Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2268,2,Mod(865,2268)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2268, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2268.865");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2268 = 2^{2} \cdot 3^{4} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2268.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: | \(18.1100711784\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 9x^{14} + 31x^{12} - 282x^{10} + 1695x^{8} - 3318x^{6} + 4606x^{4} - 4116x^{2} + 2401 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 3^{7} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 2053.8 | ||
Root | \(-0.817131 - 0.735533i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2268.2053 |
Dual form | 2268.2.i.n.865.8 |
$q$-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 \(\left(\mathbb{Z}/2268\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(1135\) | \(1541\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.83843 | + | 3.18426i | 0.822173 | + | 1.42405i | 0.904061 | + | 0.427404i | \(0.140572\pi\) |
−0.0818877 | + | 0.996642i | \(0.526095\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.55575 | − | 2.14001i | −0.588020 | − | 0.808846i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.301572 | − | 0.522337i | 0.0909273 | − | 0.157491i | −0.816974 | − | 0.576674i | \(-0.804350\pi\) |
0.907902 | + | 0.419183i | \(0.137684\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.62851 | − | 4.55271i | 0.729017 | − | 1.26269i | −0.228282 | − | 0.973595i | \(-0.573311\pi\) |
0.957299 | − | 0.289099i | \(-0.0933558\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.12557 | + | 3.68159i | 0.515526 | + | 0.892918i | 0.999838 | + | 0.0180219i | \(0.00573685\pi\) |
−0.484311 | + | 0.874896i | \(0.660930\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.68426 | − | 6.38133i | 0.845228 | − | 1.46398i | −0.0401954 | − | 0.999192i | \(-0.512798\pi\) |
0.885423 | − | 0.464786i | \(-0.153869\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.578891 | + | 1.00267i | 0.120707 | + | 0.209071i | 0.920047 | − | 0.391809i | \(-0.128150\pi\) |
−0.799340 | + | 0.600880i | \(0.794817\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.25969 | + | 7.37799i | −0.851937 | + | 1.47560i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.98826 | − | 6.90786i | −0.740601 | − | 1.28276i | −0.952222 | − | 0.305406i | \(-0.901208\pi\) |
0.211622 | − | 0.977352i | \(-0.432126\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.15085 | 0.565909 | 0.282954 | − | 0.959133i | \(-0.408686\pi\) | ||||
0.282954 | + | 0.959133i | \(0.408686\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.95419 | − | 8.88819i | 0.668380 | − | 1.50238i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.00266923 | − | 0.00462323i | 0.000438818 | − | 0.000760055i | −0.865806 | − | 0.500380i | \(-0.833194\pi\) |
0.866245 | + | 0.499620i | \(0.166527\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.00937 | + | 3.48033i | −0.313811 | + | 0.543537i | −0.979184 | − | 0.202974i | \(-0.934939\pi\) |
0.665373 | + | 0.746511i | \(0.268272\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.66193 | − | 6.34264i | −0.558438 | − | 0.967244i | −0.997627 | − | 0.0688488i | \(-0.978067\pi\) |
0.439189 | − | 0.898395i | \(-0.355266\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 12.2173 | 1.78207 | 0.891036 | − | 0.453933i | \(-0.149979\pi\) | ||||
0.891036 | + | 0.453933i | \(0.149979\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.15926 | + | 6.65865i | −0.308465 | + | 0.951236i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.64928 | − | 8.05279i | −0.638628 | − | 1.10614i | −0.985734 | − | 0.168310i | \(-0.946169\pi\) |
0.347107 | − | 0.937826i | \(-0.387164\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.21768 | 0.299032 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 6.61521 | 0.861227 | 0.430613 | − | 0.902537i | \(-0.358297\pi\) | ||||
0.430613 | + | 0.902537i | \(0.358297\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.93850 | −0.248200 | −0.124100 | − | 0.992270i | \(-0.539604\pi\) | ||||
−0.124100 | + | 0.992270i | \(0.539604\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 19.3294 | 2.39751 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.63088 | 1.05443 | 0.527215 | − | 0.849732i | \(-0.323236\pi\) | ||||
0.527215 | + | 0.849732i | \(0.323236\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.13815 | 0.135074 | 0.0675370 | − | 0.997717i | \(-0.478486\pi\) | ||||
0.0675370 | + | 0.997717i | \(0.478486\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.33511 | − | 9.24068i | −0.624427 | − | 1.08154i | −0.988651 | − | 0.150228i | \(-0.951999\pi\) |
0.364224 | − | 0.931311i | \(-0.381334\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.58698 | + | 0.167264i | −0.180853 | + | 0.0190614i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.14551 | 0.466406 | 0.233203 | − | 0.972428i | \(-0.425079\pi\) | ||||
0.233203 | + | 0.972428i | \(0.425079\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.24088 | + | 10.8095i | 0.685026 | + | 1.18650i | 0.973429 | + | 0.228990i | \(0.0735423\pi\) |
−0.288403 | + | 0.957509i | \(0.593124\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −7.81544 | + | 13.5367i | −0.847703 | + | 1.46827i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −4.09464 | + | 7.09212i | −0.434031 | + | 0.751764i | −0.997216 | − | 0.0745672i | \(-0.976242\pi\) |
0.563185 | + | 0.826331i | \(0.309576\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −13.8321 | + | 1.45787i | −1.45000 | + | 0.152827i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 27.0931 | 2.77969 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.77935 | + | 11.7422i | 0.688339 | + | 1.19224i | 0.972375 | + | 0.233425i | \(0.0749932\pi\) |
−0.284036 | + | 0.958814i | \(0.591673\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.66975 | − | 13.2844i | 0.763169 | − | 1.32185i | −0.178041 | − | 0.984023i | \(-0.556976\pi\) |
0.941209 | − | 0.337824i | \(-0.109691\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.48033 | + | 4.29606i | 0.244394 | + | 0.423303i | 0.961961 | − | 0.273186i | \(-0.0880775\pi\) |
−0.717567 | + | 0.696490i | \(0.754744\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 3.41399 | − | 5.91320i | 0.330043 | − | 0.571651i | −0.652477 | − | 0.757808i | \(-0.726270\pi\) |
0.982520 | + | 0.186158i | \(0.0596035\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.90194 | + | 15.4186i | 0.852651 | + | 1.47684i | 0.878807 | + | 0.477178i | \(0.158340\pi\) |
−0.0261554 | + | 0.999658i | \(0.508326\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −4.63946 | + | 8.03579i | −0.436444 | + | 0.755943i | −0.997412 | − | 0.0718940i | \(-0.977096\pi\) |
0.560968 | + | 0.827837i | \(0.310429\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.12851 | + | 3.68668i | −0.198484 | + | 0.343785i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 4.57177 | − | 10.2764i | 0.419093 | − | 0.942035i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.31811 | + | 9.21124i | 0.483464 | + | 0.837385i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −12.9403 | −1.15741 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −14.9941 | −1.33051 | −0.665254 | − | 0.746617i | \(-0.731677\pi\) | ||||
−0.665254 | + | 0.746617i | \(0.731677\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −11.4164 | − | 19.7737i | −0.997452 | − | 1.72764i | −0.560508 | − | 0.828149i | \(-0.689394\pi\) |
−0.436944 | − | 0.899489i | \(-0.643939\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −19.3879 | + | 2.04344i | −1.68114 | + | 0.177188i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −0.762784 | + | 1.32118i | −0.0651690 | + | 0.112876i | −0.896769 | − | 0.442499i | \(-0.854092\pi\) |
0.831600 | + | 0.555375i | \(0.187425\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.31277 | + | 5.73789i | −0.280986 | + | 0.486681i | −0.971628 | − | 0.236515i | \(-0.923995\pi\) |
0.690642 | + | 0.723197i | \(0.257328\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.58537 | − | 2.74594i | −0.132575 | − | 0.229627i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 14.6643 | − | 25.3993i | 1.21780 | − | 2.10930i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 8.88746 | + | 15.3935i | 0.728089 | + | 1.26109i | 0.957690 | + | 0.287802i | \(0.0929246\pi\) |
−0.229601 | + | 0.973285i | \(0.573742\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.31811 | + | 4.01508i | −0.188645 | + | 0.326743i | −0.944799 | − | 0.327651i | \(-0.893743\pi\) |
0.756154 | + | 0.654394i | \(0.227076\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5.79262 | + | 10.0331i | 0.465275 | + | 0.805880i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.41320 | 0.272403 | 0.136202 | − | 0.990681i | \(-0.456511\pi\) | ||||
0.136202 | + | 0.990681i | \(0.456511\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.24511 | − | 2.79874i | 0.0981281 | − | 0.220571i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.55012 | − | 13.0772i | 0.591371 | − | 1.02428i | −0.402677 | − | 0.915342i | \(-0.631920\pi\) |
0.994048 | − | 0.108942i | \(-0.0347464\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2.85782 | + | 4.94988i | −0.221144 | + | 0.383033i | −0.955156 | − | 0.296104i | \(-0.904313\pi\) |
0.734011 | + | 0.679137i | \(0.237646\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.31811 | − | 12.6753i | −0.562931 | − | 0.975026i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.89631 | 0.144174 | 0.0720871 | − | 0.997398i | \(-0.477034\pi\) | ||||
0.0720871 | + | 0.997398i | \(0.477034\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 22.4160 | − | 2.36259i | 1.69449 | − | 0.178595i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 7.29747 | + | 12.6396i | 0.545438 | + | 0.944727i | 0.998579 | + | 0.0532881i | \(0.0169702\pi\) |
−0.453141 | + | 0.891439i | \(0.649696\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 7.89857 | 0.587096 | 0.293548 | − | 0.955944i | \(-0.405164\pi\) | ||||
0.293548 | + | 0.955944i | \(0.405164\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.0196288 | 0.00144314 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.56405 | 0.187502 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −8.47340 | −0.613114 | −0.306557 | − | 0.951852i | \(-0.599177\pi\) | ||||
−0.306557 | + | 0.951852i | \(0.599177\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −6.96600 | −0.501424 | −0.250712 | − | 0.968062i | \(-0.580665\pi\) | ||||
−0.250712 | + | 0.968062i | \(0.580665\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 16.2371 | 1.15685 | 0.578424 | − | 0.815736i | \(-0.303668\pi\) | ||||
0.578424 | + | 0.815736i | \(0.303668\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −7.35153 | − | 12.7332i | −0.521136 | − | 0.902634i | −0.999698 | − | 0.0245800i | \(-0.992175\pi\) |
0.478562 | − | 0.878054i | \(-0.341158\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −8.57812 | + | 19.2818i | −0.602066 | + | 1.35332i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −14.7764 | −1.03203 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.22214 | − | 3.84886i | −0.153709 | − | 0.266231i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.41053 | − | 14.5675i | 0.579005 | − | 1.00287i | −0.416589 | − | 0.909095i | \(-0.636775\pi\) |
0.995594 | − | 0.0937708i | \(-0.0298921\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 13.4644 | − | 23.3211i | 0.918266 | − | 1.59048i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.90194 | − | 6.74283i | −0.332766 | − | 0.457733i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 22.3483 | 1.50331 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.45799 | + | 5.98942i | 0.231564 | + | 0.401081i | 0.958269 | − | 0.285869i | \(-0.0922823\pi\) |
−0.726704 | + | 0.686950i | \(0.758949\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3.49817 | − | 6.05900i | 0.232182 | − | 0.402150i | −0.726268 | − | 0.687411i | \(-0.758747\pi\) |
0.958450 | + | 0.285261i | \(0.0920803\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.41350 | + | 2.44825i | 0.0934066 | + | 0.161785i | 0.908942 | − | 0.416922i | \(-0.136891\pi\) |
−0.815536 | + | 0.578706i | \(0.803558\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −11.1679 | + | 19.3434i | −0.731635 | + | 1.26723i | 0.224550 | + | 0.974463i | \(0.427909\pi\) |
−0.956184 | + | 0.292766i | \(0.905424\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 22.4606 | + | 38.9030i | 1.46517 | + | 2.53775i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0.954829 | − | 1.65381i | 0.0617628 | − | 0.106976i | −0.833491 | − | 0.552534i | \(-0.813661\pi\) |
0.895253 | + | 0.445557i | \(0.146994\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 9.84352 | − | 17.0495i | 0.634077 | − | 1.09825i | −0.352633 | − | 0.935762i | \(-0.614714\pi\) |
0.986710 | − | 0.162492i | \(-0.0519530\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −25.1725 | + | 5.36586i | −1.60821 | + | 0.342812i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −19.3682 | − | 33.5468i | −1.23237 | − | 2.13453i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −12.2990 | −0.776306 | −0.388153 | − | 0.921595i | \(-0.626887\pi\) | ||||
−0.388153 | + | 0.921595i | \(0.626887\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.698309 | 0.0439023 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −5.71210 | − | 9.89365i | −0.356311 | − | 0.617149i | 0.631030 | − | 0.775758i | \(-0.282632\pi\) |
−0.987341 | + | 0.158609i | \(0.949299\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.0140464 | + | 0.00148046i | −0.000872802 | + | 9.19912e-5i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 9.65544 | − | 16.7237i | 0.595380 | − | 1.03123i | −0.398114 | − | 0.917336i | \(-0.630335\pi\) |
0.993493 | − | 0.113892i | \(-0.0363317\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 17.0948 | − | 29.6091i | 1.05012 | − | 1.81887i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −4.00745 | − | 6.94110i | −0.244338 | − | 0.423206i | 0.717607 | − | 0.696448i | \(-0.245237\pi\) |
−0.961945 | + | 0.273242i | \(0.911904\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.96658 | − | 5.13827i | 0.180207 | − | 0.312128i | −0.761744 | − | 0.647878i | \(-0.775657\pi\) |
0.941951 | + | 0.335750i | \(0.108990\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.56920 | + | 4.44999i | 0.154929 | + | 0.268344i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6.02768 | − | 10.4402i | 0.362168 | − | 0.627293i | −0.626149 | − | 0.779703i | \(-0.715370\pi\) |
0.988317 | + | 0.152410i | \(0.0487034\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −9.73700 | − | 16.8650i | −0.580861 | − | 1.00608i | −0.995378 | − | 0.0960386i | \(-0.969383\pi\) |
0.414517 | − | 0.910042i | \(-0.363951\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −28.7036 | −1.70625 | −0.853127 | − | 0.521704i | \(-0.825297\pi\) | ||||
−0.853127 | + | 0.521704i | \(0.825297\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 10.5740 | − | 1.11448i | 0.624165 | − | 0.0657854i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −0.536086 | + | 0.928529i | −0.0315345 | + | 0.0546193i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −11.3503 | + | 19.6593i | −0.663090 | + | 1.14851i | 0.316709 | + | 0.948523i | \(0.397422\pi\) |
−0.979799 | + | 0.199983i | \(0.935911\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 12.1616 | + | 21.0646i | 0.708077 | + | 1.22643i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 6.08648 | 0.351990 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −7.87624 | + | 17.7041i | −0.453979 | + | 1.02045i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3.56381 | − | 6.17271i | −0.204063 | − | 0.353448i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −27.9486 | −1.59511 | −0.797555 | − | 0.603246i | \(-0.793874\pi\) | ||||
−0.797555 | + | 0.603246i | \(0.793874\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −15.2982 | −0.867479 | −0.433739 | − | 0.901038i | \(-0.642806\pi\) | ||||
−0.433739 | + | 0.901038i | \(0.642806\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.34103 | 0.188846 | 0.0944230 | − | 0.995532i | \(-0.469899\pi\) | ||||
0.0944230 | + | 0.995532i | \(0.469899\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −9.01444 | −0.506301 | −0.253151 | − | 0.967427i | \(-0.581467\pi\) | ||||
−0.253151 | + | 0.967427i | \(0.581467\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.81098 | −0.269363 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 31.3246 | 1.74295 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 22.3932 | + | 38.7862i | 1.24215 | + | 2.15147i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −19.0071 | − | 26.1450i | −1.04789 | − | 1.44142i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 18.2952 | 1.00559 | 0.502797 | − | 0.864404i | \(-0.332304\pi\) | ||||
0.502797 | + | 0.864404i | \(0.332304\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 15.8673 | + | 27.4830i | 0.866924 | + | 1.50156i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −0.868823 | + | 1.50485i | −0.0473278 | + | 0.0819741i | −0.888719 | − | 0.458453i | \(-0.848404\pi\) |
0.841391 | + | 0.540427i | \(0.181737\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.950206 | − | 1.64580i | 0.0514565 | − | 0.0891253i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 17.6088 | − | 5.73840i | 0.950787 | − | 0.309845i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.09272 | −0.0586600 | −0.0293300 | − | 0.999570i | \(-0.509337\pi\) | ||||
−0.0293300 | + | 0.999570i | \(0.509337\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4.70096 | − | 8.14231i | −0.251637 | − | 0.435848i | 0.712340 | − | 0.701835i | \(-0.247636\pi\) |
−0.963977 | + | 0.265987i | \(0.914302\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −9.64549 | + | 16.7065i | −0.513378 | + | 0.889196i | 0.486502 | + | 0.873680i | \(0.338273\pi\) |
−0.999880 | + | 0.0155167i | \(0.995061\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.09242 | + | 3.62418i | 0.111054 | + | 0.192352i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −2.94976 | + | 5.10914i | −0.155682 | + | 0.269650i | −0.933307 | − | 0.359079i | \(-0.883091\pi\) |
0.777625 | + | 0.628729i | \(0.216424\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.6476 | − | 30.5665i | −0.928820 | − | 1.60876i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 19.6165 | − | 33.9768i | 1.02677 | − | 1.77843i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −5.48300 | + | 9.49684i | −0.286210 | + | 0.495731i | −0.972902 | − | 0.231218i | \(-0.925729\pi\) |
0.686692 | + | 0.726949i | \(0.259062\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −9.99988 | + | 22.4776i | −0.519168 | + | 1.16698i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 15.9691 | + | 27.6592i | 0.826847 | + | 1.43214i | 0.900500 | + | 0.434856i | \(0.143201\pi\) |
−0.0736533 | + | 0.997284i | \(0.523466\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −41.9326 | −2.15964 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −14.4354 | −0.741495 | −0.370747 | − | 0.928734i | \(-0.620898\pi\) | ||||
−0.370747 | + | 0.928734i | \(0.620898\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −8.86006 | − | 15.3461i | −0.452728 | − | 0.784148i | 0.545826 | − | 0.837898i | \(-0.316216\pi\) |
−0.998554 | + | 0.0537502i | \(0.982883\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.45016 | − | 4.74585i | −0.175837 | − | 0.241871i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −9.48751 | + | 16.4329i | −0.481036 | + | 0.833179i | −0.999763 | − | 0.0217610i | \(-0.993073\pi\) |
0.518727 | + | 0.854940i | \(0.326406\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.46095 | + | 4.26249i | −0.124455 | + | 0.215563i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 7.62124 | + | 13.2004i | 0.383466 | + | 0.664183i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −10.5889 | + | 18.3405i | −0.531440 | + | 0.920482i | 0.467886 | + | 0.883789i | \(0.345016\pi\) |
−0.999327 | + | 0.0366930i | \(0.988318\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −7.39038 | − | 12.8005i | −0.369058 | − | 0.639227i | 0.620361 | − | 0.784317i | \(-0.286986\pi\) |
−0.989419 | + | 0.145090i | \(0.953653\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 8.28202 | − | 14.3449i | 0.412557 | − | 0.714570i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −0.00160993 | − | 0.00278847i | −7.98011e−5 | − | 0.000138219i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3.73150 | −0.184511 | −0.0922554 | − | 0.995735i | \(-0.529408\pi\) | ||||
−0.0922554 | + | 0.995735i | \(0.529408\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −10.2916 | − | 14.1566i | −0.506418 | − | 0.696600i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −22.9469 | + | 39.7452i | −1.12642 | + | 1.95102i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −14.1678 | + | 24.5393i | −0.692142 | + | 1.19883i | 0.278993 | + | 0.960293i | \(0.409999\pi\) |
−0.971135 | + | 0.238532i | \(0.923334\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8.09776 | − | 14.0257i | −0.394661 | − | 0.683572i | 0.598397 | − | 0.801200i | \(-0.295805\pi\) |
−0.993058 | + | 0.117627i | \(0.962471\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −36.2170 | −1.75678 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.01584 | + | 4.14841i | 0.145947 | + | 0.200756i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 13.5528 | + | 23.4741i | 0.652815 | + | 1.13071i | 0.982437 | + | 0.186595i | \(0.0597453\pi\) |
−0.329622 | + | 0.944113i | \(0.606921\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −11.5028 | −0.552789 | −0.276394 | − | 0.961044i | \(-0.589140\pi\) | ||||
−0.276394 | + | 0.961044i | \(0.589140\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 8.53115 | 0.408100 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2.86714 | −0.136841 | −0.0684205 | − | 0.997657i | \(-0.521796\pi\) | ||||
−0.0684205 | + | 0.997657i | \(0.521796\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −8.84301 | −0.420144 | −0.210072 | − | 0.977686i | \(-0.567370\pi\) | ||||
−0.210072 | + | 0.977686i | \(0.567370\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −30.1109 | −1.42739 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −40.5033 | −1.91147 | −0.955735 | − | 0.294229i | \(-0.904937\pi\) | ||||
−0.955735 | + | 0.294229i | \(0.904937\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.21194 | + | 2.09914i | 0.0570680 | + | 0.0988446i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −30.0717 | − | 41.3650i | −1.40979 | − | 1.93922i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 38.8098 | 1.81545 | 0.907723 | − | 0.419571i | \(-0.137819\pi\) | ||||
0.907723 | + | 0.419571i | \(0.137819\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −16.1328 | − | 27.9428i | −0.751378 | − | 1.30142i | −0.947155 | − | 0.320776i | \(-0.896056\pi\) |
0.195777 | − | 0.980648i | \(-0.437277\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −16.7430 | + | 28.9997i | −0.778112 | + | 1.34773i | 0.154917 | + | 0.987927i | \(0.450489\pi\) |
−0.933029 | + | 0.359802i | \(0.882844\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −5.04280 | + | 8.73438i | −0.233353 | + | 0.404179i | −0.958793 | − | 0.284107i | \(-0.908303\pi\) |
0.725440 | + | 0.688286i | \(0.241636\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −13.4275 | − | 18.4701i | −0.620026 | − | 0.852872i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −4.41733 | −0.203109 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 31.3876 | + | 54.3649i | 1.44016 | + | 2.49443i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −4.29759 | + | 7.44365i | −0.196362 | + | 0.340109i | −0.947346 | − | 0.320211i | \(-0.896246\pi\) |
0.750984 | + | 0.660320i | \(0.229579\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.0140322 | − | 0.0243044i | −0.000639812 | − | 0.00110819i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −24.9268 | + | 43.1745i | −1.13187 | + | 1.96045i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −0.298843 | − | 0.517612i | −0.0135419 | − | 0.0234552i | 0.859175 | − | 0.511682i | \(-0.170977\pi\) |
−0.872717 | + | 0.488227i | \(0.837644\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 17.1521 | − | 29.7084i | 0.774066 | − | 1.34072i | −0.161253 | − | 0.986913i | \(-0.551553\pi\) |
0.935318 | − | 0.353808i | \(-0.115113\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 16.9546 | − | 29.3663i | 0.763598 | − | 1.32259i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.77069 | − | 2.43566i | −0.0794262 | − | 0.109254i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −15.0247 | − | 26.0236i | −0.672598 | − | 1.16497i | −0.977165 | − | 0.212483i | \(-0.931845\pi\) |
0.304566 | − | 0.952491i | \(-0.401488\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 18.5650 | 0.827773 | 0.413887 | − | 0.910328i | \(-0.364171\pi\) | ||||
0.413887 | + | 0.910328i | \(0.364171\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 56.4013 | 2.50983 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 3.50908 | + | 6.07790i | 0.155537 | + | 0.269398i | 0.933254 | − | 0.359216i | \(-0.116956\pi\) |
−0.777717 | + | 0.628614i | \(0.783623\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −11.4750 | + | 25.7934i | −0.507624 | + | 1.14103i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −9.11986 | + | 15.7961i | −0.401869 | + | 0.696057i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3.68438 | − | 6.38154i | 0.162039 | − | 0.280660i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 15.0742 | + | 26.1092i | 0.660411 | + | 1.14387i | 0.980508 | + | 0.196481i | \(0.0629514\pi\) |
−0.320096 | + | 0.947385i | \(0.603715\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −14.1726 | + | 24.5476i | −0.619724 | + | 1.07339i | 0.369812 | + | 0.929107i | \(0.379422\pi\) |
−0.989536 | + | 0.144287i | \(0.953911\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 6.69734 | + | 11.6001i | 0.291741 | + | 0.505310i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 10.8298 | − | 18.7577i | 0.470860 | − | 0.815553i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 10.5633 | + | 18.2962i | 0.457547 | + | 0.792495i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 25.1056 | 1.08541 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.82689 | + | 3.13592i | 0.121763 | + | 0.135074i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −14.5245 | + | 25.1572i | −0.624458 | + | 1.08159i | 0.364187 | + | 0.931326i | \(0.381347\pi\) |
−0.988645 | + | 0.150268i | \(0.951986\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −32.7313 | + | 56.6922i | −1.40205 | + | 2.42843i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −8.68455 | − | 15.0421i | −0.371324 | − | 0.643153i | 0.618445 | − | 0.785828i | \(-0.287763\pi\) |
−0.989770 | + | 0.142675i | \(0.954430\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −58.7751 | −2.50390 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6.44939 | − | 8.87141i | −0.274256 | − | 0.377251i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 19.5927 | + | 33.9355i | 0.830169 | + | 1.43789i | 0.897904 | + | 0.440191i | \(0.145089\pi\) |
−0.0677355 | + | 0.997703i | \(0.521577\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −38.5016 | −1.62844 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 38.4078 | 1.61870 | 0.809349 | − | 0.587328i | \(-0.199820\pi\) | ||||
0.809349 | + | 0.587328i | \(0.199820\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −34.1174 | −1.43533 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 9.08064 | 0.380680 | 0.190340 | − | 0.981718i | \(-0.439041\pi\) | ||||
0.190340 | + | 0.981718i | \(0.439041\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −37.0548 | −1.55069 | −0.775347 | − | 0.631536i | \(-0.782425\pi\) | ||||
−0.775347 | + | 0.631536i | \(0.782425\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −9.86358 | −0.411340 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.04241 | + | 1.80550i | 0.0433960 | + | 0.0751641i | 0.886908 | − | 0.461947i | \(-0.152849\pi\) |
−0.843512 | + | 0.537111i | \(0.819516\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 13.4232 | − | 30.1725i | 0.556887 | − | 1.25177i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −5.60836 | −0.232275 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 4.75919 | + | 8.24316i | 0.196433 | + | 0.340232i | 0.947369 | − | 0.320143i | \(-0.103731\pi\) |
−0.750936 | + | 0.660374i | \(0.770398\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 11.6085 | − | 20.1066i | 0.478322 | − | 0.828477i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 7.63267 | − | 13.2202i | 0.313436 | − | 0.542887i | −0.665668 | − | 0.746248i | \(-0.731853\pi\) |
0.979104 | + | 0.203361i | \(0.0651865\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 41.1276 | − | 4.33475i | 1.68607 | − | 0.177707i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −20.1195 | −0.822059 | −0.411030 | − | 0.911622i | \(-0.634831\pi\) | ||||
−0.411030 | + | 0.911622i | \(0.634831\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −10.1529 | − | 17.5854i | −0.414146 | − | 0.717322i | 0.581192 | − | 0.813766i | \(-0.302586\pi\) |
−0.995338 | + | 0.0964440i | \(0.969253\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −19.5540 | + | 33.8685i | −0.794983 | + | 1.37695i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.03649 | + | 1.79525i | 0.0420698 | + | 0.0728670i | 0.886294 | − | 0.463124i | \(-0.153271\pi\) |
−0.844224 | + | 0.535991i | \(0.819938\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 32.1132 | − | 55.6217i | 1.29916 | − | 2.25021i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.10053 | − | 1.90618i | −0.0444502 | − | 0.0769900i | 0.842944 | − | 0.538001i | \(-0.180820\pi\) |
−0.887395 | + | 0.461011i | \(0.847487\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −21.1904 | + | 36.7029i | −0.853095 | + | 1.47760i | 0.0253061 | + | 0.999680i | \(0.491944\pi\) |
−0.878401 | + | 0.477924i | \(0.841389\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −6.93536 | + | 12.0124i | −0.278756 | + | 0.482819i | −0.971076 | − | 0.238772i | \(-0.923255\pi\) |
0.692320 | + | 0.721590i | \(0.256589\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 21.5474 | − | 2.27105i | 0.863280 | − | 0.0909876i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −2.49141 | − | 4.31525i | −0.0996565 | − | 0.172610i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0.0226945 | 0.000904889 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 45.1845 | 1.79876 | 0.899382 | − | 0.437163i | \(-0.144017\pi\) | ||||
0.899382 | + | 0.437163i | \(0.144017\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −27.5656 | − | 47.7450i | −1.09391 | − | 1.89470i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 24.6393 | + | 27.3328i | 0.976244 | + | 1.08296i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 13.2564 | − | 22.9608i | 0.523597 | − | 0.906896i | −0.476026 | − | 0.879431i | \(-0.657923\pi\) |
0.999623 | − | 0.0274647i | \(-0.00874340\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 24.3184 | − | 42.1207i | 0.959024 | − | 1.66108i | 0.234145 | − | 0.972202i | \(-0.424771\pi\) |
0.724879 | − | 0.688876i | \(-0.241896\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −10.7224 | − | 18.5717i | −0.421540 | − | 0.730128i | 0.574551 | − | 0.818469i | \(-0.305177\pi\) |
−0.996090 | + | 0.0883409i | \(0.971844\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.99496 | − | 3.45537i | 0.0783090 | − | 0.135635i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.74496 | + | 3.02235i | 0.0682854 | + | 0.118274i | 0.898147 | − | 0.439696i | \(-0.144914\pi\) |
−0.829861 | + | 0.557970i | \(0.811580\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 41.9765 | − | 72.7054i | 1.64016 | − | 2.84083i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −18.2754 | − | 31.6539i | −0.711908 | − | 1.23306i | −0.964140 | − | 0.265394i | \(-0.914498\pi\) |
0.252232 | − | 0.967667i | \(-0.418835\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5.57496 | −0.216841 | −0.108420 | − | 0.994105i | \(-0.534579\pi\) | ||||
−0.108420 | + | 0.994105i | \(0.534579\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −42.1502 | − | 57.9794i | −1.63452 | − | 2.24835i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4.61753 | − | 7.99780i | 0.178792 | − | 0.309676i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −0.584598 | + | 1.01255i | −0.0225682 | + | 0.0390892i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.25661 | + | 2.17652i | 0.0484389 | + | 0.0838986i | 0.889228 | − | 0.457464i | \(-0.151242\pi\) |
−0.840789 | + | 0.541362i | \(0.817909\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −31.7213 | −1.21915 | −0.609574 | − | 0.792729i | \(-0.708659\pi\) | ||||
−0.609574 | + | 0.792729i | \(0.708659\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 14.5813 | − | 32.7758i | 0.559581 | − | 1.25782i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 21.4275 | + | 37.1136i | 0.819902 | + | 1.42011i | 0.905754 | + | 0.423804i | \(0.139305\pi\) |
−0.0858521 | + | 0.996308i | \(0.527361\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −5.60932 | −0.214321 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −48.8827 | −1.86228 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −14.7637 | −0.561639 | −0.280820 | − | 0.959761i | \(-0.590606\pi\) | ||||
−0.280820 | + | 0.959761i | \(0.590606\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −24.3613 | −0.924075 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −17.0842 | −0.647111 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 19.8352 | 0.749167 | 0.374583 | − | 0.927193i | \(-0.377786\pi\) | ||||
0.374583 | + | 0.927193i | \(0.377786\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.0196683 | − | 0.0340664i | −0.000741802 | − | 0.00128484i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −40.3609 | + | 4.25394i | −1.51793 | + | 0.159986i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 10.2058 | 0.383288 | 0.191644 | − | 0.981464i | \(-0.438618\pi\) | ||||
0.191644 | + | 0.981464i | \(0.438618\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.82400 | + | 3.15926i | 0.0683092 | + | 0.118315i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 5.82919 | − | 10.0965i | 0.217999 | − | 0.377586i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 16.2769 | − | 28.1924i | 0.607025 | − | 1.05140i | −0.384703 | − | 0.923040i | \(-0.625696\pi\) |
0.991728 | − | 0.128358i | \(-0.0409706\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.33481 | − | 11.9915i | 0.198679 | − | 0.446588i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 67.9549 | 2.52378 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −7.65095 | − | 13.2518i | −0.283758 | − | 0.491483i | 0.688549 | − | 0.725190i | \(-0.258248\pi\) |
−0.972307 | + | 0.233706i | \(0.924915\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 15.5673 | − | 26.9634i | 0.575779 | − | 0.997279i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 4.34677 | + | 7.52882i | 0.160552 | + | 0.278083i | 0.935067 | − | 0.354472i | \(-0.115339\pi\) |
−0.774515 | + | 0.632555i | \(0.782006\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2.60283 | − | 4.50823i | 0.0958764 | − | 0.166063i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −6.61922 | − | 11.4648i | −0.243492 | − | 0.421740i | 0.718215 | − | 0.695822i | \(-0.244960\pi\) |
−0.961707 | + | 0.274081i | \(0.911626\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 10.7693 | − | 18.6530i | 0.395089 | − | 0.684314i | −0.598024 | − | 0.801478i | \(-0.704047\pi\) |
0.993112 | + | 0.117165i | \(0.0373805\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −32.6780 | + | 56.6000i | −1.19723 | + | 2.07366i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −17.9656 | + | 1.89353i | −0.656449 | + | 0.0691881i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −19.8241 | − | 34.3364i | −0.723393 | − | 1.25295i | −0.959632 | − | 0.281258i | \(-0.909248\pi\) |
0.236239 | − | 0.971695i | \(-0.424085\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −17.0468 | −0.620395 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 13.0719 | 0.475108 | 0.237554 | − | 0.971374i | \(-0.423654\pi\) | ||||
0.237554 | + | 0.971374i | \(0.423654\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −9.17145 | − | 15.8854i | −0.332465 | − | 0.575846i | 0.650530 | − | 0.759481i | \(-0.274547\pi\) |
−0.982995 | + | 0.183635i | \(0.941214\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 19.1467 | − | 43.0378i | 0.693157 | − | 1.55807i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 17.3881 | − | 30.1171i | 0.627849 | − | 1.08747i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 7.46351 | − | 12.9272i | 0.269141 | − | 0.466166i | −0.699499 | − | 0.714633i | \(-0.746594\pi\) |
0.968640 | + | 0.248467i | \(0.0799269\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 14.7818 | + | 25.6029i | 0.531666 | + | 0.920873i | 0.999317 | + | 0.0369592i | \(0.0117672\pi\) |
−0.467651 | + | 0.883913i | \(0.654900\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −13.4216 | + | 23.2469i | −0.482118 | + | 0.835054i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 14.8061 | + | 25.6449i | 0.530483 | + | 0.918824i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.343235 | − | 0.594500i | 0.0122819 | − | 0.0212729i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 6.27495 | + | 10.8685i | 0.223962 | + | 0.387914i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −9.32859 | −0.332528 | −0.166264 | − | 0.986081i | \(-0.553170\pi\) | ||||
−0.166264 | + | 0.986081i | \(0.553170\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 24.4145 | − | 2.57323i | 0.868080 | − | 0.0914935i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −5.09537 | + | 8.82545i | −0.180942 | + | 0.313401i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −11.9334 | + | 20.6692i | −0.422701 | + | 0.732140i | −0.996203 | − | 0.0870647i | \(-0.972251\pi\) |
0.573502 | + | 0.819204i | \(0.305585\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 25.9686 | + | 44.9790i | 0.918705 | + | 1.59124i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −6.43567 | −0.227110 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 11.2010 | − | 1.18055i | 0.394782 | − | 0.0416091i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 17.9594 | + | 31.1066i | 0.631418 | + | 1.09365i | 0.987262 | + | 0.159103i | \(0.0508602\pi\) |
−0.355844 | + | 0.934545i | \(0.615806\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −36.5589 | −1.28376 | −0.641879 | − | 0.766806i | \(-0.721845\pi\) | ||||
−0.641879 | + | 0.766806i | \(0.721845\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 55.5216 | 1.94484 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −53.9660 | −1.88803 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 17.9516 | 0.626517 | 0.313258 | − | 0.949668i | \(-0.398579\pi\) | ||||
0.313258 | + | 0.949668i | \(0.398579\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.93871 | 0.0675793 | 0.0337897 | − | 0.999429i | \(-0.489242\pi\) | ||||
0.0337897 | + | 0.999429i | \(0.489242\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −34.4779 | −1.19891 | −0.599457 | − | 0.800407i | \(-0.704617\pi\) | ||||
−0.599457 | + | 0.800407i | \(0.704617\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 15.6165 | + | 27.0487i | 0.542385 | + | 0.939439i | 0.998766 | + | 0.0496544i | \(0.0158120\pi\) |
−0.456381 | + | 0.889784i | \(0.650855\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −29.1041 | + | 6.20392i | −1.00840 | + | 0.214953i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −21.0156 | −0.727276 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 28.2433 | + | 48.9187i | 0.975065 | + | 1.68886i | 0.679719 | + | 0.733472i | \(0.262102\pi\) |
0.295346 | + | 0.955390i | \(0.404565\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −17.3124 | + | 29.9859i | −0.596978 | + | 1.03400i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 26.9077 | − | 46.6056i | 0.925654 | − | 1.60328i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 11.4384 | − | 25.7112i | 0.393029 | − | 0.883448i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.00618077 | 0.000211874 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 5.83541 | + | 10.1072i | 0.199800 | + | 0.346065i | 0.948464 | − | 0.316886i | \(-0.102637\pi\) |
−0.748663 | + | 0.662951i | \(0.769304\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −5.98166 | + | 10.3605i | −0.204329 | + | 0.353909i | −0.949919 | − | 0.312497i | \(-0.898835\pi\) |
0.745589 | + | 0.666406i | \(0.232168\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 28.7004 | + | 49.7105i | 0.979244 | + | 1.69610i | 0.665151 | + | 0.746709i | \(0.268367\pi\) |
0.314094 | + | 0.949392i | \(0.398299\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −25.1871 | + | 43.6253i | −0.857379 | + | 1.48502i | 0.0170411 | + | 0.999855i | \(0.494575\pi\) |
−0.874420 | + | 0.485169i | \(0.838758\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 3.48625 | + | 6.03836i | 0.118536 | + | 0.205311i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.25017 | − | 2.16535i | 0.0424090 | − | 0.0734546i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 22.6863 | − | 39.2939i | 0.768697 | − | 1.33142i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 20.1319 | + | 27.6923i | 0.680582 | + | 0.936169i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 4.22569 | + | 7.31911i | 0.142691 | + | 0.247149i | 0.928509 | − | 0.371309i | \(-0.121091\pi\) |
−0.785818 | + | 0.618458i | \(0.787758\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −3.99396 | −0.134560 | −0.0672800 | − | 0.997734i | \(-0.521432\pi\) | ||||
−0.0672800 | + | 0.997734i | \(0.521432\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −6.72637 | −0.226360 | −0.113180 | − | 0.993574i | \(-0.536104\pi\) | ||||
−0.113180 | + | 0.993574i | \(0.536104\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 23.1725 | + | 40.1359i | 0.778055 | + | 1.34763i | 0.933061 | + | 0.359718i | \(0.117127\pi\) |
−0.155006 | + | 0.987914i | \(0.549540\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 23.3271 | + | 32.0874i | 0.782365 | + | 1.07618i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 45.0116 | − | 77.9624i | 1.50626 | − | 2.60891i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −26.8318 | + | 46.4741i | −0.896890 | + | 1.55346i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −12.5664 | − | 21.7656i | −0.419112 | − | 0.725924i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 19.7647 | − | 34.2335i | 0.658458 | − | 1.14048i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 14.5210 | + | 25.1511i | 0.482695 | + | 0.836052i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −2.13622 | + | 3.70004i | −0.0709320 | + | 0.122858i | −0.899310 | − | 0.437312i | \(-0.855931\pi\) |
0.828378 | + | 0.560169i | \(0.189264\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 8.26635 | + | 14.3177i | 0.273876 | + | 0.474368i | 0.969851 | − | 0.243699i | \(-0.0783607\pi\) |
−0.695975 | + | 0.718066i | \(0.745027\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 7.52829 | 0.249150 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −24.5548 | + | 55.1941i | −0.810872 | + | 1.82267i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.48862 | − | 4.31042i | 0.0820921 | − | 0.142188i | −0.822056 | − | 0.569406i | \(-0.807173\pi\) |
0.904148 | + | 0.427219i | \(0.140507\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2.99165 | − | 5.18168i | 0.0984713 | − | 0.170557i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.0227401 | + | 0.0393870i | 0.000747691 | + | 0.00129504i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 35.9629 | 1.17990 | 0.589952 | − | 0.807438i | \(-0.299147\pi\) | ||||
0.589952 | + | 0.807438i | \(0.299147\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 34.5358 | + | 38.3111i | 1.13186 | + | 1.25560i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 4.71383 | + | 8.16459i | 0.154159 | + | 0.267011i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −24.5419 | −0.801748 | −0.400874 | − | 0.916133i | \(-0.631294\pi\) | ||||
−0.400874 | + | 0.916133i | \(0.631294\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 6.32907 | 0.206322 | 0.103161 | − | 0.994665i | \(-0.467104\pi\) | ||||
0.103161 | + | 0.994665i | \(0.467104\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −4.65283 | −0.151517 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 27.2086 | 0.884161 | 0.442080 | − | 0.896975i | \(-0.354241\pi\) | ||||
0.442080 | + | 0.896975i | \(0.354241\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −56.0935 | −1.82087 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −24.9963 | −0.809711 | −0.404855 | − | 0.914381i | \(-0.632678\pi\) | ||||
−0.404855 | + | 0.914381i | \(0.632678\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −15.5778 | − | 26.9815i | −0.504086 | − | 0.873102i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 4.01404 | − | 0.423070i | 0.129620 | − | 0.0136616i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −21.0722 | −0.679747 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −12.8065 | − | 22.1816i | −0.412257 | − | 0.714050i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 6.11169 | − | 10.5858i | 0.196539 | − | 0.340415i | −0.750865 | − | 0.660455i | \(-0.770363\pi\) |
0.947404 | + | 0.320041i | \(0.103697\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −0.137437 | + | 0.238048i | −0.00441057 | + | 0.00763933i | −0.868222 | − | 0.496175i | \(-0.834737\pi\) |
0.863812 | + | 0.503815i | \(0.168071\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 17.4330 | − | 1.83739i | 0.558875 | − | 0.0589041i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 31.0169 | 0.992317 | 0.496159 | − | 0.868232i | \(-0.334743\pi\) | ||||
0.496159 | + | 0.868232i | \(0.334743\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.46965 | + | 4.27757i | 0.0789305 | + | 0.136712i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −18.0069 | + | 31.1889i | −0.574332 | + | 0.994772i | 0.421782 | + | 0.906697i | \(0.361405\pi\) |
−0.996114 | + | 0.0880747i | \(0.971929\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 29.8509 | + | 51.7033i | 0.951130 | + | 1.64741i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 4.23971 | − | 7.34340i | 0.134815 | − | 0.233507i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.19313 | − | 3.79862i | −0.0696672 | − | 0.120667i | 0.829088 | − | 0.559119i | \(-0.188860\pi\) |
−0.898755 | + | 0.438452i | \(0.855527\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 27.0306 | − | 46.8184i | 0.856928 | − | 1.48424i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 12.3882 | − | 21.4570i | 0.392338 | − | 0.679549i | −0.600419 | − | 0.799685i | \(-0.705000\pi\) |
0.992757 | + | 0.120136i | \(0.0383330\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 2268.2.i.n.2053.8 | 16 | ||
3.2 | odd | 2 | inner | 2268.2.i.n.2053.1 | 16 | ||
7.4 | even | 3 | 2268.2.l.n.109.1 | 16 | |||
9.2 | odd | 6 | 2268.2.l.n.541.8 | 16 | |||
9.4 | even | 3 | 2268.2.k.g.1297.8 | yes | 16 | ||
9.5 | odd | 6 | 2268.2.k.g.1297.1 | ✓ | 16 | ||
9.7 | even | 3 | 2268.2.l.n.541.1 | 16 | |||
21.11 | odd | 6 | 2268.2.l.n.109.8 | 16 | |||
63.4 | even | 3 | 2268.2.k.g.1621.8 | yes | 16 | ||
63.11 | odd | 6 | inner | 2268.2.i.n.865.1 | 16 | ||
63.25 | even | 3 | inner | 2268.2.i.n.865.8 | 16 | ||
63.32 | odd | 6 | 2268.2.k.g.1621.1 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2268.2.i.n.865.1 | 16 | 63.11 | odd | 6 | inner | ||
2268.2.i.n.865.8 | 16 | 63.25 | even | 3 | inner | ||
2268.2.i.n.2053.1 | 16 | 3.2 | odd | 2 | inner | ||
2268.2.i.n.2053.8 | 16 | 1.1 | even | 1 | trivial | ||
2268.2.k.g.1297.1 | ✓ | 16 | 9.5 | odd | 6 | ||
2268.2.k.g.1297.8 | yes | 16 | 9.4 | even | 3 | ||
2268.2.k.g.1621.1 | yes | 16 | 63.32 | odd | 6 | ||
2268.2.k.g.1621.8 | yes | 16 | 63.4 | even | 3 | ||
2268.2.l.n.109.1 | 16 | 7.4 | even | 3 | |||
2268.2.l.n.109.8 | 16 | 21.11 | odd | 6 | |||
2268.2.l.n.541.1 | 16 | 9.7 | even | 3 | |||
2268.2.l.n.541.8 | 16 | 9.2 | odd | 6 |