Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1600,2,Mod(401,1600)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1600, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1600.401");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1600 = 2^{6} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1600.l (of order \(4\), 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: | \(12.7760643234\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(i)\) |
Coefficient field: | 12.0.4767670494822400.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 4 x^{11} + 7 x^{10} - 4 x^{9} - 8 x^{8} + 24 x^{7} - 38 x^{6} + 48 x^{5} - 32 x^{4} - 32 x^{3} + \cdots + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 2^{7} \) |
Twist minimal: | no (minimal twist has level 400) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 1201.5 | ||
Root | \(1.35979 - 0.388551i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1600.1201 |
Dual form | 1600.2.l.g.401.5 |
$q$-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 \(\left(\mathbb{Z}/1600\mathbb{Z}\right)^\times\).
\(n\) | \(577\) | \(901\) | \(1151\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{4}\right)\) | \(1\) |
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 | ||||||||
\(3\) | 1.03997 | − | 1.03997i | 0.600427 | − | 0.600427i | −0.339999 | − | 0.940426i | \(-0.610427\pi\) |
0.940426 | + | 0.339999i | \(0.110427\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.49668i | 0.565693i | 0.959165 | + | 0.282846i | \(0.0912786\pi\) | ||||
−0.959165 | + | 0.282846i | \(0.908721\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.836925i | 0.278975i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.423260 | − | 0.423260i | −0.127618 | − | 0.127618i | 0.640413 | − | 0.768031i | \(-0.278763\pi\) |
−0.768031 | + | 0.640413i | \(0.778763\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.85704 | + | 1.85704i | −0.515051 | + | 0.515051i | −0.916070 | − | 0.401019i | \(-0.868656\pi\) |
0.401019 | + | 0.916070i | \(0.368656\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.50950 | 1.57879 | 0.789393 | − | 0.613888i | \(-0.210395\pi\) | ||||
0.789393 | + | 0.613888i | \(0.210395\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.75725 | − | 1.75725i | 0.403141 | − | 0.403141i | −0.476198 | − | 0.879338i | \(-0.657985\pi\) |
0.879338 | + | 0.476198i | \(0.157985\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.55650 | + | 1.55650i | 0.339657 | + | 0.339657i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 7.19295i | − | 1.49983i | −0.661532 | − | 0.749917i | \(-0.730094\pi\) | ||
0.661532 | − | 0.749917i | \(-0.269906\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.99029 | + | 3.99029i | 0.767931 | + | 0.767931i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.57892 | + | 6.57892i | −1.22167 | + | 1.22167i | −0.254639 | + | 0.967036i | \(0.581957\pi\) |
−0.967036 | + | 0.254639i | \(0.918043\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.75252 | 1.21279 | 0.606394 | − | 0.795164i | \(-0.292615\pi\) | ||||
0.606394 | + | 0.795164i | \(0.292615\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.880355 | −0.153250 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.95300 | + | 1.95300i | 0.321071 | + | 0.321071i | 0.849178 | − | 0.528107i | \(-0.177098\pi\) |
−0.528107 | + | 0.849178i | \(0.677098\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.86254i | 0.618501i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.70745i | 1.20370i | 0.798609 | + | 0.601851i | \(0.205570\pi\) | ||||
−0.798609 | + | 0.601851i | \(0.794430\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.13581 | + | 6.13581i | 0.935702 | + | 0.935702i | 0.998054 | − | 0.0623522i | \(-0.0198602\pi\) |
−0.0623522 | + | 0.998054i | \(0.519860\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.65476 | 0.970697 | 0.485348 | − | 0.874321i | \(-0.338693\pi\) | ||||
0.485348 | + | 0.874321i | \(0.338693\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.75994 | 0.679992 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 6.76969 | − | 6.76969i | 0.947946 | − | 0.947946i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.29390 | + | 5.29390i | 0.727173 | + | 0.727173i | 0.970056 | − | 0.242882i | \(-0.0780929\pi\) |
−0.242882 | + | 0.970056i | \(0.578093\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 3.65497i | − | 0.484113i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.91841 | − | 5.91841i | −0.770511 | − | 0.770511i | 0.207685 | − | 0.978196i | \(-0.433407\pi\) |
−0.978196 | + | 0.207685i | \(0.933407\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.43686 | + | 1.43686i | −0.183971 | + | 0.183971i | −0.793084 | − | 0.609113i | \(-0.791526\pi\) |
0.609113 | + | 0.793084i | \(0.291526\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.25261 | −0.157814 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.35614 | − | 6.35614i | 0.776526 | − | 0.776526i | −0.202712 | − | 0.979238i | \(-0.564976\pi\) |
0.979238 | + | 0.202712i | \(0.0649756\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −7.48045 | − | 7.48045i | −0.900540 | − | 0.900540i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.08932i | 0.485313i | 0.970112 | + | 0.242657i | \(0.0780188\pi\) | ||||
−0.970112 | + | 0.242657i | \(0.921981\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 2.43800i | − | 0.285346i | −0.989770 | − | 0.142673i | \(-0.954430\pi\) | ||
0.989770 | − | 0.142673i | \(-0.0455698\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.633485 | − | 0.633485i | 0.0721924 | − | 0.0721924i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −11.6722 | −1.31323 | −0.656615 | − | 0.754226i | \(-0.728012\pi\) | ||||
−0.656615 | + | 0.754226i | \(0.728012\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.78878 | 0.643198 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −2.81439 | + | 2.81439i | −0.308919 | + | 0.308919i | −0.844490 | − | 0.535571i | \(-0.820096\pi\) |
0.535571 | + | 0.844490i | \(0.320096\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 13.6838i | 1.46705i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 10.5543i | − | 1.11876i | −0.828912 | − | 0.559379i | \(-0.811040\pi\) | ||
0.828912 | − | 0.559379i | \(-0.188960\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.77940 | − | 2.77940i | −0.291360 | − | 0.291360i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 7.02242 | − | 7.02242i | 0.728191 | − | 0.728191i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 18.1512 | 1.84298 | 0.921488 | − | 0.388407i | \(-0.126975\pi\) | ||||
0.921488 | + | 0.388407i | \(0.126975\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.354237 | − | 0.354237i | 0.0356021 | − | 0.0356021i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.04036 | − | 1.04036i | −0.103520 | − | 0.103520i | 0.653450 | − | 0.756970i | \(-0.273321\pi\) |
−0.756970 | + | 0.653450i | \(0.773321\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 0.955267i | − | 0.0941253i | −0.998892 | − | 0.0470626i | \(-0.985014\pi\) | ||
0.998892 | − | 0.0470626i | \(-0.0149860\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −7.20266 | − | 7.20266i | −0.696308 | − | 0.696308i | 0.267305 | − | 0.963612i | \(-0.413867\pi\) |
−0.963612 | + | 0.267305i | \(0.913867\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.67807 | + | 5.67807i | −0.543861 | + | 0.543861i | −0.924658 | − | 0.380798i | \(-0.875649\pi\) |
0.380798 | + | 0.924658i | \(0.375649\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.06212 | 0.385560 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.94751 | 0.183206 | 0.0916029 | − | 0.995796i | \(-0.470801\pi\) | ||||
0.0916029 | + | 0.995796i | \(0.470801\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.55420 | − | 1.55420i | −0.143686 | − | 0.143686i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 9.74266i | 0.893108i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 10.6417i | − | 0.967427i | ||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 8.01552 | + | 8.01552i | 0.722735 | + | 0.722735i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.31796 | 0.116950 | 0.0584750 | − | 0.998289i | \(-0.481376\pi\) | ||||
0.0584750 | + | 0.998289i | \(0.481376\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 12.7621 | 1.12364 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.03026 | + | 1.03026i | −0.0900139 | + | 0.0900139i | −0.750680 | − | 0.660666i | \(-0.770274\pi\) |
0.660666 | + | 0.750680i | \(0.270274\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.63004 | + | 2.63004i | 0.228054 | + | 0.228054i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.75559i | 0.320862i | 0.987047 | + | 0.160431i | \(0.0512884\pi\) | ||||
−0.987047 | + | 0.160431i | \(0.948712\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −12.9485 | − | 12.9485i | −1.09828 | − | 1.09828i | −0.994612 | − | 0.103669i | \(-0.966942\pi\) |
−0.103669 | − | 0.994612i | \(-0.533058\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.92075 | − | 6.92075i | 0.582832 | − | 0.582832i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.57202 | 0.131459 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 4.95020 | − | 4.95020i | 0.408285 | − | 0.408285i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −15.8472 | − | 15.8472i | −1.29825 | − | 1.29825i | −0.929545 | − | 0.368709i | \(-0.879800\pi\) |
−0.368709 | − | 0.929545i | \(-0.620200\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.5316i | 0.938424i | 0.883085 | + | 0.469212i | \(0.155462\pi\) | ||||
−0.883085 | + | 0.469212i | \(0.844538\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 5.44797i | 0.440442i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.41891 | + | 5.41891i | −0.432476 | + | 0.432476i | −0.889470 | − | 0.456994i | \(-0.848926\pi\) |
0.456994 | + | 0.889470i | \(0.348926\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 11.0110 | 0.873229 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 10.7656 | 0.848445 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −6.47288 | + | 6.47288i | −0.506995 | + | 0.506995i | −0.913603 | − | 0.406608i | \(-0.866711\pi\) |
0.406608 | + | 0.913603i | \(0.366711\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 8.29734i | − | 0.642068i | −0.947068 | − | 0.321034i | \(-0.895970\pi\) | ||
0.947068 | − | 0.321034i | \(-0.104030\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.10279i | 0.469445i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.47069 | + | 1.47069i | 0.112466 | + | 0.112466i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 11.9420 | − | 11.9420i | 0.907935 | − | 0.907935i | −0.0881700 | − | 0.996105i | \(-0.528102\pi\) |
0.996105 | + | 0.0881700i | \(0.0281019\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −12.3099 | −0.925271 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 10.8703 | − | 10.8703i | 0.812481 | − | 0.812481i | −0.172524 | − | 0.985005i | \(-0.555192\pi\) |
0.985005 | + | 0.172524i | \(0.0551922\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.09403 | − | 4.09403i | −0.304307 | − | 0.304307i | 0.538389 | − | 0.842696i | \(-0.319033\pi\) |
−0.842696 | + | 0.538389i | \(0.819033\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.98858i | 0.220922i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.75521 | − | 2.75521i | −0.201481 | − | 0.201481i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −5.97219 | + | 5.97219i | −0.434413 | + | 0.434413i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −19.2542 | −1.39319 | −0.696594 | − | 0.717466i | \(-0.745302\pi\) | ||||
−0.696594 | + | 0.717466i | \(0.745302\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −24.8152 | −1.78624 | −0.893119 | − | 0.449820i | \(-0.851488\pi\) | ||||
−0.893119 | + | 0.449820i | \(0.851488\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2.81324 | − | 2.81324i | −0.200435 | − | 0.200435i | 0.599751 | − | 0.800186i | \(-0.295266\pi\) |
−0.800186 | + | 0.599751i | \(0.795266\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 21.2194i | 1.50420i | 0.659048 | + | 0.752101i | \(0.270959\pi\) | ||||
−0.659048 | + | 0.752101i | \(0.729041\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 13.2204i | − | 0.932495i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −9.84655 | − | 9.84655i | −0.691092 | − | 0.691092i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 6.01996 | 0.418416 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.48755 | −0.102896 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −15.5715 | + | 15.5715i | −1.07199 | + | 1.07199i | −0.0747872 | + | 0.997200i | \(0.523828\pi\) |
−0.997200 | + | 0.0747872i | \(0.976172\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 4.25277 | + | 4.25277i | 0.291395 | + | 0.291395i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 10.1064i | 0.686065i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2.53545 | − | 2.53545i | −0.171330 | − | 0.171330i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −12.0884 | + | 12.0884i | −0.813155 | + | 0.813155i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.88779 | 0.528205 | 0.264103 | − | 0.964495i | \(-0.414924\pi\) | ||||
0.264103 | + | 0.964495i | \(0.414924\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 5.98838 | − | 5.98838i | 0.397463 | − | 0.397463i | −0.479874 | − | 0.877337i | \(-0.659318\pi\) |
0.877337 | + | 0.479874i | \(0.159318\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 19.4584 | + | 19.4584i | 1.28585 | + | 1.28585i | 0.937286 | + | 0.348563i | \(0.113330\pi\) |
0.348563 | + | 0.937286i | \(0.386670\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 1.31761i | − | 0.0866925i | ||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2.68717i | 0.176042i | 0.996119 | + | 0.0880212i | \(0.0280543\pi\) | ||||
−0.996119 | + | 0.0880212i | \(0.971946\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −12.1388 | + | 12.1388i | −0.788499 | + | 0.788499i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 12.6359 | 0.817346 | 0.408673 | − | 0.912681i | \(-0.365992\pi\) | ||||
0.408673 | + | 0.912681i | \(0.365992\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.53314 | 0.485252 | 0.242626 | − | 0.970120i | \(-0.421991\pi\) | ||||
0.242626 | + | 0.970120i | \(0.421991\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −5.95070 | + | 5.95070i | −0.381738 | + | 0.381738i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.52658i | 0.415276i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 5.85376i | 0.370967i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 9.95683 | + | 9.95683i | 0.628470 | + | 0.628470i | 0.947683 | − | 0.319213i | \(-0.103419\pi\) |
−0.319213 | + | 0.947683i | \(0.603419\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.04449 | + | 3.04449i | −0.191405 | + | 0.191405i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 4.51630 | 0.281719 | 0.140860 | − | 0.990030i | \(-0.455013\pi\) | ||||
0.140860 | + | 0.990030i | \(0.455013\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.92302 | + | 2.92302i | −0.181628 | + | 0.181628i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −5.50606 | − | 5.50606i | −0.340817 | − | 0.340817i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 20.2127i | − | 1.24637i | −0.782075 | − | 0.623185i | \(-0.785838\pi\) | ||
0.782075 | − | 0.623185i | \(-0.214162\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −10.9762 | − | 10.9762i | −0.671732 | − | 0.671732i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 16.9430 | − | 16.9430i | 1.03304 | − | 1.03304i | 0.0335999 | − | 0.999435i | \(-0.489303\pi\) |
0.999435 | − | 0.0335999i | \(-0.0106972\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.64054 | 0.221147 | 0.110573 | − | 0.993868i | \(-0.464731\pi\) | ||||
0.110573 | + | 0.993868i | \(0.464731\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −5.78099 | −0.349881 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −16.0090 | − | 16.0090i | −0.961888 | − | 0.961888i | 0.0374115 | − | 0.999300i | \(-0.488089\pi\) |
−0.999300 | + | 0.0374115i | \(0.988089\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 5.65135i | 0.338338i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5.51857i | 0.329210i | 0.986360 | + | 0.164605i | \(0.0526350\pi\) | ||||
−0.986360 | + | 0.164605i | \(0.947365\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.36694 | − | 2.36694i | −0.140700 | − | 0.140700i | 0.633249 | − | 0.773949i | \(-0.281721\pi\) |
−0.773949 | + | 0.633249i | \(0.781721\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −11.5356 | −0.680925 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 25.3736 | 1.49257 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 18.8767 | − | 18.8767i | 1.10657 | − | 1.10657i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −19.1812 | − | 19.1812i | −1.12058 | − | 1.12058i | −0.991655 | − | 0.128922i | \(-0.958848\pi\) |
−0.128922 | − | 0.991655i | \(-0.541152\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 3.37786i | − | 0.196003i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 13.3576 | + | 13.3576i | 0.772491 | + | 0.772491i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −9.18335 | + | 9.18335i | −0.529320 | + | 0.529320i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2.16390 | −0.124313 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −19.9292 | + | 19.9292i | −1.13742 | + | 1.13742i | −0.148507 | + | 0.988911i | \(0.547447\pi\) |
−0.988911 | + | 0.148507i | \(0.952553\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −0.993449 | − | 0.993449i | −0.0565153 | − | 0.0565153i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5.73314i | 0.325096i | 0.986701 | + | 0.162548i | \(0.0519713\pi\) | ||||
−0.986701 | + | 0.162548i | \(0.948029\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0.212621i | 0.0120180i | 0.999982 | + | 0.00600902i | \(0.00191274\pi\) | ||||
−0.999982 | + | 0.00600902i | \(0.998087\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −3.21582 | + | 3.21582i | −0.180618 | + | 0.180618i | −0.791625 | − | 0.611007i | \(-0.790765\pi\) |
0.611007 | + | 0.791625i | \(0.290765\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5.56919 | 0.311815 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −14.9811 | −0.836164 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 11.4388 | − | 11.4388i | 0.636473 | − | 0.636473i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 11.8101i | 0.653097i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 9.96006i | 0.549116i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −22.0295 | − | 22.0295i | −1.21085 | − | 1.21085i | −0.970747 | − | 0.240106i | \(-0.922818\pi\) |
−0.240106 | − | 0.970747i | \(-0.577182\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1.63451 | + | 1.63451i | −0.0895708 | + | 0.0895708i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −11.2122 | −0.610767 | −0.305384 | − | 0.952229i | \(-0.598785\pi\) | ||||
−0.305384 | + | 0.952229i | \(0.598785\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2.02535 | − | 2.02535i | 0.110002 | − | 0.110002i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.85807 | − | 2.85807i | −0.154773 | − | 0.154773i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 17.6009i | 0.950359i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.23653 | − | 1.23653i | −0.0663803 | − | 0.0663803i | 0.673137 | − | 0.739518i | \(-0.264946\pi\) |
−0.739518 | + | 0.673137i | \(0.764946\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −5.61778 | + | 5.61778i | −0.300713 | + | 0.300713i | −0.841293 | − | 0.540580i | \(-0.818205\pi\) |
0.540580 | + | 0.841293i | \(0.318205\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −14.8203 | −0.791047 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0.748709 | 0.0398497 | 0.0199249 | − | 0.999801i | \(-0.493657\pi\) | ||||
0.0199249 | + | 0.999801i | \(0.493657\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 10.1321 | + | 10.1321i | 0.536246 | + | 0.536246i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2.69883i | 0.142439i | 0.997461 | + | 0.0712195i | \(0.0226891\pi\) | ||||
−0.997461 | + | 0.0712195i | \(0.977311\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 12.8241i | 0.674955i | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −11.0671 | − | 11.0671i | −0.580870 | − | 0.580870i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −20.6101 | −1.07584 | −0.537920 | − | 0.842996i | \(-0.680790\pi\) | ||||
−0.537920 | + | 0.842996i | \(0.680790\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −6.45056 | −0.335802 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −7.92329 | + | 7.92329i | −0.411357 | + | 0.411357i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5.24143 | + | 5.24143i | 0.271391 | + | 0.271391i | 0.829660 | − | 0.558269i | \(-0.188534\pi\) |
−0.558269 | + | 0.829660i | \(0.688534\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 24.4347i | − | 1.25845i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5.41344 | − | 5.41344i | −0.278070 | − | 0.278070i | 0.554268 | − | 0.832338i | \(-0.312998\pi\) |
−0.832338 | + | 0.554268i | \(0.812998\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.37064 | − | 1.37064i | 0.0702199 | − | 0.0702199i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −29.5087 | −1.50782 | −0.753912 | − | 0.656975i | \(-0.771836\pi\) | ||||
−0.753912 | + | 0.656975i | \(0.771836\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −5.13521 | + | 5.13521i | −0.261037 | + | 0.261037i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.37884 | + | 1.37884i | 0.0699099 | + | 0.0699099i | 0.741197 | − | 0.671287i | \(-0.234258\pi\) |
−0.671287 | + | 0.741197i | \(0.734258\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 46.8225i | − | 2.36792i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2.14287i | 0.108094i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 21.9750 | − | 21.9750i | 1.10289 | − | 1.10289i | 0.108832 | − | 0.994060i | \(-0.465289\pi\) |
0.994060 | − | 0.108832i | \(-0.0347111\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 5.47033 | 0.273859 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −31.4584 | −1.57096 | −0.785479 | − | 0.618889i | \(-0.787583\pi\) | ||||
−0.785479 | + | 0.618889i | \(0.787583\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −12.5397 | + | 12.5397i | −0.624648 | + | 0.624648i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 1.65325i | − | 0.0819487i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 12.8017i | − | 0.633003i | −0.948592 | − | 0.316502i | \(-0.897492\pi\) | ||
0.948592 | − | 0.316502i | \(-0.102508\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3.90570 | + | 3.90570i | 0.192654 | + | 0.192654i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 8.85797 | − | 8.85797i | 0.435872 | − | 0.435872i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −26.9322 | −1.31888 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 11.4979 | − | 11.4979i | 0.561709 | − | 0.561709i | −0.368084 | − | 0.929793i | \(-0.619986\pi\) |
0.929793 | + | 0.368084i | \(0.119986\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 12.5714 | + | 12.5714i | 0.612690 | + | 0.612690i | 0.943646 | − | 0.330956i | \(-0.107371\pi\) |
−0.330956 | + | 0.943646i | \(0.607371\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 5.56953i | 0.270800i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.15052 | − | 2.15052i | −0.104071 | − | 0.104071i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.63486 | − | 1.63486i | 0.0789316 | − | 0.0789316i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 15.2579 | 0.734946 | 0.367473 | − | 0.930034i | \(-0.380223\pi\) | ||||
0.367473 | + | 0.930034i | \(0.380223\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 12.1705 | 0.584877 | 0.292439 | − | 0.956284i | \(-0.405533\pi\) | ||||
0.292439 | + | 0.956284i | \(0.405533\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −12.6398 | − | 12.6398i | −0.604644 | − | 0.604644i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 39.7535i | − | 1.89733i | −0.316283 | − | 0.948665i | \(-0.602435\pi\) | ||
0.316283 | − | 0.948665i | \(-0.397565\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.98371i | 0.189701i | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3.62318 | + | 3.62318i | 0.172142 | + | 0.172142i | 0.787920 | − | 0.615778i | \(-0.211158\pi\) |
−0.615778 | + | 0.787920i | \(0.711158\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −32.9612 | −1.55901 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −5.38425 | −0.254098 | −0.127049 | − | 0.991896i | \(-0.540551\pi\) | ||||
−0.127049 | + | 0.991896i | \(0.540551\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.26225 | − | 3.26225i | 0.153614 | − | 0.153614i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 11.9925 | + | 11.9925i | 0.563455 | + | 0.563455i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 14.3039i | 0.669108i | 0.942377 | + | 0.334554i | \(0.108586\pi\) | ||||
−0.942377 | + | 0.334554i | \(0.891414\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 25.9748 | + | 25.9748i | 1.21240 | + | 1.21240i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −4.50363 | + | 4.50363i | −0.209755 | + | 0.209755i | −0.804163 | − | 0.594408i | \(-0.797386\pi\) |
0.594408 | + | 0.804163i | \(0.297386\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 19.3500 | 0.899271 | 0.449636 | − | 0.893212i | \(-0.351554\pi\) | ||||
0.449636 | + | 0.893212i | \(0.351554\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −17.1773 | + | 17.1773i | −0.794871 | + | 0.794871i | −0.982282 | − | 0.187410i | \(-0.939991\pi\) |
0.187410 | + | 0.982282i | \(0.439991\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 9.51312 | + | 9.51312i | 0.439275 | + | 0.439275i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 11.2710i | 0.519341i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 5.19408i | − | 0.238824i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −4.43060 | + | 4.43060i | −0.202863 | + | 0.202863i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −5.54474 | −0.253346 | −0.126673 | − | 0.991945i | \(-0.540430\pi\) | ||||
−0.126673 | + | 0.991945i | \(0.540430\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7.25361 | −0.330736 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 11.1959 | − | 11.1959i | 0.509429 | − | 0.509429i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 31.7138i | − | 1.43709i | −0.695480 | − | 0.718546i | \(-0.744808\pi\) | ||
0.695480 | − | 0.718546i | \(-0.255192\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 13.4632i | 0.608827i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7.39419 | − | 7.39419i | −0.333695 | − | 0.333695i | 0.520293 | − | 0.853988i | \(-0.325823\pi\) |
−0.853988 | + | 0.520293i | \(0.825823\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −42.8255 | + | 42.8255i | −1.92876 | + | 1.92876i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −6.12041 | −0.274538 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −14.0103 | + | 14.0103i | −0.627189 | + | 0.627189i | −0.947360 | − | 0.320171i | \(-0.896260\pi\) |
0.320171 | + | 0.947360i | \(0.396260\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −8.62899 | − | 8.62899i | −0.385515 | − | 0.385515i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 8.43795i | − | 0.376230i | −0.982147 | − | 0.188115i | \(-0.939762\pi\) | ||
0.982147 | − | 0.188115i | \(-0.0602377\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 6.34671 | + | 6.34671i | 0.281868 | + | 0.281868i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 2.09367 | − | 2.09367i | 0.0928004 | − | 0.0928004i | −0.659183 | − | 0.751983i | \(-0.729098\pi\) |
0.751983 | + | 0.659183i | \(0.229098\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.64891 | 0.161418 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 14.0239 | 0.619169 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.81669 | − | 2.81669i | −0.123878 | − | 0.123878i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 24.8387i | − | 1.09030i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 28.2558i | 1.23791i | 0.785428 | + | 0.618954i | \(0.212443\pi\) | ||||
−0.785428 | + | 0.618954i | \(0.787557\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 10.1929 | + | 10.1929i | 0.445703 | + | 0.445703i | 0.893923 | − | 0.448220i | \(-0.147942\pi\) |
−0.448220 | + | 0.893923i | \(0.647942\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 43.9555 | 1.91473 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −28.7385 | −1.24950 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.95326 | − | 4.95326i | 0.214953 | − | 0.214953i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −14.3131 | − | 14.3131i | −0.619967 | − | 0.619967i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 22.6095i | − | 0.975671i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2.01469 | − | 2.01469i | −0.0867790 | − | 0.0867790i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.86053 | − | 3.86053i | 0.165977 | − | 0.165977i | −0.619231 | − | 0.785209i | \(-0.712556\pi\) |
0.785209 | + | 0.619231i | \(0.212556\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −8.51534 | −0.365428 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 20.6231 | − | 20.6231i | 0.881781 | − | 0.881781i | −0.111935 | − | 0.993716i | \(-0.535705\pi\) |
0.993716 | + | 0.111935i | \(0.0357048\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.20254 | − | 1.20254i | −0.0513233 | − | 0.0513233i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 23.1216i | 0.985014i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 17.4696i | − | 0.742884i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.28512 | − | 1.28512i | 0.0544523 | − | 0.0544523i | −0.679356 | − | 0.733809i | \(-0.737741\pi\) |
0.733809 | + | 0.679356i | \(0.237741\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −22.7889 | −0.963868 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −5.73068 | −0.241949 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 21.9152 | − | 21.9152i | 0.923615 | − | 0.923615i | −0.0736677 | − | 0.997283i | \(-0.523470\pi\) |
0.997283 | + | 0.0736677i | \(0.0234704\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 8.66397i | 0.363852i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 35.6668i | − | 1.49523i | −0.664132 | − | 0.747615i | \(-0.731199\pi\) | ||
0.664132 | − | 0.747615i | \(-0.268801\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5.60524 | − | 5.60524i | −0.234572 | − | 0.234572i | 0.580026 | − | 0.814598i | \(-0.303042\pi\) |
−0.814598 | + | 0.580026i | \(0.803042\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −20.0238 | + | 20.0238i | −0.836507 | + | 0.836507i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.43681 | 0.101446 | 0.0507230 | − | 0.998713i | \(-0.483847\pi\) | ||||
0.0507230 | + | 0.998713i | \(0.483847\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −25.8071 | + | 25.8071i | −1.07251 | + | 1.07251i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4.21225 | − | 4.21225i | −0.174753 | − | 0.174753i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 4.48139i | − | 0.185600i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0.415982 | + | 0.415982i | 0.0171694 | + | 0.0171694i | 0.715639 | − | 0.698470i | \(-0.246135\pi\) |
−0.698470 | + | 0.715639i | \(0.746135\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 11.8659 | − | 11.8659i | 0.488924 | − | 0.488924i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −5.85136 | −0.240693 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 15.3439 | 0.630098 | 0.315049 | − | 0.949075i | \(-0.397979\pi\) | ||||
0.315049 | + | 0.949075i | \(0.397979\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 22.0675 | + | 22.0675i | 0.903163 | + | 0.903163i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 43.3487i | − | 1.77118i | −0.464468 | − | 0.885590i | \(-0.653754\pi\) | ||
0.464468 | − | 0.885590i | \(-0.346246\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 38.7291i | − | 1.57979i | −0.613239 | − | 0.789897i | \(-0.710134\pi\) | ||
0.613239 | − | 0.789897i | \(-0.289866\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 5.31961 | + | 5.31961i | 0.216631 | + | 0.216631i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −34.9068 | −1.41682 | −0.708412 | − | 0.705800i | \(-0.750588\pi\) | ||||
−0.708412 | + | 0.705800i | \(0.750588\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −20.4802 | −0.829901 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −12.3582 | + | 12.3582i | −0.499958 | + | 0.499958i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0.151779 | + | 0.151779i | 0.00613031 | + | 0.00613031i | 0.710165 | − | 0.704035i | \(-0.248620\pi\) |
−0.704035 | + | 0.710165i | \(0.748620\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 0.288199i | − | 0.0116025i | −0.999983 | − | 0.00580123i | \(-0.998153\pi\) | ||
0.999983 | − | 0.00580123i | \(-0.00184660\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 11.5307 | + | 11.5307i | 0.463460 | + | 0.463460i | 0.899788 | − | 0.436328i | \(-0.143721\pi\) |
−0.436328 | + | 0.899788i | \(0.643721\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 28.7019 | − | 28.7019i | 1.15177 | − | 1.15177i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 15.7965 | 0.632873 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.54700 | + | 1.54700i | −0.0617814 | + | 0.0617814i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 12.7131 | + | 12.7131i | 0.506903 | + | 0.506903i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 14.2062i | − | 0.565541i | −0.959188 | − | 0.282771i | \(-0.908746\pi\) | ||
0.959188 | − | 0.282771i | \(-0.0912536\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 32.3878i | 1.28730i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −8.83942 | + | 8.83942i | −0.350230 | + | 0.350230i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −3.42245 | −0.135390 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 19.7372 | 0.779572 | 0.389786 | − | 0.920905i | \(-0.372549\pi\) | ||||
0.389786 | + | 0.920905i | \(0.372549\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −5.80043 | + | 5.80043i | −0.228747 | + | 0.228747i | −0.812169 | − | 0.583422i | \(-0.801713\pi\) |
0.583422 | + | 0.812169i | \(0.301713\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 46.3186i | − | 1.82097i | −0.413541 | − | 0.910485i | \(-0.635708\pi\) | ||
0.413541 | − | 0.910485i | \(-0.364292\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5.01005i | 0.196662i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 10.5103 | + | 10.5103i | 0.411932 | + | 0.411932i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 4.42354 | − | 4.42354i | 0.173106 | − | 0.173106i | −0.615236 | − | 0.788343i | \(-0.710939\pi\) |
0.788343 | + | 0.615236i | \(0.210939\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 2.04042 | 0.0796045 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 15.2461 | − | 15.2461i | 0.593905 | − | 0.593905i | −0.344779 | − | 0.938684i | \(-0.612046\pi\) |
0.938684 | + | 0.344779i | \(0.112046\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 19.1271 | + | 19.1271i | 0.743958 | + | 0.743958i | 0.973337 | − | 0.229379i | \(-0.0736696\pi\) |
−0.229379 | + | 0.973337i | \(0.573670\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 25.1432i | 0.976481i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 47.3218 | + | 47.3218i | 1.83231 | + | 1.83231i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 8.20306 | − | 8.20306i | 0.317149 | − | 0.317149i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.21633 | 0.0469559 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 18.5586 | 0.715382 | 0.357691 | − | 0.933840i | \(-0.383564\pi\) | ||||
0.357691 | + | 0.933840i | \(0.383564\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 2.71844 | + | 2.71844i | 0.104478 | + | 0.104478i | 0.757414 | − | 0.652935i | \(-0.226463\pi\) |
−0.652935 | + | 0.757414i | \(0.726463\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 27.1666i | 1.04256i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 12.4555i | − | 0.477295i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −12.6646 | − | 12.6646i | −0.484598 | − | 0.484598i | 0.421999 | − | 0.906596i | \(-0.361329\pi\) |
−0.906596 | + | 0.421999i | \(0.861329\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 40.4723 | 1.54412 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −19.6620 | −0.749063 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −26.8892 | + | 26.8892i | −1.02291 | + | 1.02291i | −0.0231826 | + | 0.999731i | \(0.507380\pi\) |
−0.999731 | + | 0.0231826i | \(0.992620\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0.530180 | + | 0.530180i | 0.0201399 | + | 0.0201399i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 50.1717i | 1.90039i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 2.79458 | + | 2.79458i | 0.105701 | + | 0.105701i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 25.3725 | − | 25.3725i | 0.958305 | − | 0.958305i | −0.0408602 | − | 0.999165i | \(-0.513010\pi\) |
0.999165 | + | 0.0408602i | \(0.0130098\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 6.86382 | 0.258874 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.55709 | − | 1.55709i | 0.0585606 | − | 0.0585606i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 16.1117 | + | 16.1117i | 0.605089 | + | 0.605089i | 0.941659 | − | 0.336570i | \(-0.109267\pi\) |
−0.336570 | + | 0.941659i | \(0.609267\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 9.76879i | − | 0.366358i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 48.5705i | − | 1.81898i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 13.1409 | − | 13.1409i | 0.490757 | − | 0.490757i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −29.1676 | −1.08777 | −0.543884 | − | 0.839160i | \(-0.683047\pi\) | ||||
−0.543884 | + | 0.839160i | \(0.683047\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.42973 | 0.0532460 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 7.83424 | − | 7.83424i | 0.291358 | − | 0.291358i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 4.13463i | 0.153345i | 0.997056 | + | 0.0766724i | \(0.0244296\pi\) | ||||
−0.997056 | + | 0.0766724i | \(0.975570\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 29.7434i | 1.10161i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 39.9411 | + | 39.9411i | 1.47727 | + | 1.47727i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 19.3838 | − | 19.3838i | 0.715957 | − | 0.715957i | −0.251817 | − | 0.967775i | \(-0.581028\pi\) |
0.967775 | + | 0.251817i | \(0.0810282\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −5.38060 | −0.198197 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −23.9820 | + | 23.9820i | −0.882194 | + | 0.882194i | −0.993757 | − | 0.111564i | \(-0.964414\pi\) |
0.111564 | + | 0.993757i | \(0.464414\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 6.78744 | + | 6.78744i | 0.249343 | + | 0.249343i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 10.3473i | 0.379604i | 0.981822 | + | 0.189802i | \(0.0607846\pi\) | ||||
−0.981822 | + | 0.189802i | \(0.939215\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −2.35543 | − | 2.35543i | −0.0861808 | − | 0.0861808i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 10.7801 | − | 10.7801i | 0.393896 | − | 0.393896i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 37.0217 | 1.35094 | 0.675470 | − | 0.737387i | \(-0.263941\pi\) | ||||
0.675470 | + | 0.737387i | \(0.263941\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 20.7096 | 0.754700 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 30.4305 | + | 30.4305i | 1.10601 | + | 1.10601i | 0.993669 | + | 0.112345i | \(0.0358361\pi\) |
0.112345 | + | 0.993669i | \(0.464164\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 6.33235i | 0.229850i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 43.1054i | 1.56257i | 0.624174 | + | 0.781285i | \(0.285436\pi\) | ||||
−0.624174 | + | 0.781285i | \(0.714564\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −8.49827 | − | 8.49827i | −0.307658 | − | 0.307658i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 21.9815 | 0.793705 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −31.2507 | −1.12693 | −0.563465 | − | 0.826140i | \(-0.690532\pi\) | ||||
−0.563465 | + | 0.826140i | \(0.690532\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4.69682 | − | 4.69682i | 0.169152 | − | 0.169152i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −24.4047 | − | 24.4047i | −0.877778 | − | 0.877778i | 0.115527 | − | 0.993304i | \(-0.463144\pi\) |
−0.993304 | + | 0.115527i | \(0.963144\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 6.07970i | 0.218108i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 13.5439 | + | 13.5439i | 0.485261 | + | 0.485261i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.73085 | − | 1.73085i | 0.0619345 | − | 0.0619345i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −52.5036 | −1.87632 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −17.2122 | + | 17.2122i | −0.613549 | + | 0.613549i | −0.943869 | − | 0.330320i | \(-0.892843\pi\) |
0.330320 | + | 0.943869i | \(0.392843\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −21.0206 | − | 21.0206i | −0.748354 | − | 0.748354i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.91480i | 0.103638i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 5.33662i | − | 0.189509i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 20.3220 | − | 20.3220i | 0.719841 | − | 0.719841i | −0.248731 | − | 0.968573i | \(-0.580014\pi\) |
0.968573 | + | 0.248731i | \(0.0800136\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 43.3192 | 1.53252 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 8.83319 | 0.312105 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.03191 | + | 1.03191i | −0.0364153 | + | 0.0364153i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 35.2405i | − | 1.24052i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 2.80407i | − | 0.0985859i | −0.998784 | − | 0.0492930i | \(-0.984303\pi\) | ||
0.998784 | − | 0.0492930i | \(-0.0156968\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 7.29902 | + | 7.29902i | 0.256303 | + | 0.256303i | 0.823549 | − | 0.567246i | \(-0.191991\pi\) |
−0.567246 | + | 0.823549i | \(0.691991\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 3.78605 | − | 3.78605i | 0.132782 | − | 0.132782i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 21.5643 | 0.754439 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2.32615 | − | 2.32615i | 0.0812823 | − | 0.0812823i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −10.0517 | − | 10.0517i | −0.350806 | − | 0.350806i | 0.509603 | − | 0.860409i | \(-0.329792\pi\) |
−0.860409 | + | 0.509603i | \(0.829792\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 34.2064i | 1.19236i | 0.802851 | + | 0.596179i | \(0.203315\pi\) | ||||
−0.802851 | + | 0.596179i | \(0.796685\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 31.3455 | + | 31.3455i | 1.08999 | + | 1.08999i | 0.995529 | + | 0.0944595i | \(0.0301123\pi\) |
0.0944595 | + | 0.995529i | \(0.469888\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −3.87895 | + | 3.87895i | −0.134722 | + | 0.134722i | −0.771252 | − | 0.636530i | \(-0.780369\pi\) |
0.636530 | + | 0.771252i | \(0.280369\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −33.2978 | −1.15509 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 30.9849 | 1.07356 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 26.9445 | + | 26.9445i | 0.931338 | + | 0.931338i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 32.9463i | − | 1.13743i | −0.822533 | − | 0.568717i | \(-0.807440\pi\) | ||
0.822533 | − | 0.568717i | \(-0.192560\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 57.5644i | − | 1.98498i | ||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 5.73915 | + | 5.73915i | 0.197667 | + | 0.197667i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 15.9272 | 0.547267 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −4.92309 | −0.168960 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 14.0478 | − | 14.0478i | 0.481553 | − | 0.481553i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.87566 | − | 1.87566i | −0.0642212 | − | 0.0642212i | 0.674267 | − | 0.738488i | \(-0.264460\pi\) |
−0.738488 | + | 0.674267i | \(0.764460\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 23.1714i | − | 0.791521i | −0.918354 | − | 0.395760i | \(-0.870481\pi\) | ||
0.918354 | − | 0.395760i | \(-0.129519\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 10.5073 | + | 10.5073i | 0.358506 | + | 0.358506i | 0.863262 | − | 0.504756i | \(-0.168418\pi\) |
−0.504756 | + | 0.863262i | \(0.668418\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −11.9967 | + | 11.9967i | −0.408846 | + | 0.408846i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 25.2777 | 0.860463 | 0.430231 | − | 0.902719i | \(-0.358432\pi\) | ||||
0.430231 | + | 0.902719i | \(0.358432\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 26.3878 | − | 26.3878i | 0.896177 | − | 0.896177i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 4.94039 | + | 4.94039i | 0.167591 | + | 0.167591i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 23.6073i | 0.799901i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 15.1912i | 0.514144i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 16.7350 | − | 16.7350i | 0.565101 | − | 0.565101i | −0.365651 | − | 0.930752i | \(-0.619154\pi\) |
0.930752 | + | 0.365651i | \(0.119154\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −39.8957 | −1.34565 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 9.38791 | 0.316287 | 0.158143 | − | 0.987416i | \(-0.449449\pi\) | ||||
0.158143 | + | 0.987416i | \(0.449449\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −21.5593 | + | 21.5593i | −0.725527 | + | 0.725527i | −0.969725 | − | 0.244198i | \(-0.921475\pi\) |
0.244198 | + | 0.969725i | \(0.421475\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 48.2072i | 1.61864i | 0.587368 | + | 0.809320i | \(0.300164\pi\) | ||||
−0.587368 | + | 0.809320i | \(0.699836\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.97256i | 0.0661577i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.45016 | − | 2.45016i | −0.0820834 | − | 0.0820834i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 11.6941 | − | 11.6941i | 0.391327 | − | 0.391327i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 27.7830 | 0.927648 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −44.4243 | + | 44.4243i | −1.48163 | + | 1.48163i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 34.4607 | + | 34.4607i | 1.14805 | + | 1.14805i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 19.1008i | 0.635636i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −31.8381 | − | 31.8381i | −1.05717 | − | 1.05717i | −0.998264 | − | 0.0589044i | \(-0.981239\pi\) |
−0.0589044 | − | 0.998264i | \(-0.518761\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0.870707 | − | 0.870707i | 0.0288795 | − | 0.0288795i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −14.8669 | −0.492561 | −0.246281 | − | 0.969199i | \(-0.579209\pi\) | ||||
−0.246281 | + | 0.969199i | \(0.579209\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.38244 | 0.0788472 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1.54197 | − | 1.54197i | −0.0509202 | − | 0.0509202i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 5.27591i | − | 0.174036i | −0.996207 | − | 0.0870181i | \(-0.972266\pi\) | ||
0.996207 | − | 0.0870181i | \(-0.0277338\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 41.4515i | 1.36587i | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −7.59404 | − | 7.59404i | −0.249961 | − | 0.249961i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0.799487 | 0.0262586 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −9.13997 | −0.299873 | −0.149936 | − | 0.988696i | \(-0.547907\pi\) | ||||
−0.149936 | + | 0.988696i | \(0.547907\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 8.36441 | − | 8.36441i | 0.274133 | − | 0.274133i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 5.96229 | + | 5.96229i | 0.195197 | + | 0.195197i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 19.0036i | 0.620819i | 0.950603 | + | 0.310410i | \(0.100466\pi\) | ||||
−0.950603 | + | 0.310410i | \(0.899534\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0.221119 | + | 0.221119i | 0.00721596 | + | 0.00721596i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.48322 | − | 1.48322i | 0.0483517 | − | 0.0483517i | −0.682518 | − | 0.730869i | \(-0.739115\pi\) |
0.730869 | + | 0.682518i | \(0.239115\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 55.4393 | 1.80535 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −3.97577 | + | 3.97577i | −0.129195 | + | 0.129195i | −0.768748 | − | 0.639552i | \(-0.779120\pi\) |
0.639552 | + | 0.768748i | \(0.279120\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.52747 | + | 4.52747i | 0.146968 | + | 0.146968i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 6.68870i | 0.216896i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 16.5970i | − | 0.537628i | −0.963192 | − | 0.268814i | \(-0.913368\pi\) | ||
0.963192 | − | 0.268814i | \(-0.0866317\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 5.79179 | − | 5.79179i | 0.187222 | − | 0.187222i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −5.62092 | −0.181509 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 14.5965 | 0.470855 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 6.02809 | − | 6.02809i | 0.194252 | − | 0.194252i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 8.72635i | 0.280621i | 0.990108 | + | 0.140310i | \(0.0448100\pi\) | ||||
−0.990108 | + | 0.140310i | \(0.955190\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 23.7921i | − | 0.764311i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 14.5421 | + | 14.5421i | 0.466677 | + | 0.466677i | 0.900836 | − | 0.434159i | \(-0.142955\pi\) |
−0.434159 | + | 0.900836i | \(0.642955\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 19.3799 | − | 19.3799i | 0.621289 | − | 0.621289i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −25.2020 | −0.806284 | −0.403142 | − | 0.915137i | \(-0.632082\pi\) | ||||
−0.403142 | + | 0.915137i | \(0.632082\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4.46723 | + | 4.46723i | −0.142773 | + | 0.142773i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.75212 | − | 4.75212i | −0.151724 | − | 0.151724i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 4.00157i | − | 0.127630i | −0.997962 | − | 0.0638151i | \(-0.979673\pi\) | ||
0.997962 | − | 0.0638151i | \(-0.0203268\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 10.3582 | + | 10.3582i | 0.329704 | + | 0.329704i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 44.1346 | − | 44.1346i | 1.40340 | − | 1.40340i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 62.3391 | 1.98027 | 0.990134 | − | 0.140127i | \(-0.0447510\pi\) | ||||
0.990134 | + | 0.140127i | \(0.0447510\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −45.8201 | −1.45406 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −21.6855 | − | 21.6855i | −0.686787 | − | 0.686787i | 0.274733 | − | 0.961521i | \(-0.411410\pi\) |
−0.961521 | + | 0.274733i | \(0.911410\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 15.5861i | 0.493121i |
(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 | 1600.2.l.g.1201.5 | 12 | ||
4.3 | odd | 2 | 400.2.l.f.101.1 | ✓ | 12 | ||
5.2 | odd | 4 | 1600.2.q.e.49.2 | 12 | |||
5.3 | odd | 4 | 1600.2.q.f.49.5 | 12 | |||
5.4 | even | 2 | 1600.2.l.f.1201.2 | 12 | |||
16.3 | odd | 4 | 400.2.l.f.301.1 | yes | 12 | ||
16.13 | even | 4 | inner | 1600.2.l.g.401.5 | 12 | ||
20.3 | even | 4 | 400.2.q.f.149.4 | 12 | |||
20.7 | even | 4 | 400.2.q.e.149.3 | 12 | |||
20.19 | odd | 2 | 400.2.l.g.101.6 | yes | 12 | ||
80.3 | even | 4 | 400.2.q.e.349.3 | 12 | |||
80.13 | odd | 4 | 1600.2.q.e.849.2 | 12 | |||
80.19 | odd | 4 | 400.2.l.g.301.6 | yes | 12 | ||
80.29 | even | 4 | 1600.2.l.f.401.2 | 12 | |||
80.67 | even | 4 | 400.2.q.f.349.4 | 12 | |||
80.77 | odd | 4 | 1600.2.q.f.849.5 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
400.2.l.f.101.1 | ✓ | 12 | 4.3 | odd | 2 | ||
400.2.l.f.301.1 | yes | 12 | 16.3 | odd | 4 | ||
400.2.l.g.101.6 | yes | 12 | 20.19 | odd | 2 | ||
400.2.l.g.301.6 | yes | 12 | 80.19 | odd | 4 | ||
400.2.q.e.149.3 | 12 | 20.7 | even | 4 | |||
400.2.q.e.349.3 | 12 | 80.3 | even | 4 | |||
400.2.q.f.149.4 | 12 | 20.3 | even | 4 | |||
400.2.q.f.349.4 | 12 | 80.67 | even | 4 | |||
1600.2.l.f.401.2 | 12 | 80.29 | even | 4 | |||
1600.2.l.f.1201.2 | 12 | 5.4 | even | 2 | |||
1600.2.l.g.401.5 | 12 | 16.13 | even | 4 | inner | ||
1600.2.l.g.1201.5 | 12 | 1.1 | even | 1 | trivial | ||
1600.2.q.e.49.2 | 12 | 5.2 | odd | 4 | |||
1600.2.q.e.849.2 | 12 | 80.13 | odd | 4 | |||
1600.2.q.f.49.5 | 12 | 5.3 | odd | 4 | |||
1600.2.q.f.849.5 | 12 | 80.77 | odd | 4 |