Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [336,4,Mod(193,336)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(336, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 4]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("336.193");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 336 = 2^{4} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 336.q (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(19.8246417619\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{193})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} + 49x^{2} + 48x + 2304 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 84) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 193.1 | ||
Root | \(-3.22311 - 5.58259i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 336.193 |
Dual form | 336.4.q.i.289.1 |
$q$-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 \(\left(\mathbb{Z}/336\mathbb{Z}\right)^\times\).
\(n\) | \(85\) | \(113\) | \(127\) | \(241\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.50000 | − | 2.59808i | 0.288675 | − | 0.500000i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −6.22311 | − | 10.7787i | −0.556612 | − | 0.964080i | −0.997776 | − | 0.0666538i | \(-0.978768\pi\) |
0.441164 | − | 0.897426i | \(-0.354566\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −15.3924 | + | 10.2992i | −0.831114 | + | 0.556102i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −4.50000 | − | 7.79423i | −0.166667 | − | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −25.5618 | + | 44.2743i | −0.700651 | + | 1.21356i | 0.267587 | + | 0.963534i | \(0.413774\pi\) |
−0.968238 | + | 0.250030i | \(0.919559\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 37.2311 | 0.794312 | 0.397156 | − | 0.917751i | \(-0.369997\pi\) | ||||
0.397156 | + | 0.917751i | \(0.369997\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −37.3387 | −0.642720 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −11.1076 | + | 19.2389i | −0.158469 | + | 0.274477i | −0.934317 | − | 0.356444i | \(-0.883989\pi\) |
0.775848 | + | 0.630920i | \(0.217323\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 27.1693 | + | 47.0587i | 0.328056 | + | 0.568210i | 0.982126 | − | 0.188224i | \(-0.0602730\pi\) |
−0.654070 | + | 0.756434i | \(0.726940\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.66933 | + | 55.4395i | 0.0381292 | + | 0.576090i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 88.4622 | + | 153.221i | 0.801985 | + | 1.38908i | 0.918308 | + | 0.395867i | \(0.129556\pi\) |
−0.116323 | + | 0.993211i | \(0.537111\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −14.9542 | + | 25.9015i | −0.119634 | + | 0.207212i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 61.0916 | 0.391187 | 0.195593 | − | 0.980685i | \(-0.437337\pi\) | ||||
0.195593 | + | 0.980685i | \(0.437337\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 159.962 | − | 277.063i | 0.926776 | − | 1.60522i | 0.138097 | − | 0.990419i | \(-0.455901\pi\) |
0.788679 | − | 0.614805i | \(-0.210765\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 76.6853 | + | 132.823i | 0.404521 | + | 0.700651i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 206.801 | + | 101.818i | 0.998735 | + | 0.491727i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 157.540 | + | 272.867i | 0.699984 | + | 1.21241i | 0.968471 | + | 0.249125i | \(0.0801430\pi\) |
−0.268487 | + | 0.963283i | \(0.586524\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 55.8467 | − | 96.7293i | 0.229298 | − | 0.397156i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −206.032 | −0.784800 | −0.392400 | − | 0.919795i | \(-0.628355\pi\) | ||||
−0.392400 | + | 0.919795i | \(0.628355\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −339.661 | −1.20460 | −0.602301 | − | 0.798269i | \(-0.705749\pi\) | ||||
−0.602301 | + | 0.798269i | \(0.705749\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −56.0080 | + | 97.0087i | −0.185537 | + | 0.321360i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 71.0320 | + | 123.031i | 0.220449 | + | 0.381828i | 0.954944 | − | 0.296785i | \(-0.0959146\pi\) |
−0.734496 | + | 0.678613i | \(0.762581\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 130.855 | − | 317.058i | 0.381500 | − | 0.924369i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 33.3227 | + | 57.7166i | 0.0914923 | + | 0.158469i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −155.008 | + | 268.482i | −0.401736 | + | 0.695826i | −0.993936 | − | 0.109965i | \(-0.964926\pi\) |
0.592200 | + | 0.805791i | \(0.298260\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 636.295 | 1.55996 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 163.016 | 0.378807 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −140.825 | + | 243.916i | −0.310743 | + | 0.538223i | −0.978523 | − | 0.206136i | \(-0.933911\pi\) |
0.667780 | + | 0.744358i | \(0.267245\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 271.924 | + | 470.987i | 0.570760 | + | 0.988585i | 0.996488 | + | 0.0837341i | \(0.0266846\pi\) |
−0.425728 | + | 0.904851i | \(0.639982\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 149.540 | + | 73.6260i | 0.299052 | + | 0.147238i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −231.693 | − | 401.305i | −0.442123 | − | 0.765780i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −239.680 | + | 415.137i | −0.437038 | + | 0.756971i | −0.997459 | − | 0.0712360i | \(-0.977306\pi\) |
0.560422 | + | 0.828207i | \(0.310639\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 530.773 | 0.926052 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1105.63 | −1.84809 | −0.924046 | − | 0.382280i | \(-0.875139\pi\) | ||||
−0.924046 | + | 0.382280i | \(0.875139\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −119.675 | + | 207.283i | −0.191876 | + | 0.332338i | −0.945872 | − | 0.324541i | \(-0.894790\pi\) |
0.753996 | + | 0.656879i | \(0.228124\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 44.8627 | + | 77.7044i | 0.0690706 | + | 0.119634i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −62.5298 | − | 944.754i | −0.0925445 | − | 1.39824i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 580.333 | + | 1005.17i | 0.826488 | + | 1.43152i | 0.900777 | + | 0.434282i | \(0.142998\pi\) |
−0.0742888 | + | 0.997237i | \(0.523669\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −40.5000 | + | 70.1481i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.93158 | 0.00387690 | 0.00193845 | − | 0.999998i | \(-0.499383\pi\) | ||||
0.00193845 | + | 0.999998i | \(0.499383\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 276.494 | 0.352824 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 91.6373 | − | 158.721i | 0.112926 | − | 0.195593i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 639.371 | + | 1107.42i | 0.761496 | + | 1.31895i | 0.942079 | + | 0.335390i | \(0.108868\pi\) |
−0.180583 | + | 0.983560i | \(0.557798\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −573.078 | + | 383.449i | −0.660163 | + | 0.441719i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −479.887 | − | 831.188i | −0.535075 | − | 0.926776i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 338.156 | − | 585.703i | 0.365200 | − | 0.632545i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 79.0596 | 0.0827555 | 0.0413777 | − | 0.999144i | \(-0.486825\pi\) | ||||
0.0413777 | + | 0.999144i | \(0.486825\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 460.112 | 0.467101 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −686.052 | + | 1188.28i | −0.675889 | + | 1.17067i | 0.300319 | + | 0.953839i | \(0.402907\pi\) |
−0.976208 | + | 0.216835i | \(0.930427\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 129.265 | + | 223.894i | 0.123659 | + | 0.214184i | 0.921208 | − | 0.389070i | \(-0.127204\pi\) |
−0.797549 | + | 0.603254i | \(0.793870\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 574.733 | − | 384.557i | 0.534174 | − | 0.357418i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −631.184 | − | 1093.24i | −0.570270 | − | 0.987736i | −0.996538 | − | 0.0831393i | \(-0.973505\pi\) |
0.426268 | − | 0.904597i | \(-0.359828\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −138.416 | + | 239.744i | −0.121632 | + | 0.210673i | −0.920411 | − | 0.390951i | \(-0.872146\pi\) |
0.798779 | + | 0.601624i | \(0.205479\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 945.240 | 0.808272 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 52.9156 | 0.0440520 | 0.0220260 | − | 0.999757i | \(-0.492988\pi\) | ||||
0.0220260 | + | 0.999757i | \(0.492988\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1101.02 | − | 1907.02i | 0.892789 | − | 1.54636i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −167.540 | − | 290.188i | −0.132385 | − | 0.229298i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −27.1715 | − | 410.531i | −0.0209312 | − | 0.316247i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −641.309 | − | 1110.78i | −0.481825 | − | 0.834545i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −309.048 | + | 535.287i | −0.226552 | + | 0.392400i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1183.53 | −0.846866 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −443.700 | −0.310016 | −0.155008 | − | 0.987913i | \(-0.549540\pi\) | ||||
−0.155008 | + | 0.987913i | \(0.549540\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −509.492 | + | 882.466i | −0.347739 | + | 0.602301i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1076.74 | − | 1864.97i | −0.718133 | − | 1.24384i | −0.961739 | − | 0.273968i | \(-0.911664\pi\) |
0.243606 | − | 0.969874i | \(-0.421670\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −902.867 | − | 444.527i | −0.588635 | − | 0.289815i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 168.024 | + | 291.026i | 0.107120 | + | 0.185537i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −131.554 | + | 227.858i | −0.0820394 | + | 0.142096i | −0.904126 | − | 0.427266i | \(-0.859477\pi\) |
0.822086 | + | 0.569363i | \(0.192810\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1165.77 | −0.711360 | −0.355680 | − | 0.934608i | \(-0.615751\pi\) | ||||
−0.355680 | + | 0.934608i | \(0.615751\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 426.192 | 0.254552 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −951.693 | + | 1648.38i | −0.556536 | + | 0.963948i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −380.180 | − | 658.490i | −0.217739 | − | 0.377135i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −627.460 | − | 815.558i | −0.352055 | − | 0.457592i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 882.597 | + | 1528.70i | 0.485270 | + | 0.840512i | 0.999857 | − | 0.0169263i | \(-0.00538807\pi\) |
−0.514587 | + | 0.857438i | \(0.672055\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1346.16 | − | 2331.61i | 0.725488 | − | 1.25658i | −0.233285 | − | 0.972408i | \(-0.574948\pi\) |
0.958773 | − | 0.284173i | \(-0.0917191\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 199.936 | 0.105646 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3981.85 | −2.06342 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 970.691 | − | 1681.29i | 0.493437 | − | 0.854657i | −0.506535 | − | 0.862220i | \(-0.669074\pi\) |
0.999971 | + | 0.00756226i | \(0.00240716\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 465.024 | + | 805.445i | 0.231942 | + | 0.401736i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2939.70 | − | 1447.36i | −1.43901 | − | 0.708497i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1051.42 | + | 1821.11i | 0.505236 | + | 0.875094i | 0.999982 | + | 0.00605658i | \(0.00192788\pi\) |
−0.494746 | + | 0.869038i | \(0.664739\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 954.443 | − | 1653.14i | 0.450323 | − | 0.779982i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2344.22 | 1.08623 | 0.543116 | − | 0.839658i | \(-0.317244\pi\) | ||||
0.543116 | + | 0.839658i | \(0.317244\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −810.844 | −0.369069 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 244.524 | − | 423.528i | 0.109352 | − | 0.189403i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1735.32 | − | 3005.67i | −0.762626 | − | 1.32091i | −0.941493 | − | 0.337033i | \(-0.890576\pi\) |
0.178867 | − | 0.983873i | \(-0.442757\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −36.5813 | − | 552.703i | −0.0158017 | − | 0.238745i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 422.475 | + | 731.748i | 0.179408 | + | 0.310743i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −477.885 | + | 827.722i | −0.199547 | + | 0.345625i | −0.948381 | − | 0.317132i | \(-0.897280\pi\) |
0.748835 | + | 0.662757i | \(0.230614\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4220.26 | 1.73309 | 0.866546 | − | 0.499098i | \(-0.166335\pi\) | ||||
0.866546 | + | 0.499098i | \(0.166335\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1631.55 | 0.659057 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1960.78 | − | 3396.17i | 0.779239 | − | 1.34968i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −567.858 | − | 983.558i | −0.222063 | − | 0.384625i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 415.596 | − | 278.077i | 0.159948 | − | 0.107022i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1759.02 | − | 3046.71i | −0.666377 | − | 1.15420i | −0.978910 | − | 0.204291i | \(-0.934511\pi\) |
0.312534 | − | 0.949907i | \(-0.398822\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2508.84 | − | 4345.43i | 0.935699 | − | 1.62068i | 0.162317 | − | 0.986739i | \(-0.448103\pi\) |
0.773382 | − | 0.633940i | \(-0.218563\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1390.16 | −0.510520 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2838.14 | −1.02644 | −0.513221 | − | 0.858257i | \(-0.671548\pi\) | ||||
−0.513221 | + | 0.858257i | \(0.671548\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 177.451 | − | 307.354i | 0.0632118 | − | 0.109486i | −0.832688 | − | 0.553743i | \(-0.813199\pi\) |
0.895899 | + | 0.444257i | \(0.146532\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 719.039 | + | 1245.41i | 0.252324 | + | 0.437038i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −940.348 | + | 629.192i | −0.325121 | + | 0.217540i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1282.16 | + | 2220.77i | 0.436829 | + | 0.756610i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 796.160 | − | 1378.99i | 0.267328 | − | 0.463026i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2777.99 | −0.919413 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −752.672 | −0.245574 | −0.122787 | − | 0.992433i | \(-0.539183\pi\) | ||||
−0.122787 | + | 0.992433i | \(0.539183\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1658.45 | + | 2872.52i | −0.533498 | + | 0.924046i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2113.75 | + | 3661.12i | 0.670496 | + | 1.16133i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 391.303 | + | 5912.15i | 0.122412 | + | 1.84951i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 359.025 | + | 621.850i | 0.110779 | + | 0.191876i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −413.547 | + | 716.284i | −0.125874 | + | 0.218020i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3077.75 | 0.924221 | 0.462111 | − | 0.886822i | \(-0.347092\pi\) | ||||
0.462111 | + | 0.886822i | \(0.347092\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 269.176 | 0.0797558 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3108.72 | + | 5384.46i | −0.908955 | + | 1.57436i | −0.0934368 | + | 0.995625i | \(0.529785\pi\) |
−0.815518 | + | 0.578731i | \(0.803548\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −251.627 | − | 435.831i | −0.0726113 | − | 0.125766i | 0.827434 | − | 0.561563i | \(-0.189800\pi\) |
−0.900045 | + | 0.435797i | \(0.856467\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2548.34 | − | 1254.67i | −0.725837 | − | 0.357366i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 134.170 | + | 232.389i | 0.0377243 | + | 0.0653404i | 0.884271 | − | 0.466974i | \(-0.154656\pi\) |
−0.846547 | + | 0.532314i | \(0.821322\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 884.080 | − | 1531.27i | 0.245409 | − | 0.425060i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 3482.00 | 0.954346 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 5189.77 | 1.40459 | 0.702297 | − | 0.711884i | \(-0.252158\pi\) | ||||
0.702297 | + | 0.711884i | \(0.252158\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3085.47 | + | 5344.19i | −0.824699 | + | 1.42842i | 0.0774495 | + | 0.996996i | \(0.475322\pi\) |
−0.902149 | + | 0.431425i | \(0.858011\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 121.500 | + | 210.444i | 0.0320750 | + | 0.0555556i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −4231.82 | + | 562.641i | −1.10351 | + | 0.146718i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1011.54 | + | 1752.05i | 0.260579 | + | 0.451336i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 4.39737 | − | 7.61646i | 0.00111916 | − | 0.00193845i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1891.91 | −0.475763 | −0.237882 | − | 0.971294i | \(-0.576453\pi\) | ||||
−0.237882 | + | 0.971294i | \(0.576453\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −9045.01 | −2.24765 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 414.741 | − | 718.353i | 0.101851 | − | 0.176412i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3269.97 | + | 5663.75i | 0.793676 | + | 1.37469i | 0.923676 | + | 0.383174i | \(0.125169\pi\) |
−0.130000 | + | 0.991514i | \(0.541498\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5235.23 | − | 2577.56i | −1.25599 | − | 0.618386i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −274.912 | − | 476.162i | −0.0651978 | − | 0.112926i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2687.95 | − | 4655.67i | 0.630214 | − | 1.09156i | −0.357294 | − | 0.933992i | \(-0.616301\pi\) |
0.987508 | − | 0.157570i | \(-0.0503661\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3858.53 | 0.894443 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3836.22 | 0.879300 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1619.44 | − | 2804.95i | 0.367060 | − | 0.635766i | −0.622045 | − | 0.782982i | \(-0.713698\pi\) |
0.989104 | + | 0.147216i | \(0.0470311\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 678.729 | + | 1175.59i | 0.152140 | + | 0.263514i | 0.932014 | − | 0.362423i | \(-0.118050\pi\) |
−0.779874 | + | 0.625936i | \(0.784717\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 136.613 | + | 2064.07i | 0.0302865 | + | 0.457595i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −764.513 | − | 1324.18i | −0.167643 | − | 0.290366i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1280.82 | − | 2218.44i | 0.277823 | − | 0.481203i | −0.693021 | − | 0.720918i | \(-0.743721\pi\) |
0.970843 | + | 0.239715i | \(0.0770539\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2879.32 | −0.617851 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1786.17 | 0.379196 | 0.189598 | − | 0.981862i | \(-0.439282\pi\) | ||||
0.189598 | + | 0.981862i | \(0.439282\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3694.14 | + | 6398.44i | −0.775950 | + | 1.34398i | 0.158309 | + | 0.987390i | \(0.449396\pi\) |
−0.934259 | + | 0.356595i | \(0.883937\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1014.47 | − | 1757.11i | −0.210848 | − | 0.365200i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3171.34 | − | 2121.96i | 0.652258 | − | 0.436429i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2209.74 | + | 3827.39i | 0.449775 | + | 0.779033i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 118.589 | − | 205.403i | 0.0238895 | − | 0.0413777i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 492.981 | 0.0982945 | 0.0491472 | − | 0.998792i | \(-0.484350\pi\) | ||||
0.0491472 | + | 0.998792i | \(0.484350\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3505.48 | 0.691853 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 690.168 | − | 1195.41i | 0.134840 | − | 0.233550i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3293.55 | + | 5704.59i | 0.637026 | + | 1.10336i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5228.22 | − | 3498.23i | 1.00116 | − | 0.669882i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2058.16 | + | 3564.83i | 0.390225 | + | 0.675889i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3384.43 | − | 5862.01i | 0.635384 | − | 1.10052i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 988.810 | 0.183825 | 0.0919126 | − | 0.995767i | \(-0.470702\pi\) | ||||
0.0919126 | + | 0.995767i | \(0.470702\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 775.592 | 0.142789 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4798.28 | + | 8310.87i | −0.874874 | + | 1.51533i | −0.0179763 | + | 0.999838i | \(0.505722\pi\) |
−0.856897 | + | 0.515487i | \(0.827611\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −482.856 | − | 836.332i | −0.0871970 | − | 0.151030i | 0.819128 | − | 0.573610i | \(-0.194458\pi\) |
−0.906325 | + | 0.422581i | \(0.861124\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −137.008 | − | 2070.04i | −0.0245064 | − | 0.370265i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 4492.99 | + | 7782.08i | 0.796061 | + | 1.37882i | 0.922163 | + | 0.386801i | \(0.126420\pi\) |
−0.126103 | + | 0.992017i | \(0.540247\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1561.61 | + | 2704.79i | −0.274086 | + | 0.474730i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3787.10 | −0.658491 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1207.14 | −0.207947 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −556.762 | + | 964.340i | −0.0950265 | + | 0.164591i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 415.249 | + | 719.233i | 0.0702243 | + | 0.121632i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2360.47 | − | 1162.18i | −0.395553 | − | 0.194751i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1903.65 | − | 3297.22i | −0.316115 | − | 0.547527i | 0.663559 | − | 0.748124i | \(-0.269045\pi\) |
−0.979674 | + | 0.200597i | \(0.935712\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1417.86 | − | 2455.81i | 0.233328 | − | 0.404136i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 5966.21 | 0.973041 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1649.82 | −0.266681 | −0.133340 | − | 0.991070i | \(-0.542570\pi\) | ||||
−0.133340 | + | 0.991070i | \(0.542570\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 79.3734 | − | 137.479i | 0.0127167 | − | 0.0220260i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 8177.84 | + | 14164.4i | 1.29869 | + | 2.24940i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1251.26 | + | 6228.00i | 0.196973 | + | 0.980409i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −3303.06 | − | 5721.07i | −0.515452 | − | 0.892789i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2855.00 | − | 4945.00i | 0.441684 | − | 0.765019i | −0.556131 | − | 0.831095i | \(-0.687715\pi\) |
0.997815 | + | 0.0660760i | \(0.0210480\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −447.244 | −0.0685973 | −0.0342986 | − | 0.999412i | \(-0.510920\pi\) | ||||
−0.0342986 | + | 0.999412i | \(0.510920\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1005.24 | −0.152865 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 5322.85 | − | 9219.45i | 0.802569 | − | 1.39009i | −0.115352 | − | 0.993325i | \(-0.536799\pi\) |
0.917920 | − | 0.396765i | \(-0.129867\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6880.48 | + | 11917.3i | 1.02867 | + | 1.78171i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1107.35 | − | 545.203i | −0.164166 | − | 0.0808270i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −4548.73 | − | 7878.64i | −0.668727 | − | 1.15827i | −0.978260 | − | 0.207381i | \(-0.933506\pi\) |
0.309533 | − | 0.950889i | \(-0.399827\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1953.15 | − | 3382.96i | 0.284758 | − | 0.493215i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −3847.85 | −0.556363 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2979.01 | 0.427201 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2643.91 | − | 4579.39i | 0.376052 | − | 0.651341i | −0.614432 | − | 0.788970i | \(-0.710615\pi\) |
0.990484 | + | 0.137629i | \(0.0439480\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 927.144 | + | 1605.86i | 0.130800 | + | 0.226552i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −379.184 | − | 5729.04i | −0.0530627 | − | 0.801717i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2947.51 | − | 5105.23i | −0.409159 | − | 0.708683i | 0.585637 | − | 0.810573i | \(-0.300844\pi\) |
−0.994796 | + | 0.101890i | \(0.967511\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1775.30 | + | 3074.90i | −0.244469 | + | 0.423433i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2274.51 | 0.310724 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3842.41 | −0.520769 | −0.260384 | − | 0.965505i | \(-0.583849\pi\) | ||||
−0.260384 | + | 0.965505i | \(0.583849\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −665.551 | + | 1152.77i | −0.0894940 | + | 0.155008i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2506.87 | + | 4342.02i | 0.334452 | + | 0.579287i | 0.983379 | − | 0.181563i | \(-0.0581156\pi\) |
−0.648928 | + | 0.760850i | \(0.724782\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −9794.14 | + | 6553.30i | −1.29651 | + | 0.867499i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1528.48 | + | 2647.40i | 0.200767 | + | 0.347739i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −5591.24 | + | 9684.31i | −0.728758 | + | 1.26225i | 0.228650 | + | 0.973509i | \(0.426569\pi\) |
−0.957408 | + | 0.288738i | \(0.906765\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3930.40 | −0.508360 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −6460.45 | −0.829228 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 7222.95 | − | 12510.5i | 0.920066 | − | 1.59360i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1703.40 | + | 2950.37i | 0.215343 | + | 0.372985i | 0.953379 | − | 0.301777i | \(-0.0975798\pi\) |
−0.738036 | + | 0.674762i | \(0.764246\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2509.21 | + | 1678.93i | −0.314832 | + | 0.210655i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −41.5201 | − | 71.9149i | −0.00517061 | − | 0.00895575i | 0.863429 | − | 0.504471i | \(-0.168313\pi\) |
−0.868599 | + | 0.495515i | \(0.834979\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5955.57 | − | 10315.4i | 0.736149 | − | 1.27505i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1008.14 | 0.123692 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −16108.0 | −1.96178 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1228.10 | + | 2127.13i | −0.148473 | + | 0.257164i | −0.930663 | − | 0.365876i | \(-0.880769\pi\) |
0.782190 | + | 0.623040i | \(0.214103\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 394.661 | + | 683.573i | 0.0473655 | + | 0.0820394i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −344.489 | − | 5204.84i | −0.0410440 | − | 0.620129i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −18.2435 | − | 31.5987i | −0.00215793 | − | 0.00373764i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1748.65 | + | 3028.75i | −0.205352 | + | 0.355680i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 3437.96 | 0.400848 | 0.200424 | − | 0.979709i | \(-0.435768\pi\) | ||||
0.200424 | + | 0.979709i | \(0.435768\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5347.62 | −0.619067 | −0.309533 | − | 0.950889i | \(-0.600173\pi\) | ||||
−0.309533 | + | 0.950889i | \(0.600173\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 639.288 | − | 1107.28i | 0.0734828 | − | 0.127276i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −332.210 | − | 575.404i | −0.0379166 | − | 0.0656734i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −9036.35 | − | 4449.05i | −1.02412 | − | 0.504226i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2855.08 | + | 4945.14i | 0.321316 | + | 0.556536i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 425.821 | − | 737.544i | 0.0475895 | − | 0.0824275i | −0.841249 | − | 0.540647i | \(-0.818179\pi\) |
0.888839 | + | 0.458220i | \(0.151513\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3433.42 | −0.381061 | −0.190531 | − | 0.981681i | \(-0.561021\pi\) | ||||
−0.190531 | + | 0.981681i | \(0.561021\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2281.08 | −0.251424 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −4806.92 | + | 8325.83i | −0.526192 | + | 0.911392i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4869.20 | − | 8433.70i | −0.529371 | − | 0.916898i | −0.999413 | − | 0.0342540i | \(-0.989094\pi\) |
0.470042 | − | 0.882644i | \(-0.344239\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3060.07 | + | 406.852i | −0.330426 | + | 0.0439317i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 4967.48 | + | 8603.93i | 0.532759 | + | 0.922765i | 0.999268 | + | 0.0382491i | \(0.0121780\pi\) |
−0.466509 | + | 0.884516i | \(0.654489\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7957.75 | − | 13783.2i | 0.847716 | − | 1.46829i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 5295.58 | 0.560341 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −7557.33 | −0.794327 | −0.397163 | − | 0.917748i | \(-0.630005\pi\) | ||||
−0.397163 | + | 0.917748i | \(0.630005\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5266.54 | − | 9121.92i | 0.549871 | − | 0.952405i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −4038.47 | − | 6994.83i | −0.418861 | − | 0.725488i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 7699.43 | + | 3790.81i | 0.793307 | + | 0.390585i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7005.92 | − | 12134.6i | −0.717118 | − | 1.24209i | −0.962137 | − | 0.272567i | \(-0.912127\pi\) |
0.245018 | − | 0.969518i | \(-0.421206\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 299.904 | − | 519.449i | 0.0304974 | − | 0.0528231i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1669.61 | −0.168680 | −0.0843399 | − | 0.996437i | \(-0.526878\pi\) | ||||
−0.0843399 | + | 0.996437i | \(0.526878\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −14785.4 | −1.48409 | −0.742046 | − | 0.670349i | \(-0.766144\pi\) | ||||
−0.742046 | + | 0.670349i | \(0.766144\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −5972.78 | + | 10345.2i | −0.595658 | + | 1.03171i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 2301.58 | + | 3986.46i | 0.228061 | + | 0.395014i | 0.957233 | − | 0.289317i | \(-0.0934280\pi\) |
−0.729172 | + | 0.684330i | \(0.760095\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −586.309 | − | 8858.47i | −0.0577255 | − | 0.872167i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2912.07 | − | 5043.86i | −0.284886 | − | 0.493437i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 8682.35 | − | 15038.3i | 0.844006 | − | 1.46186i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1625.18 | −0.156987 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2790.14 | 0.267824 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1738.68 | − | 3011.47i | 0.165850 | − | 0.287261i | −0.771107 | − | 0.636706i | \(-0.780297\pi\) |
0.936957 | + | 0.349445i | \(0.113630\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5865.39 | + | 10159.2i | 0.556006 | + | 0.963030i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −8169.90 | + | 5466.52i | −0.769655 | + | 0.514980i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −491.996 | − | 852.163i | −0.0460627 | − | 0.0797829i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2172.08 | − | 3762.16i | 0.202108 | − | 0.350061i | −0.747100 | − | 0.664712i | \(-0.768554\pi\) |
0.949207 | + | 0.314651i | \(0.101888\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 6308.51 | 0.583396 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4982.89 | −0.457993 | −0.228997 | − | 0.973427i | \(-0.573544\pi\) | ||||
−0.228997 | + | 0.973427i | \(0.573544\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −678.578 | + | 1175.33i | −0.0619911 | + | 0.107372i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2863.33 | − | 4959.43i | −0.259994 | − | 0.450323i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 17018.4 | − | 11387.1i | 1.53598 | − | 1.02773i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 7663.08 | + | 13272.8i | 0.687468 | + | 1.19073i | 0.972654 | + | 0.232257i | \(0.0746110\pi\) |
−0.285187 | + | 0.958472i | \(0.592056\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 3516.32 | − | 6090.45i | 0.313568 | − | 0.543116i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1516.04 | 0.134387 | 0.0671936 | − | 0.997740i | \(-0.478595\pi\) | ||||
0.0671936 | + | 0.997740i | \(0.478595\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 17077.5 | 1.50483 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1216.27 | + | 2106.64i | −0.106541 | + | 0.184534i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −1326.82 | − | 2298.12i | −0.115541 | − | 0.200122i | 0.802455 | − | 0.596713i | \(-0.203527\pi\) |
−0.917996 | + | 0.396590i | \(0.870193\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −292.752 | − | 4423.15i | −0.0253436 | − | 0.382913i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −733.572 | − | 1270.58i | −0.0631345 | − | 0.109352i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1608.86 | − | 2786.64i | 0.137660 | − | 0.238435i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −7262.82 | −0.617830 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −10411.9 | −0.880604 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6566.06 | − | 11372.8i | 0.552139 | − | 0.956333i | −0.445981 | − | 0.895042i | \(-0.647145\pi\) |
0.998120 | − | 0.0612905i | \(-0.0195216\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1543.17 | − | 2672.85i | −0.129021 | − | 0.223471i | 0.794276 | − | 0.607557i | \(-0.207850\pi\) |
−0.923298 | + | 0.384085i | \(0.874517\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1490.84 | − | 734.013i | −0.123934 | − | 0.0610190i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3553.58 | + | 6154.98i | 0.293731 | + | 0.508757i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9567.63 | + | 16571.6i | −0.786359 | + | 1.36201i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2534.85 | 0.207162 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −7670.80 | −0.623376 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −7855.86 | + | 13606.7i | −0.634838 | + | 1.09957i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1433.66 | + | 2483.16i | 0.115208 | + | 0.199547i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 10692.7 | + | 13898.1i | 0.854482 | + | 1.11064i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −463.047 | − | 802.022i | −0.0367985 | − | 0.0637368i | 0.847040 | − | 0.531530i | \(-0.178383\pi\) |
−0.883838 | + | 0.467793i | \(0.845049\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 6330.39 | − | 10964.6i | 0.500300 | − | 0.866546i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 3445.52 | 0.270807 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −592.871 | −0.0463425 | −0.0231712 | − | 0.999732i | \(-0.507376\pi\) | ||||
−0.0231712 | + | 0.999732i | \(0.507376\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2447.32 | − | 4238.88i | 0.190253 | − | 0.329528i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1659.82 | + | 2874.89i | 0.128331 | + | 0.222276i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −19285.1 | − | 9495.02i | −1.48298 | − | 0.730144i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −5882.33 | − | 10188.5i | −0.449894 | − | 0.779239i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 6122.67 | − | 10604.8i | 0.465756 | − | 0.806713i | −0.533480 | − | 0.845813i | \(-0.679116\pi\) |
0.999235 | + | 0.0391003i | \(0.0124492\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −12646.0 | −0.956829 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3407.15 | −0.256417 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 7297.31 | − | 12639.3i | 0.546261 | − | 0.946152i | −0.452266 | − | 0.891883i | \(-0.649384\pi\) |
0.998526 | − | 0.0542682i | \(-0.0172826\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −329.300 | − | 570.364i | −0.0245199 | − | 0.0424697i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −99.0720 | − | 1496.87i | −0.00733798 | − | 0.110869i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −11455.6 | − | 19841.7i | −0.844015 | − | 1.46188i | −0.886474 | − | 0.462779i | \(-0.846853\pi\) |
0.0424590 | − | 0.999098i | \(-0.486481\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2952.32 | − | 5113.57i | 0.216376 | − | 0.374774i | −0.737321 | − | 0.675542i | \(-0.763910\pi\) |
0.953697 | + | 0.300768i | \(0.0972429\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −10554.1 | −0.769465 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −5291.53 | −0.383778 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4756.61 | + | 8238.68i | −0.343189 | + | 0.594421i | −0.985023 | − | 0.172423i | \(-0.944840\pi\) |
0.641834 | + | 0.766844i | \(0.278174\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −7526.51 | − | 13036.3i | −0.540226 | − | 0.935699i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −45.1242 | + | 30.1928i | −0.00322214 | + | 0.00215595i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −7924.56 | − | 13725.7i | −0.562953 | − | 0.975064i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2085.24 | + | 3611.74i | −0.147374 | + | 0.255260i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 22790.6 | 1.60250 | 0.801252 | − | 0.598327i | \(-0.204167\pi\) | ||||
0.801252 | + | 0.598327i | \(0.204167\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 17384.3 | 1.21614 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −4257.21 | + | 7373.70i | −0.296308 | + | 0.513221i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 9131.39 | + | 15816.0i | 0.632346 | + | 1.09526i | 0.987071 | + | 0.160285i | \(0.0512414\pi\) |
−0.354724 | + | 0.934971i | \(0.615425\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4255.92 | + | 2847.66i | −0.293237 | + | 0.196206i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −532.352 | − | 922.061i | −0.0364953 | − | 0.0632118i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 3479.05 | − | 6025.88i | 0.237312 | − | 0.411037i | −0.722630 | − | 0.691235i | \(-0.757067\pi\) |
0.959942 | + | 0.280198i | \(0.0904003\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2305.39 | 0.156471 | 0.0782353 | − | 0.996935i | \(-0.475071\pi\) | ||||
0.0782353 | + | 0.996935i | \(0.475071\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 4314.23 | 0.291358 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −7981.87 | + | 13825.0i | −0.536379 | + | 0.929036i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −8089.62 | − | 14011.6i | −0.540935 | − | 0.936927i | −0.998851 | − | 0.0479312i | \(-0.984737\pi\) |
0.457916 | − | 0.888996i | \(-0.348596\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 224.165 | + | 3386.88i | 0.0149157 | + | 0.225359i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2644.60 | + | 4580.58i | 0.175105 | + | 0.303291i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −10270.4 | + | 17788.8i | −0.676699 | + | 1.17208i | 0.299271 | + | 0.954168i | \(0.403257\pi\) |
−0.975969 | + | 0.217908i | \(0.930077\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 7692.96 | 0.504407 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 6918.19 | 0.451403 | 0.225702 | − | 0.974196i | \(-0.427533\pi\) | ||||
0.225702 | + | 0.974196i | \(0.427533\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4040.81 | + | 6998.89i | −0.262381 | + | 0.454457i | −0.966874 | − | 0.255254i | \(-0.917841\pi\) |
0.704493 | + | 0.709711i | \(0.251174\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2388.48 | − | 4136.97i | −0.154342 | − | 0.267328i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −21247.0 | − | 10461.0i | −1.36636 | − | 0.672728i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 9234.52 | + | 15994.7i | 0.591009 | + | 1.02366i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −4166.98 | + | 7217.42i | −0.265412 | + | 0.459706i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −6999.54 | −0.443704 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 27293.3 | 1.72191 | 0.860957 | − | 0.508677i | \(-0.169865\pi\) | ||||
0.860957 | + | 0.508677i | \(0.169865\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1129.01 | + | 1955.50i | −0.0708910 | + | 0.122787i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2761.20 | + | 4782.53i | 0.172559 | + | 0.298880i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4871.86 | − | 11804.4i | 0.303030 | − | 0.734237i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 4975.35 | + | 8617.56i | 0.308015 | + | 0.533498i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −9627.82 | + | 16675.9i | −0.593254 | + | 1.02755i | 0.400536 | + | 0.916281i | \(0.368824\pi\) |
−0.993791 | + | 0.111266i | \(0.964509\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 19996.4 | 1.22641 | 0.613204 | − | 0.789925i | \(-0.289880\pi\) | ||||
0.613204 | + | 0.789925i | \(0.289880\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 12682.5 | 0.774222 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 3532.10 | − | 6117.77i | 0.214623 | − | 0.371738i | −0.738533 | − | 0.674218i | \(-0.764481\pi\) |
0.953156 | + | 0.302479i | \(0.0978144\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −7199.47 | − | 12469.8i | −0.435445 | − | 0.754213i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 15947.2 | + | 7851.59i | 0.960090 | + | 0.472700i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 6910.53 | + | 11969.4i | 0.414134 | + | 0.717302i | 0.995337 | − | 0.0964570i | \(-0.0307510\pi\) |
−0.581203 | + | 0.813759i | \(0.697418\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −13401.4 | + | 23211.9i | −0.799443 | + | 1.38468i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 2154.15 | 0.127917 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 7802.80 | 0.461235 | 0.230617 | − | 0.973044i | \(-0.425925\pi\) | ||||
0.230617 | + | 0.973044i | \(0.425925\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −7908.65 | + | 13698.2i | −0.465372 | + | 0.806048i | −0.999218 | − | 0.0395338i | \(-0.987413\pi\) |
0.533846 | + | 0.845581i | \(0.320746\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1240.64 | + | 2148.85i | 0.0726734 | + | 0.125874i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 827.204 | + | 12498.1i | 0.0482370 | + | 0.728806i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5404.29 | + | 9360.51i | 0.313726 | + | 0.543389i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 4616.62 | − | 7996.23i | 0.266800 | − | 0.462111i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −27803.5 | −1.59962 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2943.30 | 0.168582 | 0.0842911 | − | 0.996441i | \(-0.473137\pi\) | ||||
0.0842911 | + | 0.996441i | \(0.473137\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 403.764 | − | 699.340i | 0.0230235 | − | 0.0398779i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1585.74 | + | 2746.58i | 0.0900220 | + | 0.155923i | 0.907520 | − | 0.420009i | \(-0.137973\pi\) |
−0.817498 | + | 0.575931i | \(0.804640\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1216.92 | + | 814.247i | −0.0687792 | + | 0.0460205i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 9326.15 | + | 16153.4i | 0.524785 | + | 0.908955i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −12226.6 | + | 21177.1i | −0.684975 | + | 1.18641i | 0.288470 | + | 0.957489i | \(0.406854\pi\) |
−0.973445 | + | 0.228923i | \(0.926480\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3274.70 | 0.182656 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1509.76 | −0.0838443 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −5771.12 | + | 9995.87i | −0.319103 | + | 0.552703i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 4297.95 | + | 7444.26i | 0.236616 | + | 0.409831i | 0.959741 | − | 0.280886i | \(-0.0906284\pi\) |
−0.723125 | + | 0.690717i | \(0.757295\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −7082.25 | + | 4738.77i | −0.388214 | + | 0.259756i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 7254.69 | + | 12565.5i | 0.395951 | + | 0.685808i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2288.51 | − | 3963.82i | 0.124367 | − | 0.215409i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 805.019 | 0.0435602 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −21476.1 | −1.15712 | −0.578561 | − | 0.815639i | \(-0.696385\pi\) | ||||
−0.578561 | + | 0.815639i | \(0.696385\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −8560.51 | + | 14827.2i | −0.459269 | + | 0.795477i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −2652.24 | − | 4593.81i | −0.141687 | − | 0.245409i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1678.24 | − | 25356.3i | −0.0892738 | − | 1.34883i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6769.46 | + | 11725.0i | 0.358579 | + | 0.621077i | 0.987724 | − | 0.156211i | \(-0.0499281\pi\) |
−0.629145 | + | 0.777288i | \(0.716595\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 5223.00 | − | 9046.49i | 0.275496 | − | 0.477173i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 56602.5 | 2.97304 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 23690.0 | 1.23910 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 7784.65 | − | 13483.4i | 0.405471 | − | 0.702297i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 6941.84 | + | 12023.6i | 0.360065 | + | 0.623652i | 0.987971 | − | 0.154638i | \(-0.0494210\pi\) |
−0.627906 | + | 0.778289i | \(0.716088\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4295.63 | − | 2114.95i | −0.221883 | − | 0.109244i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 9256.41 | + | 16032.6i | 0.476140 | + | 0.824699i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −913.577 | + | 1582.36i | −0.0467992 | + | 0.0810585i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 18292.9 | 0.933215 | 0.466607 | − | 0.884465i | \(-0.345476\pi\) | ||||
0.466607 | + | 0.884465i | \(0.345476\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3772.81 | − | 6534.69i | 0.190892 | − | 0.330635i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −7122.92 | − | 12337.3i | −0.358924 | − | 0.621674i | 0.628857 | − | 0.777521i | \(-0.283523\pi\) |
−0.987781 | + | 0.155846i | \(0.950190\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −4885.94 | + | 11838.5i | −0.245198 | + | 0.594110i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −12253.3 | − | 21223.3i | −0.612422 | − | 1.06075i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −681.947 | + | 1181.17i | −0.0339456 | + | 0.0587956i | −0.882499 | − | 0.470314i | \(-0.844141\pi\) |
0.848553 | + | 0.529110i | \(0.177474\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 6069.27 | 0.300891 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −21789.4 | −1.07588 | −0.537938 | − | 0.842984i | \(-0.680797\pi\) | ||||
−0.537938 | + | 0.842984i | \(0.680797\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 10985.0 | − | 19026.6i | 0.540214 | − | 0.935678i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −13.1921 | − | 22.8494i | −0.000646150 | − | 0.00111916i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 20974.9 | + | 10327.0i | 1.02324 | + | 0.503793i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1059.78 | − | 1835.59i | −0.0514937 | − | 0.0891898i | 0.839130 | − | 0.543932i | \(-0.183065\pi\) |
−0.890623 | + | 0.454742i | \(0.849732\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −2837.87 | + | 4915.34i | −0.137341 | + | 0.237882i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −33509.1 | −1.61526 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 28202.4 | 1.35408 | 0.677038 | − | 0.735948i | \(-0.263263\pi\) | ||||
0.677038 | + | 0.735948i | \(0.263263\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −13567.5 | + | 23499.6i | −0.648840 | + | 1.12382i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −5573.52 | − | 9653.62i | −0.265493 | − | 0.459847i | 0.702200 | − | 0.711980i | \(-0.252201\pi\) |
−0.967693 | + | 0.252133i | \(0.918868\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −338.597 | − | 5115.82i | −0.0160656 | − | 0.242733i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1244.22 | − | 2155.06i | −0.0588039 | − | 0.101851i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −5243.07 | + | 9081.26i | −0.246827 | + | 0.427517i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −4109.29 | −0.192698 | −0.0963491 | − | 0.995348i | \(-0.530717\pi\) | ||||
−0.0963491 | + | 0.995348i | \(0.530717\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 19619.8 | 0.916459 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −6945.68 | + | 12030.3i | −0.323181 | + | 0.559766i | −0.981143 | − | 0.193286i | \(-0.938086\pi\) |
0.657962 | + | 0.753052i | \(0.271419\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4784.22 | + | 8286.51i | 0.221747 | + | 0.384078i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −14549.6 | + | 9735.18i | −0.671766 | + | 0.449482i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −5597.75 | − | 9695.59i | −0.257459 | − | 0.445931i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 28262.0 | − | 48951.2i | 1.29487 | − | 2.24278i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1649.47 | −0.0752839 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −24162.9 | −1.09861 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −4671.18 | + | 8090.71i | −0.211575 | + | 0.366458i | −0.952208 | − | 0.305452i | \(-0.901193\pi\) |
0.740633 | + | 0.671910i | \(0.234526\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −8063.86 | − | 13967.0i | −0.363854 | − | 0.630214i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −814.500 | + | 544.986i | −0.0366123 | + | 0.0244974i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 10124.0 | + | 17535.4i | 0.453361 | + | 0.785245i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 5787.79 | − | 10024.7i | 0.258204 | − | 0.447222i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −24324.3 | −1.08107 | −0.540534 | − | 0.841322i | \(-0.681778\pi\) | ||||
−0.540534 | + | 0.841322i | \(0.681778\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3155.97 | −0.139737 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 5754.34 | − | 9966.80i | 0.253832 | − | 0.439650i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −6118.22 | − | 10597.1i | −0.268876 | − | 0.465706i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2693.34 | + | 40693.3i | 0.117923 | + | 1.78168i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −4858.32 | − | 8414.86i | −0.211922 | − | 0.367060i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −17227.5 | + | 29838.8i | −0.748684 | + | 1.29676i | 0.199770 | + | 0.979843i | \(0.435980\pi\) |
−0.948454 | + | 0.316915i | \(0.897353\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 8350.13 | 0.361545 | 0.180772 | − | 0.983525i | \(-0.442140\pi\) | ||||
0.180772 | + | 0.983525i | \(0.442140\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 4072.37 | 0.175676 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 13086.2 | − | 22665.9i | 0.562441 | − | 0.974176i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −9228.37 | − | 15984.0i | −0.395177 | − | 0.684467i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 5567.54 | + | 2741.18i | 0.237540 | + | 0.116953i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 9417.38 | + | 16311.4i | 0.400327 | + | 0.693387i | 0.993765 | − | 0.111492i | \(-0.0355631\pi\) |
−0.593438 | + | 0.804880i | \(0.702230\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 4828.38 | − | 8363.00i | 0.204504 | − | 0.354211i | −0.745471 | − | 0.666538i | \(-0.767775\pi\) |
0.949975 | + | 0.312327i | \(0.101109\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −4587.08 | −0.193578 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 20759.6 | 0.872892 | 0.436446 | − | 0.899731i | \(-0.356237\pi\) | ||||
0.436446 | + | 0.899731i | \(0.356237\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 7808.05 | − | 13523.9i | 0.327123 | − | 0.566593i | −0.654817 | − | 0.755787i | \(-0.727254\pi\) |
0.981940 | + | 0.189194i | \(0.0605876\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −3842.45 | − | 6655.32i | −0.160401 | − | 0.277823i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 4646.36 | + | 6039.24i | 0.193262 | + | 0.251197i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −14588.3 | − | 25267.7i | −0.604610 | − | 1.04722i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −4318.98 | + | 7480.69i | −0.178358 | + | 0.308925i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 417.027 | 0.0171601 | 0.00858007 | − | 0.999963i | \(-0.497269\pi\) | ||||
0.00858007 | + | 0.999963i | \(0.497269\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20656.8 | −0.846973 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 2679.26 | − | 4640.61i | 0.109464 | − | 0.189598i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 5045.98 | + | 8739.89i | 0.205428 | + | 0.355812i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 21311.4 | + | 10492.7i | 0.864544 | + | 0.425658i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 11082.4 | + | 19195.3i | 0.447995 | + | 0.775950i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −27872.7 | + | 48276.9i | −1.12275 | + | 1.94467i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −24917.4 | −1.00018 | −0.500092 | − | 0.865972i | \(-0.666700\pi\) | ||||
−0.500092 | + | 0.865972i | \(0.666700\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −6086.80 | −0.243467 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 22261.9 | − | 38558.7i | 0.887342 | − | 1.53692i | 0.0443361 | − | 0.999017i | \(-0.485883\pi\) |
0.843006 | − | 0.537904i | \(-0.180784\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −12073.2 | − | 20911.4i | −0.479548 | − | 0.830602i | 0.520176 | − | 0.854059i | \(-0.325866\pi\) |
−0.999725 | + | 0.0234566i | \(0.992533\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −756.000 | − | 11422.3i | −0.0299238 | − | 0.452115i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −13221.3 | − | 22900.0i | −0.521505 | − | 0.903273i | −0.999687 | − | 0.0250123i | \(-0.992037\pi\) |
0.478182 | − | 0.878261i | \(-0.341296\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −21598.2 | + | 37409.2i | −0.848973 | + | 1.47046i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 13258.5 | 0.519355 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −59337.4 | −2.31632 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −8923.54 | + | 15456.0i | −0.347144 | + | 0.601271i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −355.768 | − | 616.208i | −0.0137926 | − | 0.0238895i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 18217.4 | − | 12189.4i | 0.703842 | − | 0.470944i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 11258.1 | + | 19499.5i | 0.433475 | + | 0.750801i | 0.997170 | − | 0.0751826i | \(-0.0239540\pi\) |
−0.563695 | + | 0.825983i | \(0.690621\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 739.472 | − | 1280.80i | 0.0283752 | − | 0.0491472i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 10120.6 | 0.387027 | 0.193514 | − | 0.981098i | \(-0.438012\pi\) | ||||
0.193514 | + | 0.981098i | \(0.438012\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 20748.5 | 0.790761 | 0.395380 | − | 0.918517i | \(-0.370613\pi\) | ||||
0.395380 | + | 0.918517i | \(0.370613\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 5258.21 | − | 9107.49i | 0.199721 | − | 0.345927i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 12749.7 | + | 22083.1i | 0.482630 | + | 0.835939i | 0.999801 | − | 0.0199428i | \(-0.00634841\pi\) |
−0.517172 | + | 0.855882i | \(0.673015\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 6829.63 | − | 4569.74i | 0.257659 | − | 0.172401i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2070.50 | − | 3586.22i | −0.0778502 | − | 0.134840i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −3859.78 | + | 6685.34i | −0.144639 | + | 0.250522i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 11895.7 | 0.444280 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 19761.3 | 0.735574 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 9772.34 | − | 16926.2i | 0.362543 | − | 0.627942i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3443.52 | − | 5964.35i | −0.127326 | − | 0.220534i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1246.33 | − | 18830.6i | −0.0459305 | − | 0.693959i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −26263.1 | − | 45489.1i | −0.964659 | − | 1.67084i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 18903.5 | − | 32741.8i | 0.692040 | − | 1.19865i | −0.279128 | − | 0.960254i | \(-0.590046\pi\) |
0.971168 | − | 0.238395i | \(-0.0766212\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 12348.9 | 0.450593 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3230.08 | 0.117472 | 0.0587362 | − | 0.998274i | \(-0.481293\pi\) | ||||
0.0587362 | + | 0.998274i | \(0.481293\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −74.9364 | + | 129.794i | −0.00271635 | + | 0.00470486i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −10153.3 | − | 17586.0i | −0.366839 | − | 0.635384i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 35781.3 | + | 17616.9i | 1.28855 | + | 0.634419i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −17671.6 | − | 30608.0i | −0.634310 | − | 1.09866i | −0.986661 | − | 0.162789i | \(-0.947951\pi\) |
0.352351 | − | 0.935868i | \(-0.385382\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1483.21 | − | 2569.00i | 0.0530658 | − | 0.0919126i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −41164.0 | −1.46796 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −9423.55 | −0.334967 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1163.39 | − | 2015.05i | 0.0412197 | − | 0.0713946i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −16515.1 | − | 28605.0i | −0.583254 | − | 1.01023i | −0.995091 | − | 0.0989684i | \(-0.968446\pi\) |
0.411836 | − | 0.911258i | \(-0.364888\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 18475.6 | − | 2456.42i | 0.650390 | − | 0.0864725i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 14394.9 | + | 24932.6i | 0.505109 | + | 0.874874i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −7067.68 | + | 12241.6i | −0.247206 | + | 0.428174i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 54695.9 | 1.90698 | 0.953488 | − | 0.301430i | \(-0.0974640\pi\) | ||||
0.953488 | + | 0.301430i | \(0.0974640\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −2897.14 | −0.100686 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 9127.64 | − | 15809.5i | 0.316209 | − | 0.547690i | −0.663485 | − | 0.748190i | \(-0.730923\pi\) |
0.979694 | + | 0.200500i | \(0.0642566\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −18226.0 | − | 31568.4i | −0.629397 | − | 1.09015i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −5583.62 | − | 2749.10i | −0.192207 | − | 0.0946329i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 3107.88 | + | 5383.00i | 0.106645 | + | 0.184714i | 0.914409 | − | 0.404792i | \(-0.132656\pi\) |
−0.807764 | + | 0.589506i | \(0.799323\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4455.64 | + | 7717.39i | −0.152409 | + | 0.263980i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 26957.9 | 0.919212 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 8594.53 | 0.292135 | 0.146067 | − | 0.989275i | \(-0.453338\pi\) | ||||
0.146067 | + | 0.989275i | \(0.453338\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −21893.1 | + | 37920.0i | −0.741826 | + | 1.28488i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 4684.83 | + | 8114.36i | 0.158243 | + | 0.274086i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −321.810 | − | 4862.18i | −0.0108361 | − | 0.163721i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −36280.3 | − | 62839.4i | −1.21783 | − | 2.10934i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −5680.66 | + | 9839.18i | −0.190090 | + | 0.329245i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −62451.1 | −2.08329 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 17168.1 | 0.570929 | 0.285464 | − | 0.958389i | \(-0.407852\pi\) | ||||
0.285464 | + | 0.958389i | \(0.407852\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1810.71 | + | 3136.24i | −0.0600293 | + | 0.103974i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 5963.11 | + | 10328.4i | 0.197081 | + | 0.341354i | 0.947581 | − | 0.319517i | \(-0.103521\pi\) |
−0.750500 | + | 0.660871i | \(0.770187\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 17944.0 | − | 12006.4i | 0.591221 | − | 0.395589i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1670.29 | + | 2893.02i | 0.0548636 | + | 0.0950265i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −7019.12 | + | 12157.5i | −0.229848 | + | 0.398108i | −0.957763 | − | 0.287559i | \(-0.907156\pi\) |
0.727915 | + | 0.685667i | \(0.240490\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −65373.8 | −2.13417 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2491.50 | 0.0810880 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 10175.7 | − | 17624.8i | 0.330167 | − | 0.571866i | −0.652378 | − | 0.757894i | \(-0.726228\pi\) |
0.982544 | + | 0.186028i | \(0.0595617\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 17662.0 | + | 30591.6i | 0.571329 | + | 0.989571i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −6560.14 | + | 4389.42i | −0.211562 | + | 0.141557i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −30047.2 | − | 52043.3i | −0.966072 | − | 1.67329i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −16252.9 | + | 28150.8i | −0.520978 | + | 0.902360i | 0.478724 | + | 0.877965i | \(0.341099\pi\) |
−0.999702 | + | 0.0243951i | \(0.992234\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −11421.9 | −0.365018 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −4417.18 | −0.140738 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 12423.5 | − | 21518.2i | 0.394641 | − | 0.683539i | −0.598414 | − | 0.801187i | \(-0.704202\pi\) |
0.993055 | + | 0.117648i | \(0.0375356\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −4253.58 | − | 7367.42i | −0.134712 | − | 0.233328i |
(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 | 336.4.q.i.193.1 | 4 | ||
4.3 | odd | 2 | 84.4.i.a.25.1 | ✓ | 4 | ||
7.2 | even | 3 | inner | 336.4.q.i.289.1 | 4 | ||
7.3 | odd | 6 | 2352.4.a.bx.1.1 | 2 | |||
7.4 | even | 3 | 2352.4.a.bt.1.2 | 2 | |||
12.11 | even | 2 | 252.4.k.f.109.2 | 4 | |||
28.3 | even | 6 | 588.4.a.f.1.1 | 2 | |||
28.11 | odd | 6 | 588.4.a.i.1.2 | 2 | |||
28.19 | even | 6 | 588.4.i.j.373.2 | 4 | |||
28.23 | odd | 6 | 84.4.i.a.37.1 | yes | 4 | ||
28.27 | even | 2 | 588.4.i.j.361.2 | 4 | |||
84.11 | even | 6 | 1764.4.a.o.1.1 | 2 | |||
84.23 | even | 6 | 252.4.k.f.37.2 | 4 | |||
84.47 | odd | 6 | 1764.4.k.q.1549.1 | 4 | |||
84.59 | odd | 6 | 1764.4.a.y.1.2 | 2 | |||
84.83 | odd | 2 | 1764.4.k.q.361.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
84.4.i.a.25.1 | ✓ | 4 | 4.3 | odd | 2 | ||
84.4.i.a.37.1 | yes | 4 | 28.23 | odd | 6 | ||
252.4.k.f.37.2 | 4 | 84.23 | even | 6 | |||
252.4.k.f.109.2 | 4 | 12.11 | even | 2 | |||
336.4.q.i.193.1 | 4 | 1.1 | even | 1 | trivial | ||
336.4.q.i.289.1 | 4 | 7.2 | even | 3 | inner | ||
588.4.a.f.1.1 | 2 | 28.3 | even | 6 | |||
588.4.a.i.1.2 | 2 | 28.11 | odd | 6 | |||
588.4.i.j.361.2 | 4 | 28.27 | even | 2 | |||
588.4.i.j.373.2 | 4 | 28.19 | even | 6 | |||
1764.4.a.o.1.1 | 2 | 84.11 | even | 6 | |||
1764.4.a.y.1.2 | 2 | 84.59 | odd | 6 | |||
1764.4.k.q.361.1 | 4 | 84.83 | odd | 2 | |||
1764.4.k.q.1549.1 | 4 | 84.47 | odd | 6 | |||
2352.4.a.bt.1.2 | 2 | 7.4 | even | 3 | |||
2352.4.a.bx.1.1 | 2 | 7.3 | odd | 6 |