Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [63,3,Mod(10,63)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(63, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("63.10");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 63 = 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 63.m (of order \(6\), 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: | \(1.71662566547\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 21) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 19.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 63.19 |
Dual form | 63.3.m.d.10.1 |
$q$-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 \(\left(\mathbb{Z}/63\mathbb{Z}\right)^\times\).
\(n\) | \(10\) | \(29\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.50000 | − | 2.59808i | 0.750000 | − | 1.29904i | −0.197822 | − | 0.980238i | \(-0.563387\pi\) |
0.947822 | − | 0.318800i | \(-0.103280\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −2.50000 | − | 4.33013i | −0.625000 | − | 1.08253i | ||||
\(5\) | −4.50000 | − | 2.59808i | −0.900000 | − | 0.519615i | −0.0227998 | − | 0.999740i | \(-0.507258\pi\) |
−0.877200 | + | 0.480125i | \(0.840591\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 6.50000 | − | 2.59808i | 0.928571 | − | 0.371154i | ||||
\(8\) | −3.00000 | −0.375000 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −13.5000 | + | 7.79423i | −1.35000 | + | 0.779423i | ||||
\(11\) | 7.50000 | + | 12.9904i | 0.681818 | + | 1.18094i | 0.974425 | + | 0.224711i | \(0.0721438\pi\) |
−0.292607 | + | 0.956233i | \(0.594523\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 13.8564i | 1.06588i | 0.846154 | + | 0.532939i | \(0.178912\pi\) | ||||
−0.846154 | + | 0.532939i | \(0.821088\pi\) | |||||||
\(14\) | 3.00000 | − | 20.7846i | 0.214286 | − | 1.48461i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 5.50000 | − | 9.52628i | 0.343750 | − | 0.595392i | ||||
\(17\) | −9.00000 | + | 5.19615i | −0.529412 | + | 0.305656i | −0.740777 | − | 0.671751i | \(-0.765542\pi\) |
0.211365 | + | 0.977407i | \(0.432209\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −9.00000 | − | 5.19615i | −0.473684 | − | 0.273482i | 0.244096 | − | 0.969751i | \(-0.421509\pi\) |
−0.717781 | + | 0.696269i | \(0.754842\pi\) | |||||||
\(20\) | 25.9808i | 1.29904i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 45.0000 | 2.04545 | ||||||||
\(23\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | + | 1.73205i | 0.0400000 | + | 0.0692820i | ||||
\(26\) | 36.0000 | + | 20.7846i | 1.38462 | + | 0.799408i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −27.5000 | − | 21.6506i | −0.982143 | − | 0.773237i | ||||
\(29\) | 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 | \(0.395984\pi\) | |||||||
\(32\) | −22.5000 | − | 38.9711i | −0.703125 | − | 1.21785i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 31.1769i | 0.916968i | ||||||||
\(35\) | −36.0000 | − | 5.19615i | −1.02857 | − | 0.148461i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.00000 | + | 8.66025i | −0.135135 | + | 0.234061i | −0.925649 | − | 0.378383i | \(-0.876480\pi\) |
0.790514 | + | 0.612444i | \(0.209814\pi\) | |||||||
\(38\) | −27.0000 | + | 15.5885i | −0.710526 | + | 0.410223i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 13.5000 | + | 7.79423i | 0.337500 | + | 0.194856i | ||||
\(41\) | − | 10.3923i | − | 0.253471i | −0.991937 | − | 0.126735i | \(-0.959550\pi\) | ||
0.991937 | − | 0.126735i | \(-0.0404499\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −74.0000 | −1.72093 | −0.860465 | − | 0.509509i | \(-0.829827\pi\) | ||||
−0.860465 | + | 0.509509i | \(0.829827\pi\) | |||||||
\(44\) | 37.5000 | − | 64.9519i | 0.852273 | − | 1.47618i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 35.5000 | − | 33.7750i | 0.724490 | − | 0.689286i | ||||
\(50\) | 6.00000 | 0.120000 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 60.0000 | − | 34.6410i | 1.15385 | − | 0.666173i | ||||
\(53\) | 16.5000 | + | 28.5788i | 0.311321 | + | 0.539223i | 0.978649 | − | 0.205541i | \(-0.0658953\pi\) |
−0.667328 | + | 0.744764i | \(0.732562\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 77.9423i | − | 1.41713i | ||||||
\(56\) | −19.5000 | + | 7.79423i | −0.348214 | + | 0.139183i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 13.5000 | − | 23.3827i | 0.232759 | − | 0.403150i | ||||
\(59\) | −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 | \(0.402319\pi\) | |||||||
\(62\) | 36.3731i | 0.586662i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −91.0000 | −1.42188 | ||||||||
\(65\) | 36.0000 | − | 62.3538i | 0.553846 | − | 0.959290i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 38.0000 | + | 65.8179i | 0.567164 | + | 0.982357i | 0.996845 | + | 0.0793762i | \(0.0252928\pi\) |
−0.429681 | + | 0.902981i | \(0.641374\pi\) | |||||||
\(68\) | 45.0000 | + | 25.9808i | 0.661765 | + | 0.382070i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −67.5000 | + | 85.7365i | −0.964286 | + | 1.22481i | ||||
\(71\) | −84.0000 | −1.18310 | −0.591549 | − | 0.806269i | \(-0.701483\pi\) | ||||
−0.591549 | + | 0.806269i | \(0.701483\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −54.0000 | + | 31.1769i | −0.739726 | + | 0.427081i | −0.821970 | − | 0.569531i | \(-0.807125\pi\) |
0.0822437 | + | 0.996612i | \(0.473791\pi\) | |||||||
\(74\) | 15.0000 | + | 25.9808i | 0.202703 | + | 0.351091i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 51.9615i | 0.683704i | ||||||||
\(77\) | 82.5000 | + | 64.9519i | 1.07143 | + | 0.843531i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 21.5000 | − | 37.2391i | 0.272152 | − | 0.471381i | −0.697261 | − | 0.716818i | \(-0.745598\pi\) |
0.969413 | + | 0.245437i | \(0.0789313\pi\) | |||||||
\(80\) | −49.5000 | + | 28.5788i | −0.618750 | + | 0.357235i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −27.0000 | − | 15.5885i | −0.329268 | − | 0.190103i | ||||
\(83\) | − | 119.512i | − | 1.43990i | −0.694027 | − | 0.719949i | \(-0.744165\pi\) | ||
0.694027 | − | 0.719949i | \(-0.255835\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 54.0000 | 0.635294 | ||||||||
\(86\) | −111.000 | + | 192.258i | −1.29070 | + | 2.23555i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −22.5000 | − | 38.9711i | −0.255682 | − | 0.442854i | ||||
\(89\) | 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 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 27.0000 | + | 46.7654i | 0.284211 | + | 0.492267i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 185.329i | − | 1.91061i | −0.295618 | − | 0.955306i | \(-0.595525\pi\) | ||
0.295618 | − | 0.955306i | \(-0.404475\pi\) | |||||||
\(98\) | −34.5000 | − | 142.894i | −0.352041 | − | 1.45810i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 5.00000 | − | 8.66025i | 0.0500000 | − | 0.0866025i | ||||
\(101\) | 126.000 | − | 72.7461i | 1.24752 | − | 0.720259i | 0.276910 | − | 0.960896i | \(-0.410690\pi\) |
0.970615 | + | 0.240637i | \(0.0773564\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −60.0000 | − | 34.6410i | −0.582524 | − | 0.336321i | 0.179612 | − | 0.983738i | \(-0.442516\pi\) |
−0.762136 | + | 0.647417i | \(0.775849\pi\) | |||||||
\(104\) | − | 41.5692i | − | 0.399704i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 99.0000 | 0.933962 | ||||||||
\(107\) | 46.5000 | − | 80.5404i | 0.434579 | − | 0.752714i | −0.562682 | − | 0.826674i | \(-0.690230\pi\) |
0.997261 | + | 0.0739599i | \(0.0235637\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.00000 | + | 6.92820i | 0.0366972 | + | 0.0635615i | 0.883791 | − | 0.467882i | \(-0.154983\pi\) |
−0.847093 | + | 0.531444i | \(0.821650\pi\) | |||||||
\(110\) | −202.500 | − | 116.913i | −1.84091 | − | 1.06285i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 11.0000 | − | 76.2102i | 0.0982143 | − | 0.680449i | ||||
\(113\) | −42.0000 | −0.371681 | −0.185841 | − | 0.982580i | \(-0.559501\pi\) | ||||
−0.185841 | + | 0.982580i | \(0.559501\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −22.5000 | − | 38.9711i | −0.193966 | − | 0.335958i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 46.7654i | 0.396317i | ||||||||
\(119\) | −45.0000 | + | 57.1577i | −0.378151 | + | 0.480317i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −52.0000 | + | 90.0666i | −0.429752 | + | 0.744352i | ||||
\(122\) | 234.000 | − | 135.100i | 1.91803 | − | 1.10738i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 52.5000 | + | 30.3109i | 0.423387 | + | 0.244443i | ||||
\(125\) | 119.512i | 0.956092i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 35.0000 | 0.275591 | 0.137795 | − | 0.990461i | \(-0.455998\pi\) | ||||
0.137795 | + | 0.990461i | \(0.455998\pi\) | |||||||
\(128\) | −46.5000 | + | 80.5404i | −0.363281 | + | 0.629222i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −108.000 | − | 187.061i | −0.830769 | − | 1.43893i | ||||
\(131\) | −148.500 | − | 85.7365i | −1.13359 | − | 0.654477i | −0.188753 | − | 0.982025i | \(-0.560445\pi\) |
−0.944835 | + | 0.327547i | \(0.893778\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −72.0000 | − | 10.3923i | −0.541353 | − | 0.0781376i | ||||
\(134\) | 228.000 | 1.70149 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 27.0000 | − | 15.5885i | 0.198529 | − | 0.114621i | ||||
\(137\) | −48.0000 | − | 83.1384i | −0.350365 | − | 0.606850i | 0.635948 | − | 0.771732i | \(-0.280609\pi\) |
−0.986313 | + | 0.164882i | \(0.947276\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 183.597i | 1.32084i | 0.750894 | + | 0.660422i | \(0.229623\pi\) | ||||
−0.750894 | + | 0.660422i | \(0.770377\pi\) | |||||||
\(140\) | 67.5000 | + | 168.875i | 0.482143 | + | 1.20625i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −126.000 | + | 218.238i | −0.887324 | + | 1.53689i | ||||
\(143\) | −180.000 | + | 103.923i | −1.25874 | + | 0.726735i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −40.5000 | − | 23.3827i | −0.279310 | − | 0.161260i | ||||
\(146\) | 187.061i | 1.28124i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 50.0000 | 0.337838 | ||||||||
\(149\) | −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 | \(0.917580\pi\) | |||||||
\(152\) | 27.0000 | + | 15.5885i | 0.177632 | + | 0.102556i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 292.500 | − | 116.913i | 1.89935 | − | 0.759178i | ||||
\(155\) | 63.0000 | 0.406452 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −18.0000 | + | 10.3923i | −0.114650 | + | 0.0661930i | −0.556228 | − | 0.831030i | \(-0.687752\pi\) |
0.441579 | + | 0.897223i | \(0.354419\pi\) | |||||||
\(158\) | −64.5000 | − | 111.717i | −0.408228 | − | 0.707071i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 233.827i | 1.46142i | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 104.000 | − | 180.133i | 0.638037 | − | 1.10511i | −0.347826 | − | 0.937559i | \(-0.613080\pi\) |
0.985863 | − | 0.167553i | \(-0.0535866\pi\) | |||||||
\(164\) | −45.0000 | + | 25.9808i | −0.274390 | + | 0.158419i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −310.500 | − | 179.267i | −1.87048 | − | 1.07992i | ||||
\(167\) | − | 249.415i | − | 1.49350i | −0.665102 | − | 0.746752i | \(-0.731612\pi\) | ||
0.665102 | − | 0.746752i | \(-0.268388\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −23.0000 | −0.136095 | ||||||||
\(170\) | 81.0000 | − | 140.296i | 0.476471 | − | 0.825271i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 185.000 | + | 320.429i | 1.07558 | + | 1.86296i | ||||
\(173\) | 198.000 | + | 114.315i | 1.14451 | + | 0.660782i | 0.947543 | − | 0.319628i | \(-0.103558\pi\) |
0.196966 | + | 0.980410i | \(0.436891\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 11.0000 | + | 8.66025i | 0.0628571 | + | 0.0494872i | ||||
\(176\) | 165.000 | 0.937500 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 189.000 | − | 109.119i | 1.06180 | − | 0.613029i | ||||
\(179\) | 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 | \(0.990861\pi\) | |||||||
\(182\) | 288.000 | + | 41.5692i | 1.58242 | + | 0.228402i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 45.0000 | − | 25.9808i | 0.243243 | − | 0.140437i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −135.000 | − | 77.9423i | −0.721925 | − | 0.416804i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 162.000 | 0.852632 | ||||||||
\(191\) | −156.000 | + | 270.200i | −0.816754 | + | 1.41466i | 0.0913077 | + | 0.995823i | \(0.470895\pi\) |
−0.908062 | + | 0.418837i | \(0.862438\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 92.5000 | + | 160.215i | 0.479275 | + | 0.830128i | 0.999717 | − | 0.0237685i | \(-0.00756646\pi\) |
−0.520443 | + | 0.853896i | \(0.674233\pi\) | |||||||
\(194\) | −481.500 | − | 277.994i | −2.48196 | − | 1.43296i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −235.000 | − | 69.2820i | −1.19898 | − | 0.353480i | ||||
\(197\) | −330.000 | −1.67513 | −0.837563 | − | 0.546340i | \(-0.816021\pi\) | ||||
−0.837563 | + | 0.546340i | \(0.816021\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.00000 | − | 3.46410i | 0.0301508 | − | 0.0174075i | −0.484849 | − | 0.874598i | \(-0.661125\pi\) |
0.515000 | + | 0.857190i | \(0.327792\pi\) | |||||||
\(200\) | −3.00000 | − | 5.19615i | −0.0150000 | − | 0.0259808i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − | 436.477i | − | 2.16078i | ||||||
\(203\) | 58.5000 | − | 23.3827i | 0.288177 | − | 0.115186i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −27.0000 | + | 46.7654i | −0.131707 | + | 0.228124i | ||||
\(206\) | −180.000 | + | 103.923i | −0.873786 | + | 0.504481i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 132.000 | + | 76.2102i | 0.634615 | + | 0.366395i | ||||
\(209\) | − | 155.885i | − | 0.745859i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −248.000 | −1.17536 | −0.587678 | − | 0.809095i | \(-0.699958\pi\) | ||||
−0.587678 | + | 0.809095i | \(0.699958\pi\) | |||||||
\(212\) | 82.5000 | − | 142.894i | 0.389151 | − | 0.674029i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −139.500 | − | 241.621i | −0.651869 | − | 1.12907i | ||||
\(215\) | 333.000 | + | 192.258i | 1.54884 | + | 0.894222i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −52.5000 | + | 66.6840i | −0.241935 | + | 0.307299i | ||||
\(218\) | 24.0000 | 0.110092 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −337.500 | + | 194.856i | −1.53409 | + | 0.885708i | ||||
\(221\) | −72.0000 | − | 124.708i | −0.325792 | − | 0.564288i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 192.258i | 0.862142i | 0.902318 | + | 0.431071i | \(0.141864\pi\) | ||||
−0.902318 | + | 0.431071i | \(0.858136\pi\) | |||||||
\(224\) | −247.500 | − | 194.856i | −1.10491 | − | 0.869892i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −63.0000 | + | 109.119i | −0.278761 | + | 0.482828i | ||||
\(227\) | 76.5000 | − | 44.1673i | 0.337004 | − | 0.194570i | −0.321942 | − | 0.946759i | \(-0.604336\pi\) |
0.658947 | + | 0.752190i | \(0.271002\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 285.000 | + | 164.545i | 1.24454 | + | 0.718536i | 0.970015 | − | 0.243043i | \(-0.0781457\pi\) |
0.274526 | + | 0.961580i | \(0.411479\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −27.0000 | −0.116379 | ||||||||
\(233\) | 135.000 | − | 233.827i | 0.579399 | − | 1.00355i | −0.416149 | − | 0.909296i | \(-0.636621\pi\) |
0.995548 | − | 0.0942524i | \(-0.0300461\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 67.5000 | + | 38.9711i | 0.286017 | + | 0.165132i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 81.0000 | + | 202.650i | 0.340336 | + | 0.851470i | ||||
\(239\) | 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 | \(-0.0413687\pi\) | |||||||
\(242\) | 156.000 | + | 270.200i | 0.644628 | + | 1.11653i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 450.333i | − | 1.84563i | ||||||
\(245\) | −247.500 | + | 59.7558i | −1.01020 | + | 0.243901i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 72.0000 | − | 124.708i | 0.291498 | − | 0.504889i | ||||
\(248\) | 31.5000 | − | 18.1865i | 0.127016 | − | 0.0733328i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 310.500 | + | 179.267i | 1.24200 | + | 0.717069i | ||||
\(251\) | − | 5.19615i | − | 0.0207018i | −0.999946 | − | 0.0103509i | \(-0.996705\pi\) | ||
0.999946 | − | 0.0103509i | \(-0.00329485\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 52.5000 | − | 90.9327i | 0.206693 | − | 0.358003i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −42.5000 | − | 73.6122i | −0.166016 | − | 0.287547i | ||||
\(257\) | −99.0000 | − | 57.1577i | −0.385214 | − | 0.222403i | 0.294870 | − | 0.955537i | \(-0.404724\pi\) |
−0.680084 | + | 0.733134i | \(0.738057\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −10.0000 | + | 69.2820i | −0.0386100 | + | 0.267498i | ||||
\(260\) | −360.000 | −1.38462 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −445.500 | + | 257.210i | −1.70038 | + | 0.981716i | ||||
\(263\) | 93.0000 | + | 161.081i | 0.353612 | + | 0.612474i | 0.986879 | − | 0.161459i | \(-0.0516199\pi\) |
−0.633267 | + | 0.773933i | \(0.718287\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 171.473i | − | 0.647068i | ||||||
\(266\) | −135.000 | + | 171.473i | −0.507519 | + | 0.644635i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 190.000 | − | 329.090i | 0.708955 | − | 1.22795i | ||||
\(269\) | 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 | \(0.612493\pi\) | |||||||
\(272\) | 114.315i | 0.420277i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −288.000 | −1.05109 | ||||||||
\(275\) | −15.0000 | + | 25.9808i | −0.0545455 | + | 0.0944755i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −190.000 | − | 329.090i | −0.685921 | − | 1.18805i | −0.973147 | − | 0.230186i | \(-0.926066\pi\) |
0.287226 | − | 0.957863i | \(-0.407267\pi\) | |||||||
\(278\) | 477.000 | + | 275.396i | 1.71583 | + | 0.990633i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 108.000 | + | 15.5885i | 0.385714 | + | 0.0556731i | ||||
\(281\) | −300.000 | −1.06762 | −0.533808 | − | 0.845606i | \(-0.679239\pi\) | ||||
−0.533808 | + | 0.845606i | \(0.679239\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 177.000 | − | 102.191i | 0.625442 | − | 0.361099i | −0.153543 | − | 0.988142i | \(-0.549068\pi\) |
0.778985 | + | 0.627043i | \(0.215735\pi\) | |||||||
\(284\) | 210.000 | + | 363.731i | 0.739437 | + | 1.28074i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 623.538i | 2.18020i | ||||||||
\(287\) | −27.0000 | − | 67.5500i | −0.0940767 | − | 0.235366i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −90.5000 | + | 156.751i | −0.313149 | + | 0.542390i | ||||
\(290\) | −121.500 | + | 70.1481i | −0.418966 | + | 0.241890i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 270.000 | + | 155.885i | 0.924658 | + | 0.533851i | ||||
\(293\) | 545.596i | 1.86210i | 0.364889 | + | 0.931051i | \(0.381107\pi\) | ||||
−0.364889 | + | 0.931051i | \(0.618893\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 81.0000 | 0.274576 | ||||||||
\(296\) | 15.0000 | − | 25.9808i | 0.0506757 | − | 0.0877728i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 279.000 | + | 483.242i | 0.936242 | + | 1.62162i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −481.000 | + | 192.258i | −1.59801 | + | 0.638730i | ||||
\(302\) | −237.000 | −0.784768 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −99.0000 | + | 57.1577i | −0.325658 | + | 0.188019i | ||||
\(305\) | −234.000 | − | 405.300i | −0.767213 | − | 1.32885i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 173.205i | − | 0.564186i | −0.959387 | − | 0.282093i | \(-0.908971\pi\) | ||
0.959387 | − | 0.282093i | \(-0.0910287\pi\) | |||||||
\(308\) | 75.0000 | − | 519.615i | 0.243506 | − | 1.68706i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 94.5000 | − | 163.679i | 0.304839 | − | 0.527996i | ||||
\(311\) | 153.000 | − | 88.3346i | 0.491961 | − | 0.284034i | −0.233426 | − | 0.972374i | \(-0.574994\pi\) |
0.725388 | + | 0.688340i | \(0.241660\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −184.500 | − | 106.521i | −0.589457 | − | 0.340323i | 0.175426 | − | 0.984493i | \(-0.443870\pi\) |
−0.764883 | + | 0.644170i | \(0.777203\pi\) | |||||||
\(314\) | 62.3538i | 0.198579i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −215.000 | −0.680380 | ||||||||
\(317\) | 58.5000 | − | 101.325i | 0.184543 | − | 0.319637i | −0.758880 | − | 0.651231i | \(-0.774253\pi\) |
0.943422 | + | 0.331594i | \(0.107586\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 67.5000 | + | 116.913i | 0.211599 | + | 0.366500i | ||||
\(320\) | 409.500 | + | 236.425i | 1.27969 | + | 0.738828i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 108.000 | 0.334365 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −24.0000 | + | 13.8564i | −0.0738462 | + | 0.0426351i | ||||
\(326\) | −312.000 | − | 540.400i | −0.957055 | − | 1.65767i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 31.1769i | 0.0950516i | ||||||||
\(329\) | 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 | \(0.185912\pi\) | |||||||
\(332\) | −517.500 | + | 298.779i | −1.55873 | + | 0.899936i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −648.000 | − | 374.123i | −1.94012 | − | 1.12013i | ||||
\(335\) | − | 394.908i | − | 1.17883i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 91.0000 | 0.270030 | 0.135015 | − | 0.990844i | \(-0.456892\pi\) | ||||
0.135015 | + | 0.990844i | \(0.456892\pi\) | |||||||
\(338\) | −34.5000 | + | 59.7558i | −0.102071 | + | 0.176792i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −135.000 | − | 233.827i | −0.397059 | − | 0.687726i | ||||
\(341\) | −157.500 | − | 90.9327i | −0.461877 | − | 0.266665i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 143.000 | − | 311.769i | 0.416910 | − | 0.908948i | ||||
\(344\) | 222.000 | 0.645349 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 594.000 | − | 342.946i | 1.71676 | − | 0.991174i | ||||
\(347\) | 105.000 | + | 181.865i | 0.302594 | + | 0.524108i | 0.976723 | − | 0.214506i | \(-0.0688142\pi\) |
−0.674129 | + | 0.738614i | \(0.735481\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 304.841i | 0.873470i | 0.899590 | + | 0.436735i | \(0.143865\pi\) | ||||
−0.899590 | + | 0.436735i | \(0.856135\pi\) | |||||||
\(350\) | 39.0000 | − | 15.5885i | 0.111429 | − | 0.0445384i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 337.500 | − | 584.567i | 0.958807 | − | 1.66070i | ||||
\(353\) | −342.000 | + | 197.454i | −0.968839 | + | 0.559359i | −0.898882 | − | 0.438191i | \(-0.855619\pi\) |
−0.0699566 | + | 0.997550i | \(0.522286\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 378.000 | + | 218.238i | 1.06479 | + | 0.614756i | ||||
\(356\) | − | 363.731i | − | 1.02172i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 270.000 | 0.754190 | ||||||||
\(359\) | 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 | ||||
\(362\) | 27.0000 | + | 15.5885i | 0.0745856 | + | 0.0430620i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 300.000 | − | 381.051i | 0.824176 | − | 1.04684i | ||||
\(365\) | 324.000 | 0.887671 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −283.500 | + | 163.679i | −0.772480 | + | 0.445991i | −0.833758 | − | 0.552129i | \(-0.813815\pi\) |
0.0612789 | + | 0.998121i | \(0.480482\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | − | 155.885i | − | 0.421310i | ||||||
\(371\) | 181.500 | + | 142.894i | 0.489218 | + | 0.385160i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −85.0000 | + | 147.224i | −0.227882 | + | 0.394703i | −0.957180 | − | 0.289493i | \(-0.906513\pi\) |
0.729298 | + | 0.684196i | \(0.239847\pi\) | |||||||
\(374\) | −405.000 | + | 233.827i | −1.08289 | + | 0.625206i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 124.708i | 0.330790i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 82.0000 | 0.216359 | 0.108179 | − | 0.994131i | \(-0.465498\pi\) | ||||
0.108179 | + | 0.994131i | \(0.465498\pi\) | |||||||
\(380\) | 135.000 | − | 233.827i | 0.355263 | − | 0.615334i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 468.000 | + | 810.600i | 1.22513 | + | 2.12199i | ||||
\(383\) | −189.000 | − | 109.119i | −0.493473 | − | 0.284907i | 0.232541 | − | 0.972587i | \(-0.425296\pi\) |
−0.726014 | + | 0.687680i | \(0.758629\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −202.500 | − | 506.625i | −0.525974 | − | 1.31591i | ||||
\(386\) | 555.000 | 1.43782 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −802.500 | + | 463.324i | −2.06830 | + | 1.19413i | ||||
\(389\) | 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 | ||||||||
\(392\) | −106.500 | + | 101.325i | −0.271684 | + | 0.258482i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −495.000 | + | 857.365i | −1.25635 | + | 2.17605i | ||||
\(395\) | −193.500 | + | 111.717i | −0.489873 | + | 0.282829i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −222.000 | − | 128.172i | −0.559194 | − | 0.322851i | 0.193628 | − | 0.981075i | \(-0.437975\pi\) |
−0.752822 | + | 0.658224i | \(0.771308\pi\) | |||||||
\(398\) | − | 20.7846i | − | 0.0522226i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 22.0000 | 0.0550000 | ||||||||
\(401\) | 66.0000 | − | 114.315i | 0.164589 | − | 0.285076i | −0.771921 | − | 0.635719i | \(-0.780704\pi\) |
0.936509 | + | 0.350643i | \(0.114037\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −84.0000 | − | 145.492i | −0.208437 | − | 0.361023i | ||||
\(404\) | −630.000 | − | 363.731i | −1.55941 | − | 0.900323i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 27.0000 | − | 187.061i | 0.0665025 | − | 0.460743i | ||||
\(407\) | −150.000 | −0.368550 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −313.500 | + | 180.999i | −0.766504 | + | 0.442541i | −0.831626 | − | 0.555336i | \(-0.812590\pi\) |
0.0651223 | + | 0.997877i | \(0.479256\pi\) | |||||||
\(410\) | 81.0000 | + | 140.296i | 0.197561 | + | 0.342186i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 346.410i | 0.840801i | ||||||||
\(413\) | −67.5000 | + | 85.7365i | −0.163438 | + | 0.207594i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −310.500 | + | 537.802i | −0.748193 | + | 1.29591i | ||||
\(416\) | 540.000 | − | 311.769i | 1.29808 | − | 0.749445i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −405.000 | − | 233.827i | −0.968900 | − | 0.559394i | ||||
\(419\) | 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 | \(0.148517\pi\) | |||||||
\(422\) | −372.000 | + | 644.323i | −0.881517 | + | 1.52683i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −49.5000 | − | 85.7365i | −0.116745 | − | 0.202209i | ||||
\(425\) | −18.0000 | − | 10.3923i | −0.0423529 | − | 0.0244525i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 624.000 | + | 90.0666i | 1.46136 | + | 0.210929i | ||||
\(428\) | −465.000 | −1.08645 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 999.000 | − | 576.773i | 2.32326 | − | 1.34133i | ||||
\(431\) | 81.0000 | + | 140.296i | 0.187935 | + | 0.325513i | 0.944562 | − | 0.328334i | \(-0.106487\pi\) |
−0.756627 | + | 0.653847i | \(0.773154\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 339.482i | 0.784023i | 0.919960 | + | 0.392011i | \(0.128221\pi\) | ||||
−0.919960 | + | 0.392011i | \(0.871779\pi\) | |||||||
\(434\) | 94.5000 | + | 236.425i | 0.217742 | + | 0.544758i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 20.0000 | − | 34.6410i | 0.0458716 | − | 0.0794519i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 337.500 | + | 194.856i | 0.768793 | + | 0.443863i | 0.832444 | − | 0.554110i | \(-0.186941\pi\) |
−0.0636511 | + | 0.997972i | \(0.520274\pi\) | |||||||
\(440\) | 233.827i | 0.531425i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −432.000 | −0.977376 | ||||||||
\(443\) | −148.500 | + | 257.210i | −0.335214 | + | 0.580608i | −0.983526 | − | 0.180767i | \(-0.942142\pi\) |
0.648312 | + | 0.761375i | \(0.275475\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −189.000 | − | 327.358i | −0.424719 | − | 0.735635i | ||||
\(446\) | 499.500 | + | 288.386i | 1.11996 | + | 0.646606i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −591.500 | + | 236.425i | −1.32031 | + | 0.527734i | ||||
\(449\) | 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 | ||||
\(452\) | 105.000 | + | 181.865i | 0.232301 | + | 0.402357i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 265.004i | − | 0.583709i | ||||||
\(455\) | 72.0000 | − | 498.831i | 0.158242 | − | 1.09633i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 221.500 | − | 383.649i | 0.484683 | − | 0.839495i | −0.515162 | − | 0.857093i | \(-0.672268\pi\) |
0.999845 | + | 0.0175975i | \(0.00560174\pi\) | |||||||
\(458\) | 855.000 | − | 493.634i | 1.86681 | − | 1.07780i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 415.692i | 0.901718i | 0.892595 | + | 0.450859i | \(0.148882\pi\) | ||||
−0.892595 | + | 0.450859i | \(0.851118\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −82.0000 | −0.177106 | −0.0885529 | − | 0.996071i | \(-0.528224\pi\) | ||||
−0.0885529 | + | 0.996071i | \(0.528224\pi\) | |||||||
\(464\) | 49.5000 | − | 85.7365i | 0.106681 | − | 0.184777i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −405.000 | − | 701.481i | −0.869099 | − | 1.50532i | ||||
\(467\) | −234.000 | − | 135.100i | −0.501071 | − | 0.289293i | 0.228085 | − | 0.973641i | \(-0.426754\pi\) |
−0.729156 | + | 0.684348i | \(0.760087\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 418.000 | + | 329.090i | 0.891258 | + | 0.701684i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 40.5000 | − | 23.3827i | 0.0858051 | − | 0.0495396i | ||||
\(473\) | −555.000 | − | 961.288i | −1.17336 | − | 2.03232i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 20.7846i | − | 0.0437571i | ||||||
\(476\) | 360.000 | + | 51.9615i | 0.756303 | + | 0.109163i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 342.000 | − | 592.361i | 0.715481 | − | 1.23925i | ||||
\(479\) | −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 | ||||
\(482\) | − | 1335.41i | − | 2.77056i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 520.000 | 1.07438 | ||||||||
\(485\) | −481.500 | + | 833.982i | −0.992784 | + | 1.71955i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 158.500 | + | 274.530i | 0.325462 | + | 0.563717i | 0.981606 | − | 0.190919i | \(-0.0611468\pi\) |
−0.656144 | + | 0.754636i | \(0.727814\pi\) | |||||||
\(488\) | −234.000 | − | 135.100i | −0.479508 | − | 0.276844i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −216.000 | + | 732.657i | −0.440816 | + | 1.49522i | ||||
\(491\) | −27.0000 | −0.0549898 | −0.0274949 | − | 0.999622i | \(-0.508753\pi\) | ||||
−0.0274949 | + | 0.999622i | \(0.508753\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −81.0000 | + | 46.7654i | −0.164300 | + | 0.0948588i | ||||
\(494\) | −216.000 | − | 374.123i | −0.437247 | − | 0.757334i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 133.368i | 0.268887i | ||||||||
\(497\) | −546.000 | + | 218.238i | −1.09859 | + | 0.439111i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 223.000 | − | 386.247i | 0.446894 | − | 0.774043i | −0.551288 | − | 0.834315i | \(-0.685864\pi\) |
0.998182 | + | 0.0602721i | \(0.0191969\pi\) | |||||||
\(500\) | 517.500 | − | 298.779i | 1.03500 | − | 0.597558i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −13.5000 | − | 7.79423i | −0.0268924 | − | 0.0155264i | ||||
\(503\) | − | 488.438i | − | 0.971050i | −0.874223 | − | 0.485525i | \(-0.838628\pi\) | ||
0.874223 | − | 0.485525i | \(-0.161372\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −756.000 | −1.49703 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −87.5000 | − | 151.554i | −0.172244 | − | 0.298336i | ||||
\(509\) | −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 | ||||
\(512\) | −627.000 | −1.22461 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −297.000 | + | 171.473i | −0.577821 | + | 0.333605i | ||||
\(515\) | 180.000 | + | 311.769i | 0.349515 | + | 0.605377i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 165.000 | + | 129.904i | 0.318533 | + | 0.250780i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −108.000 | + | 187.061i | −0.207692 | + | 0.359734i | ||||
\(521\) | 783.000 | − | 452.065i | 1.50288 | − | 0.867688i | 0.502885 | − | 0.864354i | \(-0.332272\pi\) |
0.999994 | − | 0.00333410i | \(-0.00106128\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −606.000 | − | 349.874i | −1.15870 | − | 0.668976i | −0.207708 | − | 0.978191i | \(-0.566600\pi\) |
−0.950992 | + | 0.309215i | \(0.899934\pi\) | |||||||
\(524\) | 857.365i | 1.63619i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 558.000 | 1.06084 | ||||||||
\(527\) | 63.0000 | − | 109.119i | 0.119545 | − | 0.207057i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 264.500 | + | 458.127i | 0.500000 | + | 0.866025i | ||||
\(530\) | −445.500 | − | 257.210i | −0.840566 | − | 0.485301i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 135.000 | + | 337.750i | 0.253759 | + | 0.634868i | ||||
\(533\) | 144.000 | 0.270169 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −418.500 | + | 241.621i | −0.782243 | + | 0.451628i | ||||
\(536\) | −114.000 | − | 197.454i | −0.212687 | − | 0.368384i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 1013.25i | − | 1.88336i | ||||||
\(539\) | 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 | \(0.188453\pi\) | |||||||
\(542\) | 238.500 | − | 137.698i | 0.440037 | − | 0.254055i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 405.000 | + | 233.827i | 0.744485 | + | 0.429829i | ||||
\(545\) | − | 41.5692i | − | 0.0762738i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −934.000 | −1.70750 | −0.853748 | − | 0.520687i | \(-0.825676\pi\) | ||||
−0.853748 | + | 0.520687i | \(0.825676\pi\) | |||||||
\(548\) | −240.000 | + | 415.692i | −0.437956 | + | 0.758562i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 45.0000 | + | 77.9423i | 0.0818182 | + | 0.141713i | ||||
\(551\) | −81.0000 | − | 46.7654i | −0.147005 | − | 0.0848736i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 43.0000 | − | 297.913i | 0.0777577 | − | 0.538721i | ||||
\(554\) | −1140.00 | −2.05776 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 795.000 | − | 458.993i | 1.42986 | − | 0.825528i | ||||
\(557\) | 421.500 | + | 730.059i | 0.756732 | + | 1.31070i | 0.944508 | + | 0.328487i | \(0.106539\pi\) |
−0.187776 | + | 0.982212i | \(0.560128\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 1025.37i | − | 1.83430i | ||||||
\(560\) | −247.500 | + | 314.367i | −0.441964 | + | 0.561370i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −450.000 | + | 779.423i | −0.800712 | + | 1.38687i | ||||
\(563\) | −823.500 | + | 475.448i | −1.46270 | + | 0.844490i | −0.999135 | − | 0.0415731i | \(-0.986763\pi\) |
−0.463564 | + | 0.886063i | \(0.653430\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 189.000 | + | 109.119i | 0.334513 | + | 0.193131i | ||||
\(566\) | − | 613.146i | − | 1.08330i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 252.000 | 0.443662 | ||||||||
\(569\) | 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 | \(0.959232\pi\) | |||||||
\(572\) | 900.000 | + | 519.615i | 1.57343 | + | 0.908418i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −216.000 | − | 31.1769i | −0.376307 | − | 0.0543152i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 568.500 | − | 328.224i | 0.985269 | − | 0.568845i | 0.0814120 | − | 0.996681i | \(-0.474057\pi\) |
0.903857 | + | 0.427835i | \(0.140724\pi\) | |||||||
\(578\) | 271.500 | + | 470.252i | 0.469723 | + | 0.813584i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 233.827i | 0.403150i | ||||||||
\(581\) | −310.500 | − | 776.825i | −0.534423 | − | 1.33705i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −247.500 | + | 428.683i | −0.424528 | + | 0.735305i | ||||
\(584\) | 162.000 | − | 93.5307i | 0.277397 | − | 0.160155i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1417.50 | + | 818.394i | 2.41894 | + | 1.39658i | ||||
\(587\) | − | 1054.82i | − | 1.79697i | −0.439008 | − | 0.898483i | \(-0.644670\pi\) | ||
0.439008 | − | 0.898483i | \(-0.355330\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 126.000 | 0.213922 | ||||||||
\(590\) | 121.500 | − | 210.444i | 0.205932 | − | 0.356685i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 55.0000 | + | 95.2628i | 0.0929054 | + | 0.160917i | ||||
\(593\) | −612.000 | − | 353.338i | −1.03204 | − | 0.595849i | −0.114472 | − | 0.993426i | \(-0.536518\pi\) |
−0.917569 | + | 0.397578i | \(0.869851\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 351.000 | − | 140.296i | 0.589916 | − | 0.235792i | ||||
\(596\) | 930.000 | 1.56040 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 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 | \(0.933936\pi\) | |||||||
\(602\) | −222.000 | + | 1538.06i | −0.368771 | + | 2.55492i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −197.500 | + | 342.080i | −0.326987 | + | 0.566358i | ||||
\(605\) | 468.000 | − | 270.200i | 0.773554 | − | 0.446611i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −562.500 | − | 324.760i | −0.926689 | − | 0.535024i | −0.0409259 | − | 0.999162i | \(-0.513031\pi\) |
−0.885763 | + | 0.464138i | \(0.846364\pi\) | |||||||
\(608\) | 467.654i | 0.769167i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −1404.00 | −2.30164 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 446.000 | + | 772.495i | 0.727569 | + | 1.26019i | 0.957908 | + | 0.287076i | \(0.0926834\pi\) |
−0.230338 | + | 0.973111i | \(0.573983\pi\) | |||||||
\(614\) | −450.000 | − | 259.808i | −0.732899 | − | 0.423139i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −247.500 | − | 194.856i | −0.401786 | − | 0.316324i | ||||
\(617\) | 1224.00 | 1.98379 | 0.991896 | − | 0.127050i | \(-0.0405510\pi\) | ||||
0.991896 | + | 0.127050i | \(0.0405510\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −348.000 | + | 200.918i | −0.562197 | + | 0.324585i | −0.754027 | − | 0.656844i | \(-0.771891\pi\) |
0.191830 | + | 0.981428i | \(0.438558\pi\) | |||||||
\(620\) | −157.500 | − | 272.798i | −0.254032 | − | 0.439997i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 530.008i | − | 0.852102i | ||||||
\(623\) | 504.000 | + | 72.7461i | 0.808989 | + | 0.116767i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 335.500 | − | 581.103i | 0.536800 | − | 0.929765i | ||||
\(626\) | −553.500 | + | 319.563i | −0.884185 | + | 0.510485i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 90.0000 | + | 51.9615i | 0.143312 | + | 0.0827413i | ||||
\(629\) | − | 103.923i | − | 0.165219i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1115.00 | 1.76704 | 0.883518 | − | 0.468397i | \(-0.155168\pi\) | ||||
0.883518 | + | 0.468397i | \(0.155168\pi\) | |||||||
\(632\) | −64.5000 | + | 111.717i | −0.102057 | + | 0.176768i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −175.500 | − | 303.975i | −0.276814 | − | 0.479456i | ||||
\(635\) | −157.500 | − | 90.9327i | −0.248031 | − | 0.143201i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 468.000 | + | 491.902i | 0.734694 | + | 0.772217i | ||||
\(638\) | 405.000 | 0.634796 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 418.500 | − | 241.621i | 0.653906 | − | 0.377533i | ||||
\(641\) | −192.000 | − | 332.554i | −0.299532 | − | 0.518805i | 0.676497 | − | 0.736445i | \(-0.263497\pi\) |
−0.976029 | + | 0.217641i | \(0.930164\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 6.92820i | 0.0107748i | 0.999985 | + | 0.00538741i | \(0.00171487\pi\) | ||||
−0.999985 | + | 0.00538741i | \(0.998285\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 162.000 | − | 280.592i | 0.250774 | − | 0.434353i | ||||
\(647\) | −774.000 | + | 446.869i | −1.19629 | + | 0.690679i | −0.959726 | − | 0.280937i | \(-0.909355\pi\) |
−0.236564 | + | 0.971616i | \(0.576021\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −202.500 | − | 116.913i | −0.312018 | − | 0.180144i | ||||
\(650\) | 83.1384i | 0.127905i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1040.00 | −1.59509 | ||||||||
\(653\) | 37.5000 | − | 64.9519i | 0.0574273 | − | 0.0994669i | −0.835883 | − | 0.548908i | \(-0.815044\pi\) |
0.893310 | + | 0.449441i | \(0.148377\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 445.500 | + | 771.629i | 0.680153 | + | 1.17806i | ||||
\(656\) | −99.0000 | − | 57.1577i | −0.150915 | − | 0.0871306i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 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 | \(0.401412\pi\) | |||||||
\(662\) | 60.0000 | + | 103.923i | 0.0906344 | + | 0.156983i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 358.535i | 0.539962i | ||||||||
\(665\) | 297.000 | + | 233.827i | 0.446617 | + | 0.351619i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | −1080.00 | + | 623.538i | −1.61677 | + | 0.933441i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −1026.00 | − | 592.361i | −1.53134 | − | 0.884121i | ||||
\(671\) | 1351.00i | 2.01341i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 13.0000 | 0.0193165 | 0.00965825 | − | 0.999953i | \(-0.496926\pi\) | ||||
0.00965825 | + | 0.999953i | \(0.496926\pi\) | |||||||
\(674\) | 136.500 | − | 236.425i | 0.202522 | − | 0.350779i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 57.5000 | + | 99.5929i | 0.0850592 | + | 0.147327i | ||||
\(677\) | 1093.50 | + | 631.333i | 1.61521 | + | 0.932544i | 0.988135 | + | 0.153589i | \(0.0490832\pi\) |
0.627079 | + | 0.778955i | \(0.284250\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −481.500 | − | 1204.64i | −0.709131 | − | 1.77414i | ||||
\(680\) | −162.000 | −0.238235 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −472.500 | + | 272.798i | −0.692815 | + | 0.399997i | ||||
\(683\) | −484.500 | − | 839.179i | −0.709370 | − | 1.22867i | −0.965091 | − | 0.261915i | \(-0.915646\pi\) |
0.255721 | − | 0.966751i | \(-0.417687\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 498.831i | 0.728220i | ||||||||
\(686\) | −595.500 | − | 839.179i | −0.868076 | − | 1.22329i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −407.000 | + | 704.945i | −0.591570 | + | 1.02463i | ||||
\(689\) | −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 | \(0.689825\pi\) | |||||||
\(692\) | − | 1143.15i | − | 1.65196i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 630.000 | 0.907781 | ||||||||
\(695\) | 477.000 | − | 826.188i | 0.686331 | − | 1.18876i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 54.0000 | + | 93.5307i | 0.0774749 | + | 0.134190i | ||||
\(698\) | 792.000 | + | 457.261i | 1.13467 | + | 0.655102i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 10.0000 | − | 69.2820i | 0.0142857 | − | 0.0989743i | ||||
\(701\) | −597.000 | −0.851641 | −0.425820 | − | 0.904808i | \(-0.640014\pi\) | ||||
−0.425820 | + | 0.904808i | \(0.640014\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 90.0000 | − | 51.9615i | 0.128023 | − | 0.0739140i | ||||
\(704\) | −682.500 | − | 1182.12i | −0.969460 | − | 1.67915i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1184.72i | 1.67808i | ||||||||
\(707\) | 630.000 | − | 800.207i | 0.891089 | − | 1.13184i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 415.000 | − | 718.801i | 0.585331 | − | 1.01382i | −0.409503 | − | 0.912309i | \(-0.634298\pi\) |
0.994834 | − | 0.101515i | \(-0.0323689\pi\) | |||||||
\(710\) | 1134.00 | − | 654.715i | 1.59718 | − | 0.922134i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −189.000 | − | 109.119i | −0.265449 | − | 0.153257i | ||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1080.00 | 1.51049 | ||||||||
\(716\) | 225.000 | − | 389.711i | 0.314246 | − | 0.544290i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −738.000 | − | 1278.25i | −1.02786 | − | 1.78030i | ||||
\(719\) | −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 | ||||
\(722\) | −759.000 | −1.05125 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 45.0000 | − | 25.9808i | 0.0621547 | − | 0.0358850i | ||||
\(725\) | 9.00000 | + | 15.5885i | 0.0124138 | + | 0.0215013i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 50.2295i | − | 0.0690914i | −0.999403 | − | 0.0345457i | \(-0.989002\pi\) | ||
0.999403 | − | 0.0345457i | \(-0.0109984\pi\) | |||||||
\(728\) | −108.000 | − | 270.200i | −0.148352 | − | 0.371154i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 486.000 | − | 841.777i | 0.665753 | − | 1.15312i | ||||
\(731\) | 666.000 | − | 384.515i | 0.911081 | − | 0.526013i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −159.000 | − | 91.7987i | −0.216917 | − | 0.125237i | 0.387605 | − | 0.921826i | \(-0.373302\pi\) |
−0.604522 | + | 0.796589i | \(0.706636\pi\) | |||||||
\(734\) | 982.073i | 1.33797i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −570.000 | + | 987.269i | −0.773406 | + | 1.33958i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 167.000 | + | 289.252i | 0.225981 | + | 0.391411i | 0.956613 | − | 0.291361i | \(-0.0941079\pi\) |
−0.730632 | + | 0.682771i | \(0.760775\pi\) | |||||||
\(740\) | −225.000 | − | 129.904i | −0.304054 | − | 0.175546i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 643.500 | − | 257.210i | 0.867251 | − | 0.346644i | ||||
\(743\) | −84.0000 | −0.113055 | −0.0565276 | − | 0.998401i | \(-0.518003\pi\) | ||||
−0.0565276 | + | 0.998401i | \(0.518003\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 837.000 | − | 483.242i | 1.12349 | − | 0.648647i | ||||
\(746\) | 255.000 | + | 441.673i | 0.341823 | + | 0.592055i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 779.423i | 1.04201i | ||||||||
\(749\) | 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 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 324.000 | + | 187.061i | 0.429708 | + | 0.248092i | ||||
\(755\) | 410.496i | 0.543703i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −80.0000 | −0.105680 | −0.0528402 | − | 0.998603i | \(-0.516827\pi\) | ||||
−0.0528402 | + | 0.998603i | \(0.516827\pi\) | |||||||
\(758\) | 123.000 | − | 213.042i | 0.162269 | − | 0.281058i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −81.0000 | − | 140.296i | −0.106579 | − | 0.184600i | ||||
\(761\) | 702.000 | + | 405.300i | 0.922470 | + | 0.532589i | 0.884422 | − | 0.466687i | \(-0.154553\pi\) |
0.0380481 | + | 0.999276i | \(0.487886\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 44.0000 | + | 34.6410i | 0.0576671 | + | 0.0454011i | ||||
\(764\) | 1560.00 | 2.04188 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −567.000 | + | 327.358i | −0.740209 | + | 0.427360i | ||||
\(767\) | −108.000 | − | 187.061i | −0.140808 | − | 0.243887i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 774.227i | 1.00680i | 0.864054 | + | 0.503398i | \(0.167917\pi\) | ||||
−0.864054 | + | 0.503398i | \(0.832083\pi\) | |||||||
\(770\) | −1620.00 | − | 233.827i | −2.10390 | − | 0.303671i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 462.500 | − | 801.073i | 0.599093 | − | 1.03766i | ||||
\(773\) | 630.000 | − | 363.731i | 0.815006 | − | 0.470544i | −0.0336850 | − | 0.999433i | \(-0.510724\pi\) |
0.848691 | + | 0.528888i | \(0.177391\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −21.0000 | − | 12.1244i | −0.0270968 | − | 0.0156443i | ||||
\(776\) | 555.988i | 0.716480i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 918.000 | 1.17995 | ||||||||
\(779\) | −54.0000 | + | 93.5307i | −0.0693196 | + | 0.120065i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −630.000 | − | 1091.19i | −0.806658 | − | 1.39717i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −126.500 | − | 523.945i | −0.161352 | − | 0.668298i | ||||
\(785\) | 108.000 | 0.137580 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1236.00 | + | 713.605i | −1.57052 | + | 0.906741i | −0.574416 | + | 0.818563i | \(0.694771\pi\) |
−0.996105 | + | 0.0881773i | \(0.971896\pi\) | |||||||
\(788\) | 825.000 | + | 1428.94i | 1.04695 | + | 1.81338i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 670.304i | 0.848486i | ||||||||
\(791\) | −273.000 | + | 109.119i | −0.345133 | + | 0.137951i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −624.000 | + | 1080.80i | −0.786885 | + | 1.36293i | ||||
\(794\) | −666.000 | + | 384.515i | −0.838791 | + | 0.484276i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −30.0000 | − | 17.3205i | −0.0376884 | − | 0.0217594i | ||||
\(797\) | 607.950i | 0.762798i | 0.924411 | + | 0.381399i | \(0.124558\pi\) | ||||
−0.924411 | + | 0.381399i | \(0.875442\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 45.0000 | − | 77.9423i | 0.0562500 | − | 0.0974279i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −198.000 | − | 342.946i | −0.246883 | − | 0.427614i | ||||
\(803\) | −810.000 | − | 467.654i | −1.00872 | − | 0.582383i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −504.000 | −0.625310 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −378.000 | + | 218.238i | −0.467822 | + | 0.270097i | ||||
\(809\) | −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 | \(-0.0699015\pi\) | |||||||
\(812\) | −247.500 | − | 194.856i | −0.304803 | − | 0.239970i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −225.000 | + | 389.711i | −0.276413 | + | 0.478761i | ||||
\(815\) | −936.000 | + | 540.400i | −1.14847 | + | 0.663067i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 666.000 | + | 384.515i | 0.815177 | + | 0.470643i | ||||
\(818\) | 1086.00i | 1.32762i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 270.000 | 0.329268 | ||||||||
\(821\) | 142.500 | − | 246.817i | 0.173569 | − | 0.300630i | −0.766096 | − | 0.642726i | \(-0.777803\pi\) |
0.939665 | + | 0.342096i | \(0.111137\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 137.000 | + | 237.291i | 0.166464 | + | 0.288324i | 0.937174 | − | 0.348862i | \(-0.113432\pi\) |
−0.770710 | + | 0.637186i | \(0.780098\pi\) | |||||||
\(824\) | 180.000 | + | 103.923i | 0.218447 | + | 0.126120i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 121.500 | + | 303.975i | 0.147094 | + | 0.368008i | ||||
\(827\) | −429.000 | −0.518742 | −0.259371 | − | 0.965778i | \(-0.583515\pi\) | ||||
−0.259371 | + | 0.965778i | \(0.583515\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −819.000 | + | 472.850i | −0.987937 | + | 0.570386i | −0.904657 | − | 0.426140i | \(-0.859873\pi\) |
−0.0832802 | + | 0.996526i | \(0.526540\pi\) | |||||||
\(830\) | 931.500 | + | 1613.41i | 1.12229 | + | 1.94386i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − | 1260.93i | − | 1.51554i | ||||||
\(833\) | −144.000 | + | 488.438i | −0.172869 | + | 0.586361i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −648.000 | + | 1122.37i | −0.776048 | + | 1.34415i | ||||
\(836\) | −675.000 | + | 389.711i | −0.807416 | + | 0.466162i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 1674.00 | + | 966.484i | 1.99761 | + | 1.15332i | ||||
\(839\) | 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 | ||||||||
\(842\) | 1128.00 | − | 1953.75i | 1.33967 | − | 2.32037i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 620.000 | + | 1073.87i | 0.734597 | + | 1.27236i | ||||
\(845\) | 103.500 | + | 59.7558i | 0.122485 | + | 0.0707169i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −104.000 | + | 720.533i | −0.122786 | + | 0.850688i | ||||
\(848\) | 363.000 | 0.428066 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −54.0000 | + | 31.1769i | −0.0635294 | + | 0.0366787i | ||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 997.661i | − | 1.16959i | −0.811181 | − | 0.584796i | \(-0.801175\pi\) | ||
0.811181 | − | 0.584796i | \(-0.198825\pi\) | |||||||
\(854\) | 1170.00 | − | 1486.10i | 1.37002 | − | 1.74016i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −139.500 | + | 241.621i | −0.162967 | + | 0.282268i | ||||
\(857\) | −378.000 | + | 218.238i | −0.441074 | + | 0.254654i | −0.704053 | − | 0.710148i | \(-0.748628\pi\) |
0.262979 | + | 0.964801i | \(0.415295\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −393.000 | − | 226.899i | −0.457509 | − | 0.264143i | 0.253487 | − | 0.967339i | \(-0.418422\pi\) |
−0.710996 | + | 0.703196i | \(0.751756\pi\) | |||||||
\(860\) | − | 1922.58i | − | 2.23555i | ||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 486.000 | 0.563805 | ||||||||
\(863\) | −195.000 | + | 337.750i | −0.225956 | + | 0.391367i | −0.956606 | − | 0.291385i | \(-0.905884\pi\) |
0.730650 | + | 0.682752i | \(0.239217\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −594.000 | − | 1028.84i | −0.686705 | − | 1.18941i | ||||
\(866\) | 882.000 | + | 509.223i | 1.01848 | + | 0.588017i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 420.000 | + | 60.6218i | 0.483871 | + | 0.0698408i | ||||
\(869\) | 645.000 | 0.742232 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −912.000 | + | 526.543i | −1.04707 | + | 0.604527i | ||||
\(872\) | −12.0000 | − | 20.7846i | −0.0137615 | − | 0.0238356i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 310.500 | + | 776.825i | 0.354857 | + | 0.887800i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 272.000 | − | 471.118i | 0.310148 | − | 0.537192i | −0.668246 | − | 0.743940i | \(-0.732955\pi\) |
0.978394 | + | 0.206748i | \(0.0662880\pi\) | |||||||
\(878\) | 1012.50 | − | 584.567i | 1.15319 | − | 0.665794i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −742.500 | − | 428.683i | −0.843750 | − | 0.487139i | ||||
\(881\) | − | 187.061i | − | 0.212329i | −0.994349 | − | 0.106164i | \(-0.966143\pi\) | ||
0.994349 | − | 0.106164i | \(-0.0338569\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 322.000 | 0.364666 | 0.182333 | − | 0.983237i | \(-0.441635\pi\) | ||||
0.182333 | + | 0.983237i | \(0.441635\pi\) | |||||||
\(884\) | −360.000 | + | 623.538i | −0.407240 | + | 0.705360i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 445.500 | + | 771.629i | 0.502822 | + | 0.870913i | ||||
\(887\) | −612.000 | − | 353.338i | −0.689966 | − | 0.398352i | 0.113633 | − | 0.993523i | \(-0.463751\pi\) |
−0.803599 | + | 0.595171i | \(0.797084\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 227.500 | − | 90.9327i | 0.255906 | − | 0.102286i | ||||
\(890\) | −1134.00 | −1.27416 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 832.500 | − | 480.644i | 0.933296 | − | 0.538839i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 467.654i | − | 0.522518i | ||||||
\(896\) | −93.0000 | + | 644.323i | −0.103795 | + | 0.719110i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 738.000 | − | 1278.25i | 0.821826 | − | 1.42344i | ||||
\(899\) | −94.5000 | + | 54.5596i | −0.105117 | + | 0.0606892i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −297.000 | − | 171.473i | −0.329634 | − | 0.190314i | ||||
\(902\) | − | 467.654i | − | 0.518463i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 126.000 | 0.139381 | ||||||||
\(905\) | 27.0000 | − | 46.7654i | 0.0298343 | − | 0.0516744i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 550.000 | + | 952.628i | 0.606395 | + | 1.05031i | 0.991829 | + | 0.127571i | \(0.0407182\pi\) |
−0.385435 | + | 0.922735i | \(0.625948\pi\) | |||||||
\(908\) | −382.500 | − | 220.836i | −0.421256 | − | 0.243212i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −1188.00 | − | 935.307i | −1.30549 | − | 1.02781i | ||||
\(911\) | −900.000 | −0.987925 | −0.493963 | − | 0.869483i | \(-0.664452\pi\) | ||||
−0.493963 | + | 0.869483i | \(0.664452\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1552.50 | − | 896.336i | 1.70044 | − | 0.981748i | ||||
\(914\) | −664.500 | − | 1150.95i | −0.727024 | − | 1.25924i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 1645.45i | − | 1.79634i | ||||||
\(917\) | −1188.00 | − | 171.473i | −1.29553 | − | 0.186993i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 859.000 | − | 1487.83i | 0.934712 | − | 1.61897i | 0.159564 | − | 0.987188i | \(-0.448991\pi\) |
0.775147 | − | 0.631781i | \(-0.217676\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 1080.00 | + | 623.538i | 1.17137 | + | 0.676289i | ||||
\(923\) | − | 1163.94i | − | 1.26104i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −20.0000 | −0.0216216 | ||||||||
\(926\) | −123.000 | + | 213.042i | −0.132829 | + | 0.230067i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −202.500 | − | 350.740i | −0.218211 | − | 0.377953i | ||||
\(929\) | 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 | ||||
\(932\) | −1350.00 | −1.44850 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −702.000 | + | 405.300i | −0.751606 | + | 0.433940i | ||||
\(935\) | 405.000 | + | 701.481i | 0.433155 | + | 0.750247i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 957.824i | 1.02222i | 0.859514 | + | 0.511112i | \(0.170766\pi\) | ||||
−0.859514 | + | 0.511112i | \(0.829234\pi\) | |||||||
\(938\) | 1482.00 | − | 592.361i | 1.57996 | − | 0.631515i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −310.500 | + | 179.267i | −0.329968 | + | 0.190507i | −0.655827 | − | 0.754911i | \(-0.727680\pi\) |
0.325859 | + | 0.945418i | \(0.394347\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 171.473i | 0.181645i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −3330.00 | −3.52008 | ||||||||
\(947\) | 81.0000 | − | 140.296i | 0.0855333 | − | 0.148148i | −0.820085 | − | 0.572242i | \(-0.806074\pi\) |
0.905618 | + | 0.424094i | \(0.139407\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −432.000 | − | 748.246i | −0.455216 | − | 0.788457i | ||||
\(950\) | −54.0000 | − | 31.1769i | −0.0568421 | − | 0.0328178i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 135.000 | − | 171.473i | 0.141807 | − | 0.180119i | ||||
\(953\) | 954.000 | 1.00105 | 0.500525 | − | 0.865722i | \(-0.333140\pi\) | ||||
0.500525 | + | 0.865722i | \(0.333140\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1404.00 | − | 810.600i | 1.47016 | − | 0.848796i | ||||
\(956\) | −570.000 | − | 987.269i | −0.596234 | − | 1.03271i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 1028.84i | 1.07394i | ||||||||
\(959\) | −528.000 | − | 415.692i | −0.550574 | − | 0.433464i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −407.000 | + | 704.945i | −0.423517 | + | 0.733553i | ||||
\(962\) | −360.000 | + | 207.846i | −0.374220 | + | 0.216056i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −1927.50 | − | 1112.84i | −1.99948 | − | 1.15440i | ||||
\(965\) | − | 961.288i | − | 0.996154i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −751.000 | −0.776629 | −0.388314 | − | 0.921527i | \(-0.626943\pi\) | ||||
−0.388314 | + | 0.921527i | \(0.626943\pi\) | |||||||
\(968\) | 156.000 | − | 270.200i | 0.161157 | − | 0.279132i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 1444.50 | + | 2501.95i | 1.48918 | + | 2.57933i | ||||
\(971\) | 247.500 | + | 142.894i | 0.254892 | + | 0.147162i | 0.622002 | − | 0.783016i | \(-0.286320\pi\) |
−0.367110 | + | 0.930177i | \(0.619653\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 477.000 | + | 1193.38i | 0.490236 | + | 1.22650i | ||||
\(974\) | 951.000 | 0.976386 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 858.000 | − | 495.367i | 0.879098 | − | 0.507548i | ||||
\(977\) | −9.00000 | − | 15.5885i | −0.00921187 | − | 0.0159554i | 0.861383 | − | 0.507957i | \(-0.169599\pi\) |
−0.870595 | + | 0.492001i | \(0.836266\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1091.19i | 1.11460i | ||||||||
\(980\) | 877.500 | + | 922.317i | 0.895408 | + | 0.941140i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −40.5000 | + | 70.1481i | −0.0412424 | + | 0.0714339i | ||||
\(983\) | 855.000 | − | 493.634i | 0.869786 | − | 0.502171i | 0.00250913 | − | 0.999997i | \(-0.499201\pi\) |
0.867277 | + | 0.497825i | \(0.165868\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1485.00 | + | 857.365i | 1.50761 | + | 0.870421i | ||||
\(986\) | 280.592i | 0.284576i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −720.000 | −0.728745 | ||||||||
\(989\) | 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 | \(0.948748\pi\) | |||||||
\(992\) | 472.500 | + | 272.798i | 0.476310 | + | 0.274998i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −252.000 | + | 1745.91i | −0.253521 | + | 1.75645i | ||||
\(995\) | −36.0000 | −0.0361809 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 186.000 | − | 107.387i | 0.186560 | − | 0.107710i | −0.403811 | − | 0.914842i | \(-0.632315\pi\) |
0.590371 | + | 0.807132i | \(0.298981\pi\) | |||||||
\(998\) | −669.000 | − | 1158.74i | −0.670341 | − | 1.16106i | ||||
\(999\) | 0 | 0 |
(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 | 63.3.m.d.19.1 | 2 | ||
3.2 | odd | 2 | 21.3.f.a.19.1 | yes | 2 | ||
4.3 | odd | 2 | 1008.3.cg.a.145.1 | 2 | |||
7.2 | even | 3 | 441.3.d.a.244.2 | 2 | |||
7.3 | odd | 6 | inner | 63.3.m.d.10.1 | 2 | ||
7.4 | even | 3 | 441.3.m.g.325.1 | 2 | |||
7.5 | odd | 6 | 441.3.d.a.244.1 | 2 | |||
7.6 | odd | 2 | 441.3.m.g.19.1 | 2 | |||
12.11 | even | 2 | 336.3.bh.d.145.1 | 2 | |||
15.2 | even | 4 | 525.3.s.e.124.1 | 4 | |||
15.8 | even | 4 | 525.3.s.e.124.2 | 4 | |||
15.14 | odd | 2 | 525.3.o.h.376.1 | 2 | |||
21.2 | odd | 6 | 147.3.d.c.97.1 | 2 | |||
21.5 | even | 6 | 147.3.d.c.97.2 | 2 | |||
21.11 | odd | 6 | 147.3.f.a.31.1 | 2 | |||
21.17 | even | 6 | 21.3.f.a.10.1 | ✓ | 2 | ||
21.20 | even | 2 | 147.3.f.a.19.1 | 2 | |||
28.3 | even | 6 | 1008.3.cg.a.577.1 | 2 | |||
84.23 | even | 6 | 2352.3.f.a.97.2 | 2 | |||
84.47 | odd | 6 | 2352.3.f.a.97.1 | 2 | |||
84.59 | odd | 6 | 336.3.bh.d.241.1 | 2 | |||
105.17 | odd | 12 | 525.3.s.e.199.2 | 4 | |||
105.38 | odd | 12 | 525.3.s.e.199.1 | 4 | |||
105.59 | even | 6 | 525.3.o.h.451.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
21.3.f.a.10.1 | ✓ | 2 | 21.17 | even | 6 | ||
21.3.f.a.19.1 | yes | 2 | 3.2 | odd | 2 | ||
63.3.m.d.10.1 | 2 | 7.3 | odd | 6 | inner | ||
63.3.m.d.19.1 | 2 | 1.1 | even | 1 | trivial | ||
147.3.d.c.97.1 | 2 | 21.2 | odd | 6 | |||
147.3.d.c.97.2 | 2 | 21.5 | even | 6 | |||
147.3.f.a.19.1 | 2 | 21.20 | even | 2 | |||
147.3.f.a.31.1 | 2 | 21.11 | odd | 6 | |||
336.3.bh.d.145.1 | 2 | 12.11 | even | 2 | |||
336.3.bh.d.241.1 | 2 | 84.59 | odd | 6 | |||
441.3.d.a.244.1 | 2 | 7.5 | odd | 6 | |||
441.3.d.a.244.2 | 2 | 7.2 | even | 3 | |||
441.3.m.g.19.1 | 2 | 7.6 | odd | 2 | |||
441.3.m.g.325.1 | 2 | 7.4 | even | 3 | |||
525.3.o.h.376.1 | 2 | 15.14 | odd | 2 | |||
525.3.o.h.451.1 | 2 | 105.59 | even | 6 | |||
525.3.s.e.124.1 | 4 | 15.2 | even | 4 | |||
525.3.s.e.124.2 | 4 | 15.8 | even | 4 | |||
525.3.s.e.199.1 | 4 | 105.38 | odd | 12 | |||
525.3.s.e.199.2 | 4 | 105.17 | odd | 12 | |||
1008.3.cg.a.145.1 | 2 | 4.3 | odd | 2 | |||
1008.3.cg.a.577.1 | 2 | 28.3 | even | 6 | |||
2352.3.f.a.97.1 | 2 | 84.47 | odd | 6 | |||
2352.3.f.a.97.2 | 2 | 84.23 | even | 6 |