Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [57,3,Mod(37,57)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(57, base_ring=CyclotomicField(2))
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("57.37");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 57 = 3 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 57.c (of order \(2\), degree \(1\), 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: | \(1.55313750685\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{-19})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 4x^{2} - 5x + 25 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 37.3 | ||
Root | \(2.13746 + 0.656712i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 57.37 |
Dual form | 57.3.c.b.37.2 |
$q$-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 \(\left(\mathbb{Z}/57\mathbb{Z}\right)^\times\).
\(n\) | \(20\) | \(40\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.31342i | 0.656712i | 0.944554 | + | 0.328356i | \(0.106495\pi\) | ||||
−0.944554 | + | 0.328356i | \(0.893505\pi\) | |||||||
\(3\) | − | 1.73205i | − | 0.577350i | ||||||
\(4\) | 2.27492 | 0.568729 | ||||||||
\(5\) | 1.27492 | 0.254983 | 0.127492 | − | 0.991840i | \(-0.459307\pi\) | ||||
0.127492 | + | 0.991840i | \(0.459307\pi\) | |||||||
\(6\) | 2.27492 | 0.379153 | ||||||||
\(7\) | 4.72508 | 0.675012 | 0.337506 | − | 0.941323i | \(-0.390417\pi\) | ||||
0.337506 | + | 0.941323i | \(0.390417\pi\) | |||||||
\(8\) | 8.24163i | 1.03020i | ||||||||
\(9\) | −3.00000 | −0.333333 | ||||||||
\(10\) | 1.67451i | 0.167451i | ||||||||
\(11\) | −7.27492 | −0.661356 | −0.330678 | − | 0.943744i | \(-0.607277\pi\) | ||||
−0.330678 | + | 0.943744i | \(0.607277\pi\) | |||||||
\(12\) | − | 3.94027i | − | 0.328356i | ||||||
\(13\) | − | 4.30136i | − | 0.330873i | −0.986220 | − | 0.165437i | \(-0.947097\pi\) | ||
0.986220 | − | 0.165437i | \(-0.0529034\pi\) | |||||||
\(14\) | 6.20604i | 0.443288i | ||||||||
\(15\) | − | 2.20822i | − | 0.147215i | ||||||
\(16\) | −1.72508 | −0.107818 | ||||||||
\(17\) | −20.3746 | −1.19851 | −0.599253 | − | 0.800560i | \(-0.704535\pi\) | ||||
−0.599253 | + | 0.800560i | \(0.704535\pi\) | |||||||
\(18\) | − | 3.94027i | − | 0.218904i | ||||||
\(19\) | −7.54983 | − | 17.4356i | −0.397360 | − | 0.917663i | ||||
\(20\) | 2.90033 | 0.145017 | ||||||||
\(21\) | − | 8.18408i | − | 0.389718i | ||||||
\(22\) | − | 9.55505i | − | 0.434321i | ||||||
\(23\) | 5.45017 | 0.236964 | 0.118482 | − | 0.992956i | \(-0.462197\pi\) | ||||
0.118482 | + | 0.992956i | \(0.462197\pi\) | |||||||
\(24\) | 14.2749 | 0.594788 | ||||||||
\(25\) | −23.3746 | −0.934983 | ||||||||
\(26\) | 5.64950 | 0.217289 | ||||||||
\(27\) | 5.19615i | 0.192450i | ||||||||
\(28\) | 10.7492 | 0.383899 | ||||||||
\(29\) | 8.60271i | 0.296645i | 0.988939 | + | 0.148323i | \(0.0473874\pi\) | ||||
−0.988939 | + | 0.148323i | \(0.952613\pi\) | |||||||
\(30\) | 2.90033 | 0.0966777 | ||||||||
\(31\) | 20.0624i | 0.647176i | 0.946198 | + | 0.323588i | \(0.104889\pi\) | ||||
−0.946198 | + | 0.323588i | \(0.895111\pi\) | |||||||
\(32\) | 30.7007i | 0.959398i | ||||||||
\(33\) | 12.6005i | 0.381834i | ||||||||
\(34\) | − | 26.7605i | − | 0.787073i | ||||||
\(35\) | 6.02409 | 0.172117 | ||||||||
\(36\) | −6.82475 | −0.189576 | ||||||||
\(37\) | 40.6169i | 1.09775i | 0.835903 | + | 0.548877i | \(0.184944\pi\) | ||||
−0.835903 | + | 0.548877i | \(0.815056\pi\) | |||||||
\(38\) | 22.9003 | − | 9.91613i | 0.602640 | − | 0.260951i | ||||
\(39\) | −7.45017 | −0.191030 | ||||||||
\(40\) | 10.5074i | 0.262685i | ||||||||
\(41\) | − | 31.2920i | − | 0.763220i | −0.924324 | − | 0.381610i | \(-0.875370\pi\) | ||
0.924324 | − | 0.381610i | \(-0.124630\pi\) | |||||||
\(42\) | 10.7492 | 0.255933 | ||||||||
\(43\) | 65.1238 | 1.51451 | 0.757253 | − | 0.653122i | \(-0.226541\pi\) | ||||
0.757253 | + | 0.653122i | \(0.226541\pi\) | |||||||
\(44\) | −16.5498 | −0.376133 | ||||||||
\(45\) | −3.82475 | −0.0849945 | ||||||||
\(46\) | 7.15838i | 0.155617i | ||||||||
\(47\) | 55.4743 | 1.18030 | 0.590152 | − | 0.807292i | \(-0.299068\pi\) | ||||
0.590152 | + | 0.807292i | \(0.299068\pi\) | |||||||
\(48\) | 2.98793i | 0.0622486i | ||||||||
\(49\) | −26.6736 | −0.544359 | ||||||||
\(50\) | − | 30.7007i | − | 0.614015i | ||||||
\(51\) | 35.2898i | 0.691957i | ||||||||
\(52\) | − | 9.78523i | − | 0.188177i | ||||||
\(53\) | − | 78.1149i | − | 1.47387i | −0.675966 | − | 0.736933i | \(-0.736273\pi\) | ||
0.675966 | − | 0.736933i | \(-0.263727\pi\) | |||||||
\(54\) | −6.82475 | −0.126384 | ||||||||
\(55\) | −9.27492 | −0.168635 | ||||||||
\(56\) | 38.9424i | 0.695399i | ||||||||
\(57\) | −30.1993 | + | 13.0767i | −0.529813 | + | 0.229416i | ||||
\(58\) | −11.2990 | −0.194810 | ||||||||
\(59\) | − | 69.5122i | − | 1.17817i | −0.808070 | − | 0.589087i | \(-0.799488\pi\) | ||
0.808070 | − | 0.589087i | \(-0.200512\pi\) | |||||||
\(60\) | − | 5.02352i | − | 0.0837253i | ||||||
\(61\) | −6.17525 | −0.101234 | −0.0506168 | − | 0.998718i | \(-0.516119\pi\) | ||||
−0.0506168 | + | 0.998718i | \(0.516119\pi\) | |||||||
\(62\) | −26.3505 | −0.425008 | ||||||||
\(63\) | −14.1752 | −0.225004 | ||||||||
\(64\) | −47.2234 | −0.737866 | ||||||||
\(65\) | − | 5.48387i | − | 0.0843673i | ||||||
\(66\) | −16.5498 | −0.250755 | ||||||||
\(67\) | 123.724i | 1.84662i | 0.384053 | + | 0.923311i | \(0.374528\pi\) | ||||
−0.384053 | + | 0.923311i | \(0.625472\pi\) | |||||||
\(68\) | −46.3505 | −0.681625 | ||||||||
\(69\) | − | 9.43996i | − | 0.136811i | ||||||
\(70\) | 7.91218i | 0.113031i | ||||||||
\(71\) | 3.11884i | 0.0439273i | 0.999759 | + | 0.0219637i | \(0.00699181\pi\) | ||||
−0.999759 | + | 0.0219637i | \(0.993008\pi\) | |||||||
\(72\) | − | 24.7249i | − | 0.343401i | ||||||
\(73\) | 33.8248 | 0.463353 | 0.231676 | − | 0.972793i | \(-0.425579\pi\) | ||||
0.231676 | + | 0.972793i | \(0.425579\pi\) | |||||||
\(74\) | −53.3472 | −0.720908 | ||||||||
\(75\) | 40.4860i | 0.539813i | ||||||||
\(76\) | −17.1752 | − | 39.6645i | −0.225990 | − | 0.521902i | ||||
\(77\) | −34.3746 | −0.446423 | ||||||||
\(78\) | − | 9.78523i | − | 0.125452i | ||||||
\(79\) | − | 87.6700i | − | 1.10975i | −0.831935 | − | 0.554873i | \(-0.812767\pi\) | ||
0.831935 | − | 0.554873i | \(-0.187233\pi\) | |||||||
\(80\) | −2.19934 | −0.0274917 | ||||||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | 41.0997 | 0.501215 | ||||||||
\(83\) | 121.698 | 1.46624 | 0.733119 | − | 0.680101i | \(-0.238064\pi\) | ||||
0.733119 | + | 0.680101i | \(0.238064\pi\) | |||||||
\(84\) | − | 18.6181i | − | 0.221644i | ||||||
\(85\) | −25.9759 | −0.305599 | ||||||||
\(86\) | 85.5351i | 0.994594i | ||||||||
\(87\) | 14.9003 | 0.171268 | ||||||||
\(88\) | − | 59.9572i | − | 0.681331i | ||||||
\(89\) | 69.9726i | 0.786209i | 0.919494 | + | 0.393104i | \(0.128599\pi\) | ||||
−0.919494 | + | 0.393104i | \(0.871401\pi\) | |||||||
\(90\) | − | 5.02352i | − | 0.0558169i | ||||||
\(91\) | − | 20.3243i | − | 0.223344i | ||||||
\(92\) | 12.3987 | 0.134768 | ||||||||
\(93\) | 34.7492 | 0.373647 | ||||||||
\(94\) | 72.8612i | 0.775119i | ||||||||
\(95\) | −9.62541 | − | 22.2289i | −0.101320 | − | 0.233989i | ||||
\(96\) | 53.1752 | 0.553909 | ||||||||
\(97\) | − | 111.081i | − | 1.14517i | −0.819846 | − | 0.572585i | \(-0.805941\pi\) | ||
0.819846 | − | 0.572585i | \(-0.194059\pi\) | |||||||
\(98\) | − | 35.0337i | − | 0.357487i | ||||||
\(99\) | 21.8248 | 0.220452 | ||||||||
\(100\) | −53.1752 | −0.531752 | ||||||||
\(101\) | 75.2508 | 0.745058 | 0.372529 | − | 0.928021i | \(-0.378491\pi\) | ||||
0.372529 | + | 0.928021i | \(0.378491\pi\) | |||||||
\(102\) | −46.3505 | −0.454417 | ||||||||
\(103\) | 188.474i | 1.82985i | 0.403628 | + | 0.914923i | \(0.367749\pi\) | ||||
−0.403628 | + | 0.914923i | \(0.632251\pi\) | |||||||
\(104\) | 35.4502 | 0.340867 | ||||||||
\(105\) | − | 10.4340i | − | 0.0993717i | ||||||
\(106\) | 102.598 | 0.967906 | ||||||||
\(107\) | 8.14236i | 0.0760968i | 0.999276 | + | 0.0380484i | \(0.0121141\pi\) | ||||
−0.999276 | + | 0.0380484i | \(0.987886\pi\) | |||||||
\(108\) | 11.8208i | 0.109452i | ||||||||
\(109\) | − | 119.192i | − | 1.09351i | −0.837294 | − | 0.546753i | \(-0.815864\pi\) | ||
0.837294 | − | 0.546753i | \(-0.184136\pi\) | |||||||
\(110\) | − | 12.1819i | − | 0.110745i | ||||||
\(111\) | 70.3505 | 0.633788 | ||||||||
\(112\) | −8.15116 | −0.0727782 | ||||||||
\(113\) | 196.355i | 1.73765i | 0.495117 | + | 0.868826i | \(0.335125\pi\) | ||||
−0.495117 | + | 0.868826i | \(0.664875\pi\) | |||||||
\(114\) | −17.1752 | − | 39.6645i | −0.150660 | − | 0.347935i | ||||
\(115\) | 6.94851 | 0.0604218 | ||||||||
\(116\) | 19.5705i | 0.168711i | ||||||||
\(117\) | 12.9041i | 0.110291i | ||||||||
\(118\) | 91.2990 | 0.773720 | ||||||||
\(119\) | −96.2716 | −0.809005 | ||||||||
\(120\) | 18.1993 | 0.151661 | ||||||||
\(121\) | −68.0756 | −0.562608 | ||||||||
\(122\) | − | 8.11072i | − | 0.0664813i | ||||||
\(123\) | −54.1993 | −0.440645 | ||||||||
\(124\) | 45.6404i | 0.368068i | ||||||||
\(125\) | −61.6736 | −0.493389 | ||||||||
\(126\) | − | 18.6181i | − | 0.147763i | ||||||
\(127\) | 16.0229i | 0.126165i | 0.998008 | + | 0.0630823i | \(0.0200931\pi\) | ||||
−0.998008 | + | 0.0630823i | \(0.979907\pi\) | |||||||
\(128\) | 60.7786i | 0.474833i | ||||||||
\(129\) | − | 112.798i | − | 0.874400i | ||||||
\(130\) | 7.20265 | 0.0554050 | ||||||||
\(131\) | 165.921 | 1.26657 | 0.633287 | − | 0.773917i | \(-0.281705\pi\) | ||||
0.633287 | + | 0.773917i | \(0.281705\pi\) | |||||||
\(132\) | 28.6652i | 0.217160i | ||||||||
\(133\) | −35.6736 | − | 82.3846i | −0.268223 | − | 0.619433i | ||||
\(134\) | −162.502 | −1.21270 | ||||||||
\(135\) | 6.62466i | 0.0490716i | ||||||||
\(136\) | − | 167.920i | − | 1.23470i | ||||||
\(137\) | −199.674 | −1.45747 | −0.728736 | − | 0.684795i | \(-0.759892\pi\) | ||||
−0.728736 | + | 0.684795i | \(0.759892\pi\) | |||||||
\(138\) | 12.3987 | 0.0898455 | ||||||||
\(139\) | −54.5739 | −0.392618 | −0.196309 | − | 0.980542i | \(-0.562896\pi\) | ||||
−0.196309 | + | 0.980542i | \(0.562896\pi\) | |||||||
\(140\) | 13.7043 | 0.0978879 | ||||||||
\(141\) | − | 96.0842i | − | 0.681448i | ||||||
\(142\) | −4.09636 | −0.0288476 | ||||||||
\(143\) | 31.2920i | 0.218825i | ||||||||
\(144\) | 5.17525 | 0.0359392 | ||||||||
\(145\) | 10.9677i | 0.0756396i | ||||||||
\(146\) | 44.4262i | 0.304289i | ||||||||
\(147\) | 46.2000i | 0.314286i | ||||||||
\(148\) | 92.4000i | 0.624325i | ||||||||
\(149\) | −245.323 | −1.64646 | −0.823232 | − | 0.567705i | \(-0.807831\pi\) | ||||
−0.823232 | + | 0.567705i | \(0.807831\pi\) | |||||||
\(150\) | −53.1752 | −0.354502 | ||||||||
\(151\) | − | 79.2974i | − | 0.525149i | −0.964912 | − | 0.262574i | \(-0.915429\pi\) | ||
0.964912 | − | 0.262574i | \(-0.0845715\pi\) | |||||||
\(152\) | 143.698 | − | 62.2229i | 0.945379 | − | 0.409361i | ||||
\(153\) | 61.1238 | 0.399502 | ||||||||
\(154\) | − | 45.1484i | − | 0.293171i | ||||||
\(155\) | 25.5780i | 0.165019i | ||||||||
\(156\) | −16.9485 | −0.108644 | ||||||||
\(157\) | −53.6977 | −0.342023 | −0.171012 | − | 0.985269i | \(-0.554704\pi\) | ||||
−0.171012 | + | 0.985269i | \(0.554704\pi\) | |||||||
\(158\) | 115.148 | 0.728784 | ||||||||
\(159\) | −135.299 | −0.850937 | ||||||||
\(160\) | 39.1409i | 0.244631i | ||||||||
\(161\) | 25.7525 | 0.159953 | ||||||||
\(162\) | 11.8208i | 0.0729680i | ||||||||
\(163\) | 78.3987 | 0.480973 | 0.240487 | − | 0.970652i | \(-0.422693\pi\) | ||||
0.240487 | + | 0.970652i | \(0.422693\pi\) | |||||||
\(164\) | − | 71.1867i | − | 0.434065i | ||||||
\(165\) | 16.0646i | 0.0973614i | ||||||||
\(166\) | 159.841i | 0.962896i | ||||||||
\(167\) | − | 293.350i | − | 1.75658i | −0.478124 | − | 0.878292i | \(-0.658683\pi\) | ||
0.478124 | − | 0.878292i | \(-0.341317\pi\) | |||||||
\(168\) | 67.4502 | 0.401489 | ||||||||
\(169\) | 150.498 | 0.890523 | ||||||||
\(170\) | − | 34.1174i | − | 0.200691i | ||||||
\(171\) | 22.6495 | + | 52.3068i | 0.132453 | + | 0.305888i | ||||
\(172\) | 148.151 | 0.861344 | ||||||||
\(173\) | 10.5074i | 0.0607364i | 0.999539 | + | 0.0303682i | \(0.00966798\pi\) | ||||
−0.999539 | + | 0.0303682i | \(0.990332\pi\) | |||||||
\(174\) | 19.5705i | 0.112474i | ||||||||
\(175\) | −110.447 | −0.631125 | ||||||||
\(176\) | 12.5498 | 0.0713059 | ||||||||
\(177\) | −120.399 | −0.680219 | ||||||||
\(178\) | −91.9036 | −0.516313 | ||||||||
\(179\) | − | 12.4121i | − | 0.0693412i | −0.999399 | − | 0.0346706i | \(-0.988962\pi\) | ||
0.999399 | − | 0.0346706i | \(-0.0110382\pi\) | |||||||
\(180\) | −8.70099 | −0.0483389 | ||||||||
\(181\) | 106.780i | 0.589945i | 0.955506 | + | 0.294973i | \(0.0953105\pi\) | ||||
−0.955506 | + | 0.294973i | \(0.904689\pi\) | |||||||
\(182\) | 26.6944 | 0.146672 | ||||||||
\(183\) | 10.6958i | 0.0584472i | ||||||||
\(184\) | 44.9182i | 0.244121i | ||||||||
\(185\) | 51.7832i | 0.279909i | ||||||||
\(186\) | 45.6404i | 0.245378i | ||||||||
\(187\) | 148.223 | 0.792639 | ||||||||
\(188\) | 126.199 | 0.671273 | ||||||||
\(189\) | 24.5523i | 0.129906i | ||||||||
\(190\) | 29.1960 | − | 12.6423i | 0.153663 | − | 0.0665382i | ||||
\(191\) | −19.0274 | −0.0996199 | −0.0498099 | − | 0.998759i | \(-0.515862\pi\) | ||||
−0.0498099 | + | 0.998759i | \(0.515862\pi\) | |||||||
\(192\) | 81.7934i | 0.426007i | ||||||||
\(193\) | 110.391i | 0.571974i | 0.958234 | + | 0.285987i | \(0.0923213\pi\) | ||||
−0.958234 | + | 0.285987i | \(0.907679\pi\) | |||||||
\(194\) | 145.897 | 0.752046 | ||||||||
\(195\) | −9.49834 | −0.0487095 | ||||||||
\(196\) | −60.6802 | −0.309593 | ||||||||
\(197\) | 328.749 | 1.66878 | 0.834389 | − | 0.551176i | \(-0.185821\pi\) | ||||
0.834389 | + | 0.551176i | \(0.185821\pi\) | |||||||
\(198\) | 28.6652i | 0.144774i | ||||||||
\(199\) | −266.973 | −1.34157 | −0.670785 | − | 0.741651i | \(-0.734043\pi\) | ||||
−0.670785 | + | 0.741651i | \(0.734043\pi\) | |||||||
\(200\) | − | 192.645i | − | 0.963223i | ||||||
\(201\) | 214.296 | 1.06615 | ||||||||
\(202\) | 98.8362i | 0.489288i | ||||||||
\(203\) | 40.6485i | 0.200239i | ||||||||
\(204\) | 80.2814i | 0.393536i | ||||||||
\(205\) | − | 39.8947i | − | 0.194608i | ||||||
\(206\) | −247.547 | −1.20168 | ||||||||
\(207\) | −16.3505 | −0.0789879 | ||||||||
\(208\) | 7.42019i | 0.0356740i | ||||||||
\(209\) | 54.9244 | + | 126.843i | 0.262796 | + | 0.606902i | ||||
\(210\) | 13.7043 | 0.0652586 | ||||||||
\(211\) | 70.4329i | 0.333805i | 0.985973 | + | 0.166903i | \(0.0533766\pi\) | ||||
−0.985973 | + | 0.166903i | \(0.946623\pi\) | |||||||
\(212\) | − | 177.705i | − | 0.838231i | ||||||
\(213\) | 5.40199 | 0.0253614 | ||||||||
\(214\) | −10.6944 | −0.0499737 | ||||||||
\(215\) | 83.0274 | 0.386174 | ||||||||
\(216\) | −42.8248 | −0.198263 | ||||||||
\(217\) | 94.7967i | 0.436851i | ||||||||
\(218\) | 156.550 | 0.718119 | ||||||||
\(219\) | − | 58.5862i | − | 0.267517i | ||||||
\(220\) | −21.0997 | −0.0959076 | ||||||||
\(221\) | 87.6383i | 0.396554i | ||||||||
\(222\) | 92.4000i | 0.416216i | ||||||||
\(223\) | − | 237.432i | − | 1.06472i | −0.846519 | − | 0.532359i | \(-0.821306\pi\) | ||
0.846519 | − | 0.532359i | \(-0.178694\pi\) | |||||||
\(224\) | 145.064i | 0.647605i | ||||||||
\(225\) | 70.1238 | 0.311661 | ||||||||
\(226\) | −257.897 | −1.14114 | ||||||||
\(227\) | − | 269.740i | − | 1.18828i | −0.804362 | − | 0.594140i | \(-0.797492\pi\) | ||
0.804362 | − | 0.594140i | \(-0.202508\pi\) | |||||||
\(228\) | −68.7010 | + | 29.7484i | −0.301320 | + | 0.130475i | ||||
\(229\) | 259.419 | 1.13284 | 0.566418 | − | 0.824118i | \(-0.308329\pi\) | ||||
0.566418 | + | 0.824118i | \(0.308329\pi\) | |||||||
\(230\) | 9.12634i | 0.0396797i | ||||||||
\(231\) | 59.5385i | 0.257743i | ||||||||
\(232\) | −70.9003 | −0.305605 | ||||||||
\(233\) | −52.6769 | −0.226081 | −0.113041 | − | 0.993590i | \(-0.536059\pi\) | ||||
−0.113041 | + | 0.993590i | \(0.536059\pi\) | |||||||
\(234\) | −16.9485 | −0.0724295 | ||||||||
\(235\) | 70.7251 | 0.300958 | ||||||||
\(236\) | − | 158.135i | − | 0.670062i | ||||||
\(237\) | −151.849 | −0.640712 | ||||||||
\(238\) | − | 126.445i | − | 0.531283i | ||||||
\(239\) | −346.120 | −1.44820 | −0.724101 | − | 0.689694i | \(-0.757745\pi\) | ||||
−0.724101 | + | 0.689694i | \(0.757745\pi\) | |||||||
\(240\) | 3.80936i | 0.0158724i | ||||||||
\(241\) | − | 300.278i | − | 1.24597i | −0.782235 | − | 0.622983i | \(-0.785921\pi\) | ||
0.782235 | − | 0.622983i | \(-0.214079\pi\) | |||||||
\(242\) | − | 89.4121i | − | 0.369472i | ||||||
\(243\) | − | 15.5885i | − | 0.0641500i | ||||||
\(244\) | −14.0482 | −0.0575745 | ||||||||
\(245\) | −34.0066 | −0.138803 | ||||||||
\(246\) | − | 71.1867i | − | 0.289377i | ||||||
\(247\) | −74.9967 | + | 32.4745i | −0.303630 | + | 0.131476i | ||||
\(248\) | −165.347 | −0.666723 | ||||||||
\(249\) | − | 210.787i | − | 0.846532i | ||||||
\(250\) | − | 81.0036i | − | 0.324014i | ||||||
\(251\) | 190.223 | 0.757862 | 0.378931 | − | 0.925425i | \(-0.376292\pi\) | ||||
0.378931 | + | 0.925425i | \(0.376292\pi\) | |||||||
\(252\) | −32.2475 | −0.127966 | ||||||||
\(253\) | −39.6495 | −0.156717 | ||||||||
\(254\) | −21.0449 | −0.0828538 | ||||||||
\(255\) | 44.9916i | 0.176438i | ||||||||
\(256\) | −268.722 | −1.04969 | ||||||||
\(257\) | 25.3478i | 0.0986295i | 0.998783 | + | 0.0493147i | \(0.0157037\pi\) | ||||
−0.998783 | + | 0.0493147i | \(0.984296\pi\) | |||||||
\(258\) | 148.151 | 0.574229 | ||||||||
\(259\) | 191.918i | 0.740997i | ||||||||
\(260\) | − | 12.4754i | − | 0.0479821i | ||||||
\(261\) | − | 25.8081i | − | 0.0988817i | ||||||
\(262\) | 217.925i | 0.831774i | ||||||||
\(263\) | −450.120 | −1.71148 | −0.855742 | − | 0.517402i | \(-0.826899\pi\) | ||||
−0.855742 | + | 0.517402i | \(0.826899\pi\) | |||||||
\(264\) | −103.849 | −0.393367 | ||||||||
\(265\) | − | 99.5901i | − | 0.375812i | ||||||
\(266\) | 108.206 | − | 46.8546i | 0.406789 | − | 0.176145i | ||||
\(267\) | 121.196 | 0.453918 | ||||||||
\(268\) | 281.461i | 1.05023i | ||||||||
\(269\) | 485.141i | 1.80350i | 0.432259 | + | 0.901749i | \(0.357716\pi\) | ||||
−0.432259 | + | 0.901749i | \(0.642284\pi\) | |||||||
\(270\) | −8.70099 | −0.0322259 | ||||||||
\(271\) | 156.997 | 0.579324 | 0.289662 | − | 0.957129i | \(-0.406457\pi\) | ||||
0.289662 | + | 0.957129i | \(0.406457\pi\) | |||||||
\(272\) | 35.1478 | 0.129220 | ||||||||
\(273\) | −35.2026 | −0.128947 | ||||||||
\(274\) | − | 262.256i | − | 0.957139i | ||||||
\(275\) | 170.048 | 0.618357 | ||||||||
\(276\) | − | 21.4751i | − | 0.0778085i | ||||||
\(277\) | 156.629 | 0.565447 | 0.282723 | − | 0.959202i | \(-0.408762\pi\) | ||||
0.282723 | + | 0.959202i | \(0.408762\pi\) | |||||||
\(278\) | − | 71.6787i | − | 0.257837i | ||||||
\(279\) | − | 60.1873i | − | 0.215725i | ||||||
\(280\) | 49.6483i | 0.177315i | ||||||||
\(281\) | 457.658i | 1.62868i | 0.580390 | + | 0.814339i | \(0.302900\pi\) | ||||
−0.580390 | + | 0.814339i | \(0.697100\pi\) | |||||||
\(282\) | 126.199 | 0.447515 | ||||||||
\(283\) | −46.5739 | −0.164572 | −0.0822861 | − | 0.996609i | \(-0.526222\pi\) | ||||
−0.0822861 | + | 0.996609i | \(0.526222\pi\) | |||||||
\(284\) | 7.09510i | 0.0249827i | ||||||||
\(285\) | −38.5017 | + | 16.6717i | −0.135094 | + | 0.0584972i | ||||
\(286\) | −41.0997 | −0.143705 | ||||||||
\(287\) | − | 147.857i | − | 0.515182i | ||||||
\(288\) | − | 92.1022i | − | 0.319799i | ||||||
\(289\) | 126.124 | 0.436414 | ||||||||
\(290\) | −14.4053 | −0.0496734 | ||||||||
\(291\) | −192.399 | −0.661164 | ||||||||
\(292\) | 76.9485 | 0.263522 | ||||||||
\(293\) | 222.163i | 0.758235i | 0.925349 | + | 0.379117i | \(0.123772\pi\) | ||||
−0.925349 | + | 0.379117i | \(0.876228\pi\) | |||||||
\(294\) | −60.6802 | −0.206395 | ||||||||
\(295\) | − | 88.6223i | − | 0.300415i | ||||||
\(296\) | −334.749 | −1.13091 | ||||||||
\(297\) | − | 37.8016i | − | 0.127278i | ||||||
\(298\) | − | 322.213i | − | 1.08125i | ||||||
\(299\) | − | 23.4431i | − | 0.0784050i | ||||||
\(300\) | 92.1022i | 0.307007i | ||||||||
\(301\) | 307.715 | 1.02231 | ||||||||
\(302\) | 104.151 | 0.344871 | ||||||||
\(303\) | − | 130.338i | − | 0.430159i | ||||||
\(304\) | 13.0241 | + | 30.0778i | 0.0428424 | + | 0.0989403i | ||||
\(305\) | −7.87293 | −0.0258129 | ||||||||
\(306\) | 80.2814i | 0.262358i | ||||||||
\(307\) | 492.069i | 1.60283i | 0.598108 | + | 0.801416i | \(0.295920\pi\) | ||||
−0.598108 | + | 0.801416i | \(0.704080\pi\) | |||||||
\(308\) | −78.1993 | −0.253894 | ||||||||
\(309\) | 326.447 | 1.05646 | ||||||||
\(310\) | −33.5947 | −0.108370 | ||||||||
\(311\) | 162.773 | 0.523387 | 0.261693 | − | 0.965151i | \(-0.415719\pi\) | ||||
0.261693 | + | 0.965151i | \(0.415719\pi\) | |||||||
\(312\) | − | 61.4015i | − | 0.196800i | ||||||
\(313\) | 414.894 | 1.32554 | 0.662770 | − | 0.748823i | \(-0.269381\pi\) | ||||
0.662770 | + | 0.748823i | \(0.269381\pi\) | |||||||
\(314\) | − | 70.5278i | − | 0.224611i | ||||||
\(315\) | −18.0723 | −0.0573723 | ||||||||
\(316\) | − | 199.442i | − | 0.631145i | ||||||
\(317\) | − | 365.750i | − | 1.15379i | −0.816819 | − | 0.576893i | \(-0.804265\pi\) | ||
0.816819 | − | 0.576893i | \(-0.195735\pi\) | |||||||
\(318\) | − | 177.705i | − | 0.558821i | ||||||
\(319\) | − | 62.5840i | − | 0.196188i | ||||||
\(320\) | −60.2060 | −0.188144 | ||||||||
\(321\) | 14.1030 | 0.0439345 | ||||||||
\(322\) | 33.8239i | 0.105043i | ||||||||
\(323\) | 153.825 | + | 355.243i | 0.476238 | + | 1.09982i | ||||
\(324\) | 20.4743 | 0.0631921 | ||||||||
\(325\) | 100.542i | 0.309361i | ||||||||
\(326\) | 102.971i | 0.315861i | ||||||||
\(327\) | −206.447 | −0.631336 | ||||||||
\(328\) | 257.897 | 0.786271 | ||||||||
\(329\) | 262.120 | 0.796719 | ||||||||
\(330\) | −21.0997 | −0.0639384 | ||||||||
\(331\) | − | 220.258i | − | 0.665433i | −0.943027 | − | 0.332716i | \(-0.892035\pi\) | ||
0.943027 | − | 0.332716i | \(-0.107965\pi\) | |||||||
\(332\) | 276.852 | 0.833892 | ||||||||
\(333\) | − | 121.851i | − | 0.365918i | ||||||
\(334\) | 385.292 | 1.15357 | ||||||||
\(335\) | 157.737i | 0.470858i | ||||||||
\(336\) | 14.1182i | 0.0420185i | ||||||||
\(337\) | − | 240.980i | − | 0.715073i | −0.933899 | − | 0.357536i | \(-0.883617\pi\) | ||
0.933899 | − | 0.357536i | \(-0.116383\pi\) | |||||||
\(338\) | 197.668i | 0.584817i | ||||||||
\(339\) | 340.096 | 1.00323 | ||||||||
\(340\) | −59.0930 | −0.173803 | ||||||||
\(341\) | − | 145.953i | − | 0.428014i | ||||||
\(342\) | −68.7010 | + | 29.7484i | −0.200880 | + | 0.0869836i | ||||
\(343\) | −357.564 | −1.04246 | ||||||||
\(344\) | 536.726i | 1.56025i | ||||||||
\(345\) | − | 12.0352i | − | 0.0348846i | ||||||
\(346\) | −13.8007 | −0.0398863 | ||||||||
\(347\) | −234.876 | −0.676877 | −0.338438 | − | 0.940989i | \(-0.609899\pi\) | ||||
−0.338438 | + | 0.940989i | \(0.609899\pi\) | |||||||
\(348\) | 33.8970 | 0.0974052 | ||||||||
\(349\) | −440.677 | −1.26268 | −0.631342 | − | 0.775504i | \(-0.717496\pi\) | ||||
−0.631342 | + | 0.775504i | \(0.717496\pi\) | |||||||
\(350\) | − | 145.064i | − | 0.414467i | ||||||
\(351\) | 22.3505 | 0.0636766 | ||||||||
\(352\) | − | 223.345i | − | 0.634504i | ||||||
\(353\) | −543.292 | −1.53907 | −0.769536 | − | 0.638603i | \(-0.779512\pi\) | ||||
−0.769536 | + | 0.638603i | \(0.779512\pi\) | |||||||
\(354\) | − | 158.135i | − | 0.446708i | ||||||
\(355\) | 3.97626i | 0.0112007i | ||||||||
\(356\) | 159.182i | 0.447140i | ||||||||
\(357\) | 166.747i | 0.467079i | ||||||||
\(358\) | 16.3023 | 0.0455372 | ||||||||
\(359\) | −38.5191 | −0.107296 | −0.0536478 | − | 0.998560i | \(-0.517085\pi\) | ||||
−0.0536478 | + | 0.998560i | \(0.517085\pi\) | |||||||
\(360\) | − | 31.5222i | − | 0.0875616i | ||||||
\(361\) | −247.000 | + | 263.272i | −0.684211 | + | 0.729285i | ||||
\(362\) | −140.248 | −0.387424 | ||||||||
\(363\) | 117.910i | 0.324822i | ||||||||
\(364\) | − | 46.2360i | − | 0.127022i | ||||||
\(365\) | 43.1238 | 0.118147 | ||||||||
\(366\) | −14.0482 | −0.0383830 | ||||||||
\(367\) | −568.997 | −1.55040 | −0.775200 | − | 0.631716i | \(-0.782351\pi\) | ||||
−0.775200 | + | 0.631716i | \(0.782351\pi\) | |||||||
\(368\) | −9.40199 | −0.0255489 | ||||||||
\(369\) | 93.8760i | 0.254407i | ||||||||
\(370\) | −68.0132 | −0.183820 | ||||||||
\(371\) | − | 369.099i | − | 0.994877i | ||||||
\(372\) | 79.0515 | 0.212504 | ||||||||
\(373\) | − | 61.8618i | − | 0.165849i | −0.996556 | − | 0.0829247i | \(-0.973574\pi\) | ||
0.996556 | − | 0.0829247i | \(-0.0264261\pi\) | |||||||
\(374\) | 194.680i | 0.520535i | ||||||||
\(375\) | 106.822i | 0.284858i | ||||||||
\(376\) | 457.198i | 1.21595i | ||||||||
\(377\) | 37.0033 | 0.0981520 | ||||||||
\(378\) | −32.2475 | −0.0853109 | ||||||||
\(379\) | − | 342.601i | − | 0.903960i | −0.892028 | − | 0.451980i | \(-0.850718\pi\) | ||
0.892028 | − | 0.451980i | \(-0.149282\pi\) | |||||||
\(380\) | −21.8970 | − | 50.5690i | −0.0576237 | − | 0.133076i | ||||
\(381\) | 27.7525 | 0.0728412 | ||||||||
\(382\) | − | 24.9910i | − | 0.0654216i | ||||||
\(383\) | − | 77.1309i | − | 0.201386i | −0.994918 | − | 0.100693i | \(-0.967894\pi\) | ||
0.994918 | − | 0.100693i | \(-0.0321060\pi\) | |||||||
\(384\) | 105.272 | 0.274145 | ||||||||
\(385\) | −43.8248 | −0.113831 | ||||||||
\(386\) | −144.990 | −0.375622 | ||||||||
\(387\) | −195.371 | −0.504835 | ||||||||
\(388\) | − | 252.701i | − | 0.651291i | ||||||
\(389\) | 433.770 | 1.11509 | 0.557545 | − | 0.830147i | \(-0.311743\pi\) | ||||
0.557545 | + | 0.830147i | \(0.311743\pi\) | |||||||
\(390\) | − | 12.4754i | − | 0.0319881i | ||||||
\(391\) | −111.045 | −0.284002 | ||||||||
\(392\) | − | 219.834i | − | 0.560801i | ||||||
\(393\) | − | 287.384i | − | 0.731256i | ||||||
\(394\) | 431.787i | 1.09591i | ||||||||
\(395\) | − | 111.772i | − | 0.282967i | ||||||
\(396\) | 49.6495 | 0.125378 | ||||||||
\(397\) | −283.069 | −0.713020 | −0.356510 | − | 0.934291i | \(-0.616033\pi\) | ||||
−0.356510 | + | 0.934291i | \(0.616033\pi\) | |||||||
\(398\) | − | 350.648i | − | 0.881026i | ||||||
\(399\) | −142.694 | + | 61.7885i | −0.357630 | + | 0.154858i | ||||
\(400\) | 40.3231 | 0.100808 | ||||||||
\(401\) | − | 323.491i | − | 0.806710i | −0.915044 | − | 0.403355i | \(-0.867844\pi\) | ||
0.915044 | − | 0.403355i | \(-0.132156\pi\) | |||||||
\(402\) | 281.461i | 0.700152i | ||||||||
\(403\) | 86.2957 | 0.214133 | ||||||||
\(404\) | 171.189 | 0.423736 | ||||||||
\(405\) | 11.4743 | 0.0283315 | ||||||||
\(406\) | −53.3887 | −0.131499 | ||||||||
\(407\) | − | 295.484i | − | 0.726006i | ||||||
\(408\) | −290.846 | −0.712857 | ||||||||
\(409\) | − | 546.741i | − | 1.33678i | −0.743813 | − | 0.668388i | \(-0.766985\pi\) | ||
0.743813 | − | 0.668388i | \(-0.233015\pi\) | |||||||
\(410\) | 52.3987 | 0.127802 | ||||||||
\(411\) | 345.845i | 0.841472i | ||||||||
\(412\) | 428.763i | 1.04069i | ||||||||
\(413\) | − | 328.451i | − | 0.795281i | ||||||
\(414\) | − | 21.4751i | − | 0.0518723i | ||||||
\(415\) | 155.154 | 0.373866 | ||||||||
\(416\) | 132.055 | 0.317439 | ||||||||
\(417\) | 94.5248i | 0.226678i | ||||||||
\(418\) | −166.598 | + | 72.1391i | −0.398560 | + | 0.172581i | ||||
\(419\) | −352.997 | −0.842474 | −0.421237 | − | 0.906951i | \(-0.638404\pi\) | ||||
−0.421237 | + | 0.906951i | \(0.638404\pi\) | |||||||
\(420\) | − | 23.7366i | − | 0.0565156i | ||||||
\(421\) | 578.525i | 1.37417i | 0.726578 | + | 0.687084i | \(0.241110\pi\) | ||||
−0.726578 | + | 0.687084i | \(0.758890\pi\) | |||||||
\(422\) | −92.5083 | −0.219214 | ||||||||
\(423\) | −166.423 | −0.393434 | ||||||||
\(424\) | 643.794 | 1.51838 | ||||||||
\(425\) | 476.248 | 1.12058 | ||||||||
\(426\) | 7.09510i | 0.0166552i | ||||||||
\(427\) | −29.1786 | −0.0683339 | ||||||||
\(428\) | 18.5232i | 0.0432785i | ||||||||
\(429\) | 54.1993 | 0.126339 | ||||||||
\(430\) | 109.050i | 0.253605i | ||||||||
\(431\) | − | 628.896i | − | 1.45915i | −0.683898 | − | 0.729577i | \(-0.739717\pi\) | ||
0.683898 | − | 0.729577i | \(-0.260283\pi\) | |||||||
\(432\) | − | 8.96379i | − | 0.0207495i | ||||||
\(433\) | − | 122.803i | − | 0.283610i | −0.989895 | − | 0.141805i | \(-0.954709\pi\) | ||
0.989895 | − | 0.141805i | \(-0.0452905\pi\) | |||||||
\(434\) | −124.508 | −0.286885 | ||||||||
\(435\) | 18.9967 | 0.0436705 | ||||||||
\(436\) | − | 271.152i | − | 0.621909i | ||||||
\(437\) | −41.1478 | − | 95.0269i | −0.0941598 | − | 0.217453i | ||||
\(438\) | 76.9485 | 0.175682 | ||||||||
\(439\) | − | 63.3694i | − | 0.144350i | −0.997392 | − | 0.0721748i | \(-0.977006\pi\) | ||
0.997392 | − | 0.0721748i | \(-0.0229939\pi\) | |||||||
\(440\) | − | 76.4404i | − | 0.173728i | ||||||
\(441\) | 80.0208 | 0.181453 | ||||||||
\(442\) | −115.106 | −0.260421 | ||||||||
\(443\) | 610.320 | 1.37770 | 0.688849 | − | 0.724905i | \(-0.258117\pi\) | ||||
0.688849 | + | 0.724905i | \(0.258117\pi\) | |||||||
\(444\) | 160.042 | 0.360454 | ||||||||
\(445\) | 89.2092i | 0.200470i | ||||||||
\(446\) | 311.849 | 0.699213 | ||||||||
\(447\) | 424.912i | 0.950586i | ||||||||
\(448\) | −223.135 | −0.498068 | ||||||||
\(449\) | 410.772i | 0.914860i | 0.889246 | + | 0.457430i | \(0.151230\pi\) | ||||
−0.889246 | + | 0.457430i | \(0.848770\pi\) | |||||||
\(450\) | 92.1022i | 0.204672i | ||||||||
\(451\) | 227.647i | 0.504760i | ||||||||
\(452\) | 446.691i | 0.988254i | ||||||||
\(453\) | −137.347 | −0.303195 | ||||||||
\(454\) | 354.282 | 0.780358 | ||||||||
\(455\) | − | 25.9117i | − | 0.0569489i | ||||||
\(456\) | −107.773 | − | 248.892i | −0.236345 | − | 0.545815i | ||||
\(457\) | 251.722 | 0.550814 | 0.275407 | − | 0.961328i | \(-0.411187\pi\) | ||||
0.275407 | + | 0.961328i | \(0.411187\pi\) | |||||||
\(458\) | 340.728i | 0.743947i | ||||||||
\(459\) | − | 105.869i | − | 0.230652i | ||||||
\(460\) | 15.8073 | 0.0343637 | ||||||||
\(461\) | −224.622 | −0.487250 | −0.243625 | − | 0.969870i | \(-0.578337\pi\) | ||||
−0.243625 | + | 0.969870i | \(0.578337\pi\) | |||||||
\(462\) | −78.1993 | −0.169263 | ||||||||
\(463\) | −196.375 | −0.424135 | −0.212068 | − | 0.977255i | \(-0.568020\pi\) | ||||
−0.212068 | + | 0.977255i | \(0.568020\pi\) | |||||||
\(464\) | − | 14.8404i | − | 0.0319836i | ||||||
\(465\) | 44.3023 | 0.0952738 | ||||||||
\(466\) | − | 69.1871i | − | 0.148470i | ||||||
\(467\) | −106.381 | −0.227797 | −0.113899 | − | 0.993492i | \(-0.536334\pi\) | ||||
−0.113899 | + | 0.993492i | \(0.536334\pi\) | |||||||
\(468\) | 29.3557i | 0.0627258i | ||||||||
\(469\) | 584.605i | 1.24649i | ||||||||
\(470\) | 92.8920i | 0.197643i | ||||||||
\(471\) | 93.0071i | 0.197467i | ||||||||
\(472\) | 572.894 | 1.21376 | ||||||||
\(473\) | −473.770 | −1.00163 | ||||||||
\(474\) | − | 199.442i | − | 0.420764i | ||||||
\(475\) | 176.474 | + | 407.550i | 0.371525 | + | 0.858000i | ||||
\(476\) | −219.010 | −0.460105 | ||||||||
\(477\) | 234.345i | 0.491289i | ||||||||
\(478\) | − | 454.603i | − | 0.951052i | ||||||
\(479\) | 463.154 | 0.966920 | 0.483460 | − | 0.875367i | \(-0.339380\pi\) | ||||
0.483460 | + | 0.875367i | \(0.339380\pi\) | |||||||
\(480\) | 67.7940 | 0.141238 | ||||||||
\(481\) | 174.708 | 0.363217 | ||||||||
\(482\) | 394.392 | 0.818241 | ||||||||
\(483\) | − | 44.6046i | − | 0.0923491i | ||||||
\(484\) | −154.866 | −0.319972 | ||||||||
\(485\) | − | 141.620i | − | 0.291999i | ||||||
\(486\) | 20.4743 | 0.0421281 | ||||||||
\(487\) | 248.463i | 0.510191i | 0.966916 | + | 0.255095i | \(0.0821069\pi\) | ||||
−0.966916 | + | 0.255095i | \(0.917893\pi\) | |||||||
\(488\) | − | 50.8941i | − | 0.104291i | ||||||
\(489\) | − | 135.790i | − | 0.277690i | ||||||
\(490\) | − | 44.6651i | − | 0.0911533i | ||||||
\(491\) | 305.588 | 0.622379 | 0.311189 | − | 0.950348i | \(-0.399273\pi\) | ||||
0.311189 | + | 0.950348i | \(0.399273\pi\) | |||||||
\(492\) | −123.299 | −0.250608 | ||||||||
\(493\) | − | 175.277i | − | 0.355531i | ||||||
\(494\) | −42.6528 | − | 98.5025i | −0.0863417 | − | 0.199398i | ||||
\(495\) | 27.8248 | 0.0562116 | ||||||||
\(496\) | − | 34.6094i | − | 0.0697770i | ||||||
\(497\) | 14.7368i | 0.0296514i | ||||||||
\(498\) | 276.852 | 0.555928 | ||||||||
\(499\) | 268.918 | 0.538913 | 0.269457 | − | 0.963013i | \(-0.413156\pi\) | ||||
0.269457 | + | 0.963013i | \(0.413156\pi\) | |||||||
\(500\) | −140.302 | −0.280605 | ||||||||
\(501\) | −508.096 | −1.01416 | ||||||||
\(502\) | 249.844i | 0.497697i | ||||||||
\(503\) | −507.154 | −1.00826 | −0.504130 | − | 0.863628i | \(-0.668187\pi\) | ||||
−0.504130 | + | 0.863628i | \(0.668187\pi\) | |||||||
\(504\) | − | 116.827i | − | 0.231800i | ||||||
\(505\) | 95.9386 | 0.189977 | ||||||||
\(506\) | − | 52.0766i | − | 0.102918i | ||||||
\(507\) | − | 260.671i | − | 0.514144i | ||||||
\(508\) | 36.4508i | 0.0717535i | ||||||||
\(509\) | − | 407.256i | − | 0.800111i | −0.916491 | − | 0.400055i | \(-0.868991\pi\) | ||
0.916491 | − | 0.400055i | \(-0.131009\pi\) | |||||||
\(510\) | −59.0930 | −0.115869 | ||||||||
\(511\) | 159.825 | 0.312769 | ||||||||
\(512\) | − | 109.831i | − | 0.214514i | ||||||
\(513\) | 90.5980 | − | 39.2301i | 0.176604 | − | 0.0764719i | ||||
\(514\) | −33.2924 | −0.0647712 | ||||||||
\(515\) | 240.289i | 0.466581i | ||||||||
\(516\) | − | 256.605i | − | 0.497297i | ||||||
\(517\) | −403.571 | −0.780601 | ||||||||
\(518\) | −252.070 | −0.486621 | ||||||||
\(519\) | 18.1993 | 0.0350662 | ||||||||
\(520\) | 45.1960 | 0.0869154 | ||||||||
\(521\) | 607.190i | 1.16543i | 0.812676 | + | 0.582716i | \(0.198010\pi\) | ||||
−0.812676 | + | 0.582716i | \(0.801990\pi\) | |||||||
\(522\) | 33.8970 | 0.0649368 | ||||||||
\(523\) | 209.227i | 0.400052i | 0.979791 | + | 0.200026i | \(0.0641026\pi\) | ||||
−0.979791 | + | 0.200026i | \(0.935897\pi\) | |||||||
\(524\) | 377.457 | 0.720337 | ||||||||
\(525\) | 191.300i | 0.364380i | ||||||||
\(526\) | − | 591.199i | − | 1.12395i | ||||||
\(527\) | − | 408.764i | − | 0.775643i | ||||||
\(528\) | − | 21.7370i | − | 0.0411685i | ||||||
\(529\) | −499.296 | −0.943848 | ||||||||
\(530\) | 130.804 | 0.246800 | ||||||||
\(531\) | 208.537i | 0.392724i | ||||||||
\(532\) | −81.1545 | − | 187.418i | −0.152546 | − | 0.352290i | ||||
\(533\) | −134.598 | −0.252529 | ||||||||
\(534\) | 159.182i | 0.298093i | ||||||||
\(535\) | 10.3808i | 0.0194034i | ||||||||
\(536\) | −1019.68 | −1.90240 | ||||||||
\(537\) | −21.4983 | −0.0400342 | ||||||||
\(538\) | −637.196 | −1.18438 | ||||||||
\(539\) | 194.048 | 0.360015 | ||||||||
\(540\) | 15.0706i | 0.0279084i | ||||||||
\(541\) | −44.6637 | −0.0825576 | −0.0412788 | − | 0.999148i | \(-0.513143\pi\) | ||||
−0.0412788 | + | 0.999148i | \(0.513143\pi\) | |||||||
\(542\) | 206.203i | 0.380449i | ||||||||
\(543\) | 184.949 | 0.340605 | ||||||||
\(544\) | − | 625.515i | − | 1.14984i | ||||||
\(545\) | − | 151.960i | − | 0.278826i | ||||||
\(546\) | − | 46.2360i | − | 0.0846813i | ||||||
\(547\) | − | 595.405i | − | 1.08849i | −0.838925 | − | 0.544246i | \(-0.816816\pi\) | ||
0.838925 | − | 0.544246i | \(-0.183184\pi\) | |||||||
\(548\) | −454.241 | −0.828907 | ||||||||
\(549\) | 18.5257 | 0.0337445 | ||||||||
\(550\) | 223.345i | 0.406082i | ||||||||
\(551\) | 149.993 | − | 64.9490i | 0.272220 | − | 0.117875i | ||||
\(552\) | 77.8007 | 0.140943 | ||||||||
\(553\) | − | 414.248i | − | 0.749092i | ||||||
\(554\) | 205.720i | 0.371336i | ||||||||
\(555\) | 89.6911 | 0.161606 | ||||||||
\(556\) | −124.151 | −0.223293 | ||||||||
\(557\) | −78.4228 | −0.140795 | −0.0703975 | − | 0.997519i | \(-0.522427\pi\) | ||||
−0.0703975 | + | 0.997519i | \(0.522427\pi\) | |||||||
\(558\) | 79.0515 | 0.141669 | ||||||||
\(559\) | − | 280.120i | − | 0.501110i | ||||||
\(560\) | −10.3921 | −0.0185572 | ||||||||
\(561\) | − | 256.731i | − | 0.457630i | ||||||
\(562\) | −601.100 | −1.06957 | ||||||||
\(563\) | 457.825i | 0.813189i | 0.913609 | + | 0.406594i | \(0.133284\pi\) | ||||
−0.913609 | + | 0.406594i | \(0.866716\pi\) | |||||||
\(564\) | − | 218.584i | − | 0.387560i | ||||||
\(565\) | 250.336i | 0.443073i | ||||||||
\(566\) | − | 61.1713i | − | 0.108077i | ||||||
\(567\) | 42.5257 | 0.0750013 | ||||||||
\(568\) | −25.7043 | −0.0452541 | ||||||||
\(569\) | 307.833i | 0.541007i | 0.962719 | + | 0.270504i | \(0.0871902\pi\) | ||||
−0.962719 | + | 0.270504i | \(0.912810\pi\) | |||||||
\(570\) | −21.8970 | − | 50.5690i | −0.0384158 | − | 0.0887175i | ||||
\(571\) | 589.492 | 1.03238 | 0.516192 | − | 0.856473i | \(-0.327349\pi\) | ||||
0.516192 | + | 0.856473i | \(0.327349\pi\) | |||||||
\(572\) | 71.1867i | 0.124452i | ||||||||
\(573\) | 32.9564i | 0.0575156i | ||||||||
\(574\) | 194.199 | 0.338326 | ||||||||
\(575\) | −127.395 | −0.221557 | ||||||||
\(576\) | 141.670 | 0.245955 | ||||||||
\(577\) | −363.262 | −0.629570 | −0.314785 | − | 0.949163i | \(-0.601932\pi\) | ||||
−0.314785 | + | 0.949163i | \(0.601932\pi\) | |||||||
\(578\) | 165.654i | 0.286599i | ||||||||
\(579\) | 191.203 | 0.330229 | ||||||||
\(580\) | 24.9507i | 0.0430185i | ||||||||
\(581\) | 575.032 | 0.989727 | ||||||||
\(582\) | − | 252.701i | − | 0.434194i | ||||||
\(583\) | 568.280i | 0.974751i | ||||||||
\(584\) | 278.771i | 0.477348i | ||||||||
\(585\) | 16.4516i | 0.0281224i | ||||||||
\(586\) | −291.794 | −0.497942 | ||||||||
\(587\) | 391.625 | 0.667164 | 0.333582 | − | 0.942721i | \(-0.391743\pi\) | ||||
0.333582 | + | 0.942721i | \(0.391743\pi\) | |||||||
\(588\) | 105.101i | 0.178744i | ||||||||
\(589\) | 349.801 | − | 151.468i | 0.593889 | − | 0.257162i | ||||
\(590\) | 116.399 | 0.197286 | ||||||||
\(591\) | − | 569.410i | − | 0.963469i | ||||||
\(592\) | − | 70.0675i | − | 0.118357i | ||||||
\(593\) | −212.900 | −0.359022 | −0.179511 | − | 0.983756i | \(-0.557452\pi\) | ||||
−0.179511 | + | 0.983756i | \(0.557452\pi\) | |||||||
\(594\) | 49.6495 | 0.0835850 | ||||||||
\(595\) | −122.738 | −0.206283 | ||||||||
\(596\) | −558.090 | −0.936392 | ||||||||
\(597\) | 462.410i | 0.774556i | ||||||||
\(598\) | 30.7907 | 0.0514895 | ||||||||
\(599\) | 916.888i | 1.53070i | 0.643616 | + | 0.765349i | \(0.277434\pi\) | ||||
−0.643616 | + | 0.765349i | \(0.722566\pi\) | |||||||
\(600\) | −333.670 | −0.556117 | ||||||||
\(601\) | − | 485.078i | − | 0.807118i | −0.914954 | − | 0.403559i | \(-0.867773\pi\) | ||
0.914954 | − | 0.403559i | \(-0.132227\pi\) | |||||||
\(602\) | 404.160i | 0.671363i | ||||||||
\(603\) | − | 371.171i | − | 0.615541i | ||||||
\(604\) | − | 180.395i | − | 0.298667i | ||||||
\(605\) | −86.7907 | −0.143456 | ||||||||
\(606\) | 171.189 | 0.282491 | ||||||||
\(607\) | 193.101i | 0.318123i | 0.987269 | + | 0.159061i | \(0.0508468\pi\) | ||||
−0.987269 | + | 0.159061i | \(0.949153\pi\) | |||||||
\(608\) | 535.286 | − | 231.786i | 0.880404 | − | 0.381226i | ||||
\(609\) | 70.4053 | 0.115608 | ||||||||
\(610\) | − | 10.3405i | − | 0.0169516i | ||||||
\(611\) | − | 238.614i | − | 0.390531i | ||||||
\(612\) | 139.051 | 0.227208 | ||||||||
\(613\) | −142.368 | −0.232248 | −0.116124 | − | 0.993235i | \(-0.537047\pi\) | ||||
−0.116124 | + | 0.993235i | \(0.537047\pi\) | |||||||
\(614\) | −646.296 | −1.05260 | ||||||||
\(615\) | −69.0997 | −0.112357 | ||||||||
\(616\) | − | 283.303i | − | 0.459907i | ||||||
\(617\) | −547.770 | −0.887796 | −0.443898 | − | 0.896077i | \(-0.646405\pi\) | ||||
−0.443898 | + | 0.896077i | \(0.646405\pi\) | |||||||
\(618\) | 428.763i | 0.693792i | ||||||||
\(619\) | 814.482 | 1.31580 | 0.657901 | − | 0.753104i | \(-0.271444\pi\) | ||||
0.657901 | + | 0.753104i | \(0.271444\pi\) | |||||||
\(620\) | 58.1877i | 0.0938512i | ||||||||
\(621\) | 28.3199i | 0.0456037i | ||||||||
\(622\) | 213.790i | 0.343714i | ||||||||
\(623\) | 330.626i | 0.530700i | ||||||||
\(624\) | 12.8522 | 0.0205964 | ||||||||
\(625\) | 505.736 | 0.809177 | ||||||||
\(626\) | 544.931i | 0.870497i | ||||||||
\(627\) | 219.698 | − | 95.1319i | 0.350395 | − | 0.151725i | ||||
\(628\) | −122.158 | −0.194519 | ||||||||
\(629\) | − | 827.552i | − | 1.31566i | ||||||
\(630\) | − | 23.7366i | − | 0.0376771i | ||||||
\(631\) | 641.509 | 1.01665 | 0.508327 | − | 0.861164i | \(-0.330264\pi\) | ||||
0.508327 | + | 0.861164i | \(0.330264\pi\) | |||||||
\(632\) | 722.543 | 1.14326 | ||||||||
\(633\) | 121.993 | 0.192723 | ||||||||
\(634\) | 480.385 | 0.757706 | ||||||||
\(635\) | 20.4279i | 0.0321699i | ||||||||
\(636\) | −307.794 | −0.483953 | ||||||||
\(637\) | 114.733i | 0.180114i | ||||||||
\(638\) | 82.1993 | 0.128839 | ||||||||
\(639\) | − | 9.35652i | − | 0.0146424i | ||||||
\(640\) | 77.4877i | 0.121074i | ||||||||
\(641\) | 352.878i | 0.550512i | 0.961371 | + | 0.275256i | \(0.0887626\pi\) | ||||
−0.961371 | + | 0.275256i | \(0.911237\pi\) | |||||||
\(642\) | 18.5232i | 0.0288523i | ||||||||
\(643\) | −455.757 | −0.708797 | −0.354399 | − | 0.935094i | \(-0.615314\pi\) | ||||
−0.354399 | + | 0.935094i | \(0.615314\pi\) | |||||||
\(644\) | 58.5848 | 0.0909701 | ||||||||
\(645\) | − | 143.808i | − | 0.222958i | ||||||
\(646\) | −466.585 | + | 202.037i | −0.722267 | + | 0.312751i | ||||
\(647\) | 484.368 | 0.748637 | 0.374318 | − | 0.927300i | \(-0.377877\pi\) | ||||
0.374318 | + | 0.927300i | \(0.377877\pi\) | |||||||
\(648\) | 74.1746i | 0.114467i | ||||||||
\(649\) | 505.696i | 0.779192i | ||||||||
\(650\) | −132.055 | −0.203161 | ||||||||
\(651\) | 164.193 | 0.252216 | ||||||||
\(652\) | 178.350 | 0.273544 | ||||||||
\(653\) | 280.780 | 0.429985 | 0.214992 | − | 0.976616i | \(-0.431027\pi\) | ||||
0.214992 | + | 0.976616i | \(0.431027\pi\) | |||||||
\(654\) | − | 271.152i | − | 0.414606i | ||||||
\(655\) | 211.536 | 0.322955 | ||||||||
\(656\) | 53.9813i | 0.0822886i | ||||||||
\(657\) | −101.474 | −0.154451 | ||||||||
\(658\) | 344.275i | 0.523215i | ||||||||
\(659\) | 800.259i | 1.21435i | 0.794567 | + | 0.607177i | \(0.207698\pi\) | ||||
−0.794567 | + | 0.607177i | \(0.792302\pi\) | |||||||
\(660\) | 36.5457i | 0.0553723i | ||||||||
\(661\) | − | 812.996i | − | 1.22995i | −0.788547 | − | 0.614975i | \(-0.789166\pi\) | ||
0.788547 | − | 0.614975i | \(-0.210834\pi\) | |||||||
\(662\) | 289.292 | 0.436998 | ||||||||
\(663\) | 151.794 | 0.228950 | ||||||||
\(664\) | 1002.99i | 1.51052i | ||||||||
\(665\) | −45.4809 | − | 105.034i | −0.0683923 | − | 0.157945i | ||||
\(666\) | 160.042 | 0.240303 | ||||||||
\(667\) | 46.8862i | 0.0702941i | ||||||||
\(668\) | − | 667.346i | − | 0.999021i | ||||||
\(669\) | −411.244 | −0.614715 | ||||||||
\(670\) | −207.176 | −0.309218 | ||||||||
\(671\) | 44.9244 | 0.0669514 | ||||||||
\(672\) | 251.257 | 0.373895 | ||||||||
\(673\) | − | 79.8930i | − | 0.118712i | −0.998237 | − | 0.0593559i | \(-0.981095\pi\) | ||
0.998237 | − | 0.0593559i | \(-0.0189047\pi\) | |||||||
\(674\) | 316.508 | 0.469597 | ||||||||
\(675\) | − | 121.458i | − | 0.179938i | ||||||
\(676\) | 342.371 | 0.506466 | ||||||||
\(677\) | − | 1153.64i | − | 1.70404i | −0.523506 | − | 0.852022i | \(-0.675376\pi\) | ||
0.523506 | − | 0.852022i | \(-0.324624\pi\) | |||||||
\(678\) | 446.691i | 0.658836i | ||||||||
\(679\) | − | 524.869i | − | 0.773003i | ||||||
\(680\) | − | 214.084i | − | 0.314829i | ||||||
\(681\) | −467.203 | −0.686054 | ||||||||
\(682\) | 191.698 | 0.281082 | ||||||||
\(683\) | 382.766i | 0.560419i | 0.959939 | + | 0.280209i | \(0.0904039\pi\) | ||||
−0.959939 | + | 0.280209i | \(0.909596\pi\) | |||||||
\(684\) | 51.5257 | + | 118.994i | 0.0753300 | + | 0.173967i | ||||
\(685\) | −254.567 | −0.371631 | ||||||||
\(686\) | − | 469.633i | − | 0.684596i | ||||||
\(687\) | − | 449.328i | − | 0.654043i | ||||||
\(688\) | −112.344 | −0.163291 | ||||||||
\(689\) | −336.000 | −0.487663 | ||||||||
\(690\) | 15.8073 | 0.0229091 | ||||||||
\(691\) | 133.330 | 0.192952 | 0.0964759 | − | 0.995335i | \(-0.469243\pi\) | ||||
0.0964759 | + | 0.995335i | \(0.469243\pi\) | |||||||
\(692\) | 23.9034i | 0.0345426i | ||||||||
\(693\) | 103.124 | 0.148808 | ||||||||
\(694\) | − | 308.492i | − | 0.444513i | ||||||
\(695\) | −69.5772 | −0.100111 | ||||||||
\(696\) | 122.803i | 0.176441i | ||||||||
\(697\) | 637.562i | 0.914723i | ||||||||
\(698\) | − | 578.796i | − | 0.829220i | ||||||
\(699\) | 91.2391i | 0.130528i | ||||||||
\(700\) | −251.257 | −0.358939 | ||||||||
\(701\) | −934.042 | −1.33244 | −0.666221 | − | 0.745755i | \(-0.732089\pi\) | ||||
−0.666221 | + | 0.745755i | \(0.732089\pi\) | |||||||
\(702\) | 29.3557i | 0.0418172i | ||||||||
\(703\) | 708.179 | − | 306.651i | 1.00737 | − | 0.436203i | ||||
\(704\) | 343.547 | 0.487992 | ||||||||
\(705\) | − | 122.499i | − | 0.173758i | ||||||
\(706\) | − | 713.573i | − | 1.01073i | ||||||
\(707\) | 355.566 | 0.502923 | ||||||||
\(708\) | −273.897 | −0.386860 | ||||||||
\(709\) | 287.993 | 0.406197 | 0.203098 | − | 0.979158i | \(-0.434899\pi\) | ||||
0.203098 | + | 0.979158i | \(0.434899\pi\) | |||||||
\(710\) | −5.22252 | −0.00735566 | ||||||||
\(711\) | 263.010i | 0.369915i | ||||||||
\(712\) | −576.688 | −0.809955 | ||||||||
\(713\) | 109.344i | 0.153357i | ||||||||
\(714\) | −219.010 | −0.306737 | ||||||||
\(715\) | 39.8947i | 0.0557968i | ||||||||
\(716\) | − | 28.2364i | − | 0.0394364i | ||||||
\(717\) | 599.498i | 0.836120i | ||||||||
\(718\) | − | 50.5919i | − | 0.0704623i | ||||||
\(719\) | 78.0723 | 0.108585 | 0.0542923 | − | 0.998525i | \(-0.482710\pi\) | ||||
0.0542923 | + | 0.998525i | \(0.482710\pi\) | |||||||
\(720\) | 6.59801 | 0.00916391 | ||||||||
\(721\) | 890.556i | 1.23517i | ||||||||
\(722\) | −345.787 | − | 324.416i | −0.478930 | − | 0.449329i | ||||
\(723\) | −520.096 | −0.719359 | ||||||||
\(724\) | 242.916i | 0.335519i | ||||||||
\(725\) | − | 201.085i | − | 0.277358i | ||||||
\(726\) | −154.866 | −0.213314 | ||||||||
\(727\) | −320.169 | −0.440397 | −0.220199 | − | 0.975455i | \(-0.570671\pi\) | ||||
−0.220199 | + | 0.975455i | \(0.570671\pi\) | |||||||
\(728\) | 167.505 | 0.230089 | ||||||||
\(729\) | −27.0000 | −0.0370370 | ||||||||
\(730\) | 56.6398i | 0.0775887i | ||||||||
\(731\) | −1326.87 | −1.81514 | ||||||||
\(732\) | 24.3322i | 0.0332407i | ||||||||
\(733\) | −565.781 | −0.771870 | −0.385935 | − | 0.922526i | \(-0.626121\pi\) | ||||
−0.385935 | + | 0.922526i | \(0.626121\pi\) | |||||||
\(734\) | − | 747.334i | − | 1.01817i | ||||||
\(735\) | 58.9012i | 0.0801377i | ||||||||
\(736\) | 167.324i | 0.227343i | ||||||||
\(737\) | − | 900.080i | − | 1.22127i | ||||||
\(738\) | −123.299 | −0.167072 | ||||||||
\(739\) | −869.557 | −1.17667 | −0.588334 | − | 0.808618i | \(-0.700216\pi\) | ||||
−0.588334 | + | 0.808618i | \(0.700216\pi\) | |||||||
\(740\) | 117.802i | 0.159192i | ||||||||
\(741\) | 56.2475 | + | 129.898i | 0.0759076 | + | 0.175301i | ||||
\(742\) | 484.784 | 0.653348 | ||||||||
\(743\) | − | 7.74529i | − | 0.0104243i | −0.999986 | − | 0.00521217i | \(-0.998341\pi\) | ||
0.999986 | − | 0.00521217i | \(-0.00165909\pi\) | |||||||
\(744\) | 286.390i | 0.384932i | ||||||||
\(745\) | −312.767 | −0.419821 | ||||||||
\(746\) | 81.2508 | 0.108915 | ||||||||
\(747\) | −365.093 | −0.488746 | ||||||||
\(748\) | 337.196 | 0.450797 | ||||||||
\(749\) | 38.4733i | 0.0513663i | ||||||||
\(750\) | −140.302 | −0.187070 | ||||||||
\(751\) | 1281.23i | 1.70603i | 0.521890 | + | 0.853013i | \(0.325227\pi\) | ||||
−0.521890 | + | 0.853013i | \(0.674773\pi\) | |||||||
\(752\) | −95.6977 | −0.127258 | ||||||||
\(753\) | − | 329.477i | − | 0.437552i | ||||||
\(754\) | 48.6010i | 0.0644576i | ||||||||
\(755\) | − | 101.098i | − | 0.133904i | ||||||
\(756\) | 55.8543i | 0.0738814i | ||||||||
\(757\) | −441.172 | −0.582790 | −0.291395 | − | 0.956603i | \(-0.594119\pi\) | ||||
−0.291395 | + | 0.956603i | \(0.594119\pi\) | |||||||
\(758\) | 449.980 | 0.593641 | ||||||||
\(759\) | 68.6750i | 0.0904808i | ||||||||
\(760\) | 183.203 | − | 79.3291i | 0.241056 | − | 0.104380i | ||||
\(761\) | 476.532 | 0.626192 | 0.313096 | − | 0.949721i | \(-0.398634\pi\) | ||||
0.313096 | + | 0.949721i | \(0.398634\pi\) | |||||||
\(762\) | 36.4508i | 0.0478357i | ||||||||
\(763\) | − | 563.193i | − | 0.738129i | ||||||
\(764\) | −43.2858 | −0.0566568 | ||||||||
\(765\) | 77.9277 | 0.101866 | ||||||||
\(766\) | 101.306 | 0.132253 | ||||||||
\(767\) | −298.997 | −0.389826 | ||||||||
\(768\) | 465.440i | 0.606041i | ||||||||
\(769\) | −624.567 | −0.812181 | −0.406091 | − | 0.913833i | \(-0.633108\pi\) | ||||
−0.406091 | + | 0.913833i | \(0.633108\pi\) | |||||||
\(770\) | − | 57.5605i | − | 0.0747539i | ||||||
\(771\) | 43.9036 | 0.0569438 | ||||||||
\(772\) | 251.130i | 0.325298i | ||||||||
\(773\) | − | 334.038i | − | 0.432133i | −0.976379 | − | 0.216066i | \(-0.930677\pi\) | ||
0.976379 | − | 0.216066i | \(-0.0693227\pi\) | |||||||
\(774\) | − | 256.605i | − | 0.331531i | ||||||
\(775\) | − | 468.951i | − | 0.605098i | ||||||
\(776\) | 915.492 | 1.17976 | ||||||||
\(777\) | 332.412 | 0.427815 | ||||||||
\(778\) | 569.724i | 0.732293i | ||||||||
\(779\) | −545.595 | + | 236.249i | −0.700378 | + | 0.303273i | ||||
\(780\) | −21.6079 | −0.0277025 | ||||||||
\(781\) | − | 22.6893i | − | 0.0290516i | ||||||
\(782\) | − | 145.849i | − | 0.186508i | ||||||
\(783\) | −44.7010 | −0.0570894 | ||||||||
\(784\) | 46.0142 | 0.0586915 | ||||||||
\(785\) | −68.4601 | −0.0872103 | ||||||||
\(786\) | 377.457 | 0.480225 | ||||||||
\(787\) | − | 479.323i | − | 0.609051i | −0.952504 | − | 0.304526i | \(-0.901502\pi\) | ||
0.952504 | − | 0.304526i | \(-0.0984980\pi\) | |||||||
\(788\) | 747.877 | 0.949083 | ||||||||
\(789\) | 779.631i | 0.988126i | ||||||||
\(790\) | 146.804 | 0.185828 | ||||||||
\(791\) | 927.792i | 1.17294i | ||||||||
\(792\) | 179.871i | 0.227110i | ||||||||
\(793\) | 26.5619i | 0.0334955i | ||||||||
\(794\) | − | 371.790i | − | 0.468249i | ||||||
\(795\) | −172.495 | −0.216975 | ||||||||
\(796\) | −607.341 | −0.762991 | ||||||||
\(797\) | − | 126.025i | − | 0.158125i | −0.996870 | − | 0.0790624i | \(-0.974807\pi\) | ||
0.996870 | − | 0.0790624i | \(-0.0251926\pi\) | |||||||
\(798\) | −81.1545 | − | 187.418i | −0.101697 | − | 0.234860i | ||||
\(799\) | −1130.26 | −1.41460 | ||||||||
\(800\) | − | 717.617i | − | 0.897021i | ||||||
\(801\) | − | 209.918i | − | 0.262070i | ||||||
\(802\) | 424.880 | 0.529776 | ||||||||
\(803\) | −246.072 | −0.306441 | ||||||||
\(804\) | 487.505 | 0.606349 | ||||||||
\(805\) | 32.8323 | 0.0407854 | ||||||||
\(806\) | 113.343i | 0.140624i | ||||||||
\(807\) | 840.289 | 1.04125 | ||||||||
\(808\) | 620.189i | 0.767561i | ||||||||
\(809\) | 901.825 | 1.11474 | 0.557370 | − | 0.830264i | \(-0.311810\pi\) | ||||
0.557370 | + | 0.830264i | \(0.311810\pi\) | |||||||
\(810\) | 15.0706i | 0.0186056i | ||||||||
\(811\) | − | 183.776i | − | 0.226604i | −0.993561 | − | 0.113302i | \(-0.963857\pi\) | ||
0.993561 | − | 0.113302i | \(-0.0361427\pi\) | |||||||
\(812\) | 92.4720i | 0.113882i | ||||||||
\(813\) | − | 271.926i | − | 0.334473i | ||||||
\(814\) | 388.096 | 0.476777 | ||||||||
\(815\) | 99.9518 | 0.122640 | ||||||||
\(816\) | − | 60.8779i | − | 0.0746052i | ||||||
\(817\) | −491.674 | − | 1135.47i | −0.601804 | − | 1.38981i | ||||
\(818\) | 718.103 | 0.877877 | ||||||||
\(819\) | 60.9728i | 0.0744478i | ||||||||
\(820\) | − | 90.7572i | − | 0.110679i | ||||||
\(821\) | 1034.35 | 1.25986 | 0.629932 | − | 0.776650i | \(-0.283083\pi\) | ||||
0.629932 | + | 0.776650i | \(0.283083\pi\) | |||||||
\(822\) | −454.241 | −0.552604 | ||||||||
\(823\) | 952.107 | 1.15687 | 0.578437 | − | 0.815727i | \(-0.303663\pi\) | ||||
0.578437 | + | 0.815727i | \(0.303663\pi\) | |||||||
\(824\) | −1553.33 | −1.88511 | ||||||||
\(825\) | − | 294.532i | − | 0.357009i | ||||||
\(826\) | 431.395 | 0.522270 | ||||||||
\(827\) | 970.806i | 1.17389i | 0.809627 | + | 0.586944i | \(0.199669\pi\) | ||||
−0.809627 | + | 0.586944i | \(0.800331\pi\) | |||||||
\(828\) | −37.1960 | −0.0449227 | ||||||||
\(829\) | − | 374.908i | − | 0.452242i | −0.974099 | − | 0.226121i | \(-0.927396\pi\) | ||
0.974099 | − | 0.226121i | \(-0.0726044\pi\) | |||||||
\(830\) | 203.784i | 0.245522i | ||||||||
\(831\) | − | 271.289i | − | 0.326461i | ||||||
\(832\) | 203.125i | 0.244140i | ||||||||
\(833\) | 543.463 | 0.652417 | ||||||||
\(834\) | −124.151 | −0.148862 | ||||||||
\(835\) | − | 373.996i | − | 0.447900i | ||||||
\(836\) | 124.949 | + | 288.556i | 0.149460 | + | 0.345163i | ||||
\(837\) | −104.248 | −0.124549 | ||||||||
\(838\) | − | 463.634i | − | 0.553263i | ||||||
\(839\) | − | 1282.87i | − | 1.52904i | −0.644597 | − | 0.764522i | \(-0.722975\pi\) | ||
0.644597 | − | 0.764522i | \(-0.277025\pi\) | |||||||
\(840\) | 85.9934 | 0.102373 | ||||||||
\(841\) | 766.993 | 0.912002 | ||||||||
\(842\) | −759.849 | −0.902433 | ||||||||
\(843\) | 792.688 | 0.940318 | ||||||||
\(844\) | 160.229i | 0.189845i | ||||||||
\(845\) | 191.873 | 0.227069 | ||||||||
\(846\) | − | 218.584i | − | 0.258373i | ||||||
\(847\) | −321.663 | −0.379767 | ||||||||
\(848\) | 134.755i | 0.158909i | ||||||||
\(849\) | 80.6684i | 0.0950158i | ||||||||
\(850\) | 625.515i | 0.735900i | ||||||||
\(851\) | 221.369i | 0.260128i | ||||||||
\(852\) | 12.2891 | 0.0144238 | ||||||||
\(853\) | 827.595 | 0.970217 | 0.485108 | − | 0.874454i | \(-0.338780\pi\) | ||||
0.485108 | + | 0.874454i | \(0.338780\pi\) | |||||||
\(854\) | − | 38.3238i | − | 0.0448757i | ||||||
\(855\) | 28.8762 | + | 66.6868i | 0.0337734 | + | 0.0779963i | ||||
\(856\) | −67.1063 | −0.0783952 | ||||||||
\(857\) | 986.671i | 1.15131i | 0.817694 | + | 0.575654i | \(0.195252\pi\) | ||||
−0.817694 | + | 0.575654i | \(0.804748\pi\) | |||||||
\(858\) | 71.1867i | 0.0829682i | ||||||||
\(859\) | −1382.27 | −1.60916 | −0.804582 | − | 0.593842i | \(-0.797611\pi\) | ||||
−0.804582 | + | 0.593842i | \(0.797611\pi\) | |||||||
\(860\) | 188.880 | 0.219628 | ||||||||
\(861\) | −256.096 | −0.297441 | ||||||||
\(862\) | 826.007 | 0.958244 | ||||||||
\(863\) | 485.475i | 0.562543i | 0.959628 | + | 0.281272i | \(0.0907562\pi\) | ||||
−0.959628 | + | 0.281272i | \(0.909244\pi\) | |||||||
\(864\) | −159.526 | −0.184636 | ||||||||
\(865\) | 13.3961i | 0.0154868i | ||||||||
\(866\) | 161.292 | 0.186250 | ||||||||
\(867\) | − | 218.453i | − | 0.251964i | ||||||
\(868\) | 215.655i | 0.248450i | ||||||||
\(869\) | 637.792i | 0.733938i | ||||||||
\(870\) | 24.9507i | 0.0286790i | ||||||||
\(871\) | 532.179 | 0.610998 | ||||||||
\(872\) | 982.337 | 1.12653 | ||||||||
\(873\) | 333.244i | 0.381723i | ||||||||
\(874\) | 124.811 | − | 54.0446i | 0.142804 | − | 0.0618359i | ||||
\(875\) | −291.413 | −0.333043 | ||||||||
\(876\) | − | 133.279i | − | 0.152145i | ||||||
\(877\) | 266.756i | 0.304169i | 0.988368 | + | 0.152084i | \(0.0485985\pi\) | ||||
−0.988368 | + | 0.152084i | \(0.951401\pi\) | |||||||
\(878\) | 83.2310 | 0.0947961 | ||||||||
\(879\) | 384.797 | 0.437767 | ||||||||
\(880\) | 16.0000 | 0.0181818 | ||||||||
\(881\) | −979.248 | −1.11152 | −0.555760 | − | 0.831343i | \(-0.687573\pi\) | ||||
−0.555760 | + | 0.831343i | \(0.687573\pi\) | |||||||
\(882\) | 105.101i | 0.119162i | ||||||||
\(883\) | 1551.91 | 1.75755 | 0.878774 | − | 0.477239i | \(-0.158362\pi\) | ||||
0.878774 | + | 0.477239i | \(0.158362\pi\) | |||||||
\(884\) | 199.370i | 0.225532i | ||||||||
\(885\) | −153.498 | −0.173444 | ||||||||
\(886\) | 801.609i | 0.904750i | ||||||||
\(887\) | 700.543i | 0.789789i | 0.918727 | + | 0.394894i | \(0.129219\pi\) | ||||
−0.918727 | + | 0.394894i | \(0.870781\pi\) | |||||||
\(888\) | 579.803i | 0.652931i | ||||||||
\(889\) | 75.7095i | 0.0851626i | ||||||||
\(890\) | −117.170 | −0.131651 | ||||||||
\(891\) | −65.4743 | −0.0734840 | ||||||||
\(892\) | − | 540.138i | − | 0.605536i | ||||||
\(893\) | −418.821 | − | 967.227i | −0.469005 | − | 1.08312i | ||||
\(894\) | −558.090 | −0.624261 | ||||||||
\(895\) | − | 15.8244i | − | 0.0176809i | ||||||
\(896\) | 287.184i | 0.320518i | ||||||||
\(897\) | −40.6046 | −0.0452672 | ||||||||
\(898\) | −539.518 | −0.600800 | ||||||||
\(899\) | −172.591 | −0.191982 | ||||||||
\(900\) | 159.526 | 0.177251 | ||||||||
\(901\) | 1591.56i | 1.76644i | ||||||||
\(902\) | −298.997 | −0.331482 | ||||||||
\(903\) | − | 532.978i | − | 0.590231i | ||||||
\(904\) | −1618.28 | −1.79014 | ||||||||
\(905\) | 136.136i | 0.150426i | ||||||||
\(906\) | − | 180.395i | − | 0.199112i | ||||||
\(907\) | − | 1228.07i | − | 1.35399i | −0.735987 | − | 0.676996i | \(-0.763282\pi\) | ||
0.735987 | − | 0.676996i | \(-0.236718\pi\) | |||||||
\(908\) | − | 613.635i | − | 0.675810i | ||||||
\(909\) | −225.752 | −0.248353 | ||||||||
\(910\) | 34.0331 | 0.0373990 | ||||||||
\(911\) | 1077.26i | 1.18250i | 0.806487 | + | 0.591252i | \(0.201366\pi\) | ||||
−0.806487 | + | 0.591252i | \(0.798634\pi\) | |||||||
\(912\) | 52.0964 | − | 22.5584i | 0.0571232 | − | 0.0247351i | ||||
\(913\) | −885.341 | −0.969705 | ||||||||
\(914\) | 330.617i | 0.361726i | ||||||||
\(915\) | 13.6363i | 0.0149031i | ||||||||
\(916\) | 590.158 | 0.644277 | ||||||||
\(917\) | 783.991 | 0.854952 | ||||||||
\(918\) | 139.051 | 0.151472 | ||||||||
\(919\) | −348.488 | −0.379204 | −0.189602 | − | 0.981861i | \(-0.560720\pi\) | ||||
−0.189602 | + | 0.981861i | \(0.560720\pi\) | |||||||
\(920\) | 57.2670i | 0.0622468i | ||||||||
\(921\) | 852.289 | 0.925395 | ||||||||
\(922\) | − | 295.024i | − | 0.319983i | ||||||
\(923\) | 13.4152 | 0.0145344 | ||||||||
\(924\) | 135.445i | 0.146586i | ||||||||
\(925\) | − | 949.403i | − | 1.02638i | ||||||
\(926\) | − | 257.923i | − | 0.278535i | ||||||
\(927\) | − | 565.423i | − | 0.609949i | ||||||
\(928\) | −264.110 | −0.284601 | ||||||||
\(929\) | −1506.48 | −1.62162 | −0.810808 | − | 0.585312i | \(-0.800972\pi\) | ||||
−0.810808 | + | 0.585312i | \(0.800972\pi\) | |||||||
\(930\) | 58.1877i | 0.0625675i | ||||||||
\(931\) | 201.381 | + | 465.070i | 0.216306 | + | 0.499538i | ||||
\(932\) | −119.836 | −0.128579 | ||||||||
\(933\) | − | 281.932i | − | 0.302177i | ||||||
\(934\) | − | 139.724i | − | 0.149597i | ||||||
\(935\) | 188.973 | 0.202110 | ||||||||
\(936\) | −106.350 | −0.113622 | ||||||||
\(937\) | −145.777 | −0.155578 | −0.0777890 | − | 0.996970i | \(-0.524786\pi\) | ||||
−0.0777890 | + | 0.996970i | \(0.524786\pi\) | |||||||
\(938\) | −767.834 | −0.818586 | ||||||||
\(939\) | − | 718.617i | − | 0.765300i | ||||||
\(940\) | 160.894 | 0.171164 | ||||||||
\(941\) | − | 1501.75i | − | 1.59590i | −0.602721 | − | 0.797952i | \(-0.705917\pi\) | ||
0.602721 | − | 0.797952i | \(-0.294083\pi\) | |||||||
\(942\) | −122.158 | −0.129679 | ||||||||
\(943\) | − | 170.547i | − | 0.180855i | ||||||
\(944\) | 119.914i | 0.127028i | ||||||||
\(945\) | 31.3021i | 0.0331239i | ||||||||
\(946\) | − | 622.261i | − | 0.657781i | ||||||
\(947\) | 765.794 | 0.808653 | 0.404326 | − | 0.914615i | \(-0.367506\pi\) | ||||
0.404326 | + | 0.914615i | \(0.367506\pi\) | |||||||
\(948\) | −345.444 | −0.364392 | ||||||||
\(949\) | − | 145.492i | − | 0.153311i | ||||||
\(950\) | −535.286 | + | 231.786i | −0.563459 | + | 0.243985i | ||||
\(951\) | −633.498 | −0.666139 | ||||||||
\(952\) | − | 793.435i | − | 0.833440i | ||||||
\(953\) | 1308.88i | 1.37344i | 0.726924 | + | 0.686718i | \(0.240949\pi\) | ||||
−0.726924 | + | 0.686718i | \(0.759051\pi\) | |||||||
\(954\) | −307.794 | −0.322635 | ||||||||
\(955\) | −24.2584 | −0.0254014 | ||||||||
\(956\) | −787.395 | −0.823635 | ||||||||
\(957\) | −108.399 | −0.113269 | ||||||||
\(958\) | 608.318i | 0.634988i | ||||||||
\(959\) | −943.474 | −0.983810 | ||||||||
\(960\) | 104.280i | 0.108625i | ||||||||
\(961\) | 558.498 | 0.581164 | ||||||||
\(962\) | 229.465i | 0.238529i | ||||||||
\(963\) | − | 24.4271i | − | 0.0253656i | ||||||
\(964\) | − | 683.107i | − | 0.708617i | ||||||
\(965\) | 140.739i | 0.145844i | ||||||||
\(966\) | 58.5848 | 0.0606468 | ||||||||
\(967\) | 587.704 | 0.607760 | 0.303880 | − | 0.952710i | \(-0.401718\pi\) | ||||
0.303880 | + | 0.952710i | \(0.401718\pi\) | |||||||
\(968\) | − | 561.054i | − | 0.579601i | ||||||
\(969\) | 615.299 | − | 266.432i | 0.634983 | − | 0.274956i | ||||
\(970\) | 186.007 | 0.191759 | ||||||||
\(971\) | − | 653.823i | − | 0.673351i | −0.941621 | − | 0.336675i | \(-0.890698\pi\) | ||
0.941621 | − | 0.336675i | \(-0.109302\pi\) | |||||||
\(972\) | − | 35.4624i | − | 0.0364840i | ||||||
\(973\) | −257.866 | −0.265022 | ||||||||
\(974\) | −326.337 | −0.335049 | ||||||||
\(975\) | 174.145 | 0.178610 | ||||||||
\(976\) | 10.6528 | 0.0109148 | ||||||||
\(977\) | 101.034i | 0.103413i | 0.998662 | + | 0.0517064i | \(0.0164660\pi\) | ||||
−0.998662 | + | 0.0517064i | \(0.983534\pi\) | |||||||
\(978\) | 178.350 | 0.182362 | ||||||||
\(979\) | − | 509.045i | − | 0.519964i | ||||||
\(980\) | −77.3623 | −0.0789411 | ||||||||
\(981\) | 357.576i | 0.364502i | ||||||||
\(982\) | 401.367i | 0.408724i | ||||||||
\(983\) | 888.065i | 0.903423i | 0.892164 | + | 0.451711i | \(0.149186\pi\) | ||||
−0.892164 | + | 0.451711i | \(0.850814\pi\) | |||||||
\(984\) | − | 446.691i | − | 0.453954i | ||||||
\(985\) | 419.128 | 0.425511 | ||||||||
\(986\) | 230.213 | 0.233481 | ||||||||
\(987\) | − | 454.006i | − | 0.459986i | ||||||
\(988\) | −170.611 | + | 73.8768i | −0.172683 | + | 0.0747741i | ||||
\(989\) | 354.935 | 0.358883 | ||||||||
\(990\) | 36.5457i | 0.0369148i | ||||||||
\(991\) | − | 1782.19i | − | 1.79838i | −0.437562 | − | 0.899188i | \(-0.644158\pi\) | ||
0.437562 | − | 0.899188i | \(-0.355842\pi\) | |||||||
\(992\) | −615.932 | −0.620899 | ||||||||
\(993\) | −381.498 | −0.384188 | ||||||||
\(994\) | −19.3556 | −0.0194725 | ||||||||
\(995\) | −340.368 | −0.342078 | ||||||||
\(996\) | − | 479.522i | − | 0.481448i | ||||||
\(997\) | 891.200 | 0.893882 | 0.446941 | − | 0.894563i | \(-0.352513\pi\) | ||||
0.446941 | + | 0.894563i | \(0.352513\pi\) | |||||||
\(998\) | 353.203i | 0.353911i | ||||||||
\(999\) | −211.051 | −0.211263 |
(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 | 57.3.c.b.37.3 | yes | 4 | |
3.2 | odd | 2 | 171.3.c.f.37.2 | 4 | |||
4.3 | odd | 2 | 912.3.o.b.721.4 | 4 | |||
12.11 | even | 2 | 2736.3.o.l.721.1 | 4 | |||
19.18 | odd | 2 | inner | 57.3.c.b.37.2 | ✓ | 4 | |
57.56 | even | 2 | 171.3.c.f.37.3 | 4 | |||
76.75 | even | 2 | 912.3.o.b.721.2 | 4 | |||
228.227 | odd | 2 | 2736.3.o.l.721.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
57.3.c.b.37.2 | ✓ | 4 | 19.18 | odd | 2 | inner | |
57.3.c.b.37.3 | yes | 4 | 1.1 | even | 1 | trivial | |
171.3.c.f.37.2 | 4 | 3.2 | odd | 2 | |||
171.3.c.f.37.3 | 4 | 57.56 | even | 2 | |||
912.3.o.b.721.2 | 4 | 76.75 | even | 2 | |||
912.3.o.b.721.4 | 4 | 4.3 | odd | 2 | |||
2736.3.o.l.721.1 | 4 | 12.11 | even | 2 | |||
2736.3.o.l.721.2 | 4 | 228.227 | odd | 2 |