Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1440,2,Mod(847,1440)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1440, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 2, 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("1440.847");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1440 = 2^{5} \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1440.bi (of order \(4\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(11.4984578911\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 5x^{12} + 28x^{8} + 80x^{4} + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{49}]\) |
Coefficient ring index: | \( 2^{18} \) |
Twist minimal: | no (minimal twist has level 360) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 1423.4 | ||
Root | \(-1.17431 - 0.788026i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1440.1423 |
Dual form | 1440.2.bi.d.847.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1440\mathbb{Z}\right)^\times\).
\(n\) | \(577\) | \(641\) | \(901\) | \(991\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(1\) | \(-1\) | \(-1\) |
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 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.386289 | + | 2.20245i | −0.172754 | + | 0.984965i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.51606 | + | 1.51606i | 0.573017 | + | 0.573017i | 0.932970 | − | 0.359953i | \(-0.117207\pi\) |
−0.359953 | + | 0.932970i | \(0.617207\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.92468 | 1.18334 | 0.591668 | − | 0.806182i | \(-0.298470\pi\) | ||||
0.591668 | + | 0.806182i | \(0.298470\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.56393 | + | 3.56393i | −0.988455 | + | 0.988455i | −0.999934 | − | 0.0114791i | \(-0.996346\pi\) |
0.0114791 | + | 0.999934i | \(0.496346\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.37670 | − | 1.37670i | 0.333900 | − | 0.333900i | −0.520166 | − | 0.854065i | \(-0.674130\pi\) |
0.854065 | + | 0.520166i | \(0.174130\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.00000i | 0.917663i | 0.888523 | + | 0.458831i | \(0.151732\pi\) | ||||
−0.888523 | + | 0.458831i | \(0.848268\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.17748 | − | 5.17748i | 1.07958 | − | 1.07958i | 0.0830312 | − | 0.996547i | \(-0.473540\pi\) |
0.996547 | − | 0.0830312i | \(-0.0264601\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.70156 | − | 1.70156i | −0.940312 | − | 0.340312i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.95005 | −1.10490 | −0.552449 | − | 0.833547i | \(-0.686306\pi\) | ||||
−0.552449 | + | 0.833547i | \(0.686306\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.12785i | 1.28020i | 0.768292 | + | 0.640100i | \(0.221107\pi\) | ||||
−0.768292 | + | 0.640100i | \(0.778893\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.92468 | + | 2.75341i | −0.663392 | + | 0.465411i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.56393 | + | 3.56393i | 0.585906 | + | 0.585906i | 0.936520 | − | 0.350614i | \(-0.114027\pi\) |
−0.350614 | + | 0.936520i | \(0.614027\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.75341 | −0.430010 | −0.215005 | − | 0.976613i | \(-0.568977\pi\) | ||||
−0.215005 | + | 0.976613i | \(0.568977\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.40312 | − | 5.40312i | −0.823969 | − | 0.823969i | 0.162706 | − | 0.986675i | \(-0.447978\pi\) |
−0.986675 | + | 0.162706i | \(0.947978\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.54515 | + | 1.54515i | 0.225384 | + | 0.225384i | 0.810761 | − | 0.585377i | \(-0.199054\pi\) |
−0.585377 | + | 0.810761i | \(0.699054\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 2.40312i | − | 0.343303i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.81616 | + | 1.81616i | −0.249469 | + | 0.249469i | −0.820753 | − | 0.571284i | \(-0.806446\pi\) |
0.571284 | + | 0.820753i | \(0.306446\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.51606 | + | 8.64391i | −0.204425 | + | 1.16554i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.92468i | 0.510950i | 0.966816 | + | 0.255475i | \(0.0822318\pi\) | ||||
−0.966816 | + | 0.255475i | \(0.917768\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 13.1921i | 1.68907i | 0.535497 | + | 0.844537i | \(0.320124\pi\) | ||||
−0.535497 | + | 0.844537i | \(0.679876\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −6.47266 | − | 9.22607i | −0.802835 | − | 1.14435i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.40312 | − | 5.40312i | 0.660097 | − | 0.660097i | −0.295306 | − | 0.955403i | \(-0.595422\pi\) |
0.955403 | + | 0.295306i | \(0.0954216\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.00000 | + | 5.00000i | 0.585206 | + | 0.585206i | 0.936329 | − | 0.351123i | \(-0.114200\pi\) |
−0.351123 | + | 0.936329i | \(0.614200\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 5.95005 | + | 5.95005i | 0.678071 | + | 0.678071i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.12785 | −0.801946 | −0.400973 | − | 0.916090i | \(-0.631328\pi\) | ||||
−0.400973 | + | 0.916090i | \(0.631328\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −6.67809 | − | 6.67809i | −0.733016 | − | 0.733016i | 0.238200 | − | 0.971216i | \(-0.423442\pi\) |
−0.971216 | + | 0.238200i | \(0.923442\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.50031 | + | 3.56393i | 0.271197 | + | 0.386562i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 18.4521i | 1.95592i | 0.208787 | + | 0.977961i | \(0.433048\pi\) | ||||
−0.208787 | + | 0.977961i | \(0.566952\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −10.8062 | −1.13280 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −8.80980 | − | 1.54515i | −0.903866 | − | 0.158530i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −10.4031 | + | 10.4031i | −1.05628 | + | 1.05628i | −0.0579582 | + | 0.998319i | \(0.518459\pi\) |
−0.998319 | + | 0.0579582i | \(0.981541\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 8.03722i | − | 0.799733i | −0.916573 | − | 0.399867i | \(-0.869056\pi\) | ||
0.916573 | − | 0.399867i | \(-0.130944\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.61179 | + | 5.61179i | −0.552946 | + | 0.552946i | −0.927290 | − | 0.374344i | \(-0.877868\pi\) |
0.374344 | + | 0.927290i | \(0.377868\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 3.92468 | − | 3.92468i | 0.379413 | − | 0.379413i | −0.491477 | − | 0.870890i | \(-0.663543\pi\) |
0.870890 | + | 0.491477i | \(0.163543\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.06424 | 0.580849 | 0.290424 | − | 0.956898i | \(-0.406204\pi\) | ||||
0.290424 | + | 0.956898i | \(0.406204\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.37670 | + | 1.37670i | 0.129509 | + | 0.129509i | 0.768890 | − | 0.639381i | \(-0.220809\pi\) |
−0.639381 | + | 0.768890i | \(0.720809\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 9.40312 | + | 13.4031i | 0.876846 | + | 1.24985i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 4.17433 | 0.382660 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.40312 | 0.400284 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 5.56376 | − | 9.69766i | 0.497638 | − | 0.867385i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 11.6760 | + | 11.6760i | 1.03608 | + | 1.03608i | 0.999324 | + | 0.0367559i | \(0.0117024\pi\) |
0.0367559 | + | 0.999324i | \(0.488298\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 17.2809 | 1.50984 | 0.754918 | − | 0.655819i | \(-0.227677\pi\) | ||||
0.754918 | + | 0.655819i | \(0.227677\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −6.06424 | + | 6.06424i | −0.525836 | + | 0.525836i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 14.3220 | − | 14.3220i | 1.22361 | − | 1.22361i | 0.257275 | − | 0.966338i | \(-0.417176\pi\) |
0.966338 | − | 0.257275i | \(-0.0828245\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 4.00000i | − | 0.339276i | −0.985506 | − | 0.169638i | \(-0.945740\pi\) | ||
0.985506 | − | 0.169638i | \(-0.0542598\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −13.9873 | + | 13.9873i | −1.16967 | + | 1.16967i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.29844 | − | 13.1047i | 0.190875 | − | 1.08828i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 8.03722 | 0.658435 | 0.329217 | − | 0.944254i | \(-0.393215\pi\) | ||||
0.329217 | + | 0.944254i | \(0.393215\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 10.1600i | − | 0.826807i | −0.910548 | − | 0.413403i | \(-0.864340\pi\) | ||
0.910548 | − | 0.413403i | \(-0.135660\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −15.6987 | − | 2.75341i | −1.26095 | − | 0.221159i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −9.62817 | − | 9.62817i | −0.768411 | − | 0.768411i | 0.209416 | − | 0.977827i | \(-0.432844\pi\) |
−0.977827 | + | 0.209416i | \(0.932844\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 15.6987 | 1.23723 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.54515 | − | 1.54515i | −0.119568 | − | 0.119568i | 0.644791 | − | 0.764359i | \(-0.276944\pi\) |
−0.764359 | + | 0.644791i | \(0.776944\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 12.4031i | − | 0.954086i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 4.13389 | − | 4.13389i | 0.314294 | − | 0.314294i | −0.532277 | − | 0.846571i | \(-0.678663\pi\) |
0.846571 | + | 0.532277i | \(0.178663\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.54818 | − | 9.70752i | −0.343810 | − | 0.733820i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 14.1166i | 1.05512i | 0.849517 | + | 0.527562i | \(0.176894\pi\) | ||||
−0.849517 | + | 0.527562i | \(0.823106\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 6.06424i | − | 0.450751i | −0.974272 | − | 0.225376i | \(-0.927639\pi\) | ||
0.974272 | − | 0.225376i | \(-0.0723610\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −9.22607 | + | 6.47266i | −0.678314 | + | 0.475879i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.40312 | − | 5.40312i | 0.395116 | − | 0.395116i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 23.8002i | 1.72212i | 0.508501 | + | 0.861061i | \(0.330200\pi\) | ||||
−0.508501 | + | 0.861061i | \(0.669800\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.403124 | + | 0.403124i | 0.0290175 | + | 0.0290175i | 0.721467 | − | 0.692449i | \(-0.243468\pi\) |
−0.692449 | + | 0.721467i | \(0.743468\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −5.44848 | − | 5.44848i | −0.388188 | − | 0.388188i | 0.485853 | − | 0.874041i | \(-0.338509\pi\) |
−0.874041 | + | 0.485853i | \(0.838509\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 18.3514 | 1.30090 | 0.650449 | − | 0.759550i | \(-0.274581\pi\) | ||||
0.650449 | + | 0.759550i | \(0.274581\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −9.02064 | − | 9.02064i | −0.633125 | − | 0.633125i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.06361 | − | 6.06424i | 0.0742858 | − | 0.423545i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 15.6987i | 1.08590i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −12.0000 | −0.826114 | −0.413057 | − | 0.910705i | \(-0.635539\pi\) | ||||
−0.413057 | + | 0.910705i | \(0.635539\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 13.9873 | − | 9.81294i | 0.953924 | − | 0.669237i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −10.8062 | + | 10.8062i | −0.733576 | + | 0.733576i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 9.81294i | 0.660090i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 11.6760 | − | 11.6760i | 0.781885 | − | 0.781885i | −0.198264 | − | 0.980149i | \(-0.563530\pi\) |
0.980149 | + | 0.198264i | \(0.0635303\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 12.9453 | − | 12.9453i | 0.859211 | − | 0.859211i | −0.132034 | − | 0.991245i | \(-0.542151\pi\) |
0.991245 | + | 0.132034i | \(0.0421509\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −13.1921 | −0.871758 | −0.435879 | − | 0.900005i | \(-0.643562\pi\) | ||||
−0.435879 | + | 0.900005i | \(0.643562\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −14.3220 | − | 14.3220i | −0.938267 | − | 0.938267i | 0.0599354 | − | 0.998202i | \(-0.480911\pi\) |
−0.998202 | + | 0.0599354i | \(0.980911\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.00000 | + | 2.80625i | −0.260931 | + | 0.183059i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −27.9745 | −1.80952 | −0.904761 | − | 0.425919i | \(-0.859951\pi\) | ||||
−0.904761 | + | 0.425919i | \(0.859951\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 18.8062 | 1.21142 | 0.605708 | − | 0.795687i | \(-0.292890\pi\) | ||||
0.605708 | + | 0.795687i | \(0.292890\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 5.29276 | + | 0.928300i | 0.338142 | + | 0.0593069i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −14.2557 | − | 14.2557i | −0.907068 | − | 0.907068i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.58213 | −0.0998634 | −0.0499317 | − | 0.998753i | \(-0.515900\pi\) | ||||
−0.0499317 | + | 0.998753i | \(0.515900\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 20.3199 | − | 20.3199i | 1.27750 | − | 1.27750i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −4.13011 | + | 4.13011i | −0.257629 | + | 0.257629i | −0.824089 | − | 0.566460i | \(-0.808313\pi\) |
0.566460 | + | 0.824089i | \(0.308313\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 10.8062i | 0.671468i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 19.1647 | − | 19.1647i | 1.18175 | − | 1.18175i | 0.202458 | − | 0.979291i | \(-0.435107\pi\) |
0.979291 | − | 0.202458i | \(-0.0648929\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.29844 | − | 4.70156i | −0.202621 | − | 0.288815i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3.86289 | −0.235524 | −0.117762 | − | 0.993042i | \(-0.537572\pi\) | ||||
−0.117762 | + | 0.993042i | \(0.537572\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 16.2242i | − | 0.985551i | −0.870157 | − | 0.492775i | \(-0.835982\pi\) | ||
0.870157 | − | 0.492775i | \(-0.164018\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −18.4521 | − | 6.67809i | −1.11271 | − | 0.402704i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −10.6918 | − | 10.6918i | −0.642407 | − | 0.642407i | 0.308740 | − | 0.951146i | \(-0.400093\pi\) |
−0.951146 | + | 0.308740i | \(0.900093\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8.26022 | 0.492764 | 0.246382 | − | 0.969173i | \(-0.420758\pi\) | ||||
0.246382 | + | 0.969173i | \(0.420758\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.40312 | + | 5.40312i | 0.321182 | + | 0.321182i | 0.849221 | − | 0.528038i | \(-0.177072\pi\) |
−0.528038 | + | 0.849221i | \(0.677072\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4.17433 | − | 4.17433i | −0.246403 | − | 0.246403i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 13.2094i | 0.777022i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.81616 | − | 1.81616i | 0.106101 | − | 0.106101i | −0.652063 | − | 0.758165i | \(-0.726096\pi\) |
0.758165 | + | 0.652063i | \(0.226096\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −8.64391 | − | 1.51606i | −0.503268 | − | 0.0882684i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 36.9043i | 2.13423i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 16.3829i | − | 0.944296i | ||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −29.0549 | − | 5.09596i | −1.66368 | − | 0.291794i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 20.0000 | − | 20.0000i | 1.14146 | − | 1.14146i | 0.153277 | − | 0.988183i | \(-0.451017\pi\) |
0.988183 | − | 0.153277i | \(-0.0489827\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 27.9745i | − | 1.58629i | −0.609032 | − | 0.793145i | \(-0.708442\pi\) | ||
0.609032 | − | 0.793145i | \(-0.291558\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.80625 | + | 5.80625i | 0.328189 | + | 0.328189i | 0.851897 | − | 0.523709i | \(-0.175452\pi\) |
−0.523709 | + | 0.851897i | \(0.675452\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −11.3985 | − | 11.3985i | −0.640205 | − | 0.640205i | 0.310400 | − | 0.950606i | \(-0.399537\pi\) |
−0.950606 | + | 0.310400i | \(0.899537\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −23.3521 | −1.30746 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5.50682 | + | 5.50682i | 0.306407 | + | 0.306407i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 22.8203 | − | 10.6918i | 1.26584 | − | 0.593073i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 4.68509i | 0.258298i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 22.8062 | 1.25354 | 0.626772 | − | 0.779202i | \(-0.284376\pi\) | ||||
0.626772 | + | 0.779202i | \(0.284376\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 9.81294 | + | 13.9873i | 0.536138 | + | 0.764206i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 10.4031 | − | 10.4031i | 0.566694 | − | 0.566694i | −0.364507 | − | 0.931201i | \(-0.618762\pi\) |
0.931201 | + | 0.364507i | \(0.118762\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 27.9745i | 1.51491i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 14.2557 | − | 14.2557i | 0.769735 | − | 0.769735i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 18.4521 | − | 18.4521i | 0.990562 | − | 0.990562i | −0.00939345 | − | 0.999956i | \(-0.502990\pi\) |
0.999956 | + | 0.00939345i | \(0.00299007\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 13.1921 | 0.706156 | 0.353078 | − | 0.935594i | \(-0.385135\pi\) | ||||
0.353078 | + | 0.935594i | \(0.385135\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −4.13011 | − | 4.13011i | −0.219824 | − | 0.219824i | 0.588600 | − | 0.808424i | \(-0.299679\pi\) |
−0.808424 | + | 0.588600i | \(0.799679\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 32.1489 | 1.69675 | 0.848376 | − | 0.529394i | \(-0.177581\pi\) | ||||
0.848376 | + | 0.529394i | \(0.177581\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.00000 | 0.157895 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −12.9437 | + | 9.08080i | −0.677504 | + | 0.475311i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −7.58030 | − | 7.58030i | −0.395688 | − | 0.395688i | 0.481021 | − | 0.876709i | \(-0.340266\pi\) |
−0.876709 | + | 0.481021i | \(0.840266\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −5.50682 | −0.285900 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2.50031 | + | 2.50031i | −0.129461 | + | 0.129461i | −0.768868 | − | 0.639407i | \(-0.779180\pi\) |
0.639407 | + | 0.768868i | \(0.279180\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 21.2055 | − | 21.2055i | 1.09214 | − | 1.09214i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6.80625i | 0.349614i | 0.984603 | + | 0.174807i | \(0.0559301\pi\) | ||||
−0.984603 | + | 0.174807i | \(0.944070\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −9.35181 | + | 9.35181i | −0.477855 | + | 0.477855i | −0.904445 | − | 0.426590i | \(-0.859715\pi\) |
0.426590 | + | 0.904445i | \(0.359715\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −15.4031 | + | 10.8062i | −0.785016 | + | 0.550737i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −27.6631 | −1.40257 | −0.701287 | − | 0.712879i | \(-0.747391\pi\) | ||||
−0.701287 | + | 0.712879i | \(0.747391\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 14.2557i | − | 0.720942i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.75341 | − | 15.6987i | 0.138539 | − | 0.789889i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.62754 | + | 4.62754i | 0.232249 | + | 0.232249i | 0.813631 | − | 0.581382i | \(-0.197488\pi\) |
−0.581382 | + | 0.813631i | \(0.697488\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 31.3975 | 1.56791 | 0.783957 | − | 0.620815i | \(-0.213198\pi\) | ||||
0.783957 | + | 0.620815i | \(0.213198\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −25.4031 | − | 25.4031i | −1.26542 | − | 1.26542i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 13.9873 | + | 13.9873i | 0.693323 | + | 0.693323i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 9.40312i | 0.464955i | 0.972602 | + | 0.232477i | \(0.0746831\pi\) | ||||
−0.972602 | + | 0.232477i | \(0.925317\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −5.95005 | + | 5.95005i | −0.292783 | + | 0.292783i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 17.2878 | − | 12.1285i | 0.848626 | − | 0.595364i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 22.7877i | 1.11325i | 0.830764 | + | 0.556625i | \(0.187904\pi\) | ||||
−0.830764 | + | 0.556625i | \(0.812096\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 25.3206i | − | 1.23405i | −0.786944 | − | 0.617025i | \(-0.788338\pi\) | ||
0.786944 | − | 0.617025i | \(-0.211662\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −8.81521 | + | 4.13011i | −0.427600 | + | 0.200340i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −20.0000 | + | 20.0000i | −0.967868 | + | 0.967868i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 4.17433i | − | 0.201070i | −0.994933 | − | 0.100535i | \(-0.967944\pi\) | ||
0.994933 | − | 0.100535i | \(-0.0320555\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −0.403124 | − | 0.403124i | −0.0193729 | − | 0.0193729i | 0.697354 | − | 0.716727i | \(-0.254361\pi\) |
−0.716727 | + | 0.697354i | \(0.754361\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 20.7099 | + | 20.7099i | 0.990689 | + | 0.990689i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4.09573 | −0.195479 | −0.0977393 | − | 0.995212i | \(-0.531161\pi\) | ||||
−0.0977393 | + | 0.995212i | \(0.531161\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 12.9453 | + | 12.9453i | 0.615051 | + | 0.615051i | 0.944258 | − | 0.329207i | \(-0.106781\pi\) |
−0.329207 | + | 0.944258i | \(0.606781\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −40.6399 | − | 7.12785i | −1.92652 | − | 0.337893i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 15.6987i | 0.740869i | 0.928859 | + | 0.370434i | \(0.120791\pi\) | ||||
−0.928859 | + | 0.370434i | \(0.879209\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −10.8062 | −0.508846 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 4.17433 | − | 23.8002i | 0.195696 | − | 1.11577i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 15.8062 | − | 15.8062i | 0.739385 | − | 0.739385i | −0.233074 | − | 0.972459i | \(-0.574878\pi\) |
0.972459 | + | 0.233074i | \(0.0748784\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 3.86289i | − | 0.179913i | −0.995946 | − | 0.0899563i | \(-0.971327\pi\) | ||
0.995946 | − | 0.0899563i | \(-0.0286727\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −7.58030 | + | 7.58030i | −0.352286 | + | 0.352286i | −0.860960 | − | 0.508673i | \(-0.830136\pi\) |
0.508673 | + | 0.860960i | \(0.330136\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1.17127 | + | 1.17127i | −0.0542001 | + | 0.0542001i | −0.733687 | − | 0.679487i | \(-0.762202\pi\) |
0.679487 | + | 0.733687i | \(0.262202\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 16.3829 | 0.756493 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −21.2055 | − | 21.2055i | −0.975032 | − | 0.975032i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6.80625 | − | 18.8062i | 0.312292 | − | 0.862890i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −27.9745 | −1.27819 | −0.639095 | − | 0.769128i | \(-0.720691\pi\) | ||||
−0.639095 | + | 0.769128i | \(0.720691\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −25.4031 | −1.15828 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −18.8937 | − | 26.9310i | −0.857921 | − | 1.22287i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 8.64391 | + | 8.64391i | 0.391693 | + | 0.391693i | 0.875290 | − | 0.483598i | \(-0.160670\pi\) |
−0.483598 | + | 0.875290i | \(0.660670\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 27.4728 | 1.23983 | 0.619914 | − | 0.784669i | \(-0.287167\pi\) | ||||
0.619914 | + | 0.784669i | \(0.287167\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −8.19146 | + | 8.19146i | −0.368925 | + | 0.368925i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 6.80625i | − | 0.304690i | −0.988327 | − | 0.152345i | \(-0.951318\pi\) | ||
0.988327 | − | 0.152345i | \(-0.0486824\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 8.80980 | − | 8.80980i | 0.392809 | − | 0.392809i | −0.482878 | − | 0.875688i | \(-0.660409\pi\) |
0.875688 | + | 0.482878i | \(0.160409\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 17.7016 | + | 3.10469i | 0.787709 | + | 0.138157i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 22.0245 | 0.976218 | 0.488109 | − | 0.872783i | \(-0.337687\pi\) | ||||
0.488109 | + | 0.872783i | \(0.337687\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 15.1606i | 0.670665i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −10.1919 | − | 14.5275i | −0.449109 | − | 0.640156i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6.06424 | + | 6.06424i | 0.266705 | + | 0.266705i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 15.6987 | 0.687774 | 0.343887 | − | 0.939011i | \(-0.388256\pi\) | ||||
0.343887 | + | 0.939011i | \(0.388256\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 30.8062 | + | 30.8062i | 1.34706 | + | 1.34706i | 0.888834 | + | 0.458229i | \(0.151516\pi\) |
0.458229 | + | 0.888834i | \(0.348484\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 9.81294 | + | 9.81294i | 0.427458 | + | 0.427458i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 30.6125i | − | 1.33098i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 9.81294 | − | 9.81294i | 0.425046 | − | 0.425046i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 7.12785 | + | 10.1600i | 0.308164 | + | 0.439254i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 9.43150i | − | 0.406243i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 34.5756i | 1.48652i | 0.669001 | + | 0.743261i | \(0.266722\pi\) | ||||
−0.669001 | + | 0.743261i | \(0.733278\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −2.34255 | + | 13.3562i | −0.100344 | + | 0.572116i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −16.2094 | + | 16.2094i | −0.693063 | + | 0.693063i | −0.962905 | − | 0.269842i | \(-0.913029\pi\) |
0.269842 | + | 0.962905i | \(0.413029\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 23.8002i | − | 1.01392i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −10.8062 | − | 10.8062i | −0.459528 | − | 0.459528i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 15.2614 | + | 15.2614i | 0.646647 | + | 0.646647i | 0.952181 | − | 0.305534i | \(-0.0988350\pi\) |
−0.305534 | + | 0.952181i | \(0.598835\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 38.5127 | 1.62891 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −18.4521 | − | 18.4521i | −0.777665 | − | 0.777665i | 0.201769 | − | 0.979433i | \(-0.435331\pi\) |
−0.979433 | + | 0.201769i | \(0.935331\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3.56393 | + | 2.50031i | −0.149935 | + | 0.105189i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 11.0136i | 0.461715i | 0.972988 | + | 0.230858i | \(0.0741532\pi\) | ||||
−0.972988 | + | 0.230858i | \(0.925847\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 33.6125 | 1.40664 | 0.703320 | − | 0.710874i | \(-0.251700\pi\) | ||||
0.703320 | + | 0.710874i | \(0.251700\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −33.1520 | + | 15.5324i | −1.38253 | + | 0.647747i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −0.403124 | + | 0.403124i | −0.0167823 | + | 0.0167823i | −0.715448 | − | 0.698666i | \(-0.753777\pi\) |
0.698666 | + | 0.715448i | \(0.253777\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 20.2488i | − | 0.840060i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −7.12785 | + | 7.12785i | −0.295205 | + | 0.295205i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −3.92468 | + | 3.92468i | −0.161989 | + | 0.161989i | −0.783447 | − | 0.621458i | \(-0.786541\pi\) |
0.621458 | + | 0.783447i | \(0.286541\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −28.5114 | −1.17479 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1.37670 | − | 1.37670i | −0.0565345 | − | 0.0565345i | 0.678274 | − | 0.734809i | \(-0.262728\pi\) |
−0.734809 | + | 0.678274i | \(0.762728\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.61250 | + | 9.19375i | −0.0661059 | + | 0.376907i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 4.17433 | 0.170559 | 0.0852793 | − | 0.996357i | \(-0.472822\pi\) | ||||
0.0852793 | + | 0.996357i | \(0.472822\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −18.2094 | −0.742776 | −0.371388 | − | 0.928478i | \(-0.621118\pi\) | ||||
−0.371388 | + | 0.928478i | \(0.621118\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.70088 | + | 9.69766i | −0.0691505 | + | 0.394266i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −9.70752 | − | 9.70752i | −0.394016 | − | 0.394016i | 0.482100 | − | 0.876116i | \(-0.339874\pi\) |
−0.876116 | + | 0.482100i | \(0.839874\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −11.0136 | −0.445564 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −4.62754 | + | 4.62754i | −0.186904 | + | 0.186904i | −0.794356 | − | 0.607452i | \(-0.792192\pi\) |
0.607452 | + | 0.794356i | \(0.292192\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −19.8288 | + | 19.8288i | −0.798279 | + | 0.798279i | −0.982824 | − | 0.184545i | \(-0.940919\pi\) |
0.184545 | + | 0.982824i | \(0.440919\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 14.8062i | − | 0.595113i | −0.954704 | − | 0.297557i | \(-0.903828\pi\) | ||
0.954704 | − | 0.297557i | \(-0.0961717\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −27.9745 | + | 27.9745i | −1.12078 | + | 1.12078i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 19.2094 | + | 16.0000i | 0.768375 | + | 0.640000i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 9.81294 | 0.391268 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 35.6393i | 1.41878i | 0.704818 | + | 0.709388i | \(0.251029\pi\) | ||||
−0.704818 | + | 0.709388i | \(0.748971\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −30.2262 | + | 21.2055i | −1.19949 | + | 0.841516i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 8.56455 | + | 8.56455i | 0.339340 | + | 0.339340i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −18.4521 | −0.728815 | −0.364408 | − | 0.931240i | \(-0.618729\pi\) | ||||
−0.364408 | + | 0.931240i | \(0.618729\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 5.71949 | + | 5.71949i | 0.224856 | + | 0.224856i | 0.810540 | − | 0.585684i | \(-0.199174\pi\) |
−0.585684 | + | 0.810540i | \(0.699174\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 15.4031i | 0.604626i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 5.67905 | − | 5.67905i | 0.222238 | − | 0.222238i | −0.587202 | − | 0.809440i | \(-0.699771\pi\) |
0.809440 | + | 0.587202i | \(0.199771\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −6.67540 | + | 38.0602i | −0.260829 | + | 1.48714i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 11.7740i | 0.458652i | 0.973350 | + | 0.229326i | \(0.0736521\pi\) | ||||
−0.973350 | + | 0.229326i | \(0.926348\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 15.3193i | 0.595852i | 0.954589 | + | 0.297926i | \(0.0962949\pi\) | ||||
−0.954589 | + | 0.297926i | \(0.903705\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −11.0136 | − | 15.6987i | −0.427090 | − | 0.608770i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −30.8062 | + | 30.8062i | −1.19282 | + | 1.19282i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 51.7748i | 1.99874i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 15.0000 | + | 15.0000i | 0.578208 | + | 0.578208i | 0.934409 | − | 0.356202i | \(-0.115928\pi\) |
−0.356202 | + | 0.934409i | \(0.615928\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −13.4857 | − | 13.4857i | −0.518298 | − | 0.518298i | 0.398758 | − | 0.917056i | \(-0.369441\pi\) |
−0.917056 | + | 0.398758i | \(0.869441\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −31.5435 | −1.21053 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −22.3768 | − | 22.3768i | −0.856225 | − | 0.856225i | 0.134666 | − | 0.990891i | \(-0.457004\pi\) |
−0.990891 | + | 0.134666i | \(0.957004\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 26.0111 | + | 37.0760i | 0.993833 | + | 1.41660i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 12.9453i | − | 0.493177i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −28.0000 | −1.06517 | −0.532585 | − | 0.846376i | \(-0.678779\pi\) | ||||
−0.532585 | + | 0.846376i | \(0.678779\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 8.80980 | + | 1.54515i | 0.334175 | + | 0.0586111i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3.79063 | + | 3.79063i | −0.143580 | + | 0.143580i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 33.9246i | − | 1.28131i | −0.767827 | − | 0.640657i | \(-0.778662\pi\) | ||
0.767827 | − | 0.640657i | \(-0.221338\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −14.2557 | + | 14.2557i | −0.537664 | + | 0.537664i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 12.1849 | − | 12.1849i | 0.458261 | − | 0.458261i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −15.3193 | −0.575329 | −0.287664 | − | 0.957731i | \(-0.592879\pi\) | ||||
−0.287664 | + | 0.957731i | \(0.592879\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 36.9043 | + | 36.9043i | 1.38208 | + | 1.38208i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −25.4031 | − | 36.2094i | −0.950023 | − | 1.35415i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −27.9745 | −1.04327 | −0.521637 | − | 0.853167i | \(-0.674679\pi\) | ||||
−0.521637 | + | 0.853167i | \(0.674679\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −17.0156 | −0.633695 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 27.9745 | + | 10.1244i | 1.03895 | + | 0.376010i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 10.7711 | + | 10.7711i | 0.399479 | + | 0.399479i | 0.878049 | − | 0.478570i | \(-0.158845\pi\) |
−0.478570 | + | 0.878049i | \(0.658845\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −14.8770 | −0.550246 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −3.56393 | + | 3.56393i | −0.131637 | + | 0.131637i | −0.769855 | − | 0.638219i | \(-0.779672\pi\) |
0.638219 | + | 0.769855i | \(0.279672\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 21.2055 | − | 21.2055i | 0.781116 | − | 0.781116i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 28.4187i | − | 1.04540i | −0.852517 | − | 0.522700i | \(-0.824925\pi\) | ||
0.852517 | − | 0.522700i | \(-0.175075\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 22.7971 | − | 22.7971i | 0.836343 | − | 0.836343i | −0.152032 | − | 0.988376i | \(-0.548582\pi\) |
0.988376 | + | 0.152032i | \(0.0485818\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.10469 | + | 17.7016i | −0.113747 | + | 0.648535i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 11.9001 | 0.434820 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 21.3836i | 0.780297i | 0.920752 | + | 0.390148i | \(0.127576\pi\) | ||||
−0.920752 | + | 0.390148i | \(0.872424\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 22.3768 | + | 3.92468i | 0.814376 | + | 0.142834i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 29.9481 | + | 29.9481i | 1.08848 | + | 1.08848i | 0.995685 | + | 0.0927974i | \(0.0295809\pi\) |
0.0927974 | + | 0.995685i | \(0.470419\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 4.68509 | 0.169835 | 0.0849173 | − | 0.996388i | \(-0.472937\pi\) | ||||
0.0849173 | + | 0.996388i | \(0.472937\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 9.19375 | + | 9.19375i | 0.332836 | + | 0.332836i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −13.9873 | − | 13.9873i | −0.505051 | − | 0.505051i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 11.4031i | 0.411207i | 0.978635 | + | 0.205604i | \(0.0659157\pi\) | ||||
−0.978635 | + | 0.205604i | \(0.934084\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 11.9405 | − | 11.9405i | 0.429472 | − | 0.429472i | −0.458977 | − | 0.888448i | \(-0.651784\pi\) |
0.888448 | + | 0.458977i | \(0.151784\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 12.1285 | − | 33.5120i | 0.435668 | − | 1.20379i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 11.0136i | − | 0.394604i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 24.9248 | − | 17.4863i | 0.889604 | − | 0.624112i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 20.0000 | − | 20.0000i | 0.712923 | − | 0.712923i | −0.254223 | − | 0.967146i | \(-0.581820\pi\) |
0.967146 | + | 0.254223i | \(0.0818196\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 4.17433i | 0.148422i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −47.0156 | − | 47.0156i | −1.66957 | − | 1.66957i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −28.4761 | − | 28.4761i | −1.00868 | − | 1.00868i | −0.999962 | − | 0.00871364i | \(-0.997226\pi\) |
−0.00871364 | − | 0.999962i | \(-0.502774\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.25444 | 0.150511 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 19.6234 | + | 19.6234i | 0.692495 | + | 0.692495i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −6.06424 | + | 34.5756i | −0.213736 | + | 1.21863i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 18.4521i | 0.648742i | 0.945930 | + | 0.324371i | \(0.105153\pi\) | ||||
−0.945930 | + | 0.324371i | \(0.894847\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 17.1938 | 0.603754 | 0.301877 | − | 0.953347i | \(-0.402387\pi\) | ||||
0.301877 | + | 0.953347i | \(0.402387\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 21.6125 | − | 21.6125i | 0.756126 | − | 0.756126i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 26.1988i | 0.914345i | 0.889378 | + | 0.457173i | \(0.151138\pi\) | ||||
−0.889378 | + | 0.457173i | \(0.848862\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −31.9960 | + | 31.9960i | −1.11531 | + | 1.11531i | −0.122889 | + | 0.992420i | \(0.539216\pi\) |
−0.992420 | + | 0.122889i | \(0.960784\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −11.0136 | + | 11.0136i | −0.382981 | + | 0.382981i | −0.872175 | − | 0.489194i | \(-0.837291\pi\) |
0.489194 | + | 0.872175i | \(0.337291\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 34.5756 | 1.20086 | 0.600431 | − | 0.799677i | \(-0.294996\pi\) | ||||
0.600431 | + | 0.799677i | \(0.294996\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3.30839 | − | 3.30839i | −0.114629 | − | 0.114629i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4.00000 | − | 2.80625i | 0.138426 | − | 0.0971142i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 4.17433 | 0.144114 | 0.0720570 | − | 0.997401i | \(-0.477044\pi\) | ||||
0.0720570 | + | 0.997401i | \(0.477044\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 6.40312 | 0.220797 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 27.3172 | + | 4.79119i | 0.939742 | + | 0.164822i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 6.67540 | + | 6.67540i | 0.229369 | + | 0.229369i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 36.9043 | 1.26506 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −2.50031 | + | 2.50031i | −0.0856091 | + | 0.0856091i | −0.748615 | − | 0.663005i | \(-0.769281\pi\) |
0.663005 | + | 0.748615i | \(0.269281\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −4.13011 | + | 4.13011i | −0.141082 | + | 0.141082i | −0.774120 | − | 0.633038i | \(-0.781807\pi\) |
0.633038 | + | 0.774120i | \(0.281807\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 25.6125i | − | 0.873887i | −0.899489 | − | 0.436944i | \(-0.856061\pi\) | ||
0.899489 | − | 0.436944i | \(-0.143939\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −4.63546 | + | 4.63546i | −0.157793 | + | 0.157793i | −0.781588 | − | 0.623795i | \(-0.785590\pi\) |
0.623795 | + | 0.781588i | \(0.285590\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 7.50781 | + | 10.7016i | 0.255273 | + | 0.363864i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −27.9745 | −0.948971 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 38.5127i | 1.30495i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 23.1372 | − | 6.26723i | 0.782181 | − | 0.211871i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.50031 | + | 2.50031i | 0.0844296 | + | 0.0844296i | 0.748060 | − | 0.663631i | \(-0.230985\pi\) |
−0.663631 | + | 0.748060i | \(0.730985\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −38.8360 | −1.30842 | −0.654208 | − | 0.756314i | \(-0.726998\pi\) | ||||
−0.654208 | + | 0.756314i | \(0.726998\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 10.8062 | + | 10.8062i | 0.363659 | + | 0.363659i | 0.865158 | − | 0.501499i | \(-0.167218\pi\) |
−0.501499 | + | 0.865158i | \(0.667218\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −25.3454 | − | 25.3454i | −0.851014 | − | 0.851014i | 0.139244 | − | 0.990258i | \(-0.455533\pi\) |
−0.990258 | + | 0.139244i | \(0.955533\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 35.4031i | 1.18738i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −6.18062 | + | 6.18062i | −0.206827 | + | 0.206827i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −31.0911 | − | 5.45308i | −1.03926 | − | 0.182276i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 42.4111i | − | 1.41449i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.00063i | 0.166595i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 13.3562 | + | 2.34255i | 0.443974 | + | 0.0778689i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −25.4031 | + | 25.4031i | −0.843497 | + | 0.843497i | −0.989312 | − | 0.145815i | \(-0.953420\pi\) |
0.145815 | + | 0.989312i | \(0.453420\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 4.17433i | 0.138302i | 0.997606 | + | 0.0691509i | \(0.0220290\pi\) | ||||
−0.997606 | + | 0.0691509i | \(0.977971\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −26.2094 | − | 26.2094i | −0.867404 | − | 0.867404i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 26.1988 | + | 26.1988i | 0.865161 | + | 0.865161i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 17.1291 | 0.565037 | 0.282519 | − | 0.959262i | \(-0.408830\pi\) | ||||
0.282519 | + | 0.959262i | \(0.408830\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −10.6918 | − | 22.8203i | −0.351543 | − | 0.750325i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 4.68509i | 0.153713i | 0.997042 | + | 0.0768565i | \(0.0244883\pi\) | ||||
−0.997042 | + | 0.0768565i | \(0.975512\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 9.61250 | 0.315037 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 9.81294 | + | 13.9873i | 0.320917 | + | 0.457433i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 9.59688 | − | 9.59688i | 0.313516 | − | 0.313516i | −0.532754 | − | 0.846270i | \(-0.678843\pi\) |
0.846270 | + | 0.532754i | \(0.178843\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 31.8374i | 1.03787i | 0.854814 | + | 0.518935i | \(0.173671\pi\) | ||||
−0.854814 | + | 0.518935i | \(0.826329\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −14.2557 | + | 14.2557i | −0.464229 | + | 0.464229i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −5.50682 | + | 5.50682i | −0.178947 | + | 0.178947i | −0.790897 | − | 0.611949i | \(-0.790386\pi\) |
0.611949 | + | 0.790897i | \(0.290386\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −35.6393 | −1.15690 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 17.0754 | + | 17.0754i | 0.553127 | + | 0.553127i | 0.927342 | − | 0.374215i | \(-0.122088\pi\) |
−0.374215 | + | 0.927342i | \(0.622088\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −52.4187 | − | 9.19375i | −1.69623 | − | 0.297503i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 43.4261 | 1.40230 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −19.8062 | −0.638911 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1.04358 | + | 0.732138i | −0.0335941 | + | 0.0235684i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 8.64391 | + | 8.64391i | 0.277969 | + | 0.277969i | 0.832298 | − | 0.554329i | \(-0.187025\pi\) |
−0.554329 | + | 0.832298i | \(0.687025\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 7.08895 | 0.227495 | 0.113748 | − | 0.993510i | \(-0.463714\pi\) | ||||
0.113748 | + | 0.993510i | \(0.463714\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 6.06424 | − | 6.06424i | 0.194411 | − | 0.194411i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 19.8288 | − | 19.8288i | 0.634381 | − | 0.634381i | −0.314783 | − | 0.949164i | \(-0.601932\pi\) |
0.949164 | + | 0.314783i | \(0.101932\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 72.4187i | 2.31451i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 22.7971 | − | 22.7971i | 0.727113 | − | 0.727113i | −0.242930 | − | 0.970044i | \(-0.578109\pi\) |
0.970044 | + | 0.242930i | \(0.0781086\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 14.1047 | − | 9.89531i | 0.449413 | − | 0.315291i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −55.9491 | −1.77908 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 26.5429i | − | 0.843163i | −0.906791 | − | 0.421581i | \(-0.861475\pi\) | ||
0.906791 | − | 0.421581i | \(-0.138525\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −7.08895 | + | 40.4181i | −0.224735 | + | 1.28134i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 3.56393 | + | 3.56393i | 0.112871 | + | 0.112871i | 0.761286 | − | 0.648416i | \(-0.224568\pi\) |
−0.648416 | + | 0.761286i | \(0.724568\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1440.2.bi.d.1423.4 | 16 | ||
3.2 | odd | 2 | inner | 1440.2.bi.d.1423.6 | 16 | ||
4.3 | odd | 2 | 360.2.w.d.163.3 | yes | 16 | ||
5.2 | odd | 4 | inner | 1440.2.bi.d.847.5 | 16 | ||
8.3 | odd | 2 | inner | 1440.2.bi.d.1423.5 | 16 | ||
8.5 | even | 2 | 360.2.w.d.163.2 | ✓ | 16 | ||
12.11 | even | 2 | 360.2.w.d.163.6 | yes | 16 | ||
15.2 | even | 4 | inner | 1440.2.bi.d.847.3 | 16 | ||
20.7 | even | 4 | 360.2.w.d.307.2 | yes | 16 | ||
24.5 | odd | 2 | 360.2.w.d.163.7 | yes | 16 | ||
24.11 | even | 2 | inner | 1440.2.bi.d.1423.3 | 16 | ||
40.27 | even | 4 | inner | 1440.2.bi.d.847.4 | 16 | ||
40.37 | odd | 4 | 360.2.w.d.307.3 | yes | 16 | ||
60.47 | odd | 4 | 360.2.w.d.307.7 | yes | 16 | ||
120.77 | even | 4 | 360.2.w.d.307.6 | yes | 16 | ||
120.107 | odd | 4 | inner | 1440.2.bi.d.847.6 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
360.2.w.d.163.2 | ✓ | 16 | 8.5 | even | 2 | ||
360.2.w.d.163.3 | yes | 16 | 4.3 | odd | 2 | ||
360.2.w.d.163.6 | yes | 16 | 12.11 | even | 2 | ||
360.2.w.d.163.7 | yes | 16 | 24.5 | odd | 2 | ||
360.2.w.d.307.2 | yes | 16 | 20.7 | even | 4 | ||
360.2.w.d.307.3 | yes | 16 | 40.37 | odd | 4 | ||
360.2.w.d.307.6 | yes | 16 | 120.77 | even | 4 | ||
360.2.w.d.307.7 | yes | 16 | 60.47 | odd | 4 | ||
1440.2.bi.d.847.3 | 16 | 15.2 | even | 4 | inner | ||
1440.2.bi.d.847.4 | 16 | 40.27 | even | 4 | inner | ||
1440.2.bi.d.847.5 | 16 | 5.2 | odd | 4 | inner | ||
1440.2.bi.d.847.6 | 16 | 120.107 | odd | 4 | inner | ||
1440.2.bi.d.1423.3 | 16 | 24.11 | even | 2 | inner | ||
1440.2.bi.d.1423.4 | 16 | 1.1 | even | 1 | trivial | ||
1440.2.bi.d.1423.5 | 16 | 8.3 | odd | 2 | inner | ||
1440.2.bi.d.1423.6 | 16 | 3.2 | odd | 2 | inner |