Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [525,3,Mod(124,525)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(525, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 5]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("525.124");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 525 = 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 525.s (of order \(6\), degree \(2\), not 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: | \(14.3052138789\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 21) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 124.2 | ||
Root | \(0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 525.124 |
Dual form | 525.3.s.e.199.2 |
$q$-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 \(\left(\mathbb{Z}/525\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(176\) | \(451\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.59808 | + | 1.50000i | 1.29904 | + | 0.750000i | 0.980238 | − | 0.197822i | \(-0.0633868\pi\) |
0.318800 | + | 0.947822i | \(0.396720\pi\) | |||||||
\(3\) | −0.866025 | − | 1.50000i | −0.288675 | − | 0.500000i | ||||
\(4\) | 2.50000 | + | 4.33013i | 0.625000 | + | 1.08253i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | − | 5.19615i | − | 0.866025i | ||||||
\(7\) | −2.59808 | − | 6.50000i | −0.371154 | − | 0.928571i | ||||
\(8\) | 3.00000i | 0.375000i | ||||||||
\(9\) | −1.50000 | + | 2.59808i | −0.166667 | + | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −7.50000 | − | 12.9904i | −0.681818 | − | 1.18094i | −0.974425 | − | 0.224711i | \(-0.927856\pi\) |
0.292607 | − | 0.956233i | \(-0.405477\pi\) | |||||||
\(12\) | 4.33013 | − | 7.50000i | 0.360844 | − | 0.625000i | ||||
\(13\) | −13.8564 | −1.06588 | −0.532939 | − | 0.846154i | \(-0.678912\pi\) | ||||
−0.532939 | + | 0.846154i | \(0.678912\pi\) | |||||||
\(14\) | 3.00000 | − | 20.7846i | 0.214286 | − | 1.48461i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 5.50000 | − | 9.52628i | 0.343750 | − | 0.595392i | ||||
\(17\) | −5.19615 | − | 9.00000i | −0.305656 | − | 0.529412i | 0.671751 | − | 0.740777i | \(-0.265542\pi\) |
−0.977407 | + | 0.211365i | \(0.932209\pi\) | |||||||
\(18\) | −7.79423 | + | 4.50000i | −0.433013 | + | 0.250000i | ||||
\(19\) | 9.00000 | + | 5.19615i | 0.473684 | + | 0.273482i | 0.717781 | − | 0.696269i | \(-0.245158\pi\) |
−0.244096 | + | 0.969751i | \(0.578491\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −7.50000 | + | 9.52628i | −0.357143 | + | 0.453632i | ||||
\(22\) | − | 45.0000i | − | 2.04545i | ||||||
\(23\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(24\) | 4.50000 | − | 2.59808i | 0.187500 | − | 0.108253i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −36.0000 | − | 20.7846i | −1.38462 | − | 0.799408i | ||||
\(27\) | 5.19615 | 0.192450 | ||||||||
\(28\) | 21.6506 | − | 27.5000i | 0.773237 | − | 0.982143i | ||||
\(29\) | 9.00000 | 0.310345 | 0.155172 | − | 0.987887i | \(-0.450407\pi\) | ||||
0.155172 | + | 0.987887i | \(0.450407\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −10.5000 | + | 6.06218i | −0.338710 | + | 0.195554i | −0.659701 | − | 0.751528i | \(-0.729317\pi\) |
0.320992 | + | 0.947082i | \(0.395984\pi\) | |||||||
\(32\) | 38.9711 | − | 22.5000i | 1.21785 | − | 0.703125i | ||||
\(33\) | −12.9904 | + | 22.5000i | −0.393648 | + | 0.681818i | ||||
\(34\) | − | 31.1769i | − | 0.916968i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −15.0000 | −0.416667 | ||||||||
\(37\) | 8.66025 | + | 5.00000i | 0.234061 | + | 0.135135i | 0.612444 | − | 0.790514i | \(-0.290186\pi\) |
−0.378383 | + | 0.925649i | \(0.623520\pi\) | |||||||
\(38\) | 15.5885 | + | 27.0000i | 0.410223 | + | 0.710526i | ||||
\(39\) | 12.0000 | + | 20.7846i | 0.307692 | + | 0.532939i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 10.3923i | 0.253471i | 0.991937 | + | 0.126735i | \(0.0404499\pi\) | ||||
−0.991937 | + | 0.126735i | \(0.959550\pi\) | |||||||
\(42\) | −33.7750 | + | 13.5000i | −0.804166 | + | 0.321429i | ||||
\(43\) | − | 74.0000i | − | 1.72093i | −0.509509 | − | 0.860465i | \(-0.670173\pi\) | ||
0.509509 | − | 0.860465i | \(-0.329827\pi\) | |||||||
\(44\) | 37.5000 | − | 64.9519i | 0.852273 | − | 1.47618i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(48\) | −19.0526 | −0.396928 | ||||||||
\(49\) | −35.5000 | + | 33.7750i | −0.724490 | + | 0.689286i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −9.00000 | + | 15.5885i | −0.176471 | + | 0.305656i | ||||
\(52\) | −34.6410 | − | 60.0000i | −0.666173 | − | 1.15385i | ||||
\(53\) | 28.5788 | − | 16.5000i | 0.539223 | − | 0.311321i | −0.205541 | − | 0.978649i | \(-0.565895\pi\) |
0.744764 | + | 0.667328i | \(0.232562\pi\) | |||||||
\(54\) | 13.5000 | + | 7.79423i | 0.250000 | + | 0.144338i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 19.5000 | − | 7.79423i | 0.348214 | − | 0.139183i | ||||
\(57\) | − | 18.0000i | − | 0.315789i | ||||||
\(58\) | 23.3827 | + | 13.5000i | 0.403150 | + | 0.232759i | ||||
\(59\) | −13.5000 | + | 7.79423i | −0.228814 | + | 0.132106i | −0.610025 | − | 0.792382i | \(-0.708840\pi\) |
0.381211 | + | 0.924488i | \(0.375507\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 78.0000 | + | 45.0333i | 1.27869 | + | 0.738251i | 0.976607 | − | 0.215031i | \(-0.0689853\pi\) |
0.302081 | + | 0.953282i | \(0.402319\pi\) | |||||||
\(62\) | −36.3731 | −0.586662 | ||||||||
\(63\) | 20.7846 | + | 3.00000i | 0.329914 | + | 0.0476190i | ||||
\(64\) | 91.0000 | 1.42188 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −67.5000 | + | 38.9711i | −1.02273 | + | 0.590472i | ||||
\(67\) | 65.8179 | − | 38.0000i | 0.982357 | − | 0.567164i | 0.0793762 | − | 0.996845i | \(-0.474707\pi\) |
0.902981 | + | 0.429681i | \(0.141374\pi\) | |||||||
\(68\) | 25.9808 | − | 45.0000i | 0.382070 | − | 0.661765i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 84.0000 | 1.18310 | 0.591549 | − | 0.806269i | \(-0.298517\pi\) | ||||
0.591549 | + | 0.806269i | \(0.298517\pi\) | |||||||
\(72\) | −7.79423 | − | 4.50000i | −0.108253 | − | 0.0625000i | ||||
\(73\) | −31.1769 | − | 54.0000i | −0.427081 | − | 0.739726i | 0.569531 | − | 0.821970i | \(-0.307125\pi\) |
−0.996612 | + | 0.0822437i | \(0.973791\pi\) | |||||||
\(74\) | 15.0000 | + | 25.9808i | 0.202703 | + | 0.351091i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 51.9615i | 0.683704i | ||||||||
\(77\) | −64.9519 | + | 82.5000i | −0.843531 | + | 1.07143i | ||||
\(78\) | 72.0000i | 0.923077i | ||||||||
\(79\) | −21.5000 | + | 37.2391i | −0.272152 | + | 0.471381i | −0.969413 | − | 0.245437i | \(-0.921069\pi\) |
0.697261 | + | 0.716818i | \(0.254402\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.50000 | − | 7.79423i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | −15.5885 | + | 27.0000i | −0.190103 | + | 0.329268i | ||||
\(83\) | −119.512 | −1.43990 | −0.719949 | − | 0.694027i | \(-0.755835\pi\) | ||||
−0.719949 | + | 0.694027i | \(0.755835\pi\) | |||||||
\(84\) | −60.0000 | − | 8.66025i | −0.714286 | − | 0.103098i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 111.000 | − | 192.258i | 1.29070 | − | 2.23555i | ||||
\(87\) | −7.79423 | − | 13.5000i | −0.0895888 | − | 0.155172i | ||||
\(88\) | 38.9711 | − | 22.5000i | 0.442854 | − | 0.255682i | ||||
\(89\) | 63.0000 | + | 36.3731i | 0.707865 | + | 0.408686i | 0.810270 | − | 0.586057i | \(-0.199320\pi\) |
−0.102405 | + | 0.994743i | \(0.532654\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 36.0000 | + | 90.0666i | 0.395604 | + | 0.989743i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 18.1865 | + | 10.5000i | 0.195554 | + | 0.112903i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −67.5000 | − | 38.9711i | −0.703125 | − | 0.405949i | ||||
\(97\) | −185.329 | −1.91061 | −0.955306 | − | 0.295618i | \(-0.904475\pi\) | ||||
−0.955306 | + | 0.295618i | \(0.904475\pi\) | |||||||
\(98\) | −142.894 | + | 34.5000i | −1.45810 | + | 0.352041i | ||||
\(99\) | 45.0000 | 0.454545 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −126.000 | + | 72.7461i | −1.24752 | + | 0.720259i | −0.970615 | − | 0.240637i | \(-0.922644\pi\) |
−0.276910 | + | 0.960896i | \(0.589310\pi\) | |||||||
\(102\) | −46.7654 | + | 27.0000i | −0.458484 | + | 0.264706i | ||||
\(103\) | 34.6410 | − | 60.0000i | 0.336321 | − | 0.582524i | −0.647417 | − | 0.762136i | \(-0.724151\pi\) |
0.983738 | + | 0.179612i | \(0.0574841\pi\) | |||||||
\(104\) | − | 41.5692i | − | 0.399704i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 99.0000 | 0.933962 | ||||||||
\(107\) | 80.5404 | + | 46.5000i | 0.752714 | + | 0.434579i | 0.826674 | − | 0.562682i | \(-0.190230\pi\) |
−0.0739599 | + | 0.997261i | \(0.523564\pi\) | |||||||
\(108\) | 12.9904 | + | 22.5000i | 0.120281 | + | 0.208333i | ||||
\(109\) | −4.00000 | − | 6.92820i | −0.0366972 | − | 0.0635615i | 0.847093 | − | 0.531444i | \(-0.178350\pi\) |
−0.883791 | + | 0.467882i | \(0.845017\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 17.3205i | − | 0.156041i | ||||||
\(112\) | −76.2102 | − | 11.0000i | −0.680449 | − | 0.0982143i | ||||
\(113\) | 42.0000i | 0.371681i | 0.982580 | + | 0.185841i | \(0.0595008\pi\) | ||||
−0.982580 | + | 0.185841i | \(0.940499\pi\) | |||||||
\(114\) | 27.0000 | − | 46.7654i | 0.236842 | − | 0.410223i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 22.5000 | + | 38.9711i | 0.193966 | + | 0.335958i | ||||
\(117\) | 20.7846 | − | 36.0000i | 0.177646 | − | 0.307692i | ||||
\(118\) | −46.7654 | −0.396317 | ||||||||
\(119\) | −45.0000 | + | 57.1577i | −0.378151 | + | 0.480317i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −52.0000 | + | 90.0666i | −0.429752 | + | 0.744352i | ||||
\(122\) | 135.100 | + | 234.000i | 1.10738 | + | 1.91803i | ||||
\(123\) | 15.5885 | − | 9.00000i | 0.126735 | − | 0.0731707i | ||||
\(124\) | −52.5000 | − | 30.3109i | −0.423387 | − | 0.244443i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 49.5000 | + | 38.9711i | 0.392857 | + | 0.309295i | ||||
\(127\) | − | 35.0000i | − | 0.275591i | −0.990461 | − | 0.137795i | \(-0.955998\pi\) | ||
0.990461 | − | 0.137795i | \(-0.0440016\pi\) | |||||||
\(128\) | 80.5404 | + | 46.5000i | 0.629222 | + | 0.363281i | ||||
\(129\) | −111.000 | + | 64.0859i | −0.860465 | + | 0.496790i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 148.500 | + | 85.7365i | 1.13359 | + | 0.654477i | 0.944835 | − | 0.327547i | \(-0.106222\pi\) |
0.188753 | + | 0.982025i | \(0.439555\pi\) | |||||||
\(132\) | −129.904 | −0.984120 | ||||||||
\(133\) | 10.3923 | − | 72.0000i | 0.0781376 | − | 0.541353i | ||||
\(134\) | 228.000 | 1.70149 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 27.0000 | − | 15.5885i | 0.198529 | − | 0.114621i | ||||
\(137\) | 83.1384 | − | 48.0000i | 0.606850 | − | 0.350365i | −0.164882 | − | 0.986313i | \(-0.552724\pi\) |
0.771732 | + | 0.635948i | \(0.219391\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 183.597i | − | 1.32084i | −0.750894 | − | 0.660422i | \(-0.770377\pi\) | ||
0.750894 | − | 0.660422i | \(-0.229623\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 218.238 | + | 126.000i | 1.53689 | + | 0.887324i | ||||
\(143\) | 103.923 | + | 180.000i | 0.726735 | + | 1.25874i | ||||
\(144\) | 16.5000 | + | 28.5788i | 0.114583 | + | 0.198464i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | − | 187.061i | − | 1.28124i | ||||||
\(147\) | 81.4064 | + | 24.0000i | 0.553785 | + | 0.163265i | ||||
\(148\) | 50.0000i | 0.337838i | ||||||||
\(149\) | −93.0000 | + | 161.081i | −0.624161 | + | 1.08108i | 0.364541 | + | 0.931187i | \(0.381226\pi\) |
−0.988702 | + | 0.149892i | \(0.952108\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −39.5000 | − | 68.4160i | −0.261589 | − | 0.453086i | 0.705075 | − | 0.709133i | \(-0.250913\pi\) |
−0.966664 | + | 0.256047i | \(0.917580\pi\) | |||||||
\(152\) | −15.5885 | + | 27.0000i | −0.102556 | + | 0.177632i | ||||
\(153\) | 31.1769 | 0.203771 | ||||||||
\(154\) | −292.500 | + | 116.913i | −1.89935 | + | 0.759178i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −60.0000 | + | 103.923i | −0.384615 | + | 0.666173i | ||||
\(157\) | 10.3923 | + | 18.0000i | 0.0661930 | + | 0.114650i | 0.897223 | − | 0.441579i | \(-0.145581\pi\) |
−0.831030 | + | 0.556228i | \(0.812248\pi\) | |||||||
\(158\) | −111.717 | + | 64.5000i | −0.707071 | + | 0.408228i | ||||
\(159\) | −49.5000 | − | 28.5788i | −0.311321 | − | 0.179741i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | − | 27.0000i | − | 0.166667i | ||||||
\(163\) | 180.133 | + | 104.000i | 1.10511 | + | 0.638037i | 0.937559 | − | 0.347826i | \(-0.113080\pi\) |
0.167553 | + | 0.985863i | \(0.446413\pi\) | |||||||
\(164\) | −45.0000 | + | 25.9808i | −0.274390 | + | 0.158419i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −310.500 | − | 179.267i | −1.87048 | − | 1.07992i | ||||
\(167\) | 249.415 | 1.49350 | 0.746752 | − | 0.665102i | \(-0.231612\pi\) | ||||
0.746752 | + | 0.665102i | \(0.231612\pi\) | |||||||
\(168\) | −28.5788 | − | 22.5000i | −0.170112 | − | 0.133929i | ||||
\(169\) | 23.0000 | 0.136095 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −27.0000 | + | 15.5885i | −0.157895 | + | 0.0911606i | ||||
\(172\) | 320.429 | − | 185.000i | 1.86296 | − | 1.07558i | ||||
\(173\) | 114.315 | − | 198.000i | 0.660782 | − | 1.14451i | −0.319628 | − | 0.947543i | \(-0.603558\pi\) |
0.980410 | − | 0.196966i | \(-0.0631087\pi\) | |||||||
\(174\) | − | 46.7654i | − | 0.268767i | ||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −165.000 | −0.937500 | ||||||||
\(177\) | 23.3827 | + | 13.5000i | 0.132106 | + | 0.0762712i | ||||
\(178\) | 109.119 | + | 189.000i | 0.613029 | + | 1.06180i | ||||
\(179\) | 45.0000 | + | 77.9423i | 0.251397 | + | 0.435432i | 0.963911 | − | 0.266226i | \(-0.0857768\pi\) |
−0.712514 | + | 0.701658i | \(0.752443\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.3923i | 0.0574160i | 0.999588 | + | 0.0287080i | \(0.00913930\pi\) | ||||
−0.999588 | + | 0.0287080i | \(0.990861\pi\) | |||||||
\(182\) | −41.5692 | + | 288.000i | −0.228402 | + | 1.58242i | ||||
\(183\) | − | 156.000i | − | 0.852459i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 31.5000 | + | 54.5596i | 0.169355 | + | 0.293331i | ||||
\(187\) | −77.9423 | + | 135.000i | −0.416804 | + | 0.721925i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −13.5000 | − | 33.7750i | −0.0714286 | − | 0.178704i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 156.000 | − | 270.200i | 0.816754 | − | 1.41466i | −0.0913077 | − | 0.995823i | \(-0.529105\pi\) |
0.908062 | − | 0.418837i | \(-0.137562\pi\) | |||||||
\(192\) | −78.8083 | − | 136.500i | −0.410460 | − | 0.710938i | ||||
\(193\) | −160.215 | + | 92.5000i | −0.830128 | + | 0.479275i | −0.853896 | − | 0.520443i | \(-0.825767\pi\) |
0.0237685 | + | 0.999717i | \(0.492434\pi\) | |||||||
\(194\) | −481.500 | − | 277.994i | −2.48196 | − | 1.43296i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −235.000 | − | 69.2820i | −1.19898 | − | 0.353480i | ||||
\(197\) | − | 330.000i | − | 1.67513i | −0.546340 | − | 0.837563i | \(-0.683979\pi\) | ||
0.546340 | − | 0.837563i | \(-0.316021\pi\) | |||||||
\(198\) | 116.913 | + | 67.5000i | 0.590472 | + | 0.340909i | ||||
\(199\) | −6.00000 | + | 3.46410i | −0.0301508 | + | 0.0174075i | −0.515000 | − | 0.857190i | \(-0.672208\pi\) |
0.484849 | + | 0.874598i | \(0.338875\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −114.000 | − | 65.8179i | −0.567164 | − | 0.327452i | ||||
\(202\) | −436.477 | −2.16078 | ||||||||
\(203\) | −23.3827 | − | 58.5000i | −0.115186 | − | 0.288177i | ||||
\(204\) | −90.0000 | −0.441176 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 180.000 | − | 103.923i | 0.873786 | − | 0.504481i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −76.2102 | + | 132.000i | −0.366395 | + | 0.634615i | ||||
\(209\) | − | 155.885i | − | 0.745859i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −248.000 | −1.17536 | −0.587678 | − | 0.809095i | \(-0.699958\pi\) | ||||
−0.587678 | + | 0.809095i | \(0.699958\pi\) | |||||||
\(212\) | 142.894 | + | 82.5000i | 0.674029 | + | 0.389151i | ||||
\(213\) | −72.7461 | − | 126.000i | −0.341531 | − | 0.591549i | ||||
\(214\) | 139.500 | + | 241.621i | 0.651869 | + | 1.12907i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 15.5885i | 0.0721688i | ||||||||
\(217\) | 66.6840 | + | 52.5000i | 0.307299 | + | 0.241935i | ||||
\(218\) | − | 24.0000i | − | 0.110092i | ||||||
\(219\) | −54.0000 | + | 93.5307i | −0.246575 | + | 0.427081i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 72.0000 | + | 124.708i | 0.325792 | + | 0.564288i | ||||
\(222\) | 25.9808 | − | 45.0000i | 0.117030 | − | 0.202703i | ||||
\(223\) | −192.258 | −0.862142 | −0.431071 | − | 0.902318i | \(-0.641864\pi\) | ||||
−0.431071 | + | 0.902318i | \(0.641864\pi\) | |||||||
\(224\) | −247.500 | − | 194.856i | −1.10491 | − | 0.869892i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −63.0000 | + | 109.119i | −0.278761 | + | 0.482828i | ||||
\(227\) | 44.1673 | + | 76.5000i | 0.194570 | + | 0.337004i | 0.946759 | − | 0.321942i | \(-0.104336\pi\) |
−0.752190 | + | 0.658947i | \(0.771002\pi\) | |||||||
\(228\) | 77.9423 | − | 45.0000i | 0.341852 | − | 0.197368i | ||||
\(229\) | −285.000 | − | 164.545i | −1.24454 | − | 0.718536i | −0.274526 | − | 0.961580i | \(-0.588521\pi\) |
−0.970015 | + | 0.243043i | \(0.921854\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 180.000 | + | 25.9808i | 0.779221 | + | 0.112471i | ||||
\(232\) | 27.0000i | 0.116379i | ||||||||
\(233\) | −233.827 | − | 135.000i | −1.00355 | − | 0.579399i | −0.0942524 | − | 0.995548i | \(-0.530046\pi\) |
−0.909296 | + | 0.416149i | \(0.863379\pi\) | |||||||
\(234\) | 108.000 | − | 62.3538i | 0.461538 | − | 0.266469i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −67.5000 | − | 38.9711i | −0.286017 | − | 0.165132i | ||||
\(237\) | 74.4782 | 0.314254 | ||||||||
\(238\) | −202.650 | + | 81.0000i | −0.851470 | + | 0.340336i | ||||
\(239\) | 228.000 | 0.953975 | 0.476987 | − | 0.878910i | \(-0.341729\pi\) | ||||
0.476987 | + | 0.878910i | \(0.341729\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 385.500 | − | 222.569i | 1.59959 | − | 0.923521i | 0.608018 | − | 0.793923i | \(-0.291965\pi\) |
0.991567 | − | 0.129598i | \(-0.0413687\pi\) | |||||||
\(242\) | −270.200 | + | 156.000i | −1.11653 | + | 0.644628i | ||||
\(243\) | −7.79423 | + | 13.5000i | −0.0320750 | + | 0.0555556i | ||||
\(244\) | 450.333i | 1.84563i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 54.0000 | 0.219512 | ||||||||
\(247\) | −124.708 | − | 72.0000i | −0.504889 | − | 0.291498i | ||||
\(248\) | −18.1865 | − | 31.5000i | −0.0733328 | − | 0.127016i | ||||
\(249\) | 103.500 | + | 179.267i | 0.415663 | + | 0.719949i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5.19615i | 0.0207018i | 0.999946 | + | 0.0103509i | \(0.00329485\pi\) | ||||
−0.999946 | + | 0.0103509i | \(0.996705\pi\) | |||||||
\(252\) | 38.9711 | + | 97.5000i | 0.154647 | + | 0.386905i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 52.5000 | − | 90.9327i | 0.206693 | − | 0.358003i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −42.5000 | − | 73.6122i | −0.166016 | − | 0.287547i | ||||
\(257\) | 57.1577 | − | 99.0000i | 0.222403 | − | 0.385214i | −0.733134 | − | 0.680084i | \(-0.761943\pi\) |
0.955537 | + | 0.294870i | \(0.0952765\pi\) | |||||||
\(258\) | −384.515 | −1.49037 | ||||||||
\(259\) | 10.0000 | − | 69.2820i | 0.0386100 | − | 0.267498i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −13.5000 | + | 23.3827i | −0.0517241 | + | 0.0895888i | ||||
\(262\) | 257.210 | + | 445.500i | 0.981716 | + | 1.70038i | ||||
\(263\) | 161.081 | − | 93.0000i | 0.612474 | − | 0.353612i | −0.161459 | − | 0.986879i | \(-0.551620\pi\) |
0.773933 | + | 0.633267i | \(0.218287\pi\) | |||||||
\(264\) | −67.5000 | − | 38.9711i | −0.255682 | − | 0.147618i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 135.000 | − | 171.473i | 0.507519 | − | 0.644635i | ||||
\(267\) | − | 126.000i | − | 0.471910i | ||||||
\(268\) | 329.090 | + | 190.000i | 1.22795 | + | 0.708955i | ||||
\(269\) | 292.500 | − | 168.875i | 1.08736 | − | 0.627788i | 0.154488 | − | 0.987995i | \(-0.450627\pi\) |
0.932873 | + | 0.360207i | \(0.117294\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 79.5000 | + | 45.8993i | 0.293358 | + | 0.169370i | 0.639455 | − | 0.768828i | \(-0.279160\pi\) |
−0.346097 | + | 0.938199i | \(0.612493\pi\) | |||||||
\(272\) | −114.315 | −0.420277 | ||||||||
\(273\) | 103.923 | − | 132.000i | 0.380671 | − | 0.483516i | ||||
\(274\) | 288.000 | 1.05109 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −329.090 | + | 190.000i | −1.18805 | + | 0.685921i | −0.957863 | − | 0.287226i | \(-0.907267\pi\) |
−0.230186 | + | 0.973147i | \(0.573934\pi\) | |||||||
\(278\) | 275.396 | − | 477.000i | 0.990633 | − | 1.71583i | ||||
\(279\) | − | 36.3731i | − | 0.130369i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 300.000 | 1.06762 | 0.533808 | − | 0.845606i | \(-0.320761\pi\) | ||||
0.533808 | + | 0.845606i | \(0.320761\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 102.191 | + | 177.000i | 0.361099 | + | 0.625442i | 0.988142 | − | 0.153543i | \(-0.0490683\pi\) |
−0.627043 | + | 0.778985i | \(0.715735\pi\) | |||||||
\(284\) | 210.000 | + | 363.731i | 0.739437 | + | 1.28074i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 623.538i | 2.18020i | ||||||||
\(287\) | 67.5500 | − | 27.0000i | 0.235366 | − | 0.0940767i | ||||
\(288\) | 135.000i | 0.468750i | ||||||||
\(289\) | 90.5000 | − | 156.751i | 0.313149 | − | 0.542390i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 160.500 | + | 277.994i | 0.551546 | + | 0.955306i | ||||
\(292\) | 155.885 | − | 270.000i | 0.533851 | − | 0.924658i | ||||
\(293\) | 545.596 | 1.86210 | 0.931051 | − | 0.364889i | \(-0.118893\pi\) | ||||
0.931051 | + | 0.364889i | \(0.118893\pi\) | |||||||
\(294\) | 175.500 | + | 184.463i | 0.596939 | + | 0.627427i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −15.0000 | + | 25.9808i | −0.0506757 | + | 0.0877728i | ||||
\(297\) | −38.9711 | − | 67.5000i | −0.131216 | − | 0.227273i | ||||
\(298\) | −483.242 | + | 279.000i | −1.62162 | + | 0.936242i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −481.000 | + | 192.258i | −1.59801 | + | 0.638730i | ||||
\(302\) | − | 237.000i | − | 0.784768i | ||||||
\(303\) | 218.238 | + | 126.000i | 0.720259 | + | 0.415842i | ||||
\(304\) | 99.0000 | − | 57.1577i | 0.325658 | − | 0.188019i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 81.0000 | + | 46.7654i | 0.264706 | + | 0.152828i | ||||
\(307\) | −173.205 | −0.564186 | −0.282093 | − | 0.959387i | \(-0.591029\pi\) | ||||
−0.282093 | + | 0.959387i | \(0.591029\pi\) | |||||||
\(308\) | −519.615 | − | 75.0000i | −1.68706 | − | 0.243506i | ||||
\(309\) | −120.000 | −0.388350 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −153.000 | + | 88.3346i | −0.491961 | + | 0.284034i | −0.725388 | − | 0.688340i | \(-0.758340\pi\) |
0.233426 | + | 0.972374i | \(0.425006\pi\) | |||||||
\(312\) | −62.3538 | + | 36.0000i | −0.199852 | + | 0.115385i | ||||
\(313\) | 106.521 | − | 184.500i | 0.340323 | − | 0.589457i | −0.644170 | − | 0.764883i | \(-0.722797\pi\) |
0.984493 | + | 0.175426i | \(0.0561302\pi\) | |||||||
\(314\) | 62.3538i | 0.198579i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −215.000 | −0.680380 | ||||||||
\(317\) | 101.325 | + | 58.5000i | 0.319637 | + | 0.184543i | 0.651231 | − | 0.758880i | \(-0.274253\pi\) |
−0.331594 | + | 0.943422i | \(0.607586\pi\) | |||||||
\(318\) | −85.7365 | − | 148.500i | −0.269612 | − | 0.466981i | ||||
\(319\) | −67.5000 | − | 116.913i | −0.211599 | − | 0.366500i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 161.081i | − | 0.501809i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 108.000i | − | 0.334365i | ||||||
\(324\) | 22.5000 | − | 38.9711i | 0.0694444 | − | 0.120281i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 312.000 | + | 540.400i | 0.957055 | + | 1.65767i | ||||
\(327\) | −6.92820 | + | 12.0000i | −0.0211872 | + | 0.0366972i | ||||
\(328\) | −31.1769 | −0.0950516 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −20.0000 | + | 34.6410i | −0.0604230 | + | 0.104656i | −0.894655 | − | 0.446759i | \(-0.852578\pi\) |
0.834232 | + | 0.551414i | \(0.185912\pi\) | |||||||
\(332\) | −298.779 | − | 517.500i | −0.899936 | − | 1.55873i | ||||
\(333\) | −25.9808 | + | 15.0000i | −0.0780203 | + | 0.0450450i | ||||
\(334\) | 648.000 | + | 374.123i | 1.94012 | + | 1.12013i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 49.5000 | + | 123.842i | 0.147321 | + | 0.368576i | ||||
\(337\) | − | 91.0000i | − | 0.270030i | −0.990844 | − | 0.135015i | \(-0.956892\pi\) | ||
0.990844 | − | 0.135015i | \(-0.0431082\pi\) | |||||||
\(338\) | 59.7558 | + | 34.5000i | 0.176792 | + | 0.102071i | ||||
\(339\) | 63.0000 | − | 36.3731i | 0.185841 | − | 0.107295i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 157.500 | + | 90.9327i | 0.461877 | + | 0.266665i | ||||
\(342\) | −93.5307 | −0.273482 | ||||||||
\(343\) | 311.769 | + | 143.000i | 0.908948 | + | 0.416910i | ||||
\(344\) | 222.000 | 0.645349 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 594.000 | − | 342.946i | 1.71676 | − | 0.991174i | ||||
\(347\) | −181.865 | + | 105.000i | −0.524108 | + | 0.302594i | −0.738614 | − | 0.674129i | \(-0.764519\pi\) |
0.214506 | + | 0.976723i | \(0.431186\pi\) | |||||||
\(348\) | 38.9711 | − | 67.5000i | 0.111986 | − | 0.193966i | ||||
\(349\) | − | 304.841i | − | 0.873470i | −0.899590 | − | 0.436735i | \(-0.856135\pi\) | ||
0.899590 | − | 0.436735i | \(-0.143865\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −72.0000 | −0.205128 | ||||||||
\(352\) | −584.567 | − | 337.500i | −1.66070 | − | 0.958807i | ||||
\(353\) | 197.454 | + | 342.000i | 0.559359 | + | 0.968839i | 0.997550 | + | 0.0699566i | \(0.0222861\pi\) |
−0.438191 | + | 0.898882i | \(0.644381\pi\) | |||||||
\(354\) | 40.5000 | + | 70.1481i | 0.114407 | + | 0.198158i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 363.731i | 1.02172i | ||||||||
\(357\) | 124.708 | + | 18.0000i | 0.349321 | + | 0.0504202i | ||||
\(358\) | 270.000i | 0.754190i | ||||||||
\(359\) | 246.000 | − | 426.084i | 0.685237 | − | 1.18686i | −0.288126 | − | 0.957593i | \(-0.593032\pi\) |
0.973362 | − | 0.229272i | \(-0.0736346\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −126.500 | − | 219.104i | −0.350416 | − | 0.606937i | ||||
\(362\) | −15.5885 | + | 27.0000i | −0.0430620 | + | 0.0745856i | ||||
\(363\) | 180.133 | 0.496235 | ||||||||
\(364\) | −300.000 | + | 381.051i | −0.824176 | + | 1.04684i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 234.000 | − | 405.300i | 0.639344 | − | 1.10738i | ||||
\(367\) | 163.679 | + | 283.500i | 0.445991 | + | 0.772480i | 0.998121 | − | 0.0612789i | \(-0.0195179\pi\) |
−0.552129 | + | 0.833758i | \(0.686185\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −27.0000 | − | 15.5885i | −0.0731707 | − | 0.0422451i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −181.500 | − | 142.894i | −0.489218 | − | 0.385160i | ||||
\(372\) | 105.000i | 0.282258i | ||||||||
\(373\) | −147.224 | − | 85.0000i | −0.394703 | − | 0.227882i | 0.289493 | − | 0.957180i | \(-0.406513\pi\) |
−0.684196 | + | 0.729298i | \(0.739847\pi\) | |||||||
\(374\) | −405.000 | + | 233.827i | −1.08289 | + | 0.625206i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −124.708 | −0.330790 | ||||||||
\(378\) | 15.5885 | − | 108.000i | 0.0412393 | − | 0.285714i | ||||
\(379\) | −82.0000 | −0.216359 | −0.108179 | − | 0.994131i | \(-0.534502\pi\) | ||||
−0.108179 | + | 0.994131i | \(0.534502\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −52.5000 | + | 30.3109i | −0.137795 | + | 0.0795561i | ||||
\(382\) | 810.600 | − | 468.000i | 2.12199 | − | 1.22513i | ||||
\(383\) | −109.119 | + | 189.000i | −0.284907 | + | 0.493473i | −0.972587 | − | 0.232541i | \(-0.925296\pi\) |
0.687680 | + | 0.726014i | \(0.258629\pi\) | |||||||
\(384\) | − | 161.081i | − | 0.419481i | ||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −555.000 | −1.43782 | ||||||||
\(387\) | 192.258 | + | 111.000i | 0.496790 | + | 0.286822i | ||||
\(388\) | −463.324 | − | 802.500i | −1.19413 | − | 2.06830i | ||||
\(389\) | 153.000 | + | 265.004i | 0.393316 | + | 0.681244i | 0.992885 | − | 0.119080i | \(-0.0379944\pi\) |
−0.599568 | + | 0.800323i | \(0.704661\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −101.325 | − | 106.500i | −0.258482 | − | 0.271684i | ||||
\(393\) | − | 297.000i | − | 0.755725i | ||||||
\(394\) | 495.000 | − | 857.365i | 1.25635 | − | 2.17605i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 112.500 | + | 194.856i | 0.284091 | + | 0.492060i | ||||
\(397\) | −128.172 | + | 222.000i | −0.322851 | + | 0.559194i | −0.981075 | − | 0.193628i | \(-0.937975\pi\) |
0.658224 | + | 0.752822i | \(0.271308\pi\) | |||||||
\(398\) | −20.7846 | −0.0522226 | ||||||||
\(399\) | −117.000 | + | 46.7654i | −0.293233 | + | 0.117206i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −66.0000 | + | 114.315i | −0.164589 | + | 0.285076i | −0.936509 | − | 0.350643i | \(-0.885963\pi\) |
0.771921 | + | 0.635719i | \(0.219296\pi\) | |||||||
\(402\) | −197.454 | − | 342.000i | −0.491179 | − | 0.850746i | ||||
\(403\) | 145.492 | − | 84.0000i | 0.361023 | − | 0.208437i | ||||
\(404\) | −630.000 | − | 363.731i | −1.55941 | − | 0.900323i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 27.0000 | − | 187.061i | 0.0665025 | − | 0.460743i | ||||
\(407\) | − | 150.000i | − | 0.368550i | ||||||
\(408\) | −46.7654 | − | 27.0000i | −0.114621 | − | 0.0661765i | ||||
\(409\) | 313.500 | − | 180.999i | 0.766504 | − | 0.442541i | −0.0651223 | − | 0.997877i | \(-0.520744\pi\) |
0.831626 | + | 0.555336i | \(0.187410\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −144.000 | − | 83.1384i | −0.350365 | − | 0.202283i | ||||
\(412\) | 346.410 | 0.840801 | ||||||||
\(413\) | 85.7365 | + | 67.5000i | 0.207594 | + | 0.163438i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −540.000 | + | 311.769i | −1.29808 | + | 0.749445i | ||||
\(417\) | −275.396 | + | 159.000i | −0.660422 | + | 0.381295i | ||||
\(418\) | 233.827 | − | 405.000i | 0.559394 | − | 0.968900i | ||||
\(419\) | 644.323i | 1.53776i | 0.639391 | + | 0.768882i | \(0.279187\pi\) | ||||
−0.639391 | + | 0.768882i | \(0.720813\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 752.000 | 1.78622 | 0.893112 | − | 0.449835i | \(-0.148517\pi\) | ||||
0.893112 | + | 0.449835i | \(0.148517\pi\) | |||||||
\(422\) | −644.323 | − | 372.000i | −1.52683 | − | 0.881517i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 49.5000 | + | 85.7365i | 0.116745 | + | 0.202209i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | − | 436.477i | − | 1.02459i | ||||||
\(427\) | 90.0666 | − | 624.000i | 0.210929 | − | 1.46136i | ||||
\(428\) | 465.000i | 1.08645i | ||||||||
\(429\) | 180.000 | − | 311.769i | 0.419580 | − | 0.726735i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −81.0000 | − | 140.296i | −0.187935 | − | 0.325513i | 0.756627 | − | 0.653847i | \(-0.226846\pi\) |
−0.944562 | + | 0.328334i | \(0.893513\pi\) | |||||||
\(432\) | 28.5788 | − | 49.5000i | 0.0661547 | − | 0.114583i | ||||
\(433\) | −339.482 | −0.784023 | −0.392011 | − | 0.919960i | \(-0.628221\pi\) | ||||
−0.392011 | + | 0.919960i | \(0.628221\pi\) | |||||||
\(434\) | 94.5000 | + | 236.425i | 0.217742 | + | 0.544758i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 20.0000 | − | 34.6410i | 0.0458716 | − | 0.0794519i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | −280.592 | + | 162.000i | −0.640622 | + | 0.369863i | ||||
\(439\) | −337.500 | − | 194.856i | −0.768793 | − | 0.443863i | 0.0636511 | − | 0.997972i | \(-0.479726\pi\) |
−0.832444 | + | 0.554110i | \(0.813059\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −34.5000 | − | 142.894i | −0.0782313 | − | 0.324023i | ||||
\(442\) | 432.000i | 0.977376i | ||||||||
\(443\) | 257.210 | + | 148.500i | 0.580608 | + | 0.335214i | 0.761375 | − | 0.648312i | \(-0.224525\pi\) |
−0.180767 | + | 0.983526i | \(0.557858\pi\) | |||||||
\(444\) | 75.0000 | − | 43.3013i | 0.168919 | − | 0.0975254i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −499.500 | − | 288.386i | −1.11996 | − | 0.646606i | ||||
\(447\) | 322.161 | 0.720719 | ||||||||
\(448\) | −236.425 | − | 591.500i | −0.527734 | − | 1.32031i | ||||
\(449\) | 492.000 | 1.09577 | 0.547884 | − | 0.836554i | \(-0.315433\pi\) | ||||
0.547884 | + | 0.836554i | \(0.315433\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 135.000 | − | 77.9423i | 0.299335 | − | 0.172821i | ||||
\(452\) | −181.865 | + | 105.000i | −0.402357 | + | 0.232301i | ||||
\(453\) | −68.4160 | + | 118.500i | −0.151029 | + | 0.261589i | ||||
\(454\) | 265.004i | 0.583709i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 54.0000 | 0.118421 | ||||||||
\(457\) | −383.649 | − | 221.500i | −0.839495 | − | 0.484683i | 0.0175975 | − | 0.999845i | \(-0.494398\pi\) |
−0.857093 | + | 0.515162i | \(0.827732\pi\) | |||||||
\(458\) | −493.634 | − | 855.000i | −1.07780 | − | 1.86681i | ||||
\(459\) | −27.0000 | − | 46.7654i | −0.0588235 | − | 0.101885i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 415.692i | − | 0.901718i | −0.892595 | − | 0.450859i | \(-0.851118\pi\) | ||
0.892595 | − | 0.450859i | \(-0.148882\pi\) | |||||||
\(462\) | 428.683 | + | 337.500i | 0.927884 | + | 0.730519i | ||||
\(463\) | − | 82.0000i | − | 0.177106i | −0.996071 | − | 0.0885529i | \(-0.971776\pi\) | ||
0.996071 | − | 0.0885529i | \(-0.0282242\pi\) | |||||||
\(464\) | 49.5000 | − | 85.7365i | 0.106681 | − | 0.184777i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −405.000 | − | 701.481i | −0.869099 | − | 1.50532i | ||||
\(467\) | 135.100 | − | 234.000i | 0.289293 | − | 0.501071i | −0.684348 | − | 0.729156i | \(-0.739913\pi\) |
0.973641 | + | 0.228085i | \(0.0732464\pi\) | |||||||
\(468\) | 207.846 | 0.444116 | ||||||||
\(469\) | −418.000 | − | 329.090i | −0.891258 | − | 0.701684i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 18.0000 | − | 31.1769i | 0.0382166 | − | 0.0661930i | ||||
\(472\) | −23.3827 | − | 40.5000i | −0.0495396 | − | 0.0858051i | ||||
\(473\) | −961.288 | + | 555.000i | −2.03232 | + | 1.17336i | ||||
\(474\) | 193.500 | + | 111.717i | 0.408228 | + | 0.235690i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −360.000 | − | 51.9615i | −0.756303 | − | 0.109163i | ||||
\(477\) | 99.0000i | 0.207547i | ||||||||
\(478\) | 592.361 | + | 342.000i | 1.23925 | + | 0.715481i | ||||
\(479\) | −297.000 | + | 171.473i | −0.620042 | + | 0.357981i | −0.776885 | − | 0.629642i | \(-0.783202\pi\) |
0.156844 | + | 0.987623i | \(0.449868\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −120.000 | − | 69.2820i | −0.249480 | − | 0.144037i | ||||
\(482\) | 1335.41 | 2.77056 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −520.000 | −1.07438 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −40.5000 | + | 23.3827i | −0.0833333 | + | 0.0481125i | ||||
\(487\) | 274.530 | − | 158.500i | 0.563717 | − | 0.325462i | −0.190919 | − | 0.981606i | \(-0.561147\pi\) |
0.754636 | + | 0.656144i | \(0.227814\pi\) | |||||||
\(488\) | −135.100 | + | 234.000i | −0.276844 | + | 0.479508i | ||||
\(489\) | − | 360.267i | − | 0.736741i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 27.0000 | 0.0549898 | 0.0274949 | − | 0.999622i | \(-0.491247\pi\) | ||||
0.0274949 | + | 0.999622i | \(0.491247\pi\) | |||||||
\(492\) | 77.9423 | + | 45.0000i | 0.158419 | + | 0.0914634i | ||||
\(493\) | −46.7654 | − | 81.0000i | −0.0948588 | − | 0.164300i | ||||
\(494\) | −216.000 | − | 374.123i | −0.437247 | − | 0.757334i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 133.368i | 0.268887i | ||||||||
\(497\) | −218.238 | − | 546.000i | −0.439111 | − | 1.09859i | ||||
\(498\) | 621.000i | 1.24699i | ||||||||
\(499\) | −223.000 | + | 386.247i | −0.446894 | + | 0.774043i | −0.998182 | − | 0.0602721i | \(-0.980803\pi\) |
0.551288 | + | 0.834315i | \(0.314136\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −216.000 | − | 374.123i | −0.431138 | − | 0.746752i | ||||
\(502\) | −7.79423 | + | 13.5000i | −0.0155264 | + | 0.0268924i | ||||
\(503\) | −488.438 | −0.971050 | −0.485525 | − | 0.874223i | \(-0.661372\pi\) | ||||
−0.485525 | + | 0.874223i | \(0.661372\pi\) | |||||||
\(504\) | −9.00000 | + | 62.3538i | −0.0178571 | + | 0.123718i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −19.9186 | − | 34.5000i | −0.0392871 | − | 0.0680473i | ||||
\(508\) | 151.554 | − | 87.5000i | 0.298336 | − | 0.172244i | ||||
\(509\) | −85.5000 | − | 49.3634i | −0.167976 | − | 0.0969812i | 0.413655 | − | 0.910434i | \(-0.364252\pi\) |
−0.581631 | + | 0.813453i | \(0.697585\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −270.000 | + | 342.946i | −0.528376 | + | 0.671127i | ||||
\(512\) | − | 627.000i | − | 1.22461i | ||||||
\(513\) | 46.7654 | + | 27.0000i | 0.0911606 | + | 0.0526316i | ||||
\(514\) | 297.000 | − | 171.473i | 0.577821 | − | 0.333605i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −555.000 | − | 320.429i | −1.07558 | − | 0.620987i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 129.904 | − | 165.000i | 0.250780 | − | 0.318533i | ||||
\(519\) | −396.000 | −0.763006 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −783.000 | + | 452.065i | −1.50288 | + | 0.867688i | −0.502885 | + | 0.864354i | \(0.667728\pi\) |
−0.999994 | + | 0.00333410i | \(0.998939\pi\) | |||||||
\(522\) | −70.1481 | + | 40.5000i | −0.134383 | + | 0.0775862i | ||||
\(523\) | 349.874 | − | 606.000i | 0.668976 | − | 1.15870i | −0.309215 | − | 0.950992i | \(-0.600066\pi\) |
0.978191 | − | 0.207708i | \(-0.0666003\pi\) | |||||||
\(524\) | 857.365i | 1.63619i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 558.000 | 1.06084 | ||||||||
\(527\) | 109.119 | + | 63.0000i | 0.207057 | + | 0.119545i | ||||
\(528\) | 142.894 | + | 247.500i | 0.270633 | + | 0.468750i | ||||
\(529\) | −264.500 | − | 458.127i | −0.500000 | − | 0.866025i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 46.7654i | − | 0.0880704i | ||||||
\(532\) | 337.750 | − | 135.000i | 0.634868 | − | 0.253759i | ||||
\(533\) | − | 144.000i | − | 0.270169i | ||||||
\(534\) | 189.000 | − | 327.358i | 0.353933 | − | 0.613029i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 114.000 | + | 197.454i | 0.212687 | + | 0.368384i | ||||
\(537\) | 77.9423 | − | 135.000i | 0.145144 | − | 0.251397i | ||||
\(538\) | 1013.25 | 1.88336 | ||||||||
\(539\) | 705.000 | + | 207.846i | 1.30798 | + | 0.385614i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −37.0000 | + | 64.0859i | −0.0683919 | + | 0.118458i | −0.898194 | − | 0.439600i | \(-0.855120\pi\) |
0.829802 | + | 0.558058i | \(0.188453\pi\) | |||||||
\(542\) | 137.698 | + | 238.500i | 0.254055 | + | 0.440037i | ||||
\(543\) | 15.5885 | − | 9.00000i | 0.0287080 | − | 0.0165746i | ||||
\(544\) | −405.000 | − | 233.827i | −0.744485 | − | 0.429829i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 468.000 | − | 187.061i | 0.857143 | − | 0.342603i | ||||
\(547\) | 934.000i | 1.70750i | 0.520687 | + | 0.853748i | \(0.325676\pi\) | ||||
−0.520687 | + | 0.853748i | \(0.674324\pi\) | |||||||
\(548\) | 415.692 | + | 240.000i | 0.758562 | + | 0.437956i | ||||
\(549\) | −234.000 | + | 135.100i | −0.426230 | + | 0.246084i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 81.0000 | + | 46.7654i | 0.147005 | + | 0.0848736i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 297.913 | + | 43.0000i | 0.538721 | + | 0.0777577i | ||||
\(554\) | −1140.00 | −2.05776 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 795.000 | − | 458.993i | 1.42986 | − | 0.825528i | ||||
\(557\) | −730.059 | + | 421.500i | −1.31070 | + | 0.756732i | −0.982212 | − | 0.187776i | \(-0.939872\pi\) |
−0.328487 | + | 0.944508i | \(0.606539\pi\) | |||||||
\(558\) | 54.5596 | − | 94.5000i | 0.0977771 | − | 0.169355i | ||||
\(559\) | 1025.37i | 1.83430i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 270.000 | 0.481283 | ||||||||
\(562\) | 779.423 | + | 450.000i | 1.38687 | + | 0.800712i | ||||
\(563\) | 475.448 | + | 823.500i | 0.844490 | + | 1.46270i | 0.886063 | + | 0.463564i | \(0.153430\pi\) |
−0.0415731 | + | 0.999135i | \(0.513237\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 613.146i | 1.08330i | ||||||||
\(567\) | −38.9711 | + | 49.5000i | −0.0687322 | + | 0.0873016i | ||||
\(568\) | 252.000i | 0.443662i | ||||||||
\(569\) | 111.000 | − | 192.258i | 0.195079 | − | 0.337887i | −0.751847 | − | 0.659337i | \(-0.770837\pi\) |
0.946926 | + | 0.321450i | \(0.104170\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −220.000 | − | 381.051i | −0.385289 | − | 0.667340i | 0.606520 | − | 0.795068i | \(-0.292565\pi\) |
−0.991809 | + | 0.127728i | \(0.959232\pi\) | |||||||
\(572\) | −519.615 | + | 900.000i | −0.908418 | + | 1.57343i | ||||
\(573\) | −540.400 | −0.943106 | ||||||||
\(574\) | 216.000 | + | 31.1769i | 0.376307 | + | 0.0543152i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −136.500 | + | 236.425i | −0.236979 | + | 0.410460i | ||||
\(577\) | −328.224 | − | 568.500i | −0.568845 | − | 0.985269i | −0.996681 | − | 0.0814120i | \(-0.974057\pi\) |
0.427835 | − | 0.903857i | \(-0.359276\pi\) | |||||||
\(578\) | 470.252 | − | 271.500i | 0.813584 | − | 0.469723i | ||||
\(579\) | 277.500 | + | 160.215i | 0.479275 | + | 0.276709i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 310.500 | + | 776.825i | 0.534423 | + | 1.33705i | ||||
\(582\) | 963.000i | 1.65464i | ||||||||
\(583\) | −428.683 | − | 247.500i | −0.735305 | − | 0.424528i | ||||
\(584\) | 162.000 | − | 93.5307i | 0.277397 | − | 0.160155i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1417.50 | + | 818.394i | 2.41894 | + | 1.39658i | ||||
\(587\) | 1054.82 | 1.79697 | 0.898483 | − | 0.439008i | \(-0.144670\pi\) | ||||
0.898483 | + | 0.439008i | \(0.144670\pi\) | |||||||
\(588\) | 99.5929 | + | 412.500i | 0.169376 | + | 0.701531i | ||||
\(589\) | −126.000 | −0.213922 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −495.000 | + | 285.788i | −0.837563 | + | 0.483567i | ||||
\(592\) | 95.2628 | − | 55.0000i | 0.160917 | − | 0.0929054i | ||||
\(593\) | −353.338 | + | 612.000i | −0.595849 | + | 1.03204i | 0.397578 | + | 0.917569i | \(0.369851\pi\) |
−0.993426 | + | 0.114472i | \(0.963482\pi\) | |||||||
\(594\) | − | 233.827i | − | 0.393648i | ||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −930.000 | −1.56040 | ||||||||
\(597\) | 10.3923 | + | 6.00000i | 0.0174075 | + | 0.0100503i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 258.000 | + | 446.869i | 0.430718 | + | 0.746025i | 0.996935 | − | 0.0782307i | \(-0.0249271\pi\) |
−0.566217 | + | 0.824256i | \(0.691594\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 247.683i | 0.412119i | 0.978540 | + | 0.206059i | \(0.0660640\pi\) | ||||
−0.978540 | + | 0.206059i | \(0.933936\pi\) | |||||||
\(602\) | −1538.06 | − | 222.000i | −2.55492 | − | 0.368771i | ||||
\(603\) | 228.000i | 0.378109i | ||||||||
\(604\) | 197.500 | − | 342.080i | 0.326987 | − | 0.566358i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 378.000 | + | 654.715i | 0.623762 | + | 1.08039i | ||||
\(607\) | −324.760 | + | 562.500i | −0.535024 | + | 0.926689i | 0.464138 | + | 0.885763i | \(0.346364\pi\) |
−0.999162 | + | 0.0409259i | \(0.986969\pi\) | |||||||
\(608\) | 467.654 | 0.769167 | ||||||||
\(609\) | −67.5000 | + | 85.7365i | −0.110837 | + | 0.140782i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 77.9423 | + | 135.000i | 0.127357 | + | 0.220588i | ||||
\(613\) | −772.495 | + | 446.000i | −1.26019 | + | 0.727569i | −0.973111 | − | 0.230338i | \(-0.926017\pi\) |
−0.287076 | + | 0.957908i | \(0.592683\pi\) | |||||||
\(614\) | −450.000 | − | 259.808i | −0.732899 | − | 0.423139i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −247.500 | − | 194.856i | −0.401786 | − | 0.316324i | ||||
\(617\) | 1224.00i | 1.98379i | 0.127050 | + | 0.991896i | \(0.459449\pi\) | ||||
−0.127050 | + | 0.991896i | \(0.540551\pi\) | |||||||
\(618\) | −311.769 | − | 180.000i | −0.504481 | − | 0.291262i | ||||
\(619\) | 348.000 | − | 200.918i | 0.562197 | − | 0.324585i | −0.191830 | − | 0.981428i | \(-0.561442\pi\) |
0.754027 | + | 0.656844i | \(0.228109\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −530.008 | −0.852102 | ||||||||
\(623\) | 72.7461 | − | 504.000i | 0.116767 | − | 0.808989i | ||||
\(624\) | 264.000 | 0.423077 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 553.500 | − | 319.563i | 0.884185 | − | 0.510485i | ||||
\(627\) | −233.827 | + | 135.000i | −0.372930 | + | 0.215311i | ||||
\(628\) | −51.9615 | + | 90.0000i | −0.0827413 | + | 0.143312i | ||||
\(629\) | − | 103.923i | − | 0.165219i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1115.00 | 1.76704 | 0.883518 | − | 0.468397i | \(-0.155168\pi\) | ||||
0.883518 | + | 0.468397i | \(0.155168\pi\) | |||||||
\(632\) | −111.717 | − | 64.5000i | −0.176768 | − | 0.102057i | ||||
\(633\) | 214.774 | + | 372.000i | 0.339296 | + | 0.587678i | ||||
\(634\) | 175.500 | + | 303.975i | 0.276814 | + | 0.479456i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | − | 285.788i | − | 0.449353i | ||||||
\(637\) | 491.902 | − | 468.000i | 0.772217 | − | 0.734694i | ||||
\(638\) | − | 405.000i | − | 0.634796i | ||||||
\(639\) | −126.000 | + | 218.238i | −0.197183 | + | 0.341531i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 192.000 | + | 332.554i | 0.299532 | + | 0.518805i | 0.976029 | − | 0.217641i | \(-0.0698361\pi\) |
−0.676497 | + | 0.736445i | \(0.736503\pi\) | |||||||
\(642\) | 241.621 | − | 418.500i | 0.376357 | − | 0.651869i | ||||
\(643\) | −6.92820 | −0.0107748 | −0.00538741 | − | 0.999985i | \(-0.501715\pi\) | ||||
−0.00538741 | + | 0.999985i | \(0.501715\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 162.000 | − | 280.592i | 0.250774 | − | 0.434353i | ||||
\(647\) | −446.869 | − | 774.000i | −0.690679 | − | 1.19629i | −0.971616 | − | 0.236564i | \(-0.923979\pi\) |
0.280937 | − | 0.959726i | \(-0.409355\pi\) | |||||||
\(648\) | 23.3827 | − | 13.5000i | 0.0360844 | − | 0.0208333i | ||||
\(649\) | 202.500 | + | 116.913i | 0.312018 | + | 0.180144i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 21.0000 | − | 145.492i | 0.0322581 | − | 0.223490i | ||||
\(652\) | 1040.00i | 1.59509i | ||||||||
\(653\) | −64.9519 | − | 37.5000i | −0.0994669 | − | 0.0574273i | 0.449441 | − | 0.893310i | \(-0.351623\pi\) |
−0.548908 | + | 0.835883i | \(0.684956\pi\) | |||||||
\(654\) | −36.0000 | + | 20.7846i | −0.0550459 | + | 0.0317807i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 99.0000 | + | 57.1577i | 0.150915 | + | 0.0871306i | ||||
\(657\) | 187.061 | 0.284721 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −642.000 | −0.974203 | −0.487102 | − | 0.873345i | \(-0.661946\pi\) | ||||
−0.487102 | + | 0.873345i | \(0.661946\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −243.000 | + | 140.296i | −0.367625 | + | 0.212248i | −0.672420 | − | 0.740170i | \(-0.734745\pi\) |
0.304795 | + | 0.952418i | \(0.401412\pi\) | |||||||
\(662\) | −103.923 | + | 60.0000i | −0.156983 | + | 0.0906344i | ||||
\(663\) | 124.708 | − | 216.000i | 0.188096 | − | 0.325792i | ||||
\(664\) | − | 358.535i | − | 0.539962i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −90.0000 | −0.135135 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 623.538 | + | 1080.00i | 0.933441 | + | 1.61677i | ||||
\(669\) | 166.500 | + | 288.386i | 0.248879 | + | 0.431071i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 1351.00i | − | 2.01341i | ||||||
\(672\) | −77.9423 | + | 540.000i | −0.115986 | + | 0.803571i | ||||
\(673\) | 13.0000i | 0.0193165i | 0.999953 | + | 0.00965825i | \(0.00307436\pi\) | ||||
−0.999953 | + | 0.00965825i | \(0.996926\pi\) | |||||||
\(674\) | 136.500 | − | 236.425i | 0.202522 | − | 0.350779i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 57.5000 | + | 99.5929i | 0.0850592 | + | 0.147327i | ||||
\(677\) | −631.333 | + | 1093.50i | −0.932544 | + | 1.61521i | −0.153589 | + | 0.988135i | \(0.549083\pi\) |
−0.778955 | + | 0.627079i | \(0.784250\pi\) | |||||||
\(678\) | 218.238 | 0.321886 | ||||||||
\(679\) | 481.500 | + | 1204.64i | 0.709131 | + | 1.77414i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 76.5000 | − | 132.502i | 0.112335 | − | 0.194570i | ||||
\(682\) | 272.798 | + | 472.500i | 0.399997 | + | 0.692815i | ||||
\(683\) | −839.179 | + | 484.500i | −1.22867 | + | 0.709370i | −0.966751 | − | 0.255721i | \(-0.917687\pi\) |
−0.261915 | + | 0.965091i | \(0.584354\pi\) | |||||||
\(684\) | −135.000 | − | 77.9423i | −0.197368 | − | 0.113951i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 595.500 | + | 839.179i | 0.868076 | + | 1.22329i | ||||
\(687\) | 570.000i | 0.829694i | ||||||||
\(688\) | −704.945 | − | 407.000i | −1.02463 | − | 0.591570i | ||||
\(689\) | −396.000 | + | 228.631i | −0.574746 | + | 0.331830i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −87.0000 | − | 50.2295i | −0.125904 | − | 0.0726910i | 0.435725 | − | 0.900080i | \(-0.356492\pi\) |
−0.561629 | + | 0.827389i | \(0.689825\pi\) | |||||||
\(692\) | 1143.15 | 1.65196 | ||||||||
\(693\) | −116.913 | − | 292.500i | −0.168706 | − | 0.422078i | ||||
\(694\) | −630.000 | −0.907781 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 40.5000 | − | 23.3827i | 0.0581897 | − | 0.0335958i | ||||
\(697\) | 93.5307 | − | 54.0000i | 0.134190 | − | 0.0774749i | ||||
\(698\) | 457.261 | − | 792.000i | 0.655102 | − | 1.13467i | ||||
\(699\) | 467.654i | 0.669033i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 597.000 | 0.851641 | 0.425820 | − | 0.904808i | \(-0.359986\pi\) | ||||
0.425820 | + | 0.904808i | \(0.359986\pi\) | |||||||
\(702\) | −187.061 | − | 108.000i | −0.266469 | − | 0.153846i | ||||
\(703\) | 51.9615 | + | 90.0000i | 0.0739140 | + | 0.128023i | ||||
\(704\) | −682.500 | − | 1182.12i | −0.969460 | − | 1.67915i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1184.72i | 1.67808i | ||||||||
\(707\) | 800.207 | + | 630.000i | 1.13184 | + | 0.891089i | ||||
\(708\) | 135.000i | 0.190678i | ||||||||
\(709\) | −415.000 | + | 718.801i | −0.585331 | + | 1.01382i | 0.409503 | + | 0.912309i | \(0.365702\pi\) |
−0.994834 | + | 0.101515i | \(0.967631\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −64.5000 | − | 111.717i | −0.0907173 | − | 0.157127i | ||||
\(712\) | −109.119 | + | 189.000i | −0.153257 | + | 0.265449i | ||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 297.000 | + | 233.827i | 0.415966 | + | 0.327489i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −225.000 | + | 389.711i | −0.314246 | + | 0.544290i | ||||
\(717\) | −197.454 | − | 342.000i | −0.275389 | − | 0.476987i | ||||
\(718\) | 1278.25 | − | 738.000i | 1.78030 | − | 1.02786i | ||||
\(719\) | −297.000 | − | 171.473i | −0.413074 | − | 0.238488i | 0.279036 | − | 0.960281i | \(-0.409985\pi\) |
−0.692110 | + | 0.721792i | \(0.743319\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −480.000 | − | 69.2820i | −0.665742 | − | 0.0960916i | ||||
\(722\) | − | 759.000i | − | 1.05125i | ||||||
\(723\) | −667.706 | − | 385.500i | −0.923521 | − | 0.533195i | ||||
\(724\) | −45.0000 | + | 25.9808i | −0.0621547 | + | 0.0358850i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 468.000 | + | 270.200i | 0.644628 | + | 0.372176i | ||||
\(727\) | −50.2295 | −0.0690914 | −0.0345457 | − | 0.999403i | \(-0.510998\pi\) | ||||
−0.0345457 | + | 0.999403i | \(0.510998\pi\) | |||||||
\(728\) | −270.200 | + | 108.000i | −0.371154 | + | 0.148352i | ||||
\(729\) | 27.0000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −666.000 | + | 384.515i | −0.911081 | + | 0.526013i | ||||
\(732\) | 675.500 | − | 390.000i | 0.922814 | − | 0.532787i | ||||
\(733\) | 91.7987 | − | 159.000i | 0.125237 | − | 0.216917i | −0.796589 | − | 0.604522i | \(-0.793364\pi\) |
0.921826 | + | 0.387605i | \(0.126698\pi\) | |||||||
\(734\) | 982.073i | 1.33797i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −987.269 | − | 570.000i | −1.33958 | − | 0.773406i | ||||
\(738\) | −46.7654 | − | 81.0000i | −0.0633677 | − | 0.109756i | ||||
\(739\) | −167.000 | − | 289.252i | −0.225981 | − | 0.391411i | 0.730632 | − | 0.682771i | \(-0.239225\pi\) |
−0.956613 | + | 0.291361i | \(0.905892\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 249.415i | 0.336593i | ||||||||
\(742\) | −257.210 | − | 643.500i | −0.346644 | − | 0.867251i | ||||
\(743\) | 84.0000i | 0.113055i | 0.998401 | + | 0.0565276i | \(0.0180029\pi\) | ||||
−0.998401 | + | 0.0565276i | \(0.981997\pi\) | |||||||
\(744\) | −31.5000 | + | 54.5596i | −0.0423387 | + | 0.0733328i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −255.000 | − | 441.673i | −0.341823 | − | 0.592055i | ||||
\(747\) | 179.267 | − | 310.500i | 0.239983 | − | 0.415663i | ||||
\(748\) | −779.423 | −1.04201 | ||||||||
\(749\) | 93.0000 | − | 644.323i | 0.124166 | − | 0.860244i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 179.500 | − | 310.903i | 0.239015 | − | 0.413986i | −0.721417 | − | 0.692501i | \(-0.756509\pi\) |
0.960432 | + | 0.278515i | \(0.0898423\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 7.79423 | − | 4.50000i | 0.0103509 | − | 0.00597610i | ||||
\(754\) | −324.000 | − | 187.061i | −0.429708 | − | 0.248092i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 112.500 | − | 142.894i | 0.148810 | − | 0.189013i | ||||
\(757\) | 80.0000i | 0.105680i | 0.998603 | + | 0.0528402i | \(0.0168274\pi\) | ||||
−0.998603 | + | 0.0528402i | \(0.983173\pi\) | |||||||
\(758\) | −213.042 | − | 123.000i | −0.281058 | − | 0.162269i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −702.000 | − | 405.300i | −0.922470 | − | 0.532589i | −0.0380481 | − | 0.999276i | \(-0.512114\pi\) |
−0.884422 | + | 0.466687i | \(0.845447\pi\) | |||||||
\(762\) | −181.865 | −0.238668 | ||||||||
\(763\) | −34.6410 | + | 44.0000i | −0.0454011 | + | 0.0576671i | ||||
\(764\) | 1560.00 | 2.04188 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −567.000 | + | 327.358i | −0.740209 | + | 0.427360i | ||||
\(767\) | 187.061 | − | 108.000i | 0.243887 | − | 0.140808i | ||||
\(768\) | −73.6122 | + | 127.500i | −0.0958492 | + | 0.166016i | ||||
\(769\) | − | 774.227i | − | 1.00680i | −0.864054 | − | 0.503398i | \(-0.832083\pi\) | ||
0.864054 | − | 0.503398i | \(-0.167917\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −198.000 | −0.256809 | ||||||||
\(772\) | −801.073 | − | 462.500i | −1.03766 | − | 0.599093i | ||||
\(773\) | −363.731 | − | 630.000i | −0.470544 | − | 0.815006i | 0.528888 | − | 0.848691i | \(-0.322609\pi\) |
−0.999433 | + | 0.0336850i | \(0.989276\pi\) | |||||||
\(774\) | 333.000 | + | 576.773i | 0.430233 | + | 0.745185i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | − | 555.988i | − | 0.716480i | ||||||
\(777\) | −112.583 | + | 45.0000i | −0.144895 | + | 0.0579151i | ||||
\(778\) | 918.000i | 1.17995i | ||||||||
\(779\) | −54.0000 | + | 93.5307i | −0.0693196 | + | 0.120065i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −630.000 | − | 1091.19i | −0.806658 | − | 1.39717i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 46.7654 | 0.0597259 | ||||||||
\(784\) | 126.500 | + | 523.945i | 0.161352 | + | 0.668298i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 445.500 | − | 771.629i | 0.566794 | − | 0.981716i | ||||
\(787\) | 713.605 | + | 1236.00i | 0.906741 | + | 1.57052i | 0.818563 | + | 0.574416i | \(0.194771\pi\) |
0.0881773 | + | 0.996105i | \(0.471896\pi\) | |||||||
\(788\) | 1428.94 | − | 825.000i | 1.81338 | − | 1.04695i | ||||
\(789\) | −279.000 | − | 161.081i | −0.353612 | − | 0.204158i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 273.000 | − | 109.119i | 0.345133 | − | 0.137951i | ||||
\(792\) | 135.000i | 0.170455i | ||||||||
\(793\) | −1080.80 | − | 624.000i | −1.36293 | − | 0.786885i | ||||
\(794\) | −666.000 | + | 384.515i | −0.838791 | + | 0.484276i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −30.0000 | − | 17.3205i | −0.0376884 | − | 0.0217594i | ||||
\(797\) | −607.950 | −0.762798 | −0.381399 | − | 0.924411i | \(-0.624558\pi\) | ||||
−0.381399 | + | 0.924411i | \(0.624558\pi\) | |||||||
\(798\) | −374.123 | − | 54.0000i | −0.468826 | − | 0.0676692i | ||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −189.000 | + | 109.119i | −0.235955 | + | 0.136229i | ||||
\(802\) | −342.946 | + | 198.000i | −0.427614 | + | 0.246883i | ||||
\(803\) | −467.654 | + | 810.000i | −0.582383 | + | 1.00872i | ||||
\(804\) | − | 658.179i | − | 0.818631i | ||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 504.000 | 0.625310 | ||||||||
\(807\) | −506.625 | − | 292.500i | −0.627788 | − | 0.362454i | ||||
\(808\) | −218.238 | − | 378.000i | −0.270097 | − | 0.467822i | ||||
\(809\) | −84.0000 | − | 145.492i | −0.103832 | − | 0.179842i | 0.809428 | − | 0.587218i | \(-0.199777\pi\) |
−0.913260 | + | 0.407376i | \(0.866444\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 353.338i | − | 0.435682i | −0.975984 | − | 0.217841i | \(-0.930099\pi\) | ||
0.975984 | − | 0.217841i | \(-0.0699015\pi\) | |||||||
\(812\) | 194.856 | − | 247.500i | 0.239970 | − | 0.304803i | ||||
\(813\) | − | 159.000i | − | 0.195572i | ||||||
\(814\) | 225.000 | − | 389.711i | 0.276413 | − | 0.478761i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 99.0000 | + | 171.473i | 0.121324 | + | 0.210139i | ||||
\(817\) | 384.515 | − | 666.000i | 0.470643 | − | 0.815177i | ||||
\(818\) | 1086.00 | 1.32762 | ||||||||
\(819\) | −288.000 | − | 41.5692i | −0.351648 | − | 0.0507561i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −142.500 | + | 246.817i | −0.173569 | + | 0.300630i | −0.939665 | − | 0.342096i | \(-0.888863\pi\) |
0.766096 | + | 0.642726i | \(0.222197\pi\) | |||||||
\(822\) | −249.415 | − | 432.000i | −0.303425 | − | 0.525547i | ||||
\(823\) | −237.291 | + | 137.000i | −0.288324 | + | 0.166464i | −0.637186 | − | 0.770710i | \(-0.719902\pi\) |
0.348862 | + | 0.937174i | \(0.386568\pi\) | |||||||
\(824\) | 180.000 | + | 103.923i | 0.218447 | + | 0.126120i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 121.500 | + | 303.975i | 0.147094 | + | 0.368008i | ||||
\(827\) | − | 429.000i | − | 0.518742i | −0.965778 | − | 0.259371i | \(-0.916485\pi\) | ||
0.965778 | − | 0.259371i | \(-0.0835153\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 819.000 | − | 472.850i | 0.987937 | − | 0.570386i | 0.0832802 | − | 0.996526i | \(-0.473460\pi\) |
0.904657 | + | 0.426140i | \(0.140127\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 570.000 | + | 329.090i | 0.685921 | + | 0.396016i | ||||
\(832\) | −1260.93 | −1.51554 | ||||||||
\(833\) | 488.438 | + | 144.000i | 0.586361 | + | 0.172869i | ||||
\(834\) | −954.000 | −1.14388 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 675.000 | − | 389.711i | 0.807416 | − | 0.466162i | ||||
\(837\) | −54.5596 | + | 31.5000i | −0.0651847 | + | 0.0376344i | ||||
\(838\) | −966.484 | + | 1674.00i | −1.15332 | + | 1.99761i | ||||
\(839\) | 259.808i | 0.309663i | 0.987941 | + | 0.154832i | \(0.0494835\pi\) | ||||
−0.987941 | + | 0.154832i | \(0.950516\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −760.000 | −0.903686 | ||||||||
\(842\) | 1953.75 | + | 1128.00i | 2.32037 | + | 1.33967i | ||||
\(843\) | −259.808 | − | 450.000i | −0.308194 | − | 0.533808i | ||||
\(844\) | −620.000 | − | 1073.87i | −0.734597 | − | 1.27236i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 720.533 | + | 104.000i | 0.850688 | + | 0.122786i | ||||
\(848\) | − | 363.000i | − | 0.428066i | ||||||
\(849\) | 177.000 | − | 306.573i | 0.208481 | − | 0.361099i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 363.731 | − | 630.000i | 0.426914 | − | 0.739437i | ||||
\(853\) | 997.661 | 1.16959 | 0.584796 | − | 0.811181i | \(-0.301175\pi\) | ||||
0.584796 | + | 0.811181i | \(0.301175\pi\) | |||||||
\(854\) | 1170.00 | − | 1486.10i | 1.37002 | − | 1.74016i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −139.500 | + | 241.621i | −0.162967 | + | 0.282268i | ||||
\(857\) | −218.238 | − | 378.000i | −0.254654 | − | 0.441074i | 0.710148 | − | 0.704053i | \(-0.248628\pi\) |
−0.964801 | + | 0.262979i | \(0.915295\pi\) | |||||||
\(858\) | 935.307 | − | 540.000i | 1.09010 | − | 0.629371i | ||||
\(859\) | 393.000 | + | 226.899i | 0.457509 | + | 0.264143i | 0.710996 | − | 0.703196i | \(-0.248244\pi\) |
−0.253487 | + | 0.967339i | \(0.581578\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −99.0000 | − | 77.9423i | −0.114983 | − | 0.0905253i | ||||
\(862\) | − | 486.000i | − | 0.563805i | ||||||
\(863\) | 337.750 | + | 195.000i | 0.391367 | + | 0.225956i | 0.682752 | − | 0.730650i | \(-0.260783\pi\) |
−0.291385 | + | 0.956606i | \(0.594116\pi\) | |||||||
\(864\) | 202.500 | − | 116.913i | 0.234375 | − | 0.135316i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −882.000 | − | 509.223i | −1.01848 | − | 0.588017i | ||||
\(867\) | −313.501 | −0.361593 | ||||||||
\(868\) | −60.6218 | + | 420.000i | −0.0698408 | + | 0.483871i | ||||
\(869\) | 645.000 | 0.742232 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −912.000 | + | 526.543i | −1.04707 | + | 0.604527i | ||||
\(872\) | 20.7846 | − | 12.0000i | 0.0238356 | − | 0.0137615i | ||||
\(873\) | 277.994 | − | 481.500i | 0.318435 | − | 0.551546i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −540.000 | −0.616438 | ||||||||
\(877\) | −471.118 | − | 272.000i | −0.537192 | − | 0.310148i | 0.206748 | − | 0.978394i | \(-0.433712\pi\) |
−0.743940 | + | 0.668246i | \(0.767045\pi\) | |||||||
\(878\) | −584.567 | − | 1012.50i | −0.665794 | − | 1.15319i | ||||
\(879\) | −472.500 | − | 818.394i | −0.537543 | − | 0.931051i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 187.061i | 0.212329i | 0.994349 | + | 0.106164i | \(0.0338569\pi\) | ||||
−0.994349 | + | 0.106164i | \(0.966143\pi\) | |||||||
\(882\) | 124.708 | − | 423.000i | 0.141392 | − | 0.479592i | ||||
\(883\) | 322.000i | 0.364666i | 0.983237 | + | 0.182333i | \(0.0583649\pi\) | ||||
−0.983237 | + | 0.182333i | \(0.941635\pi\) | |||||||
\(884\) | −360.000 | + | 623.538i | −0.407240 | + | 0.705360i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 445.500 | + | 771.629i | 0.502822 | + | 0.870913i | ||||
\(887\) | 353.338 | − | 612.000i | 0.398352 | − | 0.689966i | −0.595171 | − | 0.803599i | \(-0.702916\pi\) |
0.993523 | + | 0.113633i | \(0.0362489\pi\) | |||||||
\(888\) | 51.9615 | 0.0585152 | ||||||||
\(889\) | −227.500 | + | 90.9327i | −0.255906 | + | 0.102286i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −67.5000 | + | 116.913i | −0.0757576 | + | 0.131216i | ||||
\(892\) | −480.644 | − | 832.500i | −0.538839 | − | 0.933296i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 837.000 | + | 483.242i | 0.936242 | + | 0.540539i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 93.0000 | − | 644.323i | 0.103795 | − | 0.719110i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 1278.25 | + | 738.000i | 1.42344 | + | 0.821826i | ||||
\(899\) | −94.5000 | + | 54.5596i | −0.105117 | + | 0.0606892i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −297.000 | − | 171.473i | −0.329634 | − | 0.190314i | ||||
\(902\) | 467.654 | 0.518463 | ||||||||
\(903\) | 704.945 | + | 555.000i | 0.780670 | + | 0.614618i | ||||
\(904\) | −126.000 | −0.139381 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −355.500 | + | 205.248i | −0.392384 | + | 0.226543i | ||||
\(907\) | 952.628 | − | 550.000i | 1.05031 | − | 0.606395i | 0.127571 | − | 0.991829i | \(-0.459282\pi\) |
0.922735 | + | 0.385435i | \(0.125948\pi\) | |||||||
\(908\) | −220.836 | + | 382.500i | −0.243212 | + | 0.421256i | ||||
\(909\) | − | 436.477i | − | 0.480173i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 900.000 | 0.987925 | 0.493963 | − | 0.869483i | \(-0.335548\pi\) | ||||
0.493963 | + | 0.869483i | \(0.335548\pi\) | |||||||
\(912\) | −171.473 | − | 99.0000i | −0.188019 | − | 0.108553i | ||||
\(913\) | 896.336 | + | 1552.50i | 0.981748 | + | 1.70044i | ||||
\(914\) | −664.500 | − | 1150.95i | −0.727024 | − | 1.25924i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 1645.45i | − | 1.79634i | ||||||
\(917\) | 171.473 | − | 1188.00i | 0.186993 | − | 1.29553i | ||||
\(918\) | − | 162.000i | − | 0.176471i | ||||||
\(919\) | −859.000 | + | 1487.83i | −0.934712 | + | 1.61897i | −0.159564 | + | 0.987188i | \(0.551009\pi\) |
−0.775147 | + | 0.631781i | \(0.782324\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 150.000 | + | 259.808i | 0.162866 | + | 0.282093i | ||||
\(922\) | 623.538 | − | 1080.00i | 0.676289 | − | 1.17137i | ||||
\(923\) | −1163.94 | −1.26104 | ||||||||
\(924\) | 337.500 | + | 844.375i | 0.365260 | + | 0.913826i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 123.000 | − | 213.042i | 0.132829 | − | 0.230067i | ||||
\(927\) | 103.923 | + | 180.000i | 0.112107 | + | 0.194175i | ||||
\(928\) | 350.740 | − | 202.500i | 0.377953 | − | 0.218211i | ||||
\(929\) | 1287.00 | + | 743.050i | 1.38536 | + | 0.799838i | 0.992788 | − | 0.119883i | \(-0.0382519\pi\) |
0.392573 | + | 0.919721i | \(0.371585\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −495.000 | + | 119.512i | −0.531686 | + | 0.128369i | ||||
\(932\) | − | 1350.00i | − | 1.44850i | ||||||
\(933\) | 265.004 | + | 153.000i | 0.284034 | + | 0.163987i | ||||
\(934\) | 702.000 | − | 405.300i | 0.751606 | − | 0.433940i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 108.000 | + | 62.3538i | 0.115385 | + | 0.0666173i | ||||
\(937\) | 957.824 | 1.02222 | 0.511112 | − | 0.859514i | \(-0.329234\pi\) | ||||
0.511112 | + | 0.859514i | \(0.329234\pi\) | |||||||
\(938\) | −592.361 | − | 1482.00i | −0.631515 | − | 1.57996i | ||||
\(939\) | −369.000 | −0.392971 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 310.500 | − | 179.267i | 0.329968 | − | 0.190507i | −0.325859 | − | 0.945418i | \(-0.605653\pi\) |
0.655827 | + | 0.754911i | \(0.272320\pi\) | |||||||
\(942\) | 93.5307 | − | 54.0000i | 0.0992895 | − | 0.0573248i | ||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 171.473i | 0.181645i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −3330.00 | −3.52008 | ||||||||
\(947\) | 140.296 | + | 81.0000i | 0.148148 | + | 0.0855333i | 0.572242 | − | 0.820085i | \(-0.306074\pi\) |
−0.424094 | + | 0.905618i | \(0.639407\pi\) | |||||||
\(948\) | 186.195 | + | 322.500i | 0.196409 | + | 0.340190i | ||||
\(949\) | 432.000 | + | 748.246i | 0.455216 | + | 0.788457i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 202.650i | − | 0.213091i | ||||||
\(952\) | −171.473 | − | 135.000i | −0.180119 | − | 0.141807i | ||||
\(953\) | − | 954.000i | − | 1.00105i | −0.865722 | − | 0.500525i | \(-0.833140\pi\) | ||
0.865722 | − | 0.500525i | \(-0.166860\pi\) | |||||||
\(954\) | −148.500 | + | 257.210i | −0.155660 | + | 0.269612i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 570.000 | + | 987.269i | 0.596234 | + | 1.03271i | ||||
\(957\) | −116.913 | + | 202.500i | −0.122167 | + | 0.211599i | ||||
\(958\) | −1028.84 | −1.07394 | ||||||||
\(959\) | −528.000 | − | 415.692i | −0.550574 | − | 0.433464i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −407.000 | + | 704.945i | −0.423517 | + | 0.733553i | ||||
\(962\) | −207.846 | − | 360.000i | −0.216056 | − | 0.374220i | ||||
\(963\) | −241.621 | + | 139.500i | −0.250905 | + | 0.144860i | ||||
\(964\) | 1927.50 | + | 1112.84i | 1.99948 | + | 1.15440i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 751.000i | 0.776629i | 0.921527 | + | 0.388314i | \(0.126943\pi\) | ||||
−0.921527 | + | 0.388314i | \(0.873057\pi\) | |||||||
\(968\) | −270.200 | − | 156.000i | −0.279132 | − | 0.161157i | ||||
\(969\) | −162.000 | + | 93.5307i | −0.167183 | + | 0.0965230i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −247.500 | − | 142.894i | −0.254892 | − | 0.147162i | 0.367110 | − | 0.930177i | \(-0.380347\pi\) |
−0.622002 | + | 0.783016i | \(0.713680\pi\) | |||||||
\(972\) | −77.9423 | −0.0801875 | ||||||||
\(973\) | −1193.38 | + | 477.000i | −1.22650 | + | 0.490236i | ||||
\(974\) | 951.000 | 0.976386 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 858.000 | − | 495.367i | 0.879098 | − | 0.507548i | ||||
\(977\) | 15.5885 | − | 9.00000i | 0.0159554 | − | 0.00921187i | −0.492001 | − | 0.870595i | \(-0.663734\pi\) |
0.507957 | + | 0.861383i | \(0.330401\pi\) | |||||||
\(978\) | 540.400 | − | 936.000i | 0.552556 | − | 0.957055i | ||||
\(979\) | − | 1091.19i | − | 1.11460i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 24.0000 | 0.0244648 | ||||||||
\(982\) | 70.1481 | + | 40.5000i | 0.0714339 | + | 0.0412424i | ||||
\(983\) | −493.634 | − | 855.000i | −0.502171 | − | 0.869786i | −0.999997 | − | 0.00250913i | \(-0.999201\pi\) |
0.497825 | − | 0.867277i | \(-0.334132\pi\) | |||||||
\(984\) | 27.0000 | + | 46.7654i | 0.0274390 | + | 0.0475258i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | − | 280.592i | − | 0.284576i | ||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | − | 720.000i | − | 0.728745i | ||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −351.500 | − | 608.816i | −0.354692 | − | 0.614345i | 0.632373 | − | 0.774664i | \(-0.282081\pi\) |
−0.987065 | + | 0.160319i | \(0.948748\pi\) | |||||||
\(992\) | −272.798 | + | 472.500i | −0.274998 | + | 0.476310i | ||||
\(993\) | 69.2820 | 0.0697704 | ||||||||
\(994\) | 252.000 | − | 1745.91i | 0.253521 | − | 1.75645i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −517.500 | + | 896.336i | −0.519578 | + | 0.899936i | ||||
\(997\) | −107.387 | − | 186.000i | −0.107710 | − | 0.186560i | 0.807132 | − | 0.590371i | \(-0.201019\pi\) |
−0.914842 | + | 0.403811i | \(0.867685\pi\) | |||||||
\(998\) | −1158.74 | + | 669.000i | −1.16106 | + | 0.670341i | ||||
\(999\) | 45.0000 | + | 25.9808i | 0.0450450 | + | 0.0260068i |
(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 | 525.3.s.e.124.2 | 4 | ||
5.2 | odd | 4 | 21.3.f.a.19.1 | yes | 2 | ||
5.3 | odd | 4 | 525.3.o.h.376.1 | 2 | |||
5.4 | even | 2 | inner | 525.3.s.e.124.1 | 4 | ||
7.3 | odd | 6 | inner | 525.3.s.e.199.1 | 4 | ||
15.2 | even | 4 | 63.3.m.d.19.1 | 2 | |||
20.7 | even | 4 | 336.3.bh.d.145.1 | 2 | |||
35.2 | odd | 12 | 147.3.d.c.97.1 | 2 | |||
35.3 | even | 12 | 525.3.o.h.451.1 | 2 | |||
35.12 | even | 12 | 147.3.d.c.97.2 | 2 | |||
35.17 | even | 12 | 21.3.f.a.10.1 | ✓ | 2 | ||
35.24 | odd | 6 | inner | 525.3.s.e.199.2 | 4 | ||
35.27 | even | 4 | 147.3.f.a.19.1 | 2 | |||
35.32 | odd | 12 | 147.3.f.a.31.1 | 2 | |||
60.47 | odd | 4 | 1008.3.cg.a.145.1 | 2 | |||
105.2 | even | 12 | 441.3.d.a.244.2 | 2 | |||
105.17 | odd | 12 | 63.3.m.d.10.1 | 2 | |||
105.32 | even | 12 | 441.3.m.g.325.1 | 2 | |||
105.47 | odd | 12 | 441.3.d.a.244.1 | 2 | |||
105.62 | odd | 4 | 441.3.m.g.19.1 | 2 | |||
140.47 | odd | 12 | 2352.3.f.a.97.1 | 2 | |||
140.87 | odd | 12 | 336.3.bh.d.241.1 | 2 | |||
140.107 | even | 12 | 2352.3.f.a.97.2 | 2 | |||
420.227 | even | 12 | 1008.3.cg.a.577.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
21.3.f.a.10.1 | ✓ | 2 | 35.17 | even | 12 | ||
21.3.f.a.19.1 | yes | 2 | 5.2 | odd | 4 | ||
63.3.m.d.10.1 | 2 | 105.17 | odd | 12 | |||
63.3.m.d.19.1 | 2 | 15.2 | even | 4 | |||
147.3.d.c.97.1 | 2 | 35.2 | odd | 12 | |||
147.3.d.c.97.2 | 2 | 35.12 | even | 12 | |||
147.3.f.a.19.1 | 2 | 35.27 | even | 4 | |||
147.3.f.a.31.1 | 2 | 35.32 | odd | 12 | |||
336.3.bh.d.145.1 | 2 | 20.7 | even | 4 | |||
336.3.bh.d.241.1 | 2 | 140.87 | odd | 12 | |||
441.3.d.a.244.1 | 2 | 105.47 | odd | 12 | |||
441.3.d.a.244.2 | 2 | 105.2 | even | 12 | |||
441.3.m.g.19.1 | 2 | 105.62 | odd | 4 | |||
441.3.m.g.325.1 | 2 | 105.32 | even | 12 | |||
525.3.o.h.376.1 | 2 | 5.3 | odd | 4 | |||
525.3.o.h.451.1 | 2 | 35.3 | even | 12 | |||
525.3.s.e.124.1 | 4 | 5.4 | even | 2 | inner | ||
525.3.s.e.124.2 | 4 | 1.1 | even | 1 | trivial | ||
525.3.s.e.199.1 | 4 | 7.3 | odd | 6 | inner | ||
525.3.s.e.199.2 | 4 | 35.24 | odd | 6 | inner | ||
1008.3.cg.a.145.1 | 2 | 60.47 | odd | 4 | |||
1008.3.cg.a.577.1 | 2 | 420.227 | even | 12 | |||
2352.3.f.a.97.1 | 2 | 140.47 | odd | 12 | |||
2352.3.f.a.97.2 | 2 | 140.107 | even | 12 |