Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1560,2,Mod(1249,1560)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1560, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1560.1249");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1560 = 2^{3} \cdot 3 \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1560.l (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: | \(12.4566627153\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} + 13x^{8} + 56x^{6} + 97x^{4} + 61x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1249.10 | ||
Root | \(-1.28447i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1560.1249 |
Dual form | 1560.2.l.f.1249.5 |
$q$-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 \(\left(\mathbb{Z}/1560\mathbb{Z}\right)^\times\).
\(n\) | \(391\) | \(521\) | \(781\) | \(937\) | \(1081\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | 1.00000i | 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.23081 | + | 0.153266i | 0.997648 | + | 0.0685425i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.71215i | 1.40306i | 0.712640 | + | 0.701530i | \(0.247499\pi\) | ||||
−0.712640 | + | 0.701530i | \(0.752501\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.31842 | 1.00054 | 0.500270 | − | 0.865869i | \(-0.333234\pi\) | ||||
0.500270 | + | 0.865869i | \(0.333234\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00000i | 0.277350i | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.153266 | + | 2.23081i | −0.0395730 | + | 0.575992i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 1.55706i | − | 0.377642i | −0.982011 | − | 0.188821i | \(-0.939533\pi\) | ||
0.982011 | − | 0.188821i | \(-0.0604667\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.33709 | 1.22441 | 0.612207 | − | 0.790698i | \(-0.290282\pi\) | ||||
0.612207 | + | 0.790698i | \(0.290282\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.71215 | −0.810057 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.442940i | 0.0923594i | 0.998933 | + | 0.0461797i | \(0.0147047\pi\) | ||||
−0.998933 | + | 0.0461797i | \(0.985295\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.95302 | + | 0.683813i | 0.990604 | + | 0.136763i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.56894 | −0.477041 | −0.238521 | − | 0.971137i | \(-0.576662\pi\) | ||||
−0.238521 | + | 0.971137i | \(0.576662\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.613062 | 0.110109 | 0.0550546 | − | 0.998483i | \(-0.482467\pi\) | ||||
0.0550546 | + | 0.998483i | \(0.482467\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.31842i | 0.577662i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.568944 | + | 8.28109i | −0.0961692 | + | 1.39976i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.257322i | 0.0423034i | 0.999776 | + | 0.0211517i | \(0.00673331\pi\) | ||||
−0.999776 | + | 0.0211517i | \(0.993267\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.00000 | −0.160128 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −10.6114 | −1.65722 | −0.828611 | − | 0.559826i | \(-0.810868\pi\) | ||||
−0.828611 | + | 0.559826i | \(0.810868\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 12.6935i | 1.93574i | 0.251450 | + | 0.967870i | \(0.419093\pi\) | ||||
−0.251450 | + | 0.967870i | \(0.580907\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.23081 | − | 0.153266i | −0.332549 | − | 0.0228475i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 7.44442i | − | 1.08588i | −0.839771 | − | 0.542940i | \(-0.817311\pi\) | ||
0.839771 | − | 0.542940i | \(-0.182689\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.78003 | −0.968576 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.55706 | 0.218032 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 5.39521i | − | 0.741089i | −0.928815 | − | 0.370545i | \(-0.879171\pi\) | ||
0.928815 | − | 0.370545i | \(-0.120829\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 7.40275 | + | 0.508599i | 0.998187 | + | 0.0685795i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 5.33709i | 0.706915i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 13.1358 | 1.71014 | 0.855068 | − | 0.518516i | \(-0.173515\pi\) | ||||
0.855068 | + | 0.518516i | \(0.173515\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.27452 | −0.675333 | −0.337667 | − | 0.941266i | \(-0.609638\pi\) | ||||
−0.337667 | + | 0.941266i | \(0.609638\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 3.71215i | − | 0.467687i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.153266 | + | 2.23081i | −0.0190103 | + | 0.276698i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 10.5384i | − | 1.28747i | −0.765248 | − | 0.643736i | \(-0.777383\pi\) | ||
0.765248 | − | 0.643736i | \(-0.222617\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.442940 | −0.0533237 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.311845 | 0.0370092 | 0.0185046 | − | 0.999829i | \(-0.494109\pi\) | ||||
0.0185046 | + | 0.999829i | \(0.494109\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 9.46841i | 1.10819i | 0.832452 | + | 0.554097i | \(0.186936\pi\) | ||||
−0.832452 | + | 0.554097i | \(0.813064\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.683813 | + | 4.95302i | −0.0789599 | + | 0.571925i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 12.3184i | 1.40382i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −16.1871 | −1.82119 | −0.910597 | − | 0.413295i | \(-0.864378\pi\) | ||||
−0.910597 | + | 0.413295i | \(0.864378\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 11.7546i | 1.29023i | 0.764084 | + | 0.645117i | \(0.223191\pi\) | ||||
−0.764084 | + | 0.645117i | \(0.776809\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.238644 | − | 3.47350i | 0.0258845 | − | 0.376754i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 2.56894i | − | 0.275420i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.58762 | 0.486287 | 0.243144 | − | 0.969990i | \(-0.421821\pi\) | ||||
0.243144 | + | 0.969990i | \(0.421821\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.71215 | −0.389139 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.613062i | 0.0635716i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 11.9060 | + | 0.817993i | 1.22153 | + | 0.0839243i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 10.8500i | − | 1.10165i | −0.834619 | − | 0.550827i | \(-0.814312\pi\) | ||
0.834619 | − | 0.550827i | \(-0.185688\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.31842 | −0.333513 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.68306 | 0.167471 | 0.0837356 | − | 0.996488i | \(-0.473315\pi\) | ||||
0.0837356 | + | 0.996488i | \(0.473315\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.78535i | 0.175916i | 0.996124 | + | 0.0879578i | \(0.0280341\pi\) | ||||
−0.996124 | + | 0.0879578i | \(0.971966\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −8.28109 | − | 0.568944i | −0.808152 | − | 0.0555233i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 1.11943i | − | 0.108220i | −0.998535 | − | 0.0541098i | \(-0.982768\pi\) | ||
0.998535 | − | 0.0541098i | \(-0.0172321\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.914914 | 0.0876329 | 0.0438164 | − | 0.999040i | \(-0.486048\pi\) | ||||
0.0438164 | + | 0.999040i | \(0.486048\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.257322 | −0.0244239 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.41386i | 0.227077i | 0.993534 | + | 0.113538i | \(0.0362185\pi\) | ||||
−0.993534 | + | 0.113538i | \(0.963782\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.0678875 | + | 0.988115i | −0.00633054 | + | 0.0921422i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − | 1.00000i | − | 0.0924500i | ||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 5.78003 | 0.529855 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.0118848 | 0.00108043 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 10.6114i | − | 0.956797i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 10.9444 | + | 2.28458i | 0.978900 | + | 0.204339i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 14.0418i | 1.24601i | 0.782218 | + | 0.623005i | \(0.214088\pi\) | ||||
−0.782218 | + | 0.623005i | \(0.785912\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −12.6935 | −1.11760 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 13.7650 | 1.20265 | 0.601327 | − | 0.799003i | \(-0.294639\pi\) | ||||
0.601327 | + | 0.799003i | \(0.294639\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 19.8121i | 1.71792i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0.153266 | − | 2.23081i | 0.0131910 | − | 0.191997i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.50470i | 0.555734i | 0.960620 | + | 0.277867i | \(0.0896275\pi\) | ||||
−0.960620 | + | 0.277867i | \(0.910373\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −9.78003 | −0.829532 | −0.414766 | − | 0.909928i | \(-0.636137\pi\) | ||||
−0.414766 | + | 0.909928i | \(0.636137\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 7.44442 | 0.626933 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.31842i | 0.277500i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −5.73082 | − | 0.393731i | −0.475919 | − | 0.0326976i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − | 6.78003i | − | 0.559208i | ||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 5.93148 | 0.485926 | 0.242963 | − | 0.970036i | \(-0.421881\pi\) | ||||
0.242963 | + | 0.970036i | \(0.421881\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.272818 | −0.0222016 | −0.0111008 | − | 0.999938i | \(-0.503534\pi\) | ||||
−0.0111008 | + | 0.999938i | \(0.503534\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.55706i | 0.125881i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.36763 | + | 0.0939614i | 0.109850 | + | 0.00754716i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 14.6561i | − | 1.16969i | −0.811146 | − | 0.584844i | \(-0.801156\pi\) | ||
0.811146 | − | 0.584844i | \(-0.198844\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 5.39521 | 0.427868 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.64426 | −0.129586 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 3.48345i | − | 0.272845i | −0.990651 | − | 0.136422i | \(-0.956440\pi\) | ||
0.990651 | − | 0.136422i | \(-0.0435604\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.508599 | + | 7.40275i | −0.0395944 | + | 0.576304i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 4.69135i | − | 0.363028i | −0.983388 | − | 0.181514i | \(-0.941900\pi\) | ||
0.983388 | − | 0.181514i | \(-0.0580998\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.00000 | −0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5.33709 | −0.408138 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3.26475i | 0.248214i | 0.992269 | + | 0.124107i | \(0.0396067\pi\) | ||||
−0.992269 | + | 0.124107i | \(0.960393\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.53841 | + | 18.3863i | −0.191886 | + | 1.38988i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 13.1358i | 0.987348i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −19.7204 | −1.47397 | −0.736987 | − | 0.675907i | \(-0.763752\pi\) | ||||
−0.736987 | + | 0.675907i | \(0.763752\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −22.0558 | −1.63940 | −0.819698 | − | 0.572796i | \(-0.805859\pi\) | ||||
−0.819698 | + | 0.572796i | \(0.805859\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 5.27452i | − | 0.389904i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.0394386 | + | 0.574036i | −0.00289958 | + | 0.0422040i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 5.16697i | − | 0.377846i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3.71215 | 0.270019 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 22.2729 | 1.61161 | 0.805805 | − | 0.592182i | \(-0.201733\pi\) | ||||
0.805805 | + | 0.592182i | \(0.201733\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 15.7733i | − | 1.13539i | −0.823241 | − | 0.567693i | \(-0.807836\pi\) | ||
0.823241 | − | 0.567693i | \(-0.192164\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −2.23081 | − | 0.153266i | −0.159752 | − | 0.0109756i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.72871i | 0.194413i | 0.995264 | + | 0.0972063i | \(0.0309907\pi\) | ||||
−0.995264 | + | 0.0972063i | \(0.969009\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 22.1029 | 1.56684 | 0.783418 | − | 0.621495i | \(-0.213474\pi\) | ||||
0.783418 | + | 0.621495i | \(0.213474\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 10.5384 | 0.743322 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 9.53630i | − | 0.669317i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −23.6720 | − | 1.62636i | −1.65332 | − | 0.113590i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 0.442940i | − | 0.0307865i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 17.7107 | 1.22507 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.01720 | 0.0700268 | 0.0350134 | − | 0.999387i | \(-0.488853\pi\) | ||||
0.0350134 | + | 0.999387i | \(0.488853\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0.311845i | 0.0213672i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.94548 | + | 28.3168i | −0.132680 | + | 1.93119i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.27578i | 0.154490i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −9.46841 | −0.639816 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.55706 | 0.104739 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 6.85535i | − | 0.459068i | −0.973301 | − | 0.229534i | \(-0.926280\pi\) | ||
0.973301 | − | 0.229534i | \(-0.0737202\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.95302 | − | 0.683813i | −0.330201 | − | 0.0455875i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 2.88224i | − | 0.191301i | −0.995415 | − | 0.0956504i | \(-0.969507\pi\) | ||
0.995415 | − | 0.0956504i | \(-0.0304931\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −14.1857 | −0.937416 | −0.468708 | − | 0.883353i | \(-0.655280\pi\) | ||||
−0.468708 | + | 0.883353i | \(0.655280\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −12.3184 | −0.810494 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0.429354i | 0.0281279i | 0.999901 | + | 0.0140639i | \(0.00447684\pi\) | ||||
−0.999901 | + | 0.0140639i | \(0.995523\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.14097 | − | 16.6071i | 0.0744289 | − | 1.08333i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 16.1871i | − | 1.05147i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −19.7255 | −1.27594 | −0.637969 | − | 0.770062i | \(-0.720225\pi\) | ||||
−0.637969 | + | 0.770062i | \(0.720225\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 19.6598 | 1.26640 | 0.633200 | − | 0.773988i | \(-0.281741\pi\) | ||||
0.633200 | + | 0.773988i | \(0.281741\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −15.1250 | − | 1.03915i | −0.966298 | − | 0.0663886i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5.33709i | 0.339591i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −11.7546 | −0.744917 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 23.4175 | 1.47810 | 0.739051 | − | 0.673650i | \(-0.235274\pi\) | ||||
0.739051 | + | 0.673650i | \(0.235274\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.46986i | 0.0924093i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 3.47350 | + | 0.238644i | 0.217519 | + | 0.0149444i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 30.7987i | − | 1.92117i | −0.277981 | − | 0.960586i | \(-0.589665\pi\) | ||
0.277981 | − | 0.960586i | \(-0.410335\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.955216 | −0.0593543 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.56894 | 0.159014 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 24.1471i | − | 1.48897i | −0.667638 | − | 0.744486i | \(-0.732695\pi\) | ||
0.667638 | − | 0.744486i | \(-0.267305\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.826900 | − | 12.0357i | 0.0507961 | − | 0.739346i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4.58762i | 0.280758i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −12.7557 | −0.777726 | −0.388863 | − | 0.921295i | \(-0.627132\pi\) | ||||
−0.388863 | + | 0.921295i | \(0.627132\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −10.4222 | −0.633102 | −0.316551 | − | 0.948575i | \(-0.602525\pi\) | ||||
−0.316551 | + | 0.948575i | \(0.602525\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − | 3.71215i | − | 0.224669i | ||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 16.4362 | + | 2.26918i | 0.991139 | + | 0.136836i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 19.9404i | − | 1.19810i | −0.800710 | − | 0.599052i | \(-0.795544\pi\) | ||
0.800710 | − | 0.599052i | \(-0.204456\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −0.613062 | −0.0367031 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 28.5272 | 1.70179 | 0.850895 | − | 0.525336i | \(-0.176060\pi\) | ||||
0.850895 | + | 0.525336i | \(0.176060\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 19.1888i | 1.14066i | 0.821416 | + | 0.570329i | \(0.193184\pi\) | ||||
−0.821416 | + | 0.570329i | \(0.806816\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.817993 | + | 11.9060i | −0.0484537 | + | 0.705253i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 39.3910i | − | 2.32518i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 14.5756 | 0.857386 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 10.8500 | 0.636040 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 11.9828i | − | 0.700045i | −0.936741 | − | 0.350022i | \(-0.886174\pi\) | ||
0.936741 | − | 0.350022i | \(-0.113826\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 29.3035 | + | 2.01327i | 1.70611 | + | 0.117217i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 3.31842i | − | 0.192554i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.442940 | −0.0256159 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −47.1201 | −2.71596 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.68306i | 0.0966895i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −11.7664 | − | 0.808403i | −0.673745 | − | 0.0462890i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 25.0299i | − | 1.42853i | −0.699874 | − | 0.714267i | \(-0.746760\pi\) | ||
0.699874 | − | 0.714267i | \(-0.253240\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.78535 | −0.101565 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 27.6360 | 1.56710 | 0.783548 | − | 0.621331i | \(-0.213408\pi\) | ||||
0.783548 | + | 0.621331i | \(0.213408\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 14.5441i | 0.822083i | 0.911617 | + | 0.411042i | \(0.134835\pi\) | ||||
−0.911617 | + | 0.411042i | \(0.865165\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.568944 | − | 8.28109i | 0.0320564 | − | 0.466587i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 8.00364i | − | 0.449529i | −0.974413 | − | 0.224765i | \(-0.927839\pi\) | ||
0.974413 | − | 0.224765i | \(-0.0721613\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −8.52483 | −0.477299 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.11943 | 0.0624806 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 8.31017i | − | 0.462390i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.683813 | + | 4.95302i | −0.0379311 | + | 0.274744i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0.914914i | 0.0505949i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 27.6348 | 1.52355 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.59929 | 0.307765 | 0.153882 | − | 0.988089i | \(-0.450822\pi\) | ||||
0.153882 | + | 0.988089i | \(0.450822\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 0.257322i | − | 0.0141011i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.61518 | − | 23.5092i | 0.0882465 | − | 1.28444i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 34.5802i | − | 1.88370i | −0.336027 | − | 0.941852i | \(-0.609083\pi\) | ||
0.336027 | − | 0.941852i | \(-0.390917\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2.41386 | −0.131103 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.03440 | 0.110169 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0.816545i | 0.0440893i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −0.988115 | − | 0.0678875i | −0.0531983 | − | 0.00365494i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 31.0537i | − | 1.66705i | −0.552482 | − | 0.833525i | \(-0.686319\pi\) | ||
0.552482 | − | 0.833525i | \(-0.313681\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.94804 | −0.157805 | −0.0789026 | − | 0.996882i | \(-0.525142\pi\) | ||||
−0.0789026 | + | 0.996882i | \(0.525142\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.00000 | 0.0533761 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.80547i | 0.0960957i | 0.998845 | + | 0.0480478i | \(0.0153000\pi\) | ||||
−0.998845 | + | 0.0480478i | \(0.984700\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.695666 | + | 0.0477951i | 0.0369221 | + | 0.00253670i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 5.78003i | 0.305912i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 9.29216 | 0.490422 | 0.245211 | − | 0.969470i | \(-0.421143\pi\) | ||||
0.245211 | + | 0.969470i | \(0.421143\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.48457 | 0.499188 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0.0118848i | 0.000623788i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.45118 | + | 21.1222i | −0.0759583 | + | 1.10559i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 18.0955i | 0.944579i | 0.881444 | + | 0.472289i | \(0.156572\pi\) | ||||
−0.881444 | + | 0.472289i | \(0.843428\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 10.6114 | 0.552407 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 20.0278 | 1.03979 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 29.4689i | − | 1.52584i | −0.646491 | − | 0.762922i | \(-0.723764\pi\) | ||
0.646491 | − | 0.762922i | \(-0.276236\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2.28458 | + | 10.9444i | −0.117975 | + | 0.565168i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 2.56894i | − | 0.132307i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 21.2489 | 1.09148 | 0.545740 | − | 0.837954i | \(-0.316249\pi\) | ||||
0.545740 | + | 0.837954i | \(0.316249\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −14.0418 | −0.719384 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 8.19163i | − | 0.418573i | −0.977854 | − | 0.209286i | \(-0.932886\pi\) | ||
0.977854 | − | 0.209286i | \(-0.0671141\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.88799 | + | 27.4801i | −0.0962211 | + | 1.40052i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 12.6935i | − | 0.645247i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 24.4557 | 1.23995 | 0.619976 | − | 0.784621i | \(-0.287142\pi\) | ||||
0.619976 | + | 0.784621i | \(0.287142\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.689684 | 0.0348788 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 13.7650i | 0.694352i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −36.1104 | − | 2.48093i | −1.81691 | − | 0.124829i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 34.4916i | − | 1.73108i | −0.500837 | − | 0.865541i | \(-0.666975\pi\) | ||
0.500837 | − | 0.865541i | \(-0.333025\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −19.8121 | −0.991844 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −16.9434 | −0.846114 | −0.423057 | − | 0.906103i | \(-0.639043\pi\) | ||||
−0.423057 | + | 0.906103i | \(0.639043\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.613062i | 0.0305388i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2.23081 | + | 0.153266i | 0.110850 | + | 0.00761583i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.853901i | 0.0423263i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.05299 | 0.150961 | 0.0754804 | − | 0.997147i | \(-0.475951\pi\) | ||||
0.0754804 | + | 0.997147i | \(0.475951\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −6.50470 | −0.320853 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 48.7620i | 2.39942i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.80158 | + | 26.2223i | −0.0884358 | + | 1.28720i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 9.78003i | − | 0.478930i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −20.9567 | −1.02380 | −0.511902 | − | 0.859044i | \(-0.671059\pi\) | ||||
−0.511902 | + | 0.859044i | \(0.671059\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −37.4462 | −1.82502 | −0.912508 | − | 0.409059i | \(-0.865857\pi\) | ||||
−0.912508 | + | 0.409059i | \(0.865857\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 7.44442i | 0.361960i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.06474 | − | 7.71215i | 0.0516473 | − | 0.374094i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 19.5798i | − | 0.947533i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −3.31842 | −0.160215 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −27.2671 | −1.31341 | −0.656706 | − | 0.754147i | \(-0.728051\pi\) | ||||
−0.656706 | + | 0.754147i | \(0.728051\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 12.5679i | 0.603975i | 0.953312 | + | 0.301988i | \(0.0976501\pi\) | ||||
−0.953312 | + | 0.301988i | \(0.902350\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.393731 | − | 5.73082i | 0.0188780 | − | 0.274772i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.36401i | 0.113086i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −14.7241 | −0.702742 | −0.351371 | − | 0.936236i | \(-0.614284\pi\) | ||||
−0.351371 | + | 0.936236i | \(0.614284\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.78003 | 0.322859 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 8.65996i | 0.411447i | 0.978610 | + | 0.205724i | \(0.0659548\pi\) | ||||
−0.978610 | + | 0.205724i | \(0.934045\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 10.2341 | + | 0.703125i | 0.485143 | + | 0.0333313i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 5.93148i | 0.280549i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 21.5690 | 1.01791 | 0.508953 | − | 0.860795i | \(-0.330033\pi\) | ||||
0.508953 | + | 0.860795i | \(0.330033\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −35.2130 | −1.65812 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 0.272818i | − | 0.0128181i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −8.28109 | − | 0.568944i | −0.388224 | − | 0.0266725i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0.192394i | 0.00899982i | 0.999990 | + | 0.00449991i | \(0.00143237\pi\) | ||||
−0.999990 | + | 0.00449991i | \(0.998568\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.55706 | −0.0726773 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −12.0821 | −0.562720 | −0.281360 | − | 0.959602i | \(-0.590785\pi\) | ||||
−0.281360 | + | 0.959602i | \(0.590785\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 25.7245i | 1.19552i | 0.801676 | + | 0.597759i | \(0.203942\pi\) | ||||
−0.801676 | + | 0.597759i | \(0.796058\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −0.0939614 | + | 1.36763i | −0.00435736 | + | 0.0634221i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 18.4317i | − | 0.852918i | −0.904507 | − | 0.426459i | \(-0.859761\pi\) | ||
0.904507 | − | 0.426459i | \(-0.140239\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 39.1201 | 1.80640 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 14.6561 | 0.675319 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 42.1223i | 1.93679i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 26.4347 | + | 3.64957i | 1.21291 | + | 0.167454i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 5.39521i | 0.247030i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −25.5826 | −1.16890 | −0.584450 | − | 0.811430i | \(-0.698690\pi\) | ||||
−0.584450 | + | 0.811430i | \(0.698690\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.257322 | −0.0117329 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − | 1.64426i | − | 0.0748164i | ||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.66294 | − | 24.2044i | 0.0755101 | − | 1.09906i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 30.1997i | 1.36848i | 0.729258 | + | 0.684239i | \(0.239866\pi\) | ||||
−0.729258 | + | 0.684239i | \(0.760134\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 3.48345 | 0.157527 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −10.7256 | −0.484039 | −0.242020 | − | 0.970271i | \(-0.577810\pi\) | ||||
−0.242020 | + | 0.970271i | \(0.577810\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.00000i | 0.180151i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −7.40275 | − | 0.508599i | −0.332729 | − | 0.0228598i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.15761i | 0.0519260i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −7.01044 | −0.313830 | −0.156915 | − | 0.987612i | \(-0.550155\pi\) | ||||
−0.156915 | + | 0.987612i | \(0.550155\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 4.69135 | 0.209594 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 32.2604i | − | 1.43842i | −0.694793 | − | 0.719210i | \(-0.744504\pi\) | ||
0.694793 | − | 0.719210i | \(-0.255496\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.75459 | + | 0.257956i | 0.167077 | + | 0.0114789i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 1.00000i | − | 0.0444116i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −17.3631 | −0.769604 | −0.384802 | − | 0.922999i | \(-0.625730\pi\) | ||||
−0.384802 | + | 0.922999i | \(0.625730\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −35.1481 | −1.55486 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 5.33709i | − | 0.235638i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −0.273632 | + | 3.98277i | −0.0120577 | + | 0.175502i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 24.7037i | − | 1.08647i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −3.26475 | −0.143307 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 27.6513 | 1.21142 | 0.605712 | − | 0.795684i | \(-0.292888\pi\) | ||||
0.605712 | + | 0.795684i | \(0.292888\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 7.49745i | − | 0.327840i | −0.986474 | − | 0.163920i | \(-0.947586\pi\) | ||
0.986474 | − | 0.163920i | \(-0.0524140\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −18.3863 | − | 2.53841i | −0.802445 | − | 0.110785i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 0.954575i | − | 0.0415819i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 22.8038 | 0.991470 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −13.1358 | −0.570045 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 10.6114i | − | 0.459630i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0.171571 | − | 2.49724i | 0.00741764 | − | 0.107965i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 19.7204i | − | 0.850999i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −22.4990 | −0.969099 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 18.8836 | 0.811871 | 0.405936 | − | 0.913902i | \(-0.366946\pi\) | ||||
0.405936 | + | 0.913902i | \(0.366946\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 22.0558i | − | 0.946506i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2.04100 | + | 0.140225i | 0.0874268 | + | 0.00600658i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 21.3808i | 0.914178i | 0.889421 | + | 0.457089i | \(0.151108\pi\) | ||||
−0.889421 | + | 0.457089i | \(0.848892\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 5.27452 | 0.225111 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −13.7107 | −0.584095 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 60.0890i | − | 2.55524i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −0.574036 | − | 0.0394386i | −0.0243665 | − | 0.00167407i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 3.80681i | − | 0.161300i | −0.996743 | − | 0.0806498i | \(-0.974300\pi\) | ||
0.996743 | − | 0.0806498i | \(-0.0256995\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −12.6935 | −0.536878 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 5.16697 | 0.218150 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 29.3983i | 1.23899i | 0.785001 | + | 0.619495i | \(0.212662\pi\) | ||||
−0.785001 | + | 0.619495i | \(0.787338\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −0.369961 | + | 5.38486i | −0.0155644 | + | 0.226543i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 3.71215i | 0.155896i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −12.4014 | −0.519892 | −0.259946 | − | 0.965623i | \(-0.583705\pi\) | ||||
−0.259946 | + | 0.965623i | \(0.583705\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4.56899 | −0.191206 | −0.0956032 | − | 0.995420i | \(-0.530478\pi\) | ||||
−0.0956032 | + | 0.995420i | \(0.530478\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 22.2729i | 0.930463i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.302888 | + | 2.19389i | −0.0126313 | + | 0.0914916i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 27.4496i | − | 1.14274i | −0.820692 | − | 0.571370i | \(-0.806412\pi\) | ||
0.820692 | − | 0.571370i | \(-0.193588\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 15.7733 | 0.655515 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −43.6348 | −1.81028 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 17.9036i | − | 0.741489i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0.153266 | − | 2.23081i | 0.00633675 | − | 0.0922326i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 19.5191i | 0.805641i | 0.915279 | + | 0.402820i | \(0.131970\pi\) | ||||
−0.915279 | + | 0.402820i | \(0.868030\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.27197 | 0.134819 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.72871 | −0.112244 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 14.8539i | − | 0.609975i | −0.952356 | − | 0.304987i | \(-0.901348\pi\) | ||
0.952356 | − | 0.304987i | \(-0.0986523\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 12.8942 | + | 0.885881i | 0.528609 | + | 0.0363176i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 22.1029i | 0.904613i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 42.6098 | 1.74099 | 0.870494 | − | 0.492178i | \(-0.163799\pi\) | ||||
0.870494 | + | 0.492178i | \(0.163799\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 34.4960 | 1.40712 | 0.703561 | − | 0.710635i | \(-0.251592\pi\) | ||||
0.703561 | + | 0.710635i | \(0.251592\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 10.5384i | 0.429157i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0.0265126 | + | 0.00182153i | 0.00107789 | + | 7.40555e-5i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 44.0061i | 1.78615i | 0.449906 | + | 0.893076i | \(0.351457\pi\) | ||||
−0.449906 | + | 0.893076i | \(0.648543\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 9.53630 | 0.386430 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 7.44442 | 0.301169 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 11.4907i | 0.464104i | 0.972703 | + | 0.232052i | \(0.0745439\pi\) | ||||
−0.972703 | + | 0.232052i | \(0.925456\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.62636 | − | 23.6720i | 0.0655812 | − | 0.954547i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 47.2506i | 1.90224i | 0.308823 | + | 0.951120i | \(0.400065\pi\) | ||||
−0.308823 | + | 0.951120i | \(0.599935\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −25.5964 | −1.02881 | −0.514403 | − | 0.857549i | \(-0.671986\pi\) | ||||
−0.514403 | + | 0.857549i | \(0.671986\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.442940 | 0.0177746 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 17.0299i | 0.682290i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 24.0648 | + | 6.77388i | 0.962592 | + | 0.270955i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 17.7107i | 0.707297i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0.400665 | 0.0159756 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6.54777 | 0.260663 | 0.130331 | − | 0.991470i | \(-0.458396\pi\) | ||||
0.130331 | + | 0.991470i | \(0.458396\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.01720i | 0.0404300i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −2.15213 | + | 31.3246i | −0.0854046 | + | 1.24308i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 6.78003i | − | 0.268635i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −0.311845 | −0.0123364 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −0.899023 | −0.0355093 | −0.0177546 | − | 0.999842i | \(-0.505652\pi\) | ||||
−0.0177546 | + | 0.999842i | \(0.505652\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 2.48862i | − | 0.0981416i | −0.998795 | − | 0.0490708i | \(-0.984374\pi\) | ||
0.998795 | − | 0.0490708i | \(-0.0156260\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −28.3168 | − | 1.94548i | −1.11497 | − | 0.0766031i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0.773002i | 0.0303898i | 0.999885 | + | 0.0151949i | \(0.00483688\pi\) | ||||
−0.999885 | + | 0.0151949i | \(0.995163\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 43.5901 | 1.71106 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.27578 | −0.0891948 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 43.1740i | − | 1.68953i | −0.535139 | − | 0.844764i | \(-0.679741\pi\) | ||
0.535139 | − | 0.844764i | \(-0.320259\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 30.7071 | + | 2.10970i | 1.19983 | + | 0.0824328i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 9.46841i | − | 0.369398i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 39.3552 | 1.53306 | 0.766530 | − | 0.642208i | \(-0.221981\pi\) | ||||
0.766530 | + | 0.642208i | \(0.221981\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −20.7673 | −0.807756 | −0.403878 | − | 0.914813i | \(-0.632338\pi\) | ||||
−0.403878 | + | 0.914813i | \(0.632338\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.55706i | 0.0604712i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −3.03651 | + | 44.1970i | −0.117751 | + | 1.71388i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 1.13789i | − | 0.0440592i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 6.85535 | 0.265043 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −17.5031 | −0.675698 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 49.6479i | − | 1.91379i | −0.290439 | − | 0.956893i | \(-0.593801\pi\) | ||
0.290439 | − | 0.956893i | \(-0.406199\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0.683813 | − | 4.95302i | 0.0263200 | − | 0.190642i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 30.5884i | 1.17561i | 0.809004 | + | 0.587803i | \(0.200007\pi\) | ||||
−0.809004 | + | 0.587803i | \(0.799993\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 40.2769 | 1.54569 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.88224 | 0.110448 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 28.9405i | 1.10738i | 0.832724 | + | 0.553688i | \(0.186780\pi\) | ||||
−0.832724 | + | 0.553688i | \(0.813220\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −0.996947 | + | 14.5107i | −0.0380914 | + | 0.554427i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 14.1857i | − | 0.541218i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 5.39521 | 0.205541 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −31.9739 | −1.21635 | −0.608173 | − | 0.793805i | \(-0.708097\pi\) | ||||
−0.608173 | + | 0.793805i | \(0.708097\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − | 12.3184i | − | 0.467939i | ||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −21.8174 | − | 1.49894i | −0.827581 | − | 0.0568581i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 16.5226i | 0.625837i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −0.429354 | −0.0162396 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 4.51673 | 0.170595 | 0.0852973 | − | 0.996356i | \(-0.472816\pi\) | ||||
0.0852973 | + | 0.996356i | \(0.472816\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.37335i | 0.0517969i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 16.6071 | + | 1.14097i | 0.625459 | + | 0.0429716i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 6.24778i | 0.234972i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 29.7979 | 1.11908 | 0.559542 | − | 0.828802i | \(-0.310977\pi\) | ||||
0.559542 | + | 0.828802i | \(0.310977\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 16.1871 | 0.607065 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0.271550i | 0.0101696i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.508599 | + | 7.40275i | −0.0190205 | + | 0.276847i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 19.7255i | − | 0.736663i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −41.8431 | −1.56049 | −0.780243 | − | 0.625477i | \(-0.784904\pi\) | ||||
−0.780243 | + | 0.625477i | \(0.784904\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6.62747 | −0.246820 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 19.6598i | 0.731157i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −12.7240 | − | 1.75668i | −0.472559 | − | 0.0652413i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 15.4317i | − | 0.572330i | −0.958180 | − | 0.286165i | \(-0.907619\pi\) | ||
0.958180 | − | 0.286165i | \(-0.0923806\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 19.7645 | 0.731018 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 39.1794i | 1.44712i | 0.690260 | + | 0.723561i | \(0.257496\pi\) | ||||
−0.690260 | + | 0.723561i | \(0.742504\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.03915 | − | 15.1250i | 0.0383295 | − | 0.557893i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 34.9708i | − | 1.28817i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −32.5361 | −1.19686 | −0.598430 | − | 0.801175i | \(-0.704209\pi\) | ||||
−0.598430 | + | 0.801175i | \(0.704209\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −5.33709 | −0.196063 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 8.13346i | 0.298388i | 0.988808 | + | 0.149194i | \(0.0476679\pi\) | ||||
−0.988808 | + | 0.149194i | \(0.952332\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 13.2320 | + | 0.909092i | 0.484783 | + | 0.0333065i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 11.7546i | − | 0.430078i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4.15550 | 0.151839 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −48.9359 | −1.78570 | −0.892848 | − | 0.450358i | \(-0.851296\pi\) | ||||
−0.892848 | + | 0.450358i | \(0.851296\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 23.4175i | 0.853382i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −0.608605 | − | 0.0418136i | −0.0221494 | − | 0.00152175i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3.54775i | 0.128945i | 0.997919 | + | 0.0644726i | \(0.0205365\pi\) | ||||
−0.997919 | + | 0.0644726i | \(0.979463\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.46986 | −0.0533525 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 40.8645 | 1.48134 | 0.740669 | − | 0.671870i | \(-0.234509\pi\) | ||||
0.740669 | + | 0.671870i | \(0.234509\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3.39630i | 0.122954i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −0.238644 | + | 3.47350i | −0.00862818 | + | 0.125585i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 13.1358i | 0.474306i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 42.6263 | 1.53714 | 0.768571 | − | 0.639764i | \(-0.220968\pi\) | ||||
0.768571 | + | 0.639764i | \(0.220968\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 30.7987 | 1.10919 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 36.3873i | 1.30876i | 0.756166 | + | 0.654379i | \(0.227070\pi\) | ||||
−0.756166 | + | 0.654379i | \(0.772930\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.03651 | + | 0.419220i | 0.109075 | + | 0.0150588i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 0.955216i | − | 0.0342682i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −56.6340 | −2.02912 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.03483 | 0.0370291 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2.56894i | 0.0918066i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.24628 | − | 32.6951i | 0.0801733 | − | 1.16694i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 12.7280i | − | 0.453705i | −0.973929 | − | 0.226853i | \(-0.927156\pi\) | ||
0.973929 | − | 0.226853i | \(-0.0728436\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 24.1471 | 0.859658 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −8.96059 | −0.318602 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 5.27452i | − | 0.187304i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 12.0357 | + | 0.826900i | 0.426862 | + | 0.0293271i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 20.3707i | − | 0.721566i | −0.932650 | − | 0.360783i | \(-0.882510\pi\) | ||
0.932650 | − | 0.360783i | \(-0.117490\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −11.5914 | −0.410074 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −4.58762 | −0.162096 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 31.4201i | 1.10879i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.66803 | − | 0.252008i | −0.129281 | − | 0.00888213i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 12.7557i | − | 0.449021i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 36.4656 | 1.28206 | 0.641030 | − | 0.767516i | \(-0.278507\pi\) | ||||
0.641030 | + | 0.767516i | \(0.278507\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 32.4823 | 1.14061 | 0.570304 | − | 0.821433i | \(-0.306825\pi\) | ||||
0.570304 | + | 0.821433i | \(0.306825\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 10.4222i | − | 0.365522i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0.533893 | − | 7.77091i | 0.0187014 | − | 0.272203i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 67.7464i | 2.37015i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 3.71215 | 0.129713 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 15.7750 | 0.550550 | 0.275275 | − | 0.961366i | \(-0.411231\pi\) | ||||
0.275275 | + | 0.961366i | \(0.411231\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 33.4570i | 1.16624i | 0.812386 | + | 0.583120i | \(0.198168\pi\) | ||||
−0.812386 | + | 0.583120i | \(0.801832\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −2.26918 | + | 16.4362i | −0.0790025 | + | 0.572234i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 30.0516i | − | 1.04500i | −0.852640 | − | 0.522499i | \(-0.825000\pi\) | ||
0.852640 | − | 0.522499i | \(-0.175000\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −3.52850 | −0.122550 | −0.0612750 | − | 0.998121i | \(-0.519517\pi\) | ||||
−0.0612750 | + | 0.998121i | \(0.519517\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 19.9404 | 0.691726 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 10.5569i | 0.365776i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0.719023 | − | 10.4655i | 0.0248828 | − | 0.362174i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 0.613062i | − | 0.0211905i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −7.19133 | −0.248272 | −0.124136 | − | 0.992265i | \(-0.539616\pi\) | ||||
−0.124136 | + | 0.992265i | \(0.539616\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −22.4005 | −0.772432 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 28.5272i | 0.982529i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −2.23081 | − | 0.153266i | −0.0767422 | − | 0.00527250i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0.0441180i | 0.00151591i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −19.1888 | −0.658559 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −0.113978 | −0.00390712 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 16.1780i | 0.553924i | 0.960881 | + | 0.276962i | \(0.0893276\pi\) | ||||
−0.960881 | + | 0.276962i | \(0.910672\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −11.9060 | − | 0.817993i | −0.407178 | − | 0.0279748i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 1.79125i | − | 0.0611881i | −0.999532 | − | 0.0305940i | \(-0.990260\pi\) | ||
0.999532 | − | 0.0305940i | \(-0.00973990\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −17.7341 | −0.605078 | −0.302539 | − | 0.953137i | \(-0.597834\pi\) | ||||
−0.302539 | + | 0.953137i | \(0.597834\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 39.3910 | 1.34244 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 2.45249i | − | 0.0834837i | −0.999128 | − | 0.0417419i | \(-0.986709\pi\) | ||
0.999128 | − | 0.0417419i | \(-0.0132907\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −0.500374 | + | 7.28303i | −0.0170132 | + | 0.247631i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 14.5756i | 0.495012i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −53.7156 | −1.82218 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 10.5384 | 0.357081 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 10.8500i | 0.367218i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −8.48071 | + | 40.6274i | −0.286700 | + | 1.37346i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 48.8367i | 1.64910i | 0.565791 | + | 0.824549i | \(0.308571\pi\) | ||||
−0.565791 | + | 0.824549i | \(0.691429\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 11.9828 | 0.404171 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 6.25328 | 0.210678 | 0.105339 | − | 0.994436i | \(-0.466407\pi\) | ||||
0.105339 | + | 0.994436i | \(0.466407\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 25.0964i | − | 0.844560i | −0.906465 | − | 0.422280i | \(-0.861230\pi\) | ||
0.906465 | − | 0.422280i | \(-0.138770\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2.01327 | + | 29.3035i | −0.0676752 | + | 0.985026i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.57354i | 0.0528344i | 0.999651 | + | 0.0264172i | \(0.00840984\pi\) | ||||
−0.999651 | + | 0.0264172i | \(0.991590\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −52.1253 | −1.74823 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.31842 | 0.111171 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 39.7316i | − | 1.32957i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −43.9925 | − | 3.02246i | −1.47051 | − | 0.101030i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 0.442940i | − | 0.0147893i | ||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.57492 | −0.0525266 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −8.40067 | −0.279867 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 47.1201i | − | 1.56806i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −49.2023 | − | 3.38040i | −1.63554 | − | 0.112368i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 20.6504i | 0.685686i | 0.939393 | + | 0.342843i | \(0.111390\pi\) | ||||
−0.939393 | + | 0.342843i | \(0.888610\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1.68306 | −0.0558237 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 39.4108 | 1.30574 | 0.652869 | − | 0.757471i | \(-0.273565\pi\) | ||||
0.652869 | + | 0.757471i | \(0.273565\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 39.0066i | 1.29093i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0.808403 | − | 11.7664i | 0.0267250 | − | 0.388987i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 51.0977i | 1.68739i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 7.84896 | 0.258913 | 0.129457 | − | 0.991585i | \(-0.458677\pi\) | ||||
0.129457 | + | 0.991585i | \(0.458677\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 25.0299 | 0.824764 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0.311845i | 0.0102645i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.175960 | + | 1.27452i | −0.00578553 | + | 0.0419060i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − | 1.78535i | − | 0.0586385i | ||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 29.2279 | 0.958935 | 0.479467 | − | 0.877560i | \(-0.340830\pi\) | ||||
0.479467 | + | 0.877560i | \(0.340830\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −36.1857 | −1.18594 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 27.6360i | 0.904764i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0.791919 | − | 11.5265i | 0.0258985 | − | 0.376958i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 8.62318i | 0.281707i | 0.990030 | + | 0.140853i | \(0.0449846\pi\) | ||||
−0.990030 | + | 0.140853i | \(0.955015\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −14.5441 | −0.474630 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −31.5064 | −1.02708 | −0.513540 | − | 0.858066i | \(-0.671666\pi\) | ||||
−0.513540 | + | 0.858066i | \(0.671666\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 4.70021i | − | 0.153060i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 8.28109 | + | 0.568944i | 0.269384 | + | 0.0185078i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 31.8565i | 1.03520i | 0.855624 | + | 0.517598i | \(0.173174\pi\) | ||||
−0.855624 | + | 0.517598i | \(0.826826\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −9.46841 | −0.307358 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 8.00364 | 0.259536 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 32.9471i | 1.06726i | 0.845717 | + | 0.533631i | \(0.179173\pi\) | ||||
−0.845717 | + | 0.533631i | \(0.820827\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 49.6865 | + | 3.41367i | 1.60782 | + | 0.110464i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 8.52483i | − | 0.275569i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −24.1464 | −0.779728 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.6242 | −0.987876 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.11943i | 0.0360732i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 2.41750 | − | 35.1872i | 0.0778221 | − | 1.13271i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 17.3801i | 0.558907i | 0.960159 | + | 0.279453i | \(0.0901532\pi\) | ||||
−0.960159 | + | 0.279453i | \(0.909847\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 8.31017 | 0.266961 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −29.4311 | −0.944490 | −0.472245 | − | 0.881467i | \(-0.656556\pi\) | ||||
−0.472245 | + | 0.881467i | \(0.656556\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 36.3049i | − | 1.16388i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −4.95302 | − | 0.683813i | −0.158624 | − | 0.0218995i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 3.49492i | − | 0.111812i | −0.998436 | − | 0.0559062i | \(-0.982195\pi\) | ||
0.998436 | − | 0.0559062i | \(-0.0178048\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 15.2236 | 0.486550 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −0.914914 | −0.0292110 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 12.1407i | − | 0.387230i | −0.981078 | − | 0.193615i | \(-0.937979\pi\) | ||
0.981078 | − | 0.193615i | \(-0.0620212\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −0.418218 | + | 6.08723i | −0.0133255 | + | 0.193955i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 27.6348i | 0.879625i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −5.62246 | −0.178784 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 46.5633 | 1.47913 | 0.739566 | − | 0.673084i | \(-0.235031\pi\) | ||||
0.739566 | + | 0.673084i | \(0.235031\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 5.59929i | 0.177688i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 49.3074 | + | 3.38762i | 1.56315 | + | 0.107395i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 10.8908i | 0.344915i | 0.985017 | + | 0.172457i | \(0.0551707\pi\) | ||||
−0.985017 | + | 0.172457i | \(0.944829\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0.257322 | 0.00814130 |
(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 | 1560.2.l.f.1249.10 | yes | 10 | |
3.2 | odd | 2 | 4680.2.l.h.2809.1 | 10 | |||
4.3 | odd | 2 | 3120.2.l.q.1249.5 | 10 | |||
5.2 | odd | 4 | 7800.2.a.ca.1.1 | 5 | |||
5.3 | odd | 4 | 7800.2.a.bz.1.5 | 5 | |||
5.4 | even | 2 | inner | 1560.2.l.f.1249.5 | ✓ | 10 | |
15.14 | odd | 2 | 4680.2.l.h.2809.2 | 10 | |||
20.19 | odd | 2 | 3120.2.l.q.1249.10 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1560.2.l.f.1249.5 | ✓ | 10 | 5.4 | even | 2 | inner | |
1560.2.l.f.1249.10 | yes | 10 | 1.1 | even | 1 | trivial | |
3120.2.l.q.1249.5 | 10 | 4.3 | odd | 2 | |||
3120.2.l.q.1249.10 | 10 | 20.19 | odd | 2 | |||
4680.2.l.h.2809.1 | 10 | 3.2 | odd | 2 | |||
4680.2.l.h.2809.2 | 10 | 15.14 | odd | 2 | |||
7800.2.a.bz.1.5 | 5 | 5.3 | odd | 4 | |||
7800.2.a.ca.1.1 | 5 | 5.2 | odd | 4 |