Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [588,4,Mod(361,588)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(588, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([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("588.361");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 588 = 2^{2} \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 588.i (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: | \(34.6931230834\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 361.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 588.361 |
Dual form | 588.4.i.g.373.1 |
$q$-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 \(\left(\mathbb{Z}/588\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(295\) | \(493\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 | ||||||||
\(5\) | −2.00000 | − | 3.46410i | −0.178885 | − | 0.309839i | 0.762614 | − | 0.646854i | \(-0.223916\pi\) |
−0.941499 | + | 0.337016i | \(0.890582\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −4.50000 | − | 7.79423i | −0.166667 | − | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 10.0000 | − | 17.3205i | 0.274101 | − | 0.474757i | −0.695807 | − | 0.718229i | \(-0.744953\pi\) |
0.969908 | + | 0.243472i | \(0.0782863\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.00000 | −0.0853385 | −0.0426692 | − | 0.999089i | \(-0.513586\pi\) | ||||
−0.0426692 | + | 0.999089i | \(0.513586\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −12.0000 | −0.206559 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −12.0000 | + | 20.7846i | −0.171202 | + | 0.296530i | −0.938840 | − | 0.344353i | \(-0.888098\pi\) |
0.767639 | + | 0.640883i | \(0.221432\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −22.0000 | − | 38.1051i | −0.265639 | − | 0.460101i | 0.702092 | − | 0.712087i | \(-0.252250\pi\) |
−0.967731 | + | 0.251986i | \(0.918916\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −36.0000 | − | 62.3538i | −0.326370 | − | 0.565290i | 0.655418 | − | 0.755266i | \(-0.272492\pi\) |
−0.981789 | + | 0.189976i | \(0.939159\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 54.5000 | − | 94.3968i | 0.436000 | − | 0.755174i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −38.0000 | −0.243325 | −0.121662 | − | 0.992572i | \(-0.538823\pi\) | ||||
−0.121662 | + | 0.992572i | \(0.538823\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −92.0000 | + | 159.349i | −0.533022 | + | 0.923222i | 0.466234 | + | 0.884661i | \(0.345610\pi\) |
−0.999256 | + | 0.0385601i | \(0.987723\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −30.0000 | − | 51.9615i | −0.158252 | − | 0.274101i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 15.0000 | + | 25.9808i | 0.0666482 | + | 0.115438i | 0.897424 | − | 0.441169i | \(-0.145436\pi\) |
−0.830776 | + | 0.556607i | \(0.812103\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −6.00000 | + | 10.3923i | −0.0246351 | + | 0.0426692i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −216.000 | −0.822769 | −0.411385 | − | 0.911462i | \(-0.634955\pi\) | ||||
−0.411385 | + | 0.911462i | \(0.634955\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −164.000 | −0.581622 | −0.290811 | − | 0.956780i | \(-0.593925\pi\) | ||||
−0.290811 | + | 0.956780i | \(0.593925\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −18.0000 | + | 31.1769i | −0.0596285 | + | 0.103280i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −260.000 | − | 450.333i | −0.806913 | − | 1.39761i | −0.914992 | − | 0.403472i | \(-0.867803\pi\) |
0.108079 | − | 0.994142i | \(-0.465530\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 36.0000 | + | 62.3538i | 0.0988433 | + | 0.171202i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 73.0000 | − | 126.440i | 0.189195 | − | 0.327695i | −0.755787 | − | 0.654817i | \(-0.772746\pi\) |
0.944982 | + | 0.327122i | \(0.106079\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −80.0000 | −0.196131 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −132.000 | −0.306734 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −230.000 | + | 398.372i | −0.507516 | + | 0.879044i | 0.492446 | + | 0.870343i | \(0.336103\pi\) |
−0.999962 | + | 0.00870069i | \(0.997230\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −314.000 | − | 543.864i | −0.659075 | − | 1.14155i | −0.980855 | − | 0.194737i | \(-0.937615\pi\) |
0.321780 | − | 0.946814i | \(-0.395719\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 8.00000 | + | 13.8564i | 0.0152658 | + | 0.0264412i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −278.000 | + | 481.510i | −0.506912 | + | 0.877997i | 0.493056 | + | 0.869998i | \(0.335880\pi\) |
−0.999968 | + | 0.00799979i | \(0.997454\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −216.000 | −0.376860 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 592.000 | 0.989542 | 0.494771 | − | 0.869023i | \(-0.335252\pi\) | ||||
0.494771 | + | 0.869023i | \(0.335252\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −512.000 | + | 886.810i | −0.820891 | + | 1.42183i | 0.0841280 | + | 0.996455i | \(0.473190\pi\) |
−0.905019 | + | 0.425371i | \(0.860144\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −163.500 | − | 283.190i | −0.251725 | − | 0.436000i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 52.0000 | + | 90.0666i | 0.0740564 | + | 0.128269i | 0.900676 | − | 0.434492i | \(-0.143072\pi\) |
−0.826619 | + | 0.562762i | \(0.809739\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −40.5000 | + | 70.1481i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −324.000 | −0.428477 | −0.214239 | − | 0.976781i | \(-0.568727\pi\) | ||||
−0.214239 | + | 0.976781i | \(0.568727\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 96.0000 | 0.122502 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −57.0000 | + | 98.7269i | −0.0702419 | + | 0.121662i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −448.000 | − | 775.959i | −0.533572 | − | 0.924174i | −0.999231 | − | 0.0392095i | \(-0.987516\pi\) |
0.465659 | − | 0.884964i | \(-0.345817\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 276.000 | + | 478.046i | 0.307741 | + | 0.533022i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −88.0000 | + | 152.420i | −0.0950380 | + | 0.164611i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −920.000 | −0.963009 | −0.481504 | − | 0.876444i | \(-0.659909\pi\) | ||||
−0.481504 | + | 0.876444i | \(0.659909\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −180.000 | −0.182734 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −554.000 | + | 959.556i | −0.545793 | + | 0.945341i | 0.452764 | + | 0.891630i | \(0.350438\pi\) |
−0.998557 | + | 0.0537102i | \(0.982895\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −724.000 | − | 1254.00i | −0.692600 | − | 1.19962i | −0.970983 | − | 0.239149i | \(-0.923132\pi\) |
0.278383 | − | 0.960470i | \(-0.410202\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −658.000 | − | 1139.69i | −0.594498 | − | 1.02970i | −0.993618 | − | 0.112802i | \(-0.964018\pi\) |
0.399120 | − | 0.916899i | \(-0.369316\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 43.0000 | − | 74.4782i | 0.0377858 | − | 0.0654469i | −0.846514 | − | 0.532366i | \(-0.821303\pi\) |
0.884300 | + | 0.466919i | \(0.154636\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 90.0000 | 0.0769588 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1778.00 | 1.48018 | 0.740089 | − | 0.672509i | \(-0.234783\pi\) | ||||
0.740089 | + | 0.672509i | \(0.234783\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −144.000 | + | 249.415i | −0.116766 | + | 0.202244i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 18.0000 | + | 31.1769i | 0.0142231 | + | 0.0246351i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 465.500 | + | 806.270i | 0.349737 | + | 0.605762i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −324.000 | + | 561.184i | −0.237513 | + | 0.411385i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −936.000 | −0.669747 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −928.000 | −0.648399 | −0.324200 | − | 0.945989i | \(-0.605095\pi\) | ||||
−0.324200 | + | 0.945989i | \(0.605095\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −246.000 | + | 426.084i | −0.167900 | + | 0.290811i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −702.000 | − | 1215.90i | −0.468199 | − | 0.810944i | 0.531141 | − | 0.847284i | \(-0.321764\pi\) |
−0.999339 | + | 0.0363397i | \(0.988430\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 54.0000 | + | 93.5307i | 0.0344265 | + | 0.0596285i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 685.000 | − | 1186.45i | 0.427179 | − | 0.739895i | −0.569442 | − | 0.822031i | \(-0.692841\pi\) |
0.996621 | + | 0.0821359i | \(0.0261741\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 516.000 | 0.314867 | 0.157434 | − | 0.987530i | \(-0.449678\pi\) | ||||
0.157434 | + | 0.987530i | \(0.449678\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1560.00 | −0.931743 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −40.0000 | + | 69.2820i | −0.0233914 | + | 0.0405151i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 76.0000 | + | 131.636i | 0.0435273 | + | 0.0753915i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −695.000 | − | 1203.78i | −0.382125 | − | 0.661860i | 0.609241 | − | 0.792985i | \(-0.291474\pi\) |
−0.991366 | + | 0.131125i | \(0.958141\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −68.0000 | + | 117.779i | −0.0366474 | + | 0.0634752i | −0.883767 | − | 0.467927i | \(-0.845001\pi\) |
0.847120 | + | 0.531402i | \(0.178335\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 216.000 | 0.114134 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 736.000 | 0.381400 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 74.0000 | − | 128.172i | 0.0376168 | − | 0.0651543i | −0.846604 | − | 0.532223i | \(-0.821357\pi\) |
0.884221 | + | 0.467069i | \(0.154690\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −219.000 | − | 379.319i | −0.109232 | − | 0.189195i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 606.000 | + | 1049.62i | 0.291200 | + | 0.504373i | 0.974094 | − | 0.226145i | \(-0.0726122\pi\) |
−0.682894 | + | 0.730518i | \(0.739279\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −120.000 | + | 207.846i | −0.0566181 | + | 0.0980654i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1976.00 | 0.915614 | 0.457807 | − | 0.889052i | \(-0.348635\pi\) | ||||
0.457807 | + | 0.889052i | \(0.348635\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2181.00 | −0.992717 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −198.000 | + | 342.946i | −0.0885464 | + | 0.153367i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1346.00 | + | 2331.34i | 0.591529 | + | 1.02456i | 0.994027 | + | 0.109137i | \(0.0348087\pi\) |
−0.402498 | + | 0.915421i | \(0.631858\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 690.000 | + | 1195.12i | 0.293015 | + | 0.507516i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1290.00 | − | 2234.35i | 0.538654 | − | 0.932977i | −0.460322 | − | 0.887752i | \(-0.652266\pi\) |
0.998977 | − | 0.0452249i | \(-0.0144004\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2036.00 | −0.836103 | −0.418052 | − | 0.908423i | \(-0.637287\pi\) | ||||
−0.418052 | + | 0.908423i | \(0.637287\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1884.00 | −0.761034 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 60.0000 | − | 103.923i | 0.0238448 | − | 0.0413004i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 240.000 | + | 415.692i | 0.0938531 | + | 0.162558i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1980.00 | − | 3429.46i | −0.750093 | − | 1.29920i | −0.947777 | − | 0.318933i | \(-0.896675\pi\) |
0.197684 | − | 0.980266i | \(-0.436658\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.00000 | + | 1.73205i | −0.000372962 | + | 0.000645988i | −0.866212 | − | 0.499677i | \(-0.833452\pi\) |
0.865839 | + | 0.500323i | \(0.166785\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 48.0000 | 0.0176274 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3774.00 | 1.36491 | 0.682453 | − | 0.730930i | \(-0.260913\pi\) | ||||
0.682453 | + | 0.730930i | \(0.260913\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1780.00 | − | 3083.05i | 0.634075 | − | 1.09825i | −0.352636 | − | 0.935761i | \(-0.614715\pi\) |
0.986710 | − | 0.162489i | \(-0.0519521\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 834.000 | + | 1444.53i | 0.292666 | + | 0.506912i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 432.000 | + | 748.246i | 0.147181 | + | 0.254926i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −324.000 | + | 561.184i | −0.108790 | + | 0.188430i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −880.000 | −0.291248 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2692.00 | −0.878317 | −0.439159 | − | 0.898410i | \(-0.644723\pi\) | ||||
−0.439159 | + | 0.898410i | \(0.644723\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 888.000 | − | 1538.06i | 0.285656 | − | 0.494771i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 328.000 | + | 568.113i | 0.104044 | + | 0.180209i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1536.00 | + | 2660.43i | 0.473942 | + | 0.820891i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 48.0000 | − | 83.1384i | 0.0146101 | − | 0.0253054i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4528.00 | 1.35972 | 0.679859 | − | 0.733342i | \(-0.262041\pi\) | ||||
0.679859 | + | 0.733342i | \(0.262041\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −981.000 | −0.290667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1826.00 | − | 3162.72i | 0.533903 | − | 0.924746i | −0.465313 | − | 0.885146i | \(-0.654058\pi\) |
0.999216 | − | 0.0396002i | \(-0.0126084\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2402.00 | + | 4160.39i | 0.693138 | + | 1.20055i | 0.970804 | + | 0.239873i | \(0.0771057\pi\) |
−0.277666 | + | 0.960678i | \(0.589561\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1379.00 | − | 2388.50i | −0.387731 | − | 0.671570i | 0.604413 | − | 0.796671i | \(-0.293408\pi\) |
−0.992144 | + | 0.125102i | \(0.960074\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1040.00 | + | 1801.33i | −0.288690 | + | 0.500026i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 312.000 | 0.0855130 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6528.00 | 1.76678 | 0.883392 | − | 0.468635i | \(-0.155254\pi\) | ||||
0.883392 | + | 0.468635i | \(0.155254\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 28.0000 | − | 48.4974i | 0.00748398 | − | 0.0129626i | −0.862259 | − | 0.506467i | \(-0.830951\pi\) |
0.869743 | + | 0.493505i | \(0.164284\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 121.500 | + | 210.444i | 0.0320750 | + | 0.0555556i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 88.0000 | + | 152.420i | 0.0226693 | + | 0.0392643i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −486.000 | + | 841.777i | −0.123691 | + | 0.214239i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4900.00 | 1.23221 | 0.616106 | − | 0.787663i | \(-0.288709\pi\) | ||||
0.616106 | + | 0.787663i | \(0.288709\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1440.00 | −0.357834 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 144.000 | − | 249.415i | 0.0353633 | − | 0.0612510i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3392.00 | + | 5875.12i | 0.823296 | + | 1.42599i | 0.903214 | + | 0.429190i | \(0.141201\pi\) |
−0.0799181 | + | 0.996801i | \(0.525466\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 171.000 | + | 296.181i | 0.0405542 | + | 0.0702419i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2272.00 | − | 3935.22i | 0.532690 | − | 0.922646i | −0.466581 | − | 0.884478i | \(-0.654514\pi\) |
0.999271 | − | 0.0381681i | \(-0.0121522\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −584.000 | −0.135377 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2688.00 | −0.616116 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 2026.00 | − | 3509.13i | 0.459210 | − | 0.795374i | −0.539710 | − | 0.841851i | \(-0.681466\pi\) |
0.998919 | + | 0.0464767i | \(0.0147993\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1376.00 | + | 2383.30i | 0.308436 | + | 0.534226i | 0.978020 | − | 0.208510i | \(-0.0668612\pi\) |
−0.669585 | + | 0.742736i | \(0.733528\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1090.00 | − | 1887.94i | −0.239016 | − | 0.413988i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2183.00 | + | 3781.07i | −0.473515 | + | 0.820153i | −0.999540 | − | 0.0303164i | \(-0.990348\pi\) |
0.526025 | + | 0.850469i | \(0.323682\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1656.00 | 0.355348 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7734.00 | 1.64189 | 0.820946 | − | 0.571006i | \(-0.193447\pi\) | ||||
0.820946 | + | 0.571006i | \(0.193447\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2026.00 | − | 3509.13i | 0.425559 | − | 0.737090i | −0.570913 | − | 0.821010i | \(-0.693411\pi\) |
0.996472 | + | 0.0839204i | \(0.0267442\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 264.000 | + | 457.261i | 0.0548702 | + | 0.0950380i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2168.50 | + | 3755.95i | 0.441380 | + | 0.764493i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1380.00 | + | 2390.23i | −0.277997 | + | 0.481504i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −3420.00 | −0.681906 | −0.340953 | − | 0.940080i | \(-0.610750\pi\) | ||||
−0.340953 | + | 0.940080i | \(0.610750\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1840.00 | 0.363149 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −270.000 | + | 467.654i | −0.0527508 | + | 0.0913671i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 144.000 | + | 249.415i | 0.0278520 | + | 0.0482410i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1662.00 | + | 2878.67i | 0.315114 | + | 0.545793i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1256.00 | + | 2175.46i | −0.235798 | + | 0.408414i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7324.00 | 1.36157 | 0.680786 | − | 0.732482i | \(-0.261638\pi\) | ||||
0.680786 | + | 0.732482i | \(0.261638\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4344.00 | −0.799746 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2096.00 | − | 3630.38i | 0.382165 | − | 0.661929i | −0.609207 | − | 0.793012i | \(-0.708512\pi\) |
0.991371 | + | 0.131083i | \(0.0418453\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3420.00 | + | 5923.61i | 0.617603 | + | 1.06972i | 0.989922 | + | 0.141615i | \(0.0452296\pi\) |
−0.372318 | + | 0.928105i | \(0.621437\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −3315.00 | − | 5741.75i | −0.587347 | − | 1.01731i | −0.994578 | − | 0.103990i | \(-0.966839\pi\) |
0.407232 | − | 0.913325i | \(-0.366494\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −380.000 | + | 658.179i | −0.0666957 | + | 0.115520i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3948.00 | −0.686467 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1056.00 | 0.181911 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −218.000 | + | 377.587i | −0.0372076 | + | 0.0644454i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −129.000 | − | 223.435i | −0.0218156 | − | 0.0377858i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3434.00 | + | 5947.86i | 0.570241 | + | 0.987686i | 0.996541 | + | 0.0831042i | \(0.0264834\pi\) |
−0.426300 | + | 0.904582i | \(0.640183\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 135.000 | − | 233.827i | 0.0222161 | − | 0.0384794i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2224.00 | 0.362717 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −7378.00 | −1.19260 | −0.596299 | − | 0.802763i | \(-0.703363\pi\) | ||||
−0.596299 | + | 0.802763i | \(0.703363\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2667.00 | − | 4619.38i | 0.427291 | − | 0.740089i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1840.00 | + | 3186.97i | 0.292204 | + | 0.506112i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 432.000 | + | 748.246i | 0.0674148 | + | 0.116766i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1338.00 | − | 2317.48i | 0.206996 | − | 0.358528i | −0.743771 | − | 0.668435i | \(-0.766965\pi\) |
0.950767 | + | 0.309907i | \(0.100298\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −5124.00 | −0.785907 | −0.392953 | − | 0.919558i | \(-0.628547\pi\) | ||||
−0.392953 | + | 0.919558i | \(0.628547\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 108.000 | 0.0164234 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −2280.00 | + | 3949.08i | −0.343774 | + | 0.595434i | −0.985130 | − | 0.171809i | \(-0.945039\pi\) |
0.641356 | + | 0.767243i | \(0.278372\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1184.00 | − | 2050.75i | −0.177015 | − | 0.306598i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1828.00 | − | 3166.19i | −0.268741 | − | 0.465474i | 0.699796 | − | 0.714343i | \(-0.253274\pi\) |
−0.968537 | + | 0.248869i | \(0.919941\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2461.50 | − | 4263.44i | 0.358872 | − | 0.621584i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2793.00 | 0.403842 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4096.00 | 0.587382 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 808.000 | − | 1399.50i | 0.114924 | − | 0.199055i | −0.802825 | − | 0.596215i | \(-0.796671\pi\) |
0.917750 | + | 0.397160i | \(0.130004\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 972.000 | + | 1683.55i | 0.137128 | + | 0.237513i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1367.00 | − | 2367.71i | −0.189760 | − | 0.328674i | 0.755410 | − | 0.655252i | \(-0.227438\pi\) |
−0.945170 | + | 0.326578i | \(0.894104\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1404.00 | + | 2431.80i | −0.193339 | + | 0.334874i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 152.000 | 0.0207650 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1380.00 | −0.187034 | −0.0935169 | − | 0.995618i | \(-0.529811\pi\) | ||||
−0.0935169 | + | 0.995618i | \(0.529811\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1392.00 | + | 2411.01i | −0.187177 | + | 0.324200i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −3444.00 | − | 5965.18i | −0.459478 | − | 0.795840i | 0.539455 | − | 0.842014i | \(-0.318630\pi\) |
−0.998933 | + | 0.0461746i | \(0.985297\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 738.000 | + | 1278.25i | 0.0969371 | + | 0.167900i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1023.00 | − | 1771.89i | 0.133337 | − | 0.230947i | −0.791624 | − | 0.611009i | \(-0.790764\pi\) |
0.924961 | + | 0.380062i | \(0.124097\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1728.00 | 0.223501 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −4212.00 | −0.540629 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 208.000 | − | 360.267i | 0.0264952 | − | 0.0458911i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1558.00 | − | 2698.54i | −0.196962 | − | 0.341148i | 0.750580 | − | 0.660779i | \(-0.229774\pi\) |
−0.947542 | + | 0.319632i | \(0.896441\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1479.00 | − | 2561.70i | −0.184184 | − | 0.319016i | 0.759117 | − | 0.650954i | \(-0.225631\pi\) |
−0.943301 | + | 0.331938i | \(0.892298\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 368.000 | − | 637.395i | 0.0454873 | − | 0.0787863i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 324.000 | 0.0397523 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 600.000 | 0.0730735 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3972.00 | + | 6879.71i | −0.480202 | + | 0.831735i | −0.999742 | − | 0.0227114i | \(-0.992770\pi\) |
0.519540 | + | 0.854446i | \(0.326103\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2055.00 | − | 3559.36i | −0.246632 | − | 0.427179i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 648.000 | + | 1122.37i | 0.0766484 | + | 0.132759i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 774.000 | − | 1340.61i | 0.0908943 | − | 0.157434i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 4084.00 | 0.476173 | 0.238086 | − | 0.971244i | \(-0.423480\pi\) | ||||
0.238086 | + | 0.971244i | \(0.423480\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6306.00 | −0.730013 | −0.365007 | − | 0.931005i | \(-0.618933\pi\) | ||||
−0.365007 | + | 0.931005i | \(0.618933\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2340.00 | + | 4053.00i | −0.268971 | + | 0.465871i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1308.00 | + | 2265.52i | 0.149288 | + | 0.258574i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 120.000 | + | 207.846i | 0.0135050 | + | 0.0233914i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5912.00 | − | 10239.9i | 0.660722 | − | 1.14440i | −0.319705 | − | 0.947517i | \(-0.603584\pi\) |
0.980426 | − | 0.196886i | \(-0.0630830\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −4504.00 | −0.499881 | −0.249940 | − | 0.968261i | \(-0.580411\pi\) | ||||
−0.249940 | + | 0.968261i | \(0.580411\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 456.000 | 0.0502610 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1584.00 | + | 2743.57i | −0.173394 | + | 0.300326i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6528.00 | − | 11306.8i | −0.709714 | − | 1.22926i | −0.964963 | − | 0.262385i | \(-0.915491\pi\) |
0.255249 | − | 0.966875i | \(-0.417842\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −66.0000 | − | 114.315i | −0.00707845 | − | 0.0122602i | 0.862464 | − | 0.506118i | \(-0.168920\pi\) |
−0.869543 | + | 0.493857i | \(0.835586\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1792.00 | + | 3103.84i | −0.190897 | + | 0.330642i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −4170.00 | −0.441240 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 4866.00 | 0.511449 | 0.255725 | − | 0.966750i | \(-0.417686\pi\) | ||||
0.255725 | + | 0.966750i | \(0.417686\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2160.00 | + | 3741.23i | −0.225522 | + | 0.390616i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 204.000 | + | 353.338i | 0.0211584 | + | 0.0366474i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5053.00 | − | 8752.05i | −0.517220 | − | 0.895851i | −0.999800 | − | 0.0199990i | \(-0.993634\pi\) |
0.482580 | − | 0.875852i | \(-0.339700\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 324.000 | − | 561.184i | 0.0329478 | − | 0.0570672i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −18036.0 | −1.82217 | −0.911085 | − | 0.412219i | \(-0.864754\pi\) | ||||
−0.911085 | + | 0.412219i | \(0.864754\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5288.00 | 0.530787 | 0.265393 | − | 0.964140i | \(-0.414498\pi\) | ||||
0.265393 | + | 0.964140i | \(0.414498\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1104.00 | − | 1912.18i | 0.110101 | − | 0.190700i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −7582.00 | − | 13132.4i | −0.751291 | − | 1.30128i | −0.947197 | − | 0.320652i | \(-0.896098\pi\) |
0.195906 | − | 0.980623i | \(-0.437235\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −222.000 | − | 384.515i | −0.0217181 | − | 0.0376168i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1640.00 | + | 2840.56i | −0.159423 | + | 0.276129i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4796.00 | −0.463275 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1314.00 | −0.126130 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −3948.00 | + | 6838.14i | −0.376594 | + | 0.652281i | −0.990564 | − | 0.137049i | \(-0.956238\pi\) |
0.613970 | + | 0.789329i | \(0.289572\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −60.0000 | − | 103.923i | −0.00568766 | − | 0.00985132i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1840.00 | + | 3186.97i | 0.172268 | + | 0.298377i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1460.00 | + | 2528.79i | −0.135850 | + | 0.235299i | −0.925922 | − | 0.377715i | \(-0.876710\pi\) |
0.790072 | + | 0.613014i | \(0.210043\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 3636.00 | 0.336249 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7932.00 | −0.729055 | −0.364528 | − | 0.931193i | \(-0.618770\pi\) | ||||
−0.364528 | + | 0.931193i | \(0.618770\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 456.000 | − | 789.815i | 0.0416576 | − | 0.0721531i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 360.000 | + | 623.538i | 0.0326885 | + | 0.0566181i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1002.00 | + | 1735.51i | 0.0898911 | + | 0.155696i | 0.907465 | − | 0.420128i | \(-0.138015\pi\) |
−0.817574 | + | 0.575824i | \(0.804681\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2964.00 | − | 5133.80i | 0.264315 | − | 0.457807i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 4496.00 | 0.398542 | 0.199271 | − | 0.979944i | \(-0.436143\pi\) | ||||
0.199271 | + | 0.979944i | \(0.436143\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4432.00 | 0.390537 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −3271.50 | + | 5666.40i | −0.286573 | + | 0.496359i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −6310.00 | − | 10929.2i | −0.549481 | − | 0.951729i | −0.998310 | − | 0.0581114i | \(-0.981492\pi\) |
0.448829 | − | 0.893618i | \(-0.351841\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 594.000 | + | 1028.84i | 0.0511223 | + | 0.0885464i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −2896.00 | + | 5016.02i | −0.247792 | + | 0.429189i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −10400.0 | −0.884703 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 8076.00 | 0.683039 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −9004.00 | + | 15595.4i | −0.757145 | + | 1.31141i | 0.187156 | + | 0.982330i | \(0.440073\pi\) |
−0.944301 | + | 0.329083i | \(0.893260\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −6646.00 | − | 11511.2i | −0.555658 | − | 0.962428i | −0.997852 | − | 0.0655088i | \(-0.979133\pi\) |
0.442194 | − | 0.896920i | \(-0.354200\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2208.00 | − | 3824.37i | −0.182509 | − | 0.316114i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3491.50 | − | 6047.46i | 0.286965 | − | 0.497038i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4140.00 | 0.338344 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 864.000 | 0.0702139 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2632.00 | + | 4558.76i | −0.212694 | + | 0.368397i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −3870.00 | − | 6703.04i | −0.310992 | − | 0.538654i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4285.00 | + | 7421.84i | 0.340530 | + | 0.589815i | 0.984531 | − | 0.175210i | \(-0.0560603\pi\) |
−0.644002 | + | 0.765024i | \(0.722727\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −3054.00 | + | 5289.68i | −0.241362 | + | 0.418052i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −344.000 | −0.0270373 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1916.00 | −0.149766 | −0.0748832 | − | 0.997192i | \(-0.523858\pi\) | ||||
−0.0748832 | + | 0.997192i | \(0.523858\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −2826.00 | + | 4894.78i | −0.219692 | + | 0.380517i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 836.000 | + | 1447.99i | 0.0646367 | + | 0.111954i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −180.000 | − | 311.769i | −0.0137668 | − | 0.0238448i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −9963.00 | + | 17256.4i | −0.757892 | + | 1.31271i | 0.186032 | + | 0.982544i | \(0.440437\pi\) |
−0.943924 | + | 0.330164i | \(0.892896\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 656.000 | 0.0496348 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1440.00 | 0.108372 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −2122.00 | + | 3675.41i | −0.158848 | + | 0.275133i | −0.934454 | − | 0.356085i | \(-0.884111\pi\) |
0.775605 | + | 0.631218i | \(0.217445\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3556.00 | − | 6159.17i | −0.264782 | − | 0.458617i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 11397.0 | + | 19740.2i | 0.839696 | + | 1.45440i | 0.890149 | + | 0.455670i | \(0.150600\pi\) |
−0.0504527 | + | 0.998726i | \(0.516066\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7014.00 | + | 12148.6i | −0.514057 | + | 0.890374i | 0.485810 | + | 0.874065i | \(0.338525\pi\) |
−0.999867 | + | 0.0163089i | \(0.994809\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −11880.0 | −0.866133 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −7848.00 | −0.569190 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4184.00 | + | 7246.90i | −0.301876 | + | 0.522864i | −0.976561 | − | 0.215242i | \(-0.930946\pi\) |
0.674685 | + | 0.738106i | \(0.264279\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 3.00000 | + | 5.19615i | 0.000215329 | + | 0.000372962i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1460.00 | − | 2528.79i | −0.103717 | − | 0.179643i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 72.0000 | − | 124.708i | 0.00508860 | − | 0.00881372i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 52.0000 | 0.00365634 | 0.00182817 | − | 0.999998i | \(-0.499418\pi\) | ||||
0.00182817 | + | 0.999998i | \(0.499418\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8096.00 | 0.566366 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 5661.00 | − | 9805.14i | 0.394014 | − | 0.682453i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −2904.00 | − | 5029.88i | −0.201101 | − | 0.348317i | 0.747782 | − | 0.663944i | \(-0.231119\pi\) |
−0.948883 | + | 0.315627i | \(0.897785\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −5340.00 | − | 9249.15i | −0.366083 | − | 0.634075i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 5232.00 | − | 9062.09i | 0.356884 | − | 0.618142i | −0.630554 | − | 0.776145i | \(-0.717172\pi\) |
0.987439 | + | 0.158003i | \(0.0505057\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1184.00 | 0.0803600 | 0.0401800 | − | 0.999192i | \(-0.487207\pi\) | ||||
0.0401800 | + | 0.999192i | \(0.487207\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 5004.00 | 0.337941 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1862.00 | − | 3225.08i | 0.125126 | − | 0.216724i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −6576.00 | − | 11390.0i | −0.439723 | − | 0.761622i | 0.557945 | − | 0.829878i | \(-0.311590\pi\) |
−0.997668 | + | 0.0682559i | \(0.978257\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1040.00 | + | 1801.33i | 0.0688607 | + | 0.119270i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 9167.00 | − | 15877.7i | 0.603999 | − | 1.04616i | −0.388209 | − | 0.921571i | \(-0.626906\pi\) |
0.992209 | − | 0.124586i | \(-0.0397604\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 2592.00 | 0.169950 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −8122.00 | −0.529950 | −0.264975 | − | 0.964255i | \(-0.585364\pi\) | ||||
−0.264975 | + | 0.964255i | \(0.585364\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −2990.00 | + | 5178.83i | −0.194149 | + | 0.336276i | −0.946621 | − | 0.322348i | \(-0.895528\pi\) |
0.752472 | + | 0.658624i | \(0.228861\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 972.000 | + | 1683.55i | 0.0628100 | + | 0.108790i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −4940.50 | − | 8557.20i | −0.316192 | − | 0.547661i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1320.00 | + | 2286.31i | −0.0840761 | + | 0.145624i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −720.000 | −0.0456411 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 12528.0 | 0.790383 | 0.395192 | − | 0.918599i | \(-0.370678\pi\) | ||||
0.395192 | + | 0.918599i | \(0.370678\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −4038.00 | + | 6994.02i | −0.253548 | + | 0.439159i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1856.00 | + | 3214.69i | 0.115989 | + | 0.200899i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −2664.00 | − | 4614.18i | −0.164924 | − | 0.285656i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −10399.0 | + | 18011.6i | −0.640773 | + | 1.10985i | 0.344487 | + | 0.938791i | \(0.388053\pi\) |
−0.985260 | + | 0.171061i | \(0.945280\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1932.00 | −0.118492 | −0.0592462 | − | 0.998243i | \(-0.518870\pi\) | ||||
−0.0592462 | + | 0.998243i | \(0.518870\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1968.00 | 0.120139 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 4212.00 | − | 7295.40i | 0.255936 | − | 0.443295i | −0.709213 | − | 0.704994i | \(-0.750950\pi\) |
0.965149 | + | 0.261699i | \(0.0842829\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4600.00 | + | 7967.43i | 0.278222 | + | 0.481894i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 8875.00 | + | 15372.0i | 0.531862 | + | 0.921211i | 0.999308 | + | 0.0371899i | \(0.0118407\pi\) |
−0.467447 | + | 0.884021i | \(0.654826\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2808.00 | + | 4863.60i | −0.167508 | + | 0.290132i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 9216.00 | 0.547261 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −27580.0 | −1.63029 | −0.815147 | − | 0.579254i | \(-0.803344\pi\) | ||||
−0.815147 | + | 0.579254i | \(0.803344\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4646.00 | − | 8047.11i | 0.273386 | − | 0.473519i | −0.696340 | − | 0.717712i | \(-0.745190\pi\) |
0.969727 | + | 0.244193i | \(0.0785229\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −144.000 | − | 249.415i | −0.00843514 | − | 0.0146101i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1368.00 | + | 2369.45i | 0.0794141 | + | 0.137549i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 6792.00 | − | 11764.1i | 0.392517 | − | 0.679859i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −12560.0 | −0.722613 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 11486.0 | 0.657879 | 0.328940 | − | 0.944351i | \(-0.393309\pi\) | ||||
0.328940 | + | 0.944351i | \(0.393309\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1471.50 | + | 2548.71i | −0.0839082 | + | 0.145333i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −3558.00 | − | 6162.64i | −0.201987 | − | 0.349851i | 0.747182 | − | 0.664620i | \(-0.231406\pi\) |
−0.949168 | + | 0.314768i | \(0.898073\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −5478.00 | − | 9488.17i | −0.308249 | − | 0.533903i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 3806.00 | − | 6592.19i | 0.213225 | − | 0.369316i | −0.739497 | − | 0.673160i | \(-0.764937\pi\) |
0.952722 | + | 0.303843i | \(0.0982700\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −5480.00 | −0.305664 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 14412.0 | 0.800367 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −292.000 | + | 505.759i | −0.0161456 | + | 0.0279650i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 10786.0 | + | 18681.9i | 0.593804 | + | 1.02850i | 0.993714 | + | 0.111945i | \(0.0357080\pi\) |
−0.399910 | + | 0.916554i | \(0.630959\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1032.00 | − | 1787.48i | −0.0563252 | − | 0.0975581i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2592.00 | − | 4489.48i | 0.140859 | − | 0.243976i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −8274.00 | −0.447713 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1702.00 | −0.0917028 | −0.0458514 | − | 0.998948i | \(-0.514600\pi\) | ||||
−0.0458514 | + | 0.998948i | \(0.514600\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 660.000 | − | 1143.15i | 0.0354088 | − | 0.0613298i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 3120.00 | + | 5404.00i | 0.166675 | + | 0.288690i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3185.00 | − | 5516.58i | −0.168710 | − | 0.292214i | 0.769257 | − | 0.638940i | \(-0.220627\pi\) |
−0.937966 | + | 0.346726i | \(0.887293\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 468.000 | − | 810.600i | 0.0246855 | − | 0.0427565i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 13248.0 | 0.695851 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 320.000 | 0.0167375 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 9792.00 | − | 16960.2i | 0.510026 | − | 0.883392i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 4404.00 | + | 7627.95i | 0.228430 | + | 0.395653i | 0.957343 | − | 0.288954i | \(-0.0933073\pi\) |
−0.728913 | + | 0.684607i | \(0.759974\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −84.0000 | − | 145.492i | −0.00432088 | − | 0.00748398i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2071.00 | + | 3587.08i | −0.106090 | + | 0.183753i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 17768.0 | 0.906436 | 0.453218 | − | 0.891400i | \(-0.350276\pi\) | ||||
0.453218 | + | 0.891400i | \(0.350276\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1968.00 | − | 3408.68i | 0.0995747 | − | 0.172468i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2782.00 | + | 4818.57i | 0.140185 | + | 0.242807i | 0.927566 | − | 0.373659i | \(-0.121897\pi\) |
−0.787381 | + | 0.616466i | \(0.788564\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 5560.00 | + | 9630.20i | 0.277890 | + | 0.481320i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 8782.00 | − | 15210.9i | 0.437146 | − | 0.757160i | −0.560322 | − | 0.828275i | \(-0.689323\pi\) |
0.997468 | + | 0.0711154i | \(0.0226559\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 528.000 | 0.0261762 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −38280.0 | −1.89012 | −0.945059 | − | 0.326901i | \(-0.893996\pi\) | ||||
−0.945059 | + | 0.326901i | \(0.893996\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2780.00 | + | 4815.10i | −0.136713 | + | 0.236794i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1458.00 | + | 2525.33i | 0.0714129 | + | 0.123691i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −18096.0 | − | 31343.2i | −0.879271 | − | 1.52294i | −0.852142 | − | 0.523310i | \(-0.824697\pi\) |
−0.0271284 | − | 0.999632i | \(-0.508636\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 7350.00 | − | 12730.6i | 0.355709 | − | 0.616106i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 544.000 | 0.0262228 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −14.0000 | −0.000672178 | −0.000336089 | − | 1.00000i | \(-0.500107\pi\) | ||||
−0.000336089 | 1.00000i | \(0.500107\pi\) | ||||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2160.00 | + | 3741.23i | −0.103298 | + | 0.178917i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 13252.0 | + | 22953.1i | 0.631254 | + | 1.09336i | 0.987296 | + | 0.158894i | \(0.0507930\pi\) |
−0.356041 | + | 0.934470i | \(0.615874\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −432.000 | − | 748.246i | −0.0204170 | − | 0.0353633i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 920.000 | − | 1593.49i | 0.0433107 | − | 0.0750163i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 40184.0 | 1.88436 | 0.942180 | − | 0.335109i | \(-0.108773\pi\) | ||||
0.942180 | + | 0.335109i | \(0.108773\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 20352.0 | 0.950661 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 17670.0 | − | 30605.3i | 0.822181 | − | 1.42406i | −0.0818742 | − | 0.996643i | \(-0.526091\pi\) |
0.904055 | − | 0.427416i | \(-0.140576\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 10028.0 | + | 17369.0i | 0.464795 | + | 0.805049i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 4752.00 | + | 8230.71i | 0.218560 | + | 0.378557i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5920.00 | − | 10253.7i | 0.271235 | − | 0.469792i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1026.00 | 0.0468279 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −592.000 | −0.0269164 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 7426.00 | − | 12862.2i | 0.336351 | − | 0.582577i | −0.647392 | − | 0.762157i | \(-0.724140\pi\) |
0.983743 | + | 0.179580i | \(0.0574738\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −6816.00 | − | 11805.7i | −0.307549 | − | 0.532690i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1256.00 | + | 2175.46i | 0.0562445 | + | 0.0974183i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −876.000 | + | 1517.28i | −0.0390799 | + | 0.0676884i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 19788.0 | 0.879457 | 0.439728 | − | 0.898131i | \(-0.355075\pi\) | ||||
0.439728 | + | 0.898131i | \(0.355075\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 12480.0 | 0.552579 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −4032.00 | + | 6983.63i | −0.177857 | + | 0.308058i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 10240.0 | + | 17736.2i | 0.450015 | + | 0.779448i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −6078.00 | − | 10527.4i | −0.265125 | − | 0.459210i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −8493.00 | + | 14710.3i | −0.369095 | + | 0.639292i | −0.989424 | − | 0.145050i | \(-0.953666\pi\) |
0.620329 | + | 0.784342i | \(0.286999\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −26596.0 | −1.15156 | −0.575778 | − | 0.817606i | \(-0.695301\pi\) | ||||
−0.575778 | + | 0.817606i | \(0.695301\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 8256.00 | 0.356151 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2424.00 | − | 4198.49i | 0.104183 | − | 0.180450i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3608.00 | + | 6249.24i | 0.154502 | + | 0.267605i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 17449.0 | + | 30222.6i | 0.741747 | + | 1.28474i | 0.951699 | + | 0.307032i | \(0.0993358\pi\) |
−0.209952 | + | 0.977712i | \(0.567331\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −6464.00 | + | 11196.0i | −0.273780 | + | 0.474201i | −0.969827 | − | 0.243796i | \(-0.921607\pi\) |
0.696047 | + | 0.717997i | \(0.254941\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −6540.00 | −0.275992 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −43164.0 | −1.81494 | −0.907472 | − | 0.420112i | \(-0.861991\pi\) | ||||
−0.907472 | + | 0.420112i | \(0.861991\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 20614.0 | − | 35704.5i | 0.863635 | − | 1.49586i | −0.00476022 | − | 0.999989i | \(-0.501515\pi\) |
0.868396 | − | 0.495872i | \(-0.165151\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 6549.00 | + | 11343.2i | 0.273384 | + | 0.473515i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3952.00 | − | 6845.06i | −0.163790 | − | 0.283692i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2484.00 | − | 4302.41i | 0.102580 | − | 0.177674i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1368.00 | −0.0562915 | −0.0281458 | − | 0.999604i | \(-0.508960\pi\) | ||||
−0.0281458 | + | 0.999604i | \(0.508960\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −22945.0 | −0.940793 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 11601.0 | − | 20093.5i | 0.473974 | − | 0.820946i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 4362.00 | + | 7555.21i | 0.177583 | + | 0.307582i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −6078.00 | − | 10527.4i | −0.245697 | − | 0.425559i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1080.00 | − | 1870.61i | 0.0435040 | − | 0.0753512i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 5276.00 | 0.211778 | 0.105889 | − | 0.994378i | \(-0.466231\pi\) | ||||
0.105889 | + | 0.994378i | \(0.466231\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1584.00 | 0.0633587 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −420.000 | + | 727.461i | −0.0167409 | + | 0.0289960i | −0.874274 | − | 0.485432i | \(-0.838662\pi\) |
0.857534 | + | 0.514428i | \(0.171996\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 13014.0 | + | 22540.9i | 0.516917 | + | 0.895327i | 0.999807 | + | 0.0196458i | \(0.00625386\pi\) |
−0.482890 | + | 0.875681i | \(0.660413\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 14724.0 | + | 25502.7i | 0.580777 | + | 1.00594i | 0.995387 | + | 0.0959366i | \(0.0305846\pi\) |
−0.414610 | + | 0.909999i | \(0.636082\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 5384.00 | − | 9325.36i | 0.211632 | − | 0.366557i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 13011.0 | 0.509662 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2080.00 | 0.0811958 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1112.00 | − | 1926.04i | 0.0432591 | − | 0.0749270i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 4140.00 | + | 7170.69i | 0.160501 | + | 0.277997i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −12933.0 | − | 22400.6i | −0.497966 | − | 0.862503i | 0.502031 | − | 0.864850i | \(-0.332586\pi\) |
−0.999997 | + | 0.00234681i | \(0.999253\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −5130.00 | + | 8885.42i | −0.196849 | + | 0.340953i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 9472.00 | 0.362225 | 0.181112 | − | 0.983462i | \(-0.442030\pi\) | ||||
0.181112 | + | 0.983462i | \(0.442030\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 49372.0 | 1.88165 | 0.940827 | − | 0.338888i | \(-0.110051\pi\) | ||||
0.940827 | + | 0.338888i | \(0.110051\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2760.00 | − | 4780.46i | 0.104832 | − | 0.181574i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 5580.00 | + | 9664.84i | 0.211227 | + | 0.365855i | 0.952099 | − | 0.305791i | \(-0.0989208\pi\) |
−0.740872 | + | 0.671646i | \(0.765588\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 810.000 | + | 1402.96i | 0.0304557 | + | 0.0527508i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −11440.0 | + | 19814.7i | −0.428695 | + | 0.742522i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −10320.0 | −0.385430 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 864.000 | 0.0321607 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3496.00 | − | 6055.25i | 0.129698 | − | 0.224643i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1752.00 | + | 3034.55i | 0.0647809 | + | 0.112204i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 4072.00 | + | 7052.91i | 0.149567 | + | 0.259057i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −11354.0 | + | 19665.7i | −0.415660 | + | 0.719944i | −0.995497 | − | 0.0947882i | \(-0.969783\pi\) |
0.579838 | + | 0.814732i | \(0.303116\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 9972.00 | 0.363862 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −16192.0 | −0.588875 | −0.294437 | − | 0.955671i | \(-0.595132\pi\) | ||||
−0.294437 | + | 0.955671i | \(0.595132\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3240.00 | + | 5611.84i | −0.117446 | + | 0.203423i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 3768.00 | + | 6526.37i | 0.136138 | + | 0.235798i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 23160.0 | + | 40114.3i | 0.831314 | + | 1.43988i | 0.896996 | + | 0.442038i | \(0.145744\pi\) |
−0.0656819 | + | 0.997841i | \(0.520922\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 10986.0 | − | 19028.3i | 0.393052 | − | 0.680786i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −2368.00 | −0.0844460 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3270.00 | 0.116235 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −6516.00 | + | 11286.0i | −0.230867 | + | 0.399873i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1140.00 | + | 1974.54i | 0.0402607 | + | 0.0697336i | 0.885454 | − | 0.464728i | \(-0.153848\pi\) |
−0.845193 | + | 0.534461i | \(0.820514\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −6288.00 | − | 10891.1i | −0.220643 | − | 0.382165i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 960.000 | − | 1662.77i | 0.0335779 | − | 0.0581587i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 49056.0 | 1.71034 | 0.855171 | − | 0.518347i | \(-0.173452\pi\) | ||||
0.855171 | + | 0.518347i | \(0.173452\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 20520.0 | 0.713147 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 12438.0 | − | 21543.2i | 0.430890 | − | 0.746323i | −0.566060 | − | 0.824364i | \(-0.691533\pi\) |
0.996950 | + | 0.0780409i | \(0.0248665\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 7776.00 | + | 13468.4i | 0.268527 | + | 0.465103i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −11714.0 | − | 20289.2i | −0.401958 | − | 0.696211i | 0.592005 | − | 0.805935i | \(-0.298337\pi\) |
−0.993962 | + | 0.109724i | \(0.965003\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2048.00 | − | 3547.24i | 0.0700536 | − | 0.121336i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −19890.0 | −0.678210 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −6678.00 | −0.226990 | −0.113495 | − | 0.993539i | \(-0.536205\pi\) | ||||
−0.113495 | + | 0.993539i | \(0.536205\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −7920.00 | + | 13717.8i | −0.268361 | + | 0.464816i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1140.00 | + | 1974.54i | 0.0385068 | + | 0.0666957i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2032.50 | − | 3520.39i | −0.0682253 | − | 0.118170i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −5922.00 | + | 10257.2i | −0.198166 | + | 0.343233i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 8.00000 | 0.000266870 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 15544.0 | 0.516920 | 0.258460 | − | 0.966022i | \(-0.416785\pi\) | ||||
0.258460 | + | 0.966022i | \(0.416785\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1584.00 | − | 2743.57i | 0.0525133 | − | 0.0909557i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 15562.0 | + | 26954.2i | 0.514324 | + | 0.890835i | 0.999862 | + | 0.0166194i | \(0.00529035\pi\) |
−0.485538 | + | 0.874215i | \(0.661376\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 654.000 | + | 1132.76i | 0.0214818 | + | 0.0372076i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −25031.0 | + | 43355.0i | −0.819665 | + | 1.41970i | 0.0862643 | + | 0.996272i | \(0.472507\pi\) |
−0.905929 | + | 0.423429i | \(0.860826\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −17920.0 | −0.585011 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −774.000 | −0.0251905 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −164.000 | + | 284.056i | −0.00532125 | + | 0.00921667i | −0.868674 | − | 0.495385i | \(-0.835027\pi\) |
0.863353 | + | 0.504601i | \(0.168360\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −7548.00 | − | 13073.5i | −0.244162 | − | 0.422900i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 5904.00 | + | 10226.0i | 0.189824 | + | 0.328785i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 10436.0 | − | 18075.7i | 0.334521 | − | 0.579408i | −0.648872 | − | 0.760898i | \(-0.724759\pi\) |
0.983393 | + | 0.181490i | \(0.0580921\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 20604.0 | 0.658457 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −14240.0 | −0.453707 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 23462.0 | − | 40637.4i | 0.745285 | − | 1.29087i | −0.204777 | − | 0.978809i | \(-0.565647\pi\) |
0.950062 | − | 0.312063i | \(-0.101020\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −405.000 | − | 701.481i | −0.0128265 | − | 0.0222161i |
(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 | 588.4.i.g.361.1 | 2 | ||
3.2 | odd | 2 | 1764.4.k.j.361.1 | 2 | |||
7.2 | even | 3 | inner | 588.4.i.g.373.1 | 2 | ||
7.3 | odd | 6 | 588.4.a.e.1.1 | yes | 1 | ||
7.4 | even | 3 | 588.4.a.b.1.1 | ✓ | 1 | ||
7.5 | odd | 6 | 588.4.i.b.373.1 | 2 | |||
7.6 | odd | 2 | 588.4.i.b.361.1 | 2 | |||
21.2 | odd | 6 | 1764.4.k.j.1549.1 | 2 | |||
21.5 | even | 6 | 1764.4.k.g.1549.1 | 2 | |||
21.11 | odd | 6 | 1764.4.a.d.1.1 | 1 | |||
21.17 | even | 6 | 1764.4.a.i.1.1 | 1 | |||
21.20 | even | 2 | 1764.4.k.g.361.1 | 2 | |||
28.3 | even | 6 | 2352.4.a.g.1.1 | 1 | |||
28.11 | odd | 6 | 2352.4.a.be.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
588.4.a.b.1.1 | ✓ | 1 | 7.4 | even | 3 | ||
588.4.a.e.1.1 | yes | 1 | 7.3 | odd | 6 | ||
588.4.i.b.361.1 | 2 | 7.6 | odd | 2 | |||
588.4.i.b.373.1 | 2 | 7.5 | odd | 6 | |||
588.4.i.g.361.1 | 2 | 1.1 | even | 1 | trivial | ||
588.4.i.g.373.1 | 2 | 7.2 | even | 3 | inner | ||
1764.4.a.d.1.1 | 1 | 21.11 | odd | 6 | |||
1764.4.a.i.1.1 | 1 | 21.17 | even | 6 | |||
1764.4.k.g.361.1 | 2 | 21.20 | even | 2 | |||
1764.4.k.g.1549.1 | 2 | 21.5 | even | 6 | |||
1764.4.k.j.361.1 | 2 | 3.2 | odd | 2 | |||
1764.4.k.j.1549.1 | 2 | 21.2 | odd | 6 | |||
2352.4.a.g.1.1 | 1 | 28.3 | even | 6 | |||
2352.4.a.be.1.1 | 1 | 28.11 | odd | 6 |