Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2100,2,Mod(1301,2100)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2100, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2100.1301");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2100.d (of order \(2\), degree \(1\), 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: | \(16.7685844245\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{5})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 3x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 420) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1301.4 | ||
Root | \(1.61803i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2100.1301 |
Dual form | 2100.2.d.g.1301.3 |
$q$-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 \(\left(\mathbb{Z}/2100\mathbb{Z}\right)^\times\).
\(n\) | \(701\) | \(1051\) | \(1177\) | \(1501\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.618034 | + | 1.61803i | 0.356822 | + | 0.934172i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.61803 | − | 0.381966i | 0.989524 | − | 0.144370i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.23607 | + | 2.00000i | −0.745356 | + | 0.666667i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.23607i | 1.57873i | 0.613922 | + | 0.789367i | \(0.289591\pi\) | ||||
−0.613922 | + | 0.789367i | \(0.710409\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.23607i | 0.897524i | 0.893651 | + | 0.448762i | \(0.148135\pi\) | ||||
−0.893651 | + | 0.448762i | \(0.851865\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.47214 | 1.08465 | 0.542326 | − | 0.840168i | \(-0.317544\pi\) | ||||
0.542326 | + | 0.840168i | \(0.317544\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.76393i | 0.634089i | 0.948411 | + | 0.317045i | \(0.102691\pi\) | ||||
−0.948411 | + | 0.317045i | \(0.897309\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.23607 | + | 4.00000i | 0.487950 | + | 0.872872i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 5.70820i | − | 1.19024i | −0.803636 | − | 0.595121i | \(-0.797104\pi\) | ||
0.803636 | − | 0.595121i | \(-0.202896\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.61803 | − | 2.38197i | −0.888741 | − | 0.458410i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 4.00000i | − | 0.742781i | −0.928477 | − | 0.371391i | \(-0.878881\pi\) | ||
0.928477 | − | 0.371391i | \(-0.121119\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.23607i | 0.222004i | 0.993820 | + | 0.111002i | \(0.0354061\pi\) | ||||
−0.993820 | + | 0.111002i | \(0.964594\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −8.47214 | + | 3.23607i | −1.47481 | + | 0.563327i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.47214 | 0.735215 | 0.367607 | − | 0.929981i | \(-0.380177\pi\) | ||||
0.367607 | + | 0.929981i | \(0.380177\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −5.23607 | + | 2.00000i | −0.838442 | + | 0.320256i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −12.4721 | −1.94782 | −0.973910 | − | 0.226934i | \(-0.927130\pi\) | ||||
−0.973910 | + | 0.226934i | \(0.927130\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.76393 | 0.421496 | 0.210748 | − | 0.977540i | \(-0.432410\pi\) | ||||
0.210748 | + | 0.977540i | \(0.432410\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.23607 | −0.180299 | −0.0901495 | − | 0.995928i | \(-0.528734\pi\) | ||||
−0.0901495 | + | 0.995928i | \(0.528734\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.70820 | − | 2.00000i | 0.958315 | − | 0.285714i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.76393 | + | 7.23607i | 0.387028 | + | 1.01325i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.76393i | 0.654376i | 0.944959 | + | 0.327188i | \(0.106101\pi\) | ||||
−0.944959 | + | 0.327188i | \(0.893899\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −4.47214 | + | 1.70820i | −0.592349 | + | 0.226257i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −8.94427 | −1.16445 | −0.582223 | − | 0.813029i | \(-0.697817\pi\) | ||||
−0.582223 | + | 0.813029i | \(0.697817\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 12.9443i | 1.65734i | 0.559734 | + | 0.828672i | \(0.310903\pi\) | ||||
−0.559734 | + | 0.828672i | \(0.689097\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −5.09017 | + | 6.09017i | −0.641301 | + | 0.767289i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.70820 | 0.453029 | 0.226515 | − | 0.974008i | \(-0.427267\pi\) | ||||
0.226515 | + | 0.974008i | \(0.427267\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 9.23607 | − | 3.52786i | 1.11189 | − | 0.424705i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 10.1803i | − | 1.20818i | −0.796915 | − | 0.604092i | \(-0.793536\pi\) | ||
0.796915 | − | 0.604092i | \(-0.206464\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 11.2361i | 1.31508i | 0.753419 | + | 0.657541i | \(0.228403\pi\) | ||||
−0.753419 | + | 0.657541i | \(0.771597\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.00000 | + | 13.7082i | 0.227921 | + | 1.56219i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.52786 | 0.171898 | 0.0859491 | − | 0.996300i | \(-0.472608\pi\) | ||||
0.0859491 | + | 0.996300i | \(0.472608\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | − | 8.94427i | 0.111111 | − | 0.993808i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.76393 | 0.303381 | 0.151690 | − | 0.988428i | \(-0.451528\pi\) | ||||
0.151690 | + | 0.988428i | \(0.451528\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 6.47214 | − | 2.47214i | 0.693886 | − | 0.265041i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3.52786 | −0.373953 | −0.186976 | − | 0.982364i | \(-0.559869\pi\) | ||||
−0.186976 | + | 0.982364i | \(0.559869\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.23607 | + | 8.47214i | 0.129575 | + | 0.888121i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.00000 | + | 0.763932i | −0.207390 | + | 0.0792161i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 8.18034i | − | 0.830588i | −0.909687 | − | 0.415294i | \(-0.863679\pi\) | ||
0.909687 | − | 0.415294i | \(-0.136321\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −10.4721 | − | 11.7082i | −1.05249 | − | 1.17672i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 10.9443 | 1.08900 | 0.544498 | − | 0.838762i | \(-0.316720\pi\) | ||||
0.544498 | + | 0.838762i | \(0.316720\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 15.2361i | 1.50125i | 0.660726 | + | 0.750627i | \(0.270249\pi\) | ||||
−0.660726 | + | 0.750627i | \(0.729751\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 13.7082i | − | 1.32522i | −0.748964 | − | 0.662611i | \(-0.769448\pi\) | ||
0.748964 | − | 0.662611i | \(-0.230552\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 14.9443 | 1.43140 | 0.715701 | − | 0.698407i | \(-0.246107\pi\) | ||||
0.715701 | + | 0.698407i | \(0.246107\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.76393 | + | 7.23607i | 0.262341 | + | 0.686817i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 12.7639i | 1.20073i | 0.799726 | + | 0.600365i | \(0.204978\pi\) | ||||
−0.799726 | + | 0.600365i | \(0.795022\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −6.47214 | − | 7.23607i | −0.598349 | − | 0.668975i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 11.7082 | − | 1.70820i | 1.07329 | − | 0.156591i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −16.4164 | −1.49240 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −7.70820 | − | 20.1803i | −0.695025 | − | 1.81960i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −19.1246 | −1.69703 | −0.848517 | − | 0.529167i | \(-0.822504\pi\) | ||||
−0.848517 | + | 0.529167i | \(0.822504\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.70820 | + | 4.47214i | 0.150399 | + | 0.393750i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −11.4164 | −0.997456 | −0.498728 | − | 0.866758i | \(-0.666199\pi\) | ||||
−0.498728 | + | 0.866758i | \(0.666199\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.05573 | + | 7.23607i | 0.0915432 | + | 0.627447i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.23607i | 0.276476i | 0.990399 | + | 0.138238i | \(0.0441439\pi\) | ||||
−0.990399 | + | 0.138238i | \(0.955856\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 10.7639i | 0.912985i | 0.889727 | + | 0.456492i | \(0.150894\pi\) | ||||
−0.889727 | + | 0.456492i | \(0.849106\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.763932 | − | 2.00000i | −0.0643347 | − | 0.168430i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −16.9443 | −1.41695 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 7.38197 | + | 9.61803i | 0.608854 | + | 0.793282i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 11.4164i | 0.935269i | 0.883922 | + | 0.467634i | \(0.154894\pi\) | ||||
−0.883922 | + | 0.467634i | \(0.845106\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.94427 | −0.727875 | −0.363937 | − | 0.931423i | \(-0.618568\pi\) | ||||
−0.363937 | + | 0.931423i | \(0.618568\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −10.0000 | + | 8.94427i | −0.808452 | + | 0.723102i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 24.1803i | − | 1.92980i | −0.262615 | − | 0.964901i | \(-0.584585\pi\) | ||
0.262615 | − | 0.964901i | \(-0.415415\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −7.70820 | + | 2.94427i | −0.611300 | + | 0.233496i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.18034 | − | 14.9443i | −0.171835 | − | 1.17777i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 12.6525 | 0.991018 | 0.495509 | − | 0.868603i | \(-0.334981\pi\) | ||||
0.495509 | + | 0.868603i | \(0.334981\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 13.2361 | 1.02424 | 0.512119 | − | 0.858915i | \(-0.328861\pi\) | ||||
0.512119 | + | 0.858915i | \(0.328861\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.52786 | 0.194451 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5.52786 | − | 6.18034i | −0.422726 | − | 0.472622i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2.00000 | −0.152057 | −0.0760286 | − | 0.997106i | \(-0.524224\pi\) | ||||
−0.0760286 | + | 0.997106i | \(0.524224\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −5.52786 | − | 14.4721i | −0.415500 | − | 1.08779i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 17.2361i | 1.28828i | 0.764906 | + | 0.644142i | \(0.222785\pi\) | ||||
−0.764906 | + | 0.644142i | \(0.777215\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 2.47214i | − | 0.183752i | −0.995770 | − | 0.0918762i | \(-0.970714\pi\) | ||
0.995770 | − | 0.0918762i | \(-0.0292864\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −20.9443 | + | 8.00000i | −1.54825 | + | 0.591377i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 23.4164i | 1.71238i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −13.0000 | − | 4.47214i | −0.945611 | − | 0.325300i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.76393i | 0.199991i | 0.994988 | + | 0.0999956i | \(0.0318829\pi\) | ||||
−0.994988 | + | 0.0999956i | \(0.968117\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.00000 | 0.431889 | 0.215945 | − | 0.976406i | \(-0.430717\pi\) | ||||
0.215945 | + | 0.976406i | \(0.430717\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 20.7639i | − | 1.47937i | −0.672954 | − | 0.739684i | \(-0.734975\pi\) | ||
0.672954 | − | 0.739684i | \(-0.265025\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 13.2361i | 0.938280i | 0.883124 | + | 0.469140i | \(0.155436\pi\) | ||||
−0.883124 | + | 0.469140i | \(0.844564\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.29180 | + | 6.00000i | 0.161651 | + | 0.423207i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.52786 | − | 10.4721i | −0.107235 | − | 0.735000i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 11.4164 | + | 12.7639i | 0.793495 | + | 0.887155i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −14.4721 | −1.00106 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.00000 | −0.550743 | −0.275371 | − | 0.961338i | \(-0.588801\pi\) | ||||
−0.275371 | + | 0.961338i | \(0.588801\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 16.4721 | − | 6.29180i | 1.12865 | − | 0.431107i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.472136 | + | 3.23607i | 0.0320507 | + | 0.219679i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −18.1803 | + | 6.94427i | −1.22851 | + | 0.469250i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 14.4721i | 0.973501i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 1.70820i | − | 0.114390i | −0.998363 | − | 0.0571949i | \(-0.981784\pi\) | ||
0.998363 | − | 0.0571949i | \(-0.0182156\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −18.7639 | −1.24541 | −0.622703 | − | 0.782458i | \(-0.713965\pi\) | ||||
−0.622703 | + | 0.782458i | \(0.713965\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 21.8885i | − | 1.44644i | −0.690620 | − | 0.723218i | \(-0.742662\pi\) | ||
0.690620 | − | 0.723218i | \(-0.257338\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −20.9443 | + | 11.7082i | −1.37803 | + | 0.770343i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 24.1803i | − | 1.58411i | −0.610452 | − | 0.792053i | \(-0.709012\pi\) | ||
0.610452 | − | 0.792053i | \(-0.290988\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0.944272 | + | 2.47214i | 0.0613371 | + | 0.160582i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 22.1803i | − | 1.43473i | −0.696699 | − | 0.717363i | \(-0.745349\pi\) | ||
0.696699 | − | 0.717363i | \(-0.254651\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 28.3607i | − | 1.82687i | −0.406982 | − | 0.913436i | \(-0.633419\pi\) | ||
0.406982 | − | 0.913436i | \(-0.366581\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 15.0902 | − | 3.90983i | 0.968035 | − | 0.250816i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −8.94427 | −0.569110 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.70820 | + | 4.47214i | 0.108253 | + | 0.283410i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 24.3607 | 1.53763 | 0.768816 | − | 0.639470i | \(-0.220846\pi\) | ||||
0.768816 | + | 0.639470i | \(0.220846\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 29.8885 | 1.87908 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 7.52786 | 0.469575 | 0.234788 | − | 0.972047i | \(-0.424561\pi\) | ||||
0.234788 | + | 0.972047i | \(0.424561\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 11.7082 | − | 1.70820i | 0.727512 | − | 0.106143i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 8.00000 | + | 8.94427i | 0.495188 | + | 0.553637i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0.180340i | 0.0111202i | 0.999985 | + | 0.00556012i | \(0.00176985\pi\) | ||||
−0.999985 | + | 0.00556012i | \(0.998230\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2.18034 | − | 5.70820i | −0.133435 | − | 0.349336i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 28.4721 | 1.73598 | 0.867988 | − | 0.496584i | \(-0.165413\pi\) | ||||
0.867988 | + | 0.496584i | \(0.165413\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 19.1246i | 1.16174i | 0.813997 | + | 0.580869i | \(0.197287\pi\) | ||||
−0.813997 | + | 0.580869i | \(0.802713\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −12.9443 | + | 7.23607i | −0.783423 | + | 0.437947i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 25.4164 | 1.52712 | 0.763562 | − | 0.645735i | \(-0.223449\pi\) | ||||
0.763562 | + | 0.645735i | \(0.223449\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2.47214 | − | 2.76393i | −0.148003 | − | 0.165472i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 15.4164i | 0.919666i | 0.888005 | + | 0.459833i | \(0.152091\pi\) | ||||
−0.888005 | + | 0.459833i | \(0.847909\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 22.6525i | − | 1.34655i | −0.739392 | − | 0.673275i | \(-0.764887\pi\) | ||
0.739392 | − | 0.673275i | \(-0.235113\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −32.6525 | + | 4.76393i | −1.92741 | + | 0.281206i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.00000 | 0.176471 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 13.2361 | − | 5.05573i | 0.775912 | − | 0.296372i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 14.0000 | 0.817889 | 0.408944 | − | 0.912559i | \(-0.365897\pi\) | ||||
0.408944 | + | 0.912559i | \(0.365897\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 12.4721 | − | 24.1803i | 0.723707 | − | 1.40309i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 18.4721 | 1.06827 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 7.23607 | − | 1.05573i | 0.417080 | − | 0.0608512i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 6.76393 | + | 17.7082i | 0.388578 | + | 1.01731i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4.18034i | 0.238585i | 0.992859 | + | 0.119292i | \(0.0380626\pi\) | ||||
−0.992859 | + | 0.119292i | \(0.961937\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −24.6525 | + | 9.41641i | −1.40243 | + | 0.535681i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 12.3607 | 0.700910 | 0.350455 | − | 0.936580i | \(-0.386027\pi\) | ||||
0.350455 | + | 0.936580i | \(0.386027\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 17.7082i | − | 1.00093i | −0.865758 | − | 0.500463i | \(-0.833163\pi\) | ||
0.865758 | − | 0.500463i | \(-0.166837\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 16.1803i | 0.908778i | 0.890803 | + | 0.454389i | \(0.150142\pi\) | ||||
−0.890803 | + | 0.454389i | \(0.849858\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 20.9443 | 1.17265 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 22.1803 | − | 8.47214i | 1.23799 | − | 0.472869i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 12.3607i | 0.687767i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 9.23607 | + | 24.1803i | 0.510756 | + | 1.33718i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3.23607 | + | 0.472136i | −0.178410 | + | 0.0260297i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.05573 | −0.167958 | −0.0839790 | − | 0.996468i | \(-0.526763\pi\) | ||||
−0.0839790 | + | 0.996468i | \(0.526763\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −10.0000 | + | 8.94427i | −0.547997 | + | 0.490143i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.00000 | −0.108947 | −0.0544735 | − | 0.998515i | \(-0.517348\pi\) | ||||
−0.0544735 | + | 0.998515i | \(0.517348\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −20.6525 | + | 7.88854i | −1.12169 | + | 0.428447i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −6.47214 | −0.350486 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 16.7984 | − | 7.79837i | 0.907027 | − | 0.421073i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.34752i | 0.0723389i | 0.999346 | + | 0.0361694i | \(0.0115156\pi\) | ||||
−0.999346 | + | 0.0361694i | \(0.988484\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 8.94427i | − | 0.478776i | −0.970924 | − | 0.239388i | \(-0.923053\pi\) | ||
0.970924 | − | 0.239388i | \(-0.0769468\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 7.70820 | − | 14.9443i | 0.411433 | − | 0.797666i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.41641 | 0.0753878 | 0.0376939 | − | 0.999289i | \(-0.487999\pi\) | ||||
0.0376939 | + | 0.999289i | \(0.487999\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 10.0000 | + | 17.8885i | 0.529256 | + | 0.946762i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 24.0689i | − | 1.27031i | −0.772386 | − | 0.635154i | \(-0.780937\pi\) | ||
0.772386 | − | 0.635154i | \(-0.219063\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 11.3607 | 0.597931 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −10.1459 | − | 26.5623i | −0.532522 | − | 1.39416i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 6.65248i | − | 0.347256i | −0.984811 | − | 0.173628i | \(-0.944451\pi\) | ||
0.984811 | − | 0.173628i | \(-0.0555491\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 27.8885 | − | 24.9443i | 1.45182 | − | 1.29855i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.81966 | + | 12.4721i | 0.0944720 | + | 0.647521i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −16.4721 | −0.852895 | −0.426447 | − | 0.904512i | \(-0.640235\pi\) | ||||
−0.426447 | + | 0.904512i | \(0.640235\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 12.9443 | 0.666664 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10.4721 | 0.537917 | 0.268959 | − | 0.963152i | \(-0.413320\pi\) | ||||
0.268959 | + | 0.963152i | \(0.413320\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −11.8197 | − | 30.9443i | −0.605540 | − | 1.58532i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 10.7639 | 0.550011 | 0.275006 | − | 0.961443i | \(-0.411320\pi\) | ||||
0.275006 | + | 0.961443i | \(0.411320\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −6.18034 | + | 5.52786i | −0.314164 | + | 0.280997i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 6.47214i | − | 0.328150i | −0.986448 | − | 0.164075i | \(-0.947536\pi\) | ||
0.986448 | − | 0.164075i | \(-0.0524640\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 25.5279i | − | 1.29100i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −7.05573 | − | 18.4721i | −0.355914 | − | 0.931796i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 9.70820i | 0.487241i | 0.969871 | + | 0.243620i | \(0.0783351\pi\) | ||||
−0.969871 | + | 0.243620i | \(0.921665\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −11.0557 | + | 6.18034i | −0.553479 | + | 0.309404i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 11.0557i | − | 0.552097i | −0.961144 | − | 0.276048i | \(-0.910975\pi\) | ||
0.961144 | − | 0.276048i | \(-0.0890250\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.00000 | −0.199254 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 23.4164i | 1.16071i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 12.0000i | 0.593362i | 0.954977 | + | 0.296681i | \(0.0958798\pi\) | ||||
−0.954977 | + | 0.296681i | \(0.904120\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −5.23607 | + | 2.00000i | −0.258276 | + | 0.0986527i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −23.4164 | + | 3.41641i | −1.15225 | + | 0.168110i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −17.4164 | + | 6.65248i | −0.852885 | + | 0.325773i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −28.0000 | −1.36789 | −0.683945 | − | 0.729534i | \(-0.739737\pi\) | ||||
−0.683945 | + | 0.729534i | \(0.739737\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 23.5279 | 1.14668 | 0.573339 | − | 0.819318i | \(-0.305648\pi\) | ||||
0.573339 | + | 0.819318i | \(0.305648\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2.76393 | − | 2.47214i | 0.134387 | − | 0.120199i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.94427 | + | 33.8885i | 0.239270 | + | 1.63998i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −10.4721 | − | 27.4164i | −0.505599 | − | 1.32368i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 5.23607i | − | 0.252213i | −0.992017 | − | 0.126106i | \(-0.959752\pi\) | ||
0.992017 | − | 0.126106i | \(-0.0402480\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.34752i | 0.0647579i | 0.999476 | + | 0.0323789i | \(0.0103083\pi\) | ||||
−0.999476 | + | 0.0323789i | \(0.989692\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 15.7771 | 0.754720 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 18.1803i | 0.867700i | 0.900985 | + | 0.433850i | \(0.142845\pi\) | ||||
−0.900985 | + | 0.433850i | \(0.857155\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −11.0000 | + | 17.8885i | −0.523810 | + | 0.851835i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 34.0689i | 1.61866i | 0.587353 | + | 0.809331i | \(0.300170\pi\) | ||||
−0.587353 | + | 0.809331i | \(0.699830\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −18.4721 | + | 7.05573i | −0.873702 | + | 0.333724i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 5.88854i | 0.277898i | 0.990300 | + | 0.138949i | \(0.0443723\pi\) | ||||
−0.990300 | + | 0.138949i | \(0.955628\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 65.3050i | − | 3.07509i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −5.52786 | − | 14.4721i | −0.259722 | − | 0.679960i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 26.9443 | 1.26040 | 0.630200 | − | 0.776433i | \(-0.282973\pi\) | ||||
0.630200 | + | 0.776433i | \(0.282973\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −20.6525 | − | 10.6525i | −0.963975 | − | 0.497215i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −15.5279 | −0.723205 | −0.361602 | − | 0.932332i | \(-0.617770\pi\) | ||||
−0.361602 | + | 0.932332i | \(0.617770\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 25.2361 | 1.17282 | 0.586410 | − | 0.810015i | \(-0.300541\pi\) | ||||
0.586410 | + | 0.810015i | \(0.300541\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −30.5410 | −1.41327 | −0.706635 | − | 0.707578i | \(-0.749788\pi\) | ||||
−0.706635 | + | 0.707578i | \(0.749788\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 9.70820 | − | 1.41641i | 0.448283 | − | 0.0654036i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 39.1246 | − | 14.9443i | 1.80277 | − | 0.688596i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 14.4721i | 0.665430i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −9.52786 | − | 10.6525i | −0.436251 | − | 0.487743i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −4.94427 | −0.225910 | −0.112955 | − | 0.993600i | \(-0.536032\pi\) | ||||
−0.112955 | + | 0.993600i | \(0.536032\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 14.4721i | 0.659873i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 22.8328 | − | 12.7639i | 1.03893 | − | 0.580779i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.23607 | −0.0560116 | −0.0280058 | − | 0.999608i | \(-0.508916\pi\) | ||||
−0.0280058 | + | 0.999608i | \(0.508916\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 7.81966 | + | 20.4721i | 0.353617 | + | 0.925782i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 0.875388i | − | 0.0395057i | −0.999805 | − | 0.0197529i | \(-0.993712\pi\) | ||
0.999805 | − | 0.0197529i | \(-0.00628794\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 17.8885i | − | 0.805659i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −3.88854 | − | 26.6525i | −0.174425 | − | 1.19553i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 28.3607 | 1.26960 | 0.634799 | − | 0.772677i | \(-0.281083\pi\) | ||||
0.634799 | + | 0.772677i | \(0.281083\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 8.18034 | + | 21.4164i | 0.365471 | + | 0.956815i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 12.6525 | 0.564146 | 0.282073 | − | 0.959393i | \(-0.408978\pi\) | ||||
0.282073 | + | 0.959393i | \(0.408978\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.56231 | + | 4.09017i | 0.0693844 | + | 0.181651i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −5.05573 | −0.224091 | −0.112046 | − | 0.993703i | \(-0.535740\pi\) | ||||
−0.112046 | + | 0.993703i | \(0.535740\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.29180 | + | 29.4164i | 0.189858 | + | 1.30131i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 6.58359 | − | 12.7639i | 0.290673 | − | 0.563541i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 6.47214i | − | 0.284644i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.23607 | − | 3.23607i | −0.0542574 | − | 0.142048i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 27.8885 | 1.22182 | 0.610910 | − | 0.791700i | \(-0.290804\pi\) | ||||
0.610910 | + | 0.791700i | \(0.290804\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 21.7082i | − | 0.949233i | −0.880193 | − | 0.474617i | \(-0.842587\pi\) | ||
0.880193 | − | 0.474617i | \(-0.157413\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 5.52786i | 0.240798i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9.58359 | −0.416678 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 20.0000 | − | 17.8885i | 0.867926 | − | 0.776297i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 40.3607i | − | 1.74822i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −27.8885 | + | 10.6525i | −1.20348 | + | 0.459688i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 10.4721 | + | 35.1246i | 0.451067 | + | 1.51292i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8.11146 | −0.348739 | −0.174369 | − | 0.984680i | \(-0.555789\pi\) | ||||
−0.174369 | + | 0.984680i | \(0.555789\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 4.00000 | − | 1.52786i | 0.171656 | − | 0.0655669i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −4.29180 | −0.183504 | −0.0917520 | − | 0.995782i | \(-0.529247\pi\) | ||||
−0.0917520 | + | 0.995782i | \(0.529247\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −25.8885 | − | 28.9443i | −1.10490 | − | 1.23531i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 11.0557 | 0.470990 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.00000 | − | 0.583592i | 0.170097 | − | 0.0248169i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 8.18034i | 0.346612i | 0.984868 | + | 0.173306i | \(0.0554450\pi\) | ||||
−0.984868 | + | 0.173306i | \(0.944555\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8.94427i | 0.378302i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −37.8885 | + | 14.4721i | −1.59966 | + | 0.611014i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 40.0689 | 1.68870 | 0.844351 | − | 0.535790i | \(-0.179986\pi\) | ||||
0.844351 | + | 0.535790i | \(0.179986\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −0.798374 | − | 23.7984i | −0.0335286 | − | 0.999438i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 13.8885i | 0.582238i | 0.956687 | + | 0.291119i | \(0.0940276\pi\) | ||||
−0.956687 | + | 0.291119i | \(0.905972\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −46.8328 | −1.95989 | −0.979946 | − | 0.199262i | \(-0.936145\pi\) | ||||
−0.979946 | + | 0.199262i | \(0.936145\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −4.47214 | + | 1.70820i | −0.186826 | + | 0.0713612i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 26.0689i | − | 1.08526i | −0.839971 | − | 0.542631i | \(-0.817428\pi\) | ||
0.839971 | − | 0.542631i | \(-0.182572\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 3.70820 | + | 9.70820i | 0.154108 | + | 0.403459i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 7.23607 | − | 1.05573i | 0.300203 | − | 0.0437990i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −24.9443 | −1.03309 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 19.7082 | 0.813445 | 0.406722 | − | 0.913552i | \(-0.366672\pi\) | ||||
0.406722 | + | 0.913552i | \(0.366672\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.41641 | −0.140771 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 33.5967 | − | 12.8328i | 1.38199 | − | 0.527872i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 28.4721 | 1.16921 | 0.584605 | − | 0.811318i | \(-0.301249\pi\) | ||||
0.584605 | + | 0.811318i | \(0.301249\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −21.4164 | + | 8.18034i | −0.876515 | + | 0.334799i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0.652476i | 0.0266594i | 0.999911 | + | 0.0133297i | \(0.00424311\pi\) | ||||
−0.999911 | + | 0.0133297i | \(0.995757\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 17.3050i | − | 0.705884i | −0.935645 | − | 0.352942i | \(-0.885181\pi\) | ||
0.935645 | − | 0.352942i | \(-0.114819\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −8.29180 | + | 7.41641i | −0.337668 | + | 0.302019i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 18.0689i | 0.733393i | 0.930341 | + | 0.366697i | \(0.119511\pi\) | ||||
−0.930341 | + | 0.366697i | \(0.880489\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 16.0000 | − | 8.94427i | 0.648353 | − | 0.362440i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 4.00000i | − | 0.161823i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 22.3607 | 0.903139 | 0.451570 | − | 0.892236i | \(-0.350864\pi\) | ||||
0.451570 | + | 0.892236i | \(0.350864\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 40.5410i | − | 1.63212i | −0.577967 | − | 0.816060i | \(-0.696154\pi\) | ||
0.577967 | − | 0.816060i | \(-0.303846\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 7.70820i | 0.309819i | 0.987929 | + | 0.154909i | \(0.0495086\pi\) | ||||
−0.987929 | + | 0.154909i | \(0.950491\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −13.5967 | + | 26.3607i | −0.545619 | + | 1.05782i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −9.23607 | + | 1.34752i | −0.370035 | + | 0.0539874i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −8.94427 | − | 23.4164i | −0.357200 | − | 0.935161i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 20.0000 | 0.797452 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −8.94427 | −0.356066 | −0.178033 | − | 0.984025i | \(-0.556973\pi\) | ||||
−0.178033 | + | 0.984025i | \(0.556973\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −4.94427 | − | 12.9443i | −0.196517 | − | 0.514489i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.47214 | + | 21.7082i | 0.256435 | + | 0.860110i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 20.3607 | + | 22.7639i | 0.805456 | + | 0.900527i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 39.4164i | − | 1.55685i | −0.627735 | − | 0.778427i | \(-0.716018\pi\) | ||
0.627735 | − | 0.778427i | \(-0.283982\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 37.7082i | − | 1.48707i | −0.668699 | − | 0.743533i | \(-0.733149\pi\) | ||
0.668699 | − | 0.743533i | \(-0.266851\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 31.1246 | 1.22363 | 0.611817 | − | 0.790999i | \(-0.290439\pi\) | ||||
0.611817 | + | 0.790999i | \(0.290439\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 46.8328i | − | 1.83835i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −4.94427 | + | 2.76393i | −0.193781 | + | 0.108327i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 27.5967i | 1.07994i | 0.841683 | + | 0.539972i | \(0.181565\pi\) | ||||
−0.841683 | + | 0.539972i | \(0.818435\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −22.4721 | − | 25.1246i | −0.876722 | − | 0.980204i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 41.2361i | 1.60633i | 0.595757 | + | 0.803165i | \(0.296852\pi\) | ||||
−0.595757 | + | 0.803165i | \(0.703148\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 30.8328i | − | 1.19926i | −0.800278 | − | 0.599629i | \(-0.795315\pi\) | ||
0.800278 | − | 0.599629i | \(-0.204685\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −23.4164 | + | 8.94427i | −0.909418 | + | 0.347367i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −22.8328 | −0.884090 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 2.76393 | − | 1.05573i | 0.106860 | − | 0.0408168i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −67.7771 | −2.61651 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.94427 | 0.113493 | 0.0567467 | − | 0.998389i | \(-0.481927\pi\) | ||||
0.0567467 | + | 0.998389i | \(0.481927\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 6.00000 | 0.230599 | 0.115299 | − | 0.993331i | \(-0.463217\pi\) | ||||
0.115299 | + | 0.993331i | \(0.463217\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3.12461 | − | 21.4164i | −0.119912 | − | 0.821886i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −11.5967 | − | 30.3607i | −0.444388 | − | 1.16342i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 33.7082i | − | 1.28981i | −0.764263 | − | 0.644904i | \(-0.776897\pi\) | ||
0.764263 | − | 0.644904i | \(-0.223103\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 35.4164 | − | 13.5279i | 1.35122 | − | 0.516120i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −15.4164 | −0.587318 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 14.1803i | − | 0.539446i | −0.962938 | − | 0.269723i | \(-0.913068\pi\) | ||
0.962938 | − | 0.269723i | \(-0.0869321\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −31.8885 | − | 26.6525i | −1.21135 | − | 1.01244i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −55.7771 | −2.11271 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 39.1246 | − | 14.9443i | 1.47983 | − | 0.565244i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 20.9443i | 0.791054i | 0.918454 | + | 0.395527i | \(0.129438\pi\) | ||||
−0.918454 | + | 0.395527i | \(0.870562\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 12.3607i | 0.466192i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 28.6525 | − | 4.18034i | 1.07759 | − | 0.157218i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −5.05573 | −0.189872 | −0.0949359 | − | 0.995483i | \(-0.530265\pi\) | ||||
−0.0949359 | + | 0.995483i | \(0.530265\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3.41641 | + | 3.05573i | −0.128125 | + | 0.114599i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 7.05573 | 0.264239 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 35.8885 | − | 13.7082i | 1.34028 | − | 0.511942i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −41.8885 | −1.56218 | −0.781090 | − | 0.624419i | \(-0.785336\pi\) | ||||
−0.781090 | + | 0.624419i | \(0.785336\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.81966 | + | 39.8885i | 0.216735 | + | 1.48553i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 45.8885 | − | 17.5279i | 1.70661 | − | 0.651868i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 9.70820i | − | 0.360057i | −0.983661 | − | 0.180029i | \(-0.942381\pi\) | ||
0.983661 | − | 0.180029i | \(-0.0576191\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 15.6525 | + | 22.0000i | 0.579721 | + | 0.814815i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 12.3607 | 0.457176 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 17.3475i | 0.640745i | 0.947292 | + | 0.320373i | \(0.103808\pi\) | ||||
−0.947292 | + | 0.320373i | \(0.896192\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 19.4164i | 0.715213i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −4.36068 | −0.160410 | −0.0802051 | − | 0.996778i | \(-0.525558\pi\) | ||||
−0.0802051 | + | 0.996778i | \(0.525558\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −5.52786 | − | 14.4721i | −0.203071 | − | 0.531647i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 6.65248i | − | 0.244056i | −0.992527 | − | 0.122028i | \(-0.961060\pi\) | ||
0.992527 | − | 0.122028i | \(-0.0389397\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −6.18034 | + | 5.52786i | −0.226127 | + | 0.202254i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −5.23607 | − | 35.8885i | −0.191322 | − | 1.31134i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −44.0000 | −1.60558 | −0.802791 | − | 0.596260i | \(-0.796653\pi\) | ||||
−0.802791 | + | 0.596260i | \(0.796653\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 15.0557 | + | 39.4164i | 0.548661 | + | 1.43641i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 27.3050 | 0.992415 | 0.496208 | − | 0.868204i | \(-0.334725\pi\) | ||||
0.496208 | + | 0.868204i | \(0.334725\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 18.4721 | + | 48.3607i | 0.670496 | + | 1.75538i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −31.3050 | −1.13480 | −0.567402 | − | 0.823441i | \(-0.692051\pi\) | ||||
−0.567402 | + | 0.823441i | \(0.692051\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 39.1246 | − | 5.70820i | 1.41641 | − | 0.206651i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 28.9443i | − | 1.04512i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 4.58359i | − | 0.165289i | −0.996579 | − | 0.0826443i | \(-0.973663\pi\) | ||
0.996579 | − | 0.0826443i | \(-0.0263365\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4.65248 | + | 12.1803i | 0.167555 | + | 0.438664i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −18.0000 | −0.647415 | −0.323708 | − | 0.946157i | \(-0.604929\pi\) | ||||
−0.323708 | + | 0.946157i | \(0.604929\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 10.0000 | + | 17.8885i | 0.358748 | + | 0.641748i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 34.4721i | − | 1.23509i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 53.3050 | 1.90740 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −9.52786 | + | 18.4721i | −0.340498 | + | 0.660140i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 29.7082i | − | 1.05898i | −0.848315 | − | 0.529492i | \(-0.822383\pi\) | ||
0.848315 | − | 0.529492i | \(-0.177617\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −0.291796 | + | 0.111456i | −0.0103882 | + | 0.00396795i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 4.87539 | + | 33.4164i | 0.173349 | + | 1.18815i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −41.8885 | −1.48751 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −24.8328 | −0.879623 | −0.439812 | − | 0.898090i | \(-0.644955\pi\) | ||||
−0.439812 | + | 0.898090i | \(0.644955\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5.52786 | −0.195562 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 7.88854 | − | 7.05573i | 0.278728 | − | 0.249302i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −58.8328 | −2.07616 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 17.5967 | + | 46.0689i | 0.619435 | + | 1.62170i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 32.3607i | − | 1.13774i | −0.822427 | − | 0.568870i | \(-0.807381\pi\) | ||
0.822427 | − | 0.568870i | \(-0.192619\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 11.7082i | 0.411131i | 0.978643 | + | 0.205565i | \(0.0659033\pi\) | ||||
−0.978643 | + | 0.205565i | \(0.934097\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −30.9443 | + | 11.8197i | −1.08526 | + | 0.414534i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 7.63932i | 0.267266i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −19.7082 | − | 16.4721i | −0.688660 | − | 0.575583i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 6.83282i | − | 0.238467i | −0.992866 | − | 0.119233i | \(-0.961956\pi\) | ||
0.992866 | − | 0.119233i | \(-0.0380437\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −37.5967 | −1.31054 | −0.655270 | − | 0.755395i | \(-0.727445\pi\) | ||||
−0.655270 | + | 0.755395i | \(0.727445\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 26.2918i | 0.914255i | 0.889401 | + | 0.457128i | \(0.151122\pi\) | ||||
−0.889401 | + | 0.457128i | \(0.848878\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 24.3607i | 0.846081i | 0.906111 | + | 0.423041i | \(0.139037\pi\) | ||||
−0.906111 | + | 0.423041i | \(0.860963\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 15.7082 | + | 41.1246i | 0.544912 | + | 1.42660i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 30.0000 | − | 8.94427i | 1.03944 | − | 0.309901i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.94427 | − | 5.70820i | 0.101769 | − | 0.197304i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 4.94427 | 0.170695 | 0.0853476 | − | 0.996351i | \(-0.472800\pi\) | ||||
0.0853476 | + | 0.996351i | \(0.472800\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 13.0000 | 0.448276 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −24.9443 | + | 9.52786i | −0.859126 | + | 0.328157i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −42.9787 | + | 6.27051i | −1.47677 | + | 0.215457i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 36.6525 | − | 14.0000i | 1.25791 | − | 0.480479i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 25.5279i | − | 0.875084i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 21.1246i | 0.723293i | 0.932315 | + | 0.361646i | \(0.117785\pi\) | ||||
−0.932315 | + | 0.361646i | \(0.882215\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −19.5279 | −0.667059 | −0.333530 | − | 0.942740i | \(-0.608240\pi\) | ||||
−0.333530 | + | 0.942740i | \(0.608240\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 44.6525i | 1.52352i | 0.647858 | + | 0.761761i | \(0.275665\pi\) | ||||
−0.647858 | + | 0.761761i | \(0.724335\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −27.8885 | − | 49.8885i | −0.950439 | − | 1.70020i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 21.3475i | 0.726678i | 0.931657 | + | 0.363339i | \(0.118363\pi\) | ||||
−0.931657 | + | 0.363339i | \(0.881637\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.85410 | + | 4.85410i | 0.0629686 | + | 0.164854i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 8.00000i | 0.271381i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 12.0000i | 0.406604i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 16.3607 | + | 18.2918i | 0.553725 | + | 0.619083i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 23.5279 | 0.794480 | 0.397240 | − | 0.917715i | \(-0.369968\pi\) | ||||
0.397240 | + | 0.917715i | \(0.369968\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 8.65248 | + | 22.6525i | 0.291841 | + | 0.764049i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 36.8328 | 1.24093 | 0.620465 | − | 0.784234i | \(-0.286944\pi\) | ||||
0.620465 | + | 0.784234i | \(0.286944\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −13.5967 | −0.457567 | −0.228783 | − | 0.973477i | \(-0.573475\pi\) | ||||
−0.228783 | + | 0.973477i | \(0.573475\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −6.18034 | −0.207516 | −0.103758 | − | 0.994603i | \(-0.533087\pi\) | ||||
−0.103758 | + | 0.994603i | \(0.533087\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −50.0689 | + | 7.30495i | −1.67926 | + | 0.245000i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 46.8328 | + | 5.23607i | 1.56896 | + | 0.175415i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 3.41641i | − | 0.114326i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 11.4164 | + | 29.8885i | 0.381183 | + | 0.997949i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 4.94427 | 0.164901 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 21.3050i | 0.709771i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 6.18034 | + | 11.0557i | 0.205669 | + | 0.367912i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 22.7639 | 0.755864 | 0.377932 | − | 0.925833i | \(-0.376635\pi\) | ||||
0.377932 | + | 0.925833i | \(0.376635\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −24.4721 | + | 21.8885i | −0.811690 | + | 0.725997i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 12.0689i | − | 0.399860i | −0.979810 | − | 0.199930i | \(-0.935929\pi\) | ||
0.979810 | − | 0.199930i | \(-0.0640715\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 14.4721i | 0.478958i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −29.8885 | + | 4.36068i | −0.987007 | + | 0.144002i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −25.5279 | −0.842087 | −0.421043 | − | 0.907041i | \(-0.638336\pi\) | ||||
−0.421043 | + | 0.907041i | \(0.638336\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −6.76393 | + | 2.58359i | −0.222879 | + | 0.0851323i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 32.9443 | 1.08437 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −30.4721 | − | 34.0689i | −1.00084 | − | 1.11897i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 15.8885 | 0.521286 | 0.260643 | − | 0.965435i | \(-0.416065\pi\) | ||||
0.260643 | + | 0.965435i | \(0.416065\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.52786 | + | 18.5410i | 0.181168 | + | 0.607657i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 7.63932 | + | 20.0000i | 0.250100 | + | 0.654771i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 19.2361i | − | 0.628415i | −0.949354 | − | 0.314207i | \(-0.898261\pi\) | ||
0.949354 | − | 0.314207i | \(-0.101739\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 28.6525 | − | 10.9443i | 0.935038 | − | 0.357153i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 36.2492 | 1.18169 | 0.590845 | − | 0.806785i | \(-0.298794\pi\) | ||||
0.590845 | + | 0.806785i | \(0.298794\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 71.1935i | 2.31838i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 20.7639i | − | 0.674737i | −0.941373 | − | 0.337369i | \(-0.890463\pi\) | ||
0.941373 | − | 0.337369i | \(-0.109537\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −36.3607 | −1.18032 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −26.1803 | + | 10.0000i | −0.848956 | + | 0.324272i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 9.70820i | 0.314480i | 0.987560 | + | 0.157240i | \(0.0502596\pi\) | ||||
−0.987560 | + | 0.157240i | \(0.949740\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 12.9443 | + | 33.8885i | 0.418429 | + | 1.09546i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.23607 | + | 8.47214i | 0.0399147 | + | 0.273580i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 29.4721 | 0.950714 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 27.4164 | + | 30.6525i | 0.883481 | + | 0.987762i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −21.8197 | −0.701673 | −0.350836 | − | 0.936437i | \(-0.614103\pi\) | ||||
−0.350836 | + | 0.936437i | \(0.614103\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −20.0000 | + | 7.63932i | −0.642493 | + | 0.245410i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −27.4164 | −0.879834 | −0.439917 | − | 0.898038i | \(-0.644992\pi\) | ||||
−0.439917 | + | 0.898038i | \(0.644992\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4.11146 | + | 28.1803i | 0.131807 | + | 0.903420i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 43.9574i | 1.40632i | 0.711030 | + | 0.703161i | \(0.248229\pi\) | ||||
−0.711030 | + | 0.703161i | \(0.751771\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 18.4721i | − | 0.590372i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −33.4164 | + | 29.8885i | −1.06690 | + | 0.954268i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −26.5410 | −0.846527 | −0.423264 | − | 0.906007i | \(-0.639116\pi\) | ||||
−0.423264 | + | 0.906007i | \(0.639116\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −2.76393 | − | 4.94427i | −0.0879769 | − | 0.157378i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 15.7771i | − | 0.501682i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −31.7771 | −1.00943 | −0.504716 | − | 0.863285i | \(-0.668403\pi\) | ||||
−0.504716 | + | 0.863285i | \(0.668403\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −1.88854 | − | 4.94427i | −0.0599311 | − | 0.156902i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 42.0689i | − | 1.33233i | −0.745802 | − | 0.666167i | \(-0.767934\pi\) | ||
0.745802 | − | 0.666167i | \(-0.232066\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −20.6525 | − | 10.6525i | −0.653415 | − | 0.337029i |
(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 | 2100.2.d.g.1301.4 | 4 | ||
3.2 | odd | 2 | 2100.2.d.h.1301.2 | 4 | |||
5.2 | odd | 4 | 2100.2.f.h.1049.3 | 4 | |||
5.3 | odd | 4 | 2100.2.f.b.1049.2 | 4 | |||
5.4 | even | 2 | 420.2.d.d.41.1 | yes | 4 | ||
7.6 | odd | 2 | 2100.2.d.h.1301.1 | 4 | |||
15.2 | even | 4 | 2100.2.f.g.1049.4 | 4 | |||
15.8 | even | 4 | 2100.2.f.a.1049.1 | 4 | |||
15.14 | odd | 2 | 420.2.d.c.41.3 | ✓ | 4 | ||
20.19 | odd | 2 | 1680.2.f.f.881.4 | 4 | |||
21.20 | even | 2 | inner | 2100.2.d.g.1301.3 | 4 | ||
35.13 | even | 4 | 2100.2.f.g.1049.3 | 4 | |||
35.27 | even | 4 | 2100.2.f.a.1049.2 | 4 | |||
35.34 | odd | 2 | 420.2.d.c.41.4 | yes | 4 | ||
60.59 | even | 2 | 1680.2.f.j.881.2 | 4 | |||
105.62 | odd | 4 | 2100.2.f.b.1049.1 | 4 | |||
105.83 | odd | 4 | 2100.2.f.h.1049.4 | 4 | |||
105.104 | even | 2 | 420.2.d.d.41.2 | yes | 4 | ||
140.139 | even | 2 | 1680.2.f.j.881.1 | 4 | |||
420.419 | odd | 2 | 1680.2.f.f.881.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
420.2.d.c.41.3 | ✓ | 4 | 15.14 | odd | 2 | ||
420.2.d.c.41.4 | yes | 4 | 35.34 | odd | 2 | ||
420.2.d.d.41.1 | yes | 4 | 5.4 | even | 2 | ||
420.2.d.d.41.2 | yes | 4 | 105.104 | even | 2 | ||
1680.2.f.f.881.3 | 4 | 420.419 | odd | 2 | |||
1680.2.f.f.881.4 | 4 | 20.19 | odd | 2 | |||
1680.2.f.j.881.1 | 4 | 140.139 | even | 2 | |||
1680.2.f.j.881.2 | 4 | 60.59 | even | 2 | |||
2100.2.d.g.1301.3 | 4 | 21.20 | even | 2 | inner | ||
2100.2.d.g.1301.4 | 4 | 1.1 | even | 1 | trivial | ||
2100.2.d.h.1301.1 | 4 | 7.6 | odd | 2 | |||
2100.2.d.h.1301.2 | 4 | 3.2 | odd | 2 | |||
2100.2.f.a.1049.1 | 4 | 15.8 | even | 4 | |||
2100.2.f.a.1049.2 | 4 | 35.27 | even | 4 | |||
2100.2.f.b.1049.1 | 4 | 105.62 | odd | 4 | |||
2100.2.f.b.1049.2 | 4 | 5.3 | odd | 4 | |||
2100.2.f.g.1049.3 | 4 | 35.13 | even | 4 | |||
2100.2.f.g.1049.4 | 4 | 15.2 | even | 4 | |||
2100.2.f.h.1049.3 | 4 | 5.2 | odd | 4 | |||
2100.2.f.h.1049.4 | 4 | 105.83 | odd | 4 |