5.65544 | − | 9.79551i | −0.194209 | − | 0.336379i | ||||
\(849\) | 39.5855 | − | 68.5640i | 1.35857 | − | 2.35311i | ||||
\(850\) | −17.4189 | −0.597464 | ||||||||
\(851\) | −2.38490 | + | 10.3149i | −0.0817532 | + | 0.353589i | ||||
\(852\) | 21.5164 | 0.737139 | ||||||||
\(853\) | 7.54207 | − | 13.0632i | 0.258236 | − | 0.447277i | −0.707534 | − | 0.706680i | \(-0.750192\pi\) |
0.965769 | + | 0.259402i | \(0.0835256\pi\) | |||||||
\(854\) | −9.23250 | − | 15.9912i | −0.315930 | − | 0.547206i | ||||
\(855\) | −19.0444 | − | 32.9858i | −0.651304 | − | 1.12809i | ||||
\(856\) | −0.181130 | − | 0.313726i | −0.00619088 | − | 0.0107229i | ||||
\(857\) | 1.17009 | 0.0399697 | 0.0199848 | − | 0.999800i | \(-0.493638\pi\) | ||||
0.0199848 | + | 0.999800i | \(0.493638\pi\) | |||||||
\(858\) | 16.2055 | + | 28.0687i | 0.553247 | + | 0.958251i | ||||
\(859\) | −36.0487 | −1.22997 | −0.614983 | − | 0.788540i | \(-0.710837\pi\) | ||||
−0.614983 | + | 0.788540i | \(0.710837\pi\) | |||||||
\(860\) | 2.74716 | − | 4.75821i | 0.0936772 | − | 0.162254i | ||||
\(861\) | 1.93793 | 0.0660446 | ||||||||
\(862\) | −20.7919 | −0.708174 | ||||||||
\(863\) | 5.22147 | − | 9.04385i | 0.177741 | − | 0.307856i | −0.763366 | − | 0.645967i | \(-0.776454\pi\) |
0.941106 | + | 0.338111i | \(0.109788\pi\) | |||||||
\(864\) | 5.05137 | + | 8.74924i | 0.171851 | + | 0.297655i | ||||
\(865\) | 5.62705 | 0.191325 | ||||||||
\(866\) | −13.8286 | + | 23.9518i | −0.469914 | + | 0.813916i | ||||
\(867\) | 13.7892 | − | 23.8836i | 0.468307 | − | 0.811131i | ||||
\(868\) | 1.20814 | − | 2.09255i | 0.0410068 | − | 0.0710259i | ||||
\(869\) | 30.3082 | + | 52.4954i | 1.02814 | + | 1.78079i | ||||
\(870\) | −7.78520 | − | 13.4844i | −0.263943 | − | 0.457163i | ||||
\(871\) | 9.31088 | − | 16.1269i | 0.315487 | − | 0.546440i | ||||
\(872\) | −0.233823 | + | 0.404994i | −0.00791826 | + | 0.0137148i | ||||
\(873\) | −6.96765 | + | 12.0683i | −0.235819 | + | 0.408451i | ||||
\(874\) | 8.34019 | 0.282111 | ||||||||
\(875\) | 16.1678 | + | 28.0034i | 0.546571 | + | 0.946689i | ||||
\(876\) | −5.05137 | + | 8.74924i | −0.170670 | + | 0.295609i | ||||
\(877\) | −40.9140 | −1.38157 | −0.690785 | − | 0.723061i | \(-0.742735\pi\) | ||||
−0.690785 | + | 0.723061i | \(0.742735\pi\) | |||||||
\(878\) | −6.93529 | −0.234055 | ||||||||
\(879\) | 33.6435 | − | 58.2722i | 1.13477 | − | 1.96547i | ||||
\(880\) | 6.68912 | 0.225490 | ||||||||
\(881\) | −9.60275 | − | 16.6324i | −0.323525 | − | 0.560361i | 0.657688 | − | 0.753291i | \(-0.271535\pi\) |
−0.981213 | + | 0.192929i | \(0.938201\pi\) | |||||||
\(882\) | 14.5837 | 0.491060 | ||||||||
\(883\) | −9.77187 | − | 16.9254i | −0.328849 | − | 0.569584i | 0.653434 | − | 0.756983i | \(-0.273328\pi\) |
−0.982284 | + | 0.187399i | \(0.939994\pi\) | |||||||
\(884\) | −5.10275 | − | 8.83822i | −0.171624 | − | 0.297261i | ||||
\(885\) | −24.4517 | − | 42.3515i | −0.821934 | − | 1.42363i | ||||
\(886\) | 9.93265 | − | 17.2039i | 0.333694 | − | 0.577975i | ||||
\(887\) | −29.1134 | −0.977534 | −0.488767 | − | 0.872414i | \(-0.662553\pi\) | ||||
−0.488767 | + | 0.872414i | \(0.662553\pi\) | |||||||
\(888\) | −17.7515 | + | 5.42090i | −0.595702 | + | 0.181913i | ||||
\(889\) | −45.7219 | −1.53346 | ||||||||
\(890\) | −2.06109 | + | 3.56991i | −0.0690879 | + | 0.119664i | ||||
\(891\) | −31.5855 | − | 54.7076i | −1.05815 | − | 1.83277i | ||||
\(892\) | −0.972993 | − | 1.68527i | −0.0325782 | − | 0.0564271i | ||||
\(893\) | 7.68648 | + | 13.3134i | 0.257218 | + | 0.445515i | ||||
\(894\) | −41.2923 | −1.38102 | ||||||||
\(895\) | 8.88128 | + | 15.3828i | 0.296868 | + | 0.514191i | ||||
\(896\) | 3.05137 | 0.101939 | ||||||||
\(897\) | 5.31088 | − | 9.19872i | 0.177325 | − | 0.307136i | ||||
\(898\) | −26.1382 | −0.872241 | ||||||||
\(899\) | 3.20814 | 0.106997 | ||||||||
\(900\) | 10.7715 | − | 18.6568i | 0.359051 | − | 0.621894i | ||||
\(901\) | −28.8583 | − | 49.9840i | −0.961409 | − | 1.66521i | ||||
\(902\) | −1.10539 | −0.0368054 | ||||||||
\(903\) | −20.3082 | + | 35.1749i | −0.675816 | + | 1.17055i | ||||
\(904\) | 0.344558 | − | 0.596791i | 0.0114598 | − | 0.0198490i | ||||
\(905\) | −8.47966 | + | 14.6872i | −0.281873 | + | 0.488219i | ||||
\(906\) | 1.86358 | + | 3.22781i | 0.0619133 | + | 0.107237i | ||||
\(907\) | 7.17446 | + | 12.4265i | 0.238224 | + | 0.412616i | 0.960205 | − | 0.279297i | \(-0.0901014\pi\) |
−0.721981 | + | 0.691913i | \(0.756768\pi\) | |||||||
\(908\) | −2.29318 | + | 3.97191i | −0.0761020 | + | 0.131812i | ||||
\(909\) | −10.6094 | + | 18.3760i | −0.351892 | + | 0.609495i | ||||
\(910\) | −3.84324 | + | 6.65668i | −0.127402 | + | 0.220667i | ||||
\(911\) | 22.3303 | 0.739836 | 0.369918 | − | 0.929064i | \(-0.379386\pi\) | ||||
0.369918 | + | 0.929064i | \(0.379386\pi\) | |||||||
\(912\) | 7.31088 | + | 12.6628i | 0.242088 | + | 0.419308i | ||||
\(913\) | 9.48098 | − | 16.4215i | 0.313775 | − | 0.543474i | ||||
\(914\) | −20.6865 | −0.684248 | ||||||||
\(915\) | −23.2569 | −0.768848 | ||||||||
\(916\) | 0.817551 | − | 1.41604i | 0.0270126 | − | 0.0467873i | ||||
\(917\) | 36.8893 | 1.21819 | ||||||||
\(918\) | 25.7759 | + | 44.6452i | 0.850731 | + | 1.47351i | ||||
\(919\) | 38.0168 | 1.25406 | 0.627029 | − | 0.778996i | \(-0.284271\pi\) | ||||
0.627029 | + | 0.778996i | \(0.284271\pi\) | |||||||
\(920\) | −1.09608 | − | 1.89847i | −0.0361368 | − | 0.0625907i | ||||
\(921\) | −8.75819 | − | 15.1696i | −0.288592 | − | 0.499856i | ||||
\(922\) | −11.1027 | − | 19.2305i | −0.365650 | − | 0.633324i | ||||
\(923\) | 7.05137 | − | 12.2133i | 0.232099 | − | 0.402007i | ||||
\(924\) | −49.4490 | −1.62675 | ||||||||
\(925\) | 15.1815 | + | 14.1662i | 0.499164 | + | 0.465780i | ||||
\(926\) | 22.1922 | 0.729280 | ||||||||
\(927\) | −54.1288 | + | 93.7539i | −1.77782 | + | 3.07928i | ||||
\(928\) | 2.02569 | + | 3.50859i | 0.0664964 | + | 0.115175i | ||||
\(929\) | −0.728477 | − | 1.26176i | −0.0239006 | − | 0.0413970i | 0.853828 | − | 0.520556i | \(-0.174275\pi\) |
−0.877728 | + | 0.479159i | \(0.840942\pi\) | |||||||
\(930\) | −1.52166 | − | 2.63559i | −0.0498972 | − | 0.0864245i | ||||
\(931\) | 11.0734 | 0.362917 | ||||||||
\(932\) | −4.01902 | − | 6.96115i | −0.131647 | − | 0.228020i | ||||
\(933\) | 32.1382 | 1.05216 | ||||||||
\(934\) | 5.94599 | − | 10.2988i | 0.194559 | − | 0.336985i | ||||
\(935\) | 34.1329 | 1.11626 | ||||||||
\(936\) | 12.6218 | 0.412555 | ||||||||
\(937\) | −22.6745 | + | 39.2733i | −0.740742 | + | 1.28300i | 0.211415 | + | 0.977396i | \(0.432193\pi\) |
−0.952158 | + | 0.305607i | \(0.901141\pi\) | |||||||
\(938\) | 14.2055 | + | 24.6046i | 0.463826 | + | 0.803370i | ||||
\(939\) | −75.7653 | −2.47251 | ||||||||
\(940\) | 2.02034 | − | 3.49933i | 0.0658962 | − | 0.114136i | ||||
\(941\) | 15.1125 | − | 26.1756i | 0.492652 | − | 0.853299i | −0.507312 | − | 0.861762i | \(-0.669361\pi\) |
0.999964 | + | 0.00846377i | \(0.00269413\pi\) | |||||||
\(942\) | 28.6461 | − | 49.6166i | 0.933342 | − | 1.61660i | ||||
\(943\) | 0.181130 | + | 0.313726i | 0.00589839 | + | 0.0102163i | ||||
\(944\) | 6.36226 | + | 11.0198i | 0.207074 | + | 0.358663i | ||||
\(945\) | 19.4136 | − | 33.6254i | 0.631526 | − | 1.09383i | ||||
\(946\) | 11.5837 | − | 20.0636i | 0.376619 | − | 0.652324i | ||||
\(947\) | 7.74049 | − | 13.4069i | 0.251532 | − | 0.435666i | −0.712416 | − | 0.701758i | \(-0.752399\pi\) |
0.963948 | + | 0.266091i | \(0.0857323\pi\) | |||||||
\(948\) | 34.8273 | 1.13114 | ||||||||
\(949\) | 3.31088 | + | 5.73462i | 0.107476 | + | 0.186154i | ||||
\(950\) | 8.17883 | − | 14.1662i | 0.265356 | − | 0.459611i | ||||
\(951\) | 80.2276 | 2.60156 | ||||||||
\(952\) | 15.5704 | 0.504639 | ||||||||
\(953\) | 2.86358 | − | 4.95986i | 0.0927604 | − | 0.160666i | −0.815911 | − | 0.578177i | \(-0.803764\pi\) |
0.908672 | + | 0.417511i | \(0.137098\pi\) | |||||||
\(954\) | 71.3817 | 2.31107 | ||||||||
\(955\) | −5.93668 | − | 10.2826i | −0.192106 | − | 0.332738i | ||||
\(956\) | 0.635102 | 0.0205407 | ||||||||
\(957\) | −32.8273 | − | 56.8585i | −1.06115 | − | 1.83797i | ||||
\(958\) | −16.5678 | − | 28.6962i | −0.535280 | − | 0.927132i | ||||
\(959\) | 25.4583 | + | 44.0951i | 0.822093 | + | 1.42391i | ||||
\(960\) | 1.92162 | − | 3.32834i | 0.0620200 | − | 0.107422i | ||||
\(961\) | −30.3730 | −0.979773 | ||||||||
\(962\) | −2.74049 | + | 11.8528i | −0.0883569 | + | 0.382151i | ||||
\(963\) | 2.28617 | 0.0736710 | ||||||||
\(964\) | 3.75819 | − | 6.50938i | 0.121043 | − | 0.209653i | ||||
\(965\) | −1.56241 | − | 2.70617i | −0.0502957 | − | 0.0871148i | ||||
\(966\) | 8.10275 | + | 14.0344i | 0.260702 | + | 0.451549i | ||||
\(967\) | −4.63510 | − | 8.02823i | −0.149055 | − | 0.258171i | 0.781824 | − | 0.623500i | \(-0.214290\pi\) |
−0.930878 | + | 0.365329i | \(0.880956\pi\) | |||||||
\(968\) | 17.2055 | 0.553006 | ||||||||
\(969\) | 37.3056 | + | 64.6152i | 1.19843 | + | 2.07574i | ||||
\(970\) | 2.78117 | 0.0892980 | ||||||||
\(971\) | −3.52569 | + | 6.10667i | −0.113145 | + | 0.195972i | −0.917037 | − | 0.398803i | \(-0.869426\pi\) |
0.803892 | + | 0.594775i | \(0.202759\pi\) | |||||||
\(972\) | −5.98667 | −0.192022 | ||||||||
\(973\) | −55.5111 | −1.77960 | ||||||||
\(974\) | −9.81887 | + | 17.0068i | −0.314617 | + | 0.544932i | ||||
\(975\) | −10.4163 | − | 18.0415i | −0.333588 | − | 0.577791i | ||||
\(976\) | 6.05137 | 0.193700 | ||||||||
\(977\) | −14.8636 | + | 25.7445i | −0.475528 | + | 0.823639i | −0.999607 | − | 0.0280310i | \(-0.991076\pi\) |
0.524079 | + | 0.851670i | \(0.324410\pi\) | |||||||
\(978\) | −11.9663 | + | 20.7263i | −0.382641 | + | 0.662754i | ||||
\(979\) | −8.69085 | + | 15.0530i | −0.277761 | + | 0.481095i | ||||
\(980\) | −1.45529 | − | 2.52064i | −0.0464876 | − | 0.0805189i | ||||
\(981\) | −1.47563 | − | 2.55587i | −0.0471133 | − | 0.0816027i | ||||
\(982\) | 2.65544 | − | 4.59936i | 0.0847386 | − | 0.146772i | ||||
\(983\) | 3.67141 | − | 6.35908i | 0.117100 | − | 0.202823i | −0.801517 | − | 0.597972i | \(-0.795974\pi\) |
0.918617 | + | 0.395149i | \(0.129307\pi\) | |||||||
\(984\) | −0.317551 | + | 0.550014i | −0.0101232 | + | 0.0175338i | ||||
\(985\) | −2.45431 | −0.0782010 | ||||||||
\(986\) | 10.3366 | + | 17.9035i | 0.329184 | + | 0.570163i | ||||
\(987\) | −14.9353 | + | 25.8687i | −0.475396 | + | 0.823409i | ||||
\(988\) | 9.58373 | 0.304899 | ||||||||
\(989\) | −7.59247 | −0.241426 | ||||||||
\(990\) | −21.1071 | + | 36.5586i | −0.670828 | + | 1.16191i | ||||
\(991\) | −3.07804 | −0.0977771 | −0.0488886 | − | 0.998804i | \(-0.515568\pi\) | ||||
−0.0488886 | + | 0.998804i | \(0.515568\pi\) | |||||||
\(992\) | 0.395932 | + | 0.685774i | 0.0125708 | + | 0.0217733i | ||||
\(993\) | −90.8981 | −2.88456 | ||||||||
\(994\) | 10.7582 | + | 18.6337i | 0.341229 | + | 0.591026i | ||||
\(995\) | 1.25111 | + | 2.16699i | 0.0396630 | + | 0.0686983i | ||||
\(996\) | −5.44731 | − | 9.43501i | −0.172604 | − | 0.298960i | ||||
\(997\) | −24.8920 | + | 43.1142i | −0.788337 | + | 1.36544i | 0.138649 | + | 0.990342i | \(0.455724\pi\) |
−0.926985 | + | 0.375098i | \(0.877609\pi\) | |||||||
\(998\) | 22.3756 | 0.708287 | ||||||||
\(999\) | 13.8432 | − | 59.8731i | 0.437981 | − | 1.89430i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 74.2.c.c.47.3 | ✓ | 6 | |
3.2 | odd | 2 | 666.2.f.j.343.2 | 6 | |||
4.3 | odd | 2 | 592.2.i.e.417.1 | 6 | |||
37.10 | even | 3 | 2738.2.a.o.1.1 | 3 | |||
37.26 | even | 3 | inner | 74.2.c.c.63.3 | yes | 6 | |
37.27 | even | 6 | 2738.2.a.n.1.1 | 3 | |||
111.26 | odd | 6 | 666.2.f.j.433.2 | 6 | |||
148.63 | odd | 6 | 592.2.i.e.433.1 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
74.2.c.c.47.3 | ✓ | 6 | 1.1 | even | 1 | trivial | |
74.2.c.c.63.3 | yes | 6 | 37.26 | even | 3 | inner | |
592.2.i.e.417.1 | 6 | 4.3 | odd | 2 | |||
592.2.i.e.433.1 | 6 | 148.63 | odd | 6 | |||
666.2.f.j.343.2 | 6 | 3.2 | odd | 2 | |||
666.2.f.j.433.2 | 6 | 111.26 | odd | 6 | |||
2738.2.a.n.1.1 | 3 | 37.27 | even | 6 | |||
2738.2.a.o.1.1 | 3 | 37.10 | even | 3 |