Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1500,2,Mod(301,1500)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1500, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 0, 8]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1500.301");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1500 = 2^{2} \cdot 3 \cdot 5^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1500.m (of order \(5\), degree \(4\), 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: | \(11.9775603032\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{5})\) |
Twist minimal: | no (minimal twist has level 300) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 601.4 | ||
Character | \(\chi\) | \(=\) | 1500.601 |
Dual form | 1500.2.m.c.901.4 |
$q$-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 \(\left(\mathbb{Z}/1500\mathbb{Z}\right)^\times\).
\(n\) | \(751\) | \(877\) | \(1001\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{5}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.809017 | − | 0.587785i | −0.467086 | − | 0.339358i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.44380 | 0.923670 | 0.461835 | − | 0.886966i | \(-0.347191\pi\) | ||||
0.461835 | + | 0.886966i | \(0.347191\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.309017 | + | 0.951057i | 0.103006 | + | 0.317019i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.178298 | + | 0.548744i | −0.0537588 | + | 0.165452i | −0.974331 | − | 0.225120i | \(-0.927723\pi\) |
0.920572 | + | 0.390572i | \(0.127723\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.99206 | + | 6.13093i | 0.552498 | + | 1.70042i | 0.702460 | + | 0.711723i | \(0.252085\pi\) |
−0.149962 | + | 0.988692i | \(0.547915\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.53529 | + | 1.11545i | −0.372362 | + | 0.270537i | −0.758190 | − | 0.652034i | \(-0.773916\pi\) |
0.385828 | + | 0.922571i | \(0.373916\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.69438 | + | 4.86375i | −1.53580 | + | 1.11582i | −0.582890 | + | 0.812551i | \(0.698078\pi\) |
−0.952905 | + | 0.303269i | \(0.901922\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.97708 | − | 1.43643i | −0.431434 | − | 0.313455i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.30065 | − | 4.00298i | 0.271203 | − | 0.834678i | −0.718996 | − | 0.695015i | \(-0.755398\pi\) |
0.990199 | − | 0.139664i | \(-0.0446021\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.309017 | − | 0.951057i | 0.0594703 | − | 0.183031i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.28988 | − | 3.84332i | −0.982306 | − | 0.713687i | −0.0240828 | − | 0.999710i | \(-0.507667\pi\) |
−0.958223 | + | 0.286023i | \(0.907667\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.93738 | + | 2.86068i | −0.707175 | + | 0.513793i | −0.882261 | − | 0.470760i | \(-0.843980\pi\) |
0.175086 | + | 0.984553i | \(0.443980\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.466789 | − | 0.339142i | 0.0812576 | − | 0.0590371i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.0673673 | − | 0.207335i | −0.0110751 | − | 0.0340857i | 0.945366 | − | 0.326010i | \(-0.105704\pi\) |
−0.956441 | + | 0.291925i | \(0.905704\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.99206 | − | 6.13093i | 0.318985 | − | 0.981735i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.99456 | + | 6.13862i | 0.311498 | + | 0.958691i | 0.977172 | + | 0.212449i | \(0.0681439\pi\) |
−0.665675 | + | 0.746242i | \(0.731856\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.42419 | −0.522184 | −0.261092 | − | 0.965314i | \(-0.584083\pi\) | ||||
−0.261092 | + | 0.965314i | \(0.584083\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 7.78140 | + | 5.65351i | 1.13503 | + | 0.824650i | 0.986419 | − | 0.164245i | \(-0.0525189\pi\) |
0.148614 | + | 0.988895i | \(0.452519\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.02783 | −0.146833 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.89772 | 0.265734 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 11.3199 | + | 8.22441i | 1.55491 | + | 1.12971i | 0.940031 | + | 0.341090i | \(0.110796\pi\) |
0.614881 | + | 0.788620i | \(0.289204\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 8.27470 | 1.09601 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.72459 | − | 11.4631i | −0.484901 | − | 1.49237i | −0.832125 | − | 0.554589i | \(-0.812876\pi\) |
0.347224 | − | 0.937782i | \(-0.387124\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.48657 | + | 4.57520i | −0.190336 | + | 0.585795i | −0.999999 | − | 0.00110016i | \(-0.999650\pi\) |
0.809663 | + | 0.586895i | \(0.199650\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.755176 | + | 2.32419i | 0.0951433 | + | 0.292821i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.13165 | + | 2.27528i | −0.382592 | + | 0.277970i | −0.762413 | − | 0.647090i | \(-0.775986\pi\) |
0.379821 | + | 0.925060i | \(0.375986\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −3.40513 | + | 2.47398i | −0.409930 | + | 0.297832i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.24443 | + | 3.81030i | 0.622399 | + | 0.452200i | 0.853759 | − | 0.520669i | \(-0.174317\pi\) |
−0.231359 | + | 0.972868i | \(0.574317\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.10590 | + | 9.55897i | −0.363518 | + | 1.11879i | 0.587386 | + | 0.809307i | \(0.300157\pi\) |
−0.950904 | + | 0.309486i | \(0.899843\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.435724 | + | 1.34102i | −0.0496554 | + | 0.152824i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.83854 | + | 2.78887i | 0.431870 | + | 0.313772i | 0.782396 | − | 0.622781i | \(-0.213997\pi\) |
−0.350526 | + | 0.936553i | \(0.613997\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.809017 | + | 0.587785i | −0.0898908 | + | 0.0653095i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −2.77831 | + | 2.01856i | −0.304959 | + | 0.221566i | −0.729730 | − | 0.683735i | \(-0.760354\pi\) |
0.424772 | + | 0.905301i | \(0.360354\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.02055 | + | 6.21862i | 0.216626 | + | 0.666706i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.75719 | + | 5.40807i | −0.186262 | + | 0.573254i | −0.999968 | − | 0.00802201i | \(-0.997446\pi\) |
0.813706 | + | 0.581276i | \(0.197446\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.86820 | + | 14.9828i | 0.510326 | + | 1.57062i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 4.86687 | 0.504671 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.32717 | − | 3.87042i | −0.540893 | − | 0.392982i | 0.283524 | − | 0.958965i | \(-0.408497\pi\) |
−0.824416 | + | 0.565984i | \(0.808497\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.576983 | −0.0579890 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −12.0363 | −1.19766 | −0.598828 | − | 0.800877i | \(-0.704367\pi\) | ||||
−0.598828 | + | 0.800877i | \(0.704367\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.68117 | + | 3.40107i | 0.461249 | + | 0.335117i | 0.794021 | − | 0.607890i | \(-0.207984\pi\) |
−0.332772 | + | 0.943007i | \(0.607984\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 4.07081 | 0.393540 | 0.196770 | − | 0.980450i | \(-0.436955\pi\) | ||||
0.196770 | + | 0.980450i | \(0.436955\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −0.450471 | − | 1.38641i | −0.0431473 | − | 0.132794i | 0.927162 | − | 0.374660i | \(-0.122241\pi\) |
−0.970310 | + | 0.241866i | \(0.922241\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.0673673 | + | 0.207335i | −0.00639422 | + | 0.0196794i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.81017 | − | 5.57114i | −0.170287 | − | 0.524089i | 0.829100 | − | 0.559100i | \(-0.188853\pi\) |
−0.999387 | + | 0.0350111i | \(0.988853\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −5.21528 | + | 3.78913i | −0.482153 | + | 0.350305i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.75194 | + | 2.72595i | −0.343940 | + | 0.249887i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.62986 | + | 6.26996i | 0.784532 | + | 0.569996i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.99456 | − | 6.13862i | 0.179843 | − | 0.553500i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.72346 | − | 14.5373i | 0.419139 | − | 1.28998i | −0.489357 | − | 0.872084i | \(-0.662768\pi\) |
0.908496 | − | 0.417894i | \(-0.137232\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.77023 | + | 2.01269i | 0.243905 | + | 0.177207i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.03698 | − | 2.20650i | 0.265343 | − | 0.192783i | −0.447156 | − | 0.894456i | \(-0.647563\pi\) |
0.712499 | + | 0.701673i | \(0.247563\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −16.3597 | + | 11.8860i | −1.41857 | + | 1.03065i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.25793 | + | 19.2599i | 0.534651 | + | 1.64549i | 0.744402 | + | 0.667732i | \(0.232735\pi\) |
−0.209751 | + | 0.977755i | \(0.567265\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.287036 | + | 0.883406i | −0.0243461 | + | 0.0749295i | −0.962491 | − | 0.271312i | \(-0.912542\pi\) |
0.938145 | + | 0.346242i | \(0.112542\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.97223 | − | 9.14758i | −0.250307 | − | 0.770365i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3.71949 | −0.311040 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.831532 | + | 0.604143i | 0.0685836 | + | 0.0498289i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 13.1432 | 1.07673 | 0.538364 | − | 0.842712i | \(-0.319042\pi\) | ||||
0.538364 | + | 0.842712i | \(0.319042\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 17.5864 | 1.43116 | 0.715580 | − | 0.698531i | \(-0.246163\pi\) | ||||
0.715580 | + | 0.698531i | \(0.246163\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.53529 | − | 1.11545i | −0.124121 | − | 0.0901790i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 8.68198 | 0.692897 | 0.346449 | − | 0.938069i | \(-0.387387\pi\) | ||||
0.346449 | + | 0.938069i | \(0.387387\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −4.32383 | − | 13.3074i | −0.342902 | − | 1.05534i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.17852 | − | 9.78248i | 0.250503 | − | 0.770968i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −0.435068 | − | 1.33900i | −0.0340771 | − | 0.104879i | 0.932571 | − | 0.360986i | \(-0.117560\pi\) |
−0.966648 | + | 0.256108i | \(0.917560\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 7.13128 | − | 5.18118i | 0.551835 | − | 0.400932i | −0.276626 | − | 0.960978i | \(-0.589216\pi\) |
0.828462 | + | 0.560046i | \(0.189216\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −23.1028 | + | 16.7852i | −1.77714 | + | 1.29117i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −6.69438 | − | 4.86375i | −0.511932 | − | 0.371940i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2.44219 | + | 7.51629i | −0.185676 | + | 0.571453i | −0.999959 | − | 0.00901487i | \(-0.997130\pi\) |
0.814283 | + | 0.580468i | \(0.197130\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −3.72459 | + | 11.4631i | −0.279958 | + | 0.861621i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 9.29450 | + | 6.75285i | 0.694704 | + | 0.504732i | 0.878203 | − | 0.478288i | \(-0.158742\pi\) |
−0.183499 | + | 0.983020i | \(0.558742\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.17383 | + | 2.30592i | −0.235909 | + | 0.171398i | −0.699459 | − | 0.714673i | \(-0.746576\pi\) |
0.463550 | + | 0.886071i | \(0.346576\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.89190 | − | 2.82763i | 0.287698 | − | 0.209024i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.338359 | − | 1.04136i | −0.0247433 | − | 0.0761520i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0.755176 | − | 2.32419i | 0.0549310 | − | 0.169060i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −7.89402 | − | 24.2953i | −0.571191 | − | 1.75795i | −0.648797 | − | 0.760961i | \(-0.724728\pi\) |
0.0776060 | − | 0.996984i | \(-0.475272\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.421651 | 0.0303511 | 0.0151756 | − | 0.999885i | \(-0.495169\pi\) | ||||
0.0151756 | + | 0.999885i | \(0.495169\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −5.84224 | − | 4.24463i | −0.416242 | − | 0.302418i | 0.359882 | − | 0.932998i | \(-0.382817\pi\) |
−0.776124 | + | 0.630580i | \(0.782817\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.93505 | 0.278949 | 0.139474 | − | 0.990226i | \(-0.455459\pi\) | ||||
0.139474 | + | 0.990226i | \(0.455459\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3.87094 | 0.273035 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −12.9274 | − | 9.39232i | −0.907327 | − | 0.659211i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 4.20898 | 0.292544 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.47536 | − | 4.54069i | −0.102053 | − | 0.314086i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.65156 | + | 23.5491i | −0.526755 | + | 1.62119i | 0.234064 | + | 0.972221i | \(0.424798\pi\) |
−0.760819 | + | 0.648964i | \(0.775202\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −2.00319 | − | 6.16520i | −0.137257 | − | 0.422432i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −9.62219 | + | 6.99093i | −0.653197 | + | 0.474575i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 8.13134 | − | 5.90777i | 0.549465 | − | 0.399210i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −9.89715 | − | 7.19070i | −0.665755 | − | 0.483699i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 6.07919 | − | 18.7098i | 0.407093 | − | 1.25290i | −0.512043 | − | 0.858960i | \(-0.671111\pi\) |
0.919135 | − | 0.393942i | \(-0.128889\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 8.15025 | − | 25.0839i | 0.540951 | − | 1.66488i | −0.189476 | − | 0.981885i | \(-0.560679\pi\) |
0.730427 | − | 0.682991i | \(-0.239321\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 12.9614 | + | 9.41703i | 0.856515 | + | 0.622295i | 0.926935 | − | 0.375223i | \(-0.122434\pi\) |
−0.0704195 | + | 0.997517i | \(0.522434\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.14074 | − | 0.828797i | 0.0750552 | − | 0.0545308i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 23.7129 | − | 17.2285i | 1.55349 | − | 1.12867i | 0.612379 | − | 0.790564i | \(-0.290213\pi\) |
0.941107 | − | 0.338109i | \(-0.109787\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.46619 | − | 4.51248i | −0.0952395 | − | 0.293117i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 7.98989 | − | 24.5904i | 0.516823 | − | 1.59062i | −0.263117 | − | 0.964764i | \(-0.584750\pi\) |
0.779940 | − | 0.625854i | \(-0.215250\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.88671 | − | 8.88437i | −0.185949 | − | 0.572292i | 0.814014 | − | 0.580845i | \(-0.197278\pi\) |
−0.999963 | + | 0.00855232i | \(0.997278\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −43.1549 | − | 31.3539i | −2.74588 | − | 1.99500i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 3.43418 | 0.217632 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −13.5088 | −0.852666 | −0.426333 | − | 0.904566i | \(-0.640195\pi\) | ||||
−0.426333 | + | 0.904566i | \(0.640195\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.96471 | + | 1.42744i | 0.123520 | + | 0.0897425i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −13.0662 | −0.815044 | −0.407522 | − | 0.913195i | \(-0.633607\pi\) | ||||
−0.407522 | + | 0.913195i | \(0.633607\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.164632 | − | 0.506686i | −0.0102298 | − | 0.0314839i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.02055 | − | 6.21862i | 0.125069 | − | 0.384923i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.36915 | + | 4.21380i | 0.0844251 | + | 0.259834i | 0.984354 | − | 0.176203i | \(-0.0563816\pi\) |
−0.899929 | + | 0.436037i | \(0.856382\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4.60038 | − | 3.34237i | 0.281539 | − | 0.204550i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −22.6936 | + | 16.4879i | −1.38366 | + | 1.00528i | −0.387127 | + | 0.922026i | \(0.626533\pi\) |
−0.996528 | + | 0.0832584i | \(0.973467\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.84207 | − | 3.51797i | −0.294135 | − | 0.213701i | 0.430924 | − | 0.902388i | \(-0.358188\pi\) |
−0.725059 | + | 0.688687i | \(0.758188\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 4.86820 | − | 14.9828i | 0.294637 | − | 0.906800i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.56694 | + | 4.82254i | −0.0941481 | + | 0.289758i | −0.987031 | − | 0.160531i | \(-0.948679\pi\) |
0.892883 | + | 0.450290i | \(0.148679\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −3.93738 | − | 2.86068i | −0.235725 | − | 0.171264i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 14.6885 | − | 10.6718i | 0.876239 | − | 0.636625i | −0.0560144 | − | 0.998430i | \(-0.517839\pi\) |
0.932254 | + | 0.361805i | \(0.117839\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3.80009 | + | 2.76092i | −0.225892 | + | 0.164120i | −0.694975 | − | 0.719034i | \(-0.744584\pi\) |
0.469083 | + | 0.883154i | \(0.344584\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.87430 | + | 15.0016i | 0.287721 | + | 0.885514i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4.14041 | + | 12.7429i | −0.243554 | + | 0.749581i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.03480 | + | 6.26247i | 0.119282 | + | 0.367112i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −9.60771 | −0.561288 | −0.280644 | − | 0.959812i | \(-0.590548\pi\) | ||||
−0.280644 | + | 0.959812i | \(0.590548\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0.466789 | + | 0.339142i | 0.0270859 | + | 0.0196790i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 27.1329 | 1.56914 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.36804 | −0.482326 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 9.73757 | + | 7.07476i | 0.559409 | + | 0.406434i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −13.5400 | −0.772771 | −0.386386 | − | 0.922337i | \(-0.626277\pi\) | ||||
−0.386386 | + | 0.922337i | \(0.626277\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.78805 | − | 5.50304i | −0.101718 | − | 0.313057i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −0.916931 | + | 2.82202i | −0.0519944 | + | 0.160022i | −0.973682 | − | 0.227910i | \(-0.926811\pi\) |
0.921688 | + | 0.387933i | \(0.126811\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4.32802 | + | 13.3203i | 0.244634 | + | 0.752906i | 0.995696 | + | 0.0926747i | \(0.0295417\pi\) |
−0.751063 | + | 0.660231i | \(0.770458\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −21.8577 | + | 15.8806i | −1.22765 | + | 0.891941i | −0.996712 | − | 0.0810273i | \(-0.974180\pi\) |
−0.230939 | + | 0.972968i | \(0.574180\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.05217 | − | 2.21753i | 0.170889 | − | 0.124158i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3.29336 | − | 2.39276i | −0.183817 | − | 0.133551i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4.85252 | − | 14.9345i | 0.270001 | − | 0.830979i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −0.450471 | + | 1.38641i | −0.0249111 | + | 0.0766686i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 19.0162 | + | 13.8161i | 1.04840 | + | 0.761705i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.38394 | − | 3.91166i | 0.295928 | − | 0.215004i | −0.429907 | − | 0.902873i | \(-0.641454\pi\) |
0.725835 | + | 0.687869i | \(0.241454\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0.176370 | − | 0.128140i | 0.00966501 | − | 0.00702204i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5.93398 | − | 18.2629i | −0.323245 | − | 0.994844i | −0.972227 | − | 0.234041i | \(-0.924805\pi\) |
0.648982 | − | 0.760804i | \(-0.275195\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.81017 | + | 5.57114i | −0.0983152 | + | 0.302583i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.867752 | − | 2.67067i | −0.0469914 | − | 0.144625i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −19.6184 | −1.05930 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −13.5584 | − | 9.85076i | −0.727853 | − | 0.528816i | 0.161030 | − | 0.986949i | \(-0.448518\pi\) |
−0.888884 | + | 0.458133i | \(0.848518\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 22.9371 | 1.22780 | 0.613898 | − | 0.789385i | \(-0.289601\pi\) | ||||
0.613898 | + | 0.789385i | \(0.289601\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6.44645 | 0.344086 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −5.67455 | − | 4.12280i | −0.302026 | − | 0.219434i | 0.426442 | − | 0.904515i | \(-0.359767\pi\) |
−0.728467 | + | 0.685081i | \(0.759767\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 4.63766 | 0.245451 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −4.61051 | − | 14.1897i | −0.243333 | − | 0.748903i | −0.995906 | − | 0.0903940i | \(-0.971187\pi\) |
0.752573 | − | 0.658509i | \(-0.228813\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 15.2873 | − | 47.0494i | 0.804594 | − | 2.47629i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −3.29631 | − | 10.1450i | −0.173012 | − | 0.532475i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −0.550914 | + | 0.400262i | −0.0287575 | + | 0.0208935i | −0.602071 | − | 0.798442i | \(-0.705658\pi\) |
0.573314 | + | 0.819336i | \(0.305658\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −5.22182 | + | 3.79387i | −0.271837 | + | 0.197501i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 27.6637 | + | 20.0988i | 1.43623 | + | 1.04348i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −8.84935 | + | 27.2355i | −0.458202 | + | 1.41020i | 0.409133 | + | 0.912475i | \(0.365831\pi\) |
−0.867335 | + | 0.497725i | \(0.834169\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 13.0254 | − | 40.0880i | 0.670842 | − | 2.06464i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 17.7191 | + | 12.8737i | 0.910167 | + | 0.661275i | 0.941057 | − | 0.338247i | \(-0.109834\pi\) |
−0.0308898 | + | 0.999523i | \(0.509834\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −12.3662 | + | 8.98455i | −0.633538 | + | 0.460293i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3.69391 | − | 2.68378i | 0.188750 | − | 0.137135i | −0.489397 | − | 0.872061i | \(-0.662783\pi\) |
0.678147 | + | 0.734926i | \(0.262783\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.05813 | − | 3.25660i | −0.0537879 | − | 0.165542i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 6.71865 | − | 20.6779i | 0.340649 | − | 1.04841i | −0.623223 | − | 0.782044i | \(-0.714177\pi\) |
0.963872 | − | 0.266366i | \(-0.0858229\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.46826 | + | 7.59653i | 0.124825 | + | 0.384173i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −3.75392 | −0.189360 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 12.6396 | + | 9.18318i | 0.634361 | + | 0.460891i | 0.857908 | − | 0.513803i | \(-0.171764\pi\) |
−0.223547 | + | 0.974693i | \(0.571764\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 20.2217 | 1.01235 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −19.9417 | −0.995841 | −0.497920 | − | 0.867223i | \(-0.665903\pi\) | ||||
−0.497920 | + | 0.867223i | \(0.665903\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −25.3821 | − | 18.4412i | −1.26437 | − | 0.918622i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.125785 | 0.00623495 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5.32001 | − | 16.3733i | −0.263058 | − | 0.809608i | −0.992134 | − | 0.125176i | \(-0.960050\pi\) |
0.729077 | − | 0.684432i | \(-0.239950\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 6.25793 | − | 19.2599i | 0.308681 | − | 0.950022i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −9.10217 | − | 28.0136i | −0.447888 | − | 1.37846i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0.751470 | − | 0.545975i | 0.0367996 | − | 0.0267365i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −10.6230 | + | 7.71804i | −0.518966 | + | 0.377051i | −0.816214 | − | 0.577749i | \(-0.803931\pi\) |
0.297248 | + | 0.954800i | \(0.403931\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −13.7712 | − | 10.0054i | −0.671169 | − | 0.487633i | 0.199248 | − | 0.979949i | \(-0.436150\pi\) |
−0.870416 | + | 0.492317i | \(0.836150\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2.97223 | + | 9.14758i | −0.144515 | + | 0.444770i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.63289 | + | 11.1809i | −0.175808 | + | 0.541081i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 3.00913 | + | 2.18626i | 0.145282 | + | 0.105554i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 10.1246 | − | 7.35594i | 0.487684 | − | 0.354323i | −0.316609 | − | 0.948556i | \(-0.602544\pi\) |
0.804293 | + | 0.594233i | \(0.202544\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 16.7848 | − | 12.1949i | 0.806626 | − | 0.586048i | −0.106225 | − | 0.994342i | \(-0.533876\pi\) |
0.912850 | + | 0.408294i | \(0.133876\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 10.7625 | + | 33.1234i | 0.514838 | + | 1.58451i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −10.2225 | + | 31.4615i | −0.487891 | + | 1.50157i | 0.339858 | + | 0.940477i | \(0.389621\pi\) |
−0.827749 | + | 0.561098i | \(0.810379\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.317617 | − | 0.977524i | −0.0151246 | − | 0.0465488i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 23.4802 | 1.11558 | 0.557788 | − | 0.829984i | \(-0.311650\pi\) | ||||
0.557788 | + | 0.829984i | \(0.311650\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −10.6330 | − | 7.72535i | −0.502925 | − | 0.365397i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −31.6965 | −1.49585 | −0.747925 | − | 0.663783i | \(-0.768950\pi\) | ||||
−0.747925 | + | 0.663783i | \(0.768950\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.72415 | −0.175363 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −14.2277 | − | 10.3370i | −0.668475 | − | 0.485676i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 28.2267 | 1.32039 | 0.660196 | − | 0.751094i | \(-0.270473\pi\) | ||||
0.660196 | + | 0.751094i | \(0.270473\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0.586428 | + | 1.80484i | 0.0273721 | + | 0.0842427i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1.52737 | + | 4.70075i | −0.0711365 | + | 0.218936i | −0.980304 | − | 0.197495i | \(-0.936719\pi\) |
0.909167 | + | 0.416431i | \(0.136719\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5.70022 | − | 17.5435i | −0.264912 | − | 0.815314i | −0.991714 | − | 0.128467i | \(-0.958994\pi\) |
0.726802 | − | 0.686847i | \(-0.241006\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −13.9969 | + | 10.1693i | −0.647699 | + | 0.470581i | −0.862487 | − | 0.506080i | \(-0.831094\pi\) |
0.214788 | + | 0.976661i | \(0.431094\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −7.65314 | + | 5.56033i | −0.353389 | + | 0.256752i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −7.02387 | − | 5.10314i | −0.323643 | − | 0.235140i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0.610525 | − | 1.87900i | 0.0280719 | − | 0.0863966i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −4.32383 | + | 13.3074i | −0.197974 | + | 0.609303i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 27.8105 | + | 20.2055i | 1.27069 | + | 0.923212i | 0.999230 | − | 0.0392366i | \(-0.0124926\pi\) |
0.271463 | + | 0.962449i | \(0.412493\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.13696 | − | 0.826049i | 0.0518408 | − | 0.0376646i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −8.32148 | + | 6.04591i | −0.378640 | + | 0.275098i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.55809 | − | 4.79530i | −0.0706037 | − | 0.217296i | 0.909528 | − | 0.415642i | \(-0.136443\pi\) |
−0.980132 | + | 0.198346i | \(0.936443\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −0.435068 | + | 1.33900i | −0.0196744 | + | 0.0605517i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −8.03949 | − | 24.7430i | −0.362817 | − | 1.11664i | −0.951337 | − | 0.308153i | \(-0.900289\pi\) |
0.588520 | − | 0.808483i | \(-0.299711\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 12.4085 | 0.558852 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 12.8163 | + | 9.31162i | 0.574892 | + | 0.417683i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.49658 | 0.111762 | 0.0558812 | − | 0.998437i | \(-0.482203\pi\) | ||||
0.0558812 | + | 0.998437i | \(0.482203\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −8.81475 | −0.393814 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −11.5366 | − | 8.38184i | −0.514392 | − | 0.373728i | 0.300095 | − | 0.953909i | \(-0.402982\pi\) |
−0.814487 | + | 0.580181i | \(0.802982\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 28.5567 | 1.26825 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −4.82569 | − | 14.8520i | −0.213895 | − | 0.658301i | −0.999230 | − | 0.0392303i | \(-0.987509\pi\) |
0.785335 | − | 0.619071i | \(-0.212491\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7.59020 | + | 23.3602i | −0.335771 | + | 1.03340i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.55702 | + | 7.86971i | 0.112895 | + | 0.347456i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4.48974 | + | 3.26198i | −0.197458 | + | 0.143462i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 6.39374 | − | 4.64533i | 0.280654 | − | 0.203907i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −11.6277 | − | 8.44804i | −0.509420 | − | 0.370115i | 0.303183 | − | 0.952932i | \(-0.401951\pi\) |
−0.812604 | + | 0.582817i | \(0.801951\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.36427 | + | 4.19878i | −0.0596552 | + | 0.183600i | −0.976443 | − | 0.215774i | \(-0.930772\pi\) |
0.916788 | + | 0.399374i | \(0.130772\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.85407 | − | 8.78393i | 0.124325 | − | 0.382634i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4.27526 | + | 3.10615i | 0.185881 | + | 0.135050i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 9.75111 | − | 7.08460i | 0.423162 | − | 0.307445i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −33.6622 | + | 24.4570i | −1.45807 | + | 1.05935i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −3.55018 | − | 10.9263i | −0.153202 | − | 0.471507i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0.183260 | − | 0.564015i | 0.00789355 | − | 0.0242939i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 11.1361 | + | 34.2734i | 0.478778 | + | 1.47353i | 0.840794 | + | 0.541355i | \(0.182088\pi\) |
−0.362016 | + | 0.932172i | \(0.617912\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 3.92307 | 0.168355 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 9.79172 | + | 7.11410i | 0.418664 | + | 0.304177i | 0.777100 | − | 0.629377i | \(-0.216690\pi\) |
−0.358436 | + | 0.933554i | \(0.616690\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −4.81065 | −0.205314 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 54.1054 | 2.30497 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 9.38064 | + | 6.81544i | 0.398906 | + | 0.289822i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −24.0437 | −1.01876 | −0.509382 | − | 0.860541i | \(-0.670126\pi\) | ||||
−0.509382 | + | 0.860541i | \(0.670126\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −6.82119 | − | 20.9935i | −0.288506 | − | 0.887929i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.338359 | + | 1.04136i | −0.0142855 | + | 0.0439664i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 5.85371 | + | 18.0159i | 0.246704 | + | 0.759278i | 0.995351 | + | 0.0963092i | \(0.0307038\pi\) |
−0.748647 | + | 0.662969i | \(0.769296\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.97708 | + | 1.43643i | −0.0830295 | + | 0.0603244i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 25.2591 | − | 18.3518i | 1.05892 | − | 0.769348i | 0.0850293 | − | 0.996378i | \(-0.472902\pi\) |
0.973888 | + | 0.227030i | \(0.0729016\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.0316916 | + | 0.0230253i | 0.00132625 | + | 0.000963578i | 0.588448 | − | 0.808535i | \(-0.299739\pi\) |
−0.587122 | + | 0.809499i | \(0.699739\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −7.89402 | + | 24.2953i | −0.329777 | + | 1.01495i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 6.22035 | − | 19.1443i | 0.258957 | − | 0.796986i | −0.734068 | − | 0.679076i | \(-0.762381\pi\) |
0.993024 | − | 0.117910i | \(-0.0376194\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −0.341123 | − | 0.247840i | −0.0141766 | − | 0.0102999i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −6.78964 | + | 4.93296i | −0.281682 | + | 0.204654i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6.53141 | + | 4.74535i | −0.270503 | + | 0.196532i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 3.08070 | + | 9.48143i | 0.127154 | + | 0.391341i | 0.994287 | − | 0.106736i | \(-0.0340399\pi\) |
−0.867133 | + | 0.498076i | \(0.834040\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 12.4447 | − | 38.3009i | 0.512776 | − | 1.57816i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2.23154 | + | 6.86796i | 0.0917931 | + | 0.282510i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 20.3619 | 0.836163 | 0.418082 | − | 0.908410i | \(-0.362703\pi\) | ||||
0.418082 | + | 0.908410i | \(0.362703\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −3.18353 | − | 2.31297i | −0.130293 | − | 0.0946634i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −24.1075 | −0.985007 | −0.492503 | − | 0.870311i | \(-0.663918\pi\) | ||||
−0.492503 | + | 0.870311i | \(0.663918\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 37.2054 | 1.51764 | 0.758820 | − | 0.651300i | \(-0.225776\pi\) | ||||
0.758820 | + | 0.651300i | \(0.225776\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −3.13165 | − | 2.27528i | −0.127531 | − | 0.0926565i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 40.5752 | 1.64690 | 0.823448 | − | 0.567392i | \(-0.192048\pi\) | ||||
0.823448 | + | 0.567392i | \(0.192048\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 4.93783 | + | 15.1971i | 0.200091 | + | 0.615817i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −19.1603 | + | 58.9694i | −0.775143 | + | 2.38565i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.58698 | − | 4.88423i | −0.0640977 | − | 0.197272i | 0.913879 | − | 0.405987i | \(-0.133072\pi\) |
−0.977977 | + | 0.208714i | \(0.933072\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −13.2531 | + | 9.62895i | −0.533550 | + | 0.387647i | −0.821684 | − | 0.569943i | \(-0.806965\pi\) |
0.288134 | + | 0.957590i | \(0.406965\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −14.9251 | + | 10.8437i | −0.599892 | + | 0.435847i | −0.845841 | − | 0.533436i | \(-0.820901\pi\) |
0.245948 | + | 0.969283i | \(0.420901\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3.40513 | − | 2.47398i | −0.136643 | − | 0.0992772i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −4.29422 | + | 13.2163i | −0.172044 | + | 0.529498i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.47536 | + | 4.54069i | −0.0589202 | + | 0.181338i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0.334701 | + | 0.243174i | 0.0133454 | + | 0.00969600i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −31.1970 | + | 22.6659i | −1.24193 | + | 0.902316i | −0.997726 | − | 0.0674068i | \(-0.978527\pi\) |
−0.244206 | + | 0.969723i | \(0.578527\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 20.0320 | − | 14.5541i | 0.796202 | − | 0.578475i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.04750 | − | 6.30156i | −0.0811249 | − | 0.249677i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −2.00319 | + | 6.16520i | −0.0792451 | + | 0.243891i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 5.87099 | + | 18.0690i | 0.231890 | + | 0.713684i | 0.997519 | + | 0.0704016i | \(0.0224281\pi\) |
−0.765629 | + | 0.643283i | \(0.777572\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 37.6504 | 1.48479 | 0.742393 | − | 0.669964i | \(-0.233691\pi\) | ||||
0.742393 | + | 0.669964i | \(0.233691\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 4.63937 | + | 3.37070i | 0.182392 | + | 0.132516i | 0.675235 | − | 0.737603i | \(-0.264042\pi\) |
−0.492843 | + | 0.870118i | \(0.664042\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 6.95440 | 0.272984 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 11.8937 | 0.466150 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 32.4262 | + | 23.5590i | 1.26894 | + | 0.921936i | 0.999160 | − | 0.0409866i | \(-0.0130501\pi\) |
0.269777 | + | 0.962923i | \(0.413050\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −10.0509 | −0.392123 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −9.75714 | − | 30.0294i | −0.380084 | − | 1.16978i | −0.939984 | − | 0.341218i | \(-0.889160\pi\) |
0.559900 | − | 0.828560i | \(-0.310840\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 9.68781 | − | 29.8160i | 0.376812 | − | 1.15971i | −0.565436 | − | 0.824792i | \(-0.691292\pi\) |
0.942248 | − | 0.334916i | \(-0.108708\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 3.78038 | + | 11.6348i | 0.146818 | + | 0.451858i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −22.2650 | + | 16.1765i | −0.862103 | + | 0.626355i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −15.9155 | + | 11.5633i | −0.615330 | + | 0.447063i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.24556 | − | 1.63150i | −0.0866889 | − | 0.0629832i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.38278 | + | 4.25575i | −0.0533021 | + | 0.164047i | −0.974164 | − | 0.225842i | \(-0.927487\pi\) |
0.920862 | + | 0.389889i | \(0.127487\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 4.35181 | − | 13.3935i | 0.167254 | − | 0.514754i | −0.831942 | − | 0.554863i | \(-0.812771\pi\) |
0.999195 | + | 0.0401092i | \(0.0127706\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −13.0186 | − | 9.45854i | −0.499607 | − | 0.362985i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −21.3376 | + | 15.5027i | −0.817660 | + | 0.594065i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −9.57528 | + | 6.95685i | −0.366388 | + | 0.266196i | −0.755711 | − | 0.654905i | \(-0.772709\pi\) |
0.389324 | + | 0.921101i | \(0.372709\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −4.95082 | − | 15.2371i | −0.188886 | − | 0.581330i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −27.8733 | + | 85.7853i | −1.06189 | + | 3.26816i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −11.6676 | − | 35.9091i | −0.443855 | − | 1.36605i | −0.883734 | − | 0.467989i | \(-0.844979\pi\) |
0.439879 | − | 0.898057i | \(-0.355021\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1.41003 | −0.0535627 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −9.90956 | − | 7.19971i | −0.375351 | − | 0.272709i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −29.3108 | −1.10864 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −39.1678 | −1.47935 | −0.739674 | − | 0.672965i | \(-0.765020\pi\) | ||||
−0.739674 | + | 0.672965i | \(0.765020\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.45941 | + | 1.06032i | 0.0550426 | + | 0.0399908i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −29.4143 | −1.10624 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −13.1296 | − | 40.4089i | −0.493094 | − | 1.51759i | −0.819906 | − | 0.572498i | \(-0.805974\pi\) |
0.326812 | − | 0.945089i | \(-0.394026\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.46619 | + | 4.51248i | −0.0549866 | + | 0.169231i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 6.33008 | + | 19.4820i | 0.237063 | + | 0.729606i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −20.9178 | + | 15.1977i | −0.781190 | + | 0.567568i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −24.0261 | + | 17.4560i | −0.896022 | + | 0.650998i | −0.937441 | − | 0.348143i | \(-0.886812\pi\) |
0.0414189 | + | 0.999142i | \(0.486812\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 11.4399 | + | 8.31154i | 0.426042 | + | 0.309538i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −2.88671 | + | 8.88437i | −0.107358 | + | 0.330413i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −12.9577 | + | 39.8796i | −0.480573 | + | 1.47905i | 0.357719 | + | 0.933829i | \(0.383555\pi\) |
−0.838292 | + | 0.545222i | \(0.816445\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −0.809017 | − | 0.587785i | −0.0299636 | − | 0.0217698i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 5.25712 | − | 3.81952i | 0.194441 | − | 0.141270i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 23.6317 | − | 17.1695i | 0.872858 | − | 0.634168i | −0.0584945 | − | 0.998288i | \(-0.518630\pi\) |
0.931352 | + | 0.364119i | \(0.118630\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −0.690179 | − | 2.12415i | −0.0254231 | − | 0.0782441i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 8.00979 | − | 24.6516i | 0.294645 | − | 0.906824i | −0.688695 | − | 0.725051i | \(-0.741816\pi\) |
0.983340 | − | 0.181773i | \(-0.0581837\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 16.4837 | + | 50.7317i | 0.605544 | + | 1.86367i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 9.22935 | 0.338592 | 0.169296 | − | 0.985565i | \(-0.445851\pi\) | ||||
0.169296 | + | 0.985565i | \(0.445851\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −2.77831 | − | 2.01856i | −0.101653 | − | 0.0738552i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 9.94826 | 0.363502 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −37.2805 | −1.36038 | −0.680192 | − | 0.733034i | \(-0.738103\pi\) | ||||
−0.680192 | + | 0.733034i | \(0.738103\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 10.9288 | + | 7.94025i | 0.398268 | + | 0.289359i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 27.6758 | 1.00589 | 0.502947 | − | 0.864317i | \(-0.332249\pi\) | ||||
0.502947 | + | 0.864317i | \(0.332249\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −0.750451 | − | 2.30965i | −0.0272396 | − | 0.0838350i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −4.21264 | + | 12.9652i | −0.152708 | + | 0.469988i | −0.997921 | − | 0.0644416i | \(-0.979473\pi\) |
0.845213 | + | 0.534429i | \(0.179473\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.10086 | − | 3.38811i | −0.0398539 | − | 0.122658i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 62.8600 | − | 45.6705i | 2.26974 | − | 1.64906i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 24.6838 | − | 17.9339i | 0.890122 | − | 0.646712i | −0.0457876 | − | 0.998951i | \(-0.514580\pi\) |
0.935910 | + | 0.352239i | \(0.114580\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 10.5707 | + | 7.68009i | 0.380696 | + | 0.276592i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 2.60967 | − | 8.03172i | 0.0938631 | − | 0.288881i | −0.893093 | − | 0.449873i | \(-0.851469\pi\) |
0.986956 | + | 0.160992i | \(0.0514693\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −0.164632 | + | 0.506686i | −0.00590615 | + | 0.0181773i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −43.2090 | − | 31.3932i | −1.54812 | − | 1.12478i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.02595 | + | 2.19848i | −0.108277 | + | 0.0786678i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −5.28988 | + | 3.84332i | −0.189045 | + | 0.137349i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 12.6251 | + | 38.8560i | 0.450036 | + | 1.38507i | 0.876865 | + | 0.480736i | \(0.159631\pi\) |
−0.426829 | + | 0.904332i | \(0.640369\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.36915 | − | 4.21380i | 0.0487429 | − | 0.150015i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −4.42371 | − | 13.6148i | −0.157289 | − | 0.484086i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −31.0116 | −1.10125 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 23.9082 | + | 17.3703i | 0.846871 | + | 0.615288i | 0.924281 | − | 0.381712i | \(-0.124665\pi\) |
−0.0774107 | + | 0.996999i | \(0.524665\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −18.2529 | −0.645742 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −5.68638 | −0.200918 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −4.69165 | − | 3.40868i | −0.165565 | − | 0.120290i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 28.0509 | 0.987438 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 7.69396 | + | 23.6796i | 0.270505 | + | 0.832529i | 0.990374 | + | 0.138419i | \(0.0442020\pi\) |
−0.719869 | + | 0.694110i | \(0.755798\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 7.52723 | − | 23.1664i | 0.264317 | − | 0.813483i | −0.727533 | − | 0.686072i | \(-0.759333\pi\) |
0.991850 | − | 0.127411i | \(-0.0406667\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.84950 | + | 5.69219i | 0.0648650 | + | 0.199634i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 22.9228 | − | 16.6544i | 0.801967 | − | 0.582663i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −12.7451 | + | 9.25987i | −0.445351 | + | 0.323566i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 44.8023 | + | 32.5508i | 1.56361 | + | 1.13603i | 0.932969 | + | 0.359956i | \(0.117208\pi\) |
0.630642 | + | 0.776074i | \(0.282792\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 5.39695 | − | 16.6101i | 0.188126 | − | 0.578992i | −0.811862 | − | 0.583849i | \(-0.801546\pi\) |
0.999988 | + | 0.00485678i | \(0.00154597\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 7.22601 | − | 22.2394i | 0.251273 | − | 0.773338i | −0.743268 | − | 0.668993i | \(-0.766725\pi\) |
0.994541 | − | 0.104345i | \(-0.0332746\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −29.1866 | − | 21.2053i | −1.01369 | − | 0.736491i | −0.0487125 | − | 0.998813i | \(-0.515512\pi\) |
−0.964980 | + | 0.262322i | \(0.915512\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 4.10230 | − | 2.98049i | 0.142307 | − | 0.103392i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.57802 | − | 1.14650i | 0.0546750 | − | 0.0397237i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.50395 | + | 4.62867i | 0.0519840 | + | 0.159990i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 5.88419 | − | 18.1097i | 0.203145 | − | 0.625215i | −0.796640 | − | 0.604454i | \(-0.793391\pi\) |
0.999784 | − | 0.0207608i | \(-0.00660885\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 4.25019 | + | 13.0808i | 0.146558 | + | 0.451060i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −18.1559 | −0.625323 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 21.0897 | + | 15.3225i | 0.724649 | + | 0.526489i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 4.69717 | 0.161206 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −0.917579 | −0.0314542 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 14.6027 | + | 10.6095i | 0.499986 | + | 0.363261i | 0.809012 | − | 0.587793i | \(-0.200003\pi\) |
−0.309026 | + | 0.951054i | \(0.600003\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 12.4435 | 0.425061 | 0.212531 | − | 0.977154i | \(-0.431829\pi\) | ||||
0.212531 | + | 0.977154i | \(0.431829\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 14.2156 | + | 43.7511i | 0.485029 | + | 1.49277i | 0.831938 | + | 0.554868i | \(0.187231\pi\) |
−0.346909 | + | 0.937899i | \(0.612769\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 4.87430 | − | 15.0016i | 0.166116 | − | 0.511252i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 14.6311 | + | 45.0298i | 0.498048 | + | 1.53283i | 0.812153 | + | 0.583445i | \(0.198296\pi\) |
−0.314105 | + | 0.949388i | \(0.601704\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 10.8397 | − | 7.87553i | 0.368137 | − | 0.267467i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2.21478 | + | 1.60913i | −0.0751311 | + | 0.0545860i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −20.1880 | − | 14.6675i | −0.684045 | − | 0.496988i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2.03480 | − | 6.26247i | 0.0688675 | − | 0.211952i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −9.87543 | + | 30.3934i | −0.333470 | + | 1.02631i | 0.634001 | + | 0.773332i | \(0.281411\pi\) |
−0.967471 | + | 0.252982i | \(0.918589\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 7.77280 | + | 5.64727i | 0.262170 | + | 0.190478i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 6.41518 | − | 4.66090i | 0.216133 | − | 0.157030i | −0.474451 | − | 0.880282i | \(-0.657353\pi\) |
0.690584 | + | 0.723252i | \(0.257353\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 30.1363 | − | 21.8953i | 1.01417 | − | 0.736836i | 0.0490886 | − | 0.998794i | \(-0.484368\pi\) |
0.965079 | + | 0.261958i | \(0.0843683\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 5.07245 | + | 15.6114i | 0.170316 | + | 0.524179i | 0.999389 | − | 0.0349619i | \(-0.0111310\pi\) |
−0.829072 | + | 0.559141i | \(0.811131\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 11.5432 | − | 35.5263i | 0.387147 | − | 1.19151i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −0.178298 | − | 0.548744i | −0.00597320 | − | 0.0183836i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −79.5889 | −2.66334 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −21.9510 | − | 15.9483i | −0.732923 | − | 0.532500i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 31.8228 | 1.06135 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −26.5533 | −0.884619 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 6.76988 | + | 4.91861i | 0.225288 | + | 0.163681i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.85782 | −0.0616880 | −0.0308440 | − | 0.999524i | \(-0.509819\pi\) | ||||
−0.0308440 | + | 0.999524i | \(0.509819\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −3.71942 | − | 11.4472i | −0.123365 | − | 0.379680i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −6.95487 | + | 21.4049i | −0.230425 | + | 0.709176i | 0.767270 | + | 0.641324i | \(0.221615\pi\) |
−0.997695 | + | 0.0678519i | \(0.978385\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −0.612306 | − | 1.88448i | −0.0202644 | − | 0.0623673i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 7.42179 | − | 5.39225i | 0.245089 | − | 0.178068i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −16.9124 | + | 12.2876i | −0.557890 | + | 0.405331i | −0.830686 | − | 0.556741i | \(-0.812052\pi\) |
0.272796 | + | 0.962072i | \(0.412052\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 10.9541 | + | 7.95864i | 0.360951 | + | 0.262246i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −12.9135 | + | 39.7436i | −0.425052 | + | 1.30818i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.78805 | + | 5.50304i | −0.0587272 | + | 0.180744i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −11.3058 | − | 8.21417i | −0.370933 | − | 0.269498i | 0.386665 | − | 0.922220i | \(-0.373627\pi\) |
−0.757598 | + | 0.652722i | \(0.773627\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.88068 | − | 4.99911i | 0.225505 | − | 0.163839i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 2.40056 | − | 1.74411i | 0.0785907 | − | 0.0570995i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 10.1229 | + | 31.1551i | 0.330701 | + | 1.01779i | 0.968801 | + | 0.247840i | \(0.0797206\pi\) |
−0.638100 | + | 0.769954i | \(0.720279\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 4.32802 | − | 13.3203i | 0.141239 | − | 0.434690i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −7.99456 | − | 24.6047i | −0.260615 | − | 0.802091i | −0.992671 | − | 0.120847i | \(-0.961439\pi\) |
0.732056 | − | 0.681244i | \(-0.238561\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 27.1669 | 0.884677 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 45.1202 | + | 32.7818i | 1.46621 | + | 1.06526i | 0.981690 | + | 0.190485i | \(0.0610059\pi\) |
0.484521 | + | 0.874780i | \(0.338994\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −64.7925 | −2.10325 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 27.0176 | 0.876106 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −20.1685 | − | 14.6533i | −0.653322 | − | 0.474666i | 0.211079 | − | 0.977469i | \(-0.432302\pi\) |
−0.864401 | + | 0.502803i | \(0.832302\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −3.77269 | −0.121954 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 15.2931 | + | 47.0675i | 0.493841 | + | 1.51989i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.26000 | + | 6.95558i | −0.0729034 | + | 0.224373i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.25795 | + | 3.87157i | 0.0405369 | + | 0.124760i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −7.02876 | + | 5.10669i | −0.226030 | + | 0.164220i | −0.695037 | − | 0.718974i | \(-0.744612\pi\) |
0.469007 | + | 0.883194i | \(0.344612\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −12.7041 | + | 9.23004i | −0.408113 | + | 0.296512i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −19.9663 | − | 14.5064i | −0.640750 | − | 0.465532i | 0.219358 | − | 0.975645i | \(-0.429604\pi\) |
−0.860108 | + | 0.510112i | \(0.829604\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −0.701459 | + | 2.15887i | −0.0224877 | + | 0.0692102i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 11.0003 | − | 33.8554i | 0.351930 | − | 1.08313i | −0.605838 | − | 0.795588i | \(-0.707162\pi\) |
0.957768 | − | 0.287542i | \(-0.0928381\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.65434 | − | 1.92849i | −0.0848332 | − | 0.0616349i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.17935 | − | 0.856848i | 0.0376537 | − | 0.0273570i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −4.80656 | + | 3.49217i | −0.153305 | + | 0.111383i | −0.661794 | − | 0.749686i | \(-0.730205\pi\) |
0.508488 | + | 0.861069i | \(0.330205\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −7.26354 | − | 22.3549i | −0.231201 | − | 0.711563i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −4.45365 | + | 13.7069i | −0.141618 | + | 0.435855i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.30614 | + | 4.01987i | 0.0414908 | + | 0.127695i | 0.969656 | − | 0.244472i | \(-0.0786147\pi\) |
−0.928166 | + | 0.372168i | \(0.878615\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −6.65492 | −0.211187 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 10.1495 | + | 7.37405i | 0.321438 | + | 0.233538i | 0.736789 | − | 0.676123i | \(-0.236341\pi\) |
−0.415351 | + | 0.909661i | \(0.636341\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −0.218005 | −0.00689738 |
(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 | 1500.2.m.c.601.4 | 24 | ||
5.2 | odd | 4 | 1500.2.o.c.649.1 | 24 | |||
5.3 | odd | 4 | 300.2.o.a.229.6 | yes | 24 | ||
5.4 | even | 2 | 1500.2.m.d.601.3 | 24 | |||
15.8 | even | 4 | 900.2.w.c.829.2 | 24 | |||
25.6 | even | 5 | inner | 1500.2.m.c.901.4 | 24 | ||
25.8 | odd | 20 | 1500.2.o.c.349.1 | 24 | |||
25.9 | even | 10 | 7500.2.a.m.1.5 | 12 | |||
25.12 | odd | 20 | 7500.2.d.g.1249.8 | 24 | |||
25.13 | odd | 20 | 7500.2.d.g.1249.17 | 24 | |||
25.16 | even | 5 | 7500.2.a.n.1.8 | 12 | |||
25.17 | odd | 20 | 300.2.o.a.169.6 | ✓ | 24 | ||
25.19 | even | 10 | 1500.2.m.d.901.3 | 24 | |||
75.17 | even | 20 | 900.2.w.c.469.2 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
300.2.o.a.169.6 | ✓ | 24 | 25.17 | odd | 20 | ||
300.2.o.a.229.6 | yes | 24 | 5.3 | odd | 4 | ||
900.2.w.c.469.2 | 24 | 75.17 | even | 20 | |||
900.2.w.c.829.2 | 24 | 15.8 | even | 4 | |||
1500.2.m.c.601.4 | 24 | 1.1 | even | 1 | trivial | ||
1500.2.m.c.901.4 | 24 | 25.6 | even | 5 | inner | ||
1500.2.m.d.601.3 | 24 | 5.4 | even | 2 | |||
1500.2.m.d.901.3 | 24 | 25.19 | even | 10 | |||
1500.2.o.c.349.1 | 24 | 25.8 | odd | 20 | |||
1500.2.o.c.649.1 | 24 | 5.2 | odd | 4 | |||
7500.2.a.m.1.5 | 12 | 25.9 | even | 10 | |||
7500.2.a.n.1.8 | 12 | 25.16 | even | 5 | |||
7500.2.d.g.1249.8 | 24 | 25.12 | odd | 20 | |||
7500.2.d.g.1249.17 | 24 | 25.13 | odd | 20 |